Properties

Label 1441.1.u.a.654.5
Level $1441$
Weight $1$
Character 1441.654
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 654.5
Root \(-0.0627905 - 0.998027i\) of defining polynomial
Character \(\chi\) \(=\) 1441.654
Dual form 1441.1.u.a.130.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50441 + 1.09302i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.541587 - 1.66683i) q^{5} +(-1.17950 + 0.856954i) q^{7} +(0.759544 + 2.33764i) q^{9} +O(q^{10})\) \(q+(1.50441 + 1.09302i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.541587 - 1.66683i) q^{5} +(-1.17950 + 0.856954i) q^{7} +(0.759544 + 2.33764i) q^{9} +(0.968583 - 0.248690i) q^{11} -1.85955 q^{12} +(0.331159 + 1.01920i) q^{13} +(2.63665 - 1.91564i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.541587 + 1.66683i) q^{20} -2.71111 q^{21} +(-1.67600 - 1.21769i) q^{25} +(-0.837780 + 2.57842i) q^{27} +(0.450527 - 1.38658i) q^{28} +(1.72897 + 0.684547i) q^{33} +(0.789600 + 2.43014i) q^{35} +(-1.98851 - 1.44474i) q^{36} +(-0.615808 + 1.89526i) q^{39} +(1.03137 + 0.749337i) q^{41} -1.98423 q^{43} +(-0.637424 + 0.770513i) q^{44} +4.30781 q^{45} +(1.50441 - 1.09302i) q^{48} +(0.347824 - 1.07049i) q^{49} +(-0.866986 - 0.629902i) q^{52} +(-0.500000 - 1.53884i) q^{53} +(0.110048 - 1.74915i) q^{55} +(0.303189 - 0.220280i) q^{59} +(-1.00711 + 3.09957i) q^{60} +(0.541587 - 1.66683i) q^{61} +(-2.89913 - 2.10634i) q^{63} +(0.309017 + 0.951057i) q^{64} +1.87819 q^{65} +(-1.19044 - 3.66380i) q^{75} +(-0.929324 + 1.12336i) q^{77} +(-1.41789 - 1.03016i) q^{80} +(-2.09011 + 1.51855i) q^{81} +(2.19334 - 1.59355i) q^{84} +0.618034 q^{89} +(-1.26401 - 0.918358i) q^{91} +(1.31703 + 2.07531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} - 5q^{25} + 20q^{33} + 15q^{35} - 5q^{36} - 10q^{39} - 10q^{45} - 5q^{49} - 10q^{53} - 10q^{63} - 5q^{64} - 10q^{75} - 5q^{81} - 10q^{89} + O(q^{100}) \)

Character values

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

\(n\) \(133\) \(1311\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{5}\right)\)

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 \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(3\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(4\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(5\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(6\) 0 0
\(7\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(8\) 0 0
\(9\) 0.759544 + 2.33764i 0.759544 + 2.33764i
\(10\) 0 0
\(11\) 0.968583 0.248690i 0.968583 0.248690i
\(12\) −1.85955 −1.85955
\(13\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(14\) 0 0
\(15\) 2.63665 1.91564i 2.63665 1.91564i
\(16\) 0.309017 0.951057i 0.309017 0.951057i
\(17\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(18\) 0 0
\(19\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(20\) 0.541587 + 1.66683i 0.541587 + 1.66683i
\(21\) −2.71111 −2.71111
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) −1.67600 1.21769i −1.67600 1.21769i
\(26\) 0 0
\(27\) −0.837780 + 2.57842i −0.837780 + 2.57842i
\(28\) 0.450527 1.38658i 0.450527 1.38658i
\(29\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(30\) 0 0
\(31\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(32\) 0 0
\(33\) 1.72897 + 0.684547i 1.72897 + 0.684547i
\(34\) 0 0
\(35\) 0.789600 + 2.43014i 0.789600 + 2.43014i
\(36\) −1.98851 1.44474i −1.98851 1.44474i
\(37\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(38\) 0 0
\(39\) −0.615808 + 1.89526i −0.615808 + 1.89526i
\(40\) 0 0
\(41\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(42\) 0 0
\(43\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(44\) −0.637424 + 0.770513i −0.637424 + 0.770513i
\(45\) 4.30781 4.30781
\(46\) 0 0
\(47\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(48\) 1.50441 1.09302i 1.50441 1.09302i
\(49\) 0.347824 1.07049i 0.347824 1.07049i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.866986 0.629902i −0.866986 0.629902i
\(53\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(54\) 0 0
\(55\) 0.110048 1.74915i 0.110048 1.74915i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(60\) −1.00711 + 3.09957i −1.00711 + 3.09957i
\(61\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(62\) 0 0
