Properties

Label 1375.1.ch.a.1286.1
Level $1375$
Weight $1$
Character 1375.1286
Analytic conductor $0.686$
Analytic rank $0$
Dimension $20$
Projective image $D_{25}$
CM discriminant -11
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1375 = 5^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1375.ch (of order \(50\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.686214392370\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\Q(\zeta_{50})\)
Defining polynomial: \(x^{20} - x^{15} + x^{10} - x^{5} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
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 1286.1
Root \(-0.968583 + 0.248690i\) of defining polynomial
Character \(\chi\) \(=\) 1375.1286
Dual form 1375.1.ch.a.1066.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.348445 + 0.137959i) q^{3} +(0.535827 + 0.844328i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-0.626587 - 0.588404i) q^{9} +O(q^{10})\) \(q+(0.348445 + 0.137959i) q^{3} +(0.535827 + 0.844328i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-0.626587 - 0.588404i) q^{9} +(0.876307 + 0.481754i) q^{11} +(0.0702235 + 0.368125i) q^{12} +(0.238883 - 0.288760i) q^{15} +(-0.425779 + 0.904827i) q^{16} +(0.968583 - 0.248690i) q^{20} +(1.84489 - 0.233064i) q^{23} +(-0.809017 - 0.587785i) q^{25} +(-0.296722 - 0.630566i) q^{27} +(-1.06320 + 1.67534i) q^{31} +(0.238883 + 0.288760i) q^{33} +(0.161064 - 0.844328i) q^{36} +(0.688925 - 1.46404i) q^{37} +(0.0627905 + 0.998027i) q^{44} +(-0.753232 + 0.414093i) q^{45} +(0.0388067 - 0.616814i) q^{47} +(-0.273190 + 0.256543i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-1.11716 + 1.35041i) q^{53} +(0.728969 - 0.684547i) q^{55} +(0.159566 + 0.836475i) q^{59} +(0.371808 + 0.0469702i) q^{60} +(-0.992115 + 0.125333i) q^{64} +(-1.23480 - 0.317042i) q^{67} +(0.674997 + 0.173310i) q^{69} +(-0.0235315 + 0.374023i) q^{71} +(-0.200808 - 0.316423i) q^{75} +(0.728969 + 0.684547i) q^{80} +(0.0375729 + 0.597204i) q^{81} +(-0.0235315 + 0.123357i) q^{89} +(1.18532 + 1.43281i) q^{92} +(-0.601597 + 0.437086i) q^{93} +(-0.824805 + 0.211774i) q^{97} +(-0.265616 - 0.817483i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 5q^{5} + O(q^{10}) \) \( 20q - 5q^{5} + 20q^{12} - 5q^{25} - 5q^{27} - 5q^{48} - 5q^{49} - 5q^{59} - 5q^{60} - 5q^{67} - 5q^{69} - 5q^{81} - 5q^{92} - 10q^{93} - 5q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1375\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(1002\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{25}\right)\)

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 0 −0.876307 0.481754i \(-0.840000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(3\) 0.348445 + 0.137959i 0.348445 + 0.137959i 0.535827 0.844328i \(-0.320000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(4\) 0.535827 + 0.844328i 0.535827 + 0.844328i
\(5\) 0.309017 0.951057i 0.309017 0.951057i
\(6\) 0 0
\(7\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(8\) 0 0
\(9\) −0.626587 0.588404i −0.626587 0.588404i
\(10\) 0 0
\(11\) 0.876307 + 0.481754i 0.876307 + 0.481754i
\(12\) 0.0702235 + 0.368125i 0.0702235 + 0.368125i
\(13\) 0 0 −0.728969 0.684547i \(-0.760000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(14\) 0 0
\(15\) 0.238883 0.288760i 0.238883 0.288760i
\(16\) −0.425779 + 0.904827i −0.425779 + 0.904827i
\(17\) 0 0 0.535827 0.844328i \(-0.320000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(18\) 0 0
\(19\) 0 0 0.929776 0.368125i \(-0.120000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(20\) 0.968583 0.248690i 0.968583 0.248690i
\(21\) 0 0
\(22\) 0 0
\(23\) 1.84489 0.233064i 1.84489 0.233064i 0.876307 0.481754i \(-0.160000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(24\) 0 0
\(25\) −0.809017 0.587785i −0.809017 0.587785i
\(26\) 0 0
\(27\) −0.296722 0.630566i −0.296722 0.630566i
\(28\) 0 0
\(29\) 0 0 0.968583 0.248690i \(-0.0800000\pi\)
−0.968583 + 0.248690i \(0.920000\pi\)
