Properties

Label 8018.2.a.j.1.3
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 47
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(0\)
Dimension: \(47\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.07943 q^{3} +1.00000 q^{4} -3.30634 q^{5} -3.07943 q^{6} -2.62160 q^{7} +1.00000 q^{8} +6.48290 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.07943 q^{3} +1.00000 q^{4} -3.30634 q^{5} -3.07943 q^{6} -2.62160 q^{7} +1.00000 q^{8} +6.48290 q^{9} -3.30634 q^{10} +3.59685 q^{11} -3.07943 q^{12} -3.17175 q^{13} -2.62160 q^{14} +10.1816 q^{15} +1.00000 q^{16} +4.85924 q^{17} +6.48290 q^{18} -1.00000 q^{19} -3.30634 q^{20} +8.07304 q^{21} +3.59685 q^{22} -3.16632 q^{23} -3.07943 q^{24} +5.93186 q^{25} -3.17175 q^{26} -10.7254 q^{27} -2.62160 q^{28} -1.52137 q^{29} +10.1816 q^{30} -6.15407 q^{31} +1.00000 q^{32} -11.0763 q^{33} +4.85924 q^{34} +8.66789 q^{35} +6.48290 q^{36} +7.44862 q^{37} -1.00000 q^{38} +9.76720 q^{39} -3.30634 q^{40} +0.725201 q^{41} +8.07304 q^{42} -1.68387 q^{43} +3.59685 q^{44} -21.4347 q^{45} -3.16632 q^{46} -10.0853 q^{47} -3.07943 q^{48} -0.127213 q^{49} +5.93186 q^{50} -14.9637 q^{51} -3.17175 q^{52} +9.64128 q^{53} -10.7254 q^{54} -11.8924 q^{55} -2.62160 q^{56} +3.07943 q^{57} -1.52137 q^{58} -9.95767 q^{59} +10.1816 q^{60} -12.4578 q^{61} -6.15407 q^{62} -16.9956 q^{63} +1.00000 q^{64} +10.4869 q^{65} -11.0763 q^{66} +5.58038 q^{67} +4.85924 q^{68} +9.75047 q^{69} +8.66789 q^{70} +3.62595 q^{71} +6.48290 q^{72} +7.67422 q^{73} +7.44862 q^{74} -18.2668 q^{75} -1.00000 q^{76} -9.42950 q^{77} +9.76720 q^{78} -12.0529 q^{79} -3.30634 q^{80} +13.5793 q^{81} +0.725201 q^{82} -4.32343 q^{83} +8.07304 q^{84} -16.0663 q^{85} -1.68387 q^{86} +4.68497 q^{87} +3.59685 q^{88} -12.5944 q^{89} -21.4347 q^{90} +8.31507 q^{91} -3.16632 q^{92} +18.9511 q^{93} -10.0853 q^{94} +3.30634 q^{95} -3.07943 q^{96} -9.41884 q^{97} -0.127213 q^{98} +23.3180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 47q + 47q^{2} + 10q^{3} + 47q^{4} + 15q^{5} + 10q^{6} + 47q^{8} + 69q^{9} + O(q^{10}) \) \( 47q + 47q^{2} + 10q^{3} + 47q^{4} + 15q^{5} + 10q^{6} + 47q^{8} + 69q^{9} + 15q^{10} + 17q^{11} + 10q^{12} + 27q^{13} + 10q^{15} + 47q^{16} + 16q^{17} + 69q^{18} - 47q^{19} + 15q^{20} + 26q^{21} + 17q^{22} + 24q^{23} + 10q^{24} + 86q^{25} + 27q^{26} + 43q^{27} + 58q^{29} + 10q^{30} + 21q^{31} + 47q^{32} + 18q^{33} + 16q^{34} + 24q^{35} + 69q^{36} + 78q^{37} - 47q^{38} - 4q^{39} + 15q^{40} + 53q^{41} + 26q^{42} + 47q^{43} + 17q^{44} + 23q^{45} + 24q^{46} + 16q^{47} + 10q^{48} + 93q^{49} + 86q^{50} + 28q^{51} + 27q^{52} + 43q^{53} + 43q^{54} + 23q^{55} - 10q^{57} + 58q^{58} + 3q^{59} + 10q^{60} + 12q^{61} + 21q^{62} - 5q^{63} + 47q^{64} + 62q^{65} + 18q^{66} + 68q^{67} + 16q^{68} + 12q^{69} + 24q^{70} - 13q^{71} + 69q^{72} + 35q^{73} + 78q^{74} + 22q^{75} - 47q^{76} + 26q^{77} - 4q^{78} + 21q^{79} + 15q^{80} + 123q^{81} + 53q^{82} + 23q^{83} + 26q^{84} + 38q^{85} + 47q^{86} + 39q^{87} + 17q^{88} + 24q^{89} + 23q^{90} + 49q^{91} + 24q^{92} + 91q^{93} + 16q^{94} - 15q^{95} + 10q^{96} + 88q^{97} + 93q^{98} + 26q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −3.07943 −1.77791 −0.888956 0.457993i \(-0.848568\pi\)
−0.888956 + 0.457993i \(0.848568\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.30634 −1.47864 −0.739319 0.673355i \(-0.764853\pi\)
−0.739319 + 0.673355i \(0.764853\pi\)
\(6\) −3.07943 −1.25717
\(7\) −2.62160 −0.990872 −0.495436 0.868645i \(-0.664992\pi\)
−0.495436 + 0.868645i \(0.664992\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.48290 2.16097
\(10\) −3.30634 −1.04556
\(11\) 3.59685 1.08449 0.542245 0.840220i \(-0.317574\pi\)
0.542245 + 0.840220i \(0.317574\pi\)
\(12\) −3.07943 −0.888956
\(13\) −3.17175 −0.879686 −0.439843 0.898075i \(-0.644966\pi\)
−0.439843 + 0.898075i \(0.644966\pi\)
\(14\) −2.62160 −0.700652
\(15\) 10.1816 2.62889
\(16\) 1.00000 0.250000
\(17\) 4.85924 1.17854 0.589269 0.807937i \(-0.299416\pi\)
0.589269 + 0.807937i \(0.299416\pi\)
\(18\) 6.48290 1.52804
\(19\) −1.00000 −0.229416
\(20\) −3.30634 −0.739319
\(21\) 8.07304 1.76168
\(22\) 3.59685 0.766851
\(23\) −3.16632 −0.660223 −0.330112 0.943942i \(-0.607086\pi\)
−0.330112 + 0.943942i \(0.607086\pi\)
\(24\) −3.07943 −0.628587
\(25\) 5.93186 1.18637
\(26\) −3.17175 −0.622032
\(27\) −10.7254 −2.06410
\(28\) −2.62160 −0.495436
\(29\) −1.52137 −0.282512 −0.141256 0.989973i \(-0.545114\pi\)
−0.141256 + 0.989973i \(0.545114\pi\)
\(30\) 10.1816 1.85890
\(31\) −6.15407 −1.10530 −0.552652 0.833412i \(-0.686384\pi\)
−0.552652 + 0.833412i \(0.686384\pi\)
\(32\) 1.00000 0.176777
\(33\) −11.0763 −1.92813
\(34\) 4.85924 0.833353
\(35\) 8.66789 1.46514
\(36\) 6.48290 1.08048
\(37\) 7.44862 1.22455 0.612273 0.790647i \(-0.290255\pi\)
0.612273 + 0.790647i \(0.290255\pi\)
\(38\) −1.00000 −0.162221
\(39\) 9.76720 1.56400
\(40\) −3.30634 −0.522778
\(41\) 0.725201 0.113257 0.0566287 0.998395i \(-0.481965\pi\)
0.0566287 + 0.998395i \(0.481965\pi\)
\(42\) 8.07304 1.24570
\(43\) −1.68387 −0.256789 −0.128394 0.991723i \(-0.540982\pi\)
−0.128394 + 0.991723i \(0.540982\pi\)
\(44\) 3.59685 0.542245
\(45\) −21.4347 −3.19529
\(46\) −3.16632 −0.466848
