Properties

Label 500.1.h.a.99.1
Level $500$
Weight $1$
Character 500.99
Analytic conductor $0.250$
Analytic rank $0$
Dimension $8$
Projective image $D_{5}$
CM discriminant -4
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 500 = 2^{2} \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 500.h (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.249532506317\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 100)
Projective image: \(D_{5}\)
Projective field: Galois closure of 5.1.6250000.1

Embedding invariants

Embedding label 99.1
Root \(0.951057 - 0.309017i\) of defining polynomial
Character \(\chi\) \(=\) 500.99
Dual form 500.1.h.a.399.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(-0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(-0.587785 + 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(1.53884 + 0.500000i) q^{13} +(0.309017 - 0.951057i) q^{16} +(0.363271 - 0.500000i) q^{17} -1.00000i q^{18} -1.61803 q^{26} +(0.500000 - 0.363271i) q^{29} +1.00000i q^{32} +(-0.190983 + 0.587785i) q^{34} +(0.309017 + 0.951057i) q^{36} +(0.587785 + 0.190983i) q^{37} +(-0.500000 + 1.53884i) q^{41} -1.00000 q^{49} +(1.53884 - 0.500000i) q^{52} +(-0.951057 - 1.30902i) q^{53} +(-0.363271 + 0.500000i) q^{58} +(-0.500000 - 1.53884i) q^{61} +(-0.309017 - 0.951057i) q^{64} -0.618034i q^{68} +(-0.587785 - 0.809017i) q^{72} +(-1.53884 + 0.500000i) q^{73} -0.618034 q^{74} +(-0.809017 - 0.587785i) q^{81} -1.61803i q^{82} +(-0.190983 - 0.587785i) q^{89} +(-0.363271 - 0.500000i) q^{97} +(0.951057 - 0.309017i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{4} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{4} + 2 q^{9} - 2 q^{16} - 4 q^{26} + 4 q^{29} - 6 q^{34} - 2 q^{36} - 4 q^{41} - 8 q^{49} - 4 q^{61} + 2 q^{64} + 4 q^{74} - 2 q^{81} - 6 q^{89}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/500\mathbb{Z}\right)^\times\).

\(n\) \(251\) \(377\)
\(\chi(n)\) \(-1\) \(e\left(\frac{9}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(3\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(4\) 0.809017 0.587785i 0.809017 0.587785i
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(9\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(10\) 0 0
\(11\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(12\) 0 0
\(13\) 1.53884 + 0.500000i 1.53884 + 0.500000i 0.951057 0.309017i \(-0.100000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.309017 0.951057i 0.309017 0.951057i
\(17\) 0.363271 0.500000i 0.363271 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(18\) 1.00000i 1.00000i
\(19\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −1.61803 −1.61803
\(27\) 0 0
\(28\) 0 0
\(29\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(30\) 0 0
\(31\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(32\) 1.00000i 1.00000i
\(33\) 0 0
\(34\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(35\) 0 0
\(36\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(37\) 0.587785 + 0.190983i 0.587785 + 0.190983i 0.587785 0.809017i \(-0.300000\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(48\) 0 0
\(49\) −1.00000 −1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 1.53884 0.500000i 1.53884 0.500000i
\(53\) −0.951057 1.30902i −0.951057 1.30902i −0.951057 0.309017i \(-0.900000\pi\)
1.00000i \(-0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(59\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(60\) 0 0
\(61\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.309017 0.951057i −0.309017 0.951057i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(68\) 0.618034i 0.618034i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(72\) −0.587785 0.809017i −0.587785 0.809017i
\(73\) −1.53884 + 0.500000i −1.53884 + 0.500000i −0.951057 0.309017i \(-0.900000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(74\) −0.618034 −0.618034
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.809017 0.587785i
\(82\) 1.61803i 1.61803i
\(83\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.363271 0.500000i −0.363271 0.500000i 0.587785 0.809017i \(-0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(98\) 0.951057 0.309017i 0.951057 0.309017i
\(99\) 0 0
\(100\) 0 0
\(101\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(102\) 0 0
\(103\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(104\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(105\) 0 0
\(106\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.587785 0.190983i −0.587785 0.190983i 1.00000i \(-0.5\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.190983 0.587785i 0.190983 0.587785i
\(117\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(122\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(128\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(137\) −1.53884 0.500000i −1.53884 0.500000i −0.587785 0.809017i \(-0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(138\) 0 0
\(139\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(145\) 0 0
\(146\) 1.30902 0.951057i 1.30902 0.951057i
\(147\) 0 0
\(148\) 0.587785 0.190983i 0.587785 0.190983i
\(149\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(163\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(164\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(168\) 0 0
