Properties

Label 8018.2.a.d.1.25
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.25
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.54327 q^{3} +1.00000 q^{4} -0.0183668 q^{5} +1.54327 q^{6} -4.28156 q^{7} +1.00000 q^{8} -0.618317 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.54327 q^{3} +1.00000 q^{4} -0.0183668 q^{5} +1.54327 q^{6} -4.28156 q^{7} +1.00000 q^{8} -0.618317 q^{9} -0.0183668 q^{10} +2.99582 q^{11} +1.54327 q^{12} +4.32372 q^{13} -4.28156 q^{14} -0.0283449 q^{15} +1.00000 q^{16} -4.98650 q^{17} -0.618317 q^{18} +1.00000 q^{19} -0.0183668 q^{20} -6.60760 q^{21} +2.99582 q^{22} -3.35613 q^{23} +1.54327 q^{24} -4.99966 q^{25} +4.32372 q^{26} -5.58404 q^{27} -4.28156 q^{28} +3.45887 q^{29} -0.0283449 q^{30} -7.49814 q^{31} +1.00000 q^{32} +4.62336 q^{33} -4.98650 q^{34} +0.0786384 q^{35} -0.618317 q^{36} +0.329578 q^{37} +1.00000 q^{38} +6.67267 q^{39} -0.0183668 q^{40} +11.3967 q^{41} -6.60760 q^{42} -9.79706 q^{43} +2.99582 q^{44} +0.0113565 q^{45} -3.35613 q^{46} -1.16608 q^{47} +1.54327 q^{48} +11.3317 q^{49} -4.99966 q^{50} -7.69551 q^{51} +4.32372 q^{52} -13.1012 q^{53} -5.58404 q^{54} -0.0550236 q^{55} -4.28156 q^{56} +1.54327 q^{57} +3.45887 q^{58} -8.47759 q^{59} -0.0283449 q^{60} +1.61162 q^{61} -7.49814 q^{62} +2.64736 q^{63} +1.00000 q^{64} -0.0794128 q^{65} +4.62336 q^{66} +10.1292 q^{67} -4.98650 q^{68} -5.17941 q^{69} +0.0786384 q^{70} +4.96060 q^{71} -0.618317 q^{72} -16.4077 q^{73} +0.329578 q^{74} -7.71583 q^{75} +1.00000 q^{76} -12.8268 q^{77} +6.67267 q^{78} +8.25238 q^{79} -0.0183668 q^{80} -6.76273 q^{81} +11.3967 q^{82} -3.64838 q^{83} -6.60760 q^{84} +0.0915859 q^{85} -9.79706 q^{86} +5.33796 q^{87} +2.99582 q^{88} -8.09860 q^{89} +0.0113565 q^{90} -18.5123 q^{91} -3.35613 q^{92} -11.5717 q^{93} -1.16608 q^{94} -0.0183668 q^{95} +1.54327 q^{96} +2.65533 q^{97} +11.3317 q^{98} -1.85237 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} + O(q^{10}) \) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} - 12q^{10} - 17q^{11} - 10q^{12} - 19q^{13} - 15q^{14} - 8q^{15} + 30q^{16} - 18q^{17} + 10q^{18} + 30q^{19} - 12q^{20} - 14q^{21} - 17q^{22} - 15q^{23} - 10q^{24} - 4q^{25} - 19q^{26} - 37q^{27} - 15q^{28} - 37q^{29} - 8q^{30} - 11q^{31} + 30q^{32} + 6q^{33} - 18q^{34} - 4q^{35} + 10q^{36} - 46q^{37} + 30q^{38} - 12q^{40} - 28q^{41} - 14q^{42} - 61q^{43} - 17q^{44} - 14q^{45} - 15q^{46} - 4q^{47} - 10q^{48} - q^{49} - 4q^{50} - 8q^{51} - 19q^{52} - 19q^{53} - 37q^{54} - 17q^{55} - 15q^{56} - 10q^{57} - 37q^{58} - 6q^{59} - 8q^{60} - 32q^{61} - 11q^{62} - 24q^{63} + 30q^{64} - 24q^{65} + 6q^{66} - 44q^{67} - 18q^{68} - 2q^{69} - 4q^{70} + 10q^{71} + 10q^{72} - 58q^{73} - 46q^{74} - 42q^{75} + 30q^{76} - 32q^{77} - 42q^{79} - 12q^{80} - 38q^{81} - 28q^{82} - 25q^{83} - 14q^{84} - 48q^{85} - 61q^{86} - 15q^{87} - 17q^{88} - 39q^{89} - 14q^{90} - 21q^{91} - 15q^{92} - 45q^{93} - 4q^{94} - 12q^{95} - 10q^{96} - 33q^{97} - q^{98} - 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.54327 0.891007 0.445504 0.895280i \(-0.353025\pi\)
0.445504 + 0.895280i \(0.353025\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.0183668 −0.00821387 −0.00410694 0.999992i \(-0.501307\pi\)
−0.00410694 + 0.999992i \(0.501307\pi\)
\(6\) 1.54327 0.630037
\(7\) −4.28156 −1.61828 −0.809138 0.587618i \(-0.800066\pi\)
−0.809138 + 0.587618i \(0.800066\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.618317 −0.206106
\(10\) −0.0183668 −0.00580809
\(11\) 2.99582 0.903274 0.451637 0.892202i \(-0.350840\pi\)
0.451637 + 0.892202i \(0.350840\pi\)
\(12\) 1.54327 0.445504
\(13\) 4.32372 1.19918 0.599592 0.800306i \(-0.295329\pi\)
0.599592 + 0.800306i \(0.295329\pi\)
\(14\) −4.28156 −1.14429
\(15\) −0.0283449 −0.00731862
\(16\) 1.00000 0.250000
\(17\) −4.98650 −1.20940 −0.604702 0.796452i \(-0.706708\pi\)
−0.604702 + 0.796452i \(0.706708\pi\)
\(18\) −0.618317 −0.145739
\(19\) 1.00000 0.229416
\(20\) −0.0183668 −0.00410694
\(21\) −6.60760 −1.44190
\(22\) 2.99582 0.638711
\(23\) −3.35613 −0.699801 −0.349900 0.936787i \(-0.613785\pi\)
−0.349900 + 0.936787i \(0.613785\pi\)
\(24\) 1.54327 0.315019
\(25\) −4.99966 −0.999933
\(26\) 4.32372 0.847951
\(27\) −5.58404 −1.07465
\(28\) −4.28156 −0.809138
\(29\) 3.45887 0.642295 0.321148 0.947029i \(-0.395931\pi\)
0.321148 + 0.947029i \(0.395931\pi\)
\(30\) −0.0283449 −0.00517505
\(31\) −7.49814 −1.34671 −0.673353 0.739321i \(-0.735147\pi\)
−0.673353 + 0.739321i \(0.735147\pi\)
\(32\) 1.00000 0.176777
\(33\) 4.62336 0.804824
\(34\) −4.98650 −0.855177
\(35\) 0.0786384 0.0132923
\(36\) −0.618317 −0.103053
\(37\) 0.329578 0.0541823 0.0270911 0.999633i \(-0.491376\pi\)
0.0270911 + 0.999633i \(0.491376\pi\)
\(38\) 1.00000 0.162221
\(39\) 6.67267 1.06848
\(40\) −0.0183668 −0.00290404
\(41\) 11.3967 1.77986 0.889930 0.456098i \(-0.150753\pi\)
0.889930 + 0.456098i \(0.150753\pi\)
\(42\) −6.60760 −1.01957
\(43\) −9.79706 −1.49404 −0.747019 0.664803i \(-0.768516\pi\)
−0.747019 + 0.664803i \(0.768516\pi\)
\(44\) 2.99582 0.451637
\(45\) 0.0113565 0.00169293
\(46\) −3.35613 −0.494834
\(47\) −1.16608 −0.170091 −0.0850453 0.996377i \(-0.527103\pi\)
−0.0850453 + 0.996377i \(0.527103\pi\)
\(48\) 1.54327 0.222752
\(49\) 11.3317 1.61882
\(50\) −4.99966 −0.707059
