Properties

Label 8041.2.a.i.1.11
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(78\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.24742 q^{2} +2.50303 q^{3} +3.05092 q^{4} +1.29850 q^{5} -5.62537 q^{6} +3.89591 q^{7} -2.36186 q^{8} +3.26514 q^{9} +O(q^{10})\) \(q-2.24742 q^{2} +2.50303 q^{3} +3.05092 q^{4} +1.29850 q^{5} -5.62537 q^{6} +3.89591 q^{7} -2.36186 q^{8} +3.26514 q^{9} -2.91829 q^{10} +1.00000 q^{11} +7.63653 q^{12} +5.45777 q^{13} -8.75577 q^{14} +3.25019 q^{15} -0.793731 q^{16} -1.00000 q^{17} -7.33817 q^{18} +5.05012 q^{19} +3.96163 q^{20} +9.75157 q^{21} -2.24742 q^{22} +6.25714 q^{23} -5.91180 q^{24} -3.31389 q^{25} -12.2659 q^{26} +0.663664 q^{27} +11.8861 q^{28} -3.12906 q^{29} -7.30455 q^{30} +1.86183 q^{31} +6.50757 q^{32} +2.50303 q^{33} +2.24742 q^{34} +5.05885 q^{35} +9.96169 q^{36} -6.20357 q^{37} -11.3498 q^{38} +13.6609 q^{39} -3.06688 q^{40} -5.29435 q^{41} -21.9159 q^{42} -1.00000 q^{43} +3.05092 q^{44} +4.23980 q^{45} -14.0624 q^{46} +1.06975 q^{47} -1.98673 q^{48} +8.17812 q^{49} +7.44772 q^{50} -2.50303 q^{51} +16.6512 q^{52} +12.4670 q^{53} -1.49153 q^{54} +1.29850 q^{55} -9.20160 q^{56} +12.6406 q^{57} +7.03232 q^{58} +8.63365 q^{59} +9.91606 q^{60} -3.21326 q^{61} -4.18432 q^{62} +12.7207 q^{63} -13.0378 q^{64} +7.08693 q^{65} -5.62537 q^{66} -7.84936 q^{67} -3.05092 q^{68} +15.6618 q^{69} -11.3694 q^{70} +9.27564 q^{71} -7.71182 q^{72} -11.4308 q^{73} +13.9421 q^{74} -8.29476 q^{75} +15.4075 q^{76} +3.89591 q^{77} -30.7019 q^{78} -10.2426 q^{79} -1.03066 q^{80} -8.13427 q^{81} +11.8987 q^{82} +3.46832 q^{83} +29.7513 q^{84} -1.29850 q^{85} +2.24742 q^{86} -7.83212 q^{87} -2.36186 q^{88} +6.43379 q^{89} -9.52863 q^{90} +21.2630 q^{91} +19.0900 q^{92} +4.66021 q^{93} -2.40418 q^{94} +6.55760 q^{95} +16.2886 q^{96} +1.16747 q^{97} -18.3797 q^{98} +3.26514 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.24742 −1.58917 −0.794585 0.607153i \(-0.792311\pi\)
−0.794585 + 0.607153i \(0.792311\pi\)
\(3\) 2.50303 1.44512 0.722562 0.691306i \(-0.242965\pi\)
0.722562 + 0.691306i \(0.242965\pi\)
\(4\) 3.05092 1.52546
\(5\) 1.29850 0.580708 0.290354 0.956919i \(-0.406227\pi\)
0.290354 + 0.956919i \(0.406227\pi\)
\(6\) −5.62537 −2.29655
\(7\) 3.89591 1.47252 0.736258 0.676701i \(-0.236591\pi\)
0.736258 + 0.676701i \(0.236591\pi\)
\(8\) −2.36186 −0.835044
\(9\) 3.26514 1.08838
\(10\) −2.91829 −0.922843
\(11\) 1.00000 0.301511
\(12\) 7.63653 2.20448
\(13\) 5.45777 1.51371 0.756856 0.653581i \(-0.226734\pi\)
0.756856 + 0.653581i \(0.226734\pi\)
\(14\) −8.75577 −2.34008
\(15\) 3.25019 0.839195
\(16\) −0.793731 −0.198433
\(17\) −1.00000 −0.242536
\(18\) −7.33817 −1.72962
\(19\) 5.05012 1.15858 0.579289 0.815122i \(-0.303330\pi\)
0.579289 + 0.815122i \(0.303330\pi\)
\(20\) 3.96163 0.885847
\(21\) 9.75157 2.12797
\(22\) −2.24742 −0.479153
\(23\) 6.25714 1.30470 0.652352 0.757917i \(-0.273783\pi\)
0.652352 + 0.757917i \(0.273783\pi\)
\(24\) −5.91180 −1.20674
\(25\) −3.31389 −0.662778
\(26\) −12.2659 −2.40555
\(27\) 0.663664 0.127722
\(28\) 11.8861 2.24626
\(29\) −3.12906 −0.581051 −0.290526 0.956867i \(-0.593830\pi\)
−0.290526 + 0.956867i \(0.593830\pi\)
\(30\) −7.30455 −1.33362
\(31\) 1.86183 0.334394 0.167197 0.985923i \(-0.446528\pi\)
0.167197 + 0.985923i \(0.446528\pi\)
\(32\) 6.50757 1.15039
\(33\) 2.50303 0.435721
\(34\) 2.24742 0.385430
\(35\) 5.05885 0.855102
\(36\) 9.96169 1.66028
\(37\) −6.20357 −1.01986 −0.509930 0.860216i \(-0.670329\pi\)
−0.509930 + 0.860216i \(0.670329\pi\)
\(38\) −11.3498 −1.84118
\(39\) 13.6609 2.18750
\(40\) −3.06688 −0.484917
\(41\) −5.29435 −0.826839 −0.413419 0.910541i \(-0.635666\pi\)
−0.413419 + 0.910541i \(0.635666\pi\)
\(42\) −21.9159 −3.38170
\(43\) −1.00000 −0.152499
\(44\) 3.05092 0.459943
\(45\) 4.23980 0.632032
\(46\) −14.0624 −2.07339
\(47\) 1.06975 0.156039 0.0780196 0.996952i \(-0.475140\pi\)
0.0780196 + 0.996952i \(0.475140\pi\)
\(48\) −1.98673 −0.286760
\(49\) 8.17812 1.16830
\(50\) 7.44772 1.05327
\(51\) −2.50303 −0.350494
\(52\) 16.6512 2.30911
\(53\) 12.4670 1.71248 0.856240 0.516578i \(-0.172794\pi\)
0.856240 + 0.516578i \(0.172794\pi\)
\(54\) −1.49153 −0.202972
\(55\) 1.29850 0.175090
\(56\) −9.20160 −1.22962
\(57\) 12.6406 1.67429
\(58\) 7.03232 0.923389
\(59\) 8.63365 1.12401 0.562003 0.827135i \(-0.310031\pi\)
0.562003 + 0.827135i \(0.310031\pi\)
\(60\) 9.91606 1.28016
\(61\) −3.21326 −0.411416 −0.205708 0.978613i \(-0.565950\pi\)
−0.205708 + 0.978613i \(0.565950\pi\)
\(62\) −4.18432 −0.531409
\(63\) 12.7207 1.60266
\(64\) −13.0378 −1.62973
\(65\) 7.08693 0.879025
\(66\) −5.62537 −0.692435
\(67\) −7.84936 −0.958952 −0.479476 0.877555i \(-0.659173\pi\)
−0.479476 + 0.877555i \(0.659173\pi\)
\(68\) −3.05092 −0.369978
\(69\) 15.6618 1.88546
\(70\) −11.3694 −1.35890
\(71\) 9.27564 1.10082 0.550408 0.834896i \(-0.314472\pi\)
0.550408 + 0.834896i \(0.314472\pi\)
\(72\) −7.71182 −0.908847
\(73\) −11.4308 −1.33787 −0.668936 0.743320i \(-0.733250\pi\)
−0.668936 + 0.743320i \(0.733250\pi\)
