Properties

Label 869.1.j.a.157.3
Level $869$
Weight $1$
Character 869.157
Analytic conductor $0.434$
Analytic rank $0$
Dimension $20$
Projective image $D_{25}$
CM discriminant -79
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 869 = 11 \cdot 79 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 869.j (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.433687495978\)
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 157.3
Root \(-0.968583 + 0.248690i\) of defining polynomial
Character \(\chi\) \(=\) 869.157
Dual form 869.1.j.a.631.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.101597 + 0.0738147i) q^{2} +(-0.304144 + 0.936058i) q^{4} +(-1.17950 - 0.856954i) q^{5} +(-0.0770013 - 0.236986i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.101597 + 0.0738147i) q^{2} +(-0.304144 + 0.936058i) q^{4} +(-1.17950 - 0.856954i) q^{5} +(-0.0770013 - 0.236986i) q^{8} +(-0.809017 + 0.587785i) q^{9} +0.183089 q^{10} +(0.0627905 - 0.998027i) q^{11} +(-1.56720 + 1.13864i) q^{13} +(-0.770942 - 0.560122i) q^{16} +(0.0388067 - 0.119435i) q^{18} +(-0.263146 - 0.809880i) q^{19} +(1.16089 - 0.843439i) q^{20} +(0.0672897 + 0.106032i) q^{22} -0.851559 q^{23} +(0.347824 + 1.07049i) q^{25} +(0.0751750 - 0.231365i) q^{26} +(-0.866986 + 0.629902i) q^{31} +0.368852 q^{32} +(-0.304144 - 0.936058i) q^{36} +(0.0865160 + 0.0628575i) q^{38} +(-0.112263 + 0.345510i) q^{40} +(0.915113 + 0.362319i) q^{44} +1.45794 q^{45} +(0.0865160 - 0.0628575i) q^{46} +(-0.809017 - 0.587785i) q^{49} +(-0.114356 - 0.0830844i) q^{50} +(-0.589177 - 1.81330i) q^{52} +(-0.929324 + 1.12336i) q^{55} +(0.0415873 - 0.127993i) q^{62} +(0.733468 - 0.532896i) q^{64} +2.82427 q^{65} +1.75261 q^{67} +(0.201592 + 0.146465i) q^{72} +(-0.613161 + 1.88711i) q^{73} +0.838129 q^{76} +(-0.809017 + 0.587785i) q^{79} +(0.429324 + 1.32132i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.30902 + 0.951057i) q^{83} +(-0.241353 + 0.0619689i) q^{88} -1.85955 q^{89} +(-0.148122 + 0.107617i) q^{90} +(0.258996 - 0.797108i) q^{92} +(-0.383650 + 1.18075i) q^{95} +(0.303189 - 0.220280i) q^{97} +0.125581 q^{98} +(0.535827 + 0.844328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} + 15q^{20} - 5q^{22} - 5q^{25} + 15q^{26} - 10q^{32} - 5q^{36} - 10q^{40} - 5q^{49} - 10q^{50} - 10q^{62} - 5q^{64} - 10q^{76} - 5q^{79} - 10q^{80} - 5q^{81} + 15q^{83} - 5q^{88} + 15q^{92} + 15q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/869\mathbb{Z}\right)^\times\).

