Properties

Label 3645.1.n.c.1619.1
Level $3645$
Weight $1$
Character 3645.1619
Analytic conductor $1.819$
Analytic rank $0$
Dimension $6$
Projective image $D_{9}$
CM discriminant -15
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3645,1,Mod(404,3645)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3645, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([5, 9]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3645.404");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3645 = 3^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3645.n (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: \(1.81909197105\)
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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1215)
Projective image: \(D_{9}\)
Projective field: Galois closure of 9.1.242137805625.3

Embedding invariants

Embedding label 1619.1
Root \(0.939693 - 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 3645.1619
Dual form 3645.1.n.c.2024.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.43969 - 0.524005i) q^{2} +(1.03209 + 0.866025i) q^{4} +(0.173648 - 0.984808i) q^{5} +(-0.266044 - 0.460802i) q^{8} +O(q^{10})\) \(q+(-1.43969 - 0.524005i) q^{2} +(1.03209 + 0.866025i) q^{4} +(0.173648 - 0.984808i) q^{5} +(-0.266044 - 0.460802i) q^{8} +(-0.766044 + 1.32683i) q^{10} +(-0.0923963 - 0.524005i) q^{16} +(0.939693 - 1.62760i) q^{17} +(0.939693 + 1.62760i) q^{19} +(1.03209 - 0.866025i) q^{20} +(0.266044 + 0.223238i) q^{23} +(-0.939693 - 0.342020i) q^{25} +(1.17365 + 0.984808i) q^{31} +(-0.233956 + 1.32683i) q^{32} +(-2.20574 + 1.85083i) q^{34} +(-0.500000 - 2.83564i) q^{38} +(-0.500000 + 0.181985i) q^{40} +(-0.266044 - 0.460802i) q^{46} +(-0.766044 + 0.642788i) q^{47} +(0.173648 - 0.984808i) q^{49} +(1.17365 + 0.984808i) q^{50} +0.347296 q^{53} +(1.17365 - 0.984808i) q^{61} +(-1.17365 - 2.03282i) q^{62} +(0.766044 - 1.32683i) q^{64} +(2.37939 - 0.866025i) q^{68} +(-0.439693 + 2.49362i) q^{76} +(-0.326352 - 0.118782i) q^{79} -0.532089 q^{80} +(1.76604 + 0.642788i) q^{83} +(-1.43969 - 1.20805i) q^{85} +(0.0812519 + 0.460802i) q^{92} +(1.43969 - 0.524005i) q^{94} +(1.76604 - 0.642788i) q^{95} +(-0.766044 + 1.32683i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} - 3 q^{4} + 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} - 3 q^{4} + 3 q^{8} + 3 q^{16} - 3 q^{20} - 3 q^{23} + 6 q^{31} - 6 q^{32} - 3 q^{34} - 3 q^{38} - 3 q^{40} + 3 q^{46} + 6 q^{50} + 6 q^{61} - 6 q^{62} + 3 q^{68} + 3 q^{76} - 3 q^{79} + 6 q^{80} + 6 q^{83} - 3 q^{85} + 3 q^{92} + 3 q^{94} + 6 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3645\mathbb{Z}\right)^\times\).

