Properties

Label 5077.2.a.c.1.11
Level 5077
Weight 2
Character 5077.1
Self dual Yes
Analytic conductor 40.540
Analytic rank 0
Dimension 216
CM No

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Newspace parameters

Level: \( N \) = \( 5077 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5077.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(40.5400491062\)
Analytic rank: \(0\)
Dimension: \(216\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.50572 q^{2} +0.313570 q^{3} +4.27863 q^{4} +0.450260 q^{5} -0.785719 q^{6} -2.26718 q^{7} -5.70960 q^{8} -2.90167 q^{9} +O(q^{10})\) \(q-2.50572 q^{2} +0.313570 q^{3} +4.27863 q^{4} +0.450260 q^{5} -0.785719 q^{6} -2.26718 q^{7} -5.70960 q^{8} -2.90167 q^{9} -1.12823 q^{10} -2.74396 q^{11} +1.34165 q^{12} -2.41966 q^{13} +5.68090 q^{14} +0.141188 q^{15} +5.74941 q^{16} -7.94330 q^{17} +7.27078 q^{18} -1.73497 q^{19} +1.92650 q^{20} -0.710918 q^{21} +6.87560 q^{22} -2.77360 q^{23} -1.79036 q^{24} -4.79727 q^{25} +6.06299 q^{26} -1.85059 q^{27} -9.70040 q^{28} -0.443430 q^{29} -0.353778 q^{30} -5.40312 q^{31} -2.98719 q^{32} -0.860425 q^{33} +19.9037 q^{34} -1.02082 q^{35} -12.4152 q^{36} -6.10114 q^{37} +4.34736 q^{38} -0.758733 q^{39} -2.57081 q^{40} +0.142888 q^{41} +1.78136 q^{42} +0.303010 q^{43} -11.7404 q^{44} -1.30651 q^{45} +6.94987 q^{46} +5.28366 q^{47} +1.80284 q^{48} -1.85992 q^{49} +12.0206 q^{50} -2.49078 q^{51} -10.3528 q^{52} +6.89349 q^{53} +4.63705 q^{54} -1.23550 q^{55} +12.9447 q^{56} -0.544036 q^{57} +1.11111 q^{58} -10.4058 q^{59} +0.604092 q^{60} -7.98425 q^{61} +13.5387 q^{62} +6.57860 q^{63} -4.01375 q^{64} -1.08948 q^{65} +2.15598 q^{66} +2.58071 q^{67} -33.9864 q^{68} -0.869719 q^{69} +2.55789 q^{70} -10.4845 q^{71} +16.5674 q^{72} -1.45158 q^{73} +15.2878 q^{74} -1.50428 q^{75} -7.42331 q^{76} +6.22105 q^{77} +1.90117 q^{78} -11.3006 q^{79} +2.58873 q^{80} +8.12473 q^{81} -0.358037 q^{82} -3.05458 q^{83} -3.04176 q^{84} -3.57655 q^{85} -0.759257 q^{86} -0.139046 q^{87} +15.6669 q^{88} +1.92687 q^{89} +3.27374 q^{90} +5.48579 q^{91} -11.8672 q^{92} -1.69426 q^{93} -13.2394 q^{94} -0.781190 q^{95} -0.936694 q^{96} -14.5873 q^{97} +4.66043 q^{98} +7.96209 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.50572 −1.77181 −0.885906 0.463866i \(-0.846462\pi\)
−0.885906 + 0.463866i \(0.846462\pi\)
\(3\) 0.313570 0.181040 0.0905199 0.995895i \(-0.471147\pi\)
0.0905199 + 0.995895i \(0.471147\pi\)
\(4\) 4.27863 2.13931
\(5\) 0.450260 0.201363 0.100681 0.994919i \(-0.467898\pi\)
0.100681 + 0.994919i \(0.467898\pi\)
\(6\) −0.785719 −0.320768
\(7\) −2.26718 −0.856912 −0.428456 0.903563i \(-0.640942\pi\)
−0.428456 + 0.903563i \(0.640942\pi\)
\(8\) −5.70960 −2.01865
\(9\) −2.90167 −0.967225
\(10\) −1.12823 −0.356776
\(11\) −2.74396 −0.827336 −0.413668 0.910428i \(-0.635753\pi\)
−0.413668 + 0.910428i \(0.635753\pi\)
\(12\) 1.34165 0.387301
\(13\) −2.41966 −0.671093 −0.335546 0.942024i \(-0.608921\pi\)
−0.335546 + 0.942024i \(0.608921\pi\)
\(14\) 5.68090 1.51829
\(15\) 0.141188 0.0364546
\(16\) 5.74941 1.43735
\(17\) −7.94330 −1.92653 −0.963267 0.268547i \(-0.913457\pi\)
−0.963267 + 0.268547i \(0.913457\pi\)
\(18\) 7.27078 1.71374
\(19\) −1.73497 −0.398030 −0.199015 0.979996i \(-0.563774\pi\)
−0.199015 + 0.979996i \(0.563774\pi\)
\(20\) 1.92650 0.430778
\(21\) −0.710918 −0.155135
\(22\) 6.87560 1.46588
\(23\) −2.77360 −0.578336 −0.289168 0.957278i \(-0.593379\pi\)
−0.289168 + 0.957278i \(0.593379\pi\)
\(24\) −1.79036 −0.365456
\(25\) −4.79727 −0.959453
\(26\) 6.06299 1.18905
\(27\) −1.85059 −0.356146
\(28\) −9.70040 −1.83320
\(29\) −0.443430 −0.0823428 −0.0411714 0.999152i \(-0.513109\pi\)
−0.0411714 + 0.999152i \(0.513109\pi\)
\(30\) −0.353778 −0.0645907
\(31\) −5.40312 −0.970428 −0.485214 0.874395i \(-0.661258\pi\)
