Properties

Label 6027.2.a.bo.1.2
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.37986 q^{2} +1.00000 q^{3} +3.66372 q^{4} +3.68734 q^{5} -2.37986 q^{6} -3.95941 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.37986 q^{2} +1.00000 q^{3} +3.66372 q^{4} +3.68734 q^{5} -2.37986 q^{6} -3.95941 q^{8} +1.00000 q^{9} -8.77534 q^{10} -6.26313 q^{11} +3.66372 q^{12} -3.25624 q^{13} +3.68734 q^{15} +2.09539 q^{16} +0.146265 q^{17} -2.37986 q^{18} -1.78602 q^{19} +13.5094 q^{20} +14.9053 q^{22} -3.11368 q^{23} -3.95941 q^{24} +8.59647 q^{25} +7.74938 q^{26} +1.00000 q^{27} +4.08462 q^{29} -8.77534 q^{30} +1.31731 q^{31} +2.93209 q^{32} -6.26313 q^{33} -0.348089 q^{34} +3.66372 q^{36} +3.67591 q^{37} +4.25047 q^{38} -3.25624 q^{39} -14.5997 q^{40} -1.00000 q^{41} -9.08247 q^{43} -22.9463 q^{44} +3.68734 q^{45} +7.41011 q^{46} +11.5238 q^{47} +2.09539 q^{48} -20.4584 q^{50} +0.146265 q^{51} -11.9299 q^{52} +4.41701 q^{53} -2.37986 q^{54} -23.0943 q^{55} -1.78602 q^{57} -9.72081 q^{58} +1.71894 q^{59} +13.5094 q^{60} +6.02287 q^{61} -3.13502 q^{62} -11.1687 q^{64} -12.0069 q^{65} +14.9053 q^{66} +1.38835 q^{67} +0.535872 q^{68} -3.11368 q^{69} +8.92495 q^{71} -3.95941 q^{72} +8.93911 q^{73} -8.74814 q^{74} +8.59647 q^{75} -6.54346 q^{76} +7.74938 q^{78} -10.3689 q^{79} +7.72642 q^{80} +1.00000 q^{81} +2.37986 q^{82} -10.6436 q^{83} +0.539327 q^{85} +21.6150 q^{86} +4.08462 q^{87} +24.7983 q^{88} -1.75624 q^{89} -8.77534 q^{90} -11.4076 q^{92} +1.31731 q^{93} -27.4251 q^{94} -6.58565 q^{95} +2.93209 q^{96} +5.53442 q^{97} -6.26313 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} - 4q^{10} + 12q^{11} + 32q^{12} + 4q^{15} + 44q^{16} + 8q^{17} + 8q^{18} - 4q^{19} + 28q^{20} + 16q^{22} + 20q^{23} + 24q^{24} + 48q^{25} + 32q^{26} + 24q^{27} + 24q^{29} - 4q^{30} - 4q^{31} + 36q^{32} + 12q^{33} + 16q^{34} + 32q^{36} + 64q^{37} + 20q^{38} - 48q^{40} - 24q^{41} + 20q^{43} + 48q^{44} + 4q^{45} + 28q^{46} + 32q^{47} + 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} + 8q^{54} - 24q^{55} - 4q^{57} + 28q^{58} + 28q^{59} + 28q^{60} - 28q^{61} - 4q^{62} + 48q^{64} + 28q^{65} + 16q^{66} + 44q^{67} - 32q^{68} + 20q^{69} + 20q^{71} + 24q^{72} - 16q^{73} + 44q^{74} + 48q^{75} - 16q^{76} + 32q^{78} + 4q^{79} + 44q^{80} + 24q^{81} - 8q^{82} + 8q^{83} + 28q^{85} + 56q^{86} + 24q^{87} + 60q^{88} + 60q^{89} - 4q^{90} + 60q^{92} - 4q^{93} + 24q^{94} + 28q^{95} + 36q^{96} - 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.37986 −1.68281 −0.841406 0.540403i \(-0.818272\pi\)
−0.841406 + 0.540403i \(0.818272\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.66372 1.83186
\(5\) 3.68734 1.64903 0.824514 0.565841i \(-0.191449\pi\)
0.824514 + 0.565841i \(0.191449\pi\)
\(6\) −2.37986 −0.971572
\(7\) 0 0
\(8\) −3.95941 −1.39986
\(9\) 1.00000 0.333333
\(10\) −8.77534 −2.77501
\(11\) −6.26313 −1.88840 −0.944202 0.329366i \(-0.893165\pi\)
−0.944202 + 0.329366i \(0.893165\pi\)
\(12\) 3.66372 1.05762
\(13\) −3.25624 −0.903118 −0.451559 0.892241i \(-0.649132\pi\)
−0.451559 + 0.892241i \(0.649132\pi\)
\(14\) 0 0
\(15\) 3.68734 0.952067
\(16\) 2.09539 0.523848
\(17\) 0.146265 0.0354744 0.0177372 0.999843i \(-0.494354\pi\)
0.0177372 + 0.999843i \(0.494354\pi\)
\(18\) −2.37986 −0.560938
\(19\) −1.78602 −0.409741 −0.204870 0.978789i \(-0.565677\pi\)
−0.204870 + 0.978789i \(0.565677\pi\)
\(20\) 13.5094 3.02079
\(21\) 0 0
\(22\) 14.9053 3.17783
\(23\) −3.11368 −0.649247 −0.324623 0.945843i \(-0.605238\pi\)
−0.324623 + 0.945843i \(0.605238\pi\)
\(24\) −3.95941 −0.808211
\(25\) 8.59647 1.71929
\(26\) 7.74938 1.51978
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 4.08462 0.758495 0.379247 0.925295i \(-0.376183\pi\)
0.379247 + 0.925295i \(0.376183\pi\)
\(30\) −8.77534 −1.60215
\(31\) 1.31731 0.236596 0.118298 0.992978i \(-0.462256\pi\)
0.118298 + 0.992978i \(0.462256\pi\)
\(32\) 2.93209 0.518325
\(33\) −6.26313 −1.09027
\(34\) −0.348089 −0.0596967
\(35\) 0 0
\(36\) 3.66372 0.610620
\(37\) 3.67591 0.604316 0.302158 0.953258i \(-0.402293\pi\)
0.302158 + 0.953258i \(0.402293\pi\)
\(38\) 4.25047 0.689517
\(39\) −3.25624 −0.521415
\(40\) −14.5997 −2.30841
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −9.08247 −1.38506 −0.692532 0.721388i \(-0.743505\pi\)
−0.692532 + 0.721388i \(0.743505\pi\)
\(44\) −22.9463 −3.45929
\(45\) 3.68734 0.549676
\(46\) 7.41011 1.09256
\(47\) 11.5238 1.68093 0.840463 0.541869i \(-0.182283\pi\)
0.840463 + 0.541869i \(0.182283\pi\)
\(48\) 2.09539 0.302444
\(49\) 0 0
\(50\) −20.4584 −2.89325
\(51\) 0.146265 0.0204811
\(52\) −11.9299 −1.65438
\(53\) 4.41701 0.606723 0.303361 0.952876i \(-0.401891\pi\)
0.303361 + 0.952876i \(0.401891\pi\)
\(54\) −2.37986 −0.323857
\(55\) −23.0943 −3.11403
\(56\) 0 0
\(57\) −1.78602 −0.236564
\(58\) −9.72081 −1.27640
\(59\) 1.71894 0.223786 0.111893 0.993720i \(-0.464309\pi\)
