Properties

Label 8041.2.a.g.1.14
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 1.14
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.02215 q^{2} +2.02595 q^{3} +2.08909 q^{4} -3.90857 q^{5} -4.09678 q^{6} -0.616656 q^{7} -0.180153 q^{8} +1.10448 q^{9} +O(q^{10})\) \(q-2.02215 q^{2} +2.02595 q^{3} +2.08909 q^{4} -3.90857 q^{5} -4.09678 q^{6} -0.616656 q^{7} -0.180153 q^{8} +1.10448 q^{9} +7.90371 q^{10} -1.00000 q^{11} +4.23240 q^{12} +3.49708 q^{13} +1.24697 q^{14} -7.91857 q^{15} -3.81388 q^{16} +1.00000 q^{17} -2.23343 q^{18} -1.94885 q^{19} -8.16535 q^{20} -1.24932 q^{21} +2.02215 q^{22} +3.59332 q^{23} -0.364982 q^{24} +10.2769 q^{25} -7.07163 q^{26} -3.84023 q^{27} -1.28825 q^{28} -6.45369 q^{29} +16.0125 q^{30} +1.16394 q^{31} +8.07255 q^{32} -2.02595 q^{33} -2.02215 q^{34} +2.41024 q^{35} +2.30736 q^{36} -0.868718 q^{37} +3.94087 q^{38} +7.08492 q^{39} +0.704142 q^{40} +4.28511 q^{41} +2.52630 q^{42} +1.00000 q^{43} -2.08909 q^{44} -4.31694 q^{45} -7.26622 q^{46} -8.11901 q^{47} -7.72674 q^{48} -6.61973 q^{49} -20.7815 q^{50} +2.02595 q^{51} +7.30572 q^{52} +5.73888 q^{53} +7.76552 q^{54} +3.90857 q^{55} +0.111093 q^{56} -3.94828 q^{57} +13.0503 q^{58} -2.86909 q^{59} -16.5426 q^{60} +11.5842 q^{61} -2.35365 q^{62} -0.681085 q^{63} -8.69614 q^{64} -13.6686 q^{65} +4.09678 q^{66} +11.3423 q^{67} +2.08909 q^{68} +7.27988 q^{69} -4.87387 q^{70} +11.2718 q^{71} -0.198976 q^{72} +4.37038 q^{73} +1.75668 q^{74} +20.8205 q^{75} -4.07132 q^{76} +0.616656 q^{77} -14.3268 q^{78} +6.90937 q^{79} +14.9068 q^{80} -11.0936 q^{81} -8.66514 q^{82} -5.62609 q^{83} -2.60993 q^{84} -3.90857 q^{85} -2.02215 q^{86} -13.0749 q^{87} +0.180153 q^{88} -11.1870 q^{89} +8.72950 q^{90} -2.15650 q^{91} +7.50676 q^{92} +2.35808 q^{93} +16.4179 q^{94} +7.61722 q^{95} +16.3546 q^{96} -2.05879 q^{97} +13.3861 q^{98} -1.10448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.02215 −1.42988 −0.714938 0.699188i \(-0.753545\pi\)
−0.714938 + 0.699188i \(0.753545\pi\)
\(3\) 2.02595 1.16968 0.584842 0.811147i \(-0.301157\pi\)
0.584842 + 0.811147i \(0.301157\pi\)
\(4\) 2.08909 1.04455
\(5\) −3.90857 −1.74797 −0.873983 0.485957i \(-0.838471\pi\)
−0.873983 + 0.485957i \(0.838471\pi\)
\(6\) −4.09678 −1.67250
\(7\) −0.616656 −0.233074 −0.116537 0.993186i \(-0.537179\pi\)
−0.116537 + 0.993186i \(0.537179\pi\)
\(8\) −0.180153 −0.0636938
\(9\) 1.10448 0.368160
\(10\) 7.90371 2.49937
\(11\) −1.00000 −0.301511
\(12\) 4.23240 1.22179
\(13\) 3.49708 0.969917 0.484958 0.874537i \(-0.338835\pi\)
0.484958 + 0.874537i \(0.338835\pi\)
\(14\) 1.24697 0.333267
\(15\) −7.91857 −2.04457
\(16\) −3.81388 −0.953471
\(17\) 1.00000 0.242536
\(18\) −2.23343 −0.526424
\(19\) −1.94885 −0.447097 −0.223548 0.974693i \(-0.571764\pi\)
−0.223548 + 0.974693i \(0.571764\pi\)
\(20\) −8.16535 −1.82583
\(21\) −1.24932 −0.272623
\(22\) 2.02215 0.431124
\(23\) 3.59332 0.749258 0.374629 0.927175i \(-0.377770\pi\)
0.374629 + 0.927175i \(0.377770\pi\)
\(24\) −0.364982 −0.0745016
\(25\) 10.2769 2.05538
\(26\) −7.07163 −1.38686
\(27\) −3.84023 −0.739053
\(28\) −1.28825 −0.243456
\(29\) −6.45369 −1.19842 −0.599210 0.800592i \(-0.704519\pi\)
−0.599210 + 0.800592i \(0.704519\pi\)
\(30\) 16.0125 2.92348
\(31\) 1.16394 0.209049 0.104525 0.994522i \(-0.466668\pi\)
0.104525 + 0.994522i \(0.466668\pi\)
\(32\) 8.07255 1.42704
\(33\) −2.02595 −0.352673
\(34\) −2.02215 −0.346796
\(35\) 2.41024 0.407406
\(36\) 2.30736 0.384560
\(37\) −0.868718 −0.142816 −0.0714081 0.997447i \(-0.522749\pi\)
−0.0714081 + 0.997447i \(0.522749\pi\)
\(38\) 3.94087 0.639293
\(39\) 7.08492 1.13450
\(40\) 0.704142 0.111335
\(41\) 4.28511 0.669222 0.334611 0.942356i \(-0.391395\pi\)
0.334611 + 0.942356i \(0.391395\pi\)
\(42\) 2.52630 0.389817
\(43\) 1.00000 0.152499
\(44\) −2.08909 −0.314942
\(45\) −4.31694 −0.643531
\(46\) −7.26622 −1.07135
\(47\) −8.11901 −1.18428 −0.592140 0.805835i \(-0.701717\pi\)
−0.592140 + 0.805835i \(0.701717\pi\)
\(48\) −7.72674 −1.11526
\(49\) −6.61973 −0.945676
\(50\) −20.7815 −2.93894
\(51\) 2.02595 0.283690
\(52\) 7.30572 1.01312
\(53\) 5.73888 0.788296 0.394148 0.919047i \(-0.371040\pi\)
0.394148 + 0.919047i \(0.371040\pi\)
\(54\) 7.76552 1.05675
\(55\) 3.90857 0.527031
\(56\) 0.111093 0.0148454
\(57\) −3.94828 −0.522962
\(58\) 13.0503 1.71359
\(59\) −2.86909 −0.373524 −0.186762 0.982405i \(-0.559799\pi\)
−0.186762 + 0.982405i \(0.559799\pi\)
\(60\) −16.5426 −2.13564
\(61\) 11.5842 1.48321 0.741605 0.670837i \(-0.234065\pi\)
0.741605 + 0.670837i \(0.234065\pi\)
\(62\) −2.35365 −0.298914
\(63\) −0.681085 −0.0858087
\(64\) −8.69614 −1.08702
\(65\) −13.6686 −1.69538
\(66\) 4.09678 0.504279
\(67\) 11.3423 1.38568 0.692841 0.721090i \(-0.256359\pi\)
0.692841 + 0.721090i \(0.256359\pi\)
\(68\) 2.08909 0.253339
\(69\) 7.27988 0.876395
\(70\) −4.87387 −0.582539
\(71\) 11.2718 1.33771 0.668857 0.743391i \(-0.266784\pi\)
0.668857 + 0.743391i \(0.266784\pi\)
\(72\) −0.198976 −0.0234495
\(73\) 4.37038 0.511515 0.255757 0.966741i \(-0.417675\pi\)
0.255757 + 0.966741i \(0.417675\pi\)
