Properties

Label 6027.2.a.bc.1.8
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 8
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: \(8\)
Coefficient field: 8.8.7457527933.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-0.314356\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.55413 q^{2} +1.00000 q^{3} +4.52358 q^{4} +2.03983 q^{5} +2.55413 q^{6} +6.44554 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.55413 q^{2} +1.00000 q^{3} +4.52358 q^{4} +2.03983 q^{5} +2.55413 q^{6} +6.44554 q^{8} +1.00000 q^{9} +5.20999 q^{10} +2.19710 q^{11} +4.52358 q^{12} +4.05386 q^{13} +2.03983 q^{15} +7.41559 q^{16} -4.84721 q^{17} +2.55413 q^{18} +7.41918 q^{19} +9.22734 q^{20} +5.61167 q^{22} -4.70245 q^{23} +6.44554 q^{24} -0.839085 q^{25} +10.3541 q^{26} +1.00000 q^{27} -10.1020 q^{29} +5.20999 q^{30} -3.76089 q^{31} +6.04930 q^{32} +2.19710 q^{33} -12.3804 q^{34} +4.52358 q^{36} -6.51492 q^{37} +18.9495 q^{38} +4.05386 q^{39} +13.1478 q^{40} +1.00000 q^{41} +10.7302 q^{43} +9.93873 q^{44} +2.03983 q^{45} -12.0107 q^{46} +0.528264 q^{47} +7.41559 q^{48} -2.14313 q^{50} -4.84721 q^{51} +18.3379 q^{52} +7.25162 q^{53} +2.55413 q^{54} +4.48171 q^{55} +7.41918 q^{57} -25.8019 q^{58} +7.53546 q^{59} +9.22734 q^{60} +1.26730 q^{61} -9.60579 q^{62} +0.619503 q^{64} +8.26919 q^{65} +5.61167 q^{66} -8.72784 q^{67} -21.9267 q^{68} -4.70245 q^{69} -1.95591 q^{71} +6.44554 q^{72} -13.1873 q^{73} -16.6399 q^{74} -0.839085 q^{75} +33.5612 q^{76} +10.3541 q^{78} -2.93987 q^{79} +15.1266 q^{80} +1.00000 q^{81} +2.55413 q^{82} +12.0571 q^{83} -9.88750 q^{85} +27.4064 q^{86} -10.1020 q^{87} +14.1615 q^{88} -4.93696 q^{89} +5.20999 q^{90} -21.2719 q^{92} -3.76089 q^{93} +1.34925 q^{94} +15.1339 q^{95} +6.04930 q^{96} -4.56808 q^{97} +2.19710 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + q^{2} + 8q^{3} + 13q^{4} + 7q^{5} + q^{6} + 6q^{8} + 8q^{9} + O(q^{10}) \) \( 8q + q^{2} + 8q^{3} + 13q^{4} + 7q^{5} + q^{6} + 6q^{8} + 8q^{9} + 8q^{10} + 11q^{11} + 13q^{12} + 10q^{13} + 7q^{15} - 17q^{16} + 3q^{17} + q^{18} + 6q^{19} + 11q^{20} + 15q^{22} + 14q^{23} + 6q^{24} + 25q^{25} + 24q^{26} + 8q^{27} + 2q^{29} + 8q^{30} + 16q^{31} + 3q^{32} + 11q^{33} - 4q^{34} + 13q^{36} - 20q^{37} + 10q^{38} + 10q^{39} - 3q^{40} + 8q^{41} + 7q^{43} + 7q^{45} - 5q^{46} + 14q^{47} - 17q^{48} - 5q^{50} + 3q^{51} + 23q^{52} + 7q^{53} + q^{54} + 48q^{55} + 6q^{57} - 20q^{58} + 22q^{59} + 11q^{60} - 33q^{62} - 10q^{64} - 14q^{65} + 15q^{66} + 12q^{67} - 27q^{68} + 14q^{69} - 5q^{71} + 6q^{72} + 2q^{73} + 6q^{74} + 25q^{75} + 43q^{76} + 24q^{78} - 15q^{79} - 7q^{80} + 8q^{81} + q^{82} + 15q^{83} - 43q^{85} + 31q^{86} + 2q^{87} + 17q^{88} + 29q^{89} + 8q^{90} + 19q^{92} + 16q^{93} + 20q^{94} + 14q^{95} + 3q^{96} + 19q^{97} + 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.55413 1.80604 0.903021 0.429596i \(-0.141344\pi\)
0.903021 + 0.429596i \(0.141344\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.52358 2.26179
\(5\) 2.03983 0.912241 0.456120 0.889918i \(-0.349239\pi\)
0.456120 + 0.889918i \(0.349239\pi\)
\(6\) 2.55413 1.04272
\(7\) 0 0
\(8\) 6.44554 2.27884
\(9\) 1.00000 0.333333
\(10\) 5.20999 1.64755
\(11\) 2.19710 0.662449 0.331225 0.943552i \(-0.392538\pi\)
0.331225 + 0.943552i \(0.392538\pi\)
\(12\) 4.52358 1.30584
\(13\) 4.05386 1.12434 0.562169 0.827022i \(-0.309967\pi\)
0.562169 + 0.827022i \(0.309967\pi\)
\(14\) 0 0
\(15\) 2.03983 0.526682
\(16\) 7.41559 1.85390
\(17\) −4.84721 −1.17562 −0.587811 0.808999i \(-0.700010\pi\)
−0.587811 + 0.808999i \(0.700010\pi\)
\(18\) 2.55413 0.602014
\(19\) 7.41918 1.70208 0.851038 0.525104i \(-0.175974\pi\)
0.851038 + 0.525104i \(0.175974\pi\)
\(20\) 9.22734 2.06330
\(21\) 0 0
\(22\) 5.61167 1.19641
\(23\) −4.70245 −0.980529 −0.490264 0.871574i \(-0.663100\pi\)
−0.490264 + 0.871574i \(0.663100\pi\)
\(24\) 6.44554 1.31569
\(25\) −0.839085 −0.167817
\(26\) 10.3541 2.03060
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −10.1020 −1.87590 −0.937950 0.346769i \(-0.887279\pi\)
−0.937950 + 0.346769i \(0.887279\pi\)
\(30\) 5.20999 0.951211
\(31\) −3.76089 −0.675475 −0.337738 0.941240i \(-0.609662\pi\)
−0.337738 + 0.941240i \(0.609662\pi\)
\(32\) 6.04930 1.06937
\(33\) 2.19710 0.382465
\(34\) −12.3804 −2.12322
\(35\) 0 0
\(36\) 4.52358 0.753929
\(37\) −6.51492 −1.07105 −0.535523 0.844521i \(-0.679885\pi\)
−0.535523 + 0.844521i \(0.679885\pi\)
\(38\) 18.9495 3.07402
\(39\) 4.05386 0.649137
\(40\) 13.1478 2.07885
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 10.7302 1.63635 0.818173 0.574972i \(-0.194987\pi\)
0.818173 + 0.574972i \(0.194987\pi\)
\(44\) 9.93873 1.49832
\(45\) 2.03983 0.304080
\(46\) −12.0107 −1.77088
\(47\) 0.528264 0.0770552 0.0385276 0.999258i \(-0.487733\pi\)
0.0385276 + 0.999258i \(0.487733\pi\)
\(48\) 7.41559 1.07035
\(49\) 0 0
\(50\) −2.14313 −0.303085
\(51\) −4.84721 −0.678745
