Properties

Label 3332.1.bp.b.3007.1
Level $3332$
Weight $1$
Character 3332.3007
Analytic conductor $1.663$
Analytic rank $0$
Dimension $8$
Projective image $D_{8}$
CM discriminant -4
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3332,1,Mod(263,3332)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3332, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([12, 16, 15]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3332.263");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3332.bp (of order \(24\), degree \(8\), 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: \(1.66288462209\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{8}\)
Projective field: Galois closure of 8.2.3089659810545728.4

Embedding invariants

Embedding label 3007.1
Root \(-0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 3332.3007
Dual form 3332.1.bp.b.2235.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.607206 + 0.465926i) q^{5} +(0.707107 - 0.707107i) q^{8} +(0.965926 + 0.258819i) q^{9} +O(q^{10})\) \(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.607206 + 0.465926i) q^{5} +(0.707107 - 0.707107i) q^{8} +(0.965926 + 0.258819i) q^{9} +(-0.607206 + 0.465926i) q^{10} +(0.500000 + 0.866025i) q^{16} +(0.965926 - 0.258819i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.292893 - 0.707107i) q^{20} +(-0.107206 - 0.400100i) q^{25} +(0.707107 - 0.292893i) q^{29} +(-0.965926 + 0.258819i) q^{32} +1.00000i q^{34} +(-0.707107 - 0.707107i) q^{36} +(0.465926 - 0.607206i) q^{37} +(0.758819 - 0.0999004i) q^{40} +(-1.70711 - 0.707107i) q^{41} +(0.465926 + 0.607206i) q^{45} +0.414214 q^{50} +(1.36603 - 0.366025i) q^{53} +(0.0999004 + 0.758819i) q^{58} +(0.241181 + 1.83195i) q^{61} -1.00000i q^{64} +(-0.965926 - 0.258819i) q^{68} +(0.866025 - 0.500000i) q^{72} +(-0.0999004 + 0.758819i) q^{73} +(0.465926 + 0.607206i) q^{74} +(-0.0999004 + 0.758819i) q^{80} +(0.866025 + 0.500000i) q^{81} +(1.12484 - 1.46593i) q^{82} +(0.707107 + 0.292893i) q^{85} +(-1.73205 + 1.00000i) q^{89} +(-0.707107 + 0.292893i) q^{90} +(-0.707107 + 0.292893i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{16} - 4 q^{18} - 8 q^{20} + 4 q^{25} - 4 q^{37} + 4 q^{40} - 8 q^{41} - 4 q^{45} - 8 q^{50} + 4 q^{53} + 4 q^{61} - 4 q^{74}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(885\) \(1667\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(3\) 0 0 −0.991445 0.130526i \(-0.958333\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(4\) −0.866025 0.500000i −0.866025 0.500000i
\(5\) 0.607206 + 0.465926i 0.607206 + 0.465926i 0.866025 0.500000i \(-0.166667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0.707107 0.707107i 0.707107 0.707107i
\(9\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(10\) −0.607206 + 0.465926i −0.607206 + 0.465926i
\(11\) 0 0 −0.608761 0.793353i \(-0.708333\pi\)
0.608761 + 0.793353i \(0.291667\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(17\) 0.965926 0.258819i 0.965926 0.258819i
\(18\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(19\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(20\) −0.292893 0.707107i −0.292893 0.707107i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 0.991445 0.130526i \(-0.0416667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(24\) 0 0
\(25\) −0.107206 0.400100i −0.107206 0.400100i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.707107 0.292893i 0.707107 0.292893i 1.00000i \(-0.5\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(30\) 0 0
\(31\) 0 0 −0.991445 0.130526i \(-0.958333\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(32\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(33\) 0 0
\(34\) 1.00000i 1.00000i
\(35\) 0 0
\(36\) −0.707107 0.707107i −0.707107 0.707107i
\(37\) 0.465926 0.607206i 0.465926 0.607206i −0.500000 0.866025i \(-0.666667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.758819 0.0999004i 0.758819 0.0999004i
\(41\) −1.70711 0.707107i −1.70711 0.707107i −0.707107 0.707107i \(-0.750000\pi\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(44\) 0 0
\(45\) 0.465926 + 0.607206i 0.465926 + 0.607206i
\(46\) 0 0
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.414214 0.414214
\(51\) 0 0
\(52\) 0 0
\(53\) 1.36603 0.366025i 1.36603 0.366025i 0.500000 0.866025i \(-0.333333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0.0999004 + 0.758819i 0.0999004 + 0.758819i
\(59\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(60\) 0 0