0.111893 + 0.993720i \(0.464309\pi\)
\(60\) 13.5094 1.74405
\(61\) 6.02287 0.771150 0.385575 0.922677i \(-0.374003\pi\)
0.385575 + 0.922677i \(0.374003\pi\)
\(62\) −3.13502 −0.398147
\(63\) 0 0
\(64\) −11.1687 −1.39609
\(65\) −12.0069 −1.48927
\(66\) 14.9053 1.83472
\(67\) 1.38835 0.169615 0.0848073 0.996397i \(-0.472973\pi\)
0.0848073 + 0.996397i \(0.472973\pi\)
\(68\) 0.535872 0.0649840
\(69\) −3.11368 −0.374843
\(70\) 0 0
\(71\) 8.92495 1.05920 0.529598 0.848249i \(-0.322343\pi\)
0.529598 + 0.848249i \(0.322343\pi\)
\(72\) −3.95941 −0.466621
\(73\) 8.93911 1.04624 0.523122 0.852258i \(-0.324767\pi\)
0.523122 + 0.852258i \(0.324767\pi\)
\(74\) −8.74814 −1.01695
\(75\) 8.59647 0.992635
\(76\) −6.54346 −0.750587
\(77\) 0 0
\(78\) 7.74938 0.877445
\(79\) −10.3689 −1.16659 −0.583294 0.812261i \(-0.698237\pi\)
−0.583294 + 0.812261i \(0.698237\pi\)
\(80\) 7.72642 0.863840
\(81\) 1.00000 0.111111
\(82\) 2.37986 0.262811
\(83\) −10.6436 −1.16829 −0.584146 0.811649i \(-0.698570\pi\)
−0.584146 + 0.811649i \(0.698570\pi\)
\(84\) 0 0
\(85\) 0.539327 0.0584982
\(86\) 21.6150 2.33080
\(87\) 4.08462 0.437917
\(88\) 24.7983 2.64351
\(89\) −1.75624 −0.186161 −0.0930805 0.995659i \(-0.529671\pi\)
−0.0930805 + 0.995659i \(0.529671\pi\)
\(90\) −8.77534 −0.925002
\(91\) 0 0
\(92\) −11.4076 −1.18933
\(93\) 1.31731 0.136599
\(94\) −27.4251 −2.82868
\(95\) −6.58565 −0.675674
\(96\) 2.93209 0.299255
\(97\) 5.53442 0.561935 0.280968 0.959717i \(-0.409345\pi\)
0.280968 + 0.959717i \(0.409345\pi\)
\(98\) 0 0
\(99\) −6.26313 −0.629468
\(100\) 31.4950 3.14950
\(101\) 15.9955 1.59161 0.795806 0.605552i \(-0.207048\pi\)
0.795806 + 0.605552i \(0.207048\pi\)
\(102\) −0.348089 −0.0344659
\(103\) 18.2558 1.79880 0.899400 0.437127i \(-0.144004\pi\)
0.899400 + 0.437127i \(0.144004\pi\)
\(104\) 12.8928 1.26424
\(105\) 0 0
\(106\) −10.5118 −1.02100
\(107\) −3.48468 −0.336877 −0.168439 0.985712i \(-0.553872\pi\)
−0.168439 + 0.985712i \(0.553872\pi\)
\(108\) 3.66372 0.352541
\(109\) 12.1345 1.16228 0.581138 0.813805i \(-0.302608\pi\)
0.581138 + 0.813805i \(0.302608\pi\)
\(110\) 54.9611 5.24033
\(111\) 3.67591 0.348902
\(112\) 0 0
\(113\) 11.1948 1.05312 0.526558 0.850139i \(-0.323482\pi\)
0.526558 + 0.850139i \(0.323482\pi\)
\(114\) 4.25047 0.398093
\(115\) −11.4812 −1.07063
\(116\) 14.9649 1.38946
\(117\) −3.25624 −0.301039
\(118\) −4.09082 −0.376591
\(119\) 0 0
\(120\) −14.5997 −1.33276
\(121\) 28.2268 2.56607
\(122\) −14.3336 −1.29770
\(123\) −1.00000 −0.0901670
\(124\) 4.82626 0.433411
\(125\) 13.2614 1.18614
\(126\) 0 0
\(127\) −19.7467 −1.75224 −0.876119 0.482095i \(-0.839876\pi\)
−0.876119 + 0.482095i \(0.839876\pi\)
\(128\) 20.7158 1.83104
\(129\) −9.08247 −0.799667
\(130\) 28.5746 2.50616
\(131\) 19.2431 1.68128 0.840640 0.541594i \(-0.182179\pi\)
0.840640 + 0.541594i \(0.182179\pi\)
\(132\) −22.9463 −1.99722
\(133\) 0 0
\(134\) −3.30408 −0.285429
\(135\) 3.68734 0.317356
\(136\) −0.579121 −0.0496592
\(137\) −3.63718 −0.310745 −0.155373 0.987856i \(-0.549658\pi\)
−0.155373 + 0.987856i \(0.549658\pi\)
\(138\) 7.41011 0.630790
\(139\) 15.6912 1.33091 0.665457 0.746436i \(-0.268237\pi\)
0.665457 + 0.746436i \(0.268237\pi\)
\(140\) 0 0
\(141\) 11.5238 0.970483
\(142\) −21.2401 −1.78243
\(143\) 20.3942 1.70545
\(144\) 2.09539 0.174616
\(145\) 15.0614 1.25078
\(146\) −21.2738 −1.76063
\(147\) 0 0
\(148\) 13.4675 1.10702
\(149\) 15.4694 1.26730 0.633651 0.773619i \(-0.281555\pi\)
0.633651 + 0.773619i \(0.281555\pi\)
\(150\) −20.4584 −1.67042
\(151\) −6.09366 −0.495895 −0.247947 0.968774i \(-0.579756\pi\)
−0.247947 + 0.968774i \(0.579756\pi\)
\(152\) 7.07157 0.573580
\(153\) 0.146265 0.0118248
\(154\) 0 0
\(155\) 4.85738 0.390154
\(156\) −11.9299 −0.955160
\(157\) 2.07672 0.165740 0.0828701 0.996560i \(-0.473591\pi\)
0.0828701 + 0.996560i \(0.473591\pi\)
\(158\) 24.6764 1.96315
\(159\) 4.41701 0.350292
\(160\) 10.8116 0.854732
\(161\) 0 0
\(162\) −2.37986 −0.186979
\(163\) 11.3480 0.888841 0.444421 0.895818i \(-0.353410\pi\)
0.444421 + 0.895818i \(0.353410\pi\)
\(164\) −3.66372 −0.286088
\(165\) −23.0943 −1.79789
\(166\) 25.3303 1.96602
\(167\) 19.2640 1.49069 0.745347 0.666677i \(-0.232284\pi\)
0.745347 + 0.666677i \(0.232284\pi\)
\(168\) 0 0
\(169\) −2.39691 −0.184378
\(170\) −1.28352 −0.0984416
\(171\) −1.78602 −0.136580
\(172\) −33.2756 −2.53724
\(173\) −11.0874 −0.842961 −0.421481 0.906837i \(-0.638489\pi\)
−0.421481 + 0.906837i \(0.638489\pi\)
\(174\) −9.72081 −0.736933
\(175\) 0 0
\(176\) −13.1237 −0.989236
\(177\) 1.71894 0.129203
\(178\) 4.17960 0.313274
\(179\) 15.7592 1.17790 0.588951 0.808169i \(-0.299541\pi\)
0.588951 + 0.808169i \(0.299541\pi\)
\(180\) 13.5094 1.00693
\(181\) −3.24953 −0.241536 −0.120768 0.992681i \(-0.538536\pi\)
−0.120768 + 0.992681i \(0.538536\pi\)
\(182\) 0 0
\(183\) 6.02287 0.445223
\(184\) 12.3283 0.908856
\(185\) 13.5543 0.996534
