Properties

Label 619.2.a.b.1.20
Level 619
Weight 2
Character 619.1
Self dual Yes
Analytic conductor 4.943
Analytic rank 0
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 619.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(4.94273988512\)
Analytic rank: \(0\)
Dimension: \(30\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.45503 q^{2} -3.26388 q^{3} +0.117111 q^{4} -2.69944 q^{5} -4.74905 q^{6} -1.44249 q^{7} -2.73966 q^{8} +7.65293 q^{9} +O(q^{10})\) \(q+1.45503 q^{2} -3.26388 q^{3} +0.117111 q^{4} -2.69944 q^{5} -4.74905 q^{6} -1.44249 q^{7} -2.73966 q^{8} +7.65293 q^{9} -3.92777 q^{10} +4.50441 q^{11} -0.382238 q^{12} +0.198137 q^{13} -2.09886 q^{14} +8.81067 q^{15} -4.22051 q^{16} -1.93683 q^{17} +11.1352 q^{18} +3.86501 q^{19} -0.316135 q^{20} +4.70811 q^{21} +6.55406 q^{22} +0.808761 q^{23} +8.94193 q^{24} +2.28699 q^{25} +0.288296 q^{26} -15.1866 q^{27} -0.168932 q^{28} +6.96153 q^{29} +12.8198 q^{30} +1.02658 q^{31} -0.661646 q^{32} -14.7019 q^{33} -2.81814 q^{34} +3.89391 q^{35} +0.896245 q^{36} +6.22281 q^{37} +5.62370 q^{38} -0.646697 q^{39} +7.39555 q^{40} +5.92980 q^{41} +6.85044 q^{42} +1.11330 q^{43} +0.527518 q^{44} -20.6586 q^{45} +1.17677 q^{46} -7.77508 q^{47} +13.7752 q^{48} -4.91923 q^{49} +3.32764 q^{50} +6.32158 q^{51} +0.0232041 q^{52} +5.75008 q^{53} -22.0970 q^{54} -12.1594 q^{55} +3.95193 q^{56} -12.6149 q^{57} +10.1292 q^{58} -7.95759 q^{59} +1.03183 q^{60} +6.64190 q^{61} +1.49371 q^{62} -11.0393 q^{63} +7.47830 q^{64} -0.534861 q^{65} -21.3917 q^{66} -13.5542 q^{67} -0.226825 q^{68} -2.63970 q^{69} +5.66576 q^{70} -7.35863 q^{71} -20.9664 q^{72} +8.20815 q^{73} +9.05438 q^{74} -7.46447 q^{75} +0.452636 q^{76} -6.49757 q^{77} -0.940964 q^{78} +7.47172 q^{79} +11.3930 q^{80} +26.6086 q^{81} +8.62803 q^{82} +15.5874 q^{83} +0.551373 q^{84} +5.22836 q^{85} +1.61988 q^{86} -22.7216 q^{87} -12.3406 q^{88} +16.4390 q^{89} -30.0589 q^{90} -0.285811 q^{91} +0.0947151 q^{92} -3.35065 q^{93} -11.3130 q^{94} -10.4334 q^{95} +2.15954 q^{96} -18.6262 q^{97} -7.15762 q^{98} +34.4720 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.45503 1.02886 0.514431 0.857532i \(-0.328003\pi\)
0.514431 + 0.857532i \(0.328003\pi\)
\(3\) −3.26388 −1.88440 −0.942202 0.335046i \(-0.891248\pi\)
−0.942202 + 0.335046i \(0.891248\pi\)
\(4\) 0.117111 0.0585557
\(5\) −2.69944 −1.20723 −0.603614 0.797277i \(-0.706273\pi\)
−0.603614 + 0.797277i \(0.706273\pi\)
\(6\) −4.74905 −1.93879
\(7\) −1.44249 −0.545209 −0.272605 0.962126i \(-0.587885\pi\)
−0.272605 + 0.962126i \(0.587885\pi\)
\(8\) −2.73966 −0.968616
\(9\) 7.65293 2.55098
\(10\) −3.92777 −1.24207
\(11\) 4.50441 1.35813 0.679066 0.734077i \(-0.262385\pi\)
0.679066 + 0.734077i \(0.262385\pi\)
\(12\) −0.382238 −0.110343
\(13\) 0.198137 0.0549534 0.0274767 0.999622i \(-0.491253\pi\)
0.0274767 + 0.999622i \(0.491253\pi\)
\(14\) −2.09886 −0.560945
\(15\) 8.81067 2.27490
\(16\) −4.22051 −1.05513
\(17\) −1.93683 −0.469750 −0.234875 0.972026i \(-0.575468\pi\)
−0.234875 + 0.972026i \(0.575468\pi\)
\(18\) 11.1352 2.62460
\(19\) 3.86501 0.886693 0.443347 0.896350i \(-0.353791\pi\)
0.443347 + 0.896350i \(0.353791\pi\)
\(20\) −0.316135 −0.0706900
\(21\) 4.70811 1.02739
\(22\) 6.55406 1.39733
\(23\) 0.808761 0.168638 0.0843192 0.996439i \(-0.473128\pi\)
0.0843192 + 0.996439i \(0.473128\pi\)
\(24\) 8.94193 1.82526
\(25\) 2.28699 0.457398
\(26\) 0.288296 0.0565395
\(27\) −15.1866 −2.92267
\(28\) −0.168932 −0.0319251
\(29\) 6.96153 1.29272 0.646362 0.763031i \(-0.276290\pi\)
0.646362 + 0.763031i \(0.276290\pi\)
\(30\) 12.8198 2.34056
\(31\) 1.02658 0.184380 0.0921900 0.995741i \(-0.470613\pi\)
0.0921900 + 0.995741i \(0.470613\pi\)
\(32\) −0.661646 −0.116964
\(33\) −14.7019 −2.55927
\(34\) −2.81814 −0.483307
\(35\) 3.89391 0.658192
\(36\) 0.896245 0.149374
\(37\) 6.22281 1.02302 0.511512 0.859276i \(-0.329086\pi\)
0.511512 + 0.859276i \(0.329086\pi\)
\(38\) 5.62370 0.912284
\(39\) −0.646697 −0.103554
\(40\) 7.39555 1.16934
\(41\) 5.92980 0.926079 0.463039 0.886338i \(-0.346759\pi\)
0.463039 + 0.886338i \(0.346759\pi\)
\(42\) 6.85044 1.05705
\(43\) 1.11330 0.169776 0.0848882 0.996390i \(-0.472947\pi\)
0.0848882 + 0.996390i \(0.472947\pi\)
\(44\) 0.527518 0.0795263
\(45\) −20.6586 −3.07961
\(46\) 1.17677 0.173506
\(47\) −7.77508 −1.13411 −0.567056 0.823679i \(-0.691918\pi\)
−0.567056 + 0.823679i \(0.691918\pi\)
\(48\) 13.7752 1.98828
\(49\) −4.91923 −0.702747
\(50\) 3.32764 0.470599
\(51\) 6.32158 0.885198
\(52\) 0.0232041 0.00321784
\(53\) 5.75008 0.789834 0.394917 0.918717i \(-0.370773\pi\)
0.394917 + 0.918717i \(0.370773\pi\)
\(54\) −22.0970 −3.00702
\(55\) −12.1594 −1.63957
\(56\) 3.95193 0.528098
\(57\) −12.6149 −1.67089
\(58\) 10.1292 1.33003
\(59\) −7.95759 −1.03599 −0.517995 0.855384i \(-0.673321\pi\)
−0.517995 + 0.855384i \(0.673321\pi\)
\(60\) 1.03183 0.133209
\(61\) 6.64190 0.850408 0.425204 0.905097i \(-0.360202\pi\)
0.425204 + 0.905097i \(0.360202\pi\)
\(62\) 1.49371 0.189702
\(63\) −11.0393 −1.39082
\(64\) 7.47830 0.934788
\(65\) −0.534861 −0.0663413
\(66\) −21.3917 −2.63313
