Properties

Label 869.1.j.a.631.5
Level $869$
Weight $1$
Character 869.631
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 631.5
Root \(-0.0627905 - 0.998027i\) of defining polynomial
Character \(\chi\) \(=\) 869.631
Dual form 869.1.j.a.157.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50441 + 1.09302i) q^{2} +(0.759544 + 2.33764i) q^{4} +(0.303189 - 0.220280i) q^{5} +(-0.837780 + 2.57842i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(1.50441 + 1.09302i) q^{2} +(0.759544 + 2.33764i) q^{4} +(0.303189 - 0.220280i) q^{5} +(-0.837780 + 2.57842i) q^{8} +(-0.809017 - 0.587785i) q^{9} +0.696891 q^{10} +(-0.929776 + 0.368125i) q^{11} +(-0.101597 - 0.0738147i) q^{13} +(-2.09011 + 1.51855i) q^{16} +(-0.574633 - 1.76854i) q^{18} +(0.541587 - 1.66683i) q^{19} +(0.745220 + 0.541434i) q^{20} +(-1.80113 - 0.462452i) q^{22} +1.75261 q^{23} +(-0.265616 + 0.817483i) q^{25} +(-0.0721631 - 0.222095i) q^{26} +(-1.56720 - 1.13864i) q^{31} -2.09308 q^{32} +(0.759544 - 2.33764i) q^{36} +(2.63665 - 1.91564i) q^{38} +(0.313968 + 0.966296i) q^{40} +(-1.56675 - 1.89387i) q^{44} -0.374763 q^{45} +(2.63665 + 1.91564i) q^{46} +(-0.809017 + 0.587785i) q^{49} +(-1.29312 + 0.939507i) q^{50} +(0.0953844 - 0.293563i) q^{52} +(-0.200808 + 0.316423i) q^{55} +(-1.11316 - 3.42596i) q^{62} +(-1.05874 - 0.769217i) q^{64} -0.0470631 q^{65} -1.98423 q^{67} +(2.19334 - 1.59355i) q^{72} +(0.450527 + 1.38658i) q^{73} +4.30781 q^{76} +(-0.809017 - 0.587785i) q^{79} +(-0.299192 + 0.920819i) q^{80} +(0.309017 + 0.951057i) q^{81} +(1.30902 - 0.951057i) q^{83} +(-0.170232 - 2.70576i) q^{88} -1.27485 q^{89} +(-0.563797 - 0.409622i) q^{90} +(1.33119 + 4.09697i) q^{92} +(-0.202967 - 0.624667i) q^{95} +(0.688925 + 0.500534i) q^{97} -1.85955 q^{98} +(0.968583 + 0.248690i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} + 15q^{20} - 5q^{22} - 5q^{25} + 15q^{26} - 10q^{32} - 5q^{36} - 10q^{40} - 5q^{49} - 10q^{50} - 10q^{62} - 5q^{64} - 10q^{76} - 5q^{79} - 10q^{80} - 5q^{81} + 15q^{83} - 5q^{88} + 15q^{92} + 15q^{95} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(3\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(4\) 0.759544 + 2.33764i 0.759544 + 2.33764i
\(5\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(6\) 0 0
\(7\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(8\) −0.837780 + 2.57842i −0.837780 + 2.57842i
\(9\) −0.809017 0.587785i −0.809017 0.587785i
\(10\) 0.696891 0.696891
\(11\) −0.929776 + 0.368125i −0.929776 + 0.368125i
\(12\) 0 0
\(13\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.09011 + 1.51855i −2.09011 + 1.51855i
\(17\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(18\) −0.574633 1.76854i −0.574633 1.76854i
\(19\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(20\) 0.745220 + 0.541434i 0.745220 + 0.541434i
\(21\) 0 0
\(22\) −1.80113 0.462452i −1.80113 0.462452i
\(23\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(24\) 0 0
\(25\) −0.265616 + 0.817483i −0.265616 + 0.817483i
\(26\) −0.0721631 0.222095i −0.0721631 0.222095i
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(30\) 0 0
\(31\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(32\) −2.09308 −2.09308
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.759544 2.33764i 0.759544 2.33764i
\(37\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(38\) 2.63665 1.91564i 2.63665 1.91564i
\(39\) 0 0
\(40\) 0.313968 + 0.966296i 0.313968 + 0.966296i
\(41\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −1.56675 1.89387i −1.56675 1.89387i
\(45\) −0.374763 −0.374763
\(46\) 2.63665 + 1.91564i 2.63665 + 1.91564i
\(47\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(48\) 0 0
\(49\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(50\) −1.29312 + 0.939507i −1.29312 + 0.939507i
\(51\) 0 0
\(52\) 0.0953844 0.293563i 0.0953844 0.293563i
\(53\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(54\) 0 0
\(55\) −0.200808 + 0.316423i −0.200808 + 0.316423i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(60\) 0 0
\(61\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(62\) −1.11316 3.42596i −1.11316 3.42596i
\(63\) 0 0
\(64\) −1.05874 0.769217i −1.05874 0.769217i
\(65\) −0.0470631 −0.0470631
\(66\) 0 0