\(47\) −10.0853 −1.47109 −0.735547 0.677474i \(-0.763075\pi\)
−0.735547 + 0.677474i \(0.763075\pi\)
\(48\) −3.07943 −0.444478
\(49\) −0.127213 −0.0181732
\(50\) 5.93186 0.838892
\(51\) −14.9637 −2.09534
\(52\) −3.17175 −0.439843
\(53\) 9.64128 1.32433 0.662166 0.749357i \(-0.269638\pi\)
0.662166 + 0.749357i \(0.269638\pi\)
\(54\) −10.7254 −1.45954
\(55\) −11.8924 −1.60357
\(56\) −2.62160 −0.350326
\(57\) 3.07943 0.407881
\(58\) −1.52137 −0.199766
\(59\) −9.95767 −1.29638 −0.648189 0.761479i \(-0.724474\pi\)
−0.648189 + 0.761479i \(0.724474\pi\)
\(60\) 10.1816 1.31444
\(61\) −12.4578 −1.59506 −0.797528 0.603282i \(-0.793859\pi\)
−0.797528 + 0.603282i \(0.793859\pi\)
\(62\) −6.15407 −0.781568
\(63\) −16.9956 −2.14124
\(64\) 1.00000 0.125000
\(65\) 10.4869 1.30074
\(66\) −11.0763 −1.36339
\(67\) 5.58038 0.681752 0.340876 0.940108i \(-0.389276\pi\)
0.340876 + 0.940108i \(0.389276\pi\)
\(68\) 4.85924 0.589269
\(69\) 9.75047 1.17382
\(70\) 8.66789 1.03601
\(71\) 3.62595 0.430321 0.215160 0.976579i \(-0.430973\pi\)
0.215160 + 0.976579i \(0.430973\pi\)
\(72\) 6.48290 0.764018
\(73\) 7.67422 0.898200 0.449100 0.893481i \(-0.351745\pi\)
0.449100 + 0.893481i \(0.351745\pi\)
\(74\) 7.44862 0.865885
\(75\) −18.2668 −2.10926
\(76\) −1.00000 −0.114708
\(77\) −9.42950 −1.07459
\(78\) 9.76720 1.10592
\(79\) −12.0529 −1.35606 −0.678031 0.735033i \(-0.737167\pi\)
−0.678031 + 0.735033i \(0.737167\pi\)
\(80\) −3.30634 −0.369660
\(81\) 13.5793 1.50882
\(82\) 0.725201 0.0800851
\(83\) −4.32343 −0.474558 −0.237279 0.971442i \(-0.576256\pi\)
−0.237279 + 0.971442i \(0.576256\pi\)
\(84\) 8.07304 0.880841
\(85\) −16.0663 −1.74263
\(86\) −1.68387 −0.181577
\(87\) 4.68497 0.502281
\(88\) 3.59685 0.383425
\(89\) −12.5944 −1.33501 −0.667504 0.744606i \(-0.732637\pi\)
−0.667504 + 0.744606i \(0.732637\pi\)
\(90\) −21.4347 −2.25941
\(91\) 8.31507 0.871656
\(92\) −3.16632 −0.330112
\(93\) 18.9511 1.96513
\(94\) −10.0853 −1.04022
\(95\) 3.30634 0.339223
\(96\) −3.07943 −0.314293
\(97\) −9.41884 −0.956338 −0.478169 0.878268i \(-0.658699\pi\)
−0.478169 + 0.878268i \(0.658699\pi\)
\(98\) −0.127213 −0.0128504
\(99\) 23.3180 2.34355
\(100\) 5.93186 0.593186
\(101\) −9.38248 −0.933592 −0.466796 0.884365i \(-0.654592\pi\)
−0.466796 + 0.884365i \(0.654592\pi\)
\(102\) −14.9637 −1.48163
\(103\) 4.29595 0.423292 0.211646 0.977346i \(-0.432118\pi\)
0.211646 + 0.977346i \(0.432118\pi\)
\(104\) −3.17175 −0.311016
\(105\) −26.6922 −2.60489
\(106\) 9.64128 0.936444
\(107\) 15.3169 1.48074 0.740369 0.672201i \(-0.234651\pi\)
0.740369 + 0.672201i \(0.234651\pi\)
\(108\) −10.7254 −1.03205
\(109\) −10.9789 −1.05158 −0.525792 0.850613i \(-0.676231\pi\)
−0.525792 + 0.850613i \(0.676231\pi\)
\(110\) −11.8924 −1.13390
\(111\) −22.9375 −2.17713
\(112\) −2.62160 −0.247718
\(113\) −3.89336 −0.366256 −0.183128 0.983089i \(-0.558622\pi\)
−0.183128 + 0.983089i \(0.558622\pi\)
\(114\) 3.07943 0.288415
\(115\) 10.4689 0.976232
\(116\) −1.52137 −0.141256
\(117\) −20.5622 −1.90097
\(118\) −9.95767 −0.916678
\(119\) −12.7390 −1.16778
\(120\) 10.1816 0.929452
\(121\) 1.93733 0.176121
\(122\) −12.4578 −1.12788
\(123\) −2.23321 −0.201362
\(124\) −6.15407 −0.552652
\(125\) −3.08104 −0.275577
\(126\) −16.9956 −1.51409
\(127\) −21.9029 −1.94357 −0.971785 0.235869i \(-0.924206\pi\)
−0.971785 + 0.235869i \(0.924206\pi\)
\(128\) 1.00000 0.0883883
\(129\) 5.18538 0.456547
\(130\) 10.4869 0.919760
\(131\) 18.1070 1.58201 0.791007 0.611808i \(-0.209557\pi\)
0.791007 + 0.611808i \(0.209557\pi\)
\(132\) −11.0763 −0.964064
\(133\) 2.62160 0.227322
\(134\) 5.58038 0.482071
\(135\) 35.4617 3.05206
\(136\) 4.85924 0.416676
\(137\) 16.0615 1.37222 0.686112 0.727496i \(-0.259316\pi\)
0.686112 + 0.727496i \(0.259316\pi\)
\(138\) 9.75047 0.830015
\(139\) 17.4362 1.47892 0.739461 0.673199i \(-0.235080\pi\)
0.739461 + 0.673199i \(0.235080\pi\)
\(140\) 8.66789 0.732571
\(141\) 31.0570 2.61547
\(142\) 3.62595 0.304283
\(143\) −11.4083 −0.954011
\(144\) 6.48290 0.540242
\(145\) 5.03017 0.417733
\(146\) 7.67422 0.635123
\(147\) 0.391742 0.0323104
\(148\) 7.44862 0.612273
\(149\) 7.05726 0.578153 0.289077 0.957306i \(-0.406652\pi\)
0.289077 + 0.957306i \(0.406652\pi\)
\(150\) −18.2668 −1.49147
\(151\) −7.40687 −0.602762 −0.301381 0.953504i \(-0.597448\pi\)
−0.301381 + 0.953504i \(0.597448\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 31.5020 2.54678
\(154\) −9.42950 −0.759851
\(155\) 20.3474 1.63435
\(156\) 9.76720 0.782002
\(157\) −7.77822 −0.620769 −0.310385 0.950611i \(-0.600458\pi\)
−0.310385 + 0.950611i \(0.600458\pi\)
\(158\) −12.0529 −0.958881
\(159\) −29.6897 −2.35454
\(160\) −3.30634 −0.261389
\(161\) 8.30083 0.654197
\(162\) 13.5793 1.06689
\(163\) −13.6308 −1.06764 −0.533822 0.845597i \(-0.679245\pi\)
−0.533822 + 0.845597i \(0.679245\pi\)
\(164\) 0.725201 0.0566287
\(165\) 36.6218 2.85101
\(166\) −4.32343 −0.335563
\(167\) 17.3668 1.34388 0.671942 0.740604i \(-0.265460\pi\)
0.671942 + 0.740604i \(0.265460\pi\)
\(168\) 8.07304 0.622849
\(169\) −2.93998 −0.226153
\(170\) −16.0663 −1.23223
\(171\) −6.48290 −0.495760
\(172\) −1.68387 −0.128394
\(173\) 4.48265 0.340810 0.170405 0.985374i \(-0.445492\pi\)
0.170405 + 0.985374i \(0.445492\pi\)
