Properties

Label 869.1.j.a.157.1
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 157.1
Root \(-0.535827 - 0.844328i\) of defining polynomial
Character \(\chi\) \(=\) 869.157
Dual form 869.1.j.a.631.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.56720 + 1.13864i) q^{2} +(0.850604 - 2.61789i) q^{4} +(1.60528 + 1.16630i) q^{5} +(1.04914 + 3.22894i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-1.56720 + 1.13864i) q^{2} +(0.850604 - 2.61789i) q^{4} +(1.60528 + 1.16630i) q^{5} +(1.04914 + 3.22894i) q^{8} +(-0.809017 + 0.587785i) q^{9} -3.84378 q^{10} +(0.968583 - 0.248690i) q^{11} +(-0.866986 + 0.629902i) q^{13} +(-3.09390 - 2.24785i) q^{16} +(0.598617 - 1.84235i) q^{18} +(-0.115808 - 0.356420i) q^{19} +(4.41870 - 3.21038i) q^{20} +(-1.23480 + 1.49261i) q^{22} -0.374763 q^{23} +(0.907634 + 2.79341i) q^{25} +(0.641510 - 1.97437i) q^{26} +(1.03137 - 0.749337i) q^{31} +4.01314 q^{32} +(0.850604 + 2.61789i) q^{36} +(0.587328 + 0.426719i) q^{38} +(-2.08174 + 6.40695i) q^{40} +(0.172838 - 2.74718i) q^{44} -1.98423 q^{45} +(0.587328 - 0.426719i) q^{46} +(-0.809017 - 0.587785i) q^{49} +(-4.60313 - 3.34437i) q^{50} +(0.911553 + 2.80547i) q^{52} +(1.84489 + 0.730444i) q^{55} +(-0.763146 + 2.34872i) q^{62} +(-3.19549 + 2.32166i) q^{64} -2.12641 q^{65} -0.851559 q^{67} +(-2.74670 - 1.99559i) q^{72} +(0.541587 - 1.66683i) q^{73} -1.03158 q^{76} +(-0.809017 + 0.587785i) q^{79} +(-2.34489 - 7.21683i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.30902 + 0.951057i) q^{83} +(1.81919 + 2.86658i) q^{88} +0.125581 q^{89} +(3.10969 - 2.25932i) q^{90} +(-0.318775 + 0.981088i) q^{92} +(0.229790 - 0.707220i) q^{95} +(-1.17950 + 0.856954i) q^{97} +1.93717 q^{98} +(-0.637424 + 0.770513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} + 15q^{20} - 5q^{22} - 5q^{25} + 15q^{26} - 10q^{32} - 5q^{36} - 10q^{40} - 5q^{49} - 10q^{50} - 10q^{62} - 5q^{64} - 10q^{76} - 5q^{79} - 10q^{80} - 5q^{81} + 15q^{83} - 5q^{88} + 15q^{92} + 15q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(3\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(4\) 0.850604 2.61789i 0.850604 2.61789i
\(5\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(6\) 0 0
\(7\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(8\) 1.04914 + 3.22894i 1.04914 + 3.22894i
\(9\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(10\) −3.84378 −3.84378
\(11\) 0.968583 0.248690i 0.968583 0.248690i
\(12\) 0 0
\(13\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −3.09390 2.24785i −3.09390 2.24785i
\(17\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(18\) 0.598617 1.84235i 0.598617 1.84235i
\(19\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(20\) 4.41870 3.21038i 4.41870 3.21038i
\(21\) 0 0
\(22\) −1.23480 + 1.49261i −1.23480 + 1.49261i
\(23\) −0.374763 −0.374763 −0.187381 0.982287i \(-0.560000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(24\) 0 0
\(25\) 0.907634 + 2.79341i 0.907634 + 2.79341i
\(26\) 0.641510 1.97437i 0.641510 1.97437i
\(27\) 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
\(31\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(32\) 4.01314 4.01314
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.850604 + 2.61789i 0.850604 + 2.61789i
\(37\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(38\) 0.587328 + 0.426719i 0.587328 + 0.426719i
\(39\) 0 0
\(40\) −2.08174 + 6.40695i −2.08174 + 6.40695i
\(41\) 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 \(\pi\)
\(44\) 0.172838 2.74718i 0.172838 2.74718i
\(45\) −1.98423 −1.98423
\(46\) 0.587328 0.426719i 0.587328 0.426719i
\(47\) 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
\(50\) −4.60313 3.34437i −4.60313 3.34437i
\(51\) 0 0
\(52\) 0.911553 + 2.80547i 0.911553 + 2.80547i
\(53\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(54\) 0 0
\(55\) 1.84489 + 0.730444i 1.84489 + 0.730444i
\(56\) 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 \(0.200000\pi\)
\(62\) −0.763146 + 2.34872i −0.763146 + 2.34872i
\(63\) 0 0
\(64\) −3.19549 + 2.32166i −3.19549 + 2.32166i
\(65\) −2.12641 −2.12641
\(66\) 0 0
\(67\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(72\) −2.74670 1.99559i −2.74670 1.99559i
