Properties

Label 2013.1.bm.b.548.1
Level 2013
Weight 1
Character 2013.548
Analytic conductor 1.005
Analytic rank 0
Dimension 4
Projective image \(D_{5}\)
CM discriminant -183
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 2013 = 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2013.bm (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.00461787043\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \(x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(D_{5}\)
Projective field Galois closure of 5.1.490312449.1

Embedding invariants

Embedding label 548.1
Root \(0.809017 + 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 2013.548
Dual form 2013.1.bm.b.731.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.190983 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.500000 + 0.363271i) q^{4} +(0.190983 + 0.587785i) q^{6} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(0.190983 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.500000 + 0.363271i) q^{4} +(0.190983 + 0.587785i) q^{6} +(0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.809017 - 0.587785i) q^{11} -0.618034 q^{12} +(0.190983 - 0.587785i) q^{13} +(-0.500000 - 1.53884i) q^{17} +(-0.500000 - 0.363271i) q^{18} +(1.30902 - 0.951057i) q^{19} +(-0.500000 + 0.363271i) q^{22} +0.618034 q^{23} +(-0.309017 + 0.951057i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-0.309017 - 0.224514i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.500000 - 0.363271i) q^{29} +1.00000 q^{32} +1.00000 q^{33} -1.00000 q^{34} +(0.500000 - 0.363271i) q^{36} +(-0.309017 - 0.951057i) q^{38} +(0.190983 + 0.587785i) q^{39} +(-0.190983 - 0.587785i) q^{44} +(0.118034 - 0.363271i) q^{46} +(0.309017 + 0.951057i) q^{49} +(0.190983 + 0.587785i) q^{50} +(1.30902 + 0.951057i) q^{51} +(0.309017 - 0.224514i) q^{52} +(0.190983 - 0.587785i) q^{53} +0.618034 q^{54} +(-0.500000 + 1.53884i) q^{57} +(-0.309017 + 0.224514i) q^{58} +(1.30902 + 0.951057i) q^{59} +(0.309017 + 0.951057i) q^{61} +(0.190983 - 0.587785i) q^{64} +(0.190983 - 0.587785i) q^{66} +(0.309017 - 0.951057i) q^{68} +(-0.500000 + 0.363271i) q^{69} +(0.618034 + 1.90211i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(-0.500000 - 0.363271i) q^{73} +(0.309017 - 0.951057i) q^{75} +1.00000 q^{76} +0.381966 q^{78} +(-0.809017 - 0.587785i) q^{81} +0.618034 q^{87} -1.00000 q^{88} -1.61803 q^{89} +(0.309017 + 0.224514i) q^{92} +(-0.809017 + 0.587785i) q^{96} +(0.618034 - 1.90211i) q^{97} +0.618034 q^{98} +(-0.809017 + 0.587785i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 3q^{2} - q^{3} + 2q^{4} + 3q^{6} + q^{8} - q^{9} + O(q^{10}) \) \( 4q + 3q^{2} - q^{3} + 2q^{4} + 3q^{6} + q^{8} - q^{9} - q^{11} + 2q^{12} + 3q^{13} - 2q^{17} - 2q^{18} + 3q^{19} - 2q^{22} - 2q^{23} + q^{24} - q^{25} + q^{26} - q^{27} - 2q^{29} + 4q^{32} + 4q^{33} - 4q^{34} + 2q^{36} + q^{38} + 3q^{39} - 3q^{44} - 4q^{46} - q^{49} + 3q^{50} + 3q^{51} - q^{52} + 3q^{53} - 2q^{54} - 2q^{57} + q^{58} + 3q^{59} - q^{61} + 3q^{64} + 3q^{66} - q^{68} - 2q^{69} - 2q^{71} + q^{72} - 2q^{73} - q^{75} + 4q^{76} + 6q^{78} - q^{81} - 2q^{87} - 4q^{88} - 2q^{89} - q^{92} - q^{96} - 2q^{97} - 2q^{98} - q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2013\mathbb{Z}\right)^\times\).

