Properties

Label 476.1.o.c.135.1
Level $476$
Weight $1$
Character 476.135
Analytic conductor $0.238$
Analytic rank $0$
Dimension $4$
Projective image $D_{6}$
CM discriminant -68
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [476,1,Mod(67,476)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(476, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4, 3]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("476.67");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 476.o (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: \(0.237554946013\)
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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{6}\)
Projective field: Galois closure of 6.2.188737808.1

Embedding invariants

Embedding label 135.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 476.135
Dual form 476.1.o.c.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.73205 q^{6} -1.00000i q^{7} -1.00000 q^{8} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.73205 q^{6} -1.00000i q^{7} -1.00000 q^{8} +(-1.00000 + 1.73205i) q^{9} +(0.866025 + 1.50000i) q^{11} +(-0.866025 + 1.50000i) q^{12} +1.00000 q^{13} +(-0.866025 - 0.500000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{17} +(1.00000 + 1.73205i) q^{18} +(-1.50000 + 0.866025i) q^{21} +1.73205 q^{22} +(0.866025 + 1.50000i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.500000 - 0.866025i) q^{26} +1.73205 q^{27} +(-0.866025 + 0.500000i) q^{28} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} -1.00000 q^{34} +2.00000 q^{36} +(-0.866025 - 1.50000i) q^{39} +1.73205i q^{42} +(0.866025 - 1.50000i) q^{44} +1.73205 q^{48} -1.00000 q^{49} -1.00000 q^{50} +(-0.866025 + 1.50000i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(0.500000 + 0.866025i) q^{53} +(0.866025 - 1.50000i) q^{54} +1.00000i q^{56} +(1.73205 + 1.00000i) q^{63} +1.00000 q^{64} +(-1.50000 - 2.59808i) q^{66} +(-0.500000 + 0.866025i) q^{68} +1.73205 q^{71} +(1.00000 - 1.73205i) q^{72} +(-0.866025 + 1.50000i) q^{75} +(1.50000 - 0.866025i) q^{77} -1.73205 q^{78} +(0.866025 - 1.50000i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.50000 + 0.866025i) q^{84} +(-0.866025 - 1.50000i) q^{88} +(-0.500000 + 0.866025i) q^{89} -1.00000i q^{91} +(0.866025 - 1.50000i) q^{96} +(-0.500000 + 0.866025i) q^{98} -3.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 4 q^{9} + 4 q^{13} - 2 q^{16} - 2 q^{17} + 4 q^{18} - 6 q^{21} - 2 q^{25} + 2 q^{26} + 2 q^{32} + 6 q^{33} - 4 q^{34} + 8 q^{36} - 4 q^{49} - 4 q^{50} - 2 q^{52} + 2 q^{53} + 4 q^{64} - 6 q^{66} - 2 q^{68} + 4 q^{72} + 6 q^{77} - 2 q^{81} + 6 q^{84} - 2 q^{89} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/476\mathbb{Z}\right)^\times\).

