Properties

Label 3800.1.cv.f.1051.1
Level $3800$
Weight $1$
Character 3800.1051
Analytic conductor $1.896$
Analytic rank $0$
Dimension $12$
Projective image $D_{9}$
CM discriminant -40
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3800,1,Mod(251,3800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3800, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 9, 0, 2]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3800.251");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3800.cv (of order \(18\), degree \(6\), 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: \(1.89644704801\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{18})\)
Coefficient field: \(\Q(\zeta_{36})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{6} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 760)
Projective image: \(D_{9}\)
Projective field: Galois closure of 9.1.43477921384960000.1

Embedding invariants

Embedding label 1051.1
Root \(0.642788 + 0.766044i\) of defining polynomial
Character \(\chi\) \(=\) 3800.1051
Dual form 3800.1.cv.f.1251.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.642788 - 0.766044i) q^{2} +(-0.173648 + 0.984808i) q^{4} +(0.300767 + 0.173648i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})\) \(q+(-0.642788 - 0.766044i) q^{2} +(-0.173648 + 0.984808i) q^{4} +(0.300767 + 0.173648i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-0.766044 - 1.32683i) q^{11} +(0.342020 + 0.939693i) q^{13} +(-0.0603074 - 0.342020i) q^{14} +(-0.939693 - 0.342020i) q^{16} +1.00000i q^{18} +(-0.766044 + 0.642788i) q^{19} +(-0.524005 + 1.43969i) q^{22} +(-1.85083 - 0.326352i) q^{23} +(0.500000 - 0.866025i) q^{26} +(-0.223238 + 0.266044i) q^{28} +(0.342020 + 0.939693i) q^{32} +(0.766044 - 0.642788i) q^{36} +1.87939i q^{37} +(0.984808 + 0.173648i) q^{38} +(-1.43969 - 0.524005i) q^{41} +(1.43969 - 0.524005i) q^{44} +(0.939693 + 1.62760i) q^{46} +(-0.642788 + 0.766044i) q^{47} +(-0.439693 - 0.761570i) q^{49} +(-0.984808 + 0.173648i) q^{52} +(0.342020 + 0.0603074i) q^{53} +0.347296 q^{56} +(0.766044 - 0.642788i) q^{59} +(-0.118782 - 0.326352i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-0.984808 - 0.173648i) q^{72} +(1.43969 - 1.20805i) q^{74} +(-0.500000 - 0.866025i) q^{76} -0.532089i q^{77} +(0.173648 + 0.984808i) q^{81} +(0.524005 + 1.43969i) q^{82} +(-1.32683 - 0.766044i) q^{88} +(-1.76604 + 0.642788i) q^{89} +(-0.0603074 + 0.342020i) q^{91} +(0.642788 - 1.76604i) q^{92} +1.00000 q^{94} +(-0.300767 + 0.826352i) q^{98} +(-0.266044 + 1.50881i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 12 q^{14} + 6 q^{26} - 6 q^{41} + 6 q^{44} + 6 q^{49} + 6 q^{64} + 6 q^{74} - 6 q^{76} - 12 q^{89} - 12 q^{91} + 12 q^{94} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3800\mathbb{Z}\right)^\times\).

