Properties

Label 869.1.j.a.394.2
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 394.2
Root \(0.187381 + 0.982287i\) of defining polynomial
Character \(\chi\) \(=\) 869.394
Dual form 869.1.j.a.236.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.263146 + 0.809880i) q^{2} +(0.222357 + 0.161552i) q^{4} +(0.331159 + 1.01920i) q^{5} +(-0.878275 + 0.638104i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.263146 + 0.809880i) q^{2} +(0.222357 + 0.161552i) q^{4} +(0.331159 + 1.01920i) q^{5} +(-0.878275 + 0.638104i) q^{8} +(0.309017 - 0.951057i) q^{9} -0.912576 q^{10} +(-0.425779 + 0.904827i) q^{11} +(-0.115808 + 0.356420i) q^{13} +(-0.200741 - 0.617816i) q^{16} +(0.688925 + 0.500534i) q^{18} +(-0.101597 + 0.0738147i) q^{19} +(-0.0910184 + 0.280126i) q^{20} +(-0.620759 - 0.582932i) q^{22} +0.125581 q^{23} +(-0.120092 + 0.0872517i) q^{25} +(-0.258183 - 0.187581i) q^{26} +(0.450527 - 1.38658i) q^{31} -0.532426 q^{32} +(0.222357 - 0.161552i) q^{36} +(-0.0330462 - 0.101706i) q^{38} +(-0.941207 - 0.683827i) q^{40} +(-0.240851 + 0.132409i) q^{44} +1.07165 q^{45} +(-0.0330462 + 0.101706i) q^{46} +(0.309017 + 0.951057i) q^{49} +(-0.0390618 - 0.120220i) q^{50} +(-0.0833310 + 0.0605435i) q^{52} +(-1.06320 - 0.134314i) q^{55} +(1.00441 + 0.729747i) q^{62} +(0.340847 - 1.04902i) q^{64} -0.401616 q^{65} -1.85955 q^{67} +(0.335471 + 1.03247i) q^{72} +(1.03137 + 0.749337i) q^{73} -0.0345157 q^{76} +(0.309017 - 0.951057i) q^{79} +(0.563203 - 0.409191i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.190983 + 0.587785i) q^{83} +(-0.203423 - 1.06638i) q^{88} +1.75261 q^{89} +(-0.282001 + 0.867911i) q^{90} +(0.0279238 + 0.0202878i) q^{92} +(-0.108877 - 0.0791038i) q^{95} +(0.598617 - 1.84235i) q^{97} -0.851559 q^{98} +(0.728969 + 0.684547i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} + 15q^{20} - 5q^{22} - 5q^{25} + 15q^{26} - 10q^{32} - 5q^{36} - 10q^{40} - 5q^{49} - 10q^{50} - 10q^{62} - 5q^{64} - 10q^{76} - 5q^{79} - 10q^{80} - 5q^{81} + 15q^{83} - 5q^{88} + 15q^{92} + 15q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(3\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(4\) 0.222357 + 0.161552i 0.222357 + 0.161552i
\(5\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(6\) 0 0
\(7\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(8\) −0.878275 + 0.638104i −0.878275 + 0.638104i
\(9\) 0.309017 0.951057i 0.309017 0.951057i
\(10\) −0.912576 −0.912576
\(11\) −0.425779 + 0.904827i −0.425779 + 0.904827i
\(12\) 0 0
\(13\) −0.115808 + 0.356420i −0.115808 + 0.356420i −0.992115 0.125333i \(-0.960000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.200741 0.617816i −0.200741 0.617816i
\(17\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(18\) 0.688925 + 0.500534i 0.688925 + 0.500534i
\(19\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(20\) −0.0910184 + 0.280126i −0.0910184 + 0.280126i
\(21\) 0 0
\(22\) −0.620759 0.582932i −0.620759 0.582932i
\(23\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(24\) 0 0
\(25\) −0.120092 + 0.0872517i −0.120092 + 0.0872517i
\(26\) −0.258183 0.187581i −0.258183 0.187581i
\(27\) 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
\(31\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(32\) −0.532426 −0.532426
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.222357 0.161552i 0.222357 0.161552i
\(37\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(38\) −0.0330462 0.101706i −0.0330462 0.101706i
\(39\) 0 0
\(40\) −0.941207 0.683827i −0.941207 0.683827i
\(41\) 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 \(\pi\)
\(44\) −0.240851 + 0.132409i −0.240851 + 0.132409i
\(45\) 1.07165 1.07165