\(51\) −7.69551 −1.07759
\(52\) 4.32372 0.599592
\(53\) −13.1012 −1.79959 −0.899793 0.436317i \(-0.856283\pi\)
−0.899793 + 0.436317i \(0.856283\pi\)
\(54\) −5.58404 −0.759892
\(55\) −0.0550236 −0.00741938
\(56\) −4.28156 −0.572147
\(57\) 1.54327 0.204411
\(58\) 3.45887 0.454171
\(59\) −8.47759 −1.10369 −0.551844 0.833947i \(-0.686076\pi\)
−0.551844 + 0.833947i \(0.686076\pi\)
\(60\) −0.0283449 −0.00365931
\(61\) 1.61162 0.206347 0.103173 0.994663i \(-0.467100\pi\)
0.103173 + 0.994663i \(0.467100\pi\)
\(62\) −7.49814 −0.952265
\(63\) 2.64736 0.333536
\(64\) 1.00000 0.125000
\(65\) −0.0794128 −0.00984995
\(66\) 4.62336 0.569096
\(67\) 10.1292 1.23748 0.618738 0.785598i \(-0.287644\pi\)
0.618738 + 0.785598i \(0.287644\pi\)
\(68\) −4.98650 −0.604702
\(69\) −5.17941 −0.623528
\(70\) 0.0786384 0.00939909
\(71\) 4.96060 0.588715 0.294357 0.955695i \(-0.404894\pi\)
0.294357 + 0.955695i \(0.404894\pi\)
\(72\) −0.618317 −0.0728693
\(73\) −16.4077 −1.92038 −0.960190 0.279348i \(-0.909882\pi\)
−0.960190 + 0.279348i \(0.909882\pi\)
\(74\) 0.329578 0.0383127
\(75\) −7.71583 −0.890947
\(76\) 1.00000 0.114708
\(77\) −12.8268 −1.46175
\(78\) 6.67267 0.755531
\(79\) 8.25238 0.928466 0.464233 0.885713i \(-0.346330\pi\)
0.464233 + 0.885713i \(0.346330\pi\)
\(80\) −0.0183668 −0.00205347
\(81\) −6.76273 −0.751415
\(82\) 11.3967 1.25855
\(83\) −3.64838 −0.400462 −0.200231 0.979749i \(-0.564169\pi\)
−0.200231 + 0.979749i \(0.564169\pi\)
\(84\) −6.60760 −0.720948
\(85\) 0.0915859 0.00993389
\(86\) −9.79706 −1.05644
\(87\) 5.33796 0.572290
\(88\) 2.99582 0.319356
\(89\) −8.09860 −0.858450 −0.429225 0.903198i \(-0.641213\pi\)
−0.429225 + 0.903198i \(0.641213\pi\)
\(90\) 0.0113565 0.00119708
\(91\) −18.5123 −1.94061
\(92\) −3.35613 −0.349900
\(93\) −11.5717 −1.19993
\(94\) −1.16608 −0.120272
\(95\) −0.0183668 −0.00188439
\(96\) 1.54327 0.157509
\(97\) 2.65533 0.269608 0.134804 0.990872i \(-0.456960\pi\)
0.134804 + 0.990872i \(0.456960\pi\)
\(98\) 11.3317 1.14468
\(99\) −1.85237 −0.186170
\(100\) −4.99966 −0.499966
\(101\) −7.01241 −0.697760 −0.348880 0.937167i \(-0.613438\pi\)
−0.348880 + 0.937167i \(0.613438\pi\)
\(102\) −7.69551 −0.761969
\(103\) 6.04519 0.595650 0.297825 0.954620i \(-0.403739\pi\)
0.297825 + 0.954620i \(0.403739\pi\)
\(104\) 4.32372 0.423976
\(105\) 0.121360 0.0118436
\(106\) −13.1012 −1.27250
\(107\) 6.69195 0.646936 0.323468 0.946239i \(-0.395151\pi\)
0.323468 + 0.946239i \(0.395151\pi\)
\(108\) −5.58404 −0.537325
\(109\) −6.28126 −0.601636 −0.300818 0.953682i \(-0.597260\pi\)
−0.300818 + 0.953682i \(0.597260\pi\)
\(110\) −0.0550236 −0.00524629
\(111\) 0.508628 0.0482768
\(112\) −4.28156 −0.404569
\(113\) −8.76071 −0.824138 −0.412069 0.911153i \(-0.635194\pi\)
−0.412069 + 0.911153i \(0.635194\pi\)
\(114\) 1.54327 0.144541
\(115\) 0.0616412 0.00574808
\(116\) 3.45887 0.321148
\(117\) −2.67343 −0.247159
\(118\) −8.47759 −0.780426
\(119\) 21.3500 1.95715
\(120\) −0.0283449 −0.00258752
\(121\) −2.02506 −0.184096
\(122\) 1.61162 0.145909
\(123\) 17.5881 1.58587
\(124\) −7.49814 −0.673353
\(125\) 0.183662 0.0164272
\(126\) 2.64736 0.235846
\(127\) −7.07855 −0.628119 −0.314060 0.949403i \(-0.601689\pi\)
−0.314060 + 0.949403i \(0.601689\pi\)
\(128\) 1.00000 0.0883883
\(129\) −15.1195 −1.33120
\(130\) −0.0794128 −0.00696496
\(131\) 11.2562 0.983457 0.491729 0.870748i \(-0.336365\pi\)
0.491729 + 0.870748i \(0.336365\pi\)
\(132\) 4.62336 0.402412
\(133\) −4.28156 −0.371258
\(134\) 10.1292 0.875027
\(135\) 0.102561 0.00882703
\(136\) −4.98650 −0.427589
\(137\) −1.46424 −0.125098 −0.0625492 0.998042i \(-0.519923\pi\)
−0.0625492 + 0.998042i \(0.519923\pi\)
\(138\) −5.17941 −0.440901
\(139\) −18.8318 −1.59729 −0.798647 0.601800i \(-0.794451\pi\)
−0.798647 + 0.601800i \(0.794451\pi\)
\(140\) 0.0786384 0.00664616
\(141\) −1.79958 −0.151552
\(142\) 4.96060 0.416284
\(143\) 12.9531 1.08319
\(144\) −0.618317 −0.0515264
\(145\) −0.0635282 −0.00527573
\(146\) −16.4077 −1.35791
\(147\) 17.4879 1.44238
\(148\) 0.329578 0.0270911
\(149\) −23.1725 −1.89837 −0.949183 0.314725i \(-0.898088\pi\)
−0.949183 + 0.314725i \(0.898088\pi\)
\(150\) −7.71583 −0.629995
\(151\) 7.66353 0.623650 0.311825 0.950140i \(-0.399060\pi\)
0.311825 + 0.950140i \(0.399060\pi\)
\(152\) 1.00000 0.0811107
\(153\) 3.08324 0.249265
\(154\) −12.8268 −1.03361
\(155\) 0.137717 0.0110617
\(156\) 6.67267 0.534241
\(157\) 9.09348 0.725739 0.362869 0.931840i \(-0.381797\pi\)
0.362869 + 0.931840i \(0.381797\pi\)
\(158\) 8.25238 0.656524
\(159\) −20.2187 −1.60344
\(160\) −0.0183668 −0.00145202
\(161\) 14.3695 1.13247
\(162\) −6.76273 −0.531331
\(163\) 10.6542 0.834500 0.417250 0.908792i \(-0.362994\pi\)
0.417250 + 0.908792i \(0.362994\pi\)
\(164\) 11.3967 0.889930
\(165\) −0.0849163 −0.00661072
\(166\) −3.64838 −0.283169
\(167\) −11.4669 −0.887337 −0.443669 0.896191i \(-0.646323\pi\)
−0.443669 + 0.896191i \(0.646323\pi\)
\(168\) −6.60760 −0.509787
\(169\) 5.69456 0.438043
\(170\) 0.0915859 0.00702432
\(171\) −0.618317 −0.0472839
\(172\) −9.79706 −0.747019
\(173\) −1.51469 −0.115160 −0.0575799 0.998341i \(-0.518338\pi\)
−0.0575799 + 0.998341i \(0.518338\pi\)
\(174\) 5.33796 0.404670
\(175\) 21.4063 1.61817
\(176\) 2.99582 0.225818
\(177\) −13.0832 −0.983395
\(178\) −8.09860 −0.607016