\(n\) \(731\) \(2917\)
\(\chi(n)\) \(e\left(\frac{11}{18}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.43969 0.524005i −1.43969 0.524005i −0.500000 0.866025i \(-0.666667\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(3\) 0 0
\(4\) 1.03209 + 0.866025i 1.03209 + 0.866025i
\(5\) 0.173648 0.984808i 0.173648 0.984808i
\(6\) 0 0
\(7\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(8\) −0.266044 0.460802i −0.266044 0.460802i
\(9\) 0 0
\(10\) −0.766044 + 1.32683i −0.766044 + 1.32683i
\(11\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(12\) 0 0
\(13\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.0923963 0.524005i −0.0923963 0.524005i
\(17\) 0.939693 1.62760i 0.939693 1.62760i 0.173648 0.984808i \(-0.444444\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(18\) 0 0
\(19\) 0.939693 + 1.62760i 0.939693 + 1.62760i 0.766044 + 0.642788i \(0.222222\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(20\) 1.03209 0.866025i 1.03209 0.866025i
\(21\) 0 0
\(22\) 0 0
\(23\) 0.266044 + 0.223238i 0.266044 + 0.223238i 0.766044 0.642788i \(-0.222222\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 0 0
\(25\) −0.939693 0.342020i −0.939693 0.342020i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(30\) 0 0
\(31\) 1.17365 + 0.984808i 1.17365 + 0.984808i 1.00000 \(0\)
0.173648 + 0.984808i \(0.444444\pi\)
\(32\) −0.233956 + 1.32683i −0.233956 + 1.32683i
\(33\) 0 0
\(34\) −2.20574 + 1.85083i −2.20574 + 1.85083i
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) −0.500000 2.83564i −0.500000 2.83564i
\(39\) 0 0
\(40\) −0.500000 + 0.181985i −0.500000 + 0.181985i
\(41\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(42\) 0 0
\(43\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −0.266044 0.460802i −0.266044 0.460802i
\(47\) −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i \(-0.888889\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(48\) 0 0
\(49\) 0.173648 0.984808i 0.173648 0.984808i
\(50\) 1.17365 + 0.984808i 1.17365 + 0.984808i
\(51\) 0 0
\(52\) 0 0
\(53\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(60\) 0 0
\(61\) 1.17365 0.984808i 1.17365 0.984808i 0.173648 0.984808i \(-0.444444\pi\)
1.00000 \(0\)
\(62\) −1.17365 2.03282i −1.17365 2.03282i
\(63\) 0 0
\(64\) 0.766044 1.32683i 0.766044 1.32683i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(68\) 2.37939 0.866025i 2.37939 0.866025i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(72\) 0 0
\(73\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −0.439693 + 2.49362i −0.439693 + 2.49362i
\(77\) 0 0
\(78\) 0 0
\(79\) −0.326352 0.118782i −0.326352 0.118782i 0.173648 0.984808i \(-0.444444\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(80\) −0.532089 −0.532089
\(81\) 0 0
\(82\) 0 0
\(83\) 1.76604 + 0.642788i 1.76604 + 0.642788i 1.00000 \(0\)
0.766044 + 0.642788i \(0.222222\pi\)
\(84\) 0 0
\(85\) −1.43969 1.20805i −1.43969 1.20805i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.0812519 + 0.460802i 0.0812519 + 0.460802i
\(93\) 0 0
\(94\) 1.43969 0.524005i 1.43969 0.524005i
\(95\) 1.76604 0.642788i 1.76604 0.642788i
\(96\) 0 0
\(97\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(98\) −0.766044 + 1.32683i −0.766044 + 1.32683i
\(99\) 0 0
\(100\) −0.673648 1.16679i −0.673648 1.16679i
\(101\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(102\) 0 0
\(103\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −0.500000 0.181985i −0.500000 0.181985i
\(107\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) 0 0
\(109\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i \(0.222222\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(114\) 0 0
\(115\) 0.266044 0.223238i 0.266044 0.223238i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(122\) −2.20574 + 0.802823i −2.20574 + 0.802823i
\(123\) 0 0
\(124\) 0.358441 + 2.03282i 0.358441 + 2.03282i
\(125\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(126\) 0 0