\(74\) 13.9421 1.62073
\(75\) −8.29476 −0.957796
\(76\) 15.4075 1.76736
\(77\) 3.89591 0.443980
\(78\) −30.7019 −3.47631
\(79\) −10.2426 −1.15239 −0.576193 0.817314i \(-0.695462\pi\)
−0.576193 + 0.817314i \(0.695462\pi\)
\(80\) −1.03066 −0.115231
\(81\) −8.13427 −0.903807
\(82\) 11.8987 1.31399
\(83\) 3.46832 0.380697 0.190349 0.981717i \(-0.439038\pi\)
0.190349 + 0.981717i \(0.439038\pi\)
\(84\) 29.7513 3.24613
\(85\) −1.29850 −0.140842
\(86\) 2.24742 0.242346
\(87\) −7.83212 −0.839691
\(88\) −2.36186 −0.251775
\(89\) 6.43379 0.681980 0.340990 0.940067i \(-0.389238\pi\)
0.340990 + 0.940067i \(0.389238\pi\)
\(90\) −9.52863 −1.00441
\(91\) 21.2630 2.22897
\(92\) 19.0900 1.99027
\(93\) 4.66021 0.483241
\(94\) −2.40418 −0.247973
\(95\) 6.55760 0.672795
\(96\) 16.2886 1.66245
\(97\) 1.16747 0.118539 0.0592693 0.998242i \(-0.481123\pi\)
0.0592693 + 0.998242i \(0.481123\pi\)
\(98\) −18.3797 −1.85663
\(99\) 3.26514 0.328159
\(100\) −10.1104 −1.01104
\(101\) 3.52949 0.351197 0.175599 0.984462i \(-0.443814\pi\)
0.175599 + 0.984462i \(0.443814\pi\)
\(102\) 5.62537 0.556994
\(103\) −7.70041 −0.758744 −0.379372 0.925244i \(-0.623860\pi\)
−0.379372 + 0.925244i \(0.623860\pi\)
\(104\) −12.8905 −1.26402
\(105\) 12.6624 1.23573
\(106\) −28.0188 −2.72142
\(107\) 2.14806 0.207661 0.103830 0.994595i \(-0.466890\pi\)
0.103830 + 0.994595i \(0.466890\pi\)
\(108\) 2.02478 0.194835
\(109\) −10.4562 −1.00152 −0.500760 0.865586i \(-0.666946\pi\)
−0.500760 + 0.865586i \(0.666946\pi\)
\(110\) −2.91829 −0.278248
\(111\) −15.5277 −1.47382
\(112\) −3.09230 −0.292195
\(113\) 1.95017 0.183456 0.0917282 0.995784i \(-0.470761\pi\)
0.0917282 + 0.995784i \(0.470761\pi\)
\(114\) −28.4088 −2.66073
\(115\) 8.12491 0.757652
\(116\) −9.54650 −0.886370
\(117\) 17.8204 1.64750
\(118\) −19.4035 −1.78623
\(119\) −3.89591 −0.357138
\(120\) −7.67649 −0.700765
\(121\) 1.00000 0.0909091
\(122\) 7.22156 0.653809
\(123\) −13.2519 −1.19488
\(124\) 5.68029 0.510105
\(125\) −10.7956 −0.965589
\(126\) −28.5888 −2.54690
\(127\) 18.4418 1.63645 0.818223 0.574901i \(-0.194960\pi\)
0.818223 + 0.574901i \(0.194960\pi\)
\(128\) 16.2864 1.43953
\(129\) −2.50303 −0.220379
\(130\) −15.9273 −1.39692
\(131\) 9.06011 0.791586 0.395793 0.918340i \(-0.370470\pi\)
0.395793 + 0.918340i \(0.370470\pi\)
\(132\) 7.63653 0.664675
\(133\) 19.6748 1.70602
\(134\) 17.6408 1.52394
\(135\) 0.861769 0.0741693
\(136\) 2.36186 0.202528
\(137\) 13.4506 1.14916 0.574580 0.818448i \(-0.305165\pi\)
0.574580 + 0.818448i \(0.305165\pi\)
\(138\) −35.1987 −2.99631
\(139\) −18.2149 −1.54497 −0.772485 0.635033i \(-0.780987\pi\)
−0.772485 + 0.635033i \(0.780987\pi\)
\(140\) 15.4341 1.30442
\(141\) 2.67761 0.225496
\(142\) −20.8463 −1.74938
\(143\) 5.45777 0.456402
\(144\) −2.59165 −0.215970
\(145\) −4.06309 −0.337421
\(146\) 25.6898 2.12611
\(147\) 20.4701 1.68834
\(148\) −18.9266 −1.55576
\(149\) 7.74413 0.634424 0.317212 0.948355i \(-0.397253\pi\)
0.317212 + 0.948355i \(0.397253\pi\)
\(150\) 18.6418 1.52210
\(151\) −23.3657 −1.90148 −0.950738 0.309996i \(-0.899672\pi\)
−0.950738 + 0.309996i \(0.899672\pi\)
\(152\) −11.9277 −0.967464
\(153\) −3.26514 −0.263971
\(154\) −8.75577 −0.705560
\(155\) 2.41759 0.194186
\(156\) 41.6784 3.33695
\(157\) 5.08626 0.405928 0.202964 0.979186i \(-0.434943\pi\)
0.202964 + 0.979186i \(0.434943\pi\)
\(158\) 23.0196 1.83134
\(159\) 31.2054 2.47475
\(160\) 8.45010 0.668039
\(161\) 24.3772 1.92120
\(162\) 18.2812 1.43630
\(163\) −1.41971 −0.111200 −0.0556001 0.998453i \(-0.517707\pi\)
−0.0556001 + 0.998453i \(0.517707\pi\)
\(164\) −16.1526 −1.26131
\(165\) 3.25019 0.253027
\(166\) −7.79478 −0.604992
\(167\) 5.40974 0.418618 0.209309 0.977850i \(-0.432878\pi\)
0.209309 + 0.977850i \(0.432878\pi\)
\(168\) −23.0319 −1.77695
\(169\) 16.7872 1.29133
\(170\) 2.91829 0.223822
\(171\) 16.4894 1.26097
\(172\) −3.05092 −0.232630
\(173\) −4.26716 −0.324426 −0.162213 0.986756i \(-0.551863\pi\)
−0.162213 + 0.986756i \(0.551863\pi\)
\(174\) 17.6021 1.33441
\(175\) −12.9106 −0.975951
\(176\) −0.793731 −0.0598297
\(177\) 21.6103 1.62433
\(178\) −14.4595 −1.08378
\(179\) −13.2461 −0.990060 −0.495030 0.868876i \(-0.664843\pi\)
−0.495030 + 0.868876i \(0.664843\pi\)
\(180\) 12.9353 0.964139
\(181\) 11.2586 0.836846 0.418423 0.908252i \(-0.362583\pi\)
0.418423 + 0.908252i \(0.362583\pi\)
\(182\) −47.7870 −3.54221
\(183\) −8.04288 −0.594546
\(184\) −14.7785 −1.08948
\(185\) −8.05535 −0.592241
\(186\) −10.4735 −0.767952
\(187\) −1.00000 −0.0731272
\(188\) 3.26372 0.238031
\(189\) 2.58557 0.188073
\(190\) −14.7377 −1.06919
\(191\) −9.65206 −0.698398 −0.349199 0.937049i \(-0.613546\pi\)
−0.349199 + 0.937049i \(0.613546\pi\)
\(192\) −32.6340 −2.35516
\(193\) −9.66911 −0.695998 −0.347999 0.937495i \(-0.613139\pi\)
−0.347999 + 0.937495i \(0.613139\pi\)
\(194\) −2.62380 −0.188378
\(195\) 17.7388 1.27030
\(196\) 24.9508 1.78220
\(197\) −26.0453 −1.85565 −0.927826 0.373012i \(-0.878325\pi\)
−0.927826 + 0.373012i \(0.878325\pi\)
\(198\) −7.33817 −0.521501
