Properties

Label 429.1.v.c.389.1
Level $429$
Weight $1$
Character 429.389
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 389.1
Root \(0.951057 - 0.309017i\) of defining polynomial
Character \(\chi\) \(=\) 429.389
Dual form 429.1.v.c.311.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.951057 - 0.690983i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.118034 + 0.363271i) q^{4} +(1.53884 - 1.11803i) q^{5} +(0.951057 - 0.690983i) q^{6} +(-0.224514 + 0.690983i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.951057 - 0.690983i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.118034 + 0.363271i) q^{4} +(1.53884 - 1.11803i) q^{5} +(0.951057 - 0.690983i) q^{6} +(-0.224514 + 0.690983i) q^{8} +(-0.809017 - 0.587785i) q^{9} -2.23607 q^{10} +(-0.587785 - 0.809017i) q^{11} -0.381966 q^{12} +(0.809017 + 0.587785i) q^{13} +(0.587785 + 1.80902i) q^{15} +(1.00000 - 0.726543i) q^{16} +(0.363271 + 1.11803i) q^{18} +(0.587785 + 0.427051i) q^{20} +1.17557i q^{22} +(-0.587785 - 0.427051i) q^{24} +(0.809017 - 2.48990i) q^{25} +(-0.363271 - 1.11803i) q^{26} +(0.809017 - 0.587785i) q^{27} +(0.690983 - 2.12663i) q^{30} -0.726543 q^{32} +(0.951057 - 0.309017i) q^{33} +(0.118034 - 0.363271i) q^{36} +(-0.809017 + 0.587785i) q^{39} +(0.427051 + 1.31433i) q^{40} +0.618034 q^{43} +(0.224514 - 0.309017i) q^{44} -1.90211 q^{45} +(-0.363271 + 1.11803i) q^{47} +(0.381966 + 1.17557i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-2.48990 + 1.80902i) q^{50} +(-0.118034 + 0.363271i) q^{52} -1.17557 q^{54} +(-1.80902 - 0.587785i) q^{55} +(0.363271 + 1.11803i) q^{59} +(-0.587785 + 0.427051i) q^{60} +(-1.30902 + 0.951057i) q^{61} +(-0.309017 - 0.224514i) q^{64} +1.90211 q^{65} +(-1.11803 - 0.363271i) q^{66} +(0.587785 - 0.427051i) q^{72} +(2.11803 + 1.53884i) q^{75} +1.17557 q^{78} +(-1.30902 - 0.951057i) q^{79} +(0.726543 - 2.23607i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-1.53884 + 1.11803i) q^{83} +(-0.587785 - 0.427051i) q^{86} +(0.690983 - 0.224514i) q^{88} +(1.80902 + 1.31433i) q^{90} +(1.11803 - 0.812299i) q^{94} +(0.224514 - 0.690983i) q^{96} +1.17557 q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{3} - 8q^{4} - 2q^{9} + O(q^{10}) \) \( 8q + 2q^{3} - 8q^{4} - 2q^{9} - 12q^{12} + 2q^{13} + 8q^{16} + 2q^{25} + 2q^{27} + 10q^{30} - 8q^{36} - 2q^{39} - 10q^{40} - 4q^{43} + 12q^{48} - 2q^{49} + 8q^{52} - 10q^{55} - 6q^{61} + 2q^{64} + 8q^{75} - 6q^{79} - 2q^{81} + 10q^{88} + 10q^{90} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.951057 0.690983i −0.951057 0.690983i 1.00000i \(-0.5\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(3\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(4\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(5\) 1.53884 1.11803i 1.53884 1.11803i 0.587785 0.809017i \(-0.300000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(6\) 0.951057 0.690983i 0.951057 0.690983i
\(7\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(8\) −0.224514 + 0.690983i −0.224514 + 0.690983i
\(9\) −0.809017 0.587785i −0.809017 0.587785i
\(10\) −2.23607 −2.23607
\(11\) −0.587785 0.809017i −0.587785 0.809017i
\(12\) −0.381966 −0.381966
\(13\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(14\) 0 0
\(15\) 0.587785 + 1.80902i 0.587785 + 1.80902i
\(16\) 1.00000 0.726543i 1.00000 0.726543i
\(17\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(18\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(19\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(20\) 0.587785 + 0.427051i 0.587785 + 0.427051i
\(21\) 0 0
\(22\) 1.17557i 1.17557i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) −0.587785 0.427051i −0.587785 0.427051i
\(25\) 0.809017 2.48990i 0.809017 2.48990i
\(26\) −0.363271 1.11803i −0.363271 1.11803i
\(27\) 0.809017 0.587785i 0.809017 0.587785i
\(28\) 0 0
\(29\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(30\) 0.690983 2.12663i 0.690983 2.12663i
\(31\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(32\) −0.726543 −0.726543
\(33\) 0.951057 0.309017i 0.951057 0.309017i
\(34\) 0 0
\(35\) 0 0
\(36\) 0.118034 0.363271i 0.118034 0.363271i
\(37\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(38\) 0 0
\(39\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(40\) 0.427051 + 1.31433i 0.427051 + 1.31433i
