Properties

Label 869.1.j.a.157.4
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 157.4
Root \(0.929776 + 0.368125i\) of defining polynomial
Character \(\chi\) \(=\) 869.157
Dual form 869.1.j.a.631.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.03137 - 0.749337i) q^{2} +(0.193209 - 0.594636i) q^{4} +(0.688925 + 0.500534i) q^{5} +(0.147638 + 0.454382i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(1.03137 - 0.749337i) q^{2} +(0.193209 - 0.594636i) q^{4} +(0.688925 + 0.500534i) q^{5} +(0.147638 + 0.454382i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.08561 q^{10} +(-0.637424 + 0.770513i) q^{11} +(1.50441 - 1.09302i) q^{13} +(0.998582 + 0.725513i) q^{16} +(-0.393950 + 1.21245i) q^{18} +(-0.613161 - 1.88711i) q^{19} +(0.430742 - 0.312952i) q^{20} +(-0.0800484 + 1.27233i) q^{22} -1.98423 q^{23} +(-0.0849327 - 0.261396i) q^{25} +(0.732570 - 2.25462i) q^{26} +(-0.101597 + 0.0738147i) q^{31} +1.09580 q^{32} +(0.193209 + 0.594636i) q^{36} +(-2.04648 - 1.48686i) q^{38} +(-0.125722 + 0.386933i) q^{40} +(0.335019 + 0.527905i) q^{44} -0.851559 q^{45} +(-2.04648 + 1.48686i) q^{46} +(-0.809017 - 0.587785i) q^{49} +(-0.283471 - 0.205954i) q^{50} +(-0.359282 - 1.10576i) q^{52} +(-0.824805 + 0.211774i) q^{55} +(-0.0494726 + 0.152261i) q^{62} +(0.131596 - 0.0956103i) q^{64} +1.58352 q^{65} +1.45794 q^{67} +(-0.386520 - 0.280823i) q^{72} +(-0.115808 + 0.356420i) q^{73} -1.24061 q^{76} +(-0.809017 + 0.587785i) q^{79} +(0.324805 + 0.999648i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.30902 + 0.951057i) q^{83} +(-0.444215 - 0.175877i) q^{88} +1.07165 q^{89} +(-0.878275 + 0.638104i) q^{90} +(-0.383371 + 1.17989i) q^{92} +(0.522142 - 1.60699i) q^{95} +(-1.41789 + 1.03016i) q^{97} -1.27485 q^{98} +(0.0627905 - 0.998027i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} + 15q^{20} - 5q^{22} - 5q^{25} + 15q^{26} - 10q^{32} - 5q^{36} - 10q^{40} - 5q^{49} - 10q^{50} - 10q^{62} - 5q^{64} - 10q^{76} - 5q^{79} - 10q^{80} - 5q^{81} + 15q^{83} - 5q^{88} + 15q^{92} + 15q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(3\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(4\) 0.193209 0.594636i 0.193209 0.594636i
\(5\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(6\) 0 0
\(7\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(8\) 0.147638 + 0.454382i 0.147638 + 0.454382i
\(9\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(10\) 1.08561 1.08561
\(11\) −0.637424 + 0.770513i −0.637424 + 0.770513i
\(12\) 0 0
\(13\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.998582 + 0.725513i 0.998582 + 0.725513i
\(17\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(18\) −0.393950 + 1.21245i −0.393950 + 1.21245i
\(19\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(20\) 0.430742 0.312952i 0.430742 0.312952i
\(21\) 0 0
\(22\) −0.0800484 + 1.27233i −0.0800484 + 1.27233i
\(23\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(24\) 0 0
\(25\) −0.0849327 0.261396i −0.0849327 0.261396i
\(26\) 0.732570 2.25462i 0.732570 2.25462i
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(30\) 0 0
\(31\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(32\) 1.09580 1.09580
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.193209 + 0.594636i 0.193209 + 0.594636i
\(37\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(38\) −2.04648 1.48686i −2.04648 1.48686i
\(39\) 0 0
\(40\) −0.125722 + 0.386933i −0.125722 + 0.386933i
\(41\) 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 \(\pi\)
\(44\) 0.335019 + 0.527905i 0.335019 + 0.527905i
\(45\) −0.851559 −0.851559
\(46\) −2.04648 + 1.48686i −2.04648 + 1.48686i
\(47\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(48\) 0 0
\(49\) −0.809017 0.587785i −0.809017 0.587785i
\(50\) −0.283471 0.205954i −0.283471 0.205954i
\(51\) 0 0
\(52\) −0.359282 1.10576i −0.359282 1.10576i
\(53\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(54\) 0 0
\(55\) −0.824805 + 0.211774i −0.824805 + 0.211774i
\(56\) 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 \(0.200000\pi\)
\(62\) −0.0494726 + 0.152261i −0.0494726 + 0.152261i
\(63\) 0 0
\(64\) 0.131596 0.0956103i 0.131596 0.0956103i
\(65\) 1.58352 1.58352
\(66\) 0 0
\(67\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(72\) −0.386520 0.280823i −0.386520 0.280823i
