Properties

Label 1441.1.u.a.785.5
Level $1441$
Weight $1$
Character 1441.785
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 785.5
Root \(0.425779 - 0.904827i\) of defining polynomial
Character \(\chi\) \(=\) 1441.785
Dual form 1441.1.u.a.916.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.541587 - 1.66683i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.50441 - 1.09302i) q^{5} +(0.331159 + 1.01920i) q^{7} +(-1.67600 - 1.21769i) q^{9} +O(q^{10})\) \(q+(0.541587 - 1.66683i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.50441 - 1.09302i) q^{5} +(0.331159 + 1.01920i) q^{7} +(-1.67600 - 1.21769i) q^{9} +(-0.187381 + 0.982287i) q^{11} +1.75261 q^{12} +(-1.17950 - 0.856954i) q^{13} +(-1.00711 - 3.09957i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.50441 + 1.09302i) q^{20} +1.87819 q^{21} +(0.759544 - 2.33764i) q^{25} +(-1.51949 + 1.10397i) q^{27} +(-0.866986 + 0.629902i) q^{28} +(1.53583 + 0.844328i) q^{33} +(1.61221 + 1.17134i) q^{35} +(0.640176 - 1.97026i) q^{36} +(-2.06720 + 1.50191i) q^{39} +(-0.613161 + 1.88711i) q^{41} -1.27485 q^{43} +(-0.992115 + 0.125333i) q^{44} -3.85235 q^{45} +(0.541587 + 1.66683i) q^{48} +(-0.120092 + 0.0872517i) q^{49} +(0.450527 - 1.38658i) q^{52} +(-0.500000 - 0.363271i) q^{53} +(0.791759 + 1.68257i) q^{55} +(0.598617 + 1.84235i) q^{59} +(2.63665 - 1.91564i) q^{60} +(1.50441 - 1.09302i) q^{61} +(0.686047 - 2.11144i) q^{63} +(-0.809017 - 0.587785i) q^{64} -2.71111 q^{65} +(-3.48509 - 2.53207i) q^{75} +(-1.06320 + 0.134314i) q^{77} +(-0.574633 + 1.76854i) q^{80} +(0.377030 + 1.16038i) q^{81} +(0.580394 + 1.78627i) q^{84} -1.61803 q^{89} +(0.482809 - 1.48593i) q^{91} +(1.51017 - 1.41814i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} - 5q^{25} + 20q^{33} + 15q^{35} - 5q^{36} - 10q^{39} - 10q^{45} - 5q^{49} - 10q^{53} - 10q^{63} - 5q^{64} - 10q^{75} - 5q^{81} - 10q^{89} + O(q^{100}) \)

Character values

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

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

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 \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(3\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(4\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(5\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(6\) 0 0
\(7\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(8\) 0 0
\(9\) −1.67600 1.21769i −1.67600 1.21769i
\(10\) 0 0
\(11\) −0.187381 + 0.982287i −0.187381 + 0.982287i
\(12\) 1.75261 1.75261
\(13\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(14\) 0 0
\(15\) −1.00711 3.09957i −1.00711 3.09957i
\(16\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(17\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(18\) 0 0
\(19\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(20\) 1.50441 + 1.09302i 1.50441 + 1.09302i
\(21\) 1.87819 1.87819
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 0.759544 2.33764i 0.759544 2.33764i
\(26\) 0 0
\(27\) −1.51949 + 1.10397i −1.51949 + 1.10397i
\(28\) −0.866986 + 0.629902i −0.866986 + 0.629902i
\(29\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(30\) 0 0
\(31\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(32\) 0 0
\(33\) 1.53583 + 0.844328i 1.53583 + 0.844328i
\(34\) 0 0
\(35\) 1.61221 + 1.17134i 1.61221 + 1.17134i
\(36\) 0.640176 1.97026i 0.640176 1.97026i
\(37\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(38\) 0 0
\(39\) −2.06720 + 1.50191i −2.06720 + 1.50191i
\(40\) 0 0
\(41\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(42\) 0 0
\(43\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(44\) −0.992115 + 0.125333i −0.992115 + 0.125333i
\(45\) −3.85235 −3.85235
\(46\) 0 0
\(47\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(48\) 0.541587 + 1.66683i 0.541587 + 1.66683i
\(49\) −0.120092 + 0.0872517i −0.120092 + 0.0872517i
\(50\) 0 0
\(51\) 0 0
\(52\) 0.450527 1.38658i 0.450527 1.38658i
\(53\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(54\) 0 0
\(55\) 0.791759 + 1.68257i 0.791759 + 1.68257i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(60\) 2.63665 1.91564i 2.63665 1.91564i
\(61\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(62\) 0 0
\(63\) 0.686047 2.11144i 0.686047 2.11144i