\(41\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(42\) 0 0
\(43\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(44\) 0.224514 0.309017i 0.224514 0.309017i
\(45\) −1.90211 −1.90211
\(46\) 0 0
\(47\) −0.363271 + 1.11803i −0.363271 + 1.11803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(48\) 0.381966 + 1.17557i 0.381966 + 1.17557i
\(49\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(50\) −2.48990 + 1.80902i −2.48990 + 1.80902i
\(51\) 0 0
\(52\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(53\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(54\) −1.17557 −1.17557
\(55\) −1.80902 0.587785i −1.80902 0.587785i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.363271 + 1.11803i 0.363271 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(60\) −0.587785 + 0.427051i −0.587785 + 0.427051i
\(61\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.309017 0.224514i −0.309017 0.224514i
\(65\) 1.90211 1.90211
\(66\) −1.11803 0.363271i −1.11803 0.363271i
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(72\) 0.587785 0.427051i 0.587785 0.427051i
\(73\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(74\) 0 0
\(75\) 2.11803 + 1.53884i 2.11803 + 1.53884i
\(76\) 0 0
\(77\) 0 0
\(78\) 1.17557 1.17557
\(79\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(80\) 0.726543 2.23607i 0.726543 2.23607i
\(81\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(82\) 0 0
\(83\) −1.53884 + 1.11803i −1.53884 + 1.11803i −0.587785 + 0.809017i \(0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.587785 0.427051i −0.587785 0.427051i
\(87\) 0 0
\(88\) 0.690983 0.224514i 0.690983 0.224514i
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 1.80902 + 1.31433i 1.80902 + 1.31433i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 1.11803 0.812299i 1.11803 0.812299i
\(95\) 0 0
\(96\) 0.224514 0.690983i 0.224514 0.690983i
\(97\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(98\) 1.17557 1.17557
\(99\) 1.00000i 1.00000i
\(100\) 1.00000 1.00000
\(101\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(102\) 0 0
\(103\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(104\) −0.587785 + 0.427051i −0.587785 + 0.427051i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(108\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 1.31433 + 1.80902i 1.31433 + 1.80902i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −0.309017 0.951057i −0.309017 0.951057i
\(118\) 0.427051 1.31433i 0.427051 1.31433i
\(119\) 0 0
\(120\) −1.38197 −1.38197
\(121\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(122\) 1.90211 1.90211
\(123\) 0 0
\(124\) 0 0
\(125\) −0.951057 2.92705i −0.951057 2.92705i
\(126\) 0 0
\(127\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(128\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(129\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(130\) −1.80902 1.31433i −1.80902 1.31433i
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0.224514 + 0.309017i 0.224514 + 0.309017i
\(133\) 0 0
\(134\) 0 0
\(135\) 0.587785 1.80902i 0.587785 1.80902i
\(136\) 0 0
\(137\) −0.951057 + 0.690983i −0.951057 + 0.690983i −0.951057 0.309017i \(-0.900000\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(140\) 0 0
\(141\) −0.951057 0.690983i −0.951057 0.690983i
\(142\) 0 0
\(143\) 1.00000i 1.00000i
\(144\) −1.23607 −1.23607
\(145\) 0 0
\(146\) 0 0
\(147\) −0.309017 0.951057i −0.309017 0.951057i
\(148\) 0 0
\(149\) 1.53884 1.11803i 1.53884 1.11803i 0.587785 0.809017i \(-0.300000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(150\) −0.951057 2.92705i −0.951057 2.92705i
\(151\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.309017 0.224514i −0.309017 0.224514i
\(157\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(158\) 0.587785 + 1.80902i 0.587785 + 1.80902i
\(159\) 0 0
\(160\) −1.11803 + 0.812299i −1.11803 + 0.812299i
\(161\) 0 0
\(162\) 0.363271 1.11803i 0.363271 1.11803i
\(163\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(164\) 0 0
\(165\) 1.11803 1.53884i 1.11803 1.53884i
\(166\) 2.23607 2.23607
\(167\) 1.53884 + 1.11803i 1.53884 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(168\) 0 0
\(169\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.0729490 + 0.224514i 0.0729490 + 0.224514i
