Properties

Label 6027.2.a.u.1.2
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 4
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: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.8468.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.704624\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.704624 q^{2} +1.00000 q^{3} -1.50350 q^{4} -1.50350 q^{5} -0.704624 q^{6} +2.46865 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.704624 q^{2} +1.00000 q^{3} -1.50350 q^{4} -1.50350 q^{5} -0.704624 q^{6} +2.46865 q^{8} +1.00000 q^{9} +1.05941 q^{10} -4.26753 q^{11} -1.50350 q^{12} -2.30238 q^{13} -1.50350 q^{15} +1.26753 q^{16} -0.905744 q^{17} -0.704624 q^{18} -1.17328 q^{19} +2.26053 q^{20} +3.00701 q^{22} -0.893136 q^{23} +2.46865 q^{24} -2.73947 q^{25} +1.62232 q^{26} +1.00000 q^{27} +3.32694 q^{29} +1.05941 q^{30} +3.09426 q^{31} -5.83045 q^{32} -4.26753 q^{33} +0.638209 q^{34} -1.50350 q^{36} -2.36179 q^{37} +0.826721 q^{38} -2.30238 q^{39} -3.71163 q^{40} +1.00000 q^{41} -7.84305 q^{43} +6.41626 q^{44} -1.50350 q^{45} +0.629325 q^{46} +1.30567 q^{47} +1.26753 q^{48} +1.93030 q^{50} -0.905744 q^{51} +3.46165 q^{52} -6.64894 q^{53} -0.704624 q^{54} +6.41626 q^{55} -1.17328 q^{57} -2.34424 q^{58} +0.638209 q^{59} +2.26053 q^{60} +9.84305 q^{61} -2.18029 q^{62} +1.57320 q^{64} +3.46165 q^{65} +3.00701 q^{66} -13.4478 q^{67} +1.36179 q^{68} -0.893136 q^{69} -0.245293 q^{71} +2.46865 q^{72} +2.08725 q^{73} +1.66418 q^{74} -2.73947 q^{75} +1.76403 q^{76} +1.62232 q^{78} -14.5736 q^{79} -1.90574 q^{80} +1.00000 q^{81} -0.704624 q^{82} +6.41626 q^{83} +1.36179 q^{85} +5.52641 q^{86} +3.32694 q^{87} -10.5351 q^{88} +1.81149 q^{89} +1.05941 q^{90} +1.34283 q^{92} +3.09426 q^{93} -0.920006 q^{94} +1.76403 q^{95} -5.83045 q^{96} +6.29416 q^{97} -4.26753 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + q^{2} + 4q^{3} + 3q^{4} + 3q^{5} + q^{6} + 3q^{8} + 4q^{9} + O(q^{10}) \) \( 4q + q^{2} + 4q^{3} + 3q^{4} + 3q^{5} + q^{6} + 3q^{8} + 4q^{9} + 5q^{10} - 5q^{11} + 3q^{12} + 5q^{13} + 3q^{15} - 7q^{16} - 5q^{17} + q^{18} + 6q^{19} + 15q^{20} - 6q^{22} + 3q^{23} + 3q^{24} - 5q^{25} - q^{26} + 4q^{27} + 2q^{29} + 5q^{30} + 11q^{31} - 3q^{32} - 5q^{33} + 16q^{34} + 3q^{36} + 4q^{37} + 14q^{38} + 5q^{39} + 7q^{40} + 4q^{41} - 19q^{43} + 3q^{45} - 23q^{46} + 4q^{47} - 7q^{48} + 12q^{50} - 5q^{51} + 25q^{52} + 9q^{53} + q^{54} + 6q^{57} + 25q^{58} + 16q^{59} + 15q^{60} + 27q^{61} + 20q^{62} - 7q^{64} + 25q^{65} - 6q^{66} - 13q^{67} - 8q^{68} + 3q^{69} + q^{71} + 3q^{72} + 25q^{73} - 21q^{74} - 5q^{75} + 4q^{76} - q^{78} - q^{79} - 9q^{80} + 4q^{81} + q^{82} - 8q^{85} + 16q^{86} + 2q^{87} - 18q^{88} + 10q^{89} + 5q^{90} + 15q^{92} + 11q^{93} - 13q^{94} + 4q^{95} - 3q^{96} - 15q^{97} - 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.704624 −0.498245 −0.249122 0.968472i \(-0.580142\pi\)
−0.249122 + 0.968472i \(0.580142\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.50350 −0.751752
\(5\) −1.50350 −0.672388 −0.336194 0.941793i \(-0.609140\pi\)
−0.336194 + 0.941793i \(0.609140\pi\)
\(6\) −0.704624 −0.287662
\(7\) 0 0
\(8\) 2.46865 0.872801
\(9\) 1.00000 0.333333
\(10\) 1.05941 0.335014
\(11\) −4.26753 −1.28671 −0.643355 0.765568i \(-0.722458\pi\)
−0.643355 + 0.765568i \(0.722458\pi\)
\(12\) −1.50350 −0.434024
\(13\) −2.30238 −0.638567 −0.319283 0.947659i \(-0.603442\pi\)
−0.319283 + 0.947659i \(0.603442\pi\)
\(14\) 0 0
\(15\) −1.50350 −0.388203
\(16\) 1.26753 0.316884
\(17\) −0.905744 −0.219675 −0.109838 0.993950i \(-0.535033\pi\)
−0.109838 + 0.993950i \(0.535033\pi\)
\(18\) −0.704624 −0.166082
\(19\) −1.17328 −0.269169 −0.134584 0.990902i \(-0.542970\pi\)
−0.134584 + 0.990902i \(0.542970\pi\)
\(20\) 2.26053 0.505469
\(21\) 0 0
\(22\) 3.00701 0.641096
\(23\) −0.893136 −0.186232 −0.0931159 0.995655i \(-0.529683\pi\)
−0.0931159 + 0.995655i \(0.529683\pi\)
\(24\) 2.46865 0.503912
\(25\) −2.73947 −0.547895
\(26\) 1.62232 0.318162
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 3.32694 0.617797 0.308899 0.951095i \(-0.400040\pi\)
0.308899 + 0.951095i \(0.400040\pi\)
\(30\) 1.05941 0.193420
\(31\) 3.09426 0.555745 0.277872 0.960618i \(-0.410371\pi\)
0.277872 + 0.960618i \(0.410371\pi\)
\(32\) −5.83045 −1.03069
\(33\) −4.26753 −0.742882
\(34\) 0.638209 0.109452
\(35\) 0 0
\(36\) −1.50350 −0.250584
\(37\) −2.36179 −0.388276 −0.194138 0.980974i \(-0.562191\pi\)
−0.194138 + 0.980974i \(0.562191\pi\)
\(38\) 0.826721 0.134112
\(39\) −2.30238 −0.368677
\(40\) −3.71163 −0.586861
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −7.84305 −1.19605 −0.598027 0.801476i \(-0.704049\pi\)
−0.598027 + 0.801476i \(0.704049\pi\)
\(44\) 6.41626 0.967287
\(45\) −1.50350 −0.224129
\(46\) 0.629325 0.0927890
\(47\) 1.30567 0.190451 0.0952257 0.995456i \(-0.469643\pi\)
0.0952257 + 0.995456i \(0.469643\pi\)
\(48\) 1.26753 0.182953
\(49\) 0 0
\(50\) 1.93030 0.272986
\(51\) −0.905744 −0.126830
\(52\) 3.46165 0.480044
