Properties

Label 869.1.j.a.394.3
Level $869$
Weight $1$
Character 869.394
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 394.3
Root \(-0.728969 - 0.684547i\) of defining polynomial
Character \(\chi\) \(=\) 869.394
Dual form 869.1.j.a.236.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.115808 + 0.356420i) q^{2} +(0.695393 + 0.505233i) q^{4} +(-0.393950 - 1.21245i) q^{5} +(-0.563797 + 0.409622i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.115808 + 0.356420i) q^{2} +(0.695393 + 0.505233i) q^{4} +(-0.393950 - 1.21245i) q^{5} +(-0.563797 + 0.409622i) q^{8} +(0.309017 - 0.951057i) q^{9} +0.477765 q^{10} +(-0.187381 - 0.982287i) q^{11} +(0.450527 - 1.38658i) q^{13} +(0.184911 + 0.569097i) q^{16} +(0.303189 + 0.220280i) q^{18} +(-1.56720 + 1.13864i) q^{19} +(0.338621 - 1.04217i) q^{20} +(0.371808 + 0.0469702i) q^{22} +1.93717 q^{23} +(-0.505828 + 0.367505i) q^{25} +(0.442031 + 0.321154i) q^{26} +(-0.613161 + 1.88711i) q^{31} -0.921143 q^{32} +(0.695393 - 0.505233i) q^{36} +(-0.224339 - 0.690446i) q^{38} +(0.718755 + 0.522206i) q^{40} +(0.365980 - 0.777747i) q^{44} -1.27485 q^{45} +(-0.224339 + 0.690446i) q^{46} +(0.309017 + 0.951057i) q^{49} +(-0.0724075 - 0.222847i) q^{50} +(1.01384 - 0.736597i) q^{52} +(-1.11716 + 0.614163i) q^{55} +(-0.601597 - 0.437086i) q^{62} +(-0.0782352 + 0.240783i) q^{64} -1.85865 q^{65} +0.125581 q^{67} +(0.215351 + 0.662783i) q^{72} +(1.50441 + 1.09302i) q^{73} -1.66510 q^{76} +(0.309017 - 0.951057i) q^{79} +(0.617158 - 0.448391i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.190983 + 0.587785i) q^{83} +(0.508012 + 0.477055i) q^{88} -0.851559 q^{89} +(0.147638 - 0.454382i) q^{90} +(1.34709 + 0.978720i) q^{92} +(1.99794 + 1.45159i) q^{95} +(0.331159 - 1.01920i) q^{97} -0.374763 q^{98} +(-0.992115 - 0.125333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} + 15q^{20} - 5q^{22} - 5q^{25} + 15q^{26} - 10q^{32} - 5q^{36} - 10q^{40} - 5q^{49} - 10q^{50} - 10q^{62} - 5q^{64} - 10q^{76} - 5q^{79} - 10q^{80} - 5q^{81} + 15q^{83} - 5q^{88} + 15q^{92} + 15q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(475\) \(793\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(3\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(4\) 0.695393 + 0.505233i 0.695393 + 0.505233i
\(5\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(6\) 0 0
\(7\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(8\) −0.563797 + 0.409622i −0.563797 + 0.409622i
\(9\) 0.309017 0.951057i 0.309017 0.951057i
\(10\) 0.477765 0.477765
\(11\) −0.187381 0.982287i −0.187381 0.982287i
\(12\) 0 0
\(13\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.184911 + 0.569097i 0.184911 + 0.569097i
\(17\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(18\) 0.303189 + 0.220280i 0.303189 + 0.220280i
\(19\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(20\) 0.338621 1.04217i 0.338621 1.04217i
\(21\) 0 0
\(22\) 0.371808 + 0.0469702i 0.371808 + 0.0469702i
\(23\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(24\) 0 0
\(25\) −0.505828 + 0.367505i −0.505828 + 0.367505i
\(26\) 0.442031 + 0.321154i 0.442031 + 0.321154i
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(30\) 0 0
\(31\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(32\) −0.921143 −0.921143
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.695393 0.505233i 0.695393 0.505233i
\(37\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(38\) −0.224339 0.690446i −0.224339 0.690446i
\(39\) 0 0
\(40\) 0.718755 + 0.522206i 0.718755 + 0.522206i
\(41\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0.365980 0.777747i 0.365980 0.777747i
\(45\) −1.27485 −1.27485
\(46\) −0.224339 + 0.690446i −0.224339 + 0.690446i
\(47\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(48\) 0 0
\(49\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(50\) −0.0724075 0.222847i −0.0724075 0.222847i
\(51\) 0 0
\(52\) 1.01384 0.736597i 1.01384 0.736597i
\(53\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(54\) 0 0
\(55\) −1.11716 + 0.614163i −1.11716 + 0.614163i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(60\) 0 0
\(61\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(62\) −0.601597 0.437086i −0.601597 0.437086i
\(63\) 0 0
\(64\) −0.0782352 + 0.240783i −0.0782352 + 0.240783i
\(65\) −1.85865 −1.85865