\(n\) \(401\) \(951\) \(1901\) \(1977\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(-1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.642788 0.766044i −0.642788 0.766044i
\(3\) 0 0 0.342020 0.939693i \(-0.388889\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(4\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(5\) 0 0
\(6\) 0 0
\(7\) 0.300767 + 0.173648i 0.300767 + 0.173648i 0.642788 0.766044i \(-0.277778\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(8\) 0.866025 0.500000i 0.866025 0.500000i
\(9\) −0.766044 0.642788i −0.766044 0.642788i
\(10\) 0 0
\(11\) −0.766044 1.32683i −0.766044 1.32683i −0.939693 0.342020i \(-0.888889\pi\)
0.173648 0.984808i \(-0.444444\pi\)
\(12\) 0 0
\(13\) 0.342020 + 0.939693i 0.342020 + 0.939693i 0.984808 + 0.173648i \(0.0555556\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(14\) −0.0603074 0.342020i −0.0603074 0.342020i
\(15\) 0 0
\(16\) −0.939693 0.342020i −0.939693 0.342020i
\(17\) 0 0 −0.642788 0.766044i \(-0.722222\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(18\) 1.00000i 1.00000i
\(19\) −0.766044 + 0.642788i −0.766044 + 0.642788i
\(20\) 0 0
\(21\) 0 0
\(22\) −0.524005 + 1.43969i −0.524005 + 1.43969i
\(23\) −1.85083 0.326352i −1.85083 0.326352i −0.866025 0.500000i \(-0.833333\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0.500000 0.866025i 0.500000 0.866025i
\(27\) 0 0
\(28\) −0.223238 + 0.266044i −0.223238 + 0.266044i
\(29\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(30\) 0 0
\(31\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 0.342020 + 0.939693i 0.342020 + 0.939693i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.766044 0.642788i 0.766044 0.642788i
\(37\) 1.87939i 1.87939i 0.342020 + 0.939693i \(0.388889\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(38\) 0.984808 + 0.173648i 0.984808 + 0.173648i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.43969 0.524005i −1.43969 0.524005i −0.500000 0.866025i \(-0.666667\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(42\) 0 0
\(43\) 0 0 0.984808 0.173648i \(-0.0555556\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(44\) 1.43969 0.524005i 1.43969 0.524005i
\(45\) 0 0
\(46\) 0.939693 + 1.62760i 0.939693 + 1.62760i
\(47\) −0.642788 + 0.766044i −0.642788 + 0.766044i −0.984808 0.173648i \(-0.944444\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(48\) 0 0
\(49\) −0.439693 0.761570i −0.439693 0.761570i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.984808 + 0.173648i −0.984808 + 0.173648i
\(53\) 0.342020 + 0.0603074i 0.342020 + 0.0603074i 0.342020 0.939693i \(-0.388889\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0.347296 0.347296
\(57\) 0 0
\(58\) 0 0
\(59\) 0.766044 0.642788i 0.766044 0.642788i −0.173648 0.984808i \(-0.555556\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(60\) 0 0
\(61\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(62\) 0 0
\(63\) −0.118782 0.326352i −0.118782 0.326352i
\(64\) 0.500000 0.866025i 0.500000 0.866025i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.642788 0.766044i \(-0.277778\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(72\) −0.984808 0.173648i −0.984808 0.173648i
\(73\) 0 0 0.342020 0.939693i \(-0.388889\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(74\) 1.43969 1.20805i 1.43969 1.20805i
\(75\) 0 0
\(76\) −0.500000 0.866025i −0.500000 0.866025i
\(77\) 0.532089i 0.532089i
\(78\) 0 0
\(79\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(80\) 0 0
\(81\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(82\) 0.524005 + 1.43969i 0.524005 + 1.43969i
\(83\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −1.32683 0.766044i −1.32683 0.766044i
\(89\) −1.76604 + 0.642788i −1.76604 + 0.642788i −0.766044 + 0.642788i \(0.777778\pi\)
−1.00000 \(1.00000\pi\)
\(90\) 0 0
\(91\) −0.0603074 + 0.342020i −0.0603074 + 0.342020i
\(92\) 0.642788 1.76604i 0.642788 1.76604i
\(93\) 0 0
\(94\) 1.00000 1.00000