\(53\) −6.64894 −0.913303 −0.456651 0.889646i \(-0.650951\pi\)
−0.456651 + 0.889646i \(0.650951\pi\)
\(54\) −0.704624 −0.0958872
\(55\) 6.41626 0.865168
\(56\) 0 0
\(57\) −1.17328 −0.155405
\(58\) −2.34424 −0.307814
\(59\) 0.638209 0.0830878 0.0415439 0.999137i \(-0.486772\pi\)
0.0415439 + 0.999137i \(0.486772\pi\)
\(60\) 2.26053 0.291833
\(61\) 9.84305 1.26027 0.630137 0.776484i \(-0.282999\pi\)
0.630137 + 0.776484i \(0.282999\pi\)
\(62\) −2.18029 −0.276897
\(63\) 0 0
\(64\) 1.57320 0.196651
\(65\) 3.46165 0.429364
\(66\) 3.00701 0.370137
\(67\) −13.4478 −1.64291 −0.821457 0.570271i \(-0.806838\pi\)
−0.821457 + 0.570271i \(0.806838\pi\)
\(68\) 1.36179 0.165141
\(69\) −0.893136 −0.107521
\(70\) 0 0
\(71\) −0.245293 −0.0291110 −0.0145555 0.999894i \(-0.504633\pi\)
−0.0145555 + 0.999894i \(0.504633\pi\)
\(72\) 2.46865 0.290934
\(73\) 2.08725 0.244294 0.122147 0.992512i \(-0.461022\pi\)
0.122147 + 0.992512i \(0.461022\pi\)
\(74\) 1.66418 0.193456
\(75\) −2.73947 −0.316327
\(76\) 1.76403 0.202348
\(77\) 0 0
\(78\) 1.62232 0.183691
\(79\) −14.5736 −1.63966 −0.819832 0.572605i \(-0.805933\pi\)
−0.819832 + 0.572605i \(0.805933\pi\)
\(80\) −1.90574 −0.213069
\(81\) 1.00000 0.111111
\(82\) −0.704624 −0.0778127
\(83\) 6.41626 0.704276 0.352138 0.935948i \(-0.385455\pi\)
0.352138 + 0.935948i \(0.385455\pi\)
\(84\) 0 0
\(85\) 1.36179 0.147707
\(86\) 5.52641 0.595928
\(87\) 3.32694 0.356685
\(88\) −10.5351 −1.12304
\(89\) 1.81149 0.192017 0.0960087 0.995380i \(-0.469392\pi\)
0.0960087 + 0.995380i \(0.469392\pi\)
\(90\) 1.05941 0.111671
\(91\) 0 0
\(92\) 1.34283 0.140000
\(93\) 3.09426 0.320859
\(94\) −0.920006 −0.0948914
\(95\) 1.76403 0.180986
\(96\) −5.83045 −0.595067
\(97\) 6.29416 0.639075 0.319538 0.947574i \(-0.396472\pi\)
0.319538 + 0.947574i \(0.396472\pi\)
\(98\) 0 0
\(99\) −4.26753 −0.428903
\(100\) 4.11881 0.411881
\(101\) −10.2816 −1.02305 −0.511526 0.859268i \(-0.670920\pi\)
−0.511526 + 0.859268i \(0.670920\pi\)
\(102\) 0.638209 0.0631922
\(103\) 8.68708 0.855963 0.427982 0.903787i \(-0.359225\pi\)
0.427982 + 0.903787i \(0.359225\pi\)
\(104\) −5.68379 −0.557342
\(105\) 0 0
\(106\) 4.68501 0.455048
\(107\) 17.9551 1.73578 0.867890 0.496756i \(-0.165476\pi\)
0.867890 + 0.496756i \(0.165476\pi\)
\(108\) −1.50350 −0.144675
\(109\) −1.29866 −0.124389 −0.0621946 0.998064i \(-0.519810\pi\)
−0.0621946 + 0.998064i \(0.519810\pi\)
\(110\) −4.52105 −0.431065
\(111\) −2.36179 −0.224171
\(112\) 0 0
\(113\) 3.46493 0.325953 0.162977 0.986630i \(-0.447890\pi\)
0.162977 + 0.986630i \(0.447890\pi\)
\(114\) 0.826721 0.0774295
\(115\) 1.34283 0.125220
\(116\) −5.00207 −0.464431
\(117\) −2.30238 −0.212856
\(118\) −0.449698 −0.0413981
\(119\) 0 0
\(120\) −3.71163 −0.338824
\(121\) 7.21185 0.655623
\(122\) −6.93566 −0.627925
\(123\) 1.00000 0.0901670
\(124\) −4.65223 −0.417782
\(125\) 11.6363 1.04079
\(126\) 0 0
\(127\) 11.1398 0.988501 0.494250 0.869320i \(-0.335443\pi\)
0.494250 + 0.869320i \(0.335443\pi\)
\(128\) 10.5524 0.932707
\(129\) −7.84305 −0.690542
\(130\) −2.43916 −0.213928
\(131\) −4.43850 −0.387793 −0.193897 0.981022i \(-0.562113\pi\)
−0.193897 + 0.981022i \(0.562113\pi\)
\(132\) 6.41626 0.558464
\(133\) 0 0
\(134\) 9.47566 0.818573
\(135\) −1.50350 −0.129401
\(136\) −2.23597 −0.191733
\(137\) 10.7362 0.917255 0.458627 0.888629i \(-0.348341\pi\)
0.458627 + 0.888629i \(0.348341\pi\)
\(138\) 0.629325 0.0535717
\(139\) 12.1836 1.03340 0.516699 0.856167i \(-0.327161\pi\)
0.516699 + 0.856167i \(0.327161\pi\)
\(140\) 0 0
\(141\) 1.30567 0.109957
\(142\) 0.172840 0.0145044
\(143\) 9.82551 0.821650
\(144\) 1.26753 0.105628
\(145\) −5.00207 −0.415399
\(146\) −1.47072 −0.121718
\(147\) 0 0
\(148\) 3.55096 0.291887
\(149\) 6.11716 0.501137 0.250569 0.968099i \(-0.419382\pi\)
0.250569 + 0.968099i \(0.419382\pi\)
\(150\) 1.93030 0.157608
\(151\) −8.41626 −0.684905 −0.342453 0.939535i \(-0.611258\pi\)
−0.342453 + 0.939535i \(0.611258\pi\)
\(152\) −2.89642 −0.234931
\(153\) −0.905744 −0.0732251
\(154\) 0 0
\(155\) −4.65223 −0.373676
\(156\) 3.46165 0.277153
\(157\) −8.46372 −0.675478 −0.337739 0.941240i \(-0.609662\pi\)
−0.337739 + 0.941240i \(0.609662\pi\)
\(158\) 10.2689 0.816953
\(159\) −6.64894 −0.527295
\(160\) 8.76610 0.693021
\(161\) 0 0
\(162\) −0.704624 −0.0553605
\(163\) 8.70603 0.681909 0.340955 0.940080i \(-0.389250\pi\)
0.340955 + 0.940080i \(0.389250\pi\)
\(164\) −1.50350 −0.117404
\(165\) 6.41626 0.499505
\(166\) −4.52105 −0.350902
\(167\) −7.09304 −0.548876 −0.274438 0.961605i \(-0.588492\pi\)
−0.274438 + 0.961605i \(0.588492\pi\)
\(168\) 0 0
\(169\) −7.69903 −0.592233
\(170\) −0.959551 −0.0735942
\(171\) −1.17328 −0.0897229
\(172\) 11.7921 0.899137
\(173\) 16.8030 1.27751 0.638756 0.769409i \(-0.279449\pi\)
0.638756 + 0.769409i \(0.279449\pi\)
\(174\) −2.34424 −0.177717
\(175\) 0 0
\(176\) −5.40925 −0.407737
\(177\) 0.638209 0.0479708
\(178\) −1.27642 −0.0956716
\(179\) 4.85663 0.363002 0.181501 0.983391i \(-0.441904\pi\)