\(186\) −3.13502 −0.229871
\(187\) −0.916074 −0.0669900
\(188\) 42.2201 3.07922
\(189\) 0 0
\(190\) 15.6729 1.13703
\(191\) −0.889555 −0.0643660 −0.0321830 0.999482i \(-0.510246\pi\)
−0.0321830 + 0.999482i \(0.510246\pi\)
\(192\) −11.1687 −0.806034
\(193\) −2.48347 −0.178764 −0.0893821 0.995997i \(-0.528489\pi\)
−0.0893821 + 0.995997i \(0.528489\pi\)
\(194\) −13.1711 −0.945632
\(195\) −12.0069 −0.859829
\(196\) 0 0
\(197\) −16.0761 −1.14537 −0.572686 0.819775i \(-0.694099\pi\)
−0.572686 + 0.819775i \(0.694099\pi\)
\(198\) 14.9053 1.05928
\(199\) 6.08609 0.431432 0.215716 0.976456i \(-0.430792\pi\)
0.215716 + 0.976456i \(0.430792\pi\)
\(200\) −34.0370 −2.40678
\(201\) 1.38835 0.0979270
\(202\) −38.0670 −2.67838
\(203\) 0 0
\(204\) 0.535872 0.0375186
\(205\) −3.68734 −0.257535
\(206\) −43.4462 −3.02704
\(207\) −3.11368 −0.216416
\(208\) −6.82309 −0.473096
\(209\) 11.1861 0.773756
\(210\) 0 0
\(211\) −26.1991 −1.80362 −0.901809 0.432135i \(-0.857761\pi\)
−0.901809 + 0.432135i \(0.857761\pi\)
\(212\) 16.1827 1.11143
\(213\) 8.92495 0.611527
\(214\) 8.29305 0.566901
\(215\) −33.4901 −2.28401
\(216\) −3.95941 −0.269404
\(217\) 0 0
\(218\) −28.8784 −1.95589
\(219\) 8.93911 0.604049
\(220\) −84.6109 −5.70447
\(221\) −0.476272 −0.0320375
\(222\) −8.74814 −0.587137
\(223\) −18.3279 −1.22733 −0.613663 0.789568i \(-0.710305\pi\)
−0.613663 + 0.789568i \(0.710305\pi\)
\(224\) 0 0
\(225\) 8.59647 0.573098
\(226\) −26.6420 −1.77220
\(227\) 18.3473 1.21776 0.608878 0.793264i \(-0.291620\pi\)
0.608878 + 0.793264i \(0.291620\pi\)
\(228\) −6.54346 −0.433351
\(229\) 4.23971 0.280168 0.140084 0.990140i \(-0.455263\pi\)
0.140084 + 0.990140i \(0.455263\pi\)
\(230\) 27.3236 1.80166
\(231\) 0 0
\(232\) −16.1727 −1.06179
\(233\) 16.9183 1.10836 0.554179 0.832398i \(-0.313032\pi\)
0.554179 + 0.832398i \(0.313032\pi\)
\(234\) 7.74938 0.506593
\(235\) 42.4923 2.77189
\(236\) 6.29769 0.409945
\(237\) −10.3689 −0.673530
\(238\) 0 0
\(239\) −12.6129 −0.815859 −0.407929 0.913014i \(-0.633749\pi\)
−0.407929 + 0.913014i \(0.633749\pi\)
\(240\) 7.72642 0.498738
\(241\) 28.8035 1.85539 0.927697 0.373334i \(-0.121786\pi\)
0.927697 + 0.373334i \(0.121786\pi\)
\(242\) −67.1757 −4.31822
\(243\) 1.00000 0.0641500
\(244\) 22.0661 1.41264
\(245\) 0 0
\(246\) 2.37986 0.151734
\(247\) 5.81570 0.370044
\(248\) −5.21578 −0.331202
\(249\) −10.6436 −0.674513
\(250\) −31.5603 −1.99605
\(251\) 30.2514 1.90945 0.954726 0.297488i \(-0.0961487\pi\)
0.954726 + 0.297488i \(0.0961487\pi\)
\(252\) 0 0
\(253\) 19.5014 1.22604
\(254\) 46.9943 2.94869
\(255\) 0.539327 0.0337740
\(256\) −26.9632 −1.68520
\(257\) 18.8356 1.17493 0.587466 0.809249i \(-0.300126\pi\)
0.587466 + 0.809249i \(0.300126\pi\)
\(258\) 21.6150 1.34569
\(259\) 0 0
\(260\) −43.9897 −2.72813
\(261\) 4.08462 0.252832
\(262\) −45.7959 −2.82928
\(263\) 20.7414 1.27897 0.639486 0.768803i \(-0.279147\pi\)
0.639486 + 0.768803i \(0.279147\pi\)
\(264\) 24.7983 1.52623
\(265\) 16.2870 1.00050
\(266\) 0 0
\(267\) −1.75624 −0.107480
\(268\) 5.08654 0.310710
\(269\) −2.26170 −0.137898 −0.0689492 0.997620i \(-0.521965\pi\)
−0.0689492 + 0.997620i \(0.521965\pi\)
\(270\) −8.77534 −0.534050
\(271\) −25.1898 −1.53017 −0.765086 0.643928i \(-0.777304\pi\)
−0.765086 + 0.643928i \(0.777304\pi\)
\(272\) 0.306481 0.0185832
\(273\) 0 0
\(274\) 8.65597 0.522926
\(275\) −53.8408 −3.24672
\(276\) −11.4076 −0.686659
\(277\) −10.2447 −0.615544 −0.307772 0.951460i \(-0.599583\pi\)
−0.307772 + 0.951460i \(0.599583\pi\)
\(278\) −37.3429 −2.23968
\(279\) 1.31731 0.0788655
\(280\) 0 0
\(281\) 6.76403 0.403508 0.201754 0.979436i \(-0.435336\pi\)
0.201754 + 0.979436i \(0.435336\pi\)
\(282\) −27.4251 −1.63314
\(283\) 2.07715 0.123474 0.0617369 0.998092i \(-0.480336\pi\)
0.0617369 + 0.998092i \(0.480336\pi\)
\(284\) 32.6985 1.94030
\(285\) −6.58565 −0.390100
\(286\) −48.5354 −2.86996
\(287\) 0 0
\(288\) 2.93209 0.172775
\(289\) −16.9786 −0.998742
\(290\) −35.8439 −2.10483
\(291\) 5.53442 0.324434
\(292\) 32.7504 1.91657
\(293\) −8.71064 −0.508881 −0.254440 0.967088i \(-0.581891\pi\)
−0.254440 + 0.967088i \(0.581891\pi\)
\(294\) 0 0
\(295\) 6.33830 0.369030
\(296\) −14.5544 −0.845959
\(297\) −6.26313 −0.363424
\(298\) −36.8150 −2.13263
\(299\) 10.1389 0.586346
\(300\) 31.4950 1.81837
\(301\) 0 0
\(302\) 14.5020 0.834498
\(303\) 15.9955 0.918918
\(304\) −3.74240 −0.214642
\(305\) 22.2084 1.27165
\(306\) −0.348089 −0.0198989
\(307\) −27.2743 −1.55662 −0.778312 0.627877i \(-0.783924\pi\)
−0.778312 + 0.627877i \(0.783924\pi\)
\(308\) 0 0
\(309\) 18.2558 1.03854
\(310\) −11.5599 −0.656556
\(311\) 10.3281 0.585654 0.292827 0.956166i \(-0.405404\pi\)
0.292827 + 0.956166i \(0.405404\pi\)
\(312\) 12.8928 0.729910
\(313\) −30.1284 −1.70296 −0.851480 0.524387i \(-0.824295\pi\)
−0.851480 + 0.524387i \(0.824295\pi\)
\(314\) −4.94229 −0.278910
\(315\) 0 0