\(179\) 11.9286 0.891586 0.445793 0.895136i \(-0.352922\pi\)
0.445793 + 0.895136i \(0.352922\pi\)
\(180\) 0.0113565 0.000846463 0
\(181\) −10.4087 −0.773676 −0.386838 0.922148i \(-0.626433\pi\)
−0.386838 + 0.922148i \(0.626433\pi\)
\(182\) −18.5123 −1.37222
\(183\) 2.48716 0.183856
\(184\) −3.35613 −0.247417
\(185\) −0.00605328 −0.000445046 0
\(186\) −11.5717 −0.848476
\(187\) −14.9387 −1.09242
\(188\) −1.16608 −0.0850453
\(189\) 23.9084 1.73908
\(190\) −0.0183668 −0.00133247
\(191\) −6.81941 −0.493435 −0.246718 0.969087i \(-0.579352\pi\)
−0.246718 + 0.969087i \(0.579352\pi\)
\(192\) 1.54327 0.111376
\(193\) −0.388352 −0.0279542 −0.0139771 0.999902i \(-0.504449\pi\)
−0.0139771 + 0.999902i \(0.504449\pi\)
\(194\) 2.65533 0.190641
\(195\) −0.122555 −0.00877638
\(196\) 11.3317 0.809410
\(197\) −7.14947 −0.509379 −0.254689 0.967023i \(-0.581973\pi\)
−0.254689 + 0.967023i \(0.581973\pi\)
\(198\) −1.85237 −0.131642
\(199\) 15.4828 1.09755 0.548774 0.835971i \(-0.315095\pi\)
0.548774 + 0.835971i \(0.315095\pi\)
\(200\) −4.99966 −0.353530
\(201\) 15.6320 1.10260
\(202\) −7.01241 −0.493391
\(203\) −14.8093 −1.03941
\(204\) −7.69551 −0.538794
\(205\) −0.209320 −0.0146195
\(206\) 6.04519 0.421188
\(207\) 2.07515 0.144233
\(208\) 4.32372 0.299796
\(209\) 2.99582 0.207225
\(210\) 0.121360 0.00837466
\(211\) −1.00000 −0.0688428
\(212\) −13.1012 −0.899793
\(213\) 7.65555 0.524549
\(214\) 6.69195 0.457453
\(215\) 0.179940 0.0122718
\(216\) −5.58404 −0.379946
\(217\) 32.1037 2.17934
\(218\) −6.28126 −0.425421
\(219\) −25.3216 −1.71107
\(220\) −0.0550236 −0.00370969
\(221\) −21.5602 −1.45030
\(222\) 0.508628 0.0341369
\(223\) −8.09141 −0.541841 −0.270921 0.962602i \(-0.587328\pi\)
−0.270921 + 0.962602i \(0.587328\pi\)
\(224\) −4.28156 −0.286074
\(225\) 3.09138 0.206092
\(226\) −8.76071 −0.582754
\(227\) 5.20647 0.345566 0.172783 0.984960i \(-0.444724\pi\)
0.172783 + 0.984960i \(0.444724\pi\)
\(228\) 1.54327 0.102206
\(229\) 17.2283 1.13848 0.569238 0.822173i \(-0.307238\pi\)
0.569238 + 0.822173i \(0.307238\pi\)
\(230\) 0.0616412 0.00406450
\(231\) −19.7952 −1.30243
\(232\) 3.45887 0.227086
\(233\) −2.72435 −0.178478 −0.0892389 0.996010i \(-0.528443\pi\)
−0.0892389 + 0.996010i \(0.528443\pi\)
\(234\) −2.67343 −0.174768
\(235\) 0.0214172 0.00139710
\(236\) −8.47759 −0.551844
\(237\) 12.7357 0.827270
\(238\) 21.3500 1.38391
\(239\) −19.9630 −1.29130 −0.645650 0.763634i \(-0.723413\pi\)
−0.645650 + 0.763634i \(0.723413\pi\)
\(240\) −0.0283449 −0.00182966
\(241\) −11.8516 −0.763429 −0.381714 0.924280i \(-0.624666\pi\)
−0.381714 + 0.924280i \(0.624666\pi\)
\(242\) −2.02506 −0.130176
\(243\) 6.31540 0.405133
\(244\) 1.61162 0.103173
\(245\) −0.208128 −0.0132968
\(246\) 17.5881 1.12138
\(247\) 4.32372 0.275112
\(248\) −7.49814 −0.476133
\(249\) −5.63044 −0.356815
\(250\) 0.183662 0.0116158
\(251\) 14.8904 0.939874 0.469937 0.882700i \(-0.344277\pi\)
0.469937 + 0.882700i \(0.344277\pi\)
\(252\) 2.64736 0.166768
\(253\) −10.0544 −0.632112
\(254\) −7.07855 −0.444148
\(255\) 0.141342 0.00885117
\(256\) 1.00000 0.0625000
\(257\) 22.5355 1.40572 0.702862 0.711327i \(-0.251905\pi\)
0.702862 + 0.711327i \(0.251905\pi\)
\(258\) −15.1195 −0.941300
\(259\) −1.41111 −0.0876819
\(260\) −0.0794128 −0.00492497
\(261\) −2.13868 −0.132381
\(262\) 11.2562 0.695409
\(263\) −1.27361 −0.0785344 −0.0392672 0.999229i \(-0.512502\pi\)
−0.0392672 + 0.999229i \(0.512502\pi\)
\(264\) 4.62336 0.284548
\(265\) 0.240627 0.0147816
\(266\) −4.28156 −0.262519
\(267\) −12.4983 −0.764886
\(268\) 10.1292 0.618738
\(269\) 17.6740 1.07760 0.538802 0.842432i \(-0.318877\pi\)
0.538802 + 0.842432i \(0.318877\pi\)
\(270\) 0.102561 0.00624165
\(271\) 1.59875 0.0971172 0.0485586 0.998820i \(-0.484537\pi\)
0.0485586 + 0.998820i \(0.484537\pi\)
\(272\) −4.98650 −0.302351
\(273\) −28.5694 −1.72910
\(274\) −1.46424 −0.0884579
\(275\) −14.9781 −0.903213
\(276\) −5.17941 −0.311764
\(277\) −7.10665 −0.426997 −0.213498 0.976943i \(-0.568486\pi\)
−0.213498 + 0.976943i \(0.568486\pi\)
\(278\) −18.8318 −1.12946
\(279\) 4.63623 0.277564
\(280\) 0.0786384 0.00469954
\(281\) 10.6124 0.633081 0.316540 0.948579i \(-0.397479\pi\)
0.316540 + 0.948579i \(0.397479\pi\)
\(282\) −1.79958 −0.107163
\(283\) −25.6020 −1.52188 −0.760941 0.648821i \(-0.775262\pi\)
−0.760941 + 0.648821i \(0.775262\pi\)
\(284\) 4.96060 0.294357
\(285\) −0.0283449 −0.00167901
\(286\) 12.9531 0.765932
\(287\) −48.7955 −2.88031
\(288\) −0.618317 −0.0364347
\(289\) 7.86516 0.462656
\(290\) −0.0635282 −0.00373051
\(291\) 4.09789 0.240222
\(292\) −16.4077 −0.960190
\(293\) −25.4146 −1.48474 −0.742368 0.669992i \(-0.766297\pi\)
−0.742368 + 0.669992i \(0.766297\pi\)
\(294\) 17.4879 1.01992
\(295\) 0.155706 0.00906556
\(296\) 0.329578 0.0191563
\(297\) −16.7288 −0.970703
\(298\) −23.1725 −1.34235
\(299\) −14.5110 −0.839190
\(300\) −7.71583 −0.445474
\(301\) 41.9467 2.41777
\(302\) 7.66353 0.440987
\(303\) −10.8220 −0.621710
\(304\) 1.00000 0.0573539
\(305\) −0.0296002 −0.00169490
\(306\) 3.08324 0.176257
\(307\) 24.5408 1.40062 0.700310 0.713839i \(-0.253045\pi\)
0.700310 + 0.713839i \(0.253045\pi\)
\(308\) −12.8268 −0.730874
\(309\) 9.32936 0.530729
\(310\) 0.137717 0.00782179
\(311\) 12.3101 0.698042 0.349021 0.937115i \(-0.386514\pi\)
