Properties

Label 2520.1.hf.b.797.2
Level $2520$
Weight $1$
Character 2520.797
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 797.2
Root \(-0.793353 + 0.608761i\) of defining polynomial
Character \(\chi\) \(=\) 2520.797
Dual form 2520.1.hf.b.1973.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.965926 - 0.258819i) q^{2} +(0.923880 - 0.382683i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.793353 + 0.608761i) q^{5} +(-0.991445 + 0.130526i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.707107 - 0.707107i) q^{9} +O(q^{10})\) \(q+(-0.965926 - 0.258819i) q^{2} +(0.923880 - 0.382683i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.793353 + 0.608761i) q^{5} +(-0.991445 + 0.130526i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.707107 - 0.707107i) q^{9} +(-0.608761 - 0.793353i) q^{10} +(0.991445 + 0.130526i) q^{12} +(0.198092 + 0.739288i) q^{13} +(0.500000 - 0.866025i) q^{14} +(0.965926 + 0.258819i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.866025 + 0.500000i) q^{18} -0.261052i q^{19} +(0.382683 + 0.923880i) q^{20} +(0.130526 + 0.991445i) q^{21} +(-0.500000 + 0.133975i) q^{23} +(-0.923880 - 0.382683i) q^{24} +(0.258819 + 0.965926i) q^{25} -0.765367i q^{26} +(0.382683 - 0.923880i) q^{27} +(-0.707107 + 0.707107i) q^{28} +(-0.866025 - 0.500000i) q^{30} +(-0.258819 - 0.965926i) q^{32} +(-0.793353 + 0.608761i) q^{35} +(0.965926 - 0.258819i) q^{36} +(-0.0675653 + 0.252157i) q^{38} +(0.465926 + 0.607206i) q^{39} +(-0.130526 - 0.991445i) q^{40} +(0.130526 - 0.991445i) q^{42} +(0.991445 - 0.130526i) q^{45} +0.517638 q^{46} +(0.793353 + 0.608761i) q^{48} +(-0.866025 - 0.500000i) q^{49} -1.00000i q^{50} +(-0.198092 + 0.739288i) q^{52} +(-0.608761 + 0.793353i) q^{54} +(0.866025 - 0.500000i) q^{56} +(-0.0999004 - 0.241181i) q^{57} +(0.923880 - 1.60021i) q^{59} +(0.707107 + 0.707107i) q^{60} +(0.991445 + 1.71723i) q^{61} +(0.500000 + 0.866025i) q^{63} +1.00000i q^{64} +(-0.292893 + 0.707107i) q^{65} +(-0.410670 + 0.315118i) q^{69} +(0.923880 - 0.382683i) q^{70} -1.93185i q^{71} -1.00000 q^{72} +(0.608761 + 0.793353i) q^{75} +(0.130526 - 0.226078i) q^{76} +(-0.292893 - 0.707107i) q^{78} +(-1.67303 + 0.965926i) q^{79} +(-0.130526 + 0.991445i) q^{80} -1.00000i q^{81} +(-0.478235 + 1.78480i) q^{83} +(-0.382683 + 0.923880i) q^{84} +(-0.991445 - 0.130526i) q^{90} -0.765367 q^{91} +(-0.500000 - 0.133975i) q^{92} +(0.158919 - 0.207107i) q^{95} +(-0.608761 - 0.793353i) q^{96} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q + 8q^{14} + 8q^{16} - 8q^{23} - 8q^{39} + 8q^{63} - 16q^{65} - 16q^{72} - 16q^{78} - 8q^{92} + O(q^{100}) \)

Character values

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

\(n\) \(281\) \(631\) \(1081\) \(1261\) \(2017\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 0.258819i −0.965926 0.258819i
\(3\) 0.923880 0.382683i 0.923880 0.382683i
\(4\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(5\) 0.793353 + 0.608761i 0.793353 + 0.608761i
\(6\) −0.991445 + 0.130526i −0.991445 + 0.130526i
\(7\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(8\) −0.707107 0.707107i −0.707107 0.707107i
\(9\) 0.707107 0.707107i 0.707107 0.707107i
\(10\) −0.608761 0.793353i −0.608761 0.793353i
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 0.991445 + 0.130526i 0.991445 + 0.130526i
\(13\) 0.198092 + 0.739288i 0.198092 + 0.739288i 0.991445 + 0.130526i \(0.0416667\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(14\) 0.500000 0.866025i 0.500000 0.866025i
\(15\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(16\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(19\) 0.261052i 0.261052i −0.991445 0.130526i \(-0.958333\pi\)
0.991445 0.130526i \(-0.0416667\pi\)
\(20\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(21\) 0.130526 + 0.991445i 0.130526 + 0.991445i
\(22\) 0 0