\(67\) −13.5542 −1.65591 −0.827956 0.560793i \(-0.810496\pi\)
−0.827956 + 0.560793i \(0.810496\pi\)
\(68\) −0.226825 −0.0275065
\(69\) −2.63970 −0.317783
\(70\) 5.66576 0.677188
\(71\) −7.35863 −0.873309 −0.436654 0.899629i \(-0.643837\pi\)
−0.436654 + 0.899629i \(0.643837\pi\)
\(72\) −20.9664 −2.47092
\(73\) 8.20815 0.960691 0.480346 0.877079i \(-0.340511\pi\)
0.480346 + 0.877079i \(0.340511\pi\)
\(74\) 9.05438 1.05255
\(75\) −7.46447 −0.861923
\(76\) 0.452636 0.0519209
\(77\) −6.49757 −0.740466
\(78\) −0.940964 −0.106543
\(79\) 7.47172 0.840635 0.420317 0.907377i \(-0.361919\pi\)
0.420317 + 0.907377i \(0.361919\pi\)
\(80\) 11.3930 1.27378
\(81\) 26.6086 2.95651
\(82\) 8.62803 0.952806
\(83\) 15.5874 1.71093 0.855467 0.517857i \(-0.173270\pi\)
0.855467 + 0.517857i \(0.173270\pi\)
\(84\) 0.551373 0.0601598
\(85\) 5.22836 0.567095
\(86\) 1.61988 0.174676
\(87\) −22.7216 −2.43601
\(88\) −12.3406 −1.31551
\(89\) 16.4390 1.74253 0.871266 0.490811i \(-0.163299\pi\)
0.871266 + 0.490811i \(0.163299\pi\)
\(90\) −30.0589 −3.16849
\(91\) −0.285811 −0.0299611
\(92\) 0.0947151 0.00987474
\(93\) −3.35065 −0.347446
\(94\) −11.3130 −1.16684
\(95\) −10.4334 −1.07044
\(96\) 2.15954 0.220407
\(97\) −18.6262 −1.89120 −0.945600 0.325332i \(-0.894524\pi\)
−0.945600 + 0.325332i \(0.894524\pi\)
\(98\) −7.15762 −0.723029
\(99\) 34.4720 3.46456
\(100\) 0.267833 0.0267833
\(101\) 7.22564 0.718978 0.359489 0.933149i \(-0.382951\pi\)
0.359489 + 0.933149i \(0.382951\pi\)
\(102\) 9.19809 0.910746
\(103\) 18.4839 1.82127 0.910636 0.413209i \(-0.135592\pi\)
0.910636 + 0.413209i \(0.135592\pi\)
\(104\) −0.542829 −0.0532288
\(105\) −12.7093 −1.24030
\(106\) 8.36653 0.812629
\(107\) 13.6163 1.31634 0.658171 0.752869i \(-0.271331\pi\)
0.658171 + 0.752869i \(0.271331\pi\)
\(108\) −1.77853 −0.171139
\(109\) 10.9783 1.05153 0.525763 0.850631i \(-0.323780\pi\)
0.525763 + 0.850631i \(0.323780\pi\)
\(110\) −17.6923 −1.68689
\(111\) −20.3105 −1.92779
\(112\) 6.08803 0.575265
\(113\) 9.20959 0.866365 0.433183 0.901306i \(-0.357391\pi\)
0.433183 + 0.901306i \(0.357391\pi\)
\(114\) −18.3551 −1.71911
\(115\) −2.18321 −0.203585
\(116\) 0.815275 0.0756964
\(117\) 1.51633 0.140185
\(118\) −11.5785 −1.06589
\(119\) 2.79385 0.256112
\(120\) −24.1382 −2.20351
\(121\) 9.28975 0.844523
\(122\) 9.66416 0.874952
\(123\) −19.3542 −1.74511
\(124\) 0.120225 0.0107965
\(125\) 7.32361 0.655044
\(126\) −16.0625 −1.43096
\(127\) −8.31505 −0.737842 −0.368921 0.929461i \(-0.620273\pi\)
−0.368921 + 0.929461i \(0.620273\pi\)
\(128\) 12.2044 1.07873
\(129\) −3.63368 −0.319927
\(130\) −0.778238 −0.0682560
\(131\) −16.2234 −1.41745 −0.708723 0.705487i \(-0.750728\pi\)
−0.708723 + 0.705487i \(0.750728\pi\)
\(132\) −1.72176 −0.149860
\(133\) −5.57523 −0.483433
\(134\) −19.7218 −1.70370
\(135\) 40.9954 3.52832
\(136\) 5.30625 0.455007
\(137\) 14.9392 1.27634 0.638170 0.769895i \(-0.279692\pi\)
0.638170 + 0.769895i \(0.279692\pi\)
\(138\) −3.84085 −0.326954
\(139\) −11.9566 −1.01415 −0.507075 0.861902i \(-0.669273\pi\)
−0.507075 + 0.861902i \(0.669273\pi\)
\(140\) 0.456022 0.0385409
\(141\) 25.3769 2.13712
\(142\) −10.7070 −0.898514
\(143\) 0.892493 0.0746340
\(144\) −32.2993 −2.69160
\(145\) −18.7923 −1.56061
\(146\) 11.9431 0.988418
\(147\) 16.0558 1.32426
\(148\) 0.728762 0.0599039
\(149\) 8.24104 0.675132 0.337566 0.941302i \(-0.390396\pi\)
0.337566 + 0.941302i \(0.390396\pi\)
\(150\) −10.8610 −0.886799
\(151\) −13.8051 −1.12344 −0.561720 0.827327i \(-0.689860\pi\)
−0.561720 + 0.827327i \(0.689860\pi\)
\(152\) −10.5888 −0.858865
\(153\) −14.8224 −1.19832
\(154\) −9.45415 −0.761837
\(155\) −2.77121 −0.222589
\(156\) −0.0757356 −0.00606370
\(157\) −14.6039 −1.16552 −0.582759 0.812645i \(-0.698027\pi\)
−0.582759 + 0.812645i \(0.698027\pi\)
\(158\) 10.8716 0.864896
\(159\) −18.7676 −1.48837
\(160\) 1.78608 0.141202
\(161\) −1.16663 −0.0919432
\(162\) 38.7162 3.04184
\(163\) 12.7376 0.997689 0.498844 0.866692i \(-0.333758\pi\)
0.498844 + 0.866692i \(0.333758\pi\)
\(164\) 0.694446 0.0542272
\(165\) 39.6869 3.08962
\(166\) 22.6801 1.76031
\(167\) −10.4856 −0.811400 −0.405700 0.914006i \(-0.632972\pi\)
−0.405700 + 0.914006i \(0.632972\pi\)
\(168\) −12.8986 −0.995150
\(169\) −12.9607 −0.996980
\(170\) 7.60741 0.583462
\(171\) 29.5786 2.26193
\(172\) 0.130380 0.00994137
\(173\) 0.373888 0.0284261 0.0142131 0.999899i \(-0.495476\pi\)
0.0142131 + 0.999899i \(0.495476\pi\)
\(174\) −33.0606 −2.50632
\(175\) −3.29896 −0.249378
\(176\) −19.0109 −1.43300
\(177\) 25.9726 1.95222
\(178\) 23.9193 1.79282
\(179\) −2.36663 −0.176890 −0.0884449 0.996081i \(-0.528190\pi\)
−0.0884449 + 0.996081i \(0.528190\pi\)
\(180\) −2.41936 −0.180329
\(181\) 21.0280 1.56300 0.781498 0.623908i \(-0.214456\pi\)
0.781498 + 0.623908i \(0.214456\pi\)
\(182\) −0.415863 −0.0308258
\(183\) −21.6784 −1.60251
\(184\) −2.21573 −0.163346
\(185\) −16.7981 −1.23502
\(186\) −4.87530 −0.357474
\(187\) −8.72428 −0.637982
\(188\) −0.910550 −0.0664087
\(189\) 21.9065 1.59347
\(190\) −15.1809 −1.10133
\(191\) −13.6361 −0.986674 −0.493337 0.869838i \(-0.664223\pi\)
