Properties

Label 429.1.v.c.350.2
Level $429$
Weight $1$
Character 429.350
Analytic conductor $0.214$
Analytic rank $0$
Dimension $8$
Projective image $D_{10}$
CM discriminant -39
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 429.v (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.214098890420\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
Defining polynomial: \(x^{8} - x^{6} + x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(D_{10}\)
Projective field Galois closure of 10.0.1487719872058563.1

Embedding invariants

Embedding label 350.2
Root \(-0.587785 + 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 429.350
Dual form 429.1.v.c.38.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.587785 - 1.80902i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-2.11803 - 1.53884i) q^{4} +(0.363271 + 1.11803i) q^{5} +(-0.587785 - 1.80902i) q^{6} +(-2.48990 + 1.80902i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(0.587785 - 1.80902i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-2.11803 - 1.53884i) q^{4} +(0.363271 + 1.11803i) q^{5} +(-0.587785 - 1.80902i) q^{6} +(-2.48990 + 1.80902i) q^{8} +(0.309017 - 0.951057i) q^{9} +2.23607 q^{10} +(-0.951057 + 0.309017i) q^{11} -2.61803 q^{12} +(-0.309017 + 0.951057i) q^{13} +(0.951057 + 0.690983i) q^{15} +(1.00000 + 3.07768i) q^{16} +(-1.53884 - 1.11803i) q^{18} +(0.951057 - 2.92705i) q^{20} +1.90211i q^{22} +(-0.951057 + 2.92705i) q^{24} +(-0.309017 + 0.224514i) q^{25} +(1.53884 + 1.11803i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.80902 - 1.31433i) q^{30} +3.07768 q^{32} +(-0.587785 + 0.809017i) q^{33} +(-2.11803 + 1.53884i) q^{36} +(0.309017 + 0.951057i) q^{39} +(-2.92705 - 2.12663i) q^{40} -1.61803 q^{43} +(2.48990 + 0.809017i) q^{44} +1.17557 q^{45} +(1.53884 - 1.11803i) q^{47} +(2.61803 + 1.90211i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.224514 + 0.690983i) q^{50} +(2.11803 - 1.53884i) q^{52} -1.90211 q^{54} +(-0.690983 - 0.951057i) q^{55} +(-1.53884 - 1.11803i) q^{59} +(-0.951057 - 2.92705i) q^{60} +(-0.190983 - 0.587785i) q^{61} +(0.809017 - 2.48990i) q^{64} -1.17557 q^{65} +(1.11803 + 1.53884i) q^{66} +(0.951057 + 2.92705i) q^{72} +(-0.118034 + 0.363271i) q^{75} +1.90211 q^{78} +(-0.190983 + 0.587785i) q^{79} +(-3.07768 + 2.23607i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.363271 - 1.11803i) q^{83} +(-0.951057 + 2.92705i) q^{86} +(1.80902 - 2.48990i) q^{88} +(0.690983 - 2.12663i) q^{90} +(-1.11803 - 3.44095i) q^{94} +(2.48990 - 1.80902i) q^{96} +1.90211 q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{3} - 8q^{4} - 2q^{9} + O(q^{10}) \) \( 8q + 2q^{3} - 8q^{4} - 2q^{9} - 12q^{12} + 2q^{13} + 8q^{16} + 2q^{25} + 2q^{27} + 10q^{30} - 8q^{36} - 2q^{39} - 10q^{40} - 4q^{43} + 12q^{48} - 2q^{49} + 8q^{52} - 10q^{55} - 6q^{61} + 2q^{64} + 8q^{75} - 6q^{79} - 2q^{81} + 10q^{88} + 10q^{90} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.587785 1.80902i 0.587785 1.80902i 1.00000i \(-0.5\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(3\) 0.809017 0.587785i 0.809017 0.587785i
\(4\) −2.11803 1.53884i −2.11803 1.53884i
\(5\) 0.363271 + 1.11803i 0.363271 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(6\) −0.587785 1.80902i −0.587785 1.80902i
\(7\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(8\) −2.48990 + 1.80902i −2.48990 + 1.80902i
\(9\) 0.309017 0.951057i 0.309017 0.951057i
\(10\) 2.23607 2.23607
\(11\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(12\) −2.61803 −2.61803
\(13\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(14\) 0 0
\(15\) 0.951057 + 0.690983i 0.951057 + 0.690983i
\(16\) 1.00000 + 3.07768i 1.00000 + 3.07768i
\(17\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(18\) −1.53884 1.11803i −1.53884 1.11803i
\(19\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(20\) 0.951057 2.92705i 0.951057 2.92705i
\(21\) 0 0
\(22\) 1.90211i 1.90211i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) −0.951057 + 2.92705i −0.951057 + 2.92705i
\(25\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(26\) 1.53884 + 1.11803i 1.53884 + 1.11803i
\(27\) −0.309017 0.951057i −0.309017 0.951057i
\(28\) 0 0
\(29\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(30\) 1.80902 1.31433i 1.80902 1.31433i