\(67\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(72\) 2.19334 1.59355i 2.19334 1.59355i
\(73\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 4.30781 4.30781
\(77\) 0 0
\(78\) 0 0
\(79\) −0.809017 0.587785i −0.809017 0.587785i
\(80\) −0.299192 + 0.920819i −0.299192 + 0.920819i
\(81\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(82\) 0 0
\(83\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −0.170232 2.70576i −0.170232 2.70576i
\(89\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(90\) −0.563797 0.409622i −0.563797 0.409622i
\(91\) 0 0
\(92\) 1.33119 + 4.09697i 1.33119 + 4.09697i
\(93\) 0 0
\(94\) 0 0
\(95\) −0.202967 0.624667i −0.202967 0.624667i
\(96\) 0 0
\(97\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(98\) −1.85955 −1.85955
\(99\) 0.968583 + 0.248690i 0.968583 + 0.248690i
\(100\) −2.11273 −2.11273
\(101\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(102\) 0 0
\(103\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(104\) 0.275441 0.200120i 0.275441 0.200120i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) −0.647953 + 0.256543i −0.647953 + 0.256543i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(114\) 0 0
\(115\) 0.531374 0.386066i 0.531374 0.386066i
\(116\) 0 0
\(117\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.728969 0.684547i 0.728969 0.684547i
\(122\) 0 0
\(123\) 0 0
\(124\) 1.47136 4.52839i 1.47136 4.52839i
\(125\) 0.215351 + 0.662783i 0.215351 + 0.662783i
\(126\) 0 0
\(127\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(128\) −0.105209 0.323801i −0.105209 0.323801i
\(129\) 0 0
\(130\) −0.0708022 0.0514408i −0.0708022 0.0514408i
\(131\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −2.98509 2.16880i −2.98509 2.16880i
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(138\) 0 0
\(139\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.121636 + 0.0312307i 0.121636 + 0.0312307i
\(144\) 2.58352 2.58352
\(145\) 0 0
\(146\) −0.837780 + 2.57842i −0.837780 + 2.57842i
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(150\) 0 0
\(151\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(152\) 3.84407 + 2.79288i 3.84407 + 2.79288i
\(153\) 0 0
\(154\) 0 0
\(155\) −0.725978 −0.725978
\(156\) 0 0
\(157\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(158\) −0.574633 1.76854i −0.574633 1.76854i
\(159\) 0 0
\(160\) −0.634599 + 0.461063i −0.634599 + 0.461063i
\(161\) 0 0
\(162\) −0.574633 + 1.76854i −0.574633 + 1.76854i
\(163\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 3.00882 3.00882
\(167\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(168\) 0 0
\(169\) −0.304144 0.936058i −0.304144 0.936058i
\(170\) 0 0
\(171\) −1.41789 + 1.03016i −1.41789 + 1.03016i
\(172\) 0 0
\(173\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.38432 2.18134i 1.38432 2.18134i
\(177\) 0 0
\(178\) −1.91789 1.39343i −1.91789 1.39343i
\(179\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(180\) −0.284649 0.876059i −0.284649 0.876059i
\(181\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.46830 + 4.51897i −1.46830 + 4.51897i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0.377427 1.16160i 0.377427 1.16160i
\(191\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(192\) 0 0
\(193\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(194\) 0.489334 + 1.50602i 0.489334 + 1.50602i
\(195\) 0 0
\(196\) −1.98851 1.44474i −1.98851 1.44474i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 1.18532 + 1.43281i 1.18532 + 1.43281i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −1.88529 1.36974i −1.88529 1.36974i
\(201\) 0 0
\(202\) 0.732570 + 2.25462i 0.732570 + 2.25462i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.41789 1.03016i −1.41789 1.03016i
\(208\) 0.324441 0.324441
\(209\) 0.110048 + 1.74915i 0.110048 + 1.74915i
\(210\) 0 0
\(211\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −0.892204 0.229079i −0.892204 0.229079i
\(221\) 0 0
\(222\) 0 0
\(223\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(224\) 0 0
\(225\) 0.695393 0.505233i 0.695393 0.505233i
\(226\) 0 0
\(227\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(228\) 0 0
\(229\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(230\) 1.22138 1.22138