\(61\) 0.241181 + 1.83195i 0.241181 + 1.83195i 0.500000 + 0.866025i \(0.333333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000i 1.00000i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) −0.965926 0.258819i −0.965926 0.258819i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(72\) 0.866025 0.500000i 0.866025 0.500000i
\(73\) −0.0999004 + 0.758819i −0.0999004 + 0.758819i 0.866025 + 0.500000i \(0.166667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(74\) 0.465926 + 0.607206i 0.465926 + 0.607206i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.991445 0.130526i \(-0.0416667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(80\) −0.0999004 + 0.758819i −0.0999004 + 0.758819i
\(81\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(82\) 1.12484 1.46593i 1.12484 1.46593i
\(83\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(84\) 0 0
\(85\) 0.707107 + 0.292893i 0.707107 + 0.292893i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.73205 + 1.00000i −1.73205 + 1.00000i −0.866025 + 0.500000i \(0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) −0.707107 + 0.292893i −0.707107 + 0.292893i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.707107 + 0.292893i −0.707107 + 0.292893i −0.707107 0.707107i \(-0.750000\pi\)
1.00000i \(0.5\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −0.107206 + 0.400100i −0.107206 + 0.400100i
\(101\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(102\) 0 0
\(103\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 1.41421i 1.41421i
\(107\) 0 0 −0.793353 0.608761i \(-0.791667\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(108\) 0 0
\(109\) 1.46593 1.12484i 1.46593 1.12484i 0.500000 0.866025i \(-0.333333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.707107 + 1.70711i −0.707107 + 1.70711i 1.00000i \(0.5\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.758819 0.0999004i −0.758819 0.0999004i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(122\) −1.83195 0.241181i −1.83195 0.241181i
\(123\) 0 0
\(124\) 0 0
\(125\) 0.414214 1.00000i 0.414214 1.00000i
\(126\) 0 0
\(127\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(128\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.793353 0.608761i \(-0.791667\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0.500000 0.866025i 0.500000 0.866025i
\(137\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(138\) 0 0
\(139\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(145\) 0.565826 + 0.151613i 0.565826 + 0.151613i
\(146\) −0.707107 0.292893i −0.707107 0.292893i
\(147\) 0 0
\(148\) −0.707107 + 0.292893i −0.707107 + 0.292893i
\(149\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) 0 0
\(151\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(152\) 0 0
\(153\) 1.00000 1.00000
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −0.707107 0.292893i −0.707107 0.292893i
\(161\) 0 0
\(162\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(163\) 0 0 −0.130526 0.991445i \(-0.541667\pi\)
0.130526 + 0.991445i \(0.458333\pi\)
\(164\) 1.12484 + 1.46593i 1.12484 + 1.46593i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(168\) 0 0
\(169\) 1.00000 1.00000
\(170\) −0.465926 + 0.607206i −0.465926 + 0.607206i
\(171\) 0 0
\(172\) 0 0
\(173\) −1.12484 + 1.46593i −1.12484 + 1.46593i −0.258819 + 0.965926i \(0.583333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) −0.517638 1.93185i −0.517638 1.93185i
\(179\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(180\) −0.0999004 0.758819i −0.0999004 0.758819i
\(181\) −0.707107 + 1.70711i −0.707107 + 1.70711i 1.00000i \(0.5\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.565826 0.151613i 0.565826 0.151613i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) 0 0
\(193\) 0.465926 + 0.607206i 0.465926 + 0.607206i 0.965926 0.258819i \(-0.0833333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) −0.0999004 0.758819i −0.0999004 0.758819i
\(195\) 0 0
\(196\) 0 0
\(197\) −1.70711 0.707107i −1.70711 0.707107i −0.707107 0.707107i \(-0.750000\pi\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 0.130526 0.991445i \(-0.458333\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(200\) −0.358719 0.207107i −0.358719 0.207107i
\(201\) 0 0
\(202\) 1.41421 + 1.41421i 1.41421 + 1.41421i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.707107 1.22474i −0.707107 1.22474i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(212\) −1.36603 0.366025i −1.36603 0.366025i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0.707107 + 1.70711i 0.707107 + 1.70711i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(224\) 0 0
