Properties

Label 4010.2.a.k.1.15
Level 4010
Weight 2
Character 4010.1
Self dual Yes
Analytic conductor 32.020
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Root \(0.495927\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +3.15350 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.15350 q^{6} -0.474552 q^{7} -1.00000 q^{8} +6.94456 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +3.15350 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.15350 q^{6} -0.474552 q^{7} -1.00000 q^{8} +6.94456 q^{9} +1.00000 q^{10} -1.05395 q^{11} +3.15350 q^{12} -3.43732 q^{13} +0.474552 q^{14} -3.15350 q^{15} +1.00000 q^{16} -4.69477 q^{17} -6.94456 q^{18} -6.53467 q^{19} -1.00000 q^{20} -1.49650 q^{21} +1.05395 q^{22} -6.00037 q^{23} -3.15350 q^{24} +1.00000 q^{25} +3.43732 q^{26} +12.4392 q^{27} -0.474552 q^{28} +8.30861 q^{29} +3.15350 q^{30} +0.592756 q^{31} -1.00000 q^{32} -3.32362 q^{33} +4.69477 q^{34} +0.474552 q^{35} +6.94456 q^{36} +0.575428 q^{37} +6.53467 q^{38} -10.8396 q^{39} +1.00000 q^{40} +2.13638 q^{41} +1.49650 q^{42} -3.03439 q^{43} -1.05395 q^{44} -6.94456 q^{45} +6.00037 q^{46} -1.96294 q^{47} +3.15350 q^{48} -6.77480 q^{49} -1.00000 q^{50} -14.8050 q^{51} -3.43732 q^{52} -6.30721 q^{53} -12.4392 q^{54} +1.05395 q^{55} +0.474552 q^{56} -20.6071 q^{57} -8.30861 q^{58} -4.62666 q^{59} -3.15350 q^{60} +13.0715 q^{61} -0.592756 q^{62} -3.29555 q^{63} +1.00000 q^{64} +3.43732 q^{65} +3.32362 q^{66} -14.9844 q^{67} -4.69477 q^{68} -18.9222 q^{69} -0.474552 q^{70} -10.7215 q^{71} -6.94456 q^{72} -6.62649 q^{73} -0.575428 q^{74} +3.15350 q^{75} -6.53467 q^{76} +0.500153 q^{77} +10.8396 q^{78} -10.7602 q^{79} -1.00000 q^{80} +18.3932 q^{81} -2.13638 q^{82} +12.6166 q^{83} -1.49650 q^{84} +4.69477 q^{85} +3.03439 q^{86} +26.2012 q^{87} +1.05395 q^{88} +2.47205 q^{89} +6.94456 q^{90} +1.63119 q^{91} -6.00037 q^{92} +1.86926 q^{93} +1.96294 q^{94} +6.53467 q^{95} -3.15350 q^{96} -7.44033 q^{97} +6.77480 q^{98} -7.31919 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + O(q^{10}) \) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + 15q^{10} - 2q^{11} - 6q^{12} - 13q^{13} + 5q^{14} + 6q^{15} + 15q^{16} + 11q^{17} - 19q^{18} - 15q^{19} - 15q^{20} - 2q^{21} + 2q^{22} - 3q^{23} + 6q^{24} + 15q^{25} + 13q^{26} - 12q^{27} - 5q^{28} + 28q^{29} - 6q^{30} - 12q^{31} - 15q^{32} - 22q^{33} - 11q^{34} + 5q^{35} + 19q^{36} - 23q^{37} + 15q^{38} - 2q^{39} + 15q^{40} + 24q^{41} + 2q^{42} - 24q^{43} - 2q^{44} - 19q^{45} + 3q^{46} - 3q^{47} - 6q^{48} + 20q^{49} - 15q^{50} - 5q^{51} - 13q^{52} + 10q^{53} + 12q^{54} + 2q^{55} + 5q^{56} - 11q^{57} - 28q^{58} + 2q^{59} + 6q^{60} + 15q^{61} + 12q^{62} - 2q^{63} + 15q^{64} + 13q^{65} + 22q^{66} - 48q^{67} + 11q^{68} + 21q^{69} - 5q^{70} + 15q^{71} - 19q^{72} - 47q^{73} + 23q^{74} - 6q^{75} - 15q^{76} + 7q^{77} + 2q^{78} - 34q^{79} - 15q^{80} + 43q^{81} - 24q^{82} - 32q^{83} - 2q^{84} - 11q^{85} + 24q^{86} + 14q^{87} + 2q^{88} + 25q^{89} + 19q^{90} - 32q^{91} - 3q^{92} - 42q^{93} + 3q^{94} + 15q^{95} + 6q^{96} - 34q^{97} - 20q^{98} + 4q^{99} + O(q^{100}) \)

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
\(3\) 3.15350 1.82067 0.910337 0.413868i \(-0.135823\pi\)
0.910337 + 0.413868i \(0.135823\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −3.15350 −1.28741
\(7\) −0.474552 −0.179364 −0.0896820 0.995970i \(-0.528585\pi\)
−0.0896820 + 0.995970i \(0.528585\pi\)
\(8\) −1.00000 −0.353553
\(9\) 6.94456 2.31485
\(10\) 1.00000 0.316228
\(11\) −1.05395 −0.317777 −0.158888 0.987297i \(-0.550791\pi\)
−0.158888 + 0.987297i \(0.550791\pi\)
\(12\) 3.15350 0.910337
\(13\) −3.43732 −0.953340 −0.476670 0.879082i \(-0.658156\pi\)
−0.476670 + 0.879082i \(0.658156\pi\)
\(14\) 0.474552 0.126829
\(15\) −3.15350 −0.814230
\(16\) 1.00000 0.250000
\(17\) −4.69477 −1.13865 −0.569325 0.822113i \(-0.692795\pi\)
−0.569325 + 0.822113i \(0.692795\pi\)
\(18\) −6.94456 −1.63685
\(19\) −6.53467 −1.49916 −0.749578 0.661916i \(-0.769744\pi\)
−0.749578 + 0.661916i \(0.769744\pi\)
\(20\) −1.00000 −0.223607
\(21\) −1.49650 −0.326563
\(22\) 1.05395 0.224702
\(23\) −6.00037 −1.25116 −0.625582 0.780159i \(-0.715138\pi\)
−0.625582 + 0.780159i \(0.715138\pi\)
\(24\) −3.15350 −0.643705
\(25\) 1.00000 0.200000
\(26\) 3.43732 0.674113
\(27\) 12.4392 2.39392
\(28\) −0.474552 −0.0896820
\(29\) 8.30861 1.54287 0.771435 0.636309i \(-0.219539\pi\)
0.771435 + 0.636309i \(0.219539\pi\)
\(30\) 3.15350 0.575748
\(31\) 0.592756 0.106462 0.0532311 0.998582i \(-0.483048\pi\)
0.0532311 + 0.998582i \(0.483048\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.32362 −0.578568
\(34\) 4.69477 0.805147
\(35\) 0.474552 0.0802140
\(36\) 6.94456 1.15743
\(37\) 0.575428 0.0945998 0.0472999 0.998881i \(-0.484938\pi\)
0.0472999 + 0.998881i \(0.484938\pi\)
\(38\) 6.53467 1.06006
\(39\) −10.8396 −1.73572
\(40\) 1.00000 0.158114
\(41\) 2.13638 0.333646 0.166823 0.985987i \(-0.446649\pi\)
0.166823 + 0.985987i \(0.446649\pi\)
\(42\) 1.49650 0.230915
\(43\) −3.03439 −0.462740 −0.231370 0.972866i \(-0.574321\pi\)
−0.231370 + 0.972866i \(0.574321\pi\)
\(44\) −1.05395 −0.158888
\(45\) −6.94456 −1.03523
\(46\) 6.00037 0.884706
\(47\) −1.96294 −0.286325 −0.143162 0.989699i \(-0.545727\pi\)
