Properties

Label 1441.1.u.a.130.3
Level $1441$
Weight $1$
Character 1441.130
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 130.3
Root \(-0.968583 + 0.248690i\) of defining polynomial
Character \(\chi\) \(=\) 1441.130
Dual form 1441.1.u.a.654.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.101597 + 0.0738147i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.263146 - 0.809880i) q^{5} +(1.60528 + 1.16630i) q^{7} +(-0.304144 + 0.936058i) q^{9} +O(q^{10})\) \(q+(-0.101597 + 0.0738147i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.263146 - 0.809880i) q^{5} +(1.60528 + 1.16630i) q^{7} +(-0.304144 + 0.936058i) q^{9} +(0.535827 - 0.844328i) q^{11} +0.125581 q^{12} +(-0.393950 + 1.21245i) q^{13} +(0.0865160 + 0.0628575i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.263146 + 0.809880i) q^{20} -0.249182 q^{21} +(0.222357 - 0.161552i) q^{25} +(-0.0770013 - 0.236986i) q^{27} +(-0.613161 - 1.88711i) q^{28} +(0.00788530 + 0.125333i) q^{33} +(0.522142 - 1.60699i) q^{35} +(0.796258 - 0.578516i) q^{36} +(-0.0494726 - 0.152261i) q^{39} +(1.50441 - 1.09302i) q^{41} +1.75261 q^{43} +(-0.929776 + 0.368125i) q^{44} +0.838129 q^{45} +(-0.101597 - 0.0738147i) q^{48} +(0.907634 + 2.79341i) q^{49} +(1.03137 - 0.749337i) q^{52} +(-0.500000 + 1.53884i) q^{53} +(-0.824805 - 0.211774i) q^{55} +(-1.17950 - 0.856954i) q^{59} +(-0.0330462 - 0.101706i) q^{60} +(-0.263146 - 0.809880i) q^{61} +(-1.57996 + 1.14791i) q^{63} +(0.309017 - 0.951057i) q^{64} +1.08561 q^{65} +(-0.0106659 + 0.0328264i) q^{75} +(1.84489 - 0.730444i) q^{77} +(0.688925 - 0.500534i) q^{80} +(-0.770942 - 0.560122i) q^{81} +(0.201592 + 0.146465i) q^{84} +0.618034 q^{89} +(-2.04648 + 1.48686i) q^{91} +(0.627371 + 0.758362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} - 5q^{25} + 20q^{33} + 15q^{35} - 5q^{36} - 10q^{39} - 10q^{45} - 5q^{49} - 10q^{53} - 10q^{63} - 5q^{64} - 10q^{75} - 5q^{81} - 10q^{89} + O(q^{100}) \)

Character values

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

\(n\) \(133\) \(1311\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{5}\right)\)

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 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(3\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(4\) −0.809017 0.587785i −0.809017 0.587785i
\(5\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(6\) 0 0
\(7\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(8\) 0 0
\(9\) −0.304144 + 0.936058i −0.304144 + 0.936058i
\(10\) 0 0
\(11\) 0.535827 0.844328i 0.535827 0.844328i
\(12\) 0.125581 0.125581
\(13\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(14\) 0 0
\(15\) 0.0865160 + 0.0628575i 0.0865160 + 0.0628575i
\(16\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(17\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(18\) 0 0
\(19\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(20\) −0.263146 + 0.809880i −0.263146 + 0.809880i
\(21\) −0.249182 −0.249182
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 0.222357 0.161552i 0.222357 0.161552i
\(26\) 0 0
\(27\) −0.0770013 0.236986i −0.0770013 0.236986i
\(28\) −0.613161 1.88711i −0.613161 1.88711i
\(29\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(30\) 0 0
\(31\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(32\) 0 0
\(33\) 0.00788530 + 0.125333i 0.00788530 + 0.125333i
\(34\) 0 0
\(35\) 0.522142 1.60699i 0.522142 1.60699i
\(36\) 0.796258 0.578516i 0.796258 0.578516i
\(37\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(38\) 0 0
\(39\) −0.0494726 0.152261i −0.0494726 0.152261i
\(40\) 0 0
\(41\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(42\) 0 0
\(43\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(44\) −0.929776 + 0.368125i −0.929776 + 0.368125i
\(45\) 0.838129 0.838129
\(46\) 0 0
\(47\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(48\) −0.101597 0.0738147i −0.101597 0.0738147i
\(49\) 0.907634 + 2.79341i 0.907634 + 2.79341i
\(50\) 0 0
\(51\) 0 0
\(52\) 1.03137 0.749337i 1.03137 0.749337i
\(53\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(54\) 0 0
\(55\) −0.824805 0.211774i −0.824805 0.211774i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(60\) −0.0330462 0.101706i −0.0330462 0.101706i
\(61\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(62\) 0 0