\(n\) \(239\) \(309\) \(409\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.500000 0.866025i
\(3\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(4\) −0.500000 0.866025i −0.500000 0.866025i
\(5\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(6\) −1.73205 −1.73205
\(7\) 1.00000i 1.00000i
\(8\) −1.00000 −1.00000
\(9\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(10\) 0 0
\(11\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(12\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(13\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(14\) −0.866025 0.500000i −0.866025 0.500000i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(17\) −0.500000 0.866025i −0.500000 0.866025i
\(18\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(19\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(20\) 0 0
\(21\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(22\) 1.73205 1.73205
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(25\) −0.500000 0.866025i −0.500000 0.866025i
\(26\) 0.500000 0.866025i 0.500000 0.866025i
\(27\) 1.73205 1.73205
\(28\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(33\) 1.50000 2.59808i 1.50000 2.59808i
\(34\) −1.00000 −1.00000
\(35\) 0 0
\(36\) 2.00000 2.00000
\(37\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) 0 0
\(39\) −0.866025 1.50000i −0.866025 1.50000i
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 1.73205i 1.73205i
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0.866025 1.50000i 0.866025 1.50000i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(48\) 1.73205 1.73205
\(49\) −1.00000 −1.00000
\(50\) −1.00000 −1.00000
\(51\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(52\) −0.500000 0.866025i −0.500000 0.866025i
\(53\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 0.866025 1.50000i 0.866025 1.50000i
\(55\) 0 0
\(56\) 1.00000i 1.00000i
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(60\) 0 0
\(61\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 0 0
\(63\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) −1.50000 2.59808i −1.50000 2.59808i
\(67\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(68\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(72\) 1.00000 1.73205i 1.00000 1.73205i
\(73\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(74\) 0 0
\(75\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(76\) 0 0
\(77\) 1.50000 0.866025i 1.50000 0.866025i
\(78\) −1.73205 −1.73205
\(79\) 0.866025 1.50000i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.500000 0.866025i
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −0.866025 1.50000i −0.866025 1.50000i
\(89\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 1.00000i 1.00000i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.866025 1.50000i 0.866025 1.50000i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(99\) −3.46410 −3.46410
\(100\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(101\) 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(102\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(103\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(104\) −1.00000 −1.00000
\(105\) 0 0
\(106\) 1.00000 1.00000
\(107\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(108\) −0.866025 1.50000i −0.866025 1.50000i
\(109\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(118\) 0 0
\(119\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(120\) 0 0
\(121\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 1.73205 1.00000i 1.73205 1.00000i
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0.500000 0.866025i 0.500000 0.866025i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(132\) −3.00000 −3.00000
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 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
\(139\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.866025 1.50000i 0.866025 1.50000i
\(143\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(144\) −1.00000 1.73205i −1.00000 1.73205i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(148\) 0 0
\(149\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(150\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(151\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(152\) 0 0
\(153\) 2.00000 2.00000
\(154\) 1.73205i 1.73205i
\(155\) 0 0
\(156\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(157\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) −0.866025 1.50000i −0.866025 1.50000i
\(159\) 0.866025 1.50000i 0.866025 1.50000i
\(160\) 0 0
\(161\) 0 0
\(162\) −1.00000 −1.00000
\(163\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 1.50000 0.866025i 1.50000 0.866025i
\(169\) 0 0
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(174\) 0 0
\(175\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(176\) −1.73205 −1.73205
\(177\) 0 0
\(178\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(179\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) −0.866025 0.500000i −0.866025 0.500000i
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.866025 1.50000i 0.866025 1.50000i
\(188\) 0 0
\(189\) 1.73205i 1.73205i
\(190\) 0 0
\(191\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) −0.866025 1.50000i −0.866025 1.50000i
\(193\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −1.73205 + 3.00000i −1.73205 + 3.00000i
\(199\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(200\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(201\) 0 0
\(202\) 2.00000 2.00000
\(203\) 0 0
\(204\) 1.73205 1.73205
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 0.500000 0.866025i 0.500000 0.866025i
\(213\) −1.50000 2.59808i −1.50000 2.59808i
\(214\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(215\) 0 0
\(216\) −1.73205 −1.73205
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −0.500000 0.866025i −0.500000 0.866025i
