Properties

Label 2008.1.j.a.219.1
Level 2008
Weight 1
Character 2008.219
Analytic conductor 1.002
Analytic rank 0
Dimension 4
Projective image \(D_{5}\)
CM discriminant -8
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 2008 = 2^{3} \cdot 251 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2008.j (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.00212254537\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \(x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(D_{5}\)
Projective field Galois closure of 5.1.254024064064.1

Embedding invariants

Embedding label 219.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 2008.219
Dual form 2008.1.j.a.651.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-0.500000 - 0.363271i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.363271i) q^{6} +1.00000 q^{8} +(-0.190983 - 0.587785i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-0.500000 - 0.363271i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.363271i) q^{6} +1.00000 q^{8} +(-0.190983 - 0.587785i) q^{9} +(1.30902 + 0.951057i) q^{11} +(-0.500000 - 0.363271i) q^{12} +1.00000 q^{16} +(-1.61803 + 1.17557i) q^{17} +(-0.190983 - 0.587785i) q^{18} +(0.618034 - 1.90211i) q^{19} +(1.30902 + 0.951057i) q^{22} +(-0.500000 - 0.363271i) q^{24} +1.00000 q^{25} +(-0.309017 + 0.951057i) q^{27} +1.00000 q^{32} +(-0.309017 - 0.951057i) q^{33} +(-1.61803 + 1.17557i) q^{34} +(-0.190983 - 0.587785i) q^{36} +(0.618034 - 1.90211i) q^{38} +(-0.500000 + 0.363271i) q^{41} +(-0.500000 - 1.53884i) q^{43} +(1.30902 + 0.951057i) q^{44} +(-0.500000 - 0.363271i) q^{48} +(-0.809017 - 0.587785i) q^{49} +1.00000 q^{50} +1.23607 q^{51} +(-0.309017 + 0.951057i) q^{54} +(-1.00000 + 0.726543i) q^{57} +(1.30902 + 0.951057i) q^{59} +1.00000 q^{64} +(-0.309017 - 0.951057i) q^{66} +(-0.500000 + 0.363271i) q^{67} +(-1.61803 + 1.17557i) q^{68} +(-0.190983 - 0.587785i) q^{72} +(-1.61803 + 1.17557i) q^{73} +(-0.500000 - 0.363271i) q^{75} +(0.618034 - 1.90211i) q^{76} +(-0.500000 + 0.363271i) q^{82} +(1.30902 - 0.951057i) q^{83} +(-0.500000 - 1.53884i) q^{86} +(1.30902 + 0.951057i) q^{88} +(-0.500000 + 0.363271i) q^{89} +(-0.500000 - 0.363271i) q^{96} +(-0.500000 + 0.363271i) q^{97} +(-0.809017 - 0.587785i) q^{98} +(0.309017 - 0.951057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} - 2q^{3} + 4q^{4} - 2q^{6} + 4q^{8} - 3q^{9} + O(q^{10}) \) \( 4q + 4q^{2} - 2q^{3} + 4q^{4} - 2q^{6} + 4q^{8} - 3q^{9} + 3q^{11} - 2q^{12} + 4q^{16} - 2q^{17} - 3q^{18} - 2q^{19} + 3q^{22} - 2q^{24} + 4q^{25} + q^{27} + 4q^{32} + q^{33} - 2q^{34} - 3q^{36} - 2q^{38} - 2q^{41} - 2q^{43} + 3q^{44} - 2q^{48} - q^{49} + 4q^{50} - 4q^{51} + q^{54} - 4q^{57} + 3q^{59} + 4q^{64} + q^{66} - 2q^{67} - 2q^{68} - 3q^{72} - 2q^{73} - 2q^{75} - 2q^{76} - 2q^{82} + 3q^{83} - 2q^{86} + 3q^{88} - 2q^{89} - 2q^{96} - 2q^{97} - q^{98} - q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(503\) \(1005\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000
\(3\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(4\) 1.00000 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) −0.500000 0.363271i −0.500000 0.363271i
\(7\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(8\) 1.00000 1.00000
\(9\) −0.190983 0.587785i −0.190983 0.587785i
\(10\) 0 0
\(11\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(12\) −0.500000 0.363271i −0.500000 0.363271i
\(13\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(18\) −0.190983 0.587785i −0.190983 0.587785i
\(19\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(23\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(24\) −0.500000 0.363271i −0.500000 0.363271i
\(25\) 1.00000 1.00000
\(26\) 0 0
\(27\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(28\) 0 0
\(29\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(30\) 0 0
\(31\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(32\) 1.00000 1.00000
\(33\) −0.309017 0.951057i −0.309017 0.951057i
\(34\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(35\) 0 0
\(36\) −0.190983 0.587785i −0.190983 0.587785i
\(37\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(38\) 0.618034 1.90211i 0.618034 1.90211i
\(39\) 0 0
\(40\) 0 0
\(41\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(42\) 0 0
\(43\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(44\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −0.500000 0.363271i −0.500000 0.363271i
\(49\) −0.809017 0.587785i −0.809017 0.587785i
\(50\) 1.00000 1.00000
\(51\) 1.23607 1.23607
\(52\) 0 0
\(53\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(54\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(55\) 0 0
\(56\) 0 0
\(57\) −1.00000 + 0.726543i −1.00000 + 0.726543i
\(58\) 0 0
\(59\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(60\) 0 0
\(61\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) −0.309017 0.951057i −0.309017 0.951057i
\(67\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(68\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(72\) −0.190983 0.587785i −0.190983 0.587785i
\(73\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(74\) 0 0
\(75\) −0.500000 0.363271i −0.500000 0.363271i