\(64\) −0.809017 0.587785i −0.809017 0.587785i
\(65\) −2.71111 −2.71111
\(66\) 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 \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(72\) 0 0
\(73\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(74\) 0 0
\(75\) −3.48509 2.53207i −3.48509 2.53207i
\(76\) 0 0
\(77\) −1.06320 + 0.134314i −1.06320 + 0.134314i
\(78\) 0 0
\(79\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(80\) −0.574633 + 1.76854i −0.574633 + 1.76854i
\(81\) 0.377030 + 1.16038i 0.377030 + 1.16038i
\(82\) 0 0
\(83\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(84\) 0.580394 + 1.78627i 0.580394 + 1.78627i
\(85\) 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
\(91\) 0.482809 1.48593i 0.482809 1.48593i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(98\) 0 0
\(99\) 1.51017 1.41814i 1.51017 1.41814i
\(100\) 2.45794 2.45794
\(101\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(102\) 0 0
\(103\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(104\) 0 0
\(105\) 2.82557 2.05290i 2.82557 2.05290i
\(106\) 0 0
\(107\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(108\) −1.51949 1.10397i −1.51949 1.10397i
\(109\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.866986 0.629902i −0.866986 0.629902i
\(113\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.933337 + 2.87251i 0.933337 + 2.87251i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.929776 0.368125i −0.929776 0.368125i
\(122\) 0 0
\(123\) 2.81343 + 2.04407i 2.81343 + 2.04407i
\(124\) 0 0
\(125\) −0.837780 2.57842i −0.837780 2.57842i
\(126\) 0 0
\(127\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(128\) 0 0
\(129\) −0.690441 + 2.12496i −0.690441 + 2.12496i
\(130\) 0 0
\(131\) 1.00000 1.00000
\(132\) −0.328407 + 1.72157i −0.328407 + 1.72157i
\(133\) 0 0
\(134\) 0 0
\(135\) −1.07927 + 3.32166i −1.07927 + 3.32166i
\(136\) 0 0
\(137\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(138\) 0 0
\(139\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(140\) −0.615808 + 1.89526i −0.615808 + 1.89526i
\(141\) 0 0
\(142\) 0 0
\(143\) 1.06279 0.998027i 1.06279 0.998027i
\(144\) 2.07165 2.07165
\(145\) 0 0
\(146\) 0 0
\(147\) 0.0803940 + 0.247427i 0.0803940 + 0.247427i
\(148\) 0 0
\(149\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(150\) 0 0
\(151\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −2.06720 1.50191i −2.06720 1.50191i
\(157\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(158\) 0 0
\(159\) −0.876307 + 0.636674i −0.876307 + 0.636674i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(164\) −1.98423 −1.98423
\(165\) 3.23338 0.408471i 3.23338 0.408471i
\(166\) 0 0
\(167\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(168\) 0 0
\(169\) 0.347824 + 1.07049i 0.347824 + 1.07049i
\(170\) 0 0
\(171\) 0 0
\(172\) −0.393950 1.21245i −0.393950 1.21245i
\(173\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(174\) 0 0
\(175\) 2.63406 2.63406
\(176\) −0.425779 0.904827i −0.425779 0.904827i
\(177\) 3.39510 3.39510
\(178\) 0 0
\(179\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(180\) −1.19044 3.66380i −1.19044 3.66380i
\(181\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(182\) 0 0
\(183\) −1.00711 3.09957i −1.00711 3.09957i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −1.62837 1.18308i −1.62837 1.18308i
\(190\) 0 0
\(191\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(192\) −1.41789 + 1.03016i −1.41789 + 1.03016i
\(193\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(194\) 0 0
\(195\) −1.46830 + 4.51897i −1.46830 + 4.51897i
\(196\) −0.120092 0.0872517i −0.120092 0.0872517i
\(197\) 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
\(205\) 1.14020 + 3.50919i 1.14020 + 3.50919i
\(206\) 0 0
\(207\) 0 0
\(208\) 1.45794 1.45794
\(209\) 0 0
\(210\) 0 0
\(211\) 0.303189 + 0.220280i 0.303189 + 0.220280i 0.728969 0.684547i \(-0.240000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(212\) 0.190983 0.587785i 0.190983 0.587785i
\(213\) 0 0
\(214\) 0 0
\(215\) −1.91789 + 1.39343i −1.91789 + 1.39343i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −1.35556 + 1.27295i −1.35556 + 1.27295i
\(221\) 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