\(30\) 0 0
\(31\) −1.06320 + 1.67534i −1.06320 + 1.67534i −0.425779 + 0.904827i \(0.640000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(32\) 0 0
\(33\) 0.238883 + 0.288760i 0.238883 + 0.288760i
\(34\) 0 0
\(35\) 0 0
\(36\) 0.161064 0.844328i 0.161064 0.844328i
\(37\) 0.688925 1.46404i 0.688925 1.46404i −0.187381 0.982287i \(-0.560000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.992115 0.125333i \(-0.960000\pi\)
0.992115 + 0.125333i \(0.0400000\pi\)
\(42\) 0 0
\(43\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(44\) 0.0627905 + 0.998027i 0.0627905 + 0.998027i
\(45\) −0.753232 + 0.414093i −0.753232 + 0.414093i
\(46\) 0 0
\(47\) 0.0388067 0.616814i 0.0388067 0.616814i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(48\) −0.273190 + 0.256543i −0.273190 + 0.256543i
\(49\) −0.809017 0.587785i −0.809017 0.587785i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.11716 + 1.35041i −1.11716 + 1.35041i −0.187381 + 0.982287i \(0.560000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(54\) 0 0
\(55\) 0.728969 0.684547i 0.728969 0.684547i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.159566 + 0.836475i 0.159566 + 0.836475i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(60\) 0.371808 + 0.0469702i 0.371808 + 0.0469702i
\(61\) 0 0 0.992115 0.125333i \(-0.0400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.992115 + 0.125333i −0.992115 + 0.125333i
\(65\) 0 0
\(66\) 0 0
\(67\) −1.23480 0.317042i −1.23480 0.317042i −0.425779 0.904827i \(-0.640000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(68\) 0 0
\(69\) 0.674997 + 0.173310i 0.674997 + 0.173310i
\(70\) 0 0
\(71\) −0.0235315 + 0.374023i −0.0235315 + 0.374023i 0.968583 + 0.248690i \(0.0800000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(72\) 0 0
\(73\) 0 0 0.187381 0.982287i \(-0.440000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(74\) 0 0
\(75\) −0.200808 0.316423i −0.200808 0.316423i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.929776 0.368125i \(-0.880000\pi\)
0.929776 + 0.368125i \(0.120000\pi\)
\(80\) 0.728969 + 0.684547i 0.728969 + 0.684547i
\(81\) 0.0375729 + 0.597204i 0.0375729 + 0.597204i
\(82\) 0 0
\(83\) 0 0 0.929776 0.368125i \(-0.120000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.0235315 + 0.123357i −0.0235315 + 0.123357i −0.992115 0.125333i \(-0.960000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.18532 + 1.43281i 1.18532 + 1.43281i
\(93\) −0.601597 + 0.437086i −0.601597 + 0.437086i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.824805 + 0.211774i −0.824805 + 0.211774i −0.637424 0.770513i \(-0.720000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(98\) 0 0
\(99\) −0.265616 0.817483i −0.265616 0.817483i
\(100\) 0.0627905 0.998027i 0.0627905 0.998027i
\(101\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(102\) 0 0
\(103\) −0.683098 1.07639i −0.683098 1.07639i −0.992115 0.125333i \(-0.960000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(108\) 0.373413 0.588404i 0.373413 0.588404i
\(109\) 0 0 0.425779 0.904827i \(-0.360000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(110\) 0 0
\(111\) 0.442031 0.415095i 0.442031 0.415095i
\(112\) 0 0
\(113\) −0.0235315 0.123357i −0.0235315 0.123357i 0.968583 0.248690i \(-0.0800000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(114\) 0 0
\(115\) 0.348445 1.82662i 0.348445 1.82662i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.535827 + 0.844328i 0.535827 + 0.844328i
\(122\) 0 0
\(123\) 0 0
\(124\) −1.98423 −1.98423
\(125\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(126\) 0 0
\(127\) 0 0 −0.876307 0.481754i \(-0.840000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.637424 0.770513i \(-0.720000\pi\)
0.637424 + 0.770513i \(0.280000\pi\)
\(132\) −0.115808 + 0.356420i −0.115808 + 0.356420i
\(133\) 0 0
\(134\) 0 0
\(135\) −0.691396 + 0.0873436i −0.691396 + 0.0873436i
\(136\) 0 0