\(74\) 1.75668 0.204210
\(75\) 20.8205 2.40415
\(76\) −4.07132 −0.467013
\(77\) 0.616656 0.0702745
\(78\) −14.3268 −1.62219
\(79\) 6.90937 0.777365 0.388683 0.921372i \(-0.372930\pi\)
0.388683 + 0.921372i \(0.372930\pi\)
\(80\) 14.9068 1.66663
\(81\) −11.0936 −1.23262
\(82\) −8.66514 −0.956905
\(83\) −5.62609 −0.617544 −0.308772 0.951136i \(-0.599918\pi\)
−0.308772 + 0.951136i \(0.599918\pi\)
\(84\) −2.60993 −0.284767
\(85\) −3.90857 −0.423944
\(86\) −2.02215 −0.218054
\(87\) −13.0749 −1.40177
\(88\) 0.180153 0.0192044
\(89\) −11.1870 −1.18582 −0.592909 0.805270i \(-0.702021\pi\)
−0.592909 + 0.805270i \(0.702021\pi\)
\(90\) 8.72950 0.920170
\(91\) −2.15650 −0.226063
\(92\) 7.50676 0.782634
\(93\) 2.35808 0.244521
\(94\) 16.4179 1.69337
\(95\) 7.61722 0.781510
\(96\) 16.3546 1.66918
\(97\) −2.05879 −0.209039 −0.104519 0.994523i \(-0.533330\pi\)
−0.104519 + 0.994523i \(0.533330\pi\)
\(98\) 13.3861 1.35220
\(99\) −1.10448 −0.111005
\(100\) 21.4694 2.14694
\(101\) −7.19940 −0.716367 −0.358184 0.933651i \(-0.616604\pi\)
−0.358184 + 0.933651i \(0.616604\pi\)
\(102\) −4.09678 −0.405641
\(103\) −16.1720 −1.59348 −0.796739 0.604324i \(-0.793443\pi\)
−0.796739 + 0.604324i \(0.793443\pi\)
\(104\) −0.630011 −0.0617777
\(105\) 4.88304 0.476536
\(106\) −11.6049 −1.12717
\(107\) −12.9163 −1.24867 −0.624334 0.781157i \(-0.714630\pi\)
−0.624334 + 0.781157i \(0.714630\pi\)
\(108\) −8.02259 −0.771974
\(109\) 1.47785 0.141552 0.0707761 0.997492i \(-0.477452\pi\)
0.0707761 + 0.997492i \(0.477452\pi\)
\(110\) −7.90371 −0.753589
\(111\) −1.75998 −0.167050
\(112\) 2.35186 0.222229
\(113\) 0.190850 0.0179537 0.00897685 0.999960i \(-0.497143\pi\)
0.00897685 + 0.999960i \(0.497143\pi\)
\(114\) 7.98401 0.747771
\(115\) −14.0447 −1.30968
\(116\) −13.4823 −1.25180
\(117\) 3.86246 0.357085
\(118\) 5.80173 0.534093
\(119\) −0.616656 −0.0565288
\(120\) 1.42656 0.130226
\(121\) 1.00000 0.0909091
\(122\) −23.4251 −2.12081
\(123\) 8.68143 0.782779
\(124\) 2.43157 0.218361
\(125\) −20.6252 −1.84477
\(126\) 1.37726 0.122696
\(127\) 14.5894 1.29460 0.647299 0.762236i \(-0.275899\pi\)
0.647299 + 0.762236i \(0.275899\pi\)
\(128\) 1.43980 0.127261
\(129\) 2.02595 0.178375
\(130\) 27.6399 2.42418
\(131\) 10.7120 0.935913 0.467957 0.883751i \(-0.344990\pi\)
0.467957 + 0.883751i \(0.344990\pi\)
\(132\) −4.23240 −0.368383
\(133\) 1.20177 0.104207
\(134\) −22.9358 −1.98135
\(135\) 15.0098 1.29184
\(136\) −0.180153 −0.0154480
\(137\) 6.42922 0.549286 0.274643 0.961546i \(-0.411440\pi\)
0.274643 + 0.961546i \(0.411440\pi\)
\(138\) −14.7210 −1.25314
\(139\) −1.29245 −0.109624 −0.0548120 0.998497i \(-0.517456\pi\)
−0.0548120 + 0.998497i \(0.517456\pi\)
\(140\) 5.03522 0.425553
\(141\) −16.4487 −1.38523
\(142\) −22.7932 −1.91276
\(143\) −3.49708 −0.292441
\(144\) −4.21236 −0.351030
\(145\) 25.2247 2.09480
\(146\) −8.83757 −0.731403
\(147\) −13.4113 −1.10614
\(148\) −1.81483 −0.149178
\(149\) 11.6166 0.951666 0.475833 0.879536i \(-0.342147\pi\)
0.475833 + 0.879536i \(0.342147\pi\)
\(150\) −42.1022 −3.43763
\(151\) 7.29036 0.593281 0.296641 0.954989i \(-0.404134\pi\)
0.296641 + 0.954989i \(0.404134\pi\)
\(152\) 0.351092 0.0284773
\(153\) 1.10448 0.0892920
\(154\) −1.24697 −0.100484
\(155\) −4.54933 −0.365411
\(156\) 14.8010 1.18503
\(157\) 21.7884 1.73890 0.869452 0.494017i \(-0.164472\pi\)
0.869452 + 0.494017i \(0.164472\pi\)
\(158\) −13.9718 −1.11154
\(159\) 11.6267 0.922057
\(160\) −31.5521 −2.49441
\(161\) −2.21584 −0.174633
\(162\) 22.4329 1.76249
\(163\) −8.97580 −0.703039 −0.351519 0.936181i \(-0.614335\pi\)
−0.351519 + 0.936181i \(0.614335\pi\)
\(164\) 8.95199 0.699033
\(165\) 7.91857 0.616460
\(166\) 11.3768 0.883011
\(167\) −8.84965 −0.684807 −0.342403 0.939553i \(-0.611241\pi\)
−0.342403 + 0.939553i \(0.611241\pi\)
\(168\) 0.225068 0.0173644
\(169\) −0.770401 −0.0592616
\(170\) 7.90371 0.606187
\(171\) −2.15247 −0.164603
\(172\) 2.08909 0.159292
\(173\) 7.78391 0.591800 0.295900 0.955219i \(-0.404381\pi\)
0.295900 + 0.955219i \(0.404381\pi\)
\(174\) 26.4393 2.00436
\(175\) −6.33732 −0.479057
\(176\) 3.81388 0.287482
\(177\) −5.81264 −0.436905
\(178\) 22.6218 1.69557
\(179\) 11.0255 0.824083 0.412041 0.911165i \(-0.364816\pi\)
0.412041 + 0.911165i \(0.364816\pi\)
\(180\) −9.01848 −0.672197
\(181\) −23.2986 −1.73177 −0.865887 0.500239i \(-0.833245\pi\)
−0.865887 + 0.500239i \(0.833245\pi\)
\(182\) 4.36076 0.323241
\(183\) 23.4691 1.73489
\(184\) −0.647348 −0.0477231
\(185\) 3.39544 0.249638
\(186\) −4.76839 −0.349635
\(187\) −1.00000 −0.0731272
\(188\) −16.9614 −1.23703
\(189\) 2.36810 0.172254
\(190\) −15.4032 −1.11746
\(191\) −12.3276 −0.891992 −0.445996 0.895035i \(-0.647150\pi\)
−0.445996 + 0.895035i \(0.647150\pi\)
\(192\) −17.6180 −1.27147
\(193\) −1.20220 −0.0865360 −0.0432680 0.999064i \(-0.513777\pi\)
−0.0432680 + 0.999064i \(0.513777\pi\)
\(194\) 4.16319 0.298899
\(195\) −27.6919 −1.98306
\(196\) −13.8292 −0.987802
\(197\) −4.53617 −0.323189 −0.161594 0.986857i \(-0.551664\pi\)
−0.161594 + 0.986857i \(0.551664\pi\)
\(198\) 2.23343 0.158723