−0.493337 + 0.869838i \(0.664223\pi\)
\(192\) −24.4083 −1.76152
\(193\) 3.03369 0.218370 0.109185 0.994021i \(-0.465176\pi\)
0.109185 + 0.994021i \(0.465176\pi\)
\(194\) −27.1016 −1.94578
\(195\) 1.74572 0.125014
\(196\) −0.576097 −0.0411498
\(197\) 10.7235 0.764016 0.382008 0.924159i \(-0.375233\pi\)
0.382008 + 0.924159i \(0.375233\pi\)
\(198\) 50.1577 3.56456
\(199\) 23.2432 1.64766 0.823832 0.566834i \(-0.191832\pi\)
0.823832 + 0.566834i \(0.191832\pi\)
\(200\) −6.26558 −0.443043
\(201\) 44.2394 3.12041
\(202\) 10.5135 0.739729
\(203\) −10.0419 −0.704805
\(204\) 0.740329 0.0518334
\(205\) −16.0071 −1.11799
\(206\) 26.8946 1.87384
\(207\) 6.18939 0.430193
\(208\) −0.836240 −0.0579828
\(209\) 17.4096 1.20425
\(210\) −18.4924 −1.27610
\(211\) −10.8969 −0.750177 −0.375088 0.926989i \(-0.622388\pi\)
−0.375088 + 0.926989i \(0.622388\pi\)
\(212\) 0.673399 0.0462492
\(213\) 24.0177 1.64567
\(214\) 19.8122 1.35433
\(215\) −3.00529 −0.204959
\(216\) 41.6062 2.83094
\(217\) −1.48084 −0.100526
\(218\) 15.9737 1.08187
\(219\) −26.7904 −1.81033
\(220\) −1.42400 −0.0960064
\(221\) −0.383758 −0.0258144
\(222\) −29.5524 −1.98343
\(223\) 7.05320 0.472317 0.236159 0.971715i \(-0.424111\pi\)
0.236159 + 0.971715i \(0.424111\pi\)
\(224\) 0.954417 0.0637697
\(225\) 17.5022 1.16681
\(226\) 13.4002 0.891370
\(227\) 15.6090 1.03601 0.518004 0.855378i \(-0.326675\pi\)
0.518004 + 0.855378i \(0.326675\pi\)
\(228\) −1.47735 −0.0978400
\(229\) 22.1927 1.46654 0.733268 0.679940i \(-0.237994\pi\)
0.733268 + 0.679940i \(0.237994\pi\)
\(230\) −3.17663 −0.209461
\(231\) 21.2073 1.39534
\(232\) −19.0722 −1.25215
\(233\) −2.04681 −0.134091 −0.0670455 0.997750i \(-0.521357\pi\)
−0.0670455 + 0.997750i \(0.521357\pi\)
\(234\) 2.20631 0.144231
\(235\) 20.9884 1.36913
\(236\) −0.931924 −0.0606631
\(237\) −24.3868 −1.58409
\(238\) 4.06514 0.263504
\(239\) 4.19951 0.271644 0.135822 0.990733i \(-0.456632\pi\)
0.135822 + 0.990733i \(0.456632\pi\)
\(240\) −37.1855 −2.40031
\(241\) −8.22325 −0.529706 −0.264853 0.964289i \(-0.585323\pi\)
−0.264853 + 0.964289i \(0.585323\pi\)
\(242\) 13.5169 0.868897
\(243\) −41.2874 −2.64859
\(244\) 0.777842 0.0497962
\(245\) 13.2792 0.848375
\(246\) −28.1609 −1.79547
\(247\) 0.765802 0.0487268
\(248\) −2.81249 −0.178593
\(249\) −50.8753 −3.22409
\(250\) 10.6561 0.673949
\(251\) 12.5908 0.794726 0.397363 0.917661i \(-0.369925\pi\)
0.397363 + 0.917661i \(0.369925\pi\)
\(252\) −1.29282 −0.0814402
\(253\) 3.64300 0.229033
\(254\) −12.0986 −0.759137
\(255\) −17.0647 −1.06864
\(256\) 2.80122 0.175076
\(257\) −16.3841 −1.02201 −0.511005 0.859578i \(-0.670727\pi\)
−0.511005 + 0.859578i \(0.670727\pi\)
\(258\) −5.28711 −0.329161
\(259\) −8.97634 −0.557762
\(260\) −0.0626383 −0.00388466
\(261\) 53.2761 3.29771
\(262\) −23.6055 −1.45836
\(263\) −4.40532 −0.271644 −0.135822 0.990733i \(-0.543367\pi\)
−0.135822 + 0.990733i \(0.543367\pi\)
\(264\) 40.2781 2.47895
\(265\) −15.5220 −0.953509
\(266\) −8.11212 −0.497386
\(267\) −53.6550 −3.28363
\(268\) −1.58735 −0.0969631
\(269\) −12.1275 −0.739424 −0.369712 0.929146i \(-0.620544\pi\)
−0.369712 + 0.929146i \(0.620544\pi\)
\(270\) 59.6495 3.63016
\(271\) −15.1314 −0.919167 −0.459583 0.888135i \(-0.652001\pi\)
−0.459583 + 0.888135i \(0.652001\pi\)
\(272\) 8.17440 0.495646
\(273\) 0.932853 0.0564588
\(274\) 21.7369 1.31318
\(275\) 10.3016 0.621207
\(276\) −0.309139 −0.0186080
\(277\) 24.2812 1.45892 0.729459 0.684025i \(-0.239772\pi\)
0.729459 + 0.684025i \(0.239772\pi\)
\(278\) −17.3973 −1.04342
\(279\) 7.85638 0.470349
\(280\) −10.6680 −0.637535
\(281\) −24.6461 −1.47026 −0.735130 0.677926i \(-0.762879\pi\)
−0.735130 + 0.677926i \(0.762879\pi\)
\(282\) 36.9242 2.19880
\(283\) 1.64814 0.0979715 0.0489858 0.998799i \(-0.484401\pi\)
0.0489858 + 0.998799i \(0.484401\pi\)
\(284\) −0.861779 −0.0511372
\(285\) 34.0533 2.01714
\(286\) 1.29860 0.0767881
\(287\) −8.55366 −0.504907
\(288\) −5.06353 −0.298372
\(289\) −13.2487 −0.779335
\(290\) −27.3433 −1.60565
\(291\) 60.7936 3.56378
\(292\) 0.961267 0.0562539
\(293\) −1.23309 −0.0720377 −0.0360189 0.999351i \(-0.511468\pi\)
−0.0360189 + 0.999351i \(0.511468\pi\)
\(294\) 23.3616 1.36248
\(295\) 21.4811 1.25068
\(296\) −17.0484 −0.990917
\(297\) −68.4068 −3.96937
\(298\) 11.9910 0.694618
\(299\) 0.160246 0.00926726
\(300\) −0.874175 −0.0504705
\(301\) −1.60592 −0.0925637
\(302\) −20.0868 −1.15586
\(303\) −23.5836 −1.35484
\(304\) −16.3123 −0.935574
\(305\) −17.9294 −1.02664
\(306\) −21.5670 −1.23291
\(307\) 2.61165 0.149055 0.0745274 0.997219i \(-0.476255\pi\)
0.0745274 + 0.997219i \(0.476255\pi\)
\(308\) −0.760939 −0.0433585
\(309\) −60.3293 −3.43201
\(310\) −4.03219 −0.229013
\(311\) 21.4251 1.21491 0.607454 0.794355i \(-0.292191\pi\)
0.607454 + 0.794355i \(0.292191\pi\)
\(312\) 1.77173 0.100304
\(313\) −25.5877 −1.44630 −0.723152 0.690689i \(-0.757308\pi\)
−0.723152 + 0.690689i \(0.757308\pi\)
\(314\) −21.2491 −1.19916
\(315\) 29.7999 1.67903
\(316\) 0.875024 0.0492239
\(317\) 23.4782 1.31866 0.659332 0.751852i \(-0.270839\pi\)
0.659332 + 0.751852i \(0.270839\pi\)
\(318\) −27.3074 −1.53132