\(316\) −37.9886 −2.13703
\(317\) 19.6474 1.10351 0.551755 0.834006i \(-0.313958\pi\)
0.551755 + 0.834006i \(0.313958\pi\)
\(318\) −10.5118 −0.589475
\(319\) −25.5825 −1.43234
\(320\) −41.1829 −2.30219
\(321\) −3.48468 −0.194496
\(322\) 0 0
\(323\) −0.261231 −0.0145353
\(324\) 3.66372 0.203540
\(325\) −27.9922 −1.55273
\(326\) −27.0065 −1.49575
\(327\) 12.1345 0.671040
\(328\) 3.95941 0.218622
\(329\) 0 0
\(330\) 54.9611 3.02551
\(331\) −33.1392 −1.82150 −0.910748 0.412962i \(-0.864494\pi\)
−0.910748 + 0.412962i \(0.864494\pi\)
\(332\) −38.9953 −2.14015
\(333\) 3.67591 0.201439
\(334\) −45.8456 −2.50856
\(335\) 5.11933 0.279699
\(336\) 0 0
\(337\) 21.6674 1.18030 0.590148 0.807295i \(-0.299069\pi\)
0.590148 + 0.807295i \(0.299069\pi\)
\(338\) 5.70430 0.310273
\(339\) 11.1948 0.608017
\(340\) 1.97594 0.107161
\(341\) −8.25050 −0.446790
\(342\) 4.25047 0.229839
\(343\) 0 0
\(344\) 35.9612 1.93890
\(345\) −11.4812 −0.618126
\(346\) 26.3865 1.41855
\(347\) 21.5837 1.15867 0.579337 0.815088i \(-0.303311\pi\)
0.579337 + 0.815088i \(0.303311\pi\)
\(348\) 14.9649 0.802202
\(349\) −22.1900 −1.18781 −0.593903 0.804537i \(-0.702414\pi\)
−0.593903 + 0.804537i \(0.702414\pi\)
\(350\) 0 0
\(351\) −3.25624 −0.173805
\(352\) −18.3640 −0.978807
\(353\) 17.7402 0.944215 0.472108 0.881541i \(-0.343493\pi\)
0.472108 + 0.881541i \(0.343493\pi\)
\(354\) −4.09082 −0.217425
\(355\) 32.9093 1.74665
\(356\) −6.43436 −0.341021
\(357\) 0 0
\(358\) −37.5047 −1.98219
\(359\) 8.89293 0.469351 0.234675 0.972074i \(-0.424597\pi\)
0.234675 + 0.972074i \(0.424597\pi\)
\(360\) −14.5997 −0.769471
\(361\) −15.8101 −0.832113
\(362\) 7.73343 0.406460
\(363\) 28.2268 1.48152
\(364\) 0 0
\(365\) 32.9615 1.72529
\(366\) −14.3336 −0.749228
\(367\) −0.601211 −0.0313830 −0.0156915 0.999877i \(-0.504995\pi\)
−0.0156915 + 0.999877i \(0.504995\pi\)
\(368\) −6.52437 −0.340106
\(369\) −1.00000 −0.0520579
\(370\) −32.2574 −1.67698
\(371\) 0 0
\(372\) 4.82626 0.250230
\(373\) 2.16528 0.112114 0.0560570 0.998428i \(-0.482147\pi\)
0.0560570 + 0.998428i \(0.482147\pi\)
\(374\) 2.18012 0.112732
\(375\) 13.2614 0.684817
\(376\) −45.6276 −2.35307
\(377\) −13.3005 −0.685010
\(378\) 0 0
\(379\) −5.85097 −0.300544 −0.150272 0.988645i \(-0.548015\pi\)
−0.150272 + 0.988645i \(0.548015\pi\)
\(380\) −24.1280 −1.23774
\(381\) −19.7467 −1.01165
\(382\) 2.11701 0.108316
\(383\) 5.09873 0.260533 0.130267 0.991479i \(-0.458417\pi\)
0.130267 + 0.991479i \(0.458417\pi\)
\(384\) 20.7158 1.05715
\(385\) 0 0
\(386\) 5.91030 0.300827
\(387\) −9.08247 −0.461688
\(388\) 20.2766 1.02939
\(389\) −38.2594 −1.93983 −0.969914 0.243449i \(-0.921721\pi\)
−0.969914 + 0.243449i \(0.921721\pi\)
\(390\) 28.5746 1.44693
\(391\) −0.455421 −0.0230316
\(392\) 0 0
\(393\) 19.2431 0.970687
\(394\) 38.2587 1.92745
\(395\) −38.2335 −1.92374
\(396\) −22.9463 −1.15310
\(397\) 25.6318 1.28642 0.643210 0.765689i \(-0.277602\pi\)
0.643210 + 0.765689i \(0.277602\pi\)
\(398\) −14.4840 −0.726018
\(399\) 0 0
\(400\) 18.0130 0.900649
\(401\) −6.94500 −0.346817 −0.173408 0.984850i \(-0.555478\pi\)
−0.173408 + 0.984850i \(0.555478\pi\)
\(402\) −3.30408 −0.164793
\(403\) −4.28949 −0.213675
\(404\) 58.6030 2.91561
\(405\) 3.68734 0.183225
\(406\) 0 0
\(407\) −23.0227 −1.14119
\(408\) −0.579121 −0.0286708
\(409\) −35.3203 −1.74648 −0.873238 0.487294i \(-0.837984\pi\)
−0.873238 + 0.487294i \(0.837984\pi\)
\(410\) 8.77534 0.433383
\(411\) −3.63718 −0.179409
\(412\) 66.8842 3.29515
\(413\) 0 0
\(414\) 7.41011 0.364187
\(415\) −39.2467 −1.92655
\(416\) −9.54758 −0.468109
\(417\) 15.6912 0.768403
\(418\) −26.6212 −1.30209
\(419\) −9.50778 −0.464485 −0.232243 0.972658i \(-0.574606\pi\)
−0.232243 + 0.972658i \(0.574606\pi\)
\(420\) 0 0
\(421\) −20.1034 −0.979781 −0.489891 0.871784i \(-0.662963\pi\)
−0.489891 + 0.871784i \(0.662963\pi\)
\(422\) 62.3500 3.03515
\(423\) 11.5238 0.560309
\(424\) −17.4887 −0.849329
\(425\) 1.25736 0.0609909
\(426\) −21.2401 −1.02909
\(427\) 0 0
\(428\) −12.7669 −0.617111
\(429\) 20.3942 0.984643
\(430\) 79.7017 3.84356
\(431\) −26.1665 −1.26040 −0.630199 0.776434i \(-0.717027\pi\)
−0.630199 + 0.776434i \(0.717027\pi\)
\(432\) 2.09539 0.100815
\(433\) 35.2333 1.69320 0.846601 0.532227i \(-0.178645\pi\)
0.846601 + 0.532227i \(0.178645\pi\)
\(434\) 0 0
\(435\) 15.0614 0.722138
\(436\) 44.4574 2.12912
\(437\) 5.56108 0.266023
\(438\) −21.2738 −1.01650
\(439\) −10.1078 −0.482419 −0.241210 0.970473i \(-0.577544\pi\)
−0.241210 + 0.970473i \(0.577544\pi\)
\(440\) 91.4397 4.35922
\(441\) 0 0
\(442\) 1.13346 0.0539132
\(443\) 24.3692 1.15782 0.578908 0.815393i \(-0.303479\pi\)
0.578908 + 0.815393i \(0.303479\pi\)
\(444\) 13.4675 0.639139
\(445\) −6.47585 −0.306985
\(446\) 43.6177 2.06536
\(447\) 15.4694 0.731678
\(448\) 0 0
\(449\) −19.5381 −0.922061 −0.461031 0.887384i \(-0.652520\pi\)
−0.461031 + 0.887384i \(0.652520\pi\)