0.181501 + 0.983391i \(0.441904\pi\)
\(180\) 2.26053 0.168490
\(181\) −5.94597 −0.441961 −0.220980 0.975278i \(-0.570926\pi\)
−0.220980 + 0.975278i \(0.570926\pi\)
\(182\) 0 0
\(183\) 9.84305 0.727619
\(184\) −2.20484 −0.162543
\(185\) 3.55096 0.261072
\(186\) −2.18029 −0.159866
\(187\) 3.86530 0.282658
\(188\) −1.96308 −0.143172
\(189\) 0 0
\(190\) −1.24298 −0.0901752
\(191\) −14.0854 −1.01918 −0.509591 0.860417i \(-0.670203\pi\)
−0.509591 + 0.860417i \(0.670203\pi\)
\(192\) 1.57320 0.113536
\(193\) 9.65924 0.695287 0.347644 0.937627i \(-0.386982\pi\)
0.347644 + 0.937627i \(0.386982\pi\)
\(194\) −4.43502 −0.318416
\(195\) 3.46165 0.247894
\(196\) 0 0
\(197\) −1.13984 −0.0812102 −0.0406051 0.999175i \(-0.512929\pi\)
−0.0406051 + 0.999175i \(0.512929\pi\)
\(198\) 3.00701 0.213699
\(199\) −6.81027 −0.482768 −0.241384 0.970430i \(-0.577601\pi\)
−0.241384 + 0.970430i \(0.577601\pi\)
\(200\) −6.76282 −0.478203
\(201\) −13.4478 −0.948536
\(202\) 7.24463 0.509731
\(203\) 0 0
\(204\) 1.36179 0.0953444
\(205\) −1.50350 −0.105009
\(206\) −6.12113 −0.426479
\(207\) −0.893136 −0.0620772
\(208\) −2.91835 −0.202351
\(209\) 5.00701 0.346342
\(210\) 0 0
\(211\) 3.45439 0.237810 0.118905 0.992906i \(-0.462062\pi\)
0.118905 + 0.992906i \(0.462062\pi\)
\(212\) 9.99672 0.686577
\(213\) −0.245293 −0.0168072
\(214\) −12.6516 −0.864843
\(215\) 11.7921 0.804212
\(216\) 2.46865 0.167971
\(217\) 0 0
\(218\) 0.915068 0.0619762
\(219\) 2.08725 0.141043
\(220\) −9.64687 −0.650392
\(221\) 2.08537 0.140277
\(222\) 1.66418 0.111692
\(223\) −3.01195 −0.201695 −0.100847 0.994902i \(-0.532155\pi\)
−0.100847 + 0.994902i \(0.532155\pi\)
\(224\) 0 0
\(225\) −2.73947 −0.182632
\(226\) −2.44147 −0.162404
\(227\) −14.0619 −0.933322 −0.466661 0.884436i \(-0.654543\pi\)
−0.466661 + 0.884436i \(0.654543\pi\)
\(228\) 1.76403 0.116826
\(229\) 1.07999 0.0713680 0.0356840 0.999363i \(-0.488639\pi\)
0.0356840 + 0.999363i \(0.488639\pi\)
\(230\) −0.946193 −0.0623901
\(231\) 0 0
\(232\) 8.21307 0.539214
\(233\) 5.55030 0.363612 0.181806 0.983334i \(-0.441806\pi\)
0.181806 + 0.983334i \(0.441806\pi\)
\(234\) 1.62232 0.106054
\(235\) −1.96308 −0.128057
\(236\) −0.959551 −0.0624614
\(237\) −14.5736 −0.946660
\(238\) 0 0
\(239\) −1.45836 −0.0943335 −0.0471668 0.998887i \(-0.515019\pi\)
−0.0471668 + 0.998887i \(0.515019\pi\)
\(240\) −1.90574 −0.123015
\(241\) −1.68335 −0.108434 −0.0542172 0.998529i \(-0.517266\pi\)
−0.0542172 + 0.998529i \(0.517266\pi\)
\(242\) −5.08165 −0.326661
\(243\) 1.00000 0.0641500
\(244\) −14.7991 −0.947414
\(245\) 0 0
\(246\) −0.704624 −0.0449252
\(247\) 2.70134 0.171882
\(248\) 7.63865 0.485055
\(249\) 6.41626 0.406614
\(250\) −8.19924 −0.518566
\(251\) 18.8882 1.19221 0.596106 0.802906i \(-0.296714\pi\)
0.596106 + 0.802906i \(0.296714\pi\)
\(252\) 0 0
\(253\) 3.81149 0.239626
\(254\) −7.84940 −0.492515
\(255\) 1.36179 0.0852786
\(256\) −10.5819 −0.661367
\(257\) −15.1796 −0.946879 −0.473440 0.880826i \(-0.656988\pi\)
−0.473440 + 0.880826i \(0.656988\pi\)
\(258\) 5.52641 0.344059
\(259\) 0 0
\(260\) −5.20460 −0.322776
\(261\) 3.32694 0.205932
\(262\) 3.12747 0.193216
\(263\) −1.96021 −0.120872 −0.0604359 0.998172i \(-0.519249\pi\)
−0.0604359 + 0.998172i \(0.519249\pi\)
\(264\) −10.5351 −0.648389
\(265\) 9.99672 0.614093
\(266\) 0 0
\(267\) 1.81149 0.110861
\(268\) 20.2189 1.23506
\(269\) 30.4771 1.85822 0.929110 0.369804i \(-0.120575\pi\)
0.929110 + 0.369804i \(0.120575\pi\)
\(270\) 1.05941 0.0644734
\(271\) −5.84634 −0.355140 −0.177570 0.984108i \(-0.556824\pi\)
−0.177570 + 0.984108i \(0.556824\pi\)
\(272\) −1.14806 −0.0696115
\(273\) 0 0
\(274\) −7.56498 −0.457017
\(275\) 11.6908 0.704982
\(276\) 1.34283 0.0808291
\(277\) 7.11638 0.427582 0.213791 0.976879i \(-0.431419\pi\)
0.213791 + 0.976879i \(0.431419\pi\)
\(278\) −8.58484 −0.514885
\(279\) 3.09426 0.185248
\(280\) 0 0
\(281\) −4.47632 −0.267035 −0.133518 0.991046i \(-0.542627\pi\)
−0.133518 + 0.991046i \(0.542627\pi\)
\(282\) −0.920006 −0.0547856
\(283\) −0.675569 −0.0401584 −0.0200792 0.999798i \(-0.506392\pi\)
−0.0200792 + 0.999798i \(0.506392\pi\)
\(284\) 0.368800 0.0218842
\(285\) 1.76403 0.104492
\(286\) −6.92329 −0.409383
\(287\) 0 0
\(288\) −5.83045 −0.343562
\(289\) −16.1796 −0.951743
\(290\) 3.52458 0.206971
\(291\) 6.29416 0.368970
\(292\) −3.13818 −0.183648
\(293\) 2.58722 0.151147 0.0755736 0.997140i \(-0.475921\pi\)
0.0755736 + 0.997140i \(0.475921\pi\)
\(294\) 0 0
\(295\) −0.959551 −0.0558672
\(296\) −5.83045 −0.338888
\(297\) −4.26753 −0.247627
\(298\) −4.31030 −0.249689
\(299\) 2.05634 0.118921
\(300\) 4.11881 0.237800
\(301\) 0 0
\(302\) 5.93030 0.341250
\(303\) −10.2816 −0.590660
\(304\) −1.48717 −0.0852952
\(305\) −14.7991 −0.847393
\(306\) 0.638209 0.0364840
\(307\) 27.0130 1.54172 0.770858 0.637007i \(-0.219828\pi\)
0.770858 + 0.637007i \(0.219828\pi\)
\(308\) 0 0
\(309\) 8.68708 0.494191
\(310\) 3.27807 0.186182
\(311\) 29.6830 1.68317 0.841585 0.540125i \(-0.181623\pi\)
