Properties

Label 8041.2.a.g.1.8
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
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: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.45687 q^{2} -0.886506 q^{3} +4.03623 q^{4} -0.806805 q^{5} +2.17803 q^{6} -3.77933 q^{7} -5.00275 q^{8} -2.21411 q^{9} +O(q^{10})\) \(q-2.45687 q^{2} -0.886506 q^{3} +4.03623 q^{4} -0.806805 q^{5} +2.17803 q^{6} -3.77933 q^{7} -5.00275 q^{8} -2.21411 q^{9} +1.98222 q^{10} -1.00000 q^{11} -3.57814 q^{12} -4.65728 q^{13} +9.28533 q^{14} +0.715238 q^{15} +4.21868 q^{16} +1.00000 q^{17} +5.43978 q^{18} -0.862138 q^{19} -3.25645 q^{20} +3.35040 q^{21} +2.45687 q^{22} +6.34147 q^{23} +4.43497 q^{24} -4.34906 q^{25} +11.4424 q^{26} +4.62234 q^{27} -15.2542 q^{28} +2.76760 q^{29} -1.75725 q^{30} -1.65984 q^{31} -0.359255 q^{32} +0.886506 q^{33} -2.45687 q^{34} +3.04918 q^{35} -8.93664 q^{36} -8.36983 q^{37} +2.11816 q^{38} +4.12871 q^{39} +4.03625 q^{40} -11.1901 q^{41} -8.23150 q^{42} +1.00000 q^{43} -4.03623 q^{44} +1.78635 q^{45} -15.5802 q^{46} -2.05804 q^{47} -3.73988 q^{48} +7.28332 q^{49} +10.6851 q^{50} -0.886506 q^{51} -18.7978 q^{52} +11.3753 q^{53} -11.3565 q^{54} +0.806805 q^{55} +18.9071 q^{56} +0.764290 q^{57} -6.79963 q^{58} -6.13074 q^{59} +2.88686 q^{60} +13.9893 q^{61} +4.07802 q^{62} +8.36784 q^{63} -7.55472 q^{64} +3.75752 q^{65} -2.17803 q^{66} +2.02853 q^{67} +4.03623 q^{68} -5.62175 q^{69} -7.49146 q^{70} +5.35238 q^{71} +11.0766 q^{72} -6.65044 q^{73} +20.5636 q^{74} +3.85547 q^{75} -3.47978 q^{76} +3.77933 q^{77} -10.1437 q^{78} -2.71492 q^{79} -3.40365 q^{80} +2.54460 q^{81} +27.4927 q^{82} +13.0548 q^{83} +13.5230 q^{84} -0.806805 q^{85} -2.45687 q^{86} -2.45349 q^{87} +5.00275 q^{88} -4.76136 q^{89} -4.38885 q^{90} +17.6014 q^{91} +25.5956 q^{92} +1.47146 q^{93} +5.05635 q^{94} +0.695577 q^{95} +0.318482 q^{96} +14.4975 q^{97} -17.8942 q^{98} +2.21411 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.45687 −1.73727 −0.868636 0.495451i \(-0.835003\pi\)
−0.868636 + 0.495451i \(0.835003\pi\)
\(3\) −0.886506 −0.511824 −0.255912 0.966700i \(-0.582376\pi\)
−0.255912 + 0.966700i \(0.582376\pi\)
\(4\) 4.03623 2.01811
\(5\) −0.806805 −0.360814 −0.180407 0.983592i \(-0.557742\pi\)
−0.180407 + 0.983592i \(0.557742\pi\)
\(6\) 2.17803 0.889178
\(7\) −3.77933 −1.42845 −0.714226 0.699915i \(-0.753221\pi\)
−0.714226 + 0.699915i \(0.753221\pi\)
\(8\) −5.00275 −1.76874
\(9\) −2.21411 −0.738036
\(10\) 1.98222 0.626833
\(11\) −1.00000 −0.301511
\(12\) −3.57814 −1.03292
\(13\) −4.65728 −1.29170 −0.645849 0.763465i \(-0.723496\pi\)
−0.645849 + 0.763465i \(0.723496\pi\)
\(14\) 9.28533 2.48161
\(15\) 0.715238 0.184674
\(16\) 4.21868 1.05467
\(17\) 1.00000 0.242536
\(18\) 5.43978 1.28217
\(19\) −0.862138 −0.197788 −0.0988940 0.995098i \(-0.531530\pi\)
−0.0988940 + 0.995098i \(0.531530\pi\)
\(20\) −3.25645 −0.728165
\(21\) 3.35040 0.731116
\(22\) 2.45687 0.523807
\(23\) 6.34147 1.32229 0.661144 0.750259i \(-0.270071\pi\)
0.661144 + 0.750259i \(0.270071\pi\)
\(24\) 4.43497 0.905285
\(25\) −4.34906 −0.869813
\(26\) 11.4424 2.24403
\(27\) 4.62234 0.889569
\(28\) −15.2542 −2.88278
\(29\) 2.76760 0.513930 0.256965 0.966421i \(-0.417278\pi\)
0.256965 + 0.966421i \(0.417278\pi\)
\(30\) −1.75725 −0.320828
\(31\) −1.65984 −0.298116 −0.149058 0.988828i \(-0.547624\pi\)
−0.149058 + 0.988828i \(0.547624\pi\)
\(32\) −0.359255 −0.0635079
\(33\) 0.886506 0.154321
\(34\) −2.45687 −0.421350
\(35\) 3.04918 0.515406
\(36\) −8.93664 −1.48944
\(37\) −8.36983 −1.37599 −0.687996 0.725715i \(-0.741509\pi\)
−0.687996 + 0.725715i \(0.741509\pi\)
\(38\) 2.11816 0.343611
\(39\) 4.12871 0.661122
\(40\) 4.03625 0.638187
\(41\) −11.1901 −1.74760 −0.873801 0.486284i \(-0.838352\pi\)
−0.873801 + 0.486284i \(0.838352\pi\)
\(42\) −8.23150 −1.27015
\(43\) 1.00000 0.152499
\(44\) −4.03623 −0.608484
\(45\) 1.78635 0.266294
\(46\) −15.5802 −2.29717
\(47\) −2.05804 −0.300196 −0.150098 0.988671i \(-0.547959\pi\)
−0.150098 + 0.988671i \(0.547959\pi\)
\(48\) −3.73988 −0.539806
\(49\) 7.28332 1.04047
\(50\) 10.6851 1.51110
\(51\) −0.886506 −0.124136
\(52\) −18.7978 −2.60679
\(53\) 11.3753 1.56252 0.781258 0.624208i \(-0.214578\pi\)
0.781258 + 0.624208i \(0.214578\pi\)
\(54\) −11.3565 −1.54542
\(55\) 0.806805 0.108790
\(56\) 18.9071 2.52656
\(57\) 0.764290 0.101233
\(58\) −6.79963 −0.892836
\(59\) −6.13074 −0.798154 −0.399077 0.916917i \(-0.630669\pi\)
−0.399077 + 0.916917i \(0.630669\pi\)
\(60\) 2.88686 0.372692
\(61\) 13.9893 1.79114 0.895571 0.444919i \(-0.146767\pi\)
0.895571 + 0.444919i \(0.146767\pi\)
\(62\) 4.07802 0.517909
\(63\) 8.36784 1.05425
\(64\) −7.55472 −0.944340
\(65\) 3.75752 0.466063
\(66\) −2.17803 −0.268097
\(67\) 2.02853 0.247824 0.123912 0.992293i \(-0.460456\pi\)
0.123912 + 0.992293i \(0.460456\pi\)
\(68\) 4.03623 0.489465
\(69\) −5.62175 −0.676779
\(70\) −7.49146 −0.895400
\(71\) 5.35238 0.635211 0.317605 0.948223i \(-0.397121\pi\)
0.317605 + 0.948223i \(0.397121\pi\)
\(72\) 11.0766 1.30539
\(73\) −6.65044 −0.778375 −0.389187 0.921159i \(-0.627244\pi\)