\(173\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.17557 0.381966i −1.17557 0.381966i
\(177\) −1.17557 −1.17557
\(178\) 0 0
\(179\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(180\) −0.224514 0.690983i −0.224514 0.690983i
\(181\) −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
\(183\) −0.500000 1.53884i −0.500000 1.53884i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.449028 −0.449028
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(192\) 0.309017 0.224514i 0.309017 0.224514i
\(193\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(194\) 0 0
\(195\) −0.587785 + 1.80902i −0.587785 + 1.80902i
\(196\) −0.309017 0.224514i −0.309017 0.224514i
\(197\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(198\) 0.690983 0.951057i 0.690983 0.951057i
\(199\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(200\) 1.53884 + 1.11803i 1.53884 + 1.11803i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0.224514 0.690983i 0.224514 0.690983i
\(207\) 0 0
\(208\) 1.23607 1.23607
\(209\) 0 0
\(210\) 0 0
\(211\) 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i \(-0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0.951057 0.690983i 0.951057 0.690983i
\(216\) 0.224514 + 0.690983i 0.224514 + 0.690983i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0.726543i 0.726543i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(224\) 0 0
\(225\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(226\) 0 0
\(227\) −0.363271 1.11803i −0.363271 1.11803i −0.951057 0.309017i \(-0.900000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(228\) 0 0
\(229\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(234\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(235\) 0.690983 + 2.12663i 0.690983 + 2.12663i
\(236\) −0.363271 + 0.263932i −0.363271 + 0.263932i
\(237\) 1.30902 0.951057i 1.30902 0.951057i
\(238\) 0 0
\(239\) 0.587785 1.80902i 0.587785 1.80902i 1.00000i \(-0.5\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(240\) 1.90211 + 1.38197i 1.90211 + 1.38197i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0.951057 0.690983i 0.951057 0.690983i
\(243\) −1.00000 −1.00000
\(244\) −0.500000 0.363271i −0.500000 0.363271i
\(245\) −0.587785 + 1.80902i −0.587785 + 1.80902i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −0.587785 1.80902i −0.587785 1.80902i
\(250\) −1.11803 + 3.44095i −1.11803 + 3.44095i
\(251\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −0.726543 −0.726543
\(255\) 0 0
\(256\) 0.309017 0.951057i 0.309017 0.951057i
\(257\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(258\) 0.587785 0.427051i 0.587785 0.427051i
\(259\) 0 0
\(260\) 0.224514 + 0.690983i 0.224514 + 0.690983i
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0.726543i 0.726543i
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(270\) −1.80902 + 1.31433i −1.80902 + 1.31433i
\(271\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 1.38197 1.38197
\(275\) −2.48990 + 0.809017i −2.48990 + 0.809017i
\(276\) 0 0
\(277\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(278\) −0.587785 + 1.80902i −0.587785 + 1.80902i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.951057 0.690983i 0.951057 0.690983i 1.00000i \(-0.5\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(282\) 0.427051 + 1.31433i 0.427051 + 1.31433i
\(283\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −0.690983 + 0.951057i −0.690983 + 0.951057i
\(287\) 0 0
\(288\) 0.587785 + 0.427051i 0.587785 + 0.427051i
\(289\) 0.309017 0.951057i 0.309017 0.951057i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0.587785 + 1.80902i 0.587785 + 1.80902i 0.587785 + 0.809017i \(0.300000\pi\)
1.00000i \(0.5\pi\)
\(294\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(295\) 1.80902 + 1.31433i 1.80902 + 1.31433i
\(296\) 0 0
\(297\) −0.951057 0.309017i −0.951057 0.309017i
\(298\) −2.23607 −2.23607
\(299\) 0 0
\(300\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.951057 + 2.92705i −0.951057 + 2.92705i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) −0.618034 −0.618034
\(310\) 0 0
\(311\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(312\) −0.224514 0.690983i −0.224514 0.690983i