\(52\) 18.3379 2.54301
\(53\) 7.25162 0.996086 0.498043 0.867152i \(-0.334052\pi\)
0.498043 + 0.867152i \(0.334052\pi\)
\(54\) 2.55413 0.347573
\(55\) 4.48171 0.604313
\(56\) 0 0
\(57\) 7.41918 0.982694
\(58\) −25.8019 −3.38796
\(59\) 7.53546 0.981033 0.490516 0.871432i \(-0.336808\pi\)
0.490516 + 0.871432i \(0.336808\pi\)
\(60\) 9.22734 1.19124
\(61\) 1.26730 0.162261 0.0811304 0.996703i \(-0.474147\pi\)
0.0811304 + 0.996703i \(0.474147\pi\)
\(62\) −9.60579 −1.21994
\(63\) 0 0
\(64\) 0.619503 0.0774378
\(65\) 8.26919 1.02567
\(66\) 5.61167 0.690748
\(67\) −8.72784 −1.06628 −0.533138 0.846029i \(-0.678987\pi\)
−0.533138 + 0.846029i \(0.678987\pi\)
\(68\) −21.9267 −2.65901
\(69\) −4.70245 −0.566109
\(70\) 0 0
\(71\) −1.95591 −0.232123 −0.116062 0.993242i \(-0.537027\pi\)
−0.116062 + 0.993242i \(0.537027\pi\)
\(72\) 6.44554 0.759614
\(73\) −13.1873 −1.54346 −0.771731 0.635949i \(-0.780609\pi\)
−0.771731 + 0.635949i \(0.780609\pi\)
\(74\) −16.6399 −1.93435
\(75\) −0.839085 −0.0968892
\(76\) 33.5612 3.84974
\(77\) 0 0
\(78\) 10.3541 1.17237
\(79\) −2.93987 −0.330761 −0.165380 0.986230i \(-0.552885\pi\)
−0.165380 + 0.986230i \(0.552885\pi\)
\(80\) 15.1266 1.69120
\(81\) 1.00000 0.111111
\(82\) 2.55413 0.282056
\(83\) 12.0571 1.32344 0.661722 0.749750i \(-0.269826\pi\)
0.661722 + 0.749750i \(0.269826\pi\)
\(84\) 0 0
\(85\) −9.88750 −1.07245
\(86\) 27.4064 2.95531
\(87\) −10.1020 −1.08305
\(88\) 14.1615 1.50962
\(89\) −4.93696 −0.523317 −0.261658 0.965161i \(-0.584269\pi\)
−0.261658 + 0.965161i \(0.584269\pi\)
\(90\) 5.20999 0.549182
\(91\) 0 0
\(92\) −21.2719 −2.21775
\(93\) −3.76089 −0.389986
\(94\) 1.34925 0.139165
\(95\) 15.1339 1.55270
\(96\) 6.04930 0.617404
\(97\) −4.56808 −0.463818 −0.231909 0.972737i \(-0.574497\pi\)
−0.231909 + 0.972737i \(0.574497\pi\)
\(98\) 0 0
\(99\) 2.19710 0.220816
\(100\) −3.79567 −0.379567
\(101\) 14.8399 1.47663 0.738313 0.674459i \(-0.235623\pi\)
0.738313 + 0.674459i \(0.235623\pi\)
\(102\) −12.3804 −1.22584
\(103\) −15.1660 −1.49435 −0.747174 0.664629i \(-0.768590\pi\)
−0.747174 + 0.664629i \(0.768590\pi\)
\(104\) 26.1293 2.56219
\(105\) 0 0
\(106\) 18.5216 1.79897
\(107\) −10.5325 −1.01822 −0.509109 0.860702i \(-0.670025\pi\)
−0.509109 + 0.860702i \(0.670025\pi\)
\(108\) 4.52358 0.435281
\(109\) −20.4788 −1.96151 −0.980757 0.195234i \(-0.937453\pi\)
−0.980757 + 0.195234i \(0.937453\pi\)
\(110\) 11.4469 1.09141
\(111\) −6.51492 −0.618369
\(112\) 0 0
\(113\) 3.99357 0.375683 0.187842 0.982199i \(-0.439851\pi\)
0.187842 + 0.982199i \(0.439851\pi\)
\(114\) 18.9495 1.77479
\(115\) −9.59221 −0.894478
\(116\) −45.6973 −4.24289
\(117\) 4.05386 0.374779
\(118\) 19.2465 1.77179
\(119\) 0 0
\(120\) 13.1478 1.20023
\(121\) −6.17277 −0.561161
\(122\) 3.23684 0.293050
\(123\) 1.00000 0.0901670
\(124\) −17.0127 −1.52778
\(125\) −11.9108 −1.06533
\(126\) 0 0
\(127\) 1.59918 0.141905 0.0709523 0.997480i \(-0.477396\pi\)
0.0709523 + 0.997480i \(0.477396\pi\)
\(128\) −10.5163 −0.929519
\(129\) 10.7302 0.944745
\(130\) 21.1206 1.85240
\(131\) 9.63387 0.841715 0.420858 0.907127i \(-0.361729\pi\)
0.420858 + 0.907127i \(0.361729\pi\)
\(132\) 9.93873 0.865055
\(133\) 0 0
\(134\) −22.2920 −1.92574
\(135\) 2.03983 0.175561
\(136\) −31.2429 −2.67906
\(137\) −7.92292 −0.676900 −0.338450 0.940984i \(-0.609903\pi\)
−0.338450 + 0.940984i \(0.609903\pi\)
\(138\) −12.0107 −1.02242
\(139\) −3.47465 −0.294716 −0.147358 0.989083i \(-0.547077\pi\)
−0.147358 + 0.989083i \(0.547077\pi\)
\(140\) 0 0
\(141\) 0.528264 0.0444878
\(142\) −4.99564 −0.419225
\(143\) 8.90671 0.744817
\(144\) 7.41559 0.617966
\(145\) −20.6065 −1.71127
\(146\) −33.6822 −2.78756
\(147\) 0 0
\(148\) −29.4707 −2.42248
\(149\) 4.81236 0.394244 0.197122 0.980379i \(-0.436840\pi\)
0.197122 + 0.980379i \(0.436840\pi\)
\(150\) −2.14313 −0.174986
\(151\) −6.30410 −0.513021 −0.256510 0.966542i \(-0.582573\pi\)
−0.256510 + 0.966542i \(0.582573\pi\)
\(152\) 47.8206 3.87876
\(153\) −4.84721 −0.391874
\(154\) 0 0
\(155\) −7.67158 −0.616196
\(156\) 18.3379 1.46821
\(157\) 4.07061 0.324870 0.162435 0.986719i \(-0.448065\pi\)
0.162435 + 0.986719i \(0.448065\pi\)
\(158\) −7.50880 −0.597368
\(159\) 7.25162 0.575090
\(160\) 12.3395 0.975527
\(161\) 0 0
\(162\) 2.55413 0.200671
\(163\) 9.43025 0.738634 0.369317 0.929303i \(-0.379592\pi\)
0.369317 + 0.929303i \(0.379592\pi\)
\(164\) 4.52358 0.353232
\(165\) 4.48171 0.348900
\(166\) 30.7955 2.39019
\(167\) 12.2859 0.950715 0.475357 0.879793i \(-0.342319\pi\)
0.475357 + 0.879793i \(0.342319\pi\)
\(168\) 0 0
\(169\) 3.43376 0.264135
\(170\) −25.2539 −1.93689
\(171\) 7.41918 0.567359
\(172\) 48.5390 3.70107
\(173\) 21.7797 1.65588 0.827940 0.560817i \(-0.189513\pi\)
0.827940 + 0.560817i \(0.189513\pi\)
\(174\) −25.8019 −1.95604
\(175\) 0 0
\(176\) 16.2928 1.22811
\(177\) 7.53546 0.566400
\(178\) −12.6096 −0.945133
\(179\) −8.27123 −0.618221 −0.309110 0.951026i \(-0.600031\pi\)