−0.389187 + 0.921159i \(0.627244\pi\)
\(74\) 20.5636 2.39047
\(75\) 3.85547 0.445191
\(76\) −3.47978 −0.399159
\(77\) 3.77933 0.430694
\(78\) −10.1437 −1.14855
\(79\) −2.71492 −0.305453 −0.152726 0.988269i \(-0.548805\pi\)
−0.152726 + 0.988269i \(0.548805\pi\)
\(80\) −3.40365 −0.380540
\(81\) 2.54460 0.282733
\(82\) 27.4927 3.03606
\(83\) 13.0548 1.43295 0.716477 0.697611i \(-0.245753\pi\)
0.716477 + 0.697611i \(0.245753\pi\)
\(84\) 13.5230 1.47548
\(85\) −0.806805 −0.0875103
\(86\) −2.45687 −0.264931
\(87\) −2.45349 −0.263042
\(88\) 5.00275 0.533295
\(89\) −4.76136 −0.504703 −0.252351 0.967636i \(-0.581204\pi\)
−0.252351 + 0.967636i \(0.581204\pi\)
\(90\) −4.38885 −0.462625
\(91\) 17.6014 1.84513
\(92\) 25.5956 2.66853
\(93\) 1.47146 0.152583
\(94\) 5.05635 0.521522
\(95\) 0.695577 0.0713647
\(96\) 0.318482 0.0325049
\(97\) 14.4975 1.47200 0.736001 0.676981i \(-0.236712\pi\)
0.736001 + 0.676981i \(0.236712\pi\)
\(98\) −17.8942 −1.80759
\(99\) 2.21411 0.222526
\(100\) −17.5538 −1.75538
\(101\) −8.11803 −0.807774 −0.403887 0.914809i \(-0.632341\pi\)
−0.403887 + 0.914809i \(0.632341\pi\)
\(102\) 2.17803 0.215657
\(103\) 13.9564 1.37517 0.687583 0.726106i \(-0.258672\pi\)
0.687583 + 0.726106i \(0.258672\pi\)
\(104\) 23.2992 2.28468
\(105\) −2.70312 −0.263797
\(106\) −27.9476 −2.71452
\(107\) −3.66100 −0.353922 −0.176961 0.984218i \(-0.556627\pi\)
−0.176961 + 0.984218i \(0.556627\pi\)
\(108\) 18.6568 1.79525
\(109\) −1.17742 −0.112777 −0.0563883 0.998409i \(-0.517958\pi\)
−0.0563883 + 0.998409i \(0.517958\pi\)
\(110\) −1.98222 −0.188997
\(111\) 7.41990 0.704266
\(112\) −15.9438 −1.50655
\(113\) 1.98154 0.186408 0.0932038 0.995647i \(-0.470289\pi\)
0.0932038 + 0.995647i \(0.470289\pi\)
\(114\) −1.87776 −0.175869
\(115\) −5.11633 −0.477101
\(116\) 11.1706 1.03717
\(117\) 10.3117 0.953319
\(118\) 15.0625 1.38661
\(119\) −3.77933 −0.346450
\(120\) −3.57816 −0.326640
\(121\) 1.00000 0.0909091
\(122\) −34.3699 −3.11170
\(123\) 9.92010 0.894465
\(124\) −6.69950 −0.601632
\(125\) 7.54288 0.674655
\(126\) −20.5587 −1.83152
\(127\) 15.4418 1.37023 0.685117 0.728433i \(-0.259751\pi\)
0.685117 + 0.728433i \(0.259751\pi\)
\(128\) 19.2795 1.70408
\(129\) −0.886506 −0.0780525
\(130\) −9.23175 −0.809678
\(131\) −4.91099 −0.429075 −0.214538 0.976716i \(-0.568824\pi\)
−0.214538 + 0.976716i \(0.568824\pi\)
\(132\) 3.57814 0.311437
\(133\) 3.25830 0.282531
\(134\) −4.98384 −0.430538
\(135\) −3.72933 −0.320969
\(136\) −5.00275 −0.428983
\(137\) −1.29999 −0.111066 −0.0555328 0.998457i \(-0.517686\pi\)
−0.0555328 + 0.998457i \(0.517686\pi\)
\(138\) 13.8119 1.17575
\(139\) 6.85794 0.581683 0.290841 0.956771i \(-0.406065\pi\)
0.290841 + 0.956771i \(0.406065\pi\)
\(140\) 12.3072 1.04015
\(141\) 1.82446 0.153648
\(142\) −13.1501 −1.10353
\(143\) 4.65728 0.389461
\(144\) −9.34061 −0.778384
\(145\) −2.23291 −0.185433
\(146\) 16.3393 1.35225
\(147\) −6.45671 −0.532540
\(148\) −33.7825 −2.77691
\(149\) −8.93399 −0.731901 −0.365950 0.930634i \(-0.619256\pi\)
−0.365950 + 0.930634i \(0.619256\pi\)
\(150\) −9.47240 −0.773419
\(151\) −0.0761129 −0.00619398 −0.00309699 0.999995i \(-0.500986\pi\)
−0.00309699 + 0.999995i \(0.500986\pi\)
\(152\) 4.31306 0.349836
\(153\) −2.21411 −0.179000
\(154\) −9.28533 −0.748233
\(155\) 1.33917 0.107565
\(156\) 16.6644 1.33422
\(157\) 18.1493 1.44848 0.724238 0.689551i \(-0.242192\pi\)
0.724238 + 0.689551i \(0.242192\pi\)
\(158\) 6.67022 0.530654
\(159\) −10.0843 −0.799734
\(160\) 0.289849 0.0229146
\(161\) −23.9665 −1.88883
\(162\) −6.25175 −0.491184
\(163\) −7.64318 −0.598660 −0.299330 0.954150i \(-0.596763\pi\)
−0.299330 + 0.954150i \(0.596763\pi\)
\(164\) −45.1658 −3.52686
\(165\) −0.715238 −0.0556812
\(166\) −32.0741 −2.48943
\(167\) 5.18148 0.400955 0.200477 0.979698i \(-0.435751\pi\)
0.200477 + 0.979698i \(0.435751\pi\)
\(168\) −16.7612 −1.29316
\(169\) 8.69027 0.668482
\(170\) 1.98222 0.152029
\(171\) 1.90887 0.145975
\(172\) 4.03623 0.307759
\(173\) −19.9666 −1.51803 −0.759015 0.651073i \(-0.774319\pi\)
−0.759015 + 0.651073i \(0.774319\pi\)
\(174\) 6.02791 0.456975
\(175\) 16.4365 1.24249
\(176\) −4.21868 −0.317995
\(177\) 5.43494 0.408515
\(178\) 11.6981 0.876806
\(179\) 12.3915 0.926185 0.463093 0.886310i \(-0.346740\pi\)
0.463093 + 0.886310i \(0.346740\pi\)
\(180\) 7.21013 0.537412
\(181\) 21.9532 1.63177 0.815884 0.578216i \(-0.196251\pi\)
0.815884 + 0.578216i \(0.196251\pi\)
\(182\) −43.2444 −3.20549
\(183\) −12.4016 −0.916750
\(184\) −31.7248 −2.33879
\(185\) 6.75283 0.496478
\(186\) −3.61519 −0.265078
\(187\) −1.00000 −0.0731272
\(188\) −8.30672 −0.605830
\(189\) −17.4693 −1.27071
\(190\) −1.70895 −0.123980
\(191\) −2.75524 −0.199362 −0.0996810 0.995019i \(-0.531782\pi\)
−0.0996810 + 0.995019i \(0.531782\pi\)
\(192\) 6.69730 0.483336
\(193\) −9.65803 −0.695200 −0.347600 0.937643i \(-0.613003\pi\)
−0.347600 + 0.937643i \(0.613003\pi\)
\(194\) −35.6186 −2.55727
\(195\) −3.33106 −0.238542
\(196\) 29.3971 2.09980
\(197\) −11.6721 −0.831604 −0.415802 0.909455i \(-0.636499\pi\)