\(73\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −1.24061 −1.24061
\(77\) 0 0
\(78\) 0 0
\(79\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(80\) 0.324805 + 0.999648i 0.324805 + 0.999648i
\(81\) 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
\(88\) −0.444215 0.175877i −0.444215 0.175877i
\(89\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(90\) −0.878275 + 0.638104i −0.878275 + 0.638104i
\(91\) 0 0
\(92\) −0.383371 + 1.17989i −0.383371 + 1.17989i
\(93\) 0 0
\(94\) 0 0
\(95\) 0.522142 1.60699i 0.522142 1.60699i
\(96\) 0 0
\(97\) −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i \(0.640000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(98\) −1.27485 −1.27485
\(99\) 0.0627905 0.998027i 0.0627905 0.998027i
\(100\) −0.171845 −0.171845
\(101\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(102\) 0 0
\(103\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(104\) 0.718755 + 0.522206i 0.718755 + 0.522206i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) −0.691992 + 0.836475i −0.691992 + 0.836475i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(114\) 0 0
\(115\) −1.36699 0.993173i −1.36699 0.993173i
\(116\) 0 0
\(117\) −0.574633 + 1.76854i −0.574633 + 1.76854i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.187381 0.982287i −0.187381 0.982287i
\(122\) 0 0
\(123\) 0 0
\(124\) 0.0242634 + 0.0746750i 0.0242634 + 0.0746750i
\(125\) 0.335471 1.03247i 0.335471 1.03247i
\(126\) 0 0
\(127\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(128\) −0.274540 + 0.844947i −0.274540 + 0.844947i
\(129\) 0 0
\(130\) 1.63320 1.18659i 1.63320 1.18659i
\(131\) −0.374763 −0.374763 −0.187381 0.982287i \(-0.560000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1.50368 1.09249i 1.50368 1.09249i
\(135\) 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
\(143\) −0.116762 + 1.85588i −0.116762 + 1.85588i
\(144\) −1.23432 −1.23432
\(145\) 0 0
\(146\) 0.147638 + 0.454382i 0.147638 + 0.454382i
\(147\) 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
\(151\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(152\) 0.766945 0.557218i 0.766945 0.557218i
\(153\) 0 0
\(154\) 0 0
\(155\) −0.106940 −0.106940
\(156\) 0 0
\(157\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(158\) −0.393950 + 1.21245i −0.393950 + 1.21245i
\(159\) 0 0
\(160\) 0.754924 + 0.548484i 0.754924 + 0.548484i
\(161\) 0 0
\(162\) −0.393950 1.21245i −0.393950 1.21245i
\(163\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 2.06275 2.06275
\(167\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(168\) 0 0
\(169\) 0.759544 2.33764i 0.759544 2.33764i
\(170\) 0 0
\(171\) 1.60528 + 1.16630i 1.60528 + 1.16630i
\(172\) 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
\(176\) −1.19554 + 0.306962i −1.19554 + 0.306962i
\(177\) 0 0
\(178\) 1.10528 0.803030i 1.10528 0.803030i
\(179\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(180\) −0.164529 + 0.506367i −0.164529 + 0.506367i
\(181\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.292947 0.901598i −0.292947 0.901598i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) −0.665652 2.04867i −0.665652 2.04867i
\(191\) 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 \(0.200000\pi\)
\(194\) −0.690441 + 2.12496i −0.690441 + 2.12496i
\(195\) 0 0
\(196\) −0.505828 + 0.367505i −0.505828 + 0.367505i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −0.683098 1.07639i −0.683098 1.07639i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0.106234 0.0771838i 0.106234 0.0771838i
\(201\) 0 0
\(202\) −0.422178 + 1.29933i −0.422178 + 1.29933i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.60528 1.16630i 1.60528 1.16630i
\(208\) 2.29528 2.29528
\(209\) 1.84489 + 0.730444i 1.84489 + 0.730444i
\(210\) 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
\(220\) −0.0334313 + 0.531376i −0.0334313 + 0.531376i
\(221\) 0 0
\(222\) 0 0
\(223\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(224\) 0 0
\(225\) 0.222357 + 0.161552i 0.222357 + 0.161552i
\(226\) 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 \(0.800000\pi\)
\(230\) −2.15409 −2.15409
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(234\) 0.732570 + 2.25462i 0.732570 + 2.25462i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(240\) 0 0