−0.485214 + 0.874395i \(0.661258\pi\)
\(32\) −2.98719 −0.528066
\(33\) −0.860425 −0.149781
\(34\) 19.9037 3.41345
\(35\) −1.02082 −0.172550
\(36\) −12.4152 −2.06920
\(37\) −6.10114 −1.00302 −0.501511 0.865151i \(-0.667222\pi\)
−0.501511 + 0.865151i \(0.667222\pi\)
\(38\) 4.34736 0.705234
\(39\) −0.758733 −0.121494
\(40\) −2.57081 −0.406481
\(41\) 0.142888 0.0223154 0.0111577 0.999938i \(-0.496448\pi\)
0.0111577 + 0.999938i \(0.496448\pi\)
\(42\) 1.78136 0.274870
\(43\) 0.303010 0.0462085 0.0231043 0.999733i \(-0.492645\pi\)
0.0231043 + 0.999733i \(0.492645\pi\)
\(44\) −11.7404 −1.76993
\(45\) −1.30651 −0.194763
\(46\) 6.94987 1.02470
\(47\) 5.28366 0.770702 0.385351 0.922770i \(-0.374080\pi\)
0.385351 + 0.922770i \(0.374080\pi\)
\(48\) 1.80284 0.260218
\(49\) −1.85992 −0.265702
\(50\) 12.0206 1.69997
\(51\) −2.49078 −0.348779
\(52\) −10.3528 −1.43568
\(53\) 6.89349 0.946894 0.473447 0.880822i \(-0.343010\pi\)
0.473447 + 0.880822i \(0.343010\pi\)
\(54\) 4.63705 0.631023
\(55\) −1.23550 −0.166595
\(56\) 12.9447 1.72980
\(57\) −0.544036 −0.0720593
\(58\) 1.11111 0.145896
\(59\) −10.4058 −1.35472 −0.677360 0.735652i \(-0.736876\pi\)
−0.677360 + 0.735652i \(0.736876\pi\)
\(60\) 0.604092 0.0779879
\(61\) −7.98425 −1.02228 −0.511139 0.859498i \(-0.670776\pi\)
−0.511139 + 0.859498i \(0.670776\pi\)
\(62\) 13.5387 1.71942
\(63\) 6.57860 0.828826
\(64\) −4.01375 −0.501719
\(65\) −1.08948 −0.135133
\(66\) 2.15598 0.265383
\(67\) 2.58071 0.315284 0.157642 0.987496i \(-0.449611\pi\)
0.157642 + 0.987496i \(0.449611\pi\)
\(68\) −33.9864 −4.12146
\(69\) −0.869719 −0.104702
\(70\) 2.55789 0.305726
\(71\) −10.4845 −1.24428 −0.622140 0.782906i \(-0.713737\pi\)
−0.622140 + 0.782906i \(0.713737\pi\)
\(72\) 16.5674 1.95249
\(73\) −1.45158 −0.169894 −0.0849472 0.996385i \(-0.527072\pi\)
−0.0849472 + 0.996385i \(0.527072\pi\)
\(74\) 15.2878 1.77717
\(75\) −1.50428 −0.173699
\(76\) −7.42331 −0.851512
\(77\) 6.22105 0.708954
\(78\) 1.90117 0.215265
\(79\) −11.3006 −1.27142 −0.635711 0.771928i \(-0.719293\pi\)
−0.635711 + 0.771928i \(0.719293\pi\)
\(80\) 2.58873 0.289429
\(81\) 8.12473 0.902748
\(82\) −0.358037 −0.0395386
\(83\) −3.05458 −0.335283 −0.167642 0.985848i \(-0.553615\pi\)
−0.167642 + 0.985848i \(0.553615\pi\)
\(84\) −3.04176 −0.331883
\(85\) −3.57655 −0.387932
\(86\) −0.759257 −0.0818728
\(87\) −0.139046 −0.0149073
\(88\) 15.6669 1.67010
\(89\) 1.92687 0.204248 0.102124 0.994772i \(-0.467436\pi\)
0.102124 + 0.994772i \(0.467436\pi\)
\(90\) 3.27374 0.345083
\(91\) 5.48579 0.575067
\(92\) −11.8672 −1.23724
\(93\) −1.69426 −0.175686
\(94\) −13.2394 −1.36554
\(95\) −0.781190 −0.0801484
\(96\) −0.936694 −0.0956010
\(97\) −14.5873 −1.48112 −0.740559 0.671991i \(-0.765439\pi\)
−0.740559 + 0.671991i \(0.765439\pi\)
\(98\) 4.66043 0.470774
\(99\) 7.96209 0.800220
\(100\) −20.5257 −2.05257
\(101\) 11.6875 1.16295 0.581474 0.813565i \(-0.302476\pi\)
0.581474 + 0.813565i \(0.302476\pi\)
\(102\) 6.24120 0.617971
\(103\) 8.80260 0.867346 0.433673 0.901070i \(-0.357217\pi\)
0.433673 + 0.901070i \(0.357217\pi\)
\(104\) 13.8153 1.35470
\(105\) −0.320098 −0.0312384
\(106\) −17.2732 −1.67772
\(107\) 2.22688 0.215281 0.107640 0.994190i \(-0.465670\pi\)
0.107640 + 0.994190i \(0.465670\pi\)
\(108\) −7.91798 −0.761908
\(109\) 17.0924 1.63715 0.818577 0.574397i \(-0.194763\pi\)
0.818577 + 0.574397i \(0.194763\pi\)
\(110\) 3.09581 0.295174
\(111\) −1.91314 −0.181587
\(112\) −13.0349 −1.23168
\(113\) 20.3906 1.91819 0.959094 0.283086i \(-0.0913583\pi\)
0.959094 + 0.283086i \(0.0913583\pi\)
\(114\) 1.36320 0.127675
\(115\) −1.24884 −0.116455
\(116\) −1.89727 −0.176157
\(117\) 7.02106 0.649097
\(118\) 26.0740 2.40031
\(119\) 18.0089 1.65087
\(120\) −0.806129 −0.0735892
\(121\) −3.47066 −0.315515
\(122\) 20.0063 1.81128
\(123\) 0.0448054 0.00403997