\(174\) 4.68497 0.355166
\(175\) −15.5510 −1.17554
\(176\) 3.59685 0.271123
\(177\) 30.6640 2.30485
\(178\) −12.5944 −0.943993
\(179\) −16.8384 −1.25856 −0.629282 0.777177i \(-0.716651\pi\)
−0.629282 + 0.777177i \(0.716651\pi\)
\(180\) −21.4347 −1.59765
\(181\) 22.8206 1.69624 0.848122 0.529801i \(-0.177733\pi\)
0.848122 + 0.529801i \(0.177733\pi\)
\(182\) 8.31507 0.616354
\(183\) 38.3629 2.83587
\(184\) −3.16632 −0.233424
\(185\) −24.6276 −1.81066
\(186\) 18.9511 1.38956
\(187\) 17.4780 1.27811
\(188\) −10.0853 −0.735547
\(189\) 28.1176 2.04526
\(190\) 3.30634 0.239867
\(191\) −25.2853 −1.82958 −0.914792 0.403926i \(-0.867645\pi\)
−0.914792 + 0.403926i \(0.867645\pi\)
\(192\) −3.07943 −0.222239
\(193\) 8.29723 0.597248 0.298624 0.954371i \(-0.403472\pi\)
0.298624 + 0.954371i \(0.403472\pi\)
\(194\) −9.41884 −0.676233
\(195\) −32.2936 −2.31260
\(196\) −0.127213 −0.00908661
\(197\) −7.81057 −0.556480 −0.278240 0.960512i \(-0.589751\pi\)
−0.278240 + 0.960512i \(0.589751\pi\)
\(198\) 23.3180 1.65714
\(199\) −17.2026 −1.21946 −0.609730 0.792609i \(-0.708722\pi\)
−0.609730 + 0.792609i \(0.708722\pi\)
\(200\) 5.93186 0.419446
\(201\) −17.1844 −1.21209
\(202\) −9.38248 −0.660149
\(203\) 3.98843 0.279933
\(204\) −14.9637 −1.04767
\(205\) −2.39776 −0.167467
\(206\) 4.29595 0.299313
\(207\) −20.5270 −1.42672
\(208\) −3.17175 −0.219921
\(209\) −3.59685 −0.248799
\(210\) −26.6922 −1.84194
\(211\) −1.00000 −0.0688428
\(212\) 9.64128 0.662166
\(213\) −11.1659 −0.765072
\(214\) 15.3169 1.04704
\(215\) 5.56746 0.379697
\(216\) −10.7254 −0.729769
\(217\) 16.1335 1.09521
\(218\) −10.9789 −0.743583
\(219\) −23.6323 −1.59692
\(220\) −11.8924 −0.801785
\(221\) −15.4123 −1.03674
\(222\) −22.9375 −1.53947
\(223\) 28.9438 1.93822 0.969112 0.246623i \(-0.0793208\pi\)
0.969112 + 0.246623i \(0.0793208\pi\)
\(224\) −2.62160 −0.175163
\(225\) 38.4557 2.56371
\(226\) −3.89336 −0.258982
\(227\) 5.79137 0.384387 0.192193 0.981357i \(-0.438440\pi\)
0.192193 + 0.981357i \(0.438440\pi\)
\(228\) 3.07943 0.203940
\(229\) −18.6651 −1.23342 −0.616712 0.787189i \(-0.711536\pi\)
−0.616712 + 0.787189i \(0.711536\pi\)
\(230\) 10.4689 0.690300
\(231\) 29.0375 1.91053
\(232\) −1.52137 −0.0998830
\(233\) 21.7720 1.42633 0.713165 0.700996i \(-0.247261\pi\)
0.713165 + 0.700996i \(0.247261\pi\)
\(234\) −20.5622 −1.34419
\(235\) 33.3454 2.17522
\(236\) −9.95767 −0.648189
\(237\) 37.1162 2.41096
\(238\) −12.7390 −0.825746
\(239\) −8.04048 −0.520096 −0.260048 0.965596i \(-0.583738\pi\)
−0.260048 + 0.965596i \(0.583738\pi\)
\(240\) 10.1816 0.657222
\(241\) 19.9326 1.28397 0.641986 0.766716i \(-0.278111\pi\)
0.641986 + 0.766716i \(0.278111\pi\)
\(242\) 1.93733 0.124536
\(243\) −9.64055 −0.618442
\(244\) −12.4578 −0.797528
\(245\) 0.420607 0.0268716
\(246\) −2.23321 −0.142384
\(247\) 3.17175 0.201814
\(248\) −6.15407 −0.390784
\(249\) 13.3137 0.843721
\(250\) −3.08104 −0.194862
\(251\) 22.5793 1.42519 0.712597 0.701573i \(-0.247519\pi\)
0.712597 + 0.701573i \(0.247519\pi\)
\(252\) −16.9956 −1.07062
\(253\) −11.3888 −0.716006
\(254\) −21.9029 −1.37431
\(255\) 49.4750 3.09825
\(256\) 1.00000 0.0625000
\(257\) −6.05765 −0.377866 −0.188933 0.981990i \(-0.560503\pi\)
−0.188933 + 0.981990i \(0.560503\pi\)
\(258\) 5.18538 0.322828
\(259\) −19.5273 −1.21337
\(260\) 10.4869 0.650369
\(261\) −9.86292 −0.610499
\(262\) 18.1070 1.11865
\(263\) 7.77313 0.479312 0.239656 0.970858i \(-0.422965\pi\)
0.239656 + 0.970858i \(0.422965\pi\)
\(264\) −11.0763 −0.681696
\(265\) −31.8773 −1.95821
\(266\) 2.62160 0.160741
\(267\) 38.7837 2.37353
\(268\) 5.58038 0.340876
\(269\) 17.7961 1.08505 0.542525 0.840040i \(-0.317469\pi\)
0.542525 + 0.840040i \(0.317469\pi\)
\(270\) 35.4617 2.15813
\(271\) 7.28986 0.442827 0.221414 0.975180i \(-0.428933\pi\)
0.221414 + 0.975180i \(0.428933\pi\)
\(272\) 4.85924 0.294635
\(273\) −25.6057 −1.54973
\(274\) 16.0615 0.970309
\(275\) 21.3360 1.28661
\(276\) 9.75047 0.586909
\(277\) 8.85228 0.531882 0.265941 0.963989i \(-0.414317\pi\)
0.265941 + 0.963989i \(0.414317\pi\)
\(278\) 17.4362 1.04576
\(279\) −39.8963 −2.38853
\(280\) 8.66789 0.518006
\(281\) 26.7309 1.59463 0.797316 0.603563i \(-0.206253\pi\)
0.797316 + 0.603563i \(0.206253\pi\)
\(282\) 31.0570 1.84942
\(283\) 10.0108 0.595083 0.297541 0.954709i \(-0.403833\pi\)
0.297541 + 0.954709i \(0.403833\pi\)
\(284\) 3.62595 0.215160
\(285\) −10.1816 −0.603108
\(286\) −11.4083 −0.674588
\(287\) −1.90119 −0.112224
\(288\) 6.48290 0.382009
\(289\) 6.61221 0.388954
\(290\) 5.03017 0.295382
\(291\) 29.0047 1.70028
\(292\) 7.67422 0.449100
\(293\) 30.3026 1.77029 0.885147 0.465311i \(-0.154058\pi\)
0.885147 + 0.465311i \(0.154058\pi\)
\(294\) 0.391742 0.0228469
\(295\) 32.9234 1.91688
\(296\) 7.44862 0.432942
\(297\) −38.5775 −2.23850
\(298\) 7.05726 0.408816
\(299\) 10.0428 0.580789
\(300\) −18.2668 −1.05463
\(301\) 4.41445 0.254444
\(302\) −7.40687 −0.426217
\(303\) 28.8927 1.65984
\(304\) −1.00000 −0.0573539
\(305\) 41.1896 2.35851
\(306\) 31.5020 1.80085
\(307\) 31.1710 1.77902 0.889512 0.456911i \(-0.151044\pi\)
0.889512 + 0.456911i \(0.151044\pi\)
\(308\) −9.42950 −0.537296
\(309\) −13.2291 −0.752576
\(310\) 20.3474 1.15566