\(241\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(242\) −0.929324 0.872693i −0.929324 0.872693i
\(243\) 0 0
\(244\) 0 0
\(245\) −0.263146 0.809880i −0.263146 0.809880i
\(246\) 0 0
\(247\) −2.98509 2.16880i −2.98509 2.16880i
\(248\) −0.0485396 0.0352661i −0.0485396 0.0352661i
\(249\) 0 0
\(250\) −0.427675 1.31625i −0.427675 1.31625i
\(251\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(252\) 0 0
\(253\) 1.26480 1.52888i 1.26480 1.52888i
\(254\) 0 0
\(255\) 0 0
\(256\) 0.400262 + 1.23188i 0.400262 + 1.23188i
\(257\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0.305950 0.941617i 0.305950 0.941617i
\(261\) 0 0
\(262\) −0.386520 + 0.280823i −0.386520 + 0.280823i
\(263\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0.281687 0.866942i 0.281687 0.866942i
\(269\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(270\) 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
\(275\) 0.255547 + 0.101178i 0.255547 + 0.101178i
\(276\) 0 0
\(277\) 0.688925 0.500534i 0.688925 0.500534i −0.187381 0.982287i \(-0.560000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(278\) 0 0
\(279\) 0.0388067 0.119435i 0.0388067 0.119435i
\(280\) 0 0
\(281\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(282\) 0 0
\(283\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 1.27026 + 2.00160i 1.27026 + 2.00160i
\(287\) 0 0
\(288\) −0.886520 + 0.644095i −0.886520 + 0.644095i
\(289\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(290\) 0 0
\(291\) 0 0
\(292\) 0.189565 + 0.137727i 0.189565 + 0.137727i
\(293\) 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
\(299\) −2.98509 + 2.16880i −2.98509 + 2.16880i
\(300\) 0 0
\(301\) 0 0
\(302\) 1.50368 + 1.09249i 1.50368 + 1.09249i
\(303\) 0 0
\(304\) 0.756834 2.32929i 0.756834 2.32929i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.110295 + 0.0801338i −0.110295 + 0.0801338i
\(311\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(312\) 0 0
\(313\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.193209 + 0.594636i 0.193209 + 0.594636i
\(317\) −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
\(320\) 0.138516 0.138516
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.505828 0.367505i −0.505828 0.367505i
\(325\) −0.413484 0.300414i −0.413484 0.300414i
\(326\) −0.763146 + 2.34872i −0.763146 + 2.34872i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0.818446 0.594636i 0.818446 0.594636i
\(333\) 0 0
\(334\) −0.0494726 + 0.152261i −0.0494726 + 0.152261i
\(335\) 1.00441 + 0.729747i 1.00441 + 0.729747i
\(336\) 0 0
\(337\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(338\) −0.968304 2.98013i −0.968304 2.98013i
\(339\) 0 0
\(340\) 0 0
\(341\) 0.00788530 0.125333i 0.00788530 0.125333i
\(342\) 2.52959 2.52959
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(348\) 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
\(352\) −0.698489 + 0.844328i −0.698489 + 0.844328i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.207053 0.637244i 0.207053 0.637244i
\(357\) 0 0
\(358\) −1.66880 1.21245i −1.66880 1.21245i
\(359\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(360\) −0.125722 0.386933i −0.125722 0.386933i
\(361\) −2.37622 + 1.72642i −2.37622 + 1.72642i
\(362\) 2.37065 2.37065
\(363\) 0 0
\(364\) 0 0
\(365\) −0.258183 + 0.187581i −0.258183 + 0.187581i
\(366\) 0 0
\(367\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(368\) −1.98142 1.43958i −1.98142 1.43958i
\(369\) 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 \(0.200000\pi\)
\(380\) −0.854691 0.620969i −0.854691 0.620969i
\(381\) 0 0
\(382\) 0 0
\(383\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0.338621 + 1.04217i 0.338621 + 1.04217i
\(389\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.147638 0.454382i 0.147638 0.454382i
\(393\) 0 0
\(394\) 0 0
\(395\) −0.851559 −0.851559
\(396\) −0.581331 0.230165i −0.581331 0.230165i
\(397\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.104834 0.322645i 0.104834 0.322645i
\(401\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(402\) 0 0
\(403\) −0.0721631 + 0.222095i −0.0721631 + 0.222095i
\(404\) 0.207053 + 0.637244i 0.207053 + 0.637244i
\(405\) 0.688925 0.500534i 0.688925 0.500534i
\(406\) 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
\(414\) 0.781687 2.40578i 0.781687 2.40578i