\(124\) −23.1179 −2.07605
\(125\) −4.41132 −0.394561
\(126\) −16.4841 −1.46852
\(127\) 11.4737 1.01813 0.509064 0.860729i \(-0.329992\pi\)
0.509064 + 0.860729i \(0.329992\pi\)
\(128\) 16.0317 1.41702
\(129\) 0.0950148 0.00836558
\(130\) 2.72992 0.239430
\(131\) −2.77884 −0.242789 −0.121394 0.992604i \(-0.538737\pi\)
−0.121394 + 0.992604i \(0.538737\pi\)
\(132\) −3.68144 −0.320428
\(133\) 3.93349 0.341077
\(134\) −6.46655 −0.558624
\(135\) −0.833247 −0.0717145
\(136\) 45.3531 3.88900
\(137\) 13.5591 1.15843 0.579214 0.815175i \(-0.303359\pi\)
0.579214 + 0.815175i \(0.303359\pi\)
\(138\) 2.17927 0.185512
\(139\) −0.298093 −0.0252839 −0.0126419 0.999920i \(-0.504024\pi\)
−0.0126419 + 0.999920i \(0.504024\pi\)
\(140\) −4.36771 −0.369139
\(141\) 1.65680 0.139528
\(142\) 26.2712 2.20463
\(143\) 6.63946 0.555219
\(144\) −16.6829 −1.39024
\(145\) −0.199659 −0.0165808
\(146\) 3.63725 0.301021
\(147\) −0.583214 −0.0481027
\(148\) −26.1045 −2.14578
\(149\) −10.8572 −0.889460 −0.444730 0.895665i \(-0.646700\pi\)
−0.444730 + 0.895665i \(0.646700\pi\)
\(150\) 3.76930 0.307762
\(151\) 4.99615 0.406581 0.203290 0.979119i \(-0.434836\pi\)
0.203290 + 0.979119i \(0.434836\pi\)
\(152\) 9.90601 0.803484
\(153\) 23.0489 1.86339
\(154\) −15.5882 −1.25613
\(155\) −2.43281 −0.195408
\(156\) −3.24634 −0.259915
\(157\) −10.1695 −0.811616 −0.405808 0.913958i \(-0.633010\pi\)
−0.405808 + 0.913958i \(0.633010\pi\)
\(158\) 28.3162 2.25272
\(159\) 2.16159 0.171425
\(160\) −1.34502 −0.106333
\(161\) 6.28825 0.495583
\(162\) −20.3583 −1.59950
\(163\) 0.976437 0.0764804 0.0382402 0.999269i \(-0.487825\pi\)
0.0382402 + 0.999269i \(0.487825\pi\)
\(164\) 0.611365 0.0477396
\(165\) −0.387415 −0.0301602
\(166\) 7.65391 0.594059
\(167\) 7.15683 0.553812 0.276906 0.960897i \(-0.410691\pi\)
0.276906 + 0.960897i \(0.410691\pi\)
\(168\) 4.05906 0.313163
\(169\) −7.14525 −0.549635
\(170\) 8.96184 0.687342
\(171\) 5.03433 0.384985
\(172\) 1.29647 0.0988546
\(173\) −12.6323 −0.960413 −0.480206 0.877156i \(-0.659438\pi\)
−0.480206 + 0.877156i \(0.659438\pi\)
\(174\) 0.348411 0.0264130
\(175\) 10.8762 0.822167
\(176\) −15.7762 −1.18917
\(177\) −3.26295 −0.245258
\(178\) −4.82820 −0.361889
\(179\) −7.05421 −0.527257 −0.263628 0.964624i \(-0.584919\pi\)
−0.263628 + 0.964624i \(0.584919\pi\)
\(180\) −5.59007 −0.416659
\(181\) 0.615411 0.0457431 0.0228716 0.999738i \(-0.492719\pi\)
0.0228716 + 0.999738i \(0.492719\pi\)
\(182\) −13.7459 −1.01891
\(183\) −2.50362 −0.185073
\(184\) 15.8362 1.16746
\(185\) −2.74710 −0.201971
\(186\) 4.24533 0.311283
\(187\) 21.7961 1.59389
\(188\) 22.6068 1.64877
\(189\) 4.19561 0.305186
\(190\) 1.95744 0.142008
\(191\) −17.5576 −1.27043 −0.635213 0.772337i \(-0.719088\pi\)
−0.635213 + 0.772337i \(0.719088\pi\)
\(192\) −1.25859 −0.0908310
\(193\) −13.7120 −0.987014 −0.493507 0.869742i \(-0.664285\pi\)
−0.493507 + 0.869742i \(0.664285\pi\)
\(194\) 36.5517 2.62426
\(195\) −0.341627 −0.0244644
\(196\) −7.95789 −0.568421
\(197\) 14.3532 1.02262 0.511311 0.859396i \(-0.329160\pi\)
0.511311 + 0.859396i \(0.329160\pi\)
\(198\) −19.9508 −1.41784
\(199\) −1.32532 −0.0939497 −0.0469749 0.998896i \(-0.514958\pi\)
−0.0469749 + 0.998896i \(0.514958\pi\)
\(200\) 27.3905 1.93680
\(201\) 0.809235 0.0570790
\(202\) −29.2855 −2.06052
\(203\) 1.00533 0.0705605
\(204\) −10.6571 −0.746148
\(205\) 0.0643368 0.00449348
\(206\) −22.0568 −1.53677
\(207\) 8.04809 0.559381
\(208\) −13.9116 −0.964596
\(209\) 4.76070 0.329305
\(210\) 0.802077 0.0553486
\(211\) −4.74629 −0.326748 −0.163374 0.986564i \(-0.552238\pi\)
−0.163374 + 0.986564i \(0.552238\pi\)
\(212\) 29.4947 2.02570
\(213\) −3.28762 −0.225264
\(214\) −5.57994 −0.381437
\(215\) 0.136433 0.00930467
\(216\) 10.5661 0.718934
\(217\) 12.2498 0.831572
\(218\) −42.8287 −2.90073
\(219\) −0.455171 −0.0307576