\(225\) 0.414214i 0.414214i
\(226\) −1.46593 1.12484i −1.46593 1.12484i
\(227\) 0 0 −0.608761 0.793353i \(-0.708333\pi\)
0.608761 + 0.793353i \(0.291667\pi\)
\(228\) 0 0
\(229\) 1.36603 + 0.366025i 1.36603 + 0.366025i 0.866025 0.500000i \(-0.166667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.292893 0.707107i 0.292893 0.707107i
\(233\) −1.46593 1.12484i −1.46593 1.12484i −0.965926 0.258819i \(-0.916667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −0.758819 0.0999004i −0.758819 0.0999004i −0.258819 0.965926i \(-0.583333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) −0.866025 0.500000i −0.866025 0.500000i
\(243\) 0 0
\(244\) 0.707107 1.70711i 0.707107 1.70711i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0.858719 + 0.658919i 0.858719 + 0.658919i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(257\) 0.366025 1.36603i 0.366025 1.36603i −0.500000 0.866025i \(-0.666667\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0.758819 0.0999004i 0.758819 0.0999004i
\(262\) 0 0
\(263\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(264\) 0 0
\(265\) 1.00000 + 0.414214i 1.00000 + 0.414214i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0.758819 + 0.0999004i 0.758819 + 0.0999004i 0.500000 0.866025i \(-0.333333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(270\) 0 0
\(271\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(272\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(273\) 0 0
\(274\) −1.00000 1.00000i −1.00000 1.00000i
\(275\) 0 0
\(276\) 0 0
\(277\) 0.241181 1.83195i 0.241181 1.83195i −0.258819 0.965926i \(-0.583333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 −0.608761 0.793353i \(-0.708333\pi\)
0.608761 + 0.793353i \(0.291667\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −1.00000
\(289\) 0.866025 0.500000i 0.866025 0.500000i
\(290\) −0.292893 + 0.507306i −0.292893 + 0.507306i
\(291\) 0 0
\(292\) 0.465926 0.607206i 0.465926 0.607206i
\(293\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −0.0999004 0.758819i −0.0999004 0.758819i
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(306\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.130526 0.991445i \(-0.458333\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(312\) 0 0
\(313\) −0.241181 1.83195i −0.241181 1.83195i −0.500000 0.866025i \(-0.666667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(314\) 1.00000 1.00000i 1.00000 1.00000i
\(315\) 0 0
\(316\) 0 0
\(317\) −0.758819 + 0.0999004i −0.758819 + 0.0999004i −0.500000 0.866025i \(-0.666667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.465926 0.607206i 0.465926 0.607206i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.500000 0.866025i −0.500000 0.866025i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) −1.70711 + 0.707107i −1.70711 + 0.707107i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(332\) 0 0
\(333\) 0.607206 0.465926i 0.607206 0.465926i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.707107 1.70711i −0.707107 1.70711i −0.707107 0.707107i \(-0.750000\pi\)
1.00000i \(-0.5\pi\)
\(338\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(339\) 0 0
\(340\) −0.465926 0.607206i −0.465926 0.607206i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −1.12484 1.46593i −1.12484 1.46593i
\(347\) 0 0 0.793353 0.608761i \(-0.208333\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(348\) 0 0
\(349\) 1.41421 1.41421i 1.41421 1.41421i 0.707107 0.707107i \(-0.250000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 2.00000 2.00000
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(360\) 0.758819 + 0.0999004i 0.758819 + 0.0999004i
\(361\) −0.866025 0.500000i −0.866025 0.500000i
\(362\) −1.46593 1.12484i −1.46593 1.12484i
\(363\) 0 0
\(364\) 0 0
\(365\) −0.414214 + 0.414214i −0.414214 + 0.414214i
\(366\) 0 0
\(367\) 0 0 0.793353 0.608761i \(-0.208333\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(368\) 0 0
\(369\) −1.46593 1.12484i −1.46593 1.12484i
\(370\) 0.585786i 0.585786i
\(371\) 0 0
\(372\) 0 0
\(373\) −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.707107 + 0.292893i −0.707107 + 0.292893i
\(387\) 0 0
\(388\) 0.758819 + 0.0999004i 0.758819 + 0.0999004i
\(389\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 1.12484 1.46593i 1.12484 1.46593i
\(395\) 0 0
\(396\) 0 0
\(397\) 1.83195 0.241181i 1.83195 0.241181i 0.866025 0.500000i \(-0.166667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.292893 0.292893i 0.292893 0.292893i
