Properties

Label 8041.2.a.g.1.17
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.71913 q^{2} +3.18493 q^{3} +0.955421 q^{4} -4.00741 q^{5} -5.47533 q^{6} -0.822562 q^{7} +1.79577 q^{8} +7.14381 q^{9} +O(q^{10})\) \(q-1.71913 q^{2} +3.18493 q^{3} +0.955421 q^{4} -4.00741 q^{5} -5.47533 q^{6} -0.822562 q^{7} +1.79577 q^{8} +7.14381 q^{9} +6.88927 q^{10} -1.00000 q^{11} +3.04295 q^{12} -6.89242 q^{13} +1.41409 q^{14} -12.7633 q^{15} -4.99801 q^{16} +1.00000 q^{17} -12.2812 q^{18} +4.72993 q^{19} -3.82876 q^{20} -2.61981 q^{21} +1.71913 q^{22} -3.39021 q^{23} +5.71941 q^{24} +11.0593 q^{25} +11.8490 q^{26} +13.1978 q^{27} -0.785893 q^{28} +8.69009 q^{29} +21.9419 q^{30} -8.91260 q^{31} +5.00071 q^{32} -3.18493 q^{33} -1.71913 q^{34} +3.29634 q^{35} +6.82535 q^{36} +5.10906 q^{37} -8.13138 q^{38} -21.9519 q^{39} -7.19639 q^{40} +7.65390 q^{41} +4.50380 q^{42} +1.00000 q^{43} -0.955421 q^{44} -28.6282 q^{45} +5.82822 q^{46} +8.72236 q^{47} -15.9183 q^{48} -6.32339 q^{49} -19.0124 q^{50} +3.18493 q^{51} -6.58516 q^{52} -13.0580 q^{53} -22.6887 q^{54} +4.00741 q^{55} -1.47713 q^{56} +15.0645 q^{57} -14.9394 q^{58} +10.4689 q^{59} -12.1944 q^{60} +3.72905 q^{61} +15.3219 q^{62} -5.87623 q^{63} +1.39913 q^{64} +27.6207 q^{65} +5.47533 q^{66} +7.77990 q^{67} +0.955421 q^{68} -10.7976 q^{69} -5.66685 q^{70} -3.49805 q^{71} +12.8286 q^{72} -14.7520 q^{73} -8.78315 q^{74} +35.2232 q^{75} +4.51907 q^{76} +0.822562 q^{77} +37.7383 q^{78} +7.74481 q^{79} +20.0291 q^{80} +20.6026 q^{81} -13.1581 q^{82} -5.25584 q^{83} -2.50302 q^{84} -4.00741 q^{85} -1.71913 q^{86} +27.6774 q^{87} -1.79577 q^{88} -4.17801 q^{89} +49.2156 q^{90} +5.66944 q^{91} -3.23907 q^{92} -28.3860 q^{93} -14.9949 q^{94} -18.9547 q^{95} +15.9269 q^{96} +8.41756 q^{97} +10.8708 q^{98} -7.14381 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.71913 −1.21561 −0.607806 0.794086i \(-0.707950\pi\)
−0.607806 + 0.794086i \(0.707950\pi\)
\(3\) 3.18493 1.83882 0.919412 0.393297i \(-0.128666\pi\)
0.919412 + 0.393297i \(0.128666\pi\)
\(4\) 0.955421 0.477711
\(5\) −4.00741 −1.79217 −0.896084 0.443885i \(-0.853600\pi\)
−0.896084 + 0.443885i \(0.853600\pi\)
\(6\) −5.47533 −2.23529
\(7\) −0.822562 −0.310899 −0.155450 0.987844i \(-0.549683\pi\)
−0.155450 + 0.987844i \(0.549683\pi\)
\(8\) 1.79577 0.634901
\(9\) 7.14381 2.38127
\(10\) 6.88927 2.17858
\(11\) −1.00000 −0.301511
\(12\) 3.04295 0.878425
\(13\) −6.89242 −1.91161 −0.955806 0.293997i \(-0.905015\pi\)
−0.955806 + 0.293997i \(0.905015\pi\)
\(14\) 1.41409 0.377933
\(15\) −12.7633 −3.29548
\(16\) −4.99801 −1.24950
\(17\) 1.00000 0.242536
\(18\) −12.2812 −2.89470
\(19\) 4.72993 1.08512 0.542560 0.840017i \(-0.317455\pi\)
0.542560 + 0.840017i \(0.317455\pi\)
\(20\) −3.82876 −0.856137
\(21\) −2.61981 −0.571689
\(22\) 1.71913 0.366521
\(23\) −3.39021 −0.706907 −0.353453 0.935452i \(-0.614993\pi\)
−0.353453 + 0.935452i \(0.614993\pi\)
\(24\) 5.71941 1.16747
\(25\) 11.0593 2.21186
\(26\) 11.8490 2.32378
\(27\) 13.1978 2.53991
\(28\) −0.785893 −0.148520
\(29\) 8.69009 1.61371 0.806854 0.590751i \(-0.201168\pi\)
0.806854 + 0.590751i \(0.201168\pi\)
\(30\) 21.9419 4.00602
\(31\) −8.91260 −1.60075 −0.800375 0.599500i \(-0.795366\pi\)
−0.800375 + 0.599500i \(0.795366\pi\)
\(32\) 5.00071 0.884009
\(33\) −3.18493 −0.554426
\(34\) −1.71913 −0.294829
\(35\) 3.29634 0.557183
\(36\) 6.82535 1.13756
\(37\) 5.10906 0.839924 0.419962 0.907542i \(-0.362043\pi\)
0.419962 + 0.907542i \(0.362043\pi\)
\(38\) −8.13138 −1.31908
\(39\) −21.9519 −3.51512
\(40\) −7.19639 −1.13785
\(41\) 7.65390 1.19534 0.597669 0.801743i \(-0.296094\pi\)
0.597669 + 0.801743i \(0.296094\pi\)
\(42\) 4.50380 0.694951
\(43\) 1.00000 0.152499
\(44\) −0.955421 −0.144035
\(45\) −28.6282 −4.26763
\(46\) 5.82822 0.859324
\(47\) 8.72236 1.27229 0.636144 0.771571i \(-0.280529\pi\)
0.636144 + 0.771571i \(0.280529\pi\)
\(48\) −15.9183 −2.29762
\(49\) −6.32339 −0.903342
\(50\) −19.0124 −2.68877
\(51\) 3.18493 0.445980
\(52\) −6.58516 −0.913198
\(53\) −13.0580 −1.79365 −0.896827 0.442381i \(-0.854134\pi\)
−0.896827 + 0.442381i \(0.854134\pi\)
\(54\) −22.6887 −3.08754
\(55\) 4.00741 0.540359
\(56\) −1.47713 −0.197390
\(57\) 15.0645 1.99534
\(58\) −14.9394 −1.96164
\(59\) 10.4689 1.36293 0.681466 0.731850i \(-0.261343\pi\)
0.681466 + 0.731850i \(0.261343\pi\)
\(60\) −12.1944 −1.57428
\(61\) 3.72905 0.477456 0.238728 0.971086i \(-0.423270\pi\)
0.238728 + 0.971086i \(0.423270\pi\)
\(62\) 15.3219 1.94589
\(63\) −5.87623 −0.740335
\(64\) 1.39913 0.174892
\(65\) 27.6207 3.42593
\(66\) 5.47533 0.673966
\(67\) 7.77990 0.950466 0.475233 0.879860i \(-0.342364\pi\)
0.475233 + 0.879860i \(0.342364\pi\)
\(68\) 0.955421 0.115862
\(69\) −10.7976 −1.29988
\(70\) −5.66685 −0.677318
\(71\) −3.49805 −0.415142 −0.207571 0.978220i \(-0.566556\pi\)
−0.207571 + 0.978220i \(0.566556\pi\)
\(72\) 12.8286 1.51187
\(73\) −14.7520 −1.72659 −0.863294 0.504701i \(-0.831603\pi\)
−0.863294 + 0.504701i \(0.831603\pi\)
\(74\) −8.78315 −1.02102
\(75\) 35.2232 4.06723