\(73\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −1.03158 −1.03158
\(77\) 0 0
\(78\) 0 0
\(79\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(80\) −2.34489 7.21683i −2.34489 7.21683i
\(81\) 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
\(88\) 1.81919 + 2.86658i 1.81919 + 2.86658i
\(89\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(90\) 3.10969 2.25932i 3.10969 2.25932i
\(91\) 0 0
\(92\) −0.318775 + 0.981088i −0.318775 + 0.981088i
\(93\) 0 0
\(94\) 0 0
\(95\) 0.229790 0.707220i 0.229790 0.707220i
\(96\) 0 0
\(97\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(98\) 1.93717 1.93717
\(99\) −0.637424 + 0.770513i −0.637424 + 0.770513i
\(100\) 8.08488 8.08488
\(101\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(102\) 0 0
\(103\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(104\) −2.94351 2.13858i −2.94351 2.13858i
\(105\) 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 \(\pi\)
\(110\) −3.72302 + 0.955910i −3.72302 + 0.955910i
\(111\) 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
\(115\) −0.601597 0.437086i −0.601597 0.437086i
\(116\) 0 0
\(117\) 0.331159 1.01920i 0.331159 1.01920i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.876307 0.481754i 0.876307 0.481754i
\(122\) 0 0
\(123\) 0 0
\(124\) −1.08439 3.33741i −1.08439 3.33741i
\(125\) −1.18779 + 3.65565i −1.18779 + 3.65565i
\(126\) 0 0
\(127\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(128\) 1.12432 3.46030i 1.12432 3.46030i
\(129\) 0 0
\(130\) 3.33251 2.42121i 3.33251 2.42121i
\(131\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1.33456 0.969617i 1.33456 0.969617i
\(135\) 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
\(143\) −0.683098 + 0.825723i −0.683098 + 0.825723i
\(144\) 3.82427 3.82427
\(145\) 0 0
\(146\) 1.04914 + 3.22894i 1.04914 + 3.22894i
\(147\) 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
\(151\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(152\) 1.02936 0.747873i 1.02936 0.747873i
\(153\) 0 0
\(154\) 0 0
\(155\) 2.52959 2.52959
\(156\) 0 0
\(157\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(158\) 0.598617 1.84235i 0.598617 1.84235i
\(159\) 0 0
\(160\) 6.44219 + 4.68053i 6.44219 + 4.68053i
\(161\) 0 0
\(162\) 0.598617 + 1.84235i 0.598617 + 1.84235i
\(163\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −3.13440 −3.13440
\(167\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(168\) 0 0
\(169\) 0.0458709 0.141176i 0.0458709 0.141176i
\(170\) 0 0
\(171\) 0.303189 + 0.220280i 0.303189 + 0.220280i
\(172\) 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
\(176\) −3.55571 1.40781i −3.55571 1.40781i
\(177\) 0 0
\(178\) −0.196811 + 0.142991i −0.196811 + 0.142991i
\(179\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(180\) −1.68779 + 5.19450i −1.68779 + 5.19450i
\(181\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.393180 1.21008i −0.393180 1.21008i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0.445141 + 1.37000i 0.445141 + 1.37000i
\(191\) 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 \(0.200000\pi\)
\(194\) 0.872746 2.68604i 0.872746 2.68604i
\(195\) 0 0
\(196\) −2.22691 + 1.61795i −2.22691 + 1.61795i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0.121636 1.93334i 0.121636 1.93334i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −8.06750 + 5.86139i −8.06750 + 5.86139i
\(201\) 0 0
\(202\) 0.0751750 0.231365i 0.0751750 0.231365i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.303189 0.220280i 0.303189 0.220280i
\(208\) 4.09829 4.09829
\(209\) −0.200808 0.316423i −0.200808 0.316423i
\(210\) 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
\(220\) 3.48149 4.20840i 3.48149 4.20840i
\(221\) 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
\(225\) −2.37622 1.72642i −2.37622 1.72642i
\(226\) 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 \(0.800000\pi\)
\(230\) 1.44051 1.44051
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(234\) 0.641510 + 1.97437i 0.641510 + 1.97437i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(240\) 0 0
\(241\) −1.85955 −1.85955 −0.929776 0.368125i \(-0.880000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(242\) −0.824805 + 1.75280i −0.824805 + 1.75280i