\(199\) 12.4139 0.879997 0.439999 0.897998i \(-0.354979\pi\)
0.439999 + 0.897998i \(0.354979\pi\)
\(200\) −1.85142 −0.130915
\(201\) 22.9789 1.62081
\(202\) 14.5583 1.02432
\(203\) 3.97971 0.279321
\(204\) 4.23240 0.296327
\(205\) −16.7487 −1.16978
\(206\) 32.7023 2.27848
\(207\) 3.96875 0.275847
\(208\) −13.3375 −0.924787
\(209\) 1.94885 0.134805
\(210\) −9.87423 −0.681387
\(211\) 25.1602 1.73210 0.866051 0.499956i \(-0.166651\pi\)
0.866051 + 0.499956i \(0.166651\pi\)
\(212\) 11.9890 0.823411
\(213\) 22.8361 1.56470
\(214\) 26.1188 1.78544
\(215\) −3.90857 −0.266562
\(216\) 0.691830 0.0470731
\(217\) −0.717749 −0.0487240
\(218\) −2.98843 −0.202402
\(219\) 8.85419 0.598311
\(220\) 8.16535 0.550508
\(221\) 3.49708 0.235239
\(222\) 3.55894 0.238861
\(223\) 0.799018 0.0535062 0.0267531 0.999642i \(-0.491483\pi\)
0.0267531 + 0.999642i \(0.491483\pi\)
\(224\) −4.97799 −0.332606
\(225\) 11.3507 0.756710
\(226\) −0.385928 −0.0256715
\(227\) −21.3790 −1.41897 −0.709486 0.704719i \(-0.751073\pi\)
−0.709486 + 0.704719i \(0.751073\pi\)
\(228\) −8.24831 −0.546257
\(229\) −4.65134 −0.307369 −0.153685 0.988120i \(-0.549114\pi\)
−0.153685 + 0.988120i \(0.549114\pi\)
\(230\) 28.4005 1.87268
\(231\) 1.24932 0.0821990
\(232\) 1.16265 0.0763319
\(233\) −20.3553 −1.33352 −0.666760 0.745272i \(-0.732319\pi\)
−0.666760 + 0.745272i \(0.732319\pi\)
\(234\) −7.81048 −0.510587
\(235\) 31.7337 2.07008
\(236\) −5.99379 −0.390162
\(237\) 13.9981 0.909271
\(238\) 1.24697 0.0808292
\(239\) −28.7116 −1.85720 −0.928599 0.371084i \(-0.878986\pi\)
−0.928599 + 0.371084i \(0.878986\pi\)
\(240\) 30.2005 1.94943
\(241\) 8.80483 0.567169 0.283584 0.958947i \(-0.408476\pi\)
0.283584 + 0.958947i \(0.408476\pi\)
\(242\) −2.02215 −0.129989
\(243\) −10.9543 −0.702721
\(244\) 24.2005 1.54928
\(245\) 25.8737 1.65301
\(246\) −17.5552 −1.11928
\(247\) −6.81529 −0.433647
\(248\) −0.209687 −0.0133151
\(249\) −11.3982 −0.722331
\(250\) 41.7072 2.63779
\(251\) 12.3337 0.778496 0.389248 0.921133i \(-0.372735\pi\)
0.389248 + 0.921133i \(0.372735\pi\)
\(252\) −1.42285 −0.0896310
\(253\) −3.59332 −0.225910
\(254\) −29.5019 −1.85111
\(255\) −7.91857 −0.495880
\(256\) 14.4808 0.905050
\(257\) 27.5418 1.71801 0.859005 0.511967i \(-0.171083\pi\)
0.859005 + 0.511967i \(0.171083\pi\)
\(258\) −4.09678 −0.255054
\(259\) 0.535700 0.0332868
\(260\) −28.5549 −1.77090
\(261\) −7.12798 −0.441211
\(262\) −21.6613 −1.33824
\(263\) −17.6915 −1.09090 −0.545452 0.838142i \(-0.683642\pi\)
−0.545452 + 0.838142i \(0.683642\pi\)
\(264\) 0.364982 0.0224631
\(265\) −22.4308 −1.37791
\(266\) −2.43016 −0.149003
\(267\) −22.6643 −1.38703
\(268\) 23.6951 1.44741
\(269\) −4.71397 −0.287416 −0.143708 0.989620i \(-0.545903\pi\)
−0.143708 + 0.989620i \(0.545903\pi\)
\(270\) −30.3521 −1.84717
\(271\) −23.0375 −1.39943 −0.699715 0.714422i \(-0.746690\pi\)
−0.699715 + 0.714422i \(0.746690\pi\)
\(272\) −3.81388 −0.231251
\(273\) −4.36896 −0.264422
\(274\) −13.0009 −0.785410
\(275\) −10.2769 −0.619721
\(276\) 15.2083 0.915434
\(277\) −20.7722 −1.24808 −0.624041 0.781392i \(-0.714510\pi\)
−0.624041 + 0.781392i \(0.714510\pi\)
\(278\) 2.61352 0.156749
\(279\) 1.28555 0.0769636
\(280\) −0.434213 −0.0259492
\(281\) 11.6394 0.694349 0.347174 0.937801i \(-0.387141\pi\)
0.347174 + 0.937801i \(0.387141\pi\)
\(282\) 33.2618 1.98071
\(283\) 13.8878 0.825544 0.412772 0.910834i \(-0.364561\pi\)
0.412772 + 0.910834i \(0.364561\pi\)
\(284\) 23.5477 1.39730
\(285\) 15.4321 0.914120
\(286\) 7.07163 0.418154
\(287\) −2.64244 −0.155978
\(288\) 8.91598 0.525379
\(289\) 1.00000 0.0588235
\(290\) −51.0081 −2.99530
\(291\) −4.17101 −0.244509
\(292\) 9.13013 0.534300
\(293\) −9.65732 −0.564187 −0.282093 0.959387i \(-0.591029\pi\)
−0.282093 + 0.959387i \(0.591029\pi\)
\(294\) 27.1196 1.58165
\(295\) 11.2140 0.652906
\(296\) 0.156502 0.00909651
\(297\) 3.84023 0.222833
\(298\) −23.4904 −1.36076
\(299\) 12.5661 0.726718
\(300\) 43.4960 2.51124
\(301\) −0.616656 −0.0355435
\(302\) −14.7422 −0.848318
\(303\) −14.5856 −0.837923
\(304\) 7.43269 0.426294
\(305\) −45.2778 −2.59260
\(306\) −2.23343 −0.127676
\(307\) −24.5011 −1.39835 −0.699175 0.714951i \(-0.746449\pi\)
−0.699175 + 0.714951i \(0.746449\pi\)
\(308\) 1.28825 0.0734049
\(309\) −32.7638 −1.86387
\(310\) 9.19942 0.522492
\(311\) 18.1724 1.03046 0.515230 0.857052i \(-0.327707\pi\)
0.515230 + 0.857052i \(0.327707\pi\)
\(312\) −1.27637 −0.0722604
\(313\) 21.0156 1.18787 0.593937 0.804512i \(-0.297573\pi\)
0.593937 + 0.804512i \(0.297573\pi\)
\(314\) −44.0594 −2.48642
\(315\) 2.66207 0.149991
\(316\) 14.4343 0.811993
\(317\) −23.1003 −1.29744 −0.648720 0.761027i \(-0.724695\pi\)
−0.648720 + 0.761027i \(0.724695\pi\)
\(318\) −23.5109 −1.31843
\(319\) 6.45369 0.361337
\(320\) 33.9895 1.90007
\(321\) −26.1679 −1.46055
\(322\) 4.48076 0.249703
\(323\) −1.94885 −0.108437
\(324\) −23.1755 −1.28753
\(325\) 35.9392 1.99355
\(326\) 18.1504 1.00526
\(327\) 2.99405 0.165571
\(328\) −0.771978 −0.0426253
\(329\) 5.00664 0.276025
\(330\) −16.0125 −0.881461
