Properties

Label 2520.1.hf.a.2477.4
Level $2520$
Weight $1$
Character 2520.2477
Analytic conductor $1.258$
Analytic rank $0$
Dimension $16$
Projective image $D_{24}$
CM discriminant -56
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2520.hf (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.25764383184\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{48})\)
Defining polynomial: \(x^{16} - x^{8} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{24}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{24} - \cdots)\)

Embedding invariants

Embedding label 2477.4
Root \(-0.793353 - 0.608761i\) of defining polynomial
Character \(\chi\) \(=\) 2520.2477
Dual form 2520.1.hf.a.293.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.258819 + 0.965926i) q^{2} +(0.923880 + 0.382683i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.382683 - 0.923880i) q^{5} +(-0.130526 + 0.991445i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.707107 + 0.707107i) q^{9} +O(q^{10})\) \(q+(0.258819 + 0.965926i) q^{2} +(0.923880 + 0.382683i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.382683 - 0.923880i) q^{5} +(-0.130526 + 0.991445i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.707107 + 0.707107i) q^{9} +(0.793353 - 0.608761i) q^{10} +(-0.991445 + 0.130526i) q^{12} +(1.78480 + 0.478235i) q^{13} +(-0.500000 - 0.866025i) q^{14} -1.00000i q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{18} +1.98289i q^{19} +(0.793353 + 0.608761i) q^{20} +(-0.991445 - 0.130526i) q^{21} +(-0.133975 + 0.500000i) q^{23} +(-0.382683 - 0.923880i) q^{24} +(-0.707107 + 0.707107i) q^{25} +1.84776i q^{26} +(0.382683 + 0.923880i) q^{27} +(0.707107 - 0.707107i) q^{28} +(0.965926 - 0.258819i) q^{30} +(0.965926 + 0.258819i) q^{32} +(0.608761 + 0.793353i) q^{35} +(-0.965926 - 0.258819i) q^{36} +(-1.91532 + 0.513210i) q^{38} +(1.46593 + 1.12484i) q^{39} +(-0.382683 + 0.923880i) q^{40} +(-0.130526 - 0.991445i) q^{42} +(0.382683 - 0.923880i) q^{45} -0.517638 q^{46} +(0.793353 - 0.608761i) q^{48} +(0.866025 - 0.500000i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(-1.78480 + 0.478235i) q^{52} +(-0.793353 + 0.608761i) q^{54} +(0.866025 + 0.500000i) q^{56} +(-0.758819 + 1.83195i) q^{57} +(0.382683 + 0.662827i) q^{59} +(0.500000 + 0.866025i) q^{60} +(0.130526 - 0.226078i) q^{61} +(-0.866025 - 0.500000i) q^{63} +1.00000i q^{64} +(-0.241181 - 1.83195i) q^{65} +(-0.315118 + 0.410670i) q^{69} +(-0.608761 + 0.793353i) q^{70} -1.93185i q^{71} -1.00000i q^{72} +(-0.923880 + 0.382683i) q^{75} +(-0.991445 - 1.71723i) q^{76} +(-0.707107 + 1.70711i) q^{78} +(-1.67303 - 0.965926i) q^{79} +(-0.991445 - 0.130526i) q^{80} +1.00000i q^{81} +(-0.739288 + 0.198092i) q^{83} +(0.923880 - 0.382683i) q^{84} +(0.991445 + 0.130526i) q^{90} -1.84776 q^{91} +(-0.133975 - 0.500000i) q^{92} +(1.83195 - 0.758819i) q^{95} +(0.793353 + 0.608761i) q^{96} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 8q^{14} + 8q^{16} - 8q^{18} - 16q^{23} + 8q^{39} - 8q^{57} + 8q^{60} - 8q^{65} - 16q^{92} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(1081\) \(1261\) \(2017\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(3\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(4\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(5\) −0.382683 0.923880i −0.382683 0.923880i
\(6\) −0.130526 + 0.991445i −0.130526 + 0.991445i
\(7\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(8\) −0.707107 0.707107i −0.707107 0.707107i
\(9\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(10\) 0.793353 0.608761i 0.793353 0.608761i
\(11\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) −0.991445 + 0.130526i −0.991445 + 0.130526i
\(13\) 1.78480 + 0.478235i 1.78480 + 0.478235i 0.991445 0.130526i \(-0.0416667\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(14\) −0.500000 0.866025i −0.500000 0.866025i
\(15\) 1.00000i 1.00000i
\(16\) 0.500000 0.866025i 0.500000 0.866025i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(19\) 1.98289i 1.98289i 0.130526 + 0.991445i \(0.458333\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(20\) 0.793353 + 0.608761i 0.793353 + 0.608761i