\(220\) −5.28624 −0.356398
\(221\) 19.2201 1.29288
\(222\) 4.79378 0.321738
\(223\) −8.27587 −0.554193 −0.277097 0.960842i \(-0.589372\pi\)
−0.277097 + 0.960842i \(0.589372\pi\)
\(224\) 6.77249 0.452506
\(225\) 13.9201 0.928007
\(226\) −51.0932 −3.39867
\(227\) −16.3732 −1.08673 −0.543363 0.839498i \(-0.682849\pi\)
−0.543363 + 0.839498i \(0.682849\pi\)
\(228\) −2.32773 −0.154158
\(229\) 11.2075 0.740616 0.370308 0.928909i \(-0.379252\pi\)
0.370308 + 0.928909i \(0.379252\pi\)
\(230\) 3.12925 0.206337
\(231\) 1.95073 0.128349
\(232\) 2.53181 0.166221
\(233\) −16.1590 −1.05861 −0.529307 0.848431i \(-0.677548\pi\)
−0.529307 + 0.848431i \(0.677548\pi\)
\(234\) −17.5928 −1.15008
\(235\) 2.37903 0.155190
\(236\) −44.5226 −2.89817
\(237\) −3.54354 −0.230178
\(238\) −45.1251 −2.92503
\(239\) −5.16096 −0.333835 −0.166917 0.985971i \(-0.553381\pi\)
−0.166917 + 0.985971i \(0.553381\pi\)
\(240\) 0.811749 0.0523981
\(241\) −13.7237 −0.884024 −0.442012 0.897009i \(-0.645735\pi\)
−0.442012 + 0.897009i \(0.645735\pi\)
\(242\) 8.69651 0.559033
\(243\) 8.09944 0.519579
\(244\) −34.1616 −2.18698
\(245\) −0.837447 −0.0535025
\(246\) −0.112270 −0.00715806
\(247\) 4.19804 0.267115
\(248\) 30.8497 1.95896
\(249\) −0.957824 −0.0606996
\(250\) 11.0535 0.699087
\(251\) 7.40750 0.467557 0.233779 0.972290i \(-0.424891\pi\)
0.233779 + 0.972290i \(0.424891\pi\)
\(252\) 28.1474 1.77312
\(253\) 7.61067 0.478479
\(254\) −28.7499 −1.80393
\(255\) −1.12150 −0.0702311
\(256\) −32.1435 −2.00897
\(257\) 28.2807 1.76410 0.882049 0.471157i \(-0.156163\pi\)
0.882049 + 0.471157i \(0.156163\pi\)
\(258\) −0.238080 −0.0148222
\(259\) 13.8324 0.859501
\(260\) −4.66147 −0.289092
\(261\) 1.28669 0.0796440
\(262\) 6.96300 0.430176
\(263\) −20.4513 −1.26108 −0.630539 0.776157i \(-0.717166\pi\)
−0.630539 + 0.776157i \(0.717166\pi\)
\(264\) 4.91269 0.302355
\(265\) 3.10387 0.190669
\(266\) −9.85622 −0.604324
\(267\) 0.604210 0.0369770
\(268\) 11.0419 0.674493
\(269\) 13.4126 0.817780 0.408890 0.912584i \(-0.365916\pi\)
0.408890 + 0.912584i \(0.365916\pi\)
\(270\) 2.08788 0.127064
\(271\) −10.8581 −0.659585 −0.329793 0.944053i \(-0.606979\pi\)
−0.329793 + 0.944053i \(0.606979\pi\)
\(272\) −45.6693 −2.76911
\(273\) 1.72018 0.104110
\(274\) −33.9752 −2.05252
\(275\) 13.1635 0.793790
\(276\) −3.72121 −0.223990
\(277\) 4.47678 0.268983 0.134492 0.990915i \(-0.457060\pi\)
0.134492 + 0.990915i \(0.457060\pi\)
\(278\) 0.746937 0.0447983
\(279\) 15.6781 0.938622
\(280\) 5.82848 0.348318
\(281\) −25.0148 −1.49226 −0.746130 0.665800i \(-0.768090\pi\)
−0.746130 + 0.665800i \(0.768090\pi\)
\(282\) −4.15147 −0.247217
\(283\) −11.0347 −0.655946 −0.327973 0.944687i \(-0.606365\pi\)
−0.327973 + 0.944687i \(0.606365\pi\)
\(284\) −44.8593 −2.66191
\(285\) −0.244958 −0.0145100
\(286\) −16.6366 −0.983744
\(287\) −0.323952 −0.0191223
\(288\) 8.66786 0.510759
\(289\) 46.0960 2.71153
\(290\) 0.500289 0.0293780
\(291\) −4.57415 −0.268141
\(292\) −6.21076 −0.363457
\(293\) 7.78307 0.454692 0.227346 0.973814i \(-0.426995\pi\)
0.227346 + 0.973814i \(0.426995\pi\)
\(294\) 1.46137 0.0852289
\(295\) −4.68532 −0.272790
\(296\) 34.8351 2.02475
\(297\) 5.07795 0.294652
\(298\) 27.2052 1.57595
\(299\) 6.71118 0.388117
\(300\) −6.43625 −0.371597
\(301\) −0.686976 −0.0395966
\(302\) −12.5189 −0.720384
\(303\) 3.66484 0.210540
\(304\) −9.97507 −0.572110
\(305\) −3.59499 −0.205849
\(306\) −57.7540 −3.30158
\(307\) −25.9073 −1.47861 −0.739304 0.673372i \(-0.764845\pi\)
−0.739304 + 0.673372i \(0.764845\pi\)
\(308\) 26.6176 1.51668
\(309\) 2.76023 0.157024
\(310\) 6.09594 0.346226
\(311\) −16.6273 −0.942846 −0.471423 0.881907i \(-0.656260\pi\)
−0.471423 + 0.881907i \(0.656260\pi\)
\(312\) 4.33206 0.245255
\(313\) −12.3582 −0.698524 −0.349262 0.937025i \(-0.613568\pi\)
−0.349262 + 0.937025i \(0.613568\pi\)