0.841585 + 0.540125i \(0.181623\pi\)
\(312\) −5.68379 −0.321781
\(313\) 14.0091 0.791840 0.395920 0.918285i \(-0.370426\pi\)
0.395920 + 0.918285i \(0.370426\pi\)
\(314\) 5.96374 0.336553
\(315\) 0 0
\(316\) 21.9115 1.23262
\(317\) 21.2836 1.19541 0.597704 0.801717i \(-0.296080\pi\)
0.597704 + 0.801717i \(0.296080\pi\)
\(318\) 4.68501 0.262722
\(319\) −14.1978 −0.794926
\(320\) −2.36532 −0.132225
\(321\) 17.9551 1.00215
\(322\) 0 0
\(323\) 1.06269 0.0591297
\(324\) −1.50350 −0.0835280
\(325\) 6.30732 0.349867
\(326\) −6.13448 −0.339758
\(327\) −1.29866 −0.0718161
\(328\) 2.46865 0.136309
\(329\) 0 0
\(330\) −4.52105 −0.248876
\(331\) 8.80304 0.483859 0.241930 0.970294i \(-0.422220\pi\)
0.241930 + 0.970294i \(0.422220\pi\)
\(332\) −9.64687 −0.529441
\(333\) −2.36179 −0.129425
\(334\) 4.99793 0.273475
\(335\) 20.2189 1.10467
\(336\) 0 0
\(337\) 32.7158 1.78214 0.891072 0.453863i \(-0.149954\pi\)
0.891072 + 0.453863i \(0.149954\pi\)
\(338\) 5.42492 0.295077
\(339\) 3.46493 0.188189
\(340\) −2.04746 −0.111039
\(341\) −13.2048 −0.715082
\(342\) 0.826721 0.0447040
\(343\) 0 0
\(344\) −19.3618 −1.04392
\(345\) 1.34283 0.0722957
\(346\) −11.8398 −0.636513
\(347\) 32.9033 1.76634 0.883171 0.469051i \(-0.155404\pi\)
0.883171 + 0.469051i \(0.155404\pi\)
\(348\) −5.00207 −0.268139
\(349\) 32.5250 1.74102 0.870511 0.492149i \(-0.163789\pi\)
0.870511 + 0.492149i \(0.163789\pi\)
\(350\) 0 0
\(351\) −2.30238 −0.122892
\(352\) 24.8816 1.32620
\(353\) 7.58131 0.403513 0.201756 0.979436i \(-0.435335\pi\)
0.201756 + 0.979436i \(0.435335\pi\)
\(354\) −0.449698 −0.0239012
\(355\) 0.368800 0.0195738
\(356\) −2.72358 −0.144350
\(357\) 0 0
\(358\) −3.42210 −0.180864
\(359\) 24.6482 1.30088 0.650440 0.759557i \(-0.274584\pi\)
0.650440 + 0.759557i \(0.274584\pi\)
\(360\) −3.71163 −0.195620
\(361\) −17.6234 −0.927548
\(362\) 4.18968 0.220205
\(363\) 7.21185 0.378524
\(364\) 0 0
\(365\) −3.13818 −0.164260
\(366\) −6.93566 −0.362533
\(367\) −21.6318 −1.12917 −0.564586 0.825374i \(-0.690964\pi\)
−0.564586 + 0.825374i \(0.690964\pi\)
\(368\) −1.13208 −0.0590138
\(369\) 1.00000 0.0520579
\(370\) −2.50209 −0.130078
\(371\) 0 0
\(372\) −4.65223 −0.241207
\(373\) −32.2405 −1.66935 −0.834676 0.550741i \(-0.814345\pi\)
−0.834676 + 0.550741i \(0.814345\pi\)
\(374\) −2.72358 −0.140833
\(375\) 11.6363 0.600898
\(376\) 3.22325 0.166226
\(377\) −7.65990 −0.394505
\(378\) 0 0
\(379\) 28.8416 1.48149 0.740747 0.671784i \(-0.234472\pi\)
0.740747 + 0.671784i \(0.234472\pi\)
\(380\) −2.65223 −0.136056
\(381\) 11.1398 0.570711
\(382\) 9.92490 0.507802
\(383\) −31.1691 −1.59267 −0.796333 0.604858i \(-0.793230\pi\)
−0.796333 + 0.604858i \(0.793230\pi\)
\(384\) 10.5524 0.538498
\(385\) 0 0
\(386\) −6.80613 −0.346423
\(387\) −7.84305 −0.398685
\(388\) −9.46330 −0.480426
\(389\) 0.0362595 0.00183843 0.000919215 1.00000i \(-0.499707\pi\)
0.000919215 1.00000i \(0.499707\pi\)
\(390\) −2.43916 −0.123512
\(391\) 0.808953 0.0409105
\(392\) 0 0
\(393\) −4.43850 −0.223893
\(394\) 0.803158 0.0404625
\(395\) 21.9115 1.10249
\(396\) 6.41626 0.322429
\(397\) 34.1952 1.71621 0.858104 0.513477i \(-0.171643\pi\)
0.858104 + 0.513477i \(0.171643\pi\)
\(398\) 4.79868 0.240536
\(399\) 0 0
\(400\) −3.47238 −0.173619
\(401\) 20.3606 1.01676 0.508379 0.861133i \(-0.330245\pi\)
0.508379 + 0.861133i \(0.330245\pi\)
\(402\) 9.47566 0.472603
\(403\) −7.12417 −0.354880
\(404\) 15.4584 0.769082
\(405\) −1.50350 −0.0747097
\(406\) 0 0
\(407\) 10.0790 0.499599
\(408\) −2.23597 −0.110697
\(409\) −10.5257 −0.520465 −0.260232 0.965546i \(-0.583799\pi\)
−0.260232 + 0.965546i \(0.583799\pi\)
\(410\) 1.05941 0.0523203
\(411\) 10.7362 0.529577
\(412\) −13.0611 −0.643472
\(413\) 0 0
\(414\) 0.629325 0.0309297
\(415\) −9.64687 −0.473546
\(416\) 13.4239 0.658162
\(417\) 12.1836 0.596632
\(418\) −3.52806 −0.172563
\(419\) 27.5895 1.34784 0.673919 0.738806i \(-0.264610\pi\)
0.673919 + 0.738806i \(0.264610\pi\)
\(420\) 0 0
\(421\) 33.0924 1.61282 0.806412 0.591354i \(-0.201406\pi\)
0.806412 + 0.591354i \(0.201406\pi\)
\(422\) −2.43405 −0.118488
\(423\) 1.30567 0.0634838
\(424\) −16.4139 −0.797132
\(425\) 2.48126 0.120359
\(426\) 0.172840 0.00837411
\(427\) 0 0
\(428\) −26.9955 −1.30488
\(429\) 9.82551 0.474380
\(430\) −8.30898 −0.400694
\(431\) −4.91044 −0.236528 −0.118264 0.992982i \(-0.537733\pi\)
−0.118264 + 0.992982i \(0.537733\pi\)
\(432\) 1.26753 0.0609843
\(433\) −12.2511 −0.588750 −0.294375 0.955690i \(-0.595111\pi\)
−0.294375 + 0.955690i \(0.595111\pi\)
\(434\) 0 0
\(435\) −5.00207 −0.239831
\(436\) 1.95254 0.0935098
\(437\) 1.04790 0.0501277
\(438\) −1.47072 −0.0702740
\(439\) −15.5133 −0.740408 −0.370204 0.928951i \(-0.620712\pi\)
−0.370204 + 0.928951i \(0.620712\pi\)
\(440\) 15.8395 0.755120
\(441\) 0 0
\(442\) −1.46940 −0.0698924
\(443\) −18.4525 −0.876706 −0.438353 0.898803i \(-0.644438\pi\)
−0.438353 + 0.898803i \(0.644438\pi\)
\(444\) 3.55096 0.168521
\(445\) −2.72358 −0.129110