\(313\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(314\) 1.53884 1.11803i 1.53884 1.11803i
\(315\) 0 0
\(316\) 0.190983 0.587785i 0.190983 0.587785i
\(317\) −1.53884 1.11803i −1.53884 1.11803i −0.951057 0.309017i \(-0.900000\pi\)
−0.587785 0.809017i \(-0.700000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.726543 −0.726543
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(325\) 2.11803 1.53884i 2.11803 1.53884i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) −2.12663 + 0.690983i −2.12663 + 0.690983i
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −0.587785 0.427051i −0.587785 0.427051i
\(333\) 0 0
\(334\) −0.690983 2.12663i −0.690983 2.12663i
\(335\) 0 0
\(336\) 0 0
\(337\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(338\) 0.363271 1.11803i 0.363271 1.11803i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) −0.138757 + 0.427051i −0.138757 + 0.427051i
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(348\) 0 0
\(349\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(350\) 0 0
\(351\) 1.00000 1.00000
\(352\) 0.427051 + 0.587785i 0.427051 + 0.587785i
\(353\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(354\) 1.11803 + 0.812299i 1.11803 + 0.812299i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(360\) 0.427051 1.31433i 0.427051 1.31433i
\(361\) −0.809017 0.587785i −0.809017 0.587785i
\(362\) 0.726543 0.726543
\(363\) −0.809017 0.587785i −0.809017 0.587785i
\(364\) 0 0
\(365\) 0 0
\(366\) −0.587785 + 1.80902i −0.587785 + 1.80902i
\(367\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(374\) 0 0
\(375\) 3.07768 3.07768
\(376\) −0.690983 0.502029i −0.690983 0.502029i
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(380\) 0 0
\(381\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(382\) 0 0
\(383\) −0.951057 0.690983i −0.951057 0.690983i 1.00000i \(-0.5\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(384\) −1.17557 −1.17557
\(385\) 0 0
\(386\) 0 0
\(387\) −0.500000 0.363271i −0.500000 0.363271i
\(388\) 0 0
\(389\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(390\) 1.80902 1.31433i 1.80902 1.31433i
\(391\) 0 0
\(392\) −0.224514 0.690983i −0.224514 0.690983i
\(393\) 0 0
\(394\) 1.11803 + 0.812299i 1.11803 + 0.812299i
\(395\) −3.07768 −3.07768
\(396\) −0.363271 + 0.118034i −0.363271 + 0.118034i
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) −1.53884 1.11803i −1.53884 1.11803i
\(399\) 0 0
\(400\) −1.00000 3.07768i −1.00000 3.07768i
\(401\) −1.53884 + 1.11803i −1.53884 + 1.11803i −0.587785 + 0.809017i \(0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 1.53884 + 1.11803i 1.53884 + 1.11803i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(410\) 0 0
\(411\) −0.363271 1.11803i −0.363271 1.11803i
\(412\) −0.190983 + 0.138757i −0.190983 + 0.138757i
\(413\) 0 0
\(414\) 0 0
\(415\) −1.11803 + 3.44095i −1.11803 + 3.44095i
\(416\) −0.587785 0.427051i −0.587785 0.427051i
\(417\) 1.61803 1.61803
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(422\) −0.224514 0.690983i −0.224514 0.690983i
\(423\) 0.951057 0.690983i 0.951057 0.690983i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(430\) −1.38197 −1.38197
\(431\) 0.951057 + 0.690983i 0.951057 + 0.690983i 0.951057 0.309017i \(-0.100000\pi\)
1.00000i \(0.5\pi\)
\(432\) 0.381966 1.17557i 0.381966 1.17557i
\(433\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(440\) 0.812299 1.11803i 0.812299 1.11803i
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0.587785 + 1.80902i 0.587785 + 1.80902i
\(448\) 0 0
\(449\) 0.951057 + 0.690983i 0.951057 + 0.690983i 0.951057 0.309017i \(-0.100000\pi\)
1.00000i \(0.5\pi\)
\(450\) 3.07768 3.07768
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −0.427051 + 1.31433i −0.427051 + 1.31433i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(458\) 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 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(468\) 0.309017 0.224514i 0.309017 0.224514i
\(469\) 0 0
\(470\) 0.812299 2.50000i 0.812299 2.50000i
\(471\) −1.30902 0.951057i −1.30902 0.951057i
\(472\) −0.854102 −0.854102
\(473\) −0.363271 0.500000i −0.363271 0.500000i
\(474\) −1.90211 −1.90211
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −1.80902 + 1.31433i −1.80902 + 1.31433i