\(331\) −7.67137 −0.421656 −0.210828 0.977523i \(-0.567616\pi\)
−0.210828 + 0.977523i \(0.567616\pi\)
\(332\) −11.7534 −0.645052
\(333\) −0.959482 −0.0525793
\(334\) 17.8953 0.979189
\(335\) −44.3322 −2.42212
\(336\) 4.76475 0.259938
\(337\) −12.8868 −0.701987 −0.350994 0.936378i \(-0.614156\pi\)
−0.350994 + 0.936378i \(0.614156\pi\)
\(338\) 1.55787 0.0847367
\(339\) 0.386654 0.0210001
\(340\) −8.16535 −0.442828
\(341\) −1.16394 −0.0630307
\(342\) 4.35261 0.235362
\(343\) 8.39870 0.453487
\(344\) −0.180153 −0.00971322
\(345\) −28.4539 −1.53191
\(346\) −15.7402 −0.846200
\(347\) −17.2251 −0.924690 −0.462345 0.886700i \(-0.652992\pi\)
−0.462345 + 0.886700i \(0.652992\pi\)
\(348\) −27.3146 −1.46421
\(349\) 3.75398 0.200946 0.100473 0.994940i \(-0.467964\pi\)
0.100473 + 0.994940i \(0.467964\pi\)
\(350\) 12.8150 0.684991
\(351\) −13.4296 −0.716820
\(352\) −8.07255 −0.430268
\(353\) −4.01624 −0.213763 −0.106881 0.994272i \(-0.534087\pi\)
−0.106881 + 0.994272i \(0.534087\pi\)
\(354\) 11.7540 0.624719
\(355\) −44.0565 −2.33828
\(356\) −23.3706 −1.23864
\(357\) −1.24932 −0.0661208
\(358\) −22.2952 −1.17834
\(359\) −25.4201 −1.34162 −0.670810 0.741630i \(-0.734053\pi\)
−0.670810 + 0.741630i \(0.734053\pi\)
\(360\) 0.777711 0.0409890
\(361\) −15.2020 −0.800104
\(362\) 47.1134 2.47622
\(363\) 2.02595 0.106335
\(364\) −4.50512 −0.236133
\(365\) −17.0819 −0.894110
\(366\) −47.4581 −2.48067
\(367\) −22.7531 −1.18770 −0.593850 0.804576i \(-0.702393\pi\)
−0.593850 + 0.804576i \(0.702393\pi\)
\(368\) −13.7045 −0.714396
\(369\) 4.73283 0.246381
\(370\) −6.86609 −0.356951
\(371\) −3.53892 −0.183732
\(372\) 4.92624 0.255414
\(373\) −23.2096 −1.20175 −0.600874 0.799344i \(-0.705181\pi\)
−0.600874 + 0.799344i \(0.705181\pi\)
\(374\) 2.02215 0.104563
\(375\) −41.7856 −2.15780
\(376\) 1.46267 0.0754313
\(377\) −22.5691 −1.16237
\(378\) −4.78866 −0.246302
\(379\) −2.90409 −0.149173 −0.0745865 0.997215i \(-0.523764\pi\)
−0.0745865 + 0.997215i \(0.523764\pi\)
\(380\) 15.9131 0.816322
\(381\) 29.5574 1.51427
\(382\) 24.9282 1.27544
\(383\) −37.0210 −1.89169 −0.945843 0.324625i \(-0.894762\pi\)
−0.945843 + 0.324625i \(0.894762\pi\)
\(384\) 2.91696 0.148855
\(385\) −2.41024 −0.122837
\(386\) 2.43102 0.123736
\(387\) 1.10448 0.0561439
\(388\) −4.30100 −0.218350
\(389\) −5.87758 −0.298005 −0.149002 0.988837i \(-0.547606\pi\)
−0.149002 + 0.988837i \(0.547606\pi\)
\(390\) 55.9972 2.83553
\(391\) 3.59332 0.181722
\(392\) 1.19257 0.0602337
\(393\) 21.7020 1.09472
\(394\) 9.17282 0.462120
\(395\) −27.0058 −1.35881
\(396\) −2.30736 −0.115949
\(397\) −9.10055 −0.456744 −0.228372 0.973574i \(-0.573340\pi\)
−0.228372 + 0.973574i \(0.573340\pi\)
\(398\) −25.1027 −1.25829
\(399\) 2.43473 0.121889
\(400\) −39.1949 −1.95975
\(401\) −20.0744 −1.00247 −0.501234 0.865312i \(-0.667120\pi\)
−0.501234 + 0.865312i \(0.667120\pi\)
\(402\) −46.4669 −2.31756
\(403\) 4.07038 0.202760
\(404\) −15.0402 −0.748278
\(405\) 43.3600 2.15457
\(406\) −8.04757 −0.399394
\(407\) 0.868718 0.0430607
\(408\) −0.364982 −0.0180693
\(409\) 19.7634 0.977239 0.488620 0.872497i \(-0.337501\pi\)
0.488620 + 0.872497i \(0.337501\pi\)
\(410\) 33.8683 1.67264
\(411\) 13.0253 0.642491
\(412\) −33.7848 −1.66446
\(413\) 1.76924 0.0870587
\(414\) −8.02540 −0.394427
\(415\) 21.9900 1.07945
\(416\) 28.2304 1.38411
\(417\) −2.61844 −0.128225
\(418\) −3.94087 −0.192754
\(419\) −34.8150 −1.70082 −0.850411 0.526119i \(-0.823647\pi\)
−0.850411 + 0.526119i \(0.823647\pi\)
\(420\) 10.2011 0.497763
\(421\) 13.4050 0.653318 0.326659 0.945142i \(-0.394077\pi\)
0.326659 + 0.945142i \(0.394077\pi\)
\(422\) −50.8777 −2.47669
\(423\) −8.96730 −0.436005
\(424\) −1.03388 −0.0502096
\(425\) 10.2769 0.498503
\(426\) −46.1780 −2.23733
\(427\) −7.14350 −0.345698
\(428\) −26.9834 −1.30429
\(429\) −7.08492 −0.342063
\(430\) 7.90371 0.381151
\(431\) −30.1712 −1.45329 −0.726647 0.687011i \(-0.758923\pi\)
−0.726647 + 0.687011i \(0.758923\pi\)
\(432\) 14.6462 0.704665
\(433\) 31.0713 1.49319 0.746595 0.665278i \(-0.231687\pi\)
0.746595 + 0.665278i \(0.231687\pi\)
\(434\) 1.45140 0.0696692
\(435\) 51.1040 2.45025
\(436\) 3.08736 0.147858
\(437\) −7.00283 −0.334991
\(438\) −17.9045 −0.855510
\(439\) −0.322716 −0.0154024 −0.00770121 0.999970i \(-0.502451\pi\)
−0.00770121 + 0.999970i \(0.502451\pi\)
\(440\) −0.704142 −0.0335686
\(441\) −7.31137 −0.348161
\(442\) −7.07163 −0.336363
\(443\) 12.1698 0.578203 0.289101 0.957298i \(-0.406643\pi\)
0.289101 + 0.957298i \(0.406643\pi\)
\(444\) −3.67676 −0.174491
\(445\) 43.7251 2.07277
\(446\) −1.61573 −0.0765073
\(447\) 23.5346 1.11315
\(448\) 5.36253 0.253356
\(449\) 4.18739 0.197615 0.0988076 0.995107i \(-0.468497\pi\)
0.0988076 + 0.995107i \(0.468497\pi\)
\(450\) −22.9527 −1.08200
\(451\) −4.28511 −0.201778
\(452\) 0.398704 0.0187534
\(453\) 14.7699 0.693951
\(454\) 43.2315 2.02896
\(455\) 8.42883 0.395149
\(456\) 0.711295 0.0333095
\(457\) −7.48258 −0.350020 −0.175010 0.984567i \(-0.555996\pi\)
−0.175010 + 0.984567i \(0.555996\pi\)
\(458\) 9.40571 0.439500
\(459\) −3.84023 −0.179247