\(401\) 0.0999004 + 0.758819i 0.0999004 + 0.758819i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(405\) 0.292893 + 0.707107i 0.292893 + 0.707107i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(410\) 1.36603 0.366025i 1.36603 0.366025i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(420\) 0 0
\(421\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0.707107 1.22474i 0.707107 1.22474i
\(425\) −0.207107 0.358719i −0.207107 0.358719i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.608761 0.793353i \(-0.708333\pi\)
0.608761 + 0.793353i \(0.291667\pi\)
\(432\) 0 0
\(433\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.83195 + 0.241181i −1.83195 + 0.241181i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.608761 0.793353i \(-0.291667\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(444\) 0 0
\(445\) −1.51764 0.199801i −1.51764 0.199801i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.707107 0.292893i −0.707107 0.292893i 1.00000i \(-0.5\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(450\) 0.400100 + 0.107206i 0.400100 + 0.107206i
\(451\) 0 0
\(452\) 1.46593 1.12484i 1.46593 1.12484i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(458\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(459\) 0 0
\(460\) 0 0
\(461\) −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0.607206 + 0.465926i 0.607206 + 0.465926i
\(465\) 0 0
\(466\) 1.46593 1.12484i 1.46593 1.12484i
\(467\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 1.41421 1.41421
\(478\) 0 0
\(479\) 0 0 −0.991445 0.130526i \(-0.958333\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.292893 0.707107i 0.292893 0.707107i
\(483\) 0 0
\(484\) 0.707107 0.707107i 0.707107 0.707107i
\(485\) −0.565826 0.151613i −0.565826 0.151613i
\(486\) 0 0
\(487\) 0 0 −0.608761 0.793353i \(-0.708333\pi\)
0.608761 + 0.793353i \(0.291667\pi\)
\(488\) 1.46593 + 1.12484i 1.46593 + 1.12484i
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(492\) 0 0
\(493\) 0.607206 0.465926i 0.607206 0.465926i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 0.991445 0.130526i \(-0.0416667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(500\) −0.858719 + 0.658919i −0.858719 + 0.658919i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(504\) 0 0
\(505\) 1.41421 0.585786i 1.41421 0.585786i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.707107 0.707107i −0.707107 0.707107i
\(513\) 0 0
\(514\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.12484 + 1.46593i 1.12484 + 1.46593i 0.866025 + 0.500000i \(0.166667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(522\) −0.0999004 + 0.758819i −0.0999004 + 0.758819i
\(523\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.965926 0.258819i 0.965926 0.258819i
\(530\) −0.658919 + 0.858719i −0.658919 + 0.858719i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −0.292893 + 0.707107i −0.292893 + 0.707107i
\(539\) 0 0
\(540\) 0 0
\(541\) −1.12484 + 1.46593i −1.12484 + 1.46593i −0.258819 + 0.965926i \(0.583333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(545\) 1.41421 1.41421
\(546\) 0 0
\(547\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(548\) 1.22474 0.707107i 1.22474 0.707107i
\(549\) −0.241181 + 1.83195i −0.241181 + 1.83195i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 1.70711 + 0.707107i 1.70711 + 0.707107i
\(555\) 0 0
\(556\) 0 0
\(557\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −0.707107 1.22474i −0.707107 1.22474i
\(563\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(564\) 0 0
\(565\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.36603 + 0.366025i 1.36603 + 0.366025i 0.866025 0.500000i \(-0.166667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(570\) 0 0
\(571\) 0 0 0.793353 0.608761i \(-0.208333\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.258819 0.965926i 0.258819 0.965926i
\(577\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(578\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(579\) 0 0
\(580\) −0.414214 0.414214i −0.414214 0.414214i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0.465926 + 0.607206i 0.465926 + 0.607206i
\(585\) 0 0
\(586\) −1.36603 0.366025i −1.36603 0.366025i
\(587\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.758819 + 0.0999004i 0.758819 + 0.0999004i
\(593\) 0.517638 1.93185i 0.517638 1.93185i 0.258819 0.965926i \(-0.416667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 0 0
\(601\) 0.707107 1.70711i 0.707107 1.70711i 1.00000i \(-0.5\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.607206 + 0.465926i −0.607206 + 0.465926i
\(606\) 0 0