\(21\) −0.991445 0.130526i −0.991445 0.130526i
\(22\) 0 0
\(23\) −0.133975 + 0.500000i −0.133975 + 0.500000i 0.866025 + 0.500000i \(0.166667\pi\)
−1.00000 \(\pi\)
\(24\) −0.382683 0.923880i −0.382683 0.923880i
\(25\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(26\) 1.84776i 1.84776i
\(27\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(28\) 0.707107 0.707107i 0.707107 0.707107i
\(29\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 0.965926 0.258819i 0.965926 0.258819i
\(31\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(32\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(33\) 0 0
\(34\) 0 0
\(35\) 0.608761 + 0.793353i 0.608761 + 0.793353i
\(36\) −0.965926 0.258819i −0.965926 0.258819i
\(37\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(38\) −1.91532 + 0.513210i −1.91532 + 0.513210i
\(39\) 1.46593 + 1.12484i 1.46593 + 1.12484i
\(40\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(41\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(42\) −0.130526 0.991445i −0.130526 0.991445i
\(43\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(44\) 0 0
\(45\) 0.382683 0.923880i 0.382683 0.923880i
\(46\) −0.517638 −0.517638
\(47\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(48\) 0.793353 0.608761i 0.793353 0.608761i
\(49\) 0.866025 0.500000i 0.866025 0.500000i
\(50\) −0.866025 0.500000i −0.866025 0.500000i
\(51\) 0 0
\(52\) −1.78480 + 0.478235i −1.78480 + 0.478235i
\(53\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(54\) −0.793353 + 0.608761i −0.793353 + 0.608761i
\(55\) 0 0
\(56\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(57\) −0.758819 + 1.83195i −0.758819 + 1.83195i
\(58\) 0 0
\(59\) 0.382683 + 0.662827i 0.382683 + 0.662827i 0.991445 0.130526i \(-0.0416667\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(60\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(61\) 0.130526 0.226078i 0.130526 0.226078i −0.793353 0.608761i \(-0.791667\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(62\) 0 0
\(63\) −0.866025 0.500000i −0.866025 0.500000i
\(64\) 1.00000i 1.00000i
\(65\) −0.241181 1.83195i −0.241181 1.83195i
\(66\) 0 0
\(67\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(68\) 0 0
\(69\) −0.315118 + 0.410670i −0.315118 + 0.410670i
\(70\) −0.608761 + 0.793353i −0.608761 + 0.793353i
\(71\) 1.93185i 1.93185i −0.258819 0.965926i \(-0.583333\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(72\) 1.00000i 1.00000i
\(73\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(74\) 0 0
\(75\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(76\) −0.991445 1.71723i −0.991445 1.71723i
\(77\) 0 0
\(78\) −0.707107 + 1.70711i −0.707107 + 1.70711i
\(79\) −1.67303 0.965926i −1.67303 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(80\) −0.991445 0.130526i −0.991445 0.130526i
\(81\) 1.00000i 1.00000i
\(82\) 0 0
\(83\) −0.739288 + 0.198092i −0.739288 + 0.198092i −0.608761 0.793353i \(-0.708333\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(84\) 0.923880 0.382683i 0.923880 0.382683i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0.991445 + 0.130526i 0.991445 + 0.130526i
\(91\) −1.84776 −1.84776
\(92\) −0.133975 0.500000i −0.133975 0.500000i
\(93\) 0 0
\(94\) 0 0
\(95\) 1.83195 0.758819i 1.83195 0.758819i
\(96\) 0.793353 + 0.608761i 0.793353 + 0.608761i
\(97\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(98\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(99\) 0 0
\(100\) 0.258819 0.965926i 0.258819 0.965926i
\(101\) 1.05441 + 0.608761i 1.05441 + 0.608761i 0.923880 0.382683i \(-0.125000\pi\)
0.130526 + 0.991445i \(0.458333\pi\)
\(102\) 0 0
\(103\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(104\) −0.923880 1.60021i −0.923880 1.60021i
\(105\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(106\) 0 0