\(63\) −2.89913 2.10634i −2.89913 2.10634i
\(64\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(65\) 1.87819 1.87819
\(66\) 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 \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(72\) 0 0
\(73\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(74\) 0 0
\(75\) −1.19044 3.66380i −1.19044 3.66380i
\(76\) 0 0
\(77\) −0.929324 + 1.12336i −0.929324 + 1.12336i
\(78\) 0 0
\(79\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(80\) −1.41789 1.03016i −1.41789 1.03016i
\(81\) −2.09011 + 1.51855i −2.09011 + 1.51855i
\(82\) 0 0
\(83\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(84\) 2.19334 1.59355i 2.19334 1.59355i
\(85\) 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
\(91\) −1.26401 0.918358i −1.26401 0.918358i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(98\) 0 0
\(99\) 1.31703 + 2.07531i 1.31703 + 2.07531i
\(100\) 2.07165 2.07165
\(101\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(102\) 0 0
\(103\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(104\) 0 0
\(105\) −1.46830 + 4.51897i −1.46830 + 4.51897i
\(106\) 0 0
\(107\) 0.303189 + 0.220280i 0.303189 + 0.220280i 0.728969 0.684547i \(-0.240000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(108\) −0.837780 2.57842i −0.837780 2.57842i
\(109\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.450527 + 1.38658i 0.450527 + 1.38658i
\(113\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −2.13100 + 1.54826i −2.13100 + 1.54826i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.876307 0.481754i 0.876307 0.481754i
\(122\) 0 0
\(123\) 0.732570 + 2.25462i 0.732570 + 2.25462i
\(124\) 0 0
\(125\) −1.51949 + 1.10397i −1.51949 + 1.10397i
\(126\) 0 0
\(127\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(128\) 0 0
\(129\) −2.98509 2.16880i −2.98509 2.16880i
\(130\) 0 0
\(131\) 1.00000 1.00000
\(132\) −1.80113 + 0.462452i −1.80113 + 0.462452i
\(133\) 0 0
\(134\) 0 0
\(135\) 3.84407 + 2.79288i 3.84407 + 2.79288i
\(136\) 0 0
\(137\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(138\) 0 0
\(139\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(140\) −2.06720 1.50191i −2.06720 1.50191i
\(141\) 0 0
\(142\) 0 0
\(143\) 0.574221 + 0.904827i 0.574221 + 0.904827i
\(144\) 2.45794 2.45794
\(145\) 0 0
\(146\) 0 0
\(147\) 1.69334 1.23028i 1.69334 1.23028i
\(148\) 0 0
\(149\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(150\) 0 0
\(151\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.615808 1.89526i −0.615808 1.89526i
\(157\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(158\) 0 0
\(159\) 0.929776 2.86156i 0.929776 2.86156i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(164\) −1.27485 −1.27485
\(165\) 2.07741 2.51116i 2.07741 2.51116i
\(166\) 0 0
\(167\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(168\) 0 0
\(169\) −0.120092 + 0.0872517i −0.120092 + 0.0872517i
\(170\) 0 0
\(171\) 0 0
\(172\) 1.60528 1.16630i 1.60528 1.16630i
\(173\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(174\) 0 0
\(175\) 3.02034 3.02034
\(176\) 0.0627905 0.998027i 0.0627905 0.998027i
\(177\) 0.696891 0.696891
\(178\) 0 0
\(179\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(180\) −3.48509 + 2.53207i −3.48509 + 2.53207i
\(181\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(182\) 0 0
\(183\) 2.63665 1.91564i 2.63665 1.91564i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −1.22143 3.75918i −1.22143 3.75918i
\(190\) 0 0
\(191\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(192\) −0.574633 + 1.76854i −0.574633 + 1.76854i
\(193\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(194\) 0 0
\(195\) 2.82557 + 2.05290i 2.82557 + 2.05290i
\(196\) 0.347824 + 1.07049i 0.347824 + 1.07049i
\(197\) 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
\(205\) 1.80760 1.31330i 1.80760 1.31330i
\(206\) 0 0
\(207\) 0 0
\(208\) 1.07165 1.07165
\(209\) 0 0
\(210\) 0 0
\(211\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(212\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(213\) 0 0
\(214\) 0 0
\(215\) −1.07463 + 3.30738i −1.07463 + 3.30738i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0.939097 + 1.47978i 0.939097 + 1.47978i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(224\) 0 0