\(46\) −0.0330462 + 0.101706i −0.0330462 + 0.101706i
\(47\) 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
\(50\) −0.0390618 0.120220i −0.0390618 0.120220i
\(51\) 0 0
\(52\) −0.0833310 + 0.0605435i −0.0833310 + 0.0605435i
\(53\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(54\) 0 0
\(55\) −1.06320 0.134314i −1.06320 0.134314i
\(56\) 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 \(0.400000\pi\)
\(62\) 1.00441 + 0.729747i 1.00441 + 0.729747i
\(63\) 0 0
\(64\) 0.340847 1.04902i 0.340847 1.04902i
\(65\) −0.401616 −0.401616
\(66\) 0 0
\(67\) −1.85955 −1.85955 −0.929776 0.368125i \(-0.880000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(72\) 0.335471 + 1.03247i 0.335471 + 1.03247i
\(73\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −0.0345157 −0.0345157
\(77\) 0 0
\(78\) 0 0
\(79\) 0.309017 0.951057i 0.309017 0.951057i
\(80\) 0.563203 0.409191i 0.563203 0.409191i
\(81\) −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
\(88\) −0.203423 1.06638i −0.203423 1.06638i
\(89\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(90\) −0.282001 + 0.867911i −0.282001 + 0.867911i
\(91\) 0 0
\(92\) 0.0279238 + 0.0202878i 0.0279238 + 0.0202878i
\(93\) 0 0
\(94\) 0 0
\(95\) −0.108877 0.0791038i −0.108877 0.0791038i
\(96\) 0 0
\(97\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(98\) −0.851559 −0.851559
\(99\) 0.728969 + 0.684547i 0.728969 + 0.684547i
\(100\) −0.0407988 −0.0407988
\(101\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(102\) 0 0
\(103\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(104\) −0.125722 0.386933i −0.125722 0.386933i
\(105\) 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 \(\pi\)
\(110\) 0.388556 0.825723i 0.388556 0.825723i
\(111\) 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
\(115\) 0.0415873 + 0.127993i 0.0415873 + 0.127993i
\(116\) 0 0
\(117\) 0.303189 + 0.220280i 0.303189 + 0.220280i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.637424 0.770513i −0.637424 0.770513i
\(122\) 0 0
\(123\) 0 0
\(124\) 0.324182 0.235532i 0.324182 0.235532i
\(125\) 0.738289 + 0.536399i 0.738289 + 0.536399i
\(126\) 0 0
\(127\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(128\) 0.329145 + 0.239138i 0.329145 + 0.239138i
\(129\) 0 0
\(130\) 0.105684 0.325261i 0.105684 0.325261i
\(131\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.489334 1.50602i 0.489334 1.50602i
\(135\) 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
\(143\) −0.273190 0.256543i −0.273190 0.256543i
\(144\) −0.649611 −0.649611
\(145\) 0 0
\(146\) −0.878275 + 0.638104i −0.878275 + 0.638104i
\(147\) 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
\(151\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(152\) 0.0421288 0.129659i 0.0421288 0.129659i
\(153\) 0 0
\(154\) 0 0
\(155\) 1.56240 1.56240
\(156\) 0 0
\(157\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(158\) 0.688925 + 0.500534i 0.688925 + 0.500534i
\(159\) 0 0
\(160\) −0.176318 0.542651i −0.176318 0.542651i
\(161\) 0 0
\(162\) 0.688925 0.500534i 0.688925 0.500534i
\(163\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −0.526292 −0.526292
\(167\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(168\) 0 0
\(169\) 0.695393 + 0.505233i 0.695393 + 0.505233i
\(170\) 0 0
\(171\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i
\(172\) 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
\(176\) 0.644488 + 0.0814178i 0.644488 + 0.0814178i
\(177\) 0 0
\(178\) −0.461193 + 1.41941i −0.461193 + 1.41941i
\(179\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(180\) 0.238289 + 0.173127i 0.238289 + 0.173127i