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 −0.642788 0.766044i \(-0.722222\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(98\) −0.300767 + 0.826352i −0.300767 + 0.826352i
\(99\) −0.266044 + 1.50881i −0.266044 + 1.50881i
\(100\) 0 0
\(101\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(102\) 0 0
\(103\) 0.300767 0.173648i 0.300767 0.173648i −0.342020 0.939693i \(-0.611111\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(104\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(105\) 0 0
\(106\) −0.173648 0.300767i −0.173648 0.300767i
\(107\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(108\) 0 0
\(109\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.223238 0.266044i −0.223238 0.266044i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.342020 0.939693i 0.342020 0.939693i
\(118\) −0.984808 0.173648i −0.984808 0.173648i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.673648 + 1.16679i −0.673648 + 1.16679i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −0.173648 + 0.300767i −0.173648 + 0.300767i
\(127\) −0.642788 1.76604i −0.642788 1.76604i −0.642788 0.766044i \(-0.722222\pi\)
1.00000i \(-0.5\pi\)
\(128\) −0.984808 + 0.173648i −0.984808 + 0.173648i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.43969 + 1.20805i −1.43969 + 1.20805i −0.500000 + 0.866025i \(0.666667\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(132\) 0 0
\(133\) −0.342020 + 0.0603074i −0.342020 + 0.0603074i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.984808 0.173648i \(-0.944444\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(138\) 0 0
\(139\) −0.939693 + 0.342020i −0.939693 + 0.342020i −0.766044 0.642788i \(-0.777778\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.984808 1.17365i 0.984808 1.17365i
\(144\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −1.85083 0.326352i −1.85083 0.326352i
\(149\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) −0.342020 + 0.939693i −0.342020 + 0.939693i
\(153\) 0 0
\(154\) −0.407604 + 0.342020i −0.407604 + 0.342020i
\(155\) 0 0
\(156\) 0 0
\(157\) −1.85083 + 0.326352i −1.85083 + 0.326352i −0.984808 0.173648i \(-0.944444\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −0.500000 0.419550i −0.500000 0.419550i
\(162\) 0.642788 0.766044i 0.642788 0.766044i
\(163\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(164\) 0.766044 1.32683i 0.766044 1.32683i
\(165\) 0 0
\(166\) 0 0
\(167\) −1.50881 0.266044i −1.50881 0.266044i −0.642788 0.766044i \(-0.722222\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 1.00000 1.00000
\(172\) 0 0
\(173\) 0.984808 + 1.17365i 0.984808 + 1.17365i 0.984808 + 0.173648i \(0.0555556\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.266044 + 1.50881i 0.266044 + 1.50881i
\(177\) 0 0
\(178\) 1.62760 + 0.939693i 1.62760 + 0.939693i
\(179\) −0.939693 1.62760i −0.939693 1.62760i −0.766044 0.642788i \(-0.777778\pi\)
−0.173648 0.984808i \(-0.555556\pi\)
\(180\) 0 0
\(181\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(182\) 0.300767 0.173648i 0.300767 0.173648i
\(183\) 0 0
\(184\) −1.76604 + 0.642788i −1.76604 + 0.642788i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.642788 0.766044i −0.642788 0.766044i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) 0 0 0.342020 0.939693i \(-0.388889\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.826352 0.300767i 0.826352 0.300767i
\(197\) 1.32683 + 0.766044i 1.32683 + 0.766044i 0.984808 0.173648i \(-0.0555556\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(198\) 1.32683 0.766044i 1.32683 0.766044i
\(199\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −0.326352 0.118782i −0.326352 0.118782i
\(207\) 1.20805 + 1.43969i 1.20805 + 1.43969i
\(208\) 1.00000i 1.00000i
\(209\) 1.43969 + 0.524005i 1.43969 + 0.524005i
\(210\) 0 0
\(211\) 1.17365 0.984808i 1.17365 0.984808i 0.173648 0.984808i \(-0.444444\pi\)
1.00000 \(0\)