\(n\) \(475\) \(793\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(3\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(4\) −0.304144 + 0.936058i −0.304144 + 0.936058i
\(5\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(6\) 0 0
\(7\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(8\) −0.0770013 0.236986i −0.0770013 0.236986i
\(9\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(10\) 0.183089 0.183089
\(11\) 0.0627905 0.998027i 0.0627905 0.998027i
\(12\) 0 0
\(13\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.770942 0.560122i −0.770942 0.560122i
\(17\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(18\) 0.0388067 0.119435i 0.0388067 0.119435i
\(19\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(20\) 1.16089 0.843439i 1.16089 0.843439i
\(21\) 0 0
\(22\) 0.0672897 + 0.106032i 0.0672897 + 0.106032i
\(23\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(24\) 0 0
\(25\) 0.347824 + 1.07049i 0.347824 + 1.07049i
\(26\) 0.0751750 0.231365i 0.0751750 0.231365i
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(30\) 0 0
\(31\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(32\) 0.368852 0.368852
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.304144 0.936058i −0.304144 0.936058i
\(37\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(38\) 0.0865160 + 0.0628575i 0.0865160 + 0.0628575i
\(39\) 0 0
\(40\) −0.112263 + 0.345510i −0.112263 + 0.345510i
\(41\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0.915113 + 0.362319i 0.915113 + 0.362319i
\(45\) 1.45794 1.45794
\(46\) 0.0865160 0.0628575i 0.0865160 0.0628575i
\(47\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(48\) 0 0
\(49\) −0.809017 0.587785i −0.809017 0.587785i
\(50\) −0.114356 0.0830844i −0.114356 0.0830844i
\(51\) 0 0
\(52\) −0.589177 1.81330i −0.589177 1.81330i
\(53\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(54\) 0 0
\(55\) −0.929324 + 1.12336i −0.929324 + 1.12336i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(60\) 0 0
\(61\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(62\) 0.0415873 0.127993i 0.0415873 0.127993i
\(63\) 0 0
\(64\) 0.733468 0.532896i 0.733468 0.532896i
\(65\) 2.82427 2.82427
\(66\) 0 0
\(67\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(72\) 0.201592 + 0.146465i 0.201592 + 0.146465i
\(73\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0.838129 0.838129
\(77\) 0 0
\(78\) 0 0
\(79\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(80\) 0.429324 + 1.32132i 0.429324 + 1.32132i
\(81\) 0.309017 0.951057i 0.309017 0.951057i
\(82\) 0 0
\(83\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −0.241353 + 0.0619689i −0.241353 + 0.0619689i
\(89\) −1.85955 −1.85955 −0.929776 0.368125i \(-0.880000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(90\) −0.148122 + 0.107617i −0.148122 + 0.107617i
\(91\) 0 0
\(92\) 0.258996 0.797108i 0.258996 0.797108i
\(93\) 0 0
\(94\) 0 0
\(95\) −0.383650 + 1.18075i −0.383650 + 1.18075i
\(96\) 0 0
\(97\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(98\) 0.125581 0.125581
\(99\) 0.535827 + 0.844328i 0.535827 + 0.844328i
\(100\) −1.10783 −1.10783
\(101\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(102\) 0 0
\(103\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(104\) 0.390518 + 0.283728i 0.390518 + 0.283728i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0.0114963 0.182728i 0.0114963 0.182728i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(114\) 0 0
\(115\) 1.00441 + 0.729747i 1.00441 + 0.729747i
\(116\) 0 0
\(117\) 0.598617 1.84235i 0.598617 1.84235i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.992115 0.125333i −0.992115 0.125333i
\(122\) 0 0
\(123\) 0 0
\(124\) −0.325937 1.00313i −0.325937 1.00313i
\(125\) 0.0565777 0.174128i 0.0565777 0.174128i
\(126\) 0 0
\(127\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(128\) −0.149164 + 0.459081i −0.149164 + 0.459081i
\(129\) 0 0
\(130\) −0.286938 + 0.208472i −0.286938 + 0.208472i
\(131\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.178061 + 0.129369i −0.178061 + 0.129369i
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(138\) 0 0
\(139\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.03799 + 1.63560i 1.03799 + 1.63560i
\(144\) 0.952937 0.952937
\(145\) 0 0
\(146\) −0.0770013 0.236986i −0.0770013 0.236986i
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(150\) 0 0
\(151\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(152\) −0.171668 + 0.124724i −0.171668 + 0.124724i
\(153\) 0 0
\(154\) 0 0
\(155\) 1.56240 1.56240
\(156\) 0 0
\(157\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(158\) 0.0388067 0.119435i 0.0388067 0.119435i
\(159\) 0 0
\(160\) −0.435060 0.316090i −0.435060 0.316090i
\(161\) 0 0
\(162\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i