0.349021 + 0.937115i \(0.386514\pi\)
\(312\) 6.67267 0.377765
\(313\) 0.609964 0.0344772 0.0172386 0.999851i \(-0.494513\pi\)
0.0172386 + 0.999851i \(0.494513\pi\)
\(314\) 9.09348 0.513175
\(315\) −0.0486235 −0.00273962
\(316\) 8.25238 0.464233
\(317\) −25.1406 −1.41203 −0.706017 0.708194i \(-0.749510\pi\)
−0.706017 + 0.708194i \(0.749510\pi\)
\(318\) −20.2187 −1.13381
\(319\) 10.3621 0.580169
\(320\) −0.0183668 −0.00102673
\(321\) 10.3275 0.576424
\(322\) 14.3695 0.800778
\(323\) −4.98650 −0.277456
\(324\) −6.76273 −0.375707
\(325\) −21.6171 −1.19910
\(326\) 10.6542 0.590080
\(327\) −9.69368 −0.536062
\(328\) 11.3967 0.629275
\(329\) 4.99265 0.275254
\(330\) −0.0849163 −0.00467449
\(331\) −20.7309 −1.13947 −0.569737 0.821827i \(-0.692955\pi\)
−0.569737 + 0.821827i \(0.692955\pi\)
\(332\) −3.64838 −0.200231
\(333\) −0.203784 −0.0111673
\(334\) −11.4669 −0.627442
\(335\) −0.186040 −0.0101645
\(336\) −6.60760 −0.360474
\(337\) −16.8322 −0.916910 −0.458455 0.888718i \(-0.651597\pi\)
−0.458455 + 0.888718i \(0.651597\pi\)
\(338\) 5.69456 0.309743
\(339\) −13.5201 −0.734313
\(340\) 0.0915859 0.00496694
\(341\) −22.4631 −1.21644
\(342\) −0.618317 −0.0334347
\(343\) −18.5466 −1.00142
\(344\) −9.79706 −0.528222
\(345\) 0.0951291 0.00512158
\(346\) −1.51469 −0.0814303
\(347\) −34.3472 −1.84385 −0.921927 0.387363i \(-0.873386\pi\)
−0.921927 + 0.387363i \(0.873386\pi\)
\(348\) 5.33796 0.286145
\(349\) 4.32477 0.231500 0.115750 0.993278i \(-0.463073\pi\)
0.115750 + 0.993278i \(0.463073\pi\)
\(350\) 21.4063 1.14422
\(351\) −24.1438 −1.28870
\(352\) 2.99582 0.159678
\(353\) −35.6842 −1.89928 −0.949638 0.313349i \(-0.898549\pi\)
−0.949638 + 0.313349i \(0.898549\pi\)
\(354\) −13.0832 −0.695365
\(355\) −0.0911102 −0.00483563
\(356\) −8.09860 −0.429225
\(357\) 32.9488 1.74383
\(358\) 11.9286 0.630447
\(359\) 7.05580 0.372391 0.186195 0.982513i \(-0.440384\pi\)
0.186195 + 0.982513i \(0.440384\pi\)
\(360\) 0.0113565 0.000598540 0
\(361\) 1.00000 0.0526316
\(362\) −10.4087 −0.547071
\(363\) −3.12521 −0.164031
\(364\) −18.5123 −0.970306
\(365\) 0.301357 0.0157738
\(366\) 2.48716 0.130006
\(367\) −27.3530 −1.42782 −0.713908 0.700240i \(-0.753076\pi\)
−0.713908 + 0.700240i \(0.753076\pi\)
\(368\) −3.35613 −0.174950
\(369\) −7.04675 −0.366839
\(370\) −0.00605328 −0.000314695 0
\(371\) 56.0935 2.91223
\(372\) −11.5717 −0.599963
\(373\) 25.0734 1.29825 0.649126 0.760681i \(-0.275135\pi\)
0.649126 + 0.760681i \(0.275135\pi\)
\(374\) −14.9387 −0.772459
\(375\) 0.283439 0.0146368
\(376\) −1.16608 −0.0601361
\(377\) 14.9552 0.770230
\(378\) 23.9084 1.22972
\(379\) −24.1253 −1.23923 −0.619616 0.784905i \(-0.712712\pi\)
−0.619616 + 0.784905i \(0.712712\pi\)
\(380\) −0.0183668 −0.000942196 0
\(381\) −10.9241 −0.559659
\(382\) −6.81941 −0.348911
\(383\) 12.0159 0.613982 0.306991 0.951712i \(-0.400678\pi\)
0.306991 + 0.951712i \(0.400678\pi\)
\(384\) 1.54327 0.0787547
\(385\) 0.235587 0.0120066
\(386\) −0.388352 −0.0197666
\(387\) 6.05769 0.307930
\(388\) 2.65533 0.134804
\(389\) 26.8420 1.36095 0.680473 0.732774i \(-0.261775\pi\)
0.680473 + 0.732774i \(0.261775\pi\)
\(390\) −0.122555 −0.00620584
\(391\) 16.7353 0.846341
\(392\) 11.3317 0.572339
\(393\) 17.3713 0.876268
\(394\) −7.14947 −0.360185
\(395\) −0.151570 −0.00762630
\(396\) −1.85237 −0.0930849
\(397\) 13.3275 0.668890 0.334445 0.942415i \(-0.391451\pi\)
0.334445 + 0.942415i \(0.391451\pi\)
\(398\) 15.4828 0.776084
\(399\) −6.60760 −0.330794
\(400\) −4.99966 −0.249983
\(401\) 10.0490 0.501824 0.250912 0.968010i \(-0.419269\pi\)
0.250912 + 0.968010i \(0.419269\pi\)
\(402\) 15.6320 0.779656
\(403\) −32.4199 −1.61495
\(404\) −7.01241 −0.348880
\(405\) 0.124210 0.00617203
\(406\) −14.8093 −0.734975
\(407\) 0.987356 0.0489414
\(408\) −7.69551 −0.380985
\(409\) −26.9528 −1.33273 −0.666365 0.745625i \(-0.732151\pi\)
−0.666365 + 0.745625i \(0.732151\pi\)
\(410\) −0.209320 −0.0103376
\(411\) −2.25972 −0.111464
\(412\) 6.04519 0.297825
\(413\) 36.2973 1.78607
\(414\) 2.07515 0.101988
\(415\) 0.0670091 0.00328935
\(416\) 4.32372 0.211988
\(417\) −29.0626 −1.42320
\(418\) 2.99582 0.146530
\(419\) 13.2440 0.647013 0.323507 0.946226i \(-0.395138\pi\)
0.323507 + 0.946226i \(0.395138\pi\)
\(420\) 0.121360 0.00592178
\(421\) 1.92237 0.0936908 0.0468454 0.998902i \(-0.485083\pi\)
0.0468454 + 0.998902i \(0.485083\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 0.721008 0.0350566
\(424\) −13.1012 −0.636250
\(425\) 24.9308 1.20932
\(426\) 7.65555 0.370912
\(427\) −6.90024 −0.333926
\(428\) 6.69195 0.323468
\(429\) 19.9901 0.965132
\(430\) 0.179940 0.00867750
\(431\) 19.3188 0.930556 0.465278 0.885165i \(-0.345954\pi\)
0.465278 + 0.885165i \(0.345954\pi\)
\(432\) −5.58404 −0.268662
\(433\) 6.94110 0.333568 0.166784 0.985993i \(-0.446662\pi\)
0.166784 + 0.985993i \(0.446662\pi\)
\(434\) 32.1037 1.54103
\(435\) −0.0980412 −0.00470072
\(436\) −6.28126 −0.300818
\(437\) −3.35613 −0.160545
\(438\) −25.3216 −1.20991
\(439\) 15.0788 0.719670 0.359835 0.933016i \(-0.382833\pi\)
0.359835 + 0.933016i \(0.382833\pi\)
\(440\) −0.0550236 −0.00262315
\(441\) −7.00660 −0.333648
\(442\) −21.5602 −1.02552
\(443\) −23.4720 −1.11519 −0.557594 0.830114i \(-0.688275\pi\)
−0.557594 + 0.830114i \(0.688275\pi\)
\(444\) 0.508628 0.0241384