\(127\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(128\) −0.766044 + 0.642788i −0.766044 + 0.642788i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −1.00000 −1.00000
\(137\) −0.326352 0.118782i −0.326352 0.118782i 0.173648 0.984808i \(-0.444444\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) 0 0
\(139\) −0.766044 0.642788i −0.766044 0.642788i 0.173648 0.984808i \(-0.444444\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(150\) 0 0
\(151\) −0.173648 0.984808i −0.173648 0.984808i −0.939693 0.342020i \(-0.888889\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(152\) 0.500000 0.866025i 0.500000 0.866025i
\(153\) 0 0
\(154\) 0 0
\(155\) 1.17365 0.984808i 1.17365 0.984808i
\(156\) 0 0
\(157\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(158\) 0.407604 + 0.342020i 0.407604 + 0.342020i
\(159\) 0 0
\(160\) 1.26604 + 0.460802i 1.26604 + 0.460802i
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −2.20574 1.85083i −2.20574 1.85083i
\(167\) 0.266044 1.50881i 0.266044 1.50881i −0.500000 0.866025i \(-0.666667\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(168\) 0 0
\(169\) 0.766044 0.642788i 0.766044 0.642788i
\(170\) 1.43969 + 2.49362i 1.43969 + 2.49362i
\(171\) 0 0
\(172\) 0 0
\(173\) 0.266044 + 1.50881i 0.266044 + 1.50881i 0.766044 + 0.642788i \(0.222222\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(180\) 0 0
\(181\) −0.173648 0.300767i −0.173648 0.300767i 0.766044 0.642788i \(-0.222222\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.0320889 0.181985i 0.0320889 0.181985i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −1.34730 −1.34730
\(189\) 0 0
\(190\) −2.87939 −2.87939
\(191\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(192\) 0 0
\(193\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1.03209 0.866025i 1.03209 0.866025i
\(197\) −0.766044 1.32683i −0.766044 1.32683i −0.939693 0.342020i \(-0.888889\pi\)
0.173648 0.984808i \(-0.444444\pi\)
\(198\) 0 0
\(199\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(200\) 0.0923963 + 0.524005i 0.0923963 + 0.524005i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0.266044 1.50881i 0.266044 1.50881i −0.500000 0.866025i \(-0.666667\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(212\) 0.358441 + 0.300767i 0.358441 + 0.300767i
\(213\) 0 0
\(214\) 1.43969 + 0.524005i 1.43969 + 0.524005i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −0.500000 0.181985i −0.500000 0.181985i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0.766044 1.32683i 0.766044 1.32683i
\(227\) 0.0603074 + 0.342020i 0.0603074 + 0.342020i 1.00000 \(0\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(228\) 0 0
\(229\) 1.76604 0.642788i 1.76604 0.642788i 0.766044 0.642788i \(-0.222222\pi\)
1.00000 \(0\)
\(230\) −0.500000 + 0.181985i −0.500000 + 0.181985i
\(231\) 0 0
\(232\) 0 0
\(233\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(234\) 0 0
\(235\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(240\) 0 0
\(241\) 1.76604 + 0.642788i 1.76604 + 0.642788i 1.00000 \(0\)
0.766044 + 0.642788i \(0.222222\pi\)
\(242\) 1.53209 1.53209
\(243\) 0 0
\(244\) 2.06418 2.06418
\(245\) −0.939693 0.342020i −0.939693 0.342020i
\(246\) 0 0
\(247\) 0 0
\(248\) 0.141559 0.802823i 0.141559 0.802823i
\(249\) 0 0
\(250\) 1.17365 0.984808i 1.17365 0.984808i
\(251\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.43969 + 0.524005i −1.43969 + 0.524005i −0.939693 0.342020i \(-0.888889\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 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
\(265\) 0.0603074 0.342020i 0.0603074 0.342020i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(272\) −0.939693 0.342020i −0.939693 0.342020i
\(273\) 0 0
\(274\) 0.407604 + 0.342020i 0.407604 + 0.342020i
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(278\) 0.766044 + 1.32683i 0.766044 + 1.32683i
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(282\) 0 0