\(479\) 1.53884 1.11803i 1.53884 1.11803i 0.587785 0.809017i \(-0.300000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(480\) −0.427051 1.31433i −0.427051 1.31433i
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.381966 −0.381966
\(485\) 0 0
\(486\) 0.951057 + 0.690983i 0.951057 + 0.690983i
\(487\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(488\) −0.363271 1.11803i −0.363271 1.11803i
\(489\) 0 0
\(490\) 1.80902 1.31433i 1.80902 1.31433i
\(491\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 1.11803 + 1.53884i 1.11803 + 1.53884i
\(496\) 0 0
\(497\) 0 0
\(498\) −0.690983 + 2.12663i −0.690983 + 2.12663i
\(499\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(500\) 0.951057 0.690983i 0.951057 0.690983i
\(501\) −1.53884 + 1.11803i −1.53884 + 1.11803i
\(502\) 0 0
\(503\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −1.00000
\(508\) 0.190983 + 0.138757i 0.190983 + 0.138757i
\(509\) 0.587785 1.80902i 0.587785 1.80902i 1.00000i \(-0.5\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0.951057 + 0.690983i 0.951057 + 0.690983i
\(516\) −0.236068 −0.236068
\(517\) 1.11803 0.363271i 1.11803 0.363271i
\(518\) 0 0
\(519\) 0 0
\(520\) −0.427051 + 1.31433i −0.427051 + 1.31433i
\(521\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(522\) 0 0
\(523\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0.726543 1.00000i 0.726543 1.00000i
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 0.363271 1.11803i 0.363271 1.11803i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(540\) 0.726543 0.726543
\(541\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(542\) 0 0
\(543\) −0.190983 0.587785i −0.190983 0.587785i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(548\) −0.363271 0.263932i −0.363271 0.263932i
\(549\) 1.61803 1.61803
\(550\) 2.92705 + 0.951057i 2.92705 + 0.951057i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0.726543 + 2.23607i 0.726543 + 2.23607i
\(555\) 0 0
\(556\) 0.500000 0.363271i 0.500000 0.363271i
\(557\) −0.363271 1.11803i −0.363271 1.11803i −0.951057 0.309017i \(-0.900000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(558\) 0 0
\(559\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(560\) 0 0
\(561\) 0 0
\(562\) −1.38197 −1.38197
\(563\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(564\) 0.138757 0.427051i 0.138757 0.427051i
\(565\) 0 0
\(566\) −1.53884 + 1.11803i −1.53884 + 1.11803i
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(570\) 0 0
\(571\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(572\) 0.363271 0.118034i 0.363271 0.118034i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(577\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(578\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −1.53884 1.11803i −1.53884 1.11803i
\(586\) 0.690983 2.12663i 0.690983 2.12663i
\(587\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(588\) 0.309017 0.224514i 0.309017 0.224514i
\(589\) 0 0
\(590\) −0.812299 2.50000i −0.812299 2.50000i
\(591\) 0.363271 1.11803i 0.363271 1.11803i
\(592\) 0 0
\(593\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(594\) 0.690983 + 0.951057i 0.690983 + 0.951057i
\(595\) 0 0
\(596\) 0.587785 + 0.427051i 0.587785 + 0.427051i
\(597\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(598\) 0 0
\(599\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(600\) −1.53884 + 1.11803i −1.53884 + 1.11803i
\(601\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.587785 + 1.80902i 0.587785 + 1.80902i
\(606\) 0 0
\(607\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 2.92705 2.12663i 2.92705 2.12663i
\(611\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(612\) 0 0
\(613\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(618\) 0.587785 + 0.427051i 0.587785 + 0.427051i
\(619\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −0.381966 + 1.17557i −0.381966 + 1.17557i
\(625\) −2.61803 1.90211i −2.61803 1.90211i
\(626\) −0.726543 −0.726543
\(627\) 0 0
\(628\) −0.618034 −0.618034
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(632\) 0.951057 0.690983i 0.951057 0.690983i
\(633\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(634\) 0.690983 + 2.12663i 0.690983 + 2.12663i
\(635\) 0.363271 1.11803i 0.363271 1.11803i