\(212\) −0.118782 + 0.326352i −0.118782 + 0.326352i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1.50881 + 0.266044i −1.50881 + 0.266044i −0.866025 0.500000i \(-0.833333\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(224\) −0.0603074 + 0.342020i −0.0603074 + 0.342020i
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.984808 0.173648i \(-0.0555556\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(234\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(235\) 0 0
\(236\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) 0 0
\(241\) 0.939693 0.342020i 0.939693 0.342020i 0.173648 0.984808i \(-0.444444\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(242\) 1.32683 0.233956i 1.32683 0.233956i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −0.866025 0.500000i −0.866025 0.500000i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i \(0.222222\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(252\) 0.342020 0.0603074i 0.342020 0.0603074i
\(253\) 0.984808 + 2.70574i 0.984808 + 2.70574i
\(254\) −0.939693 + 1.62760i −0.939693 + 1.62760i
\(255\) 0 0
\(256\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(257\) 0 0 0.642788 0.766044i \(-0.277778\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(258\) 0 0
\(259\) −0.326352 + 0.565258i −0.326352 + 0.565258i
\(260\) 0 0
\(261\) 0 0
\(262\) 1.85083 + 0.326352i 1.85083 + 0.326352i
\(263\) 0.524005 1.43969i 0.524005 1.43969i −0.342020 0.939693i \(-0.611111\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0.266044 + 0.223238i 0.266044 + 0.223238i
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(270\) 0 0
\(271\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(278\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.0603074 0.342020i 0.0603074 0.342020i −0.939693 0.342020i \(-0.888889\pi\)
1.00000 \(0\)
\(282\) 0 0
\(283\) 0 0 −0.642788 0.766044i \(-0.722222\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −1.53209 −1.53209
\(287\) −0.342020 0.407604i −0.342020 0.407604i
\(288\) 0.342020 0.939693i 0.342020 0.939693i
\(289\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0.300767 0.173648i 0.300767 0.173648i −0.342020 0.939693i \(-0.611111\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.939693 + 1.62760i 0.939693 + 1.62760i
\(297\) 0 0
\(298\) 0 0
\(299\) −0.326352 1.85083i −0.326352 1.85083i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.939693 0.342020i 0.939693 0.342020i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.342020 0.939693i \(-0.388889\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(308\) 0.524005 + 0.0923963i 0.524005 + 0.0923963i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) 0 0
\(313\) 0 0 0.642788 0.766044i \(-0.277778\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(314\) 1.43969 + 1.20805i 1.43969 + 1.20805i
\(315\) 0 0
\(316\) 0 0
\(317\) 0.524005 + 1.43969i 0.524005 + 1.43969i 0.866025 + 0.500000i \(0.166667\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0.652704i 0.652704i
\(323\) 0 0
\(324\) −1.00000 −1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) −1.50881 + 0.266044i −1.50881 + 0.266044i
\(329\) −0.326352 + 0.118782i −0.326352 + 0.118782i
\(330\) 0 0
\(331\) −0.173648 0.300767i −0.173648 0.300767i 0.766044 0.642788i \(-0.222222\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(332\) 0 0
\(333\) 1.20805 1.43969i 1.20805 1.43969i
\(334\) 0.766044 + 1.32683i 0.766044 + 1.32683i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.984808 0.173648i \(-0.0555556\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) −0.642788 0.766044i −0.642788 0.766044i
\(343\) 0.652704i 0.652704i
\(344\) 0 0
\(345\) 0 0
\(346\) 0.266044 1.50881i 0.266044 1.50881i
\(347\) 0 0 0.984808 0.173648i \(-0.0555556\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(348\) 0 0
\(349\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.984808 1.17365i 0.984808 1.17365i
\(353\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.326352 1.85083i −0.326352 1.85083i