−0.415802 + 0.909455i \(0.636499\pi\)
\(198\) −5.43978 −0.386589
\(199\) −1.42085 −0.100722 −0.0503608 0.998731i \(-0.516037\pi\)
−0.0503608 + 0.998731i \(0.516037\pi\)
\(200\) 21.7573 1.53847
\(201\) −1.79830 −0.126842
\(202\) 19.9450 1.40332
\(203\) −10.4597 −0.734124
\(204\) −3.57814 −0.250520
\(205\) 9.02824 0.630560
\(206\) −34.2891 −2.38904
\(207\) −14.0407 −0.975896
\(208\) −19.6476 −1.36231
\(209\) 0.862138 0.0596353
\(210\) 6.64122 0.458288
\(211\) −2.19054 −0.150803 −0.0754015 0.997153i \(-0.524024\pi\)
−0.0754015 + 0.997153i \(0.524024\pi\)
\(212\) 45.9133 3.15334
\(213\) −4.74492 −0.325116
\(214\) 8.99460 0.614858
\(215\) −0.806805 −0.0550237
\(216\) −23.1244 −1.57342
\(217\) 6.27308 0.425845
\(218\) 2.89278 0.195924
\(219\) 5.89565 0.398391
\(220\) 3.25645 0.219550
\(221\) −4.65728 −0.313283
\(222\) −18.2298 −1.22350
\(223\) 7.37189 0.493659 0.246829 0.969059i \(-0.420611\pi\)
0.246829 + 0.969059i \(0.420611\pi\)
\(224\) 1.35774 0.0907180
\(225\) 9.62930 0.641953
\(226\) −4.86840 −0.323841
\(227\) −11.5953 −0.769604 −0.384802 0.922999i \(-0.625730\pi\)
−0.384802 + 0.922999i \(0.625730\pi\)
\(228\) 3.08485 0.204299
\(229\) 13.8873 0.917698 0.458849 0.888514i \(-0.348262\pi\)
0.458849 + 0.888514i \(0.348262\pi\)
\(230\) 12.5702 0.828854
\(231\) −3.35040 −0.220440
\(232\) −13.8456 −0.909008
\(233\) 26.1512 1.71322 0.856612 0.515961i \(-0.172565\pi\)
0.856612 + 0.515961i \(0.172565\pi\)
\(234\) −25.3346 −1.65617
\(235\) 1.66044 0.108315
\(236\) −24.7451 −1.61077
\(237\) 2.40679 0.156338
\(238\) 9.28533 0.601879
\(239\) −10.7883 −0.697839 −0.348919 0.937153i \(-0.613451\pi\)
−0.348919 + 0.937153i \(0.613451\pi\)
\(240\) 3.01736 0.194770
\(241\) 9.11748 0.587309 0.293654 0.955912i \(-0.405129\pi\)
0.293654 + 0.955912i \(0.405129\pi\)
\(242\) −2.45687 −0.157934
\(243\) −16.1228 −1.03428
\(244\) 56.4639 3.61473
\(245\) −5.87622 −0.375418
\(246\) −24.3724 −1.55393
\(247\) 4.01522 0.255482
\(248\) 8.30378 0.527290
\(249\) −11.5732 −0.733421
\(250\) −18.5319 −1.17206
\(251\) −28.6068 −1.80564 −0.902822 0.430014i \(-0.858509\pi\)
−0.902822 + 0.430014i \(0.858509\pi\)
\(252\) 33.7745 2.12759
\(253\) −6.34147 −0.398685
\(254\) −37.9385 −2.38047
\(255\) 0.715238 0.0447899
\(256\) −32.2578 −2.01612
\(257\) 20.2935 1.26587 0.632937 0.774204i \(-0.281849\pi\)
0.632937 + 0.774204i \(0.281849\pi\)
\(258\) 2.17803 0.135598
\(259\) 31.6323 1.96554
\(260\) 15.1662 0.940568
\(261\) −6.12775 −0.379299
\(262\) 12.0657 0.745421
\(263\) 21.9631 1.35430 0.677152 0.735843i \(-0.263214\pi\)
0.677152 + 0.735843i \(0.263214\pi\)
\(264\) −4.43497 −0.272954
\(265\) −9.17765 −0.563778
\(266\) −8.00523 −0.490832
\(267\) 4.22097 0.258319
\(268\) 8.18761 0.500138
\(269\) 11.0199 0.671894 0.335947 0.941881i \(-0.390944\pi\)
0.335947 + 0.941881i \(0.390944\pi\)
\(270\) 9.16248 0.557611
\(271\) 2.67016 0.162200 0.0811002 0.996706i \(-0.474157\pi\)
0.0811002 + 0.996706i \(0.474157\pi\)
\(272\) 4.21868 0.255795
\(273\) −15.6037 −0.944381
\(274\) 3.19391 0.192951
\(275\) 4.34906 0.262258
\(276\) −22.6907 −1.36582
\(277\) −6.73935 −0.404928 −0.202464 0.979290i \(-0.564895\pi\)
−0.202464 + 0.979290i \(0.564895\pi\)
\(278\) −16.8491 −1.01054
\(279\) 3.67507 0.220020
\(280\) −15.2543 −0.911620
\(281\) −32.0838 −1.91396 −0.956978 0.290159i \(-0.906292\pi\)
−0.956978 + 0.290159i \(0.906292\pi\)
\(282\) −4.48248 −0.266928
\(283\) 15.3570 0.912878 0.456439 0.889755i \(-0.349125\pi\)
0.456439 + 0.889755i \(0.349125\pi\)
\(284\) 21.6034 1.28193
\(285\) −0.616633 −0.0365262
\(286\) −11.4424 −0.676600
\(287\) 42.2911 2.49637
\(288\) 0.795429 0.0468711
\(289\) 1.00000 0.0588235
\(290\) 5.48598 0.322148
\(291\) −12.8521 −0.753406
\(292\) −26.8427 −1.57085
\(293\) −32.7665 −1.91424 −0.957121 0.289689i \(-0.906448\pi\)
−0.957121 + 0.289689i \(0.906448\pi\)
\(294\) 15.8633 0.925167
\(295\) 4.94631 0.287986
\(296\) 41.8722 2.43377
\(297\) −4.62234 −0.268215
\(298\) 21.9497 1.27151
\(299\) −29.5340 −1.70800
\(300\) 15.5616 0.898447
\(301\) −3.77933 −0.217837
\(302\) 0.187000 0.0107606
\(303\) 7.19668 0.413438
\(304\) −3.63708 −0.208601
\(305\) −11.2866 −0.646270
\(306\) 5.43978 0.310972
\(307\) −8.07639 −0.460944 −0.230472 0.973079i \(-0.574027\pi\)
−0.230472 + 0.973079i \(0.574027\pi\)
\(308\) 15.2542 0.869190
\(309\) −12.3724 −0.703843
\(310\) −3.29017 −0.186869
\(311\) −10.3457 −0.586649 −0.293325 0.956013i \(-0.594762\pi\)
−0.293325 + 0.956013i \(0.594762\pi\)
\(312\) −20.6549 −1.16935
\(313\) 24.2793 1.37235 0.686174 0.727438i \(-0.259289\pi\)
0.686174 + 0.727438i \(0.259289\pi\)
\(314\) −44.5906 −2.51640
\(315\) −6.75122 −0.380388
\(316\) −10.9580 −0.616438
\(317\) 6.98517 0.392326 0.196163 0.980571i \(-0.437152\pi\)
0.196163 + 0.980571i \(0.437152\pi\)
\(318\) 24.7757 1.38936
\(319\) −2.76760 −0.154956
\(320\) 6.09519 0.340731
\(321\) 3.24549 0.181146
\(322\) 58.8827 3.28140
\(323\) −0.862138 −0.0479706
\(324\) 10.2706 0.570587
\(325\) 20.2548 1.12354
\(326\) 18.7783 1.04004
\(327\) 1.04379 0.0577218
\(328\) 55.9814 3.09105
\(329\) 7.77801 0.428816