\(314\) 25.4820 1.43803
\(315\) 2.96209 0.166895
\(316\) −48.3512 −2.71997
\(317\) −2.83807 −0.159402 −0.0797009 0.996819i \(-0.525397\pi\)
−0.0797009 + 0.996819i \(0.525397\pi\)
\(318\) −5.41634 −0.303733
\(319\) 1.21675 0.0681252
\(320\) −1.80723 −0.101027
\(321\) 0.698284 0.0389744
\(322\) −15.7566 −0.878080
\(323\) 13.7814 0.766819
\(324\) 34.7627 1.93126
\(325\) 11.6077 0.643882
\(326\) −2.44668 −0.135509
\(327\) 5.35966 0.296390
\(328\) −0.815834 −0.0450469
\(329\) −11.9790 −0.660423
\(330\) 0.970754 0.0534382
\(331\) −14.7257 −0.809396 −0.404698 0.914450i \(-0.632623\pi\)
−0.404698 + 0.914450i \(0.632623\pi\)
\(332\) −13.0694 −0.717277
\(333\) 17.7035 0.970147
\(334\) −17.9330 −0.981250
\(335\) 1.16199 0.0634865
\(336\) −4.08736 −0.222984
\(337\) −31.7608 −1.73012 −0.865060 0.501669i \(-0.832720\pi\)
−0.865060 + 0.501669i \(0.832720\pi\)
\(338\) 17.9040 0.973849
\(339\) 6.39389 0.347268
\(340\) −15.3027 −0.829908
\(341\) 14.8260 0.802871
\(342\) −12.6146 −0.682120
\(343\) 20.0870 1.08460
\(344\) −1.73007 −0.0932789
\(345\) −0.391600 −0.0210830
\(346\) 31.6529 1.70167
\(347\) −15.6529 −0.840292 −0.420146 0.907457i \(-0.638021\pi\)
−0.420146 + 0.907457i \(0.638021\pi\)
\(348\) −0.594927 −0.0318914
\(349\) −13.1459 −0.703685 −0.351842 0.936059i \(-0.614445\pi\)
−0.351842 + 0.936059i \(0.614445\pi\)
\(350\) −27.2528 −1.45672
\(351\) 4.47779 0.239007
\(352\) 8.19675 0.436888
\(353\) 28.0385 1.49234 0.746168 0.665757i \(-0.231891\pi\)
0.746168 + 0.665757i \(0.231891\pi\)
\(354\) 8.17603 0.434551
\(355\) −4.72075 −0.250552
\(356\) 8.24438 0.436951
\(357\) 5.64704 0.298873
\(358\) 17.6759 0.934199
\(359\) 4.10661 0.216739 0.108369 0.994111i \(-0.465437\pi\)
0.108369 + 0.994111i \(0.465437\pi\)
\(360\) 7.45965 0.393158
\(361\) −15.9899 −0.841572
\(362\) −1.54205 −0.0810481
\(363\) −1.08830 −0.0571207
\(364\) 23.4717 1.23025
\(365\) −0.653588 −0.0342104
\(366\) 6.27337 0.327915
\(367\) 23.1623 1.20906 0.604532 0.796581i \(-0.293360\pi\)
0.604532 + 0.796581i \(0.293360\pi\)
\(368\) −15.9466 −0.831273
\(369\) −0.414614 −0.0215840
\(370\) 6.88347 0.357855
\(371\) −15.6288 −0.811404
\(372\) −7.24909 −0.375848
\(373\) −33.7730 −1.74870 −0.874350 0.485295i \(-0.838712\pi\)
−0.874350 + 0.485295i \(0.838712\pi\)
\(374\) −54.6150 −2.82407
\(375\) −1.38326 −0.0714312
\(376\) −30.1676 −1.55578
\(377\) 1.07295 0.0552596
\(378\) −10.5130 −0.540731
\(379\) −31.0955 −1.59727 −0.798634 0.601816i \(-0.794444\pi\)
−0.798634 + 0.601816i \(0.794444\pi\)
\(380\) −3.34242 −0.171463
\(381\) 3.59782 0.184322
\(382\) 43.9945 2.25096
\(383\) 29.9493 1.53034 0.765170 0.643828i \(-0.222655\pi\)
0.765170 + 0.643828i \(0.222655\pi\)
\(384\) 5.02707 0.256536
\(385\) 2.80109 0.142757
\(386\) 34.3585 1.74880
\(387\) −0.879235 −0.0446940
\(388\) −62.4137 −3.16858
\(389\) −33.3230 −1.68954 −0.844771 0.535128i \(-0.820264\pi\)
−0.844771 + 0.535128i \(0.820264\pi\)
\(390\) 0.856022 0.0433464
\(391\) 22.0316 1.11418
\(392\) 10.6194 0.536360
\(393\) −0.871362 −0.0439544
\(394\) −35.9650 −1.81189
\(395\) −5.08823 −0.256017
\(396\) 34.0668 1.71192
\(397\) 6.52875 0.327668 0.163834 0.986488i \(-0.447614\pi\)
0.163834 + 0.986488i \(0.447614\pi\)
\(398\) 3.32089 0.166461
\(399\) 1.23342 0.0617485
\(400\) −27.5814 −1.37907
\(401\) −30.5305 −1.52462 −0.762309 0.647213i \(-0.775934\pi\)
−0.762309 + 0.647213i \(0.775934\pi\)
\(402\) −2.02772 −0.101133
\(403\) 13.0737 0.651247
\(404\) 50.0064 2.48791
\(405\) 3.65825 0.181780
\(406\) −2.51908 −0.125020
\(407\) 16.7413 0.829836
\(408\) 14.2214 0.704063
\(409\) 6.27097 0.310080 0.155040 0.987908i \(-0.450449\pi\)
0.155040 + 0.987908i \(0.450449\pi\)
\(410\) −0.161210 −0.00796159
\(411\) 4.25172 0.209722
\(412\) 37.6631 1.85553
\(413\) 23.5918 1.16088
\(414\) −20.1663 −0.991118
\(415\) −1.37536 −0.0675135