\(357\) 0 0
\(358\) −0.642788 + 1.76604i −0.642788 + 1.76604i
\(359\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(360\) 0 0
\(361\) 0.173648 0.984808i 0.173648 0.984808i
\(362\) 0 0
\(363\) 0 0
\(364\) −0.326352 0.118782i −0.326352 0.118782i
\(365\) 0 0
\(366\) 0 0
\(367\) −0.342020 0.939693i −0.342020 0.939693i −0.984808 0.173648i \(-0.944444\pi\)
0.642788 0.766044i \(-0.277778\pi\)
\(368\) 1.62760 + 0.939693i 1.62760 + 0.939693i
\(369\) 0.766044 + 1.32683i 0.766044 + 1.32683i
\(370\) 0 0
\(371\) 0.0923963 + 0.0775297i 0.0923963 + 0.0775297i
\(372\) 0 0
\(373\) −0.300767 0.173648i −0.300767 0.173648i 0.342020 0.939693i \(-0.388889\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(377\) 0 0
\(378\) 0 0
\(379\) 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 0
\(383\) −0.342020 + 0.939693i −0.342020 + 0.939693i 0.642788 + 0.766044i \(0.277778\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.761570 0.439693i −0.761570 0.439693i
\(393\) 0 0
\(394\) −0.266044 1.50881i −0.266044 1.50881i
\(395\) 0 0
\(396\) −1.43969 0.524005i −1.43969 0.524005i
\(397\) −0.984808 1.17365i −0.984808 1.17365i −0.984808 0.173648i \(-0.944444\pi\)
1.00000i \(-0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.53209 1.28558i 1.53209 1.28558i 0.766044 0.642788i \(-0.222222\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.49362 1.43969i 2.49362 1.43969i
\(408\) 0 0
\(409\) −0.266044 0.223238i −0.266044 0.223238i 0.500000 0.866025i \(-0.333333\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0.118782 + 0.326352i 0.118782 + 0.326352i
\(413\) 0.342020 0.0603074i 0.342020 0.0603074i
\(414\) 0.326352 1.85083i 0.326352 1.85083i
\(415\) 0 0
\(416\) −0.766044 + 0.642788i −0.766044 + 0.642788i
\(417\) 0 0
\(418\) −0.524005 1.43969i −0.524005 1.43969i
\(419\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(420\) 0 0
\(421\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(422\) −1.50881 0.266044i −1.50881 0.266044i
\(423\) 0.984808 0.173648i 0.984808 0.173648i
\(424\) 0.326352 0.118782i 0.326352 0.118782i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(432\) 0 0
\(433\) 0 0 −0.984808 0.173648i \(-0.944444\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.62760 0.939693i 1.62760 0.939693i
\(438\) 0 0
\(439\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(440\) 0 0
\(441\) −0.152704 + 0.866025i −0.152704 + 0.866025i
\(442\) 0 0
\(443\) 0 0 −0.342020 0.939693i \(-0.611111\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 1.17365 + 0.984808i 1.17365 + 0.984808i
\(447\) 0 0
\(448\) 0.300767 0.173648i 0.300767 0.173648i
\(449\) 0.766044 1.32683i 0.766044 1.32683i −0.173648 0.984808i \(-0.555556\pi\)
0.939693 0.342020i \(-0.111111\pi\)
\(450\) 0 0
\(451\) 0.407604 + 2.31164i 0.407604 + 2.31164i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(462\) 0 0
\(463\) −1.32683 0.766044i −1.32683 0.766044i −0.342020 0.939693i \(-0.611111\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(468\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0.342020 0.939693i 0.342020 0.939693i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.223238 0.266044i −0.223238 0.266044i
\(478\) 0 0
\(479\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(480\) 0 0
\(481\) −1.76604 + 0.642788i −1.76604 + 0.642788i
\(482\) −0.866025 0.500000i −0.866025 0.500000i
\(483\) 0 0
\(484\) −1.03209 0.866025i −1.03209 0.866025i
\(485\) 0 0
\(486\) 0 0
\(487\) 0.300767 + 0.173648i 0.300767 + 0.173648i 0.642788 0.766044i \(-0.277778\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.76604 + 0.642788i 1.76604 + 0.642788i 1.00000 \(0\)
0.766044 + 0.642788i \(0.222222\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −0.0603074 0.342020i −0.0603074 0.342020i 0.939693 0.342020i \(-0.111111\pi\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0.866025 0.500000i 0.866025 0.500000i
\(503\) −0.984808 + 1.17365i −0.984808 + 1.17365i 1.00000i \(0.5\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(504\) −0.266044 0.223238i −0.266044 0.223238i