\(137\) −0.362989 1.90285i −0.362989 1.90285i −0.425779 0.904827i \(-0.640000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(138\) 0 0
\(139\) 0 0 0.728969 0.684547i \(-0.240000\pi\)
−0.728969 + 0.684547i \(0.760000\pi\)
\(140\) 0 0
\(141\) 0.0986173 0.209572i 0.0986173 0.209572i
\(142\) 0 0
\(143\) 0 0
\(144\) 0.799192 0.316423i 0.799192 0.316423i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.200808 0.316423i −0.200808 0.316423i
\(148\) 1.60528 0.202793i 1.60528 0.202793i
\(149\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(150\) 0 0
\(151\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1.26480 + 1.52888i 1.26480 + 1.52888i
\(156\) 0 0
\(157\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(158\) 0 0
\(159\) −0.575570 + 0.316423i −0.575570 + 0.316423i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 1.96858 + 0.248690i 1.96858 + 0.248690i 1.00000 \(0\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(164\) 0 0
\(165\) 0.348445 0.137959i 0.348445 0.137959i
\(166\) 0 0
\(167\) 0 0 0.929776 0.368125i \(-0.120000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(168\) 0 0
\(169\) 0.0627905 + 0.998027i 0.0627905 + 0.998027i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 0.728969 0.684547i \(-0.240000\pi\)
−0.728969 + 0.684547i \(0.760000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(177\) −0.0597994 + 0.313480i −0.0597994 + 0.313480i
\(178\) 0 0
\(179\) 0.121636 1.93334i 0.121636 1.93334i −0.187381 0.982287i \(-0.560000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(180\) −0.753232 0.414093i −0.753232 0.414093i
\(181\) −1.56720 0.402389i −1.56720 0.402389i −0.637424 0.770513i \(-0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.17950 1.10762i −1.17950 1.10762i
\(186\) 0 0
\(187\) 0 0
\(188\) 0.541587 0.297740i 0.541587 0.297740i
\(189\) 0 0
\(190\) 0 0
\(191\) −0.0235315 0.123357i −0.0235315 0.123357i 0.968583 0.248690i \(-0.0800000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(192\) −0.362989 0.0931997i −0.362989 0.0931997i
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.0627905 0.998027i 0.0627905 0.998027i
\(197\) 0 0 0.637424 0.770513i \(-0.280000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(198\) 0 0
\(199\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(200\) 0 0
\(201\) −0.386520 0.280823i −0.386520 0.280823i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.29312 0.939507i −1.29312 0.939507i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.425779 0.904827i \(-0.640000\pi\)
0.425779 + 0.904827i \(0.360000\pi\)
\(212\) −1.73879 0.219661i −1.73879 0.219661i
\(213\) −0.0597994 + 0.127080i −0.0597994 + 0.127080i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0.968583 + 0.248690i 0.968583 + 0.248690i
\(221\) 0 0
\(222\) 0 0
\(223\) −0.620759 1.31918i −0.620759 1.31918i −0.929776 0.368125i \(-0.880000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(224\) 0 0
\(225\) 0.161064 + 0.844328i 0.161064 + 0.844328i
\(226\) 0 0
\(227\) 0 0 0.992115 0.125333i \(-0.0400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(228\) 0 0
\(229\) −0.683098 + 0.825723i −0.683098 + 0.825723i −0.992115 0.125333i \(-0.960000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.535827 0.844328i \(-0.320000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(234\) 0 0
\(235\) −0.574633 0.227513i −0.574633 0.227513i
\(236\) −0.620759 + 0.582932i −0.620759 + 0.582932i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.876307 0.481754i \(-0.840000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(240\) 0.159566 + 0.339095i 0.159566 + 0.339095i
\(241\) 0 0 −0.728969 0.684547i \(-0.760000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(242\) 0 0
\(243\) −0.284649 + 0.876059i −0.284649 + 0.876059i
\(244\) 0 0
\(245\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(252\) 0 0
\(253\) 1.72897 + 0.684547i 1.72897 + 0.684547i
\(254\) 0 0
\(255\) 0 0
\(256\) −0.637424 0.770513i −0.637424 0.770513i