\(636\) 0 0
\(637\) −1.00000 −1.00000
\(638\) 0 0
\(639\) 0 0
\(640\) 1.80902 + 1.31433i 1.80902 + 1.31433i
\(641\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(642\) 0 0
\(643\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(644\) 0 0
\(645\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(646\) 0 0
\(647\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(648\) −0.726543 −0.726543
\(649\) 0.690983 0.951057i 0.690983 0.951057i
\(650\) −3.07768 −3.07768
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0.690983 + 0.224514i 0.690983 + 0.224514i
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −0.427051 1.31433i −0.427051 1.31433i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −0.224514 + 0.690983i −0.224514 + 0.690983i
\(669\) 0 0
\(670\) 0 0
\(671\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(672\) 0 0
\(673\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(674\) 0.587785 1.80902i 0.587785 1.80902i
\(675\) −0.809017 2.48990i −0.809017 2.48990i
\(676\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(677\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1.17557 1.17557
\(682\) 0 0
\(683\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(684\) 0 0
\(685\) −0.690983 + 2.12663i −0.690983 + 2.12663i
\(686\) 0 0
\(687\) 0 0
\(688\) 0.618034 0.449028i 0.618034 0.449028i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.48990 1.80902i −2.48990 1.80902i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(702\) −0.951057 0.690983i −0.951057 0.690983i
\(703\) 0 0
\(704\) 0.381966i 0.381966i
\(705\) −2.23607 −2.23607
\(706\) −1.80902 1.31433i −1.80902 1.31433i
\(707\) 0 0
\(708\) −0.138757 0.427051i −0.138757 0.427051i
\(709\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(710\) 0 0
\(711\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −1.11803 1.53884i −1.11803 1.53884i
\(716\) 0 0
\(717\) 1.53884 + 1.11803i 1.53884 + 1.11803i
\(718\) 0 0
\(719\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(720\) −1.90211 + 1.38197i −1.90211 + 1.38197i
\(721\) 0 0
\(722\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(723\) 0 0
\(724\) −0.190983 0.138757i −0.190983 0.138757i
\(725\) 0 0
\(726\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(727\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(728\) 0 0
\(729\) 0.309017 0.951057i 0.309017 0.951057i
\(730\) 0 0
\(731\) 0 0
\(732\) 0.500000 0.363271i 0.500000 0.363271i
\(733\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(734\) −0.587785 + 1.80902i −0.587785 + 1.80902i
\(735\) −1.53884 1.11803i −1.53884 1.11803i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.951057 + 0.690983i −0.951057 + 0.690983i −0.951057 0.309017i \(-0.900000\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 1.11803 3.44095i 1.11803 3.44095i
\(746\) 0.587785 + 0.427051i 0.587785 + 0.427051i
\(747\) 1.90211 1.90211
\(748\) 0 0
\(749\) 0 0
\(750\) −2.92705 2.12663i −2.92705 2.12663i
\(751\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(752\) 0.449028 + 1.38197i 0.449028 + 1.38197i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.951057 0.690983i −0.951057 0.690983i 1.00000i \(-0.5\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(762\) 0.224514 0.690983i 0.224514 0.690983i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0.427051 + 1.31433i 0.427051 + 1.31433i
\(767\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(768\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0.363271 1.11803i 0.363271 1.11803i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(774\) 0.224514 + 0.690983i 0.224514 + 0.690983i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) −0.726543 −0.726543
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.381966 + 1.17557i −0.381966 + 1.17557i
\(785\) 0.951057 + 2.92705i 0.951057 + 2.92705i
\(786\) 0 0
\(787\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(788\) −0.138757 0.427051i −0.138757 0.427051i
\(789\) 0 0
\(790\) 2.92705 + 2.12663i 2.92705 + 2.12663i
\(791\) 0 0
\(792\) −0.690983 0.224514i −0.690983 0.224514i
\(793\) −1.61803 −1.61803
\(794\) 0 0
\(795\) 0 0
\(796\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(797\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(798\) 0 0
\(799\) 0 0