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0.866025 0.500000i 0.866025 0.500000i
\(225\) 2.00000 2.00000
\(226\) 0 0
\(227\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(230\) 0 0
\(231\) −2.59808 1.50000i −2.59808 1.50000i
\(232\) 0 0
\(233\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(234\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(235\) 0 0
\(236\) 0 0
\(237\) −3.00000 −3.00000
\(238\) 1.00000i 1.00000i
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(242\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(243\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 2.00000i 2.00000i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.500000 0.866025i
\(257\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(265\) 0 0
\(266\) 0 0
\(267\) 1.73205 1.73205
\(268\) 0 0
\(269\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(270\) 0 0
\(271\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) 1.00000 1.00000
\(273\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(274\) −1.00000 −1.00000
\(275\) 0.866025 1.50000i 0.866025 1.50000i
\(276\) 0 0
\(277\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(278\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(279\) 0 0
\(280\) 0 0
\(281\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(282\) 0 0
\(283\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(284\) −0.866025 1.50000i −0.866025 1.50000i
\(285\) 0 0
\(286\) 1.73205 1.73205
\(287\) 0 0
\(288\) −2.00000 −2.00000
\(289\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(294\) 1.73205 1.73205
\(295\) 0 0
\(296\) 0 0
\(297\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(298\) −0.500000 0.866025i −0.500000 0.866025i
\(299\) 0 0
\(300\) 1.73205 1.73205
\(301\) 0 0
\(302\) 0 0
\(303\) 1.73205 3.00000i 1.73205 3.00000i
\(304\) 0 0
\(305\) 0 0
\(306\) 1.00000 1.73205i 1.00000 1.73205i
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) −1.50000 0.866025i −1.50000 0.866025i
\(309\) 0 0
\(310\) 0 0
\(311\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(312\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(313\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) 1.00000 1.00000
\(315\) 0 0
\(316\) −1.73205 −1.73205
\(317\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(318\) −0.866025 1.50000i −0.866025 1.50000i
\(319\) 0 0
\(320\) 0 0
\(321\) 3.00000 3.00000
\(322\) 0 0
\(323\) 0 0
\(324\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(325\) −0.500000 0.866025i −0.500000 0.866025i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(335\) 0 0
\(336\) 1.73205i 1.73205i
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000i 1.00000i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) 0 0
\(349\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(350\) 1.00000i 1.00000i
\(351\) 1.73205 1.73205
\(352\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(353\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.00000 1.00000
\(357\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(358\) 0 0
\(359\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(360\) 0 0
\(361\) −0.500000 0.866025i −0.500000 0.866025i
\(362\) 0 0
\(363\) 3.46410 3.46410
\(364\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(365\) 0 0
\(366\) 0 0
\(367\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.866025 0.500000i 0.866025 0.500000i
\(372\) 0 0
\(373\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(374\) −0.866025 1.50000i −0.866025 1.50000i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) −1.50000 0.866025i −1.50000 0.866025i
\(379\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(384\) −1.73205 −1.73205
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 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
\(392\) 1.00000 1.00000
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 1.73205 + 3.00000i 1.73205 + 3.00000i
\(397\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) 1.73205 1.73205
\(399\) 0 0
\(400\) 1.00000 1.00000
\(401\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 1.00000 1.73205i 1.00000 1.73205i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.866025 1.50000i 0.866025 1.50000i
\(409\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) 0 0
\(411\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(417\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(418\) 0 0
\(419\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(420\) 0 0
\(421\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −0.500000 0.866025i −0.500000 0.866025i
\(425\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(426\) −3.00000 −3.00000
\(427\) 0 0
\(428\) 1.73205 1.73205
\(429\) 1.50000 2.59808i 1.50000 2.59808i
\(430\) 0 0
\(431\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(432\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(433\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) 1.00000 1.73205i 1.00000 1.73205i
\(442\) −1.00000 −1.00000
\(443\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −1.73205 −1.73205
\(448\) 1.00000i 1.00000i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 1.00000 1.73205i 1.00000 1.73205i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 1.73205 1.73205
\(455\) 0 0
\(456\) 0 0
\(457\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(458\) −1.00000 1.73205i −1.00000 1.73205i
\(459\) −0.866025 1.50000i −0.866025 1.50000i
\(460\) 0 0
\(461\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(462\) −2.59808 + 1.50000i −2.59808 + 1.50000i
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(468\) 2.00000 2.00000
\(469\) 0 0
\(470\) 0 0
\(471\) 0.866025 1.50000i 0.866025 1.50000i
\(472\) 0 0
\(473\) 0 0
\(474\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(475\) 0 0
\(476\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(477\) −2.00000 −2.00000
\(478\) 0 0
\(479\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 2.00000 2.00000