−0.143162 + 0.989699i \(0.545727\pi\)
\(48\) 3.15350 0.455168
\(49\) −6.77480 −0.967829
\(50\) −1.00000 −0.141421
\(51\) −14.8050 −2.07311
\(52\) −3.43732 −0.476670
\(53\) −6.30721 −0.866362 −0.433181 0.901307i \(-0.642609\pi\)
−0.433181 + 0.901307i \(0.642609\pi\)
\(54\) −12.4392 −1.69275
\(55\) 1.05395 0.142114
\(56\) 0.474552 0.0634147
\(57\) −20.6071 −2.72948
\(58\) −8.30861 −1.09097
\(59\) −4.62666 −0.602340 −0.301170 0.953571i \(-0.597377\pi\)
−0.301170 + 0.953571i \(0.597377\pi\)
\(60\) −3.15350 −0.407115
\(61\) 13.0715 1.67364 0.836819 0.547480i \(-0.184413\pi\)
0.836819 + 0.547480i \(0.184413\pi\)
\(62\) −0.592756 −0.0752801
\(63\) −3.29555 −0.415201
\(64\) 1.00000 0.125000
\(65\) 3.43732 0.426347
\(66\) 3.32362 0.409109
\(67\) −14.9844 −1.83063 −0.915316 0.402737i \(-0.868059\pi\)
−0.915316 + 0.402737i \(0.868059\pi\)
\(68\) −4.69477 −0.569325
\(69\) −18.9222 −2.27796
\(70\) −0.474552 −0.0567198
\(71\) −10.7215 −1.27240 −0.636201 0.771523i \(-0.719495\pi\)
−0.636201 + 0.771523i \(0.719495\pi\)
\(72\) −6.94456 −0.818424
\(73\) −6.62649 −0.775572 −0.387786 0.921749i \(-0.626760\pi\)
−0.387786 + 0.921749i \(0.626760\pi\)
\(74\) −0.575428 −0.0668922
\(75\) 3.15350 0.364135
\(76\) −6.53467 −0.749578
\(77\) 0.500153 0.0569977
\(78\) 10.8396 1.22734
\(79\) −10.7602 −1.21062 −0.605308 0.795991i \(-0.706950\pi\)
−0.605308 + 0.795991i \(0.706950\pi\)
\(80\) −1.00000 −0.111803
\(81\) 18.3932 2.04369
\(82\) −2.13638 −0.235923
\(83\) 12.6166 1.38485 0.692427 0.721488i \(-0.256542\pi\)
0.692427 + 0.721488i \(0.256542\pi\)
\(84\) −1.49650 −0.163282
\(85\) 4.69477 0.509220
\(86\) 3.03439 0.327207
\(87\) 26.2012 2.80906
\(88\) 1.05395 0.112351
\(89\) 2.47205 0.262037 0.131018 0.991380i \(-0.458175\pi\)
0.131018 + 0.991380i \(0.458175\pi\)
\(90\) 6.94456 0.732020
\(91\) 1.63119 0.170995
\(92\) −6.00037 −0.625582
\(93\) 1.86926 0.193833
\(94\) 1.96294 0.202462
\(95\) 6.53467 0.670443
\(96\) −3.15350 −0.321853
\(97\) −7.44033 −0.755451 −0.377725 0.925918i \(-0.623294\pi\)
−0.377725 + 0.925918i \(0.623294\pi\)
\(98\) 6.77480 0.684358
\(99\) −7.31919 −0.735606
\(100\) 1.00000 0.100000
\(101\) 17.3668 1.72806 0.864032 0.503437i \(-0.167931\pi\)
0.864032 + 0.503437i \(0.167931\pi\)
\(102\) 14.8050 1.46591
\(103\) −18.4129 −1.81428 −0.907138 0.420833i \(-0.861738\pi\)
−0.907138 + 0.420833i \(0.861738\pi\)
\(104\) 3.43732 0.337057
\(105\) 1.49650 0.146043
\(106\) 6.30721 0.612611
\(107\) −12.0183 −1.16185 −0.580927 0.813956i \(-0.697310\pi\)
−0.580927 + 0.813956i \(0.697310\pi\)
\(108\) 12.4392 1.19696
\(109\) 13.1575 1.26026 0.630132 0.776488i \(-0.283001\pi\)
0.630132 + 0.776488i \(0.283001\pi\)
\(110\) −1.05395 −0.100490
\(111\) 1.81461 0.172235
\(112\) −0.474552 −0.0448410
\(113\) 3.81072 0.358482 0.179241 0.983805i \(-0.442636\pi\)
0.179241 + 0.983805i \(0.442636\pi\)
\(114\) 20.6071 1.93003
\(115\) 6.00037 0.559537
\(116\) 8.30861 0.771435
\(117\) −23.8706 −2.20684
\(118\) 4.62666 0.425918
\(119\) 2.22792 0.204233
\(120\) 3.15350 0.287874
\(121\) −9.88920 −0.899018
\(122\) −13.0715 −1.18344
\(123\) 6.73706 0.607460
\(124\) 0.592756 0.0532311
\(125\) −1.00000 −0.0894427
\(126\) 3.29555 0.293591
\(127\) 13.1465 1.16656 0.583281 0.812271i \(-0.301769\pi\)
0.583281 + 0.812271i \(0.301769\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −9.56895 −0.842499
\(130\) −3.43732 −0.301473
\(131\) −0.566335 −0.0494809 −0.0247405 0.999694i \(-0.507876\pi\)
−0.0247405 + 0.999694i \(0.507876\pi\)
\(132\) −3.32362 −0.289284
\(133\) 3.10104 0.268895
\(134\) 14.9844 1.29445
\(135\) −12.4392 −1.07059
\(136\) 4.69477 0.402573
\(137\) −1.40749 −0.120250 −0.0601251 0.998191i \(-0.519150\pi\)
−0.0601251 + 0.998191i \(0.519150\pi\)
\(138\) 18.9222 1.61076
\(139\) 10.3966 0.881827 0.440913 0.897550i \(-0.354655\pi\)
0.440913 + 0.897550i \(0.354655\pi\)
\(140\) 0.474552 0.0401070
\(141\) −6.19014 −0.521304
\(142\) 10.7215 0.899725
\(143\) 3.62275 0.302949
\(144\) 6.94456 0.578713
\(145\) −8.30861 −0.689992
\(146\) 6.62649 0.548412
\(147\) −21.3643 −1.76210
\(148\) 0.575428 0.0472999
\(149\) −22.1535 −1.81489 −0.907445 0.420172i \(-0.861970\pi\)
−0.907445 + 0.420172i \(0.861970\pi\)
\(150\) −3.15350 −0.257482
\(151\) −9.77674 −0.795620 −0.397810 0.917468i \(-0.630230\pi\)
−0.397810 + 0.917468i \(0.630230\pi\)
\(152\) 6.53467 0.530032
\(153\) −32.6031 −2.63581
\(154\) −0.500153 −0.0403034
\(155\) −0.592756 −0.0476113
\(156\) −10.8396 −0.867861
\(157\) −3.67323 −0.293156 −0.146578 0.989199i \(-0.546826\pi\)
−0.146578 + 0.989199i \(0.546826\pi\)
\(158\) 10.7602 0.856035
\(159\) −19.8898 −1.57736
\(160\) 1.00000 0.0790569
\(161\) 2.84749 0.224414
\(162\) −18.3932 −1.44511
\(163\) 4.65548 0.364646 0.182323 0.983239i \(-0.441638\pi\)
0.182323 + 0.983239i \(0.441638\pi\)
\(164\) 2.13638 0.166823
\(165\) 3.32362 0.258743
\(166\) −12.6166 −0.979239
\(167\) −4.29110 −0.332055 −0.166028 0.986121i \(-0.553094\pi\)
−0.166028 + 0.986121i \(0.553094\pi\)
\(168\) 1.49650 0.115457
\(169\) −1.18486 −0.0911427
\(170\) −4.69477 −0.360073
\(171\) −45.3804 −3.47033
\(172\) −3.03439 −0.231370
\(173\) 23.3544 1.77561 0.887803 0.460224i \(-0.152231\pi\)
0.887803 + 0.460224i \(0.152231\pi\)
\(174\) −26.2012 −1.98631