\(243\) 0 0
\(244\) 0 0
\(245\) −0.613161 1.88711i −0.613161 1.88711i
\(246\) 0 0
\(247\) 0.324914 + 0.236064i 0.324914 + 0.236064i
\(248\) 3.50162 + 2.54408i 3.50162 + 2.54408i
\(249\) 0 0
\(250\) −2.30095 7.08161i −2.30095 7.08161i
\(251\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(252\) 0 0
\(253\) −0.362989 + 0.0931997i −0.362989 + 0.0931997i
\(254\) 0 0
\(255\) 0 0
\(256\) 0.957424 + 2.94665i 0.957424 + 2.94665i
\(257\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −1.80873 + 5.56670i −1.80873 + 5.56670i
\(261\) 0 0
\(262\) −2.74670 + 1.99559i −2.74670 + 1.99559i
\(263\) −1.85955 −1.85955 −0.929776 0.368125i \(-0.880000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −0.724339 + 2.22929i −0.724339 + 2.22929i
\(269\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(270\) 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
\(275\) 1.57381 + 2.47993i 1.57381 + 2.47993i
\(276\) 0 0
\(277\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(278\) 0 0
\(279\) −0.393950 + 1.21245i −0.393950 + 1.21245i
\(280\) 0 0
\(281\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(282\) 0 0
\(283\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0.130351 2.07187i 0.130351 2.07187i
\(287\) 0 0
\(288\) −3.24670 + 2.35886i −3.24670 + 2.35886i
\(289\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(290\) 0 0
\(291\) 0 0
\(292\) −3.90291 2.83563i −3.90291 2.83563i
\(293\) 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
\(299\) 0.324914 0.236064i 0.324914 0.236064i
\(300\) 0 0
\(301\) 0 0
\(302\) 1.33456 + 0.969617i 1.33456 + 0.969617i
\(303\) 0 0
\(304\) −0.442881 + 1.36305i −0.442881 + 1.36305i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −3.96438 + 2.88029i −3.96438 + 2.88029i
\(311\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(312\) 0 0
\(313\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.850604 + 2.61789i 0.850604 + 2.61789i
\(317\) −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
\(320\) −7.83740 −7.83740
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −2.22691 1.61795i −2.22691 1.61795i
\(325\) −2.54648 1.85013i −2.54648 1.85013i
\(326\) −1.11316 + 3.42596i −1.11316 + 3.42596i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 3.60322 2.61789i 3.60322 2.61789i
\(333\) 0 0
\(334\) −0.763146 + 2.34872i −0.763146 + 2.34872i
\(335\) −1.36699 0.993173i −1.36699 0.993173i
\(336\) 0 0
\(337\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(338\) 0.0888596 + 0.273482i 0.0888596 + 0.273482i
\(339\) 0 0
\(340\) 0 0
\(341\) 0.812619 0.982287i 0.812619 0.982287i
\(342\) −0.725978 −0.725978
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(348\) 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
\(352\) 3.88706 0.998027i 3.88706 0.998027i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.106820 0.328757i 0.106820 0.328757i
\(357\) 0 0
\(358\) 2.53578 + 1.84235i 2.53578 + 1.84235i
\(359\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(360\) −2.08174 6.40695i −2.08174 6.40695i
\(361\) 0.695393 0.505233i 0.695393 0.505233i
\(362\) 2.07597 2.07597
\(363\) 0 0
\(364\) 0 0
\(365\) 2.81343 2.04407i 2.81343 2.04407i
\(366\) 0 0
\(367\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(368\) 1.15948 + 0.842409i 1.15948 + 0.842409i
\(369\) 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 \(0.200000\pi\)
\(380\) −1.65596 1.20313i −1.65596 1.20313i
\(381\) 0 0
\(382\) 0 0
\(383\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 1.24013 + 3.81672i 1.24013 + 3.81672i
\(389\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.04914 3.22894i 1.04914 3.22894i
\(393\) 0 0
\(394\) 0 0
\(395\) −1.98423 −1.98423
\(396\) 1.47492 + 2.32411i 1.47492 + 2.32411i
\(397\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 3.47104 10.6828i 3.47104 10.6828i
\(401\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(402\) 0 0
\(403\) −0.422178 + 1.29933i −0.422178 + 1.29933i
\(404\) 0.106820 + 0.328757i 0.106820 + 0.328757i
\(405\) 1.60528 1.16630i 1.60528 1.16630i
\(406\) 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