\(181\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.110295 + 0.0801338i −0.110295 + 0.0801338i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0.0927151 0.0673615i 0.0927151 0.0673615i
\(191\) 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 \(0.400000\pi\)
\(194\) 1.33456 + 0.969617i 1.33456 + 0.969617i
\(195\) 0 0
\(196\) −0.0849327 + 0.261396i −0.0849327 + 0.261396i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −0.746226 + 0.410241i −0.746226 + 0.410241i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0.0497978 0.153262i 0.0497978 0.153262i
\(201\) 0 0
\(202\) 1.20742 + 0.877242i 1.20742 + 0.877242i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.0388067 0.119435i 0.0388067 0.119435i
\(208\) 0.243450 0.243450
\(209\) −0.0235315 0.123357i −0.0235315 0.123357i
\(210\) 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
\(220\) −0.214712 0.201628i −0.214712 0.201628i
\(221\) 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
\(225\) 0.0458709 + 0.141176i 0.0458709 + 0.141176i
\(226\) 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 \(0.600000\pi\)
\(230\) −0.114602 −0.114602
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(234\) −0.258183 + 0.187581i −0.258183 + 0.187581i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(240\) 0 0
\(241\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(242\) 0.791759 0.313480i 0.791759 0.313480i
\(243\) 0 0
\(244\) 0 0
\(245\) −0.866986 + 0.629902i −0.866986 + 0.629902i
\(246\) 0 0
\(247\) −0.0145433 0.0447596i −0.0145433 0.0447596i
\(248\) 0.489096 + 1.50528i 0.489096 + 1.50528i
\(249\) 0 0
\(250\) −0.628697 + 0.456775i −0.628697 + 0.456775i
\(251\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(252\) 0 0
\(253\) −0.0534698 + 0.113629i −0.0534698 + 0.113629i
\(254\) 0 0
\(255\) 0 0
\(256\) 0.612062 0.444689i 0.612062 0.444689i
\(257\) 0.303189 + 0.220280i 0.303189 + 0.220280i 0.728969 0.684547i \(-0.240000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.0893019 0.0648817i −0.0893019 0.0648817i
\(261\) 0 0
\(262\) 0.335471 1.03247i 0.335471 1.03247i
\(263\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −0.413484 0.300414i −0.413484 0.300414i
\(269\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(270\) 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
\(275\) −0.0278151 0.145812i −0.0278151 0.145812i
\(276\) 0 0
\(277\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(278\) 0 0
\(279\) −1.17950 0.856954i −1.17950 0.856954i
\(280\) 0 0
\(281\) 0.331159 + 1.01920i 0.331159 + 1.01920i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(282\) 0 0
\(283\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0.279658 0.153743i 0.279658 0.153743i
\(287\) 0 0
\(288\) −0.164529 + 0.506367i −0.164529 + 0.506367i
\(289\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(290\) 0 0
\(291\) 0 0
\(292\) 0.108276 + 0.333240i 0.108276 + 0.333240i
\(293\) 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
\(299\) −0.0145433 + 0.0447596i −0.0145433 + 0.0447596i
\(300\) 0 0
\(301\) 0 0
\(302\) 0.489334 + 1.50602i 0.489334 + 1.50602i
\(303\) 0 0
\(304\) 0.0659986 + 0.0479508i 0.0659986 + 0.0479508i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.411140 + 1.26536i −0.411140 + 1.26536i
\(311\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(312\) 0 0
\(313\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.222357 0.161552i 0.222357 0.161552i
\(317\) −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
\(320\) 1.18204 1.18204
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.0849327 0.261396i −0.0849327 0.261396i
\(325\) −0.0171907 0.0529076i −0.0171907 0.0529076i
\(326\) −1.36699 0.993173i −1.36699 0.993173i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −0.0524913 + 0.161552i −0.0524913 + 0.161552i