\(107\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(108\) −0.793353 0.608761i −0.793353 0.608761i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(113\) 0.448288 1.67303i 0.448288 1.67303i −0.258819 0.965926i \(-0.583333\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(114\) −1.96593 0.258819i −1.96593 0.258819i
\(115\) 0.513210 0.0675653i 0.513210 0.0675653i
\(116\) 0 0
\(117\) 0.923880 + 1.60021i 0.923880 + 1.60021i
\(118\) −0.541196 + 0.541196i −0.541196 + 0.541196i
\(119\) 0 0
\(120\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(121\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(122\) 0.252157 + 0.0675653i 0.252157 + 0.0675653i
\(123\) 0 0
\(124\) 0 0
\(125\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(126\) 0.258819 0.965926i 0.258819 0.965926i
\(127\) −0.366025 0.366025i −0.366025 0.366025i 0.500000 0.866025i \(-0.333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(128\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(129\) 0 0
\(130\) 1.70711 0.707107i 1.70711 0.707107i
\(131\) 1.37413 0.793353i 1.37413 0.793353i 0.382683 0.923880i \(-0.375000\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(132\) 0 0
\(133\) −0.513210 1.91532i −0.513210 1.91532i
\(134\) 0 0
\(135\) 0.707107 0.707107i 0.707107 0.707107i
\(136\) 0 0
\(137\) −0.366025 1.36603i −0.366025 1.36603i −0.866025 0.500000i \(-0.833333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(138\) −0.478235 0.198092i −0.478235 0.198092i
\(139\) 1.37413 0.793353i 1.37413 0.793353i 0.382683 0.923880i \(-0.375000\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(140\) −0.923880 0.382683i −0.923880 0.382683i
\(141\) 0 0
\(142\) 1.86603 0.500000i 1.86603 0.500000i
\(143\) 0 0
\(144\) 0.965926 0.258819i 0.965926 0.258819i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.991445 0.130526i 0.991445 0.130526i
\(148\) 0 0
\(149\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) −0.608761 0.793353i −0.608761 0.793353i
\(151\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(152\) 1.40211 1.40211i 1.40211 1.40211i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −1.83195 0.241181i −1.83195 0.241181i
\(157\) 0.315118 1.17604i 0.315118 1.17604i −0.608761 0.793353i \(-0.708333\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(158\) 0.500000 1.86603i 0.500000 1.86603i
\(159\) 0 0
\(160\) −0.130526 0.991445i −0.130526 0.991445i
\(161\) 0.517638i 0.517638i
\(162\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(163\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −0.382683 0.662827i −0.382683 0.662827i
\(167\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(168\) 0.608761 + 0.793353i 0.608761 + 0.793353i
\(169\) 2.09077 + 1.20711i 2.09077 + 1.20711i
\(170\) 0 0
\(171\) −1.40211 + 1.40211i −1.40211 + 1.40211i
\(172\) 0 0
\(173\) −1.78480 + 0.478235i −1.78480 + 0.478235i −0.991445 0.130526i \(-0.958333\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(174\) 0 0
\(175\) 0.500000 0.866025i 0.500000 0.866025i
\(176\) 0 0
\(177\) 0.0999004 + 0.758819i 0.0999004 + 0.758819i
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0.130526 + 0.991445i 0.130526 + 0.991445i
\(181\) 1.21752 1.21752 0.608761 0.793353i \(-0.291667\pi\)
0.608761 + 0.793353i \(0.291667\pi\)
\(182\) −0.478235 1.78480i −0.478235 1.78480i
\(183\) 0.207107 0.158919i 0.207107 0.158919i
\(184\) 0.448288 0.258819i 0.448288 0.258819i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −0.608761 0.793353i −0.608761 0.793353i
\(190\) 1.20711 + 1.57313i 1.20711 + 1.57313i
\(191\) 0.448288 + 0.258819i 0.448288 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(192\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(193\) −1.67303 0.448288i −1.67303 0.448288i −0.707107 0.707107i \(-0.750000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(194\) 0 0
\(195\) 0.478235 1.78480i 0.478235 1.78480i
\(196\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(197\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 1.00000 1.00000
\(201\) 0 0
\(202\) −0.315118 + 1.17604i −0.315118 + 1.17604i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.448288 + 0.258819i −0.448288 + 0.258819i