\(330\) 1.75725 0.0967334
\(331\) 2.19206 0.120486 0.0602432 0.998184i \(-0.480812\pi\)
0.0602432 + 0.998184i \(0.480812\pi\)
\(332\) 52.6923 2.89186
\(333\) 18.5317 1.01553
\(334\) −12.7302 −0.696568
\(335\) −1.63663 −0.0894186
\(336\) 14.1343 0.771087
\(337\) −20.3694 −1.10959 −0.554796 0.831986i \(-0.687204\pi\)
−0.554796 + 0.831986i \(0.687204\pi\)
\(338\) −21.3509 −1.16134
\(339\) −1.75665 −0.0954080
\(340\) −3.25645 −0.176606
\(341\) 1.65984 0.0898854
\(342\) −4.68984 −0.253598
\(343\) −1.07077 −0.0578159
\(344\) −5.00275 −0.269730
\(345\) 4.53566 0.244192
\(346\) 49.0553 2.63723
\(347\) 16.1734 0.868235 0.434117 0.900856i \(-0.357060\pi\)
0.434117 + 0.900856i \(0.357060\pi\)
\(348\) −9.90284 −0.530848
\(349\) −30.7769 −1.64745 −0.823726 0.566988i \(-0.808109\pi\)
−0.823726 + 0.566988i \(0.808109\pi\)
\(350\) −40.3825 −2.15854
\(351\) −21.5275 −1.14905
\(352\) 0.359255 0.0191484
\(353\) 26.3520 1.40258 0.701288 0.712878i \(-0.252609\pi\)
0.701288 + 0.712878i \(0.252609\pi\)
\(354\) −13.3529 −0.709701
\(355\) −4.31833 −0.229193
\(356\) −19.2179 −1.01855
\(357\) 3.35040 0.177322
\(358\) −30.4444 −1.60904
\(359\) 15.7461 0.831046 0.415523 0.909583i \(-0.363599\pi\)
0.415523 + 0.909583i \(0.363599\pi\)
\(360\) −8.93669 −0.471005
\(361\) −18.2567 −0.960880
\(362\) −53.9362 −2.83482
\(363\) −0.886506 −0.0465295
\(364\) 71.0432 3.72368
\(365\) 5.36561 0.280849
\(366\) 30.4691 1.59264
\(367\) −25.6519 −1.33902 −0.669509 0.742804i \(-0.733495\pi\)
−0.669509 + 0.742804i \(0.733495\pi\)
\(368\) 26.7526 1.39458
\(369\) 24.7761 1.28979
\(370\) −16.5908 −0.862517
\(371\) −42.9910 −2.23198
\(372\) 5.93914 0.307930
\(373\) 37.3390 1.93334 0.966670 0.256026i \(-0.0824131\pi\)
0.966670 + 0.256026i \(0.0824131\pi\)
\(374\) 2.45687 0.127042
\(375\) −6.68680 −0.345305
\(376\) 10.2959 0.530969
\(377\) −12.8895 −0.663842
\(378\) 42.9199 2.20756
\(379\) 2.83870 0.145814 0.0729072 0.997339i \(-0.476772\pi\)
0.0729072 + 0.997339i \(0.476772\pi\)
\(380\) 2.80751 0.144022
\(381\) −13.6892 −0.701319
\(382\) 6.76927 0.346346
\(383\) 8.18481 0.418224 0.209112 0.977892i \(-0.432943\pi\)
0.209112 + 0.977892i \(0.432943\pi\)
\(384\) −17.0914 −0.872191
\(385\) −3.04918 −0.155401
\(386\) 23.7286 1.20775
\(387\) −2.21411 −0.112549
\(388\) 58.5153 2.97067
\(389\) 12.6477 0.641265 0.320633 0.947204i \(-0.396104\pi\)
0.320633 + 0.947204i \(0.396104\pi\)
\(390\) 8.18400 0.414413
\(391\) 6.34147 0.320702
\(392\) −36.4367 −1.84033
\(393\) 4.35362 0.219611
\(394\) 28.6769 1.44472
\(395\) 2.19041 0.110212
\(396\) 8.93664 0.449083
\(397\) −3.73996 −0.187703 −0.0938517 0.995586i \(-0.529918\pi\)
−0.0938517 + 0.995586i \(0.529918\pi\)
\(398\) 3.49086 0.174981
\(399\) −2.88850 −0.144606
\(400\) −18.3473 −0.917366
\(401\) 4.81273 0.240336 0.120168 0.992754i \(-0.461657\pi\)
0.120168 + 0.992754i \(0.461657\pi\)
\(402\) 4.41820 0.220360
\(403\) 7.73034 0.385076
\(404\) −32.7662 −1.63018
\(405\) −2.05299 −0.102014
\(406\) 25.6980 1.27537
\(407\) 8.36983 0.414877
\(408\) 4.43497 0.219564
\(409\) 1.22734 0.0606881 0.0303441 0.999540i \(-0.490340\pi\)
0.0303441 + 0.999540i \(0.490340\pi\)
\(410\) −22.1813 −1.09545
\(411\) 1.15245 0.0568461
\(412\) 56.3312 2.77524
\(413\) 23.1701 1.14012
\(414\) 34.4962 1.69540
\(415\) −10.5327 −0.517030
\(416\) 1.67315 0.0820330
\(417\) −6.07960 −0.297719
\(418\) −2.11816 −0.103603
\(419\) −1.27285 −0.0621826 −0.0310913 0.999517i \(-0.509898\pi\)
−0.0310913 + 0.999517i \(0.509898\pi\)
\(420\) −10.9104 −0.532373
\(421\) −36.7832 −1.79270 −0.896352 0.443343i \(-0.853792\pi\)
−0.896352 + 0.443343i \(0.853792\pi\)
\(422\) 5.38188 0.261986
\(423\) 4.55672 0.221555
\(424\) −56.9078 −2.76369
\(425\) −4.34906 −0.210961
\(426\) 11.6577 0.564816
\(427\) −52.8700 −2.55856
\(428\) −14.7766 −0.714255
\(429\) −4.12871 −0.199336
\(430\) 1.98222 0.0955911
\(431\) 15.5099 0.747085 0.373542 0.927613i \(-0.378143\pi\)
0.373542 + 0.927613i \(0.378143\pi\)
\(432\) 19.5002 0.938202
\(433\) −32.1192 −1.54355 −0.771776 0.635894i \(-0.780631\pi\)
−0.771776 + 0.635894i \(0.780631\pi\)
\(434\) −15.4122 −0.739808
\(435\) 1.97949 0.0949092
\(436\) −4.75234 −0.227596
\(437\) −5.46722 −0.261533
\(438\) −14.4849 −0.692114
\(439\) 14.4252 0.688477 0.344238 0.938882i \(-0.388137\pi\)
0.344238 + 0.938882i \(0.388137\pi\)
\(440\) −4.03625 −0.192421
\(441\) −16.1261 −0.767908
\(442\) 11.4424 0.544257
\(443\) −20.0106 −0.950730 −0.475365 0.879789i \(-0.657684\pi\)
−0.475365 + 0.879789i \(0.657684\pi\)
\(444\) 29.9484 1.42129
\(445\) 3.84149 0.182104
\(446\) −18.1118 −0.857619
\(447\) 7.92003 0.374605
\(448\) 28.5518 1.34894
\(449\) 35.4480 1.67289 0.836447 0.548048i \(-0.184629\pi\)
0.836447 + 0.548048i \(0.184629\pi\)
\(450\) −23.6580 −1.11525
\(451\) 11.1901 0.526922
\(452\) 7.99795 0.376192
\(453\) 0.0674745 0.00317023
\(454\) 28.4881 1.33701
\(455\) −14.2009 −0.665749
\(456\) −3.82356 −0.179054
\(457\) −31.3899 −1.46836 −0.734178 0.678957i \(-0.762432\pi\)
−0.734178 + 0.678957i \(0.762432\pi\)
\(458\) −34.1193 −1.59429
\(459\) 4.62234 0.215752