\(23\) −0.500000 + 0.133975i −0.500000 + 0.133975i −0.500000 0.866025i \(-0.666667\pi\)
1.00000i \(0.5\pi\)
\(24\) −0.923880 0.382683i −0.923880 0.382683i
\(25\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(26\) 0.765367i 0.765367i
\(27\) 0.382683 0.923880i 0.382683 0.923880i
\(28\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(29\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) −0.866025 0.500000i −0.866025 0.500000i
\(31\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) −0.258819 0.965926i −0.258819 0.965926i
\(33\) 0 0
\(34\) 0 0
\(35\) −0.793353 + 0.608761i −0.793353 + 0.608761i
\(36\) 0.965926 0.258819i 0.965926 0.258819i
\(37\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(38\) −0.0675653 + 0.252157i −0.0675653 + 0.252157i
\(39\) 0.465926 + 0.607206i 0.465926 + 0.607206i
\(40\) −0.130526 0.991445i −0.130526 0.991445i
\(41\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(42\) 0.130526 0.991445i 0.130526 0.991445i
\(43\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(44\) 0 0
\(45\) 0.991445 0.130526i 0.991445 0.130526i
\(46\) 0.517638 0.517638
\(47\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(48\) 0.793353 + 0.608761i 0.793353 + 0.608761i
\(49\) −0.866025 0.500000i −0.866025 0.500000i
\(50\) 1.00000i 1.00000i
\(51\) 0 0
\(52\) −0.198092 + 0.739288i −0.198092 + 0.739288i
\(53\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(54\) −0.608761 + 0.793353i −0.608761 + 0.793353i
\(55\) 0 0
\(56\) 0.866025 0.500000i 0.866025 0.500000i
\(57\) −0.0999004 0.241181i −0.0999004 0.241181i
\(58\) 0 0
\(59\) 0.923880 1.60021i 0.923880 1.60021i 0.130526 0.991445i \(-0.458333\pi\)
0.793353 0.608761i \(-0.208333\pi\)
\(60\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(61\) 0.991445 + 1.71723i 0.991445 + 1.71723i 0.608761 + 0.793353i \(0.291667\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(62\) 0 0
\(63\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(64\) 1.00000i 1.00000i
\(65\) −0.292893 + 0.707107i −0.292893 + 0.707107i
\(66\) 0 0
\(67\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(68\) 0 0
\(69\) −0.410670 + 0.315118i −0.410670 + 0.315118i
\(70\) 0.923880 0.382683i 0.923880 0.382683i
\(71\) 1.93185i 1.93185i −0.258819 0.965926i \(-0.583333\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(72\) −1.00000 −1.00000
\(73\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(74\) 0 0
\(75\) 0.608761 + 0.793353i 0.608761 + 0.793353i
\(76\) 0.130526 0.226078i 0.130526 0.226078i
\(77\) 0 0
\(78\) −0.292893 0.707107i −0.292893 0.707107i
\(79\) −1.67303 + 0.965926i −1.67303 + 0.965926i −0.707107 + 0.707107i \(0.750000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(80\) −0.130526 + 0.991445i −0.130526 + 0.991445i
\(81\) 1.00000i 1.00000i
\(82\) 0 0
\(83\) −0.478235 + 1.78480i −0.478235 + 1.78480i 0.130526 + 0.991445i \(0.458333\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(84\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(85\) 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
\(91\) −0.765367 −0.765367
\(92\) −0.500000 0.133975i −0.500000 0.133975i
\(93\) 0 0
\(94\) 0 0
\(95\) 0.158919 0.207107i 0.158919 0.207107i
\(96\) −0.608761 0.793353i −0.608761 0.793353i
\(97\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(98\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(99\) 0 0
\(100\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(101\) 1.37413 0.793353i 1.37413 0.793353i 0.382683 0.923880i \(-0.375000\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(102\) 0 0
\(103\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(104\) 0.382683 0.662827i 0.382683 0.662827i
\(105\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(106\) 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
\(112\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(113\) −1.67303 + 0.448288i −1.67303 + 0.448288i −0.965926 0.258819i \(-0.916667\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(114\) 0.0340742 + 0.258819i 0.0340742 + 0.258819i