\(460\) −29.3407 −1.36802
\(461\) 9.06496 0.422197 0.211099 0.977465i \(-0.432296\pi\)
0.211099 + 0.977465i \(0.432296\pi\)
\(462\) −2.52630 −0.117534
\(463\) 5.22220 0.242696 0.121348 0.992610i \(-0.461278\pi\)
0.121348 + 0.992610i \(0.461278\pi\)
\(464\) 24.6136 1.14266
\(465\) −9.21672 −0.427415
\(466\) 41.1615 1.90677
\(467\) 1.32197 0.0611737 0.0305869 0.999532i \(-0.490262\pi\)
0.0305869 + 0.999532i \(0.490262\pi\)
\(468\) 8.06903 0.372991
\(469\) −6.99430 −0.322967
\(470\) −64.1703 −2.95996
\(471\) 44.1423 2.03397
\(472\) 0.516876 0.0237912
\(473\) −1.00000 −0.0459800
\(474\) −28.3062 −1.30015
\(475\) −20.0282 −0.918955
\(476\) −1.28825 −0.0590469
\(477\) 6.33849 0.290219
\(478\) 58.0592 2.65556
\(479\) −18.3500 −0.838431 −0.419216 0.907887i \(-0.637695\pi\)
−0.419216 + 0.907887i \(0.637695\pi\)
\(480\) −63.9231 −2.91768
\(481\) −3.03798 −0.138520
\(482\) −17.8047 −0.810981
\(483\) −4.48919 −0.204265
\(484\) 2.08909 0.0949586
\(485\) 8.04693 0.365392
\(486\) 22.1513 1.00480
\(487\) −5.42957 −0.246037 −0.123019 0.992404i \(-0.539258\pi\)
−0.123019 + 0.992404i \(0.539258\pi\)
\(488\) −2.08694 −0.0944713
\(489\) −18.1845 −0.822333
\(490\) −52.3205 −2.36360
\(491\) −8.75286 −0.395011 −0.197506 0.980302i \(-0.563284\pi\)
−0.197506 + 0.980302i \(0.563284\pi\)
\(492\) 18.1363 0.817647
\(493\) −6.45369 −0.290660
\(494\) 13.7815 0.620061
\(495\) 4.31694 0.194032
\(496\) −4.43912 −0.199322
\(497\) −6.95081 −0.311786
\(498\) 23.0489 1.03284
\(499\) 27.6112 1.23605 0.618024 0.786160i \(-0.287934\pi\)
0.618024 + 0.786160i \(0.287934\pi\)
\(500\) −43.0878 −1.92695
\(501\) −17.9290 −0.801007
\(502\) −24.9406 −1.11315
\(503\) −33.8389 −1.50880 −0.754401 0.656414i \(-0.772072\pi\)
−0.754401 + 0.656414i \(0.772072\pi\)
\(504\) 0.122700 0.00546548
\(505\) 28.1394 1.25218
\(506\) 7.26622 0.323023
\(507\) −1.56080 −0.0693173
\(508\) 30.4785 1.35227
\(509\) −18.4703 −0.818680 −0.409340 0.912382i \(-0.634241\pi\)
−0.409340 + 0.912382i \(0.634241\pi\)
\(510\) 16.0125 0.709047
\(511\) −2.69503 −0.119221
\(512\) −32.1619 −1.42137
\(513\) 7.48404 0.330428
\(514\) −55.6936 −2.45654
\(515\) 63.2095 2.78534
\(516\) 4.23240 0.186321
\(517\) 8.11901 0.357074
\(518\) −1.08327 −0.0475960
\(519\) 15.7698 0.692219
\(520\) 2.46244 0.107985
\(521\) 29.2264 1.28043 0.640216 0.768195i \(-0.278845\pi\)
0.640216 + 0.768195i \(0.278845\pi\)
\(522\) 14.4138 0.630876
\(523\) 16.1581 0.706545 0.353272 0.935520i \(-0.385069\pi\)
0.353272 + 0.935520i \(0.385069\pi\)
\(524\) 22.3784 0.977603
\(525\) −12.8391 −0.560345
\(526\) 35.7748 1.55986
\(527\) 1.16394 0.0507019
\(528\) 7.72674 0.336263
\(529\) −10.0881 −0.438612
\(530\) 45.3585 1.97025
\(531\) −3.16886 −0.137517
\(532\) 2.51061 0.108849
\(533\) 14.9854 0.649090
\(534\) 45.8306 1.98328
\(535\) 50.4844 2.18263
\(536\) −2.04335 −0.0882594
\(537\) 22.3371 0.963916
\(538\) 9.53236 0.410969
\(539\) 6.61973 0.285132
\(540\) 31.3568 1.34938
\(541\) −29.6948 −1.27668 −0.638339 0.769755i \(-0.720378\pi\)
−0.638339 + 0.769755i \(0.720378\pi\)
\(542\) 46.5853 2.00101
\(543\) −47.2019 −2.02563
\(544\) 8.07255 0.346108
\(545\) −5.77627 −0.247428
\(546\) 8.83470 0.378090
\(547\) −46.3890 −1.98345 −0.991724 0.128387i \(-0.959020\pi\)
−0.991724 + 0.128387i \(0.959020\pi\)
\(548\) 13.4312 0.573754
\(549\) 12.7946 0.546059
\(550\) 20.7815 0.886124
\(551\) 12.5773 0.535810
\(552\) −1.31150 −0.0558210
\(553\) −4.26071 −0.181184
\(554\) 42.0045 1.78460
\(555\) 6.87900 0.291997
\(556\) −2.70004 −0.114507
\(557\) 4.41040 0.186875 0.0934373 0.995625i \(-0.470215\pi\)
0.0934373 + 0.995625i \(0.470215\pi\)
\(558\) −2.59957 −0.110048
\(559\) 3.49708 0.147911
\(560\) −9.19239 −0.388449
\(561\) −2.02595 −0.0855358
\(562\) −23.5366 −0.992832
\(563\) 11.8063 0.497576 0.248788 0.968558i \(-0.419968\pi\)
0.248788 + 0.968558i \(0.419968\pi\)
\(564\) −34.3629 −1.44694
\(565\) −0.745952 −0.0313824
\(566\) −28.0832 −1.18043
\(567\) 6.84092 0.287292
\(568\) −2.03065 −0.0852041
\(569\) 32.2082 1.35024 0.675119 0.737709i \(-0.264092\pi\)
0.675119 + 0.737709i \(0.264092\pi\)
\(570\) −31.2060 −1.30708
\(571\) −12.6367 −0.528829 −0.264415 0.964409i \(-0.585179\pi\)
−0.264415 + 0.964409i \(0.585179\pi\)
\(572\) −7.30572 −0.305468
\(573\) −24.9751 −1.04335
\(574\) 5.34342 0.223030
\(575\) 36.9282 1.54001
\(576\) −9.60472 −0.400197
\(577\) 22.2664 0.926962 0.463481 0.886107i \(-0.346600\pi\)
0.463481 + 0.886107i \(0.346600\pi\)
\(578\) −2.02215 −0.0841103
\(579\) −2.43559 −0.101220
\(580\) 52.6966 2.18811
\(581\) 3.46937 0.143934
\(582\) 8.43441 0.349618
\(583\) −5.73888 −0.237680
\(584\) −0.787339 −0.0325803
\(585\) −15.0967 −0.624172
\(586\) 19.5286 0.806717
\(587\) −24.2252 −0.999882 −0.499941 0.866060i \(-0.666645\pi\)
−0.499941 + 0.866060i \(0.666645\pi\)
\(588\) −28.0173 −1.15542
\(589\) −2.26834 −0.0934653
\(590\) −22.6765 −0.933575
\(591\) −9.19007 −0.378029
\(592\) 3.31319 0.136171
\(593\) −6.21644 −0.255279 −0.127639 0.991821i \(-0.540740\pi\)
−0.127639 + 0.991821i \(0.540740\pi\)
\(594\) −7.76552 −0.318623
