Properties

Label 869.1.j.a.236.4
Level $869$
Weight $1$
Character 869.236
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 236.4
Root \(0.992115 - 0.125333i\) of defining polynomial
Character \(\chi\) \(=\) 869.236
Dual form 869.1.j.a.394.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.450527 + 1.38658i) q^{2} +(-0.910614 + 0.661600i) q^{4} +(-0.574633 + 1.76854i) q^{5} +(-0.148122 - 0.107617i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(0.450527 + 1.38658i) q^{2} +(-0.910614 + 0.661600i) q^{4} +(-0.574633 + 1.76854i) q^{5} +(-0.148122 - 0.107617i) q^{8} +(0.309017 + 0.951057i) q^{9} -2.71111 q^{10} +(0.728969 - 0.684547i) q^{11} +(-0.613161 - 1.88711i) q^{13} +(-0.265337 + 0.816623i) q^{16} +(-1.17950 + 0.856954i) q^{18} +(-0.866986 - 0.629902i) q^{19} +(-0.646797 - 1.99064i) q^{20} +(1.27760 + 0.702367i) q^{22} +1.07165 q^{23} +(-1.98851 - 1.44474i) q^{25} +(2.34039 - 1.70039i) q^{26} +(0.541587 + 1.66683i) q^{31} -1.43494 q^{32} +(-0.910614 - 0.661600i) q^{36} +(0.482809 - 1.48593i) q^{38} +(0.275441 - 0.200120i) q^{40} +(-0.210913 + 1.10564i) q^{44} -1.85955 q^{45} +(0.482809 + 1.48593i) q^{46} +(0.309017 - 0.951057i) q^{49} +(1.10737 - 3.40813i) q^{50} +(1.80687 + 1.31277i) q^{52} +(0.791759 + 1.68257i) q^{55} +(-2.06720 + 1.50191i) q^{62} +(-0.381145 - 1.17304i) q^{64} +3.68978 q^{65} +1.93717 q^{67} +(0.0565777 - 0.174128i) q^{72} +(-0.101597 + 0.0738147i) q^{73} +1.20623 q^{76} +(0.309017 + 0.951057i) q^{79} +(-1.29176 - 0.938518i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(0.190983 - 0.587785i) q^{83} +(-0.181646 + 0.0229472i) q^{88} -0.374763 q^{89} +(-0.837780 - 2.57842i) q^{90} +(-0.975863 + 0.709006i) q^{92} +(1.61221 - 1.17134i) q^{95} +(-0.393950 - 1.21245i) q^{97} +1.45794 q^{98} +(0.876307 + 0.481754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} + 15q^{20} - 5q^{22} - 5q^{25} + 15q^{26} - 10q^{32} - 5q^{36} - 10q^{40} - 5q^{49} - 10q^{50} - 10q^{62} - 5q^{64} - 10q^{76} - 5q^{79} - 10q^{80} - 5q^{81} + 15q^{83} - 5q^{88} + 15q^{92} + 15q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(475\) \(793\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(3\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(4\) −0.910614 + 0.661600i −0.910614 + 0.661600i
\(5\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(6\) 0 0
\(7\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(8\) −0.148122 0.107617i −0.148122 0.107617i
\(9\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(10\) −2.71111 −2.71111
\(11\) 0.728969 0.684547i 0.728969 0.684547i
\(12\) 0 0
\(13\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.265337 + 0.816623i −0.265337 + 0.816623i
\(17\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(18\) −1.17950 + 0.856954i −1.17950 + 0.856954i
\(19\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(20\) −0.646797 1.99064i −0.646797 1.99064i
\(21\) 0 0
\(22\) 1.27760 + 0.702367i 1.27760 + 0.702367i
\(23\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(24\) 0 0
\(25\) −1.98851 1.44474i −1.98851 1.44474i
\(26\) 2.34039 1.70039i 2.34039 1.70039i
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(30\) 0 0
\(31\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(32\) −1.43494 −1.43494
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.910614 0.661600i −0.910614 0.661600i
\(37\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(38\) 0.482809 1.48593i 0.482809 1.48593i
\(39\) 0 0
\(40\) 0.275441 0.200120i 0.275441 0.200120i
\(41\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −0.210913 + 1.10564i −0.210913 + 1.10564i
\(45\) −1.85955 −1.85955
\(46\) 0.482809 + 1.48593i 0.482809 + 1.48593i
\(47\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(48\) 0 0
\(49\) 0.309017 0.951057i 0.309017 0.951057i
\(50\) 1.10737 3.40813i 1.10737 3.40813i
\(51\) 0 0
\(52\) 1.80687 + 1.31277i 1.80687 + 1.31277i
\(53\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(54\) 0 0
\(55\) 0.791759 + 1.68257i 0.791759 + 1.68257i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(60\) 0 0
\(61\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(62\) −2.06720 + 1.50191i −2.06720 + 1.50191i
\(63\) 0 0
\(64\) −0.381145 1.17304i −0.381145 1.17304i
\(65\) 3.68978 3.68978