−0.309110 + 0.951026i \(0.600031\pi\)
\(180\) 9.22734 0.687765
\(181\) 2.34065 0.173979 0.0869894 0.996209i \(-0.472275\pi\)
0.0869894 + 0.996209i \(0.472275\pi\)
\(182\) 0 0
\(183\) 1.26730 0.0936813
\(184\) −30.3098 −2.23447
\(185\) −13.2893 −0.977052
\(186\) −9.60579 −0.704331
\(187\) −10.6498 −0.778789
\(188\) 2.38964 0.174282
\(189\) 0 0
\(190\) 38.6539 2.80425
\(191\) 14.5214 1.05073 0.525367 0.850876i \(-0.323928\pi\)
0.525367 + 0.850876i \(0.323928\pi\)
\(192\) 0.619503 0.0447087
\(193\) 18.0211 1.29719 0.648593 0.761136i \(-0.275358\pi\)
0.648593 + 0.761136i \(0.275358\pi\)
\(194\) −11.6675 −0.837676
\(195\) 8.26919 0.592169
\(196\) 0 0
\(197\) 25.2224 1.79702 0.898510 0.438953i \(-0.144650\pi\)
0.898510 + 0.438953i \(0.144650\pi\)
\(198\) 5.61167 0.398804
\(199\) 2.07686 0.147225 0.0736125 0.997287i \(-0.476547\pi\)
0.0736125 + 0.997287i \(0.476547\pi\)
\(200\) −5.40836 −0.382429
\(201\) −8.72784 −0.615614
\(202\) 37.9030 2.66685
\(203\) 0 0
\(204\) −21.9267 −1.53518
\(205\) 2.03983 0.142468
\(206\) −38.7358 −2.69885
\(207\) −4.70245 −0.326843
\(208\) 30.0617 2.08441
\(209\) 16.3006 1.12754
\(210\) 0 0
\(211\) 9.20520 0.633712 0.316856 0.948474i \(-0.397373\pi\)
0.316856 + 0.948474i \(0.397373\pi\)
\(212\) 32.8032 2.25294
\(213\) −1.95591 −0.134017
\(214\) −26.9014 −1.83894
\(215\) 21.8879 1.49274
\(216\) 6.44554 0.438563
\(217\) 0 0
\(218\) −52.3055 −3.54258
\(219\) −13.1873 −0.891118
\(220\) 20.2733 1.36683
\(221\) −19.6499 −1.32180
\(222\) −16.6399 −1.11680
\(223\) 23.2274 1.55542 0.777710 0.628624i \(-0.216381\pi\)
0.777710 + 0.628624i \(0.216381\pi\)
\(224\) 0 0
\(225\) −0.839085 −0.0559390
\(226\) 10.2001 0.678500
\(227\) −4.57677 −0.303771 −0.151885 0.988398i \(-0.548534\pi\)
−0.151885 + 0.988398i \(0.548534\pi\)
\(228\) 33.5612 2.22265
\(229\) 10.8001 0.713688 0.356844 0.934164i \(-0.383853\pi\)
0.356844 + 0.934164i \(0.383853\pi\)
\(230\) −24.4997 −1.61547
\(231\) 0 0
\(232\) −65.1131 −4.27488
\(233\) −19.0904 −1.25065 −0.625325 0.780364i \(-0.715034\pi\)
−0.625325 + 0.780364i \(0.715034\pi\)
\(234\) 10.3541 0.676867
\(235\) 1.07757 0.0702929
\(236\) 34.0872 2.21889
\(237\) −2.93987 −0.190965
\(238\) 0 0
\(239\) −7.39421 −0.478291 −0.239146 0.970984i \(-0.576867\pi\)
−0.239146 + 0.970984i \(0.576867\pi\)
\(240\) 15.1266 0.976415
\(241\) 8.85999 0.570722 0.285361 0.958420i \(-0.407887\pi\)
0.285361 + 0.958420i \(0.407887\pi\)
\(242\) −15.7661 −1.01348
\(243\) 1.00000 0.0641500
\(244\) 5.73271 0.366999
\(245\) 0 0
\(246\) 2.55413 0.162845
\(247\) 30.0763 1.91371
\(248\) −24.2410 −1.53930
\(249\) 12.0571 0.764090
\(250\) −30.4216 −1.92403
\(251\) −2.14037 −0.135099 −0.0675495 0.997716i \(-0.521518\pi\)
−0.0675495 + 0.997716i \(0.521518\pi\)
\(252\) 0 0
\(253\) −10.3317 −0.649550
\(254\) 4.08452 0.256286
\(255\) −9.88750 −0.619179
\(256\) −28.0990 −1.75619
\(257\) −14.2797 −0.890744 −0.445372 0.895346i \(-0.646929\pi\)
−0.445372 + 0.895346i \(0.646929\pi\)
\(258\) 27.4064 1.70625
\(259\) 0 0
\(260\) 37.4063 2.31984
\(261\) −10.1020 −0.625300
\(262\) 24.6061 1.52017
\(263\) 16.4154 1.01222 0.506109 0.862469i \(-0.331083\pi\)
0.506109 + 0.862469i \(0.331083\pi\)
\(264\) 14.1615 0.871578
\(265\) 14.7921 0.908670
\(266\) 0 0
\(267\) −4.93696 −0.302137
\(268\) −39.4810 −2.41169
\(269\) −5.20640 −0.317440 −0.158720 0.987324i \(-0.550737\pi\)
−0.158720 + 0.987324i \(0.550737\pi\)
\(270\) 5.20999 0.317070
\(271\) 30.7434 1.86753 0.933765 0.357888i \(-0.116503\pi\)
0.933765 + 0.357888i \(0.116503\pi\)
\(272\) −35.9449 −2.17948
\(273\) 0 0
\(274\) −20.2362 −1.22251
\(275\) −1.84355 −0.111170
\(276\) −21.2719 −1.28042
\(277\) −11.4285 −0.686669 −0.343335 0.939213i \(-0.611556\pi\)
−0.343335 + 0.939213i \(0.611556\pi\)
\(278\) −8.87472 −0.532270
\(279\) −3.76089 −0.225158
\(280\) 0 0
\(281\) 1.76574 0.105335 0.0526677 0.998612i \(-0.483228\pi\)
0.0526677 + 0.998612i \(0.483228\pi\)
\(282\) 1.34925 0.0803469
\(283\) −9.61324 −0.571448 −0.285724 0.958312i \(-0.592234\pi\)
−0.285724 + 0.958312i \(0.592234\pi\)
\(284\) −8.84770 −0.525014
\(285\) 15.1339 0.896454
\(286\) 22.7489 1.34517
\(287\) 0 0
\(288\) 6.04930 0.356458
\(289\) 6.49545 0.382086
\(290\) −52.6316 −3.09063
\(291\) −4.56808 −0.267786
\(292\) −59.6540 −3.49098
\(293\) −0.406494 −0.0237476 −0.0118738 0.999930i \(-0.503780\pi\)
−0.0118738 + 0.999930i \(0.503780\pi\)
\(294\) 0 0
\(295\) 15.3711 0.894938
\(296\) −41.9922 −2.44075
\(297\) 2.19710 0.127488
\(298\) 12.2914 0.712021
\(299\) −19.0631 −1.10245
\(300\) −3.79567 −0.219143
\(301\) 0 0
\(302\) −16.1015 −0.926537
\(303\) 14.8399 0.852530
\(304\) 55.0176 3.15547
\(305\) 2.58507 0.148021
\(306\) −12.3804 −0.707741
\(307\) −1.20072 −0.0685287 −0.0342644 0.999413i \(-0.510909\pi\)
−0.0342644 + 0.999413i \(0.510909\pi\)
\(308\) 0 0
\(309\) −15.1660 −0.862762
\(310\) −19.5942 −1.11288
\(311\) −28.8728 −1.63722 −0.818612 0.574346i \(-0.805256\pi\)