\(595\) 2.41024 0.0988104
\(596\) 24.2681 0.994058
\(597\) 25.1499 1.02932
\(598\) −25.4106 −1.03912
\(599\) 33.8019 1.38111 0.690553 0.723282i \(-0.257367\pi\)
0.690553 + 0.723282i \(0.257367\pi\)
\(600\) −3.75089 −0.153129
\(601\) −11.4599 −0.467460 −0.233730 0.972301i \(-0.575093\pi\)
−0.233730 + 0.972301i \(0.575093\pi\)
\(602\) 1.24697 0.0508228
\(603\) 12.5274 0.510153
\(604\) 15.2302 0.619709
\(605\) −3.90857 −0.158906
\(606\) 29.4943 1.19813
\(607\) −39.3802 −1.59839 −0.799197 0.601070i \(-0.794741\pi\)
−0.799197 + 0.601070i \(0.794741\pi\)
\(608\) −15.7322 −0.638025
\(609\) 8.06270 0.326717
\(610\) 91.5585 3.70710
\(611\) −28.3929 −1.14865
\(612\) 2.30736 0.0932695
\(613\) −29.4621 −1.18996 −0.594982 0.803739i \(-0.702841\pi\)
−0.594982 + 0.803739i \(0.702841\pi\)
\(614\) 49.5448 1.99947
\(615\) −33.9320 −1.36827
\(616\) −0.111093 −0.00447605
\(617\) −2.64954 −0.106667 −0.0533333 0.998577i \(-0.516985\pi\)
−0.0533333 + 0.998577i \(0.516985\pi\)
\(618\) 66.2532 2.66510
\(619\) −28.6501 −1.15155 −0.575773 0.817610i \(-0.695299\pi\)
−0.575773 + 0.817610i \(0.695299\pi\)
\(620\) −9.50395 −0.381688
\(621\) −13.7992 −0.553741
\(622\) −36.7472 −1.47343
\(623\) 6.89852 0.276383
\(624\) −27.0211 −1.08171
\(625\) 29.2303 1.16921
\(626\) −42.4967 −1.69851
\(627\) 3.94828 0.157679
\(628\) 45.5180 1.81636
\(629\) −0.868718 −0.0346380
\(630\) −5.38310 −0.214468
\(631\) −20.9029 −0.832132 −0.416066 0.909334i \(-0.636592\pi\)
−0.416066 + 0.909334i \(0.636592\pi\)
\(632\) −1.24475 −0.0495134
\(633\) 50.9734 2.02601
\(634\) 46.7122 1.85518
\(635\) −57.0236 −2.26291
\(636\) 24.2892 0.963130
\(637\) −23.1498 −0.917227
\(638\) −13.0503 −0.516667
\(639\) 12.4495 0.492493
\(640\) −5.62754 −0.222448
\(641\) −22.8407 −0.902155 −0.451078 0.892485i \(-0.648960\pi\)
−0.451078 + 0.892485i \(0.648960\pi\)
\(642\) 52.9153 2.08840
\(643\) 33.6497 1.32702 0.663508 0.748169i \(-0.269067\pi\)
0.663508 + 0.748169i \(0.269067\pi\)
\(644\) −4.62909 −0.182412
\(645\) −7.91857 −0.311793
\(646\) 3.94087 0.155051
\(647\) −27.6381 −1.08657 −0.543283 0.839549i \(-0.682819\pi\)
−0.543283 + 0.839549i \(0.682819\pi\)
\(648\) 1.99854 0.0785102
\(649\) 2.86909 0.112622
\(650\) −72.6745 −2.85053
\(651\) −1.45412 −0.0569916
\(652\) −18.7513 −0.734356
\(653\) 36.8604 1.44246 0.721230 0.692695i \(-0.243577\pi\)
0.721230 + 0.692695i \(0.243577\pi\)
\(654\) −6.05441 −0.236746
\(655\) −41.8687 −1.63594
\(656\) −16.3429 −0.638084
\(657\) 4.82701 0.188319
\(658\) −10.1242 −0.394682
\(659\) 30.2407 1.17801 0.589005 0.808129i \(-0.299520\pi\)
0.589005 + 0.808129i \(0.299520\pi\)
\(660\) 16.5426 0.643920
\(661\) −19.1948 −0.746592 −0.373296 0.927712i \(-0.621772\pi\)
−0.373296 + 0.927712i \(0.621772\pi\)
\(662\) 15.5126 0.602916
\(663\) 7.08492 0.275156
\(664\) 1.01356 0.0393337
\(665\) −4.69720 −0.182150
\(666\) 1.94022 0.0751818
\(667\) −23.1901 −0.897926
\(668\) −18.4877 −0.715312
\(669\) 1.61877 0.0625854
\(670\) 89.6463 3.46334
\(671\) −11.5842 −0.447205
\(672\) −10.0852 −0.389044
\(673\) −22.7730 −0.877833 −0.438917 0.898528i \(-0.644638\pi\)
−0.438917 + 0.898528i \(0.644638\pi\)
\(674\) 26.0590 1.00375
\(675\) −39.4657 −1.51904
\(676\) −1.60944 −0.0619014
\(677\) 15.4848 0.595129 0.297564 0.954702i \(-0.403826\pi\)
0.297564 + 0.954702i \(0.403826\pi\)
\(678\) −0.781872 −0.0300276
\(679\) 1.26957 0.0487215
\(680\) 0.704142 0.0270026
\(681\) −43.3128 −1.65975
\(682\) 2.35365 0.0901261
\(683\) −24.2280 −0.927057 −0.463529 0.886082i \(-0.653417\pi\)
−0.463529 + 0.886082i \(0.653417\pi\)
\(684\) −4.49670 −0.171936
\(685\) −25.1291 −0.960132
\(686\) −16.9834 −0.648430
\(687\) −9.42339 −0.359525
\(688\) −3.81388 −0.145403
\(689\) 20.0694 0.764582
\(690\) 57.5381 2.19044
\(691\) 25.4006 0.966285 0.483142 0.875542i \(-0.339495\pi\)
0.483142 + 0.875542i \(0.339495\pi\)
\(692\) 16.2613 0.618162
\(693\) 0.681085 0.0258723
\(694\) 34.8317 1.32219
\(695\) 5.05162 0.191619
\(696\) 2.35548 0.0892842
\(697\) 4.28511 0.162310
\(698\) −7.59110 −0.287328
\(699\) −41.2389 −1.55980
\(700\) −13.2392 −0.500396
\(701\) −27.4028 −1.03499 −0.517495 0.855686i \(-0.673136\pi\)
−0.517495 + 0.855686i \(0.673136\pi\)
\(702\) 27.1567 1.02496
\(703\) 1.69300 0.0638527
\(704\) 8.69614 0.327748
\(705\) 64.2910 2.42134
\(706\) 8.12144 0.305654
\(707\) 4.43956 0.166967
\(708\) −12.1431 −0.456367
\(709\) −38.8487 −1.45899 −0.729496 0.683985i \(-0.760245\pi\)
−0.729496 + 0.683985i \(0.760245\pi\)
\(710\) 89.0888 3.34344
\(711\) 7.63127 0.286195
\(712\) 2.01537 0.0755293
\(713\) 4.18239 0.156632
\(714\) 2.52630 0.0945446
\(715\) 13.6686 0.511176
\(716\) 23.0332 0.860792
\(717\) −58.1683 −2.17234
\(718\) 51.4032 1.91835
\(719\) 21.2829 0.793720 0.396860 0.917879i \(-0.370100\pi\)
0.396860 + 0.917879i \(0.370100\pi\)
\(720\) 16.4643 0.613588
\(721\) 9.97259 0.371399
\(722\) 30.7407 1.14405
\(723\) 17.8382 0.663408
\(724\) −48.6730 −1.80892
\(725\) −66.3240 −2.46321
\(726\) −4.09678 −0.152046
\(727\) 19.9248 0.738970 0.369485 0.929237i \(-0.379534\pi\)
0.369485 + 0.929237i \(0.379534\pi\)