\(607\) 0 0 −0.793353 0.608761i \(-0.791667\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −1.00000 1.00000i −1.00000 1.00000i
\(611\) 0 0
\(612\) −0.866025 0.500000i −0.866025 0.500000i
\(613\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.70711 + 0.707107i −1.70711 + 0.707107i −0.707107 + 0.707107i \(0.750000\pi\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 0.793353 0.608761i \(-0.208333\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.358719 0.207107i 0.358719 0.207107i
\(626\) 1.83195 + 0.241181i 1.83195 + 0.241181i
\(627\) 0 0
\(628\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(629\) 0.292893 0.707107i 0.292893 0.707107i
\(630\) 0 0
\(631\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0.0999004 0.758819i 0.0999004 0.758819i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0.465926 + 0.607206i 0.465926 + 0.607206i
\(641\) −0.241181 + 1.83195i −0.241181 + 1.83195i 0.258819 + 0.965926i \(0.416667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) 0 0
\(643\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(648\) 0.965926 0.258819i 0.965926 0.258819i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −0.0999004 0.758819i −0.0999004 0.758819i −0.965926 0.258819i \(-0.916667\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.241181 1.83195i −0.241181 1.83195i
\(657\) −0.292893 + 0.707107i −0.292893 + 0.707107i
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0.292893 + 0.707107i 0.292893 + 0.707107i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.70711 0.707107i −1.70711 0.707107i −0.707107 0.707107i \(-0.750000\pi\)
−1.00000 \(\pi\)
\(674\) 1.83195 0.241181i 1.83195 0.241181i
\(675\) 0 0
\(676\) −0.866025 0.500000i −0.866025 0.500000i
\(677\) −0.465926 + 0.607206i −0.465926 + 0.607206i −0.965926 0.258819i \(-0.916667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0.707107 0.292893i 0.707107 0.292893i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.991445 0.130526i \(-0.958333\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(684\) 0 0
\(685\) −1.00000 + 0.414214i −1.00000 + 0.414214i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.991445 0.130526i \(-0.0416667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(692\) 1.70711 0.707107i 1.70711 0.707107i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −1.83195 0.241181i −1.83195 0.241181i
\(698\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(699\) 0 0
\(700\) 0 0
\(701\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 1.00000 1.00000i 1.00000 1.00000i
\(707\) 0 0
\(708\) 0 0
\(709\) −0.607206 0.465926i −0.607206 0.465926i 0.258819 0.965926i \(-0.416667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.517638 + 1.93185i −0.517638 + 1.93185i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.793353 0.608761i \(-0.791667\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(720\) −0.292893 + 0.707107i −0.292893 + 0.707107i
\(721\) 0 0
\(722\) 0.707107 0.707107i 0.707107 0.707107i
\(723\) 0 0
\(724\) 1.46593 1.12484i 1.46593 1.12484i
\(725\) −0.192993 0.251513i −0.192993 0.251513i
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(730\) −0.292893 0.507306i −0.292893 0.507306i
\(731\) 0 0
\(732\) 0 0
\(733\) 0.517638 1.93185i 0.517638 1.93185i 0.258819 0.965926i \(-0.416667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 1.46593 1.12484i 1.46593 1.12484i
\(739\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(740\) −0.565826 0.151613i −0.565826 0.151613i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 1.36603 0.366025i 1.36603 0.366025i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.608761 0.793353i \(-0.291667\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.41421 1.41421i 1.41421 1.41421i 0.707107 0.707107i \(-0.250000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0.607206 + 0.465926i 0.607206 + 0.465926i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.0999004 0.758819i −0.0999004 0.758819i
\(773\) −0.366025 1.36603i −0.366025 1.36603i −0.866025 0.500000i \(-0.833333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −0.292893 + 0.707107i −0.292893 + 0.707107i
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −0.414214 1.00000i −0.414214 1.00000i
\(786\) 0 0
\(787\) 0 0 0.130526 0.991445i \(-0.458333\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(788\) 1.12484 + 1.46593i 1.12484 + 1.46593i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) −0.241181 + 1.83195i −0.241181 + 1.83195i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(798\) 0 0