\(416\) 7.22799 0.354381
\(417\) −0.0934730 −0.00457739
\(418\) −11.9290 −0.583466
\(419\) 28.7723 1.40562 0.702810 0.711378i \(-0.251929\pi\)
0.702810 + 0.711378i \(0.251929\pi\)
\(420\) −1.36958 −0.0668288
\(421\) −4.48112 −0.218396 −0.109198 0.994020i \(-0.534828\pi\)
−0.109198 + 0.994020i \(0.534828\pi\)
\(422\) 11.8929 0.578936
\(423\) −15.3315 −0.745442
\(424\) −39.3591 −1.91145
\(425\) 38.1061 1.84842
\(426\) 8.23786 0.399126
\(427\) 18.1017 0.876003
\(428\) 9.52801 0.460554
\(429\) 2.08193 0.100517
\(430\) −0.341864 −0.0164861
\(431\) −9.12226 −0.439404 −0.219702 0.975567i \(-0.570509\pi\)
−0.219702 + 0.975567i \(0.570509\pi\)
\(432\) −10.6398 −0.511907
\(433\) −11.2021 −0.538340 −0.269170 0.963093i \(-0.586749\pi\)
−0.269170 + 0.963093i \(0.586749\pi\)
\(434\) −30.6946 −1.47339
\(435\) −0.0626070 −0.00300178
\(436\) 73.1320 3.50239
\(437\) 4.81213 0.230195
\(438\) 1.14053 0.0544967
\(439\) −16.1141 −0.769085 −0.384542 0.923107i \(-0.625641\pi\)
−0.384542 + 0.923107i \(0.625641\pi\)
\(440\) 7.05421 0.336296
\(441\) 5.39687 0.256994
\(442\) −48.1601 −2.29074
\(443\) 18.2568 0.867407 0.433704 0.901056i \(-0.357206\pi\)
0.433704 + 0.901056i \(0.357206\pi\)
\(444\) −8.18560 −0.388471
\(445\) 0.867595 0.0411280
\(446\) 20.7370 0.981926
\(447\) −3.40451 −0.161028
\(448\) 9.09987 0.429929
\(449\) 31.7958 1.50054 0.750269 0.661133i \(-0.229924\pi\)
0.750269 + 0.661133i \(0.229924\pi\)
\(450\) −34.8799 −1.64425
\(451\) −0.392079 −0.0184623
\(452\) 87.2439 4.10361
\(453\) 1.56664 0.0736073
\(454\) 41.0266 1.92547
\(455\) 2.47003 0.115797
\(456\) 3.10623 0.145463
\(457\) −34.1179 −1.59597 −0.797984 0.602678i \(-0.794100\pi\)
−0.797984 + 0.602678i \(0.794100\pi\)
\(458\) −28.0830 −1.31223
\(459\) 14.6998 0.686127
\(460\) −5.34334 −0.249135
\(461\) −12.8224 −0.597200 −0.298600 0.954378i \(-0.596520\pi\)
−0.298600 + 0.954378i \(0.596520\pi\)
\(462\) −4.88799 −0.227410
\(463\) 22.8633 1.06255 0.531273 0.847201i \(-0.321714\pi\)
0.531273 + 0.847201i \(0.321714\pi\)
\(464\) −2.54946 −0.118356
\(465\) −0.762856 −0.0353766
\(466\) 40.4900 1.87566
\(467\) −20.0188 −0.926360 −0.463180 0.886264i \(-0.653292\pi\)
−0.463180 + 0.886264i \(0.653292\pi\)
\(468\) 30.0405 1.38862
\(469\) −5.85093 −0.270171
\(470\) −5.96117 −0.274968
\(471\) −3.18886 −0.146935
\(472\) 59.4130 2.73471
\(473\) −0.831448 −0.0382300
\(474\) 8.87912 0.407832
\(475\) 8.32313 0.381891
\(476\) 77.0532 3.53173
\(477\) −20.0027 −0.915859
\(478\) 12.9319 0.591492
\(479\) 18.2110 0.832080 0.416040 0.909346i \(-0.363418\pi\)
0.416040 + 0.909346i \(0.363418\pi\)
\(480\) −0.421756 −0.0192505
\(481\) 14.7627 0.673121
\(482\) 34.3879 1.56632
\(483\) 1.97181 0.0897203
\(484\) −14.8497 −0.674986
\(485\) −6.56809 −0.298242
\(486\) −20.2949 −0.920596
\(487\) 13.9922 0.634048 0.317024 0.948418i \(-0.397316\pi\)
0.317024 + 0.948418i \(0.397316\pi\)
\(488\) 45.5869 2.06362
\(489\) 0.306181 0.0138460
\(490\) 2.09841 0.0947963
\(491\) 15.2007 0.685997 0.342999 0.939336i \(-0.388557\pi\)
0.342999 + 0.939336i \(0.388557\pi\)
\(492\) 0.191706 0.00864276
\(493\) 3.52229 0.158636
\(494\) −10.5191 −0.473278
\(495\) 3.58501 0.161134
\(496\) −31.0647 −1.39485
\(497\) 23.7702 1.06624
\(498\) 2.40004 0.107548
\(499\) 4.38295 0.196208 0.0981040 0.995176i \(-0.468722\pi\)
0.0981040 + 0.995176i \(0.468722\pi\)
\(500\) −18.8744 −0.844089
\(501\) 2.24417 0.100262
\(502\) −18.5611 −0.828423
\(503\) 14.7282 0.656699 0.328350 0.944556i \(-0.393508\pi\)
0.328350 + 0.944556i \(0.393508\pi\)
\(504\) −37.5612 −1.67311
\(505\) 5.26241 0.234174
\(506\) −19.0702 −0.847774
\(507\) −2.24054 −0.0995057
\(508\) 49.0918 2.17810
\(509\) −3.67043 −0.162689 −0.0813444 0.996686i \(-0.525921\pi\)
−0.0813444 + 0.996686i \(0.525921\pi\)
\(510\) 2.81016 0.124436
\(511\) 3.29098 0.145584
\(512\) 48.4791 2.14249