\(446\) 2.12229 0.100493
\(447\) 6.11716 0.289332
\(448\) 0 0
\(449\) −13.5643 −0.640140 −0.320070 0.947394i \(-0.603706\pi\)
−0.320070 + 0.947394i \(0.603706\pi\)
\(450\) 1.93030 0.0909952
\(451\) −4.26753 −0.200950
\(452\) −5.20954 −0.245036
\(453\) −8.41626 −0.395430
\(454\) 9.90837 0.465023
\(455\) 0 0
\(456\) −2.89642 −0.135637
\(457\) −7.62298 −0.356588 −0.178294 0.983977i \(-0.557058\pi\)
−0.178294 + 0.983977i \(0.557058\pi\)
\(458\) −0.760990 −0.0355587
\(459\) −0.905744 −0.0422765
\(460\) −2.01896 −0.0941343
\(461\) 10.5533 0.491518 0.245759 0.969331i \(-0.420963\pi\)
0.245759 + 0.969331i \(0.420963\pi\)
\(462\) 0 0
\(463\) −22.4384 −1.04280 −0.521400 0.853312i \(-0.674590\pi\)
−0.521400 + 0.853312i \(0.674590\pi\)
\(464\) 4.21701 0.195770
\(465\) −4.65223 −0.215742
\(466\) −3.91088 −0.181168
\(467\) 25.3453 1.17284 0.586421 0.810006i \(-0.300536\pi\)
0.586421 + 0.810006i \(0.300536\pi\)
\(468\) 3.46165 0.160015
\(469\) 0 0
\(470\) 1.38323 0.0638038
\(471\) −8.46372 −0.389987
\(472\) 1.57552 0.0725191
\(473\) 33.4705 1.53898
\(474\) 10.2689 0.471668
\(475\) 3.21417 0.147476
\(476\) 0 0
\(477\) −6.64894 −0.304434
\(478\) 1.02760 0.0470012
\(479\) 37.6491 1.72023 0.860117 0.510098i \(-0.170391\pi\)
0.860117 + 0.510098i \(0.170391\pi\)
\(480\) 8.76610 0.400116
\(481\) 5.43775 0.247940
\(482\) 1.18613 0.0540268
\(483\) 0 0
\(484\) −10.8431 −0.492866
\(485\) −9.46330 −0.429706
\(486\) −0.704624 −0.0319624
\(487\) 7.52337 0.340916 0.170458 0.985365i \(-0.445475\pi\)
0.170458 + 0.985365i \(0.445475\pi\)
\(488\) 24.2991 1.09997
\(489\) 8.70603 0.393700
\(490\) 0 0
\(491\) 19.8758 0.896982 0.448491 0.893787i \(-0.351962\pi\)
0.448491 + 0.893787i \(0.351962\pi\)
\(492\) −1.50350 −0.0677832
\(493\) −3.01336 −0.135715
\(494\) −1.90343 −0.0856394
\(495\) 6.41626 0.288389
\(496\) 3.92208 0.176106
\(497\) 0 0
\(498\) −4.52105 −0.202593
\(499\) −37.6127 −1.68377 −0.841887 0.539654i \(-0.818555\pi\)
−0.841887 + 0.539654i \(0.818555\pi\)
\(500\) −17.4953 −0.782413
\(501\) −7.09304 −0.316894
\(502\) −13.3091 −0.594013
\(503\) 15.2628 0.680536 0.340268 0.940328i \(-0.389482\pi\)
0.340268 + 0.940328i \(0.389482\pi\)
\(504\) 0 0
\(505\) 15.4584 0.687888
\(506\) −2.68567 −0.119392
\(507\) −7.69903 −0.341926
\(508\) −16.7488 −0.743108
\(509\) −11.1269 −0.493192 −0.246596 0.969118i \(-0.579312\pi\)
−0.246596 + 0.969118i \(0.579312\pi\)
\(510\) −0.959551 −0.0424896
\(511\) 0 0
\(512\) −13.6485 −0.603184
\(513\) −1.17328 −0.0518015
\(514\) 10.6959 0.471777
\(515\) −13.0611 −0.575539
\(516\) 11.7921 0.519117
\(517\) −5.57199 −0.245056
\(518\) 0 0
\(519\) 16.8030 0.737572
\(520\) 8.54561 0.374750
\(521\) 17.0795 0.748265 0.374132 0.927375i \(-0.377941\pi\)
0.374132 + 0.927375i \(0.377941\pi\)
\(522\) −2.34424 −0.102605
\(523\) 23.7322 1.03774 0.518869 0.854854i \(-0.326353\pi\)
0.518869 + 0.854854i \(0.326353\pi\)
\(524\) 6.67330 0.291525
\(525\) 0 0
\(526\) 1.38121 0.0602237
\(527\) −2.80260 −0.122083
\(528\) −5.40925 −0.235407
\(529\) −22.2023 −0.965318
\(530\) −7.04393 −0.305969
\(531\) 0.638209 0.0276959
\(532\) 0 0
\(533\) −2.30238 −0.0997273
\(534\) −1.27642 −0.0552360
\(535\) −26.9955 −1.16712
\(536\) −33.1980 −1.43394
\(537\) 4.85663 0.209579
\(538\) −21.4749 −0.925848
\(539\) 0 0
\(540\) 2.26053 0.0972775
\(541\) −27.4226 −1.17899 −0.589495 0.807772i \(-0.700673\pi\)
−0.589495 + 0.807772i \(0.700673\pi\)
\(542\) 4.11947 0.176946
\(543\) −5.94597 −0.255166
\(544\) 5.28089 0.226416
\(545\) 1.95254 0.0836377
\(546\) 0 0
\(547\) −21.2333 −0.907871 −0.453936 0.891034i \(-0.649980\pi\)
−0.453936 + 0.891034i \(0.649980\pi\)
\(548\) −16.1419 −0.689548
\(549\) 9.84305 0.420091
\(550\) −8.23762 −0.351253
\(551\) −3.90343 −0.166292
\(552\) −2.20484 −0.0938444
\(553\) 0 0
\(554\) −5.01438 −0.213040
\(555\) 3.55096 0.150730
\(556\) −18.3181 −0.776859
\(557\) 26.6920 1.13098 0.565489 0.824756i \(-0.308688\pi\)
0.565489 + 0.824756i \(0.308688\pi\)
\(558\) −2.18029 −0.0922990
\(559\) 18.0577 0.763760
\(560\) 0 0
\(561\) 3.86530 0.163193
\(562\) 3.15413 0.133049
\(563\) −5.72358 −0.241220 −0.120610 0.992700i \(-0.538485\pi\)
−0.120610 + 0.992700i \(0.538485\pi\)
\(564\) −1.96308 −0.0826606
\(565\) −5.20954 −0.219167
\(566\) 0.476022 0.0200087
\(567\) 0 0
\(568\) −0.605544 −0.0254081
\(569\) 33.3248 1.39705 0.698523 0.715587i \(-0.253841\pi\)
0.698523 + 0.715587i \(0.253841\pi\)
\(570\) −1.24298 −0.0520626
\(571\) 8.54252 0.357493 0.178747 0.983895i \(-0.442796\pi\)
0.178747 + 0.983895i \(0.442796\pi\)
\(572\) −14.7727 −0.617677
\(573\) −14.0854 −0.588425
\(574\) 0 0
\(575\) 2.44672 0.102035
\(576\) 1.57320 0.0655502
\(577\) −6.13581 −0.255437 −0.127718 0.991810i \(-0.540765\pi\)
−0.127718 + 0.991810i \(0.540765\pi\)
\(578\) 11.4006 0.474201
\(579\) 9.65924 0.401424
\(580\) 7.52064 0.312277
\(581\) 0 0
\(582\) −4.43502 −0.183837
\(583\) 28.3746 1.17516
\(584\) 5.15269 0.213220
\(585\) 3.46165 0.143121
\(586\) −1.82302 −0.0753083
