Properties

Label 1441.1.u.a.916.2
Level $1441$
Weight $1$
Character 1441.916
Analytic conductor $0.719$
Analytic rank $0$
Dimension $20$
Projective image $D_{25}$
CM discriminant -131
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1441.u (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.719152683204\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{50})\)
Defining polynomial: \(x^{20} - x^{15} + x^{10} - x^{5} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{25}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{25} + \cdots)\)

Embedding invariants

Embedding label 916.2
Root \(0.187381 - 0.982287i\) of defining polynomial
Character \(\chi\) \(=\) 1441.916
Dual form 1441.1.u.a.785.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.263146 - 0.809880i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.101597 - 0.0738147i) q^{5} +(-0.393950 + 1.21245i) q^{7} +(0.222357 - 0.161552i) q^{9} +O(q^{10})\) \(q+(-0.263146 - 0.809880i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.101597 - 0.0738147i) q^{5} +(-0.393950 + 1.21245i) q^{7} +(0.222357 - 0.161552i) q^{9} +(0.728969 + 0.684547i) q^{11} -0.851559 q^{12} +(1.60528 - 1.16630i) q^{13} +(-0.0330462 + 0.101706i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.101597 + 0.0738147i) q^{20} +1.08561 q^{21} +(-0.304144 - 0.936058i) q^{25} +(-0.878275 - 0.638104i) q^{27} +(1.03137 + 0.749337i) q^{28} +(0.362576 - 0.770513i) q^{33} +(0.129521 - 0.0941025i) q^{35} +(-0.0849327 - 0.261396i) q^{36} +(-1.36699 - 0.993173i) q^{39} +(0.541587 + 1.66683i) q^{41} -1.85955 q^{43} +(0.876307 - 0.481754i) q^{44} -0.0345157 q^{45} +(-0.263146 + 0.809880i) q^{48} +(-0.505828 - 0.367505i) q^{49} +(-0.613161 - 1.88711i) q^{52} +(-0.500000 + 0.363271i) q^{53} +(-0.0235315 - 0.123357i) q^{55} +(0.331159 - 1.01920i) q^{59} +(0.0865160 + 0.0628575i) q^{60} +(-0.101597 - 0.0738147i) q^{61} +(0.108276 + 0.333240i) q^{63} +(-0.809017 + 0.587785i) q^{64} -0.249182 q^{65} +(-0.678061 + 0.492640i) q^{75} +(-1.11716 + 0.614163i) q^{77} +(0.0388067 + 0.119435i) q^{80} +(-0.200741 + 0.617816i) q^{81} +(0.335471 - 1.03247i) q^{84} -1.61803 q^{89} +(0.781687 + 2.40578i) q^{91} +(0.272681 + 0.0344476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} - 5q^{25} + 20q^{33} + 15q^{35} - 5q^{36} - 10q^{39} - 10q^{45} - 5q^{49} - 10q^{53} - 10q^{63} - 5q^{64} - 10q^{75} - 5q^{81} - 10q^{89} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1441\mathbb{Z}\right)^\times\).

\(n\) \(133\) \(1311\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{5}\right)\)

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 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(3\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(4\) 0.309017 0.951057i 0.309017 0.951057i
\(5\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(6\) 0 0
\(7\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(8\) 0 0
\(9\) 0.222357 0.161552i 0.222357 0.161552i
\(10\) 0 0
\(11\) 0.728969 + 0.684547i 0.728969 + 0.684547i
\(12\) −0.851559 −0.851559
\(13\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(14\) 0 0
\(15\) −0.0330462 + 0.101706i −0.0330462 + 0.101706i
\(16\) −0.809017 0.587785i −0.809017 0.587785i
\(17\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(18\) 0 0
\(19\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(20\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i
\(21\) 1.08561 1.08561
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) −0.304144 0.936058i −0.304144 0.936058i
\(26\) 0 0
\(27\) −0.878275 0.638104i −0.878275 0.638104i
\(28\) 1.03137 + 0.749337i 1.03137 + 0.749337i
\(29\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(30\) 0 0
\(31\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(32\) 0 0
\(33\) 0.362576 0.770513i 0.362576 0.770513i
\(34\) 0 0
\(35\) 0.129521 0.0941025i 0.129521 0.0941025i
\(36\) −0.0849327 0.261396i −0.0849327 0.261396i
\(37\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(38\) 0 0
\(39\) −1.36699 0.993173i −1.36699 0.993173i
\(40\) 0 0
\(41\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(42\) 0 0
\(43\) −1.85955 −1.85955 −0.929776 0.368125i \(-0.880000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(44\) 0.876307 0.481754i 0.876307 0.481754i
\(45\) −0.0345157 −0.0345157