\(450\) −20.4584 −0.964417
\(451\) 6.26313 0.294919
\(452\) 41.0145 1.92916
\(453\) −6.09366 −0.286305
\(454\) −43.6640 −2.04926
\(455\) 0 0
\(456\) 7.07157 0.331157
\(457\) 26.2573 1.22826 0.614132 0.789203i \(-0.289506\pi\)
0.614132 + 0.789203i \(0.289506\pi\)
\(458\) −10.0899 −0.471471
\(459\) 0.146265 0.00682705
\(460\) −42.0638 −1.96124
\(461\) 11.5537 0.538110 0.269055 0.963125i \(-0.413289\pi\)
0.269055 + 0.963125i \(0.413289\pi\)
\(462\) 0 0
\(463\) −1.17471 −0.0545936 −0.0272968 0.999627i \(-0.508690\pi\)
−0.0272968 + 0.999627i \(0.508690\pi\)
\(464\) 8.55887 0.397336
\(465\) 4.85738 0.225256
\(466\) −40.2632 −1.86516
\(467\) 5.32580 0.246449 0.123224 0.992379i \(-0.460677\pi\)
0.123224 + 0.992379i \(0.460677\pi\)
\(468\) −11.9299 −0.551462
\(469\) 0 0
\(470\) −101.126 −4.66458
\(471\) 2.07672 0.0956901
\(472\) −6.80597 −0.313270
\(473\) 56.8847 2.61556
\(474\) 24.6764 1.13343
\(475\) −15.3534 −0.704465
\(476\) 0 0
\(477\) 4.41701 0.202241
\(478\) 30.0168 1.37294
\(479\) 25.6439 1.17170 0.585849 0.810420i \(-0.300761\pi\)
0.585849 + 0.810420i \(0.300761\pi\)
\(480\) 10.8116 0.493480
\(481\) −11.9696 −0.545769
\(482\) −68.5481 −3.12228
\(483\) 0 0
\(484\) 103.415 4.70068
\(485\) 20.4073 0.926647
\(486\) −2.37986 −0.107952
\(487\) −3.25149 −0.147339 −0.0736696 0.997283i \(-0.523471\pi\)
−0.0736696 + 0.997283i \(0.523471\pi\)
\(488\) −23.8470 −1.07950
\(489\) 11.3480 0.513173
\(490\) 0 0
\(491\) −19.5010 −0.880069 −0.440034 0.897981i \(-0.645034\pi\)
−0.440034 + 0.897981i \(0.645034\pi\)
\(492\) −3.66372 −0.165173
\(493\) 0.597435 0.0269071
\(494\) −13.8405 −0.622715
\(495\) −23.0943 −1.03801
\(496\) 2.76029 0.123941
\(497\) 0 0
\(498\) 25.3303 1.13508
\(499\) 32.6281 1.46064 0.730318 0.683107i \(-0.239372\pi\)
0.730318 + 0.683107i \(0.239372\pi\)
\(500\) 48.5861 2.17284
\(501\) 19.2640 0.860652
\(502\) −71.9940 −3.21325
\(503\) −21.7937 −0.971732 −0.485866 0.874033i \(-0.661496\pi\)
−0.485866 + 0.874033i \(0.661496\pi\)
\(504\) 0 0
\(505\) 58.9808 2.62461
\(506\) −46.4105 −2.06320
\(507\) −2.39691 −0.106451
\(508\) −72.3464 −3.20985
\(509\) −18.9583 −0.840312 −0.420156 0.907452i \(-0.638025\pi\)
−0.420156 + 0.907452i \(0.638025\pi\)
\(510\) −1.28352 −0.0568353
\(511\) 0 0
\(512\) 22.7369 1.00484
\(513\) −1.78602 −0.0788546
\(514\) −44.8260 −1.97719
\(515\) 67.3154 2.96627
\(516\) −33.2756 −1.46488
\(517\) −72.1754 −3.17427
\(518\) 0 0
\(519\) −11.0874 −0.486684
\(520\) 47.5401 2.08477
\(521\) −3.35523 −0.146995 −0.0734975 0.997295i \(-0.523416\pi\)
−0.0734975 + 0.997295i \(0.523416\pi\)
\(522\) −9.72081 −0.425468
\(523\) −18.9321 −0.827843 −0.413922 0.910312i \(-0.635841\pi\)
−0.413922 + 0.910312i \(0.635841\pi\)
\(524\) 70.5014 3.07987
\(525\) 0 0
\(526\) −49.3617 −2.15227
\(527\) 0.192676 0.00839311
\(528\) −13.1237 −0.571136
\(529\) −13.3050 −0.578479
\(530\) −38.7608 −1.68366
\(531\) 1.71894 0.0745955
\(532\) 0 0
\(533\) 3.25624 0.141043
\(534\) 4.17960 0.180869
\(535\) −12.8492 −0.555520
\(536\) −5.49706 −0.237437
\(537\) 15.7592 0.680062
\(538\) 5.38253 0.232057
\(539\) 0 0
\(540\) 13.5094 0.581351
\(541\) 28.6878 1.23339 0.616693 0.787204i \(-0.288472\pi\)
0.616693 + 0.787204i \(0.288472\pi\)
\(542\) 59.9482 2.57499
\(543\) −3.24953 −0.139451
\(544\) 0.428861 0.0183872
\(545\) 44.7441 1.91662
\(546\) 0 0
\(547\) 25.8811 1.10659 0.553297 0.832984i \(-0.313369\pi\)
0.553297 + 0.832984i \(0.313369\pi\)
\(548\) −13.3256 −0.569242
\(549\) 6.02287 0.257050
\(550\) 128.133 5.46363
\(551\) −7.29520 −0.310786
\(552\) 12.3283 0.524728
\(553\) 0 0
\(554\) 24.3809 1.03585
\(555\) 13.5543 0.575349
\(556\) 57.4883 2.43805
\(557\) 23.2849 0.986614 0.493307 0.869855i \(-0.335788\pi\)
0.493307 + 0.869855i \(0.335788\pi\)
\(558\) −3.13502 −0.132716
\(559\) 29.5747 1.25088
\(560\) 0 0
\(561\) −0.916074 −0.0386767
\(562\) −16.0974 −0.679029
\(563\) −32.5005 −1.36973 −0.684867 0.728668i \(-0.740140\pi\)
−0.684867 + 0.728668i \(0.740140\pi\)
\(564\) 42.2201 1.77779
\(565\) 41.2790 1.73662
\(566\) −4.94332 −0.207783
\(567\) 0 0
\(568\) −35.3375 −1.48273
\(569\) −17.0193 −0.713486 −0.356743 0.934203i \(-0.616113\pi\)
−0.356743 + 0.934203i \(0.616113\pi\)
\(570\) 15.6729 0.656466
\(571\) 29.9442 1.25313 0.626564 0.779370i \(-0.284461\pi\)
0.626564 + 0.779370i \(0.284461\pi\)
\(572\) 74.7187 3.12415
\(573\) −0.889555 −0.0371617
\(574\) 0 0
\(575\) −26.7666 −1.11625
\(576\) −11.1687 −0.465364
\(577\) −22.0478 −0.917862 −0.458931 0.888472i \(-0.651767\pi\)
−0.458931 + 0.888472i \(0.651767\pi\)
\(578\) 40.4066 1.68070
\(579\) −2.48347 −0.103210
\(580\) 55.1806 2.29125
\(581\) 0 0
\(582\) −13.1711 −0.545961
\(583\) −27.6643 −1.14574
\(584\) −35.3936 −1.46460
\(585\) −12.0069 −0.496422
\(586\) 20.7301 0.856351
\(587\) −34.5456 −1.42585 −0.712924 0.701241i \(-0.752630\pi\)
−0.712924 + 0.701241i \(0.752630\pi\)