\(319\) 31.3576 1.75569
\(320\) −20.1872 −1.12850
\(321\) −44.4421 −2.48052
\(322\) −1.69748 −0.0945968
\(323\) −7.48585 −0.416524
\(324\) 3.11616 0.173120
\(325\) 0.453139 0.0251356
\(326\) 18.5336 1.02648
\(327\) −35.8317 −1.98150
\(328\) −16.2456 −0.897014
\(329\) 11.2155 0.618328
\(330\) 57.7456 3.17879
\(331\) −6.06252 −0.333227 −0.166613 0.986022i \(-0.553283\pi\)
−0.166613 + 0.986022i \(0.553283\pi\)
\(332\) 1.82546 0.100185
\(333\) 47.6228 2.60971
\(334\) −15.2569 −0.834818
\(335\) 36.5889 1.99906
\(336\) −19.8706 −1.08403
\(337\) −27.7433 −1.51127 −0.755637 0.654990i \(-0.772673\pi\)
−0.755637 + 0.654990i \(0.772673\pi\)
\(338\) −18.8583 −1.02575
\(339\) −30.0590 −1.63258
\(340\) 0.612300 0.0332066
\(341\) 4.62416 0.250412
\(342\) 43.0378 2.32722
\(343\) 17.1933 0.928353
\(344\) −3.05006 −0.164448
\(345\) 7.12573 0.383636
\(346\) 0.544017 0.0292466
\(347\) 31.7210 1.70287 0.851436 0.524458i \(-0.175732\pi\)
0.851436 + 0.524458i \(0.175732\pi\)
\(348\) −2.66096 −0.142642
\(349\) −2.75301 −0.147365 −0.0736827 0.997282i \(-0.523475\pi\)
−0.0736827 + 0.997282i \(0.523475\pi\)
\(350\) −4.80008 −0.256575
\(351\) −3.00904 −0.160611
\(352\) −2.98033 −0.158852
\(353\) 6.68412 0.355760 0.177880 0.984052i \(-0.443076\pi\)
0.177880 + 0.984052i \(0.443076\pi\)
\(354\) 37.7910 2.00857
\(355\) 19.8642 1.05428
\(356\) 1.92520 0.102035
\(357\) −9.11881 −0.482618
\(358\) −3.44351 −0.181995
\(359\) −5.53478 −0.292114 −0.146057 0.989276i \(-0.546658\pi\)
−0.146057 + 0.989276i \(0.546658\pi\)
\(360\) 56.5977 2.98296
\(361\) −4.06173 −0.213775
\(362\) 30.5963 1.60811
\(363\) −30.3207 −1.59142
\(364\) −0.0334717 −0.00175439
\(365\) −22.1574 −1.15977
\(366\) −31.5427 −1.64876
\(367\) 15.8704 0.828426 0.414213 0.910180i \(-0.364057\pi\)
0.414213 + 0.910180i \(0.364057\pi\)
\(368\) −3.41338 −0.177935
\(369\) 45.3803 2.36240
\(370\) −24.4418 −1.27067
\(371\) −8.29442 −0.430625
\(372\) −0.392399 −0.0203450
\(373\) −30.3655 −1.57227 −0.786134 0.618057i \(-0.787920\pi\)
−0.786134 + 0.618057i \(0.787920\pi\)
\(374\) −12.6941 −0.656395
\(375\) −23.9034 −1.23437
\(376\) 21.3011 1.09852
\(377\) 1.37934 0.0710396
\(378\) 31.8746 1.63945
\(379\) −27.3973 −1.40731 −0.703653 0.710544i \(-0.748449\pi\)
−0.703653 + 0.710544i \(0.748449\pi\)
\(380\) −1.22187 −0.0626804
\(381\) 27.1394 1.39039
\(382\) −19.8409 −1.01515
\(383\) 12.8193 0.655037 0.327518 0.944845i \(-0.393788\pi\)
0.327518 + 0.944845i \(0.393788\pi\)
\(384\) −39.8339 −2.03276
\(385\) 17.5398 0.893911
\(386\) 4.41411 0.224672
\(387\) 8.52000 0.433096
\(388\) −2.18133 −0.110740
\(389\) 31.8869 1.61673 0.808366 0.588680i \(-0.200352\pi\)
0.808366 + 0.588680i \(0.200352\pi\)
\(390\) 2.54008 0.128622
\(391\) −1.56643 −0.0792179
\(392\) 13.4770 0.680692
\(393\) 52.9513 2.67104
\(394\) 15.6030 0.786066
\(395\) −20.1695 −1.01484
\(396\) 4.03706 0.202870
\(397\) −5.27927 −0.264959 −0.132480 0.991186i \(-0.542294\pi\)
−0.132480 + 0.991186i \(0.542294\pi\)
\(398\) 33.8195 1.69522
\(399\) 18.1969 0.910984
\(400\) −9.65227 −0.482613
\(401\) 16.6475 0.831337 0.415668 0.909516i \(-0.363548\pi\)
0.415668 + 0.909516i \(0.363548\pi\)
\(402\) 64.3696 3.21047
\(403\) 0.203405 0.0101323
\(404\) 0.846204 0.0421002
\(405\) −71.8283 −3.56918
\(406\) −14.6113 −0.725147
\(407\) 28.0301 1.38940
\(408\) −17.3190 −0.857417
\(409\) −35.3883 −1.74984 −0.874920 0.484267i \(-0.839086\pi\)
−0.874920 + 0.484267i \(0.839086\pi\)
\(410\) −23.2909 −1.15025
\(411\) −48.7597 −2.40514
\(412\) 2.16467 0.106646
\(413\) 11.4787 0.564832
\(414\) 9.00575 0.442609
\(415\) −42.0772 −2.06549
\(416\) −0.131097 −0.00642755
\(417\) 39.0251 1.91107
\(418\) 25.3315 1.23900
\(419\) −2.99594 −0.146361 −0.0731805 0.997319i \(-0.523315\pi\)
−0.0731805 + 0.997319i \(0.523315\pi\)
\(420\) −1.48840 −0.0726265
\(421\) −22.9087 −1.11650 −0.558252 0.829672i \(-0.688528\pi\)
−0.558252 + 0.829672i \(0.688528\pi\)
\(422\) −15.8554 −0.771828
\(423\) −59.5021 −2.89309
\(424\) −15.7532 −0.765045
\(425\) −4.42951 −0.214863
\(426\) 34.9465 1.69316
\(427\) −9.58087 −0.463651
\(428\) 1.59463 0.0770792
\(429\) −2.91299 −0.140641
\(430\) −4.37278 −0.210874
\(431\) 34.0116 1.63828 0.819141 0.573592i \(-0.194451\pi\)
0.819141 + 0.573592i \(0.194451\pi\)
\(432\) 64.0953 3.08378
\(433\) 7.85344 0.377412 0.188706 0.982034i \(-0.439571\pi\)
0.188706 + 0.982034i \(0.439571\pi\)
\(434\) −2.15466 −0.103427
\(435\) 61.3357 2.94082
\(436\) 1.28568 0.0615728
\(437\) 3.12587 0.149531
\(438\) −38.9809 −1.86258
\(439\) −8.49965 −0.405666 −0.202833 0.979213i \(-0.565015\pi\)
−0.202833 + 0.979213i \(0.565015\pi\)
\(440\) 33.3126 1.58812
\(441\) −37.6465 −1.79269
\(442\) −0.558379 −0.0265594
\(443\) 0.532143 0.0252829 0.0126414 0.999920i \(-0.495976\pi\)
0.0126414 + 0.999920i \(0.495976\pi\)
\(444\) −2.37859 −0.112883
\(445\) −44.3762 −2.10363
\(446\) 10.2626 0.485949
\(447\) −26.8978 −1.27222
\(448\) −10.7874 −0.509655
\(449\) −11.0838 −0.523077 −0.261538 0.965193i \(-0.584230\pi\)
−0.261538 + 0.965193i \(0.584230\pi\)
\(450\) 25.4662 1.20049
\(451\) 26.7103 1.25774
\(452\) 1.07855 0.0507306