\(445\) 0.148745 0.00705120
\(446\) −8.09141 −0.383140
\(447\) −35.7614 −1.69146
\(448\) −4.28156 −0.202285
\(449\) 30.7862 1.45289 0.726445 0.687225i \(-0.241171\pi\)
0.726445 + 0.687225i \(0.241171\pi\)
\(450\) 3.09138 0.145729
\(451\) 34.1424 1.60770
\(452\) −8.76071 −0.412069
\(453\) 11.8269 0.555676
\(454\) 5.20647 0.244352
\(455\) 0.340011 0.0159399
\(456\) 1.54327 0.0722703
\(457\) 29.0387 1.35837 0.679185 0.733967i \(-0.262333\pi\)
0.679185 + 0.733967i \(0.262333\pi\)
\(458\) 17.2283 0.805023
\(459\) 27.8448 1.29968
\(460\) 0.0616412 0.00287404
\(461\) −31.6706 −1.47505 −0.737524 0.675321i \(-0.764005\pi\)
−0.737524 + 0.675321i \(0.764005\pi\)
\(462\) −19.7952 −0.920955
\(463\) 9.65031 0.448488 0.224244 0.974533i \(-0.428009\pi\)
0.224244 + 0.974533i \(0.428009\pi\)
\(464\) 3.45887 0.160574
\(465\) 0.212534 0.00985604
\(466\) −2.72435 −0.126203
\(467\) 22.4722 1.03989 0.519946 0.854199i \(-0.325952\pi\)
0.519946 + 0.854199i \(0.325952\pi\)
\(468\) −2.67343 −0.123579
\(469\) −43.3686 −2.00258
\(470\) 0.0214172 0.000987900 0
\(471\) 14.0337 0.646639
\(472\) −8.47759 −0.390213
\(473\) −29.3502 −1.34953
\(474\) 12.7357 0.584968
\(475\) −4.99966 −0.229400
\(476\) 21.3500 0.978575
\(477\) 8.10068 0.370905
\(478\) −19.9630 −0.913087
\(479\) 28.5859 1.30612 0.653062 0.757305i \(-0.273484\pi\)
0.653062 + 0.757305i \(0.273484\pi\)
\(480\) −0.0283449 −0.00129376
\(481\) 1.42500 0.0649745
\(482\) −11.8516 −0.539826
\(483\) 22.1759 1.00904
\(484\) −2.02506 −0.0920481
\(485\) −0.0487698 −0.00221452
\(486\) 6.31540 0.286472
\(487\) −18.7107 −0.847863 −0.423931 0.905694i \(-0.639350\pi\)
−0.423931 + 0.905694i \(0.639350\pi\)
\(488\) 1.61162 0.0729545
\(489\) 16.4423 0.743545
\(490\) −0.208128 −0.00940224
\(491\) 42.0521 1.89778 0.948892 0.315602i \(-0.102206\pi\)
0.948892 + 0.315602i \(0.102206\pi\)
\(492\) 17.5881 0.792934
\(493\) −17.2476 −0.776794
\(494\) 4.32372 0.194533
\(495\) 0.0340220 0.00152918
\(496\) −7.49814 −0.336677
\(497\) −21.2391 −0.952704
\(498\) −5.63044 −0.252306
\(499\) −28.9174 −1.29452 −0.647261 0.762268i \(-0.724086\pi\)
−0.647261 + 0.762268i \(0.724086\pi\)
\(500\) 0.183662 0.00821360
\(501\) −17.6966 −0.790624
\(502\) 14.8904 0.664591
\(503\) −11.7612 −0.524407 −0.262203 0.965013i \(-0.584449\pi\)
−0.262203 + 0.965013i \(0.584449\pi\)
\(504\) 2.64736 0.117923
\(505\) 0.128795 0.00573132
\(506\) −10.0544 −0.446971
\(507\) 8.78824 0.390299
\(508\) −7.07855 −0.314060
\(509\) −13.7154 −0.607924 −0.303962 0.952684i \(-0.598310\pi\)
−0.303962 + 0.952684i \(0.598310\pi\)
\(510\) 0.141342 0.00625872
\(511\) 70.2507 3.10771
\(512\) 1.00000 0.0441942
\(513\) −5.58404 −0.246541
\(514\) 22.5355 0.993997
\(515\) −0.111031 −0.00489259
\(516\) −15.1195 −0.665599
\(517\) −3.49337 −0.153638
\(518\) −1.41111 −0.0620005
\(519\) −2.33758 −0.102608
\(520\) −0.0794128 −0.00348248
\(521\) −40.7620 −1.78581 −0.892907 0.450240i \(-0.851338\pi\)
−0.892907 + 0.450240i \(0.851338\pi\)
\(522\) −2.13868 −0.0936073
\(523\) 4.58595 0.200530 0.100265 0.994961i \(-0.468031\pi\)
0.100265 + 0.994961i \(0.468031\pi\)
\(524\) 11.2562 0.491729
\(525\) 33.0358 1.44180
\(526\) −1.27361 −0.0555322
\(527\) 37.3895 1.62871
\(528\) 4.62336 0.201206
\(529\) −11.7364 −0.510279
\(530\) 0.240627 0.0104522
\(531\) 5.24184 0.227476
\(532\) −4.28156 −0.185629
\(533\) 49.2760 2.13438
\(534\) −12.4983 −0.540856
\(535\) −0.122910 −0.00531385
\(536\) 10.1292 0.437514
\(537\) 18.4091 0.794410
\(538\) 17.6740 0.761981
\(539\) 33.9479 1.46224
\(540\) 0.102561 0.00441352
\(541\) 26.9915 1.16046 0.580228 0.814454i \(-0.302963\pi\)
0.580228 + 0.814454i \(0.302963\pi\)
\(542\) 1.59875 0.0686723
\(543\) −16.0635 −0.689351
\(544\) −4.98650 −0.213794
\(545\) 0.115367 0.00494176
\(546\) −28.5694 −1.22266
\(547\) 11.9950 0.512871 0.256435 0.966561i \(-0.417452\pi\)
0.256435 + 0.966561i \(0.417452\pi\)
\(548\) −1.46424 −0.0625492
\(549\) −0.996491 −0.0425292
\(550\) −14.9781 −0.638668
\(551\) 3.45887 0.147353
\(552\) −5.17941 −0.220450
\(553\) −35.3331 −1.50251
\(554\) −7.10665 −0.301932
\(555\) −0.00934185 −0.000396540 0
\(556\) −18.8318 −0.798647
\(557\) 26.8346 1.13702 0.568510 0.822676i \(-0.307520\pi\)
0.568510 + 0.822676i \(0.307520\pi\)
\(558\) 4.63623 0.196267
\(559\) −42.3597 −1.79163
\(560\) 0.0786384 0.00332308
\(561\) −23.0544 −0.973357
\(562\) 10.6124 0.447656
\(563\) −15.0988 −0.636338 −0.318169 0.948034i \(-0.603068\pi\)
−0.318169 + 0.948034i \(0.603068\pi\)
\(564\) −1.79958 −0.0757760
\(565\) 0.160906 0.00676937
\(566\) −25.6020 −1.07613
\(567\) 28.9550 1.21600
\(568\) 4.96060 0.208142
\(569\) −10.4562 −0.438345 −0.219173 0.975686i \(-0.570336\pi\)
−0.219173 + 0.975686i \(0.570336\pi\)
\(570\) −0.0283449 −0.00118724
\(571\) 9.63933 0.403393 0.201697 0.979448i \(-0.435354\pi\)
0.201697 + 0.979448i \(0.435354\pi\)
\(572\) 12.9531 0.541596
\(573\) −10.5242 −0.439654
\(574\) −48.7955 −2.03668
\(575\) 16.7795 0.699754
\(576\) −0.618317 −0.0257632
\(577\) −5.67312 −0.236175 −0.118088 0.993003i \(-0.537676\pi\)
−0.118088 + 0.993003i \(0.537676\pi\)
\(578\) 7.86516 0.327147
\(579\) −0.599333 −0.0249074
\(580\) −0.0635282 −0.00263787
\(581\) 15.6208 0.648059
\(582\) 4.09789 0.169863
\(583\) −39.2488 −1.62552
\(584\) −16.4077 −0.678957
\(585\) 0.0491023 0.00203013