\(76\) 4.51907 0.518373
\(77\) 0.822562 0.0937396
\(78\) 37.7383 4.27302
\(79\) 7.74481 0.871359 0.435679 0.900102i \(-0.356508\pi\)
0.435679 + 0.900102i \(0.356508\pi\)
\(80\) 20.0291 2.23932
\(81\) 20.6026 2.28918
\(82\) −13.1581 −1.45307
\(83\) −5.25584 −0.576904 −0.288452 0.957494i \(-0.593141\pi\)
−0.288452 + 0.957494i \(0.593141\pi\)
\(84\) −2.50302 −0.273102
\(85\) −4.00741 −0.434664
\(86\) −1.71913 −0.185379
\(87\) 27.6774 2.96732
\(88\) −1.79577 −0.191430
\(89\) −4.17801 −0.442869 −0.221434 0.975175i \(-0.571074\pi\)
−0.221434 + 0.975175i \(0.571074\pi\)
\(90\) 49.2156 5.18778
\(91\) 5.66944 0.594319
\(92\) −3.23907 −0.337697
\(93\) −28.3860 −2.94350
\(94\) −14.9949 −1.54661
\(95\) −18.9547 −1.94472
\(96\) 15.9269 1.62554
\(97\) 8.41756 0.854674 0.427337 0.904093i \(-0.359452\pi\)
0.427337 + 0.904093i \(0.359452\pi\)
\(98\) 10.8708 1.09811
\(99\) −7.14381 −0.717980
\(100\) 10.5663 1.05663
\(101\) 2.02705 0.201699 0.100849 0.994902i \(-0.467844\pi\)
0.100849 + 0.994902i \(0.467844\pi\)
\(102\) −5.47533 −0.542138
\(103\) 9.74029 0.959740 0.479870 0.877340i \(-0.340684\pi\)
0.479870 + 0.877340i \(0.340684\pi\)
\(104\) −12.3772 −1.21368
\(105\) 10.4986 1.02456
\(106\) 22.4485 2.18039
\(107\) −6.14529 −0.594087 −0.297044 0.954864i \(-0.596001\pi\)
−0.297044 + 0.954864i \(0.596001\pi\)
\(108\) 12.6094 1.21334
\(109\) −14.6358 −1.40186 −0.700928 0.713232i \(-0.747230\pi\)
−0.700928 + 0.713232i \(0.747230\pi\)
\(110\) −6.88927 −0.656866
\(111\) 16.2720 1.54447
\(112\) 4.11118 0.388470
\(113\) −9.45921 −0.889848 −0.444924 0.895568i \(-0.646769\pi\)
−0.444924 + 0.895568i \(0.646769\pi\)
\(114\) −25.8979 −2.42556
\(115\) 13.5859 1.26689
\(116\) 8.30269 0.770886
\(117\) −49.2381 −4.55207
\(118\) −17.9974 −1.65680
\(119\) −0.822562 −0.0754041
\(120\) −22.9200 −2.09230
\(121\) 1.00000 0.0909091
\(122\) −6.41074 −0.580401
\(123\) 24.3772 2.19802
\(124\) −8.51528 −0.764695
\(125\) −24.2822 −2.17186
\(126\) 10.1020 0.899960
\(127\) −8.10955 −0.719607 −0.359803 0.933028i \(-0.617156\pi\)
−0.359803 + 0.933028i \(0.617156\pi\)
\(128\) −12.4067 −1.09661
\(129\) 3.18493 0.280418
\(130\) −47.4837 −4.16460
\(131\) −15.6420 −1.36665 −0.683324 0.730115i \(-0.739466\pi\)
−0.683324 + 0.730115i \(0.739466\pi\)
\(132\) −3.04295 −0.264855
\(133\) −3.89066 −0.337363
\(134\) −13.3747 −1.15540
\(135\) −52.8888 −4.55195
\(136\) 1.79577 0.153986
\(137\) −7.68724 −0.656765 −0.328383 0.944545i \(-0.606504\pi\)
−0.328383 + 0.944545i \(0.606504\pi\)
\(138\) 18.5625 1.58014
\(139\) −8.01638 −0.679941 −0.339970 0.940436i \(-0.610417\pi\)
−0.339970 + 0.940436i \(0.610417\pi\)
\(140\) 3.14939 0.266172
\(141\) 27.7802 2.33951
\(142\) 6.01362 0.504651
\(143\) 6.89242 0.576373
\(144\) −35.7049 −2.97540
\(145\) −34.8247 −2.89204
\(146\) 25.3606 2.09886
\(147\) −20.1396 −1.66109
\(148\) 4.88130 0.401241
\(149\) −19.7477 −1.61780 −0.808899 0.587947i \(-0.799936\pi\)
−0.808899 + 0.587947i \(0.799936\pi\)
\(150\) −60.5534 −4.94416
\(151\) −16.9875 −1.38242 −0.691210 0.722654i \(-0.742922\pi\)
−0.691210 + 0.722654i \(0.742922\pi\)
\(152\) 8.49386 0.688943
\(153\) 7.14381 0.577543
\(154\) −1.41409 −0.113951
\(155\) 35.7164 2.86881
\(156\) −20.9733 −1.67921
\(157\) 20.1809 1.61061 0.805307 0.592858i \(-0.202001\pi\)
0.805307 + 0.592858i \(0.202001\pi\)
\(158\) −13.3144 −1.05923
\(159\) −41.5889 −3.29821
\(160\) −20.0399 −1.58429
\(161\) 2.78865 0.219777
\(162\) −35.4186 −2.78275
\(163\) 0.0456029 0.00357189 0.00178595 0.999998i \(-0.499432\pi\)
0.00178595 + 0.999998i \(0.499432\pi\)
\(164\) 7.31270 0.571026
\(165\) 12.7633 0.993624
\(166\) 9.03550 0.701291
\(167\) −11.3955 −0.881812 −0.440906 0.897553i \(-0.645343\pi\)
−0.440906 + 0.897553i \(0.645343\pi\)
\(168\) −4.70457 −0.362966
\(169\) 34.5054 2.65426
\(170\) 6.88927 0.528383
\(171\) 33.7897 2.58396
\(172\) 0.955421 0.0728502
\(173\) 2.42878 0.184657 0.0923285 0.995729i \(-0.470569\pi\)
0.0923285 + 0.995729i \(0.470569\pi\)
\(174\) −47.5811 −3.60711
\(175\) −9.09697 −0.687667
\(176\) 4.99801 0.376739
\(177\) 33.3427 2.50619
\(178\) 7.18257 0.538356
\(179\) −4.95607 −0.370434 −0.185217 0.982698i \(-0.559299\pi\)
−0.185217 + 0.982698i \(0.559299\pi\)
\(180\) −27.3520 −2.03869
\(181\) −5.24294 −0.389704 −0.194852 0.980833i \(-0.562423\pi\)
−0.194852 + 0.980833i \(0.562423\pi\)
\(182\) −9.74653 −0.722461
\(183\) 11.8768 0.877958
\(184\) −6.08803 −0.448816
\(185\) −20.4741 −1.50528
\(186\) 48.7994 3.57815
\(187\) −1.00000 −0.0731272
\(188\) 8.33353 0.607785
\(189\) −10.8560 −0.789656
\(190\) 32.5857 2.36402
\(191\) −15.8324 −1.14559 −0.572797 0.819697i \(-0.694142\pi\)
−0.572797 + 0.819697i \(0.694142\pi\)
\(192\) 4.45615 0.321595
\(193\) 24.6147 1.77181 0.885904 0.463869i \(-0.153539\pi\)
0.885904 + 0.463869i \(0.153539\pi\)
\(194\) −14.4709 −1.03895
\(195\) 87.9702 6.29968
\(196\) −6.04150 −0.431536
\(197\) −15.1604 −1.08013 −0.540066 0.841623i \(-0.681601\pi\)
−0.540066 + 0.841623i \(0.681601\pi\)
\(198\) 12.2812 0.872784