\(76\) 0.618034 1.90211i 0.618034 1.90211i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(83\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.500000 1.53884i −0.500000 1.53884i
\(87\) 0 0
\(88\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(89\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −0.500000 0.363271i −0.500000 0.363271i
\(97\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(98\) −0.809017 0.587785i −0.809017 0.587785i
\(99\) 0.309017 0.951057i 0.309017 0.951057i
\(100\) 1.00000 1.00000
\(101\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(102\) 1.23607 1.23607
\(103\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(108\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(109\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(114\) −1.00000 + 0.726543i −1.00000 + 0.726543i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(122\) 0 0
\(123\) 0.381966 0.381966
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(128\) 1.00000 1.00000
\(129\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(130\) 0 0
\(131\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(132\) −0.309017 0.951057i −0.309017 0.951057i
\(133\) 0 0
\(134\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(135\) 0 0
\(136\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(137\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(138\) 0 0
\(139\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.190983 0.587785i −0.190983 0.587785i
\(145\) 0 0
\(146\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(147\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) −0.500000 0.363271i −0.500000 0.363271i
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0.618034 1.90211i 0.618034 1.90211i
\(153\) 1.00000 + 0.726543i 1.00000 + 0.726543i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(164\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(165\) 0 0
\(166\) 1.30902 0.951057i 1.30902 0.951057i
\(167\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(168\) 0 0
\(169\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(170\) 0 0
\(171\) −1.23607 −1.23607
\(172\) −0.500000 1.53884i −0.500000 1.53884i
\(173\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(177\) −0.309017 0.951057i −0.309017 0.951057i
\(178\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(179\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(180\) 0 0
\(181\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −3.23607 −3.23607
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(192\) −0.500000 0.363271i −0.500000 0.363271i
\(193\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(194\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(195\) 0 0
\(196\) −0.809017 0.587785i −0.809017 0.587785i
\(197\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(198\) 0.309017 0.951057i 0.309017 0.951057i
\(199\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(200\) 1.00000 1.00000
\(201\) 0.381966 0.381966
\(202\) 0 0
\(203\) 0 0
\(204\) 1.23607 1.23607
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.61803 1.90211i 2.61803 1.90211i
\(210\) 0 0
\(211\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(215\) 0 0
\(216\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(217\) 0 0
\(218\) 0 0
\(219\) 1.23607 1.23607
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(224\) 0 0
\(225\) −0.190983 0.587785i −0.190983 0.587785i
\(226\) −1.61803 −1.61803
\(227\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(228\) −1.00000 + 0.726543i −1.00000 + 0.726543i
\(229\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(240\) 0 0
\(241\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(242\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(243\) 1.00000 1.00000
\(244\) 0 0
\(245\) 0 0
\(246\) 0.381966 0.381966
\(247\) 0 0
\(248\) 0 0
\(249\) −1.00000 −1.00000
\(250\) 0 0
\(251\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(258\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −1.61803 1.17557i −1.61803 1.17557i
\(263\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(264\) −0.309017 0.951057i −0.309017 0.951057i
\(265\) 0 0
\(266\) 0 0
\(267\) 0.381966 0.381966
\(268\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(269\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(273\) 0 0
\(274\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(275\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(276\) 0 0
\(277\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(278\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(279\) 0 0
\(280\) 0 0
\(281\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(282\) 0 0
\(283\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.190983 0.587785i −0.190983 0.587785i
\(289\) 0.927051 2.85317i 0.927051 2.85317i
\(290\) 0 0
\(291\) 0.381966 0.381966
\(292\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(293\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(294\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(295\) 0 0
\(296\) 0 0
\(297\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.500000 0.363271i −0.500000 0.363271i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.618034 1.90211i 0.618034 1.90211i