\(333\) 0 0
\(334\) 1.00441 + 0.729747i 1.00441 + 0.729747i
\(335\) −0.615808 1.89526i −0.615808 1.89526i
\(336\) 0 0
\(337\) −1.56720 1.13864i −1.56720 1.13864i −0.929776 0.368125i \(-0.880000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(338\) −0.592168 + 0.430235i −0.592168 + 0.430235i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.06279 + 0.998027i 1.06279 + 0.998027i
\(342\) −0.106940 −0.106940
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.574633 1.76854i −0.574633 1.76854i −0.637424 0.770513i \(-0.720000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(348\) 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
\(352\) 0.226696 0.481754i 0.226696 0.481754i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.389705 + 0.283137i 0.389705 + 0.283137i
\(357\) 0 0
\(358\) −0.162633 0.500534i −0.162633 0.500534i
\(359\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(360\) −0.941207 + 0.683827i −0.941207 + 0.683827i
\(361\) −0.304144 + 0.936058i −0.304144 + 0.936058i
\(362\) 0.319132 0.319132
\(363\) 0 0
\(364\) 0 0
\(365\) −0.422178 + 1.29933i −0.422178 + 1.29933i
\(366\) 0 0
\(367\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(368\) −0.0252092 0.0775860i −0.0252092 0.0775860i
\(369\) 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 \(0.400000\pi\)
\(380\) −0.0114302 0.0351785i −0.0114302 0.0351785i
\(381\) 0 0
\(382\) 0 0
\(383\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0.430742 0.312952i 0.430742 0.312952i
\(389\) −1.17950 0.856954i −1.17950 0.856954i −0.187381 0.982287i \(-0.560000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.878275 0.638104i −0.878275 0.638104i
\(393\) 0 0
\(394\) 0 0
\(395\) 1.07165 1.07165
\(396\) 0.0515014 + 0.269980i 0.0515014 + 0.269980i
\(397\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.0780128 + 0.0566796i 0.0780128 + 0.0566796i
\(401\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(402\) 0 0
\(403\) 0.442031 + 0.321154i 0.442031 + 0.321154i
\(404\) 0.389705 0.283137i 0.389705 0.283137i
\(405\) 0.331159 1.01920i 0.331159 1.01920i
\(406\) 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
\(414\) 0.0865160 + 0.0628575i 0.0865160 + 0.0628575i
\(415\) −0.535827 + 0.389301i −0.535827 + 0.389301i
\(416\) 0.0616592 0.189768i 0.0616592 0.189768i
\(417\) 0 0
\(418\) 0.106096 + 0.0134031i 0.106096 + 0.0134031i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(422\) 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
\(431\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(432\) 0 0
\(433\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.0127587 + 0.00926972i −0.0127587 + 0.00926972i
\(438\) 0 0
\(439\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(440\) 1.01949 0.560470i 1.01949 0.560470i
\(441\) 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
\(445\) 0.580394 + 1.78627i 0.580394 + 1.78627i
\(446\) −0.162633 0.500534i −0.162633 0.500534i
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(450\) −0.126407 −0.126407
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −0.0114302 + 0.0351785i −0.0114302 + 0.0351785i
\(461\) 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
\(467\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(468\) 0.0318296 + 0.0979614i 0.0318296 + 0.0979614i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.00576052 0.0177291i 0.00576052 0.0177291i
\(476\) 0 0
\(477\) 0 0
\(478\) −0.282001 0.867911i −0.282001 0.867911i
\(479\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.522142 1.60699i 0.522142 1.60699i
\(483\) 0 0
\(484\) −0.0172578 0.274306i −0.0172578 0.274306i
\(485\) 2.07597 2.07597