\(199\) 14.0826 0.998292 0.499146 0.866518i \(-0.333647\pi\)
0.499146 + 0.866518i \(0.333647\pi\)
\(200\) 19.8600 1.40431
\(201\) 24.7785 1.74774
\(202\) −3.48476 −0.245187
\(203\) −7.14814 −0.501701
\(204\) 3.04295 0.213049
\(205\) −30.6723 −2.14225
\(206\) −16.7449 −1.16667
\(207\) −24.2190 −1.68334
\(208\) 34.4484 2.38857
\(209\) −4.72993 −0.327176
\(210\) −18.0486 −1.24547
\(211\) 6.60856 0.454952 0.227476 0.973784i \(-0.426953\pi\)
0.227476 + 0.973784i \(0.426953\pi\)
\(212\) −12.4759 −0.856848
\(213\) −11.1411 −0.763373
\(214\) 10.5646 0.722179
\(215\) −4.00741 −0.273303
\(216\) 23.7002 1.61259
\(217\) 7.33116 0.497672
\(218\) 25.1609 1.70411
\(219\) −46.9841 −3.17489
\(220\) 3.82876 0.258135
\(221\) −6.89242 −0.463634
\(222\) −27.9738 −1.87748
\(223\) 1.94469 0.130226 0.0651129 0.997878i \(-0.479259\pi\)
0.0651129 + 0.997878i \(0.479259\pi\)
\(224\) −4.11339 −0.274838
\(225\) 79.0057 5.26704
\(226\) 16.2617 1.08171
\(227\) −13.7058 −0.909687 −0.454843 0.890571i \(-0.650305\pi\)
−0.454843 + 0.890571i \(0.650305\pi\)
\(228\) 14.3930 0.953196
\(229\) −0.639020 −0.0422276 −0.0211138 0.999777i \(-0.506721\pi\)
−0.0211138 + 0.999777i \(0.506721\pi\)
\(230\) −23.3560 −1.54005
\(231\) 2.61981 0.172371
\(232\) 15.6054 1.02454
\(233\) 4.35493 0.285301 0.142650 0.989773i \(-0.454438\pi\)
0.142650 + 0.989773i \(0.454438\pi\)
\(234\) 84.6469 5.53354
\(235\) −34.9541 −2.28015
\(236\) 10.0022 0.651087
\(237\) 24.6667 1.60227
\(238\) 1.41409 0.0916621
\(239\) −11.4300 −0.739345 −0.369673 0.929162i \(-0.620530\pi\)
−0.369673 + 0.929162i \(0.620530\pi\)
\(240\) 63.7913 4.11771
\(241\) −12.0442 −0.775834 −0.387917 0.921694i \(-0.626805\pi\)
−0.387917 + 0.921694i \(0.626805\pi\)
\(242\) −1.71913 −0.110510
\(243\) 26.0246 1.66948
\(244\) 3.56282 0.228086
\(245\) 25.3404 1.61894
\(246\) −41.9076 −2.67193
\(247\) −32.6006 −2.07433
\(248\) −16.0050 −1.01632
\(249\) −16.7395 −1.06082
\(250\) 41.7443 2.64014
\(251\) −14.8383 −0.936582 −0.468291 0.883574i \(-0.655130\pi\)
−0.468291 + 0.883574i \(0.655130\pi\)
\(252\) −5.61427 −0.353666
\(253\) 3.39021 0.213140
\(254\) 13.9414 0.874762
\(255\) −12.7633 −0.799271
\(256\) 18.5305 1.15816
\(257\) −7.91040 −0.493437 −0.246719 0.969087i \(-0.579352\pi\)
−0.246719 + 0.969087i \(0.579352\pi\)
\(258\) −5.47533 −0.340879
\(259\) −4.20252 −0.261132
\(260\) 26.3894 1.63660
\(261\) 62.0803 3.84268
\(262\) 26.8907 1.66131
\(263\) 5.76497 0.355483 0.177742 0.984077i \(-0.443121\pi\)
0.177742 + 0.984077i \(0.443121\pi\)
\(264\) −5.71941 −0.352006
\(265\) 52.3287 3.21453
\(266\) 6.68856 0.410102
\(267\) −13.3067 −0.814357
\(268\) 7.43308 0.454048
\(269\) 9.19550 0.560660 0.280330 0.959904i \(-0.409556\pi\)
0.280330 + 0.959904i \(0.409556\pi\)
\(270\) 90.9230 5.53340
\(271\) −5.83545 −0.354478 −0.177239 0.984168i \(-0.556717\pi\)
−0.177239 + 0.984168i \(0.556717\pi\)
\(272\) −4.99801 −0.303049
\(273\) 18.0568 1.09285
\(274\) 13.2154 0.798371
\(275\) −11.0593 −0.666902
\(276\) −10.3162 −0.620965
\(277\) 27.8947 1.67603 0.838015 0.545647i \(-0.183716\pi\)
0.838015 + 0.545647i \(0.183716\pi\)
\(278\) 13.7812 0.826543
\(279\) −63.6699 −3.81182
\(280\) 5.91947 0.353756
\(281\) −21.0646 −1.25661 −0.628304 0.777968i \(-0.716251\pi\)
−0.628304 + 0.777968i \(0.716251\pi\)
\(282\) −47.7578 −2.84394
\(283\) 4.24418 0.252290 0.126145 0.992012i \(-0.459740\pi\)
0.126145 + 0.992012i \(0.459740\pi\)
\(284\) −3.34211 −0.198318
\(285\) −60.3696 −3.57599
\(286\) −11.8490 −0.700645
\(287\) −6.29581 −0.371630
\(288\) 35.7241 2.10506
\(289\) 1.00000 0.0588235
\(290\) 59.8684 3.51559
\(291\) 26.8094 1.57159
\(292\) −14.0944 −0.824810
\(293\) −30.0806 −1.75733 −0.878664 0.477441i \(-0.841564\pi\)
−0.878664 + 0.477441i \(0.841564\pi\)
\(294\) 34.6227 2.01923
\(295\) −41.9531 −2.44260
\(296\) 9.17470 0.533268
\(297\) −13.1978 −0.765812
\(298\) 33.9490 1.96661
\(299\) 23.3667 1.35133
\(300\) 33.6530 1.94296
\(301\) −0.822562 −0.0474117
\(302\) 29.2037 1.68048
\(303\) 6.45601 0.370888
\(304\) −23.6402 −1.35586
\(305\) −14.9438 −0.855681
\(306\) −12.2812 −0.702068
\(307\) −1.44626 −0.0825425 −0.0412712 0.999148i \(-0.513141\pi\)
−0.0412712 + 0.999148i \(0.513141\pi\)
\(308\) 0.785893 0.0447804
\(309\) 31.0222 1.76479
\(310\) −61.4013 −3.48736
\(311\) −12.6238 −0.715829 −0.357915 0.933754i \(-0.616512\pi\)
−0.357915 + 0.933754i \(0.616512\pi\)
\(312\) −39.4206 −2.23175
\(313\) 1.27433 0.0720293 0.0360147 0.999351i \(-0.488534\pi\)
0.0360147 + 0.999351i \(0.488534\pi\)
\(314\) −34.6937 −1.95788
\(315\) 23.5484 1.32680
\(316\) 7.39955 0.416257
\(317\) −14.5937 −0.819666 −0.409833 0.912161i \(-0.634413\pi\)
−0.409833 + 0.912161i \(0.634413\pi\)
\(318\) 71.4969 4.00934
\(319\) −8.69009 −0.486551
\(320\) −5.60690 −0.313435
\(321\) −19.5723 −1.09242
\(322\) −4.79407 −0.267163
\(323\) 4.72993 0.263180
\(324\) 19.6842 1.09356
\(325\) −76.2254 −4.22823
\(326\) −0.0783974 −0.00434203
\(327\) −46.6141 −2.57776
\(328\) 13.7447 0.758921
\(329\) −7.17468 −0.395553
\(330\) −21.9419 −1.20786