\(163\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −0.203194 −0.203194
\(167\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(168\) 0 0
\(169\) 0.850604 2.61789i 0.850604 2.61789i
\(170\) 0 0
\(171\) 0.688925 + 0.500534i 0.688925 + 0.500534i
\(172\) 0 0
\(173\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.607425 + 0.734251i −0.607425 + 0.734251i
\(177\) 0 0
\(178\) 0.188925 0.137262i 0.188925 0.137262i
\(179\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(180\) −0.443422 + 1.36471i −0.443422 + 1.36471i
\(181\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.0655712 + 0.201807i 0.0655712 + 0.201807i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) −0.0481792 0.148280i −0.0481792 0.148280i
\(191\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(192\) 0 0
\(193\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(194\) −0.0145433 + 0.0447596i −0.0145433 + 0.0447596i
\(195\) 0 0
\(196\) 0.796258 0.578516i 0.796258 0.578516i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −0.116762 0.0462295i −0.116762 0.0462295i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0.226908 0.164859i 0.226908 0.164859i
\(201\) 0 0
\(202\) −0.0721631 + 0.222095i −0.0721631 + 0.222095i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.688925 0.500534i 0.688925 0.500534i
\(208\) 1.84600 1.84600
\(209\) −0.824805 + 0.211774i −0.824805 + 0.211774i
\(210\) 0 0
\(211\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −0.768882 1.21156i −0.768882 1.21156i
\(221\) 0 0
\(222\) 0 0
\(223\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(224\) 0 0
\(225\) −0.910614 0.661600i −0.910614 0.661600i
\(226\) 0 0
\(227\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(228\) 0 0
\(229\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(230\) −0.155911 −0.155911
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(234\) 0.0751750 + 0.231365i 0.0751750 + 0.231365i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(240\) 0 0
\(241\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(242\) 0.110048 0.0604991i 0.110048 0.0604991i
\(243\) 0 0
\(244\) 0 0
\(245\) 0.450527 + 1.38658i 0.450527 + 1.38658i
\(246\) 0 0
\(247\) 1.33456 + 0.969617i 1.33456 + 0.969617i
\(248\) 0.216037 + 0.156960i 0.216037 + 0.156960i
\(249\) 0 0
\(250\) 0.00710509 + 0.0218672i 0.00710509 + 0.0218672i
\(251\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(252\) 0 0
\(253\) −0.0534698 + 0.849878i −0.0534698 + 0.849878i
\(254\) 0 0
\(255\) 0 0
\(256\) 0.261428 + 0.804591i 0.261428 + 0.804591i
\(257\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.858983 + 2.64368i −0.858983 + 2.64368i
\(261\) 0 0
\(262\) 0.201592 0.146465i 0.201592 0.146465i
\(263\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −0.533046 + 1.64055i −0.533046 + 1.64055i
\(269\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(270\) 0 0
\(271\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.09022 0.279921i 1.09022 0.279921i
\(276\) 0 0
\(277\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(278\) 0 0
\(279\) 0.331159 1.01920i 0.331159 1.01920i
\(280\) 0 0
\(281\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(282\) 0 0
\(283\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −0.226188 0.0895542i −0.226188 0.0895542i
\(287\) 0 0
\(288\) −0.298408 + 0.216806i −0.298408 + 0.216806i
\(289\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(290\) 0 0
\(291\) 0 0
\(292\) −1.57996 1.14791i −1.57996 1.14791i
\(293\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.33456 0.969617i 1.33456 0.969617i
\(300\) 0 0
\(301\) 0 0
\(302\) −0.178061 0.129369i −0.178061 0.129369i
\(303\) 0 0
\(304\) −0.250762 + 0.771765i −0.250762 + 0.771765i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.158736 + 0.115328i −0.158736 + 0.115328i
\(311\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(312\) 0 0
\(313\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −0.304144 0.936058i −0.304144 0.936058i
\(317\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.32179 −1.32179
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.796258 + 0.578516i 0.796258 + 0.578516i
\(325\) −1.76401 1.28163i −1.76401 1.28163i
\(326\) −0.0494726 + 0.152261i −0.0494726 + 0.152261i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −1.28837 + 0.936058i −1.28837 + 0.936058i
\(333\) 0 0
\(334\) 0.0415873 0.127993i 0.0415873 0.127993i
\(335\) −2.06720 1.50191i −2.06720 1.50191i
\(336\) 0 0
\(337\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(338\) 0.106820 + 0.328757i 0.106820 + 0.328757i
\(339\) 0 0
\(340\) 0 0
\(341\) 0.574221 + 0.904827i 0.574221 + 0.904827i
\(342\) −0.106940 −0.106940
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.0231604 0.368125i 0.0231604 0.368125i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.565571 1.74065i 0.565571 1.74065i