\(225\) −4.11951 + 2.99300i −4.11951 + 2.99300i
\(226\) 0 0
\(227\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(228\) 0 0
\(229\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(230\) 0 0
\(231\) −0.351939 + 1.84493i −0.351939 + 1.84493i
\(232\) 0 0
\(233\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.56720 + 1.13864i −1.56720 + 1.13864i
\(237\) 0 0
\(238\) 0 0
\(239\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(240\) 2.63665 + 1.91564i 2.63665 + 1.91564i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 0.260160 0.260160
\(244\) 1.50441 + 1.09302i 1.50441 + 1.09302i
\(245\) −0.0852994 + 0.262525i −0.0852994 + 0.262525i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(252\) 2.22010 2.22010
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.309017 0.951057i 0.309017 0.951057i
\(257\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.837780 2.57842i −0.837780 2.57842i
\(261\) 0 0
\(262\) 0 0
\(263\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(264\) 0 0
\(265\) −1.14927 −1.14927
\(266\) 0 0
\(267\) −0.876307 + 2.69699i −0.876307 + 2.69699i
\(268\) 0 0
\(269\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(270\) 0 0
\(271\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(272\) 0 0
\(273\) −2.21532 1.60953i −2.21532 1.60953i
\(274\) 0 0
\(275\) 2.15391 + 1.18412i 2.15391 + 1.18412i
\(276\) 0 0
\(277\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(282\) 0 0
\(283\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.12641 −2.12641
\(288\) 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 \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(294\) 0 0
\(295\) 2.91429 + 2.11736i 2.91429 + 2.11736i
\(296\) 0 0
\(297\) −0.799696 1.69944i −0.799696 1.69944i
\(298\) 0 0
\(299\) 0 0
\(300\) 1.33119 4.09697i 1.33119 4.09697i
\(301\) −0.422178 1.29933i −0.422178 1.29933i
\(302\) 0 0
\(303\) 1.80760 1.31330i 1.80760 1.31330i
\(304\) 0 0
\(305\) 1.06856 3.28869i 1.06856 3.28869i
\(306\) 0 0
\(307\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(308\) −0.456288 0.969661i −0.456288 0.969661i
\(309\) 0 0
\(310\) 0 0
\(311\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(312\) 0 0
\(313\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(314\) 0 0
\(315\) −1.27574 3.92633i −1.27574 3.92633i
\(316\) 0 0
\(317\) 0.303189 + 0.220280i 0.303189 + 0.220280i 0.728969 0.684547i \(-0.240000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.85955 −1.85955
\(321\) −2.74670 1.99559i −2.74670 1.99559i
\(322\) 0 0
\(323\) 0 0
\(324\) −0.987078 + 0.717154i −0.987078 + 0.717154i
\(325\) −2.89913 + 2.10634i −2.89913 + 2.10634i
\(326\) 0 0
\(327\) −1.07463 + 3.30738i −1.07463 + 3.30738i
\(328\) 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
\(336\) −1.51949 + 1.10397i −1.51949 + 1.10397i
\(337\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(338\) 0 0
\(339\) 0.531374 + 0.386066i 0.531374 + 0.386066i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.738289 + 0.536399i 0.738289 + 0.536399i
\(344\) 0 0
\(345\) 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
\(351\) 2.73829 2.73829
\(352\) 0 0
\(353\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(354\) 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 \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(360\) 0 0
\(361\) −0.809017 0.587785i −0.809017 0.587785i
\(362\) 0 0
\(363\) −1.11716 + 1.35041i −1.11716 + 1.35041i
\(364\) 1.56240 1.56240
\(365\) 0 0
\(366\) 0 0
\(367\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(368\) 0 0
\(369\) 3.32557 2.41617i 3.32557 2.41617i
\(370\) 0 0
\(371\) 0.204668 0.629902i 0.204668 0.629902i
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) −4.75153 −4.75153
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(384\) 0 0
\(385\) −1.45269 + 1.36416i −1.45269 + 1.36416i
\(386\) 0 0
\(387\) 2.13665 + 1.55237i 2.13665 + 1.55237i
\(388\) 0 0
\(389\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0.541587 1.66683i 0.541587 1.66683i
\(394\) 0 0
\(395\) 0 0
\(396\) 1.81540 + 0.998027i 1.81540 + 0.998027i
\(397\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.759544 + 2.33764i 0.759544 + 2.33764i
\(401\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −0.393950 + 1.21245i −0.393950 + 1.21245i