\(415\) 0.425779 + 1.31041i 0.425779 + 1.31041i
\(416\) 1.64853 1.19773i 1.64853 1.19773i
\(417\) 0 0
\(418\) 2.45012 0.629084i 2.45012 0.629084i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−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
\(431\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(432\) 0 0
\(433\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.21665 + 3.74447i 1.21665 + 3.74447i
\(438\) 0 0
\(439\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(440\) −0.217999 0.343511i −0.217999 0.343511i
\(441\) 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
\(445\) 0.738289 + 0.536399i 0.738289 + 0.536399i
\(446\) −1.66880 1.21245i −1.66880 1.21245i
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(450\) 0.350389 0.350389
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −0.854691 + 0.620969i −0.854691 + 0.620969i
\(461\) 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
\(467\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(468\) 0.940613 + 0.683396i 0.940613 + 0.683396i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −0.441207 + 0.320555i −0.441207 + 0.320555i
\(476\) 0 0
\(477\) 0 0
\(478\) −0.878275 0.638104i −0.878275 0.638104i
\(479\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1.99794 1.45159i 1.99794 1.45159i
\(483\) 0 0
\(484\) −0.620307 0.0783630i −0.620307 0.0783630i
\(485\) −1.49245 −1.49245
\(486\) 0 0
\(487\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −0.878275 0.638104i −0.878275 0.638104i
\(491\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −4.70391 −4.70391
\(495\) 0.542804 0.656137i 0.542804 0.656137i
\(496\) −0.155007 −0.155007
\(497\) 0 0
\(498\) 0 0
\(499\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(500\) −0.549130 0.398967i −0.549130 0.398967i
\(501\) 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
\(505\) −0.912576 −0.912576
\(506\) 0.158834 2.52460i 0.158834 2.52460i
\(507\) 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
\(512\) 0.617158 + 0.448391i 0.617158 + 0.448391i
\(513\) 0 0
\(514\) 0.732570 + 2.25462i 0.732570 + 2.25462i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0.233787 + 0.719522i 0.233787 + 0.719522i
\(521\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(522\) 0 0
\(523\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(524\) −0.0724075 + 0.222847i −0.0724075 + 0.222847i
\(525\) 0 0
\(526\) 1.99794 1.45159i 1.99794 1.45159i
\(527\) 0 0
\(528\) 0 0
\(529\) 2.93717 2.93717
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0.215246 + 0.662460i 0.215246 + 0.662460i
\(537\) 0 0
\(538\) −1.85865 −1.85865
\(539\) 0.968583 0.248690i 0.968583 0.248690i
\(540\) 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
\(547\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0.339381 0.0871383i 0.339381 0.0871383i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0.335471 1.03247i 0.335471 1.03247i
\(555\) 0 0
\(556\) 0 0
\(557\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(558\) −0.0494726 0.152261i −0.0494726 0.152261i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 1.08561 1.08561
\(563\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.129521 + 0.0941025i 0.129521 + 0.0941025i
\(567\) 0 0
\(568\) 0 0
\(569\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(570\) 0 0
\(571\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(572\) 1.08102 + 0.428004i 1.08102 + 0.428004i
\(573\) 0 0
\(574\) 0 0
\(575\) 0.168526 + 0.518670i 0.168526 + 0.518670i
\(576\) −0.0502653 + 0.154701i −0.0502653 + 0.154701i
\(577\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(578\) 1.03137 + 0.749337i 1.03137 + 0.749337i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −0.179049 −0.179049
\(585\) −1.28109 + 0.930769i −1.28109 + 0.930769i
\(586\) 0 0
\(587\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(588\) 0 0
\(589\) 0.201592 + 0.146465i 0.201592 + 0.146465i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −1.45359 + 4.47368i −1.45359 + 4.47368i
\(599\) 0.303189 + 0.220280i 0.303189 + 0.220280i 0.728969 0.684547i \(-0.240000\pi\)
−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
\(603\) −1.17950 + 0.856954i −1.17950 + 0.856954i
\(604\) 0.911557 0.911557
\(605\) 0.362576 0.770513i 0.362576 0.770513i
\(606\) 0 0