\(513\) 3.21072 0.141757
\(514\) −70.8634 −3.12565
\(515\) 3.96346 0.174651
\(516\) 0.406533 0.0178966
\(517\) −14.4982 −0.637629
\(518\) −34.6600 −1.52287
\(519\) −3.96110 −0.173873
\(520\) 6.22048 0.272786
\(521\) −13.1276 −0.575129 −0.287565 0.957761i \(-0.592846\pi\)
−0.287565 + 0.957761i \(0.592846\pi\)
\(522\) −3.22408 −0.141114
\(523\) 3.89184 0.170178 0.0850892 0.996373i \(-0.472882\pi\)
0.0850892 + 0.996373i \(0.472882\pi\)
\(524\) −11.8896 −0.519402
\(525\) 3.41046 0.148845
\(526\) 51.2451 2.23439
\(527\) 42.9186 1.86956
\(528\) −4.94693 −0.215288
\(529\) −15.3071 −0.665527
\(530\) −7.77742 −0.337829
\(531\) 30.1943 1.31032
\(532\) 16.8299 0.729671
\(533\) −0.345740 −0.0149757
\(534\) −1.51398 −0.0655163
\(535\) 1.00268 0.0433495
\(536\) −14.7349 −0.636449
\(537\) −2.21199 −0.0954544
\(538\) −33.6082 −1.44895
\(539\) 5.10354 0.219825
\(540\) −3.56515 −0.153420
\(541\) −7.52504 −0.323527 −0.161763 0.986830i \(-0.551718\pi\)
−0.161763 + 0.986830i \(0.551718\pi\)
\(542\) 27.2074 1.16866
\(543\) 0.192974 0.00828132
\(544\) 23.7282 1.01734
\(545\) 7.69602 0.329661
\(546\) −4.31029 −0.184463
\(547\) 23.3623 0.998899 0.499449 0.866343i \(-0.333536\pi\)
0.499449 + 0.866343i \(0.333536\pi\)
\(548\) 58.0142 2.47824
\(549\) 23.1677 0.988773
\(550\) −32.9841 −1.40645
\(551\) 0.769339 0.0327749
\(552\) 4.96575 0.211356
\(553\) 25.6205 1.08950
\(554\) −11.2175 −0.476588
\(555\) −0.861409 −0.0365648
\(556\) −1.27543 −0.0540902
\(557\) −14.0713 −0.596219 −0.298109 0.954532i \(-0.596356\pi\)
−0.298109 + 0.954532i \(0.596356\pi\)
\(558\) −39.2849 −1.66306
\(559\) −0.733180 −0.0310102
\(560\) −5.86911 −0.248015
\(561\) 6.83461 0.288558
\(562\) 62.6802 2.64400
\(563\) −6.33521 −0.266997 −0.133499 0.991049i \(-0.542621\pi\)
−0.133499 + 0.991049i \(0.542621\pi\)
\(564\) 7.08883 0.298493
\(565\) 9.18109 0.386251
\(566\) 27.6499 1.16221
\(567\) −18.4202 −0.773575
\(568\) 59.8623 2.51177
\(569\) 30.8370 1.29275 0.646377 0.763018i \(-0.276283\pi\)
0.646377 + 0.763018i \(0.276283\pi\)
\(570\) 0.613796 0.0257091
\(571\) −0.782704 −0.0327551 −0.0163776 0.999866i \(-0.505213\pi\)
−0.0163776 + 0.999866i \(0.505213\pi\)
\(572\) 28.4078 1.18779
\(573\) −5.50555 −0.229998
\(574\) 0.811733 0.0338811
\(575\) 13.3057 0.554887
\(576\) 11.6466 0.485275
\(577\) 11.1486 0.464121 0.232061 0.972701i \(-0.425453\pi\)
0.232061 + 0.972701i \(0.425453\pi\)
\(578\) −115.504 −4.80432
\(579\) −4.29968 −0.178689
\(580\) −0.854266 −0.0354715
\(581\) 6.92526 0.287308
\(582\) 11.4615 0.475096
\(583\) −18.9155 −0.783400
\(584\) 8.28794 0.342957
\(585\) 3.16131 0.130704
\(586\) −19.5022 −0.805628
\(587\) −32.2431 −1.33081 −0.665407 0.746480i \(-0.731742\pi\)
−0.665407 + 0.746480i \(0.731742\pi\)
\(588\) −2.49536 −0.102907
\(589\) 9.37426 0.386260
\(590\) 11.7401 0.483332
\(591\) 4.50073 0.185135
\(592\) −35.0780 −1.44170
\(593\) −31.1141 −1.27770 −0.638851 0.769331i \(-0.720590\pi\)
−0.638851 + 0.769331i \(0.720590\pi\)
\(594\) −12.7239 −0.522068
\(595\) 8.10868 0.332423
\(596\) −46.4541 −1.90283
\(597\) −0.415582 −0.0170086
\(598\) −16.8163 −0.687671
\(599\) 2.06383 0.0843259 0.0421629 0.999111i \(-0.486575\pi\)
0.0421629 + 0.999111i \(0.486575\pi\)
\(600\) 8.58884 0.350638
\(601\) −24.4708 −0.998184 −0.499092 0.866549i \(-0.666333\pi\)
−0.499092 + 0.866549i \(0.666333\pi\)
\(602\) 1.72137 0.0701578
\(603\) −7.48839 −0.304951
\(604\) 21.3767 0.869804
\(605\) −1.56270 −0.0635329
\(606\) −9.18307 −0.373037
\(607\) −17.6775 −0.717506 −0.358753 0.933433i \(-0.616798\pi\)
−0.358753 + 0.933433i \(0.616798\pi\)
\(608\) 5.18270 0.210186
\(609\) 0.315242 0.0127743
\(610\) 9.00804 0.364725
\(611\) −12.7847 −0.517212
\(612\) 98.6175 3.98638
\(613\) −4.51992 −0.182558 −0.0912790 0.995825i \(-0.529096\pi\)
−0.0912790 + 0.995825i \(0.529096\pi\)