\(405\) 1.83552 + 1.33359i 1.83552 + 1.33359i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.67950 + 1.22023i −1.67950 + 1.22023i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 2.82557 + 2.05290i 2.82557 + 2.05290i
\(421\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1.61221 + 1.17134i 1.61221 + 1.17134i
\(428\) 1.93717 1.93717
\(429\) −1.08795 2.31201i −1.08795 2.31201i
\(430\) 0 0
\(431\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(432\) 0.580394 1.78627i 0.580394 1.78627i
\(433\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.613161 1.88711i −0.613161 1.88711i
\(437\) 0 0
\(438\) 0 0
\(439\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(440\) 0 0
\(441\) 0.307519 0.307519
\(442\) 0 0
\(443\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(444\) 0 0
\(445\) −2.43419 + 1.76854i −2.43419 + 1.76854i
\(446\) 0 0
\(447\) 0 0
\(448\) 0.331159 1.01920i 0.331159 1.01920i
\(449\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(450\) 0 0
\(451\) −1.73879 0.955910i −1.73879 0.955910i
\(452\) −0.374763 −0.374763
\(453\) 1.20742 + 0.877242i 1.20742 + 0.877242i
\(454\) 0 0
\(455\) −0.897809 2.76317i −0.897809 2.76317i
\(456\) 0 0
\(457\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(458\) 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
\(467\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(468\) −2.44351 + 1.77531i −2.44351 + 1.77531i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.238883 1.25227i 0.238883 1.25227i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.395651 + 1.21769i 0.395651 + 1.21769i
\(478\) 0 0
\(479\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.0627905 0.998027i 0.0627905 0.998027i
\(485\) 0 0
\(486\) 0 0
\(487\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(492\) −1.07463 + 3.30738i −1.07463 + 3.30738i
\(493\) 0 0
\(494\) 0 0
\(495\) 0.721858 3.78411i 0.721858 3.78411i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(500\) 2.19334 1.59355i 2.19334 1.59355i
\(501\) −0.876307 + 0.636674i −0.876307 + 0.636674i
\(502\) 0 0
\(503\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(504\) 0 0
\(505\) 2.37065 2.37065
\(506\) 0 0
\(507\) 1.97271 1.97271
\(508\) 0 0
\(509\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) −2.23432 −2.23432
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(522\) 0 0
\(523\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(524\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(525\) 1.42657 4.39054i 1.42657 4.39054i
\(526\) 0 0
\(527\) 0 0
\(528\) −1.73879 + 0.219661i −1.73879 + 0.219661i
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 1.24013 3.81672i 1.24013 3.81672i
\(532\) 0 0
\(533\) 2.34039 1.70039i 2.34039 1.70039i
\(534\) 0 0
\(535\) −1.11316 3.42596i −1.11316 3.42596i
\(536\) 0 0
\(537\) −0.178061 0.129369i −0.178061 0.129369i
\(538\) 0 0
\(539\) −0.0632033 0.134314i −0.0632033 0.134314i
\(540\) −3.49260 −3.49260
\(541\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2.98509 + 2.16880i −2.98509 + 2.16880i
\(546\) 0 0
\(547\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(548\) 0 0
\(549\) −3.85235 −3.85235
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(558\) 0 0
\(559\) 1.50368 + 1.09249i 1.50368 + 1.09249i
\(560\) −1.99280 −1.99280
\(561\) 0 0
\(562\) 0 0
\(563\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(564\) 0 0
\(565\) 0.215351 + 0.662783i 0.215351 + 0.662783i
\(566\) 0 0
\(567\) −1.05781 + 0.768540i −1.05781 + 0.768540i
\(568\) 0 0
\(569\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 1.27760 + 0.702367i 1.27760 + 0.702367i
\(573\) 2.55520 2.55520
\(574\) 0 0
\(575\) 0 0
\(576\) 0.640176 + 1.97026i 0.640176 + 1.97026i
\(577\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(578\) 0 0
\(579\) 0.0680131 + 0.209323i 0.0680131 + 0.209323i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.450527 0.423073i 0.450527 0.423073i
\(584\) 0 0
\(585\) 4.54383 + 3.30129i 4.54383 + 3.30129i
\(586\) 0 0
\(587\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(588\) −0.210474 + 0.152918i −0.210474 + 0.152918i
\(589\) 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
