Properties

Label 869.1.j.a.157.2
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 157.2
Root \(0.637424 - 0.770513i\) of defining polynomial
Character \(\chi\) \(=\) 869.157
Dual form 869.1.j.a.631.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866986 + 0.629902i) q^{2} +(0.0458709 - 0.141176i) q^{4} +(-1.41789 - 1.03016i) q^{5} +(-0.282001 - 0.867911i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.866986 + 0.629902i) q^{2} +(0.0458709 - 0.141176i) q^{4} +(-1.41789 - 1.03016i) q^{5} +(-0.282001 - 0.867911i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.87819 q^{10} +(0.535827 + 0.844328i) q^{11} +(1.03137 - 0.749337i) q^{13} +(0.911282 + 0.662085i) q^{16} +(0.331159 - 1.01920i) q^{18} +(0.450527 + 1.38658i) q^{19} +(-0.210474 + 0.152918i) q^{20} +(-0.996398 - 0.394502i) q^{22} +1.45794 q^{23} +(0.640176 + 1.97026i) q^{25} +(-0.422178 + 1.29933i) q^{26} +(1.50441 - 1.09302i) q^{31} -0.294542 q^{32} +(0.0458709 + 0.141176i) q^{36} +(-1.26401 - 0.918358i) q^{38} +(-0.494239 + 1.52111i) q^{40} +(0.143778 - 0.0369159i) q^{44} +1.75261 q^{45} +(-1.26401 + 0.918358i) q^{46} +(-0.809017 - 0.587785i) q^{49} +(-1.79609 - 1.30494i) q^{50} +(-0.0584785 - 0.179978i) q^{52} +(0.110048 - 1.74915i) q^{55} +(-0.615808 + 1.89526i) q^{62} +(-0.655918 + 0.476553i) q^{64} -2.23432 q^{65} -0.374763 q^{67} +(0.738289 + 0.536399i) q^{72} +(-0.263146 + 0.809880i) q^{73} +0.216418 q^{76} +(-0.809017 + 0.587785i) q^{79} +(-0.610048 - 1.87753i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.30902 + 0.951057i) q^{83} +(0.581698 - 0.703152i) q^{88} +1.93717 q^{89} +(-1.51949 + 1.10397i) q^{90} +(0.0668769 - 0.205826i) q^{92} +(0.789600 - 2.43014i) q^{95} +(1.60528 - 1.16630i) q^{97} +1.07165 q^{98} +(-0.929776 - 0.368125i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} + 15q^{20} - 5q^{22} - 5q^{25} + 15q^{26} - 10q^{32} - 5q^{36} - 10q^{40} - 5q^{49} - 10q^{50} - 10q^{62} - 5q^{64} - 10q^{76} - 5q^{79} - 10q^{80} - 5q^{81} + 15q^{83} - 5q^{88} + 15q^{92} + 15q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(3\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(4\) 0.0458709 0.141176i 0.0458709 0.141176i
\(5\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(6\) 0 0
\(7\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(8\) −0.282001 0.867911i −0.282001 0.867911i
\(9\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(10\) 1.87819 1.87819
\(11\) 0.535827 + 0.844328i 0.535827 + 0.844328i
\(12\) 0 0
\(13\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.911282 + 0.662085i 0.911282 + 0.662085i
\(17\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(18\) 0.331159 1.01920i 0.331159 1.01920i
\(19\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(20\) −0.210474 + 0.152918i −0.210474 + 0.152918i
\(21\) 0 0
\(22\) −0.996398 0.394502i −0.996398 0.394502i
\(23\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(24\) 0 0
\(25\) 0.640176 + 1.97026i 0.640176 + 1.97026i
\(26\) −0.422178 + 1.29933i −0.422178 + 1.29933i
\(27\) 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
\(31\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(32\) −0.294542 −0.294542
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.0458709 + 0.141176i 0.0458709 + 0.141176i
\(37\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(38\) −1.26401 0.918358i −1.26401 0.918358i
\(39\) 0 0
\(40\) −0.494239 + 1.52111i −0.494239 + 1.52111i
\(41\) 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 \(\pi\)
\(44\) 0.143778 0.0369159i 0.143778 0.0369159i
\(45\) 1.75261 1.75261
\(46\) −1.26401 + 0.918358i −1.26401 + 0.918358i
\(47\) 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
\(50\) −1.79609 1.30494i −1.79609 1.30494i
\(51\) 0 0
\(52\) −0.0584785 0.179978i −0.0584785 0.179978i
\(53\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(54\) 0 0
\(55\) 0.110048 1.74915i 0.110048 1.74915i
\(56\) 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 \(0.200000\pi\)
\(62\) −0.615808 + 1.89526i −0.615808 + 1.89526i
\(63\) 0 0
\(64\) −0.655918 + 0.476553i −0.655918 + 0.476553i
\(65\) −2.23432 −2.23432
\(66\) 0 0
\(67\) −0.374763 −0.374763 −0.187381 0.982287i \(-0.560000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(72\) 0.738289 + 0.536399i 0.738289 + 0.536399i