\(588\) 0 0
\(589\) −2.35274 −0.0969431
\(590\) −15.0842 −0.621009
\(591\) −16.0761 −0.661281
\(592\) 7.70247 0.316569
\(593\) −20.0432 −0.823076 −0.411538 0.911393i \(-0.635008\pi\)
−0.411538 + 0.911393i \(0.635008\pi\)
\(594\) 14.9053 0.611574
\(595\) 0 0
\(596\) 56.6755 2.32152
\(597\) 6.08609 0.249087
\(598\) −24.1291 −0.986711
\(599\) 28.6415 1.17026 0.585130 0.810940i \(-0.301044\pi\)
0.585130 + 0.810940i \(0.301044\pi\)
\(600\) −34.0370 −1.38955
\(601\) 19.4285 0.792506 0.396253 0.918141i \(-0.370310\pi\)
0.396253 + 0.918141i \(0.370310\pi\)
\(602\) 0 0
\(603\) 1.38835 0.0565382
\(604\) −22.3254 −0.908409
\(605\) 104.082 4.23153
\(606\) −38.0670 −1.54637
\(607\) −9.75872 −0.396094 −0.198047 0.980193i \(-0.563460\pi\)
−0.198047 + 0.980193i \(0.563460\pi\)
\(608\) −5.23676 −0.212379
\(609\) 0 0
\(610\) −52.8527 −2.13994
\(611\) −37.5244 −1.51807
\(612\) 0.535872 0.0216613
\(613\) 16.3639 0.660934 0.330467 0.943818i \(-0.392794\pi\)
0.330467 + 0.943818i \(0.392794\pi\)
\(614\) 64.9089 2.61951
\(615\) −3.68734 −0.148688
\(616\) 0 0
\(617\) −6.22352 −0.250549 −0.125275 0.992122i \(-0.539981\pi\)
−0.125275 + 0.992122i \(0.539981\pi\)
\(618\) −43.4462 −1.74766
\(619\) −36.5437 −1.46882 −0.734408 0.678709i \(-0.762540\pi\)
−0.734408 + 0.678709i \(0.762540\pi\)
\(620\) 17.7961 0.714707
\(621\) −3.11368 −0.124948
\(622\) −24.5794 −0.985545
\(623\) 0 0
\(624\) −6.82309 −0.273142
\(625\) 5.91698 0.236679
\(626\) 71.7014 2.86576
\(627\) 11.1861 0.446728
\(628\) 7.60851 0.303613
\(629\) 0.537655 0.0214377
\(630\) 0 0
\(631\) 34.5755 1.37643 0.688215 0.725506i \(-0.258394\pi\)
0.688215 + 0.725506i \(0.258394\pi\)
\(632\) 41.0546 1.63306
\(633\) −26.1991 −1.04132
\(634\) −46.7581 −1.85700
\(635\) −72.8128 −2.88949
\(636\) 16.1827 0.641685
\(637\) 0 0
\(638\) 60.8827 2.41037
\(639\) 8.92495 0.353066
\(640\) 76.3862 3.01943
\(641\) −45.6225 −1.80198 −0.900990 0.433839i \(-0.857159\pi\)
−0.900990 + 0.433839i \(0.857159\pi\)
\(642\) 8.29305 0.327300
\(643\) −6.12623 −0.241595 −0.120797 0.992677i \(-0.538545\pi\)
−0.120797 + 0.992677i \(0.538545\pi\)
\(644\) 0 0
\(645\) −33.4901 −1.31867
\(646\) 0.621693 0.0244602
\(647\) −21.5628 −0.847720 −0.423860 0.905728i \(-0.639325\pi\)
−0.423860 + 0.905728i \(0.639325\pi\)
\(648\) −3.95941 −0.155540
\(649\) −10.7659 −0.422599
\(650\) 66.6173 2.61295
\(651\) 0 0
\(652\) 41.5757 1.62823
\(653\) −2.57822 −0.100894 −0.0504468 0.998727i \(-0.516065\pi\)
−0.0504468 + 0.998727i \(0.516065\pi\)
\(654\) −28.8784 −1.12923
\(655\) 70.9559 2.77248
\(656\) −2.09539 −0.0818113
\(657\) 8.93911 0.348748
\(658\) 0 0
\(659\) 7.93310 0.309030 0.154515 0.987990i \(-0.450619\pi\)
0.154515 + 0.987990i \(0.450619\pi\)
\(660\) −84.6109 −3.29348
\(661\) −2.46160 −0.0957452 −0.0478726 0.998853i \(-0.515244\pi\)
−0.0478726 + 0.998853i \(0.515244\pi\)
\(662\) 78.8666 3.06524
\(663\) −0.476272 −0.0184969
\(664\) 42.1425 1.63545
\(665\) 0 0
\(666\) −8.74814 −0.338983
\(667\) −12.7182 −0.492450
\(668\) 70.5779 2.73074
\(669\) −18.3279 −0.708597
\(670\) −12.1833 −0.470681
\(671\) −37.7220 −1.45624
\(672\) 0 0
\(673\) 46.3505 1.78668 0.893339 0.449383i \(-0.148356\pi\)
0.893339 + 0.449383i \(0.148356\pi\)
\(674\) −51.5652 −1.98622
\(675\) 8.59647 0.330878
\(676\) −8.78160 −0.337754
\(677\) −22.5487 −0.866617 −0.433309 0.901246i \(-0.642654\pi\)
−0.433309 + 0.901246i \(0.642654\pi\)
\(678\) −26.6420 −1.02318
\(679\) 0 0
\(680\) −2.13542 −0.0818895
\(681\) 18.3473 0.703072
\(682\) 19.6350 0.751864
\(683\) −5.94771 −0.227583 −0.113791 0.993505i \(-0.536300\pi\)
−0.113791 + 0.993505i \(0.536300\pi\)
\(684\) −6.54346 −0.250196
\(685\) −13.4115 −0.512428
\(686\) 0 0
\(687\) 4.23971 0.161755
\(688\) −19.0313 −0.725562
\(689\) −14.3828 −0.547942
\(690\) 27.3236 1.04019
\(691\) 46.6357 1.77411 0.887054 0.461666i \(-0.152748\pi\)
0.887054 + 0.461666i \(0.152748\pi\)
\(692\) −40.6212 −1.54419
\(693\) 0 0
\(694\) −51.3661 −1.94983
\(695\) 57.8589 2.19471
\(696\) −16.1727 −0.613024
\(697\) −0.146265 −0.00554017
\(698\) 52.8091 1.99885
\(699\) 16.9183 0.639910
\(700\) 0 0
\(701\) −19.9123 −0.752078 −0.376039 0.926604i \(-0.622714\pi\)
−0.376039 + 0.926604i \(0.622714\pi\)
\(702\) 7.74938 0.292482
\(703\) −6.56524 −0.247613
\(704\) 69.9512 2.63639
\(705\) 42.4923 1.60035
\(706\) −42.2191 −1.58894
\(707\) 0 0
\(708\) 6.29769 0.236682
\(709\) 23.9798 0.900580 0.450290 0.892882i \(-0.351321\pi\)
0.450290 + 0.892882i \(0.351321\pi\)
\(710\) −78.3195 −2.93928
\(711\) −10.3689 −0.388863
\(712\) 6.95367 0.260600
\(713\) −4.10169 −0.153609
\(714\) 0 0
\(715\) 75.2005 2.81234
\(716\) 57.7374 2.15775
\(717\) −12.6129 −0.471036
\(718\) −21.1639 −0.789830
\(719\) −16.6841 −0.622213 −0.311107 0.950375i \(-0.600700\pi\)
−0.311107 + 0.950375i \(0.600700\pi\)
\(720\) 7.72642 0.287947
\(721\) 0 0
\(722\) 37.6259 1.40029
\(723\) 28.8035 1.07121