\(n\) \(1222\) \(1343\) \(1465\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(3\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(4\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(5\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(6\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(7\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(8\) 0.809017 0.587785i 0.809017 0.587785i
\(9\) 0.309017 0.951057i 0.309017 0.951057i
\(10\) 0 0
\(11\) −0.809017 0.587785i −0.809017 0.587785i
\(12\) −0.618034 −0.618034
\(13\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(18\) −0.500000 0.363271i −0.500000 0.363271i
\(19\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(23\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(24\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(25\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(26\) −0.309017 0.224514i −0.309017 0.224514i
\(27\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(28\) 0 0
\(29\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(30\) 0 0
\(31\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(32\) 1.00000 1.00000
\(33\) 1.00000 1.00000
\(34\) −1.00000 −1.00000
\(35\) 0 0
\(36\) 0.500000 0.363271i 0.500000 0.363271i
\(37\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(38\) −0.309017 0.951057i −0.309017 0.951057i
\(39\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(40\) 0 0
\(41\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −0.190983 0.587785i −0.190983 0.587785i
\(45\) 0 0
\(46\) 0.118034 0.363271i 0.118034 0.363271i
\(47\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(48\) 0 0
\(49\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(50\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(51\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(52\) 0.309017 0.224514i 0.309017 0.224514i
\(53\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(54\) 0.618034 0.618034
\(55\) 0 0
\(56\) 0 0
\(57\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(58\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(59\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(60\) 0 0
\(61\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(62\) 0 0
\(63\) 0 0
\(64\) 0.190983 0.587785i 0.190983 0.587785i
\(65\) 0 0
\(66\) 0.190983 0.587785i 0.190983 0.587785i
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0.309017 0.951057i 0.309017 0.951057i
\(69\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(70\) 0 0
\(71\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(72\) −0.309017 0.951057i −0.309017 0.951057i
\(73\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(74\) 0 0
\(75\) 0.309017 0.951057i 0.309017 0.951057i
\(76\) 1.00000 1.00000
\(77\) 0 0
\(78\) 0.381966 0.381966
\(79\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.809017 0.587785i
\(82\) 0 0
\(83\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0.618034 0.618034
\(88\) −1.00000 −1.00000
\(89\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(97\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(98\) 0.618034 0.618034
\(99\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(100\) −0.618034 −0.618034
\(101\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(102\) 0.809017 0.587785i 0.809017 0.587785i
\(103\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(104\) −0.190983 0.587785i −0.190983 0.587785i
\(105\) 0 0
\(106\) −0.309017 0.224514i −0.309017 0.224514i
\(107\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(108\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(109\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(114\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(115\) 0 0
\(116\) −0.118034 0.363271i −0.118034 0.363271i
\(117\) −0.500000 0.363271i −0.500000 0.363271i
\(118\) 0.809017 0.587785i 0.809017 0.587785i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(122\) 0.618034 0.618034
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(128\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −1.30902 0.951057i −1.30902 0.951057i
\(137\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(138\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(139\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.23607 1.23607
\(143\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(144\) 0 0
\(145\) 0 0
\(146\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(147\) −0.809017 0.587785i −0.809017 0.587785i
\(148\) 0 0
\(149\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(150\) −0.500000 0.363271i −0.500000 0.363271i
\(151\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(152\) 0.500000 1.53884i 0.500000 1.53884i
\(153\) −1.61803 −1.61803
\(154\) 0 0
\(155\) 0 0
\(156\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(157\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(158\) 0 0
\(159\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(160\) 0 0
\(161\) 0 0
\(162\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(163\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(168\) 0 0
\(169\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(170\) 0 0
\(171\) −0.500000 1.53884i −0.500000 1.53884i
\(172\) 0 0