\(175\) −0.474552 −0.0358728
\(176\) −1.05395 −0.0794442
\(177\) −14.5902 −1.09666
\(178\) −2.47205 −0.185288
\(179\) 11.9470 0.892963 0.446481 0.894793i \(-0.352677\pi\)
0.446481 + 0.894793i \(0.352677\pi\)
\(180\) −6.94456 −0.517617
\(181\) 16.2940 1.21112 0.605560 0.795799i \(-0.292949\pi\)
0.605560 + 0.795799i \(0.292949\pi\)
\(182\) −1.63119 −0.120912
\(183\) 41.2211 3.04715
\(184\) 6.00037 0.442353
\(185\) −0.575428 −0.0423063
\(186\) −1.86926 −0.137061
\(187\) 4.94804 0.361836
\(188\) −1.96294 −0.143162
\(189\) −5.90303 −0.429382
\(190\) −6.53467 −0.474075
\(191\) 13.0588 0.944902 0.472451 0.881357i \(-0.343369\pi\)
0.472451 + 0.881357i \(0.343369\pi\)
\(192\) 3.15350 0.227584
\(193\) 19.6904 1.41734 0.708672 0.705538i \(-0.249295\pi\)
0.708672 + 0.705538i \(0.249295\pi\)
\(194\) 7.44033 0.534185
\(195\) 10.8396 0.776238
\(196\) −6.77480 −0.483914
\(197\) 16.9507 1.20769 0.603844 0.797102i \(-0.293635\pi\)
0.603844 + 0.797102i \(0.293635\pi\)
\(198\) 7.31919 0.520152
\(199\) −9.47071 −0.671361 −0.335680 0.941976i \(-0.608966\pi\)
−0.335680 + 0.941976i \(0.608966\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −47.2532 −3.33298
\(202\) −17.3668 −1.22193
\(203\) −3.94287 −0.276735
\(204\) −14.8050 −1.03655
\(205\) −2.13638 −0.149211
\(206\) 18.4129 1.28289
\(207\) −41.6699 −2.89626
\(208\) −3.43732 −0.238335
\(209\) 6.88719 0.476397
\(210\) −1.49650 −0.103268
\(211\) −22.7837 −1.56850 −0.784248 0.620447i \(-0.786951\pi\)
−0.784248 + 0.620447i \(0.786951\pi\)
\(212\) −6.30721 −0.433181
\(213\) −33.8101 −2.31663
\(214\) 12.0183 0.821555
\(215\) 3.03439 0.206944
\(216\) −12.4392 −0.846377
\(217\) −0.281294 −0.0190955
\(218\) −13.1575 −0.891141
\(219\) −20.8966 −1.41206
\(220\) 1.05395 0.0710570
\(221\) 16.1374 1.08552
\(222\) −1.81461 −0.121789
\(223\) −3.34891 −0.224259 −0.112130 0.993694i \(-0.535767\pi\)
−0.112130 + 0.993694i \(0.535767\pi\)
\(224\) 0.474552 0.0317074
\(225\) 6.94456 0.462970
\(226\) −3.81072 −0.253485
\(227\) −26.0852 −1.73133 −0.865667 0.500621i \(-0.833105\pi\)
−0.865667 + 0.500621i \(0.833105\pi\)
\(228\) −20.6071 −1.36474
\(229\) 11.1271 0.735303 0.367651 0.929964i \(-0.380162\pi\)
0.367651 + 0.929964i \(0.380162\pi\)
\(230\) −6.00037 −0.395653
\(231\) 1.57723 0.103774
\(232\) −8.30861 −0.545487
\(233\) 17.6495 1.15625 0.578127 0.815947i \(-0.303784\pi\)
0.578127 + 0.815947i \(0.303784\pi\)
\(234\) 23.8706 1.56047
\(235\) 1.96294 0.128048
\(236\) −4.62666 −0.301170
\(237\) −33.9323 −2.20414
\(238\) −2.22792 −0.144414
\(239\) −22.4986 −1.45532 −0.727658 0.685940i \(-0.759391\pi\)
−0.727658 + 0.685940i \(0.759391\pi\)
\(240\) −3.15350 −0.203557
\(241\) −17.8502 −1.14983 −0.574916 0.818212i \(-0.694965\pi\)
−0.574916 + 0.818212i \(0.694965\pi\)
\(242\) 9.88920 0.635702
\(243\) 20.6854 1.32697
\(244\) 13.0715 0.836819
\(245\) 6.77480 0.432826
\(246\) −6.73706 −0.429539
\(247\) 22.4617 1.42921
\(248\) −0.592756 −0.0376401
\(249\) 39.7865 2.52137
\(250\) 1.00000 0.0632456
\(251\) 12.9427 0.816934 0.408467 0.912773i \(-0.366064\pi\)
0.408467 + 0.912773i \(0.366064\pi\)
\(252\) −3.29555 −0.207600
\(253\) 6.32407 0.397591
\(254\) −13.1465 −0.824883
\(255\) 14.8050 0.927123
\(256\) 1.00000 0.0625000
\(257\) −17.4206 −1.08667 −0.543333 0.839517i \(-0.682838\pi\)
−0.543333 + 0.839517i \(0.682838\pi\)
\(258\) 9.56895 0.595737
\(259\) −0.273071 −0.0169678
\(260\) 3.43732 0.213173
\(261\) 57.6996 3.57151
\(262\) 0.566335 0.0349883
\(263\) 10.9851 0.677373 0.338687 0.940899i \(-0.390017\pi\)
0.338687 + 0.940899i \(0.390017\pi\)
\(264\) 3.32362 0.204555
\(265\) 6.30721 0.387449
\(266\) −3.10104 −0.190137
\(267\) 7.79561 0.477083
\(268\) −14.9844 −0.915316
\(269\) −10.8695 −0.662724 −0.331362 0.943504i \(-0.607508\pi\)
−0.331362 + 0.943504i \(0.607508\pi\)
\(270\) 12.4392 0.757023
\(271\) 12.3201 0.748394 0.374197 0.927349i \(-0.377918\pi\)
0.374197 + 0.927349i \(0.377918\pi\)
\(272\) −4.69477 −0.284662
\(273\) 5.14394 0.311326
\(274\) 1.40749 0.0850297
\(275\) −1.05395 −0.0635554
\(276\) −18.9222 −1.13898
\(277\) −6.25679 −0.375934 −0.187967 0.982175i \(-0.560190\pi\)
−0.187967 + 0.982175i \(0.560190\pi\)
\(278\) −10.3966 −0.623546
\(279\) 4.11643 0.246444
\(280\) −0.474552 −0.0283599
\(281\) 23.2116 1.38469 0.692345 0.721567i \(-0.256578\pi\)
0.692345 + 0.721567i \(0.256578\pi\)
\(282\) 6.19014 0.368617
\(283\) 10.4175 0.619253 0.309627 0.950858i \(-0.399796\pi\)
0.309627 + 0.950858i \(0.399796\pi\)
\(284\) −10.7215 −0.636201
\(285\) 20.6071 1.22066
\(286\) −3.62275 −0.214218
\(287\) −1.01382 −0.0598440
\(288\) −6.94456 −0.409212
\(289\) 5.04089 0.296523
\(290\) 8.30861 0.487898
\(291\) −23.4631 −1.37543
\(292\) −6.62649 −0.387786
\(293\) −1.15574 −0.0675189 −0.0337595 0.999430i \(-0.510748\pi\)
−0.0337595 + 0.999430i \(0.510748\pi\)
\(294\) 21.3643 1.24599
\(295\) 4.62666 0.269374
\(296\) −0.575428 −0.0334461
\(297\) −13.1102 −0.760731
\(298\) 22.1535 1.28332
\(299\) 20.6252 1.19278
\(300\) 3.15350 0.182067
\(301\) 1.43998 0.0829989
\(302\) 9.77674 0.562588
\(303\) 54.7663 3.14624
\(304\) −6.53467 −0.374789
\(305\) −13.0715 −0.748474
\(306\) 32.6031 1.86380
\(307\) −3.59248 −0.205034 −0.102517 0.994731i \(-0.532690\pi\)
−0.102517 + 0.994731i \(0.532690\pi\)