\(66\) 0 0
\(67\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(72\) 0.215351 + 0.662783i 0.215351 + 0.662783i
\(73\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −1.66510 −1.66510
\(77\) 0 0
\(78\) 0 0
\(79\) 0.309017 0.951057i 0.309017 0.951057i
\(80\) 0.617158 0.448391i 0.617158 0.448391i
\(81\) −0.809017 0.587785i −0.809017 0.587785i
\(82\) 0 0
\(83\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0.508012 + 0.477055i 0.508012 + 0.477055i
\(89\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(90\) 0.147638 0.454382i 0.147638 0.454382i
\(91\) 0 0
\(92\) 1.34709 + 0.978720i 1.34709 + 0.978720i
\(93\) 0 0
\(94\) 0 0
\(95\) 1.99794 + 1.45159i 1.99794 + 1.45159i
\(96\) 0 0
\(97\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(98\) −0.374763 −0.374763
\(99\) −0.992115 0.125333i −0.992115 0.125333i
\(100\) −0.537425 −0.537425
\(101\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(102\) 0 0
\(103\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(104\) 0.313968 + 0.966296i 0.313968 + 0.966296i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) −0.0895243 0.469303i −0.0895243 0.469303i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(114\) 0 0
\(115\) −0.763146 2.34872i −0.763146 2.34872i
\(116\) 0 0
\(117\) −1.17950 0.856954i −1.17950 0.856954i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.929776 + 0.368125i −0.929776 + 0.368125i
\(122\) 0 0
\(123\) 0 0
\(124\) −1.37982 + 1.00250i −1.37982 + 1.00250i
\(125\) −0.386520 0.280823i −0.386520 0.280823i
\(126\) 0 0
\(127\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(128\) −0.821980 0.597204i −0.821980 0.597204i
\(129\) 0 0
\(130\) 0.215246 0.662460i 0.215246 0.662460i
\(131\) −1.85955 −1.85955 −0.929776 0.368125i \(-0.880000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.0145433 + 0.0447596i −0.0145433 + 0.0447596i
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(138\) 0 0
\(139\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.44644 0.182728i −1.44644 0.182728i
\(144\) 0.598384 0.598384
\(145\) 0 0
\(146\) −0.563797 + 0.409622i −0.563797 + 0.409622i
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(150\) 0 0
\(151\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(152\) 0.417171 1.28392i 0.417171 1.28392i
\(153\) 0 0
\(154\) 0 0
\(155\) 2.52959 2.52959
\(156\) 0 0
\(157\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(158\) 0.303189 + 0.220280i 0.303189 + 0.220280i
\(159\) 0 0
\(160\) 0.362884 + 1.11684i 0.362884 + 1.11684i
\(161\) 0 0
\(162\) 0.303189 0.220280i 0.303189 0.220280i
\(163\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −0.231616 −0.231616
\(167\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(168\) 0 0
\(169\) −0.910614 0.661600i −0.910614 0.661600i
\(170\) 0 0
\(171\) 0.598617 + 1.84235i 0.598617 + 1.84235i
\(172\) 0 0
\(173\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.524368 0.288274i 0.524368 0.288274i
\(177\) 0 0
\(178\) 0.0986173 0.303513i 0.0986173 0.303513i
\(179\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(180\) −0.886520 0.644095i −0.886520 0.644095i
\(181\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.09217 + 0.793506i −1.09217 + 0.793506i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) −0.748754 + 0.544002i −0.748754 + 0.544002i
\(191\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(192\) 0 0
\(193\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(194\) 0.324914 + 0.236064i 0.324914 + 0.236064i
\(195\) 0 0
\(196\) −0.265616 + 0.817483i −0.265616 + 0.817483i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0.159566 0.339095i 0.159566 0.339095i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0.134646 0.414397i 0.134646 0.414397i
\(201\) 0 0
\(202\) −0.258183 0.187581i −0.258183 0.187581i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.598617 1.84235i 0.598617 1.84235i
\(208\) 0.872407 0.872407
\(209\) 1.41213 + 1.32608i 1.41213 + 1.32608i
\(210\) 0 0
\(211\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −1.08716 0.137340i −1.08716 0.137340i
\(221\) 0 0
\(222\) 0 0
\(223\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(224\) 0 0
\(225\) 0.193209 + 0.594636i 0.193209 + 0.594636i
\(226\) 0 0
\(227\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(228\) 0 0