\(311\) −12.8925 −0.731066 −0.365533 0.930798i \(-0.619113\pi\)
−0.365533 + 0.930798i \(0.619113\pi\)
\(312\) 9.76720 0.552959
\(313\) −23.8586 −1.34857 −0.674285 0.738471i \(-0.735548\pi\)
−0.674285 + 0.738471i \(0.735548\pi\)
\(314\) −7.77822 −0.438950
\(315\) 56.1931 3.16612
\(316\) −12.0529 −0.678031
\(317\) −16.6396 −0.934571 −0.467286 0.884106i \(-0.654768\pi\)
−0.467286 + 0.884106i \(0.654768\pi\)
\(318\) −29.6897 −1.66491
\(319\) −5.47215 −0.306382
\(320\) −3.30634 −0.184830
\(321\) −47.1673 −2.63262
\(322\) 8.30083 0.462587
\(323\) −4.85924 −0.270375
\(324\) 13.5793 0.754408
\(325\) −18.8144 −1.04363
\(326\) −13.6308 −0.754939
\(327\) 33.8087 1.86962
\(328\) 0.725201 0.0400425
\(329\) 26.4397 1.45767
\(330\) 36.6218 2.01597
\(331\) −2.23202 −0.122683 −0.0613414 0.998117i \(-0.519538\pi\)
−0.0613414 + 0.998117i \(0.519538\pi\)
\(332\) −4.32343 −0.237279
\(333\) 48.2887 2.64620
\(334\) 17.3668 0.950270
\(335\) −18.4506 −1.00806
\(336\) 8.07304 0.440420
\(337\) 9.48518 0.516691 0.258345 0.966053i \(-0.416823\pi\)
0.258345 + 0.966053i \(0.416823\pi\)
\(338\) −2.93998 −0.159914
\(339\) 11.9893 0.651171
\(340\) −16.0663 −0.871316
\(341\) −22.1353 −1.19869
\(342\) −6.48290 −0.350555
\(343\) 18.6847 1.00888
\(344\) −1.68387 −0.0907885
\(345\) −32.2383 −1.73565
\(346\) 4.48265 0.240989
\(347\) 18.1699 0.975412 0.487706 0.873008i \(-0.337834\pi\)
0.487706 + 0.873008i \(0.337834\pi\)
\(348\) 4.68497 0.251140
\(349\) 8.80359 0.471245 0.235623 0.971845i \(-0.424287\pi\)
0.235623 + 0.971845i \(0.424287\pi\)
\(350\) −15.5510 −0.831234
\(351\) 34.0182 1.81576
\(352\) 3.59685 0.191713
\(353\) −34.1955 −1.82004 −0.910020 0.414564i \(-0.863934\pi\)
−0.910020 + 0.414564i \(0.863934\pi\)
\(354\) 30.6640 1.62977
\(355\) −11.9886 −0.636289
\(356\) −12.5944 −0.667504
\(357\) 39.2288 2.07621
\(358\) −16.8384 −0.889939
\(359\) −26.0976 −1.37738 −0.688690 0.725056i \(-0.741814\pi\)
−0.688690 + 0.725056i \(0.741814\pi\)
\(360\) −21.4347 −1.12971
\(361\) 1.00000 0.0526316
\(362\) 22.8206 1.19943
\(363\) −5.96586 −0.313127
\(364\) 8.31507 0.435828
\(365\) −25.3736 −1.32811
\(366\) 38.3629 2.00526
\(367\) −5.06346 −0.264310 −0.132155 0.991229i \(-0.542190\pi\)
−0.132155 + 0.991229i \(0.542190\pi\)
\(368\) −3.16632 −0.165056
\(369\) 4.70141 0.244746
\(370\) −24.6276 −1.28033
\(371\) −25.2756 −1.31224
\(372\) 18.9511 0.982566
\(373\) −13.6706 −0.707839 −0.353919 0.935276i \(-0.615151\pi\)
−0.353919 + 0.935276i \(0.615151\pi\)
\(374\) 17.4780 0.903764
\(375\) 9.48785 0.489951
\(376\) −10.0853 −0.520110
\(377\) 4.82542 0.248522
\(378\) 28.1176 1.44621
\(379\) −9.76421 −0.501554 −0.250777 0.968045i \(-0.580686\pi\)
−0.250777 + 0.968045i \(0.580686\pi\)
\(380\) 3.30634 0.169611
\(381\) 67.4486 3.45549
\(382\) −25.2853 −1.29371
\(383\) −5.82604 −0.297697 −0.148848 0.988860i \(-0.547557\pi\)
−0.148848 + 0.988860i \(0.547557\pi\)
\(384\) −3.07943 −0.157147
\(385\) 31.1771 1.58893
\(386\) 8.29723 0.422318
\(387\) −10.9164 −0.554912
\(388\) −9.41884 −0.478169
\(389\) 24.5023 1.24231 0.621157 0.783686i \(-0.286663\pi\)
0.621157 + 0.783686i \(0.286663\pi\)
\(390\) −32.2936 −1.63525
\(391\) −15.3859 −0.778099
\(392\) −0.127213 −0.00642520
\(393\) −55.7592 −2.81268
\(394\) −7.81057 −0.393491
\(395\) 39.8511 2.00513
\(396\) 23.3180 1.17178
\(397\) 10.2721 0.515540 0.257770 0.966206i \(-0.417012\pi\)
0.257770 + 0.966206i \(0.417012\pi\)
\(398\) −17.2026 −0.862289
\(399\) −8.07304 −0.404158
\(400\) 5.93186 0.296593
\(401\) 23.9630 1.19665 0.598327 0.801252i \(-0.295832\pi\)
0.598327 + 0.801252i \(0.295832\pi\)
\(402\) −17.1844 −0.857080
\(403\) 19.5192 0.972321
\(404\) −9.38248 −0.466796
\(405\) −44.8979 −2.23099
\(406\) 3.98843 0.197943
\(407\) 26.7916 1.32801
\(408\) −14.9637 −0.740814
\(409\) 32.3667 1.60043 0.800215 0.599714i \(-0.204719\pi\)
0.800215 + 0.599714i \(0.204719\pi\)
\(410\) −2.39776 −0.118417
\(411\) −49.4602 −2.43969
\(412\) 4.29595 0.211646
\(413\) 26.1050 1.28455
\(414\) −20.5270 −1.00884
\(415\) 14.2947 0.701699
\(416\) −3.17175 −0.155508
\(417\) −53.6937 −2.62939
\(418\) −3.59685 −0.175928
\(419\) −3.17751 −0.155232 −0.0776158 0.996983i \(-0.524731\pi\)
−0.0776158 + 0.996983i \(0.524731\pi\)
\(420\) −26.6922 −1.30245
\(421\) −10.6423 −0.518673 −0.259336 0.965787i \(-0.583504\pi\)
−0.259336 + 0.965787i \(0.583504\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −65.3821 −3.17899
\(424\) 9.64128 0.468222
\(425\) 28.8243 1.39819
\(426\) −11.1659 −0.540988
\(427\) 32.6593 1.58050
\(428\) 15.3169 0.740369
\(429\) 35.1311 1.69615
\(430\) 5.56746 0.268487
\(431\) 20.6701 0.995642 0.497821 0.867280i \(-0.334134\pi\)
0.497821 + 0.867280i \(0.334134\pi\)
\(432\) −10.7254 −0.516025
\(433\) 22.9944 1.10504 0.552521 0.833499i \(-0.313666\pi\)
0.552521 + 0.833499i \(0.313666\pi\)
\(434\) 16.1335 0.774434
\(435\) −15.4901 −0.742692
\(436\) −10.9789 −0.525792
\(437\) 3.16632 0.151466
\(438\) −23.6323 −1.12919
\(439\) 15.2381 0.727277 0.363639 0.931540i \(-0.381534\pi\)
0.363639 + 0.931540i \(0.381534\pi\)
\(440\) −11.8924 −0.566948
\(441\) −0.824707 −0.0392718
\(442\) −15.4123 −0.733089
\(443\) 16.2175 0.770517 0.385259 0.922809i \(-0.374112\pi\)