\(73\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0.216418 0.216418
\(77\) 0 0
\(78\) 0 0
\(79\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(80\) −0.610048 1.87753i −0.610048 1.87753i
\(81\) 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
\(88\) 0.581698 0.703152i 0.581698 0.703152i
\(89\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(90\) −1.51949 + 1.10397i −1.51949 + 1.10397i
\(91\) 0 0
\(92\) 0.0668769 0.205826i 0.0668769 0.205826i
\(93\) 0 0
\(94\) 0 0
\(95\) 0.789600 2.43014i 0.789600 2.43014i
\(96\) 0 0
\(97\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(98\) 1.07165 1.07165
\(99\) −0.929776 0.368125i −0.929776 0.368125i
\(100\) 0.307519 0.307519
\(101\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(102\) 0 0
\(103\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(104\) −0.941207 0.683827i −0.941207 0.683827i
\(105\) 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 \(\pi\)
\(110\) 1.00639 + 1.58581i 1.00639 + 1.58581i
\(111\) 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
\(115\) −2.06720 1.50191i −2.06720 1.50191i
\(116\) 0 0
\(117\) −0.393950 + 1.21245i −0.393950 + 1.21245i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.425779 + 0.904827i −0.425779 + 0.904827i
\(122\) 0 0
\(123\) 0 0
\(124\) −0.0852994 0.262525i −0.0852994 0.262525i
\(125\) 0.580394 1.78627i 0.580394 1.78627i
\(126\) 0 0
\(127\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(128\) 0.359509 1.10645i 0.359509 1.10645i
\(129\) 0 0
\(130\) 1.93712 1.40740i 1.93712 1.40740i
\(131\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.324914 0.236064i 0.324914 0.236064i
\(135\) 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
\(143\) 1.18532 + 0.469303i 1.18532 + 0.469303i
\(144\) −1.12641 −1.12641
\(145\) 0 0
\(146\) −0.282001 0.867911i −0.282001 0.867911i
\(147\) 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
\(151\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(152\) 1.07638 0.782036i 1.07638 0.782036i
\(153\) 0 0
\(154\) 0 0
\(155\) −3.25908 −3.25908
\(156\) 0 0
\(157\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(158\) 0.331159 1.01920i 0.331159 1.01920i
\(159\) 0 0
\(160\) 0.417629 + 0.303425i 0.417629 + 0.303425i
\(161\) 0 0
\(162\) 0.331159 + 1.01920i 0.331159 + 1.01920i
\(163\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −1.73397 −1.73397
\(167\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(168\) 0 0
\(169\) 0.193209 0.594636i 0.193209 0.594636i
\(170\) 0 0
\(171\) −1.17950 0.856954i −1.17950 0.856954i
\(172\) 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
\(176\) −0.0707277 + 1.12418i −0.0707277 + 1.12418i
\(177\) 0 0
\(178\) −1.67950 + 1.22023i −1.67950 + 1.22023i
\(179\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(180\) 0.0803940 0.247427i 0.0803940 0.247427i
\(181\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.411140 1.26536i −0.411140 1.26536i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0.846178 + 2.60427i 0.846178 + 2.60427i
\(191\) 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 \(0.200000\pi\)
\(194\) −0.657096 + 2.02233i −0.657096 + 2.02233i
\(195\) 0 0
\(196\) −0.120092 + 0.0872517i −0.120092 + 0.0872517i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 1.03799 0.266509i 1.03799 0.266509i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 1.52948 1.11123i 1.52948 1.11123i
\(201\) 0 0
\(202\) 0.641510 1.97437i 0.641510 1.97437i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.17950 + 0.856954i −1.17950 + 0.856954i
\(208\) 1.43600 1.43600
\(209\) −0.929324 + 1.12336i −0.929324 + 1.12336i
\(210\) 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
\(220\) −0.241891 0.0957714i −0.241891 0.0957714i
\(221\) 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
\(225\) −1.67600 1.21769i −1.67600 1.21769i
\(226\) 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 \(0.800000\pi\)
\(230\) 2.73829 2.73829
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(234\) −0.422178 1.29933i −0.422178 1.29933i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(240\) 0 0
\(241\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(242\) −0.200808 1.05267i −0.200808 1.05267i