\(225\) 1.57351 4.84277i 1.57351 4.84277i
\(226\) 0 0
\(227\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(228\) 0 0
\(229\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(230\) 0 0
\(231\) −2.62594 + 0.674226i −2.62594 + 0.674226i
\(232\) 0 0
\(233\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.115808 + 0.356420i −0.115808 + 0.356420i
\(237\) 0 0
\(238\) 0 0
\(239\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(240\) −1.00711 3.09957i −1.00711 3.09957i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) −2.09308 −2.09308
\(244\) 0.541587 + 1.66683i 0.541587 + 1.66683i
\(245\) −1.59595 1.15953i −1.59595 1.15953i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(252\) 3.58352 3.58352
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.809017 0.587785i
\(257\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −1.51949 + 1.10397i −1.51949 + 1.10397i
\(261\) 0 0
\(262\) 0 0
\(263\) −1.85955 −1.85955 −0.929776 0.368125i \(-0.880000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(264\) 0 0
\(265\) −2.83579 −2.83579
\(266\) 0 0
\(267\) 0.929776 + 0.675522i 0.929776 + 0.675522i
\(268\) 0 0
\(269\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(270\) 0 0
\(271\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(272\) 0 0
\(273\) −0.897809 2.76317i −0.897809 2.76317i
\(274\) 0 0
\(275\) −1.92617 0.762627i −1.92617 0.762627i
\(276\) 0 0
\(277\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(282\) 0 0
\(283\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.85865 −1.85865
\(288\) 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 \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(294\) 0 0
\(295\) −0.202967 0.624667i −0.202967 0.624667i
\(296\) 0 0
\(297\) −0.170232 + 2.70576i −0.170232 + 2.70576i
\(298\) 0 0
\(299\) 0 0
\(300\) 3.11662 + 2.26435i 3.11662 + 2.26435i
\(301\) 2.34039 1.70039i 2.34039 1.70039i
\(302\) 0 0
\(303\) 1.14020 3.50919i 1.14020 3.50919i
\(304\) 0 0
\(305\) −2.48502 1.80547i −2.48502 1.80547i
\(306\) 0 0
\(307\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(308\) 0.0915446 1.45506i 0.0915446 1.45506i
\(309\) 0 0
\(310\) 0 0
\(311\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(312\) 0 0
\(313\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(314\) 0 0
\(315\) −5.08105 + 3.69160i −5.08105 + 3.69160i
\(316\) 0 0
\(317\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.75261 1.75261
\(321\) 0.215351 + 0.662783i 0.215351 + 0.662783i
\(322\) 0 0
\(323\) 0 0
\(324\) 0.798351 2.45707i 0.798351 2.45707i
\(325\) 0.686047 2.11144i 0.686047 2.11144i
\(326\) 0 0
\(327\) −1.91789 1.39343i −1.91789 1.39343i
\(328\) 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
\(336\) −0.837780 + 2.57842i −0.837780 + 2.57842i
\(337\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(338\) 0 0
\(339\) −1.11316 3.42596i −1.11316 3.42596i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.0565777 + 0.174128i 0.0565777 + 0.174128i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(350\) 0 0
\(351\) −2.90537 −2.90537
\(352\) 0 0
\(353\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(354\) 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 \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(360\) 0 0
\(361\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(362\) 0 0
\(363\) 1.84489 + 0.233064i 1.84489 + 0.233064i
\(364\) 1.56240 1.56240
\(365\) 0 0
\(366\) 0 0
\(367\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(368\) 0 0
\(369\) −0.968304 + 2.98013i −0.968304 + 2.98013i
\(370\) 0 0
\(371\) 1.90846 + 1.38658i 1.90846 + 1.38658i
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) −3.49260 −3.49260
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(384\) 0 0
\(385\) 1.36914 + 2.15743i 1.36914 + 2.15743i
\(386\) 0 0
\(387\) −1.50711 4.63841i −1.50711 4.63841i
\(388\) 0 0
\(389\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 1.50441 + 1.09302i 1.50441 + 1.09302i
\(394\) 0 0
\(395\) 0 0
\(396\) −2.28533 0.904827i −2.28533 0.904827i