\(587\) −39.5794 −1.63362 −0.816809 0.576908i \(-0.804259\pi\)
−0.816809 + 0.576908i \(0.804259\pi\)
\(588\) 0 0
\(589\) −3.63043 −0.149589
\(590\) 0.676123 0.0278355
\(591\) −1.13984 −0.0468867
\(592\) −2.99365 −0.123038
\(593\) −15.4883 −0.636027 −0.318014 0.948086i \(-0.603016\pi\)
−0.318014 + 0.948086i \(0.603016\pi\)
\(594\) 3.00701 0.123379
\(595\) 0 0
\(596\) −9.19717 −0.376731
\(597\) −6.81027 −0.278726
\(598\) −1.44895 −0.0592519
\(599\) 4.22806 0.172754 0.0863768 0.996263i \(-0.472471\pi\)
0.0863768 + 0.996263i \(0.472471\pi\)
\(600\) −6.76282 −0.276091
\(601\) −35.7858 −1.45973 −0.729867 0.683589i \(-0.760418\pi\)
−0.729867 + 0.683589i \(0.760418\pi\)
\(602\) 0 0
\(603\) −13.4478 −0.547638
\(604\) 12.6539 0.514879
\(605\) −10.8431 −0.440833
\(606\) 7.24463 0.294293
\(607\) 3.30743 0.134244 0.0671222 0.997745i \(-0.478618\pi\)
0.0671222 + 0.997745i \(0.478618\pi\)
\(608\) 6.84074 0.277429
\(609\) 0 0
\(610\) 10.4278 0.422209
\(611\) −3.00615 −0.121616
\(612\) 1.36179 0.0550471
\(613\) 21.8254 0.881519 0.440760 0.897625i \(-0.354709\pi\)
0.440760 + 0.897625i \(0.354709\pi\)
\(614\) −19.0341 −0.768152
\(615\) −1.50350 −0.0606272
\(616\) 0 0
\(617\) 36.3792 1.46457 0.732286 0.680997i \(-0.238453\pi\)
0.732286 + 0.680997i \(0.238453\pi\)
\(618\) −6.12113 −0.246228
\(619\) 33.3671 1.34114 0.670568 0.741848i \(-0.266051\pi\)
0.670568 + 0.741848i \(0.266051\pi\)
\(620\) 6.99464 0.280912
\(621\) −0.893136 −0.0358403
\(622\) −20.9154 −0.838630
\(623\) 0 0
\(624\) −2.91835 −0.116828
\(625\) −3.79791 −0.151916
\(626\) −9.87114 −0.394530
\(627\) 5.00701 0.199961
\(628\) 12.7252 0.507792
\(629\) 2.13918 0.0852946
\(630\) 0 0
\(631\) 35.8563 1.42742 0.713708 0.700443i \(-0.247014\pi\)
0.713708 + 0.700443i \(0.247014\pi\)
\(632\) −35.9773 −1.43110
\(633\) 3.45439 0.137300
\(634\) −14.9970 −0.595605
\(635\) −16.7488 −0.664656
\(636\) 9.99672 0.396396
\(637\) 0 0
\(638\) 10.0041 0.396068
\(639\) −0.245293 −0.00970365
\(640\) −15.8655 −0.627141
\(641\) 29.4974 1.16508 0.582538 0.812803i \(-0.302060\pi\)
0.582538 + 0.812803i \(0.302060\pi\)
\(642\) −12.6516 −0.499318
\(643\) −39.6993 −1.56559 −0.782795 0.622280i \(-0.786207\pi\)
−0.782795 + 0.622280i \(0.786207\pi\)
\(644\) 0 0
\(645\) 11.7921 0.464312
\(646\) −0.748798 −0.0294611
\(647\) −28.2158 −1.10928 −0.554638 0.832092i \(-0.687143\pi\)
−0.554638 + 0.832092i \(0.687143\pi\)
\(648\) 2.46865 0.0969779
\(649\) −2.72358 −0.106910
\(650\) −4.44429 −0.174320
\(651\) 0 0
\(652\) −13.0896 −0.512627
\(653\) 23.1901 0.907497 0.453748 0.891130i \(-0.350086\pi\)
0.453748 + 0.891130i \(0.350086\pi\)
\(654\) 0.915068 0.0357820
\(655\) 6.67330 0.260748
\(656\) 1.26753 0.0494889
\(657\) 2.08725 0.0814313
\(658\) 0 0
\(659\) −14.5515 −0.566847 −0.283423 0.958995i \(-0.591470\pi\)
−0.283423 + 0.958995i \(0.591470\pi\)
\(660\) −9.64687 −0.375504
\(661\) 26.5326 1.03200 0.516000 0.856589i \(-0.327420\pi\)
0.516000 + 0.856589i \(0.327420\pi\)
\(662\) −6.20284 −0.241080
\(663\) 2.08537 0.0809891
\(664\) 15.8395 0.614693
\(665\) 0 0
\(666\) 1.66418 0.0644855
\(667\) −2.97141 −0.115053
\(668\) 10.6644 0.412619
\(669\) −3.01195 −0.116449
\(670\) −14.2467 −0.550398
\(671\) −42.0056 −1.62161
\(672\) 0 0
\(673\) −17.9600 −0.692307 −0.346153 0.938178i \(-0.612512\pi\)
−0.346153 + 0.938178i \(0.612512\pi\)
\(674\) −23.0523 −0.887943
\(675\) −2.73947 −0.105442
\(676\) 11.5755 0.445212
\(677\) 7.79090 0.299429 0.149714 0.988729i \(-0.452165\pi\)
0.149714 + 0.988729i \(0.452165\pi\)
\(678\) −2.44147 −0.0937643
\(679\) 0 0
\(680\) 3.36179 0.128919
\(681\) −14.0619 −0.538854
\(682\) 9.30445 0.356286
\(683\) −4.27880 −0.163724 −0.0818618 0.996644i \(-0.526087\pi\)
−0.0818618 + 0.996644i \(0.526087\pi\)
\(684\) 1.76403 0.0674494
\(685\) −16.1419 −0.616751
\(686\) 0 0
\(687\) 1.07999 0.0412043
\(688\) −9.94134 −0.379010
\(689\) 15.3084 0.583204
\(690\) −0.946193 −0.0360210
\(691\) 23.8218 0.906222 0.453111 0.891454i \(-0.350314\pi\)
0.453111 + 0.891454i \(0.350314\pi\)
\(692\) −25.2635 −0.960372
\(693\) 0 0
\(694\) −23.1845 −0.880071
\(695\) −18.3181 −0.694843
\(696\) 8.21307 0.311316
\(697\) −0.905744 −0.0343075
\(698\) −22.9179 −0.867455
\(699\) 5.55030 0.209932
\(700\) 0 0
\(701\) 9.77225 0.369093 0.184546 0.982824i \(-0.440918\pi\)
0.184546 + 0.982824i \(0.440918\pi\)
\(702\) 1.62232 0.0612304
\(703\) 2.77104 0.104512
\(704\) −6.71370 −0.253032
\(705\) −1.96308 −0.0739339
\(706\) −5.34198 −0.201048
\(707\) 0 0
\(708\) −0.959551 −0.0360621
\(709\) −7.96953 −0.299302 −0.149651 0.988739i \(-0.547815\pi\)
−0.149651 + 0.988739i \(0.547815\pi\)
\(710\) −0.259865 −0.00975256
\(711\) −14.5736 −0.546554
\(712\) 4.47194 0.167593
\(713\) −2.76359 −0.103497
\(714\) 0 0
\(715\) −14.7727 −0.552467
\(716\) −7.30197 −0.272887
\(717\) −1.45836 −0.0544635
\(718\) −17.3677 −0.648157
\(719\) −3.66691 −0.136753 −0.0683763 0.997660i \(-0.521782\pi\)
−0.0683763 + 0.997660i \(0.521782\pi\)
\(720\) −1.90574 −0.0710229