\(31\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(32\) 3.07768 3.07768
\(33\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(34\) 0 0
\(35\) 0 0
\(36\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(37\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(38\) 0 0
\(39\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(40\) −2.92705 2.12663i −2.92705 2.12663i
\(41\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(42\) 0 0
\(43\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(44\) 2.48990 + 0.809017i 2.48990 + 0.809017i
\(45\) 1.17557 1.17557
\(46\) 0 0
\(47\) 1.53884 1.11803i 1.53884 1.11803i 0.587785 0.809017i \(-0.300000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(48\) 2.61803 + 1.90211i 2.61803 + 1.90211i
\(49\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(50\) 0.224514 + 0.690983i 0.224514 + 0.690983i
\(51\) 0 0
\(52\) 2.11803 1.53884i 2.11803 1.53884i
\(53\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(54\) −1.90211 −1.90211
\(55\) −0.690983 0.951057i −0.690983 0.951057i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.53884 1.11803i −1.53884 1.11803i −0.951057 0.309017i \(-0.900000\pi\)
−0.587785 0.809017i \(-0.700000\pi\)
\(60\) −0.951057 2.92705i −0.951057 2.92705i
\(61\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.809017 2.48990i 0.809017 2.48990i
\(65\) −1.17557 −1.17557
\(66\) 1.11803 + 1.53884i 1.11803 + 1.53884i
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(72\) 0.951057 + 2.92705i 0.951057 + 2.92705i
\(73\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(74\) 0 0
\(75\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(76\) 0 0
\(77\) 0 0
\(78\) 1.90211 1.90211
\(79\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(80\) −3.07768 + 2.23607i −3.07768 + 2.23607i
\(81\) −0.809017 0.587785i −0.809017 0.587785i
\(82\) 0 0
\(83\) −0.363271 1.11803i −0.363271 1.11803i −0.951057 0.309017i \(-0.900000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.951057 + 2.92705i −0.951057 + 2.92705i
\(87\) 0 0
\(88\) 1.80902 2.48990i 1.80902 2.48990i
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0.690983 2.12663i 0.690983 2.12663i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) −1.11803 3.44095i −1.11803 3.44095i
\(95\) 0 0
\(96\) 2.48990 1.80902i 2.48990 1.80902i
\(97\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(98\) 1.90211 1.90211
\(99\) 1.00000i 1.00000i
\(100\) 1.00000 1.00000
\(101\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(102\) 0 0
\(103\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(104\) −0.951057 2.92705i −0.951057 2.92705i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(108\) −0.809017 + 2.48990i −0.809017 + 2.48990i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) −2.12663 + 0.690983i −2.12663 + 0.690983i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(118\) −2.92705 + 2.12663i −2.92705 + 2.12663i
\(119\) 0 0
\(120\) −3.61803 −3.61803
\(121\) 0.809017 0.587785i 0.809017 0.587785i
\(122\) −1.17557 −1.17557
\(123\) 0 0
\(124\) 0 0
\(125\) 0.587785 + 0.427051i 0.587785 + 0.427051i
\(126\) 0 0
\(127\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(128\) −1.53884 1.11803i −1.53884 1.11803i
\(129\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(130\) −0.690983 + 2.12663i −0.690983 + 2.12663i
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 2.48990 0.809017i 2.48990 0.809017i
\(133\) 0 0
\(134\) 0 0
\(135\) 0.951057 0.690983i 0.951057 0.690983i
\(136\) 0 0
\(137\) 0.587785 + 1.80902i 0.587785 + 1.80902i 0.587785 + 0.809017i \(0.300000\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(140\) 0 0
\(141\) 0.587785 1.80902i 0.587785 1.80902i
\(142\) 0 0
\(143\) 1.00000i 1.00000i
\(144\) 3.23607 3.23607
\(145\) 0 0
\(146\) 0 0
\(147\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(148\) 0 0
\(149\) 0.363271 + 1.11803i 0.363271 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(150\) 0.587785 + 0.427051i 0.587785 + 0.427051i
\(151\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0.809017 2.48990i 0.809017 2.48990i
\(157\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(158\) 0.951057 + 0.690983i 0.951057 + 0.690983i
\(159\) 0 0
\(160\) 1.11803 + 3.44095i 1.11803 + 3.44095i
\(161\) 0 0