\(724\) −11.9054 −0.442460
\(725\) 35.1133 1.30408
\(726\) −67.1757 −2.49312
\(727\) −21.5134 −0.797888 −0.398944 0.916975i \(-0.630623\pi\)
−0.398944 + 0.916975i \(0.630623\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −78.4437 −2.90333
\(731\) −1.32844 −0.0491342
\(732\) 22.0661 0.815586
\(733\) 13.7896 0.509330 0.254665 0.967029i \(-0.418035\pi\)
0.254665 + 0.967029i \(0.418035\pi\)
\(734\) 1.43080 0.0528116
\(735\) 0 0
\(736\) −9.12958 −0.336521
\(737\) −8.69544 −0.320301
\(738\) 2.37986 0.0876037
\(739\) 52.1005 1.91655 0.958273 0.285854i \(-0.0922773\pi\)
0.958273 + 0.285854i \(0.0922773\pi\)
\(740\) 49.6592 1.82551
\(741\) 5.81570 0.213645
\(742\) 0 0
\(743\) −7.82960 −0.287240 −0.143620 0.989633i \(-0.545874\pi\)
−0.143620 + 0.989633i \(0.545874\pi\)
\(744\) −5.21578 −0.191220
\(745\) 57.0409 2.08982
\(746\) −5.15306 −0.188667
\(747\) −10.6436 −0.389431
\(748\) −3.35624 −0.122716
\(749\) 0 0
\(750\) −31.5603 −1.15242
\(751\) 24.7094 0.901659 0.450829 0.892610i \(-0.351128\pi\)
0.450829 + 0.892610i \(0.351128\pi\)
\(752\) 24.1470 0.880549
\(753\) 30.2514 1.10242
\(754\) 31.6533 1.15274
\(755\) −22.4694 −0.817744
\(756\) 0 0
\(757\) 3.24530 0.117952 0.0589762 0.998259i \(-0.481216\pi\)
0.0589762 + 0.998259i \(0.481216\pi\)
\(758\) 13.9245 0.505760
\(759\) 19.5014 0.707855
\(760\) 26.0753 0.945850
\(761\) −23.8904 −0.866027 −0.433013 0.901387i \(-0.642550\pi\)
−0.433013 + 0.901387i \(0.642550\pi\)
\(762\) 46.9943 1.70243
\(763\) 0 0
\(764\) −3.25908 −0.117909
\(765\) 0.539327 0.0194994
\(766\) −12.1343 −0.438429
\(767\) −5.59726 −0.202106
\(768\) −26.9632 −0.972950
\(769\) 7.71831 0.278329 0.139165 0.990269i \(-0.455558\pi\)
0.139165 + 0.990269i \(0.455558\pi\)
\(770\) 0 0
\(771\) 18.8356 0.678347
\(772\) −9.09873 −0.327471
\(773\) 17.9179 0.644461 0.322231 0.946661i \(-0.395567\pi\)
0.322231 + 0.946661i \(0.395567\pi\)
\(774\) 21.6150 0.776934
\(775\) 11.3242 0.406779
\(776\) −21.9130 −0.786632
\(777\) 0 0
\(778\) 91.0518 3.26437
\(779\) 1.78602 0.0639907
\(780\) −43.9897 −1.57509
\(781\) −55.8981 −2.00019
\(782\) 1.08384 0.0387579
\(783\) 4.08462 0.145972
\(784\) 0 0
\(785\) 7.65757 0.273310
\(786\) −45.7959 −1.63349
\(787\) −27.3832 −0.976104 −0.488052 0.872814i \(-0.662292\pi\)
−0.488052 + 0.872814i \(0.662292\pi\)
\(788\) −58.8982 −2.09816
\(789\) 20.7414 0.738415
\(790\) 90.9903 3.23729
\(791\) 0 0
\(792\) 24.7983 0.881169
\(793\) −19.6119 −0.696439
\(794\) −60.9999 −2.16481
\(795\) 16.2870 0.577641
\(796\) 22.2977 0.790322
\(797\) −11.0166 −0.390229 −0.195114 0.980781i \(-0.562508\pi\)
−0.195114 + 0.980781i \(0.562508\pi\)
\(798\) 0 0
\(799\) 1.68553 0.0596298
\(800\) 25.2056 0.891153
\(801\) −1.75624 −0.0620537
\(802\) 16.5281 0.583627
\(803\) −55.9868 −1.97573
\(804\) 5.08654 0.179388
\(805\) 0 0
\(806\) 10.2084 0.359574
\(807\) −2.26170 −0.0796157
\(808\) −63.3327 −2.22804
\(809\) −17.9023 −0.629413 −0.314706 0.949189i \(-0.601906\pi\)
−0.314706 + 0.949189i \(0.601906\pi\)
\(810\) −8.77534 −0.308334
\(811\) 30.4616 1.06965 0.534826 0.844962i \(-0.320377\pi\)
0.534826 + 0.844962i \(0.320377\pi\)
\(812\) 0 0
\(813\) −25.1898 −0.883446
\(814\) 54.7907 1.92041
\(815\) 41.8438 1.46572
\(816\) 0.306481 0.0107290
\(817\) 16.2214 0.567516
\(818\) 84.0572 2.93899
\(819\) 0 0
\(820\) −13.5094 −0.471768
\(821\) 24.3154 0.848614 0.424307 0.905518i \(-0.360518\pi\)
0.424307 + 0.905518i \(0.360518\pi\)
\(822\) 8.65597 0.301912
\(823\) −47.9101 −1.67004 −0.835020 0.550220i \(-0.814544\pi\)
−0.835020 + 0.550220i \(0.814544\pi\)
\(824\) −72.2823 −2.51807
\(825\) −53.8408 −1.87450
\(826\) 0 0
\(827\) 17.4163 0.605624 0.302812 0.953050i \(-0.402075\pi\)
0.302812 + 0.953050i \(0.402075\pi\)
\(828\) −11.4076 −0.396443
\(829\) 5.83275 0.202580 0.101290 0.994857i \(-0.467703\pi\)
0.101290 + 0.994857i \(0.467703\pi\)
\(830\) 93.4016 3.24202
\(831\) −10.2447 −0.355385
\(832\) 36.3681 1.26084
\(833\) 0 0
\(834\) −37.3429 −1.29308
\(835\) 71.0329 2.45820
\(836\) 40.9826 1.41741
\(837\) 1.31731 0.0455330
\(838\) 22.6271 0.781642
\(839\) 20.2271 0.698316 0.349158 0.937064i \(-0.386468\pi\)
0.349158 + 0.937064i \(0.386468\pi\)
\(840\) 0 0
\(841\) −12.3159 −0.424686
\(842\) 47.8433 1.64879
\(843\) 6.76403 0.232966
\(844\) −95.9860 −3.30397
\(845\) −8.83822 −0.304044
\(846\) −27.4251 −0.942895
\(847\) 0 0
\(848\) 9.25536 0.317830
\(849\) 2.07715 0.0712876
\(850\) −2.99234 −0.102636
\(851\) −11.4456 −0.392350
\(852\) 32.6985 1.12023
\(853\) −12.0327 −0.411992 −0.205996 0.978553i \(-0.566043\pi\)
−0.205996 + 0.978553i \(0.566043\pi\)
\(854\) 0 0
\(855\) −6.58565 −0.225225
\(856\) 13.7973 0.471582
\(857\) 0.405363 0.0138469 0.00692347 0.999976i \(-0.497796\pi\)
0.00692347 + 0.999976i \(0.497796\pi\)
\(858\) −48.5354 −1.65697
\(859\) −15.9365 −0.543748 −0.271874 0.962333i \(-0.587643\pi\)
−0.271874 + 0.962333i \(0.587643\pi\)