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(234\) −0.0721631 + 0.222095i −0.0721631 + 0.222095i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(240\) 0 0
\(241\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(242\) 1.84489 0.233064i 1.84489 0.233064i
\(243\) 0 0
\(244\) 0 0
\(245\) −0.115808 + 0.356420i −0.115808 + 0.356420i
\(246\) 0 0
\(247\) −0.178061 + 0.129369i −0.178061 + 0.129369i
\(248\) 4.24886 3.08697i 4.24886 3.08697i
\(249\) 0 0
\(250\) −0.400457 + 1.23248i −0.400457 + 1.23248i
\(251\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(252\) 0 0
\(253\) −1.62954 + 0.645180i −1.62954 + 0.645180i
\(254\) 0 0
\(255\) 0 0
\(256\) −0.208759 + 0.642495i −0.208759 + 0.642495i
\(257\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.0357465 0.110016i −0.0357465 0.110016i
\(261\) 0 0
\(262\) 2.19334 + 1.59355i 2.19334 + 1.59355i
\(263\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −1.50711 4.63841i −1.50711 4.63841i
\(269\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(270\) 0 0
\(271\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.0539718 0.857857i −0.0539718 0.857857i
\(276\) 0 0
\(277\) 0.303189 + 0.220280i 0.303189 + 0.220280i 0.728969 0.684547i \(-0.240000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(278\) 0 0
\(279\) 0.598617 + 1.84235i 0.598617 + 1.84235i
\(280\) 0 0
\(281\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(282\) 0 0
\(283\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0.148854 + 0.179934i 0.148854 + 0.179934i
\(287\) 0 0
\(288\) 1.69334 + 1.23028i 1.69334 + 1.23028i
\(289\) 0.309017 0.951057i 0.309017 0.951057i
\(290\) 0 0
\(291\) 0 0
\(292\) −2.89913 + 2.10634i −2.89913 + 2.10634i
\(293\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.178061 0.129369i −0.178061 0.129369i
\(300\) 0 0
\(301\) 0 0
\(302\) −2.98509 + 2.16880i −2.98509 + 2.16880i
\(303\) 0 0
\(304\) 1.39920 + 4.30630i 1.39920 + 4.30630i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1.09217 0.793506i −1.09217 0.793506i
\(311\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(312\) 0 0
\(313\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.759544 2.33764i 0.759544 2.33764i
\(317\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.490441 −0.490441
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −1.98851 + 1.44474i −1.98851 + 1.44474i
\(325\) 0.0873282 0.0634476i 0.0873282 0.0634476i
\(326\) −0.615808 1.89526i −0.615808 1.89526i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 3.21748 + 2.33764i 3.21748 + 2.33764i
\(333\) 0 0
\(334\) −1.11316 3.42596i −1.11316 3.42596i
\(335\) −0.601597 + 0.437086i −0.601597 + 0.437086i
\(336\) 0 0
\(337\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(338\) 0.565571 1.74065i 0.565571 1.74065i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.87631 + 0.481754i 1.87631 + 0.481754i
\(342\) −3.25908 −3.25908
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(348\) 0 0
\(349\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.94609 0.770513i 1.94609 0.770513i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.968304 2.98013i −0.968304 2.98013i
\(357\) 0 0
\(358\) −2.43419 + 1.76854i −2.43419 + 1.76854i
\(359\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(360\) 0.313968 0.966296i 0.313968 0.966296i
\(361\) −1.67600 1.21769i −1.67600 1.21769i
\(362\) −0.233525 −0.233525
\(363\) 0 0
\(364\) 0 0
\(365\) 0.442031 + 0.321154i 0.442031 + 0.321154i
\(366\) 0 0
\(367\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(368\) −3.66316 + 2.66144i −3.66316 + 2.66144i
\(369\) 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 \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(380\) 1.30608 0.948925i 1.30608 0.948925i
\(381\) 0 0
\(382\) 0 0
\(383\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −0.646797 + 1.99064i −0.646797 + 1.99064i
\(389\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.837780 2.57842i −0.837780 2.57842i
\(393\) 0 0
\(394\) 0 0
\(395\) −0.374763 −0.374763
\(396\) 0.154335 + 2.45309i 0.154335 + 2.45309i
\(397\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.686225 2.11198i −0.686225 2.11198i
\(401\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(402\) 0 0