\(199\) 5.26448 0.373189 0.186595 0.982437i \(-0.440255\pi\)
0.186595 + 0.982437i \(0.440255\pi\)
\(200\) 7.82695 0.553449
\(201\) −19.6472 −1.38580
\(202\) −7.93226 −0.558112
\(203\) −12.1905 −0.855607
\(204\) −7.63653 −0.534664
\(205\) −6.87473 −0.480152
\(206\) 17.3061 1.20577
\(207\) 20.4305 1.42001
\(208\) −4.33200 −0.300370
\(209\) 5.05012 0.349324
\(210\) −28.4579 −1.96378
\(211\) −20.2874 −1.39664 −0.698321 0.715784i \(-0.746069\pi\)
−0.698321 + 0.715784i \(0.746069\pi\)
\(212\) 38.0360 2.61232
\(213\) 23.2172 1.59081
\(214\) −4.82760 −0.330008
\(215\) −1.29850 −0.0885571
\(216\) −1.56748 −0.106654
\(217\) 7.25352 0.492401
\(218\) 23.4995 1.59158
\(219\) −28.6116 −1.93339
\(220\) 3.96163 0.267093
\(221\) −5.45777 −0.367129
\(222\) 34.8973 2.34216
\(223\) −9.08984 −0.608701 −0.304350 0.952560i \(-0.598439\pi\)
−0.304350 + 0.952560i \(0.598439\pi\)
\(224\) 25.3529 1.69396
\(225\) −10.8203 −0.721355
\(226\) −4.38286 −0.291543
\(227\) 20.1651 1.33841 0.669203 0.743079i \(-0.266635\pi\)
0.669203 + 0.743079i \(0.266635\pi\)
\(228\) 38.5654 2.55406
\(229\) 10.0428 0.663650 0.331825 0.943341i \(-0.392336\pi\)
0.331825 + 0.943341i \(0.392336\pi\)
\(230\) −18.2601 −1.20404
\(231\) 9.75157 0.641606
\(232\) 7.39040 0.485204
\(233\) −6.51859 −0.427047 −0.213524 0.976938i \(-0.568494\pi\)
−0.213524 + 0.976938i \(0.568494\pi\)
\(234\) −40.0500 −2.61815
\(235\) 1.38907 0.0906132
\(236\) 26.3406 1.71462
\(237\) −25.6376 −1.66534
\(238\) 8.75577 0.567552
\(239\) −18.4861 −1.19577 −0.597883 0.801583i \(-0.703991\pi\)
−0.597883 + 0.801583i \(0.703991\pi\)
\(240\) −2.57977 −0.166524
\(241\) 3.24031 0.208727 0.104364 0.994539i \(-0.466719\pi\)
0.104364 + 0.994539i \(0.466719\pi\)
\(242\) −2.24742 −0.144470
\(243\) −22.3513 −1.43384
\(244\) −9.80339 −0.627598
\(245\) 10.6193 0.678443
\(246\) 29.7827 1.89887
\(247\) 27.5624 1.75375
\(248\) −4.39738 −0.279234
\(249\) 8.68129 0.550154
\(250\) 24.2623 1.53448
\(251\) 20.5238 1.29545 0.647726 0.761873i \(-0.275720\pi\)
0.647726 + 0.761873i \(0.275720\pi\)
\(252\) 38.8099 2.44479
\(253\) 6.25714 0.393383
\(254\) −41.4466 −2.60059
\(255\) −3.25019 −0.203535
\(256\) −10.5268 −0.657923
\(257\) 10.1027 0.630188 0.315094 0.949060i \(-0.397964\pi\)
0.315094 + 0.949060i \(0.397964\pi\)
\(258\) 5.62537 0.350220
\(259\) −24.1685 −1.50176
\(260\) 21.6216 1.34092
\(261\) −10.2168 −0.632406
\(262\) −20.3619 −1.25796
\(263\) 8.50347 0.524347 0.262173 0.965021i \(-0.415561\pi\)
0.262173 + 0.965021i \(0.415561\pi\)
\(264\) −5.91180 −0.363846
\(265\) 16.1885 0.994451
\(266\) −44.2177 −2.71116
\(267\) 16.1040 0.985546
\(268\) −23.9478 −1.46284
\(269\) −2.60052 −0.158557 −0.0792784 0.996853i \(-0.525262\pi\)
−0.0792784 + 0.996853i \(0.525262\pi\)
\(270\) −1.93676 −0.117868
\(271\) −12.1214 −0.736323 −0.368162 0.929762i \(-0.620013\pi\)
−0.368162 + 0.929762i \(0.620013\pi\)
\(272\) 0.793731 0.0481270
\(273\) 53.2218 3.22113
\(274\) −30.2292 −1.82621
\(275\) −3.31389 −0.199835
\(276\) 47.7828 2.87619
\(277\) 17.9928 1.08108 0.540541 0.841317i \(-0.318219\pi\)
0.540541 + 0.841317i \(0.318219\pi\)
\(278\) 40.9367 2.45522
\(279\) 6.07914 0.363949
\(280\) −11.9483 −0.714048
\(281\) −25.8853 −1.54419 −0.772093 0.635510i \(-0.780790\pi\)
−0.772093 + 0.635510i \(0.780790\pi\)
\(282\) −6.01774 −0.358351
\(283\) 18.0848 1.07503 0.537515 0.843254i \(-0.319363\pi\)
0.537515 + 0.843254i \(0.319363\pi\)
\(284\) 28.2992 1.67925
\(285\) 16.4138 0.972272
\(286\) −12.2659 −0.725300
\(287\) −20.6263 −1.21753
\(288\) 21.2482 1.25206
\(289\) 1.00000 0.0588235
\(290\) 9.13149 0.536220
\(291\) 2.92221 0.171303
\(292\) −34.8744 −2.04087
\(293\) −1.40597 −0.0821375 −0.0410688 0.999156i \(-0.513076\pi\)
−0.0410688 + 0.999156i \(0.513076\pi\)
\(294\) −46.0049 −2.68306
\(295\) 11.2108 0.652719
\(296\) 14.6520 0.851629
\(297\) 0.663664 0.0385097
\(298\) −17.4044 −1.00821
\(299\) 34.1500 1.97495
\(300\) −25.3066 −1.46108
\(301\) −3.89591 −0.224557
\(302\) 52.5127 3.02177
\(303\) 8.83440 0.507523
\(304\) −4.00844 −0.229900
\(305\) −4.17243 −0.238912
\(306\) 7.33817 0.419495
\(307\) −10.6707 −0.609012 −0.304506 0.952510i \(-0.598491\pi\)
−0.304506 + 0.952510i \(0.598491\pi\)
\(308\) 11.8861 0.677274
\(309\) −19.2743 −1.09648
\(310\) −5.43335 −0.308594
\(311\) −19.1958 −1.08850 −0.544248 0.838924i \(-0.683185\pi\)
−0.544248 + 0.838924i \(0.683185\pi\)
\(312\) −32.2653 −1.82666
\(313\) 19.0190 1.07502 0.537508 0.843259i \(-0.319366\pi\)
0.537508 + 0.843259i \(0.319366\pi\)
\(314\) −11.4310 −0.645089
\(315\) 16.5179 0.930677
\(316\) −31.2494 −1.75792
\(317\) 0.322116 0.0180918 0.00904591 0.999959i \(-0.497121\pi\)
0.00904591 + 0.999959i \(0.497121\pi\)
\(318\) −70.1317 −3.93279
\(319\) −3.12906 −0.175194
\(320\) −16.9296 −0.946396
\(321\) 5.37665 0.300095
\(322\) −54.7860 −3.05311
\(323\) −5.05012 −0.280996
\(324\) −24.8170 −1.37872
\(325\) −18.0865 −1.00326
\(326\) 3.19069 0.176716
\(327\) −26.1721 −1.44732
\(328\) 12.5045 0.690447
\(329\) 4.16765 0.229770
\(330\) −7.30455 −0.402102