\(63\) −1.57996 + 1.14791i −1.57996 + 1.14791i
\(64\) 0.309017 0.951057i 0.309017 0.951057i
\(65\) 1.08561 1.08561
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(72\) 0 0
\(73\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(74\) 0 0
\(75\) −0.0106659 + 0.0328264i −0.0106659 + 0.0328264i
\(76\) 0 0
\(77\) 1.84489 0.730444i 1.84489 0.730444i
\(78\) 0 0
\(79\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(80\) 0.688925 0.500534i 0.688925 0.500534i
\(81\) −0.770942 0.560122i −0.770942 0.560122i
\(82\) 0 0
\(83\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(84\) 0.201592 + 0.146465i 0.201592 + 0.146465i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(90\) 0 0
\(91\) −2.04648 + 1.48686i −2.04648 + 1.48686i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(98\) 0 0
\(99\) 0.627371 + 0.758362i 0.627371 + 0.758362i
\(100\) −0.274848 −0.274848
\(101\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(102\) 0 0
\(103\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(104\) 0 0
\(105\) 0.0655712 + 0.201807i 0.0655712 + 0.201807i
\(106\) 0 0
\(107\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(108\) −0.0770013 + 0.236986i −0.0770013 + 0.236986i
\(109\) −1.85955 −1.85955 −0.929776 0.368125i \(-0.880000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.613161 + 1.88711i −0.613161 + 1.88711i
\(113\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.01511 0.737519i −1.01511 0.737519i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.425779 0.904827i −0.425779 0.904827i
\(122\) 0 0
\(123\) −0.0721631 + 0.222095i −0.0721631 + 0.222095i
\(124\) 0 0
\(125\) −0.878275 0.638104i −0.878275 0.638104i
\(126\) 0 0
\(127\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(128\) 0 0
\(129\) −0.178061 + 0.129369i −0.178061 + 0.129369i
\(130\) 0 0
\(131\) 1.00000 1.00000
\(132\) 0.0672897 0.106032i 0.0672897 0.106032i
\(133\) 0 0
\(134\) 0 0
\(135\) −0.171668 + 0.124724i −0.171668 + 0.124724i
\(136\) 0 0
\(137\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(138\) 0 0
\(139\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(140\) −1.36699 + 0.993173i −1.36699 + 0.993173i
\(141\) 0 0
\(142\) 0 0
\(143\) 0.812619 + 0.982287i 0.812619 + 0.982287i
\(144\) −0.984229 −0.984229
\(145\) 0 0
\(146\) 0 0
\(147\) −0.298408 0.216806i −0.298408 0.216806i
\(148\) 0 0
\(149\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(150\) 0 0
\(151\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.0494726 + 0.152261i −0.0494726 + 0.152261i
\(157\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(158\) 0 0
\(159\) −0.0627905 0.193249i −0.0627905 0.193249i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(164\) −1.85955 −1.85955
\(165\) 0.0994299 0.0393671i 0.0994299 0.0393671i
\(166\) 0 0
\(167\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(168\) 0 0
\(169\) −0.505828 0.367505i −0.505828 0.367505i
\(170\) 0 0
\(171\) 0 0
\(172\) −1.41789 1.03016i −1.41789 1.03016i
\(173\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(174\) 0 0
\(175\) 0.545361 0.545361
\(176\) 0.968583 + 0.248690i 0.968583 + 0.248690i
\(177\) 0.183089 0.183089
\(178\) 0 0
\(179\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(180\) −0.678061 0.492640i −0.678061 0.492640i
\(181\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(182\) 0 0
\(183\) 0.0865160 + 0.0628575i 0.0865160 + 0.0628575i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0.152788 0.470234i 0.152788 0.470234i
\(190\) 0 0
\(191\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(192\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i
\(193\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(194\) 0 0
\(195\) −0.110295 + 0.0801338i −0.110295 + 0.0801338i
\(196\) 0.907634 2.79341i 0.907634 2.79341i
\(197\) 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
\(205\) −1.28109 0.930769i −1.28109 0.930769i
\(206\) 0 0
\(207\) 0 0
\(208\) −1.27485 −1.27485
\(209\) 0 0
\(210\) 0 0
\(211\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(212\) 1.30902 0.951057i 1.30902 0.951057i
\(213\) 0 0
\(214\) 0 0
\(215\) −0.461193 1.41941i −0.461193 1.41941i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0.542804 + 0.656137i 0.542804 + 0.656137i
\(221\) 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