\(453\) 45.0581 2.11702
\(454\) 22.7116 1.06591
\(455\) 0.771530 0.0361699
\(456\) 34.5606 1.61845
\(457\) 32.6997 1.52963 0.764815 0.644250i \(-0.222831\pi\)
0.764815 + 0.644250i \(0.222831\pi\)
\(458\) 32.2911 1.50886
\(459\) 29.4139 1.37292
\(460\) −0.255678 −0.0119211
\(461\) −10.3452 −0.481824 −0.240912 0.970547i \(-0.577446\pi\)
−0.240912 + 0.970547i \(0.577446\pi\)
\(462\) 30.8572 1.43561
\(463\) 5.60035 0.260271 0.130135 0.991496i \(-0.458459\pi\)
0.130135 + 0.991496i \(0.458459\pi\)
\(464\) −29.3812 −1.36399
\(465\) 9.04489 0.419447
\(466\) −2.97817 −0.137961
\(467\) 16.9894 0.786174 0.393087 0.919501i \(-0.371407\pi\)
0.393087 + 0.919501i \(0.371407\pi\)
\(468\) 0.177580 0.00820862
\(469\) 19.5518 0.902819
\(470\) 30.5387 1.40865
\(471\) 47.6654 2.19631
\(472\) 21.8011 1.00348
\(473\) 5.01476 0.230579
\(474\) −35.4836 −1.62981
\(475\) 8.83924 0.405572
\(476\) 0.327192 0.0149968
\(477\) 44.0049 2.01485
\(478\) 6.11042 0.279484
\(479\) −16.0046 −0.731269 −0.365634 0.930759i \(-0.619148\pi\)
−0.365634 + 0.930759i \(0.619148\pi\)
\(480\) −5.82954 −0.266081
\(481\) 1.23297 0.0562187
\(482\) −11.9651 −0.544994
\(483\) 3.80774 0.173258
\(484\) 1.08794 0.0494516
\(485\) 50.2802 2.28311
\(486\) −60.0743 −2.72503
\(487\) 9.76453 0.442473 0.221237 0.975220i \(-0.428991\pi\)
0.221237 + 0.975220i \(0.428991\pi\)
\(488\) −18.1965 −0.823719
\(489\) −41.5742 −1.88005
\(490\) 19.3216 0.872861
\(491\) −8.02281 −0.362065 −0.181032 0.983477i \(-0.557944\pi\)
−0.181032 + 0.983477i \(0.557944\pi\)
\(492\) −2.26659 −0.102186
\(493\) −13.4833 −0.607257
\(494\) 1.11427 0.0501332
\(495\) −93.0551 −4.18252
\(496\) −4.33271 −0.194544
\(497\) 10.6147 0.476136
\(498\) −74.0251 −3.31714
\(499\) 11.1118 0.497432 0.248716 0.968577i \(-0.419991\pi\)
0.248716 + 0.968577i \(0.419991\pi\)
\(500\) 0.857678 0.0383565
\(501\) 34.2238 1.52900
\(502\) 18.3200 0.817663
\(503\) −13.3780 −0.596495 −0.298248 0.954489i \(-0.596402\pi\)
−0.298248 + 0.954489i \(0.596402\pi\)
\(504\) 30.2438 1.34717
\(505\) −19.5052 −0.867970
\(506\) 5.30067 0.235643
\(507\) 42.3023 1.87871
\(508\) −0.973787 −0.0432048
\(509\) 34.4226 1.52576 0.762878 0.646542i \(-0.223786\pi\)
0.762878 + 0.646542i \(0.223786\pi\)
\(510\) −24.8297 −1.09948
\(511\) −11.8402 −0.523778
\(512\) −20.3330 −0.898601
\(513\) −58.6964 −2.59151
\(514\) −23.8393 −1.05151
\(515\) −49.8962 −2.19869
\(516\) −0.425545 −0.0187336
\(517\) −35.0222 −1.54027
\(518\) −13.0608 −0.573860
\(519\) −1.22033 −0.0535663
\(520\) 1.46534 0.0642592
\(521\) 29.0308 1.27186 0.635932 0.771745i \(-0.280616\pi\)
0.635932 + 0.771745i \(0.280616\pi\)
\(522\) 77.5184 3.39289
\(523\) −12.0058 −0.524977 −0.262489 0.964935i \(-0.584543\pi\)
−0.262489 + 0.964935i \(0.584543\pi\)
\(524\) −1.89995 −0.0829995
\(525\) 10.7674 0.469928
\(526\) −6.40987 −0.279484
\(527\) −1.98832 −0.0866125
\(528\) 62.0494 2.70035
\(529\) −22.3459 −0.971561
\(530\) −22.5850 −0.981028
\(531\) −60.8989 −2.64279
\(532\) −0.652922 −0.0283078
\(533\) 1.17491 0.0508912
\(534\) −78.0697 −3.37841
\(535\) −36.7565 −1.58912
\(536\) 37.1340 1.60394
\(537\) 7.72439 0.333332
\(538\) −17.6458 −0.760765
\(539\) −22.1582 −0.954423
\(540\) 4.80103 0.206603
\(541\) 6.60138 0.283816 0.141908 0.989880i \(-0.454676\pi\)
0.141908 + 0.989880i \(0.454676\pi\)
\(542\) −22.0166 −0.945695
\(543\) −68.6328 −2.94532
\(544\) 1.28149 0.0549436
\(545\) −29.6352 −1.26943
\(546\) 1.35733 0.0580883
\(547\) 22.0708 0.943677 0.471839 0.881685i \(-0.343591\pi\)
0.471839 + 0.881685i \(0.343591\pi\)
\(548\) 1.74955 0.0747370
\(549\) 50.8300 2.16937
\(550\) 14.9891 0.639136
\(551\) 26.9064 1.14625
\(552\) 7.23188 0.307809
\(553\) −10.7779 −0.458322
\(554\) 35.3299 1.50102
\(555\) 54.8271 2.32728
\(556\) −1.40026 −0.0593842
\(557\) −10.6720 −0.452189 −0.226094 0.974105i \(-0.572596\pi\)
−0.226094 + 0.974105i \(0.572596\pi\)
\(558\) 11.4313 0.483924
\(559\) 0.220586 0.00932980
\(560\) −16.4343 −0.694476
\(561\) 28.4750 1.20222
\(562\) −35.8608 −1.51269
\(563\) −15.9951 −0.674114 −0.337057 0.941484i \(-0.609432\pi\)
−0.337057 + 0.941484i \(0.609432\pi\)
\(564\) 2.97193 0.125141
\(565\) −24.8608 −1.04590
\(566\) 2.39809 0.100799
\(567\) −38.3825 −1.61192
\(568\) 20.1601 0.845901
\(569\) 30.3674 1.27307 0.636535 0.771248i \(-0.280367\pi\)
0.636535 + 0.771248i \(0.280367\pi\)
\(570\) 49.5485 2.07536
\(571\) −25.1730 −1.05346 −0.526729 0.850033i \(-0.676582\pi\)
−0.526729 + 0.850033i \(0.676582\pi\)
\(572\) 0.104521 0.00437025
\(573\) 44.5067 1.85929
\(574\) −12.4458 −0.519479
\(575\) 1.84963 0.0771349
\(576\) 57.2309 2.38462
\(577\) 16.9543 0.705817 0.352909 0.935658i \(-0.385193\pi\)
0.352909 + 0.935658i \(0.385193\pi\)
\(578\) −19.2772 −0.801828
\(579\) −9.90161 −0.411497
\(580\) −2.20079 −0.0913827
\(581\) −22.4846 −0.932818
\(582\) 88.4565 3.66664
\(583\) 25.9007 1.07270
\(584\) −22.4875 −0.930540
\(585\) −4.09325 −0.169235
\(586\) −1.79418 −0.0741168
\(587\) 0.234134 0.00966375 0.00483187 0.999988i \(-0.498462\pi\)
0.00483187 + 0.999988i \(0.498462\pi\)
\(588\) 1.88031 0.0775429
\(589\) 3.96776 0.163489
\(590\) 31.2556 1.28677