\(46\) 0 0
\(47\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(48\) −0.263146 + 0.809880i −0.263146 + 0.809880i
\(49\) −0.505828 0.367505i −0.505828 0.367505i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.613161 1.88711i −0.613161 1.88711i
\(53\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(54\) 0 0
\(55\) −0.0235315 0.123357i −0.0235315 0.123357i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(60\) 0.0865160 + 0.0628575i 0.0865160 + 0.0628575i
\(61\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(62\) 0 0
\(63\) 0.108276 + 0.333240i 0.108276 + 0.333240i
\(64\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(65\) −0.249182 −0.249182
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(72\) 0 0
\(73\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(74\) 0 0
\(75\) −0.678061 + 0.492640i −0.678061 + 0.492640i
\(76\) 0 0
\(77\) −1.11716 + 0.614163i −1.11716 + 0.614163i
\(78\) 0 0
\(79\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(80\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i
\(81\) −0.200741 + 0.617816i −0.200741 + 0.617816i
\(82\) 0 0
\(83\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(84\) 0.335471 1.03247i 0.335471 1.03247i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(90\) 0 0
\(91\) 0.781687 + 2.40578i 0.781687 + 2.40578i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(98\) 0 0
\(99\) 0.272681 + 0.0344476i 0.272681 + 0.0344476i
\(100\) −0.984229 −0.984229
\(101\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(102\) 0 0
\(103\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(104\) 0 0
\(105\) −0.110295 0.0801338i −0.110295 0.0801338i
\(106\) 0 0
\(107\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(108\) −0.878275 + 0.638104i −0.878275 + 0.638104i
\(109\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.03137 0.749337i 1.03137 0.749337i
\(113\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.168526 0.518670i 0.168526 0.518670i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.0627905 + 0.998027i 0.0627905 + 0.998027i
\(122\) 0 0
\(123\) 1.20742 0.877242i 1.20742 0.877242i
\(124\) 0 0
\(125\) −0.0770013 + 0.236986i −0.0770013 + 0.236986i
\(126\) 0 0
\(127\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(128\) 0 0
\(129\) 0.489334 + 1.50602i 0.489334 + 1.50602i
\(130\) 0 0
\(131\) 1.00000 1.00000
\(132\) −0.620759 0.582932i −0.620759 0.582932i
\(133\) 0 0
\(134\) 0 0
\(135\) 0.0421288 + 0.129659i 0.0421288 + 0.129659i
\(136\) 0 0
\(137\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(138\) 0 0
\(139\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(140\) −0.0494726 0.152261i −0.0494726 0.152261i
\(141\) 0 0
\(142\) 0 0
\(143\) 1.96858 + 0.248690i 1.96858 + 0.248690i
\(144\) −0.274848 −0.274848
\(145\) 0 0
\(146\) 0 0
\(147\) −0.164529 + 0.506367i −0.164529 + 0.506367i
\(148\) 0 0
\(149\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(150\) 0 0
\(151\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −1.36699 + 0.993173i −1.36699 + 0.993173i
\(157\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(158\) 0 0
\(159\) 0.425779 + 0.309347i 0.425779 + 0.309347i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(164\) 1.75261 1.75261
\(165\) −0.0937119 + 0.0515186i −0.0937119 + 0.0515186i
\(166\) 0 0
\(167\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(168\) 0 0
\(169\) 0.907634 2.79341i 0.907634 2.79341i
\(170\) 0 0
\(171\) 0 0
\(172\) −0.574633 + 1.76854i −0.574633 + 1.76854i
\(173\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(174\) 0 0
\(175\) 1.25474 1.25474
\(176\) −0.187381 0.982287i −0.187381 0.982287i
\(177\) −0.912576 −0.912576
\(178\) 0 0
\(179\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(180\) −0.0106659 + 0.0328264i −0.0106659 + 0.0328264i
\(181\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(182\) 0 0
\(183\) −0.0330462 + 0.101706i −0.0330462 + 0.101706i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 1.11967 0.813486i 1.11967 0.813486i
\(190\) 0 0
\(191\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(192\) 0.688925 + 0.500534i 0.688925 + 0.500534i
\(193\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(194\) 0 0
\(195\) 0.0655712 + 0.201807i 0.0655712 + 0.201807i