\(728\) 0.388501 0.0143988
\(729\) 11.0877 0.410657
\(730\) 34.5423 1.27847
\(731\) 1.00000 0.0369863
\(732\) 49.0291 1.81217
\(733\) 38.8664 1.43556 0.717782 0.696268i \(-0.245157\pi\)
0.717782 + 0.696268i \(0.245157\pi\)
\(734\) 46.0101 1.69826
\(735\) 52.4188 1.93350
\(736\) 29.0072 1.06922
\(737\) −11.3423 −0.417799
\(738\) −9.57048 −0.352294
\(739\) 51.2332 1.88465 0.942323 0.334706i \(-0.108637\pi\)
0.942323 + 0.334706i \(0.108637\pi\)
\(740\) 7.09338 0.260758
\(741\) −13.8075 −0.507230
\(742\) 7.15622 0.262713
\(743\) −34.8354 −1.27799 −0.638994 0.769212i \(-0.720649\pi\)
−0.638994 + 0.769212i \(0.720649\pi\)
\(744\) −0.424816 −0.0155745
\(745\) −45.4041 −1.66348
\(746\) 46.9333 1.71835
\(747\) −6.21391 −0.227355
\(748\) −2.08909 −0.0763847
\(749\) 7.96494 0.291032
\(750\) 84.4967 3.08538
\(751\) 38.7739 1.41488 0.707440 0.706773i \(-0.249850\pi\)
0.707440 + 0.706773i \(0.249850\pi\)
\(752\) 30.9650 1.12918
\(753\) 24.9875 0.910594
\(754\) 45.6381 1.66204
\(755\) −28.4949 −1.03703
\(756\) 4.94718 0.179927
\(757\) 18.5025 0.672484 0.336242 0.941776i \(-0.390844\pi\)
0.336242 + 0.941776i \(0.390844\pi\)
\(758\) 5.87251 0.213299
\(759\) −7.27988 −0.264243
\(760\) −1.37227 −0.0497774
\(761\) −11.6430 −0.422059 −0.211029 0.977480i \(-0.567682\pi\)
−0.211029 + 0.977480i \(0.567682\pi\)
\(762\) −59.7694 −2.16522
\(763\) −0.911324 −0.0329922
\(764\) −25.7534 −0.931726
\(765\) −4.31694 −0.156079
\(766\) 74.8620 2.70488
\(767\) −10.0335 −0.362287
\(768\) 29.3374 1.05862
\(769\) −32.0730 −1.15658 −0.578292 0.815830i \(-0.696280\pi\)
−0.578292 + 0.815830i \(0.696280\pi\)
\(770\) 4.87387 0.175642
\(771\) 55.7984 2.00953
\(772\) −2.51150 −0.0903907
\(773\) 22.0240 0.792147 0.396073 0.918219i \(-0.370373\pi\)
0.396073 + 0.918219i \(0.370373\pi\)
\(774\) −2.23343 −0.0802788
\(775\) 11.9617 0.429676
\(776\) 0.370898 0.0133145
\(777\) 1.08530 0.0389350
\(778\) 11.8853 0.426110
\(779\) −8.35105 −0.299207
\(780\) −57.8509 −2.07139
\(781\) −11.2718 −0.403336
\(782\) −7.26622 −0.259840
\(783\) 24.7837 0.885695
\(784\) 25.2469 0.901675
\(785\) −85.1615 −3.03954
\(786\) −43.8848 −1.56532
\(787\) −29.1493 −1.03906 −0.519531 0.854452i \(-0.673893\pi\)
−0.519531 + 0.854452i \(0.673893\pi\)
\(788\) −9.47647 −0.337585
\(789\) −35.8421 −1.27601
\(790\) 54.6097 1.94293
\(791\) −0.117689 −0.00418454
\(792\) 0.198976 0.00707030
\(793\) 40.5111 1.43859
\(794\) 18.4027 0.653087
\(795\) −45.4438 −1.61172
\(796\) 25.9337 0.919197
\(797\) −22.4102 −0.793811 −0.396905 0.917859i \(-0.629916\pi\)
−0.396905 + 0.917859i \(0.629916\pi\)
\(798\) −4.92339 −0.174286
\(799\) −8.11901 −0.287230
\(800\) 82.9609 2.93311
\(801\) −12.3558 −0.436571
\(802\) 40.5934 1.43340
\(803\) −4.37038 −0.154228
\(804\) 48.0051 1.69301
\(805\) 8.66077 0.305252
\(806\) −8.23093 −0.289922
\(807\) −9.55028 −0.336186
\(808\) 1.29700 0.0456282
\(809\) −31.9802 −1.12436 −0.562182 0.827013i \(-0.690038\pi\)
−0.562182 + 0.827013i \(0.690038\pi\)
\(810\) −87.6803 −3.08077
\(811\) 39.7649 1.39634 0.698168 0.715934i \(-0.253999\pi\)
0.698168 + 0.715934i \(0.253999\pi\)
\(812\) 8.31397 0.291763
\(813\) −46.6729 −1.63689
\(814\) −1.75668 −0.0615715
\(815\) 35.0825 1.22889
\(816\) −7.72674 −0.270490
\(817\) −1.94885 −0.0681816
\(818\) −39.9646 −1.39733
\(819\) −2.38181 −0.0832273
\(820\) −34.9895 −1.22189
\(821\) −16.8400 −0.587720 −0.293860 0.955849i \(-0.594940\pi\)
−0.293860 + 0.955849i \(0.594940\pi\)
\(822\) −26.3391 −0.918682
\(823\) 23.7160 0.826688 0.413344 0.910575i \(-0.364361\pi\)
0.413344 + 0.910575i \(0.364361\pi\)
\(824\) 2.91345 0.101495
\(825\) −20.8205 −0.724878
\(826\) −3.57767 −0.124483
\(827\) −34.6843 −1.20609 −0.603046 0.797707i \(-0.706046\pi\)
−0.603046 + 0.797707i \(0.706046\pi\)
\(828\) 8.29107 0.288135
\(829\) −7.58080 −0.263292 −0.131646 0.991297i \(-0.542026\pi\)
−0.131646 + 0.991297i \(0.542026\pi\)
\(830\) −44.4670 −1.54347
\(831\) −42.0835 −1.45986
\(832\) −30.4111 −1.05432
\(833\) −6.61973 −0.229360
\(834\) 5.29487 0.183346
\(835\) 34.5895 1.19702
\(836\) 4.07132 0.140810
\(837\) −4.46979 −0.154498
\(838\) 70.4011 2.43197
\(839\) 36.7771 1.26969 0.634844 0.772640i \(-0.281064\pi\)
0.634844 + 0.772640i \(0.281064\pi\)
\(840\) −0.879696 −0.0303524
\(841\) 12.6501 0.436210
\(842\) −27.1068 −0.934163
\(843\) 23.5809 0.812168
\(844\) 52.5620 1.80926
\(845\) 3.01116 0.103587
\(846\) 18.1332 0.623433
\(847\) −0.616656 −0.0211886
\(848\) −21.8874 −0.751617
\(849\) 28.1360 0.965626
\(850\) −20.7815 −0.712798
\(851\) −3.12158 −0.107006
\(852\) 47.7066 1.63440
\(853\) 18.4854 0.632929 0.316464 0.948604i \(-0.397504\pi\)
0.316464 + 0.948604i \(0.397504\pi\)
\(854\) 14.4452 0.494305
\(855\) 8.41307 0.287721
\(856\) 2.32692 0.0795325
\(857\) 20.1190 0.687253 0.343627 0.939106i \(-0.388345\pi\)
0.343627 + 0.939106i \(0.388345\pi\)
\(858\) 14.3268 0.489108
\(859\) 12.5145 0.426988 0.213494 0.976944i \(-0.431516\pi\)
0.213494 + 0.976944i \(0.431516\pi\)
\(860\) −8.16535 −0.278436
\(861\) −5.35346 −0.182445
\(862\) 61.0107 2.07803
\(863\) −32.5646 −1.10851 −0.554256 0.832346i \(-0.686997\pi\)
