Properties

Label 6027.2.a.bm.1.12
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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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: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(-1.10456\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.10456 q^{2} +1.00000 q^{3} -0.779950 q^{4} -3.67747 q^{5} +1.10456 q^{6} -3.07062 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.10456 q^{2} +1.00000 q^{3} -0.779950 q^{4} -3.67747 q^{5} +1.10456 q^{6} -3.07062 q^{8} +1.00000 q^{9} -4.06198 q^{10} +1.52221 q^{11} -0.779950 q^{12} +3.67604 q^{13} -3.67747 q^{15} -1.83178 q^{16} -4.16206 q^{17} +1.10456 q^{18} +5.23036 q^{19} +2.86824 q^{20} +1.68137 q^{22} +1.53784 q^{23} -3.07062 q^{24} +8.52379 q^{25} +4.06040 q^{26} +1.00000 q^{27} -8.04051 q^{29} -4.06198 q^{30} +8.26086 q^{31} +4.11793 q^{32} +1.52221 q^{33} -4.59724 q^{34} -0.779950 q^{36} -9.47010 q^{37} +5.77725 q^{38} +3.67604 q^{39} +11.2921 q^{40} +1.00000 q^{41} +5.19544 q^{43} -1.18725 q^{44} -3.67747 q^{45} +1.69863 q^{46} -2.92116 q^{47} -1.83178 q^{48} +9.41503 q^{50} -4.16206 q^{51} -2.86712 q^{52} -9.52691 q^{53} +1.10456 q^{54} -5.59789 q^{55} +5.23036 q^{57} -8.88122 q^{58} +1.95320 q^{59} +2.86824 q^{60} -10.9140 q^{61} +9.12461 q^{62} +8.21205 q^{64} -13.5185 q^{65} +1.68137 q^{66} +7.95894 q^{67} +3.24619 q^{68} +1.53784 q^{69} -12.3213 q^{71} -3.07062 q^{72} +13.8614 q^{73} -10.4603 q^{74} +8.52379 q^{75} -4.07942 q^{76} +4.06040 q^{78} -5.81290 q^{79} +6.73631 q^{80} +1.00000 q^{81} +1.10456 q^{82} -11.6164 q^{83} +15.3058 q^{85} +5.73867 q^{86} -8.04051 q^{87} -4.67413 q^{88} +18.1860 q^{89} -4.06198 q^{90} -1.19944 q^{92} +8.26086 q^{93} -3.22659 q^{94} -19.2345 q^{95} +4.11793 q^{96} +4.22436 q^{97} +1.52221 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} + O(q^{10}) \) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} - 4q^{10} - 4q^{11} + 12q^{12} - 12q^{15} - 8q^{17} - 4q^{18} + 4q^{19} - 20q^{20} - 16q^{22} - 12q^{23} - 12q^{24} - 8q^{25} - 8q^{26} + 16q^{27} - 16q^{29} - 4q^{30} - 4q^{31} - 48q^{32} - 4q^{33} + 16q^{34} + 12q^{36} - 48q^{37} - 4q^{38} + 56q^{40} + 16q^{41} - 16q^{43} - 12q^{45} - 4q^{46} - 36q^{47} - 8q^{50} - 8q^{51} - 60q^{53} - 4q^{54} + 8q^{55} + 4q^{57} - 36q^{58} - 36q^{59} - 20q^{60} - 4q^{61} - 12q^{62} + 52q^{64} - 36q^{65} - 16q^{66} - 52q^{67} - 8q^{68} - 12q^{69} - 12q^{71} - 12q^{72} - 16q^{73} + 4q^{74} - 8q^{75} + 16q^{76} - 8q^{78} - 36q^{79} - 68q^{80} + 16q^{81} - 4q^{82} - 32q^{83} - 28q^{85} - 8q^{86} - 16q^{87} - 36q^{88} - 12q^{89} - 4q^{90} - 36q^{92} - 4q^{93} + 24q^{94} - 20q^{95} - 48q^{96} + 48q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.10456 0.781041 0.390521 0.920594i \(-0.372295\pi\)
0.390521 + 0.920594i \(0.372295\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.779950 −0.389975
\(5\) −3.67747 −1.64461 −0.822307 0.569044i \(-0.807314\pi\)
−0.822307 + 0.569044i \(0.807314\pi\)
\(6\) 1.10456 0.450934
\(7\) 0 0
\(8\) −3.07062 −1.08563
\(9\) 1.00000 0.333333
\(10\) −4.06198 −1.28451
\(11\) 1.52221 0.458964 0.229482 0.973313i \(-0.426297\pi\)
0.229482 + 0.973313i \(0.426297\pi\)
\(12\) −0.779950 −0.225152
\(13\) 3.67604 1.01955 0.509774 0.860308i \(-0.329729\pi\)
0.509774 + 0.860308i \(0.329729\pi\)
\(14\) 0 0
\(15\) −3.67747 −0.949519
\(16\) −1.83178 −0.457945
\(17\) −4.16206 −1.00945 −0.504724 0.863281i \(-0.668406\pi\)
−0.504724 + 0.863281i \(0.668406\pi\)
\(18\) 1.10456 0.260347
\(19\) 5.23036 1.19993 0.599964 0.800027i \(-0.295182\pi\)
0.599964 + 0.800027i \(0.295182\pi\)
\(20\) 2.86824 0.641358
\(21\) 0 0
\(22\) 1.68137 0.358470
\(23\) 1.53784 0.320662 0.160331 0.987063i \(-0.448744\pi\)
0.160331 + 0.987063i \(0.448744\pi\)
\(24\) −3.07062 −0.626787
\(25\) 8.52379 1.70476
\(26\) 4.06040 0.796309
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −8.04051 −1.49309 −0.746543 0.665337i \(-0.768288\pi\)
−0.746543 + 0.665337i \(0.768288\pi\)
\(30\) −4.06198 −0.741613
\(31\) 8.26086 1.48369 0.741847 0.670569i \(-0.233950\pi\)
0.741847 + 0.670569i \(0.233950\pi\)
\(32\) 4.11793 0.727954
\(33\) 1.52221 0.264983
\(34\) −4.59724 −0.788420
\(35\) 0 0
\(36\) −0.779950 −0.129992
\(37\) −9.47010 −1.55687 −0.778437 0.627723i \(-0.783987\pi\)
−0.778437 + 0.627723i \(0.783987\pi\)
\(38\) 5.77725 0.937193
\(39\) 3.67604 0.588637
\(40\) 11.2921 1.78544
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 5.19544 0.792297 0.396148 0.918186i \(-0.370347\pi\)
0.396148 + 0.918186i \(0.370347\pi\)
\(44\) −1.18725 −0.178984
\(45\) −3.67747 −0.548205
\(46\) 1.69863 0.250450
\(47\) −2.92116 −0.426095 −0.213047 0.977042i \(-0.568339\pi\)
−0.213047 + 0.977042i \(0.568339\pi\)
\(48\) −1.83178 −0.264395
\(49\) 0 0
\(50\) 9.41503 1.33149
\(51\) −4.16206 −0.582805
\(52\) −2.86712 −0.397598
\(53\) −9.52691 −1.30862 −0.654311 0.756226i \(-0.727041\pi\)
−0.654311 + 0.756226i \(0.727041\pi\)