\(196\) −0.505828 + 0.367505i −0.505828 + 0.367505i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.0680131 0.209323i 0.0680131 0.209323i
\(206\) 0 0
\(207\) 0 0
\(208\) −1.98423 −1.98423
\(209\) 0 0
\(210\) 0 0
\(211\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(212\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(213\) 0 0
\(214\) 0 0
\(215\) 0.188925 + 0.137262i 0.188925 + 0.137262i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −0.124591 0.0157395i −0.124591 0.0157395i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(224\) 0 0
\(225\) −0.218850 0.159004i −0.218850 0.159004i
\(226\) 0 0
\(227\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(228\) 0 0
\(229\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(230\) 0 0
\(231\) 0.791374 + 0.743150i 0.791374 + 0.743150i
\(232\) 0 0
\(233\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.866986 0.629902i −0.866986 0.629902i
\(237\) 0 0
\(238\) 0 0
\(239\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(240\) 0.0865160 0.0628575i 0.0865160 0.0628575i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) −0.532426 −0.532426
\(244\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i
\(245\) 0.0242634 + 0.0746750i 0.0242634 + 0.0746750i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(252\) 0.350389 0.350389
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(257\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.0770013 + 0.236986i −0.0770013 + 0.236986i
\(261\) 0 0
\(262\) 0 0
\(263\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(264\) 0 0
\(265\) 0.0776134 0.0776134
\(266\) 0 0
\(267\) 0.425779 + 1.31041i 0.425779 + 1.31041i
\(268\) 0 0
\(269\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(270\) 0 0
\(271\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(272\) 0 0
\(273\) 1.74270 1.26615i 1.74270 1.26615i
\(274\) 0 0
\(275\) 0.419064 0.890557i 0.419064 0.890557i
\(276\) 0 0
\(277\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(282\) 0 0
\(283\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.23432 −2.23432
\(288\) 0 0
\(289\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(294\) 0 0
\(295\) −0.108877 + 0.0791038i −0.108877 + 0.0791038i
\(296\) 0 0
\(297\) −0.203423 1.06638i −0.203423 1.06638i
\(298\) 0 0
\(299\) 0 0
\(300\) 0.258996 + 0.797108i 0.258996 + 0.797108i
\(301\) 0.732570 2.25462i 0.732570 2.25462i
\(302\) 0 0
\(303\) −1.28109 0.930769i −1.28109 0.930769i
\(304\) 0 0
\(305\) 0.00487338 + 0.0149987i 0.00487338 + 0.0149987i
\(306\) 0 0
\(307\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(308\) 0.238883 + 1.25227i 0.238883 + 1.25227i
\(309\) 0 0
\(310\) 0 0
\(311\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(312\) 0 0
\(313\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(314\) 0 0
\(315\) 0.0135974 0.0418486i 0.0135974 0.0418486i
\(316\) 0 0
\(317\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.125581 0.125581
\(321\) 0.738289 0.536399i 0.738289 0.536399i
\(322\) 0 0
\(323\) 0 0
\(324\) 0.525546 + 0.381832i 0.525546 + 0.381832i
\(325\) −1.57996 1.14791i −1.57996 1.14791i
\(326\) 0 0
\(327\) −0.461193 1.41941i −0.461193 1.41941i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) −0.878275 0.638104i −0.878275 0.638104i
\(337\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(338\) 0 0
\(339\) 1.00441 0.729747i 1.00441 0.729747i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.386520 + 0.280823i −0.386520 + 0.280823i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(350\) 0 0
\(351\) −2.15409 −2.15409
\(352\) 0 0
\(353\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(357\) 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
\(361\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(362\) 0 0
\(363\) 0.791759 0.313480i 0.791759 0.313480i
\(364\) 2.52959 2.52959
\(365\) 0 0
\(366\) 0 0
\(367\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(368\) 0 0
\(369\) 0.389705 + 0.283137i 0.389705 + 0.283137i
\(370\) 0 0
\(371\) −0.243474 0.749337i −0.243474 0.749337i
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0.212193 0.212193
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(384\) 0 0
\(385\) 0.158834 + 0.0200654i 0.158834 + 0.0200654i
\(386\) 0 0
\(387\) −0.413484 + 0.300414i −0.413484 + 0.300414i
\(388\) 0 0