\(115\) −0.478235 0.198092i −0.478235 0.198092i
\(116\) 0 0
\(117\) 0.662827 + 0.382683i 0.662827 + 0.382683i
\(118\) −1.30656 + 1.30656i −1.30656 + 1.30656i
\(119\) 0 0
\(120\) −0.500000 0.866025i −0.500000 0.866025i
\(121\) 0.500000 0.866025i 0.500000 0.866025i
\(122\) −0.513210 1.91532i −0.513210 1.91532i
\(123\) 0 0
\(124\) 0 0
\(125\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(126\) −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 \(0.833333\pi\)
\(128\) 0.258819 0.965926i 0.258819 0.965926i
\(129\) 0 0
\(130\) 0.465926 0.607206i 0.465926 0.607206i
\(131\) −1.05441 0.608761i −1.05441 0.608761i −0.130526 0.991445i \(-0.541667\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(132\) 0 0
\(133\) 0.252157 + 0.0675653i 0.252157 + 0.0675653i
\(134\) 0 0
\(135\) 0.866025 0.500000i 0.866025 0.500000i
\(136\) 0 0
\(137\) −1.36603 0.366025i −1.36603 0.366025i −0.500000 0.866025i \(-0.666667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(138\) 0.478235 0.198092i 0.478235 0.198092i
\(139\) 1.05441 + 0.608761i 1.05441 + 0.608761i 0.923880 0.382683i \(-0.125000\pi\)
0.130526 + 0.991445i \(0.458333\pi\)
\(140\) −0.991445 + 0.130526i −0.991445 + 0.130526i
\(141\) 0 0
\(142\) −0.500000 + 1.86603i −0.500000 + 1.86603i
\(143\) 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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(150\) −0.382683 0.923880i −0.382683 0.923880i
\(151\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(152\) −0.184592 + 0.184592i −0.184592 + 0.184592i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0.0999004 + 0.758819i 0.0999004 + 0.758819i
\(157\) 1.53264 0.410670i 1.53264 0.410670i 0.608761 0.793353i \(-0.291667\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(158\) 1.86603 0.500000i 1.86603 0.500000i
\(159\) 0 0
\(160\) 0.382683 0.923880i 0.382683 0.923880i
\(161\) 0.517638i 0.517638i
\(162\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(163\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0.923880 1.60021i 0.923880 1.60021i
\(167\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(168\) 0.608761 0.793353i 0.608761 0.793353i
\(169\) 0.358719 0.207107i 0.358719 0.207107i
\(170\) 0 0
\(171\) −0.184592 0.184592i −0.184592 0.184592i
\(172\) 0 0
\(173\) 0.198092 0.739288i 0.198092 0.739288i −0.793353 0.608761i \(-0.791667\pi\)
0.991445 0.130526i \(-0.0416667\pi\)
\(174\) 0 0
\(175\) −1.00000 −1.00000
\(176\) 0 0
\(177\) 0.241181 1.83195i 0.241181 1.83195i
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(181\) 1.58671 1.58671 0.793353 0.608761i \(-0.208333\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(182\) 0.739288 + 0.198092i 0.739288 + 0.198092i
\(183\) 1.57313 + 1.20711i 1.57313 + 1.20711i
\(184\) 0.448288 + 0.258819i 0.448288 + 0.258819i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0.793353 + 0.608761i 0.793353 + 0.608761i
\(190\) −0.207107 + 0.158919i −0.207107 + 0.158919i
\(191\) −0.448288 + 0.258819i −0.448288 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(192\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(193\) −0.448288 1.67303i −0.448288 1.67303i −0.707107 0.707107i \(-0.750000\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(194\) 0 0
\(195\) 0.765367i 0.765367i
\(196\) −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 \(0.5\pi\)
\(200\) 0.500000 0.866025i 0.500000 0.866025i
\(201\) 0 0
\(202\) −1.53264 + 0.410670i −1.53264 + 0.410670i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.258819 + 0.448288i −0.258819 + 0.448288i
\(208\) −0.541196 + 0.541196i −0.541196 + 0.541196i
\(209\) 0 0
\(210\) 0.707107 0.707107i 0.707107 0.707107i
\(211\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) 0 0
\(213\) −0.739288 1.78480i −0.739288 1.78480i