\(308\) 0.500153 0.0284988
\(309\) −58.0651 −3.30321
\(310\) 0.592756 0.0336663
\(311\) −16.7427 −0.949391 −0.474696 0.880150i \(-0.657442\pi\)
−0.474696 + 0.880150i \(0.657442\pi\)
\(312\) 10.8396 0.613670
\(313\) −27.9220 −1.57824 −0.789122 0.614236i \(-0.789464\pi\)
−0.789122 + 0.614236i \(0.789464\pi\)
\(314\) 3.67323 0.207292
\(315\) 3.29555 0.185683
\(316\) −10.7602 −0.605308
\(317\) 24.5975 1.38153 0.690766 0.723078i \(-0.257274\pi\)
0.690766 + 0.723078i \(0.257274\pi\)
\(318\) 19.8898 1.11536
\(319\) −8.75682 −0.490288
\(320\) −1.00000 −0.0559017
\(321\) −37.8997 −2.11536
\(322\) −2.84749 −0.158684
\(323\) 30.6788 1.70701
\(324\) 18.3932 1.02184
\(325\) −3.43732 −0.190668
\(326\) −4.65548 −0.257843
\(327\) 41.4923 2.29453
\(328\) −2.13638 −0.117962
\(329\) 0.931519 0.0513563
\(330\) −3.32362 −0.182959
\(331\) −0.197429 −0.0108517 −0.00542583 0.999985i \(-0.501727\pi\)
−0.00542583 + 0.999985i \(0.501727\pi\)
\(332\) 12.6166 0.692427
\(333\) 3.99609 0.218985
\(334\) 4.29110 0.234799
\(335\) 14.9844 0.818683
\(336\) −1.49650 −0.0816408
\(337\) 1.92974 0.105119 0.0525597 0.998618i \(-0.483262\pi\)
0.0525597 + 0.998618i \(0.483262\pi\)
\(338\) 1.18486 0.0644476
\(339\) 12.0171 0.652679
\(340\) 4.69477 0.254610
\(341\) −0.624733 −0.0338312
\(342\) 45.3804 2.45389
\(343\) 6.53686 0.352957
\(344\) 3.03439 0.163603
\(345\) 18.9222 1.01874
\(346\) −23.3544 −1.25554
\(347\) 9.84709 0.528620 0.264310 0.964438i \(-0.414856\pi\)
0.264310 + 0.964438i \(0.414856\pi\)
\(348\) 26.2012 1.40453
\(349\) 20.8401 1.11554 0.557772 0.829994i \(-0.311656\pi\)
0.557772 + 0.829994i \(0.311656\pi\)
\(350\) 0.474552 0.0253659
\(351\) −42.7573 −2.28222
\(352\) 1.05395 0.0561755
\(353\) 0.766412 0.0407920 0.0203960 0.999792i \(-0.493507\pi\)
0.0203960 + 0.999792i \(0.493507\pi\)
\(354\) 14.5902 0.775458
\(355\) 10.7215 0.569036
\(356\) 2.47205 0.131018
\(357\) 7.02573 0.371841
\(358\) −11.9470 −0.631420
\(359\) 28.3525 1.49639 0.748195 0.663479i \(-0.230921\pi\)
0.748195 + 0.663479i \(0.230921\pi\)
\(360\) 6.94456 0.366010
\(361\) 23.7020 1.24747
\(362\) −16.2940 −0.856392
\(363\) −31.1856 −1.63682
\(364\) 1.63119 0.0854974
\(365\) 6.62649 0.346846
\(366\) −41.2211 −2.15466
\(367\) −16.1601 −0.843549 −0.421774 0.906701i \(-0.638593\pi\)
−0.421774 + 0.906701i \(0.638593\pi\)
\(368\) −6.00037 −0.312791
\(369\) 14.8362 0.772341
\(370\) 0.575428 0.0299151
\(371\) 2.99310 0.155394
\(372\) 1.86926 0.0969165
\(373\) −15.0275 −0.778096 −0.389048 0.921217i \(-0.627196\pi\)
−0.389048 + 0.921217i \(0.627196\pi\)
\(374\) −4.94804 −0.255857
\(375\) −3.15350 −0.162846
\(376\) 1.96294 0.101231
\(377\) −28.5593 −1.47088
\(378\) 5.90303 0.303619
\(379\) −14.6512 −0.752581 −0.376291 0.926502i \(-0.622801\pi\)
−0.376291 + 0.926502i \(0.622801\pi\)
\(380\) 6.53467 0.335222
\(381\) 41.4574 2.12393
\(382\) −13.0588 −0.668146
\(383\) 13.9724 0.713956 0.356978 0.934113i \(-0.383807\pi\)
0.356978 + 0.934113i \(0.383807\pi\)
\(384\) −3.15350 −0.160926
\(385\) −0.500153 −0.0254901
\(386\) −19.6904 −1.00221
\(387\) −21.0725 −1.07118
\(388\) −7.44033 −0.377725
\(389\) 3.34407 0.169551 0.0847755 0.996400i \(-0.472983\pi\)
0.0847755 + 0.996400i \(0.472983\pi\)
\(390\) −10.8396 −0.548883
\(391\) 28.1704 1.42464
\(392\) 6.77480 0.342179
\(393\) −1.78594 −0.0900886
\(394\) −16.9507 −0.853964
\(395\) 10.7602 0.541404
\(396\) −7.31919 −0.367803
\(397\) 4.05193 0.203360 0.101680 0.994817i \(-0.467578\pi\)
0.101680 + 0.994817i \(0.467578\pi\)
\(398\) 9.47071 0.474724
\(399\) 9.77914 0.489569
\(400\) 1.00000 0.0500000
\(401\) −1.00000 −0.0499376
\(402\) 47.2532 2.35677
\(403\) −2.03749 −0.101495
\(404\) 17.3668 0.864032
\(405\) −18.3932 −0.913965
\(406\) 3.94287 0.195681
\(407\) −0.606470 −0.0300616
\(408\) 14.8050 0.732955
\(409\) −35.2075 −1.74090 −0.870449 0.492259i \(-0.836171\pi\)
−0.870449 + 0.492259i \(0.836171\pi\)
\(410\) 2.13638 0.105508
\(411\) −4.43853 −0.218936
\(412\) −18.4129 −0.907138
\(413\) 2.19559 0.108038
\(414\) 41.6699 2.04796
\(415\) −12.6166 −0.619325
\(416\) 3.43732 0.168528
\(417\) 32.7856 1.60552
\(418\) −6.88719 −0.336864
\(419\) 12.9090 0.630645 0.315322 0.948985i \(-0.397887\pi\)
0.315322 + 0.948985i \(0.397887\pi\)
\(420\) 1.49650 0.0730217
\(421\) −25.0552 −1.22112 −0.610559 0.791971i \(-0.709055\pi\)
−0.610559 + 0.791971i \(0.709055\pi\)
\(422\) 22.7837 1.10909
\(423\) −13.6318 −0.662799
\(424\) 6.30721 0.306305
\(425\) −4.69477 −0.227730
\(426\) 33.8101 1.63810
\(427\) −6.20312 −0.300190
\(428\) −12.0183 −0.580927
\(429\) 11.4243 0.551572
\(430\) −3.03439 −0.146331
\(431\) −18.2753 −0.880289 −0.440145 0.897927i \(-0.645073\pi\)
−0.440145 + 0.897927i \(0.645073\pi\)
\(432\) 12.4392 0.598479
\(433\) −24.2793 −1.16679 −0.583394 0.812189i \(-0.698276\pi\)
−0.583394 + 0.812189i \(0.698276\pi\)
\(434\) 0.281294 0.0135025
\(435\) −26.2012 −1.25625
\(436\) 13.1575 0.630132
\(437\) 39.2105 1.87569
\(438\) 20.8966 0.998480
\(439\) 39.0419 1.86337 0.931683 0.363272i \(-0.118340\pi\)
0.931683 + 0.363272i \(0.118340\pi\)
\(440\) −1.05395 −0.0502449
\(441\) −47.0480 −2.24038
\(442\) −16.1374 −0.767579
\(443\) 28.5384 1.35590 0.677951 0.735107i \(-0.262868\pi\)
0.677951 + 0.735107i \(0.262868\pi\)