\(283\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1.26604 2.19285i −1.26604 2.19285i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.43969 1.20805i −1.43969 1.20805i −0.939693 0.342020i \(-0.888889\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) −0.266044 + 1.50881i −0.266044 + 1.50881i
\(303\) 0 0
\(304\) 0.766044 0.642788i 0.766044 0.642788i
\(305\) −0.766044 1.32683i −0.766044 1.32683i
\(306\) 0 0
\(307\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −2.20574 + 0.802823i −2.20574 + 0.802823i
\(311\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(312\) 0 0
\(313\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −0.233956 0.405223i −0.233956 0.405223i
\(317\) −1.43969 + 1.20805i −1.43969 + 1.20805i −0.500000 + 0.866025i \(0.666667\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.17365 0.984808i −1.17365 0.984808i
\(321\) 0 0
\(322\) 0 0
\(323\) 3.53209 3.53209
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i \(-0.888889\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(332\) 1.26604 + 2.19285i 1.26604 + 2.19285i
\(333\) 0 0
\(334\) −1.17365 + 2.03282i −1.17365 + 2.03282i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(338\) −1.43969 + 0.524005i −1.43969 + 0.524005i
\(339\) 0 0
\(340\) −0.439693 2.49362i −0.439693 2.49362i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0.407604 2.31164i 0.407604 2.31164i
\(347\) −0.766044 0.642788i −0.766044 0.642788i 0.173648 0.984808i \(-0.444444\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(348\) 0 0
\(349\) −1.43969 0.524005i −1.43969 0.524005i −0.500000 0.866025i \(-0.666667\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0.939693 + 0.342020i 0.939693 + 0.342020i 0.766044 0.642788i \(-0.222222\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(360\) 0 0
\(361\) −1.26604 + 2.19285i −1.26604 + 2.19285i
\(362\) 0.0923963 + 0.524005i 0.0923963 + 0.524005i
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(368\) 0.0923963 0.160035i 0.0923963 0.160035i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0.500000 + 0.181985i 0.500000 + 0.181985i
\(377\) 0 0
\(378\) 0 0
\(379\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(380\) 2.37939 + 0.866025i 2.37939 + 0.866025i
\(381\) 0 0
\(382\) 0 0
\(383\) 0.266044 1.50881i 0.266044 1.50881i −0.500000 0.866025i \(-0.666667\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(384\) 0 0
\(385\) 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
\(391\) 0.613341 0.223238i 0.613341 0.223238i
\(392\) −0.500000 + 0.181985i −0.500000 + 0.181985i
\(393\) 0 0
\(394\) 0.407604 + 2.31164i 0.407604 + 2.31164i
\(395\) −0.173648 + 0.300767i −0.173648 + 0.300767i
\(396\) 0 0
\(397\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(398\) −1.17365 + 0.984808i −1.17365 + 0.984808i
\(399\) 0 0
\(400\) −0.0923963 + 0.524005i −0.0923963 + 0.524005i
\(401\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0.266044 + 0.223238i 0.266044 + 0.223238i 0.766044 0.642788i \(-0.222222\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0.939693 1.62760i 0.939693 1.62760i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(420\) 0 0
\(421\) 0.266044 + 1.50881i 0.266044 + 1.50881i 0.766044 + 0.642788i \(0.222222\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(422\) −1.17365 + 2.03282i −1.17365 + 2.03282i
\(423\) 0 0
\(424\) −0.0923963 0.160035i −0.0923963 0.160035i
\(425\) −1.43969 + 1.20805i −1.43969 + 1.20805i
\(426\) 0 0
\(427\) 0 0
\(428\) −1.03209 0.866025i −1.03209 0.866025i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.358441 + 0.300767i 0.358441 + 0.300767i
\(437\) −0.113341 + 0.642788i −0.113341 + 0.642788i
\(438\) 0 0
\(439\) −1.43969 + 1.20805i −1.43969 + 1.20805i −0.500000 + 0.866025i \(0.666667\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0.0603074 + 0.342020i 0.0603074 + 0.342020i 1.00000 \(0\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −1.03209 + 0.866025i −1.03209 + 0.866025i