−0.818612 + 0.574346i \(0.805256\pi\)
\(312\) 26.1293 1.47928
\(313\) −15.2516 −0.862073 −0.431037 0.902334i \(-0.641852\pi\)
−0.431037 + 0.902334i \(0.641852\pi\)
\(314\) 10.3969 0.586729
\(315\) 0 0
\(316\) −13.2987 −0.748111
\(317\) 19.2570 1.08158 0.540790 0.841158i \(-0.318125\pi\)
0.540790 + 0.841158i \(0.318125\pi\)
\(318\) 18.5216 1.03864
\(319\) −22.1951 −1.24269
\(320\) 1.26368 0.0706419
\(321\) −10.5325 −0.587868
\(322\) 0 0
\(323\) −35.9623 −2.00100
\(324\) 4.52358 0.251310
\(325\) −3.40153 −0.188683
\(326\) 24.0861 1.33400
\(327\) −20.4788 −1.13248
\(328\) 6.44554 0.355895
\(329\) 0 0
\(330\) 11.4469 0.630129
\(331\) 2.31034 0.126988 0.0634939 0.997982i \(-0.479776\pi\)
0.0634939 + 0.997982i \(0.479776\pi\)
\(332\) 54.5414 2.99335
\(333\) −6.51492 −0.357015
\(334\) 31.3799 1.71703
\(335\) −17.8033 −0.972700
\(336\) 0 0
\(337\) −6.37449 −0.347240 −0.173620 0.984813i \(-0.555547\pi\)
−0.173620 + 0.984813i \(0.555547\pi\)
\(338\) 8.77026 0.477039
\(339\) 3.99357 0.216901
\(340\) −44.7268 −2.42565
\(341\) −8.26303 −0.447468
\(342\) 18.9495 1.02467
\(343\) 0 0
\(344\) 69.1622 3.72897
\(345\) −9.59221 −0.516427
\(346\) 55.6282 2.99059
\(347\) −3.75901 −0.201794 −0.100897 0.994897i \(-0.532171\pi\)
−0.100897 + 0.994897i \(0.532171\pi\)
\(348\) −45.6973 −2.44963
\(349\) −16.7097 −0.894451 −0.447225 0.894421i \(-0.647588\pi\)
−0.447225 + 0.894421i \(0.647588\pi\)
\(350\) 0 0
\(351\) 4.05386 0.216379
\(352\) 13.2909 0.708406
\(353\) −2.05629 −0.109445 −0.0547226 0.998502i \(-0.517427\pi\)
−0.0547226 + 0.998502i \(0.517427\pi\)
\(354\) 19.2465 1.02294
\(355\) −3.98972 −0.211752
\(356\) −22.3327 −1.18363
\(357\) 0 0
\(358\) −21.1258 −1.11653
\(359\) 35.2054 1.85807 0.929036 0.369989i \(-0.120639\pi\)
0.929036 + 0.369989i \(0.120639\pi\)
\(360\) 13.1478 0.692951
\(361\) 36.0442 1.89706
\(362\) 5.97831 0.314213
\(363\) −6.17277 −0.323986
\(364\) 0 0
\(365\) −26.9000 −1.40801
\(366\) 3.23684 0.169192
\(367\) −13.9271 −0.726989 −0.363494 0.931596i \(-0.618416\pi\)
−0.363494 + 0.931596i \(0.618416\pi\)
\(368\) −34.8714 −1.81780
\(369\) 1.00000 0.0520579
\(370\) −33.9427 −1.76460
\(371\) 0 0
\(372\) −17.0127 −0.882065
\(373\) 20.9602 1.08528 0.542639 0.839966i \(-0.317425\pi\)
0.542639 + 0.839966i \(0.317425\pi\)
\(374\) −27.2009 −1.40653
\(375\) −11.9108 −0.615069
\(376\) 3.40494 0.175597
\(377\) −40.9522 −2.10915
\(378\) 0 0
\(379\) −26.2526 −1.34851 −0.674253 0.738501i \(-0.735534\pi\)
−0.674253 + 0.738501i \(0.735534\pi\)
\(380\) 68.4593 3.51189
\(381\) 1.59918 0.0819287
\(382\) 37.0896 1.89767
\(383\) 18.8996 0.965723 0.482861 0.875697i \(-0.339598\pi\)
0.482861 + 0.875697i \(0.339598\pi\)
\(384\) −10.5163 −0.536658
\(385\) 0 0
\(386\) 46.0282 2.34277
\(387\) 10.7302 0.545449
\(388\) −20.6641 −1.04906
\(389\) 14.4255 0.731400 0.365700 0.930733i \(-0.380830\pi\)
0.365700 + 0.930733i \(0.380830\pi\)
\(390\) 21.1206 1.06948
\(391\) 22.7938 1.15273
\(392\) 0 0
\(393\) 9.63387 0.485964
\(394\) 64.4212 3.24549
\(395\) −5.99683 −0.301733
\(396\) 9.93873 0.499440
\(397\) 11.9969 0.602109 0.301055 0.953607i \(-0.402661\pi\)
0.301055 + 0.953607i \(0.402661\pi\)
\(398\) 5.30458 0.265895
\(399\) 0 0
\(400\) −6.22231 −0.311116
\(401\) 29.7872 1.48750 0.743751 0.668457i \(-0.233045\pi\)
0.743751 + 0.668457i \(0.233045\pi\)
\(402\) −22.2920 −1.11183
\(403\) −15.2461 −0.759462
\(404\) 67.1294 3.33981
\(405\) 2.03983 0.101360
\(406\) 0 0
\(407\) −14.3139 −0.709514
\(408\) −31.2429 −1.54675
\(409\) −17.3151 −0.856175 −0.428087 0.903737i \(-0.640812\pi\)
−0.428087 + 0.903737i \(0.640812\pi\)
\(410\) 5.20999 0.257303
\(411\) −7.92292 −0.390809
\(412\) −68.6044 −3.37990
\(413\) 0 0
\(414\) −12.0107 −0.590292
\(415\) 24.5945 1.20730
\(416\) 24.5230 1.20234
\(417\) −3.47465 −0.170155
\(418\) 41.6339 2.03638
\(419\) −39.3854 −1.92410 −0.962051 0.272869i \(-0.912027\pi\)
−0.962051 + 0.272869i \(0.912027\pi\)
\(420\) 0 0
\(421\) −3.88794 −0.189486 −0.0947432 0.995502i \(-0.530203\pi\)
−0.0947432 + 0.995502i \(0.530203\pi\)
\(422\) 23.5113 1.14451
\(423\) 0.528264 0.0256851
\(424\) 46.7406 2.26992
\(425\) 4.06722 0.197289
\(426\) −4.99564 −0.242040
\(427\) 0 0
\(428\) −47.6447 −2.30299
\(429\) 8.90671 0.430020
\(430\) 55.9045 2.69595
\(431\) 18.5771 0.894827 0.447414 0.894327i \(-0.352345\pi\)
0.447414 + 0.894327i \(0.352345\pi\)
\(432\) 7.41559 0.356783
\(433\) −17.0462 −0.819187 −0.409593 0.912268i \(-0.634329\pi\)
−0.409593 + 0.912268i \(0.634329\pi\)
\(434\) 0 0
\(435\) −20.6065 −0.988004
\(436\) −92.6374 −4.43653
\(437\) −34.8883 −1.66893
\(438\) −33.6822 −1.60940
\(439\) −32.6415 −1.55789 −0.778947 0.627090i \(-0.784246\pi\)
−0.778947 + 0.627090i \(0.784246\pi\)
\(440\) 28.8870 1.37713
\(441\) 0 0
\(442\) −50.1884 −2.38722
\(443\) 8.03404 0.381709 0.190854 0.981618i \(-0.438874\pi\)
0.190854 + 0.981618i \(0.438874\pi\)
\(444\) −29.4707 −1.39862