\(225\) 0.0835933 + 0.257274i 0.0835933 + 0.257274i
\(226\) 0 0
\(227\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(228\) 0 0
\(229\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(230\) 0 0
\(231\) −0.133518 + 0.210391i −0.133518 + 0.210391i
\(232\) 0 0
\(233\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.450527 + 1.38658i 0.450527 + 1.38658i
\(237\) 0 0
\(238\) 0 0
\(239\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(240\) −0.0330462 + 0.101706i −0.0330462 + 0.101706i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 0.368852 0.368852
\(244\) −0.263146 + 0.809880i −0.263146 + 0.809880i
\(245\) 2.02349 1.47015i 2.02349 1.47015i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(252\) 1.95294 1.95294
\(253\) 0 0
\(254\) 0 0
\(255\) 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 0
\(259\) 0 0
\(260\) −0.878275 0.638104i −0.878275 0.638104i
\(261\) 0 0
\(262\) 0 0
\(263\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(264\) 0 0
\(265\) 1.37785 1.37785
\(266\) 0 0
\(267\) −0.0627905 + 0.0456200i −0.0627905 + 0.0456200i
\(268\) 0 0
\(269\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(270\) 0 0
\(271\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(272\) 0 0
\(273\) 0.0981650 0.302121i 0.0981650 0.302121i
\(274\) 0 0
\(275\) −0.0172578 0.274306i −0.0172578 0.274306i
\(276\) 0 0
\(277\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(282\) 0 0
\(283\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.68978 3.68978
\(288\) 0 0
\(289\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(294\) 0 0
\(295\) −0.383650 + 1.18075i −0.383650 + 1.18075i
\(296\) 0 0
\(297\) −0.241353 0.0619689i −0.241353 0.0619689i
\(298\) 0 0
\(299\) 0 0
\(300\) 0.0279238 0.0202878i 0.0279238 0.0202878i
\(301\) 2.81343 + 2.04407i 2.81343 + 2.04407i
\(302\) 0 0
\(303\) 0.0680131 + 0.209323i 0.0680131 + 0.209323i
\(304\) 0 0
\(305\) −0.586660 + 0.426234i −0.586660 + 0.426234i
\(306\) 0 0
\(307\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(308\) −1.92189 0.493458i −1.92189 0.493458i
\(309\) 0 0
\(310\) 0 0
\(311\) −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i \(0.640000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(312\) 0 0
\(313\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(314\) 0 0
\(315\) 1.34543 + 0.977511i 1.34543 + 0.977511i
\(316\) 0 0
\(317\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.851559 −0.851559
\(321\) 0.0565777 0.174128i 0.0565777 0.174128i
\(322\) 0 0
\(323\) 0 0
\(324\) 0.294474 + 0.906297i 0.294474 + 0.906297i
\(325\) 0.108276 + 0.333240i 0.108276 + 0.333240i
\(326\) 0 0
\(327\) 0.188925 0.137262i 0.188925 0.137262i
\(328\) 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
\(336\) −0.0770013 0.236986i −0.0770013 0.236986i
\(337\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(338\) 0 0
\(339\) 0.0415873 0.127993i 0.0415873 0.127993i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −1.18779 + 3.65565i −1.18779 + 3.65565i
\(344\) 0 0
\(345\) 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
\(351\) 0.317669 0.317669
\(352\) 0 0
\(353\) −1.85955 −1.85955 −0.929776 0.368125i \(-0.880000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.500000 0.363271i −0.500000 0.363271i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(360\) 0 0
\(361\) 0.309017 0.951057i 0.309017 0.951057i
\(362\) 0 0
\(363\) 0.110048 + 0.0604991i 0.110048 + 0.0604991i
\(364\) 2.52959 2.52959
\(365\) 0 0
\(366\) 0 0
\(367\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(368\) 0 0
\(369\) 0.565571 + 1.74065i 0.565571 + 1.74065i
\(370\) 0 0
\(371\) −2.59739 + 1.88711i −2.59739 + 1.88711i
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0.136332 0.136332
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(384\) 0 0
\(385\) −1.07705 1.30193i −1.07705 1.30193i
\(386\) 0 0
\(387\) −0.533046 + 1.64055i −0.533046 + 1.64055i
\(388\) 0 0
\(389\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i
\(394\) 0 0
\(395\) 0 0
\(396\) −0.0618003 0.982287i −0.0618003 0.982287i
\(397\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.222357 + 0.161552i 0.222357 + 0.161552i
\(401\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −1.41789 + 1.03016i −1.41789 + 1.03016i