\(66\) 0 0
\(67\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(72\) 0.0565777 0.174128i 0.0565777 0.174128i
\(73\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 1.20623 1.20623
\(77\) 0 0
\(78\) 0 0
\(79\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(80\) −1.29176 0.938518i −1.29176 0.938518i
\(81\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(82\) 0 0
\(83\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −0.181646 + 0.0229472i −0.181646 + 0.0229472i
\(89\) −0.374763 −0.374763 −0.187381 0.982287i \(-0.560000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(90\) −0.837780 2.57842i −0.837780 2.57842i
\(91\) 0 0
\(92\) −0.975863 + 0.709006i −0.975863 + 0.709006i
\(93\) 0 0
\(94\) 0 0
\(95\) 1.61221 1.17134i 1.61221 1.17134i
\(96\) 0 0
\(97\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(98\) 1.45794 1.45794
\(99\) 0.876307 + 0.481754i 0.876307 + 0.481754i
\(100\) 2.76661 2.76661
\(101\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(102\) 0 0
\(103\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(104\) −0.112263 + 0.345510i −0.112263 + 0.345510i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) −1.97632 + 1.85588i −1.97632 + 1.85588i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(114\) 0 0
\(115\) −0.615808 + 1.89526i −0.615808 + 1.89526i
\(116\) 0 0
\(117\) 1.60528 1.16630i 1.60528 1.16630i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.0627905 0.998027i 0.0627905 0.998027i
\(122\) 0 0
\(123\) 0 0
\(124\) −1.59595 1.15953i −1.59595 1.15953i
\(125\) 2.19334 1.59355i 2.19334 1.59355i
\(126\) 0 0
\(127\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(128\) 0.293909 0.213537i 0.293909 0.213537i
\(129\) 0 0
\(130\) 1.66235 + 5.11618i 1.66235 + 5.11618i
\(131\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.872746 + 2.68604i 0.872746 + 2.68604i
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(138\) 0 0
\(139\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.73879 0.955910i −1.73879 0.955910i
\(144\) −0.858648 −0.858648
\(145\) 0 0
\(146\) −0.148122 0.107617i −0.148122 0.107617i
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(150\) 0 0
\(151\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(152\) 0.0606317 + 0.186605i 0.0606317 + 0.186605i
\(153\) 0 0
\(154\) 0 0
\(155\) −3.25908 −3.25908
\(156\) 0 0
\(157\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(158\) −1.17950 + 0.856954i −1.17950 + 0.856954i
\(159\) 0 0
\(160\) 0.824567 2.53776i 0.824567 2.53776i
\(161\) 0 0
\(162\) −1.17950 0.856954i −1.17950 0.856954i
\(163\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0.901055 0.901055
\(167\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(168\) 0 0
\(169\) −2.37622 + 1.72642i −2.37622 + 1.72642i
\(170\) 0 0
\(171\) 0.331159 1.01920i 0.331159 1.01920i
\(172\) 0 0
\(173\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.365595 + 0.776928i 0.365595 + 0.776928i
\(177\) 0 0
\(178\) −0.168841 0.519639i −0.168841 0.519639i
\(179\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(180\) 1.69334 1.23028i 1.69334 1.23028i
\(181\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.158736 0.115328i −0.158736 0.115328i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 2.35050 + 1.70774i 2.35050 + 1.70774i
\(191\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(192\) 0 0
\(193\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(194\) 1.50368 1.09249i 1.50368 1.09249i
\(195\) 0 0
\(196\) 0.347824 + 1.07049i 0.347824 + 1.07049i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −0.273190 + 1.43211i −0.273190 + 1.43211i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0.139064 + 0.427996i 0.139064 + 0.427996i
\(201\) 0 0
\(202\) 0.442031 0.321154i 0.442031 0.321154i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.331159 + 1.01920i 0.331159 + 1.01920i
\(208\) 1.70376 1.70376
\(209\) −1.06320 + 0.134314i −1.06320 + 0.134314i
\(210\) 0 0
\(211\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −1.83418 1.00835i −1.83418 1.00835i
\(221\) 0 0
\(222\) 0 0
\(223\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(224\) 0 0
\(225\) 0.759544 2.33764i 0.759544 2.33764i
\(226\) 0 0
\(227\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(228\) 0 0