\(173\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(174\) 0.118034 0.363271i 0.118034 0.363271i
\(175\) 0 0
\(176\) 0 0
\(177\) −1.61803 −1.61803
\(178\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(179\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(180\) 0 0
\(181\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(182\) 0 0
\(183\) −0.809017 0.587785i −0.809017 0.587785i
\(184\) 0.500000 0.363271i 0.500000 0.363271i
\(185\) 0 0
\(186\) 0 0
\(187\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(192\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(193\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(194\) −1.00000 0.726543i −1.00000 0.726543i
\(195\) 0 0
\(196\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(199\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(200\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(201\) 0 0
\(202\) −1.00000 0.726543i −1.00000 0.726543i
\(203\) 0 0
\(204\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(205\) 0 0
\(206\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(207\) 0.190983 0.587785i 0.190983 0.587785i
\(208\) 0 0
\(209\) −1.61803 −1.61803
\(210\) 0 0
\(211\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(212\) 0.309017 0.224514i 0.309017 0.224514i
\(213\) −1.61803 1.17557i −1.61803 1.17557i
\(214\) 0 0
\(215\) 0 0
\(216\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(217\) 0 0
\(218\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(219\) 0.618034 0.618034
\(220\) 0 0
\(221\) −1.00000 −1.00000
\(222\) 0 0
\(223\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(224\) 0 0
\(225\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(226\) 0 0
\(227\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(228\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(229\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.618034 −0.618034
\(233\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(234\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(235\) 0 0
\(236\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(240\) 0 0
\(241\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(242\) 0.618034 0.618034
\(243\) 1.00000 1.00000
\(244\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(245\) 0 0
\(246\) 0 0
\(247\) −0.309017 0.951057i −0.309017 0.951057i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(252\) 0 0
\(253\) −0.500000 0.363271i −0.500000 0.363271i
\(254\) 1.23607 1.23607
\(255\) 0 0
\(256\) 0.809017 0.587785i 0.809017 0.587785i
\(257\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0.809017 0.587785i 0.809017 0.587785i
\(265\) 0 0
\(266\) 0 0
\(267\) 1.30902 0.951057i 1.30902 0.951057i
\(268\) 0 0
\(269\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(270\) 0 0
\(271\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.00000 1.00000
\(276\) −0.381966 −0.381966
\(277\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(282\) 0 0
\(283\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(284\) −0.381966 + 1.17557i −0.381966 + 1.17557i
\(285\) 0 0
\(286\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(287\) 0 0
\(288\) 0.309017 0.951057i 0.309017 0.951057i
\(289\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(290\) 0 0
\(291\) 0.618034 + 1.90211i 0.618034 + 1.90211i
\(292\) −0.118034 0.363271i −0.118034 0.363271i
\(293\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(294\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.309017 0.951057i 0.309017 0.951057i
\(298\) 0 0
\(299\) 0.118034 0.363271i 0.118034 0.363271i
\(300\) 0.500000 0.363271i 0.500000 0.363271i
\(301\) 0 0
\(302\) 0 0
\(303\) 0.618034 + 1.90211i 0.618034 + 1.90211i
\(304\) 0 0
\(305\) 0 0
\(306\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0.618034 0.618034
\(310\) 0 0
\(311\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(312\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(313\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(318\) 0.381966 0.381966
\(319\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2.11803 1.53884i −2.11803 1.53884i
\(324\) −0.190983 0.587785i −0.190983 0.587785i
\(325\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(326\) −0.309017 0.224514i −0.309017 0.224514i
\(327\) 1.30902 0.951057i 1.30902 0.951057i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(338\) 0.309017 0.224514i 0.309017 0.224514i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) −1.00000 −1.00000
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0.381966 + 1.17557i 0.381966 + 1.17557i
\(347\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(348\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(349\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(350\) 0 0
\(351\) 0.618034 0.618034
\(352\) −0.809017 0.587785i −0.809017 0.587785i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(355\) 0 0
\(356\) −0.809017 0.587785i −0.809017 0.587785i
\(357\) 0 0
\(358\) 0 0
\(359\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(360\) 0 0
\(361\) 0.500000 1.53884i 0.500000 1.53884i
\(362\) 0 0
\(363\) −0.809017 0.587785i −0.809017 0.587785i
\(364\) 0 0
\(365\) 0 0