\(208\) 1.30656 1.30656i 1.30656 1.30656i
\(209\) 0 0
\(210\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(211\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) 0 0
\(213\) 0.739288 1.78480i 0.739288 1.78480i
\(214\) 0 0
\(215\) 0 0
\(216\) 0.382683 0.923880i 0.382683 0.923880i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(224\) −1.00000 −1.00000
\(225\) −1.00000 −1.00000
\(226\) 1.73205 1.73205
\(227\) −0.315118 1.17604i −0.315118 1.17604i −0.923880 0.382683i \(-0.875000\pi\)
0.608761 0.793353i \(-0.291667\pi\)
\(228\) −0.258819 1.96593i −0.258819 1.96593i
\(229\) −1.37413 + 0.793353i −1.37413 + 0.793353i −0.991445 0.130526i \(-0.958333\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(230\) 0.198092 + 0.478235i 0.198092 + 0.478235i
\(231\) 0 0
\(232\) 0 0
\(233\) −1.36603 1.36603i −1.36603 1.36603i −0.866025 0.500000i \(-0.833333\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(234\) −1.30656 + 1.30656i −1.30656 + 1.30656i
\(235\) 0 0
\(236\) −0.662827 0.382683i −0.662827 0.382683i
\(237\) −1.17604 1.53264i −1.17604 1.53264i
\(238\) 0 0
\(239\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) −0.866025 0.500000i −0.866025 0.500000i
\(241\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(243\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(244\) 0.261052i 0.261052i
\(245\) −0.793353 0.608761i −0.793353 0.608761i
\(246\) 0 0
\(247\) −0.948288 + 3.53906i −0.948288 + 3.53906i
\(248\) 0 0
\(249\) −0.758819 0.0999004i −0.758819 0.0999004i
\(250\) −0.130526 + 0.991445i −0.130526 + 0.991445i
\(251\) 1.98289i 1.98289i −0.130526 0.991445i \(-0.541667\pi\)
0.130526 0.991445i \(-0.458333\pi\)
\(252\) 1.00000 1.00000
\(253\) 0 0
\(254\) 0.258819 0.448288i 0.258819 0.448288i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.500000 0.866025i
\(257\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1.12484 + 1.46593i 1.12484 + 1.46593i
\(261\) 0 0
\(262\) 1.12197 + 1.12197i 1.12197 + 1.12197i
\(263\) −1.67303 + 0.448288i −1.67303 + 0.448288i −0.965926 0.258819i \(-0.916667\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 1.71723 0.991445i 1.71723 0.991445i
\(267\) 0 0
\(268\) 0 0
\(269\) 1.58671 1.58671 0.793353 0.608761i \(-0.208333\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(270\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) −1.70711 0.707107i −1.70711 0.707107i
\(274\) 1.22474 0.707107i 1.22474 0.707107i
\(275\) 0 0
\(276\) 0.0675653 0.513210i 0.0675653 0.513210i
\(277\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(278\) 1.12197 + 1.12197i 1.12197 + 1.12197i
\(279\) 0 0
\(280\) 0.130526 0.991445i 0.130526 0.991445i
\(281\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(282\) 0 0
\(283\) 1.53264 + 0.410670i 1.53264 + 0.410670i 0.923880 0.382683i \(-0.125000\pi\)
0.608761 + 0.793353i \(0.291667\pi\)
\(284\) 0.965926 + 1.67303i 0.965926 + 1.67303i
\(285\) 1.98289 1.98289
\(286\) 0 0
\(287\) 0 0
\(288\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0.0675653 0.252157i 0.0675653 0.252157i −0.923880 0.382683i \(-0.875000\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(294\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(295\) 0.465926 0.607206i 0.465926 0.607206i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.478235 + 0.828328i −0.478235 + 0.828328i
\(300\) 0.608761 0.793353i 0.608761 0.793353i
\(301\) 0 0
\(302\) −1.67303 0.448288i −1.67303 0.448288i
\(303\) 0.741181 + 0.965926i 0.741181 + 0.965926i
\(304\) 1.71723 + 0.991445i 1.71723 + 0.991445i
\(305\) −0.258819 0.0340742i −0.258819 0.0340742i
\(306\) 0 0
\(307\) 0.184592 + 0.184592i 0.184592 + 0.184592i 0.793353 0.608761i \(-0.208333\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(312\) −0.241181 1.83195i −0.241181 1.83195i
\(313\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(314\) 1.21752 1.21752
\(315\) −0.130526 + 0.991445i −0.130526 + 0.991445i
\(316\) 1.93185 1.93185
\(317\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.923880 0.382683i 0.923880 0.382683i