\(229\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(230\) −2.90537 −2.90537
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(234\) 2.34039 + 1.70039i 2.34039 + 1.70039i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(240\) 0 0
\(241\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(242\) 1.41213 0.362574i 1.41213 0.362574i
\(243\) 0 0
\(244\) 0 0
\(245\) 1.50441 + 1.09302i 1.50441 + 1.09302i
\(246\) 0 0
\(247\) −0.657096 + 2.02233i −0.657096 + 2.02233i
\(248\) 0.0991588 0.305179i 0.0991588 0.305179i
\(249\) 0 0
\(250\) 3.19775 + 2.32330i 3.19775 + 2.32330i
\(251\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(252\) 0 0
\(253\) 0.781202 0.733597i 0.781202 0.733597i
\(254\) 0 0
\(255\) 0 0
\(256\) −0.569350 0.413657i −0.569350 0.413657i
\(257\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −3.35997 + 2.44116i −3.35997 + 2.44116i
\(261\) 0 0
\(262\) 0.0565777 + 0.174128i 0.0565777 + 0.174128i
\(263\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −1.76401 + 1.28163i −1.76401 + 1.28163i
\(269\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(270\) 0 0
\(271\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.43856 + 0.308061i −2.43856 + 0.308061i
\(276\) 0 0
\(277\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(278\) 0 0
\(279\) −1.41789 + 1.03016i −1.41789 + 1.03016i
\(280\) 0 0
\(281\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(282\) 0 0
\(283\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0.542072 2.84164i 0.542072 2.84164i
\(287\) 0 0
\(288\) −0.443422 1.36471i −0.443422 1.36471i
\(289\) −0.809017 0.587785i −0.809017 0.587785i
\(290\) 0 0
\(291\) 0 0
\(292\) 0.0436801 0.134433i 0.0436801 0.134433i
\(293\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.657096 2.02233i −0.657096 2.02233i
\(300\) 0 0
\(301\) 0 0
\(302\) 0.872746 2.68604i 0.872746 2.68604i
\(303\) 0 0
\(304\) 0.744436 0.540864i 0.744436 0.540864i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1.46830 4.51897i −1.46830 4.51897i
\(311\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(312\) 0 0
\(313\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −0.910614 0.661600i −0.910614 0.661600i
\(317\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 2.29359 2.29359
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.347824 1.07049i 0.347824 1.07049i
\(325\) −1.50711 + 4.63841i −1.50711 + 4.63841i
\(326\) 1.00441 0.729747i 1.00441 0.729747i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0.214967 + 0.661600i 0.214967 + 0.661600i
\(333\) 0 0
\(334\) −2.06720 + 1.50191i −2.06720 + 1.50191i
\(335\) −1.11316 + 3.42596i −1.11316 + 3.42596i
\(336\) 0 0
\(337\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(338\) −3.46438 2.51702i −3.46438 2.51702i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.53583 + 0.844328i 1.53583 + 0.844328i
\(342\) 1.56240 1.56240
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.04603 + 0.982287i −1.04603 + 0.982287i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.341264 0.247943i 0.341264 0.247943i
\(357\) 0 0
\(358\) 0.278441 0.856954i 0.278441 0.856954i
\(359\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(360\) 0.275441 + 0.200120i 0.275441 + 0.200120i
\(361\) 0.0458709 + 0.141176i 0.0458709 + 0.141176i
\(362\) −2.89288 −2.89288
\(363\) 0 0
\(364\) 0 0
\(365\) −0.0721631 0.222095i −0.0721631 0.222095i
\(366\) 0 0
\(367\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(368\) −0.284349 + 0.875137i −0.284349 + 0.875137i
\(369\) 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 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(380\) −0.693142 + 2.13327i −0.693142 + 2.13327i
\(381\) 0 0
\(382\) 0 0
\(383\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 1.16089 + 0.843439i 1.16089 + 0.843439i
\(389\) −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i \(0.640000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.148122 + 0.107617i −0.148122 + 0.107617i
\(393\) 0 0
\(394\) 0 0
\(395\) −1.85955 −1.85955
\(396\) −1.11671 + 0.141073i −1.11671 + 0.141073i
\(397\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.70743 1.24052i 1.70743 1.24052i
\(401\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(402\) 0 0