\(214\) 0 0
\(215\) 0 0
\(216\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(224\) 1.00000 1.00000
\(225\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(226\) 1.73205 1.73205
\(227\) 1.53264 + 0.410670i 1.53264 + 0.410670i 0.923880 0.382683i \(-0.125000\pi\)
0.608761 + 0.793353i \(0.291667\pi\)
\(228\) 0.0340742 0.258819i 0.0340742 0.258819i
\(229\) −1.05441 0.608761i −1.05441 0.608761i −0.130526 0.991445i \(-0.541667\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(230\) 0.410670 + 0.315118i 0.410670 + 0.315118i
\(231\) 0 0
\(232\) 0 0
\(233\) 1.36603 + 1.36603i 1.36603 + 1.36603i 0.866025 + 0.500000i \(0.166667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(234\) −0.541196 0.541196i −0.541196 0.541196i
\(235\) 0 0
\(236\) 1.60021 0.923880i 1.60021 0.923880i
\(237\) −1.17604 + 1.53264i −1.17604 + 1.53264i
\(238\) 0 0
\(239\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(240\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(241\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(242\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(243\) −0.382683 0.923880i −0.382683 0.923880i
\(244\) 1.98289i 1.98289i
\(245\) −0.382683 0.923880i −0.382683 0.923880i
\(246\) 0 0
\(247\) 0.192993 0.0517123i 0.192993 0.0517123i
\(248\) 0 0
\(249\) 0.241181 + 1.83195i 0.241181 + 1.83195i
\(250\) 0.608761 0.793353i 0.608761 0.793353i
\(251\) 0.261052i 0.261052i −0.991445 0.130526i \(-0.958333\pi\)
0.991445 0.130526i \(-0.0416667\pi\)
\(252\) 1.00000i 1.00000i
\(253\) 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 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.607206 + 0.465926i −0.607206 + 0.465926i
\(261\) 0 0
\(262\) 0.860919 + 0.860919i 0.860919 + 0.860919i
\(263\) 0.448288 1.67303i 0.448288 1.67303i −0.258819 0.965926i \(-0.583333\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −0.226078 0.130526i −0.226078 0.130526i
\(267\) 0 0
\(268\) 0 0
\(269\) 1.21752 1.21752 0.608761 0.793353i \(-0.291667\pi\)
0.608761 + 0.793353i \(0.291667\pi\)
\(270\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) −0.707107 + 0.292893i −0.707107 + 0.292893i
\(274\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(275\) 0 0
\(276\) −0.513210 + 0.0675653i −0.513210 + 0.0675653i
\(277\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(278\) −0.860919 0.860919i −0.860919 0.860919i
\(279\) 0 0
\(280\) 0.991445 + 0.130526i 0.991445 + 0.130526i
\(281\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) −0.315118 1.17604i −0.315118 1.17604i −0.923880 0.382683i \(-0.875000\pi\)
0.608761 0.793353i \(-0.291667\pi\)
\(284\) 0.965926 1.67303i 0.965926 1.67303i
\(285\) 0.0675653 0.252157i 0.0675653 0.252157i
\(286\) 0 0
\(287\) 0 0
\(288\) −0.866025 0.500000i −0.866025 0.500000i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.91532 + 0.513210i −1.91532 + 0.513210i −0.923880 + 0.382683i \(0.875000\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(294\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(295\) 1.70711 0.707107i 1.70711 0.707107i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.198092 0.343105i −0.198092 0.343105i
\(300\) 0.130526 + 0.991445i 0.130526 + 0.991445i
\(301\) 0 0
\(302\) 0.448288 + 1.67303i 0.448288 + 1.67303i
\(303\) 0.965926 1.25882i 0.965926 1.25882i
\(304\) 0.226078 0.130526i 0.226078 0.130526i
\(305\) −0.258819 + 1.96593i −0.258819 + 1.96593i
\(306\) 0 0
\(307\) −1.40211 1.40211i −1.40211 1.40211i −0.793353 0.608761i \(-0.791667\pi\)
−0.608761 0.793353i \(-0.708333\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 0.0999004 0.758819i 0.0999004 0.758819i
\(313\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(314\) −1.58671 −1.58671
\(315\) −0.130526 + 0.991445i −0.130526 + 0.991445i
\(316\) −1.93185 −1.93185
\(317\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.608761 + 0.793353i −0.608761 + 0.793353i