\(54\) 1.10456 0.150311
\(55\) −5.59789 −0.754819
\(56\) 0 0
\(57\) 5.23036 0.692779
\(58\) −8.88122 −1.16616
\(59\) 1.95320 0.254285 0.127142 0.991884i \(-0.459419\pi\)
0.127142 + 0.991884i \(0.459419\pi\)
\(60\) 2.86824 0.370288
\(61\) −10.9140 −1.39739 −0.698695 0.715420i \(-0.746236\pi\)
−0.698695 + 0.715420i \(0.746236\pi\)
\(62\) 9.12461 1.15883
\(63\) 0 0
\(64\) 8.21205 1.02651
\(65\) −13.5185 −1.67676
\(66\) 1.68137 0.206963
\(67\) 7.95894 0.972339 0.486169 0.873865i \(-0.338394\pi\)
0.486169 + 0.873865i \(0.338394\pi\)
\(68\) 3.24619 0.393659
\(69\) 1.53784 0.185134
\(70\) 0 0
\(71\) −12.3213 −1.46227 −0.731134 0.682233i \(-0.761009\pi\)
−0.731134 + 0.682233i \(0.761009\pi\)
\(72\) −3.07062 −0.361876
\(73\) 13.8614 1.62235 0.811175 0.584803i \(-0.198828\pi\)
0.811175 + 0.584803i \(0.198828\pi\)
\(74\) −10.4603 −1.21598
\(75\) 8.52379 0.984242
\(76\) −4.07942 −0.467942
\(77\) 0 0
\(78\) 4.06040 0.459749
\(79\) −5.81290 −0.654003 −0.327001 0.945024i \(-0.606038\pi\)
−0.327001 + 0.945024i \(0.606038\pi\)
\(80\) 6.73631 0.753143
\(81\) 1.00000 0.111111
\(82\) 1.10456 0.121978
\(83\) −11.6164 −1.27506 −0.637530 0.770425i \(-0.720044\pi\)
−0.637530 + 0.770425i \(0.720044\pi\)
\(84\) 0 0
\(85\) 15.3058 1.66015
\(86\) 5.73867 0.618816
\(87\) −8.04051 −0.862033
\(88\) −4.67413 −0.498264
\(89\) 18.1860 1.92771 0.963854 0.266432i \(-0.0858447\pi\)
0.963854 + 0.266432i \(0.0858447\pi\)
\(90\) −4.06198 −0.428171
\(91\) 0 0
\(92\) −1.19944 −0.125050
\(93\) 8.26086 0.856612
\(94\) −3.22659 −0.332798
\(95\) −19.2345 −1.97342
\(96\) 4.11793 0.420284
\(97\) 4.22436 0.428919 0.214459 0.976733i \(-0.431201\pi\)
0.214459 + 0.976733i \(0.431201\pi\)
\(98\) 0 0
\(99\) 1.52221 0.152988
\(100\) −6.64813 −0.664813
\(101\) −12.4856 −1.24236 −0.621182 0.783666i \(-0.713347\pi\)
−0.621182 + 0.783666i \(0.713347\pi\)
\(102\) −4.59724 −0.455194
\(103\) −17.5997 −1.73415 −0.867073 0.498182i \(-0.834001\pi\)
−0.867073 + 0.498182i \(0.834001\pi\)
\(104\) −11.2877 −1.10685
\(105\) 0 0
\(106\) −10.5230 −1.02209
\(107\) −8.93227 −0.863515 −0.431757 0.901990i \(-0.642106\pi\)
−0.431757 + 0.901990i \(0.642106\pi\)
\(108\) −0.779950 −0.0750507
\(109\) −13.0978 −1.25454 −0.627272 0.778801i \(-0.715828\pi\)
−0.627272 + 0.778801i \(0.715828\pi\)
\(110\) −6.18320 −0.589545
\(111\) −9.47010 −0.898862
\(112\) 0 0
\(113\) 0.658461 0.0619428 0.0309714 0.999520i \(-0.490140\pi\)
0.0309714 + 0.999520i \(0.490140\pi\)
\(114\) 5.77725 0.541089
\(115\) −5.65536 −0.527365
\(116\) 6.27119 0.582266
\(117\) 3.67604 0.339850
\(118\) 2.15742 0.198607
\(119\) 0 0
\(120\) 11.2921 1.03082
\(121\) −8.68287 −0.789352
\(122\) −12.0551 −1.09142
\(123\) 1.00000 0.0901670
\(124\) −6.44306 −0.578604
\(125\) −12.9586 −1.15906
\(126\) 0 0
\(127\) −8.74772 −0.776235 −0.388117 0.921610i \(-0.626874\pi\)
−0.388117 + 0.921610i \(0.626874\pi\)
\(128\) 0.834840 0.0737901
\(129\) 5.19544 0.457433
\(130\) −14.9320 −1.30962
\(131\) −18.4044 −1.60800 −0.804002 0.594627i \(-0.797300\pi\)
−0.804002 + 0.594627i \(0.797300\pi\)
\(132\) −1.18725 −0.103337
\(133\) 0 0
\(134\) 8.79112 0.759437
\(135\) −3.67747 −0.316506
\(136\) 12.7801 1.09588
\(137\) −2.50601 −0.214103 −0.107052 0.994253i \(-0.534141\pi\)
−0.107052 + 0.994253i \(0.534141\pi\)
\(138\) 1.69863 0.144597
\(139\) 4.25917 0.361258 0.180629 0.983551i \(-0.442187\pi\)
0.180629 + 0.983551i \(0.442187\pi\)
\(140\) 0 0
\(141\) −2.92116 −0.246006
\(142\) −13.6096 −1.14209
\(143\) 5.59570 0.467936
\(144\) −1.83178 −0.152648
\(145\) 29.5687 2.45555
\(146\) 15.3107 1.26712
\(147\) 0 0
\(148\) 7.38620 0.607142
\(149\) −4.22166 −0.345852 −0.172926 0.984935i \(-0.555322\pi\)
−0.172926 + 0.984935i \(0.555322\pi\)
\(150\) 9.41503 0.768734
\(151\) 15.5047 1.26175 0.630876 0.775884i \(-0.282696\pi\)
0.630876 + 0.775884i \(0.282696\pi\)
\(152\) −16.0605 −1.30267
\(153\) −4.16206 −0.336482
\(154\) 0 0
\(155\) −30.3791 −2.44011
\(156\) −2.86712 −0.229554
\(157\) −3.46926 −0.276877 −0.138438 0.990371i \(-0.544208\pi\)
−0.138438 + 0.990371i \(0.544208\pi\)
\(158\) −6.42069 −0.510803
\(159\) −9.52691 −0.755533
\(160\) −15.1436 −1.19720
\(161\) 0 0
\(162\) 1.10456 0.0867823
\(163\) −18.7787 −1.47086 −0.735429 0.677602i \(-0.763019\pi\)
−0.735429 + 0.677602i \(0.763019\pi\)
\(164\) −0.779950 −0.0609038
\(165\) −5.59789 −0.435795
\(166\) −12.8309 −0.995875
\(167\) 10.2446 0.792751 0.396376 0.918088i \(-0.370268\pi\)
0.396376 + 0.918088i \(0.370268\pi\)
\(168\) 0 0
\(169\) 0.513236 0.0394797
\(170\) 16.9062 1.29665
\(171\) 5.23036 0.399976
\(172\) −4.05218 −0.308976
\(173\) 14.0080 1.06501 0.532504 0.846428i \(-0.321251\pi\)
0.532504 + 0.846428i \(0.321251\pi\)
\(174\) −8.88122 −0.673283
\(175\) 0 0
\(176\) −2.78836 −0.210180
\(177\) 1.95320 0.146811
\(178\) 20.0875 1.50562
\(179\) 6.20988 0.464148 0.232074 0.972698i \(-0.425449\pi\)
0.232074 + 0.972698i \(0.425449\pi\)