\(162\) −1.53884 + 1.11803i −1.53884 + 1.11803i
\(163\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(164\) 0 0
\(165\) −1.11803 0.363271i −1.11803 0.363271i
\(166\) −2.23607 −2.23607
\(167\) 0.363271 1.11803i 0.363271 1.11803i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(168\) 0 0
\(169\) −0.809017 0.587785i −0.809017 0.587785i
\(170\) 0 0
\(171\) 0 0
\(172\) 3.42705 + 2.48990i 3.42705 + 2.48990i
\(173\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.90211 2.61803i −1.90211 2.61803i
\(177\) −1.90211 −1.90211
\(178\) 0 0
\(179\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(180\) −2.48990 1.80902i −2.48990 1.80902i
\(181\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(182\) 0 0
\(183\) −0.500000 0.363271i −0.500000 0.363271i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −4.97980 −4.97980
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(192\) −0.809017 2.48990i −0.809017 2.48990i
\(193\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(194\) 0 0
\(195\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(196\) 0.809017 2.48990i 0.809017 2.48990i
\(197\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(198\) 1.80902 + 0.587785i 1.80902 + 0.587785i
\(199\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(200\) 0.363271 1.11803i 0.363271 1.11803i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 2.48990 1.80902i 2.48990 1.80902i
\(207\) 0 0
\(208\) −3.23607 −3.23607
\(209\) 0 0
\(210\) 0 0
\(211\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −0.587785 1.80902i −0.587785 1.80902i
\(216\) 2.48990 + 1.80902i 2.48990 + 1.80902i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 3.07768i 3.07768i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(224\) 0 0
\(225\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(226\) 0 0
\(227\) 1.53884 + 1.11803i 1.53884 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(228\) 0 0
\(229\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(234\) 1.53884 1.11803i 1.53884 1.11803i
\(235\) 1.80902 + 1.31433i 1.80902 + 1.31433i
\(236\) 1.53884 + 4.73607i 1.53884 + 4.73607i
\(237\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(238\) 0 0
\(239\) 0.951057 0.690983i 0.951057 0.690983i 1.00000i \(-0.5\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(240\) −1.17557 + 3.61803i −1.17557 + 3.61803i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −0.587785 1.80902i −0.587785 1.80902i
\(243\) −1.00000 −1.00000
\(244\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(245\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −0.951057 0.690983i −0.951057 0.690983i
\(250\) 1.11803 0.812299i 1.11803 0.812299i
\(251\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 3.07768 3.07768
\(255\) 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 \(0.200000\pi\)
\(258\) 0.951057 + 2.92705i 0.951057 + 2.92705i
\(259\) 0 0
\(260\) 2.48990 + 1.80902i 2.48990 + 1.80902i
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 3.07768i 3.07768i
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(270\) −0.690983 2.12663i −0.690983 2.12663i
\(271\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 3.61803 3.61803
\(275\) 0.224514 0.309017i 0.224514 0.309017i
\(276\) 0 0
\(277\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(278\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(279\) 0 0
\(280\) 0 0
\(281\) −0.587785 1.80902i −0.587785 1.80902i −0.587785 0.809017i \(-0.700000\pi\)
1.00000i \(-0.5\pi\)
\(282\) −2.92705 2.12663i −2.92705 2.12663i
\(283\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −1.80902 0.587785i −1.80902 0.587785i
\(287\) 0 0
\(288\) 0.951057 2.92705i 0.951057 2.92705i
\(289\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0.951057 + 0.690983i 0.951057 + 0.690983i 0.951057 0.309017i \(-0.100000\pi\)
1.00000i \(0.5\pi\)
\(294\) 1.53884 1.11803i 1.53884 1.11803i
\(295\) 0.690983 2.12663i 0.690983 2.12663i
\(296\) 0 0
\(297\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(298\) 2.23607 2.23607
\(299\) 0 0
\(300\) 0.809017 0.587785i 0.809017 0.587785i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0.587785 0.427051i 0.587785 0.427051i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 1.61803 1.61803
\(310\) 0 0