\(229\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(230\) 0.925511 0.925511
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(234\) 0.442031 0.321154i 0.442031 0.321154i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(240\) 0 0
\(241\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(242\) −0.0235315 0.374023i −0.0235315 0.374023i
\(243\) 0 0
\(244\) 0 0
\(245\) 1.03137 0.749337i 1.03137 0.749337i
\(246\) 0 0
\(247\) 0.872746 + 2.68604i 0.872746 + 2.68604i
\(248\) −0.427306 1.31511i −0.427306 1.31511i
\(249\) 0 0
\(250\) 0.144853 0.105242i 0.144853 0.105242i
\(251\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(252\) 0 0
\(253\) −0.362989 1.90285i −0.362989 1.90285i
\(254\) 0 0
\(255\) 0 0
\(256\) 0.103225 0.0749974i 0.103225 0.0749974i
\(257\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −1.29249 0.939050i −1.29249 0.939050i
\(261\) 0 0
\(262\) 0.215351 0.662783i 0.215351 0.662783i
\(263\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0.0873282 + 0.0634476i 0.0873282 + 0.0634476i
\(269\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(270\) 0 0
\(271\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.455778 + 0.428004i 0.455778 + 0.428004i
\(276\) 0 0
\(277\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(278\) 0 0
\(279\) 1.60528 + 1.16630i 1.60528 + 1.16630i
\(280\) 0 0
\(281\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(282\) 0 0
\(283\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0.232637 0.494380i 0.232637 0.494380i
\(287\) 0 0
\(288\) −0.284649 + 0.876059i −0.284649 + 0.876059i
\(289\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(290\) 0 0
\(291\) 0 0
\(292\) 0.493928 + 1.52015i 0.493928 + 1.52015i
\(293\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.872746 2.68604i 0.872746 2.68604i
\(300\) 0 0
\(301\) 0 0
\(302\) −0.0145433 0.0447596i −0.0145433 0.0447596i
\(303\) 0 0
\(304\) −0.937788 0.681343i −0.937788 0.681343i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.292947 + 0.901598i −0.292947 + 0.901598i
\(311\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(312\) 0 0
\(313\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.695393 0.505233i 0.695393 0.505233i
\(317\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.322759 0.322759
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.265616 0.817483i −0.265616 0.817483i
\(325\) 0.281687 + 0.866942i 0.281687 + 0.866942i
\(326\) 0.531374 + 0.386066i 0.531374 + 0.386066i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −0.164160 + 0.505233i −0.164160 + 0.505233i
\(333\) 0 0
\(334\) −0.601597 0.437086i −0.601597 0.437086i
\(335\) −0.0494726 0.152261i −0.0494726 0.152261i
\(336\) 0 0
\(337\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(338\) 0.341264 0.247943i 0.341264 0.247943i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.96858 + 0.248690i 1.96858 + 0.248690i
\(342\) −0.725978 −0.725978
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(348\) 0 0
\(349\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.172605 + 0.904827i 0.172605 + 0.904827i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.592168 0.430235i −0.592168 0.430235i
\(357\) 0 0
\(358\) −0.0715733 0.220280i −0.0715733 0.220280i
\(359\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(360\) 0.718755 0.522206i 0.718755 0.522206i
\(361\) 0.850604 2.61789i 0.850604 2.61789i
\(362\) −0.546380 −0.546380
\(363\) 0 0
\(364\) 0 0
\(365\) 0.732570 2.25462i 0.732570 2.25462i
\(366\) 0 0
\(367\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(368\) 0.358203 + 1.10244i 0.358203 + 1.10244i
\(369\) 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 \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(380\) 0.655964 + 2.01885i 0.655964 + 2.01885i
\(381\) 0 0
\(382\) 0 0
\(383\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0.745220 0.541434i 0.745220 0.541434i
\(389\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.563797 0.409622i −0.563797 0.409622i
\(393\) 0 0
\(394\) 0 0
\(395\) −1.27485 −1.27485
\(396\) −0.626587 0.588404i −0.626587 0.588404i
\(397\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.302679 0.219909i −0.302679 0.219909i
\(401\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(402\) 0 0
\(403\) 2.34039 + 1.70039i 2.34039 + 1.70039i