\(243\) 0 0
\(244\) 0 0
\(245\) 0.541587 + 1.66683i 0.541587 + 1.66683i
\(246\) 0 0
\(247\) 1.50368 + 1.09249i 1.50368 + 1.09249i
\(248\) −1.37289 0.997462i −1.37289 0.997462i
\(249\) 0 0
\(250\) 0.621981 + 1.91426i 0.621981 + 1.91426i
\(251\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(252\) 0 0
\(253\) 0.781202 + 1.23098i 0.781202 + 1.23098i
\(254\) 0 0
\(255\) 0 0
\(256\) 0.134731 + 0.414658i 0.134731 + 0.414658i
\(257\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.102490 + 0.315432i −0.102490 + 0.315432i
\(261\) 0 0
\(262\) 0.738289 0.536399i 0.738289 0.536399i
\(263\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −0.0171907 + 0.0529076i −0.0171907 + 0.0529076i
\(269\) 0.303189 + 0.220280i 0.303189 + 0.220280i 0.728969 0.684547i \(-0.240000\pi\)
−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
\(275\) −1.32052 + 1.59624i −1.32052 + 1.59624i
\(276\) 0 0
\(277\) −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i \(0.640000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(278\) 0 0
\(279\) −0.574633 + 1.76854i −0.574633 + 1.76854i
\(280\) 0 0
\(281\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(282\) 0 0
\(283\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −1.32327 + 0.339759i −1.32327 + 0.339759i
\(287\) 0 0
\(288\) 0.238289 0.173127i 0.238289 0.173127i
\(289\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(290\) 0 0
\(291\) 0 0
\(292\) 0.102265 + 0.0742999i 0.102265 + 0.0742999i
\(293\) 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
\(299\) 1.50368 1.09249i 1.50368 1.09249i
\(300\) 0 0
\(301\) 0 0
\(302\) 0.324914 + 0.236064i 0.324914 + 0.236064i
\(303\) 0 0
\(304\) −0.507477 + 1.56185i −0.507477 + 1.56185i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 2.82557 2.05290i 2.82557 2.05290i
\(311\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(312\) 0 0
\(313\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.0458709 + 0.141176i 0.0458709 + 0.141176i
\(317\) −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
\(320\) 1.42095 1.42095
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.120092 0.0872517i −0.120092 0.0872517i
\(325\) 2.13665 + 1.55237i 2.13665 + 1.55237i
\(326\) 0.0415873 0.127993i 0.0415873 0.127993i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0.194312 0.141176i 0.194312 0.141176i
\(333\) 0 0
\(334\) −0.615808 + 1.89526i −0.615808 + 1.89526i
\(335\) 0.531374 + 0.386066i 0.531374 + 0.386066i
\(336\) 0 0
\(337\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(338\) 0.207053 + 0.637244i 0.207053 + 0.637244i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.72897 + 0.684547i 1.72897 + 0.684547i
\(342\) 1.56240 1.56240
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0.303189 + 0.220280i 0.303189 + 0.220280i 0.728969 0.684547i \(-0.240000\pi\)
−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
\(352\) −0.157823 0.248690i −0.157823 0.248690i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.0888596 0.273482i 0.0888596 0.273482i
\(357\) 0 0
\(358\) 1.40281 + 1.01920i 1.40281 + 1.01920i
\(359\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(360\) −0.494239 1.52111i −0.494239 1.52111i
\(361\) −0.910614 + 0.661600i −0.910614 + 0.661600i
\(362\) −1.36620 −1.36620
\(363\) 0 0
\(364\) 0 0
\(365\) 1.20742 0.877242i 1.20742 0.877242i
\(366\) 0 0
\(367\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(368\) 1.32859 + 0.965279i 1.32859 + 0.965279i
\(369\) 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 \(0.200000\pi\)
\(380\) −0.306858 0.222946i −0.306858 0.222946i
\(381\) 0 0
\(382\) 0 0
\(383\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −0.0910184 0.280126i −0.0910184 0.280126i
\(389\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.282001 + 0.867911i −0.282001 + 0.867911i
\(393\) 0 0
\(394\) 0 0
\(395\) 1.75261 1.75261
\(396\) −0.0946201 + 0.114376i −0.0946201 + 0.114376i
\(397\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.721099 + 2.21931i −0.721099 + 2.21931i
\(401\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(402\) 0 0
\(403\) 0.732570 2.25462i 0.732570 2.25462i
\(404\) 0.0888596 + 0.273482i 0.0888596 + 0.273482i
\(405\) −1.41789 + 1.03016i −1.41789 + 1.03016i