\(445\) −10.0706 −0.477391
\(446\) 59.3257 2.80915
\(447\) 4.81236 0.227617
\(448\) 0 0
\(449\) −13.9945 −0.660444 −0.330222 0.943903i \(-0.607124\pi\)
−0.330222 + 0.943903i \(0.607124\pi\)
\(450\) −2.14313 −0.101028
\(451\) 2.19710 0.103457
\(452\) 18.0652 0.849716
\(453\) −6.30410 −0.296193
\(454\) −11.6897 −0.548623
\(455\) 0 0
\(456\) 47.8206 2.23941
\(457\) −25.8840 −1.21080 −0.605401 0.795920i \(-0.706987\pi\)
−0.605401 + 0.795920i \(0.706987\pi\)
\(458\) 27.5848 1.28895
\(459\) −4.84721 −0.226248
\(460\) −43.3911 −2.02312
\(461\) −11.8265 −0.550817 −0.275408 0.961327i \(-0.588813\pi\)
−0.275408 + 0.961327i \(0.588813\pi\)
\(462\) 0 0
\(463\) −1.25951 −0.0585345 −0.0292672 0.999572i \(-0.509317\pi\)
−0.0292672 + 0.999572i \(0.509317\pi\)
\(464\) −74.9126 −3.47773
\(465\) −7.67158 −0.355761
\(466\) −48.7592 −2.25873
\(467\) −5.15600 −0.238591 −0.119296 0.992859i \(-0.538064\pi\)
−0.119296 + 0.992859i \(0.538064\pi\)
\(468\) 18.3379 0.847671
\(469\) 0 0
\(470\) 2.75225 0.126952
\(471\) 4.07061 0.187564
\(472\) 48.5701 2.23562
\(473\) 23.5754 1.08400
\(474\) −7.50880 −0.344890
\(475\) −6.22532 −0.285637
\(476\) 0 0
\(477\) 7.25162 0.332029
\(478\) −18.8858 −0.863815
\(479\) 24.6671 1.12707 0.563534 0.826093i \(-0.309442\pi\)
0.563534 + 0.826093i \(0.309442\pi\)
\(480\) 12.3395 0.563221
\(481\) −26.4105 −1.20422
\(482\) 22.6296 1.03075
\(483\) 0 0
\(484\) −27.9230 −1.26923
\(485\) −9.31812 −0.423114
\(486\) 2.55413 0.115858
\(487\) −36.9281 −1.67337 −0.836685 0.547684i \(-0.815510\pi\)
−0.836685 + 0.547684i \(0.815510\pi\)
\(488\) 8.16841 0.369767
\(489\) 9.43025 0.426451
\(490\) 0 0
\(491\) 38.8273 1.75225 0.876125 0.482085i \(-0.160120\pi\)
0.876125 + 0.482085i \(0.160120\pi\)
\(492\) 4.52358 0.203939
\(493\) 48.9667 2.20535
\(494\) 76.8187 3.45624
\(495\) 4.48171 0.201438
\(496\) −27.8892 −1.25226
\(497\) 0 0
\(498\) 30.7955 1.37998
\(499\) −11.8209 −0.529175 −0.264587 0.964362i \(-0.585236\pi\)
−0.264587 + 0.964362i \(0.585236\pi\)
\(500\) −53.8792 −2.40955
\(501\) 12.2859 0.548895
\(502\) −5.46679 −0.243995
\(503\) −28.3846 −1.26561 −0.632803 0.774312i \(-0.718096\pi\)
−0.632803 + 0.774312i \(0.718096\pi\)
\(504\) 0 0
\(505\) 30.2709 1.34704
\(506\) −26.3886 −1.17312
\(507\) 3.43376 0.152499
\(508\) 7.23403 0.320958
\(509\) 7.66798 0.339877 0.169939 0.985455i \(-0.445643\pi\)
0.169939 + 0.985455i \(0.445643\pi\)
\(510\) −25.2539 −1.11826
\(511\) 0 0
\(512\) −50.7359 −2.24223
\(513\) 7.41918 0.327565
\(514\) −36.4722 −1.60872
\(515\) −30.9360 −1.36320
\(516\) 48.5390 2.13681
\(517\) 1.16065 0.0510451
\(518\) 0 0
\(519\) 21.7797 0.956023
\(520\) 53.2994 2.33733
\(521\) 9.40056 0.411846 0.205923 0.978568i \(-0.433980\pi\)
0.205923 + 0.978568i \(0.433980\pi\)
\(522\) −25.8019 −1.12932
\(523\) 35.7553 1.56347 0.781735 0.623610i \(-0.214335\pi\)
0.781735 + 0.623610i \(0.214335\pi\)
\(524\) 43.5795 1.90378
\(525\) 0 0
\(526\) 41.9271 1.82811
\(527\) 18.2298 0.794103
\(528\) 16.2928 0.709051
\(529\) −0.886957 −0.0385634
\(530\) 37.7809 1.64110
\(531\) 7.53546 0.327011
\(532\) 0 0
\(533\) 4.05386 0.175592
\(534\) −12.6096 −0.545673
\(535\) −21.4846 −0.928860
\(536\) −56.2556 −2.42987
\(537\) −8.27123 −0.356930
\(538\) −13.2978 −0.573309
\(539\) 0 0
\(540\) 9.22734 0.397081
\(541\) 20.1520 0.866401 0.433201 0.901298i \(-0.357384\pi\)
0.433201 + 0.901298i \(0.357384\pi\)
\(542\) 78.5226 3.37284
\(543\) 2.34065 0.100447
\(544\) −29.3222 −1.25718
\(545\) −41.7733 −1.78937
\(546\) 0 0
\(547\) −15.9234 −0.680837 −0.340419 0.940274i \(-0.610569\pi\)
−0.340419 + 0.940274i \(0.610569\pi\)
\(548\) −35.8399 −1.53101
\(549\) 1.26730 0.0540869
\(550\) −4.70866 −0.200778
\(551\) −74.9488 −3.19293
\(552\) −30.3098 −1.29007
\(553\) 0 0
\(554\) −29.1898 −1.24015
\(555\) −13.2893 −0.564101
\(556\) −15.7179 −0.666586
\(557\) −23.1311 −0.980095 −0.490047 0.871696i \(-0.663020\pi\)
−0.490047 + 0.871696i \(0.663020\pi\)
\(558\) −9.60579 −0.406646
\(559\) 43.4988 1.83981
\(560\) 0 0
\(561\) −10.6498 −0.449634
\(562\) 4.50993 0.190240
\(563\) −30.7087 −1.29422 −0.647109 0.762398i \(-0.724022\pi\)
−0.647109 + 0.762398i \(0.724022\pi\)
\(564\) 2.38964 0.100622
\(565\) 8.14621 0.342714
\(566\) −24.5534 −1.03206
\(567\) 0 0
\(568\) −12.6069 −0.528973
\(569\) 3.03214 0.127114 0.0635570 0.997978i \(-0.479756\pi\)
0.0635570 + 0.997978i \(0.479756\pi\)
\(570\) 38.6539 1.61903
\(571\) −1.79836 −0.0752589 −0.0376294 0.999292i \(-0.511981\pi\)
−0.0376294 + 0.999292i \(0.511981\pi\)
\(572\) 40.2902 1.68462
\(573\) 14.5214 0.606642
\(574\) 0 0
\(575\) 3.94576 0.164549
\(576\) 0.619503 0.0258126
\(577\) 26.4404 1.10073 0.550365 0.834924i \(-0.314489\pi\)
0.550365 + 0.834924i \(0.314489\pi\)
\(578\) 16.5902 0.690063
\(579\) 18.0211 0.748930
\(580\) −93.2149 −3.87054
\(581\) 0 0
\(582\) −11.6675 −0.483632
\(583\) 15.9325 0.659856
\(584\) −84.9996 −3.51731
\(585\) 8.26919 0.341889