\(321\) 0 0
\(322\) 0.500000 0.133975i 0.500000 0.133975i
\(323\) 0 0
\(324\) −0.500000 0.866025i −0.500000 0.866025i
\(325\) −1.60021 + 0.923880i −1.60021 + 0.923880i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) 0.541196 0.541196i 0.541196 0.541196i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) −0.608761 + 0.793353i −0.608761 + 0.793353i
\(337\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(338\) −0.624844 + 2.33195i −0.624844 + 2.33195i
\(339\) 1.05441 1.37413i 1.05441 1.37413i
\(340\) 0 0
\(341\) 0 0
\(342\) −1.71723 0.991445i −1.71723 0.991445i
\(343\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(344\) 0 0
\(345\) 0.500000 + 0.133975i 0.500000 + 0.133975i
\(346\) −0.923880 1.60021i −0.923880 1.60021i
\(347\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(348\) 0 0
\(349\) −0.662827 0.382683i −0.662827 0.382683i 0.130526 0.991445i \(-0.458333\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(350\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(351\) 0.241181 + 1.83195i 0.241181 + 1.83195i
\(352\) 0 0
\(353\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(354\) −0.707107 + 0.292893i −0.707107 + 0.292893i
\(355\) −1.78480 + 0.739288i −1.78480 + 0.739288i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(360\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(361\) −2.93185 −2.93185
\(362\) 0.315118 + 1.17604i 0.315118 + 1.17604i
\(363\) 0.130526 + 0.991445i 0.130526 + 0.991445i
\(364\) 1.60021 0.923880i 1.60021 0.923880i
\(365\) 0 0
\(366\) 0.207107 + 0.158919i 0.207107 + 0.158919i
\(367\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(368\) 0.366025 + 0.366025i 0.366025 + 0.366025i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(374\) 0 0
\(375\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(376\) 0 0
\(377\) 0 0
\(378\) 0.608761 0.793353i 0.608761 0.793353i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) −1.20711 + 1.57313i −1.20711 + 1.57313i
\(381\) −0.198092 0.478235i −0.198092 0.478235i
\(382\) −0.133975 + 0.500000i −0.133975 + 0.500000i
\(383\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(384\) −0.991445 0.130526i −0.991445 0.130526i
\(385\) 0 0
\(386\) 1.73205i 1.73205i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(390\) 1.84776 1.84776
\(391\) 0 0
\(392\) −0.965926 0.258819i −0.965926 0.258819i
\(393\) 1.57313 0.207107i 1.57313 0.207107i
\(394\) 0 0
\(395\) −0.252157 + 1.91532i −0.252157 + 1.91532i
\(396\) 0 0
\(397\) −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i \(-0.375000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(398\) 0 0
\(399\) 0.258819 1.96593i 0.258819 1.96593i
\(400\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(401\) −1.67303 + 0.965926i −1.67303 + 0.965926i −0.707107 + 0.707107i \(0.750000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −1.21752 −1.21752
\(405\) 0.923880 0.382683i 0.923880 0.382683i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(410\) 0 0
\(411\) 0.184592 1.40211i 0.184592 1.40211i
\(412\) 0 0
\(413\) −0.541196 0.541196i −0.541196 0.541196i
\(414\) −0.366025 0.366025i −0.366025 0.366025i
\(415\) 0.465926 + 0.607206i 0.465926 + 0.607206i
\(416\) 1.60021 + 0.923880i 1.60021 + 0.923880i
\(417\) 1.57313 0.207107i 1.57313 0.207107i
\(418\) 0 0
\(419\) −0.130526 0.226078i −0.130526 0.226078i 0.793353 0.608761i \(-0.208333\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(420\) −0.707107 0.707107i −0.707107 0.707107i
\(421\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 1.91532 + 0.252157i 1.91532 + 0.252157i
\(427\) −0.0675653 + 0.252157i −0.0675653 + 0.252157i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0.991445 + 0.130526i 0.991445 + 0.130526i
\(433\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.991445 0.265657i −0.991445 0.265657i
\(438\) 0 0
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 0 0
\(441\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(442\) 0 0
\(443\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.258819 0.965926i −0.258819 0.965926i