\(366\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(367\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(375\) 0 0
\(376\) 0 0
\(377\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(378\) 0 0
\(379\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(380\) 0 0
\(381\) −1.61803 1.17557i −1.61803 1.17557i
\(382\) 0.809017 0.587785i 0.809017 0.587785i
\(383\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(384\) −0.618034 −0.618034
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 1.00000 0.726543i 1.00000 0.726543i
\(389\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(390\) 0 0
\(391\) −0.309017 0.951057i −0.309017 0.951057i
\(392\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −0.618034 −0.618034
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(399\) 0 0
\(400\) 0 0
\(401\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 1.00000 0.726543i 1.00000 0.726543i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 1.61803 1.61803
\(409\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.118034 0.363271i −0.118034 0.363271i
\(413\) 0 0
\(414\) −0.309017 0.224514i −0.309017 0.224514i
\(415\) 0 0
\(416\) 0.190983 0.587785i 0.190983 0.587785i
\(417\) 0 0
\(418\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(419\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(420\) 0 0
\(421\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −0.190983 0.587785i −0.190983 0.587785i
\(425\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(426\) −1.00000 + 0.726543i −1.00000 + 0.726543i
\(427\) 0 0
\(428\) 0 0
\(429\) 0.190983 0.587785i 0.190983 0.587785i
\(430\) 0 0
\(431\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(432\) 0 0
\(433\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.809017 0.587785i −0.809017 0.587785i
\(437\) 0.809017 0.587785i 0.809017 0.587785i
\(438\) 0.118034 0.363271i 0.118034 0.363271i
\(439\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(440\) 0 0
\(441\) 1.00000 1.00000
\(442\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(443\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(450\) 0.618034 0.618034
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −1.00000 + 0.726543i −1.00000 + 0.726543i
\(455\) 0 0
\(456\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(457\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(458\) −0.309017 0.224514i −0.309017 0.224514i
\(459\) 1.30902 0.951057i 1.30902 0.951057i
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(467\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(468\) −0.118034 0.363271i −0.118034 0.363271i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 1.61803 1.61803
\(473\) 0 0
\(474\) 0 0
\(475\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(476\) 0 0
\(477\) −0.500000 0.363271i −0.500000 0.363271i
\(478\) 0 0
\(479\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.381966 1.17557i 0.381966 1.17557i
\(483\) 0 0
\(484\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(485\) 0 0
\(486\) 0.190983 0.587785i 0.190983 0.587785i
\(487\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(488\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(489\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(490\) 0 0
\(491\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(492\) 0 0
\(493\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(494\) −0.618034 −0.618034
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(503\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(507\) −0.618034 −0.618034
\(508\) −0.381966 + 1.17557i −0.381966 + 1.17557i
\(509\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0.618034 1.90211i 0.618034 1.90211i
\(520\) 0 0
\(521\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(522\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(523\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.618034 −0.618034
\(530\) 0 0
\(531\) 1.30902 0.951057i 1.30902 0.951057i
\(532\) 0 0
\(533\) 0 0
\(534\) −0.309017 0.951057i −0.309017 0.951057i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.309017 0.951057i 0.309017 0.951057i
\(540\) 0 0
\(541\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(542\) 0.809017 0.587785i 0.809017 0.587785i
\(543\) 0 0
\(544\) −0.500000 1.53884i −0.500000 1.53884i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(548\) 0 0
\(549\) 1.00000 1.00000
\(550\) 0.190983 0.587785i 0.190983 0.587785i
\(551\) −1.00000 −1.00000
\(552\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −0.500000 1.53884i −0.500000 1.53884i
\(562\) 0.381966 0.381966
\(563\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −0.309017 0.951057i −0.309017 0.951057i
\(567\) 0 0
\(568\) 1.61803 + 1.17557i 1.61803 + 1.17557i
\(569\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(570\) 0 0
\(571\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(572\) −0.381966 −0.381966
\(573\) −1.61803 −1.61803
\(574\) 0 0
\(575\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(576\) −0.500000 0.363271i −0.500000 0.363271i
\(577\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(578\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 1.23607 1.23607
\(583\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(584\) −0.618034 −0.618034
\(585\) 0 0