\(257\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.728969 0.684547i \(-0.760000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(264\) 0 0
\(265\) 0.939097 + 1.47978i 0.939097 + 1.47978i
\(266\) 0 0
\(267\) −0.0252177 + 0.0397367i −0.0252177 + 0.0397367i
\(268\) −0.393950 1.21245i −0.393950 1.21245i
\(269\) −0.996398 + 0.394502i −0.996398 + 0.394502i −0.809017 0.587785i \(-0.800000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(270\) 0 0
\(271\) 0 0 0.637424 0.770513i \(-0.280000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.425779 0.904827i −0.425779 0.904827i
\(276\) 0.215351 + 0.662783i 0.215351 + 0.662783i
\(277\) 0 0 −0.425779 0.904827i \(-0.640000\pi\)
0.425779 + 0.904827i \(0.360000\pi\)
\(278\) 0 0
\(279\) 1.65197 0.424153i 1.65197 0.424153i
\(280\) 0 0
\(281\) 0 0 0.535827 0.844328i \(-0.320000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(282\) 0 0
\(283\) 0 0 −0.637424 0.770513i \(-0.720000\pi\)
0.637424 + 0.770513i \(0.280000\pi\)
\(284\) −0.328407 + 0.180543i −0.328407 + 0.180543i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −0.425779 0.904827i −0.425779 0.904827i
\(290\) 0 0
\(291\) −0.316616 0.0399979i −0.316616 0.0399979i
\(292\) 0 0
\(293\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(294\) 0 0
\(295\) 0.844844 + 0.106729i 0.844844 + 0.106729i
\(296\) 0 0
\(297\) 0.0437581 0.695516i 0.0437581 0.695516i
\(298\) 0 0
\(299\) 0 0
\(300\) 0.159566 0.339095i 0.159566 0.339095i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) −0.0895243 0.469303i −0.0895243 0.469303i
\(310\) 0 0
\(311\) 1.26480 0.159781i 1.26480 0.159781i 0.535827 0.844328i \(-0.320000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(312\) 0 0
\(313\) 1.69755 0.933237i 1.69755 0.933237i 0.728969 0.684547i \(-0.240000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.41213 + 0.362574i 1.41213 + 0.362574i 0.876307 0.481754i \(-0.160000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.187381 + 0.982287i −0.187381 + 0.982287i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.484103 + 0.351721i −0.484103 + 0.351721i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.0800484 1.27233i −0.0800484 1.27233i −0.809017 0.587785i \(-0.800000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(332\) 0 0
\(333\) −1.29312 + 0.511982i −1.29312 + 0.511982i
\(334\) 0 0
\(335\) −0.683098 + 1.07639i −0.683098 + 1.07639i
\(336\) 0 0
\(337\) 0 0 −0.992115 0.125333i \(-0.960000\pi\)
0.992115 + 0.125333i \(0.0400000\pi\)
\(338\) 0 0
\(339\) 0.00881874 0.0462295i 0.00881874 0.0462295i
\(340\) 0 0
\(341\) −1.73879 + 0.955910i −1.73879 + 0.955910i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0.373413 0.588404i 0.373413 0.588404i
\(346\) 0 0
\(347\) 0 0 0.968583 0.248690i \(-0.0800000\pi\)
−0.968583 + 0.248690i \(0.920000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.07165 + 1.68866i 1.07165 + 1.68866i 0.535827 + 0.844328i \(0.320000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(354\) 0 0
\(355\) 0.348445 + 0.137959i 0.348445 + 0.137959i
\(356\) −0.116762 + 0.0462295i −0.116762 + 0.0462295i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.425779 0.904827i \(-0.360000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(360\) 0 0
\(361\) 0.728969 0.684547i 0.728969 0.684547i
\(362\) 0 0
\(363\) 0.0702235 + 0.368125i 0.0702235 + 0.368125i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0.121636 + 1.93334i 0.121636 + 1.93334i 0.309017 + 0.951057i \(0.400000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(368\) −0.574633 + 1.76854i −0.574633 + 1.76854i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −0.691396 0.273743i −0.691396 0.273743i
\(373\) 0 0 −0.876307 0.481754i \(-0.840000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(374\) 0 0