\(607\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(608\) −0.671901 2.06790i −0.671901 2.06790i
\(609\) 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
\(617\) −1.85955 −1.85955 −0.929776 0.368125i \(-0.880000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(618\) 0 0
\(619\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(620\) −0.0206617 + 0.0635902i −0.0206617 + 0.0635902i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.525546 0.381832i 0.525546 0.381832i
\(626\) −0.160097 −0.160097
\(627\) 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 \(0.600000\pi\)
\(632\) −0.386520 0.280823i −0.386520 0.280823i
\(633\) 0 0
\(634\) −0.243474 + 0.749337i −0.243474 + 0.749337i
\(635\) 0 0
\(636\) 0 0
\(637\) −1.85955 −1.85955
\(638\) 0 0
\(639\) 0 0
\(640\) −0.612062 + 0.444689i −0.612062 + 0.444689i
\(641\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(642\) 0 0
\(643\) 0.303189 + 0.220280i 0.303189 + 0.220280i 0.728969 0.684547i \(-0.240000\pi\)
−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 \(0.800000\pi\)
\(648\) 0.477765 0.477765
\(649\) 0 0
\(650\) −0.651568 −0.651568
\(651\) 0 0
\(652\) 0.374278 + 1.15191i 0.374278 + 1.15191i
\(653\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(654\) 0 0
\(655\) −0.258183 0.187581i −0.258183 0.187581i
\(656\) 0 0
\(657\) −0.115808 0.356420i −0.115808 0.356420i
\(658\) 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
\(664\) −0.238883 + 0.735205i −0.238883 + 0.735205i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0.0242634 + 0.0746750i 0.0242634 + 0.0746750i
\(669\) 0 0
\(670\) 1.58275 1.58275
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(674\) −0.690441 2.12496i −0.690441 2.12496i
\(675\) 0 0
\(676\) −1.24329 0.903305i −1.24329 0.903305i
\(677\) −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
\(682\) −0.0857841 0.135174i −0.0857841 0.135174i
\(683\) −0.374763 −0.374763 −0.187381 0.982287i \(-0.560000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(684\) 1.00368 0.729215i 1.00368 0.729215i
\(685\) 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
\(694\) −1.85865 −1.85865
\(695\) 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
\(704\) −0.0102136 + 0.162341i −0.0102136 + 0.162341i
\(705\) 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
\(712\) 0.158216 + 0.486940i 0.158216 + 0.486940i
\(713\) 0.201592 0.146465i 0.201592 0.146465i
\(714\) 0 0
\(715\) −1.00937 + 1.22012i −1.00937 + 1.22012i
\(716\) −1.01166 −1.01166
\(717\) 0 0
\(718\) 0 0
\(719\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(720\) −0.850351 0.617816i −0.850351 0.617816i
\(721\) 0 0
\(722\) −1.15710 + 3.56117i −1.15710 + 3.56117i
\(723\) 0 0
\(724\) 0.940613 0.683396i 0.940613 0.683396i
\(725\) 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
\(730\) −0.125722 + 0.386933i −0.125722 + 0.386933i
\(731\) 0 0
\(732\) 0 0
\(733\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(734\) −0.422178 1.29933i −0.422178 1.29933i
\(735\) 0 0
\(736\) −2.17432 −2.17432
\(737\) −0.929324 + 1.12336i −0.929324 + 1.12336i
\(738\) 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
\(743\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
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
\(751\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.383650 + 1.18075i −0.383650 + 1.18075i
\(756\) 0 0
\(757\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0.807274 0.807274
\(761\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0.502226 1.54569i 0.502226 1.54569i
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(774\) 0 0
\(775\) 0.0279238 + 0.0202878i 0.0279238 + 0.0202878i
\(776\) −0.677421 0.492175i −0.677421 0.492175i
\(777\) 0 0
\(778\) −0.0494726 0.152261i −0.0494726 0.152261i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.381424 1.17390i −0.381424 1.17390i
\(785\) 0 0
\(786\) 0 0
\(787\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) −0.878275 + 0.638104i −0.878275 + 0.638104i
\(791\) 0 0
\(792\) 0.462756 0.118815i 0.462756 0.118815i
\(793\) 0 0
\(794\) −1.66880 + 1.21245i −1.66880 + 1.21245i
\(795\) 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
\(800\) −0.0930692 0.286438i −0.0930692 0.286438i
\(801\) −0.866986 + 0.629902i −0.866986 + 0.629902i
\(802\) 0 0