Properties

Label 6027.2.a.bn.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 \(-0.808551\pi\)
−0.824514 + 0.565841i \(0.808551\pi\)
\(6\) 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 \(-0.350868\pi\)
0.451559 + 0.892241i \(0.350868\pi\)
\(14\) 0 0
\(15\) 3.68734 0.952067
\(16\) 2.09539 0.523848
\(17\) −0.146265 −0.0354744 −0.0177372 0.999843i \(-0.505646\pi\)
−0.0177372 + 0.999843i \(0.505646\pi\)
\(18\) −2.37986 −0.560938
\(19\) 1.78602 0.409741 0.204870 0.978789i \(-0.434323\pi\)
0.204870 + 0.978789i \(0.434323\pi\)
\(20\) −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 \(-0.537744\pi\)
−0.118298 + 0.992978i \(0.537744\pi\)
\(32\) 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 \(-0.817717\pi\)
−0.840463 + 0.541869i \(0.817717\pi\)
\(48\) −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 \(-0.535691\pi\)
−0.111893 + 0.993720i \(0.535691\pi\)
\(60\) 13.5094 1.74405
\(61\) −6.02287 −0.771150 −0.385575 0.922677i \(-0.625997\pi\)
−0.385575 + 0.922677i \(0.625997\pi\)
\(62\) 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 \(-0.675233\pi\)
−0.523122 + 0.852258i \(0.675233\pi\)
\(74\) −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 \(-0.301430\pi\)
0.584146 + 0.811649i \(0.301430\pi\)
\(84\) 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 \(-0.470329\pi\)
0.0930805 + 0.995659i \(0.470329\pi\)
\(90\) 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 \(-0.590655\pi\)
−0.280968 + 0.959717i \(0.590655\pi\)
\(98\) 0 0
\(99\) −6.26313 −0.629468
\(100\) 31.4950 3.14950
\(101\) −15.9955 −1.59161 −0.795806 0.605552i \(-0.792952\pi\)
−0.795806 + 0.605552i \(0.792952\pi\)
\(102\) −0.348089 −0.0344659
\(103\) −18.2558 −1.79880 −0.899400 0.437127i \(-0.855996\pi\)
−0.899400 + 0.437127i \(0.855996\pi\)
\(104\) −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 \(-0.817821\pi\)
−0.840640 + 0.541594i \(0.817821\pi\)
\(132\) 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 \(-0.731763\pi\)
−0.665457 + 0.746436i \(0.731763\pi\)
\(140\) 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 \(-0.526409\pi\)
−0.0828701 + 0.996560i \(0.526409\pi\)
\(158\) 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 \(-0.767716\pi\)
−0.745347 + 0.666677i \(0.767716\pi\)
\(168\) 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 \(-0.361511\pi\)
0.421481 + 0.906837i \(0.361511\pi\)
\(174\) 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 \(-0.461464\pi\)
0.120768 + 0.992681i \(0.461464\pi\)
\(182\) 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 \(-0.569208\pi\)
−0.215716 + 0.976456i \(0.569208\pi\)
\(200\) −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 \(-0.289695\pi\)
0.613663 + 0.789568i \(0.289695\pi\)
\(224\) 0 0
\(225\) 8.59647 0.573098
\(226\) −26.6420 −1.77220
\(227\) −18.3473 −1.21776 −0.608878 0.793264i \(-0.708380\pi\)
−0.608878 + 0.793264i \(0.708380\pi\)
\(228\) −6.54346 −0.433351
\(229\) −4.23971 −0.280168 −0.140084 0.990140i \(-0.544737\pi\)
−0.140084 + 0.990140i \(0.544737\pi\)
\(230\) −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 \(-0.878214\pi\)
−0.927697 + 0.373334i \(0.878214\pi\)
\(242\) −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 \(-0.903851\pi\)
−0.954726 + 0.297488i \(0.903851\pi\)
\(252\) 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 \(-0.699874\pi\)
−0.587466 + 0.809249i \(0.699874\pi\)
\(258\) −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 \(-0.478035\pi\)
0.0689492 + 0.997620i \(0.478035\pi\)