\(311\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(312\) −2.48990 1.80902i −2.48990 1.80902i
\(313\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(314\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(315\) 0 0
\(316\) 1.30902 0.951057i 1.30902 0.951057i
\(317\) −0.363271 + 1.11803i −0.363271 + 1.11803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 3.07768 3.07768
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(325\) −0.118034 0.363271i −0.118034 0.363271i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) −1.31433 + 1.80902i −1.31433 + 1.80902i
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −0.951057 + 2.92705i −0.951057 + 2.92705i
\(333\) 0 0
\(334\) −1.80902 1.31433i −1.80902 1.31433i
\(335\) 0 0
\(336\) 0 0
\(337\) 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i \(-0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(338\) −1.53884 + 1.11803i −1.53884 + 1.11803i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 4.02874 2.92705i 4.02874 2.92705i
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(348\) 0 0
\(349\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(350\) 0 0
\(351\) 1.00000 1.00000
\(352\) −2.92705 + 0.951057i −2.92705 + 0.951057i
\(353\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(354\) −1.11803 + 3.44095i −1.11803 + 3.44095i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(360\) −2.92705 + 2.12663i −2.92705 + 2.12663i
\(361\) 0.309017 0.951057i 0.309017 0.951057i
\(362\) −3.07768 −3.07768
\(363\) 0.309017 0.951057i 0.309017 0.951057i
\(364\) 0 0
\(365\) 0 0
\(366\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(367\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(374\) 0 0
\(375\) 0.726543 0.726543
\(376\) −1.80902 + 5.56758i −1.80902 + 5.56758i
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(380\) 0 0
\(381\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(382\) 0 0
\(383\) 0.587785 1.80902i 0.587785 1.80902i 1.00000i \(-0.5\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(384\) −1.90211 −1.90211
\(385\) 0 0
\(386\) 0 0
\(387\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(388\) 0 0
\(389\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(390\) 0.690983 + 2.12663i 0.690983 + 2.12663i
\(391\) 0 0
\(392\) −2.48990 1.80902i −2.48990 1.80902i
\(393\) 0 0
\(394\) −1.11803 + 3.44095i −1.11803 + 3.44095i
\(395\) −0.726543 −0.726543
\(396\) 1.53884 2.11803i 1.53884 2.11803i
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(399\) 0 0
\(400\) −1.00000 0.726543i −1.00000 0.726543i
\(401\) −0.363271 1.11803i −0.363271 1.11803i −0.951057 0.309017i \(-0.900000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0.363271 1.11803i 0.363271 1.11803i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(410\) 0 0
\(411\) 1.53884 + 1.11803i 1.53884 + 1.11803i
\(412\) −1.30902 4.02874i −1.30902 4.02874i
\(413\) 0 0
\(414\) 0 0
\(415\) 1.11803 0.812299i 1.11803 0.812299i
\(416\) −0.951057 + 2.92705i −0.951057 + 2.92705i
\(417\) −0.618034 −0.618034
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(422\) −2.48990 1.80902i −2.48990 1.80902i
\(423\) −0.587785 1.80902i −0.587785 1.80902i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −0.587785 0.809017i −0.587785 0.809017i
\(430\) −3.61803 −3.61803
\(431\) −0.587785 + 1.80902i −0.587785 + 1.80902i 1.00000i \(0.5\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(432\) 2.61803 1.90211i 2.61803 1.90211i
\(433\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(440\) 3.44095 + 1.11803i 3.44095 + 1.11803i
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) 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
\(447\) 0.951057 + 0.690983i 0.951057 + 0.690983i
\(448\) 0 0
\(449\) −0.587785 + 1.80902i −0.587785 + 1.80902i 1.00000i \(0.5\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(450\) 0.726543 0.726543
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 2.92705 2.12663i 2.92705 2.12663i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(468\) −0.809017 2.48990i −0.809017 2.48990i
\(469\) 0 0
\(470\) 3.44095 2.50000i 3.44095 2.50000i
\(471\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(472\) 5.85410 5.85410
\(473\) 1.53884 0.500000i 1.53884 0.500000i
\(474\) 1.17557 1.17557