\(486\) 0 0
\(487\) 0.303189 0.220280i 0.303189 0.220280i −0.425779 0.904827i \(-0.640000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −0.282001 0.867911i −0.282001 0.867911i
\(491\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0.0400770 0.0400770
\(495\) −0.456288 + 0.969661i −0.456288 + 0.969661i
\(496\) −0.947092 −0.947092
\(497\) 0 0
\(498\) 0 0
\(499\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(500\) 0.0775075 + 0.238544i 0.0775075 + 0.238544i
\(501\) 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
\(505\) 1.87819 1.87819
\(506\) −0.0779556 0.0732052i −0.0779556 0.0732052i
\(507\) 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
\(512\) 0.324805 + 0.999648i 0.324805 + 0.999648i
\(513\) 0 0
\(514\) −0.258183 + 0.187581i −0.258183 + 0.187581i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0.352729 0.256273i 0.352729 0.256273i
\(521\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(522\) 0 0
\(523\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(524\) −0.283471 0.205954i −0.283471 0.205954i
\(525\) 0 0
\(526\) 0.522142 1.60699i 0.522142 1.60699i
\(527\) 0 0
\(528\) 0 0
\(529\) −0.984229 −0.984229
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 1.63320 1.18659i 1.63320 1.18659i
\(537\) 0 0
\(538\) 1.58352 1.58352
\(539\) −0.992115 0.125333i −0.992115 0.125333i
\(540\) 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
\(547\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0.125410 + 0.0158429i 0.125410 + 0.0158429i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0.738289 + 0.536399i 0.738289 + 0.536399i
\(555\) 0 0
\(556\) 0 0
\(557\) −0.101597 0.0738147i −0.101597 0.0738147i 0.535827 0.844328i \(-0.320000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(558\) 1.00441 0.729747i 1.00441 0.729747i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −0.912576 −0.912576
\(563\) 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
\(566\) −0.383650 1.18075i −0.383650 1.18075i
\(567\) 0 0
\(568\) 0 0
\(569\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(570\) 0 0
\(571\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(572\) −0.0193008 0.101178i −0.0193008 0.101178i
\(573\) 0 0
\(574\) 0 0
\(575\) −0.0150812 + 0.0109572i −0.0150812 + 0.0109572i
\(576\) −0.892348 0.648329i −0.892348 0.648329i
\(577\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(578\) −0.263146 0.809880i −0.263146 0.809880i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −1.38398 −1.38398
\(585\) −0.124106 + 0.381959i −0.124106 + 0.381959i
\(586\) 0 0
\(587\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(588\) 0 0
\(589\) 0.0565777 + 0.174128i 0.0565777 + 0.174128i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.07165 1.07165 0.535827 0.844328i \(-0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −0.0324229 0.0235567i −0.0324229 0.0235567i
\(599\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(600\) 0 0
\(601\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(602\) 0 0
\(603\) −0.574633 + 1.76854i −0.574633 + 1.76854i
\(604\) 0.511094 0.511094
\(605\) 0.574221 0.904827i 0.574221 0.904827i
\(606\) 0 0
\(607\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(608\) 0.0540930 0.0393009i 0.0540930 0.0393009i
\(609\) 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
\(617\) −0.374763 −0.374763 −0.187381 0.982287i \(-0.560000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(618\) 0 0
\(619\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(620\) 0.347411 + 0.252409i 0.347411 + 0.252409i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.348079 + 1.07128i −0.348079 + 1.07128i
\(626\) −1.24152 −1.24152