\(460\) −20.6507 −0.962844
\(461\) 11.0680 0.515489 0.257744 0.966213i \(-0.417021\pi\)
0.257744 + 0.966213i \(0.417021\pi\)
\(462\) 8.23150 0.382964
\(463\) −3.90936 −0.181683 −0.0908417 0.995865i \(-0.528956\pi\)
−0.0908417 + 0.995865i \(0.528956\pi\)
\(464\) 11.6756 0.542026
\(465\) −1.18718 −0.0550542
\(466\) −64.2503 −2.97634
\(467\) 16.3775 0.757859 0.378929 0.925426i \(-0.376292\pi\)
0.378929 + 0.925426i \(0.376292\pi\)
\(468\) 41.6205 1.92391
\(469\) −7.66648 −0.354005
\(470\) −4.07949 −0.188173
\(471\) −16.0895 −0.741365
\(472\) 30.6706 1.41173
\(473\) −1.00000 −0.0459800
\(474\) −5.91319 −0.271602
\(475\) 3.74949 0.172039
\(476\) −15.2542 −0.699176
\(477\) −25.1861 −1.15319
\(478\) 26.5056 1.21234
\(479\) −11.6699 −0.533213 −0.266607 0.963805i \(-0.585902\pi\)
−0.266607 + 0.963805i \(0.585902\pi\)
\(480\) −0.256953 −0.0117282
\(481\) 38.9807 1.77736
\(482\) −22.4005 −1.02031
\(483\) 21.2464 0.966747
\(484\) 4.03623 0.183465
\(485\) −11.6967 −0.531119
\(486\) 39.6117 1.79682
\(487\) 28.1759 1.27677 0.638386 0.769717i \(-0.279603\pi\)
0.638386 + 0.769717i \(0.279603\pi\)
\(488\) −69.9849 −3.16807
\(489\) 6.77572 0.306409
\(490\) 14.4371 0.652203
\(491\) −8.00194 −0.361123 −0.180561 0.983564i \(-0.557791\pi\)
−0.180561 + 0.983564i \(0.557791\pi\)
\(492\) 40.0398 1.80513
\(493\) 2.76760 0.124646
\(494\) −9.86488 −0.443842
\(495\) −1.78635 −0.0802907
\(496\) −7.00234 −0.314414
\(497\) −20.2284 −0.907368
\(498\) 28.4338 1.27415
\(499\) 26.2471 1.17498 0.587490 0.809231i \(-0.300116\pi\)
0.587490 + 0.809231i \(0.300116\pi\)
\(500\) 30.4448 1.36153
\(501\) −4.59341 −0.205218
\(502\) 70.2833 3.13690
\(503\) −31.2721 −1.39436 −0.697178 0.716898i \(-0.745561\pi\)
−0.697178 + 0.716898i \(0.745561\pi\)
\(504\) −41.8622 −1.86469
\(505\) 6.54967 0.291456
\(506\) 15.5802 0.692624
\(507\) −7.70397 −0.342145
\(508\) 62.3265 2.76529
\(509\) −37.6877 −1.67048 −0.835238 0.549888i \(-0.814670\pi\)
−0.835238 + 0.549888i \(0.814670\pi\)
\(510\) −1.75725 −0.0778123
\(511\) 25.1342 1.11187
\(512\) 40.6945 1.79846
\(513\) −3.98509 −0.175946
\(514\) −49.8585 −2.19917
\(515\) −11.2601 −0.496179
\(516\) −3.57814 −0.157519
\(517\) 2.05804 0.0905125
\(518\) −77.7166 −3.41467
\(519\) 17.7005 0.776965
\(520\) −18.7980 −0.824345
\(521\) 29.6520 1.29908 0.649539 0.760328i \(-0.274962\pi\)
0.649539 + 0.760328i \(0.274962\pi\)
\(522\) 15.0551 0.658945
\(523\) 37.2857 1.63039 0.815196 0.579186i \(-0.196629\pi\)
0.815196 + 0.579186i \(0.196629\pi\)
\(524\) −19.8219 −0.865923
\(525\) −14.5711 −0.635934
\(526\) −53.9606 −2.35279
\(527\) −1.65984 −0.0723038
\(528\) 3.73988 0.162758
\(529\) 17.2143 0.748447
\(530\) 22.5483 0.979436
\(531\) 13.5741 0.589066
\(532\) 13.1512 0.570179
\(533\) 52.1155 2.25737
\(534\) −10.3704 −0.448771
\(535\) 2.95371 0.127700
\(536\) −10.1482 −0.438337
\(537\) −10.9851 −0.474044
\(538\) −27.0745 −1.16726
\(539\) −7.28332 −0.313715
\(540\) −15.0524 −0.647753
\(541\) 37.5255 1.61335 0.806673 0.590998i \(-0.201266\pi\)
0.806673 + 0.590998i \(0.201266\pi\)
\(542\) −6.56024 −0.281786
\(543\) −19.4616 −0.835178
\(544\) −0.359255 −0.0154029
\(545\) 0.949950 0.0406914
\(546\) 38.3364 1.64065
\(547\) −13.4283 −0.574151 −0.287075 0.957908i \(-0.592683\pi\)
−0.287075 + 0.957908i \(0.592683\pi\)
\(548\) −5.24706 −0.224143
\(549\) −30.9737 −1.32193
\(550\) −10.6851 −0.455614
\(551\) −2.38605 −0.101649
\(552\) 28.1242 1.19705
\(553\) 10.2606 0.436324
\(554\) 16.5577 0.703470
\(555\) −5.98642 −0.254109
\(556\) 27.6802 1.17390
\(557\) 9.20104 0.389860 0.194930 0.980817i \(-0.437552\pi\)
0.194930 + 0.980817i \(0.437552\pi\)
\(558\) −9.02917 −0.382235
\(559\) −4.65728 −0.196982
\(560\) 12.8635 0.543583
\(561\) 0.886506 0.0374283
\(562\) 78.8258 3.32506
\(563\) −28.0597 −1.18257 −0.591287 0.806461i \(-0.701380\pi\)
−0.591287 + 0.806461i \(0.701380\pi\)
\(564\) 7.36396 0.310078
\(565\) −1.59872 −0.0672586
\(566\) −37.7302 −1.58592
\(567\) −9.61686 −0.403870
\(568\) −26.7767 −1.12352
\(569\) −8.93769 −0.374688 −0.187344 0.982294i \(-0.559988\pi\)
−0.187344 + 0.982294i \(0.559988\pi\)
\(570\) 1.51499 0.0634560
\(571\) 12.7777 0.534732 0.267366 0.963595i \(-0.413847\pi\)
0.267366 + 0.963595i \(0.413847\pi\)
\(572\) 18.7978 0.785978
\(573\) 2.44253 0.102038
\(574\) −103.904 −4.33687
\(575\) −27.5795 −1.15014
\(576\) 16.7270 0.696956
\(577\) −22.3765 −0.931546 −0.465773 0.884904i \(-0.654224\pi\)
−0.465773 + 0.884904i \(0.654224\pi\)
\(578\) −2.45687 −0.102192
\(579\) 8.56190 0.355820
\(580\) −9.01254 −0.374225
\(581\) −49.3385 −2.04691
\(582\) 31.5761 1.30887
\(583\) −11.3753 −0.471116
\(584\) 33.2705 1.37674
\(585\) −8.31955 −0.343971
\(586\) 80.5032 3.32556
\(587\) 19.5857 0.808390 0.404195 0.914673i \(-0.367552\pi\)
0.404195 + 0.914673i \(0.367552\pi\)
\(588\) −26.0607 −1.07473
\(589\) 1.43101 0.0589638
\(590\) −12.1525 −0.500309
\(591\) 10.3474 0.425635
\(592\) −35.3096 −1.45122
\(593\) 39.4378 1.61952 0.809759 0.586762i \(-0.199598\pi\)
0.809759 + 0.586762i \(0.199598\pi\)
\(594\) 11.3565 0.465963
\(595\) 3.04918 0.125004