\(444\) 1.81461 0.0861177
\(445\) −2.47205 −0.117186
\(446\) 3.34891 0.158575
\(447\) −69.8612 −3.30432
\(448\) −0.474552 −0.0224205
\(449\) −6.91622 −0.326396 −0.163198 0.986593i \(-0.552181\pi\)
−0.163198 + 0.986593i \(0.552181\pi\)
\(450\) −6.94456 −0.327370
\(451\) −2.25163 −0.106025
\(452\) 3.81072 0.179241
\(453\) −30.8309 −1.44856
\(454\) 26.0852 1.22424
\(455\) −1.63119 −0.0764712
\(456\) 20.6071 0.965015
\(457\) −3.94501 −0.184540 −0.0922698 0.995734i \(-0.529412\pi\)
−0.0922698 + 0.995734i \(0.529412\pi\)
\(458\) −11.1271 −0.519937
\(459\) −58.3990 −2.72583
\(460\) 6.00037 0.279769
\(461\) −12.2147 −0.568894 −0.284447 0.958692i \(-0.591810\pi\)
−0.284447 + 0.958692i \(0.591810\pi\)
\(462\) −1.57723 −0.0733794
\(463\) 0.135978 0.00631943 0.00315972 0.999995i \(-0.498994\pi\)
0.00315972 + 0.999995i \(0.498994\pi\)
\(464\) 8.30861 0.385717
\(465\) −1.86926 −0.0866847
\(466\) −17.6495 −0.817595
\(467\) −19.1532 −0.886305 −0.443152 0.896446i \(-0.646140\pi\)
−0.443152 + 0.896446i \(0.646140\pi\)
\(468\) −23.8706 −1.10342
\(469\) 7.11086 0.328349
\(470\) −1.96294 −0.0905438
\(471\) −11.5835 −0.533741
\(472\) 4.62666 0.212959
\(473\) 3.19808 0.147048
\(474\) 33.9323 1.55856
\(475\) −6.53467 −0.299831
\(476\) 2.22792 0.102116
\(477\) −43.8008 −2.00550
\(478\) 22.4986 1.02906
\(479\) −24.0010 −1.09663 −0.548317 0.836271i \(-0.684731\pi\)
−0.548317 + 0.836271i \(0.684731\pi\)
\(480\) 3.15350 0.143937
\(481\) −1.97793 −0.0901858
\(482\) 17.8502 0.813055
\(483\) 8.97956 0.408584
\(484\) −9.88920 −0.449509
\(485\) 7.44033 0.337848
\(486\) −20.6854 −0.938311
\(487\) −29.9631 −1.35776 −0.678878 0.734251i \(-0.737534\pi\)
−0.678878 + 0.734251i \(0.737534\pi\)
\(488\) −13.0715 −0.591720
\(489\) 14.6811 0.663900
\(490\) −6.77480 −0.306054
\(491\) 20.9770 0.946677 0.473338 0.880881i \(-0.343049\pi\)
0.473338 + 0.880881i \(0.343049\pi\)
\(492\) 6.73706 0.303730
\(493\) −39.0070 −1.75679
\(494\) −22.4617 −1.01060
\(495\) 7.31919 0.328973
\(496\) 0.592756 0.0266156
\(497\) 5.08789 0.228223
\(498\) −39.7865 −1.78288
\(499\) −37.4023 −1.67436 −0.837178 0.546930i \(-0.815796\pi\)
−0.837178 + 0.546930i \(0.815796\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −13.5320 −0.604564
\(502\) −12.9427 −0.577659
\(503\) 37.6096 1.67693 0.838464 0.544958i \(-0.183454\pi\)
0.838464 + 0.544958i \(0.183454\pi\)
\(504\) 3.29555 0.146796
\(505\) −17.3668 −0.772814
\(506\) −6.32407 −0.281139
\(507\) −3.73644 −0.165941
\(508\) 13.1465 0.583281
\(509\) 0.111220 0.00492972 0.00246486 0.999997i \(-0.499215\pi\)
0.00246486 + 0.999997i \(0.499215\pi\)
\(510\) −14.8050 −0.655575
\(511\) 3.14462 0.139110
\(512\) −1.00000 −0.0441942
\(513\) −81.2858 −3.58886
\(514\) 17.4206 0.768390
\(515\) 18.4129 0.811369
\(516\) −9.56895 −0.421249
\(517\) 2.06884 0.0909873
\(518\) 0.273071 0.0119980
\(519\) 73.6482 3.23280
\(520\) −3.43732 −0.150736
\(521\) −29.9013 −1.31000 −0.655000 0.755628i \(-0.727332\pi\)
−0.655000 + 0.755628i \(0.727332\pi\)
\(522\) −57.6996 −2.52544
\(523\) 18.6140 0.813933 0.406967 0.913443i \(-0.366587\pi\)
0.406967 + 0.913443i \(0.366587\pi\)
\(524\) −0.566335 −0.0247405
\(525\) −1.49650 −0.0653126
\(526\) −10.9851 −0.478975
\(527\) −2.78286 −0.121223
\(528\) −3.32362 −0.144642
\(529\) 13.0044 0.565411
\(530\) −6.30721 −0.273968
\(531\) −32.1301 −1.39433
\(532\) 3.10104 0.134447
\(533\) −7.34340 −0.318078
\(534\) −7.79561 −0.337349
\(535\) 12.0183 0.519597
\(536\) 14.9844 0.647226
\(537\) 37.6749 1.62579
\(538\) 10.8695 0.468616
\(539\) 7.14028 0.307553
\(540\) −12.4392 −0.535296
\(541\) 6.61840 0.284547 0.142274 0.989827i \(-0.454559\pi\)
0.142274 + 0.989827i \(0.454559\pi\)
\(542\) −12.3201 −0.529195
\(543\) 51.3830 2.20506
\(544\) 4.69477 0.201287
\(545\) −13.1575 −0.563607
\(546\) −5.14394 −0.220141
\(547\) 14.0053 0.598824 0.299412 0.954124i \(-0.403209\pi\)
0.299412 + 0.954124i \(0.403209\pi\)
\(548\) −1.40749 −0.0601251
\(549\) 90.7760 3.87422
\(550\) 1.05395 0.0449404
\(551\) −54.2940 −2.31300
\(552\) 18.9222 0.805381
\(553\) 5.10627 0.217141
\(554\) 6.25679 0.265826
\(555\) −1.81461 −0.0770260
\(556\) 10.3966 0.440913
\(557\) 13.1509 0.557222 0.278611 0.960404i \(-0.410126\pi\)
0.278611 + 0.960404i \(0.410126\pi\)
\(558\) −4.11643 −0.174262
\(559\) 10.4302 0.441149
\(560\) 0.474552 0.0200535
\(561\) 15.6036 0.658786
\(562\) −23.2116 −0.979123
\(563\) −31.6543 −1.33407 −0.667035 0.745026i \(-0.732437\pi\)
−0.667035 + 0.745026i \(0.732437\pi\)
\(564\) −6.19014 −0.260652
\(565\) −3.81072 −0.160318
\(566\) −10.4175 −0.437878
\(567\) −8.72853 −0.366564
\(568\) 10.7215 0.449862
\(569\) −12.1707 −0.510222 −0.255111 0.966912i \(-0.582112\pi\)
−0.255111 + 0.966912i \(0.582112\pi\)
\(570\) −20.6071 −0.863136
\(571\) 15.1041 0.632085 0.316043 0.948745i \(-0.397646\pi\)
0.316043 + 0.948745i \(0.397646\pi\)
\(572\) 3.62275 0.151475
\(573\) 41.1809 1.72036
\(574\) 1.01382 0.0423161
\(575\) −6.00037 −0.250233
\(576\) 6.94456 0.289357
\(577\) 32.8633 1.36812 0.684059 0.729427i \(-0.260213\pi\)
0.684059 + 0.729427i \(0.260213\pi\)
\(578\) −5.04089 −0.209673
\(579\) 62.0935 2.58052
\(580\) −8.30861 −0.344996
\(581\) −5.98724 −0.248393
\(582\) 23.4631 0.972576
\(583\) 6.64746 0.275310