\(627\) 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 \(0.200000\pi\)
\(632\) 0.335471 + 1.03247i 0.335471 + 1.03247i
\(633\) 0 0
\(634\) −1.11470 0.809880i −1.11470 0.809880i
\(635\) 0 0
\(636\) 0 0
\(637\) −0.374763 −0.374763
\(638\) 0 0
\(639\) 0 0
\(640\) −0.134731 + 0.414658i −0.134731 + 0.414658i
\(641\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(642\) 0 0
\(643\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(648\) 1.08561 1.08561
\(649\) 0 0
\(650\) 0.0473725 0.0473725
\(651\) 0 0
\(652\) −0.441207 + 0.320555i −0.441207 + 0.320555i
\(653\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(654\) 0 0
\(655\) −0.422178 1.29933i −0.422178 1.29933i
\(656\) 0 0
\(657\) 1.03137 0.749337i 1.03137 0.749337i
\(658\) 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
\(664\) −0.542804 0.394370i −0.542804 0.394370i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0.324182 0.235532i 0.324182 0.235532i
\(669\) 0 0
\(670\) 1.69698 1.69698
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(674\) 1.33456 0.969617i 1.33456 0.969617i
\(675\) 0 0
\(676\) 0.0730042 + 0.224684i 0.0730042 + 0.224684i
\(677\) −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
\(682\) −1.08795 + 0.598106i −1.08795 + 0.598106i
\(683\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(684\) −0.0106659 + 0.0328264i −0.0106659 + 0.0328264i
\(685\) 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
\(694\) 1.58352 1.58352
\(695\) 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
\(704\) 0.804054 + 0.755057i 0.804054 + 0.755057i
\(705\) 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
\(712\) −1.53928 + 1.11835i −1.53928 + 1.11835i
\(713\) 0.0565777 0.174128i 0.0565777 0.174128i
\(714\) 0 0
\(715\) 0.171000 0.363393i 0.171000 0.363393i
\(716\) −0.169865 −0.169865
\(717\) 0 0
\(718\) 0 0
\(719\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(720\) −0.215125 0.662085i −0.215125 0.662085i
\(721\) 0 0
\(722\) −0.678061 0.492640i −0.678061 0.492640i
\(723\) 0 0
\(724\) 0.0318296 0.0979614i 0.0318296 0.0979614i
\(725\) 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
\(730\) −0.941207 0.683827i −0.941207 0.683827i
\(731\) 0 0
\(732\) 0 0
\(733\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(734\) 1.20742 0.877242i 1.20742 0.877242i
\(735\) 0 0
\(736\) −0.0668626 −0.0668626
\(737\) 0.791759 1.68257i 0.791759 1.68257i
\(738\) 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
\(743\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.618034 0.618034
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0.688925 0.500534i 0.688925 0.500534i −0.187381 0.982287i \(-0.560000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.61221 + 1.17134i 1.61221 + 1.17134i
\(756\) 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
\(760\) 0.146100 0.146100
\(761\) 0.0388067 0.119435i 0.0388067 0.119435i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −0.586660 0.426234i −0.586660 0.426234i
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(774\) 0 0
\(775\) 0.0668769 + 0.205826i 0.0668769 + 0.205826i
\(776\) 0.649864 + 2.00007i 0.649864 + 2.00007i
\(777\) 0 0
\(778\) 1.00441 0.729747i 1.00441 0.729747i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.525546 0.381832i 0.525546 0.381832i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) −0.282001 + 0.867911i −0.282001 + 0.867911i
\(791\) 0 0
\(792\) −1.07705 0.136063i −1.07705 0.136063i
\(793\) 0 0
\(794\) −0.162633 + 0.500534i −0.162633 + 0.500534i
\(795\) 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
\(800\) 0.0639399 0.0464551i 0.0639399 0.0464551i
\(801\) 0.541587 1.66683i 0.541587 1.66683i
\(802\) 0