\(596\) −36.0596 −1.47706
\(597\) 1.25959 0.0515518
\(598\) 72.5614 2.96725
\(599\) −27.8142 −1.13646 −0.568230 0.822870i \(-0.692371\pi\)
−0.568230 + 0.822870i \(0.692371\pi\)
\(600\) −19.2880 −0.787428
\(601\) −14.8850 −0.607171 −0.303586 0.952804i \(-0.598184\pi\)
−0.303586 + 0.952804i \(0.598184\pi\)
\(602\) 9.28533 0.378442
\(603\) −4.49138 −0.182903
\(604\) −0.307209 −0.0125002
\(605\) −0.806805 −0.0328013
\(606\) −17.6813 −0.718255
\(607\) −45.5701 −1.84963 −0.924816 0.380415i \(-0.875781\pi\)
−0.924816 + 0.380415i \(0.875781\pi\)
\(608\) 0.309727 0.0125611
\(609\) 9.27254 0.375742
\(610\) 27.7298 1.12275
\(611\) 9.58487 0.387762
\(612\) −8.93664 −0.361242
\(613\) 2.70182 0.109125 0.0545627 0.998510i \(-0.482624\pi\)
0.0545627 + 0.998510i \(0.482624\pi\)
\(614\) 19.8427 0.800785
\(615\) −8.00359 −0.322736
\(616\) −18.9071 −0.761787
\(617\) 20.2650 0.815837 0.407919 0.913018i \(-0.366255\pi\)
0.407919 + 0.913018i \(0.366255\pi\)
\(618\) 30.3975 1.22277
\(619\) −26.8529 −1.07931 −0.539654 0.841887i \(-0.681445\pi\)
−0.539654 + 0.841887i \(0.681445\pi\)
\(620\) 5.40519 0.217078
\(621\) 29.3124 1.17627
\(622\) 25.4180 1.01917
\(623\) 17.9947 0.720944
\(624\) 17.4177 0.697266
\(625\) 15.6597 0.626388
\(626\) −59.6512 −2.38414
\(627\) −0.764290 −0.0305228
\(628\) 73.2549 2.92319
\(629\) −8.36983 −0.333727
\(630\) 16.5869 0.660838
\(631\) 34.6381 1.37892 0.689461 0.724323i \(-0.257848\pi\)
0.689461 + 0.724323i \(0.257848\pi\)
\(632\) 13.5821 0.540266
\(633\) 1.94193 0.0771846
\(634\) −17.1617 −0.681578
\(635\) −12.4585 −0.494400
\(636\) −40.7024 −1.61395
\(637\) −33.9205 −1.34398
\(638\) 6.79963 0.269200
\(639\) −11.8508 −0.468808
\(640\) −15.5548 −0.614858
\(641\) −12.5892 −0.497242 −0.248621 0.968601i \(-0.579977\pi\)
−0.248621 + 0.968601i \(0.579977\pi\)
\(642\) −7.97377 −0.314700
\(643\) 40.8840 1.61231 0.806154 0.591706i \(-0.201545\pi\)
0.806154 + 0.591706i \(0.201545\pi\)
\(644\) −96.7343 −3.81186
\(645\) 0.715238 0.0281625
\(646\) 2.11816 0.0833380
\(647\) 23.1544 0.910293 0.455146 0.890417i \(-0.349587\pi\)
0.455146 + 0.890417i \(0.349587\pi\)
\(648\) −12.7300 −0.500081
\(649\) 6.13074 0.240653
\(650\) −49.7635 −1.95189
\(651\) −5.56112 −0.217958
\(652\) −30.8496 −1.20816
\(653\) −28.3555 −1.10964 −0.554819 0.831971i \(-0.687212\pi\)
−0.554819 + 0.831971i \(0.687212\pi\)
\(654\) −2.56446 −0.100278
\(655\) 3.96222 0.154817
\(656\) −47.2075 −1.84314
\(657\) 14.7248 0.574468
\(658\) −19.1096 −0.744969
\(659\) −8.72016 −0.339689 −0.169845 0.985471i \(-0.554327\pi\)
−0.169845 + 0.985471i \(0.554327\pi\)
\(660\) −2.88686 −0.112371
\(661\) −14.6667 −0.570470 −0.285235 0.958458i \(-0.592072\pi\)
−0.285235 + 0.958458i \(0.592072\pi\)
\(662\) −5.38561 −0.209317
\(663\) 4.12871 0.160346
\(664\) −65.3101 −2.53452
\(665\) −2.62882 −0.101941
\(666\) −45.5301 −1.76425
\(667\) 17.5506 0.679563
\(668\) 20.9136 0.809173
\(669\) −6.53523 −0.252666
\(670\) 4.02099 0.155344
\(671\) −13.9893 −0.540050
\(672\) −1.20365 −0.0464317
\(673\) −30.9797 −1.19418 −0.597089 0.802175i \(-0.703676\pi\)
−0.597089 + 0.802175i \(0.703676\pi\)
\(674\) 50.0451 1.92766
\(675\) −20.1028 −0.773759
\(676\) 35.0759 1.34907
\(677\) 2.40270 0.0923434 0.0461717 0.998934i \(-0.485298\pi\)
0.0461717 + 0.998934i \(0.485298\pi\)
\(678\) 4.31586 0.165750
\(679\) −54.7909 −2.10268
\(680\) 4.03625 0.154783
\(681\) 10.2793 0.393902
\(682\) −4.07802 −0.156155
\(683\) −26.8448 −1.02719 −0.513594 0.858033i \(-0.671686\pi\)
−0.513594 + 0.858033i \(0.671686\pi\)
\(684\) 7.70462 0.294593
\(685\) 1.04884 0.0400741
\(686\) 2.63074 0.100442
\(687\) −12.3112 −0.469700
\(688\) 4.21868 0.160836
\(689\) −52.9779 −2.01830
\(690\) −11.1435 −0.424227
\(691\) 34.2946 1.30463 0.652314 0.757948i \(-0.273798\pi\)
0.652314 + 0.757948i \(0.273798\pi\)
\(692\) −80.5896 −3.06356
\(693\) −8.36784 −0.317868
\(694\) −39.7361 −1.50836
\(695\) −5.53302 −0.209879
\(696\) 12.2742 0.465253
\(697\) −11.1901 −0.423856
\(698\) 75.6151 2.86207
\(699\) −23.1832 −0.876870
\(700\) 66.3416 2.50748
\(701\) −40.4732 −1.52865 −0.764326 0.644829i \(-0.776928\pi\)
−0.764326 + 0.644829i \(0.776928\pi\)
\(702\) 52.8904 1.99622
\(703\) 7.21595 0.272155
\(704\) 7.55472 0.284729
\(705\) −1.47199 −0.0554383
\(706\) −64.7436 −2.43666
\(707\) 30.6807 1.15387
\(708\) 21.9366 0.824429
\(709\) −33.1652 −1.24554 −0.622772 0.782403i \(-0.713994\pi\)
−0.622772 + 0.782403i \(0.713994\pi\)
\(710\) 10.6096 0.398171
\(711\) 6.01113 0.225435
\(712\) 23.8199 0.892689
\(713\) −10.5258 −0.394196
\(714\) −8.23150 −0.308056
\(715\) −3.75752 −0.140523
\(716\) 50.0150 1.86915
\(717\) 9.56391 0.357171
\(718\) −38.6861 −1.44375
\(719\) −23.1103 −0.861869 −0.430934 0.902383i \(-0.641816\pi\)
−0.430934 + 0.902383i \(0.641816\pi\)
\(720\) 7.53606 0.280852
\(721\) −52.7458 −1.96436
\(722\) 44.8545 1.66931
\(723\) −8.08270 −0.300599
\(724\) 88.6081 3.29309
\(725\) −12.0365 −0.447023
\(726\) 2.17803 0.0808344
\(727\) −29.4737 −1.09312 −0.546560 0.837420i \(-0.684063\pi\)
−0.546560 + 0.837420i \(0.684063\pi\)
\(728\) −88.0555 −3.26355