\(406\) 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
\(414\) 0.482809 1.48593i 0.482809 1.48593i
\(415\) −0.876307 2.69699i −0.876307 2.69699i
\(416\) −0.303783 + 0.220711i −0.303783 + 0.220711i
\(417\) 0 0
\(418\) 0.0981041 1.55932i 0.0981041 1.55932i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(422\) 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
\(431\) 0.688925 0.500534i 0.688925 0.500534i −0.187381 0.982287i \(-0.560000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(432\) 0 0
\(433\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.656841 + 2.02155i 0.656841 + 2.02155i
\(438\) 0 0
\(439\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(440\) −1.54914 + 0.397753i −1.54914 + 0.397753i
\(441\) 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
\(445\) −2.74670 1.99559i −2.74670 1.99559i
\(446\) 1.40281 + 1.01920i 1.40281 + 1.01920i
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(450\) 2.22010 2.22010
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −0.306858 + 0.222946i −0.306858 + 0.222946i
\(461\) 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 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(468\) 0.153099 + 0.111233i 0.153099 + 0.111233i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −2.44351 + 1.77531i −2.44351 + 1.77531i
\(476\) 0 0
\(477\) 0 0
\(478\) −1.51949 1.10397i −1.51949 1.10397i
\(479\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.108877 + 0.0791038i −0.108877 + 0.0791038i
\(483\) 0 0
\(484\) 0.108209 + 0.101615i 0.108209 + 0.101615i
\(485\) −3.47759 −3.47759
\(486\) 0 0
\(487\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −1.51949 1.10397i −1.51949 1.10397i
\(491\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −1.99183 −1.99183
\(495\) 0.939097 + 1.47978i 0.939097 + 1.47978i
\(496\) 2.09461 2.09461
\(497\) 0 0
\(498\) 0 0
\(499\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(500\) −0.225555 0.163876i −0.225555 0.163876i
\(501\) 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
\(505\) 3.39510 3.39510
\(506\) −1.45269 0.575159i −1.45269 0.575159i
\(507\) 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
\(512\) 0.563203 + 0.409191i 0.563203 + 0.409191i
\(513\) 0 0
\(514\) −0.422178 1.29933i −0.422178 1.29933i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0.630080 + 1.93919i 0.630080 + 1.93919i
\(521\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(522\) 0 0
\(523\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(524\) −0.0390618 + 0.120220i −0.0390618 + 0.120220i
\(525\) 0 0
\(526\) −0.108877 + 0.0791038i −0.108877 + 0.0791038i
\(527\) 0 0
\(528\) 0 0
\(529\) 1.12558 1.12558
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0.105684 + 0.325261i 0.105684 + 0.325261i
\(537\) 0 0
\(538\) −0.401616 −0.401616
\(539\) 0.0627905 0.998027i 0.0627905 0.998027i
\(540\) 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
\(547\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0.139401 2.21571i 0.139401 2.21571i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0.580394 1.78627i 0.580394 1.78627i
\(555\) 0 0
\(556\) 0 0
\(557\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(558\) −0.615808 1.89526i −0.615808 1.89526i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 1.87819 1.87819
\(563\) −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
\(566\) 1.61221 + 1.17134i 1.61221 + 1.17134i
\(567\) 0 0
\(568\) 0 0
\(569\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(570\) 0 0
\(571\) −1.85955 −1.85955 −0.929776 0.368125i \(-0.880000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(572\) 0.120626 0.145812i 0.120626 0.145812i
\(573\) 0 0
\(574\) 0 0
\(575\) 0.933337 + 2.87251i 0.933337 + 2.87251i
\(576\) 0.250539 0.771078i 0.250539 0.771078i
\(577\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(578\) −0.866986 0.629902i −0.866986 0.629902i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0.777112 0.777112
\(585\) 1.80760 1.31330i 1.80760 1.31330i
\(586\) 0 0
\(587\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(588\) 0 0
\(589\) 2.19334 + 1.59355i 2.19334 + 1.59355i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −0.615508 + 1.89434i −0.615508 + 1.89434i
\(599\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(600\) 0 0