\(586\) −1.03824 −0.0428892
\(587\) 3.24299 0.133853 0.0669263 0.997758i \(-0.478681\pi\)
0.0669263 + 0.997758i \(0.478681\pi\)
\(588\) 0 0
\(589\) −27.9027 −1.14971
\(590\) 39.2597 1.61630
\(591\) 25.2224 1.03751
\(592\) −48.3120 −1.98561
\(593\) −25.9252 −1.06462 −0.532311 0.846549i \(-0.678676\pi\)
−0.532311 + 0.846549i \(0.678676\pi\)
\(594\) 5.61167 0.230249
\(595\) 0 0
\(596\) 21.7691 0.891697
\(597\) 2.07686 0.0850004
\(598\) −48.6895 −1.99106
\(599\) −16.7618 −0.684867 −0.342433 0.939542i \(-0.611251\pi\)
−0.342433 + 0.939542i \(0.611251\pi\)
\(600\) −5.40836 −0.220795
\(601\) −9.35320 −0.381525 −0.190762 0.981636i \(-0.561096\pi\)
−0.190762 + 0.981636i \(0.561096\pi\)
\(602\) 0 0
\(603\) −8.72784 −0.355425
\(604\) −28.5171 −1.16034
\(605\) −12.5914 −0.511914
\(606\) 37.9030 1.53970
\(607\) 5.62356 0.228253 0.114127 0.993466i \(-0.463593\pi\)
0.114127 + 0.993466i \(0.463593\pi\)
\(608\) 44.8808 1.82016
\(609\) 0 0
\(610\) 6.60261 0.267332
\(611\) 2.14151 0.0866360
\(612\) −21.9267 −0.886335
\(613\) 13.6259 0.550346 0.275173 0.961395i \(-0.411265\pi\)
0.275173 + 0.961395i \(0.411265\pi\)
\(614\) −3.06679 −0.123766
\(615\) 2.03983 0.0822540
\(616\) 0 0
\(617\) 45.9830 1.85121 0.925604 0.378494i \(-0.123558\pi\)
0.925604 + 0.378494i \(0.123558\pi\)
\(618\) −38.7358 −1.55818
\(619\) −12.0863 −0.485791 −0.242895 0.970052i \(-0.578097\pi\)
−0.242895 + 0.970052i \(0.578097\pi\)
\(620\) −34.7030 −1.39371
\(621\) −4.70245 −0.188703
\(622\) −73.7448 −2.95690
\(623\) 0 0
\(624\) 30.0617 1.20343
\(625\) −20.1005 −0.804020
\(626\) −38.9546 −1.55694
\(627\) 16.3006 0.650985
\(628\) 18.4137 0.734787
\(629\) 31.5792 1.25914
\(630\) 0 0
\(631\) −45.2956 −1.80319 −0.901596 0.432580i \(-0.857603\pi\)
−0.901596 + 0.432580i \(0.857603\pi\)
\(632\) −18.9490 −0.753752
\(633\) 9.20520 0.365874
\(634\) 49.1848 1.95338
\(635\) 3.26207 0.129451
\(636\) 32.8032 1.30073
\(637\) 0 0
\(638\) −56.6892 −2.24435
\(639\) −1.95591 −0.0773745
\(640\) −21.4515 −0.847945
\(641\) −14.8236 −0.585495 −0.292748 0.956190i \(-0.594570\pi\)
−0.292748 + 0.956190i \(0.594570\pi\)
\(642\) −26.9014 −1.06171
\(643\) −10.4299 −0.411314 −0.205657 0.978624i \(-0.565933\pi\)
−0.205657 + 0.978624i \(0.565933\pi\)
\(644\) 0 0
\(645\) 21.8879 0.861834
\(646\) −91.8524 −3.61389
\(647\) 17.4261 0.685093 0.342546 0.939501i \(-0.388711\pi\)
0.342546 + 0.939501i \(0.388711\pi\)
\(648\) 6.44554 0.253205
\(649\) 16.5561 0.649884
\(650\) −8.68795 −0.340769
\(651\) 0 0
\(652\) 42.6584 1.67063
\(653\) 15.0102 0.587394 0.293697 0.955899i \(-0.405114\pi\)
0.293697 + 0.955899i \(0.405114\pi\)
\(654\) −52.3055 −2.04531
\(655\) 19.6515 0.767847
\(656\) 7.41559 0.289530
\(657\) −13.1873 −0.514487
\(658\) 0 0
\(659\) 32.1433 1.25212 0.626062 0.779774i \(-0.284666\pi\)
0.626062 + 0.779774i \(0.284666\pi\)
\(660\) 20.2733 0.789139
\(661\) −2.34987 −0.0913992 −0.0456996 0.998955i \(-0.514552\pi\)
−0.0456996 + 0.998955i \(0.514552\pi\)
\(662\) 5.90091 0.229345
\(663\) −19.6499 −0.763139
\(664\) 77.7148 3.01592
\(665\) 0 0
\(666\) −16.6399 −0.644785
\(667\) 47.5043 1.83937
\(668\) 55.5764 2.15032
\(669\) 23.2274 0.898022
\(670\) −45.4720 −1.75674
\(671\) 2.78437 0.107489
\(672\) 0 0
\(673\) −29.7768 −1.14781 −0.573906 0.818921i \(-0.694573\pi\)
−0.573906 + 0.818921i \(0.694573\pi\)
\(674\) −16.2813 −0.627131
\(675\) −0.839085 −0.0322964
\(676\) 15.5329 0.597418
\(677\) 27.9673 1.07487 0.537435 0.843305i \(-0.319393\pi\)
0.537435 + 0.843305i \(0.319393\pi\)
\(678\) 10.2001 0.391732
\(679\) 0 0
\(680\) −63.7303 −2.44394
\(681\) −4.57677 −0.175382
\(682\) −21.1048 −0.808146
\(683\) −26.5644 −1.01646 −0.508230 0.861221i \(-0.669700\pi\)
−0.508230 + 0.861221i \(0.669700\pi\)
\(684\) 33.5612 1.28325
\(685\) −16.1614 −0.617496
\(686\) 0 0
\(687\) 10.8001 0.412048
\(688\) 79.5710 3.03362
\(689\) 29.3970 1.11994
\(690\) −24.4997 −0.932689
\(691\) −1.69085 −0.0643229 −0.0321614 0.999483i \(-0.510239\pi\)
−0.0321614 + 0.999483i \(0.510239\pi\)
\(692\) 98.5221 3.74525
\(693\) 0 0
\(694\) −9.60100 −0.364449
\(695\) −7.08771 −0.268852
\(696\) −65.1131 −2.46810
\(697\) −4.84721 −0.183601
\(698\) −42.6788 −1.61542
\(699\) −19.0904 −0.722064
\(700\) 0 0
\(701\) 3.65407 0.138012 0.0690062 0.997616i \(-0.478017\pi\)
0.0690062 + 0.997616i \(0.478017\pi\)
\(702\) 10.3541 0.390789
\(703\) −48.3353 −1.82300
\(704\) 1.36111 0.0512986
\(705\) 1.07757 0.0405836
\(706\) −5.25203 −0.197663
\(707\) 0 0
\(708\) 34.0872 1.28108
\(709\) −29.8396 −1.12065 −0.560324 0.828273i \(-0.689323\pi\)
−0.560324 + 0.828273i \(0.689323\pi\)
\(710\) −10.1903 −0.382434
\(711\) −2.93987 −0.110254
\(712\) −31.8214 −1.19256
\(713\) 17.6854 0.662323
\(714\) 0 0
\(715\) 18.1682 0.679452
\(716\) −37.4155 −1.39828
\(717\) −7.39421 −0.276142
\(718\) 89.9193 3.35576
\(719\) −21.2360 −0.791970 −0.395985 0.918257i \(-0.629597\pi\)
−0.395985 + 0.918257i \(0.629597\pi\)
