Properties

Label 2500.1.h.d.1999.1
Level $2500$
Weight $1$
Character 2500.1999
Analytic conductor $1.248$
Analytic rank $0$
Dimension $4$
Projective image $D_{5}$
CM discriminant -20
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2500 = 2^{2} \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2500.h (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.24766253158\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 500)
Projective image: \(D_{5}\)
Projective field: Galois closure of 5.1.250000.1

Embedding invariants

Embedding label 1999.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 2500.1999
Dual form 2500.1.h.d.499.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.309017 + 0.951057i) q^{2} +(0.500000 + 0.363271i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.363271i) q^{6} +1.61803 q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.190983 - 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.309017 + 0.951057i) q^{2} +(0.500000 + 0.363271i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.363271i) q^{6} +1.61803 q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.190983 - 0.587785i) q^{9} +(-0.190983 - 0.587785i) q^{12} +(-0.500000 + 1.53884i) q^{14} +(0.309017 + 0.951057i) q^{16} +0.618034 q^{18} +(0.809017 + 0.587785i) q^{21} +(0.500000 - 1.53884i) q^{23} +0.618034 q^{24} +(0.309017 - 0.951057i) q^{27} +(-1.30902 - 0.951057i) q^{28} +(-0.500000 - 0.363271i) q^{29} -1.00000 q^{32} +(-0.190983 + 0.587785i) q^{36} +(0.190983 + 0.587785i) q^{41} +(-0.809017 + 0.587785i) q^{42} -0.618034 q^{43} +(1.30902 + 0.951057i) q^{46} +(0.500000 + 0.363271i) q^{47} +(-0.190983 + 0.587785i) q^{48} +1.61803 q^{49} +(0.809017 + 0.587785i) q^{54} +(1.30902 - 0.951057i) q^{56} +(0.500000 - 0.363271i) q^{58} +(-0.500000 + 1.53884i) q^{61} +(-0.309017 - 0.951057i) q^{63} +(0.309017 - 0.951057i) q^{64} +(1.61803 - 1.17557i) q^{67} +(0.809017 - 0.587785i) q^{69} +(-0.500000 - 0.363271i) q^{72} -0.618034 q^{82} +(-1.30902 + 0.951057i) q^{83} +(-0.309017 - 0.951057i) q^{84} +(0.190983 - 0.587785i) q^{86} +(-0.118034 - 0.363271i) q^{87} +(-0.500000 + 1.53884i) q^{89} +(-1.30902 + 0.951057i) q^{92} +(-0.500000 + 0.363271i) q^{94} +(-0.500000 - 0.363271i) q^{96} +(-0.500000 + 1.53884i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} + 2 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} + 2 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + q^{8} - 3 q^{9} - 3 q^{12} - 2 q^{14} - q^{16} - 2 q^{18} + q^{21} + 2 q^{23} - 2 q^{24} - q^{27} - 3 q^{28} - 2 q^{29} - 4 q^{32} - 3 q^{36} + 3 q^{41} - q^{42} + 2 q^{43} + 3 q^{46} + 2 q^{47} - 3 q^{48} + 2 q^{49} + q^{54} + 3 q^{56} + 2 q^{58} - 2 q^{61} + q^{63} - q^{64} + 2 q^{67} + q^{69} - 2 q^{72} + 2 q^{82} - 3 q^{83} + q^{84} + 3 q^{86} + 4 q^{87} - 2 q^{89} - 3 q^{92} - 2 q^{94} - 2 q^{96} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2500\mathbb{Z}\right)^\times\).