\(397\) −0.374763 −0.374763 −0.187381 0.982287i \(-0.560000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −1.67600 + 1.21769i −1.67600 + 1.21769i
\(401\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 1.60528 + 1.16630i 1.60528 + 1.16630i
\(405\) 1.39920 + 4.30630i 1.39920 + 4.30630i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −0.168841 + 0.519639i −0.168841 + 0.519639i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) −1.46830 4.51897i −1.46830 4.51897i
\(421\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.789600 + 2.43014i 0.789600 + 2.43014i
\(428\) −0.374763 −0.374763
\(429\) −0.125129 + 1.98886i −0.125129 + 1.98886i
\(430\) 0 0
\(431\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(432\) 2.19334 + 1.59355i 2.19334 + 1.59355i
\(433\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.03137 0.749337i 1.03137 0.749337i
\(437\) 0 0
\(438\) 0 0
\(439\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(440\) 0 0
\(441\) 2.76661 2.76661
\(442\) 0 0
\(443\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(444\) 0 0
\(445\) 0.334719 1.03016i 0.334719 1.03016i
\(446\) 0 0
\(447\) 0 0
\(448\) −1.17950 0.856954i −1.17950 0.856954i
\(449\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(450\) 0 0
\(451\) 1.18532 + 0.469303i 1.18532 + 0.469303i
\(452\) 1.93717 1.93717
\(453\) −0.0721631 0.222095i −0.0721631 0.222095i
\(454\) 0 0
\(455\) −2.21532 + 1.60953i −2.21532 + 1.60953i
\(456\) 0 0
\(457\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(458\) 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
\(467\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(468\) 0.813968 2.50514i 0.813968 2.50514i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.92189 + 0.493458i −1.92189 + 0.493458i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 3.21748 2.33764i 3.21748 2.33764i
\(478\) 0 0
\(479\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.425779 + 0.904827i −0.425779 + 0.904827i
\(485\) 0 0
\(486\) 0 0
\(487\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(492\) −1.91789 1.39343i −1.91789 1.39343i
\(493\) 0 0
\(494\) 0 0
\(495\) 4.17248 1.07131i 4.17248 1.07131i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(500\) 0.580394 1.78627i 0.580394 1.78627i
\(501\) 0.929776 2.86156i 0.929776 2.86156i
\(502\) 0 0
\(503\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(504\) 0 0
\(505\) −3.47759 −3.47759
\(506\) 0 0
\(507\) −0.276035 −0.276035
\(508\) 0 0
\(509\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 3.68978 3.68978
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(522\) 0 0
\(523\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(524\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(525\) 4.54383 + 3.30129i 4.54383 + 3.30129i
\(526\) 0 0
\(527\) 0 0
\(528\) 1.18532 1.43281i 1.18532 1.43281i
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 0.745220 + 0.541434i 0.745220 + 0.541434i
\(532\) 0 0
\(533\) −0.422178 + 1.29933i −0.422178 + 1.29933i
\(534\) 0 0
\(535\) 0.531374 0.386066i 0.531374 0.386066i
\(536\) 0 0
\(537\) 0.489334 + 1.50602i 0.489334 + 1.50602i
\(538\) 0 0
\(539\) 0.0706758 1.12336i 0.0706758 1.12336i
\(540\) −4.75153 −4.75153
\(541\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −0.690441 + 2.12496i −0.690441 + 2.12496i
\(546\) 0 0
\(547\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(548\) 0 0
\(549\) 4.30781 4.30781
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(558\) 0 0
\(559\) −0.657096 2.02233i −0.657096 2.02233i
\(560\) 2.55520 2.55520
\(561\) 0 0
\(562\) 0 0
\(563\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(564\) 0 0
\(565\) −2.74670 + 1.99559i −2.74670 + 1.99559i
\(566\) 0 0
\(567\) 1.16395 3.58226i 1.16395 3.58226i
\(568\) 0 0
\(569\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) −0.996398 0.394502i −0.996398 0.394502i
\(573\) −1.99280 −1.99280
\(574\) 0 0
\(575\) 0 0
\(576\) −1.98851 + 1.44474i −1.98851 + 1.44474i
\(577\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(578\) 0 0
\(579\) −1.28109 + 0.930769i −1.28109 + 0.930769i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −0.866986 1.36615i −0.866986 1.36615i
\(584\) 0 0
\(585\) 1.42657 + 4.39054i 1.42657 + 4.39054i
\(586\) 0 0