\(169\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.587785 0.190983i 0.587785 0.190983i 1.00000i \(-0.5\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(179\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(180\) 0 0
\(181\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(192\) 0 0
\(193\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(194\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(195\) 0 0
\(196\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(197\) 0.951057 + 1.30902i 0.951057 + 1.30902i 0.951057 + 0.309017i \(0.100000\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0.951057 1.30902i 0.951057 1.30902i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(212\) −1.53884 0.500000i −1.53884 0.500000i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 1.61803i 1.61803i
\(219\) 0 0
\(220\) 0 0
\(221\) 0.809017 0.587785i 0.809017 0.587785i
\(222\) 0 0
\(223\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0.618034 0.618034
\(227\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(228\) 0 0
\(229\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.618034i 0.618034i
\(233\) 0.951057 1.30902i 0.951057 1.30902i 1.00000i \(-0.5\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(234\) 0.500000 1.53884i 0.500000 1.53884i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(240\) 0 0
\(241\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(242\) 0.587785 0.809017i 0.587785 0.809017i
\(243\) 0 0
\(244\) −1.30902 0.951057i −1.30902 0.951057i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.809017 0.587785i
\(257\) 1.61803i 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(262\) 0 0
\(263\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(272\) −0.363271 0.500000i −0.363271 0.500000i
\(273\) 0 0
\(274\) 1.61803 1.61803
\(275\) 0 0
\(276\) 0 0
\(277\) −0.587785 + 0.190983i −0.587785 + 0.190983i −0.587785 0.809017i \(-0.700000\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(282\) 0 0
\(283\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.951057 0.309017i −0.951057 0.309017i
\(289\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(290\) 0 0
\(291\) 0 0
\(292\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(293\) 0.618034i 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(297\) 0 0
\(298\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) −0.500000 0.363271i −0.500000 0.363271i
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(312\) 0 0
\(313\) −1.90211 0.618034i −1.90211 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 0.309017i \(-0.900000\pi\)
\(314\) −0.190983 0.587785i −0.190983 0.587785i
\(315\) 0 0
\(316\) 0 0
\(317\) 1.17557 1.61803i 1.17557 1.61803i 0.587785 0.809017i \(-0.300000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −1.00000 −1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) −0.951057 1.30902i −0.951057 1.30902i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(332\) 0 0
\(333\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.90211 + 0.618034i 1.90211 + 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(338\) −1.53884 0.500000i −1.53884 0.500000i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(347\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(348\) 0 0
\(349\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.17557 + 1.61803i 1.17557 + 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.500000 0.363271i −0.500000 0.363271i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(360\) 0 0
\(361\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(362\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(368\) 0 0
\(369\) −1.30902 0.951057i −1.30902 0.951057i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 1.90211 0.618034i 1.90211 0.618034i 0.951057 0.309017i \(-0.100000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.951057 0.309017i 0.951057 0.309017i
\(378\) 0 0
\(379\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.500000 1.53884i −0.500000 1.53884i
\(387\) 0 0
\(388\) −0.587785 0.190983i −0.587785 0.190983i
\(389\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.587785 0.809017i 0.587785 0.809017i
\(393\) 0 0
\(394\) −1.30902 0.951057i −1.30902 0.951057i
\(395\) 0 0
\(396\) 0 0
\(397\) −1.17557 1.61803i −1.17557 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 0.809017i \(-0.700000\pi\)
\(398\) 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 0
\(403\) 0 0
\(404\) 0.500000 0.363271i 0.500000 0.363271i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(420\) 0 0
\(421\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 1.61803 1.61803
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(432\) 0 0
\(433\) 0.951057 1.30902i 0.951057 1.30902i 1.00000i \(-0.5\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.500000 1.53884i −0.500000 1.53884i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(440\) 0 0
\(441\) 0.309017 0.951057i 0.309017 0.951057i
\(442\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 0.951057 1.30902i 0.951057 1.30902i
\(459\) 0 0
\(460\) 0 0
\(461\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(462\) 0 0
\(463\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(464\) −0.190983 0.587785i −0.190983 0.587785i
\(465\) 0 0