\(180\) 2.86824 0.213786
\(181\) −21.9328 −1.63025 −0.815127 0.579283i \(-0.803333\pi\)
−0.815127 + 0.579283i \(0.803333\pi\)
\(182\) 0 0
\(183\) −10.9140 −0.806784
\(184\) −4.72212 −0.348119
\(185\) 34.8260 2.56046
\(186\) 9.12461 0.669049
\(187\) −6.33553 −0.463300
\(188\) 2.27836 0.166166
\(189\) 0 0
\(190\) −21.2457 −1.54132
\(191\) −5.12001 −0.370471 −0.185235 0.982694i \(-0.559305\pi\)
−0.185235 + 0.982694i \(0.559305\pi\)
\(192\) 8.21205 0.592654
\(193\) 11.1033 0.799234 0.399617 0.916682i \(-0.369143\pi\)
0.399617 + 0.916682i \(0.369143\pi\)
\(194\) 4.66606 0.335003
\(195\) −13.5185 −0.968081
\(196\) 0 0
\(197\) −3.72992 −0.265746 −0.132873 0.991133i \(-0.542420\pi\)
−0.132873 + 0.991133i \(0.542420\pi\)
\(198\) 1.68137 0.119490
\(199\) 14.4265 1.02267 0.511334 0.859382i \(-0.329151\pi\)
0.511334 + 0.859382i \(0.329151\pi\)
\(200\) −26.1733 −1.85073
\(201\) 7.95894 0.561380
\(202\) −13.7911 −0.970338
\(203\) 0 0
\(204\) 3.24619 0.227279
\(205\) −3.67747 −0.256846
\(206\) −19.4399 −1.35444
\(207\) 1.53784 0.106887
\(208\) −6.73369 −0.466897
\(209\) 7.96172 0.550724
\(210\) 0 0
\(211\) −13.3208 −0.917041 −0.458521 0.888684i \(-0.651621\pi\)
−0.458521 + 0.888684i \(0.651621\pi\)
\(212\) 7.43051 0.510329
\(213\) −12.3213 −0.844241
\(214\) −9.86621 −0.674441
\(215\) −19.1061 −1.30302
\(216\) −3.07062 −0.208929
\(217\) 0 0
\(218\) −14.4673 −0.979850
\(219\) 13.8614 0.936664
\(220\) 4.36607 0.294360
\(221\) −15.2999 −1.02918
\(222\) −10.4603 −0.702048
\(223\) −23.8810 −1.59919 −0.799594 0.600540i \(-0.794952\pi\)
−0.799594 + 0.600540i \(0.794952\pi\)
\(224\) 0 0
\(225\) 8.52379 0.568253
\(226\) 0.727309 0.0483799
\(227\) 3.77010 0.250230 0.125115 0.992142i \(-0.460070\pi\)
0.125115 + 0.992142i \(0.460070\pi\)
\(228\) −4.07942 −0.270166
\(229\) −6.51600 −0.430589 −0.215295 0.976549i \(-0.569071\pi\)
−0.215295 + 0.976549i \(0.569071\pi\)
\(230\) −6.24668 −0.411894
\(231\) 0 0
\(232\) 24.6893 1.62093
\(233\) −8.18148 −0.535987 −0.267993 0.963421i \(-0.586361\pi\)
−0.267993 + 0.963421i \(0.586361\pi\)
\(234\) 4.06040 0.265436
\(235\) 10.7425 0.700762
\(236\) −1.52340 −0.0991646
\(237\) −5.81290 −0.377589
\(238\) 0 0
\(239\) −13.7032 −0.886387 −0.443193 0.896426i \(-0.646154\pi\)
−0.443193 + 0.896426i \(0.646154\pi\)
\(240\) 6.73631 0.434827
\(241\) −13.2872 −0.855903 −0.427952 0.903802i \(-0.640765\pi\)
−0.427952 + 0.903802i \(0.640765\pi\)
\(242\) −9.59074 −0.616516
\(243\) 1.00000 0.0641500
\(244\) 8.51234 0.544947
\(245\) 0 0
\(246\) 1.10456 0.0704241
\(247\) 19.2270 1.22339
\(248\) −25.3660 −1.61074
\(249\) −11.6164 −0.736156
\(250\) −14.3136 −0.905270
\(251\) −7.91598 −0.499653 −0.249826 0.968291i \(-0.580374\pi\)
−0.249826 + 0.968291i \(0.580374\pi\)
\(252\) 0 0
\(253\) 2.34092 0.147172
\(254\) −9.66237 −0.606271
\(255\) 15.3058 0.958489
\(256\) −15.5020 −0.968873
\(257\) 5.83445 0.363943 0.181971 0.983304i \(-0.441752\pi\)
0.181971 + 0.983304i \(0.441752\pi\)
\(258\) 5.73867 0.357274
\(259\) 0 0
\(260\) 10.5438 0.653896
\(261\) −8.04051 −0.497695
\(262\) −20.3288 −1.25592
\(263\) −1.97786 −0.121960 −0.0609800 0.998139i \(-0.519423\pi\)
−0.0609800 + 0.998139i \(0.519423\pi\)
\(264\) −4.67413 −0.287673
\(265\) 35.0349 2.15218
\(266\) 0 0
\(267\) 18.1860 1.11296
\(268\) −6.20757 −0.379188
\(269\) 23.3647 1.42457 0.712287 0.701889i \(-0.247660\pi\)
0.712287 + 0.701889i \(0.247660\pi\)
\(270\) −4.06198 −0.247204
\(271\) 23.7310 1.44155 0.720776 0.693168i \(-0.243786\pi\)
0.720776 + 0.693168i \(0.243786\pi\)
\(272\) 7.62397 0.462271
\(273\) 0 0
\(274\) −2.76804 −0.167223
\(275\) 12.9750 0.782423
\(276\) −1.19944 −0.0721977
\(277\) 21.0539 1.26501 0.632504 0.774557i \(-0.282027\pi\)
0.632504 + 0.774557i \(0.282027\pi\)
\(278\) 4.70450 0.282157
\(279\) 8.26086 0.494565
\(280\) 0 0
\(281\) −25.8960 −1.54483 −0.772413 0.635120i \(-0.780950\pi\)
−0.772413 + 0.635120i \(0.780950\pi\)
\(282\) −3.22659 −0.192141
\(283\) −25.7797 −1.53245 −0.766223 0.642575i \(-0.777866\pi\)
−0.766223 + 0.642575i \(0.777866\pi\)
\(284\) 9.60999 0.570248
\(285\) −19.2345 −1.13935
\(286\) 6.18078 0.365477
\(287\) 0 0
\(288\) 4.11793 0.242651
\(289\) 0.322719 0.0189835
\(290\) 32.6604 1.91789
\(291\) 4.22436 0.247636
\(292\) −10.8112 −0.632676
\(293\) 20.8476 1.21793 0.608964 0.793198i \(-0.291585\pi\)
0.608964 + 0.793198i \(0.291585\pi\)
\(294\) 0 0
\(295\) −7.18283 −0.418200
\(296\) 29.0790 1.69019
\(297\) 1.52221 0.0883277
\(298\) −4.66307 −0.270125
\(299\) 5.65315 0.326930
\(300\) −6.64813 −0.383830
\(301\) 0 0
\(302\) 17.1258 0.985480
\(303\) −12.4856 −0.717279
\(304\) −9.58087 −0.549501
\(305\) 40.1358 2.29817
\(306\) −4.59724 −0.262807
\(307\) −9.56642 −0.545984 −0.272992 0.962016i \(-0.588013\pi\)
−0.272992 + 0.962016i \(0.588013\pi\)
\(308\) 0 0
\(309\) −17.5997 −1.00121
\(310\) −33.5555 −1.90582
\(311\) −16.1256 −0.914400 −0.457200 0.889364i \(-0.651148\pi\)
−0.457200 + 0.889364i \(0.651148\pi\)