\(586\) −25.4146 −1.04987
\(587\) 14.4963 0.598326 0.299163 0.954202i \(-0.403293\pi\)
0.299163 + 0.954202i \(0.403293\pi\)
\(588\) 17.4879 0.721190
\(589\) −7.49814 −0.308956
\(590\) 0.155706 0.00641032
\(591\) −11.0336 −0.453860
\(592\) 0.329578 0.0135456
\(593\) 2.22876 0.0915241 0.0457620 0.998952i \(-0.485428\pi\)
0.0457620 + 0.998952i \(0.485428\pi\)
\(594\) −16.7288 −0.686390
\(595\) −0.392130 −0.0160758
\(596\) −23.1725 −0.949183
\(597\) 23.8942 0.977924
\(598\) −14.5110 −0.593397
\(599\) −7.07178 −0.288945 −0.144473 0.989509i \(-0.546149\pi\)
−0.144473 + 0.989509i \(0.546149\pi\)
\(600\) −7.71583 −0.314997
\(601\) 38.4735 1.56937 0.784683 0.619897i \(-0.212826\pi\)
0.784683 + 0.619897i \(0.212826\pi\)
\(602\) 41.9467 1.70962
\(603\) −6.26304 −0.255051
\(604\) 7.66353 0.311825
\(605\) 0.0371938 0.00151214
\(606\) −10.8220 −0.439615
\(607\) 40.3893 1.63935 0.819676 0.572828i \(-0.194154\pi\)
0.819676 + 0.572828i \(0.194154\pi\)
\(608\) 1.00000 0.0405554
\(609\) −22.8548 −0.926123
\(610\) −0.0296002 −0.00119848
\(611\) −5.04181 −0.203970
\(612\) 3.08324 0.124632
\(613\) 38.8530 1.56926 0.784628 0.619967i \(-0.212854\pi\)
0.784628 + 0.619967i \(0.212854\pi\)
\(614\) 24.5408 0.990388
\(615\) −0.323037 −0.0130261
\(616\) −12.8268 −0.516806
\(617\) 18.0179 0.725372 0.362686 0.931911i \(-0.381860\pi\)
0.362686 + 0.931911i \(0.381860\pi\)
\(618\) 9.32936 0.375282
\(619\) −7.60231 −0.305562 −0.152781 0.988260i \(-0.548823\pi\)
−0.152781 + 0.988260i \(0.548823\pi\)
\(620\) 0.137717 0.00553084
\(621\) 18.7408 0.752040
\(622\) 12.3101 0.493590
\(623\) 34.6746 1.38921
\(624\) 6.67267 0.267121
\(625\) 24.9949 0.999798
\(626\) 0.609964 0.0243791
\(627\) 4.62336 0.184639
\(628\) 9.09348 0.362869
\(629\) −1.64344 −0.0655282
\(630\) −0.0486235 −0.00193721
\(631\) 19.4370 0.773775 0.386888 0.922127i \(-0.373550\pi\)
0.386888 + 0.922127i \(0.373550\pi\)
\(632\) 8.25238 0.328262
\(633\) −1.54327 −0.0613395
\(634\) −25.1406 −0.998459
\(635\) 0.130010 0.00515929
\(636\) −20.2187 −0.801722
\(637\) 48.9953 1.94126
\(638\) 10.3621 0.410241
\(639\) −3.06722 −0.121337
\(640\) −0.0183668 −0.000726011 0
\(641\) 27.0542 1.06858 0.534288 0.845302i \(-0.320580\pi\)
0.534288 + 0.845302i \(0.320580\pi\)
\(642\) 10.3275 0.407594
\(643\) −14.8373 −0.585124 −0.292562 0.956247i \(-0.594508\pi\)
−0.292562 + 0.956247i \(0.594508\pi\)
\(644\) 14.3695 0.566236
\(645\) 0.277697 0.0109343
\(646\) −4.98650 −0.196191
\(647\) −6.15956 −0.242157 −0.121079 0.992643i \(-0.538635\pi\)
−0.121079 + 0.992643i \(0.538635\pi\)
\(648\) −6.76273 −0.265665
\(649\) −25.3973 −0.996933
\(650\) −21.6171 −0.847894
\(651\) 49.5447 1.94181
\(652\) 10.6542 0.417250
\(653\) −14.7092 −0.575615 −0.287808 0.957688i \(-0.592926\pi\)
−0.287808 + 0.957688i \(0.592926\pi\)
\(654\) −9.69368 −0.379053
\(655\) −0.206740 −0.00807799
\(656\) 11.3967 0.444965
\(657\) 10.1452 0.395801
\(658\) 4.99265 0.194634
\(659\) 11.4941 0.447747 0.223874 0.974618i \(-0.428130\pi\)
0.223874 + 0.974618i \(0.428130\pi\)
\(660\) −0.0849163 −0.00330536
\(661\) 48.8731 1.90094 0.950471 0.310813i \(-0.100601\pi\)
0.950471 + 0.310813i \(0.100601\pi\)
\(662\) −20.7309 −0.805729
\(663\) −33.2732 −1.29223
\(664\) −3.64838 −0.141585
\(665\) 0.0786384 0.00304947
\(666\) −0.203784 −0.00789645
\(667\) −11.6084 −0.449479
\(668\) −11.4669 −0.443669
\(669\) −12.4872 −0.482785
\(670\) −0.186040 −0.00718736
\(671\) 4.82812 0.186387
\(672\) −6.60760 −0.254894
\(673\) −17.6053 −0.678635 −0.339318 0.940672i \(-0.610196\pi\)
−0.339318 + 0.940672i \(0.610196\pi\)
\(674\) −16.8322 −0.648353
\(675\) 27.9183 1.07458
\(676\) 5.69456 0.219021
\(677\) −9.65642 −0.371126 −0.185563 0.982632i \(-0.559411\pi\)
−0.185563 + 0.982632i \(0.559411\pi\)
\(678\) −13.5201 −0.519238
\(679\) −11.3689 −0.436300
\(680\) 0.0915859 0.00351216
\(681\) 8.03499 0.307902
\(682\) −22.4631 −0.860156
\(683\) 21.3129 0.815516 0.407758 0.913090i \(-0.366311\pi\)
0.407758 + 0.913090i \(0.366311\pi\)
\(684\) −0.618317 −0.0236419
\(685\) 0.0268934 0.00102754
\(686\) −18.5466 −0.708112
\(687\) 26.5879 1.01439
\(688\) −9.79706 −0.373509
\(689\) −56.6459 −2.15804
\(690\) 0.0951291 0.00362150
\(691\) −14.3588 −0.546235 −0.273117 0.961981i \(-0.588055\pi\)
−0.273117 + 0.961981i \(0.588055\pi\)
\(692\) −1.51469 −0.0575799
\(693\) 7.93101 0.301274
\(694\) −34.3472 −1.30380
\(695\) 0.345880 0.0131200
\(696\) 5.33796 0.202335
\(697\) −56.8294 −2.15257
\(698\) 4.32477 0.163695
\(699\) −4.20440 −0.159025
\(700\) 21.4063 0.809084
\(701\) 46.7020 1.76391 0.881956 0.471332i \(-0.156227\pi\)
0.881956 + 0.471332i \(0.156227\pi\)
\(702\) −24.1438 −0.911250
\(703\) 0.329578 0.0124303
\(704\) 2.99582 0.112909
\(705\) 0.0330525 0.00124483
\(706\) −35.6842 −1.34299
\(707\) 30.0240 1.12917
\(708\) −13.0832 −0.491697
\(709\) 46.8548 1.75967 0.879835 0.475279i \(-0.157653\pi\)
0.879835 + 0.475279i \(0.157653\pi\)
\(710\) −0.0911102 −0.00341931
\(711\) −5.10259 −0.191362
\(712\) −8.09860 −0.303508
\(713\) 25.1647 0.942426
\(714\) 32.9488 1.23308
\(715\) −0.237907 −0.00889720
\(716\) 11.9286 0.445793
\(717\) −30.8083 −1.15056
\(718\) 7.05580 0.263320
\(719\) 41.6234 1.55229 0.776145 0.630555i \(-0.217173\pi\)
0.776145 + 0.630555i \(0.217173\pi\)
\(720\) 0.0113565 0.000423231 0