\(403\) 2.81343 2.04407i 2.81343 2.04407i
\(404\) 0.341264 + 0.247943i 0.341264 + 0.247943i
\(405\) −0.574633 1.76854i −0.574633 1.76854i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −1.26401 + 0.918358i −1.26401 + 0.918358i
\(415\) 0.929776 + 0.675522i 0.929776 + 0.675522i
\(416\) 0.879852 + 2.70790i 0.879852 + 2.70790i
\(417\) 0 0
\(418\) −0.665239 1.41371i −0.665239 1.41371i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(422\) 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
\(431\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(432\) 0 0
\(433\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.929109 0.675037i −0.929109 0.675037i
\(438\) 0 0
\(439\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(440\) 0.0637966 0.334434i 0.0637966 0.334434i
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(444\) 0 0
\(445\) 0.215351 0.662783i 0.215351 0.662783i
\(446\) 0.278441 0.856954i 0.278441 0.856954i
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(450\) 3.58352 3.58352
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −0.693142 2.13327i −0.693142 2.13327i
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(468\) −0.690162 + 2.12410i −0.690162 + 2.12410i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.813968 + 2.50514i 0.813968 + 2.50514i
\(476\) 0 0
\(477\) 0 0
\(478\) −0.837780 + 2.57842i −0.837780 + 2.57842i
\(479\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.383650 1.18075i −0.383650 1.18075i
\(483\) 0 0
\(484\) 0.603116 + 0.950360i 0.603116 + 0.950360i
\(485\) 2.37065 2.37065
\(486\) 0 0
\(487\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −0.837780 + 2.57842i −0.837780 + 2.57842i
\(491\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −3.10017 −3.10017
\(495\) −1.35556 + 1.27295i −1.35556 + 1.27295i
\(496\) −1.50488 −1.50488
\(497\) 0 0
\(498\) 0 0
\(499\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(500\) −0.942989 + 2.90222i −0.942989 + 2.90222i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(504\) 0 0
\(505\) 0.696891 0.696891
\(506\) 1.36914 + 0.752694i 1.36914 + 0.752694i
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.429324 1.32132i 0.429324 1.32132i
\(513\) 0 0
\(514\) 2.34039 + 1.70039i 2.34039 + 1.70039i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −0.546539 0.397084i −0.546539 0.397084i
\(521\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(522\) 0 0
\(523\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(524\) −0.114356 + 0.0830844i −0.114356 + 0.0830844i
\(525\) 0 0
\(526\) −0.383650 1.18075i −0.383650 1.18075i
\(527\) 0 0
\(528\) 0 0
\(529\) 0.148441 0.148441
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −0.286938 0.208472i −0.286938 0.208472i
\(537\) 0 0
\(538\) 2.82427 2.82427
\(539\) −0.425779 0.904827i −0.425779 0.904827i
\(540\) 0 0
\(541\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) −1.52579 3.24246i −1.52579 3.24246i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 2.19334 1.59355i 2.19334 1.59355i
\(555\) 0 0
\(556\) 0 0
\(557\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(558\) −2.06720 1.50191i −2.06720 1.50191i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −2.71111 −2.71111
\(563\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.789600 2.43014i 0.789600 2.43014i
\(567\) 0 0
\(568\) 0 0
\(569\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(570\) 0 0
\(571\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(572\) 2.21580 0.279921i 2.21580 0.279921i
\(573\) 0 0
\(574\) 0 0
\(575\) −2.13100 1.54826i −2.13100 1.54826i
\(576\) 0.997850 0.724981i 0.997850 0.724981i
\(577\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(578\) 0.450527 1.38658i 0.450527 1.38658i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0.0229925 0.0229925
\(585\) 1.14020 + 3.50919i 1.14020 + 3.50919i
\(586\) 0 0
\(587\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(588\) 0 0
\(589\) 0.580394 1.78627i 0.580394 1.78627i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.85955 −1.85955 −0.929776 0.368125i \(-0.880000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 2.50809 1.82223i 2.50809 1.82223i
\(599\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(600\) 0 0