\(305\) 0 0
\(306\) 1.00000 + 0.726543i 1.00000 + 0.726543i
\(307\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(312\) 0 0
\(313\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0.118034 0.363271i 0.118034 0.363271i
\(322\) 0 0
\(323\) 1.23607 + 3.80423i 1.23607 + 3.80423i
\(324\) 0 0
\(325\) 0 0
\(326\) −0.500000 0.363271i −0.500000 0.363271i
\(327\) 0 0
\(328\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(329\) 0 0
\(330\) 0 0
\(331\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(332\) 1.30902 0.951057i 1.30902 0.951057i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(338\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(339\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(340\) 0 0
\(341\) 0 0
\(342\) −1.23607 −1.23607
\(343\) 0 0
\(344\) −0.500000 1.53884i −0.500000 1.53884i
\(345\) 0 0
\(346\) 0 0
\(347\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(353\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(354\) −0.309017 0.951057i −0.309017 0.951057i
\(355\) 0 0
\(356\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(357\) 0 0
\(358\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(359\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(360\) 0 0
\(361\) −2.42705 1.76336i −2.42705 1.76336i
\(362\) 0 0
\(363\) 0.309017 0.951057i 0.309017 0.951057i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(368\) 0 0
\(369\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(374\) −3.23607 −3.23607
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(384\) −0.500000 0.363271i −0.500000 0.363271i
\(385\) 0 0
\(386\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(387\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(388\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.809017 0.587785i −0.809017 0.587785i
\(393\) 0.381966 + 1.17557i 0.381966 + 1.17557i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.309017 0.951057i 0.309017 0.951057i
\(397\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.00000 1.00000
\(401\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(402\) 0.381966 0.381966
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 1.23607 1.23607
\(409\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(410\) 0 0
\(411\) 0.381966 0.381966
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.809017 0.587785i 0.809017 0.587785i
\(418\) 2.61803 1.90211i 2.61803 1.90211i
\(419\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(420\) 0 0
\(421\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(422\) 0.618034 0.618034
\(423\) 0 0
\(424\) 0 0
\(425\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(426\) 0 0
\(427\) 0 0
\(428\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(432\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(433\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 1.23607 1.23607
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(442\) 0 0
\(443\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(450\) −0.190983 0.587785i −0.190983 0.587785i
\(451\) −1.00000 −1.00000
\(452\) −1.61803 −1.61803
\(453\) 0 0
\(454\) −1.61803 1.17557i −1.61803 1.17557i
\(455\) 0 0
\(456\) −1.00000 + 0.726543i −1.00000 + 0.726543i
\(457\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(458\) 0 0
\(459\) −0.618034 1.90211i −0.618034 1.90211i
\(460\) 0 0
\(461\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(462\) 0 0
\(463\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.500000 1.53884i −0.500000 1.53884i
\(467\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(473\) 0.809017 2.48990i 0.809017 2.48990i
\(474\) 0 0
\(475\) 0.618034 1.90211i 0.618034 1.90211i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.618034 0.618034
\(483\) 0 0
\(484\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(485\) 0 0
\(486\) 1.00000 1.00000
\(487\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(488\) 0 0
\(489\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(490\) 0 0
\(491\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(492\) 0.381966 0.381966
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −1.00000 −1.00000
\(499\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.618034 0.618034
\(508\) 0 0
\(509\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 1.00000
\(513\) 1.61803 + 1.17557i 1.61803 + 1.17557i
\(514\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(515\) 0 0
\(516\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(522\) 0 0
\(523\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(524\) −1.61803 1.17557i −1.61803 1.17557i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −0.309017 0.951057i −0.309017 0.951057i
\(529\) 0.309017 0.951057i 0.309017 0.951057i
\(530\) 0 0
\(531\) 0.309017 0.951057i 0.309017 0.951057i
\(532\) 0 0
\(533\) 0 0
\(534\) 0.381966 0.381966
\(535\) 0 0
\(536\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(537\) 0.118034 0.363271i 0.118034 0.363271i
\(538\) 0 0
\(539\) −0.500000 1.53884i −0.500000 1.53884i
\(540\) 0 0
\(541\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(545\) 0 0
\(546\) 0 0