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −0.690983 2.12663i −0.690983 2.12663i
\(479\) 0.363271 + 1.11803i 0.363271 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(480\) 2.92705 + 2.12663i 2.92705 + 2.12663i
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −2.61803 −2.61803
\(485\) 0 0
\(486\) −0.587785 + 1.80902i −0.587785 + 1.80902i
\(487\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(488\) 1.53884 + 1.11803i 1.53884 + 1.11803i
\(489\) 0 0
\(490\) 0.690983 + 2.12663i 0.690983 + 2.12663i
\(491\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −1.11803 + 0.363271i −1.11803 + 0.363271i
\(496\) 0 0
\(497\) 0 0
\(498\) −1.80902 + 1.31433i −1.80902 + 1.31433i
\(499\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(500\) −0.587785 1.80902i −0.587785 1.80902i
\(501\) −0.363271 1.11803i −0.363271 1.11803i
\(502\) 0 0
\(503\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −1.00000
\(508\) 1.30902 4.02874i 1.30902 4.02874i
\(509\) 0.951057 0.690983i 0.951057 0.690983i 1.00000i \(-0.5\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −0.587785 + 1.80902i −0.587785 + 1.80902i
\(516\) 4.23607 4.23607
\(517\) −1.11803 + 1.53884i −1.11803 + 1.53884i
\(518\) 0 0
\(519\) 0 0
\(520\) 2.92705 2.12663i 2.92705 2.12663i
\(521\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(522\) 0 0
\(523\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −3.07768 1.00000i −3.07768 1.00000i
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) −1.53884 + 1.11803i −1.53884 + 1.11803i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.587785 0.809017i −0.587785 0.809017i
\(540\) −3.07768 −3.07768
\(541\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(542\) 0 0
\(543\) −1.30902 0.951057i −1.30902 0.951057i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(548\) 1.53884 4.73607i 1.53884 4.73607i
\(549\) −0.618034 −0.618034
\(550\) −0.427051 0.587785i −0.427051 0.587785i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −3.07768 2.23607i −3.07768 2.23607i
\(555\) 0 0
\(556\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(557\) 1.53884 + 1.11803i 1.53884 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(558\) 0 0
\(559\) 0.500000 1.53884i 0.500000 1.53884i
\(560\) 0 0
\(561\) 0 0
\(562\) −3.61803 −3.61803
\(563\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(564\) −4.02874 + 2.92705i −4.02874 + 2.92705i
\(565\) 0 0
\(566\) −0.363271 1.11803i −0.363271 1.11803i
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(570\) 0 0
\(571\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(572\) −1.53884 + 2.11803i −1.53884 + 2.11803i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −2.11803 1.53884i −2.11803 1.53884i
\(577\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(578\) 0.587785 + 1.80902i 0.587785 + 1.80902i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(586\) 1.80902 1.31433i 1.80902 1.31433i
\(587\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(588\) −0.809017 2.48990i −0.809017 2.48990i
\(589\) 0 0
\(590\) −3.44095 2.50000i −3.44095 2.50000i
\(591\) −1.53884 + 1.11803i −1.53884 + 1.11803i
\(592\) 0 0
\(593\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(594\) 1.80902 0.587785i 1.80902 0.587785i
\(595\) 0 0
\(596\) 0.951057 2.92705i 0.951057 2.92705i
\(597\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(598\) 0 0
\(599\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(600\) −0.363271 1.11803i −0.363271 1.11803i
\(601\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.951057 + 0.690983i 0.951057 + 0.690983i
\(606\) 0 0
\(607\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −0.427051 1.31433i −0.427051 1.31433i
\(611\) 0.587785 + 1.80902i 0.587785 + 1.80902i
\(612\) 0 0
\(613\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(618\) 0.951057 2.92705i 0.951057 2.92705i
\(619\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −2.61803 + 1.90211i −2.61803 + 1.90211i
\(625\) −0.381966 + 1.17557i −0.381966 + 1.17557i
\(626\) 3.07768 3.07768
\(627\) 0 0
\(628\) 1.61803 1.61803
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(632\) −0.587785 1.80902i −0.587785 1.80902i
\(633\) −0.500000 1.53884i −0.500000 1.53884i
\(634\) 1.80902 + 1.31433i 1.80902 + 1.31433i
\(635\) −1.53884 + 1.11803i −1.53884 + 1.11803i