\(414\) −0.224339 + 0.690446i −0.224339 + 0.690446i
\(415\) 0.992115 + 3.05342i 0.992115 + 3.05342i
\(416\) −3.47933 + 2.52788i −3.47933 + 2.52788i
\(417\) 0 0
\(418\) 0.674997 + 0.267250i 0.674997 + 0.267250i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(422\) 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
\(431\) −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i \(0.640000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(432\) 0 0
\(433\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.0434005 + 0.133573i 0.0434005 + 0.133573i
\(438\) 0 0
\(439\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(440\) −0.422999 + 6.72337i −0.422999 + 6.72337i
\(441\) 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
\(445\) 0.201592 + 0.146465i 0.201592 + 0.146465i
\(446\) 2.53578 + 1.84235i 2.53578 + 1.84235i
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(450\) 5.68978 5.68978
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −1.65596 + 1.20313i −1.65596 + 1.20313i
\(461\) 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
\(467\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(468\) −2.38648 1.73388i −2.38648 1.73388i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.890518 0.646999i 0.890518 0.646999i
\(476\) 0 0
\(477\) 0 0
\(478\) 3.10969 + 2.25932i 3.10969 + 2.25932i
\(479\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 2.91429 2.11736i 2.91429 2.11736i
\(483\) 0 0
\(484\) −0.515788 2.70386i −0.515788 2.70386i
\(485\) −2.89288 −2.89288
\(486\) 0 0
\(487\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 3.10969 + 2.25932i 3.10969 + 2.25932i
\(491\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −0.777996 −0.777996
\(495\) −1.92189 + 0.493458i −1.92189 + 0.493458i
\(496\) −4.87536 −4.87536
\(497\) 0 0
\(498\) 0 0
\(499\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(500\) 8.55976 + 6.21903i 8.55976 + 6.21903i
\(501\) 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
\(505\) −0.249182 −0.249182
\(506\) 0.462756 0.559375i 0.462756 0.559375i
\(507\) 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
\(512\) −1.91213 1.38925i −1.91213 1.38925i
\(513\) 0 0
\(514\) 0.641510 + 1.97437i 0.641510 + 1.97437i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −2.23091 6.86603i −2.23091 6.86603i
\(521\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(522\) 0 0
\(523\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(524\) 1.49078 4.58815i 1.49078 4.58815i
\(525\) 0 0
\(526\) 2.91429 2.11736i 2.91429 2.11736i
\(527\) 0 0
\(528\) 0 0
\(529\) −0.859553 −0.859553
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −0.893408 2.74963i −0.893408 2.74963i
\(537\) 0 0
\(538\) −1.64961 −1.64961
\(539\) −0.929776 0.368125i −0.929776 0.368125i
\(540\) 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
\(547\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) −5.29022 2.09455i −5.29022 2.09455i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −1.18779 + 3.65565i −1.18779 + 3.65565i
\(555\) 0 0
\(556\) 0 0
\(557\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(558\) −0.763146 2.34872i −0.763146 2.34872i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −3.84378 −3.84378
\(563\) −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
\(566\) 1.99794 + 1.45159i 1.99794 + 1.45159i
\(567\) 0 0
\(568\) 0 0
\(569\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(570\) 0 0
\(571\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(572\) 1.58061 + 2.49064i 1.58061 + 2.49064i
\(573\) 0 0
\(574\) 0 0
\(575\) −0.340147 1.04687i −0.340147 1.04687i
\(576\) 1.22057 3.75653i 1.22057 3.75653i
\(577\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(578\) −1.56720 1.13864i −1.56720 1.13864i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 5.95030 5.95030
\(585\) 1.72030 1.24987i 1.72030 1.24987i
\(586\) 0 0
\(587\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(588\) 0 0
\(589\) −0.386520 0.280823i −0.386520 0.280823i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −0.240414 + 0.739919i −0.240414 + 0.739919i
\(599\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(600\) 0 0