\(584\) 6.62649 0.274206
\(585\) 23.8706 0.986929
\(586\) 1.15574 0.0477431
\(587\) −23.0518 −0.951448 −0.475724 0.879594i \(-0.657814\pi\)
−0.475724 + 0.879594i \(0.657814\pi\)
\(588\) −21.3643 −0.881050
\(589\) −3.87347 −0.159604
\(590\) −4.62666 −0.190477
\(591\) 53.4541 2.19881
\(592\) 0.575428 0.0236500
\(593\) 29.0499 1.19294 0.596469 0.802636i \(-0.296570\pi\)
0.596469 + 0.802636i \(0.296570\pi\)
\(594\) 13.1102 0.537918
\(595\) −2.22792 −0.0913356
\(596\) −22.1535 −0.907445
\(597\) −29.8659 −1.22233
\(598\) −20.6252 −0.843426
\(599\) 7.22925 0.295379 0.147689 0.989034i \(-0.452816\pi\)
0.147689 + 0.989034i \(0.452816\pi\)
\(600\) −3.15350 −0.128741
\(601\) 8.42647 0.343723 0.171862 0.985121i \(-0.445022\pi\)
0.171862 + 0.985121i \(0.445022\pi\)
\(602\) −1.43998 −0.0586891
\(603\) −104.060 −4.23764
\(604\) −9.77674 −0.397810
\(605\) 9.88920 0.402053
\(606\) −54.7663 −2.22473
\(607\) 12.1519 0.493230 0.246615 0.969114i \(-0.420682\pi\)
0.246615 + 0.969114i \(0.420682\pi\)
\(608\) 6.53467 0.265016
\(609\) −12.4338 −0.503844
\(610\) 13.0715 0.529251
\(611\) 6.74725 0.272965
\(612\) −32.6031 −1.31790
\(613\) −3.31433 −0.133865 −0.0669323 0.997758i \(-0.521321\pi\)
−0.0669323 + 0.997758i \(0.521321\pi\)
\(614\) 3.59248 0.144981
\(615\) −6.73706 −0.271665
\(616\) −0.500153 −0.0201517
\(617\) −23.3807 −0.941273 −0.470637 0.882327i \(-0.655976\pi\)
−0.470637 + 0.882327i \(0.655976\pi\)
\(618\) 58.0651 2.33572
\(619\) 31.8826 1.28147 0.640736 0.767762i \(-0.278630\pi\)
0.640736 + 0.767762i \(0.278630\pi\)
\(620\) −0.592756 −0.0238057
\(621\) −74.6395 −2.99518
\(622\) 16.7427 0.671321
\(623\) −1.17312 −0.0469999
\(624\) −10.8396 −0.433930
\(625\) 1.00000 0.0400000
\(626\) 27.9220 1.11599
\(627\) 21.7188 0.867364
\(628\) −3.67323 −0.146578
\(629\) −2.70150 −0.107716
\(630\) −3.29555 −0.131298
\(631\) 13.7124 0.545881 0.272941 0.962031i \(-0.412004\pi\)
0.272941 + 0.962031i \(0.412004\pi\)
\(632\) 10.7602 0.428018
\(633\) −71.8485 −2.85572
\(634\) −24.5975 −0.976890
\(635\) −13.1465 −0.521702
\(636\) −19.8898 −0.788681
\(637\) 23.2871 0.922670
\(638\) 8.75682 0.346686
\(639\) −74.4558 −2.94542
\(640\) 1.00000 0.0395285
\(641\) 35.4099 1.39861 0.699304 0.714825i \(-0.253494\pi\)
0.699304 + 0.714825i \(0.253494\pi\)
\(642\) 37.8997 1.49578
\(643\) −45.3047 −1.78664 −0.893321 0.449420i \(-0.851631\pi\)
−0.893321 + 0.449420i \(0.851631\pi\)
\(644\) 2.84749 0.112207
\(645\) 9.56895 0.376777
\(646\) −30.6788 −1.20704
\(647\) 24.7742 0.973974 0.486987 0.873409i \(-0.338096\pi\)
0.486987 + 0.873409i \(0.338096\pi\)
\(648\) −18.3932 −0.722553
\(649\) 4.87625 0.191410
\(650\) 3.43732 0.134823
\(651\) −0.887060 −0.0347666
\(652\) 4.65548 0.182323
\(653\) 8.37484 0.327733 0.163866 0.986483i \(-0.447603\pi\)
0.163866 + 0.986483i \(0.447603\pi\)
\(654\) −41.4923 −1.62248
\(655\) 0.566335 0.0221285
\(656\) 2.13638 0.0834115
\(657\) −46.0180 −1.79533
\(658\) −0.931519 −0.0363144
\(659\) 2.31861 0.0903201 0.0451601 0.998980i \(-0.485620\pi\)
0.0451601 + 0.998980i \(0.485620\pi\)
\(660\) 3.32362 0.129372
\(661\) −7.46012 −0.290165 −0.145082 0.989420i \(-0.546345\pi\)
−0.145082 + 0.989420i \(0.546345\pi\)
\(662\) 0.197429 0.00767328
\(663\) 50.8893 1.97638
\(664\) −12.6166 −0.489620
\(665\) −3.10104 −0.120253
\(666\) −3.99609 −0.154845
\(667\) −49.8547 −1.93038
\(668\) −4.29110 −0.166028
\(669\) −10.5608 −0.408303
\(670\) −14.9844 −0.578896
\(671\) −13.7767 −0.531843
\(672\) 1.49650 0.0577287
\(673\) 9.18273 0.353968 0.176984 0.984214i \(-0.443366\pi\)
0.176984 + 0.984214i \(0.443366\pi\)
\(674\) −1.92974 −0.0743307
\(675\) 12.4392 0.478783
\(676\) −1.18486 −0.0455714
\(677\) −27.6474 −1.06258 −0.531288 0.847191i \(-0.678292\pi\)
−0.531288 + 0.847191i \(0.678292\pi\)
\(678\) −12.0171 −0.461514
\(679\) 3.53083 0.135501
\(680\) −4.69477 −0.180036
\(681\) −82.2596 −3.15219
\(682\) 0.624733 0.0239223
\(683\) −2.41739 −0.0924988 −0.0462494 0.998930i \(-0.514727\pi\)
−0.0462494 + 0.998930i \(0.514727\pi\)
\(684\) −45.3804 −1.73516
\(685\) 1.40749 0.0537775
\(686\) −6.53686 −0.249579
\(687\) 35.0894 1.33875
\(688\) −3.03439 −0.115685
\(689\) 21.6799 0.825938
\(690\) −18.9222 −0.720354
\(691\) −41.2899 −1.57074 −0.785370 0.619026i \(-0.787528\pi\)
−0.785370 + 0.619026i \(0.787528\pi\)
\(692\) 23.3544 0.887803
\(693\) 3.47334 0.131941
\(694\) −9.84709 −0.373791
\(695\) −10.3966 −0.394365
\(696\) −26.2012 −0.993153
\(697\) −10.0298 −0.379906
\(698\) −20.8401 −0.788808
\(699\) 55.6575 2.10516
\(700\) −0.474552 −0.0179364
\(701\) −15.7272 −0.594009 −0.297005 0.954876i \(-0.595988\pi\)
−0.297005 + 0.954876i \(0.595988\pi\)
\(702\) 42.7573 1.61377
\(703\) −3.76024 −0.141820
\(704\) −1.05395 −0.0397221
\(705\) 6.19014 0.233134
\(706\) −0.766412 −0.0288443
\(707\) −8.24147 −0.309952
\(708\) −14.5902 −0.548332
\(709\) 42.7621 1.60596 0.802982 0.596003i \(-0.203246\pi\)
0.802982 + 0.596003i \(0.203246\pi\)
\(710\) −10.7215 −0.402369
\(711\) −74.7248 −2.80240
\(712\) −2.47205 −0.0926440
\(713\) −3.55676 −0.133202
\(714\) −7.02573 −0.262931
\(715\) −3.62275 −0.135483
\(716\) 11.9470 0.446481
\(717\) −70.9495 −2.64966
\(718\) −28.3525 −1.05811
\(719\) 45.7972 1.70795 0.853974 0.520316i \(-0.174186\pi\)