\(321\) 0 0
\(322\) −0.133975 + 0.500000i −0.133975 + 0.500000i
\(323\) 0 0
\(324\) 0.500000 0.866025i 0.500000 0.866025i
\(325\) −0.662827 + 0.382683i −0.662827 + 0.382683i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) −1.30656 + 1.30656i −1.30656 + 1.30656i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) −0.793353 + 0.608761i −0.793353 + 0.608761i
\(337\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(338\) −0.400100 + 0.107206i −0.400100 + 0.107206i
\(339\) −1.37413 + 1.05441i −1.37413 + 1.05441i
\(340\) 0 0
\(341\) 0 0
\(342\) 0.130526 + 0.226078i 0.130526 + 0.226078i
\(343\) 0.707107 0.707107i 0.707107 0.707107i
\(344\) 0 0
\(345\) −0.517638 −0.517638
\(346\) −0.382683 + 0.662827i −0.382683 + 0.662827i
\(347\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(348\) 0 0
\(349\) −1.60021 + 0.923880i −1.60021 + 0.923880i −0.608761 + 0.793353i \(0.708333\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(350\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(351\) 0.758819 + 0.0999004i 0.758819 + 0.0999004i
\(352\) 0 0
\(353\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(354\) −0.707107 + 1.70711i −0.707107 + 1.70711i
\(355\) 1.17604 1.53264i 1.17604 1.53264i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(360\) −0.793353 0.608761i −0.793353 0.608761i
\(361\) 0.931852 0.931852
\(362\) −1.53264 0.410670i −1.53264 0.410670i
\(363\) 0.130526 0.991445i 0.130526 0.991445i
\(364\) −0.662827 0.382683i −0.662827 0.382683i
\(365\) 0 0
\(366\) −1.20711 1.57313i −1.20711 1.57313i
\(367\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(368\) −0.366025 0.366025i −0.366025 0.366025i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(374\) 0 0
\(375\) 1.00000i 1.00000i
\(376\) 0 0
\(377\) 0 0
\(378\) −0.608761 0.793353i −0.608761 0.793353i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0.241181 0.0999004i 0.241181 0.0999004i
\(381\) −0.478235 0.198092i −0.478235 0.198092i
\(382\) 0.500000 0.133975i 0.500000 0.133975i
\(383\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(384\) −0.130526 0.991445i −0.130526 0.991445i
\(385\) 0 0
\(386\) 1.73205i 1.73205i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(390\) 0.198092 0.739288i 0.198092 0.739288i
\(391\) 0 0
\(392\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(393\) −1.20711 0.158919i −1.20711 0.158919i
\(394\) 0 0
\(395\) −1.91532 0.252157i −1.91532 0.252157i
\(396\) 0 0
\(397\) −1.30656 1.30656i −1.30656 1.30656i −0.923880 0.382683i \(-0.875000\pi\)
−0.382683 0.923880i \(-0.625000\pi\)
\(398\) 0 0
\(399\) 0.258819 0.0340742i 0.258819 0.0340742i
\(400\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(401\) 1.67303 + 0.965926i 1.67303 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 1.58671 1.58671
\(405\) 0.608761 0.793353i 0.608761 0.793353i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(410\) 0 0
\(411\) −1.40211 + 0.184592i −1.40211 + 0.184592i
\(412\) 0 0
\(413\) 1.30656 + 1.30656i 1.30656 + 1.30656i
\(414\) 0.366025 0.366025i 0.366025 0.366025i
\(415\) −1.46593 + 1.12484i −1.46593 + 1.12484i
\(416\) 0.662827 0.382683i 0.662827 0.382683i
\(417\) 1.20711 + 0.158919i 1.20711 + 0.158919i
\(418\) 0 0
\(419\) 0.991445 1.71723i 0.991445 1.71723i 0.382683 0.923880i \(-0.375000\pi\)
0.608761 0.793353i \(-0.291667\pi\)
\(420\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(421\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0.252157 + 1.91532i 0.252157 + 1.91532i
\(427\) −1.91532 + 0.513210i −1.91532 + 0.513210i
\(428\) 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
\(437\) 0.0349744 + 0.130526i 0.0349744 + 0.130526i
\(438\) 0 0
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(442\) 0 0
\(443\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.965926 0.258819i −0.965926 0.258819i