\(389\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −0.263146 0.809880i −0.263146 0.809880i
\(394\) 0 0
\(395\) 0 0
\(396\) 0.117025 0.248690i 0.117025 0.248690i
\(397\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.304144 + 0.936058i −0.304144 + 0.936058i
\(401\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −0.574633 1.76854i −0.574633 1.76854i
\(405\) 0.0659986 0.0479508i 0.0659986 0.0479508i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.10528 + 0.803030i 1.10528 + 0.803030i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) −0.110295 + 0.0801338i −0.110295 + 0.0801338i
\(421\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.129521 0.0941025i 0.129521 0.0941025i
\(428\) 1.07165 1.07165
\(429\) −0.316616 1.65976i −0.316616 1.65976i
\(430\) 0 0
\(431\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(432\) 0.335471 + 1.03247i 0.335471 + 1.03247i
\(433\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.541587 1.66683i 0.541587 1.66683i
\(437\) 0 0
\(438\) 0 0
\(439\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(440\) 0 0
\(441\) −0.171845 −0.171845
\(442\) 0 0
\(443\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(444\) 0 0
\(445\) 0.164388 + 0.119435i 0.164388 + 0.119435i
\(446\) 0 0
\(447\) 0 0
\(448\) −0.393950 1.21245i −0.393950 1.21245i
\(449\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(450\) 0 0
\(451\) −0.746226 + 1.58581i −0.746226 + 1.58581i
\(452\) 1.45794 1.45794
\(453\) −0.258183 + 0.187581i −0.258183 + 0.187581i
\(454\) 0 0
\(455\) 0.0981650 0.302121i 0.0981650 0.302121i
\(456\) 0 0
\(457\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(468\) −0.441207 0.320555i −0.441207 0.320555i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.35556 1.27295i −1.35556 1.27295i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.0524913 + 0.161552i −0.0524913 + 0.161552i
\(478\) 0 0
\(479\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.968583 + 0.248690i 0.968583 + 0.248690i
\(485\) 0 0
\(486\) 0 0
\(487\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(492\) −0.461193 1.41941i −0.461193 1.41941i
\(493\) 0 0
\(494\) 0 0
\(495\) −0.0251609 0.0236276i −0.0251609 0.0236276i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(500\) 0.201592 + 0.146465i 0.201592 + 0.146465i
\(501\) 0.425779 + 0.309347i 0.425779 + 0.309347i
\(502\) 0 0
\(503\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(504\) 0 0
\(505\) −0.233525 −0.233525
\(506\) 0 0
\(507\) −2.50117 −2.50117
\(508\) 0 0
\(509\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 1.58352 1.58352
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(522\) 0 0
\(523\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(524\) 0.309017 0.951057i 0.309017 0.951057i
\(525\) −0.330181 1.01619i −0.330181 1.01619i
\(526\) 0 0
\(527\) 0 0
\(528\) −0.746226 + 0.410241i −0.746226 + 0.410241i
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) −0.0910184 0.280126i −0.0910184 0.280126i
\(532\) 0 0
\(533\) 2.81343 + 2.04407i 2.81343 + 2.04407i
\(534\) 0 0
\(535\) 0.0415873 0.127993i 0.0415873 0.127993i
\(536\) 0 0
\(537\) 1.33456 0.969617i 1.33456 0.969617i
\(538\) 0 0
\(539\) −0.117158 0.614163i −0.117158 0.614163i
\(540\) 0.136332 0.136332
\(541\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −0.178061 0.129369i −0.178061 0.129369i
\(546\) 0 0
\(547\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(548\) 0 0
\(549\) −0.0345157 −0.0345157
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(558\) 0 0
\(559\) −2.98509 + 2.16880i −2.98509 + 2.16880i
\(560\) −0.160097 −0.160097
\(561\) 0 0
\(562\) 0 0
\(563\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(564\) 0 0
\(565\) 0.0565777 0.174128i 0.0565777 0.174128i
\(566\) 0 0
\(567\) −0.669991 0.486777i −0.669991 0.486777i
\(568\) 0 0
\(569\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0.844844 1.79538i 0.844844 1.79538i
\(573\) 1.68969 1.68969
\(574\) 0 0
\(575\) 0 0
\(576\) −0.0849327 + 0.261396i −0.0849327 + 0.261396i
\(577\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(578\) 0 0
\(579\) −0.509758 + 1.56887i −0.509758 + 1.56887i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −0.613161 0.0774602i −0.613161 0.0774602i
\(584\) 0 0
\(585\) −0.0554072 + 0.0402557i −0.0554072 + 0.0402557i