\(636\) 0 0
\(637\) −1.00000 −1.00000
\(638\) 0 0
\(639\) 0 0
\(640\) 0.690983 2.12663i 0.690983 2.12663i
\(641\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−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
\(645\) −1.53884 1.11803i −1.53884 1.11803i
\(646\) 0 0
\(647\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(648\) 3.07768 3.07768
\(649\) 1.80902 + 0.587785i 1.80902 + 0.587785i
\(650\) −0.726543 −0.726543
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 1.80902 + 2.48990i 1.80902 + 2.48990i
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 2.92705 + 2.12663i 2.92705 + 2.12663i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −2.48990 + 1.80902i −2.48990 + 1.80902i
\(669\) 0 0
\(670\) 0 0
\(671\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(672\) 0 0
\(673\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(674\) 0.951057 0.690983i 0.951057 0.690983i
\(675\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(676\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(677\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1.90211 1.90211
\(682\) 0 0
\(683\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(684\) 0 0
\(685\) −1.80902 + 1.31433i −1.80902 + 1.31433i
\(686\) 0 0
\(687\) 0 0
\(688\) −1.61803 4.97980i −1.61803 4.97980i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0.224514 0.690983i 0.224514 0.690983i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(702\) 0.587785 1.80902i 0.587785 1.80902i
\(703\) 0 0
\(704\) 2.61803i 2.61803i
\(705\) 2.23607 2.23607
\(706\) −0.690983 + 2.12663i −0.690983 + 2.12663i
\(707\) 0 0
\(708\) 4.02874 + 2.92705i 4.02874 + 2.92705i
\(709\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(710\) 0 0
\(711\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 1.11803 0.363271i 1.11803 0.363271i
\(716\) 0 0
\(717\) 0.363271 1.11803i 0.363271 1.11803i
\(718\) 0 0
\(719\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(720\) 1.17557 + 3.61803i 1.17557 + 3.61803i
\(721\) 0 0
\(722\) −1.53884 1.11803i −1.53884 1.11803i
\(723\) 0 0
\(724\) −1.30902 + 4.02874i −1.30902 + 4.02874i
\(725\) 0 0
\(726\) −1.53884 1.11803i −1.53884 1.11803i
\(727\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(728\) 0 0
\(729\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(730\) 0 0
\(731\) 0 0
\(732\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(733\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(734\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(735\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(736\) 0 0
\(737\) 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 0
\(742\) 0 0
\(743\) 0.587785 + 1.80902i 0.587785 + 1.80902i 0.587785 + 0.809017i \(0.300000\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) −1.11803 + 0.812299i −1.11803 + 0.812299i
\(746\) 0.951057 2.92705i 0.951057 2.92705i
\(747\) −1.17557 −1.17557
\(748\) 0 0
\(749\) 0 0
\(750\) 0.427051 1.31433i 0.427051 1.31433i
\(751\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(752\) 4.97980 + 3.61803i 4.97980 + 3.61803i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.587785 1.80902i 0.587785 1.80902i 1.00000i \(-0.5\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(762\) 2.48990 1.80902i 2.48990 1.80902i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −2.92705 2.12663i −2.92705 2.12663i
\(767\) 1.53884 1.11803i 1.53884 1.11803i
\(768\) −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
\(773\) −1.53884 + 1.11803i −1.53884 + 1.11803i −0.587785 + 0.809017i \(0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(774\) 2.48990 + 1.80902i 2.48990 + 1.80902i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 3.07768 3.07768
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −2.61803 + 1.90211i −2.61803 + 1.90211i
\(785\) −0.587785 0.427051i −0.587785 0.427051i
\(786\) 0 0
\(787\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(788\) 4.02874 + 2.92705i 4.02874 + 2.92705i
\(789\) 0 0
\(790\) −0.427051 + 1.31433i −0.427051 + 1.31433i
\(791\) 0 0
\(792\) −1.80902 2.48990i −1.80902 2.48990i
\(793\) 0.618034 0.618034
\(794\) 0 0
\(795\) 0 0
\(796\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(797\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\)