\(466\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(467\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(468\) 1.61803i 1.61803i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 1.53884 0.500000i 1.53884 0.500000i
\(478\) 0 0
\(479\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(480\) 0 0
\(481\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(482\) 0.618034i 0.618034i
\(483\) 0 0
\(484\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(488\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(492\) 0 0
\(493\) 0.381966i 0.381966i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(513\) 0 0
\(514\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(522\) −0.363271 0.500000i −0.363271 0.500000i
\(523\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.809017 0.587785i 0.809017 0.587785i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.53884 + 2.11803i −1.53884 + 2.11803i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(548\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(549\) 1.61803 1.61803
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0.500000 0.363271i 0.500000 0.363271i
\(555\) 0 0
\(556\) 0 0
\(557\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −1.53884 0.500000i −1.53884 0.500000i
\(563\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i \(-0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(570\) 0 0
\(571\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 1.00000
\(577\) −1.90211 + 0.618034i −1.90211 + 0.618034i −0.951057 + 0.309017i \(0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(578\) −0.363271 0.500000i −0.363271 0.500000i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0.500000 1.53884i 0.500000 1.53884i
\(585\) 0 0
\(586\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(587\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.363271 0.500000i 0.363271 0.500000i
\(593\) 0.618034i 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(594\) 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
\(601\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(613\) −0.587785 0.190983i −0.587785 0.190983i 1.00000i \(-0.5\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −0.951057 + 1.30902i −0.951057 + 1.30902i 1.00000i \(0.5\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(618\) 0 0
\(619\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 2.00000 2.00000
\(627\) 0 0
\(628\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(629\) 0.309017 0.224514i 0.309017 0.224514i
\(630\) 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
\(634\) −0.618034 + 1.90211i −0.618034 + 1.90211i
\(635\) 0 0
\(636\) 0 0
\(637\) −1.53884 0.500000i −1.53884 0.500000i
\(638\) 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 0
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(648\) 0.951057 0.309017i 0.951057 0.309017i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0.363271 + 0.500000i 0.363271 + 0.500000i 0.951057 0.309017i \(-0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(657\) 1.61803i 1.61803i
\(658\) 0 0
\(659\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(660\) 0 0
\(661\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0.190983 0.587785i 0.190983 0.587785i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.587785 0.190983i 0.587785 0.190983i 1.00000i \(-0.5\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(674\) −2.00000 −2.00000
\(675\) 0 0
\(676\) 1.61803 1.61803
\(677\) −1.90211 + 0.618034i −1.90211 + 0.618034i −0.951057 + 0.309017i \(0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −0.809017 2.48990i −0.809017 2.48990i
\(690\) 0 0
\(691\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(692\) 0.363271 0.500000i 0.363271 0.500000i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(698\) 0.587785 0.190983i 0.587785 0.190983i
\(699\) 0 0
\(700\) 0 0
\(701\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −1.61803 1.17557i −1.61803 1.17557i
\(707\) 0 0
\(708\) 0 0
\(709\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.587785 0.809017i −0.587785 0.809017i
\(723\) 0 0
\(724\) −0.618034 −0.618034
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(728\) 0 0
\(729\) 0.809017 0.587785i 0.809017 0.587785i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −1.17557 + 1.61803i −1.17557 + 1.61803i −0.587785 + 0.809017i \(0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(739\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(755\) 0 0
\(756\) 0 0
\(757\) 1.61803i 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 1.61803 + 1.17557i 1.61803 + 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(773\) −1.53884 + 0.500000i −1.53884 + 0.500000i −0.951057 0.309017i \(-0.900000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0.618034 0.618034
\(777\) 0 0
\(778\) −0.951057 1.30902i −0.951057 1.30902i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(788\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 2.61803i 2.61803i
\(794\) 1.61803 + 1.17557i 1.61803 + 1.17557i
\(795\) 0 0
\(796\) 0 0
\(797\) 0.951057 + 1.30902i 0.951057 + 1.30902i 0.951057 + 0.309017i \(0.100000\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0.618034 0.618034
\(802\) 1.53884 0.500000i 1.53884 0.500000i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0