\(547\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(548\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(549\) 0 0
\(550\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(557\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 1.61803 + 1.17557i 1.61803 + 1.17557i
\(562\) −0.500000 0.363271i −0.500000 0.363271i
\(563\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.618034 0.618034
\(567\) 0 0
\(568\) 0 0
\(569\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(570\) 0 0
\(571\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.190983 0.587785i −0.190983 0.587785i
\(577\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(578\) 0.927051 2.85317i 0.927051 2.85317i
\(579\) 0.809017 0.587785i 0.809017 0.587785i
\(580\) 0 0
\(581\) 0 0
\(582\) 0.381966 0.381966
\(583\) 0 0
\(584\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(585\) 0 0
\(586\) 0 0
\(587\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(588\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(594\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(600\) −0.500000 0.363271i −0.500000 0.363271i
\(601\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(602\) 0 0
\(603\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(608\) 0.618034 1.90211i 0.618034 1.90211i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 1.00000 + 0.726543i 1.00000 + 0.726543i
\(613\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(614\) 0.190983 0.587785i 0.190983 0.587785i
\(615\) 0 0
\(616\) 0 0
\(617\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(618\) 0 0
\(619\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) −0.500000 0.363271i −0.500000 0.363271i
\(627\) −2.00000 −2.00000
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(632\) 0 0
\(633\) −0.309017 0.224514i −0.309017 0.224514i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(642\) 0.118034 0.363271i 0.118034 0.363271i
\(643\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1.23607 + 3.80423i 1.23607 + 3.80423i
\(647\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(648\) 0 0
\(649\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.500000 0.363271i −0.500000 0.363271i
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(657\) 1.00000 + 0.726543i 1.00000 + 0.726543i
\(658\) 0 0
\(659\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(660\) 0 0
\(661\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(662\) −1.61803 −1.61803
\(663\) 0 0
\(664\) 1.30902 0.951057i 1.30902 0.951057i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(674\) −0.500000 1.53884i −0.500000 1.53884i
\(675\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(676\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(677\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(678\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.381966 + 1.17557i 0.381966 + 1.17557i
\(682\) 0 0
\(683\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(684\) −1.23607 −1.23607
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −0.500000 1.53884i −0.500000 1.53884i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(695\) 0 0
\(696\) 0 0
\(697\) 0.381966 1.17557i 0.381966 1.17557i
\(698\) 0 0
\(699\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(700\) 0 0
\(701\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(705\) 0 0
\(706\) 2.00000 2.00000
\(707\) 0 0
\(708\) −0.309017 0.951057i −0.309017 0.951057i
\(709\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −2.42705 1.76336i −2.42705 1.76336i
\(723\) −0.309017 0.224514i −0.309017 0.224514i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.309017 0.951057i 0.309017 0.951057i
\(727\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(728\) 0 0
\(729\) −0.500000 0.363271i −0.500000 0.363271i
\(730\) 0 0
\(731\) 2.61803 + 1.90211i 2.61803 + 1.90211i
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.00000 −1.00000
\(738\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(739\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.809017 0.587785i −0.809017 0.587785i
\(748\) −3.23607 −3.23607
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0.190983 0.587785i 0.190983 0.587785i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0.618034 0.618034
\(759\) 0 0
\(760\) 0 0
\(761\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.500000 0.363271i −0.500000 0.363271i
\(769\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(770\) 0 0
\(771\) −0.309017 0.951057i −0.309017 0.951057i
\(772\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(775\) 0 0
\(776\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(777\) 0 0
\(778\) 0 0
\(779\) 0.381966 + 1.17557i 0.381966 + 1.17557i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.809017 0.587785i −0.809017 0.587785i
\(785\) 0 0
\(786\) 0.381966 + 1.17557i 0.381966 + 1.17557i
\(787\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.309017 0.951057i 0.309017 0.951057i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.00000 1.00000
\(801\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(802\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(803\) −3.23607 −3.23607
\(804\) 0.381966 0.381966
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(810\) 0 0
\(8