0.385259 + 0.922809i \(0.374112\pi\)
\(444\) −22.9375 −1.08857
\(445\) 41.6414 1.97399
\(446\) 28.9438 1.37053
\(447\) −21.7323 −1.02790
\(448\) −2.62160 −0.123859
\(449\) −26.3657 −1.24427 −0.622136 0.782909i \(-0.713735\pi\)
−0.622136 + 0.782909i \(0.713735\pi\)
\(450\) 38.4557 1.81282
\(451\) 2.60844 0.122827
\(452\) −3.89336 −0.183128
\(453\) 22.8090 1.07166
\(454\) 5.79137 0.271802
\(455\) −27.4924 −1.28886
\(456\) 3.07943 0.144208
\(457\) −28.5587 −1.33592 −0.667960 0.744197i \(-0.732832\pi\)
−0.667960 + 0.744197i \(0.732832\pi\)
\(458\) −18.6651 −0.872162
\(459\) −52.1171 −2.43262
\(460\) 10.4689 0.488116
\(461\) −28.1105 −1.30924 −0.654618 0.755960i \(-0.727170\pi\)
−0.654618 + 0.755960i \(0.727170\pi\)
\(462\) 29.0375 1.35095
\(463\) −6.56312 −0.305014 −0.152507 0.988302i \(-0.548735\pi\)
−0.152507 + 0.988302i \(0.548735\pi\)
\(464\) −1.52137 −0.0706280
\(465\) −62.6586 −2.90572
\(466\) 21.7720 1.00857
\(467\) −36.3201 −1.68070 −0.840348 0.542048i \(-0.817649\pi\)
−0.840348 + 0.542048i \(0.817649\pi\)
\(468\) −20.5622 −0.950487
\(469\) −14.6295 −0.675528
\(470\) 33.3454 1.53811
\(471\) 23.9525 1.10367
\(472\) −9.95767 −0.458339
\(473\) −6.05664 −0.278485
\(474\) 37.1162 1.70481
\(475\) −5.93186 −0.272172
\(476\) −12.7390 −0.583890
\(477\) 62.5035 2.86184
\(478\) −8.04048 −0.367763
\(479\) 14.6465 0.669216 0.334608 0.942357i \(-0.391396\pi\)
0.334608 + 0.942357i \(0.391396\pi\)
\(480\) 10.1816 0.464726
\(481\) −23.6252 −1.07722
\(482\) 19.9326 0.907906
\(483\) −25.5618 −1.16310
\(484\) 1.93733 0.0880603
\(485\) 31.1418 1.41408
\(486\) −9.64055 −0.437304
\(487\) −13.9606 −0.632616 −0.316308 0.948657i \(-0.602443\pi\)
−0.316308 + 0.948657i \(0.602443\pi\)
\(488\) −12.4578 −0.563938
\(489\) 41.9751 1.89818
\(490\) 0.420607 0.0190011
\(491\) −8.28220 −0.373770 −0.186885 0.982382i \(-0.559839\pi\)
−0.186885 + 0.982382i \(0.559839\pi\)
\(492\) −2.23321 −0.100681
\(493\) −7.39272 −0.332951
\(494\) 3.17175 0.142704
\(495\) −77.0973 −3.46526
\(496\) −6.15407 −0.276326
\(497\) −9.50579 −0.426393
\(498\) 13.3137 0.596601
\(499\) −8.79475 −0.393707 −0.196854 0.980433i \(-0.563072\pi\)
−0.196854 + 0.980433i \(0.563072\pi\)
\(500\) −3.08104 −0.137788
\(501\) −53.4799 −2.38931
\(502\) 22.5793 1.00776
\(503\) 16.2843 0.726079 0.363039 0.931774i \(-0.381739\pi\)
0.363039 + 0.931774i \(0.381739\pi\)
\(504\) −16.9956 −0.757043
\(505\) 31.0216 1.38044
\(506\) −11.3888 −0.506293
\(507\) 9.05348 0.402079
\(508\) −21.9029 −0.971785
\(509\) 14.8423 0.657875 0.328938 0.944352i \(-0.393309\pi\)
0.328938 + 0.944352i \(0.393309\pi\)
\(510\) 49.4750 2.19079
\(511\) −20.1187 −0.890001
\(512\) 1.00000 0.0441942
\(513\) 10.7254 0.473537
\(514\) −6.05765 −0.267191
\(515\) −14.2038 −0.625896
\(516\) 5.18538 0.228274
\(517\) −36.2753 −1.59539
\(518\) −19.5273 −0.857981
\(519\) −13.8040 −0.605930
\(520\) 10.4869 0.459880
\(521\) −9.87276 −0.432533 −0.216267 0.976334i \(-0.569388\pi\)
−0.216267 + 0.976334i \(0.569388\pi\)
\(522\) −9.86292 −0.431688
\(523\) −8.67971 −0.379537 −0.189769 0.981829i \(-0.560774\pi\)
−0.189769 + 0.981829i \(0.560774\pi\)
\(524\) 18.1070 0.791007
\(525\) 47.8881 2.09001
\(526\) 7.77313 0.338924
\(527\) −29.9041 −1.30264
\(528\) −11.0763 −0.482032
\(529\) −12.9744 −0.564105
\(530\) −31.8773 −1.38466
\(531\) −64.5547 −2.80143
\(532\) 2.62160 0.113661
\(533\) −2.30016 −0.0996310
\(534\) 38.7837 1.67834
\(535\) −50.6427 −2.18948
\(536\) 5.58038 0.241036
\(537\) 51.8528 2.23761
\(538\) 17.7961 0.767246
\(539\) −0.457564 −0.0197087
\(540\) 35.4617 1.52603
\(541\) 38.0847 1.63739 0.818695 0.574229i \(-0.194698\pi\)
0.818695 + 0.574229i \(0.194698\pi\)
\(542\) 7.28986 0.313126
\(543\) −70.2746 −3.01577
\(544\) 4.85924 0.208338
\(545\) 36.2998 1.55491
\(546\) −25.6057 −1.09582
\(547\) −12.2235 −0.522637 −0.261319 0.965253i \(-0.584157\pi\)
−0.261319 + 0.965253i \(0.584157\pi\)
\(548\) 16.0615 0.686112
\(549\) −80.7627 −3.44687
\(550\) 21.3360 0.909770
\(551\) 1.52137 0.0648127
\(552\) 9.75047 0.415008
\(553\) 31.5980 1.34368
\(554\) 8.85228 0.376097
\(555\) 75.8392 3.21919
\(556\) 17.4362 0.739461
\(557\) −7.54648 −0.319755 −0.159877 0.987137i \(-0.551110\pi\)
−0.159877 + 0.987137i \(0.551110\pi\)
\(558\) −39.8963 −1.68894
\(559\) 5.34084 0.225893
\(560\) 8.66789 0.366285
\(561\) −53.8222 −2.27237
\(562\) 26.7309 1.12757
\(563\) 18.6248 0.784941 0.392471 0.919765i \(-0.371621\pi\)
0.392471 + 0.919765i \(0.371621\pi\)
\(564\) 31.0570 1.30774
\(565\) 12.8727 0.541561
\(566\) 10.0108 0.420787
\(567\) −35.5996 −1.49504
\(568\) 3.62595 0.152141
\(569\) 8.28382 0.347276 0.173638 0.984810i \(-0.444448\pi\)
0.173638 + 0.984810i \(0.444448\pi\)
\(570\) −10.1816 −0.426462
\(571\) −18.6107 −0.778832 −0.389416 0.921062i \(-0.627323\pi\)
−0.389416 + 0.921062i \(0.627323\pi\)
\(572\) −11.4083 −0.477006
\(573\) 77.8645 3.25284
\(574\) −1.90119 −0.0793541
\(575\) −18.7822 −0.783270
\(576\) 6.48290 0.270121
\(577\) −18.5544 −0.772430 −0.386215 0.922409i \(-0.626218\pi\)
−0.386215 + 0.922409i \(0.626218\pi\)
\(578\) 6.61221 0.275032
\(579\) −25.5508 −1.06185
\(580\) 5.03017 0.208866
\(581\) 11.3343 0.470226
\(582\) 29.0047 1.20228
\(583\) 34.6782 1.43623
\(584\) 7.67422 0.317562