\(270\) −8.77534 −0.534050
\(271\) 25.1898 1.53017 0.765086 0.643928i \(-0.222696\pi\)
0.765086 + 0.643928i \(0.222696\pi\)
\(272\) −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 \(-0.519664\pi\)
−0.0617369 + 0.998092i \(0.519664\pi\)
\(284\) 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 \(-0.418109\pi\)
0.254440 + 0.967088i \(0.418109\pi\)
\(294\) 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 \(-0.216076\pi\)
0.778312 + 0.627877i \(0.216076\pi\)
\(308\) 0 0
\(309\) 18.2558 1.03854
\(310\) −11.5599 −0.656556
\(311\) −10.3281 −0.585654 −0.292827 0.956166i \(-0.594596\pi\)
−0.292827 + 0.956166i \(0.594596\pi\)
\(312\) 12.8928 0.729910
\(313\) 30.1284 1.70296 0.851480 0.524387i \(-0.175705\pi\)
0.851480 + 0.524387i \(0.175705\pi\)
\(314\) 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 \(-0.297586\pi\)
0.593903 + 0.804537i \(0.297586\pi\)
\(350\) 0 0
\(351\) −3.25624 −0.173805
\(352\) −18.3640 −0.978807
\(353\) −17.7402 −0.944215 −0.472108 0.881541i \(-0.656507\pi\)
−0.472108 + 0.881541i \(0.656507\pi\)
\(354\) −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 \(-0.495005\pi\)
0.0156915 + 0.999877i \(0.495005\pi\)
\(368\) −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 \(-0.541583\pi\)
−0.130267 + 0.991479i \(0.541583\pi\)
\(384\) −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 \(-0.722398\pi\)
−0.643210 + 0.765689i \(0.722398\pi\)
\(398\) 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 \(-0.162016\pi\)
0.873238 + 0.487294i \(0.162016\pi\)
\(410\) 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 \(-0.425394\pi\)
0.232243 + 0.972658i \(0.425394\pi\)
\(420\) 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 \(-0.821355\pi\)
−0.846601 + 0.532227i \(0.821355\pi\)
\(434\) 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 \(-0.422456\pi\)
0.241210 + 0.970473i \(0.422456\pi\)
\(440\) −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 \(-0.586711\pi\)
−0.269055 + 0.963125i \(0.586711\pi\)
\(462\) 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 \(-0.539323\pi\)
−0.123224 + 0.992379i \(0.539323\pi\)
\(468\) 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 \(-0.699239\pi\)
−0.585849 + 0.810420i \(0.699239\pi\)
\(480\) 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 \(-0.338504\pi\)
0.485866 + 0.874033i \(0.338504\pi\)
\(504\) 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 \(-0.361975\pi\)
0.420156 + 0.907452i \(0.361975\pi\)
\(510\) 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 \(-0.476584\pi\)
0.0734975 + 0.997295i \(0.476584\pi\)
\(522\) −9.72081 −0.425468
\(523\) 18.9321 0.827843 0.413922 0.910312i \(-0.364159\pi\)
0.413922 + 0.910312i \(0.364159\pi\)
\(524\) −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 \(-0.259860\pi\)
0.684867 + 0.728668i \(0.259860\pi\)
\(564\) 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 \(-0.348233\pi\)
0.458931 + 0.888472i \(0.348233\pi\)
\(578\) 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 \(-0.247370\pi\)
0.712924 + 0.701241i \(0.247370\pi\)
\(588\) 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 \(-0.364992\pi\)
0.411538 + 0.911393i \(0.364992\pi\)
\(594\) −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 \(-0.629690\pi\)
−0.396253 + 0.918141i \(0.629690\pi\)
\(602\) 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 \(-0.436540\pi\)
0.198047 + 0.980193i \(0.436540\pi\)
\(608\) 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 \(-0.237460\pi\)