\(587\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(588\) −0.646797 + 1.99064i −0.646797 + 1.99064i
\(589\) 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
\(599\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(600\) 0 0
\(601\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.125581 0.125581
\(605\) −0.328407 1.72157i −0.328407 1.72157i
\(606\) 0 0
\(607\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(614\) 0 0
\(615\) 4.15483 4.15483
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −0.728969 + 0.529627i −0.728969 + 0.529627i
\(624\) 1.61221 + 1.17134i 1.61221 + 1.17134i
\(625\) 0.377030 + 1.16038i 0.377030 + 1.16038i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(632\) 0 0
\(633\) −1.11316 + 3.42596i −1.11316 + 3.42596i
\(634\) 0 0
\(635\) 0 0
\(636\) 0.929776 + 2.86156i 0.929776 + 2.86156i
\(637\) 1.20623 1.20623
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(642\) 0 0
\(643\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(644\) 0 0
\(645\) −5.23172 + 3.80106i −5.23172 + 3.80106i
\(646\) 0 0
\(647\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(648\) 0 0
\(649\) 0.238883 0.288760i 0.238883 0.288760i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(654\) 0 0
\(655\) 0.541587 1.66683i 0.541587 1.66683i
\(656\) 1.03137 0.749337i 1.03137 0.749337i
\(657\) 0 0
\(658\) 0 0
\(659\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(660\) −0.204639 + 3.25265i −0.204639 + 3.25265i
\(661\) 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
\(671\) 0.110048 1.74915i 0.110048 1.74915i
\(672\) 0 0
\(673\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(674\) 0 0
\(675\) 4.54383 3.30129i 4.54383 3.30129i
\(676\) 0.0458709 0.141176i 0.0458709 0.141176i
\(677\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(678\) 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
\(688\) −0.613161 + 1.88711i −0.613161 + 1.88711i
\(689\) 1.40281 1.01920i 1.40281 1.01920i
\(690\) 0 0
\(691\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(692\) 0 0
\(693\) −3.33187 1.31918i −3.33187 1.31918i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0.489334 1.50602i 0.489334 1.50602i
\(700\) −2.44351 + 1.77531i −2.44351 + 1.77531i
\(701\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.535827 + 0.844328i 0.535827 + 0.844328i
\(705\) 0 0
\(706\) 0 0
\(707\) 2.34039 + 1.70039i 2.34039 + 1.70039i
\(708\) −0.563797 + 0.409622i −0.563797 + 0.409622i
\(709\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 1.81919 0.467088i 1.81919 0.467088i
\(716\) −0.851559 −0.851559
\(717\) 0.489334 + 1.50602i 0.489334 + 1.50602i
\(718\) 0 0
\(719\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(720\) 1.33119 4.09697i 1.33119 4.09697i
\(721\) 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
\(729\) −1.05874 0.769217i −1.05874 0.769217i
\(730\) 0 0
\(731\) 0 0
\(732\) −1.00711 + 3.09957i −1.00711 + 3.09957i
\(733\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(734\) 0 0
\(735\) −1.13358 3.48881i −1.13358 3.48881i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −0.546380 −0.546380
\(750\) 0 0
\(751\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.178061 + 0.129369i −0.178061 + 0.129369i
\(756\) 3.19775 + 2.32330i 3.19775 + 2.32330i
\(757\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(762\) 0 0
\(763\) 1.50368 1.09249i 1.50368 1.09249i
\(764\) 0.331159 1.01920i 0.331159 1.01920i
\(765\) 0 0
\(766\) 0 0
\(767\) 0.324914 + 0.236064i 0.324914 + 0.236064i
\(768\) −0.574633 1.76854i −0.574633 1.76854i
\(769\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.263146 0.809880i −0.263146 0.809880i
\(773\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) −3.49260 −3.49260
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.910614 0.661600i −0.910614 0.661600i
\(785\) 0 0
\(786\) 0 0
\(787\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(788\) 0 0
\(789\) −2.79753 2.03252i −2.79753 2.03252i
\(790\) 0 0
\(791\) 2.82427 2.82427
\(792\) 0 0
\(793\) 1.87819 1.87819
\(794\) 0 0
\(795\) −4.26619 3.09957i −4.26619 3.09957i
\(796\) 0 0
\(797\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0.469424 + 1.44474i 0.469424 + 1.44474i
\(802\) 0 0
\(803\) 0 0
\(804\) 0