\(585\) 67.9855 2.81085
\(586\) 30.3026 1.25179
\(587\) −1.44658 −0.0597066 −0.0298533 0.999554i \(-0.509504\pi\)
−0.0298533 + 0.999554i \(0.509504\pi\)
\(588\) 0.391742 0.0161552
\(589\) 6.15407 0.253574
\(590\) 32.9234 1.35544
\(591\) 24.0521 0.989372
\(592\) 7.44862 0.306136
\(593\) −18.4786 −0.758826 −0.379413 0.925227i \(-0.623874\pi\)
−0.379413 + 0.925227i \(0.623874\pi\)
\(594\) −38.5775 −1.58286
\(595\) 42.1194 1.72673
\(596\) 7.05726 0.289077
\(597\) 52.9743 2.16809
\(598\) 10.0428 0.410680
\(599\) −28.5876 −1.16806 −0.584028 0.811733i \(-0.698524\pi\)
−0.584028 + 0.811733i \(0.698524\pi\)
\(600\) −18.2668 −0.745737
\(601\) 8.46071 0.345119 0.172560 0.984999i \(-0.444796\pi\)
0.172560 + 0.984999i \(0.444796\pi\)
\(602\) 4.41445 0.179919
\(603\) 36.1771 1.47324
\(604\) −7.40687 −0.301381
\(605\) −6.40545 −0.260419
\(606\) 28.8927 1.17369
\(607\) −12.9877 −0.527156 −0.263578 0.964638i \(-0.584903\pi\)
−0.263578 + 0.964638i \(0.584903\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −12.2821 −0.497696
\(610\) 41.1896 1.66772
\(611\) 31.9881 1.29410
\(612\) 31.5020 1.27339
\(613\) 40.1813 1.62291 0.811453 0.584417i \(-0.198677\pi\)
0.811453 + 0.584417i \(0.198677\pi\)
\(614\) 31.1710 1.25796
\(615\) 7.38374 0.297741
\(616\) −9.42950 −0.379925
\(617\) 31.7165 1.27686 0.638428 0.769681i \(-0.279585\pi\)
0.638428 + 0.769681i \(0.279585\pi\)
\(618\) −13.2291 −0.532151
\(619\) 13.8137 0.555218 0.277609 0.960694i \(-0.410458\pi\)
0.277609 + 0.960694i \(0.410458\pi\)
\(620\) 20.3474 0.817173
\(621\) 33.9600 1.36277
\(622\) −12.8925 −0.516942
\(623\) 33.0176 1.32282
\(624\) 9.76720 0.391001
\(625\) −19.4723 −0.778894
\(626\) −23.8586 −0.953583
\(627\) 11.0763 0.442343
\(628\) −7.77822 −0.310385
\(629\) 36.1946 1.44317
\(630\) 56.1931 2.23879
\(631\) −22.1676 −0.882479 −0.441240 0.897389i \(-0.645461\pi\)
−0.441240 + 0.897389i \(0.645461\pi\)
\(632\) −12.0529 −0.479441
\(633\) 3.07943 0.122396
\(634\) −16.6396 −0.660841
\(635\) 72.4184 2.87384
\(636\) −29.6897 −1.17727
\(637\) 0.403487 0.0159867
\(638\) −5.47215 −0.216644
\(639\) 23.5067 0.929910
\(640\) −3.30634 −0.130694
\(641\) 9.67713 0.382224 0.191112 0.981568i \(-0.438791\pi\)
0.191112 + 0.981568i \(0.438791\pi\)
\(642\) −47.1673 −1.86154
\(643\) 9.36419 0.369288 0.184644 0.982806i \(-0.440887\pi\)
0.184644 + 0.982806i \(0.440887\pi\)
\(644\) 8.30083 0.327098
\(645\) −17.1446 −0.675068
\(646\) −4.85924 −0.191184
\(647\) −21.7018 −0.853187 −0.426594 0.904443i \(-0.640287\pi\)
−0.426594 + 0.904443i \(0.640287\pi\)
\(648\) 13.5793 0.533447
\(649\) −35.8163 −1.40591
\(650\) −18.8144 −0.737961
\(651\) −49.6821 −1.94719
\(652\) −13.6308 −0.533822
\(653\) 17.5043 0.684997 0.342498 0.939518i \(-0.388727\pi\)
0.342498 + 0.939518i \(0.388727\pi\)
\(654\) 33.8087 1.32202
\(655\) −59.8677 −2.33923
\(656\) 0.725201 0.0283144
\(657\) 49.7513 1.94098
\(658\) 26.4397 1.03073
\(659\) −19.7418 −0.769031 −0.384516 0.923118i \(-0.625632\pi\)
−0.384516 + 0.923118i \(0.625632\pi\)
\(660\) 36.6218 1.42550
\(661\) 6.51672 0.253471 0.126735 0.991937i \(-0.459550\pi\)
0.126735 + 0.991937i \(0.459550\pi\)
\(662\) −2.23202 −0.0867498
\(663\) 47.4612 1.84324
\(664\) −4.32343 −0.167781
\(665\) −8.66789 −0.336126
\(666\) 48.2887 1.87115
\(667\) 4.81715 0.186521
\(668\) 17.3668 0.671942
\(669\) −89.1306 −3.44599
\(670\) −18.4506 −0.712809
\(671\) −44.8088 −1.72982
\(672\) 8.07304 0.311424
\(673\) −4.78895 −0.184601 −0.0923003 0.995731i \(-0.529422\pi\)
−0.0923003 + 0.995731i \(0.529422\pi\)
\(674\) 9.48518 0.365355
\(675\) −63.6214 −2.44879
\(676\) −2.93998 −0.113076
\(677\) −4.03118 −0.154931 −0.0774654 0.996995i \(-0.524683\pi\)
−0.0774654 + 0.996995i \(0.524683\pi\)
\(678\) 11.9893 0.460448
\(679\) 24.6924 0.947608
\(680\) −16.0663 −0.616114
\(681\) −17.8341 −0.683405
\(682\) −22.1353 −0.847603
\(683\) −5.79267 −0.221650 −0.110825 0.993840i \(-0.535349\pi\)
−0.110825 + 0.993840i \(0.535349\pi\)
\(684\) −6.48290 −0.247880
\(685\) −53.1046 −2.02902
\(686\) 18.6847 0.713385
\(687\) 57.4779 2.19292
\(688\) −1.68387 −0.0641971
\(689\) −30.5797 −1.16500
\(690\) −32.2383 −1.22729
\(691\) 39.8481 1.51589 0.757947 0.652316i \(-0.226203\pi\)
0.757947 + 0.652316i \(0.226203\pi\)
\(692\) 4.48265 0.170405
\(693\) −61.1306 −2.32216
\(694\) 18.1699 0.689721
\(695\) −57.6501 −2.18679
\(696\) 4.68497 0.177583
\(697\) 3.52393 0.133478
\(698\) 8.80359 0.333221
\(699\) −67.0454 −2.53589
\(700\) −15.5510 −0.587771
\(701\) 44.3959 1.67681 0.838405 0.545049i \(-0.183489\pi\)
0.838405 + 0.545049i \(0.183489\pi\)
\(702\) 34.0182 1.28394
\(703\) −7.44862 −0.280930
\(704\) 3.59685 0.135561
\(705\) −102.685 −3.86734
\(706\) −34.1955 −1.28696
\(707\) 24.5971 0.925070
\(708\) 30.6640 1.15242
\(709\) 32.1101 1.20592 0.602960 0.797772i \(-0.293988\pi\)
0.602960 + 0.797772i \(0.293988\pi\)
\(710\) −11.9886 −0.449924
\(711\) −78.1381 −2.93041
\(712\) −12.5944 −0.471997
\(713\) 19.4858 0.729748
\(714\) 39.2288 1.46810
\(715\) 37.7197 1.41064
\(716\) −16.8384 −0.629282
\(717\) 24.7601 0.924684
\(718\) −26.0976 −0.973955
\(719\) −14.8190 −0.552655 −0.276328 0.961063i \(-0.589118\pi\)
−0.276328 + 0.961063i \(0.589118\pi\)