\(312\) −11.2877 −0.639040
\(313\) 21.2132 1.19904 0.599520 0.800360i \(-0.295358\pi\)
0.599520 + 0.800360i \(0.295358\pi\)
\(314\) −3.83200 −0.216252
\(315\) 0 0
\(316\) 4.53377 0.255045
\(317\) 13.4949 0.757951 0.378975 0.925407i \(-0.376276\pi\)
0.378975 + 0.925407i \(0.376276\pi\)
\(318\) −10.5230 −0.590102
\(319\) −12.2394 −0.685273
\(320\) −30.1996 −1.68821
\(321\) −8.93227 −0.498551
\(322\) 0 0
\(323\) −21.7691 −1.21126
\(324\) −0.779950 −0.0433305
\(325\) 31.3337 1.73808
\(326\) −20.7421 −1.14880
\(327\) −13.0978 −0.724311
\(328\) −3.07062 −0.169547
\(329\) 0 0
\(330\) −6.18320 −0.340374
\(331\) 5.17282 0.284324 0.142162 0.989843i \(-0.454595\pi\)
0.142162 + 0.989843i \(0.454595\pi\)
\(332\) 9.06017 0.497241
\(333\) −9.47010 −0.518958
\(334\) 11.3158 0.619171
\(335\) −29.2688 −1.59912
\(336\) 0 0
\(337\) −0.770683 −0.0419818 −0.0209909 0.999780i \(-0.506682\pi\)
−0.0209909 + 0.999780i \(0.506682\pi\)
\(338\) 0.566900 0.0308353
\(339\) 0.658461 0.0357627
\(340\) −11.9378 −0.647417
\(341\) 12.5748 0.680963
\(342\) 5.77725 0.312398
\(343\) 0 0
\(344\) −15.9532 −0.860139
\(345\) −5.65536 −0.304474
\(346\) 15.4726 0.831814
\(347\) −7.00830 −0.376225 −0.188113 0.982147i \(-0.560237\pi\)
−0.188113 + 0.982147i \(0.560237\pi\)
\(348\) 6.27119 0.336171
\(349\) 22.4246 1.20036 0.600181 0.799864i \(-0.295095\pi\)
0.600181 + 0.799864i \(0.295095\pi\)
\(350\) 0 0
\(351\) 3.67604 0.196212
\(352\) 6.26836 0.334105
\(353\) 23.2159 1.23566 0.617828 0.786313i \(-0.288013\pi\)
0.617828 + 0.786313i \(0.288013\pi\)
\(354\) 2.15742 0.114666
\(355\) 45.3112 2.40487
\(356\) −14.1841 −0.751757
\(357\) 0 0
\(358\) 6.85918 0.362519
\(359\) −9.57666 −0.505437 −0.252719 0.967540i \(-0.581325\pi\)
−0.252719 + 0.967540i \(0.581325\pi\)
\(360\) 11.2921 0.595146
\(361\) 8.35671 0.439827
\(362\) −24.2261 −1.27330
\(363\) −8.68287 −0.455733
\(364\) 0 0
\(365\) −50.9748 −2.66814
\(366\) −12.0551 −0.630131
\(367\) 4.64264 0.242344 0.121172 0.992632i \(-0.461335\pi\)
0.121172 + 0.992632i \(0.461335\pi\)
\(368\) −2.81698 −0.146845
\(369\) 1.00000 0.0520579
\(370\) 38.4674 1.99982
\(371\) 0 0
\(372\) −6.44306 −0.334057
\(373\) −16.1711 −0.837307 −0.418653 0.908146i \(-0.637498\pi\)
−0.418653 + 0.908146i \(0.637498\pi\)
\(374\) −6.99797 −0.361856
\(375\) −12.9586 −0.669181
\(376\) 8.96976 0.462580
\(377\) −29.5572 −1.52227
\(378\) 0 0
\(379\) 0.105888 0.00543911 0.00271956 0.999996i \(-0.499134\pi\)
0.00271956 + 0.999996i \(0.499134\pi\)
\(380\) 15.0019 0.769584
\(381\) −8.74772 −0.448159
\(382\) −5.65535 −0.289353
\(383\) −9.96830 −0.509356 −0.254678 0.967026i \(-0.581970\pi\)
−0.254678 + 0.967026i \(0.581970\pi\)
\(384\) 0.834840 0.0426027
\(385\) 0 0
\(386\) 12.2643 0.624234
\(387\) 5.19544 0.264099
\(388\) −3.29479 −0.167268
\(389\) −27.7414 −1.40654 −0.703271 0.710921i \(-0.748278\pi\)
−0.703271 + 0.710921i \(0.748278\pi\)
\(390\) −14.9320 −0.756111
\(391\) −6.40058 −0.323691
\(392\) 0 0
\(393\) −18.4044 −0.928381
\(394\) −4.11991 −0.207558
\(395\) 21.3768 1.07558
\(396\) −1.18725 −0.0596615
\(397\) 6.99697 0.351168 0.175584 0.984464i \(-0.443819\pi\)
0.175584 + 0.984464i \(0.443819\pi\)
\(398\) 15.9349 0.798746
\(399\) 0 0
\(400\) −15.6137 −0.780685
\(401\) −12.0665 −0.602570 −0.301285 0.953534i \(-0.597416\pi\)
−0.301285 + 0.953534i \(0.597416\pi\)
\(402\) 8.79112 0.438461
\(403\) 30.3672 1.51270
\(404\) 9.73814 0.484491
\(405\) −3.67747 −0.182735
\(406\) 0 0
\(407\) −14.4155 −0.714549
\(408\) 12.7801 0.632709
\(409\) −12.8745 −0.636603 −0.318302 0.947989i \(-0.603112\pi\)
−0.318302 + 0.947989i \(0.603112\pi\)
\(410\) −4.06198 −0.200607
\(411\) −2.50601 −0.123612
\(412\) 13.7268 0.676273
\(413\) 0 0
\(414\) 1.69863 0.0834833
\(415\) 42.7188 2.09698
\(416\) 15.1376 0.742184
\(417\) 4.25917 0.208572
\(418\) 8.79419 0.430138
\(419\) 28.8557 1.40969 0.704847 0.709359i \(-0.251015\pi\)
0.704847 + 0.709359i \(0.251015\pi\)
\(420\) 0 0
\(421\) 6.97023 0.339708 0.169854 0.985469i \(-0.445670\pi\)
0.169854 + 0.985469i \(0.445670\pi\)
\(422\) −14.7136 −0.716247
\(423\) −2.92116 −0.142032
\(424\) 29.2535 1.42068
\(425\) −35.4765 −1.72086
\(426\) −13.6096 −0.659387
\(427\) 0 0
\(428\) 6.96672 0.336749
\(429\) 5.59570 0.270163
\(430\) −21.1038 −1.01771
\(431\) 34.6761 1.67029 0.835145 0.550031i \(-0.185384\pi\)
0.835145 + 0.550031i \(0.185384\pi\)
\(432\) −1.83178 −0.0881315
\(433\) −38.1831 −1.83496 −0.917480 0.397782i \(-0.869780\pi\)
−0.917480 + 0.397782i \(0.869780\pi\)
\(434\) 0 0
\(435\) 29.5687 1.41771
\(436\) 10.2156 0.489240
\(437\) 8.04346 0.384771
\(438\) 15.3107 0.731573
\(439\) −30.6755 −1.46406 −0.732031 0.681271i \(-0.761428\pi\)
−0.732031 + 0.681271i \(0.761428\pi\)
\(440\) 17.1890 0.819452
\(441\) 0 0
\(442\) −16.8996 −0.803832
\(443\) −19.6537 −0.933773 −0.466887 0.884317i \(-0.654624\pi\)
−0.466887 + 0.884317i \(0.654624\pi\)
\(444\) 7.38620 0.350533
\(445\) −66.8783 −3.17034