\(586\) 0 0
\(587\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(588\) −0.190983 0.587785i −0.190983 0.587785i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(594\) −0.500000 0.363271i −0.500000 0.363271i
\(595\) 0 0
\(596\) 0 0
\(597\) 1.30902 0.951057i 1.30902 0.951057i
\(598\) −0.190983 0.138757i −0.190983 0.138757i
\(599\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(600\) −0.309017 0.951057i −0.309017 0.951057i
\(601\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 1.23607 1.23607
\(607\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(608\) 1.30902 0.951057i 1.30902 0.951057i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.809017 0.587785i −0.809017 0.587785i
\(613\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(618\) 0.118034 0.363271i 0.118034 0.363271i
\(619\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(620\) 0 0
\(621\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(622\) 0.381966 + 1.17557i 0.381966 + 1.17557i
\(623\) 0 0
\(624\) 0 0
\(625\) 0.309017 0.951057i 0.309017 0.951057i
\(626\) 0 0
\(627\) 1.30902 0.951057i 1.30902 0.951057i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(637\) 0.618034 0.618034
\(638\) 0.381966 0.381966
\(639\) 2.00000 2.00000
\(640\) 0 0
\(641\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(642\) 0 0
\(643\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(647\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(648\) −1.00000 −1.00000
\(649\) −0.500000 1.53884i −0.500000 1.53884i
\(650\) 0.381966 0.381966
\(651\) 0 0
\(652\) 0.309017 0.224514i 0.309017 0.224514i
\(653\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(654\) −0.309017 0.951057i −0.309017 0.951057i
\(655\) 0 0
\(656\) 0 0
\(657\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0.809017 0.587785i 0.809017 0.587785i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.309017 0.224514i −0.309017 0.224514i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0.309017 0.951057i 0.309017 0.951057i
\(672\) 0 0
\(673\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(674\) 0 0
\(675\) −0.809017 0.587785i −0.809017 0.587785i
\(676\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(677\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 2.00000 2.00000
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0.309017 0.951057i 0.309017 0.951057i
\(685\) 0 0
\(686\) 0 0
\(687\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(688\) 0 0
\(689\) −0.309017 0.224514i −0.309017 0.224514i
\(690\) 0 0
\(691\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(692\) −1.23607 −1.23607
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0.500000 0.363271i 0.500000 0.363271i
\(697\) 0 0
\(698\) 0 0
\(699\) −0.500000 1.53884i −0.500000 1.53884i
\(700\) 0 0
\(701\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(702\) 0.118034 0.363271i 0.118034 0.363271i
\(703\) 0 0
\(704\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) −0.809017 0.587785i −0.809017 0.587785i
\(709\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0.809017 0.587785i 0.809017 0.587785i
\(719\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.809017 0.587785i −0.809017 0.587785i
\(723\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(724\) 0 0
\(725\) 0.618034 0.618034
\(726\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(727\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(728\) 0 0
\(729\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.190983 0.587785i −0.190983 0.587785i
\(733\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(734\) −1.00000 + 0.726543i −1.00000 + 0.726543i
\(735\) 0 0
\(736\) 0.618034 0.618034
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(740\) 0 0
\(741\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(742\) 0 0
\(743\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(749\) 0 0
\(750\) 0 0
\(751\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(752\) 0 0
\(753\) −0.500000 1.53884i −0.500000 1.53884i
\(754\) 0.0729490 + 0.224514i 0.0729490 + 0.224514i
\(755\) 0 0
\(756\) 0 0
\(757\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(758\) 0.381966 0.381966
\(759\) 0.618034 0.618034
\(760\) 0 0
\(761\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(762\) −1.00000 + 0.726543i −1.00000 + 0.726543i
\(763\) 0 0
\(764\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(765\) 0 0
\(766\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(767\) 0.809017 0.587785i 0.809017 0.587785i
\(768\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −0.618034 1.90211i −0.618034 1.90211i
\(777\) 0 0
\(778\) −1.00000 + 0.726543i −1.00000 + 0.726543i
\(779\) 0 0
\(780\) 0 0
\(781\) 0.618034 1.90211i 0.618034 1.90211i
\(782\) −0.618034 −0.618034
\(783\) 0.190983 0.587785i 0.190983 0.587785i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(793\) 0.618034 0.618034
\(794\) 0 0
\(795\) 0 0
\(796\) −0.809017 0.587785i −0.809017 0.587785i
\(797\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(801\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(802\) 0.381966 0.381966
\(803\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) −0.618034 1.90211i −0.618034 1.90211i
\(809\)