\(601\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(602\) 0 0
\(603\) 0.303189 0.220280i 0.303189 0.220280i
\(604\) −0.0556303 −0.0556303
\(605\) 1.53583 0.844328i 1.53583 0.844328i
\(606\) 0 0
\(607\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(608\) −0.132699 0.408406i −0.132699 0.408406i
\(609\) 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
\(617\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(618\) 0 0
\(619\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(620\) −0.149497 + 0.460104i −0.149497 + 0.460104i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.987078 + 0.717154i −0.987078 + 0.717154i
\(626\) −1.99280 −1.99280
\(627\) 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 \(0.600000\pi\)
\(632\) 0.738289 + 0.536399i 0.738289 + 0.536399i
\(633\) 0 0
\(634\) 0.204668 0.629902i 0.204668 0.629902i
\(635\) 0 0
\(636\) 0 0
\(637\) −1.27485 −1.27485
\(638\) 0 0
\(639\) 0 0
\(640\) −1.64957 + 1.19848i −1.64957 + 1.19848i
\(641\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(642\) 0 0
\(643\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(648\) −0.912576 −0.912576
\(649\) 0 0
\(650\) −2.83028 −2.83028
\(651\) 0 0
\(652\) 0.00576052 + 0.0177291i 0.00576052 + 0.0177291i
\(653\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(654\) 0 0
\(655\) 1.20742 + 0.877242i 1.20742 + 0.877242i
\(656\) 0 0
\(657\) −0.263146 0.809880i −0.263146 0.809880i
\(658\) 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
\(664\) 0.456288 1.40431i 0.456288 1.40431i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −0.0852994 0.262525i −0.0852994 0.262525i
\(669\) 0 0
\(670\) −0.703877 −0.703877
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(674\) −0.657096 2.02233i −0.657096 2.02233i
\(675\) 0 0
\(676\) −0.0750858 0.0545530i −0.0750858 0.0545530i
\(677\) −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
\(682\) −1.93019 + 0.495588i −1.93019 + 0.495588i
\(683\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(684\) −0.175086 + 0.127207i −0.175086 + 0.127207i
\(685\) 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
\(694\) −0.401616 −0.401616
\(695\) 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
\(704\) −0.753825 0.298461i −0.753825 0.298461i
\(705\) 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
\(712\) −0.546284 1.68129i −0.546284 1.68129i
\(713\) 2.19334 1.59355i 2.19334 1.59355i
\(714\) 0 0
\(715\) −1.19721 1.88650i −1.19721 1.88650i
\(716\) −0.240183 −0.240183
\(717\) 0 0
\(718\) 0 0
\(719\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(720\) 1.59713 + 1.16038i 1.59713 + 1.16038i
\(721\) 0 0
\(722\) 0.372746 1.14720i 0.372746 1.14720i
\(723\) 0 0
\(724\) 0.153099 0.111233i 0.153099 0.111233i
\(725\) 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
\(730\) −0.494239 + 1.52111i −0.494239 + 1.52111i
\(731\) 0 0
\(732\) 0 0
\(733\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(734\) 0.641510 + 1.97437i 0.641510 + 1.97437i
\(735\) 0 0
\(736\) −0.429423 −0.429423
\(737\) −0.200808 0.316423i −0.200808 0.316423i
\(738\) 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
\(743\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.61803 −1.61803
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.202967 + 0.624667i −0.202967 + 0.624667i
\(756\) 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
\(760\) −2.33181 −2.33181
\(761\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0.354888 1.09223i 0.354888 1.09223i
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(774\) 0 0
\(775\) 3.11662 + 2.26435i 3.11662 + 2.26435i
\(776\) −1.46494 1.06434i −1.46494 1.06434i
\(777\) 0 0
\(778\) −0.615808 1.89526i −0.615808 1.89526i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.348079 1.07128i −0.348079 1.07128i
\(785\) 0 0
\(786\) 0 0
\(787\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) −1.51949 + 1.10397i −1.51949 + 1.10397i
\(791\) 0 0
\(792\) −0.0573011 + 0.910775i −0.0573011 + 0.910775i
\(793\) 0 0
\(794\) 1.40281 1.01920i 1.40281 1.01920i
\(795\) 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
\(800\) −0.188559 0.580324i −0.188559 0.580324i
\(801\) −1.56720 + 1.13864i −1.56720 + 1.13864i
\(802\) 0 0