\(453\) 0 0
\(454\) 0.0923963 0.524005i 0.0923963 0.524005i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(458\) −2.87939 −2.87939
\(459\) 0 0
\(460\) 0.467911 0.467911
\(461\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(462\) 0 0
\(463\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −1.17365 + 0.984808i −1.17365 + 0.984808i
\(467\) 0.939693 + 1.62760i 0.939693 + 1.62760i 0.766044 + 0.642788i \(0.222222\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −0.266044 1.50881i −0.266044 1.50881i
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −0.326352 1.85083i −0.326352 1.85083i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −2.20574 1.85083i −2.20574 1.85083i
\(483\) 0 0
\(484\) −1.26604 0.460802i −1.26604 0.460802i
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) −0.766044 0.278817i −0.766044 0.278817i
\(489\) 0 0
\(490\) 1.17365 + 0.984808i 1.17365 + 0.984808i
\(491\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.407604 0.705990i 0.407604 0.705990i
\(497\) 0 0
\(498\) 0 0
\(499\) −1.43969 + 0.524005i −1.43969 + 0.524005i −0.939693 0.342020i \(-0.888889\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) −1.26604 + 0.460802i −1.26604 + 0.460802i
\(501\) 0 0
\(502\) 0 0
\(503\) −0.766044 + 1.32683i −0.766044 + 1.32683i 0.173648 + 0.984808i \(0.444444\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 1.00000
\(513\) 0 0
\(514\) 2.34730 2.34730
\(515\) 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
\(525\) 0 0
\(526\) −2.87939 + 1.04801i −2.87939 + 1.04801i
\(527\) 2.70574 0.984808i 2.70574 0.984808i
\(528\) 0 0
\(529\) −0.152704 0.866025i −0.152704 0.866025i
\(530\) −0.266044 + 0.460802i −0.266044 + 0.460802i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(542\) 2.70574 + 0.984808i 2.70574 + 0.984808i
\(543\) 0 0
\(544\) 1.93969 + 1.62760i 1.93969 + 1.62760i
\(545\) 0.0603074 0.342020i 0.0603074 0.342020i
\(546\) 0 0
\(547\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(548\) −0.233956 0.405223i −0.233956 0.405223i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.233956 1.32683i −0.233956 1.32683i
\(557\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.53209 + 1.28558i 1.53209 + 1.28558i 0.766044 + 0.642788i \(0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(564\) 0 0
\(565\) 0.939693 + 0.342020i 0.939693 + 0.342020i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(570\) 0 0
\(571\) 0.266044 + 0.223238i 0.266044 + 0.223238i 0.766044 0.642788i \(-0.222222\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.173648 0.300767i −0.173648 0.300767i
\(576\) 0 0
\(577\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(578\) 0.673648 + 3.82045i 0.673648 + 3.82045i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 1.43969 + 2.49362i 1.43969 + 2.49362i
\(587\) 1.17365 0.984808i 1.17365 0.984808i 0.173648 0.984808i \(-0.444444\pi\)
1.00000 \(0\)
\(588\) 0 0
\(589\) −0.500000 + 2.83564i −0.500000 + 2.83564i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(600\) 0 0
\(601\) −1.43969 + 1.20805i −1.43969 + 1.20805i −0.500000 + 0.866025i \(0.666667\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.673648 1.16679i 0.673648 1.16679i
\(605\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(606\) 0 0
\(607\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(608\) −2.37939 + 0.866025i −2.37939 + 0.866025i
\(609\) 0 0
\(610\) 0.407604 + 2.31164i 0.407604 + 2.31164i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.17365 + 0.984808i 1.17365 + 0.984808i 1.00000 \(0\)
0.173648 + 0.984808i \(0.444444\pi\)
\(618\) 0 0
\(619\) 0.939693 + 0.342020i 0.939693 + 0.342020i 0.766044 0.642788i \(-0.222222\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(620\) 2.06418 2.06418
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −0.766044 + 1.32683i −0.766044 + 1.32683i 0.173648 + 0.984808i \(0.444444\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(632\) 0.0320889 + 0.181985i 0.0320889 + 0.181985i