\(591\) −35.0002 −1.43971
\(592\) −26.2634 −1.07942
\(593\) 25.8018 1.05955 0.529777 0.848137i \(-0.322276\pi\)
0.529777 + 0.848137i \(0.322276\pi\)
\(594\) −99.5340 −4.08393
\(595\) −7.54184 −0.309185
\(596\) 0.965119 0.0395328
\(597\) −75.8630 −3.10486
\(598\) 0.233163 0.00953472
\(599\) −17.1524 −0.700829 −0.350415 0.936595i \(-0.613959\pi\)
−0.350415 + 0.936595i \(0.613959\pi\)
\(600\) 20.4501 0.834872
\(601\) −27.0121 −1.10185 −0.550923 0.834556i \(-0.685724\pi\)
−0.550923 + 0.834556i \(0.685724\pi\)
\(602\) −2.33666 −0.0952352
\(603\) −103.730 −4.22419
\(604\) −1.61673 −0.0657838
\(605\) −25.0771 −1.01953
\(606\) −34.3149 −1.39395
\(607\) −18.1553 −0.736901 −0.368451 0.929647i \(-0.620112\pi\)
−0.368451 + 0.929647i \(0.620112\pi\)
\(608\) −2.55727 −0.103711
\(609\) 32.7757 1.32814
\(610\) −26.0879 −1.05627
\(611\) −1.54053 −0.0623233
\(612\) −1.73587 −0.0701685
\(613\) −16.5866 −0.669926 −0.334963 0.942231i \(-0.608724\pi\)
−0.334963 + 0.942231i \(0.608724\pi\)
\(614\) 3.80003 0.153357
\(615\) 52.2454 2.10674
\(616\) 17.8011 0.717227
\(617\) −37.5797 −1.51290 −0.756452 0.654049i \(-0.773069\pi\)
−0.756452 + 0.654049i \(0.773069\pi\)
\(618\) −87.7809 −3.53107
\(619\) 1.00000 0.0401934
\(620\) −0.324540 −0.0130338
\(621\) −12.2824 −0.492874
\(622\) 31.1742 1.24997
\(623\) −23.7131 −0.950045
\(624\) 2.72939 0.109263
\(625\) −31.2046 −1.24819
\(626\) −37.2309 −1.48805
\(627\) −56.8229 −2.26929
\(628\) −1.71028 −0.0682477
\(629\) −12.0525 −0.480565
\(630\) 43.3597 1.72749
\(631\) −17.9210 −0.713423 −0.356711 0.934215i \(-0.616102\pi\)
−0.356711 + 0.934215i \(0.616102\pi\)
\(632\) −20.4700 −0.814252
\(633\) 35.5664 1.41364
\(634\) 34.1614 1.35672
\(635\) 22.4460 0.890743
\(636\) −2.19790 −0.0871522
\(637\) −0.974683 −0.0386183
\(638\) 45.6263 1.80636
\(639\) −56.3151 −2.22779
\(640\) −32.9452 −1.30227
\(641\) 20.3082 0.802124 0.401062 0.916051i \(-0.368641\pi\)
0.401062 + 0.916051i \(0.368641\pi\)
\(642\) −64.6646 −2.55211
\(643\) −9.94038 −0.392010 −0.196005 0.980603i \(-0.562797\pi\)
−0.196005 + 0.980603i \(0.562797\pi\)
\(644\) −0.136625 −0.00538380
\(645\) 9.80890 0.386225
\(646\) −10.8921 −0.428545
\(647\) −22.4111 −0.881070 −0.440535 0.897735i \(-0.645211\pi\)
−0.440535 + 0.897735i \(0.645211\pi\)
\(648\) −72.8984 −2.86372
\(649\) −35.8443 −1.40701
\(650\) 0.659330 0.0258611
\(651\) 4.83328 0.189431
\(652\) 1.49172 0.0584203
\(653\) 34.5540 1.35220 0.676102 0.736808i \(-0.263668\pi\)
0.676102 + 0.736808i \(0.263668\pi\)
\(654\) −52.1362 −2.03869
\(655\) 43.7942 1.71118
\(656\) −25.0267 −0.977130
\(657\) 62.8164 2.45070
\(658\) 16.3188 0.636174
\(659\) −20.8525 −0.812297 −0.406148 0.913807i \(-0.633128\pi\)
−0.406148 + 0.913807i \(0.633128\pi\)
\(660\) 4.64779 0.180915
\(661\) 30.6607 1.19256 0.596281 0.802776i \(-0.296644\pi\)
0.596281 + 0.802776i \(0.296644\pi\)
\(662\) −8.82115 −0.342844
\(663\) 1.25254 0.0486447
\(664\) −42.7040 −1.65724
\(665\) 15.0500 0.583614
\(666\) 69.2925 2.68503
\(667\) 5.63022 0.218003
\(668\) −1.22798 −0.0475121
\(669\) −23.0208 −0.890036
\(670\) 53.2379 2.05676
\(671\) 29.9179 1.15497
\(672\) −3.11510 −0.120168
\(673\) 51.4652 1.98384 0.991918 0.126879i \(-0.0404959\pi\)
0.991918 + 0.126879i \(0.0404959\pi\)
\(674\) −40.3673 −1.55489
\(675\) −34.7317 −1.33682
\(676\) −1.51785 −0.0583788
\(677\) 43.6169 1.67633 0.838166 0.545415i \(-0.183628\pi\)
0.838166 + 0.545415i \(0.183628\pi\)
\(678\) −43.7368 −1.67970
\(679\) 26.8680 1.03110
\(680\) −14.3239 −0.549297
\(681\) −50.9461 −1.95226
\(682\) 6.72829 0.257640
\(683\) 29.0416 1.11125 0.555624 0.831434i \(-0.312480\pi\)
0.555624 + 0.831434i \(0.312480\pi\)
\(684\) 3.46399 0.132449
\(685\) −40.3275 −1.54083
\(686\) 25.0168 0.955147
\(687\) −72.4344 −2.76354
\(688\) −4.69868 −0.179136
\(689\) 1.13931 0.0434041
\(690\) 10.3681 0.394708
\(691\) −31.5302 −1.19947 −0.599733 0.800200i \(-0.704726\pi\)
−0.599733 + 0.800200i \(0.704726\pi\)
\(692\) 0.0437865 0.00166451
\(693\) −49.7254 −1.88891
\(694\) 46.1550 1.75202
\(695\) 32.2763 1.22431
\(696\) 62.2495 2.35956
\(697\) −11.4850 −0.435025
\(698\) −4.00572 −0.151619
\(699\) 6.68054 0.252681
\(700\) −0.386346 −0.0146025
\(701\) 11.1053 0.419440 0.209720 0.977761i \(-0.432745\pi\)
0.209720 + 0.977761i \(0.432745\pi\)
\(702\) −4.37824 −0.165246
\(703\) 24.0512 0.907109
\(704\) 33.6854 1.26956
\(705\) −68.5036 −2.57999
\(706\) 9.72559 0.366028
\(707\) −10.4229 −0.391994
\(708\) 3.04169 0.114314
\(709\) 29.2939 1.10016 0.550079 0.835113i \(-0.314598\pi\)
0.550079 + 0.835113i \(0.314598\pi\)
\(710\) 28.9030 1.08471
\(711\) 57.1806 2.14444
\(712\) −45.0373 −1.68784
\(713\) 0.830262 0.0310936
\(714\) −13.2681 −0.496547
\(715\) −2.40923 −0.0901002
\(716\) −0.277159 −0.0103579
\(717\) −13.7067 −0.511887
\(718\) −8.05326 −0.300545
\(719\) 20.8433 0.777324 0.388662 0.921380i \(-0.372937\pi\)
0.388662 + 0.921380i \(0.372937\pi\)
\(720\) 87.1900 3.24938
\(721\) −26.6628 −0.992975
\(722\) −5.90994 −0.219945
\(723\) 26.8397 0.998180
\(724\) 2.46261 0.0915223
\(725\) 15.9210 0.591290
\(726\) −44.1174 −1.63735