\(449\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(450\) −0.707107 0.707107i −0.707107 0.707107i
\(451\) 0 0
\(452\) −1.67303 0.448288i −1.67303 0.448288i
\(453\) −1.37413 1.05441i −1.37413 1.05441i
\(454\) −1.37413 0.793353i −1.37413 0.793353i
\(455\) −0.607206 0.465926i −0.607206 0.465926i
\(456\) −0.0999004 + 0.241181i −0.0999004 + 0.241181i
\(457\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(458\) 0.860919 + 0.860919i 0.860919 + 0.860919i
\(459\) 0 0
\(460\) −0.315118 0.410670i −0.315118 0.410670i
\(461\) −1.05441 + 0.608761i −1.05441 + 0.608761i −0.923880 0.382683i \(-0.875000\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(462\) 0 0
\(463\) 0.448288 + 1.67303i 0.448288 + 1.67303i 0.707107 + 0.707107i \(0.250000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.965926 1.67303i −0.965926 1.67303i
\(467\) −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i \(-0.875000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(468\) 0.382683 + 0.662827i 0.382683 + 0.662827i
\(469\) 0 0
\(470\) 0 0
\(471\) 1.25882 0.965926i 1.25882 0.965926i
\(472\) −1.78480 + 0.478235i −1.78480 + 0.478235i
\(473\) 0 0
\(474\) 1.53264 1.17604i 1.53264 1.17604i
\(475\) 0.252157 0.0675653i 0.252157 0.0675653i
\(476\) 0 0
\(477\) 0 0
\(478\) 0.707107 0.707107i 0.707107 0.707107i
\(479\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(480\) 1.00000i 1.00000i
\(481\) 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
\(486\) 0.130526 + 0.991445i 0.130526 + 0.991445i
\(487\) −1.36603 1.36603i −1.36603 1.36603i −0.866025 0.500000i \(-0.833333\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(488\) 0.513210 1.91532i 0.513210 1.91532i
\(489\) 0 0
\(490\) 0.130526 + 0.991445i 0.130526 + 0.991445i
\(491\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −0.199801 −0.199801
\(495\) 0 0
\(496\) 0 0
\(497\) 1.86603 + 0.500000i 1.86603 + 0.500000i
\(498\) 0.241181 1.83195i 0.241181 1.83195i
\(499\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(500\) −0.793353 + 0.608761i −0.793353 + 0.608761i
\(501\) 0 0
\(502\) −0.0675653 + 0.252157i −0.0675653 + 0.252157i
\(503\) 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
\(505\) 1.57313 + 0.207107i 1.57313 + 0.207107i
\(506\) 0 0
\(507\) 0.252157 0.328618i 0.252157 0.328618i
\(508\) −0.133975 0.500000i −0.133975 0.500000i
\(509\) −0.923880 + 1.60021i −0.923880 + 1.60021i −0.130526 + 0.991445i \(0.541667\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.707107 0.707107i 0.707107 0.707107i
\(513\) −0.241181 0.0999004i −0.241181 0.0999004i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −0.0999004 0.758819i −0.0999004 0.758819i
\(520\) 0.707107 0.292893i 0.707107 0.292893i
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) 0.184592 0.184592i 0.184592 0.184592i −0.608761 0.793353i \(-0.708333\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(524\) −0.608761 1.05441i −0.608761 1.05441i
\(525\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(526\) −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
\(531\) −0.478235 1.78480i −0.478235 1.78480i
\(532\) 0.184592 + 0.184592i 0.184592 + 0.184592i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −1.17604 0.315118i −1.17604 0.315118i
\(539\) 0 0
\(540\) 1.00000 1.00000
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 1.46593 0.607206i 1.46593 0.607206i
\(544\) 0 0
\(545\) 0 0
\(546\) 0.758819 0.0999004i 0.758819 0.0999004i
\(547\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(548\) −1.00000 1.00000i −1.00000 1.00000i
\(549\) 1.91532 + 0.513210i 1.91532 + 0.513210i
\(550\) 0 0
\(551\) 0 0
\(552\) 0.513210 + 0.0675653i 0.513210 + 0.0675653i
\(553\) −0.500000 1.86603i −0.500000 1.86603i
\(554\) 0 0
\(555\) 0 0
\(556\) 0.608761 + 1.05441i 0.608761 + 1.05441i
\(557\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −0.923880 0.382683i −0.923880 0.382683i
\(561\) 0 0