\(404\) −0.592168 + 0.430235i −0.592168 + 0.430235i
\(405\) −0.393950 + 1.21245i −0.393950 + 1.21245i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0.587328 + 0.426719i 0.587328 + 0.426719i
\(415\) 0.637424 0.463116i 0.637424 0.463116i
\(416\) −0.415000 + 1.27724i −0.415000 + 1.27724i
\(417\) 0 0
\(418\) −0.636179 + 0.349742i −0.636179 + 0.349742i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
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
\(431\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(432\) 0 0
\(433\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3.03593 + 2.20573i −3.03593 + 2.20573i
\(438\) 0 0
\(439\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(440\) 0.378275 0.803876i 0.378275 0.803876i
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(444\) 0 0
\(445\) 0.335471 + 1.03247i 0.335471 + 1.03247i
\(446\) −0.0715733 0.220280i −0.0715733 0.220280i
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(450\) −0.234316 −0.234316
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0.655964 2.01885i 0.655964 2.01885i
\(461\) 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
\(467\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(468\) −0.387252 1.19184i −0.387252 1.19184i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.374278 1.15191i 0.374278 1.15191i
\(476\) 0 0
\(477\) 0 0
\(478\) 0.147638 + 0.454382i 0.147638 + 0.454382i
\(479\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.202967 + 0.624667i −0.202967 + 0.624667i
\(483\) 0 0
\(484\) −0.832549 0.213762i −0.832549 0.213762i
\(485\) −1.36620 −1.36620
\(486\) 0 0
\(487\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0.147638 + 0.454382i 0.147638 + 0.454382i
\(491\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −1.05843 −1.05843
\(495\) 0.238883 + 1.25227i 0.238883 + 1.25227i
\(496\) −1.18733 −1.18733
\(497\) 0 0
\(498\) 0 0
\(499\) 0.303189 + 0.220280i 0.303189 + 0.220280i 0.728969 0.684547i \(-0.240000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(500\) −0.126902 0.390565i −0.126902 0.390565i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(504\) 0 0
\(505\) 1.08561 1.08561
\(506\) 0.720253 + 0.0909891i 0.720253 + 0.0909891i
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.299192 0.920819i −0.299192 0.920819i
\(513\) 0 0
\(514\) 0.442031 0.321154i 0.442031 0.321154i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 1.04790 0.761344i 1.04790 0.761344i
\(521\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(522\) 0 0
\(523\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(524\) −1.29312 0.939507i −1.29312 0.939507i
\(525\) 0 0
\(526\) −0.202967 + 0.624667i −0.202967 + 0.624667i
\(527\) 0 0
\(528\) 0 0
\(529\) 2.75261 2.75261
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −0.0708022 + 0.0514408i −0.0708022 + 0.0514408i
\(537\) 0 0
\(538\) −0.0470631 −0.0470631
\(539\) 0.876307 0.481754i 0.876307 0.481754i
\(540\) 0 0
\(541\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i \(0.640000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) −0.205332 + 0.112882i −0.205332 + 0.112882i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −0.386520 0.280823i −0.386520 0.280823i
\(555\) 0 0
\(556\) 0 0
\(557\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(558\) −0.601597 + 0.437086i −0.601597 + 0.437086i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0.477765 0.477765
\(563\) 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
\(566\) 0.229790 + 0.707220i 0.229790 + 0.707220i
\(567\) 0 0
\(568\) 0 0
\(569\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(570\) 0 0
\(571\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(572\) −0.913525 0.857857i −0.913525 0.857857i
\(573\) 0 0
\(574\) 0 0
\(575\) −0.979872 + 0.711919i −0.979872 + 0.711919i
\(576\) 0.204822 + 0.148812i 0.204822 + 0.148812i
\(577\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(578\) −0.115808 0.356420i −0.115808 0.356420i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −1.29591 −1.29591
\(585\) −0.574354 + 1.76768i −0.574354 + 1.76768i
\(586\) 0 0
\(587\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(588\) 0 0
\(589\) −1.18779 3.65565i −1.18779 3.65565i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0.856288 + 0.622129i 0.856288 + 0.622129i