\(601\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(602\) 0 0
\(603\) 0.598617 + 1.84235i 0.598617 + 1.84235i
\(604\) 2.18044 2.18044
\(605\) 1.72897 + 0.684547i 1.72897 + 0.684547i
\(606\) 0 0
\(607\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(608\) 1.24408 + 0.903875i 1.24408 + 0.903875i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(618\) 0 0
\(619\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(620\) 2.96776 2.15621i 2.96776 2.15621i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.798351 + 2.45707i 0.798351 + 2.45707i
\(626\) 2.55520 2.55520
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(632\) 0.0565777 0.174128i 0.0565777 0.174128i
\(633\) 0 0
\(634\) 1.90846 1.38658i 1.90846 1.38658i
\(635\) 0 0
\(636\) 0 0
\(637\) −1.98423 −1.98423
\(638\) 0 0
\(639\) 0 0
\(640\) 0.208759 + 0.642495i 0.208759 + 0.642495i
\(641\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(642\) 0 0
\(643\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(648\) 0.183089 0.183089
\(649\) 0 0
\(650\) −7.11052 −7.11052
\(651\) 0 0
\(652\) 0.775441 + 0.563391i 0.775441 + 0.563391i
\(653\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(654\) 0 0
\(655\) −0.0721631 + 0.222095i −0.0721631 + 0.222095i
\(656\) 0 0
\(657\) −0.101597 0.0738147i −0.101597 0.0738147i
\(658\) 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
\(664\) −0.0915446 + 0.0665111i −0.0915446 + 0.0665111i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −1.59595 1.15953i −1.59595 1.15953i
\(669\) 0 0
\(670\) −5.25187 −5.25187
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(674\) 1.50368 + 1.09249i 1.50368 + 1.09249i
\(675\) 0 0
\(676\) 1.02162 3.14421i 1.02162 3.14421i
\(677\) −0.500000 + 1.53884i −0.500000 + 1.53884i 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
\(682\) −0.478797 + 2.50994i −0.478797 + 2.50994i
\(683\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(684\) 0.372746 + 1.14720i 0.372746 + 1.14720i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 2.82427 2.82427
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.08085 0.594200i −1.08085 0.594200i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(710\) 0 0
\(711\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(712\) 0.0555107 + 0.0403309i 0.0555107 + 0.0403309i
\(713\) 0.580394 + 1.78627i 0.580394 + 1.78627i
\(714\) 0 0
\(715\) 2.68973 2.52583i 2.68973 2.52583i
\(716\) 0.695647 0.695647
\(717\) 0 0
\(718\) 0 0
\(719\) 0.688925 0.500534i 0.688925 0.500534i −0.187381 0.982287i \(-0.560000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(720\) 0.493408 1.51855i 0.493408 1.51855i
\(721\) 0 0
\(722\) −0.175086 + 0.127207i −0.175086 + 0.127207i
\(723\) 0 0
\(724\) −0.690162 2.12410i −0.690162 2.12410i
\(725\) 0 0
\(726\) 0 0
\(727\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(728\) 0 0
\(729\) −0.809017 0.587785i −0.809017 0.587785i
\(730\) 0.275441 0.200120i 0.275441 0.200120i
\(731\) 0 0
\(732\) 0 0
\(733\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(734\) 0.442031 + 0.321154i 0.442031 + 0.321154i
\(735\) 0 0
\(736\) −1.53776 −1.53776
\(737\) 1.41213 1.32608i 1.41213 1.32608i
\(738\) 0 0
\(739\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.618034 0.618034
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.91429 2.11736i 2.91429 2.11736i
\(756\) 0 0
\(757\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −0.364860 −0.364860
\(761\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −1.71963 + 1.24939i −1.71963 + 1.24939i
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(774\) 0 0
\(775\) 1.33119 4.09697i 1.33119 4.09697i
\(776\) −0.0721280 + 0.221987i −0.0721280 + 0.221987i
\(777\) 0 0
\(778\) −2.06720 1.50191i −2.06720 1.50191i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.694661 + 0.504701i 0.694661 + 0.504701i
\(785\) 0 0
\(786\) 0 0
\(787\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) −0.837780 2.57842i −0.837780 2.57842i
\(791\) 0 0
\(792\) −0.0779556 0.165664i −0.0779556 0.165664i
\(793\) 0 0
\(794\) 0.278441 + 0.856954i 0.278441 + 0.856954i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 2.85341 + 2.07312i 2.85341 + 2.07312i
\(801\) −0.115808 0.356420i −0.115808 0.356420i
\(802\) 0 0
\(803\)