\(357\) 0 0
\(358\) 0.164388 + 0.119435i 0.164388 + 0.119435i
\(359\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(360\) −0.112263 0.345510i −0.112263 0.345510i
\(361\) 0.222357 0.161552i 0.222357 0.161552i
\(362\) 0.243271 0.243271
\(363\) 0 0
\(364\) 0 0
\(365\) 2.34039 1.70039i 2.34039 1.70039i
\(366\) 0 0
\(367\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(368\) 0.656502 + 0.476977i 0.656502 + 0.476977i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(380\) −0.988570 0.718238i −0.988570 0.718238i
\(381\) 0 0
\(382\) 0 0
\(383\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0.113982 + 0.350799i 0.113982 + 0.350799i
\(389\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.0770013 + 0.236986i −0.0770013 + 0.236986i
\(393\) 0 0
\(394\) 0 0
\(395\) 1.45794 1.45794
\(396\) −0.953308 + 0.244768i −0.953308 + 0.244768i
\(397\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.331454 1.02011i 0.331454 1.02011i
\(401\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(402\) 0 0
\(403\) 0.641510 1.97437i 0.641510 1.97437i
\(404\) 0.565571 + 1.74065i 0.565571 + 1.74065i
\(405\) −1.17950 + 0.856954i −1.17950 + 0.856954i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −0.0330462 + 0.101706i −0.0330462 + 0.101706i
\(415\) −0.728969 2.24353i −0.728969 2.24353i
\(416\) −0.578066 + 0.419989i −0.578066 + 0.419989i
\(417\) 0 0
\(418\) 0.0681659 0.0823984i 0.0681659 0.0823984i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(432\) 0 0
\(433\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.224084 + 0.689661i 0.224084 + 0.689661i
\(438\) 0 0
\(439\) −0.374763 −0.374763 −0.187381 0.982287i \(-0.560000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(440\) 0.337780 + 0.133736i 0.337780 + 0.133736i
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(444\) 0 0
\(445\) 2.19334 + 1.59355i 2.19334 + 1.59355i
\(446\) 0.164388 + 0.119435i 0.164388 + 0.119435i
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(450\) 0.141352 0.141352
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −0.988570 + 0.718238i −0.988570 + 0.718238i
\(461\) 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
\(467\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(468\) 1.54248 + 1.12068i 1.54248 + 1.12068i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.775441 0.563391i 0.775441 0.563391i
\(476\) 0 0
\(477\) 0 0
\(478\) −0.148122 0.107617i −0.148122 0.107617i
\(479\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.129521 0.0941025i 0.129521 0.0941025i
\(483\) 0 0
\(484\) 0.419064 0.890557i 0.419064 0.890557i
\(485\) −0.546380 −0.546380
\(486\) 0 0
\(487\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −0.148122 0.107617i −0.148122 0.107617i
\(491\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −0.207160 −0.207160
\(495\) 0.0915446 1.45506i 0.0915446 1.45506i
\(496\) 1.02122 1.02122
\(497\) 0 0
\(498\) 0 0
\(499\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(500\) 0.145786 + 0.105920i 0.145786 + 0.105920i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(504\) 0 0
\(505\) −2.71111 −2.71111
\(506\) −0.0573011 0.0902921i −0.0573011 0.0902921i
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.476468 0.346175i −0.476468 0.346175i
\(513\) 0 0
\(514\) 0.0751750 + 0.231365i 0.0751750 + 0.231365i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −0.217472 0.669311i −0.217472 0.669311i
\(521\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(522\) 0 0
\(523\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(524\) 0.603491 1.85735i 0.603491 1.85735i
\(525\) 0 0
\(526\) 0.129521 0.0941025i 0.129521 0.0941025i
\(527\) 0 0
\(528\) 0 0
\(529\) −0.274848 −0.274848
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −0.134954 0.415344i −0.134954 0.415344i
\(537\) 0 0
\(538\) 0.220095 0.220095
\(539\) −0.637424 + 0.770513i −0.637424 + 0.770513i
\(540\) 0 0
\(541\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) −0.0901009 + 0.108913i −0.0901009 + 0.108913i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0.0565777 0.174128i 0.0565777 0.174128i
\(555\) 0 0
\(556\) 0 0
\(557\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(558\) 0.0415873 + 0.127993i 0.0415873 + 0.127993i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0.183089 0.183089
\(563\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −0.108877 0.0791038i −0.108877 0.0791038i
\(567\) 0 0
\(568\) 0 0
\(569\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(570\) 0 0
\(571\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(572\) −1.84672 + 0.474156i −1.84672 + 0.474156i
\(573\) 0 0
\(574\) 0 0
\(575\) −0.296192 0.911586i −0.296192 0.911586i
\(576\) −0.280160 + 0.862243i −0.280160 + 0.862243i