\(720\) −21.4347 −0.798823
\(721\) −11.2623 −0.419428
\(722\) 1.00000 0.0372161
\(723\) −61.3811 −2.28279
\(724\) 22.8206 0.848122
\(725\) −9.02457 −0.335164
\(726\) −5.96586 −0.221414
\(727\) −4.99472 −0.185244 −0.0926219 0.995701i \(-0.529525\pi\)
−0.0926219 + 0.995701i \(0.529525\pi\)
\(728\) 8.31507 0.308177
\(729\) −11.0506 −0.409281
\(730\) −25.3736 −0.939118
\(731\) −8.18235 −0.302635
\(732\) 38.3629 1.41793
\(733\) 4.68036 0.172873 0.0864365 0.996257i \(-0.472452\pi\)
0.0864365 + 0.996257i \(0.472452\pi\)
\(734\) −5.06346 −0.186896
\(735\) −1.29523 −0.0477754
\(736\) −3.16632 −0.116712
\(737\) 20.0718 0.739353
\(738\) 4.70141 0.173061
\(739\) −12.1592 −0.447285 −0.223642 0.974671i \(-0.571795\pi\)
−0.223642 + 0.974671i \(0.571795\pi\)
\(740\) −24.6276 −0.905330
\(741\) −9.76720 −0.358807
\(742\) −25.2756 −0.927896
\(743\) 26.9877 0.990082 0.495041 0.868869i \(-0.335153\pi\)
0.495041 + 0.868869i \(0.335153\pi\)
\(744\) 18.9511 0.694779
\(745\) −23.3337 −0.854879
\(746\) −13.6706 −0.500517
\(747\) −28.0284 −1.02550
\(748\) 17.4780 0.639057
\(749\) −40.1547 −1.46722
\(750\) 9.48785 0.346447
\(751\) 3.99780 0.145882 0.0729409 0.997336i \(-0.476762\pi\)
0.0729409 + 0.997336i \(0.476762\pi\)
\(752\) −10.0853 −0.367773
\(753\) −69.5315 −2.53387
\(754\) 4.82542 0.175731
\(755\) 24.4896 0.891268
\(756\) 28.1176 1.02263
\(757\) 15.2875 0.555633 0.277816 0.960634i \(-0.410389\pi\)
0.277816 + 0.960634i \(0.410389\pi\)
\(758\) −9.76421 −0.354652
\(759\) 35.0710 1.27300
\(760\) 3.30634 0.119933
\(761\) −0.265766 −0.00963401 −0.00481700 0.999988i \(-0.501533\pi\)
−0.00481700 + 0.999988i \(0.501533\pi\)
\(762\) 67.4486 2.44340
\(763\) 28.7822 1.04199
\(764\) −25.2853 −0.914792
\(765\) −104.156 −3.76577
\(766\) −5.82604 −0.210503
\(767\) 31.5833 1.14041
\(768\) −3.07943 −0.111119
\(769\) −10.7293 −0.386910 −0.193455 0.981109i \(-0.561969\pi\)
−0.193455 + 0.981109i \(0.561969\pi\)
\(770\) 31.1771 1.12354
\(771\) 18.6541 0.671812
\(772\) 8.29723 0.298624
\(773\) 38.6791 1.39119 0.695595 0.718434i \(-0.255141\pi\)
0.695595 + 0.718434i \(0.255141\pi\)
\(774\) −10.9164 −0.392382
\(775\) −36.5051 −1.31130
\(776\) −9.41884 −0.338117
\(777\) 60.1330 2.15726
\(778\) 24.5023 0.878449
\(779\) −0.725201 −0.0259830
\(780\) −32.2936 −1.15630
\(781\) 13.0420 0.466679
\(782\) −15.3859 −0.550199
\(783\) 16.3173 0.583132
\(784\) −0.127213 −0.00454331
\(785\) 25.7174 0.917893
\(786\) −55.7592 −1.98886
\(787\) −13.5007 −0.481249 −0.240625 0.970618i \(-0.577352\pi\)
−0.240625 + 0.970618i \(0.577352\pi\)
\(788\) −7.81057 −0.278240
\(789\) −23.9368 −0.852173
\(790\) 39.8511 1.41784
\(791\) 10.2068 0.362913
\(792\) 23.3180 0.828570
\(793\) 39.5130 1.40315
\(794\) 10.2721 0.364542
\(795\) 98.1640 3.48152
\(796\) −17.2026 −0.609730
\(797\) 3.90496 0.138321 0.0691604 0.997606i \(-0.477968\pi\)
0.0691604 + 0.997606i \(0.477968\pi\)
\(798\) −8.07304 −0.285783
\(799\) −49.0070 −1.73374
\(800\) 5.93186 0.209723
\(801\) −81.6485 −2.88491
\(802\) 23.9630 0.846162
\(803\) 27.6030 0.974090
\(804\) −17.1844 −0.606047
\(805\) −27.4453 −0.967320
\(806\) 19.5192 0.687534
\(807\) −54.8020 −1.92912
\(808\) −9.38248 −0.330075
\(809\) 45.8869 1.61330 0.806649 0.591031i \(-0.201279\pi\)
0.806649 + 0.591031i \(0.201279\pi\)
\(810\) −44.8979 −1.57755
\(811\) 11.0177 0.386882 0.193441 0.981112i \(-0.438035\pi\)
0.193441 + 0.981112i \(0.438035\pi\)
\(812\) 3.98843 0.139967
\(813\) −22.4486 −0.787307
\(814\) 26.7916 0.939044
\(815\) 45.0679 1.57866
\(816\) −14.9637 −0.523834
\(817\) 1.68387 0.0589113
\(818\) 32.3667 1.13167
\(819\) 53.9058 1.88362
\(820\) −2.39776 −0.0837334
\(821\) 40.4816 1.41282 0.706408 0.707805i \(-0.250314\pi\)
0.706408 + 0.707805i \(0.250314\pi\)
\(822\) −49.4602 −1.72512
\(823\) 36.1537 1.26024 0.630119 0.776499i \(-0.283006\pi\)
0.630119 + 0.776499i \(0.283006\pi\)
\(824\) 4.29595 0.149656
\(825\) −65.7028 −2.28748
\(826\) 26.1050 0.908311
\(827\) −35.6799 −1.24071 −0.620356 0.784321i \(-0.713012\pi\)
−0.620356 + 0.784321i \(0.713012\pi\)
\(828\) −20.5270 −0.713361
\(829\) −24.3085 −0.844267 −0.422134 0.906534i \(-0.638719\pi\)
−0.422134 + 0.906534i \(0.638719\pi\)
\(830\) 14.2947 0.496176
\(831\) −27.2600 −0.945639
\(832\) −3.17175 −0.109961
\(833\) −0.618156 −0.0214178
\(834\) −53.6937 −1.85926
\(835\) −57.4205 −1.98712
\(836\) −3.59685 −0.124400
\(837\) 66.0047 2.28146
\(838\) −3.17751 −0.109765
\(839\) −17.3791 −0.599992 −0.299996 0.953940i \(-0.596985\pi\)
−0.299996 + 0.953940i \(0.596985\pi\)
\(840\) −26.6922 −0.920968
\(841\) −26.6854 −0.920187
\(842\) −10.6423 −0.366757
\(843\) −82.3160 −2.83511
\(844\) −1.00000 −0.0344214
\(845\) 9.72057 0.334398
\(846\) −65.3821 −2.24788
\(847\) −5.07889 −0.174513
\(848\) 9.64128 0.331083
\(849\) −30.8277 −1.05800
\(850\) 28.8243 0.988666
\(851\) −23.5847 −0.808474
\(852\) −11.1659 −0.382536
\(853\) 39.1600 1.34081 0.670406 0.741994i \(-0.266120\pi\)
0.670406 + 0.741994i \(0.266120\pi\)
\(854\) 32.6593 1.11758
\(855\) 21.4347 0.733050
\(856\) 15.3169 0.523520
\(857\) 12.8771 0.439872 0.219936 0.975514i \(-0.429415\pi\)
0.219936 + 0.975514i \(0.429415\pi\)
\(858\) 35.1311 1.19936
\(859\) −16.2199 −0.553415 −0.276708 0.960954i \(-0.589243\pi\)