\(331\) 17.6260 0.968815 0.484407 0.874843i \(-0.339035\pi\)
0.484407 + 0.874843i \(0.339035\pi\)
\(332\) 10.5816 0.580738
\(333\) −20.2555 −1.11000
\(334\) −12.1580 −0.665256
\(335\) −10.1924 −0.556871
\(336\) −7.74012 −0.422258
\(337\) 32.0174 1.74410 0.872050 0.489417i \(-0.162790\pi\)
0.872050 + 0.489417i \(0.162790\pi\)
\(338\) −37.7281 −2.05214
\(339\) 4.88133 0.265117
\(340\) −3.96163 −0.214849
\(341\) 1.86183 0.100824
\(342\) −37.0586 −2.00390
\(343\) 4.58985 0.247829
\(344\) 2.36186 0.127343
\(345\) 20.3369 1.09490
\(346\) 9.59012 0.515568
\(347\) −6.91527 −0.371231 −0.185616 0.982622i \(-0.559428\pi\)
−0.185616 + 0.982622i \(0.559428\pi\)
\(348\) −23.8952 −1.28091
\(349\) 15.2322 0.815363 0.407682 0.913124i \(-0.366337\pi\)
0.407682 + 0.913124i \(0.366337\pi\)
\(350\) 29.0157 1.55095
\(351\) 3.62212 0.193335
\(352\) 6.50757 0.346855
\(353\) 31.3606 1.66915 0.834577 0.550891i \(-0.185712\pi\)
0.834577 + 0.550891i \(0.185712\pi\)
\(354\) −48.5674 −2.58133
\(355\) 12.0444 0.639252
\(356\) 19.6290 1.04033
\(357\) −9.75157 −0.516108
\(358\) 29.7696 1.57337
\(359\) −11.4855 −0.606183 −0.303091 0.952961i \(-0.598019\pi\)
−0.303091 + 0.952961i \(0.598019\pi\)
\(360\) −10.0138 −0.527775
\(361\) 6.50374 0.342302
\(362\) −25.3029 −1.32989
\(363\) 2.50303 0.131375
\(364\) 64.8716 3.40020
\(365\) −14.8429 −0.776913
\(366\) 18.0758 0.944835
\(367\) −33.4544 −1.74631 −0.873153 0.487446i \(-0.837928\pi\)
−0.873153 + 0.487446i \(0.837928\pi\)
\(368\) −4.96648 −0.258896
\(369\) −17.2868 −0.899916
\(370\) 18.1038 0.941171
\(371\) 48.5705 2.52166
\(372\) 14.2179 0.737165
\(373\) −26.8485 −1.39016 −0.695082 0.718931i \(-0.744632\pi\)
−0.695082 + 0.718931i \(0.744632\pi\)
\(374\) 2.24742 0.116212
\(375\) −27.0217 −1.39539
\(376\) −2.52660 −0.130300
\(377\) −17.0777 −0.879545
\(378\) −5.81088 −0.298880
\(379\) 15.2165 0.781618 0.390809 0.920472i \(-0.372195\pi\)
0.390809 + 0.920472i \(0.372195\pi\)
\(380\) 20.0067 1.02632
\(381\) 46.1603 2.36487
\(382\) 21.6923 1.10987
\(383\) −34.7631 −1.77631 −0.888155 0.459543i \(-0.848013\pi\)
−0.888155 + 0.459543i \(0.848013\pi\)
\(384\) 40.7653 2.08029
\(385\) 5.05885 0.257823
\(386\) 21.7306 1.10606
\(387\) −3.26514 −0.165977
\(388\) 3.56186 0.180826
\(389\) 16.7497 0.849241 0.424621 0.905371i \(-0.360407\pi\)
0.424621 + 0.905371i \(0.360407\pi\)
\(390\) −39.8666 −2.01872
\(391\) −6.25714 −0.316437
\(392\) −19.3156 −0.975585
\(393\) 22.6777 1.14394
\(394\) 58.5349 2.94895
\(395\) −13.3001 −0.669200
\(396\) 9.96169 0.500594
\(397\) −6.08086 −0.305190 −0.152595 0.988289i \(-0.548763\pi\)
−0.152595 + 0.988289i \(0.548763\pi\)
\(398\) −11.8315 −0.593061
\(399\) 49.2466 2.46542
\(400\) 2.63034 0.131517
\(401\) −19.0965 −0.953636 −0.476818 0.879002i \(-0.658210\pi\)
−0.476818 + 0.879002i \(0.658210\pi\)
\(402\) 44.1555 2.20228
\(403\) 10.1614 0.506177
\(404\) 10.7682 0.535737
\(405\) −10.5624 −0.524848
\(406\) 27.3973 1.35971
\(407\) −6.20357 −0.307499
\(408\) 5.91180 0.292678
\(409\) 3.61284 0.178643 0.0893216 0.996003i \(-0.471530\pi\)
0.0893216 + 0.996003i \(0.471530\pi\)
\(410\) 15.4504 0.763043
\(411\) 33.6672 1.66068
\(412\) −23.4933 −1.15743
\(413\) 33.6359 1.65512
\(414\) −45.9159 −2.25664
\(415\) 4.50362 0.221074
\(416\) 35.5168 1.74136
\(417\) −45.5925 −2.23267
\(418\) −11.3498 −0.555136
\(419\) −33.8980 −1.65603 −0.828013 0.560709i \(-0.810528\pi\)
−0.828013 + 0.560709i \(0.810528\pi\)
\(420\) 38.6321 1.88505
\(421\) −1.22532 −0.0597186 −0.0298593 0.999554i \(-0.509506\pi\)
−0.0298593 + 0.999554i \(0.509506\pi\)
\(422\) 45.5944 2.21950
\(423\) 3.49289 0.169830
\(424\) −29.4454 −1.43000
\(425\) 3.31389 0.160747
\(426\) −52.1788 −2.52807
\(427\) −12.5186 −0.605816
\(428\) 6.55355 0.316778
\(429\) 13.6609 0.659557
\(430\) 2.91829 0.140732
\(431\) −27.0231 −1.30166 −0.650830 0.759224i \(-0.725579\pi\)
−0.650830 + 0.759224i \(0.725579\pi\)
\(432\) −0.526770 −0.0253442
\(433\) 4.86248 0.233676 0.116838 0.993151i \(-0.462724\pi\)
0.116838 + 0.993151i \(0.462724\pi\)
\(434\) −16.3017 −0.782509
\(435\) −10.1700 −0.487615
\(436\) −31.9009 −1.52778
\(437\) 31.5993 1.51160
\(438\) 64.3024 3.07249
\(439\) −16.5288 −0.788878 −0.394439 0.918922i \(-0.629061\pi\)
−0.394439 + 0.918922i \(0.629061\pi\)
\(440\) −3.06688 −0.146208
\(441\) 26.7027 1.27156
\(442\) 12.2659 0.583431
\(443\) 4.21628 0.200322 0.100161 0.994971i \(-0.468064\pi\)
0.100161 + 0.994971i \(0.468064\pi\)
\(444\) −47.3738 −2.24826
\(445\) 8.35429 0.396031
\(446\) 20.4287 0.967329
\(447\) 19.3838 0.916821
\(448\) −50.7942 −2.39980
\(449\) 3.19480 0.150772 0.0753860 0.997154i \(-0.475981\pi\)
0.0753860 + 0.997154i \(0.475981\pi\)
\(450\) 24.3179 1.14636
\(451\) −5.29435 −0.249301
\(452\) 5.94981 0.279855
\(453\) −58.4850 −2.74787
\(454\) −45.3196 −2.12696
\(455\) 27.6100 1.29438
\(456\) −29.8553 −1.39810
\(457\) 12.3202 0.576314 0.288157 0.957583i \(-0.406958\pi\)
0.288157 + 0.957583i \(0.406958\pi\)
\(458\) −22.5705 −1.05465
\(459\) −0.663664 −0.0309772
\(460\) 24.7884 1.15577