\(577\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(578\) −0.101597 0.0738147i −0.101597 0.0738147i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0.494433 0.494433
\(585\) −2.28488 + 1.66006i −2.28488 + 1.66006i
\(586\) 0 0
\(587\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(588\) 0 0
\(589\) 0.738289 + 0.536399i 0.738289 + 0.536399i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −0.0640159 + 0.197021i −0.0640159 + 0.197021i
\(599\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(600\) 0 0
\(601\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(602\) 0 0
\(603\) −1.41789 + 1.03016i −1.41789 + 1.03016i
\(604\) −1.72497 −1.72497
\(605\) 1.06279 + 0.998027i 1.06279 + 0.998027i
\(606\) 0 0
\(607\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(608\) −0.0970621 0.298726i −0.0970621 0.298726i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(618\) 0 0
\(619\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(620\) −0.475195 + 1.46250i −0.475195 + 1.46250i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.694661 0.504701i 0.694661 0.504701i
\(626\) 0.134579 0.134579
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(632\) 0.201592 + 0.146465i 0.201592 + 0.146465i
\(633\) 0 0
\(634\) 0.0239838 0.0738147i 0.0239838 0.0738147i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.93717 1.93717
\(638\) 0 0
\(639\) 0 0
\(640\) 0.569350 0.413657i 0.569350 0.413657i
\(641\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(642\) 0 0
\(643\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(648\) −0.249182 −0.249182
\(649\) 0 0
\(650\) 0.273822 0.273822
\(651\) 0 0
\(652\) 0.387737 + 1.19333i 0.387737 + 1.19333i
\(653\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(654\) 0 0
\(655\) 2.34039 + 1.70039i 2.34039 + 1.70039i
\(656\) 0 0
\(657\) −0.613161 1.88711i −0.613161 1.88711i
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.124591 0.383451i 0.124591 0.383451i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −0.325937 1.00313i −0.325937 1.00313i
\(669\) 0 0
\(670\) 0.320885 0.320885
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(674\) −0.0145433 0.0447596i −0.0145433 0.0447596i
\(675\) 0 0
\(676\) 2.19179 + 1.59243i 2.19179 + 1.59243i
\(677\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) −0.125129 0.0495420i −0.125129 0.0495420i
\(683\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(684\) −0.678061 + 0.492640i −0.678061 + 0.492640i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.220095 0.220095
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.485789 0.765481i −0.485789 0.765481i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(710\) 0 0
\(711\) 0.309017 0.951057i 0.309017 0.951057i
\(712\) 0.143188 + 0.440688i 0.143188 + 0.440688i
\(713\) 0.738289 0.536399i 0.738289 0.536399i
\(714\) 0 0
\(715\) 0.177337 2.81869i 0.177337 2.81869i
\(716\) 1.59252 1.59252
\(717\) 0 0
\(718\) 0 0
\(719\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(720\) −1.12399 0.816623i −1.12399 0.816623i
\(721\) 0 0
\(722\) −0.0106659 + 0.0328264i −0.0106659 + 0.0328264i
\(723\) 0 0
\(724\) 1.54248 1.12068i 1.54248 1.12068i
\(725\) 0 0
\(726\) 0 0
\(727\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(728\) 0 0
\(729\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(730\) −0.112263 + 0.345510i −0.112263 + 0.345510i
\(731\) 0 0
\(732\) 0 0
\(733\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(734\) −0.0721631 0.222095i −0.0721631 0.222095i
\(735\) 0 0
\(736\) −0.314099 −0.314099
\(737\) 0.110048 1.74915i 0.110048 1.74915i
\(738\) 0 0
\(739\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.61803 −1.61803
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0.789600 2.43014i 0.789600 2.43014i
\(756\) 0 0
\(757\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0.309364 0.309364
\(761\) 0.688925 0.500534i 0.688925 0.500534i −0.187381 0.982287i \(-0.560000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0.00487338 0.0149987i 0.00487338 0.0149987i
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(774\) 0 0
\(775\) −0.975863 0.709006i −0.975863 0.709006i
\(776\) −0.0755492 0.0548897i −0.0755492 0.0548897i
\(777\) 0 0
\(778\) 0.0415873 + 0.127993i 0.0415873 + 0.127993i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.294474 + 0.906297i 0.294474 + 0.906297i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.303189 + 0.220280i 0.303189 + 0.220280i 0.728969 0.684547i \(-0.240000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) −0.148122 + 0.107617i −0.148122 + 0.107617i
\(791\) 0 0
\(792\) 0.158834 0.191998i 0.158834 0.191998i
\(793\) 0 0
\(794\) 0.164388 0.119435i 0.164388 0.119435i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.128296 + 0.394853i 0.128296 + 0.394853i
\(801\) 1.50441 1.09302i 1.50441 1.09302i
\(802\) 0 0