\(405\) −0.250762 + 0.771765i −0.250762 + 0.771765i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −0.893950 2.75129i −0.893950 2.75129i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0.0655712 0.201807i 0.0655712 0.201807i
\(421\) −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i \(0.640000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.522142 1.60699i 0.522142 1.60699i
\(428\) 1.45794 1.45794
\(429\) −0.155067 0.0398144i −0.155067 0.0398144i
\(430\) 0 0
\(431\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(432\) 0.201592 0.146465i 0.201592 0.146465i
\(433\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.50441 + 1.09302i 1.50441 + 1.09302i
\(437\) 0 0
\(438\) 0 0
\(439\) −0.374763 −0.374763 −0.187381 0.982287i \(-0.560000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(440\) 0 0
\(441\) −2.89085 −2.89085
\(442\) 0 0
\(443\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(444\) 0 0
\(445\) −0.162633 0.500534i −0.162633 0.500534i
\(446\) 0 0
\(447\) 0 0
\(448\) 1.60528 1.16630i 1.60528 1.16630i
\(449\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(450\) 0 0
\(451\) −0.116762 1.85588i −0.116762 1.85588i
\(452\) 1.07165 1.07165
\(453\) 0.0751750 0.231365i 0.0751750 0.231365i
\(454\) 0 0
\(455\) 1.74270 + 1.26615i 1.74270 + 1.26615i
\(456\) 0 0
\(457\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(458\) 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
\(467\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(468\) 0.387737 + 1.19333i 0.387737 + 1.19333i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.939097 1.47978i 0.939097 1.47978i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.28837 0.936058i −1.28837 0.936058i
\(478\) 0 0
\(479\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.187381 + 0.982287i −0.187381 + 0.982287i
\(485\) 0 0
\(486\) 0 0
\(487\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(492\) 0.188925 0.137262i 0.188925 0.137262i
\(493\) 0 0
\(494\) 0 0
\(495\) 0.449092 0.707656i 0.449092 0.707656i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(500\) 0.335471 + 1.03247i 0.335471 + 1.03247i
\(501\) −0.0627905 0.193249i −0.0627905 0.193249i
\(502\) 0 0
\(503\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(504\) 0 0
\(505\) −1.49245 −1.49245
\(506\) 0 0
\(507\) 0.0785180 0.0785180
\(508\) 0 0
\(509\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0.220095 0.220095
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(522\) 0 0
\(523\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(524\) −0.809017 0.587785i −0.809017 0.587785i
\(525\) −0.0554072 + 0.0402557i −0.0554072 + 0.0402557i
\(526\) 0 0
\(527\) 0 0
\(528\) −0.116762 + 0.0462295i −0.116762 + 0.0462295i
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 1.16089 0.843439i 1.16089 0.843439i
\(532\) 0 0
\(533\) 0.732570 + 2.25462i 0.732570 + 2.25462i
\(534\) 0 0
\(535\) 1.00441 + 0.729747i 1.00441 + 0.729747i
\(536\) 0 0
\(537\) −0.0145433 + 0.0447596i −0.0145433 + 0.0447596i
\(538\) 0 0
\(539\) 2.84489 + 0.730444i 2.84489 + 0.730444i
\(540\) 0.212193 0.212193
\(541\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.489334 + 1.50602i 0.489334 + 1.50602i
\(546\) 0 0
\(547\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(548\) 0 0
\(549\) 0.838129 0.838129
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(558\) 0 0
\(559\) −0.690441 + 2.12496i −0.690441 + 2.12496i
\(560\) 1.68969 1.68969
\(561\) 0 0
\(562\) 0 0
\(563\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(564\) 0 0
\(565\) 0.738289 + 0.536399i 0.738289 + 0.536399i
\(566\) 0 0
\(567\) −0.584303 1.79830i −0.584303 1.79830i
\(568\) 0 0
\(569\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) −0.0800484 1.27233i −0.0800484 1.27233i
\(573\) −0.160097 −0.160097
\(574\) 0 0
\(575\) 0 0
\(576\) 0.796258 + 0.578516i 0.796258 + 0.578516i
\(577\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(578\) 0 0
\(579\) 0.0380748 + 0.0276630i 0.0380748 + 0.0276630i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 1.03137 + 1.24672i 1.03137 + 1.24672i
\(584\) 0 0
\(585\) −0.330181 + 1.01619i −0.330181 + 1.01619i
\(586\) 0 0
\(587\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(588\) 0.113982 + 0.350799i 0.113982 + 0.350799i
\(589\) 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