\(449\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(450\) −0.258819 0.965926i −0.258819 0.965926i
\(451\) 0 0
\(452\) 0.448288 + 1.67303i 0.448288 + 1.67303i
\(453\) −1.37413 + 1.05441i −1.37413 + 1.05441i
\(454\) 1.05441 0.608761i 1.05441 0.608761i
\(455\) 0.707107 + 1.70711i 0.707107 + 1.70711i
\(456\) 1.83195 0.758819i 1.83195 0.758819i
\(457\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(458\) −1.12197 1.12197i −1.12197 1.12197i
\(459\) 0 0
\(460\) −0.410670 + 0.315118i −0.410670 + 0.315118i
\(461\) 1.37413 + 0.793353i 1.37413 + 0.793353i 0.991445 0.130526i \(-0.0416667\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(462\) 0 0
\(463\) 1.67303 + 0.448288i 1.67303 + 0.448288i 0.965926 0.258819i \(-0.0833333\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.965926 1.67303i 0.965926 1.67303i
\(467\) −1.30656 + 1.30656i −1.30656 + 1.30656i −0.382683 + 0.923880i \(0.625000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(468\) −1.60021 0.923880i −1.60021 0.923880i
\(469\) 0 0
\(470\) 0 0
\(471\) 0.741181 0.965926i 0.741181 0.965926i
\(472\) 0.198092 0.739288i 0.198092 0.739288i
\(473\) 0 0
\(474\) 1.17604 1.53264i 1.17604 1.53264i
\(475\) −1.40211 1.40211i −1.40211 1.40211i
\(476\) 0 0
\(477\) 0 0
\(478\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(479\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(480\) 0.258819 0.965926i 0.258819 0.965926i
\(481\) 0 0
\(482\) 0 0
\(483\) 0.198092 0.478235i 0.198092 0.478235i
\(484\) −0.866025 0.500000i −0.866025 0.500000i
\(485\) 0 0
\(486\) −0.991445 0.130526i −0.991445 0.130526i
\(487\) −1.36603 1.36603i −1.36603 1.36603i −0.866025 0.500000i \(-0.833333\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(488\) −0.252157 + 0.0675653i −0.252157 + 0.0675653i
\(489\) 0 0
\(490\) 0.382683 0.923880i 0.382683 0.923880i
\(491\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −3.66390 −3.66390
\(495\) 0 0
\(496\) 0 0
\(497\) 0.500000 + 1.86603i 0.500000 + 1.86603i
\(498\) −0.0999004 0.758819i −0.0999004 0.758819i
\(499\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(500\) −0.991445 + 0.130526i −0.991445 + 0.130526i
\(501\) 0 0
\(502\) 1.91532 0.513210i 1.91532 0.513210i
\(503\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(504\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(505\) 0.158919 1.20711i 0.158919 1.20711i
\(506\) 0 0
\(507\) 1.46968 + 1.91532i 1.46968 + 1.91532i
\(508\) 0.500000 + 0.133975i 0.500000 + 0.133975i
\(509\) −0.382683 0.662827i −0.382683 0.662827i 0.608761 0.793353i \(-0.291667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.707107 0.707107i 0.707107 0.707107i
\(513\) −1.83195 + 0.758819i −1.83195 + 0.758819i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −1.83195 0.241181i −1.83195 0.241181i
\(520\) −1.12484 + 1.46593i −1.12484 + 1.46593i
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) 1.40211 1.40211i 1.40211 1.40211i 0.608761 0.793353i \(-0.291667\pi\)
0.793353 0.608761i \(-0.208333\pi\)
\(524\) −0.793353 + 1.37413i −0.793353 + 1.37413i
\(525\) 0.793353 0.608761i 0.793353 0.608761i
\(526\) −0.866025 1.50000i −0.866025 1.50000i
\(527\) 0 0
\(528\) 0 0
\(529\) 0.633975 + 0.366025i 0.633975 + 0.366025i
\(530\) 0 0
\(531\) −0.198092 + 0.739288i −0.198092 + 0.739288i
\(532\) 1.40211 + 1.40211i 1.40211 + 1.40211i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0.410670 + 1.53264i 0.410670 + 1.53264i
\(539\) 0 0
\(540\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 1.12484 + 0.465926i 1.12484 + 0.465926i
\(544\) 0 0
\(545\) 0 0
\(546\) 0.241181 1.83195i 0.241181 1.83195i
\(547\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(548\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(549\) 0.252157 0.0675653i 0.252157 0.0675653i
\(550\) 0 0
\(551\) 0 0
\(552\) 0.513210 0.0675653i 0.513210 0.0675653i
\(553\) 1.86603 + 0.500000i 1.86603 + 0.500000i
\(554\) 0 0
\(555\) 0 0
\(556\) −0.793353 + 1.37413i −0.793353 + 1.37413i