\(331\) −25.7314 −1.41433 −0.707163 0.707050i \(-0.750025\pi\)
−0.707163 + 0.707050i \(0.750025\pi\)
\(332\) −5.02154 −0.275593
\(333\) 36.4981 2.00009
\(334\) 19.5904 1.07194
\(335\) −31.1772 −1.70339
\(336\) 13.0938 0.714327
\(337\) 14.2213 0.774682 0.387341 0.921937i \(-0.373394\pi\)
0.387341 + 0.921937i \(0.373394\pi\)
\(338\) −59.3194 −3.22655
\(339\) −30.1270 −1.63627
\(340\) −3.82876 −0.207644
\(341\) 8.91260 0.482644
\(342\) −58.0890 −3.14109
\(343\) 10.9593 0.591747
\(344\) 1.79577 0.0968215
\(345\) 43.2703 2.32960
\(346\) −4.17540 −0.224471
\(347\) −2.77170 −0.148793 −0.0743964 0.997229i \(-0.523703\pi\)
−0.0743964 + 0.997229i \(0.523703\pi\)
\(348\) 26.4435 1.41752
\(349\) −28.3921 −1.51980 −0.759898 0.650042i \(-0.774751\pi\)
−0.759898 + 0.650042i \(0.774751\pi\)
\(350\) 15.6389 0.835935
\(351\) −90.9645 −4.85533
\(352\) −5.00071 −0.266539
\(353\) −17.0272 −0.906268 −0.453134 0.891442i \(-0.649694\pi\)
−0.453134 + 0.891442i \(0.649694\pi\)
\(354\) −57.3206 −3.04655
\(355\) 14.0181 0.744004
\(356\) −3.99176 −0.211563
\(357\) −2.61981 −0.138655
\(358\) 8.52015 0.450304
\(359\) 21.5498 1.13735 0.568677 0.822561i \(-0.307455\pi\)
0.568677 + 0.822561i \(0.307455\pi\)
\(360\) −51.4096 −2.70952
\(361\) 3.37221 0.177485
\(362\) 9.01331 0.473729
\(363\) 3.18493 0.167166
\(364\) 5.41670 0.283912
\(365\) 59.1172 3.09434
\(366\) −20.4178 −1.06726
\(367\) 34.0951 1.77975 0.889875 0.456205i \(-0.150791\pi\)
0.889875 + 0.456205i \(0.150791\pi\)
\(368\) 16.9443 0.883282
\(369\) 54.6780 2.84642
\(370\) 35.1977 1.82984
\(371\) 10.7410 0.557646
\(372\) −27.1206 −1.40614
\(373\) −16.1783 −0.837679 −0.418840 0.908060i \(-0.637563\pi\)
−0.418840 + 0.908060i \(0.637563\pi\)
\(374\) 1.71913 0.0888943
\(375\) −77.3371 −3.99367
\(376\) 15.6634 0.807776
\(377\) −59.8957 −3.08479
\(378\) 18.6629 0.959915
\(379\) −12.5070 −0.642442 −0.321221 0.947004i \(-0.604093\pi\)
−0.321221 + 0.947004i \(0.604093\pi\)
\(380\) −18.1098 −0.929011
\(381\) −25.8284 −1.32323
\(382\) 27.2180 1.39260
\(383\) 5.89385 0.301162 0.150581 0.988598i \(-0.451886\pi\)
0.150581 + 0.988598i \(0.451886\pi\)
\(384\) −39.5146 −2.01647
\(385\) −3.29634 −0.167997
\(386\) −42.3160 −2.15383
\(387\) 7.14381 0.363140
\(388\) 8.04231 0.408287
\(389\) 27.8834 1.41375 0.706873 0.707341i \(-0.250105\pi\)
0.706873 + 0.707341i \(0.250105\pi\)
\(390\) −151.233 −7.65796
\(391\) −3.39021 −0.171450
\(392\) −11.3554 −0.573532
\(393\) −49.8188 −2.51302
\(394\) 26.0627 1.31302
\(395\) −31.0366 −1.56162
\(396\) −6.82535 −0.342987
\(397\) 24.7785 1.24360 0.621798 0.783178i \(-0.286403\pi\)
0.621798 + 0.783178i \(0.286403\pi\)
\(398\) −24.2099 −1.21353
\(399\) −12.3915 −0.620351
\(400\) −55.2746 −2.76373
\(401\) 12.0064 0.599571 0.299785 0.954007i \(-0.403085\pi\)
0.299785 + 0.954007i \(0.403085\pi\)
\(402\) −42.5975 −2.12457
\(403\) 61.4293 3.06001
\(404\) 1.93668 0.0963535
\(405\) −82.5630 −4.10259
\(406\) 12.2886 0.609873
\(407\) −5.10906 −0.253247
\(408\) 5.71941 0.283153
\(409\) 8.41052 0.415874 0.207937 0.978142i \(-0.433325\pi\)
0.207937 + 0.978142i \(0.433325\pi\)
\(410\) 52.7298 2.60414
\(411\) −24.4834 −1.20768
\(412\) 9.30608 0.458478
\(413\) −8.61131 −0.423735
\(414\) 41.6357 2.04628
\(415\) 21.0623 1.03391
\(416\) −34.4670 −1.68988
\(417\) −25.5317 −1.25029
\(418\) 8.13138 0.397719
\(419\) 0.618466 0.0302140 0.0151070 0.999886i \(-0.495191\pi\)
0.0151070 + 0.999886i \(0.495191\pi\)
\(420\) 10.0306 0.489444
\(421\) 4.69991 0.229060 0.114530 0.993420i \(-0.463464\pi\)
0.114530 + 0.993420i \(0.463464\pi\)
\(422\) −11.3610 −0.553045
\(423\) 62.3109 3.02966
\(424\) −23.4492 −1.13879
\(425\) 11.0593 0.536456
\(426\) 19.1530 0.927965
\(427\) −3.06738 −0.148441
\(428\) −5.87134 −0.283802
\(429\) 21.9519 1.05985
\(430\) 6.88927 0.332230
\(431\) 7.18414 0.346048 0.173024 0.984918i \(-0.444646\pi\)
0.173024 + 0.984918i \(0.444646\pi\)
\(432\) −65.9626 −3.17363
\(433\) −10.1282 −0.486733 −0.243366 0.969934i \(-0.578252\pi\)
−0.243366 + 0.969934i \(0.578252\pi\)
\(434\) −12.6033 −0.604975
\(435\) −110.914 −5.31794
\(436\) −13.9834 −0.669681
\(437\) −16.0354 −0.767078
\(438\) 80.7719 3.85943
\(439\) −7.68547 −0.366807 −0.183404 0.983038i \(-0.558712\pi\)
−0.183404 + 0.983038i \(0.558712\pi\)
\(440\) 7.19639 0.343074
\(441\) −45.1731 −2.15110
\(442\) 11.8490 0.563599
\(443\) −27.7559 −1.31872 −0.659361 0.751827i \(-0.729173\pi\)
−0.659361 + 0.751827i \(0.729173\pi\)
\(444\) 15.5466 0.737810
\(445\) 16.7430 0.793695
\(446\) −3.34318 −0.158304
\(447\) −62.8953 −2.97485
\(448\) −1.15087 −0.0543737
\(449\) −1.09419 −0.0516378 −0.0258189 0.999667i \(-0.508219\pi\)
−0.0258189 + 0.999667i \(0.508219\pi\)
\(450\) −135.821 −6.40268
\(451\) −7.65390 −0.360408
\(452\) −9.03753 −0.425090
\(453\) −54.1039 −2.54203
\(454\) 23.5621 1.10583
\(455\) −22.7198 −1.06512
\(456\) 27.0524 1.26685
\(457\) −28.4495 −1.33081 −0.665407 0.746481i \(-0.731742\pi\)
−0.665407 + 0.746481i \(0.731742\pi\)
\(458\) 1.09856 0.0513324
\(459\) 13.1978 0.616019
\(460\) 12.9803 0.605209