0.853974 + 0.520316i \(0.174186\pi\)
\(720\) −6.94456 −0.258808
\(721\) 8.73788 0.325416
\(722\) −23.7020 −0.882095
\(723\) −56.2906 −2.09347
\(724\) 16.2940 0.605560
\(725\) 8.30861 0.308574
\(726\) 31.1856 1.15741
\(727\) 15.9640 0.592072 0.296036 0.955177i \(-0.404335\pi\)
0.296036 + 0.955177i \(0.404335\pi\)
\(728\) −1.63119 −0.0604558
\(729\) 10.0520 0.372295
\(730\) −6.62649 −0.245257
\(731\) 14.2458 0.526899
\(732\) 41.2211 1.52357
\(733\) −29.8776 −1.10356 −0.551778 0.833991i \(-0.686050\pi\)
−0.551778 + 0.833991i \(0.686050\pi\)
\(734\) 16.1601 0.596479
\(735\) 21.3643 0.788035
\(736\) 6.00037 0.221177
\(737\) 15.7927 0.581732
\(738\) −14.8362 −0.546128
\(739\) −1.45055 −0.0533593 −0.0266797 0.999644i \(-0.508493\pi\)
−0.0266797 + 0.999644i \(0.508493\pi\)
\(740\) −0.575428 −0.0211532
\(741\) 70.8331 2.60212
\(742\) −2.99310 −0.109880
\(743\) 39.9782 1.46666 0.733328 0.679875i \(-0.237966\pi\)
0.733328 + 0.679875i \(0.237966\pi\)
\(744\) −1.86926 −0.0685303
\(745\) 22.1535 0.811643
\(746\) 15.0275 0.550197
\(747\) 87.6168 3.20573
\(748\) 4.94804 0.180918
\(749\) 5.70332 0.208395
\(750\) 3.15350 0.115150
\(751\) 46.4906 1.69647 0.848233 0.529624i \(-0.177667\pi\)
0.848233 + 0.529624i \(0.177667\pi\)
\(752\) −1.96294 −0.0715811
\(753\) 40.8147 1.48737
\(754\) 28.5593 1.04007
\(755\) 9.77674 0.355812
\(756\) −5.90303 −0.214691
\(757\) −29.8235 −1.08395 −0.541977 0.840393i \(-0.682324\pi\)
−0.541977 + 0.840393i \(0.682324\pi\)
\(758\) 14.6512 0.532155
\(759\) 19.9429 0.723883
\(760\) −6.53467 −0.237038
\(761\) −4.20554 −0.152451 −0.0762253 0.997091i \(-0.524287\pi\)
−0.0762253 + 0.997091i \(0.524287\pi\)
\(762\) −41.4574 −1.50184
\(763\) −6.24394 −0.226046
\(764\) 13.0588 0.472451
\(765\) 32.6031 1.17877
\(766\) −13.9724 −0.504843
\(767\) 15.9033 0.574235
\(768\) 3.15350 0.113792
\(769\) −11.5511 −0.416544 −0.208272 0.978071i \(-0.566784\pi\)
−0.208272 + 0.978071i \(0.566784\pi\)
\(770\) 0.500153 0.0180242
\(771\) −54.9358 −1.97847
\(772\) 19.6904 0.708672
\(773\) −48.2056 −1.73383 −0.866917 0.498453i \(-0.833902\pi\)
−0.866917 + 0.498453i \(0.833902\pi\)
\(774\) 21.0725 0.757435
\(775\) 0.592756 0.0212924
\(776\) 7.44033 0.267092
\(777\) −0.861129 −0.0308928
\(778\) −3.34407 −0.119891
\(779\) −13.9605 −0.500188
\(780\) 10.8396 0.388119
\(781\) 11.2998 0.404340
\(782\) −28.1704 −1.00737
\(783\) 103.352 3.69350
\(784\) −6.77480 −0.241957
\(785\) 3.67323 0.131103
\(786\) 1.78594 0.0637023
\(787\) −39.1121 −1.39420 −0.697099 0.716975i \(-0.745526\pi\)
−0.697099 + 0.716975i \(0.745526\pi\)
\(788\) 16.9507 0.603844
\(789\) 34.6417 1.23328
\(790\) −10.7602 −0.382831
\(791\) −1.80838 −0.0642987
\(792\) 7.31919 0.260076
\(793\) −44.9310 −1.59555
\(794\) −4.05193 −0.143797
\(795\) 19.8898 0.705418
\(796\) −9.47071 −0.335680
\(797\) −33.1920 −1.17572 −0.587861 0.808962i \(-0.700030\pi\)
−0.587861 + 0.808962i \(0.700030\pi\)
\(798\) −9.77914 −0.346178
\(799\) 9.21557 0.326023
\(800\) −1.00000 −0.0353553
\(801\) 17.1673 0.606576
\(802\) 1.00000 0.0353112
\(803\) 6.98397 0.246459
\(804\) −47.2532 −1.66649
\(805\) −2.84749 −0.100361
\(806\) 2.03749 0.0717676
\(807\) −34.2769 −1.20660
\(808\) −17.3668 −0.610963
\(809\) −34.7471 −1.22164 −0.610822 0.791768i \(-0.709161\pi\)
−0.610822 + 0.791768i \(0.709161\pi\)
\(810\) 18.3932 0.646271
\(811\) −25.4546 −0.893831 −0.446915 0.894576i \(-0.647477\pi\)
−0.446915 + 0.894576i \(0.647477\pi\)
\(812\) −3.94287 −0.138368
\(813\) 38.8515 1.36258
\(814\) 0.606470 0.0212568
\(815\) −4.65548 −0.163074
\(816\) −14.8050 −0.518277
\(817\) 19.8288 0.693720
\(818\) 35.2075 1.23100
\(819\) 11.3279 0.395828
\(820\) −2.13638 −0.0746055
\(821\) −3.61530 −0.126175 −0.0630875 0.998008i \(-0.520095\pi\)
−0.0630875 + 0.998008i \(0.520095\pi\)
\(822\) 4.43853 0.154811
\(823\) −22.2385 −0.775186 −0.387593 0.921831i \(-0.626693\pi\)
−0.387593 + 0.921831i \(0.626693\pi\)
\(824\) 18.4129 0.641444
\(825\) −3.32362 −0.115714
\(826\) −2.19559 −0.0763944
\(827\) −35.1752 −1.22316 −0.611582 0.791181i \(-0.709466\pi\)
−0.611582 + 0.791181i \(0.709466\pi\)
\(828\) −41.6699 −1.44813
\(829\) −34.8087 −1.20896 −0.604478 0.796622i \(-0.706618\pi\)
−0.604478 + 0.796622i \(0.706618\pi\)
\(830\) 12.6166 0.437929
\(831\) −19.7308 −0.684454
\(832\) −3.43732 −0.119168
\(833\) 31.8061 1.10202
\(834\) −32.7856 −1.13527
\(835\) 4.29110 0.148500
\(836\) 6.88719 0.238199
\(837\) 7.37339 0.254862
\(838\) −12.9090 −0.445933
\(839\) 10.2957 0.355446 0.177723 0.984081i \(-0.443127\pi\)
0.177723 + 0.984081i \(0.443127\pi\)
\(840\) −1.49650 −0.0516342
\(841\) 40.0329 1.38045
\(842\) 25.0552 0.863461
\(843\) 73.1978 2.52107
\(844\) −22.7837 −0.784248
\(845\) 1.18486 0.0407603
\(846\) 13.6318 0.468670
\(847\) 4.69294 0.161251
\(848\) −6.30721 −0.216591
\(849\) 32.8514 1.12746
\(850\) 4.69477 0.161029
\(851\) −3.45278 −0.118360
\(852\) −33.8101 −1.15832
\(853\) 17.2745 0.591466 0.295733 0.955271i \(-0.404436\pi\)
0.295733 + 0.955271i \(0.404436\pi\)
\(854\) 6.20312 0.212267
\(855\) 45.3804 1.55198
\(856\) 12.0183 0.410777
\(857\) −14.6672 −0.501024 −0.250512 0.968114i \(-0.580599\pi\)
−0.250512 + 0.968114i \(0.580599\pi\)
\(858\) −11.4243 −0.390020
\(859\) 52.3161 1.78500 0.892501 0.451045i \(-0.148949\pi\)