\(557\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.991445 0.130526i 0.991445 0.130526i
\(561\) 0 0
\(562\) 0.258819 0.965926i 0.258819 0.965926i
\(563\) −0.410670 + 1.53264i −0.410670 + 1.53264i 0.382683 + 0.923880i \(0.375000\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(564\) 0 0
\(565\) −1.71723 + 0.226078i −1.71723 + 0.226078i
\(566\) 1.58671i 1.58671i
\(567\) −0.258819 0.965926i −0.258819 0.965926i
\(568\) −1.36603 + 1.36603i −1.36603 + 1.36603i
\(569\) 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(570\) 0.513210 + 1.91532i 0.513210 + 1.91532i
\(571\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(572\) 0 0
\(573\) 0.315118 + 0.410670i 0.315118 + 0.410670i
\(574\) 0 0
\(575\) −0.258819 0.448288i −0.258819 0.448288i
\(576\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(577\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(578\) 0.965926 0.258819i 0.965926 0.258819i
\(579\) −1.37413 1.05441i −1.37413 1.05441i
\(580\) 0 0
\(581\) 0.662827 0.382683i 0.662827 0.382683i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 1.12484 1.46593i 1.12484 1.46593i
\(586\) 0.261052 0.261052
\(587\) −0.0675653 0.252157i −0.0675653 0.252157i 0.923880 0.382683i \(-0.125000\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(588\) −0.793353 + 0.608761i −0.793353 + 0.608761i
\(589\) 0 0
\(590\) 0.707107 + 0.292893i 0.707107 + 0.292893i
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −0.923880 0.247553i −0.923880 0.247553i
\(599\) −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(600\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(601\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.73205i 1.73205i
\(605\) 0.608761 0.793353i 0.608761 0.793353i
\(606\) −0.741181 + 0.965926i −0.741181 + 0.965926i
\(607\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(608\) −0.513210 + 1.91532i −0.513210 + 1.91532i
\(609\) 0 0
\(610\) −0.0340742 0.258819i −0.0340742 0.258819i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(614\) −0.130526 + 0.226078i −0.130526 + 0.226078i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(618\) 0 0
\(619\) 0.226078 + 0.130526i 0.226078 + 0.130526i 0.608761 0.793353i \(-0.291667\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(620\) 0 0
\(621\) −0.513210 + 0.0675653i −0.513210 + 0.0675653i
\(622\) 0 0
\(623\) 0 0
\(624\) 1.70711 0.707107i 1.70711 0.707107i
\(625\) 1.00000i 1.00000i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.315118 + 1.17604i 0.315118 + 1.17604i
\(629\) 0 0
\(630\) −0.991445 + 0.130526i −0.991445 + 0.130526i
\(631\) 0.517638 0.517638 0.258819 0.965926i \(-0.416667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(632\) 0.500000 + 1.86603i 0.500000 + 1.86603i
\(633\) 0 0
\(634\) 0 0
\(635\) −0.198092 + 0.478235i −0.198092 + 0.478235i
\(636\) 0 0
\(637\) 1.78480 0.478235i 1.78480 0.478235i
\(638\) 0 0
\(639\) 1.36603 1.36603i 1.36603 1.36603i
\(640\) 0.608761 + 0.793353i 0.608761 + 0.793353i
\(641\) 1.67303 + 0.965926i 1.67303 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(642\) 0 0
\(643\) −0.739288 0.198092i −0.739288 0.198092i −0.130526 0.991445i \(-0.541667\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(644\) 0.258819 + 0.448288i 0.258819 + 0.448288i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(648\) 0.707107 0.707107i 0.707107 0.707107i
\(649\) 0 0
\(650\) −1.30656 1.30656i −1.30656 1.30656i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(654\) 0 0
\(655\) −1.25882 0.965926i −1.25882 0.965926i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(660\) 0 0
\(661\) 0.608761 + 1.05441i 0.608761 + 1.05441i 0.991445 + 0.130526i \(0.0416667\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.662827 + 0.382683i 0.662827 + 0.382683i
\(665\) −1.57313 + 1.20711i −1.57313 + 1.20711i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −0.923880 0.382683i −0.923880 0.382683i
\(673\) −0.133975 0.500000i −0.133975 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) −0.923880 0.382683i −0.923880 0.382683i
\(676\) −2.41421 −2.41421