\(461\) 15.3779 0.716219 0.358110 0.933680i \(-0.383421\pi\)
0.358110 + 0.933680i \(0.383421\pi\)
\(462\) −4.50380 −0.209536
\(463\) −7.20865 −0.335014 −0.167507 0.985871i \(-0.553572\pi\)
−0.167507 + 0.985871i \(0.553572\pi\)
\(464\) −43.4332 −2.01633
\(465\) 113.754 5.27524
\(466\) −7.48671 −0.346815
\(467\) 40.6280 1.88004 0.940021 0.341118i \(-0.110806\pi\)
0.940021 + 0.341118i \(0.110806\pi\)
\(468\) −47.0431 −2.17457
\(469\) −6.39945 −0.295499
\(470\) 60.0907 2.77178
\(471\) 64.2750 2.96163
\(472\) 18.7997 0.865327
\(473\) −1.00000 −0.0459800
\(474\) −42.4054 −1.94774
\(475\) 52.3098 2.40014
\(476\) −0.785893 −0.0360214
\(477\) −93.2839 −4.27118
\(478\) 19.6497 0.898757
\(479\) −40.5934 −1.85476 −0.927380 0.374120i \(-0.877945\pi\)
−0.927380 + 0.374120i \(0.877945\pi\)
\(480\) −63.8257 −2.91323
\(481\) −35.2138 −1.60561
\(482\) 20.7056 0.943113
\(483\) 8.88168 0.404130
\(484\) 0.955421 0.0434282
\(485\) −33.7326 −1.53172
\(486\) −44.7398 −2.02944
\(487\) 1.20329 0.0545264 0.0272632 0.999628i \(-0.491321\pi\)
0.0272632 + 0.999628i \(0.491321\pi\)
\(488\) 6.69652 0.303137
\(489\) 0.145242 0.00656808
\(490\) −43.5636 −1.96800
\(491\) 20.8972 0.943079 0.471539 0.881845i \(-0.343698\pi\)
0.471539 + 0.881845i \(0.343698\pi\)
\(492\) 23.2905 1.05002
\(493\) 8.69009 0.391382
\(494\) 56.0449 2.52158
\(495\) 28.6282 1.28674
\(496\) 44.5453 2.00014
\(497\) 2.87736 0.129067
\(498\) 28.7775 1.28955
\(499\) −37.7858 −1.69152 −0.845762 0.533561i \(-0.820854\pi\)
−0.845762 + 0.533561i \(0.820854\pi\)
\(500\) −23.1997 −1.03752
\(501\) −36.2940 −1.62150
\(502\) 25.5089 1.13852
\(503\) −13.6211 −0.607336 −0.303668 0.952778i \(-0.598211\pi\)
−0.303668 + 0.952778i \(0.598211\pi\)
\(504\) −10.5524 −0.470039
\(505\) −8.12320 −0.361478
\(506\) −5.82822 −0.259096
\(507\) 109.898 4.88072
\(508\) −7.74804 −0.343764
\(509\) −0.510111 −0.0226103 −0.0113051 0.999936i \(-0.503599\pi\)
−0.0113051 + 0.999936i \(0.503599\pi\)
\(510\) 21.9419 0.971603
\(511\) 12.1344 0.536795
\(512\) −7.04305 −0.311262
\(513\) 62.4245 2.75611
\(514\) 13.5990 0.599828
\(515\) −39.0333 −1.72001
\(516\) 3.04295 0.133959
\(517\) −8.72236 −0.383609
\(518\) 7.22469 0.317435
\(519\) 7.73552 0.339551
\(520\) 49.6005 2.17513
\(521\) −15.6940 −0.687565 −0.343783 0.939049i \(-0.611708\pi\)
−0.343783 + 0.939049i \(0.611708\pi\)
\(522\) −106.724 −4.67120
\(523\) −1.90606 −0.0833462 −0.0416731 0.999131i \(-0.513269\pi\)
−0.0416731 + 0.999131i \(0.513269\pi\)
\(524\) −14.9447 −0.652862
\(525\) −28.9733 −1.26450
\(526\) −9.91076 −0.432130
\(527\) −8.91260 −0.388239
\(528\) 15.9183 0.692757
\(529\) −11.5065 −0.500283
\(530\) −89.9601 −3.90762
\(531\) 74.7877 3.24551
\(532\) −3.71722 −0.161162
\(533\) −52.7539 −2.28502
\(534\) 22.8760 0.989942
\(535\) 24.6267 1.06470
\(536\) 13.9709 0.603452
\(537\) −15.7848 −0.681163
\(538\) −15.8083 −0.681544
\(539\) 6.32339 0.272368
\(540\) −50.5311 −2.17451
\(541\) −21.0959 −0.906984 −0.453492 0.891260i \(-0.649822\pi\)
−0.453492 + 0.891260i \(0.649822\pi\)
\(542\) 10.0319 0.430908
\(543\) −16.6984 −0.716597
\(544\) 5.00071 0.214404
\(545\) 58.6516 2.51236
\(546\) −31.0421 −1.32848
\(547\) 24.6020 1.05190 0.525952 0.850514i \(-0.323709\pi\)
0.525952 + 0.850514i \(0.323709\pi\)
\(548\) −7.34455 −0.313744
\(549\) 26.6396 1.13695
\(550\) 19.0124 0.810693
\(551\) 41.1035 1.75107
\(552\) −19.3900 −0.825293
\(553\) −6.37058 −0.270905
\(554\) −47.9547 −2.03740
\(555\) −65.2086 −2.76795
\(556\) −7.65902 −0.324815
\(557\) 41.3337 1.75137 0.875683 0.482886i \(-0.160411\pi\)
0.875683 + 0.482886i \(0.160411\pi\)
\(558\) 109.457 4.63369
\(559\) −6.89242 −0.291518
\(560\) −16.4752 −0.696202
\(561\) −3.18493 −0.134468
\(562\) 36.2129 1.52755
\(563\) 1.51411 0.0638122 0.0319061 0.999491i \(-0.489842\pi\)
0.0319061 + 0.999491i \(0.489842\pi\)
\(564\) 26.5418 1.11761
\(565\) 37.9069 1.59476
\(566\) −7.29631 −0.306687
\(567\) −16.9469 −0.711703
\(568\) −6.28170 −0.263574
\(569\) −37.9906 −1.59265 −0.796324 0.604871i \(-0.793225\pi\)
−0.796324 + 0.604871i \(0.793225\pi\)
\(570\) 103.783 4.34701
\(571\) −28.3497 −1.18640 −0.593199 0.805056i \(-0.702135\pi\)
−0.593199 + 0.805056i \(0.702135\pi\)
\(572\) 6.58516 0.275339
\(573\) −50.4252 −2.10654
\(574\) 10.8233 0.451757
\(575\) −37.4934 −1.56358
\(576\) 9.99515 0.416464
\(577\) 9.59058 0.399261 0.199631 0.979871i \(-0.436026\pi\)
0.199631 + 0.979871i \(0.436026\pi\)
\(578\) −1.71913 −0.0715065
\(579\) 78.3963 3.25804
\(580\) −33.2723 −1.38156
\(581\) 4.32326 0.179359
\(582\) −46.0889 −1.91045
\(583\) 13.0580 0.540807
\(584\) −26.4912 −1.09621
\(585\) 197.317 8.15806
\(586\) 51.7126 2.13623
\(587\) 10.5657 0.436094 0.218047 0.975938i \(-0.430031\pi\)
0.218047 + 0.975938i \(0.430031\pi\)
\(588\) −19.2418 −0.793518
\(589\) −42.1559 −1.73700
\(590\) 72.1230 2.96926
\(591\) −48.2848 −1.98617
\(592\) −25.5351 −1.04949
\(593\) −26.1162 −1.07247 −0.536233 0.844070i \(-0.680153\pi\)
−0.536233 + 0.844070i \(0.680153\pi\)
\(594\) 22.6887 0.930930
\(595\) 3.29634 0.135137