\(n\) \(1251\) \(1877\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(3\) 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i \(-0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(4\) −0.809017 0.587785i −0.809017 0.587785i
\(5\) 0 0
\(6\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(7\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(8\) 0.809017 0.587785i 0.809017 0.587785i
\(9\) −0.190983 0.587785i −0.190983 0.587785i
\(10\) 0 0
\(11\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(12\) −0.190983 0.587785i −0.190983 0.587785i
\(13\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(14\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(15\) 0 0
\(16\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(17\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(18\) 0.618034 0.618034
\(19\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(20\) 0 0
\(21\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(22\) 0 0
\(23\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(24\) 0.618034 0.618034
\(25\) 0 0
\(26\) 0 0
\(27\) 0.309017 0.951057i 0.309017 0.951057i
\(28\) −1.30902 0.951057i −1.30902 0.951057i
\(29\) −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 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(32\) −1.00000 −1.00000
\(33\) 0 0
\(34\) 0 0
\(35\) 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 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(42\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(43\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(47\) 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i \(-0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(48\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(49\) 1.61803 1.61803
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(54\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(55\) 0 0
\(56\) 1.30902 0.951057i 1.30902 0.951057i
\(57\) 0 0
\(58\) 0.500000 0.363271i 0.500000 0.363271i
\(59\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(60\) 0 0
\(61\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(62\) 0 0
\(63\) −0.309017 0.951057i −0.309017 0.951057i
\(64\) 0.309017 0.951057i 0.309017 0.951057i
\(65\) 0 0
\(66\) 0 0
\(67\) 1.61803 1.17557i 1.61803 1.17557i 0.809017 0.587785i \(-0.200000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(68\) 0 0
\(69\) 0.809017 0.587785i 0.809017 0.587785i
\(70\) 0 0
\(71\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(72\) −0.500000 0.363271i −0.500000 0.363271i
\(73\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −0.618034 −0.618034
\(83\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(84\) −0.309017 0.951057i −0.309017 0.951057i
\(85\) 0 0
\(86\) 0.190983 0.587785i 0.190983 0.587785i
\(87\) −0.118034 0.363271i −0.118034 0.363271i
\(88\) 0 0
\(89\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(93\) 0 0
\(94\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(95\) 0 0
\(96\) −0.500000 0.363271i −0.500000 0.363271i
\(97\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(98\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(99\) 0 0
\(100\) 0 0
\(101\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(102\) 0 0
\(103\) 1.61803 + 1.17557i 1.61803 + 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(108\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(109\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(113\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.809017 0.587785i −0.809017 0.587785i
\(122\) −1.30902 0.951057i −1.30902 0.951057i
\(123\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(124\) 0 0
\(125\) 0 0
\(126\) 1.00000 1.00000
\(127\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(128\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(129\) −0.309017 0.224514i −0.309017 0.224514i
\(130\) 0 0
\(131\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.618034 + 1.90211i 0.618034 + 1.90211i
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(138\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(139\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(140\) 0 0
\(141\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(142\) 0 0
\(143\) 0 0
\(144\) 0.500000 0.363271i 0.500000 0.363271i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(148\) 0 0
\(149\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 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
\(161\) 0.809017 2.48990i 0.809017 2.48990i
\(162\) 0 0
\(163\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(164\) 0.190983 0.587785i 0.190983 0.587785i
\(165\) 0 0
\(166\) −0.500000 1.53884i −0.500000 1.53884i
\(167\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(168\) 1.00000 1.00000
\(169\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(173\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(174\) 0.381966 0.381966
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) −1.30902 0.951057i −1.30902 0.951057i
\(179\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(180\) 0 0
\(181\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(182\) 0 0
\(183\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(184\) −0.500000 1.53884i −0.500000 1.53884i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.190983 0.587785i −0.190983 0.587785i
\(189\) 0.500000 1.53884i 0.500000 1.53884i
\(190\) 0 0
\(191\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(192\) 0.500000 0.363271i 0.500000 0.363271i
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −1.30902 0.951057i −1.30902 0.951057i
\(197\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 1.23607 1.23607
\(202\) 0.500000 1.53884i 0.500000 1.53884i
\(203\) −0.809017 0.587785i −0.809017 0.587785i
\(204\) 0 0
\(205\) 0 0
\(206\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(207\) −1.00000 −1.00000
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(212\) 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
\(218\) −0.618034 −0.618034
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(224\) −1.61803 −1.61803