\(375\) −0.362989 + 0.0931997i −0.362989 + 0.0931997i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.331159 + 0.521823i 0.331159 + 0.521823i 0.968583 0.248690i \(-0.0800000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −0.124591 1.98031i −0.124591 1.98031i −0.187381 0.982287i \(-0.560000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −0.620759 0.582932i −0.620759 0.582932i
\(389\) 1.06279 0.998027i 1.06279 0.998027i 0.0627905 0.998027i \(-0.480000\pi\)
1.00000 \(0\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0.547900 0.662297i 0.547900 0.662297i
\(397\) 0.0672897 + 0.106032i 0.0672897 + 0.106032i 0.876307 0.481754i \(-0.160000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.876307 0.481754i 0.876307 0.481754i
\(401\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0.579585 + 0.148812i 0.579585 + 0.148812i
\(406\) 0 0
\(407\) 1.30902 0.951057i 1.30902 0.951057i
\(408\) 0 0
\(409\) 0 0 0.876307 0.481754i \(-0.160000\pi\)
−0.876307 + 0.481754i \(0.840000\pi\)
\(410\) 0 0
\(411\) 0.136035 0.713118i 0.136035 0.713118i
\(412\) 0.542804 1.15352i 0.542804 1.15352i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −0.0534698 0.849878i −0.0534698 0.849878i −0.929776 0.368125i \(-0.880000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(420\) 0 0
\(421\) −0.116762 0.0462295i −0.116762 0.0462295i 0.309017 0.951057i \(-0.400000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(422\) 0 0
\(423\) −0.387252 + 0.363654i −0.387252 + 0.363654i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.968583 0.248690i \(-0.920000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(432\) 0.696891 0.696891
\(433\) −1.56720 0.402389i −1.56720 0.402389i −0.637424 0.770513i \(-0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.992115 0.125333i \(-0.0400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(440\) 0 0
\(441\) 0.161064 + 0.844328i 0.161064 + 0.844328i
\(442\) 0 0
\(443\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(444\) 0.587328 + 0.150800i 0.587328 + 0.150800i
\(445\) 0.110048 + 0.0604991i 0.110048 + 0.0604991i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0.0915446 0.0859661i 0.0915446 0.0859661i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 1.72897 0.684547i 1.72897 0.684547i
\(461\) 0 0 −0.425779 0.904827i \(-0.640000\pi\)
0.425779 + 0.904827i \(0.360000\pi\)
\(462\) 0 0
\(463\) −0.0534698 + 0.113629i −0.0534698 + 0.113629i −0.929776 0.368125i \(-0.880000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(464\) 0 0
\(465\) 0.229790 + 0.707220i 0.229790 + 0.707220i
\(466\) 0 0
\(467\) −0.393950 0.476203i −0.393950 0.476203i 0.535827 0.844328i \(-0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −0.388998 + 0.0998778i −0.388998 + 0.0998778i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 1.49459 0.188810i 1.49459 0.188810i
\(478\) 0 0
\(479\) 0 0 0.637424 0.770513i \(-0.280000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.425779 + 0.904827i −0.425779 + 0.904827i
\(485\) −0.0534698 + 0.849878i −0.0534698 + 0.849878i
\(486\) 0 0
\(487\) 1.45794 + 1.36909i 1.45794 + 1.36909i 0.728969 + 0.684547i \(0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(488\) 0 0
\(489\) 0.651635 + 0.358239i 0.651635 + 0.358239i
\(490\) 0 0
\(491\) 0 0 −0.728969 0.684547i \(-0.760000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −0.859553 −0.859553
\(496\) −1.06320 1.67534i −1.06320 1.67534i
\(497\) 0 0
\(498\) 0 0
\(499\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(500\) −0.929776 0.368125i −0.929776 0.368125i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.929776 0.368125i \(-0.880000\pi\)
0.929776 + 0.368125i \(0.120000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −0.115808 + 0.356420i −0.115808 + 0.356420i
\(508\) 0 0
\(509\) 1.41213 + 1.32608i 1.41213 + 1.32608i 0.876307 + 0.481754i \(0.160000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.23480 + 0.317042i −1.23480 + 0.317042i
\(516\) 0 0
\(517\) 0.331159 0.521823i 0.331159 0.521823i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.812619 0.982287i 0.812619 0.982287i −0.187381 0.982287i \(-0.560000\pi\)