\(446\) −26.3779 −1.24903
\(447\) −4.22166 −0.199678
\(448\) 0 0
\(449\) 33.1895 1.56631 0.783155 0.621827i \(-0.213609\pi\)
0.783155 + 0.621827i \(0.213609\pi\)
\(450\) 9.41503 0.443829
\(451\) 1.52221 0.0716782
\(452\) −0.513566 −0.0241561
\(453\) 15.5047 0.728472
\(454\) 4.16430 0.195440
\(455\) 0 0
\(456\) −16.0605 −0.752100
\(457\) −18.7154 −0.875470 −0.437735 0.899104i \(-0.644219\pi\)
−0.437735 + 0.899104i \(0.644219\pi\)
\(458\) −7.19731 −0.336308
\(459\) −4.16206 −0.194268
\(460\) 4.41090 0.205659
\(461\) −0.256027 −0.0119243 −0.00596217 0.999982i \(-0.501898\pi\)
−0.00596217 + 0.999982i \(0.501898\pi\)
\(462\) 0 0
\(463\) −21.1023 −0.980709 −0.490355 0.871523i \(-0.663133\pi\)
−0.490355 + 0.871523i \(0.663133\pi\)
\(464\) 14.7284 0.683751
\(465\) −30.3791 −1.40880
\(466\) −9.03693 −0.418628
\(467\) −1.02605 −0.0474801 −0.0237400 0.999718i \(-0.507557\pi\)
−0.0237400 + 0.999718i \(0.507557\pi\)
\(468\) −2.86712 −0.132533
\(469\) 0 0
\(470\) 11.8657 0.547324
\(471\) −3.46926 −0.159855
\(472\) −5.99753 −0.276059
\(473\) 7.90856 0.363636
\(474\) −6.42069 −0.294912
\(475\) 44.5825 2.04559
\(476\) 0 0
\(477\) −9.52691 −0.436207
\(478\) −15.1360 −0.692304
\(479\) 27.2043 1.24299 0.621497 0.783417i \(-0.286525\pi\)
0.621497 + 0.783417i \(0.286525\pi\)
\(480\) −15.1436 −0.691206
\(481\) −34.8124 −1.58731
\(482\) −14.6765 −0.668496
\(483\) 0 0
\(484\) 6.77220 0.307827
\(485\) −15.5350 −0.705406
\(486\) 1.10456 0.0501038
\(487\) 12.1352 0.549898 0.274949 0.961459i \(-0.411339\pi\)
0.274949 + 0.961459i \(0.411339\pi\)
\(488\) 33.5126 1.51705
\(489\) −18.7787 −0.849200
\(490\) 0 0
\(491\) 26.9411 1.21584 0.607919 0.793999i \(-0.292005\pi\)
0.607919 + 0.793999i \(0.292005\pi\)
\(492\) −0.779950 −0.0351628
\(493\) 33.4651 1.50719
\(494\) 21.2374 0.955514
\(495\) −5.59789 −0.251606
\(496\) −15.1321 −0.679450
\(497\) 0 0
\(498\) −12.8309 −0.574968
\(499\) −7.71740 −0.345478 −0.172739 0.984968i \(-0.555262\pi\)
−0.172739 + 0.984968i \(0.555262\pi\)
\(500\) 10.1071 0.452002
\(501\) 10.2446 0.457695
\(502\) −8.74367 −0.390249
\(503\) −25.1080 −1.11951 −0.559754 0.828659i \(-0.689104\pi\)
−0.559754 + 0.828659i \(0.689104\pi\)
\(504\) 0 0
\(505\) 45.9154 2.04321
\(506\) 2.58568 0.114948
\(507\) 0.513236 0.0227936
\(508\) 6.82278 0.302712
\(509\) 5.41173 0.239871 0.119935 0.992782i \(-0.461731\pi\)
0.119935 + 0.992782i \(0.461731\pi\)
\(510\) 16.9062 0.748619
\(511\) 0 0
\(512\) −18.7925 −0.830520
\(513\) 5.23036 0.230926
\(514\) 6.44449 0.284254
\(515\) 64.7222 2.85200
\(516\) −4.05218 −0.178387
\(517\) −4.44662 −0.195562
\(518\) 0 0
\(519\) 14.0080 0.614882
\(520\) 41.5102 1.82034
\(521\) 20.0868 0.880017 0.440008 0.897994i \(-0.354975\pi\)
0.440008 + 0.897994i \(0.354975\pi\)
\(522\) −8.88122 −0.388720
\(523\) 6.29814 0.275398 0.137699 0.990474i \(-0.456029\pi\)
0.137699 + 0.990474i \(0.456029\pi\)
\(524\) 14.3545 0.627081
\(525\) 0 0
\(526\) −2.18466 −0.0952558
\(527\) −34.3822 −1.49771
\(528\) −2.78836 −0.121348
\(529\) −20.6350 −0.897176
\(530\) 38.6981 1.68094
\(531\) 1.95320 0.0847616
\(532\) 0 0
\(533\) 3.67604 0.159227
\(534\) 20.0875 0.869269
\(535\) 32.8481 1.42015
\(536\) −24.4389 −1.05560
\(537\) 6.20988 0.267976
\(538\) 25.8077 1.11265
\(539\) 0 0
\(540\) 2.86824 0.123429
\(541\) −27.1030 −1.16525 −0.582624 0.812742i \(-0.697974\pi\)
−0.582624 + 0.812742i \(0.697974\pi\)
\(542\) 26.2122 1.12591
\(543\) −21.9328 −0.941227
\(544\) −17.1391 −0.734831
\(545\) 48.1668 2.06324
\(546\) 0 0
\(547\) 18.9156 0.808771 0.404386 0.914589i \(-0.367485\pi\)
0.404386 + 0.914589i \(0.367485\pi\)
\(548\) 1.95456 0.0834948
\(549\) −10.9140 −0.465797
\(550\) 14.3317 0.611104
\(551\) −42.0548 −1.79160
\(552\) −4.72212 −0.200987
\(553\) 0 0
\(554\) 23.2553 0.988023
\(555\) 34.8260 1.47828
\(556\) −3.32194 −0.140881
\(557\) −20.9212 −0.886458 −0.443229 0.896408i \(-0.646167\pi\)
−0.443229 + 0.896408i \(0.646167\pi\)
\(558\) 9.12461 0.386276
\(559\) 19.0986 0.807785
\(560\) 0 0
\(561\) −6.33553 −0.267486
\(562\) −28.6037 −1.20657
\(563\) −21.0926 −0.888949 −0.444474 0.895792i \(-0.646609\pi\)
−0.444474 + 0.895792i \(0.646609\pi\)
\(564\) 2.27836 0.0959361
\(565\) −2.42147 −0.101872
\(566\) −28.4752 −1.19690
\(567\) 0 0
\(568\) 37.8340 1.58748
\(569\) 14.0507 0.589036 0.294518 0.955646i \(-0.404841\pi\)
0.294518 + 0.955646i \(0.404841\pi\)
\(570\) −21.2457 −0.889882
\(571\) 20.6691 0.864973 0.432486 0.901640i \(-0.357636\pi\)
0.432486 + 0.901640i \(0.357636\pi\)
\(572\) −4.36437 −0.182483
\(573\) −5.12001 −0.213891
\(574\) 0 0
\(575\) 13.1082 0.546651
\(576\) 8.21205 0.342169
\(577\) −39.7417 −1.65447 −0.827234 0.561858i \(-0.810087\pi\)
−0.827234 + 0.561858i \(0.810087\pi\)
\(578\) 0.356462 0.0148269
\(579\) 11.1033 0.461438
\(580\) −23.0621 −0.957603
\(581\) 0 0
\(582\) 4.66606 0.193414
\(583\) −14.5020 −0.600610
\(584\) −42.5630 −1.76127
\(585\) −13.5185 −0.558922
\(586\) 23.0274 0.951252