\(596\) −18.8674 −0.772839
\(597\) 44.8523 1.83568
\(598\) −40.1705 −1.64269
\(599\) −48.0725 −1.96419 −0.982094 0.188394i \(-0.939672\pi\)
−0.982094 + 0.188394i \(0.939672\pi\)
\(600\) 63.2528 2.58229
\(601\) −44.8799 −1.83069 −0.915344 0.402672i \(-0.868082\pi\)
−0.915344 + 0.402672i \(0.868082\pi\)
\(602\) 1.41409 0.0576342
\(603\) 55.5782 2.26332
\(604\) −16.2302 −0.660396
\(605\) −4.00741 −0.162924
\(606\) −11.0987 −0.450856
\(607\) −21.6854 −0.880184 −0.440092 0.897953i \(-0.645054\pi\)
−0.440092 + 0.897953i \(0.645054\pi\)
\(608\) 23.6530 0.959256
\(609\) −22.7663 −0.922539
\(610\) 25.6905 1.04018
\(611\) −60.1182 −2.43212
\(612\) 6.82535 0.275898
\(613\) 7.97223 0.321995 0.160998 0.986955i \(-0.448529\pi\)
0.160998 + 0.986955i \(0.448529\pi\)
\(614\) 2.48632 0.100340
\(615\) −97.6893 −3.93921
\(616\) 1.47713 0.0595154
\(617\) 9.21159 0.370845 0.185422 0.982659i \(-0.440635\pi\)
0.185422 + 0.982659i \(0.440635\pi\)
\(618\) −53.3313 −2.14530
\(619\) −12.7248 −0.511451 −0.255726 0.966749i \(-0.582314\pi\)
−0.255726 + 0.966749i \(0.582314\pi\)
\(620\) 34.1242 1.37046
\(621\) −44.7431 −1.79548
\(622\) 21.7020 0.870170
\(623\) 3.43668 0.137688
\(624\) 109.716 4.39215
\(625\) 42.0119 1.68048
\(626\) −2.19074 −0.0875596
\(627\) −15.0645 −0.601619
\(628\) 19.2813 0.769407
\(629\) 5.10906 0.203711
\(630\) −40.4829 −1.61288
\(631\) 3.09587 0.123245 0.0616223 0.998100i \(-0.480373\pi\)
0.0616223 + 0.998100i \(0.480373\pi\)
\(632\) 13.9079 0.553227
\(633\) 21.0478 0.836577
\(634\) 25.0886 0.996395
\(635\) 32.4983 1.28966
\(636\) −39.7349 −1.57559
\(637\) 43.5835 1.72684
\(638\) 14.9394 0.591457
\(639\) −24.9894 −0.988565
\(640\) 49.7188 1.96531
\(641\) 5.51031 0.217644 0.108822 0.994061i \(-0.465292\pi\)
0.108822 + 0.994061i \(0.465292\pi\)
\(642\) 33.6475 1.32796
\(643\) −27.0367 −1.06622 −0.533112 0.846044i \(-0.678978\pi\)
−0.533112 + 0.846044i \(0.678978\pi\)
\(644\) 2.66434 0.104990
\(645\) −12.7633 −0.502556
\(646\) −8.13138 −0.319925
\(647\) 46.5177 1.82880 0.914400 0.404811i \(-0.132663\pi\)
0.914400 + 0.404811i \(0.132663\pi\)
\(648\) 36.9975 1.45340
\(649\) −10.4689 −0.410940
\(650\) 131.042 5.13988
\(651\) 23.3493 0.915130
\(652\) 0.0435699 0.00170633
\(653\) 32.1229 1.25707 0.628533 0.777783i \(-0.283656\pi\)
0.628533 + 0.777783i \(0.283656\pi\)
\(654\) 80.1358 3.13356
\(655\) 62.6839 2.44926
\(656\) −38.2543 −1.49358
\(657\) −105.385 −4.11147
\(658\) 12.3342 0.480839
\(659\) 12.8047 0.498801 0.249400 0.968400i \(-0.419766\pi\)
0.249400 + 0.968400i \(0.419766\pi\)
\(660\) 12.1944 0.474665
\(661\) 36.9761 1.43820 0.719101 0.694905i \(-0.244554\pi\)
0.719101 + 0.694905i \(0.244554\pi\)
\(662\) 44.2358 1.71927
\(663\) −21.9519 −0.852541
\(664\) −9.43829 −0.366277
\(665\) 15.5915 0.604611
\(666\) −62.7452 −2.43133
\(667\) −29.4612 −1.14074
\(668\) −10.8875 −0.421251
\(669\) 6.19370 0.239462
\(670\) 53.5979 2.07067
\(671\) −3.72905 −0.143958
\(672\) −13.1009 −0.505378
\(673\) 34.5176 1.33055 0.665277 0.746596i \(-0.268313\pi\)
0.665277 + 0.746596i \(0.268313\pi\)
\(674\) −24.4483 −0.941712
\(675\) 145.958 5.61794
\(676\) 32.9672 1.26797
\(677\) 18.5221 0.711863 0.355932 0.934512i \(-0.384164\pi\)
0.355932 + 0.934512i \(0.384164\pi\)
\(678\) 51.7923 1.98907
\(679\) −6.92396 −0.265717
\(680\) −7.19639 −0.275969
\(681\) −43.6521 −1.67275
\(682\) −15.3219 −0.586708
\(683\) −26.6500 −1.01974 −0.509868 0.860253i \(-0.670306\pi\)
−0.509868 + 0.860253i \(0.670306\pi\)
\(684\) 32.2834 1.23439
\(685\) 30.8059 1.17703
\(686\) −18.8405 −0.719335
\(687\) −2.03524 −0.0776491
\(688\) −4.99801 −0.190547
\(689\) 90.0012 3.42877
\(690\) −74.3875 −2.83188
\(691\) −38.0756 −1.44846 −0.724232 0.689557i \(-0.757805\pi\)
−0.724232 + 0.689557i \(0.757805\pi\)
\(692\) 2.32051 0.0882126
\(693\) 5.87623 0.223219
\(694\) 4.76493 0.180874
\(695\) 32.1249 1.21857
\(696\) 49.7022 1.88396
\(697\) 7.65390 0.289912
\(698\) 48.8099 1.84748
\(699\) 13.8702 0.524618
\(700\) −8.69144 −0.328506
\(701\) −18.2094 −0.687761 −0.343880 0.939013i \(-0.611742\pi\)
−0.343880 + 0.939013i \(0.611742\pi\)
\(702\) 156.380 5.90219
\(703\) 24.1655 0.911418
\(704\) −1.39913 −0.0527318
\(705\) −111.326 −4.19280
\(706\) 29.2721 1.10167
\(707\) −1.66737 −0.0627079
\(708\) 31.8563 1.19723
\(709\) 7.95631 0.298806 0.149403 0.988776i \(-0.452265\pi\)
0.149403 + 0.988776i \(0.452265\pi\)
\(710\) −24.0990 −0.904420
\(711\) 55.3274 2.07494
\(712\) −7.50276 −0.281178
\(713\) 30.2155 1.13158
\(714\) 4.50380 0.168550
\(715\) −27.6207 −1.03296
\(716\) −4.73513 −0.176960
\(717\) −36.4038 −1.35953
\(718\) −37.0470 −1.38258
\(719\) 30.9824 1.15545 0.577723 0.816233i \(-0.303941\pi\)
0.577723 + 0.816233i \(0.303941\pi\)
\(720\) 143.084 5.33242
\(721\) −8.01199 −0.298382
\(722\) −5.79728 −0.215752
\(723\) −38.3599 −1.42662
\(724\) −5.00921 −0.186166
\(725\) 96.1064 3.56930
\(726\) −5.47533 −0.203209
\(727\) 13.0988 0.485809 0.242905 0.970050i \(-0.421900\pi\)
0.242905 + 0.970050i \(0.421900\pi\)
\(728\) 10.1810 0.377334