\(721\) −25.8828 −0.963927
\(722\) 1.00000 0.0372161
\(723\) −18.2902 −0.680221
\(724\) −10.4087 −0.386838
\(725\) −17.2932 −0.642252
\(726\) −3.12521 −0.115988
\(727\) 25.8166 0.957486 0.478743 0.877955i \(-0.341092\pi\)
0.478743 + 0.877955i \(0.341092\pi\)
\(728\) −18.5123 −0.686110
\(729\) 30.0346 1.11239
\(730\) 0.301357 0.0111537
\(731\) 48.8530 1.80689
\(732\) 2.48716 0.0919282
\(733\) 19.5479 0.722018 0.361009 0.932562i \(-0.382432\pi\)
0.361009 + 0.932562i \(0.382432\pi\)
\(734\) −27.3530 −1.00962
\(735\) −0.321197 −0.0118475
\(736\) −3.35613 −0.123708
\(737\) 30.3452 1.11778
\(738\) −7.04675 −0.259394
\(739\) 50.7120 1.86547 0.932735 0.360563i \(-0.117415\pi\)
0.932735 + 0.360563i \(0.117415\pi\)
\(740\) −0.00605328 −0.000222523 0
\(741\) 6.67267 0.245127
\(742\) 56.0935 2.05926
\(743\) −6.50281 −0.238565 −0.119283 0.992860i \(-0.538059\pi\)
−0.119283 + 0.992860i \(0.538059\pi\)
\(744\) −11.5717 −0.424238
\(745\) 0.425604 0.0155929
\(746\) 25.0734 0.918002
\(747\) 2.25586 0.0825375
\(748\) −14.9387 −0.546211
\(749\) −28.6520 −1.04692
\(750\) 0.283439 0.0103497
\(751\) 40.6645 1.48387 0.741933 0.670474i \(-0.233909\pi\)
0.741933 + 0.670474i \(0.233909\pi\)
\(752\) −1.16608 −0.0425226
\(753\) 22.9799 0.837434
\(754\) 14.9552 0.544635
\(755\) −0.140754 −0.00512258
\(756\) 23.9084 0.869540
\(757\) −18.5282 −0.673421 −0.336710 0.941608i \(-0.609314\pi\)
−0.336710 + 0.941608i \(0.609314\pi\)
\(758\) −24.1253 −0.876269
\(759\) −15.5166 −0.563216
\(760\) −0.0183668 −0.000666233 0
\(761\) −30.0134 −1.08799 −0.543993 0.839090i \(-0.683088\pi\)
−0.543993 + 0.839090i \(0.683088\pi\)
\(762\) −10.9241 −0.395739
\(763\) 26.8936 0.973613
\(764\) −6.81941 −0.246718
\(765\) −0.0566291 −0.00204743
\(766\) 12.0159 0.434151
\(767\) −36.6547 −1.32353
\(768\) 1.54327 0.0556880
\(769\) −32.2840 −1.16419 −0.582096 0.813120i \(-0.697767\pi\)
−0.582096 + 0.813120i \(0.697767\pi\)
\(770\) 0.235587 0.00848995
\(771\) 34.7783 1.25251
\(772\) −0.388352 −0.0139771
\(773\) −13.9236 −0.500798 −0.250399 0.968143i \(-0.580562\pi\)
−0.250399 + 0.968143i \(0.580562\pi\)
\(774\) 6.05769 0.217739
\(775\) 37.4882 1.34662
\(776\) 2.65533 0.0953207
\(777\) −2.17772 −0.0781252
\(778\) 26.8420 0.962333
\(779\) 11.3967 0.408328
\(780\) −0.122555 −0.00438819
\(781\) 14.8611 0.531771
\(782\) 16.7353 0.598454
\(783\) −19.3144 −0.690242
\(784\) 11.3317 0.404705
\(785\) −0.167018 −0.00596113
\(786\) 17.3713 0.619615
\(787\) 11.6370 0.414814 0.207407 0.978255i \(-0.433498\pi\)
0.207407 + 0.978255i \(0.433498\pi\)
\(788\) −7.14947 −0.254689
\(789\) −1.96553 −0.0699748
\(790\) −0.151570 −0.00539261
\(791\) 37.5095 1.33368
\(792\) −1.85237 −0.0658210
\(793\) 6.96819 0.247448
\(794\) 13.3275 0.472977
\(795\) 0.371352 0.0131705
\(796\) 15.4828 0.548774
\(797\) 52.4829 1.85904 0.929521 0.368770i \(-0.120221\pi\)
0.929521 + 0.368770i \(0.120221\pi\)
\(798\) −6.60760 −0.233907
\(799\) 5.81467 0.205708
\(800\) −4.99966 −0.176765
\(801\) 5.00750 0.176931
\(802\) 10.0490 0.354843
\(803\) −49.1546 −1.73463
\(804\) 15.6320 0.551300
\(805\) −0.263921 −0.00930198
\(806\) −32.4199 −1.14194
\(807\) 27.2758 0.960153
\(808\) −7.01241 −0.246696
\(809\) −11.5027 −0.404413 −0.202206 0.979343i \(-0.564811\pi\)
−0.202206 + 0.979343i \(0.564811\pi\)
\(810\) 0.124210 0.00436428
\(811\) 30.5401 1.07241 0.536203 0.844089i \(-0.319858\pi\)
0.536203 + 0.844089i \(0.319858\pi\)
\(812\) −14.8093 −0.519706
\(813\) 2.46731 0.0865322
\(814\) 0.987356 0.0346068
\(815\) −0.195683 −0.00685447
\(816\) −7.69551 −0.269397
\(817\) −9.79706 −0.342756
\(818\) −26.9528 −0.942383
\(819\) 11.4464 0.399971
\(820\) −0.209320 −0.00730977
\(821\) −13.4060 −0.467873 −0.233936 0.972252i \(-0.575161\pi\)
−0.233936 + 0.972252i \(0.575161\pi\)
\(822\) −2.25972 −0.0788167
\(823\) 10.4822 0.365385 0.182692 0.983170i \(-0.441519\pi\)
0.182692 + 0.983170i \(0.441519\pi\)
\(824\) 6.04519 0.210594
\(825\) −23.1152 −0.804770
\(826\) 36.2973 1.26294
\(827\) −1.51148 −0.0525593 −0.0262796 0.999655i \(-0.508366\pi\)
−0.0262796 + 0.999655i \(0.508366\pi\)
\(828\) 2.07515 0.0721165
\(829\) −40.3604 −1.40177 −0.700887 0.713272i \(-0.747212\pi\)
−0.700887 + 0.713272i \(0.747212\pi\)
\(830\) 0.0670091 0.00232592
\(831\) −10.9675 −0.380458
\(832\) 4.32372 0.149898
\(833\) −56.5057 −1.95781
\(834\) −29.0626 −1.00636
\(835\) 0.210610 0.00728848
\(836\) 2.99582 0.103613
\(837\) 41.8699 1.44724
\(838\) 13.2440 0.457508
\(839\) 5.09661 0.175955 0.0879773 0.996122i \(-0.471960\pi\)
0.0879773 + 0.996122i \(0.471960\pi\)
\(840\) 0.121360 0.00418733
\(841\) −17.0362 −0.587457
\(842\) 1.92237 0.0662494
\(843\) 16.3777 0.564080
\(844\) −1.00000 −0.0344214
\(845\) −0.104591 −0.00359803
\(846\) 0.721008 0.0247888
\(847\) 8.67040 0.297919
\(848\) −13.1012 −0.449897
\(849\) −39.5108 −1.35601
\(850\) 24.9308 0.855120
\(851\) −1.10611 −0.0379168
\(852\) 7.65555 0.262275
\(853\) −12.5382 −0.429301 −0.214651 0.976691i \(-0.568861\pi\)
−0.214651 + 0.976691i \(0.568861\pi\)
\(854\) −6.90024 −0.236121
\(855\) 0.0113565 0.000388384 0
\(856\) 6.69195 0.228726
\(857\) −41.7933 −1.42763 −0.713816 0.700333i \(-0.753035\pi\)
−0.713816 + 0.700333i \(0.753035\pi\)
\(858\) 19.9901 0.682451
\(859\) −6.59686 −0.225082 −0.112541 0.993647i \(-0.535899\pi\)
−0.112541 + 0.993647i \(0.535899\pi\)