0.892501 + 0.451045i \(0.148949\pi\)
\(860\) 3.03439 0.103472
\(861\) −3.19709 −0.108956
\(862\) 18.2753 0.622459
\(863\) −17.3127 −0.589332 −0.294666 0.955600i \(-0.595208\pi\)
−0.294666 + 0.955600i \(0.595208\pi\)
\(864\) −12.4392 −0.423189
\(865\) −23.3544 −0.794075
\(866\) 24.2793 0.825044
\(867\) 15.8964 0.539871
\(868\) −0.281294 −0.00954774
\(869\) 11.3407 0.384706
\(870\) 26.2012 0.888303
\(871\) 51.5060 1.74521
\(872\) −13.1575 −0.445571
\(873\) −51.6698 −1.74876
\(874\) −39.2105 −1.32631
\(875\) 0.474552 0.0160428
\(876\) −20.8966 −0.706032
\(877\) −11.1664 −0.377063 −0.188532 0.982067i \(-0.560373\pi\)
−0.188532 + 0.982067i \(0.560373\pi\)
\(878\) −39.0419 −1.31760
\(879\) −3.64462 −0.122930
\(880\) 1.05395 0.0355285
\(881\) 36.1158 1.21677 0.608387 0.793641i \(-0.291817\pi\)
0.608387 + 0.793641i \(0.291817\pi\)
\(882\) 47.0480 1.58419
\(883\) −15.1612 −0.510215 −0.255108 0.966913i \(-0.582111\pi\)
−0.255108 + 0.966913i \(0.582111\pi\)
\(884\) 16.1374 0.542760
\(885\) 14.5902 0.490443
\(886\) −28.5384 −0.958767
\(887\) 24.2627 0.814662 0.407331 0.913281i \(-0.366460\pi\)
0.407331 + 0.913281i \(0.366460\pi\)
\(888\) −1.81461 −0.0608944
\(889\) −6.23869 −0.209239
\(890\) 2.47205 0.0828633
\(891\) −19.3854 −0.649437
\(892\) −3.34891 −0.112130
\(893\) 12.8272 0.429245
\(894\) 69.8612 2.33651
\(895\) −11.9470 −0.399345
\(896\) 0.474552 0.0158537
\(897\) 65.0415 2.17167
\(898\) 6.91622 0.230797
\(899\) 4.92498 0.164257
\(900\) 6.94456 0.231485
\(901\) 29.6109 0.986483
\(902\) 2.25163 0.0749709
\(903\) 4.54097 0.151114
\(904\) −3.81072 −0.126743
\(905\) −16.2940 −0.541630
\(906\) 30.8309 1.02429
\(907\) −32.4651 −1.07799 −0.538994 0.842310i \(-0.681195\pi\)
−0.538994 + 0.842310i \(0.681195\pi\)
\(908\) −26.0852 −0.865667
\(909\) 120.605 4.00021
\(910\) 1.63119 0.0540733
\(911\) 58.8363 1.94933 0.974667 0.223660i \(-0.0718006\pi\)
0.974667 + 0.223660i \(0.0718006\pi\)
\(912\) −20.6071 −0.682369
\(913\) −13.2972 −0.440074
\(914\) 3.94501 0.130489
\(915\) −41.2211 −1.36273
\(916\) 11.1271 0.367651
\(917\) 0.268756 0.00887509
\(918\) 58.3990 1.92745
\(919\) 19.4972 0.643155 0.321577 0.946883i \(-0.395787\pi\)
0.321577 + 0.946883i \(0.395787\pi\)
\(920\) −6.00037 −0.197826
\(921\) −11.3289 −0.373300
\(922\) 12.2147 0.402269
\(923\) 36.8530 1.21303
\(924\) 1.57723 0.0518871
\(925\) 0.575428 0.0189200
\(926\) −0.135978 −0.00446851
\(927\) −127.869 −4.19978
\(928\) −8.30861 −0.272743
\(929\) 24.6678 0.809325 0.404663 0.914466i \(-0.367389\pi\)
0.404663 + 0.914466i \(0.367389\pi\)
\(930\) 1.86926 0.0612954
\(931\) 44.2711 1.45093
\(932\) 17.6495 0.578127
\(933\) −52.7981 −1.72853
\(934\) 19.1532 0.626712
\(935\) −4.94804 −0.161818
\(936\) 23.8706 0.780236
\(937\) −8.19286 −0.267649 −0.133825 0.991005i \(-0.542726\pi\)
−0.133825 + 0.991005i \(0.542726\pi\)
\(938\) −7.11086 −0.232178
\(939\) −88.0520 −2.87347
\(940\) 1.96294 0.0640241
\(941\) −3.17998 −0.103664 −0.0518321 0.998656i \(-0.516506\pi\)
−0.0518321 + 0.998656i \(0.516506\pi\)
\(942\) 11.5835 0.377412
\(943\) −12.8191 −0.417446
\(944\) −4.62666 −0.150585
\(945\) 5.90303 0.192026
\(946\) −3.19808 −0.103979
\(947\) −2.37096 −0.0770459 −0.0385230 0.999258i \(-0.512265\pi\)
−0.0385230 + 0.999258i \(0.512265\pi\)
\(948\) −33.9323 −1.10207
\(949\) 22.7773 0.739384
\(950\) 6.53467 0.212013
\(951\) 77.5681 2.51532
\(952\) −2.22792 −0.0722071
\(953\) 34.3615 1.11308 0.556539 0.830821i \(-0.312129\pi\)
0.556539 + 0.830821i \(0.312129\pi\)
\(954\) 43.8008 1.41810
\(955\) −13.0588 −0.422573
\(956\) −22.4986 −0.727658
\(957\) −27.6146 −0.892654
\(958\) 24.0010 0.775437
\(959\) 0.667929 0.0215685
\(960\) −3.15350 −0.101779
\(961\) −30.6486 −0.988666
\(962\) 1.97793 0.0637710
\(963\) −83.4619 −2.68952
\(964\) −17.8502 −0.574916
\(965\) −19.6904 −0.633855
\(966\) −8.97956 −0.288912
\(967\) 37.4377 1.20392 0.601958 0.798528i \(-0.294388\pi\)
0.601958 + 0.798528i \(0.294388\pi\)
\(968\) 9.88920 0.317851
\(969\) 96.7456 3.10792
\(970\) −7.44033 −0.238895
\(971\) 37.8384 1.21429 0.607146 0.794590i \(-0.292314\pi\)
0.607146 + 0.794590i \(0.292314\pi\)
\(972\) 20.6854 0.663486
\(973\) −4.93372 −0.158168
\(974\) 29.9631 0.960079
\(975\) −10.8396 −0.347144
\(976\) 13.0715 0.418409
\(977\) 40.0521 1.28138 0.640690 0.767800i \(-0.278649\pi\)
0.640690 + 0.767800i \(0.278649\pi\)
\(978\) −14.6811 −0.469449
\(979\) −2.60541 −0.0832692
\(980\) 6.77480 0.216413
\(981\) 91.3733 2.91732
\(982\) −20.9770 −0.669402
\(983\) −12.7989 −0.408220 −0.204110 0.978948i \(-0.565430\pi\)
−0.204110 + 0.978948i \(0.565430\pi\)
\(984\) −6.73706 −0.214770
\(985\) −16.9507 −0.540095
\(986\) 39.0070 1.24224
\(987\) 2.93754 0.0935030
\(988\) 22.4617 0.714603
\(989\) 18.2075 0.578964
\(990\) −7.31919 −0.232619
\(991\) 38.3312 1.21763 0.608816 0.793312i \(-0.291645\pi\)
0.608816 + 0.793312i \(0.291645\pi\)
\(992\) −0.592756 −0.0188200
\(993\) −0.622591 −0.0197573
\(994\) −5.08789 −0.161378
\(995\) 9.47071 0.300242
\(996\) 39.7865 1.26068
\(997\) −11.4733 −0.363362 −0.181681 0.983357i \(-0.558154\pi\)
−0.181681 + 0.983357i \(0.558154\pi\)
\(998\) 37.4023 1.18395
\(999\) 7.15784 0.226464
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 \(a_p\))