−0.554256 + 0.832346i \(0.686997\pi\)
\(864\) −31.0005 −1.05466
\(865\) −30.4240 −1.03445
\(866\) −62.8308 −2.13508
\(867\) 2.02595 0.0688049
\(868\) −1.49944 −0.0508944
\(869\) −6.90937 −0.234384
\(870\) −103.340 −3.50355
\(871\) 39.6650 1.34400
\(872\) −0.266239 −0.00901600
\(873\) −2.27390 −0.0769597
\(874\) 14.1608 0.478996
\(875\) 12.7186 0.429969
\(876\) 18.4972 0.624962
\(877\) −51.2538 −1.73072 −0.865358 0.501154i \(-0.832909\pi\)
−0.865358 + 0.501154i \(0.832909\pi\)
\(878\) 0.652581 0.0220235
\(879\) −19.5653 −0.659920
\(880\) −14.9068 −0.502509
\(881\) −12.1003 −0.407671 −0.203836 0.979005i \(-0.565341\pi\)
−0.203836 + 0.979005i \(0.565341\pi\)
\(882\) 14.7847 0.497826
\(883\) −32.1222 −1.08100 −0.540499 0.841345i \(-0.681765\pi\)
−0.540499 + 0.841345i \(0.681765\pi\)
\(884\) 7.30572 0.245718
\(885\) 22.7191 0.763694
\(886\) −24.6091 −0.826758
\(887\) −25.5468 −0.857779 −0.428889 0.903357i \(-0.641095\pi\)
−0.428889 + 0.903357i \(0.641095\pi\)
\(888\) 0.317066 0.0106400
\(889\) −8.99663 −0.301737
\(890\) −88.4187 −2.96380
\(891\) 11.0936 0.371648
\(892\) 1.66922 0.0558897
\(893\) 15.8227 0.529488
\(894\) −47.5905 −1.59166
\(895\) −43.0938 −1.44047
\(896\) −0.887860 −0.0296613
\(897\) 25.4584 0.850030
\(898\) −8.46753 −0.282565
\(899\) −7.51168 −0.250529
\(900\) 23.7125 0.790418
\(901\) 5.73888 0.191190
\(902\) 8.66514 0.288518
\(903\) −1.24932 −0.0415746
\(904\) −0.0343823 −0.00114354
\(905\) 91.0644 3.02708
\(906\) −29.8670 −0.992264
\(907\) 18.3973 0.610872 0.305436 0.952213i \(-0.401198\pi\)
0.305436 + 0.952213i \(0.401198\pi\)
\(908\) −44.6626 −1.48218
\(909\) −7.95160 −0.263738
\(910\) −17.0443 −0.565015
\(911\) −28.5891 −0.947197 −0.473599 0.880741i \(-0.657045\pi\)
−0.473599 + 0.880741i \(0.657045\pi\)
\(912\) 15.0583 0.498629
\(913\) 5.62609 0.186197
\(914\) 15.1309 0.500486
\(915\) −91.7306 −3.03252
\(916\) −9.71707 −0.321061
\(917\) −6.60563 −0.218137
\(918\) 7.76552 0.256300
\(919\) −35.3462 −1.16596 −0.582982 0.812485i \(-0.698114\pi\)
−0.582982 + 0.812485i \(0.698114\pi\)
\(920\) 2.53020 0.0834183
\(921\) −49.6380 −1.63563
\(922\) −18.3307 −0.603690
\(923\) 39.4183 1.29747
\(924\) 2.60993 0.0858605
\(925\) −8.92773 −0.293542
\(926\) −10.5601 −0.347025
\(927\) −17.8617 −0.586655
\(928\) −52.0977 −1.71019
\(929\) 6.33066 0.207702 0.103851 0.994593i \(-0.466883\pi\)
0.103851 + 0.994593i \(0.466883\pi\)
\(930\) 18.6376 0.611150
\(931\) 12.9009 0.422809
\(932\) −42.5241 −1.39292
\(933\) 36.8163 1.20531
\(934\) −2.67323 −0.0874708
\(935\) 3.90857 0.127824
\(936\) −0.695836 −0.0227441
\(937\) 22.7343 0.742697 0.371348 0.928494i \(-0.378896\pi\)
0.371348 + 0.928494i \(0.378896\pi\)
\(938\) 14.1435 0.461802
\(939\) 42.5766 1.38944
\(940\) 66.2946 2.16229
\(941\) 40.9500 1.33493 0.667465 0.744641i \(-0.267379\pi\)
0.667465 + 0.744641i \(0.267379\pi\)
\(942\) −89.2623 −2.90832
\(943\) 15.3978 0.501420
\(944\) 10.9424 0.356144
\(945\) −9.25589 −0.301094
\(946\) 2.02215 0.0657458
\(947\) 28.7063 0.932831 0.466415 0.884566i \(-0.345545\pi\)
0.466415 + 0.884566i \(0.345545\pi\)
\(948\) 29.2432 0.949775
\(949\) 15.2836 0.496127
\(950\) 40.4999 1.31399
\(951\) −46.8000 −1.51760
\(952\) 0.111093 0.00360054
\(953\) −12.0592 −0.390635 −0.195318 0.980740i \(-0.562574\pi\)
−0.195318 + 0.980740i \(0.562574\pi\)
\(954\) −12.8174 −0.414978
\(955\) 48.1832 1.55917
\(956\) −59.9811 −1.93993
\(957\) 13.0749 0.422650
\(958\) 37.1064 1.19885
\(959\) −3.96462 −0.128024
\(960\) 68.8610 2.22248
\(961\) −29.6453 −0.956298
\(962\) 6.14325 0.198066
\(963\) −14.2658 −0.459710
\(964\) 18.3941 0.592433
\(965\) 4.69887 0.151262
\(966\) 9.07781 0.292074
\(967\) −28.5200 −0.917141 −0.458570 0.888658i \(-0.651638\pi\)
−0.458570 + 0.888658i \(0.651638\pi\)
\(968\) −0.180153 −0.00579035
\(969\) −3.94828 −0.126837
\(970\) −16.2721 −0.522466
\(971\) 30.9750 0.994036 0.497018 0.867740i \(-0.334428\pi\)
0.497018 + 0.867740i \(0.334428\pi\)
\(972\) −22.8846 −0.734024
\(973\) 0.796996 0.0255505
\(974\) 10.9794 0.351803
\(975\) 72.8111 2.33182
\(976\) −44.1809 −1.41420
\(977\) −45.8483 −1.46682 −0.733408 0.679789i \(-0.762072\pi\)
−0.733408 + 0.679789i \(0.762072\pi\)
\(978\) 36.7719 1.17583
\(979\) 11.1870 0.357537
\(980\) 54.0525 1.72664
\(981\) 1.63225 0.0521139
\(982\) 17.6996 0.564817
\(983\) 40.6723 1.29724 0.648622 0.761111i \(-0.275346\pi\)
0.648622 + 0.761111i \(0.275346\pi\)
\(984\) −1.56399 −0.0498582
\(985\) 17.7299 0.564923
\(986\) 13.0503 0.415607
\(987\) 10.1432 0.322862
\(988\) −14.2378 −0.452964
\(989\) 3.59332 0.114261
\(990\) −8.72950 −0.277442
\(991\) 5.32483 0.169149 0.0845745 0.996417i \(-0.473047\pi\)
0.0845745 + 0.996417i \(0.473047\pi\)
\(992\) 9.39594 0.298321
\(993\) −15.5418 −0.493205
\(994\) 14.0556 0.445816
\(995\) −48.5205 −1.53820
\(996\) −23.8119 −0.754507
\(997\) −8.92479 −0.282651 −0.141326 0.989963i \(-0.545136\pi\)
−0.141326 + 0.989963i \(0.545136\pi\)
\(998\) −55.8340 −1.76739
\(999\) 3.33608 0.105549
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 \(a_p\))