\(721\) 0 0
\(722\) 12.4179 0.462146
\(723\) −1.68335 −0.0626046
\(724\) 8.93980 0.332245
\(725\) −9.11407 −0.338488
\(726\) −5.08165 −0.188598
\(727\) −40.3400 −1.49613 −0.748064 0.663627i \(-0.769016\pi\)
−0.748064 + 0.663627i \(0.769016\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 2.21124 0.0818417
\(731\) 7.10380 0.262744
\(732\) −14.7991 −0.546990
\(733\) −35.1684 −1.29898 −0.649488 0.760372i \(-0.725017\pi\)
−0.649488 + 0.760372i \(0.725017\pi\)
\(734\) 15.2423 0.562604
\(735\) 0 0
\(736\) 5.20738 0.191947
\(737\) 57.3891 2.11395
\(738\) −0.704624 −0.0259376
\(739\) 1.71767 0.0631856 0.0315928 0.999501i \(-0.489942\pi\)
0.0315928 + 0.999501i \(0.489942\pi\)
\(740\) −5.33889 −0.196261
\(741\) 2.70134 0.0992362
\(742\) 0 0
\(743\) −20.4571 −0.750500 −0.375250 0.926924i \(-0.622443\pi\)
−0.375250 + 0.926924i \(0.622443\pi\)
\(744\) 7.63865 0.280046
\(745\) −9.19717 −0.336958
\(746\) 22.7175 0.831746
\(747\) 6.41626 0.234759
\(748\) −5.81149 −0.212489
\(749\) 0 0
\(750\) −8.19924 −0.299394
\(751\) 20.4502 0.746238 0.373119 0.927783i \(-0.378288\pi\)
0.373119 + 0.927783i \(0.378288\pi\)
\(752\) 1.65498 0.0603510
\(753\) 18.8882 0.688324
\(754\) 5.39735 0.196560
\(755\) 12.6539 0.460522
\(756\) 0 0
\(757\) 28.4022 1.03230 0.516148 0.856499i \(-0.327365\pi\)
0.516148 + 0.856499i \(0.327365\pi\)
\(758\) −20.3225 −0.738147
\(759\) 3.81149 0.138348
\(760\) 4.35478 0.157965
\(761\) 10.0943 0.365916 0.182958 0.983121i \(-0.441433\pi\)
0.182958 + 0.983121i \(0.441433\pi\)
\(762\) −7.84940 −0.284354
\(763\) 0 0
\(764\) 21.1774 0.766172
\(765\) 1.36179 0.0492356
\(766\) 21.9625 0.793537
\(767\) −1.46940 −0.0530571
\(768\) −10.5819 −0.381840
\(769\) −39.5682 −1.42687 −0.713434 0.700723i \(-0.752861\pi\)
−0.713434 + 0.700723i \(0.752861\pi\)
\(770\) 0 0
\(771\) −15.1796 −0.546681
\(772\) −14.5227 −0.522684
\(773\) −13.6450 −0.490776 −0.245388 0.969425i \(-0.578915\pi\)
−0.245388 + 0.969425i \(0.578915\pi\)
\(774\) 5.52641 0.198643
\(775\) −8.47663 −0.304490
\(776\) 15.5381 0.557786
\(777\) 0 0
\(778\) −0.0255493 −0.000915988 0
\(779\) −1.17328 −0.0420371
\(780\) −5.20460 −0.186355
\(781\) 1.04680 0.0374574
\(782\) −0.570008 −0.0203834
\(783\) 3.32694 0.118895
\(784\) 0 0
\(785\) 12.7252 0.454183
\(786\) 3.12747 0.111553
\(787\) −6.72052 −0.239561 −0.119780 0.992800i \(-0.538219\pi\)
−0.119780 + 0.992800i \(0.538219\pi\)
\(788\) 1.71375 0.0610499
\(789\) −1.96021 −0.0697854
\(790\) −15.4394 −0.549309
\(791\) 0 0
\(792\) −10.5351 −0.374347
\(793\) −22.6625 −0.804769
\(794\) −24.0948 −0.855091
\(795\) 9.99672 0.354547
\(796\) 10.2393 0.362922
\(797\) −1.63942 −0.0580714 −0.0290357 0.999578i \(-0.509244\pi\)
−0.0290357 + 0.999578i \(0.509244\pi\)
\(798\) 0 0
\(799\) −1.18260 −0.0418375
\(800\) 15.9724 0.564708
\(801\) 1.81149 0.0640058
\(802\) −14.3466 −0.506595
\(803\) −8.90740 −0.314335
\(804\) 20.2189 0.713064
\(805\) 0 0
\(806\) 5.01986 0.176817
\(807\) 30.4771 1.07284
\(808\) −25.3816 −0.892922
\(809\) −28.1798 −0.990750 −0.495375 0.868679i \(-0.664969\pi\)
−0.495375 + 0.868679i \(0.664969\pi\)
\(810\) 1.05941 0.0372237
\(811\) −22.2848 −0.782526 −0.391263 0.920279i \(-0.627962\pi\)
−0.391263 + 0.920279i \(0.627962\pi\)
\(812\) 0 0
\(813\) −5.84634 −0.205040
\(814\) −7.10193 −0.248922
\(815\) −13.0896 −0.458507
\(816\) −1.14806 −0.0401902
\(817\) 9.20209 0.321940
\(818\) 7.41670 0.259319
\(819\) 0 0
\(820\) 2.26053 0.0789410
\(821\) −29.0974 −1.01551 −0.507753 0.861503i \(-0.669524\pi\)
−0.507753 + 0.861503i \(0.669524\pi\)
\(822\) −7.56498 −0.263859
\(823\) −28.7398 −1.00181 −0.500903 0.865503i \(-0.666999\pi\)
−0.500903 + 0.865503i \(0.666999\pi\)
\(824\) 21.4454 0.747086
\(825\) 11.6908 0.407021
\(826\) 0 0
\(827\) 38.5448 1.34033 0.670167 0.742211i \(-0.266223\pi\)
0.670167 + 0.742211i \(0.266223\pi\)
\(828\) 1.34283 0.0466667
\(829\) −42.9541 −1.49186 −0.745928 0.666026i \(-0.767994\pi\)
−0.745928 + 0.666026i \(0.767994\pi\)
\(830\) 6.79742 0.235942
\(831\) 7.11638 0.246865
\(832\) −3.62212 −0.125574
\(833\) 0 0
\(834\) −8.58484 −0.297269
\(835\) 10.6644 0.369057
\(836\) −7.52806 −0.260363
\(837\) 3.09426 0.106953
\(838\) −19.4403 −0.671553
\(839\) −12.5023 −0.431627 −0.215813 0.976435i \(-0.569240\pi\)
−0.215813 + 0.976435i \(0.569240\pi\)
\(840\) 0 0
\(841\) −17.9315 −0.618326
\(842\) −23.3177 −0.803581
\(843\) −4.47632 −0.154173
\(844\) −5.19369 −0.178774
\(845\) 11.5755 0.398210
\(846\) −0.920006 −0.0316305
\(847\) 0 0
\(848\) −8.42777 −0.289411
\(849\) −0.675569 −0.0231855
\(850\) −1.74836 −0.0599682
\(851\) 2.10940 0.0723093
\(852\) 0.368800 0.0126349
\(853\) −0.740028 −0.0253381 −0.0126690 0.999920i \(-0.504033\pi\)
−0.0126690 + 0.999920i \(0.504033\pi\)
\(854\) 0 0
\(855\) 1.76403 0.0603286
\(856\) 44.3248 1.51499
\(857\) 55.2205 1.88630 0.943148 0.332374i \(-0.107850\pi\)
0.943148 + 0.332374i \(0.107850\pi\)
\(858\) −6.92329 −0.236357
\(859\) −48.3612 −1.65006 −0.825032 0.565087i \(-0.808843\pi\)