\(461\) −19.8534 −0.924663 −0.462331 0.886707i \(-0.652987\pi\)
−0.462331 + 0.886707i \(0.652987\pi\)
\(462\) −21.9159 −1.01962
\(463\) −15.1086 −0.702155 −0.351078 0.936346i \(-0.614185\pi\)
−0.351078 + 0.936346i \(0.614185\pi\)
\(464\) 2.48363 0.115300
\(465\) 6.05129 0.280622
\(466\) 14.6500 0.678650
\(467\) 19.6309 0.908412 0.454206 0.890897i \(-0.349923\pi\)
0.454206 + 0.890897i \(0.349923\pi\)
\(468\) 54.3686 2.51319
\(469\) −30.5804 −1.41207
\(470\) −3.12184 −0.144000
\(471\) 12.7311 0.586616
\(472\) −20.3915 −0.938594
\(473\) −1.00000 −0.0459800
\(474\) 57.6186 2.64651
\(475\) −16.7356 −0.767880
\(476\) −11.8861 −0.544799
\(477\) 40.7067 1.86383
\(478\) 41.5461 1.90028
\(479\) 16.1951 0.739971 0.369986 0.929037i \(-0.379363\pi\)
0.369986 + 0.929037i \(0.379363\pi\)
\(480\) 21.1508 0.965399
\(481\) −33.8576 −1.54378
\(482\) −7.28236 −0.331703
\(483\) 61.0169 2.77637
\(484\) 3.05092 0.138678
\(485\) 1.51596 0.0688363
\(486\) 50.2328 2.27861
\(487\) 8.50186 0.385256 0.192628 0.981272i \(-0.438299\pi\)
0.192628 + 0.981272i \(0.438299\pi\)
\(488\) 7.58927 0.343550
\(489\) −3.55357 −0.160698
\(490\) −23.8661 −1.07816
\(491\) −27.4917 −1.24068 −0.620341 0.784332i \(-0.713006\pi\)
−0.620341 + 0.784332i \(0.713006\pi\)
\(492\) −40.4305 −1.82275
\(493\) 3.12906 0.140926
\(494\) −61.9444 −2.78701
\(495\) 4.23980 0.190565
\(496\) −1.47779 −0.0663548
\(497\) 36.1371 1.62097
\(498\) −19.5105 −0.874289
\(499\) −39.1081 −1.75072 −0.875360 0.483472i \(-0.839376\pi\)
−0.875360 + 0.483472i \(0.839376\pi\)
\(500\) −32.9365 −1.47297
\(501\) 13.5407 0.604955
\(502\) −46.1258 −2.05869
\(503\) 13.7303 0.612202 0.306101 0.951999i \(-0.400975\pi\)
0.306101 + 0.951999i \(0.400975\pi\)
\(504\) −30.0446 −1.33829
\(505\) 4.58305 0.203943
\(506\) −14.0624 −0.625152
\(507\) 42.0189 1.86613
\(508\) 56.2645 2.49633
\(509\) −29.6756 −1.31535 −0.657673 0.753303i \(-0.728459\pi\)
−0.657673 + 0.753303i \(0.728459\pi\)
\(510\) 7.30455 0.323451
\(511\) −44.5333 −1.97004
\(512\) −8.91463 −0.393975
\(513\) 3.35158 0.147976
\(514\) −22.7050 −1.00148
\(515\) −9.99901 −0.440609
\(516\) −7.63653 −0.336180
\(517\) 1.06975 0.0470476
\(518\) 54.3170 2.38655
\(519\) −10.6808 −0.468836
\(520\) −16.7383 −0.734025
\(521\) 0.758394 0.0332258 0.0166129 0.999862i \(-0.494712\pi\)
0.0166129 + 0.999862i \(0.494712\pi\)
\(522\) 22.9615 1.00500
\(523\) −15.7541 −0.688877 −0.344439 0.938809i \(-0.611931\pi\)
−0.344439 + 0.938809i \(0.611931\pi\)
\(524\) 27.6417 1.20753
\(525\) −32.3156 −1.41037
\(526\) −19.1109 −0.833276
\(527\) −1.86183 −0.0811026
\(528\) −1.98673 −0.0864613
\(529\) 16.1518 0.702250
\(530\) −36.3824 −1.58035
\(531\) 28.1901 1.22335
\(532\) 60.0263 2.60247
\(533\) −28.8953 −1.25160
\(534\) −36.1924 −1.56620
\(535\) 2.78926 0.120590
\(536\) 18.5391 0.800767
\(537\) −33.1553 −1.43076
\(538\) 5.84448 0.251973
\(539\) 8.17812 0.352257
\(540\) 2.62919 0.113142
\(541\) −15.4550 −0.664463 −0.332232 0.943198i \(-0.607802\pi\)
−0.332232 + 0.943198i \(0.607802\pi\)
\(542\) 27.2420 1.17014
\(543\) 28.1806 1.20935
\(544\) −6.50757 −0.279010
\(545\) −13.5774 −0.581590
\(546\) −119.612 −5.11892
\(547\) 9.90966 0.423707 0.211853 0.977301i \(-0.432050\pi\)
0.211853 + 0.977301i \(0.432050\pi\)
\(548\) 41.0366 1.75300
\(549\) −10.4918 −0.447777
\(550\) 7.44772 0.317572
\(551\) −15.8021 −0.673193
\(552\) −36.9910 −1.57444
\(553\) −39.9044 −1.69691
\(554\) −40.4375 −1.71802
\(555\) −20.1628 −0.855861
\(556\) −55.5723 −2.35679
\(557\) −23.3130 −0.987803 −0.493901 0.869518i \(-0.664430\pi\)
−0.493901 + 0.869518i \(0.664430\pi\)
\(558\) −13.6624 −0.578376
\(559\) −5.45777 −0.230839
\(560\) −4.01537 −0.169680
\(561\) −2.50303 −0.105678
\(562\) 58.1752 2.45397
\(563\) 24.7387 1.04261 0.521306 0.853370i \(-0.325445\pi\)
0.521306 + 0.853370i \(0.325445\pi\)
\(564\) 8.16918 0.343985
\(565\) 2.53230 0.106535
\(566\) −40.6442 −1.70840
\(567\) −31.6904 −1.33087
\(568\) −21.9078 −0.919230
\(569\) 9.37413 0.392984 0.196492 0.980505i \(-0.437045\pi\)
0.196492 + 0.980505i \(0.437045\pi\)
\(570\) −36.8889 −1.54511
\(571\) −16.6403 −0.696374 −0.348187 0.937425i \(-0.613203\pi\)
−0.348187 + 0.937425i \(0.613203\pi\)
\(572\) 16.6512 0.696222
\(573\) −24.1594 −1.00927
\(574\) 46.3561 1.93487
\(575\) −20.7355 −0.864729
\(576\) −42.5704 −1.77377
\(577\) −14.5126 −0.604166 −0.302083 0.953282i \(-0.597682\pi\)
−0.302083 + 0.953282i \(0.597682\pi\)
\(578\) −2.24742 −0.0934806
\(579\) −24.2020 −1.00580
\(580\) −12.3962 −0.514722
\(581\) 13.5123 0.560583
\(582\) −6.56744 −0.272229
\(583\) 12.4670 0.516332
\(584\) 26.9979 1.11718
\(585\) 23.1398 0.956715
\(586\) 3.15981 0.130530
\(587\) 1.96415 0.0810693 0.0405347 0.999178i \(-0.487094\pi\)
0.0405347 + 0.999178i \(0.487094\pi\)
\(588\) 62.4525 2.57550
\(589\) 9.40247 0.387422
\(590\) −25.1955 −1.03728
\(591\) −65.1922 −2.68165
\(592\) 4.92396 0.202374
\(593\) 29.1849 1.19848 0.599240 0.800569i \(-0.295469\pi\)
0.599240 + 0.800569i \(0.295469\pi\)
\(594\) −1.49153 −0.0611984
\(595\) −5.05885 −0.207393