\(225\) 0 0
\(226\) 0 0
\(227\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(228\) 0 0
\(229\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.618034 −0.618034
\(233\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(240\) 0 0
\(241\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(242\) 0.809017 0.587785i 0.809017 0.587785i
\(243\) −1.00000 −1.00000
\(244\) 1.30902 0.951057i 1.30902 0.951057i
\(245\) 0 0
\(246\) −0.309017 0.224514i −0.309017 0.224514i
\(247\) 0 0
\(248\) 0 0
\(249\) −1.00000 −1.00000
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(253\) 0 0
\(254\) −0.500000 0.363271i −0.500000 0.363271i
\(255\) 0 0
\(256\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0.309017 0.224514i 0.309017 0.224514i
\(259\) 0 0
\(260\) 0 0
\(261\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(262\) 0 0
\(263\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(268\) −2.00000 −2.00000
\(269\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(270\) 0 0
\(271\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −1.00000 −1.00000
\(277\) 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
\(281\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(282\) −0.381966 −0.381966
\(283\) 1.61803 1.17557i 1.61803 1.17557i 0.809017 0.587785i \(-0.200000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(288\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(289\) 0.309017 0.951057i 0.309017 0.951057i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0.500000 1.53884i 0.500000 1.53884i
\(299\) 0 0
\(300\) 0 0
\(301\) −1.00000 −1.00000
\(302\) 0 0
\(303\) −0.809017 0.587785i −0.809017 0.587785i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(308\) 0 0
\(309\) 0.381966 + 1.17557i 0.381966 + 1.17557i
\(310\) 0 0
\(311\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(312\) 0 0
\(313\) 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 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −0.309017 0.224514i −0.309017 0.224514i
\(322\) 2.11803 + 1.53884i 2.11803 + 1.53884i
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) −1.61803 −1.61803
\(327\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(328\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(329\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(330\) 0 0
\(331\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(332\) 1.61803 1.61803
\(333\) 0 0
\(334\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(335\) 0 0
\(336\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(337\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(338\) −0.309017 0.951057i −0.309017 0.951057i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 1.00000
\(344\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(345\) 0 0
\(346\) 0 0
\(347\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(348\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(349\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.30902 0.951057i 1.30902 0.951057i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(360\) 0 0
\(361\) 0.309017 0.951057i 0.309017 0.951057i
\(362\) −0.190983 0.587785i −0.190983 0.587785i
\(363\) −0.190983 0.587785i −0.190983 0.587785i
\(364\) 0 0
\(365\) 0 0
\(366\) −0.309017 0.951057i −0.309017 0.951057i
\(367\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(368\) 1.61803 1.61803
\(369\) 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 \(0.600000\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0.618034 0.618034
\(377\) 0 0
\(378\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(379\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(380\) 0 0
\(381\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(382\) 0 0
\(383\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(384\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(385\) 0 0
\(386\) 0 0
\(387\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(388\) 0 0
\(389\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.30902 0.951057i 1.30902 0.951057i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(402\) −0.381966 + 1.17557i −0.381966 + 1.17557i
\(403\) 0 0
\(404\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(405\) 0 0
\(406\) 0.809017 0.587785i 0.809017 0.587785i
\(407\) 0 0
\(408\) 0 0
\(409\) −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 0
\(412\) −0.618034 1.90211i −0.618034 1.90211i
\(413\) 0 0
\(414\) 0.309017 0.951057i 0.309017 0.951057i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(420\) 0 0
\(421\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(422\) 0 0
\(423\) 0.118034 0.363271i 0.118034 0.363271i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.809017 + 2.48990i −0.809017 + 2.48990i
\(428\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(432\) 1.00000 1.00000
\(433\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.190983 0.587785i 0.190983 0.587785i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(440\) 0 0
\(441\) −0.309017 0.951057i −0.309017 0.951057i
\(442\) 0 0
\(443\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −0.500000 0.363271i −0.500000 0.363271i
\(447\) −0.809017 0.587785i −0.809017 0.587785i
\(448\) 0.500000 1.53884i 0.500000 1.53884i
\(449\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(459\) 0 0
\(460\) 0 0
\(461\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(462\) 0 0
\(463\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(464\) 0.190983 0.587785i 0.190983 0.587785i
\(465\) 0 0
\(466\) 0 0
\(467\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 2.61803 1.90211i 2.61803 1.90211i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1.61803 1.61803
\(483\) 1.30902 0.951057i 1.30902 0.951057i
\(484\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(485\) 0 0
\(486\) 0.309017 0.951057i 0.309017 0.951057i
\(487\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(488\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(489\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(490\) 0 0