1.00000 \(0\)
\(522\) 0 0
\(523\) 0 0 0.992115 0.125333i \(-0.0400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −0.362989 + 0.0931997i −0.362989 + 0.0931997i
\(529\) 2.38072 0.611264i 2.38072 0.611264i
\(530\) 0 0
\(531\) 0.392204 0.618014i 0.392204 0.618014i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0.309106 0.656884i 0.309106 0.656884i
\(538\) 0 0
\(539\) −0.425779 0.904827i −0.425779 0.904827i
\(540\) −0.444215 0.536964i −0.444215 0.536964i
\(541\) 0 0 −0.992115 0.125333i \(-0.960000\pi\)
0.992115 + 0.125333i \(0.0400000\pi\)
\(542\) 0 0
\(543\) −0.490571 0.356420i −0.490571 0.356420i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.0627905 0.998027i \(-0.480000\pi\)
−0.0627905 + 0.998027i \(0.520000\pi\)
\(548\) 1.41213 1.32608i 1.41213 1.32608i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −0.258183 0.548668i −0.258183 0.548668i
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.876307 0.481754i \(-0.160000\pi\)
−0.876307 + 0.481754i \(0.840000\pi\)
\(564\) 0.229790 0.0290292i 0.229790 0.0290292i
\(565\) −0.124591 0.0157395i −0.124591 0.0157395i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 −0.968583 0.248690i \(-0.920000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(570\) 0 0
\(571\) 0 0 0.0627905 0.998027i \(-0.480000\pi\)
−0.0627905 + 0.998027i \(0.520000\pi\)
\(572\) 0 0
\(573\) 0.00881874 0.0462295i 0.00881874 0.0462295i
\(574\) 0 0
\(575\) −1.62954 0.895846i −1.62954 0.895846i
\(576\) 0.695393 + 0.505233i 0.695393 + 0.505233i
\(577\) 1.06279 0.998027i 1.06279 0.998027i 0.0627905 0.998027i \(-0.480000\pi\)
1.00000 \(0\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −1.62954 + 0.645180i −1.62954 + 0.645180i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.844844 + 0.106729i 0.844844 + 0.106729i 0.535827 0.844328i \(-0.320000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(588\) 0.159566 0.339095i 0.159566 0.339095i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 1.03137 + 1.24672i 1.03137 + 1.24672i
\(593\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.703170 + 0.180543i −0.703170 + 0.180543i
\(598\) 0 0
\(599\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(600\) 0 0
\(601\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(602\) 0 0
\(603\) 0.587159 + 0.925214i 0.587159 + 0.925214i
\(604\) 0 0
\(605\) 0.968583 0.248690i 0.968583 0.248690i
\(606\) 0 0
\(607\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.187381 0.982287i \(-0.560000\pi\)
0.187381 + 0.982287i \(0.440000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.0915446 + 1.45506i 0.0915446 + 1.45506i 0.728969 + 0.684547i \(0.240000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(618\) 0 0
\(619\) 1.26480 + 1.52888i 1.26480 + 1.52888i 0.728969 + 0.684547i \(0.240000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(620\) −0.613161 + 1.88711i −0.613161 + 1.88711i
\(621\) −0.694381 1.09417i −0.694381 1.09417i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(626\) 0 0
\(627\) 0 0
\(628\) −0.996398 0.394502i −0.996398 0.394502i
\(629\) 0 0
\(630\) 0 0
\(631\) 0.812619 + 0.982287i 0.812619 + 0.982287i 1.00000 \(0\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −0.575570 0.316423i −0.575570 0.316423i
\(637\) 0 0
\(638\) 0 0
\(639\) 0.234821 0.220512i 0.234821 0.220512i
\(640\) 0 0
\(641\) 0.159566 0.339095i 0.159566 0.339095i −0.809017 0.587785i \(-0.800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(642\) 0 0
\(643\) −0.613161 1.88711i −0.613161 1.88711i −0.425779 0.904827i \(-0.640000\pi\)
−0.187381 0.982287i \(-0.560000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.683098 1.07639i −0.683098 1.07639i −0.992115 0.125333i \(-0.960000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(648\) 0 0
\(649\) −0.263146 + 0.809880i −0.263146 + 0.809880i
\(650\) 0 0
\(651\) 0 0
\(652\) 0.844844 + 1.79538i 0.844844 + 1.79538i