\(587\) −12.9442 −0.534266 −0.267133 0.963660i \(-0.586076\pi\)
−0.267133 + 0.963660i \(0.586076\pi\)
\(588\) 0 0
\(589\) 43.2073 1.78033
\(590\) −7.93386 −0.326632
\(591\) −3.72992 −0.153428
\(592\) 17.3471 0.712962
\(593\) 8.11030 0.333050 0.166525 0.986037i \(-0.446745\pi\)
0.166525 + 0.986037i \(0.446745\pi\)
\(594\) 1.68137 0.0689876
\(595\) 0 0
\(596\) 3.29268 0.134874
\(597\) 14.4265 0.590438
\(598\) 6.24424 0.255346
\(599\) 33.7505 1.37901 0.689504 0.724282i \(-0.257829\pi\)
0.689504 + 0.724282i \(0.257829\pi\)
\(600\) −26.1733 −1.06852
\(601\) 20.2822 0.827327 0.413664 0.910430i \(-0.364249\pi\)
0.413664 + 0.910430i \(0.364249\pi\)
\(602\) 0 0
\(603\) 7.95894 0.324113
\(604\) −12.0929 −0.492051
\(605\) 31.9310 1.29818
\(606\) −13.7911 −0.560225
\(607\) 30.2667 1.22849 0.614243 0.789117i \(-0.289461\pi\)
0.614243 + 0.789117i \(0.289461\pi\)
\(608\) 21.5383 0.873492
\(609\) 0 0
\(610\) 44.3323 1.79496
\(611\) −10.7383 −0.434424
\(612\) 3.24619 0.131220
\(613\) 1.31409 0.0530755 0.0265378 0.999648i \(-0.491552\pi\)
0.0265378 + 0.999648i \(0.491552\pi\)
\(614\) −10.5667 −0.426436
\(615\) −3.67747 −0.148290
\(616\) 0 0
\(617\) 29.5191 1.18839 0.594196 0.804320i \(-0.297470\pi\)
0.594196 + 0.804320i \(0.297470\pi\)
\(618\) −19.4399 −0.781986
\(619\) 18.3832 0.738882 0.369441 0.929254i \(-0.379549\pi\)
0.369441 + 0.929254i \(0.379549\pi\)
\(620\) 23.6942 0.951580
\(621\) 1.53784 0.0617114
\(622\) −17.8117 −0.714184
\(623\) 0 0
\(624\) −6.73369 −0.269563
\(625\) 5.03603 0.201441
\(626\) 23.4312 0.936499
\(627\) 7.96172 0.317961
\(628\) 2.70584 0.107975
\(629\) 39.4151 1.57158
\(630\) 0 0
\(631\) −19.1228 −0.761268 −0.380634 0.924726i \(-0.624294\pi\)
−0.380634 + 0.924726i \(0.624294\pi\)
\(632\) 17.8492 0.710003
\(633\) −13.3208 −0.529454
\(634\) 14.9059 0.591991
\(635\) 32.1695 1.27661
\(636\) 7.43051 0.294639
\(637\) 0 0
\(638\) −13.5191 −0.535226
\(639\) −12.3213 −0.487423
\(640\) −3.07010 −0.121356
\(641\) 21.9048 0.865187 0.432594 0.901589i \(-0.357599\pi\)
0.432594 + 0.901589i \(0.357599\pi\)
\(642\) −9.86621 −0.389388
\(643\) −29.6162 −1.16795 −0.583974 0.811772i \(-0.698503\pi\)
−0.583974 + 0.811772i \(0.698503\pi\)
\(644\) 0 0
\(645\) −19.1061 −0.752301
\(646\) −24.0452 −0.946047
\(647\) −11.5650 −0.454669 −0.227334 0.973817i \(-0.573001\pi\)
−0.227334 + 0.973817i \(0.573001\pi\)
\(648\) −3.07062 −0.120625
\(649\) 2.97318 0.116708
\(650\) 34.6100 1.35751
\(651\) 0 0
\(652\) 14.6464 0.573598
\(653\) −6.59821 −0.258208 −0.129104 0.991631i \(-0.541210\pi\)
−0.129104 + 0.991631i \(0.541210\pi\)
\(654\) −14.4673 −0.565717
\(655\) 67.6818 2.64455
\(656\) −1.83178 −0.0715190
\(657\) 13.8614 0.540783
\(658\) 0 0
\(659\) −14.7272 −0.573691 −0.286846 0.957977i \(-0.592607\pi\)
−0.286846 + 0.957977i \(0.592607\pi\)
\(660\) 4.36607 0.169949
\(661\) 8.44705 0.328552 0.164276 0.986414i \(-0.447471\pi\)
0.164276 + 0.986414i \(0.447471\pi\)
\(662\) 5.71369 0.222069
\(663\) −15.2999 −0.594198
\(664\) 35.6694 1.38424
\(665\) 0 0
\(666\) −10.4603 −0.405328
\(667\) −12.3650 −0.478775
\(668\) −7.99027 −0.309153
\(669\) −23.8810 −0.923292
\(670\) −32.3291 −1.24898
\(671\) −16.6134 −0.641352
\(672\) 0 0
\(673\) 37.3476 1.43964 0.719822 0.694159i \(-0.244223\pi\)
0.719822 + 0.694159i \(0.244223\pi\)
\(674\) −0.851265 −0.0327895
\(675\) 8.52379 0.328081
\(676\) −0.400298 −0.0153961
\(677\) 7.84359 0.301454 0.150727 0.988575i \(-0.451839\pi\)
0.150727 + 0.988575i \(0.451839\pi\)
\(678\) 0.727309 0.0279321
\(679\) 0 0
\(680\) −46.9984 −1.80231
\(681\) 3.77010 0.144471
\(682\) 13.8896 0.531860
\(683\) 1.10391 0.0422400 0.0211200 0.999777i \(-0.493277\pi\)
0.0211200 + 0.999777i \(0.493277\pi\)
\(684\) −4.07942 −0.155981
\(685\) 9.21578 0.352117
\(686\) 0 0
\(687\) −6.51600 −0.248601
\(688\) −9.51690 −0.362828
\(689\) −35.0212 −1.33420
\(690\) −6.24668 −0.237807
\(691\) −14.7201 −0.559978 −0.279989 0.960003i \(-0.590331\pi\)
−0.279989 + 0.960003i \(0.590331\pi\)
\(692\) −10.9255 −0.415326
\(693\) 0 0
\(694\) −7.74108 −0.293848
\(695\) −15.6630 −0.594130
\(696\) 24.6893 0.935847
\(697\) −4.16206 −0.157649
\(698\) 24.7693 0.937532
\(699\) −8.18148 −0.309452
\(700\) 0 0
\(701\) −15.8325 −0.597987 −0.298993 0.954255i \(-0.596651\pi\)
−0.298993 + 0.954255i \(0.596651\pi\)
\(702\) 4.06040 0.153250
\(703\) −49.5320 −1.86814
\(704\) 12.5005 0.471130
\(705\) 10.7425 0.404585
\(706\) 25.6433 0.965098
\(707\) 0 0
\(708\) −1.52340 −0.0572527
\(709\) 24.3093 0.912955 0.456478 0.889735i \(-0.349111\pi\)
0.456478 + 0.889735i \(0.349111\pi\)
\(710\) 50.0489 1.87830
\(711\) −5.81290 −0.218001
\(712\) −55.8421 −2.09277
\(713\) 12.7039 0.475764
\(714\) 0 0
\(715\) −20.5780 −0.769575
\(716\) −4.84339 −0.181006
\(717\) −13.7032 −0.511756
\(718\) −10.5780 −0.394767
\(719\) 25.4055 0.947464 0.473732 0.880669i \(-0.342906\pi\)
0.473732 + 0.880669i \(0.342906\pi\)
\(720\) 6.73631 0.251048