−0.825032 + 0.565087i \(0.808843\pi\)
\(860\) −17.7294 −0.604568
\(861\) 0 0
\(862\) 3.46001 0.117849
\(863\) −34.7431 −1.18267 −0.591334 0.806427i \(-0.701399\pi\)
−0.591334 + 0.806427i \(0.701399\pi\)
\(864\) −5.83045 −0.198356
\(865\) −25.2635 −0.858983
\(866\) 8.63241 0.293341
\(867\) −16.1796 −0.549489
\(868\) 0 0
\(869\) 62.1935 2.10977
\(870\) 3.52458 0.119494
\(871\) 30.9621 1.04911
\(872\) −3.20594 −0.108567
\(873\) 6.29416 0.213025
\(874\) −0.738374 −0.0249759
\(875\) 0 0
\(876\) −3.13818 −0.106029
\(877\) −32.5538 −1.09926 −0.549632 0.835407i \(-0.685232\pi\)
−0.549632 + 0.835407i \(0.685232\pi\)
\(878\) 10.9310 0.368904
\(879\) 2.58722 0.0872648
\(880\) 8.13283 0.274158
\(881\) −3.54142 −0.119313 −0.0596567 0.998219i \(-0.519001\pi\)
−0.0596567 + 0.998219i \(0.519001\pi\)
\(882\) 0 0
\(883\) 34.3909 1.15735 0.578673 0.815559i \(-0.303571\pi\)
0.578673 + 0.815559i \(0.303571\pi\)
\(884\) −3.13537 −0.105454
\(885\) −0.959551 −0.0322549
\(886\) 13.0021 0.436814
\(887\) −10.8911 −0.365686 −0.182843 0.983142i \(-0.558530\pi\)
−0.182843 + 0.983142i \(0.558530\pi\)
\(888\) −5.83045 −0.195657
\(889\) 0 0
\(890\) 1.91910 0.0643284
\(891\) −4.26753 −0.142968
\(892\) 4.52848 0.151625
\(893\) −1.53191 −0.0512636
\(894\) −4.31030 −0.144158
\(895\) −7.30197 −0.244078
\(896\) 0 0
\(897\) 2.05634 0.0686593
\(898\) 9.55775 0.318946
\(899\) 10.2944 0.343338
\(900\) 4.11881 0.137294
\(901\) 6.02224 0.200630
\(902\) 3.00701 0.100122
\(903\) 0 0
\(904\) 8.55372 0.284492
\(905\) 8.93980 0.297169
\(906\) 5.93030 0.197021
\(907\) −32.4770 −1.07838 −0.539190 0.842184i \(-0.681269\pi\)
−0.539190 + 0.842184i \(0.681269\pi\)
\(908\) 21.1422 0.701627
\(909\) −10.2816 −0.341018
\(910\) 0 0
\(911\) 14.4670 0.479314 0.239657 0.970858i \(-0.422965\pi\)
0.239657 + 0.970858i \(0.422965\pi\)
\(912\) −1.48717 −0.0492452
\(913\) −27.3816 −0.906199
\(914\) 5.37134 0.177668
\(915\) −14.7991 −0.489242
\(916\) −1.62378 −0.0536510
\(917\) 0 0
\(918\) 0.638209 0.0210641
\(919\) −21.8298 −0.720097 −0.360049 0.932934i \(-0.617240\pi\)
−0.360049 + 0.932934i \(0.617240\pi\)
\(920\) 3.31499 0.109292
\(921\) 27.0130 0.890110
\(922\) −7.43614 −0.244896
\(923\) 0.564759 0.0185893
\(924\) 0 0
\(925\) 6.47006 0.212734
\(926\) 15.8106 0.519570
\(927\) 8.68708 0.285321
\(928\) −19.3975 −0.636756
\(929\) −11.2589 −0.369392 −0.184696 0.982796i \(-0.559130\pi\)
−0.184696 + 0.982796i \(0.559130\pi\)
\(930\) 3.27807 0.107492
\(931\) 0 0
\(932\) −8.34490 −0.273346
\(933\) 29.6830 0.971778
\(934\) −17.8589 −0.584363
\(935\) −5.81149 −0.190056
\(936\) −5.68379 −0.185781
\(937\) −27.7504 −0.906566 −0.453283 0.891367i \(-0.649747\pi\)
−0.453283 + 0.891367i \(0.649747\pi\)
\(938\) 0 0
\(939\) 14.0091 0.457169
\(940\) 2.95150 0.0962673
\(941\) 27.2563 0.888531 0.444266 0.895895i \(-0.353465\pi\)
0.444266 + 0.895895i \(0.353465\pi\)
\(942\) 5.96374 0.194309
\(943\) −0.893136 −0.0290845
\(944\) 0.808953 0.0263292
\(945\) 0 0
\(946\) −23.5841 −0.766786
\(947\) −16.0528 −0.521645 −0.260823 0.965387i \(-0.583994\pi\)
−0.260823 + 0.965387i \(0.583994\pi\)
\(948\) 21.9115 0.711654
\(949\) −4.80564 −0.155998
\(950\) −2.26478 −0.0734792
\(951\) 21.2836 0.690169
\(952\) 0 0
\(953\) −4.62507 −0.149821 −0.0749104 0.997190i \(-0.523867\pi\)
−0.0749104 + 0.997190i \(0.523867\pi\)
\(954\) 4.68501 0.151683
\(955\) 21.1774 0.685285
\(956\) 2.19265 0.0709154
\(957\) −14.1978 −0.458951
\(958\) −26.5285 −0.857097
\(959\) 0 0
\(960\) −2.36532 −0.0763404
\(961\) −21.4256 −0.691148
\(962\) −3.83157 −0.123535
\(963\) 17.9551 0.578593
\(964\) 2.53093 0.0815157
\(965\) −14.5227 −0.467502
\(966\) 0 0
\(967\) 0.867236 0.0278884 0.0139442 0.999903i \(-0.495561\pi\)
0.0139442 + 0.999903i \(0.495561\pi\)
\(968\) 17.8036 0.572229
\(969\) 1.06269 0.0341385
\(970\) 6.66807 0.214099
\(971\) 45.9188 1.47360 0.736802 0.676109i \(-0.236335\pi\)
0.736802 + 0.676109i \(0.236335\pi\)
\(972\) −1.50350 −0.0482249
\(973\) 0 0
\(974\) −5.30115 −0.169860
\(975\) 6.30732 0.201996
\(976\) 12.4764 0.399360
\(977\) −0.727989 −0.0232904 −0.0116452 0.999932i \(-0.503707\pi\)
−0.0116452 + 0.999932i \(0.503707\pi\)
\(978\) −6.13448 −0.196159
\(979\) −7.73059 −0.247071
\(980\) 0 0
\(981\) −1.29866 −0.0414630
\(982\) −14.0050 −0.446916
\(983\) 26.3436 0.840230 0.420115 0.907471i \(-0.361990\pi\)
0.420115 + 0.907471i \(0.361990\pi\)
\(984\) 2.46865 0.0786978
\(985\) 1.71375 0.0546047
\(986\) 2.12329 0.0676192
\(987\) 0 0
\(988\) −4.06148 −0.129213
\(989\) 7.00491 0.222743
\(990\) −4.52105 −0.143688
\(991\) 29.2465 0.929044 0.464522 0.885561i \(-0.346226\pi\)
0.464522 + 0.885561i \(0.346226\pi\)
\(992\) −18.0409 −0.572799
\(993\) 8.80304 0.279356
\(994\) 0 0
\(995\) 10.2393 0.324607
\(996\) −9.64687 −0.305673
\(997\) 43.6374 1.38201 0.691005 0.722850i \(-0.257168\pi\)
0.691005 + 0.722850i \(0.257168\pi\)
\(998\) 26.5028 0.838931
\(999\) −2.36179 −0.0747237
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 \(a_p\))