\(720\) 15.1266 0.563734
\(721\) 0 0
\(722\) 92.0616 3.42618
\(723\) 8.85999 0.329506
\(724\) 10.5881 0.393503
\(725\) 8.47647 0.314808
\(726\) −15.7661 −0.585133
\(727\) 48.4942 1.79855 0.899275 0.437383i \(-0.144095\pi\)
0.899275 + 0.437383i \(0.144095\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −68.7060 −2.54292
\(731\) −52.0117 −1.92372
\(732\) 5.73271 0.211887
\(733\) 27.3083 1.00866 0.504328 0.863512i \(-0.331740\pi\)
0.504328 + 0.863512i \(0.331740\pi\)
\(734\) −35.5716 −1.31297
\(735\) 0 0
\(736\) −28.4465 −1.04855
\(737\) −19.1759 −0.706353
\(738\) 2.55413 0.0940188
\(739\) −13.4819 −0.495940 −0.247970 0.968768i \(-0.579763\pi\)
−0.247970 + 0.968768i \(0.579763\pi\)
\(740\) −60.1153 −2.20988
\(741\) 30.0763 1.10488
\(742\) 0 0
\(743\) 46.0019 1.68765 0.843823 0.536622i \(-0.180300\pi\)
0.843823 + 0.536622i \(0.180300\pi\)
\(744\) −24.2410 −0.888716
\(745\) 9.81641 0.359645
\(746\) 53.5350 1.96006
\(747\) 12.0571 0.441148
\(748\) −48.1751 −1.76146
\(749\) 0 0
\(750\) −30.4216 −1.11084
\(751\) 21.8979 0.799066 0.399533 0.916719i \(-0.369172\pi\)
0.399533 + 0.916719i \(0.369172\pi\)
\(752\) 3.91739 0.142852
\(753\) −2.14037 −0.0779995
\(754\) −104.597 −3.80921
\(755\) −12.8593 −0.467998
\(756\) 0 0
\(757\) −42.5655 −1.54707 −0.773535 0.633754i \(-0.781513\pi\)
−0.773535 + 0.633754i \(0.781513\pi\)
\(758\) −67.0525 −2.43546
\(759\) −10.3317 −0.375018
\(760\) 97.5460 3.53837
\(761\) 18.1190 0.656812 0.328406 0.944537i \(-0.393489\pi\)
0.328406 + 0.944537i \(0.393489\pi\)
\(762\) 4.08452 0.147967
\(763\) 0 0
\(764\) 65.6888 2.37654
\(765\) −9.88750 −0.357483
\(766\) 48.2719 1.74414
\(767\) 30.5477 1.10301
\(768\) −28.0990 −1.01394
\(769\) −0.938954 −0.0338596 −0.0169298 0.999857i \(-0.505389\pi\)
−0.0169298 + 0.999857i \(0.505389\pi\)
\(770\) 0 0
\(771\) −14.2797 −0.514271
\(772\) 81.5197 2.93396
\(773\) 19.5127 0.701821 0.350911 0.936409i \(-0.385872\pi\)
0.350911 + 0.936409i \(0.385872\pi\)
\(774\) 27.4064 0.985103
\(775\) 3.15570 0.113356
\(776\) −29.4438 −1.05697
\(777\) 0 0
\(778\) 36.8445 1.32094
\(779\) 7.41918 0.265820
\(780\) 37.4063 1.33936
\(781\) −4.29732 −0.153770
\(782\) 58.2182 2.08188
\(783\) −10.1020 −0.361017
\(784\) 0 0
\(785\) 8.30336 0.296360
\(786\) 24.6061 0.877672
\(787\) −46.1884 −1.64644 −0.823219 0.567724i \(-0.807824\pi\)
−0.823219 + 0.567724i \(0.807824\pi\)
\(788\) 114.095 4.06448
\(789\) 16.4154 0.584404
\(790\) −15.3167 −0.544943
\(791\) 0 0
\(792\) 14.1615 0.503206
\(793\) 5.13744 0.182436
\(794\) 30.6417 1.08743
\(795\) 14.7921 0.524621
\(796\) 9.39486 0.332992
\(797\) 4.04847 0.143404 0.0717020 0.997426i \(-0.477157\pi\)
0.0717020 + 0.997426i \(0.477157\pi\)
\(798\) 0 0
\(799\) −2.56060 −0.0905877
\(800\) −5.07587 −0.179459
\(801\) −4.93696 −0.174439
\(802\) 76.0804 2.68649
\(803\) −28.9739 −1.02247
\(804\) −39.4810 −1.39239
\(805\) 0 0
\(806\) −38.9405 −1.37162
\(807\) −5.20640 −0.183274
\(808\) 95.6512 3.36500
\(809\) −21.5809 −0.758745 −0.379373 0.925244i \(-0.623860\pi\)
−0.379373 + 0.925244i \(0.623860\pi\)
\(810\) 5.20999 0.183061
\(811\) −0.609476 −0.0214016 −0.0107008 0.999943i \(-0.503406\pi\)
−0.0107008 + 0.999943i \(0.503406\pi\)
\(812\) 0 0
\(813\) 30.7434 1.07822
\(814\) −36.5595 −1.28141
\(815\) 19.2361 0.673812
\(816\) −35.9449 −1.25832
\(817\) 79.6095 2.78519
\(818\) −44.2249 −1.54629
\(819\) 0 0
\(820\) 9.22734 0.322233
\(821\) 6.40281 0.223460 0.111730 0.993739i \(-0.464361\pi\)
0.111730 + 0.993739i \(0.464361\pi\)
\(822\) −20.2362 −0.705817
\(823\) −34.8973 −1.21644 −0.608221 0.793768i \(-0.708117\pi\)
−0.608221 + 0.793768i \(0.708117\pi\)
\(824\) −97.7529 −3.40538
\(825\) −1.84355 −0.0641842
\(826\) 0 0
\(827\) 19.4846 0.677545 0.338773 0.940868i \(-0.389988\pi\)
0.338773 + 0.940868i \(0.389988\pi\)
\(828\) −21.2719 −0.739249
\(829\) 49.9870 1.73612 0.868060 0.496460i \(-0.165367\pi\)
0.868060 + 0.496460i \(0.165367\pi\)
\(830\) 62.8176 2.18043
\(831\) −11.4285 −0.396449
\(832\) 2.51137 0.0870663
\(833\) 0 0
\(834\) −8.87472 −0.307306
\(835\) 25.0613 0.867281
\(836\) 73.7372 2.55025
\(837\) −3.76089 −0.129995
\(838\) −100.595 −3.47501
\(839\) −33.9692 −1.17275 −0.586374 0.810040i \(-0.699445\pi\)
−0.586374 + 0.810040i \(0.699445\pi\)
\(840\) 0 0
\(841\) 73.0511 2.51900
\(842\) −9.93029 −0.342221
\(843\) 1.76574 0.0608154
\(844\) 41.6404 1.43332
\(845\) 7.00429 0.240955
\(846\) 1.34925 0.0463883
\(847\) 0 0
\(848\) 53.7750 1.84664
\(849\) −9.61324 −0.329925
\(850\) 10.3882 0.356313
\(851\) 30.6361 1.05019
\(852\) −8.84770 −0.303117
\(853\) −21.9694 −0.752219 −0.376109 0.926575i \(-0.622738\pi\)
−0.376109 + 0.926575i \(0.622738\pi\)
\(854\) 0 0
\(855\) 15.1339 0.517568
\(856\) −67.8878 −2.32036
\(857\) −29.0187 −0.991261 −0.495630 0.868534i \(-0.665063\pi\)
−0.495630 + 0.868534i \(0.665063\pi\)
\(858\) 22.7489 0.776634
\(859\) −51.7596 −1.76602 −0.883008 0.469358i \(-0.844485\pi\)