\(729\) 21.0790 0.780702
\(730\) −101.630 −3.76151
\(731\) 1.00000 0.0369863
\(732\) 11.3473 0.419410
\(733\) −26.8523 −0.991814 −0.495907 0.868376i \(-0.665164\pi\)
−0.495907 + 0.868376i \(0.665164\pi\)
\(734\) −58.6140 −2.16348
\(735\) 80.7076 2.97694
\(736\) −16.9534 −0.624912
\(737\) −7.77990 −0.286576
\(738\) −93.9988 −3.46014
\(739\) −35.4966 −1.30576 −0.652882 0.757460i \(-0.726440\pi\)
−0.652882 + 0.757460i \(0.726440\pi\)
\(740\) −19.5614 −0.719090
\(741\) −103.831 −3.81432
\(742\) −18.4652 −0.677880
\(743\) −28.8571 −1.05866 −0.529332 0.848415i \(-0.677557\pi\)
−0.529332 + 0.848415i \(0.677557\pi\)
\(744\) −50.9748 −1.86883
\(745\) 79.1373 2.89937
\(746\) 27.8126 1.01829
\(747\) −37.5468 −1.37376
\(748\) −0.955421 −0.0349337
\(749\) 5.05488 0.184701
\(750\) 132.953 4.85475
\(751\) −10.9151 −0.398299 −0.199149 0.979969i \(-0.563818\pi\)
−0.199149 + 0.979969i \(0.563818\pi\)
\(752\) −43.5945 −1.58973
\(753\) −47.2589 −1.72221
\(754\) 102.969 3.74990
\(755\) 68.0757 2.47753
\(756\) −10.3720 −0.377227
\(757\) 4.74972 0.172632 0.0863158 0.996268i \(-0.472491\pi\)
0.0863158 + 0.996268i \(0.472491\pi\)
\(758\) 21.5012 0.780960
\(759\) 10.7976 0.391927
\(760\) −34.0384 −1.23470
\(761\) 14.5171 0.526246 0.263123 0.964762i \(-0.415248\pi\)
0.263123 + 0.964762i \(0.415248\pi\)
\(762\) 44.4025 1.60853
\(763\) 12.0389 0.435836
\(764\) −15.1266 −0.547262
\(765\) −28.6282 −1.03505
\(766\) −10.1323 −0.366096
\(767\) −72.1559 −2.60540
\(768\) 59.0186 2.12965
\(769\) −50.7644 −1.83061 −0.915306 0.402760i \(-0.868051\pi\)
−0.915306 + 0.402760i \(0.868051\pi\)
\(770\) 5.66685 0.204219
\(771\) −25.1941 −0.907344
\(772\) 23.5174 0.846411
\(773\) −5.74692 −0.206702 −0.103351 0.994645i \(-0.532957\pi\)
−0.103351 + 0.994645i \(0.532957\pi\)
\(774\) −12.2812 −0.441437
\(775\) −98.5672 −3.54064
\(776\) 15.1160 0.542633
\(777\) −13.3847 −0.480175
\(778\) −47.9353 −1.71857
\(779\) 36.2024 1.29709
\(780\) 84.0486 3.00942
\(781\) 3.49805 0.125170
\(782\) 5.82822 0.208417
\(783\) 114.690 4.09868
\(784\) 31.6044 1.12873
\(785\) −80.8732 −2.88649
\(786\) 85.6451 3.05486
\(787\) −15.8025 −0.563298 −0.281649 0.959517i \(-0.590881\pi\)
−0.281649 + 0.959517i \(0.590881\pi\)
\(788\) −14.4845 −0.515990
\(789\) 18.3611 0.653671
\(790\) 53.3561 1.89832
\(791\) 7.78079 0.276653
\(792\) −12.8286 −0.455846
\(793\) −25.7022 −0.912711
\(794\) −42.5975 −1.51173
\(795\) 166.664 5.91095
\(796\) 13.4548 0.476894
\(797\) 13.6540 0.483649 0.241825 0.970320i \(-0.422254\pi\)
0.241825 + 0.970320i \(0.422254\pi\)
\(798\) 21.3026 0.754105
\(799\) 8.72236 0.308575
\(800\) 55.3044 1.95531
\(801\) −29.8469 −1.05459
\(802\) −20.6406 −0.728845
\(803\) 14.7520 0.520586
\(804\) 23.6739 0.834914
\(805\) −11.1753 −0.393877
\(806\) −105.605 −3.71979
\(807\) 29.2871 1.03095
\(808\) 3.64011 0.128059
\(809\) −12.6313 −0.444093 −0.222046 0.975036i \(-0.571274\pi\)
−0.222046 + 0.975036i \(0.571274\pi\)
\(810\) 141.937 4.98715
\(811\) −31.7960 −1.11651 −0.558253 0.829670i \(-0.688528\pi\)
−0.558253 + 0.829670i \(0.688528\pi\)
\(812\) −6.82948 −0.239668
\(813\) −18.5855 −0.651823
\(814\) 8.78315 0.307849
\(815\) −0.182749 −0.00640143
\(816\) −15.9183 −0.557254
\(817\) 4.72993 0.165479
\(818\) −14.4588 −0.505541
\(819\) 40.5014 1.41523
\(820\) −29.3050 −1.02337
\(821\) −19.5069 −0.680797 −0.340398 0.940281i \(-0.610562\pi\)
−0.340398 + 0.940281i \(0.610562\pi\)
\(822\) 42.0902 1.46806
\(823\) 26.4286 0.921244 0.460622 0.887596i \(-0.347626\pi\)
0.460622 + 0.887596i \(0.347626\pi\)
\(824\) 17.4913 0.609339
\(825\) −35.2232 −1.22631
\(826\) 14.8040 0.515097
\(827\) 26.1691 0.909990 0.454995 0.890494i \(-0.349641\pi\)
0.454995 + 0.890494i \(0.349641\pi\)
\(828\) −23.1393 −0.804147
\(829\) 25.8391 0.897430 0.448715 0.893675i \(-0.351882\pi\)
0.448715 + 0.893675i \(0.351882\pi\)
\(830\) −36.2089 −1.25683
\(831\) 88.8428 3.08192
\(832\) −9.64342 −0.334325
\(833\) −6.32339 −0.219093
\(834\) 43.8923 1.51987
\(835\) 45.6665 1.58036
\(836\) −4.51907 −0.156295
\(837\) −117.626 −4.06576
\(838\) −1.06323 −0.0367285
\(839\) 8.37733 0.289218 0.144609 0.989489i \(-0.453808\pi\)
0.144609 + 0.989489i \(0.453808\pi\)
\(840\) 18.8531 0.650495
\(841\) 46.5176 1.60406
\(842\) −8.07978 −0.278448
\(843\) −67.0894 −2.31068
\(844\) 6.31396 0.217336
\(845\) −138.277 −4.75688
\(846\) −107.121 −3.68289
\(847\) −0.822562 −0.0282636
\(848\) 65.2641 2.24118
\(849\) 13.5174 0.463917
\(850\) −19.0124 −0.652122
\(851\) −17.3208 −0.593748
\(852\) −10.6444 −0.364671
\(853\) 19.3539 0.662666 0.331333 0.943514i \(-0.392502\pi\)
0.331333 + 0.943514i \(0.392502\pi\)
\(854\) 5.27323 0.180446
\(855\) −135.409 −4.63089
\(856\) −11.0355 −0.377186
\(857\) −9.21330 −0.314720 −0.157360 0.987541i \(-0.550298\pi\)
−0.157360 + 0.987541i \(0.550298\pi\)
\(858\) −37.7383 −1.28836
\(859\) −34.4835 −1.17656 −0.588281 0.808656i \(-0.700195\pi\)
−0.588281 + 0.808656i \(0.700195\pi\)
\(860\) −3.82876 −0.130560
\(861\) −20.0517 −0.683361
\(862\) −12.3505 −0.420660