\(505\) 0 0
\(506\) 1.43969 2.49362i 1.43969 2.49362i
\(507\) 0 0
\(508\) 1.85083 0.326352i 1.85083 0.326352i
\(509\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 1.00000i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 1.50881 + 0.266044i 1.50881 + 0.266044i
\(518\) 0.642788 0.113341i 0.642788 0.113341i
\(519\) 0 0
\(520\) 0 0
\(521\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(522\) 0 0
\(523\) 0 0 0.642788 0.766044i \(-0.277778\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(524\) −0.939693 1.62760i −0.939693 1.62760i
\(525\) 0 0
\(526\) −1.43969 + 0.524005i −1.43969 + 0.524005i
\(527\) 0 0
\(528\) 0 0
\(529\) 2.37939 + 0.866025i 2.37939 + 0.866025i
\(530\) 0 0
\(531\) −1.00000 −1.00000
\(532\) 0.347296i 0.347296i
\(533\) 1.53209i 1.53209i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.673648 + 1.16679i −0.673648 + 1.16679i
\(540\) 0 0
\(541\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.984808 0.173648i \(-0.944444\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −0.939693 0.342020i −0.939693 0.342020i
\(555\) 0 0
\(556\) −0.173648 0.984808i −0.173648 0.984808i
\(557\) 0.118782 + 0.326352i 0.118782 + 0.326352i 0.984808 0.173648i \(-0.0555556\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −0.300767 + 0.173648i −0.300767 + 0.173648i
\(563\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.118782 + 0.326352i −0.118782 + 0.326352i
\(568\) 0 0
\(569\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(570\) 0 0
\(571\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0.984808 + 1.17365i 0.984808 + 1.17365i
\(573\) 0 0
\(574\) −0.0923963 + 0.524005i −0.0923963 + 0.524005i
\(575\) 0 0
\(576\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(577\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(578\) 0.866025 0.500000i 0.866025 0.500000i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −0.181985 0.500000i −0.181985 0.500000i
\(584\) 0 0
\(585\) 0 0
\(586\) −0.326352 0.118782i −0.326352 0.118782i
\(587\) 0 0 −0.642788 0.766044i \(-0.722222\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.642788 1.76604i 0.642788 1.76604i
\(593\) 0 0 −0.984808 0.173648i \(-0.944444\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −1.20805 + 1.43969i −1.20805 + 1.43969i
\(599\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(600\) 0 0
\(601\) −0.766044 + 1.32683i −0.766044 + 1.32683i 0.173648 + 0.984808i \(0.444444\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0.347296i 0.347296i −0.984808 0.173648i \(-0.944444\pi\)
0.984808 0.173648i \(-0.0555556\pi\)
\(608\) −0.866025 0.500000i −0.866025 0.500000i
\(609\) 0 0
\(610\) 0 0
\(611\) −0.939693 0.342020i −0.939693 0.342020i
\(612\) 0 0
\(613\) −1.50881 + 0.266044i −1.50881 + 0.266044i −0.866025 0.500000i \(-0.833333\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −0.266044 0.460802i −0.266044 0.460802i
\(617\) 0 0 0.642788 0.766044i \(-0.277778\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(618\) 0 0
\(619\) 0.173648 + 0.300767i 0.173648 + 0.300767i 0.939693 0.342020i \(-0.111111\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −0.642788 0.113341i −0.642788 0.113341i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 1.87939i 1.87939i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0.766044 1.32683i 0.766044 1.32683i
\(635\) 0 0
\(636\) 0 0
\(637\) 0.565258 0.673648i 0.565258 0.673648i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.173648 0.984808i −0.173648 0.984808i −0.939693 0.342020i \(-0.888889\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(642\) 0 0
\(643\) 0 0 0.342020 0.939693i \(-0.388889\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(644\) 0.500000 0.419550i 0.500000 0.419550i
\(645\) 0 0
\(646\) 0 0
\(647\) 1.87939i 1.87939i 0.342020 + 0.939693i \(0.388889\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(648\) 0.642788 + 0.766044i 0.642788 + 0.766044i