\(562\) 0.965926 0.258819i 0.965926 0.258819i
\(563\) −1.17604 + 0.315118i −1.17604 + 0.315118i −0.793353 0.608761i \(-0.791667\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(564\) 0 0
\(565\) −1.60021 0.662827i −1.60021 0.662827i
\(566\) 1.21752i 1.21752i
\(567\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(568\) −1.36603 + 1.36603i −1.36603 + 1.36603i
\(569\) 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(570\) −0.130526 + 0.226078i −0.130526 + 0.226078i
\(571\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 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 \(0.250000\pi\)
\(578\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(579\) −1.05441 1.37413i −1.05441 1.37413i
\(580\) 0 0
\(581\) −1.60021 0.923880i −1.60021 0.923880i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0.292893 + 0.707107i 0.292893 + 0.707107i
\(586\) 1.98289 1.98289
\(587\) 1.91532 + 0.513210i 1.91532 + 0.513210i 0.991445 + 0.130526i \(0.0416667\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(588\) −0.793353 0.608761i −0.793353 0.608761i
\(589\) 0 0
\(590\) −1.83195 + 0.241181i −1.83195 + 0.241181i
\(591\) 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
\(598\) 0.102540 + 0.382683i 0.102540 + 0.382683i
\(599\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(600\) 0.130526 0.991445i 0.130526 0.991445i
\(601\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.73205i 1.73205i
\(605\) 0.923880 0.382683i 0.923880 0.382683i
\(606\) −1.25882 + 0.965926i −1.25882 + 0.965926i
\(607\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(608\) −0.252157 + 0.0675653i −0.252157 + 0.0675653i
\(609\) 0 0
\(610\) 0.758819 1.83195i 0.758819 1.83195i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(614\) 0.991445 + 1.71723i 0.991445 + 1.71723i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(618\) 0 0
\(619\) −1.71723 + 0.991445i −1.71723 + 0.991445i −0.793353 + 0.608761i \(0.791667\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(620\) 0 0
\(621\) −0.0675653 + 0.513210i −0.0675653 + 0.513210i
\(622\) 0 0
\(623\) 0 0
\(624\) −0.292893 + 0.707107i −0.292893 + 0.707107i
\(625\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(626\) 0 0
\(627\) 0 0
\(628\) 1.53264 + 0.410670i 1.53264 + 0.410670i
\(629\) 0 0
\(630\) 0.382683 0.923880i 0.382683 0.923880i
\(631\) −0.517638 −0.517638 −0.258819 0.965926i \(-0.583333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(632\) 1.86603 + 0.500000i 1.86603 + 0.500000i
\(633\) 0 0
\(634\) 0 0
\(635\) −0.0675653 0.513210i −0.0675653 0.513210i
\(636\) 0 0
\(637\) 0.198092 0.739288i 0.198092 0.739288i
\(638\) 0 0
\(639\) −1.36603 1.36603i −1.36603 1.36603i
\(640\) 0.793353 0.608761i 0.793353 0.608761i
\(641\) −1.67303 + 0.965926i −1.67303 + 0.965926i −0.707107 + 0.707107i \(0.750000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(642\) 0 0
\(643\) 0.478235 + 1.78480i 0.478235 + 1.78480i 0.608761 + 0.793353i \(0.291667\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(644\) 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
\(650\) 0.739288 0.198092i 0.739288 0.198092i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(654\) 0 0
\(655\) −0.465926 1.12484i −0.465926 1.12484i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(660\) 0 0
\(661\) 0.793353 1.37413i 0.793353 1.37413i −0.130526 0.991445i \(-0.541667\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 1.60021 0.923880i 1.60021 0.923880i
\(665\) 0.158919 + 0.207107i 0.158919 + 0.207107i
\(666\) 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
\(673\) 0.500000 + 0.133975i 0.500000 + 0.133975i 0.500000 0.866025i \(-0.333333\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 0.991445 + 0.130526i 0.991445 + 0.130526i
\(676\) 0.414214 0.414214
\(677\) −0.739288 0.198092i −0.739288 0.198092i −0.130526 0.991445i \(-0.541667\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(678\) 1.60021 0.662827i 1.60021 0.662827i