\(596\) 23.6267 0.967788
\(597\) 13.1771 0.539305
\(598\) −76.7496 −3.13852
\(599\) −0.721406 −0.0294759 −0.0147379 0.999891i \(-0.504691\pi\)
−0.0147379 + 0.999891i \(0.504691\pi\)
\(600\) 19.5911 0.799802
\(601\) −46.5021 −1.89686 −0.948431 0.316985i \(-0.897330\pi\)
−0.948431 + 0.316985i \(0.897330\pi\)
\(602\) 8.75577 0.356858
\(603\) −25.6293 −1.04371
\(604\) −71.2869 −2.90062
\(605\) 1.29850 0.0527916
\(606\) −19.8547 −0.806540
\(607\) 43.8105 1.77821 0.889107 0.457699i \(-0.151326\pi\)
0.889107 + 0.457699i \(0.151326\pi\)
\(608\) 32.8641 1.33281
\(609\) −30.5132 −1.23646
\(610\) 9.37721 0.379672
\(611\) 5.83845 0.236198
\(612\) −9.96169 −0.402678
\(613\) −43.1007 −1.74082 −0.870411 0.492326i \(-0.836147\pi\)
−0.870411 + 0.492326i \(0.836147\pi\)
\(614\) 23.9817 0.967823
\(615\) −17.2076 −0.693879
\(616\) −9.20160 −0.370743
\(617\) 26.7367 1.07638 0.538189 0.842824i \(-0.319109\pi\)
0.538189 + 0.842824i \(0.319109\pi\)
\(618\) 43.3176 1.74249
\(619\) −12.7618 −0.512940 −0.256470 0.966552i \(-0.582559\pi\)
−0.256470 + 0.966552i \(0.582559\pi\)
\(620\) 7.37587 0.296222
\(621\) 4.15263 0.166639
\(622\) 43.1412 1.72980
\(623\) 25.0655 1.00423
\(624\) −10.8431 −0.434072
\(625\) 2.55133 0.102053
\(626\) −42.7437 −1.70838
\(627\) 12.6406 0.504817
\(628\) 15.5178 0.619227
\(629\) 6.20357 0.247352
\(630\) −37.1227 −1.47900
\(631\) 36.4173 1.44975 0.724875 0.688881i \(-0.241898\pi\)
0.724875 + 0.688881i \(0.241898\pi\)
\(632\) 24.1917 0.962294
\(633\) −50.7799 −2.01832
\(634\) −0.723930 −0.0287510
\(635\) 23.9467 0.950297
\(636\) 95.2050 3.77512
\(637\) 44.6343 1.76848
\(638\) 7.03232 0.278412
\(639\) 30.2863 1.19811
\(640\) 21.1479 0.835945
\(641\) −45.6000 −1.80109 −0.900547 0.434759i \(-0.856834\pi\)
−0.900547 + 0.434759i \(0.856834\pi\)
\(642\) −12.0836 −0.476902
\(643\) 11.5233 0.454436 0.227218 0.973844i \(-0.427037\pi\)
0.227218 + 0.973844i \(0.427037\pi\)
\(644\) 74.3730 2.93071
\(645\) −3.25019 −0.127976
\(646\) 11.3498 0.446551
\(647\) −42.6096 −1.67515 −0.837577 0.546319i \(-0.816029\pi\)
−0.837577 + 0.546319i \(0.816029\pi\)
\(648\) 19.2120 0.754719
\(649\) 8.63365 0.338900
\(650\) 40.6479 1.59434
\(651\) 18.1558 0.711580
\(652\) −4.33142 −0.169631
\(653\) −30.8010 −1.20533 −0.602667 0.797993i \(-0.705895\pi\)
−0.602667 + 0.797993i \(0.705895\pi\)
\(654\) 58.8198 2.30004
\(655\) 11.7646 0.459680
\(656\) 4.20229 0.164072
\(657\) −37.3232 −1.45612
\(658\) −9.36648 −0.365144
\(659\) −23.8832 −0.930357 −0.465179 0.885217i \(-0.654010\pi\)
−0.465179 + 0.885217i \(0.654010\pi\)
\(660\) 9.91606 0.385982
\(661\) 37.7122 1.46684 0.733418 0.679778i \(-0.237924\pi\)
0.733418 + 0.679778i \(0.237924\pi\)
\(662\) −39.6132 −1.53961
\(663\) −13.6609 −0.530547
\(664\) −8.19169 −0.317899
\(665\) 25.5478 0.990702
\(666\) 45.5228 1.76397
\(667\) −19.5789 −0.758100
\(668\) 16.5047 0.638585
\(669\) −22.7521 −0.879648
\(670\) 22.9067 0.884962
\(671\) −3.21326 −0.124047
\(672\) 63.4591 2.44799
\(673\) 22.1018 0.851960 0.425980 0.904733i \(-0.359929\pi\)
0.425980 + 0.904733i \(0.359929\pi\)
\(674\) −71.9567 −2.77167
\(675\) −2.19931 −0.0846514
\(676\) 51.2165 1.96987
\(677\) 45.0030 1.72961 0.864803 0.502111i \(-0.167443\pi\)
0.864803 + 0.502111i \(0.167443\pi\)
\(678\) −10.9704 −0.421316
\(679\) 4.54836 0.174550
\(680\) 3.06688 0.117610
\(681\) 50.4739 1.93416
\(682\) −4.18432 −0.160226
\(683\) 17.9007 0.684953 0.342476 0.939526i \(-0.388734\pi\)
0.342476 + 0.939526i \(0.388734\pi\)
\(684\) 50.3078 1.92357
\(685\) 17.4656 0.667327
\(686\) −10.3153 −0.393842
\(687\) 25.1375 0.959056
\(688\) 0.793731 0.0302607
\(689\) 68.0423 2.59220
\(690\) −45.7056 −1.73998
\(691\) 3.89552 0.148192 0.0740962 0.997251i \(-0.476393\pi\)
0.0740962 + 0.997251i \(0.476393\pi\)
\(692\) −13.0188 −0.494899
\(693\) 12.7207 0.483220
\(694\) 15.5415 0.589949
\(695\) −23.6521 −0.897177
\(696\) 18.4984 0.701179
\(697\) 5.29435 0.200538
\(698\) −34.2333 −1.29575
\(699\) −16.3162 −0.617136
\(700\) −39.3893 −1.48877
\(701\) −17.3023 −0.653498 −0.326749 0.945111i \(-0.605953\pi\)
−0.326749 + 0.945111i \(0.605953\pi\)
\(702\) −8.14045 −0.307242
\(703\) −31.3288 −1.18159
\(704\) −13.0378 −0.491381
\(705\) 3.47689 0.130947
\(706\) −70.4805 −2.65257
\(707\) 13.7506 0.517143
\(708\) 65.9311 2.47784
\(709\) 29.8795 1.12215 0.561075 0.827765i \(-0.310388\pi\)
0.561075 + 0.827765i \(0.310388\pi\)
\(710\) −27.0690 −1.01588
\(711\) −33.4437 −1.25424
\(712\) −15.1957 −0.569484
\(713\) 11.6497 0.436285
\(714\) 21.9159 0.820183
\(715\) 7.08693 0.265036
\(716\) −40.4128 −1.51030
\(717\) −46.2712 −1.72803
\(718\) 25.8129 0.963327
\(719\) 28.8517 1.07599 0.537993 0.842950i \(-0.319183\pi\)
0.537993 + 0.842950i \(0.319183\pi\)
\(720\) −3.36526 −0.125416
\(721\) −30.0001 −1.11726
\(722\) −14.6167 −0.543976
\(723\) 8.11059 0.301636
\(724\) 34.3491 1.27657
\(725\) 10.3694 0.385108
\(726\) −5.62537 −0.208777
\(727\) 10.8843 0.403675 0.201838 0.979419i \(-0.435309\pi\)
0.201838 + 0.979419i \(0.435309\pi\)
\(728\) −50.2202 −1.86129