\(727\) 46.8273 1.73673 0.868364 0.495927i \(-0.165172\pi\)
0.868364 + 0.495927i \(0.165172\pi\)
\(728\) 0.783024 0.0290208
\(729\) 54.9314 2.03450
\(730\) −32.2397 −1.19325
\(731\) −2.15627 −0.0797524
\(732\) −2.53879 −0.0938362
\(733\) −21.0505 −0.777518 −0.388759 0.921339i \(-0.627096\pi\)
−0.388759 + 0.921339i \(0.627096\pi\)
\(734\) 23.0918 0.852335
\(735\) −43.3417 −1.59868
\(736\) −0.535114 −0.0197246
\(737\) −61.0538 −2.24895
\(738\) 66.0297 2.43059
\(739\) 23.3449 0.858758 0.429379 0.903124i \(-0.358733\pi\)
0.429379 + 0.903124i \(0.358733\pi\)
\(740\) −1.96725 −0.0723176
\(741\) −2.49949 −0.0918210
\(742\) −12.0686 −0.443053
\(743\) −26.2395 −0.962633 −0.481316 0.876547i \(-0.659841\pi\)
−0.481316 + 0.876547i \(0.659841\pi\)
\(744\) 9.17964 0.336542
\(745\) −22.2462 −0.815038
\(746\) −44.1827 −1.61765
\(747\) 119.289 4.36456
\(748\) −1.02171 −0.0373575
\(749\) −19.6414 −0.717681
\(750\) −34.7802 −1.26999
\(751\) 24.3104 0.887100 0.443550 0.896250i \(-0.353719\pi\)
0.443550 + 0.896250i \(0.353719\pi\)
\(752\) 32.8148 1.19663
\(753\) −41.0950 −1.49759
\(754\) 2.00698 0.0730899
\(755\) 37.2660 1.35625
\(756\) 2.56550 0.0933064
\(757\) −27.6139 −1.00364 −0.501821 0.864971i \(-0.667337\pi\)
−0.501821 + 0.864971i \(0.667337\pi\)
\(758\) −39.8639 −1.44792
\(759\) −11.8903 −0.431591
\(760\) 28.5839 1.03685
\(761\) 34.0614 1.23472 0.617362 0.786680i \(-0.288202\pi\)
0.617362 + 0.786680i \(0.288202\pi\)
\(762\) 39.4886 1.43052
\(763\) −15.8360 −0.573302
\(764\) −1.59694 −0.0577754
\(765\) 40.0123 1.44665
\(766\) 18.6525 0.673942
\(767\) −1.57670 −0.0569312
\(768\) −9.14287 −0.329915
\(769\) 34.9720 1.26112 0.630562 0.776139i \(-0.282824\pi\)
0.630562 + 0.776139i \(0.282824\pi\)
\(770\) 25.5209 0.919711
\(771\) 53.4757 1.92588
\(772\) 0.355280 0.0127868
\(773\) −28.9546 −1.04142 −0.520712 0.853732i \(-0.674334\pi\)
−0.520712 + 0.853732i \(0.674334\pi\)
\(774\) 12.3968 0.445595
\(775\) 2.34779 0.0843351
\(776\) 51.0293 1.83185
\(777\) 29.2977 1.05105
\(778\) 46.3964 1.66339
\(779\) 22.9187 0.821147
\(780\) 0.204444 0.00732027
\(781\) −33.1463 −1.18607
\(782\) −2.27920 −0.0815042
\(783\) −105.722 −3.77820
\(784\) 20.7616 0.741487
\(785\) 39.4224 1.40705
\(786\) 77.0457 2.74813
\(787\) −10.9034 −0.388663 −0.194331 0.980936i \(-0.562254\pi\)
−0.194331 + 0.980936i \(0.562254\pi\)
\(788\) 1.25584 0.0447375
\(789\) 14.3784 0.511886
\(790\) −29.3472 −1.04413
\(791\) −13.2847 −0.472350
\(792\) −94.4414 −3.35583
\(793\) 1.31601 0.0467329
\(794\) −7.68150 −0.272606
\(795\) 50.6620 1.79680
\(796\) 2.72204 0.0964801
\(797\) −19.1652 −0.678865 −0.339433 0.940630i \(-0.610235\pi\)
−0.339433 + 0.940630i \(0.610235\pi\)
\(798\) 26.4770 0.937276
\(799\) 15.0590 0.532749
\(800\) −1.51318 −0.0534990
\(801\) 125.807 4.44516
\(802\) 24.2226 0.855330
\(803\) 36.9729 1.30475
\(804\) 5.18094 0.182718
\(805\) 3.14925 0.110996
\(806\) 0.295960 0.0104247
\(807\) 39.5826 1.39337
\(808\) −19.7958 −0.696413
\(809\) −5.88096 −0.206764 −0.103382 0.994642i \(-0.532966\pi\)
−0.103382 + 0.994642i \(0.532966\pi\)
\(810\) −104.512 −3.67219
\(811\) 1.76023 0.0618101 0.0309051 0.999522i \(-0.490161\pi\)
0.0309051 + 0.999522i \(0.490161\pi\)
\(812\) −1.17602 −0.0412704
\(813\) 49.3871 1.73208
\(814\) 40.7847 1.42950
\(815\) −34.3845 −1.20444
\(816\) −26.6803 −0.933997
\(817\) 4.30290 0.150540
\(818\) −51.4911 −1.80034
\(819\) −2.18729 −0.0764301
\(820\) −1.87462 −0.0654645
\(821\) −33.0842 −1.15465 −0.577323 0.816516i \(-0.695903\pi\)
−0.577323 + 0.816516i \(0.695903\pi\)
\(822\) −70.9469 −2.47456
\(823\) 6.54633 0.228191 0.114095 0.993470i \(-0.463603\pi\)
0.114095 + 0.993470i \(0.463603\pi\)
\(824\) −50.6396 −1.76411
\(825\) −33.6231 −1.17061
\(826\) 16.7019 0.581133
\(827\) −0.130403 −0.00453456 −0.00226728 0.999997i \(-0.500722\pi\)
−0.00226728 + 0.999997i \(0.500722\pi\)
\(828\) 0.724848 0.0251902
\(829\) 18.1137 0.629114 0.314557 0.949239i \(-0.398144\pi\)
0.314557 + 0.949239i \(0.398144\pi\)
\(830\) −61.2235 −2.12510
\(831\) −79.2511 −2.74919
\(832\) 1.48173 0.0513698
\(833\) 9.52770 0.330115
\(834\) 56.7827 1.96622
\(835\) 28.3053 0.979544
\(836\) 2.03886 0.0705155
\(837\) −15.5904 −0.538881
\(838\) −4.35918 −0.150585
\(839\) 27.5593 0.951452 0.475726 0.879594i \(-0.342185\pi\)
0.475726 + 0.879594i \(0.342185\pi\)
\(840\) 34.8191 1.20137
\(841\) 19.4630 0.671136
\(842\) −33.3329 −1.14873
\(843\) 80.4419 2.77057
\(844\) −1.27616 −0.0439271
\(845\) 34.9868 1.20358
\(846\) −86.5774 −2.97659
\(847\) −13.4004 −0.460442
\(848\) −24.2682 −0.833375
\(849\) −5.37932 −0.184618
\(850\) −6.44507 −0.221064
\(851\) 5.03277 0.172521
\(852\) 2.81275 0.0963631
\(853\) −40.3891 −1.38290 −0.691448 0.722427i \(-0.743027\pi\)
−0.691448 + 0.722427i \(0.743027\pi\)
\(854\) −13.9404 −0.477032
\(855\) −79.8458 −2.73067
\(856\) −37.3041 −1.27503
\(857\) 35.8393 1.22425 0.612124 0.790762i \(-0.290316\pi\)
0.612124 + 0.790762i \(0.290316\pi\)
\(858\) −4.23849 −0.144700
\(859\) 32.2117 1.09905 0.549525 0.835477i \(-0.314809\pi\)
0.549525 + 0.835477i \(0.314809\pi\)
\(860\) −0.351953 −0.0120015
\(861\) 27.9181 0.951448