\(679\) 0 0
\(680\) 0 0
\(681\) 1.57313 0.207107i 1.57313 0.207107i
\(682\) 0 0
\(683\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(684\) −0.0675653 0.252157i −0.0675653 0.252157i
\(685\) −0.860919 1.12197i −0.860919 1.12197i
\(686\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(687\) −1.20711 0.158919i −1.20711 0.158919i
\(688\) 0 0
\(689\) 0 0
\(690\) 0.500000 + 0.133975i 0.500000 + 0.133975i
\(691\) 0.793353 + 1.37413i 0.793353 + 1.37413i 0.923880 + 0.382683i \(0.125000\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(692\) 0.541196 0.541196i 0.541196 0.541196i
\(693\) 0 0
\(694\) 0 0
\(695\) 0.465926 + 1.12484i 0.465926 + 1.12484i
\(696\) 0 0
\(697\) 0 0
\(698\) 1.78480 0.478235i 1.78480 0.478235i
\(699\) 1.78480 + 0.739288i 1.78480 + 0.739288i
\(700\) −0.866025 0.500000i −0.866025 0.500000i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) −0.707107 0.292893i −0.707107 0.292893i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0.410670 + 1.53264i 0.410670 + 1.53264i
\(708\) 1.12484 1.46593i 1.12484 1.46593i
\(709\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(710\) −1.53264 + 1.17604i −1.53264 + 1.17604i
\(711\) −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
\(718\) 1.67303 + 0.448288i 1.67303 + 0.448288i
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0.608761 + 0.793353i 0.608761 + 0.793353i
\(721\) 0 0
\(722\) −0.900100 0.241181i −0.900100 0.241181i
\(723\) 0 0
\(724\) 1.37413 + 0.793353i 1.37413 + 0.793353i
\(725\) 0 0
\(726\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(727\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(728\) 0.541196 + 0.541196i 0.541196 + 0.541196i
\(729\) −0.707107 0.707107i −0.707107 0.707107i
\(730\) 0 0
\(731\) 0 0
\(732\) 0.758819 + 1.83195i 0.758819 + 1.83195i
\(733\) 0.410670 + 1.53264i 0.410670 + 1.53264i 0.793353 + 0.608761i \(0.208333\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(734\) 0 0
\(735\) −0.707107 0.707107i −0.707107 0.707107i
\(736\) 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
\(741\) 0.158513 0.121631i 0.158513 0.121631i
\(742\) 0 0
\(743\) −1.36603 + 0.366025i −1.36603 + 0.366025i −0.866025 0.500000i \(-0.833333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.923880 + 1.60021i 0.923880 + 1.60021i
\(748\) 0 0
\(749\) 0 0
\(750\) 0.258819 0.965926i 0.258819 0.965926i
\(751\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(752\) 0 0
\(753\) −0.0999004 0.241181i −0.0999004 0.241181i
\(754\) 0 0
\(755\) 0.226078 1.71723i 0.226078 1.71723i
\(756\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(757\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −0.258819 + 0.0340742i −0.258819 + 0.0340742i
\(761\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(762\) 0.410670 + 0.315118i 0.410670 + 0.315118i
\(763\) 0 0
\(764\) −0.517638 −0.517638
\(765\) 0 0
\(766\) 0 0
\(767\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(768\) −0.130526 + 0.991445i −0.130526 + 0.991445i
\(769\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.448288 1.67303i 0.448288 1.67303i
\(773\) 0.184592 + 0.184592i 0.184592 + 0.184592i 0.793353 0.608761i \(-0.208333\pi\)
−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
\(780\) −0.382683 + 0.662827i −0.382683 + 0.662827i
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000i 1.00000i
\(785\) 1.46593 + 0.607206i 1.46593 + 0.607206i
\(786\) 1.12484 + 0.465926i 1.12484 + 0.465926i
\(787\) 1.78480 0.478235i 1.78480 0.478235i 0.793353 0.608761i \(-0.208333\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(788\) 0 0
\(789\) −0.226078 1.71723i −0.226078 1.71723i
\(790\) 1.78480 + 0.739288i 1.78480 + 0.739288i
\(791\) 1.73205i 1.73205i
\(792\) 0 0
\(793\) −1.07313 + 1.07313i −1.07313 + 1.07313i
\(794\) 0.923880 + 1.60021i 0.923880 +