\(729\) −31.5431 −1.16826
\(730\) 33.3583 1.23465
\(731\) 1.00000 0.0369863
\(732\) −24.5382 −0.906957
\(733\) −22.7745 −0.841195 −0.420597 0.907247i \(-0.638180\pi\)
−0.420597 + 0.907247i \(0.638180\pi\)
\(734\) 75.1863 2.77518
\(735\) 26.5804 0.980434
\(736\) 40.7188 1.50091
\(737\) −7.84936 −0.289135
\(738\) 38.8508 1.43012
\(739\) −6.55869 −0.241265 −0.120633 0.992697i \(-0.538492\pi\)
−0.120633 + 0.992697i \(0.538492\pi\)
\(740\) −24.5762 −0.903440
\(741\) 68.9895 2.53439
\(742\) −109.159 −4.00734
\(743\) 9.89598 0.363048 0.181524 0.983386i \(-0.441897\pi\)
0.181524 + 0.983386i \(0.441897\pi\)
\(744\) −11.0068 −0.403528
\(745\) 10.0558 0.368415
\(746\) 60.3400 2.20921
\(747\) 11.3246 0.414344
\(748\) −3.05092 −0.111553
\(749\) 8.36865 0.305784
\(750\) 60.7292 2.21752
\(751\) 40.9101 1.49283 0.746415 0.665481i \(-0.231774\pi\)
0.746415 + 0.665481i \(0.231774\pi\)
\(752\) −0.849094 −0.0309633
\(753\) 51.3717 1.87209
\(754\) 38.3808 1.39775
\(755\) −30.3405 −1.10420
\(756\) 7.88838 0.286898
\(757\) −6.70267 −0.243613 −0.121806 0.992554i \(-0.538869\pi\)
−0.121806 + 0.992554i \(0.538869\pi\)
\(758\) −34.1979 −1.24212
\(759\) 15.6618 0.568487
\(760\) −15.4881 −0.561814
\(761\) −37.1265 −1.34584 −0.672918 0.739717i \(-0.734959\pi\)
−0.672918 + 0.739717i \(0.734959\pi\)
\(762\) −103.742 −3.75817
\(763\) −40.7363 −1.47475
\(764\) −29.4477 −1.06538
\(765\) −4.23980 −0.153290
\(766\) 78.1274 2.82286
\(767\) 47.1205 1.70142
\(768\) −26.3488 −0.950780
\(769\) −22.2466 −0.802233 −0.401117 0.916027i \(-0.631378\pi\)
−0.401117 + 0.916027i \(0.631378\pi\)
\(770\) −11.3694 −0.409724
\(771\) 25.2873 0.910700
\(772\) −29.4997 −1.06172
\(773\) −5.65323 −0.203333 −0.101666 0.994819i \(-0.532417\pi\)
−0.101666 + 0.994819i \(0.532417\pi\)
\(774\) 7.33817 0.263765
\(775\) −6.16990 −0.221629
\(776\) −2.75740 −0.0989850
\(777\) −60.4945 −2.17023
\(778\) −37.6436 −1.34959
\(779\) −26.7371 −0.957957
\(780\) 54.1196 1.93779
\(781\) 9.27564 0.331908
\(782\) 14.0624 0.502872
\(783\) −2.07664 −0.0742131
\(784\) −6.49123 −0.231829
\(785\) 6.60453 0.235726
\(786\) −50.9664 −1.81791
\(787\) 14.9658 0.533474 0.266737 0.963769i \(-0.414055\pi\)
0.266737 + 0.963769i \(0.414055\pi\)
\(788\) −79.4622 −2.83072
\(789\) 21.2844 0.757746
\(790\) 29.8909 1.06347
\(791\) 7.59769 0.270143
\(792\) −7.71182 −0.274028
\(793\) −17.5372 −0.622765
\(794\) 13.6663 0.484998
\(795\) 40.5202 1.43710
\(796\) 16.0615 0.569285
\(797\) −2.78234 −0.0985556 −0.0492778 0.998785i \(-0.515692\pi\)
−0.0492778 + 0.998785i \(0.515692\pi\)
\(798\) −110.678 −3.91796
\(799\) −1.06975 −0.0378450
\(800\) −21.5654 −0.762452
\(801\) 21.0073 0.742255
\(802\) 42.9181 1.51549
\(803\) −11.4308 −0.403384
\(804\) −59.9419 −2.11399
\(805\) 31.6539 1.11565
\(806\) −22.8371 −0.804401
\(807\) −6.50918 −0.229134
\(808\) −8.33616 −0.293265
\(809\) 11.2250 0.394650 0.197325 0.980338i \(-0.436775\pi\)
0.197325 + 0.980338i \(0.436775\pi\)
\(810\) 23.7381 0.834073
\(811\) −17.5173 −0.615117 −0.307558 0.951529i \(-0.599512\pi\)
−0.307558 + 0.951529i \(0.599512\pi\)
\(812\) −37.1923 −1.30519
\(813\) −30.3402 −1.06408
\(814\) 13.9421 0.488669
\(815\) −1.84350 −0.0645749
\(816\) 1.98673 0.0695495
\(817\) −5.05012 −0.176681
\(818\) −8.11958 −0.283894
\(819\) 69.4267 2.42597
\(820\) −20.9742 −0.732452
\(821\) 19.7865 0.690554 0.345277 0.938501i \(-0.387785\pi\)
0.345277 + 0.938501i \(0.387785\pi\)
\(822\) −75.6644 −2.63910
\(823\) 24.6735 0.860064 0.430032 0.902814i \(-0.358502\pi\)
0.430032 + 0.902814i \(0.358502\pi\)
\(824\) 18.1873 0.633585
\(825\) −8.29476 −0.288786
\(826\) −75.5942 −2.63026
\(827\) 8.80854 0.306303 0.153152 0.988203i \(-0.451058\pi\)
0.153152 + 0.988203i \(0.451058\pi\)
\(828\) 62.3317 2.16618
\(829\) 9.55607 0.331896 0.165948 0.986135i \(-0.446932\pi\)
0.165948 + 0.986135i \(0.446932\pi\)
\(830\) −10.1215 −0.351324
\(831\) 45.0365 1.56230
\(832\) −71.1574 −2.46694
\(833\) −8.17812 −0.283355
\(834\) 102.466 3.54810
\(835\) 7.02456 0.243095
\(836\) 15.4075 0.532880
\(837\) 1.23563 0.0427096
\(838\) 76.1832 2.63170
\(839\) 40.6984 1.40506 0.702532 0.711652i \(-0.252053\pi\)
0.702532 + 0.711652i \(0.252053\pi\)
\(840\) −29.9069 −1.03189
\(841\) −19.2090 −0.662379
\(842\) 2.75382 0.0949029
\(843\) −64.7915 −2.23154
\(844\) −61.8952 −2.13052
\(845\) 21.7983 0.749884
\(846\) −7.85001 −0.269889
\(847\) 3.89591 0.133865
\(848\) −9.89548 −0.339812
\(849\) 45.2667 1.55355
\(850\) −7.44772 −0.255455
\(851\) −38.8166 −1.33062
\(852\) 70.8337 2.42672
\(853\) 37.9370 1.29894 0.649468 0.760389i \(-0.274991\pi\)
0.649468 + 0.760389i \(0.274991\pi\)
\(854\) 28.1345 0.962744
\(855\) 21.4115 0.732258
\(856\) −5.07342 −0.173406
\(857\) −54.0819 −1.84740 −0.923701 0.383114i \(-0.874852\pi\)
−0.923701 + 0.383114i \(0.874852\pi\)
\(858\) −30.7019 −1.04815
\(859\) 11.0328 0.376434 0.188217 0.982127i \(-0.439729\pi\)
0.188217 + 0.982127i \(0.439729\pi\)
\(860\) −3.96163 −0.135090
\(861\) −51.6282 −1.75949
\(862\) 60.7325 2.06856
\(863\) −29.0166 −0.987736 −0.493868 0.869537i \(-0.664417\pi\)