\(721\) 0 0
\(722\) 9.23048 0.343523
\(723\) −13.2872 −0.494156
\(724\) 17.1065 0.635758
\(725\) −68.5356 −2.54535
\(726\) −9.59074 −0.355946
\(727\) 25.5947 0.949255 0.474628 0.880187i \(-0.342583\pi\)
0.474628 + 0.880187i \(0.342583\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −56.3046 −2.08393
\(731\) −21.6237 −0.799782
\(732\) 8.51234 0.314625
\(733\) −21.1670 −0.781821 −0.390911 0.920429i \(-0.627840\pi\)
−0.390911 + 0.920429i \(0.627840\pi\)
\(734\) 5.12806 0.189280
\(735\) 0 0
\(736\) 6.33271 0.233427
\(737\) 12.1152 0.446269
\(738\) 1.10456 0.0406594
\(739\) −38.7709 −1.42621 −0.713106 0.701056i \(-0.752712\pi\)
−0.713106 + 0.701056i \(0.752712\pi\)
\(740\) −27.1625 −0.998514
\(741\) 19.2270 0.706322
\(742\) 0 0
\(743\) 34.8769 1.27951 0.639755 0.768579i \(-0.279036\pi\)
0.639755 + 0.768579i \(0.279036\pi\)
\(744\) −25.3660 −0.929961
\(745\) 15.5250 0.568793
\(746\) −17.8619 −0.653971
\(747\) −11.6164 −0.425020
\(748\) 4.94140 0.180675
\(749\) 0 0
\(750\) −14.3136 −0.522658
\(751\) 15.7762 0.575680 0.287840 0.957678i \(-0.407063\pi\)
0.287840 + 0.957678i \(0.407063\pi\)
\(752\) 5.35092 0.195128
\(753\) −7.91598 −0.288475
\(754\) −32.6477 −1.18896
\(755\) −57.0179 −2.07509
\(756\) 0 0
\(757\) −14.9534 −0.543491 −0.271746 0.962369i \(-0.587601\pi\)
−0.271746 + 0.962369i \(0.587601\pi\)
\(758\) 0.116960 0.00424817
\(759\) 2.34092 0.0849699
\(760\) 59.0618 2.14240
\(761\) −25.1974 −0.913404 −0.456702 0.889620i \(-0.650969\pi\)
−0.456702 + 0.889620i \(0.650969\pi\)
\(762\) −9.66237 −0.350031
\(763\) 0 0
\(764\) 3.99335 0.144474
\(765\) 15.3058 0.553384
\(766\) −11.0106 −0.397828
\(767\) 7.18003 0.259256
\(768\) −15.5020 −0.559379
\(769\) −9.10070 −0.328180 −0.164090 0.986445i \(-0.552469\pi\)
−0.164090 + 0.986445i \(0.552469\pi\)
\(770\) 0 0
\(771\) 5.83445 0.210122
\(772\) −8.66002 −0.311681
\(773\) 13.8184 0.497015 0.248507 0.968630i \(-0.420060\pi\)
0.248507 + 0.968630i \(0.420060\pi\)
\(774\) 5.73867 0.206272
\(775\) 70.4138 2.52934
\(776\) −12.9714 −0.465646
\(777\) 0 0
\(778\) −30.6420 −1.09857
\(779\) 5.23036 0.187397
\(780\) 10.5438 0.377527
\(781\) −18.7556 −0.671129
\(782\) −7.06981 −0.252816
\(783\) −8.04051 −0.287344
\(784\) 0 0
\(785\) 12.7581 0.455356
\(786\) −20.3288 −0.725104
\(787\) −24.4151 −0.870306 −0.435153 0.900357i \(-0.643306\pi\)
−0.435153 + 0.900357i \(0.643306\pi\)
\(788\) 2.90915 0.103634
\(789\) −1.97786 −0.0704136
\(790\) 23.6119 0.840074
\(791\) 0 0
\(792\) −4.67413 −0.166088
\(793\) −40.1201 −1.42471
\(794\) 7.72856 0.274276
\(795\) 35.0349 1.24256
\(796\) −11.2520 −0.398815
\(797\) −33.4142 −1.18359 −0.591796 0.806088i \(-0.701581\pi\)
−0.591796 + 0.806088i \(0.701581\pi\)
\(798\) 0 0
\(799\) 12.1580 0.430120
\(800\) 35.1004 1.24098
\(801\) 18.1860 0.642569
\(802\) −13.3281 −0.470632
\(803\) 21.0999 0.744601
\(804\) −6.20757 −0.218924
\(805\) 0 0
\(806\) 33.5424 1.18148
\(807\) 23.3647 0.822478
\(808\) 38.3385 1.34874
\(809\) −19.3112 −0.678947 −0.339473 0.940616i \(-0.610249\pi\)
−0.339473 + 0.940616i \(0.610249\pi\)
\(810\) −4.06198 −0.142724
\(811\) 39.8362 1.39884 0.699418 0.714713i \(-0.253442\pi\)
0.699418 + 0.714713i \(0.253442\pi\)
\(812\) 0 0
\(813\) 23.7310 0.832281
\(814\) −15.9228 −0.558092
\(815\) 69.0580 2.41900
\(816\) 7.62397 0.266892
\(817\) 27.1740 0.950699
\(818\) −14.2206 −0.497213
\(819\) 0 0
\(820\) 2.86824 0.100163
\(821\) 39.6593 1.38412 0.692059 0.721841i \(-0.256704\pi\)
0.692059 + 0.721841i \(0.256704\pi\)
\(822\) −2.76804 −0.0965464
\(823\) −19.0595 −0.664373 −0.332186 0.943214i \(-0.607786\pi\)
−0.332186 + 0.943214i \(0.607786\pi\)
\(824\) 54.0418 1.88264
\(825\) 12.9750 0.451732
\(826\) 0 0
\(827\) 17.1040 0.594763 0.297381 0.954759i \(-0.403887\pi\)
0.297381 + 0.954759i \(0.403887\pi\)
\(828\) −1.19944 −0.0416833
\(829\) −10.2235 −0.355079 −0.177539 0.984114i \(-0.556814\pi\)
−0.177539 + 0.984114i \(0.556814\pi\)
\(830\) 47.1854 1.63783
\(831\) 21.0539 0.730353
\(832\) 30.1878 1.04657
\(833\) 0 0
\(834\) 4.70450 0.162904
\(835\) −37.6742 −1.30377
\(836\) −6.20974 −0.214768
\(837\) 8.26086 0.285537
\(838\) 31.8729 1.10103
\(839\) −46.7936 −1.61549 −0.807747 0.589530i \(-0.799313\pi\)
−0.807747 + 0.589530i \(0.799313\pi\)
\(840\) 0 0
\(841\) 35.6498 1.22930
\(842\) 7.69903 0.265326
\(843\) −25.8960 −0.891906
\(844\) 10.3896 0.357623
\(845\) −1.88741 −0.0649289
\(846\) −3.22659 −0.110933
\(847\) 0 0
\(848\) 17.4512 0.599276
\(849\) −25.7797 −0.884758
\(850\) −39.1859 −1.34406
\(851\) −14.5635 −0.499230
\(852\) 9.60999 0.329233
\(853\) −5.07317 −0.173702 −0.0868509 0.996221i \(-0.527680\pi\)
−0.0868509 + 0.996221i \(0.527680\pi\)
\(854\) 0 0
\(855\) −19.2345 −0.657806
\(856\) 27.4276 0.937455
\(857\) 11.5246 0.393674 0.196837 0.980436i \(-0.436933\pi\)
0.196837 + 0.980436i \(0.436933\pi\)
\(858\) 6.18078 0.211009
\(859\) −58.4061 −1.99279 −0.996395 0.0848356i \(-0.972963\pi\)