\(677\) 0.478235 + 1.78480i 0.478235 + 1.78480i 0.608761 + 0.793353i \(0.291667\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(678\) 1.60021 + 0.662827i 1.60021 + 0.662827i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.158919 1.20711i 0.158919 1.20711i
\(682\) 0 0
\(683\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(684\) 0.513210 1.91532i 0.513210 1.91532i
\(685\) −1.12197 + 0.860919i −1.12197 + 0.860919i
\(686\) −0.866025 0.500000i −0.866025 0.500000i
\(687\) −1.57313 + 0.207107i −1.57313 + 0.207107i
\(688\) 0 0
\(689\) 0 0
\(690\) 0.517638i 0.517638i
\(691\) 0.608761 1.05441i 0.608761 1.05441i −0.382683 0.923880i \(-0.625000\pi\)
0.991445 0.130526i \(-0.0416667\pi\)
\(692\) 1.30656 1.30656i 1.30656 1.30656i
\(693\) 0 0
\(694\) 0 0
\(695\) −1.25882 0.965926i −1.25882 0.965926i
\(696\) 0 0
\(697\) 0 0
\(698\) 0.198092 0.739288i 0.198092 0.739288i
\(699\) −0.739288 1.78480i −0.739288 1.78480i
\(700\) 1.00000i 1.00000i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) −1.70711 + 0.707107i −1.70711 + 0.707107i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.17604 0.315118i −1.17604 0.315118i
\(708\) −0.465926 0.607206i −0.465926 0.607206i
\(709\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(710\) −1.17604 1.53264i −1.17604 1.53264i
\(711\) −0.500000 1.86603i −0.500000 1.86603i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0.130526 + 0.991445i 0.130526 + 0.991445i
\(718\) 0.448288 + 1.67303i 0.448288 + 1.67303i
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) −0.608761 0.793353i −0.608761 0.793353i
\(721\) 0 0
\(722\) −0.758819 2.83195i −0.758819 2.83195i
\(723\) 0 0
\(724\) −1.05441 + 0.608761i −1.05441 + 0.608761i
\(725\) 0 0
\(726\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(727\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(728\) 1.30656 + 1.30656i 1.30656 + 1.30656i
\(729\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.0999004 + 0.241181i −0.0999004 + 0.241181i
\(733\) 1.17604 + 0.315118i 1.17604 + 0.315118i 0.793353 0.608761i \(-0.208333\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(734\) 0 0
\(735\) −0.500000 0.866025i −0.500000 0.866025i
\(736\) −0.258819 + 0.448288i −0.258819 + 0.448288i
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 0 0
\(741\) −2.23044 + 2.90677i −2.23044 + 2.90677i
\(742\) 0 0
\(743\) −0.366025 + 1.36603i −0.366025 + 1.36603i 0.500000 + 0.866025i \(0.333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.662827 0.382683i −0.662827 0.382683i
\(748\) 0 0
\(749\) 0 0
\(750\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(751\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(752\) 0 0
\(753\) 0.758819 1.83195i 0.758819 1.83195i
\(754\) 0 0
\(755\) 1.71723 + 0.226078i 1.71723 + 0.226078i
\(756\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(757\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −1.83195 0.758819i −1.83195 0.758819i
\(761\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(762\) 0.410670 0.315118i 0.410670 0.315118i
\(763\) 0 0
\(764\) −0.517638 −0.517638
\(765\) 0 0
\(766\) 0 0
\(767\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(768\) −0.130526 0.991445i −0.130526 0.991445i
\(769\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.67303 0.448288i 1.67303 0.448288i
\(773\) −1.40211 1.40211i −1.40211 1.40211i −0.793353 0.608761i \(-0.791667\pi\)
−0.608761 0.793353i \(-0.708333\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0.478235 + 1.78480i 0.478235 + 1.78480i
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000i 1.00000i
\(785\) −1.20711 + 0.158919i −1.20711 + 0.158919i
\(786\) 0.607206 + 1.46593i 0.607206 + 1.46593i
\(787\) −0.198092 + 0.739288i −0.198092 + 0.739288i 0.793353 + 0.608761i \(0.208333\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(788\) 0 0
\(789\) −1.71723 0.226078i −1.71723 0.226078i
\(790\) −1.91532 + 0.252157i −1.91532 + 0.252157i
\(791\) 1.73205i 1.73205i
\(792\) 0 0
\(793\) 0.341081 0.341081i 0.341081 0.341081i
\(794\) 0.382683 0.662827i 0.382683 0.662827i