−0.493868 + 0.869537i \(0.664417\pi\)
\(864\) 4.31884 0.146930
\(865\) −5.54092 −0.188397
\(866\) −10.9281 −0.371350
\(867\) 2.50303 0.0850073
\(868\) 22.1299 0.751138
\(869\) −10.2426 −0.347458
\(870\) 22.8564 0.774903
\(871\) −42.8400 −1.45158
\(872\) 24.6960 0.836313
\(873\) 3.81196 0.129015
\(874\) −71.0171 −2.40219
\(875\) −42.0587 −1.42184
\(876\) −87.2916 −2.94931
\(877\) 49.2283 1.66232 0.831161 0.556031i \(-0.187677\pi\)
0.831161 + 0.556031i \(0.187677\pi\)
\(878\) 37.1473 1.25366
\(879\) −3.51918 −0.118699
\(880\) −1.03066 −0.0347436
\(881\) −4.53190 −0.152684 −0.0763418 0.997082i \(-0.524324\pi\)
−0.0763418 + 0.997082i \(0.524324\pi\)
\(882\) −60.0124 −2.02072
\(883\) −2.86139 −0.0962933 −0.0481466 0.998840i \(-0.515331\pi\)
−0.0481466 + 0.998840i \(0.515331\pi\)
\(884\) −16.6512 −0.560041
\(885\) 28.0610 0.943259
\(886\) −9.47577 −0.318345
\(887\) 50.6299 1.69999 0.849993 0.526794i \(-0.176606\pi\)
0.849993 + 0.526794i \(0.176606\pi\)
\(888\) 36.6743 1.23071
\(889\) 71.8476 2.40969
\(890\) −18.7756 −0.629361
\(891\) −8.13427 −0.272508
\(892\) −27.7324 −0.928548
\(893\) 5.40237 0.180783
\(894\) −43.5636 −1.45698
\(895\) −17.2001 −0.574936
\(896\) 63.4503 2.11973
\(897\) 85.4784 2.85404
\(898\) −7.18008 −0.239602
\(899\) −5.82577 −0.194300
\(900\) −33.0120 −1.10040
\(901\) −12.4670 −0.415338
\(902\) 11.8987 0.396182
\(903\) −9.75157 −0.324512
\(904\) −4.60603 −0.153194
\(905\) 14.6193 0.485963
\(906\) 131.441 4.36683
\(907\) 43.7426 1.45245 0.726224 0.687458i \(-0.241273\pi\)
0.726224 + 0.687458i \(0.241273\pi\)
\(908\) 61.5222 2.04169
\(909\) 11.5243 0.382236
\(910\) −62.0515 −2.05699
\(911\) 47.5104 1.57409 0.787045 0.616896i \(-0.211610\pi\)
0.787045 + 0.616896i \(0.211610\pi\)
\(912\) −10.0332 −0.332233
\(913\) 3.46832 0.114785
\(914\) −27.6887 −0.915860
\(915\) −10.4437 −0.345258
\(916\) 30.6399 1.01237
\(917\) 35.2974 1.16562
\(918\) 1.49153 0.0492280
\(919\) 41.0831 1.35521 0.677603 0.735428i \(-0.263019\pi\)
0.677603 + 0.735428i \(0.263019\pi\)
\(920\) −19.1899 −0.632673
\(921\) −26.7092 −0.880097
\(922\) 44.6189 1.46945
\(923\) 50.6243 1.66632
\(924\) 29.7513 0.978744
\(925\) 20.5579 0.675941
\(926\) 33.9554 1.11584
\(927\) −25.1430 −0.825803
\(928\) −20.3626 −0.668434
\(929\) 29.0175 0.952032 0.476016 0.879437i \(-0.342080\pi\)
0.476016 + 0.879437i \(0.342080\pi\)
\(930\) −13.5998 −0.445956
\(931\) 41.3005 1.35357
\(932\) −19.8877 −0.651443
\(933\) −48.0477 −1.57301
\(934\) −44.1191 −1.44362
\(935\) −1.29850 −0.0424656
\(936\) −42.0893 −1.37573
\(937\) −11.3659 −0.371308 −0.185654 0.982615i \(-0.559440\pi\)
−0.185654 + 0.982615i \(0.559440\pi\)
\(938\) 68.7271 2.24402
\(939\) 47.6050 1.55353
\(940\) 4.23795 0.138227
\(941\) −34.3599 −1.12010 −0.560051 0.828458i \(-0.689218\pi\)
−0.560051 + 0.828458i \(0.689218\pi\)
\(942\) −28.6121 −0.932232
\(943\) −33.1275 −1.07878
\(944\) −6.85279 −0.223039
\(945\) 3.35738 0.109215
\(946\) 2.24742 0.0730701
\(947\) 6.66073 0.216445 0.108222 0.994127i \(-0.465484\pi\)
0.108222 + 0.994127i \(0.465484\pi\)
\(948\) −78.2182 −2.54041
\(949\) −62.3866 −2.02516
\(950\) 37.6119 1.22029
\(951\) 0.806264 0.0261449
\(952\) 9.20160 0.298226
\(953\) −27.0813 −0.877250 −0.438625 0.898670i \(-0.644534\pi\)
−0.438625 + 0.898670i \(0.644534\pi\)
\(954\) −91.4853 −2.96195
\(955\) −12.5332 −0.405566
\(956\) −56.3996 −1.82409
\(957\) −7.83212 −0.253176
\(958\) −36.3972 −1.17594
\(959\) 52.4022 1.69216
\(960\) −42.3754 −1.36766
\(961\) −27.5336 −0.888180
\(962\) 76.0925 2.45332
\(963\) 7.01372 0.226014
\(964\) 9.88594 0.318405
\(965\) −12.5554 −0.404172
\(966\) −137.131 −4.41211
\(967\) −23.4339 −0.753584 −0.376792 0.926298i \(-0.622973\pi\)
−0.376792 + 0.926298i \(0.622973\pi\)
\(968\) −2.36186 −0.0759131
\(969\) −12.6406 −0.406074
\(970\) −3.40701 −0.109393
\(971\) 33.0060 1.05921 0.529607 0.848243i \(-0.322340\pi\)
0.529607 + 0.848243i \(0.322340\pi\)
\(972\) −68.1919 −2.18726
\(973\) −70.9638 −2.27499
\(974\) −19.1073 −0.612237
\(975\) −45.2709 −1.44983
\(976\) 2.55046 0.0816383
\(977\) 50.0477 1.60117 0.800583 0.599221i \(-0.204523\pi\)
0.800583 + 0.599221i \(0.204523\pi\)
\(978\) 7.98639 0.255376
\(979\) 6.43379 0.205625
\(980\) 32.3987 1.03494
\(981\) −34.1409 −1.09004
\(982\) 61.7855 1.97166
\(983\) −49.5716 −1.58109 −0.790544 0.612405i \(-0.790202\pi\)
−0.790544 + 0.612405i \(0.790202\pi\)
\(984\) 31.2992 0.997781
\(985\) −33.8199 −1.07759
\(986\) −7.03232 −0.223955
\(987\) 10.4317 0.332046
\(988\) 84.0907 2.67528
\(989\) −6.25714 −0.198965
\(990\) −9.52863 −0.302840
\(991\) −13.1785 −0.418628 −0.209314 0.977848i \(-0.567123\pi\)
−0.209314 + 0.977848i \(0.567123\pi\)
\(992\) 12.1160 0.384683
\(993\) 44.1185 1.40006
\(994\) −81.2153 −2.57599
\(995\) 6.83595 0.216714
\(996\) 26.4859 0.839238
\(997\) 47.6776 1.50996 0.754982 0.655745i \(-0.227646\pi\)
0.754982 + 0.655745i \(0.227646\pi\)
\(998\) 87.8926 2.78219
\(999\) −4.11708 −0.130259
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 \(a_p\))