0.734408 + 0.678709i \(0.237460\pi\)
\(620\) 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 \(-0.461455\pi\)
0.120797 + 0.992677i \(0.461455\pi\)
\(644\) 0 0
\(645\) −33.4901 −1.31867
\(646\) 0.621693 0.0244602
\(647\) 21.5628 0.847720 0.423860 0.905728i \(-0.360675\pi\)
0.423860 + 0.905728i \(0.360675\pi\)
\(648\) −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 \(-0.484756\pi\)
0.0478726 + 0.998853i \(0.484756\pi\)
\(662\) 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 \(-0.357346\pi\)
0.433309 + 0.901246i \(0.357346\pi\)
\(678\) 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 \(-0.847252\pi\)
−0.887054 + 0.461666i \(0.847252\pi\)
\(692\) 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 \(-0.399300\pi\)
0.311107 + 0.950375i \(0.399300\pi\)
\(720\) −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 \(-0.369377\pi\)
0.398944 + 0.916975i \(0.369377\pi\)
\(728\) 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 \(-0.581965\pi\)
−0.254665 + 0.967029i \(0.581965\pi\)
\(734\) −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 \(-0.357450\pi\)
0.433013 + 0.901387i \(0.357450\pi\)
\(762\) −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 \(-0.544442\pi\)
−0.139165 + 0.990269i \(0.544442\pi\)
\(770\) 0 0
\(771\) 18.8356 0.678347
\(772\) −9.09873 −0.327471
\(773\) −17.9179 −0.644461 −0.322231 0.946661i \(-0.604433\pi\)
−0.322231 + 0.946661i \(0.604433\pi\)
\(774\) 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 \(-0.337708\pi\)
0.488052 + 0.872814i \(0.337708\pi\)
\(788\) −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 \(-0.437492\pi\)
0.195114 + 0.980781i \(0.437492\pi\)
\(798\) 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 \(-0.679623\pi\)
−0.534826 + 0.844962i \(0.679623\pi\)
\(812\) 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 \(-0.532297\pi\)
−0.101290 + 0.994857i \(0.532297\pi\)
\(830\) 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 \(-0.613532\pi\)
−0.349158 + 0.937064i \(0.613532\pi\)
\(840\) 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 \(-0.433957\pi\)
0.205996 + 0.978553i \(0.433957\pi\)
\(854\) 0 0
\(855\) −6.58565 −0.225225
\(856\) 13.7973 0.471582
\(857\) −0.405363 −0.0138469 −0.00692347 0.999976i \(-0.502204\pi\)
−0.00692347 + 0.999976i \(0.502204\pi\)
\(858\) −48.5354 −1.65697
\(859\) 15.9365 0.543748 0.271874 0.962333i \(-0.412357\pi\)
0.271874 + 0.962333i \(0.412357\pi\)
\(860\) 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 \(-0.435109\pi\)
0.202452 + 0.979292i \(0.435109\pi\)
\(882\) 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 \(-0.782101\pi\)
−0.774704 + 0.632324i \(0.782101\pi\)
\(888\) 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 \(-0.376050\pi\)
0.379633 + 0.925137i \(0.376050\pi\)
\(930\) 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 \(-0.348649\pi\)
0.457768 + 0.889072i \(0.348649\pi\)
\(938\) 0 0
\(939\) −30.1284 −0.983204
\(940\) 155.680 5.07772
\(941\) −1.30089 −0.0424079 −0.0212040 0.999775i \(-0.506750\pi\)
−0.0212040 + 0.999775i \(0.506750\pi\)
\(942\) −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 \(-0.439307\pi\)
0.189521 + 0.981877i \(0.439307\pi\)
\(972\) −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 \(-0.470539\pi\)
0.0924224 + 0.995720i \(0.470539\pi\)
\(984\) 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 \(-0.719049\pi\)
−0.635119 + 0.772414i \(0.719049\pi\)
\(998\) −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 \(a_p\))