\(403\) 0.0751750 + 0.231365i 0.0751750 + 0.231365i
\(404\) −0.968304 + 2.98013i −0.968304 + 2.98013i
\(405\) 0.303189 + 0.220280i 0.303189 + 0.220280i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −1.00711 3.09957i −1.00711 3.09957i
\(415\) 0.187381 0.576700i 0.187381 0.576700i
\(416\) 0.212651 + 0.154500i 0.212651 + 0.154500i
\(417\) 0 0
\(418\) −1.74630 + 2.75173i −1.74630 + 2.75173i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−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
\(431\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(432\) 0 0
\(433\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.949193 2.92132i 0.949193 2.92132i
\(438\) 0 0
\(439\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(440\) −0.647638 0.782859i −0.647638 0.782859i
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(444\) 0 0
\(445\) −0.386520 + 0.280823i −0.386520 + 0.280823i
\(446\) −2.43419 + 1.76854i −2.43419 + 1.76854i
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(450\) 1.59838 1.59838
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 1.30608 + 0.948925i 1.30608 + 0.948925i
\(461\) 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
\(467\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(468\) −0.249720 + 0.181432i −0.249720 + 0.181432i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 1.21875 + 0.885477i 1.21875 + 0.885477i
\(476\) 0 0
\(477\) 0 0
\(478\) −0.563797 + 0.409622i −0.563797 + 0.409622i
\(479\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1.61221 + 1.17134i 1.61221 + 1.17134i
\(483\) 0 0
\(484\) 2.15391 + 1.18412i 2.15391 + 1.18412i
\(485\) 0.319132 0.319132
\(486\) 0 0
\(487\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −0.563797 + 0.409622i −0.563797 + 0.409622i
\(491\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −0.409278 −0.409278
\(495\) 0.348445 0.137959i 0.348445 0.137959i
\(496\) 5.00470 5.00470
\(497\) 0 0
\(498\) 0 0
\(499\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(500\) −1.38578 + 1.00683i −1.38578 + 1.00683i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(504\) 0 0
\(505\) 0.477765 0.477765
\(506\) −3.15669 0.810500i −3.15669 0.810500i
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.29176 + 0.938518i −1.29176 + 0.938518i
\(513\) 0 0
\(514\) −0.0721631 + 0.222095i −0.0721631 + 0.222095i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0.0394285 0.121348i 0.0394285 0.121348i
\(521\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(522\) 0 0
\(523\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(524\) 1.10737 + 3.40813i 1.10737 + 3.40813i
\(525\) 0 0
\(526\) 1.61221 + 1.17134i 1.61221 + 1.17134i
\(527\) 0 0
\(528\) 0 0
\(529\) 2.07165 2.07165
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 1.66235 5.11618i 1.66235 5.11618i
\(537\) 0 0
\(538\) 3.68978 3.68978
\(539\) 0.535827 0.844328i 0.535827 0.844328i
\(540\) 0 0
\(541\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0.856457 1.34956i 0.856457 1.34956i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0.215351 + 0.662783i 0.215351 + 0.662783i
\(555\) 0 0
\(556\) 0 0
\(557\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(558\) −1.11316 + 3.42596i −1.11316 + 3.42596i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0.696891 0.696891
\(563\) −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
\(566\) 2.91429 2.11736i 2.91429 2.11736i
\(567\) 0 0
\(568\) 0 0
\(569\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(570\) 0 0
\(571\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(572\) 0.0193816 + 0.308061i 0.0193816 + 0.308061i
\(573\) 0 0
\(574\) 0 0
\(575\) −0.465523 + 1.43273i −0.465523 + 1.43273i
\(576\) 0.404401 + 1.24462i 0.404401 + 1.24462i
\(577\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(578\) 1.50441 1.09302i 1.50441 1.09302i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −3.95263 −3.95263
\(585\) 0.0380748 + 0.0276630i 0.0380748 + 0.0276630i
\(586\) 0 0
\(587\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(588\) 0 0
\(589\) −2.74670 + 1.99559i −2.74670 + 1.99559i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.374763 −0.374763 −0.187381 0.982287i \(-0.560000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −0.126474 0.389247i −0.126474 0.389247i