\(860\) −122.698 −4.18398
\(861\) 0 0
\(862\) 62.2726 2.12101
\(863\) −28.1342 −0.957698 −0.478849 0.877897i \(-0.658946\pi\)
−0.478849 + 0.877897i \(0.658946\pi\)
\(864\) 2.93209 0.0997517
\(865\) −40.8831 −1.39007
\(866\) −83.8501 −2.84934
\(867\) −16.9786 −0.576624
\(868\) 0 0
\(869\) 64.9416 2.20299
\(870\) −35.8439 −1.21522
\(871\) −4.52081 −0.153182
\(872\) −48.0455 −1.62703
\(873\) 5.53442 0.187312
\(874\) −13.2346 −0.447666
\(875\) 0 0
\(876\) 32.7504 1.10653
\(877\) 4.69948 0.158690 0.0793451 0.996847i \(-0.474717\pi\)
0.0793451 + 0.996847i \(0.474717\pi\)
\(878\) 24.0551 0.811821
\(879\) −8.71064 −0.293802
\(880\) −48.3916 −1.63128
\(881\) −12.0182 −0.404904 −0.202452 0.979292i \(-0.564891\pi\)
−0.202452 + 0.979292i \(0.564891\pi\)
\(882\) 0 0
\(883\) 59.0988 1.98883 0.994417 0.105520i \(-0.0336507\pi\)
0.994417 + 0.105520i \(0.0336507\pi\)
\(884\) −1.74493 −0.0586883
\(885\) 6.33830 0.213060
\(886\) −57.9952 −1.94839
\(887\) 46.1453 1.54941 0.774704 0.632324i \(-0.217899\pi\)
0.774704 + 0.632324i \(0.217899\pi\)
\(888\) −14.5544 −0.488415
\(889\) 0 0
\(890\) 15.4116 0.516598
\(891\) −6.26313 −0.209823
\(892\) −67.1482 −2.24829
\(893\) −20.5818 −0.688743
\(894\) −36.8150 −1.23128
\(895\) 58.1097 1.94239
\(896\) 0 0
\(897\) 10.1389 0.338527
\(898\) 46.4980 1.55166
\(899\) 5.38072 0.179457
\(900\) 31.4950 1.04983
\(901\) 0.646052 0.0215231
\(902\) −14.9053 −0.496294
\(903\) 0 0
\(904\) −44.3247 −1.47422
\(905\) −11.9821 −0.398300
\(906\) 14.5020 0.481798
\(907\) 21.7744 0.723008 0.361504 0.932370i \(-0.382263\pi\)
0.361504 + 0.932370i \(0.382263\pi\)
\(908\) 67.2195 2.23076
\(909\) 15.9955 0.530537
\(910\) 0 0
\(911\) 39.8850 1.32145 0.660724 0.750629i \(-0.270249\pi\)
0.660724 + 0.750629i \(0.270249\pi\)
\(912\) −3.74240 −0.123923
\(913\) 66.6625 2.20621
\(914\) −62.4886 −2.06694
\(915\) 22.2084 0.734186
\(916\) 15.5331 0.513228
\(917\) 0 0
\(918\) −0.348089 −0.0114886
\(919\) −50.3237 −1.66002 −0.830012 0.557745i \(-0.811667\pi\)
−0.830012 + 0.557745i \(0.811667\pi\)
\(920\) 45.4587 1.49873
\(921\) −27.2743 −0.898718
\(922\) −27.4962 −0.905538
\(923\) −29.0618 −0.956580
\(924\) 0 0
\(925\) 31.5999 1.03900
\(926\) 2.79565 0.0918707
\(927\) 18.2558 0.599600
\(928\) 11.9765 0.393147
\(929\) −23.1421 −0.759267 −0.379633 0.925137i \(-0.623950\pi\)
−0.379633 + 0.925137i \(0.623950\pi\)
\(930\) −11.5599 −0.379063
\(931\) 0 0
\(932\) 61.9840 2.03035
\(933\) 10.3281 0.338127
\(934\) −12.6746 −0.414727
\(935\) −3.37788 −0.110468
\(936\) 12.8928 0.421414
\(937\) −28.0250 −0.915535 −0.457768 0.889072i \(-0.651351\pi\)
−0.457768 + 0.889072i \(0.651351\pi\)
\(938\) 0 0
\(939\) −30.1284 −0.983204
\(940\) 155.680 5.07772
\(941\) 1.30089 0.0424079 0.0212040 0.999775i \(-0.493250\pi\)
0.0212040 + 0.999775i \(0.493250\pi\)
\(942\) −4.94229 −0.161029
\(943\) 3.11368 0.101395
\(944\) 3.60184 0.117230
\(945\) 0 0
\(946\) −135.377 −4.40150
\(947\) −28.0944 −0.912944 −0.456472 0.889738i \(-0.650887\pi\)
−0.456472 + 0.889738i \(0.650887\pi\)
\(948\) −37.9886 −1.23381
\(949\) −29.1079 −0.944882
\(950\) 36.5390 1.18548
\(951\) 19.6474 0.637112
\(952\) 0 0
\(953\) −32.4370 −1.05074 −0.525368 0.850875i \(-0.676073\pi\)
−0.525368 + 0.850875i \(0.676073\pi\)
\(954\) −10.5118 −0.340334
\(955\) −3.28009 −0.106141
\(956\) −46.2100 −1.49454
\(957\) −25.5825 −0.826965
\(958\) −61.0287 −1.97175
\(959\) 0 0
\(960\) −41.1829 −1.32917
\(961\) −29.2647 −0.944022
\(962\) 28.4860 0.918426
\(963\) −3.48468 −0.112292
\(964\) 105.528 3.39882
\(965\) −9.15740 −0.294787
\(966\) 0 0
\(967\) −50.6459 −1.62866 −0.814331 0.580401i \(-0.802896\pi\)
−0.814331 + 0.580401i \(0.802896\pi\)
\(968\) −111.761 −3.59215
\(969\) −0.261231 −0.00839195
\(970\) −48.5664 −1.55937
\(971\) −11.8113 −0.379042 −0.189521 0.981877i \(-0.560693\pi\)
−0.189521 + 0.981877i \(0.560693\pi\)
\(972\) 3.66372 0.117514
\(973\) 0 0
\(974\) 7.73808 0.247944
\(975\) −27.9922 −0.896467
\(976\) 12.6203 0.403965
\(977\) 54.8172 1.75376 0.876879 0.480710i \(-0.159621\pi\)
0.876879 + 0.480710i \(0.159621\pi\)
\(978\) −27.0065 −0.863573
\(979\) 10.9996 0.351547
\(980\) 0 0
\(981\) 12.1345 0.387425
\(982\) 46.4096 1.48099
\(983\) −5.79541 −0.184845 −0.0924224 0.995720i \(-0.529461\pi\)
−0.0924224 + 0.995720i \(0.529461\pi\)
\(984\) 3.95941 0.126221
\(985\) −59.2779 −1.88875
\(986\) −1.42181 −0.0452797
\(987\) 0 0
\(988\) 21.3071 0.677868
\(989\) 28.2799 0.899248
\(990\) 54.9611 1.74678
\(991\) −18.5305 −0.588642 −0.294321 0.955707i \(-0.595093\pi\)
−0.294321 + 0.955707i \(0.595093\pi\)
\(992\) 3.86248 0.122634
\(993\) −33.1392 −1.05164
\(994\) 0 0
\(995\) 22.4415 0.711443
\(996\) −38.9953 −1.23561
\(997\) 40.1082 1.27024 0.635119 0.772414i \(-0.280951\pi\)
0.635119 + 0.772414i \(0.280951\pi\)
\(998\) −77.6503 −2.45798
\(999\) 3.67591 0.116301
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 \(a_p\))