\(601\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(602\) 0 0
\(603\) 0.688925 0.500534i 0.688925 0.500534i
\(604\) −2.34401 −2.34401
\(605\) 1.96858 + 0.248690i 1.96858 + 0.248690i
\(606\) 0 0
\(607\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(608\) −0.464754 1.43036i −0.464754 1.43036i
\(609\) 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
\(617\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(618\) 0 0
\(619\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(620\) 2.15168 6.62219i 2.15168 6.62219i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −3.79411 + 2.75658i −3.79411 + 2.75658i
\(626\) −2.46959 −2.46959
\(627\) 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 \(0.600000\pi\)
\(632\) −2.74670 1.99559i −2.74670 1.99559i
\(633\) 0 0
\(634\) 0.369966 1.13864i 0.369966 1.13864i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.07165 1.07165
\(638\) 0 0
\(639\) 0 0
\(640\) 5.84059 4.24344i 5.84059 4.24344i
\(641\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(642\) 0 0
\(643\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(648\) 3.39510 3.39510
\(649\) 0 0
\(650\) 6.09747 6.09747
\(651\) 0 0
\(652\) −1.58174 4.86811i −1.58174 4.86811i
\(653\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(654\) 0 0
\(655\) 2.81343 + 2.04407i 2.81343 + 2.04407i
\(656\) 0 0
\(657\) 0.541587 + 1.66683i 0.541587 + 1.66683i
\(658\) 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
\(664\) −1.69755 + 5.22453i −1.69755 + 5.22453i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −1.08439 3.33741i −1.08439 3.33741i
\(669\) 0 0
\(670\) 3.27321 3.27321
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(674\) 0.872746 + 2.68604i 0.872746 + 2.68604i
\(675\) 0 0
\(676\) −0.330566 0.240170i −0.330566 0.240170i
\(677\) −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
\(682\) −0.155067 + 2.46472i −0.155067 + 2.46472i
\(683\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(684\) 0.834563 0.606346i 0.834563 0.606346i
\(685\) 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
\(694\) −1.64961 −1.64961
\(695\) 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
\(704\) −2.51773 + 3.04341i −2.51773 + 3.04341i
\(705\) 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
\(712\) 0.131753 + 0.405493i 0.131753 + 0.405493i
\(713\) −0.386520 + 0.280823i −0.386520 + 0.280823i
\(714\) 0 0
\(715\) −2.05960 + 0.528816i −2.05960 + 0.528816i
\(716\) −4.45382 −4.45382
\(717\) 0 0
\(718\) 0 0
\(719\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(720\) 6.13900 + 4.46025i 6.13900 + 4.46025i
\(721\) 0 0
\(722\) −0.514543 + 1.58360i −0.514543 + 1.58360i
\(723\) 0 0
\(724\) −2.38648 + 1.73388i −2.38648 + 1.73388i
\(725\) 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
\(730\) −2.08174 + 6.40695i −2.08174 + 6.40695i
\(731\) 0 0
\(732\) 0 0
\(733\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(734\) 0.0751750 + 0.231365i 0.0751750 + 0.231365i
\(735\) 0 0
\(736\) −1.50397 −1.50397
\(737\) −0.824805 + 0.211774i −0.824805 + 0.211774i
\(738\) 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
\(743\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.61803 −1.61803
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0.522142 1.60699i 0.522142 1.60699i
\(756\) 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
\(760\) 2.52465 2.52465
\(761\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 1.15962 3.56895i 1.15962 3.56895i
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(774\) 0 0
\(775\) 3.02932 + 2.20093i 3.02932 + 2.20093i
\(776\) −4.00451 2.90945i −4.00451 2.90945i
\(777\) 0 0
\(778\) −0.763146 2.34872i −0.763146 2.34872i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.18176 + 3.63709i 1.18176 + 3.63709i
\(785\) 0 0
\(786\) 0 0
\(787\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 3.10969 2.25932i 3.10969 2.25932i
\(791\) 0 0
\(792\) −3.15669 1.24982i −3.15669 1.24982i
\(793\) 0 0
\(794\) 2.53578 1.84235i 2.53578 1.84235i
\(795\) 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
\(800\) 3.64246 + 11.2103i 3.64246 + 11.2103i
\(801\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i
\(802\) 0 0
\(803\) 0.110048 &minu