\(586\) 0 0
\(587\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(588\) 0.430742 + 0.312952i 0.430742 + 0.312952i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(600\) 0 0
\(601\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −0.374763 −0.374763
\(605\) 0.0672897 0.106032i 0.0672897 0.106032i
\(606\) 0 0
\(607\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(614\) 0 0
\(615\) −0.187424 −0.187424
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0.637424 1.96179i 0.637424 1.96179i
\(624\) 0.522142 + 1.60699i 0.522142 + 1.60699i
\(625\) −0.770942 + 0.560122i −0.770942 + 0.560122i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(632\) 0 0
\(633\) 1.00441 + 0.729747i 1.00441 + 0.729747i
\(634\) 0 0
\(635\) 0 0
\(636\) 0.425779 0.309347i 0.425779 0.309347i
\(637\) −1.24061 −1.24061
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(642\) 0 0
\(643\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(644\) 0 0
\(645\) 0.0614511 0.189127i 0.0614511 0.189127i
\(646\) 0 0
\(647\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(648\) 0 0
\(649\) 0.939097 0.516273i 0.939097 0.516273i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(654\) 0 0
\(655\) −0.101597 0.0738147i −0.101597 0.0738147i
\(656\) 0.541587 1.66683i 0.541587 1.66683i
\(657\) 0 0
\(658\) 0 0
\(659\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(660\) 0.0200385 + 0.105045i 0.0200385 + 0.105045i
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(669\) 0 0
\(670\) 0 0
\(671\) −0.0235315 0.123357i −0.0235315 0.123357i
\(672\) 0 0
\(673\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(674\) 0 0
\(675\) −0.330181 + 1.01619i −0.330181 + 1.01619i
\(676\) −2.37622 1.72642i −2.37622 1.72642i
\(677\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 1.50441 + 1.09302i 1.50441 + 1.09302i
\(689\) −0.378954 + 1.16630i −0.378954 + 1.16630i
\(690\) 0 0
\(691\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(692\) 0 0
\(693\) −0.149189 + 0.317042i −0.149189 + 0.317042i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 1.33456 + 0.969617i 1.33456 + 0.969617i
\(700\) 0.387737 1.19333i 0.387737 1.19333i
\(701\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.992115 0.125333i −0.992115 0.125333i
\(705\) 0 0
\(706\) 0 0
\(707\) 0.732570 + 2.25462i 0.732570 + 2.25462i
\(708\) −0.282001 + 0.867911i −0.282001 + 0.867911i
\(709\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −0.181646 0.170577i −0.181646 0.170577i
\(716\) 1.93717 1.93717
\(717\) 1.33456 0.969617i 1.33456 0.969617i
\(718\) 0 0
\(719\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(720\) 0.0279238 + 0.0202878i 0.0279238 + 0.0202878i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 0.340847 + 1.04902i 0.340847 + 1.04902i
\(730\) 0 0
\(731\) 0 0
\(732\) 0.0865160 + 0.0628575i 0.0865160 + 0.0628575i
\(733\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(734\) 0 0
\(735\) 0.0540930 0.0393009i 0.0540930 0.0393009i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.688925 0.500534i 0.688925 0.500534i −0.187381 0.982287i \(-0.560000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.36620 −1.36620
\(750\) 0 0
\(751\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.0145433 + 0.0447596i −0.0145433 + 0.0447596i
\(756\) −0.427675 1.31625i −0.427675 1.31625i
\(757\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(762\) 0 0
\(763\) −0.690441 + 2.12496i −0.690441 + 2.12496i
\(764\) 1.60528 + 1.16630i 1.60528 + 1.16630i
\(765\) 0 0
\(766\) 0 0
\(767\) −0.657096 2.02233i −0.657096 2.02233i
\(768\) 0.688925 0.500534i 0.688925 0.500534i
\(769\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.56720 + 1.13864i −1.56720 + 1.13864i
\(773\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0.212193 0.212193
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.193209 + 0.594636i 0.193209 + 0.594636i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(788\) 0 0
\(789\) 0.224084 + 0.689661i 0.224084 + 0.689661i
\(790\) 0 0
\(791\) −1.85865 −1.85865
\(792\) 0 0
\(793\) −0.249182 −0.249182
\(794\) 0 0
\(795\) −0.0204236 0.0628575i −0.0204236 0.0628575i
\(796\) 0 0
\(797\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −0.359781 + 0.261396i −0.359781 + 0.261396i
\(802\) 0 0
\(803\) 0 0