\(599\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(600\) 0 0
\(601\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(602\) 0 0
\(603\) 0.0388067 0.119435i 0.0388067 0.119435i
\(604\) −0.107944 −0.107944
\(605\) 0.812619 + 0.982287i 0.812619 + 0.982287i
\(606\) 0 0
\(607\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(608\) 1.44362 1.04885i 1.44362 1.04885i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(618\) 0 0
\(619\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(620\) 1.75906 + 1.27803i 1.75906 + 1.27803i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.381424 + 1.17390i −0.381424 + 1.17390i
\(626\) 0.743615 0.743615
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(632\) 0.215351 + 0.662783i 0.215351 + 0.662783i
\(633\) 0 0
\(634\) −0.490571 0.356420i −0.490571 0.356420i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.45794 1.45794
\(638\) 0 0
\(639\) 0 0
\(640\) −0.400262 + 1.23188i −0.400262 + 1.23188i
\(641\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(642\) 0 0
\(643\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(648\) 0.696891 0.696891
\(649\) 0 0
\(650\) −0.341617 −0.341617
\(651\) 0 0
\(652\) 1.21875 0.885477i 1.21875 0.885477i
\(653\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(654\) 0 0
\(655\) 0.732570 + 2.25462i 0.732570 + 2.25462i
\(656\) 0 0
\(657\) 1.50441 1.09302i 1.50441 1.09302i
\(658\) 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
\(664\) −0.348445 0.253160i −0.348445 0.253160i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −1.37982 + 1.00250i −1.37982 + 1.00250i
\(669\) 0 0
\(670\) 0.0599983 0.0599983
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(674\) 0.324914 0.236064i 0.324914 0.236064i
\(675\) 0 0
\(676\) −0.298973 0.920144i −0.298973 0.920144i
\(677\) −0.500000 1.53884i −0.500000 1.53884i −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
\(682\) −0.316616 + 0.672843i −0.316616 + 0.672843i
\(683\) −1.85955 −1.85955 −0.929776 0.368125i \(-0.880000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(684\) −0.514543 + 1.58360i −0.514543 + 1.58360i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.0470631 −0.0470631
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.251178 + 0.0317312i 0.251178 + 0.0317312i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(710\) 0 0
\(711\) −0.809017 0.587785i −0.809017 0.587785i
\(712\) 0.480106 0.348817i 0.480106 0.348817i
\(713\) −1.18779 + 3.65565i −1.18779 + 3.65565i
\(714\) 0 0
\(715\) 0.348276 + 1.82573i 0.348276 + 1.82573i
\(716\) −0.531233 −0.531233
\(717\) 0 0
\(718\) 0 0
\(719\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(720\) −0.235733 0.725513i −0.235733 0.725513i
\(721\) 0 0
\(722\) 0.834563 + 0.606346i 0.834563 + 0.606346i
\(723\) 0 0
\(724\) −0.387252 + 1.19184i −0.387252 + 1.19184i
\(725\) 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
\(730\) 0.718755 + 0.522206i 0.718755 + 0.522206i
\(731\) 0 0
\(732\) 0 0
\(733\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(734\) −0.258183 + 0.187581i −0.258183 + 0.187581i
\(735\) 0 0
\(736\) −1.78441 −1.78441
\(737\) −0.0235315 0.123357i −0.0235315 0.123357i
\(738\) 0 0
\(739\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−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
\(751\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0.129521 + 0.0941025i 0.129521 + 0.0941025i
\(756\) 0 0
\(757\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −1.72104 −1.72104
\(761\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −0.113624 0.0825527i −0.113624 0.0825527i
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(774\) 0 0
\(775\) −0.383371 1.17989i −0.383371 1.17989i
\(776\) 0.230782 + 0.710273i 0.230782 + 0.710273i
\(777\) 0 0
\(778\) −0.601597 + 0.437086i −0.601597 + 0.437086i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.484103 + 0.351721i −0.484103 + 0.351721i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0.147638 0.454382i 0.147638 0.454382i
\(791\) 0 0
\(792\) 0.610690 0.335730i 0.610690 0.335730i
\(793\) 0 0
\(794\) −0.0715733 + 0.220280i −0.0715733 + 0.220280i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.465940 0.338525i 0.465940 0.338525i
\(801\) −0.263146 + 0.809880i −0.263146 + 0.809880i
\(802\) 0 0