\(649\) −1.43969 0.524005i −1.43969 0.524005i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −0.300767 0.173648i −0.300767 0.173648i 0.342020 0.939693i \(-0.388889\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.17365 + 0.984808i 1.17365 + 0.984808i
\(657\) 0 0
\(658\) 0.300767 + 0.173648i 0.300767 + 0.173648i
\(659\) 1.43969 0.524005i 1.43969 0.524005i 0.500000 0.866025i \(-0.333333\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(660\) 0 0
\(661\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(662\) −0.118782 + 0.326352i −0.118782 + 0.326352i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −1.87939 −1.87939
\(667\) 0 0
\(668\) 0.524005 1.43969i 0.524005 1.43969i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.62760 0.939693i −1.62760 0.939693i −0.984808 0.173648i \(-0.944444\pi\)
−0.642788 0.766044i \(-0.722222\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) −0.173648 + 0.984808i −0.173648 + 0.984808i
\(685\) 0 0
\(686\) −0.500000 + 0.419550i −0.500000 + 0.419550i
\(687\) 0 0
\(688\) 0 0
\(689\) 0.0603074 + 0.342020i 0.0603074 + 0.342020i
\(690\) 0 0
\(691\) 0.939693 1.62760i 0.939693 1.62760i 0.173648 0.984808i \(-0.444444\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(692\) −1.32683 + 0.766044i −1.32683 + 0.766044i
\(693\) −0.342020 + 0.407604i −0.342020 + 0.407604i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(702\) 0 0
\(703\) −1.20805 1.43969i −1.20805 1.43969i
\(704\) −1.53209 −1.53209
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1.20805 + 1.43969i −1.20805 + 1.43969i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.76604 0.642788i 1.76604 0.642788i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(720\) 0 0
\(721\) 0.120615 0.120615
\(722\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1.96962 0.347296i 1.96962 0.347296i 0.984808 0.173648i \(-0.0555556\pi\)
0.984808 0.173648i \(-0.0555556\pi\)
\(728\) 0.118782 + 0.326352i 0.118782 + 0.326352i
\(729\) 0.500000 0.866025i 0.500000 0.866025i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0.300767 0.173648i 0.300767 0.173648i −0.342020 0.939693i \(-0.611111\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(734\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(735\) 0 0
\(736\) −0.326352 1.85083i −0.326352 1.85083i
\(737\) 0 0
\(738\) 0.524005 1.43969i 0.524005 1.43969i
\(739\) 1.43969 1.20805i 1.43969 1.20805i 0.500000 0.866025i \(-0.333333\pi\)
0.939693 0.342020i \(-0.111111\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.120615i 0.120615i
\(743\) 0.223238 + 0.266044i 0.223238 + 0.266044i 0.866025 0.500000i \(-0.166667\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0.0603074 + 0.342020i 0.0603074 + 0.342020i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(752\) 0.866025 0.500000i 0.866025 0.500000i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −0.524005 + 1.43969i −0.524005 + 1.43969i 0.342020 + 0.939693i \(0.388889\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(758\) −0.642788 0.766044i −0.642788 0.766044i
\(759\) 0 0
\(760\) 0 0
\(761\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0.939693 0.342020i 0.939693 0.342020i
\(767\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(768\) 0 0
\(769\) 0.766044 + 0.642788i 0.766044 + 0.642788i 0.939693 0.342020i \(-0.111111\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0.642788 + 1.76604i 0.642788 + 1.76604i 0.642788 + 0.766044i \(0.277778\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.43969 0.524005i 1.43969 0.524005i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.152704 + 0.866025i 0.152704 + 0.866025i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(788\) −0.984808 + 1.17365i −0.984808 + 1.17365i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.524005 + 1.43969i 0.524005 + 1.43969i
\(793\) 0 0
\(794\) −0.266044 + 1.50881i −0.266044 + 1.50881i
\(795\) 0 0
\(796\) 0 0