\(599\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(600\) 0 0
\(601\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −0.851559 −0.851559
\(605\) −1.80113 + 0.462452i −1.80113 + 0.462452i
\(606\) 0 0
\(607\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(614\) 0 0
\(615\) 6.46676 6.46676
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 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
\(623\) −0.535827 1.64911i −0.535827 1.64911i
\(624\) 0.789600 2.43014i 0.789600 2.43014i
\(625\) −2.09011 1.51855i −2.09011 1.51855i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(632\) 0 0
\(633\) 0.531374 0.386066i 0.531374 0.386066i
\(634\) 0 0
\(635\) 0 0
\(636\) −0.876307 0.636674i −0.876307 0.636674i
\(637\) 0.216418 0.216418
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(642\) 0 0
\(643\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(644\) 0 0
\(645\) 1.28391 + 3.95148i 1.28391 + 3.95148i
\(646\) 0 0
\(647\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(648\) 0 0
\(649\) −1.92189 + 0.242791i −1.92189 + 0.242791i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(654\) 0 0
\(655\) 1.50441 1.09302i 1.50441 1.09302i
\(656\) −0.613161 1.88711i −0.613161 1.88711i
\(657\) 0 0
\(658\) 0 0
\(659\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(660\) 1.38765 + 2.94890i 1.38765 + 2.94890i
\(661\) 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
\(671\) 0.791759 + 1.68257i 0.791759 + 1.68257i
\(672\) 0 0
\(673\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(674\) 0 0
\(675\) 1.42657 + 4.39054i 1.42657 + 4.39054i
\(676\) −0.910614 + 0.661600i −0.910614 + 0.661600i
\(677\) 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
\(681\) 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
\(688\) 1.03137 0.749337i 1.03137 0.749337i
\(689\) 0.278441 + 0.856954i 0.278441 + 0.856954i
\(690\) 0 0
\(691\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(692\) 0 0
\(693\) 1.94548 + 1.06954i 1.94548 + 1.06954i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −0.178061 + 0.129369i −0.178061 + 0.129369i
\(700\) 0.813968 + 2.50514i 0.813968 + 2.50514i
\(701\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.728969 0.684547i 0.728969 0.684547i
\(705\) 0 0
\(706\) 0 0
\(707\) −0.422178 + 1.29933i −0.422178 + 1.29933i
\(708\) 1.04914 + 3.22894i 1.04914 + 3.22894i
\(709\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0.508012 2.66309i 0.508012 2.66309i
\(716\) 0.125581 0.125581
\(717\) −0.178061 0.129369i −0.178061 0.129369i
\(718\) 0 0
\(719\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(720\) 3.11662 2.26435i 3.11662 2.26435i
\(721\) 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
\(729\) −0.236131 + 0.726735i −0.236131 + 0.726735i
\(730\) 0 0
\(731\) 0 0
\(732\) 2.63665 1.91564i 2.63665 1.91564i
\(733\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(734\) 0 0
\(735\) 0.391388 + 0.284360i 0.391388 + 0.284360i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.07597 2.07597
\(750\) 0 0
\(751\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0.489334 + 1.50602i 0.489334 + 1.50602i
\(756\) 0.621981 1.91426i 0.621981 1.91426i
\(757\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(762\) 0 0
\(763\) −0.657096 2.02233i −0.657096 2.02233i
\(764\) −1.17950 + 0.856954i −1.17950 + 0.856954i
\(765\) 0 0
\(766\) 0 0
\(767\) 0.872746 2.68604i 0.872746 2.68604i
\(768\) −1.41789 1.03016i −1.41789 1.03016i
\(769\) −0.374763 −0.374763 −0.187381 0.982287i \(-0.560000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.101597 0.0738147i −0.101597 0.0738147i
\(773\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) −4.75153 −4.75153
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.0458709 0.141176i 0.0458709 0.141176i
\(785\) 0 0
\(786\) 0 0
\(787\) −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i \(0.640000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(788\) 0 0
\(789\) 0.949193 2.92132i 0.949193 2.92132i
\(790\) 0 0
\(791\) −0.401616 −0.401616
\(792\) 0 0
\(793\) −2.71111 −2.71111
\(794\) 0 0
\(795\) −0.622428 + 1.91564i −0.622428 + 1.91564i
\(796\) 0 0
\(797\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 2.71183 + 1.97026i 2.71183 + 1.97026i
\(802\) 0 0
\(803\) 0 0
\(804\) 0