−0.276708 + 0.960954i \(0.589243\pi\)
\(860\) 5.56746 0.189849
\(861\) 5.85458 0.199524
\(862\) 20.6701 0.704025
\(863\) 7.60759 0.258965 0.129483 0.991582i \(-0.458668\pi\)
0.129483 + 0.991582i \(0.458668\pi\)
\(864\) −10.7254 −0.364885
\(865\) −14.8212 −0.503935
\(866\) 22.9944 0.781382
\(867\) −20.3619 −0.691525
\(868\) 16.1335 0.547607
\(869\) −43.3526 −1.47064
\(870\) −15.4901 −0.525163
\(871\) −17.6996 −0.599727
\(872\) −10.9789 −0.371791
\(873\) −61.0614 −2.06662
\(874\) 3.16632 0.107102
\(875\) 8.07725 0.273061
\(876\) −23.6323 −0.798460
\(877\) −53.5343 −1.80772 −0.903862 0.427824i \(-0.859280\pi\)
−0.903862 + 0.427824i \(0.859280\pi\)
\(878\) 15.2381 0.514263
\(879\) −93.3147 −3.14743
\(880\) −11.8924 −0.400892
\(881\) 29.2387 0.985078 0.492539 0.870290i \(-0.336069\pi\)
0.492539 + 0.870290i \(0.336069\pi\)
\(882\) −0.824707 −0.0277693
\(883\) −49.5773 −1.66841 −0.834205 0.551454i \(-0.814073\pi\)
−0.834205 + 0.551454i \(0.814073\pi\)
\(884\) −15.4123 −0.518372
\(885\) −101.385 −3.40803
\(886\) 16.2175 0.544838
\(887\) 1.61986 0.0543896 0.0271948 0.999630i \(-0.491343\pi\)
0.0271948 + 0.999630i \(0.491343\pi\)
\(888\) −22.9375 −0.769733
\(889\) 57.4207 1.92583
\(890\) 41.6414 1.39582
\(891\) 48.8428 1.63630
\(892\) 28.9438 0.969112
\(893\) 10.0853 0.337492
\(894\) −21.7323 −0.726838
\(895\) 55.6735 1.86096
\(896\) −2.62160 −0.0875815
\(897\) −30.9261 −1.03259
\(898\) −26.3657 −0.879833
\(899\) 9.36264 0.312262
\(900\) 38.4557 1.28186
\(901\) 46.8493 1.56078
\(902\) 2.60844 0.0868516
\(903\) −13.5940 −0.452380
\(904\) −3.89336 −0.129491
\(905\) −75.4527 −2.50813
\(906\) 22.8090 0.757777
\(907\) 21.0380 0.698557 0.349278 0.937019i \(-0.386427\pi\)
0.349278 + 0.937019i \(0.386427\pi\)
\(908\) 5.79137 0.192193
\(909\) −60.8257 −2.01746
\(910\) −27.4924 −0.911365
\(911\) 17.7870 0.589308 0.294654 0.955604i \(-0.404796\pi\)
0.294654 + 0.955604i \(0.404796\pi\)
\(912\) 3.07943 0.101970
\(913\) −15.5507 −0.514654
\(914\) −28.5587 −0.944639
\(915\) −126.841 −4.19322
\(916\) −18.6651 −0.616712
\(917\) −47.4692 −1.56757
\(918\) −52.1171 −1.72012
\(919\) 30.1580 0.994821 0.497410 0.867515i \(-0.334284\pi\)
0.497410 + 0.867515i \(0.334284\pi\)
\(920\) 10.4689 0.345150
\(921\) −95.9891 −3.16295
\(922\) −28.1105 −0.925769
\(923\) −11.5006 −0.378547
\(924\) 29.0375 0.955264
\(925\) 44.1842 1.45277
\(926\) −6.56312 −0.215677
\(927\) 27.8502 0.914721
\(928\) −1.52137 −0.0499415
\(929\) 6.92159 0.227090 0.113545 0.993533i \(-0.463779\pi\)
0.113545 + 0.993533i \(0.463779\pi\)
\(930\) −62.6586 −2.05465
\(931\) 0.127213 0.00416922
\(932\) 21.7720 0.713165
\(933\) 39.7016 1.29977
\(934\) −36.3201 −1.18843
\(935\) −57.7880 −1.88987
\(936\) −20.5622 −0.672096
\(937\) 16.4258 0.536606 0.268303 0.963335i \(-0.413537\pi\)
0.268303 + 0.963335i \(0.413537\pi\)
\(938\) −14.6295 −0.477671
\(939\) 73.4710 2.39764
\(940\) 33.3454 1.08761
\(941\) 2.02529 0.0660224 0.0330112 0.999455i \(-0.489490\pi\)
0.0330112 + 0.999455i \(0.489490\pi\)
\(942\) 23.9525 0.780415
\(943\) −2.29622 −0.0747752
\(944\) −9.95767 −0.324095
\(945\) −92.9663 −3.02420
\(946\) −6.05664 −0.196918
\(947\) −40.3818 −1.31223 −0.656117 0.754659i \(-0.727802\pi\)
−0.656117 + 0.754659i \(0.727802\pi\)
\(948\) 37.1162 1.20548
\(949\) −24.3407 −0.790134
\(950\) −5.93186 −0.192455
\(951\) 51.2404 1.66158
\(952\) −12.7390 −0.412873
\(953\) 53.8358 1.74391 0.871956 0.489584i \(-0.162851\pi\)
0.871956 + 0.489584i \(0.162851\pi\)
\(954\) 62.5035 2.02362
\(955\) 83.6019 2.70529
\(956\) −8.04048 −0.260048
\(957\) 16.8511 0.544719
\(958\) 14.6465 0.473207
\(959\) −42.1068 −1.35970
\(960\) 10.1816 0.328611
\(961\) 6.87262 0.221697
\(962\) −23.6252 −0.761707
\(963\) 99.2978 3.19983
\(964\) 19.9326 0.641986
\(965\) −27.4334 −0.883114
\(966\) −25.5618 −0.822438
\(967\) −19.1912 −0.617147 −0.308574 0.951200i \(-0.599852\pi\)
−0.308574 + 0.951200i \(0.599852\pi\)
\(968\) 1.93733 0.0622680
\(969\) 14.9637 0.480703
\(970\) 31.1418 0.999904
\(971\) −16.0719 −0.515771 −0.257885 0.966175i \(-0.583026\pi\)
−0.257885 + 0.966175i \(0.583026\pi\)
\(972\) −9.64055 −0.309221
\(973\) −45.7108 −1.46542
\(974\) −13.9606 −0.447327
\(975\) 57.9376 1.85549
\(976\) −12.4578 −0.398764
\(977\) −12.7285 −0.407220 −0.203610 0.979052i \(-0.565268\pi\)
−0.203610 + 0.979052i \(0.565268\pi\)
\(978\) 41.9751 1.34221
\(979\) −45.3003 −1.44780
\(980\) 0.420607 0.0134358
\(981\) −71.1750 −2.27244
\(982\) −8.28220 −0.264296
\(983\) −45.5321 −1.45225 −0.726124 0.687564i \(-0.758680\pi\)
−0.726124 + 0.687564i \(0.758680\pi\)
\(984\) −2.23321 −0.0711921
\(985\) 25.8244 0.822833
\(986\) −7.39272 −0.235432
\(987\) −81.4191 −2.59160
\(988\) 3.17175 0.100907
\(989\) 5.33169 0.169538
\(990\) −77.0973 −2.45031
\(991\) 4.29645 0.136481 0.0682405 0.997669i \(-0.478261\pi\)
0.0682405 + 0.997669i \(0.478261\pi\)
\(992\) −6.15407 −0.195392
\(993\) 6.87335 0.218119
\(994\) −9.50579 −0.301505
\(995\) 56.8776 1.80314
\(996\) 13.3137 0.421861
\(997\) 55.3690 1.75355 0.876777 0.480898i \(-0.159689\pi\)
0.876777 + 0.480898i \(0.159689\pi\)
\(998\) −8.79475 −0.278393
\(999\) −79.8892 −2.52758
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 \(a_p\))