\(599\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(600\) 0 0
\(601\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(602\) 0 0
\(603\) 1.60528 + 1.16630i 1.60528 + 1.16630i
\(604\) −4.87711 −4.87711
\(605\) 0.0702235 0.368125i 0.0702235 0.368125i
\(606\) 0 0
\(607\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(608\) −1.13358 + 3.48881i −1.13358 + 3.48881i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(618\) 0 0
\(619\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(620\) −0.551412 1.69707i −0.551412 1.69707i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.484103 0.351721i −0.484103 0.351721i
\(626\) −3.60226 −3.60226
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(632\) 2.19334 1.59355i 2.19334 1.59355i
\(633\) 0 0
\(634\) −0.355143 1.09302i −0.355143 1.09302i
\(635\) 0 0
\(636\) 0 0
\(637\) 0.125581 0.125581
\(638\) 0 0
\(639\) 0 0
\(640\) −0.103225 0.0749974i −0.103225 0.0749974i
\(641\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(642\) 0 0
\(643\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(648\) −2.71111 −2.71111
\(649\) 0 0
\(650\) 0.200727 0.200727
\(651\) 0 0
\(652\) 0.813968 2.50514i 0.813968 2.50514i
\(653\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(654\) 0 0
\(655\) 0.442031 0.321154i 0.442031 0.321154i
\(656\) 0 0
\(657\) 0.450527 1.38658i 0.450527 1.38658i
\(658\) 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
\(664\) 1.35556 + 4.17197i 1.35556 + 4.17197i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 1.47136 4.52839i 1.47136 4.52839i
\(669\) 0 0
\(670\) −1.38279 −1.38279
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(674\) 0.489334 1.50602i 0.489334 1.50602i
\(675\) 0 0
\(676\) 1.95715 1.42195i 1.95715 1.42195i
\(677\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 2.29617 + 2.77559i 2.29617 + 2.77559i
\(683\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(684\) −3.48509 2.53207i −3.48509 2.53207i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 3.68978 3.68978
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1.26756 + 0.325453i 1.26756 + 0.325453i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(710\) 0 0
\(711\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(712\) 1.06804 3.28709i 1.06804 3.28709i
\(713\) −2.74670 1.99559i −2.74670 1.99559i
\(714\) 0 0
\(715\) 0.0437581 0.0173251i 0.0437581 0.0173251i
\(716\) −3.97703 −3.97703
\(717\) 0 0
\(718\) 0 0
\(719\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(720\) 0.783295 0.569097i 0.783295 0.569097i
\(721\) 0 0
\(722\) −1.19044 3.66380i −1.19044 3.66380i
\(723\) 0 0
\(724\) −0.249720 0.181432i −0.249720 0.181432i
\(725\) 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
\(730\) 0.313968 + 0.966296i 0.313968 + 0.966296i
\(731\) 0 0
\(732\) 0 0
\(733\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(734\) 0.732570 2.25462i 0.732570 2.25462i
\(735\) 0 0
\(736\) −3.66836 −3.66836
\(737\) 1.84489 0.730444i 1.84489 0.730444i
\(738\) 0 0
\(739\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.61803 −1.61803
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0.229790 + 0.707220i 0.229790 + 0.707220i
\(756\) 0 0
\(757\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 1.78070 1.78070
\(761\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 1.06856 + 3.28869i 1.06856 + 3.28869i
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(774\) 0 0
\(775\) 1.34709 0.978720i 1.34709 0.978720i
\(776\) −1.86775 + 1.35700i −1.86775 + 1.35700i
\(777\) 0 0
\(778\) −1.11316 + 3.42596i −1.11316 + 3.42596i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.798351 2.45707i 0.798351 2.45707i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.688925 0.500534i 0.688925 0.500534i −0.187381 0.982287i \(-0.560000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) −0.563797 0.409622i −0.563797 0.409622i
\(791\) 0 0
\(792\) −1.45269 + 2.28907i −1.45269 + 2.28907i
\(793\) 0 0
\(794\) −2.43419 1.76854i −2.43419 1.76854i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.555956 1.71106i 0.555956 1.71106i
\(801\) 1.03137 + 0.749337i 1.03137 + 0.749337i
\(802\) 0 0