−0.996395 + 0.0848356i \(0.972963\pi\)
\(860\) 14.9018 0.508146
\(861\) 0 0
\(862\) 38.3018 1.30456
\(863\) 22.5392 0.767244 0.383622 0.923490i \(-0.374677\pi\)
0.383622 + 0.923490i \(0.374677\pi\)
\(864\) 4.11793 0.140095
\(865\) −51.5139 −1.75153
\(866\) −42.1754 −1.43318
\(867\) 0.322719 0.0109601
\(868\) 0 0
\(869\) −8.84847 −0.300164
\(870\) 32.6604 1.10729
\(871\) 29.2573 0.991347
\(872\) 40.2184 1.36197
\(873\) 4.22436 0.142973
\(874\) 8.88448 0.300522
\(875\) 0 0
\(876\) −10.8112 −0.365276
\(877\) 4.63609 0.156550 0.0782749 0.996932i \(-0.475059\pi\)
0.0782749 + 0.996932i \(0.475059\pi\)
\(878\) −33.8829 −1.14349
\(879\) 20.8476 0.703171
\(880\) 10.2541 0.345666
\(881\) −34.1449 −1.15037 −0.575185 0.818023i \(-0.695070\pi\)
−0.575185 + 0.818023i \(0.695070\pi\)
\(882\) 0 0
\(883\) −1.63476 −0.0550141 −0.0275071 0.999622i \(-0.508757\pi\)
−0.0275071 + 0.999622i \(0.508757\pi\)
\(884\) 11.9331 0.401355
\(885\) −7.18283 −0.241448
\(886\) −21.7086 −0.729315
\(887\) 2.28069 0.0765781 0.0382890 0.999267i \(-0.487809\pi\)
0.0382890 + 0.999267i \(0.487809\pi\)
\(888\) 29.0790 0.975829
\(889\) 0 0
\(890\) −73.8710 −2.47616
\(891\) 1.52221 0.0509960
\(892\) 18.6260 0.623643
\(893\) −15.2787 −0.511283
\(894\) −4.66307 −0.155956
\(895\) −22.8366 −0.763345
\(896\) 0 0
\(897\) 5.65315 0.188753
\(898\) 36.6598 1.22335
\(899\) −66.4216 −2.21528
\(900\) −6.64813 −0.221604
\(901\) 39.6515 1.32098
\(902\) 1.68137 0.0559836
\(903\) 0 0
\(904\) −2.02188 −0.0672468
\(905\) 80.6573 2.68114
\(906\) 17.1258 0.568967
\(907\) −4.61452 −0.153223 −0.0766113 0.997061i \(-0.524410\pi\)
−0.0766113 + 0.997061i \(0.524410\pi\)
\(908\) −2.94049 −0.0975836
\(909\) −12.4856 −0.414121
\(910\) 0 0
\(911\) 37.2131 1.23292 0.616462 0.787385i \(-0.288565\pi\)
0.616462 + 0.787385i \(0.288565\pi\)
\(912\) −9.58087 −0.317254
\(913\) −17.6825 −0.585207
\(914\) −20.6723 −0.683778
\(915\) 40.1358 1.32685
\(916\) 5.08215 0.167919
\(917\) 0 0
\(918\) −4.59724 −0.151731
\(919\) −25.5836 −0.843926 −0.421963 0.906613i \(-0.638659\pi\)
−0.421963 + 0.906613i \(0.638659\pi\)
\(920\) 17.3655 0.572522
\(921\) −9.56642 −0.315224
\(922\) −0.282796 −0.00931341
\(923\) −45.2935 −1.49085
\(924\) 0 0
\(925\) −80.7211 −2.65409
\(926\) −23.3088 −0.765974
\(927\) −17.5997 −0.578048
\(928\) −33.1103 −1.08690
\(929\) −59.7088 −1.95898 −0.979491 0.201488i \(-0.935422\pi\)
−0.979491 + 0.201488i \(0.935422\pi\)
\(930\) −33.5555 −1.10033
\(931\) 0 0
\(932\) 6.38115 0.209021
\(933\) −16.1256 −0.527929
\(934\) −1.13334 −0.0370839
\(935\) 23.2987 0.761950
\(936\) −11.2877 −0.368950
\(937\) −2.29189 −0.0748728 −0.0374364 0.999299i \(-0.511919\pi\)
−0.0374364 + 0.999299i \(0.511919\pi\)
\(938\) 0 0
\(939\) 21.2132 0.692266
\(940\) −8.37859 −0.273279
\(941\) 31.1495 1.01544 0.507722 0.861521i \(-0.330488\pi\)
0.507722 + 0.861521i \(0.330488\pi\)
\(942\) −3.83200 −0.124853
\(943\) 1.53784 0.0500790
\(944\) −3.57783 −0.116448
\(945\) 0 0
\(946\) 8.73547 0.284015
\(947\) −18.6973 −0.607580 −0.303790 0.952739i \(-0.598252\pi\)
−0.303790 + 0.952739i \(0.598252\pi\)
\(948\) 4.53377 0.147250
\(949\) 50.9549 1.65407
\(950\) 49.2440 1.59769
\(951\) 13.4949 0.437603
\(952\) 0 0
\(953\) 15.2900 0.495291 0.247646 0.968851i \(-0.420343\pi\)
0.247646 + 0.968851i \(0.420343\pi\)
\(954\) −10.5230 −0.340696
\(955\) 18.8287 0.609282
\(956\) 10.6878 0.345668
\(957\) −12.2394 −0.395642
\(958\) 30.0487 0.970829
\(959\) 0 0
\(960\) −30.1996 −0.974687
\(961\) 37.2419 1.20135
\(962\) −38.4524 −1.23975
\(963\) −8.93227 −0.287838
\(964\) 10.3633 0.333781
\(965\) −40.8321 −1.31443
\(966\) 0 0
\(967\) −36.5656 −1.17587 −0.587934 0.808909i \(-0.700059\pi\)
−0.587934 + 0.808909i \(0.700059\pi\)
\(968\) 26.6618 0.856942
\(969\) −21.7691 −0.699323
\(970\) −17.1593 −0.550951
\(971\) 8.08521 0.259467 0.129733 0.991549i \(-0.458588\pi\)
0.129733 + 0.991549i \(0.458588\pi\)
\(972\) −0.779950 −0.0250169
\(973\) 0 0
\(974\) 13.4040 0.429493
\(975\) 31.3337 1.00348
\(976\) 19.9920 0.639928
\(977\) 50.6243 1.61962 0.809808 0.586695i \(-0.199571\pi\)
0.809808 + 0.586695i \(0.199571\pi\)
\(978\) −20.7421 −0.663260
\(979\) 27.6829 0.884749
\(980\) 0 0
\(981\) −13.0978 −0.418181
\(982\) 29.7581 0.949619
\(983\) −41.8918 −1.33614 −0.668070 0.744098i \(-0.732879\pi\)
−0.668070 + 0.744098i \(0.732879\pi\)
\(984\) −3.07062 −0.0978877
\(985\) 13.7167 0.437049
\(986\) 36.9641 1.17718
\(987\) 0 0
\(988\) −14.9961 −0.477089
\(989\) 7.98975 0.254059
\(990\) −6.18320 −0.196515
\(991\) −29.9239 −0.950564 −0.475282 0.879833i \(-0.657654\pi\)
−0.475282 + 0.879833i \(0.657654\pi\)
\(992\) 34.0176 1.08006
\(993\) 5.17282 0.164155
\(994\) 0 0
\(995\) −53.0531 −1.68190
\(996\) 9.06017 0.287082
\(997\) 11.3961 0.360919 0.180459 0.983582i \(-0.442242\pi\)
0.180459 + 0.983582i \(0.442242\pi\)
\(998\) −8.52433 −0.269833
\(999\) −9.47010 −0.299621
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 \(a_p\))