\(633\) 0 0
\(634\) 2.70574 0.984808i 2.70574 0.984808i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(641\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(642\) 0 0
\(643\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −5.08512 1.85083i −5.08512 1.85083i
\(647\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −0.326352 + 1.85083i −0.326352 + 1.85083i 0.173648 + 0.984808i \(0.444444\pi\)
−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 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(660\) 0 0
\(661\) 0.939693 0.342020i 0.939693 0.342020i 0.173648 0.984808i \(-0.444444\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(662\) 1.43969 0.524005i 1.43969 0.524005i
\(663\) 0 0
\(664\) −0.173648 0.984808i −0.173648 0.984808i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 1.58125 1.32683i 1.58125 1.32683i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 1.34730 1.34730
\(677\) 0.939693 + 0.342020i 0.939693 + 0.342020i 0.766044 0.642788i \(-0.222222\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(681\) 0 0
\(682\) 0 0
\(683\) 0.939693 + 1.62760i 0.939693 + 1.62760i 0.766044 + 0.642788i \(0.222222\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(684\) 0 0
\(685\) −0.173648 + 0.300767i −0.173648 + 0.300767i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.0603074 + 0.342020i 0.0603074 + 0.342020i 1.00000 \(0\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(692\) −1.03209 + 1.78763i −1.03209 + 1.78763i
\(693\) 0 0
\(694\) 0.766044 + 1.32683i 0.766044 + 1.32683i
\(695\) −0.766044 + 0.642788i −0.766044 + 0.642788i
\(696\) 0 0
\(697\) 0 0
\(698\) 1.79813 + 1.50881i 1.79813 + 1.50881i
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −1.17365 0.984808i −1.17365 0.984808i
\(707\) 0 0
\(708\) 0 0
\(709\) −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i \(-0.888889\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0.0923963 + 0.524005i 0.0923963 + 0.524005i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 2.97178 2.49362i 2.97178 2.49362i
\(723\) 0 0
\(724\) 0.0812519 0.460802i 0.0812519 0.460802i
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.358441 + 0.300767i −0.358441 + 0.300767i
\(737\) 0 0
\(738\) 0 0
\(739\) −0.173648 + 0.300767i −0.173648 + 0.300767i −0.939693 0.342020i \(-0.888889\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.87939 + 0.684040i −1.87939 + 0.684040i −0.939693 + 0.342020i \(0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −0.326352 + 1.85083i −0.326352 + 1.85083i 0.173648 + 0.984808i \(0.444444\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 0.407604 + 0.342020i 0.407604 + 0.342020i
\(753\) 0 0
\(754\) 0 0
\(755\) −1.00000 −1.00000
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) −2.20574 0.802823i −2.20574 0.802823i
\(759\) 0 0
\(760\) −0.766044 0.642788i −0.766044 0.642788i
\(761\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −1.17365 + 2.03282i −1.17365 + 2.03282i
\(767\) 0 0
\(768\) 0 0
\(769\) −0.326352 + 0.118782i −0.326352 + 0.118782i −0.500000 0.866025i \(-0.666667\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0.939693 1.62760i 0.939693 1.62760i 0.173648 0.984808i \(-0.444444\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(774\) 0 0
\(775\) −0.766044 1.32683i −0.766044 1.32683i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) −1.00000 −1.00000
\(783\) 0 0
\(784\) −0.532089 −0.532089
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(788\) 0.358441 2.03282i 0.358441 2.03282i
\(789\) 0 0
\(790\) 0.407604 0.342020i 0.407604 0.342020i
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 1.26604 0.460802i 1.26604 0.460802i
\(797\) −0.326352 + 0.118782i −0.326352 + 0.118782i −0.500000 0.866025i \(-0.666667\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(798\) 0 0