\(729\) 6.65917 0.246636
\(730\) −13.1826 −0.487911
\(731\) 1.00000 0.0369863
\(732\) −50.0555 −1.85011
\(733\) 50.0111 1.84720 0.923601 0.383356i \(-0.125232\pi\)
0.923601 + 0.383356i \(0.125232\pi\)
\(734\) 63.0234 2.32624
\(735\) 5.20931 0.192148
\(736\) −2.27821 −0.0839758
\(737\) −2.02853 −0.0747218
\(738\) −60.8718 −2.24072
\(739\) −37.3021 −1.37218 −0.686090 0.727516i \(-0.740675\pi\)
−0.686090 + 0.727516i \(0.740675\pi\)
\(740\) 27.2559 1.00195
\(741\) −3.55951 −0.130762
\(742\) 105.623 3.87755
\(743\) 19.3397 0.709506 0.354753 0.934960i \(-0.384565\pi\)
0.354753 + 0.934960i \(0.384565\pi\)
\(744\) −7.36134 −0.269880
\(745\) 7.20799 0.264080
\(746\) −91.7372 −3.35874
\(747\) −28.9048 −1.05757
\(748\) −4.03623 −0.147579
\(749\) 13.8361 0.505560
\(750\) 16.4286 0.599889
\(751\) −2.40462 −0.0877457 −0.0438729 0.999037i \(-0.513970\pi\)
−0.0438729 + 0.999037i \(0.513970\pi\)
\(752\) −8.68222 −0.316608
\(753\) 25.3601 0.924173
\(754\) 31.6678 1.15327
\(755\) 0.0614083 0.00223488
\(756\) −70.5102 −2.56443
\(757\) 10.1310 0.368216 0.184108 0.982906i \(-0.441060\pi\)
0.184108 + 0.982906i \(0.441060\pi\)
\(758\) −6.97433 −0.253319
\(759\) 5.62175 0.204057
\(760\) −3.47980 −0.126226
\(761\) 27.0771 0.981545 0.490772 0.871288i \(-0.336715\pi\)
0.490772 + 0.871288i \(0.336715\pi\)
\(762\) 33.6327 1.21838
\(763\) 4.44986 0.161096
\(764\) −11.1208 −0.402335
\(765\) 1.78635 0.0645858
\(766\) −20.1091 −0.726570
\(767\) 28.5526 1.03097
\(768\) 28.5968 1.03190
\(769\) 40.4282 1.45788 0.728939 0.684579i \(-0.240014\pi\)
0.728939 + 0.684579i \(0.240014\pi\)
\(770\) 7.49146 0.269973
\(771\) −17.9903 −0.647905
\(772\) −38.9820 −1.40299
\(773\) 29.8571 1.07389 0.536943 0.843618i \(-0.319579\pi\)
0.536943 + 0.843618i \(0.319579\pi\)
\(774\) 5.43978 0.195529
\(775\) 7.21875 0.259305
\(776\) −72.5276 −2.60359
\(777\) −28.0422 −1.00601
\(778\) −31.0739 −1.11405
\(779\) 9.64742 0.345655
\(780\) −13.4449 −0.481406
\(781\) −5.35238 −0.191523
\(782\) −15.5802 −0.557147
\(783\) 12.7928 0.457176
\(784\) 30.7260 1.09736
\(785\) −14.6430 −0.522631
\(786\) −10.6963 −0.381524
\(787\) −47.0094 −1.67571 −0.837853 0.545896i \(-0.816189\pi\)
−0.837853 + 0.545896i \(0.816189\pi\)
\(788\) −47.1113 −1.67827
\(789\) −19.4704 −0.693166
\(790\) −5.38157 −0.191468
\(791\) −7.48889 −0.266274
\(792\) −11.0766 −0.393591
\(793\) −65.1519 −2.31361
\(794\) 9.18862 0.326092
\(795\) 8.13604 0.288555
\(796\) −5.73489 −0.203268
\(797\) 10.8342 0.383768 0.191884 0.981418i \(-0.438540\pi\)
0.191884 + 0.981418i \(0.438540\pi\)
\(798\) 7.09669 0.251220
\(799\) −2.05804 −0.0728082
\(800\) 1.56242 0.0552400
\(801\) 10.5422 0.372489
\(802\) −11.8243 −0.417529
\(803\) 6.65044 0.234689
\(804\) −7.25836 −0.255983
\(805\) 19.3363 0.681515
\(806\) −18.9925 −0.668982
\(807\) −9.76919 −0.343892
\(808\) 40.6125 1.42874
\(809\) −40.9838 −1.44091 −0.720457 0.693499i \(-0.756068\pi\)
−0.720457 + 0.693499i \(0.756068\pi\)
\(810\) 5.04395 0.177226
\(811\) −22.1634 −0.778261 −0.389131 0.921183i \(-0.627225\pi\)
−0.389131 + 0.921183i \(0.627225\pi\)
\(812\) −42.2175 −1.48155
\(813\) −2.36711 −0.0830181
\(814\) −20.5636 −0.720754
\(815\) 6.16656 0.216005
\(816\) −3.73988 −0.130922
\(817\) −0.862138 −0.0301624
\(818\) −3.01542 −0.105432
\(819\) −38.9714 −1.36177
\(820\) 36.4401 1.27254
\(821\) −18.0694 −0.630625 −0.315312 0.948988i \(-0.602109\pi\)
−0.315312 + 0.948988i \(0.602109\pi\)
\(822\) −2.83142 −0.0987571
\(823\) 29.2263 1.01876 0.509382 0.860541i \(-0.329874\pi\)
0.509382 + 0.860541i \(0.329874\pi\)
\(824\) −69.8205 −2.43231
\(825\) −3.85547 −0.134230
\(826\) −56.9259 −1.98071
\(827\) −54.5303 −1.89621 −0.948103 0.317965i \(-0.897001\pi\)
−0.948103 + 0.317965i \(0.897001\pi\)
\(828\) −56.6715 −1.96947
\(829\) 48.5058 1.68468 0.842338 0.538950i \(-0.181179\pi\)
0.842338 + 0.538950i \(0.181179\pi\)
\(830\) 25.8775 0.898222
\(831\) 5.97447 0.207252
\(832\) 35.1844 1.21980
\(833\) 7.28332 0.252352
\(834\) 14.9368 0.517219
\(835\) −4.18045 −0.144670
\(836\) 3.47978 0.120351
\(837\) −7.67234 −0.265195
\(838\) 3.12722 0.108028
\(839\) −6.60532 −0.228041 −0.114020 0.993478i \(-0.536373\pi\)
−0.114020 + 0.993478i \(0.536373\pi\)
\(840\) 13.5230 0.466589
\(841\) −21.3404 −0.735876
\(842\) 90.3717 3.11441
\(843\) 28.4424 0.979610
\(844\) −8.84152 −0.304338
\(845\) −7.01136 −0.241198
\(846\) −11.1953 −0.384902
\(847\) −3.77933 −0.129859
\(848\) 47.9887 1.64794
\(849\) −13.6141 −0.467233
\(850\) 10.6851 0.366496
\(851\) −53.0770 −1.81946
\(852\) −19.1516 −0.656122
\(853\) −16.4219 −0.562277 −0.281138 0.959667i \(-0.590712\pi\)
−0.281138 + 0.959667i \(0.590712\pi\)
\(854\) 129.895 4.44491
\(855\) −1.54008 −0.0526697
\(856\) 18.3151 0.625996
\(857\) 26.0854 0.891060 0.445530 0.895267i \(-0.353015\pi\)
0.445530 + 0.895267i \(0.353015\pi\)
\(858\) 10.1437 0.346301
\(859\) −50.5524 −1.72483 −0.862413 0.506206i \(-0.831048\pi\)
−0.862413 + 0.506206i \(0.831048\pi\)
\(860\) −3.25645 −0.111044
\(861\) −37.4913 −1.27770
\(862\) −38.1058 −1.29789
\(863\) 10.8897 0.370688 0.185344 0.982674i \(-0.440660\pi\)