\(860\) 0.179940 0.00613592
\(861\) −75.3046 −2.56637
\(862\) 19.3188 0.658002
\(863\) −36.9702 −1.25848 −0.629241 0.777210i \(-0.716634\pi\)
−0.629241 + 0.777210i \(0.716634\pi\)
\(864\) −5.58404 −0.189973
\(865\) 0.0278200 0.000945908 0
\(866\) 6.94110 0.235868
\(867\) 12.1381 0.412230
\(868\) 32.1037 1.08967
\(869\) 24.7227 0.838659
\(870\) −0.0980412 −0.00332391
\(871\) 43.7957 1.48396
\(872\) −6.28126 −0.212710
\(873\) −1.64183 −0.0555677
\(874\) −3.35613 −0.113523
\(875\) −0.786358 −0.0265837
\(876\) −25.3216 −0.855536
\(877\) −22.7670 −0.768787 −0.384393 0.923169i \(-0.625589\pi\)
−0.384393 + 0.923169i \(0.625589\pi\)
\(878\) 15.0788 0.508883
\(879\) −39.2216 −1.32291
\(880\) −0.0550236 −0.00185484
\(881\) −2.98165 −0.100454 −0.0502271 0.998738i \(-0.515995\pi\)
−0.0502271 + 0.998738i \(0.515995\pi\)
\(882\) −7.00660 −0.235925
\(883\) −57.4053 −1.93184 −0.965920 0.258839i \(-0.916660\pi\)
−0.965920 + 0.258839i \(0.916660\pi\)
\(884\) −21.5602 −0.725149
\(885\) 0.240297 0.00807748
\(886\) −23.4720 −0.788556
\(887\) −47.4645 −1.59370 −0.796852 0.604175i \(-0.793503\pi\)
−0.796852 + 0.604175i \(0.793503\pi\)
\(888\) 0.508628 0.0170684
\(889\) 30.3072 1.01647
\(890\) 0.148745 0.00498595
\(891\) −20.2599 −0.678733
\(892\) −8.09141 −0.270921
\(893\) −1.16608 −0.0390214
\(894\) −35.7614 −1.19604
\(895\) −0.219090 −0.00732338
\(896\) −4.28156 −0.143037
\(897\) −22.3943 −0.747725
\(898\) 30.7862 1.02735
\(899\) −25.9351 −0.864983
\(900\) 3.09138 0.103046
\(901\) 65.3290 2.17643
\(902\) 34.1424 1.13682
\(903\) 64.7351 2.15425
\(904\) −8.76071 −0.291377
\(905\) 0.191175 0.00635487
\(906\) 11.8269 0.392923
\(907\) 33.3822 1.10844 0.554220 0.832370i \(-0.313017\pi\)
0.554220 + 0.832370i \(0.313017\pi\)
\(908\) 5.20647 0.172783
\(909\) 4.33589 0.143812
\(910\) 0.340011 0.0112712
\(911\) −21.2119 −0.702783 −0.351392 0.936229i \(-0.614291\pi\)
−0.351392 + 0.936229i \(0.614291\pi\)
\(912\) 1.54327 0.0511028
\(913\) −10.9299 −0.361727
\(914\) 29.0387 0.960513
\(915\) −0.0456812 −0.00151017
\(916\) 17.2283 0.569238
\(917\) −48.1940 −1.59151
\(918\) 27.8448 0.919016
\(919\) −19.8236 −0.653921 −0.326960 0.945038i \(-0.606024\pi\)
−0.326960 + 0.945038i \(0.606024\pi\)
\(920\) 0.0616412 0.00203225
\(921\) 37.8731 1.24796
\(922\) −31.6706 −1.04302
\(923\) 21.4482 0.705978
\(924\) −19.7952 −0.651214
\(925\) −1.64778 −0.0541786
\(926\) 9.65031 0.317129
\(927\) −3.73784 −0.122767
\(928\) 3.45887 0.113543
\(929\) −21.4766 −0.704624 −0.352312 0.935883i \(-0.614604\pi\)
−0.352312 + 0.935883i \(0.614604\pi\)
\(930\) 0.212534 0.00696927
\(931\) 11.3317 0.371383
\(932\) −2.72435 −0.0892389
\(933\) 18.9978 0.621961
\(934\) 22.4722 0.735314
\(935\) 0.274375 0.00897302
\(936\) −2.67343 −0.0873838
\(937\) 12.9240 0.422210 0.211105 0.977463i \(-0.432294\pi\)
0.211105 + 0.977463i \(0.432294\pi\)
\(938\) −43.3686 −1.41604
\(939\) 0.941339 0.0307194
\(940\) 0.0214172 0.000698551 0
\(941\) −37.3371 −1.21715 −0.608577 0.793495i \(-0.708259\pi\)
−0.608577 + 0.793495i \(0.708259\pi\)
\(942\) 14.0337 0.457243
\(943\) −38.2486 −1.24555
\(944\) −8.47759 −0.275922
\(945\) −0.439120 −0.0142846
\(946\) −29.3502 −0.954258
\(947\) −51.8654 −1.68540 −0.842700 0.538383i \(-0.819035\pi\)
−0.842700 + 0.538383i \(0.819035\pi\)
\(948\) 12.7357 0.413635
\(949\) −70.9424 −2.30289
\(950\) −4.99966 −0.162210
\(951\) −38.7987 −1.25813
\(952\) 21.3500 0.691957
\(953\) −36.3691 −1.17811 −0.589055 0.808093i \(-0.700500\pi\)
−0.589055 + 0.808093i \(0.700500\pi\)
\(954\) 8.10068 0.262269
\(955\) 0.125251 0.00405301
\(956\) −19.9630 −0.645650
\(957\) 15.9916 0.516934
\(958\) 28.5859 0.923569
\(959\) 6.26922 0.202444
\(960\) −0.0283449 −0.000914828 0
\(961\) 25.2222 0.813619
\(962\) 1.42500 0.0459439
\(963\) −4.13775 −0.133337
\(964\) −11.8516 −0.381714
\(965\) 0.00713278 0.000229612 0
\(966\) 22.1759 0.713499
\(967\) 43.1048 1.38616 0.693078 0.720863i \(-0.256254\pi\)
0.693078 + 0.720863i \(0.256254\pi\)
\(968\) −2.02506 −0.0650878
\(969\) −7.69551 −0.247215
\(970\) −0.0487698 −0.00156590
\(971\) 21.9570 0.704635 0.352318 0.935880i \(-0.385394\pi\)
0.352318 + 0.935880i \(0.385394\pi\)
\(972\) 6.31540 0.202566
\(973\) 80.6295 2.58486
\(974\) −18.7107 −0.599530
\(975\) −33.3611 −1.06841
\(976\) 1.61162 0.0515866
\(977\) −38.1719 −1.22123 −0.610614 0.791928i \(-0.709077\pi\)
−0.610614 + 0.791928i \(0.709077\pi\)
\(978\) 16.4423 0.525766
\(979\) −24.2620 −0.775416
\(980\) −0.208128 −0.00664839
\(981\) 3.88381 0.124001
\(982\) 42.0521 1.34194
\(983\) −5.48626 −0.174984 −0.0874922 0.996165i \(-0.527885\pi\)
−0.0874922 + 0.996165i \(0.527885\pi\)
\(984\) 17.5881 0.560689
\(985\) 0.131313 0.00418397
\(986\) −17.2476 −0.549276
\(987\) 7.70500 0.245253
\(988\) 4.32372 0.137556
\(989\) 32.8802 1.04553
\(990\) 0.0340220 0.00108129
\(991\) 22.3505 0.709987 0.354994 0.934869i \(-0.384483\pi\)
0.354994 + 0.934869i \(0.384483\pi\)
\(992\) −7.49814 −0.238066
\(993\) −31.9934 −1.01528
\(994\) −21.2391 −0.673663
\(995\) −0.284370 −0.00901512
\(996\) −5.63044 −0.178407
\(997\) 14.6811 0.464954 0.232477 0.972602i \(-0.425317\pi\)
0.232477 + 0.972602i \(0.425317\pi\)
\(998\) −28.9174 −0.915365
\(999\) −1.84038 −0.0582269
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 \(a_p\))