\(491\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(492\) 0.309017 0.224514i 0.309017 0.224514i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.309017 0.951057i 0.309017 0.951057i
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 0.381966 0.381966
\(502\) 0 0
\(503\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(504\) −0.809017 0.587785i −0.809017 0.587785i
\(505\) 0 0
\(506\) 0 0
\(507\) −0.618034 −0.618034
\(508\) 0.500000 0.363271i 0.500000 0.363271i
\(509\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.309017 0.951057i −0.309017 0.951057i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(522\) −0.309017 0.224514i −0.309017 0.224514i
\(523\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0.618034 0.618034
\(527\) 0 0
\(528\) 0 0
\(529\) −1.30902 0.951057i −1.30902 0.951057i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.309017 0.951057i −0.309017 0.951057i
\(535\) 0 0
\(536\) 0.618034 1.90211i 0.618034 1.90211i
\(537\) 0 0
\(538\) −0.618034 1.90211i −0.618034 1.90211i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(542\) 0 0
\(543\) −0.381966 −0.381966
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 1.00000 1.00000
\(550\) 0 0
\(551\) 0 0
\(552\) 0.309017 0.951057i 0.309017 0.951057i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(563\) −0.618034 1.90211i −0.618034 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 0.951057i \(-0.600000\pi\)
\(564\) 0.118034 0.363271i 0.118034 0.363271i
\(565\) 0 0
\(566\) 0.618034 + 1.90211i 0.618034 + 1.90211i
\(567\) 0 0
\(568\) 0 0
\(569\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(570\) 0 0
\(571\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −1.00000 −1.00000
\(575\) 0 0
\(576\) −0.618034 −0.618034
\(577\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(578\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(579\) 0 0
\(580\) 0 0
\(581\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −0.618034 1.90211i −0.618034 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 0.951057i \(-0.600000\pi\)
\(588\) −0.309017 0.951057i −0.309017 0.951057i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(602\) 0.309017 0.951057i 0.309017 0.951057i
\(603\) −1.00000 0.726543i −1.00000 0.726543i
\(604\) 0 0
\(605\) 0 0
\(606\) 0.809017 0.587785i 0.809017 0.587785i
\(607\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) −0.190983 0.587785i −0.190983 0.587785i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(614\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(618\) −1.23607 −1.23607
\(619\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(620\) 0 0
\(621\) −1.30902 0.951057i −1.30902 0.951057i
\(622\) 0 0
\(623\) −0.809017 + 2.48990i −0.809017 + 2.48990i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(642\) 0.309017 0.224514i 0.309017 0.224514i
\(643\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(644\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(645\) 0 0
\(646\) 0 0
\(647\) 1.61803 + 1.17557i 1.61803 + 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.500000 1.53884i 0.500000 1.53884i
\(653\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(654\) −0.309017 0.224514i −0.309017 0.224514i
\(655\) 0 0
\(656\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(657\) 0 0
\(658\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(659\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(660\) 0 0
\(661\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(662\) 0 0
\(663\) 0 0
\(664\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(665\) 0 0
\(666\) 0 0
\(667\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(668\) −0.618034 −0.618034
\(669\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(670\) 0 0
\(671\) 0 0
\(672\) −0.809017 0.587785i −0.809017 0.587785i
\(673\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 1.00000 1.00000
\(677\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.809017 0.587785i 0.809017 0.587785i
\(682\) 0 0
\(683\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(687\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(688\) −0.190983 0.587785i −0.190983 0.587785i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 1.30902 0.951057i 1.30902 0.951057i
\(695\) 0 0
\(696\) −0.309017 0.224514i −0.309017 0.224514i
\(697\) 0 0
\(698\) 0.500000 1.53884i 0.500000 1.53884i
\(699\) 0 0
\(700\) 0 0
\(701\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.61803 −2.61803
\(708\) 0 0
\(709\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 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
\(721\) 2.61803 + 1.90211i 2.61803 + 1.90211i
\(722\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(723\) 0.309017 0.951057i 0.309017 0.951057i
\(724\) 0.618034 0.618034
\(725\) 0 0
\(726\) 0.618034 0.618034
\(727\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) −0.500000 0.363271i −0.500000 0.363271i
\(730\) 0 0
\(731\) 0 0
\(732\) 1.00000 1.00000
\(733\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(734\) −0.500000 1.53884i −0.500000 1.53884i
\(735\) 0 0
\(736\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(737\) 0 0
\(738\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(739\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(748\) 0 0
\(749\) −1.00000 −1.00000
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(762\) −0.118034 0.363271i −0.118034 0.363271i
\(763\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(764\) 0 0
\(765\) 0 0
\(766\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(767\) 0 0
\(768\) −0.618034 −0.618034
\(769\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(774\) −0.381966 −0.381966
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(784\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(785\) 0 0
\(786\) 0 0
\(787\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 0.118034 0.363271i 0.118034 0.363271i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 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
\(800\) 0 0
\(801\) 1.00000