−0.883008 + 0.469358i \(0.844485\pi\)
\(860\) 99.0115 3.37626
\(861\) 0 0
\(862\) 47.4483 1.61610
\(863\) 2.65807 0.0904819 0.0452409 0.998976i \(-0.485594\pi\)
0.0452409 + 0.998976i \(0.485594\pi\)
\(864\) 6.04930 0.205801
\(865\) 44.4269 1.51056
\(866\) −43.5381 −1.47949
\(867\) 6.49545 0.220597
\(868\) 0 0
\(869\) −6.45916 −0.219112
\(870\) −52.6316 −1.78438
\(871\) −35.3814 −1.19885
\(872\) −131.997 −4.46998
\(873\) −4.56808 −0.154606
\(874\) −89.1093 −3.01417
\(875\) 0 0
\(876\) −59.6540 −2.01552
\(877\) 36.3290 1.22674 0.613371 0.789795i \(-0.289813\pi\)
0.613371 + 0.789795i \(0.289813\pi\)
\(878\) −83.3706 −2.81362
\(879\) −0.406494 −0.0137107
\(880\) 33.2345 1.12033
\(881\) 54.4117 1.83318 0.916588 0.399833i \(-0.130932\pi\)
0.916588 + 0.399833i \(0.130932\pi\)
\(882\) 0 0
\(883\) 25.0694 0.843654 0.421827 0.906676i \(-0.361389\pi\)
0.421827 + 0.906676i \(0.361389\pi\)
\(884\) −88.8878 −2.98962
\(885\) 15.3711 0.516693
\(886\) 20.5200 0.689382
\(887\) 44.5935 1.49730 0.748651 0.662964i \(-0.230702\pi\)
0.748651 + 0.662964i \(0.230702\pi\)
\(888\) −41.9922 −1.40916
\(889\) 0 0
\(890\) −25.7216 −0.862188
\(891\) 2.19710 0.0736055
\(892\) 105.071 3.51803
\(893\) 3.91928 0.131154
\(894\) 12.2914 0.411086
\(895\) −16.8719 −0.563966
\(896\) 0 0
\(897\) −19.0631 −0.636497
\(898\) −35.7439 −1.19279
\(899\) 37.9926 1.26712
\(900\) −3.79567 −0.126522
\(901\) −35.1501 −1.17102
\(902\) 5.61167 0.186848
\(903\) 0 0
\(904\) 25.7407 0.856123
\(905\) 4.77452 0.158711
\(906\) −16.1015 −0.534936
\(907\) −51.9895 −1.72628 −0.863141 0.504962i \(-0.831506\pi\)
−0.863141 + 0.504962i \(0.831506\pi\)
\(908\) −20.7034 −0.687065
\(909\) 14.8399 0.492208
\(910\) 0 0
\(911\) −12.5978 −0.417383 −0.208692 0.977981i \(-0.566921\pi\)
−0.208692 + 0.977981i \(0.566921\pi\)
\(912\) 55.0176 1.82181
\(913\) 26.4907 0.876714
\(914\) −66.1111 −2.18676
\(915\) 2.58507 0.0854599
\(916\) 48.8549 1.61421
\(917\) 0 0
\(918\) −12.3804 −0.408614
\(919\) −40.2751 −1.32855 −0.664277 0.747487i \(-0.731260\pi\)
−0.664277 + 0.747487i \(0.731260\pi\)
\(920\) −61.8270 −2.03837
\(921\) −1.20072 −0.0395651
\(922\) −30.2065 −0.994799
\(923\) −7.92897 −0.260985
\(924\) 0 0
\(925\) 5.46657 0.179740
\(926\) −3.21696 −0.105716
\(927\) −15.1660 −0.498116
\(928\) −61.1102 −2.00604
\(929\) 37.4105 1.22740 0.613700 0.789539i \(-0.289680\pi\)
0.613700 + 0.789539i \(0.289680\pi\)
\(930\) −19.5942 −0.642519
\(931\) 0 0
\(932\) −86.3567 −2.82871
\(933\) −28.8728 −0.945252
\(934\) −13.1691 −0.430906
\(935\) −21.7238 −0.710443
\(936\) 26.1293 0.854063
\(937\) −6.39519 −0.208922 −0.104461 0.994529i \(-0.533312\pi\)
−0.104461 + 0.994529i \(0.533312\pi\)
\(938\) 0 0
\(939\) −15.2516 −0.497718
\(940\) 4.87447 0.158988
\(941\) −28.2888 −0.922189 −0.461095 0.887351i \(-0.652543\pi\)
−0.461095 + 0.887351i \(0.652543\pi\)
\(942\) 10.3969 0.338748
\(943\) −4.70245 −0.153133
\(944\) 55.8799 1.81873
\(945\) 0 0
\(946\) 60.2145 1.95774
\(947\) −11.5695 −0.375957 −0.187979 0.982173i \(-0.560194\pi\)
−0.187979 + 0.982173i \(0.560194\pi\)
\(948\) −13.2987 −0.431922
\(949\) −53.4596 −1.73537
\(950\) −15.9003 −0.515873
\(951\) 19.2570 0.624450
\(952\) 0 0
\(953\) −26.3771 −0.854437 −0.427219 0.904148i \(-0.640507\pi\)
−0.427219 + 0.904148i \(0.640507\pi\)
\(954\) 18.5216 0.599658
\(955\) 29.6213 0.958522
\(956\) −33.4483 −1.08179
\(957\) −22.1951 −0.717467
\(958\) 63.0029 2.03553
\(959\) 0 0
\(960\) 1.26368 0.0407851
\(961\) −16.8557 −0.543733
\(962\) −67.4560 −2.17487
\(963\) −10.5325 −0.339406
\(964\) 40.0788 1.29085
\(965\) 36.7600 1.18335
\(966\) 0 0
\(967\) −33.1048 −1.06458 −0.532290 0.846562i \(-0.678668\pi\)
−0.532290 + 0.846562i \(0.678668\pi\)
\(968\) −39.7868 −1.27880
\(969\) −35.9623 −1.15528
\(970\) −23.7997 −0.764162
\(971\) 13.5891 0.436095 0.218047 0.975938i \(-0.430031\pi\)
0.218047 + 0.975938i \(0.430031\pi\)
\(972\) 4.52358 0.145094
\(973\) 0 0
\(974\) −94.3191 −3.02218
\(975\) −3.40153 −0.108936
\(976\) 9.39775 0.300815
\(977\) −58.3154 −1.86567 −0.932837 0.360299i \(-0.882675\pi\)
−0.932837 + 0.360299i \(0.882675\pi\)
\(978\) 24.0861 0.770188
\(979\) −10.8470 −0.346671
\(980\) 0 0
\(981\) −20.4788 −0.653838
\(982\) 99.1698 3.16464
\(983\) 16.9974 0.542132 0.271066 0.962561i \(-0.412624\pi\)
0.271066 + 0.962561i \(0.412624\pi\)
\(984\) 6.44554 0.205476
\(985\) 51.4494 1.63932
\(986\) 125.067 3.98295
\(987\) 0 0
\(988\) 136.052 4.32840
\(989\) −50.4584 −1.60448
\(990\) 11.4469 0.363805
\(991\) −9.52580 −0.302597 −0.151299 0.988488i \(-0.548345\pi\)
−0.151299 + 0.988488i \(0.548345\pi\)
\(992\) −22.7507 −0.722336
\(993\) 2.31034 0.0733164
\(994\) 0 0
\(995\) 4.23646 0.134305
\(996\) 54.5414 1.72821
\(997\) 43.2360 1.36930 0.684648 0.728874i \(-0.259956\pi\)
0.684648 + 0.728874i \(0.259956\pi\)
\(998\) −30.1920 −0.955712
\(999\) −6.51492 −0.206123
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 \(a_p\))