\(653\) −1.92189 + 0.493458i −1.92189 + 0.493458i −0.929776 + 0.368125i \(0.880000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 0.876307 0.481754i \(-0.160000\pi\)
−0.876307 + 0.481754i \(0.840000\pi\)
\(660\) 0.303189 + 0.220280i 0.303189 + 0.220280i
\(661\) −0.362989 + 1.90285i −0.362989 + 1.90285i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −0.0343075 0.545302i −0.0343075 0.545302i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.728969 0.684547i \(-0.240000\pi\)
−0.728969 + 0.684547i \(0.760000\pi\)
\(674\) 0 0
\(675\) −0.130584 + 0.684547i −0.130584 + 0.684547i
\(676\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(677\) 0 0 0.187381 0.982287i \(-0.440000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.03799 + 0.266509i 1.03799 + 0.266509i 0.728969 0.684547i \(-0.240000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(684\) 0 0
\(685\) −1.92189 0.242791i −1.92189 0.242791i
\(686\) 0 0
\(687\) −0.351939 + 0.193480i −0.351939 + 0.193480i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.348445 + 1.82662i 0.348445 + 1.82662i 0.535827 + 0.844328i \(0.320000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 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
\(704\) −0.929776 0.368125i −0.929776 0.368125i
\(705\) −0.168841 0.158552i −0.168841 0.158552i
\(706\) 0 0
\(707\) 0 0
\(708\) −0.296722 + 0.117480i −0.296722 + 0.117480i
\(709\) −1.73879 0.219661i −1.73879 0.219661i −0.809017 0.587785i \(-0.800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.57103 + 3.33861i −1.57103 + 3.33861i
\(714\) 0 0
\(715\) 0 0
\(716\) 1.69755 0.933237i 1.69755 0.933237i
\(717\) 0 0
\(718\) 0 0
\(719\) 0.574221 0.904827i 0.574221 0.904827i −0.425779 0.904827i \(-0.640000\pi\)
1.00000 \(0\)
\(720\) −0.0539718 0.857857i −0.0539718 0.857857i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) −0.500000 1.53884i −0.500000 1.53884i
\(725\) 0 0
\(726\) 0 0
\(727\) 0.844844 0.106729i 0.844844 0.106729i 0.309017 0.951057i \(-0.400000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(728\) 0 0
\(729\) 0.161379 0.195074i 0.161379 0.195074i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.535827 0.844328i \(-0.320000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(734\) 0 0
\(735\) −0.362989 + 0.0931997i −0.362989 + 0.0931997i
\(736\) 0 0
\(737\) −0.929324 0.872693i −0.929324 0.872693i
\(738\) 0 0
\(739\) 0 0 −0.876307 0.481754i \(-0.840000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(740\) 0.303189 1.58937i 0.303189 1.58937i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(752\) 0.541587 + 0.297740i 0.541587 + 0.297740i
\(753\) 0.610690 + 0.241789i 0.610690 + 0.241789i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(758\) 0 0
\(759\) 0.508012 + 0.477055i 0.508012 + 0.477055i
\(760\) 0 0
\(761\) 0 0 −0.876307 0.481754i \(-0.840000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0.0915446 0.0859661i 0.0915446 0.0859661i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.115808 0.356420i −0.115808 0.356420i
\(769\) 0 0 0.929776 0.368125i \(-0.120000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(770\) 0 0
\(771\) −0.444215 + 0.536964i −0.444215 + 0.536964i
\(772\) 0 0
\(773\) −1.73879 + 0.219661i −1.73879 + 0.219661i −0.929776 0.368125i \(-0.880000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(774\) 0 0
\(775\) 1.84489 0.730444i 1.84489 0.730444i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −0.200808 + 0.316423i −0.200808 + 0.316423i
\(782\) 0 0
\(783\) 0 0
\(784\) 0.876307 0.481754i 0.876307 0.481754i
\(785\) 0.331159 + 1.01920i 0.331159 + 1.01920i
\(786\) 0 0
\(787\) 0 0 0.425779 0.904827i \(-0.360000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0.123075 + 0.645180i 0.123075 + 0.645180i
\(796\) −1.80113 0.713118i −1.80113 0.713118i
\(797\) 0.00788530 0.125333i 0.00788530 0.125333i −0.992115 0.125333i \(-0.960000\pi\)
1.00000 \(0\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0.0873282 0.0634476i 0.0873282 0.0634476i
\(802\) 0