\(863\) −41.1491 −1.40073 −0.700365 0.713784i \(-0.746980\pi\)
−0.700365 + 0.713784i \(0.746980\pi\)
\(864\) 65.9982 2.24530
\(865\) −9.73312 −0.330936
\(866\) 17.4118 0.591678
\(867\) 3.18493 0.108166
\(868\) 7.00435 0.237743
\(869\) −7.74481 −0.262725
\(870\) 190.677 6.46455
\(871\) −53.6223 −1.81692
\(872\) −26.2825 −0.890039
\(873\) 60.1334 2.03521
\(874\) 27.5670 0.932469
\(875\) 19.9736 0.675230
\(876\) −44.8896 −1.51668
\(877\) 10.9195 0.368726 0.184363 0.982858i \(-0.440978\pi\)
0.184363 + 0.982858i \(0.440978\pi\)
\(878\) 13.2123 0.445895
\(879\) −95.8048 −3.23141
\(880\) −20.0291 −0.675180
\(881\) −29.1905 −0.983452 −0.491726 0.870750i \(-0.663634\pi\)
−0.491726 + 0.870750i \(0.663634\pi\)
\(882\) 77.6586 2.61490
\(883\) 12.1443 0.408688 0.204344 0.978899i \(-0.434494\pi\)
0.204344 + 0.978899i \(0.434494\pi\)
\(884\) −6.58516 −0.221483
\(885\) −133.618 −4.49151
\(886\) 47.7161 1.60305
\(887\) 27.7654 0.932272 0.466136 0.884713i \(-0.345646\pi\)
0.466136 + 0.884713i \(0.345646\pi\)
\(888\) 29.2208 0.980586
\(889\) 6.67061 0.223725
\(890\) −28.7835 −0.964824
\(891\) −20.6026 −0.690213
\(892\) 1.85800 0.0622103
\(893\) 41.2561 1.38058
\(894\) 108.125 3.61626
\(895\) 19.8610 0.663880
\(896\) 10.2053 0.340935
\(897\) 74.4215 2.48486
\(898\) 1.88105 0.0627715
\(899\) −77.4512 −2.58314
\(900\) 75.4837 2.51612
\(901\) −13.0580 −0.435025
\(902\) 13.1581 0.438116
\(903\) −2.61981 −0.0871817
\(904\) −16.9866 −0.564965
\(905\) 21.0106 0.698416
\(906\) 93.0119 3.09011
\(907\) 49.3816 1.63969 0.819844 0.572587i \(-0.194060\pi\)
0.819844 + 0.572587i \(0.194060\pi\)
\(908\) −13.0948 −0.434567
\(909\) 14.4808 0.480299
\(910\) 39.0583 1.29477
\(911\) −5.46742 −0.181144 −0.0905719 0.995890i \(-0.528870\pi\)
−0.0905719 + 0.995890i \(0.528870\pi\)
\(912\) −75.2926 −2.49319
\(913\) 5.25584 0.173943
\(914\) 48.9086 1.61775
\(915\) −47.5951 −1.57345
\(916\) −0.610533 −0.0201726
\(917\) 12.8665 0.424890
\(918\) −22.6887 −0.748840
\(919\) 19.9275 0.657348 0.328674 0.944443i \(-0.393398\pi\)
0.328674 + 0.944443i \(0.393398\pi\)
\(920\) 24.3972 0.804353
\(921\) −4.60625 −0.151781
\(922\) −26.4366 −0.870644
\(923\) 24.1100 0.793591
\(924\) 2.50302 0.0823433
\(925\) 56.5027 1.85780
\(926\) 12.3926 0.407247
\(927\) 69.5828 2.28540
\(928\) 43.4566 1.42653
\(929\) −22.3310 −0.732655 −0.366327 0.930486i \(-0.619385\pi\)
−0.366327 + 0.930486i \(0.619385\pi\)
\(930\) −195.559 −6.41264
\(931\) −29.9092 −0.980234
\(932\) 4.16079 0.136291
\(933\) −40.2059 −1.31628
\(934\) −69.8450 −2.28540
\(935\) 4.00741 0.131056
\(936\) −88.4204 −2.89011
\(937\) −14.1693 −0.462890 −0.231445 0.972848i \(-0.574345\pi\)
−0.231445 + 0.972848i \(0.574345\pi\)
\(938\) 11.0015 0.359212
\(939\) 4.05865 0.132449
\(940\) −33.3959 −1.08925
\(941\) −20.1180 −0.655829 −0.327915 0.944707i \(-0.606346\pi\)
−0.327915 + 0.944707i \(0.606346\pi\)
\(942\) −110.497 −3.60020
\(943\) −25.9483 −0.844993
\(944\) −52.3236 −1.70299
\(945\) 43.5043 1.41520
\(946\) 1.71913 0.0558939
\(947\) 24.0244 0.780688 0.390344 0.920669i \(-0.372356\pi\)
0.390344 + 0.920669i \(0.372356\pi\)
\(948\) 23.5671 0.765424
\(949\) 101.677 3.30057
\(950\) −89.9275 −2.91763
\(951\) −46.4801 −1.50722
\(952\) −1.47713 −0.0478742
\(953\) −59.0554 −1.91299 −0.956496 0.291746i \(-0.905764\pi\)
−0.956496 + 0.291746i \(0.905764\pi\)
\(954\) 160.367 5.19209
\(955\) 63.4470 2.05310
\(956\) −10.9205 −0.353193
\(957\) −27.6774 −0.894682
\(958\) 69.7855 2.25467
\(959\) 6.32323 0.204188
\(960\) −17.8576 −0.576352
\(961\) 48.4344 1.56240
\(962\) 60.5372 1.95180
\(963\) −43.9008 −1.41468
\(964\) −11.5073 −0.370624
\(965\) −98.6413 −3.17538
\(966\) −15.2688 −0.491266
\(967\) 34.9430 1.12369 0.561846 0.827242i \(-0.310091\pi\)
0.561846 + 0.827242i \(0.310091\pi\)
\(968\) 1.79577 0.0577183
\(969\) 15.0645 0.483942
\(970\) 57.9908 1.86197
\(971\) −53.7492 −1.72489 −0.862447 0.506148i \(-0.831069\pi\)
−0.862447 + 0.506148i \(0.831069\pi\)
\(972\) 24.8645 0.797529
\(973\) 6.59397 0.211393
\(974\) −2.06862 −0.0662829
\(975\) −242.773 −7.77496
\(976\) −18.6379 −0.596583
\(977\) −17.9431 −0.574052 −0.287026 0.957923i \(-0.592667\pi\)
−0.287026 + 0.957923i \(0.592667\pi\)
\(978\) −0.249691 −0.00798423
\(979\) 4.17801 0.133530
\(980\) 24.2108 0.773384
\(981\) −104.555 −3.33820
\(982\) −35.9251 −1.14642
\(983\) 4.70761 0.150150 0.0750748 0.997178i \(-0.476080\pi\)
0.0750748 + 0.997178i \(0.476080\pi\)
\(984\) 43.7758 1.39552
\(985\) 60.7538 1.93578
\(986\) −14.9394 −0.475768
\(987\) −22.8509 −0.727352
\(988\) −31.1473 −0.990929
\(989\) −3.39021 −0.107802
\(990\) −49.2156 −1.56418
\(991\) 19.5584 0.621292 0.310646 0.950526i \(-0.399455\pi\)
0.310646 + 0.950526i \(0.399455\pi\)
\(992\) −44.5693 −1.41508
\(993\) −81.9529 −2.60070
\(994\) −4.94657 −0.156896
\(995\) −56.4349 −1.78911
\(996\) −15.9933 −0.506767
\(997\) 13.8085 0.437320 0.218660 0.975801i \(-0.429831\pi\)
0.218660 + 0.975801i \(0.429831\pi\)
\(998\) 64.9588 2.05623
\(999\) 67.4282 2.13333
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 \(a_p\))