\(485\) 0 0
\(486\) 0 0
\(487\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.73205i 1.73205i
\(498\) 0 0
\(499\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(500\) 0 0
\(501\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(502\) 0 0
\(503\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(504\) −1.73205 1.00000i −1.73205 1.00000i
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) 0 0
\(514\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(522\) 0 0
\(523\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(524\) 0 0
\(525\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(526\) 0 0
\(527\) 0 0
\(528\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(529\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0.866025 1.50000i 0.866025 1.50000i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.866025 1.50000i −0.866025 1.50000i
\(540\) 0 0
\(541\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.500000 0.866025i 0.500000 0.866025i
\(545\) 0 0
\(546\) 1.73205i 1.73205i
\(547\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(548\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(549\) 0 0
\(550\) −0.866025 1.50000i −0.866025 1.50000i
\(551\) 0 0
\(552\) 0 0
\(553\) −1.50000 0.866025i −1.50000 0.866025i
\(554\) 0 0
\(555\) 0 0
\(556\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(557\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −3.00000 −3.00000
\(562\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(563\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −1.73205 −1.73205
\(567\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(568\) −1.73205 −1.73205
\(569\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(570\) 0 0
\(571\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(572\) 0.866025 1.50000i 0.866025 1.50000i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(577\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(578\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(584\) 0 0
\(585\) 0 0
\(586\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0.866025 1.50000i 0.866025 1.50000i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(594\) 3.00000 3.00000
\(595\) 0 0
\(596\) −1.00000 −1.00000
\(597\) 1.50000 2.59808i 1.50000 2.59808i
\(598\) 0 0
\(599\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(600\) 0.866025 1.50000i 0.866025 1.50000i
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) −1.73205 3.00000i −1.73205 3.00000i
\(607\) 0.866025 1.50000i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −1.00000 1.73205i −1.00000 1.73205i
\(613\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −1.73205 −1.73205
\(623\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(624\) 1.73205 1.73205
\(625\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.500000 0.866025i 0.500000 0.866025i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −1.73205 −1.73205
\(637\) −1.00000 −1.00000
\(638\) 0 0
\(639\) −1.73205 + 3.00000i −1.73205 + 3.00000i
\(640\) 0 0
\(641\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(642\) 1.50000 2.59808i 1.50000 2.59808i
\(643\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(648\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(649\) 0 0
\(650\) −1.00000 −1.00000
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(662\) 0 0
\(663\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −1.50000 0.866025i −1.50000 0.866025i
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) −0.866025 1.50000i −0.866025 1.50000i
\(676\) 0 0
\(677\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1.50000 2.59808i 1.50000 2.59808i
\(682\) 0 0
\(683\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(687\) −3.46410 −3.46410
\(688\) 0 0
\(689\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(690\) 0 0
\(691\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(692\) 0 0
\(693\) 3.46410i 3.46410i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 1.00000 1.73205i 1.00000 1.73205i
\(699\) 0 0
\(700\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(701\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(702\) 0.866025 1.50000i 0.866025 1.50000i
\(703\) 0 0
\(704\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(705\) 0 0
\(706\) 1.00000 1.00000
\(707\) 1.73205 1.00000i 1.73205 1.00000i
\(708\) 0 0
\(709\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) 0 0
\(711\) 1.73205 + 3.00000i 1.73205 + 3.00000i
\(712\) 0.500000 0.866025i 0.500000 0.866025i
\(713\) 0 0
\(714\) 1.50000 0.866025i 1.50000 0.866025i
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0.866025 1.50000i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.00000 −1.00000
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 1.73205 3.00000i 1.73205 3.00000i
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 1.00000i 1.00000i
\(729\) −1.00000 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(734\) 1.73205 1.73205
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 1.00000i 1.00000i
\(743\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(747\) 0 0
\(748\) −1.73205 −1.73205
\(749\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(750\) 0 0
\(751\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(757\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(758\) 0.866025 1.50000i 0.866025 1.50000i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(769\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(770\) 0 0
\(771\) 1.73205 1.73205
\(772\) 0 0
\(773\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −1.00000 −1.00000
\(779\) 0 0
\(780\) 0 0
\(781\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(782\) 0 0
\(783\) 0 0
\(784\) 0.500000 0.866025i 0.500000 0.866025i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 3.46410 3.46410
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0.866025 1.50000i 0.866025 1.50000i
\(797\) −1.00000