\(862\) 49.4879 1.68557
\(863\) −21.6667 −0.737544 −0.368772 0.929520i \(-0.620222\pi\)
−0.368772 + 0.929520i \(0.620222\pi\)
\(864\) 10.0482 0.341846
\(865\) −1.00929 −0.0343168
\(866\) 11.4270 0.388305
\(867\) 43.2422 1.46858
\(868\) −0.173423 −0.00588635
\(869\) 33.6557 1.14169
\(870\) 89.2453 3.02570
\(871\) −2.68560 −0.0909981
\(872\) −30.0767 −1.01852
\(873\) −142.545 −4.82441
\(874\) 4.54823 0.153846
\(875\) −10.5642 −0.357136
\(876\) −3.13746 −0.106005
\(877\) 33.9945 1.14791 0.573957 0.818886i \(-0.305408\pi\)
0.573957 + 0.818886i \(0.305408\pi\)
\(878\) −12.3672 −0.417374
\(879\) 4.02465 0.135748
\(880\) 51.3189 1.72996
\(881\) 17.3024 0.582932 0.291466 0.956581i \(-0.405857\pi\)
0.291466 + 0.956581i \(0.405857\pi\)
\(882\) −54.7768 −1.84443
\(883\) −41.4804 −1.39593 −0.697963 0.716134i \(-0.745910\pi\)
−0.697963 + 0.716134i \(0.745910\pi\)
\(884\) −0.0449424 −0.00151158
\(885\) −70.1117 −2.35678
\(886\) 0.774283 0.0260126
\(887\) 20.6409 0.693053 0.346526 0.938040i \(-0.387361\pi\)
0.346526 + 0.938040i \(0.387361\pi\)
\(888\) 55.6439 1.86729
\(889\) 11.9944 0.402278
\(890\) −64.5687 −2.16435
\(891\) 119.856 4.01533
\(892\) 0.826010 0.0276569
\(893\) −30.0507 −1.00561
\(894\) −39.1371 −1.30894
\(895\) 6.38857 0.213546
\(896\) −17.6048 −0.588134
\(897\) −0.523024 −0.0174633
\(898\) −16.1272 −0.538173
\(899\) 7.14660 0.238353
\(900\) 2.04971 0.0683235
\(901\) −11.1369 −0.371024
\(902\) 38.8642 1.29404
\(903\) 5.24153 0.174427
\(904\) −25.2311 −0.839175
\(905\) −56.7638 −1.88689
\(906\) 65.5609 2.17812
\(907\) 12.8852 0.427846 0.213923 0.976851i \(-0.431376\pi\)
0.213923 + 0.976851i \(0.431376\pi\)
\(908\) 1.82800 0.0606642
\(909\) 55.2973 1.83410
\(910\) 1.12260 0.0372138
\(911\) 32.6028 1.08018 0.540089 0.841608i \(-0.318391\pi\)
0.540089 + 0.841608i \(0.318391\pi\)
\(912\) 53.2414 1.76300
\(913\) 70.2119 2.32368
\(914\) 47.5791 1.57378
\(915\) 58.5196 1.93460
\(916\) 2.59902 0.0858740
\(917\) 23.4021 0.772805
\(918\) 42.7981 1.41255
\(919\) −54.1757 −1.78709 −0.893545 0.448973i \(-0.851790\pi\)
−0.893545 + 0.448973i \(0.851790\pi\)
\(920\) 5.98124 0.197196
\(921\) −8.52412 −0.280879
\(922\) −15.0526 −0.495730
\(923\) −1.45802 −0.0479913
\(924\) 2.48361 0.0817049
\(925\) 14.2315 0.467930
\(926\) 8.14868 0.267782
\(927\) 141.456 4.64602
\(928\) −4.60607 −0.151202
\(929\) −9.40444 −0.308550 −0.154275 0.988028i \(-0.549304\pi\)
−0.154275 + 0.988028i \(0.549304\pi\)
\(930\) 13.1606 0.431553
\(931\) −19.0128 −0.623121
\(932\) −0.239705 −0.00785178
\(933\) −69.9291 −2.28938
\(934\) 24.7200 0.808864
\(935\) 23.5507 0.770190
\(936\) −4.15423 −0.135785
\(937\) −26.6094 −0.869292 −0.434646 0.900601i \(-0.643126\pi\)
−0.434646 + 0.900601i \(0.643126\pi\)
\(938\) 28.4485 0.928875
\(939\) 83.5154 2.72542
\(940\) 2.45798 0.0801704
\(941\) 46.7143 1.52284 0.761422 0.648257i \(-0.224502\pi\)
0.761422 + 0.648257i \(0.224502\pi\)
\(942\) 69.3546 2.25969
\(943\) 4.79579 0.156172
\(944\) 33.5851 1.09310
\(945\) −59.1354 −1.92368
\(946\) 7.29662 0.237234
\(947\) −46.1737 −1.50044 −0.750221 0.661187i \(-0.770053\pi\)
−0.750221 + 0.661187i \(0.770053\pi\)
\(948\) −2.85597 −0.0927577
\(949\) 1.62634 0.0527933
\(950\) 12.8614 0.417277
\(951\) −76.6299 −2.48490
\(952\) −7.65420 −0.248074
\(953\) 43.7291 1.41653 0.708263 0.705949i \(-0.249479\pi\)
0.708263 + 0.705949i \(0.249479\pi\)
\(954\) 64.0285 2.07300
\(955\) 36.8099 1.19114
\(956\) 0.491811 0.0159063
\(957\) −102.348 −3.30843
\(958\) −23.2872 −0.752374
\(959\) −21.5496 −0.695873
\(960\) 65.8888 2.12655
\(961\) −29.9461 −0.966004
\(962\) 1.79401 0.0578412
\(963\) 104.205 3.35796
\(964\) −0.963036 −0.0310173
\(965\) −8.18927 −0.263622
\(966\) 5.54037 0.178259
\(967\) −6.19072 −0.199080 −0.0995400 0.995034i \(-0.531737\pi\)
−0.0995400 + 0.995034i \(0.531737\pi\)
\(968\) −25.4507 −0.818018
\(969\) 24.4329 0.784899
\(970\) 73.1592 2.34900
\(971\) −18.1743 −0.583240 −0.291620 0.956534i \(-0.594194\pi\)
−0.291620 + 0.956534i \(0.594194\pi\)
\(972\) −4.83522 −0.155090
\(973\) 17.2473 0.552924
\(974\) 14.2077 0.455244
\(975\) −1.47899 −0.0473656
\(976\) −28.0322 −0.897289
\(977\) −33.3552 −1.06713 −0.533563 0.845760i \(-0.679147\pi\)
−0.533563 + 0.845760i \(0.679147\pi\)
\(978\) −60.4916 −1.93431
\(979\) 74.0482 2.36659
\(980\) 1.55514 0.0496772
\(981\) 84.0158 2.68242
\(982\) −11.6734 −0.372514
\(983\) 27.2974 0.870651 0.435325 0.900273i \(-0.356633\pi\)
0.435325 + 0.900273i \(0.356633\pi\)
\(984\) 53.0238 1.69034
\(985\) −28.9474 −0.922341
\(986\) −19.6186 −0.624783
\(987\) −36.6059 −1.16518
\(988\) 0.0896841 0.00285323
\(989\) 0.900393 0.0286308
\(990\) −135.398 −4.30323
\(991\) −10.0739 −0.320007 −0.160003 0.987116i \(-0.551150\pi\)
−0.160003 + 0.987116i \(0.551150\pi\)
\(992\) −0.679236 −0.0215658
\(993\) 19.7874 0.627933
\(994\) 15.4448 0.489878
\(995\) −62.7436 −1.98911
\(996\) −5.95808 −0.188789
\(997\) −47.1640 −1.49370 −0.746850 0.664992i \(-0.768435\pi\)
−0.746850 + 0.664992i \(0.768435\pi\)
\(998\) 16.1680 0.511788
\(999\) −94.5035 −2.98996
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 \(a_p\))