0.185344 + 0.982674i \(0.440660\pi\)
\(864\) −1.66060 −0.0564947
\(865\) 16.1091 0.547727
\(866\) 78.9129 2.68157
\(867\) −0.886506 −0.0301073
\(868\) 25.3196 0.859403
\(869\) 2.71492 0.0920974
\(870\) −4.86335 −0.164883
\(871\) −9.44743 −0.320114
\(872\) 5.89035 0.199472
\(873\) −32.0991 −1.08639
\(874\) 13.4323 0.454353
\(875\) −28.5070 −0.963713
\(876\) 23.7962 0.803999
\(877\) −36.9488 −1.24767 −0.623836 0.781555i \(-0.714427\pi\)
−0.623836 + 0.781555i \(0.714427\pi\)
\(878\) −35.4409 −1.19607
\(879\) 29.0477 0.979755
\(880\) 3.40365 0.114737
\(881\) −13.3098 −0.448419 −0.224209 0.974541i \(-0.571980\pi\)
−0.224209 + 0.974541i \(0.571980\pi\)
\(882\) 39.6197 1.33406
\(883\) −35.4485 −1.19294 −0.596469 0.802636i \(-0.703430\pi\)
−0.596469 + 0.802636i \(0.703430\pi\)
\(884\) −18.7978 −0.632240
\(885\) −4.38494 −0.147398
\(886\) 49.1634 1.65168
\(887\) 17.4160 0.584773 0.292386 0.956300i \(-0.405551\pi\)
0.292386 + 0.956300i \(0.405551\pi\)
\(888\) −37.1200 −1.24566
\(889\) −58.3595 −1.95731
\(890\) −9.43805 −0.316364
\(891\) −2.54460 −0.0852472
\(892\) 29.7546 0.996259
\(893\) 1.77431 0.0593752
\(894\) −19.4585 −0.650790
\(895\) −9.99754 −0.334181
\(896\) −72.8635 −2.43420
\(897\) 26.1821 0.874194
\(898\) −87.0912 −2.90627
\(899\) −4.59377 −0.153211
\(900\) 38.8660 1.29553
\(901\) 11.3753 0.378966
\(902\) −27.4927 −0.915406
\(903\) 3.35040 0.111494
\(904\) −9.91316 −0.329707
\(905\) −17.7120 −0.588765
\(906\) −0.165776 −0.00550755
\(907\) 4.05748 0.134726 0.0673632 0.997729i \(-0.478541\pi\)
0.0673632 + 0.997729i \(0.478541\pi\)
\(908\) −46.8011 −1.55315
\(909\) 17.9742 0.596166
\(910\) 34.8898 1.15659
\(911\) −36.4373 −1.20722 −0.603611 0.797279i \(-0.706272\pi\)
−0.603611 + 0.797279i \(0.706272\pi\)
\(912\) 3.22430 0.106767
\(913\) −13.0548 −0.432052
\(914\) 77.1210 2.55093
\(915\) 10.0057 0.330777
\(916\) 56.0523 1.85202
\(917\) 18.5602 0.612913
\(918\) −11.3565 −0.374820
\(919\) −24.5738 −0.810614 −0.405307 0.914181i \(-0.632835\pi\)
−0.405307 + 0.914181i \(0.632835\pi\)
\(920\) 25.5958 0.843868
\(921\) 7.15977 0.235922
\(922\) −27.1927 −0.895544
\(923\) −24.9276 −0.820500
\(924\) −13.5230 −0.444873
\(925\) 36.4009 1.19686
\(926\) 9.60480 0.315633
\(927\) −30.9010 −1.01492
\(928\) −0.994273 −0.0326386
\(929\) 6.03459 0.197988 0.0989942 0.995088i \(-0.468437\pi\)
0.0989942 + 0.995088i \(0.468437\pi\)
\(930\) 2.91675 0.0956441
\(931\) −6.27923 −0.205793
\(932\) 105.552 3.45748
\(933\) 9.17150 0.300261
\(934\) −40.2374 −1.31661
\(935\) 0.806805 0.0263854
\(936\) −51.5870 −1.68617
\(937\) −56.4994 −1.84575 −0.922877 0.385094i \(-0.874169\pi\)
−0.922877 + 0.385094i \(0.874169\pi\)
\(938\) 18.8356 0.615003
\(939\) −21.5237 −0.702401
\(940\) 6.70191 0.218592
\(941\) −33.1839 −1.08176 −0.540882 0.841099i \(-0.681909\pi\)
−0.540882 + 0.841099i \(0.681909\pi\)
\(942\) 39.5299 1.28795
\(943\) −70.9618 −2.31083
\(944\) −25.8636 −0.841789
\(945\) 14.0943 0.458489
\(946\) 2.45687 0.0798799
\(947\) −32.6341 −1.06047 −0.530233 0.847852i \(-0.677896\pi\)
−0.530233 + 0.847852i \(0.677896\pi\)
\(948\) 9.71437 0.315508
\(949\) 30.9730 1.00542
\(950\) −9.21203 −0.298878
\(951\) −6.19239 −0.200802
\(952\) 18.9071 0.612781
\(953\) −15.3278 −0.496515 −0.248258 0.968694i \(-0.579858\pi\)
−0.248258 + 0.968694i \(0.579858\pi\)
\(954\) 61.8791 2.00341
\(955\) 2.22294 0.0719327
\(956\) −43.5441 −1.40832
\(957\) 2.45349 0.0793101
\(958\) 28.6716 0.926337
\(959\) 4.91309 0.158652
\(960\) −5.40342 −0.174395
\(961\) −28.2449 −0.911127
\(962\) −95.7705 −3.08777
\(963\) 8.10584 0.261207
\(964\) 36.8002 1.18526
\(965\) 7.79215 0.250838
\(966\) −52.1998 −1.67950
\(967\) 22.9748 0.738820 0.369410 0.929267i \(-0.379560\pi\)
0.369410 + 0.929267i \(0.379560\pi\)
\(968\) −5.00275 −0.160795
\(969\) 0.764290 0.0245525
\(970\) 28.7373 0.922698
\(971\) −25.5688 −0.820542 −0.410271 0.911964i \(-0.634566\pi\)
−0.410271 + 0.911964i \(0.634566\pi\)
\(972\) −65.0753 −2.08729
\(973\) −25.9184 −0.830905
\(974\) −69.2246 −2.21810
\(975\) −17.9560 −0.575053
\(976\) 59.0162 1.88906
\(977\) −2.52292 −0.0807153 −0.0403576 0.999185i \(-0.512850\pi\)
−0.0403576 + 0.999185i \(0.512850\pi\)
\(978\) −16.6471 −0.532315
\(979\) 4.76136 0.152174
\(980\) −23.7178 −0.757637
\(981\) 2.60694 0.0832331
\(982\) 19.6598 0.627368
\(983\) −55.1314 −1.75842 −0.879210 0.476435i \(-0.841929\pi\)
−0.879210 + 0.476435i \(0.841929\pi\)
\(984\) −49.6278 −1.58208
\(985\) 9.41713 0.300055
\(986\) −6.79963 −0.216544
\(987\) −6.89525 −0.219478
\(988\) 16.2063 0.515592
\(989\) 6.34147 0.201647
\(990\) 4.38885 0.139487
\(991\) −61.7472 −1.96147 −0.980733 0.195354i \(-0.937414\pi\)
−0.980733 + 0.195354i \(0.937414\pi\)
\(992\) 0.596306 0.0189327
\(993\) −1.94327 −0.0616678
\(994\) 49.6987 1.57635
\(995\) 1.14635 0.0363418
\(996\) −46.7120 −1.48013
\(997\) 26.3416 0.834247 0.417123 0.908850i \(-0.363038\pi\)
0.417123 + 0.908850i \(0.363038\pi\)
\(998\) −64.4857 −2.04126
\(999\) −38.6882 −1.22404
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 \(a_p\))