\(599\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(600\) 0 0
\(601\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.93717 1.93717
\(605\) −0.620759 + 0.582932i −0.620759 + 0.582932i
\(606\) 0 0
\(607\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(614\) 0 0
\(615\) 0.198860 0.198860
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 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
\(623\) 0.992115 + 0.720814i 0.992115 + 0.720814i
\(624\) 0.129521 0.0941025i 0.129521 0.0941025i
\(625\) −0.200741 + 0.617816i −0.200741 + 0.617816i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(632\) 0 0
\(633\) 0.0415873 + 0.127993i 0.0415873 + 0.127993i
\(634\) 0 0
\(635\) 0 0
\(636\) −0.0627905 + 0.193249i −0.0627905 + 0.193249i
\(637\) −3.74444 −3.74444
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(642\) 0 0
\(643\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(644\) 0 0
\(645\) 0.151629 + 0.110165i 0.151629 + 0.110165i
\(646\) 0 0
\(647\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(648\) 0 0
\(649\) −1.35556 + 0.536702i −1.35556 + 0.536702i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(654\) 0 0
\(655\) −0.263146 0.809880i −0.263146 0.809880i
\(656\) 1.50441 + 1.09302i 1.50441 + 1.09302i
\(657\) 0 0
\(658\) 0 0
\(659\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(660\) −0.103580 0.0265948i −0.103580 0.0265948i
\(661\) 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
\(668\) 1.30902 0.951057i 1.30902 0.951057i
\(669\) 0 0
\(670\) 0 0
\(671\) −0.824805 0.211774i −0.824805 0.211774i
\(672\) 0 0
\(673\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(674\) 0 0
\(675\) −0.0554072 0.0402557i −0.0554072 0.0402557i
\(676\) 0.193209 + 0.594636i 0.193209 + 0.594636i
\(677\) 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
\(681\) 0 0
\(682\) 0 0
\(683\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0.541587 + 1.66683i 0.541587 + 1.66683i
\(689\) −1.66880 1.21245i −1.66880 1.21245i
\(690\) 0 0
\(691\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(692\) 0 0
\(693\) 0.122626 + 1.94908i 0.122626 + 1.94908i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −0.0145433 0.0447596i −0.0145433 0.0447596i
\(700\) −0.441207 0.320555i −0.441207 0.320555i
\(701\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.637424 0.770513i −0.637424 0.770513i
\(705\) 0 0
\(706\) 0 0
\(707\) 2.81343 2.04407i 2.81343 2.04407i
\(708\) −0.148122 0.107617i −0.148122 0.107617i
\(709\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0.581698 0.916609i 0.581698 0.916609i
\(716\) −0.374763 −0.374763
\(717\) −0.0145433 + 0.0447596i −0.0145433 + 0.0447596i
\(718\) 0 0
\(719\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(720\) 0.258996 + 0.797108i 0.258996 + 0.797108i
\(721\) 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
\(729\) 0.733468 0.532896i 0.733468 0.532896i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.0330462 0.101706i −0.0330462 0.101706i
\(733\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(734\) 0 0
\(735\) −0.0970621 + 0.298726i −0.0970621 + 0.298726i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2.89288 −2.89288
\(750\) 0 0
\(751\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.33456 + 0.969617i 1.33456 + 0.969617i
\(756\) −0.400005 + 0.290621i −0.400005 + 0.290621i
\(757\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(762\) 0 0
\(763\) −2.98509 2.16880i −2.98509 2.16880i
\(764\) −0.393950 1.21245i −0.393950 1.21245i
\(765\) 0 0
\(766\) 0 0
\(767\) 1.50368 1.09249i 1.50368 1.09249i
\(768\) 0.0388067 0.119435i 0.0388067 0.119435i
\(769\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.115808 + 0.356420i −0.115808 + 0.356420i
\(773\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0.136332 0.136332
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −2.37622 + 1.72642i −2.37622 + 1.72642i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(788\) 0 0
\(789\) −0.0127587 + 0.00926972i −0.0127587 + 0.00926972i
\(790\) 0 0
\(791\) −2.12641 −2.12641
\(792\) 0 0
\(793\) 1.08561 1.08561
\(794\) 0 0
\(795\) −0.139986 + 0.101706i −0.139986 + 0.101706i
\(796\) 0 0
\(797\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −0.187971 + 0.578516i −0.187971 + 0.578516i
\(802\) 0 0
\(803\) 0 0