\(614\) 64.9164 2.61981
\(615\) 0.0201741 0.000813498 0
\(616\) −35.5197 −1.43113
\(617\) 17.7745 0.715573 0.357786 0.933803i \(-0.383532\pi\)
0.357786 + 0.933803i \(0.383532\pi\)
\(618\) −6.91637 −0.278217
\(619\) −26.0447 −1.04682 −0.523412 0.852079i \(-0.675341\pi\)
−0.523412 + 0.852079i \(0.675341\pi\)
\(620\) −10.4091 −0.418039
\(621\) 5.13280 0.205972
\(622\) 41.6633 1.67055
\(623\) −4.36856 −0.175023
\(624\) −4.36226 −0.174630
\(625\) 22.0001 0.880003
\(626\) 30.9661 1.23765
\(627\) 1.49281 0.0596173
\(628\) −43.5116 −1.73630
\(629\) 48.4632 1.93235
\(630\) −7.42215 −0.295706
\(631\) 49.1776 1.95773 0.978864 0.204513i \(-0.0655611\pi\)
0.978864 + 0.204513i \(0.0655611\pi\)
\(632\) 64.5222 2.56655
\(633\) −1.48829 −0.0591544
\(634\) 7.11140 0.282430
\(635\) 5.16616 0.205013
\(636\) 9.24865 0.366733
\(637\) 4.50036 0.178311
\(638\) −3.04885 −0.120705
\(639\) 30.4226 1.20350
\(640\) 7.21845 0.285334
\(641\) −19.9382 −0.787512 −0.393756 0.919215i \(-0.628825\pi\)
−0.393756 + 0.919215i \(0.628825\pi\)
\(642\) −1.74970 −0.0690553
\(643\) 23.4457 0.924608 0.462304 0.886722i \(-0.347023\pi\)
0.462304 + 0.886722i \(0.347023\pi\)
\(644\) 26.9051 1.06021
\(645\) 0.0427814 0.00168452
\(646\) −34.5324 −1.35866
\(647\) 22.6253 0.889493 0.444746 0.895657i \(-0.353294\pi\)
0.444746 + 0.895657i \(0.353294\pi\)
\(648\) −46.3890 −1.82233
\(649\) 28.5531 1.12081
\(650\) −29.0858 −1.14084
\(651\) 3.84117 0.150548
\(652\) 4.17781 0.163616
\(653\) 32.3837 1.26727 0.633635 0.773632i \(-0.281562\pi\)
0.633635 + 0.773632i \(0.281562\pi\)
\(654\) −13.4298 −0.525147
\(655\) −1.25120 −0.0488886
\(656\) 0.821521 0.0320750
\(657\) 4.21201 0.164326
\(658\) 30.0160 1.17015
\(659\) −40.7978 −1.58926 −0.794628 0.607097i \(-0.792334\pi\)
−0.794628 + 0.607097i \(0.792334\pi\)
\(660\) −1.65761 −0.0645222
\(661\) 22.9972 0.894489 0.447244 0.894412i \(-0.352405\pi\)
0.447244 + 0.894412i \(0.352405\pi\)
\(662\) 36.8984 1.43410
\(663\) 6.02684 0.234063
\(664\) 17.4404 0.676820
\(665\) 1.77109 0.0686801
\(666\) −44.3601 −1.71892
\(667\) 1.22990 0.0476218
\(668\) 30.6214 1.18478
\(669\) −2.59507 −0.100331
\(670\) −2.91163 −0.112486
\(671\) 21.9085 0.845768
\(672\) 2.12365 0.0819216
\(673\) 2.94046 0.113346 0.0566731 0.998393i \(-0.481951\pi\)
0.0566731 + 0.998393i \(0.481951\pi\)
\(674\) 79.5836 3.06545
\(675\) 8.87776 0.341705
\(676\) −30.5719 −1.17584
\(677\) −35.4035 −1.36067 −0.680333 0.732903i \(-0.738165\pi\)
−0.680333 + 0.732903i \(0.738165\pi\)
\(678\) −16.0213 −0.615294
\(679\) 33.0720 1.26919
\(680\) 20.4207 0.783098
\(681\) −5.13413 −0.196740
\(682\) −37.1497 −1.42253
\(683\) 25.6966 0.983254 0.491627 0.870806i \(-0.336402\pi\)
0.491627 + 0.870806i \(0.336402\pi\)
\(684\) 21.5400 0.823603
\(685\) 6.10511 0.233264
\(686\) −50.3323 −1.92170
\(687\) 3.51435 0.134081
\(688\) 1.74213 0.0664179
\(689\) −16.6799 −0.635454
\(690\) 0.981240 0.0373552
\(691\) 46.1735 1.75652 0.878261 0.478182i \(-0.158704\pi\)
0.878261 + 0.478182i \(0.158704\pi\)
\(692\) −54.0487 −2.05463
\(693\) −18.0514 −0.685718
\(694\) 39.2218 1.48884
\(695\) −0.134219 −0.00509123
\(696\) 0.793899 0.0300927
\(697\) −1.13500 −0.0429913
\(698\) 32.9400 1.24680
\(699\) −5.06699 −0.191651
\(700\) 46.5354 1.75887
\(701\) 7.75805 0.293017 0.146509 0.989209i \(-0.453196\pi\)
0.146509 + 0.989209i \(0.453196\pi\)
\(702\) −11.2201 −0.423475
\(703\) 10.5853 0.399233
\(704\) 11.0136 0.415090
\(705\) 0.745991 0.0280956
\(706\) −70.2565 −2.64414
\(707\) −26.4976 −0.996543
\(708\) −13.9609 −0.524685
\(709\) 12.5360 0.470800 0.235400 0.971899i \(-0.424360\pi\)
0.235400 + 0.971899i \(0.424360\pi\)
\(710\) 11.8289 0.443930
\(711\) 32.7908 1.22975
\(712\) −11.0017 −0.412306
\(713\) 14.9861 0.561234
\(714\) −14.1499 −0.529546
\(715\) 2.98948 0.111800
\(716\) −30.1824 −1.12797
\(717\) −1.61832 −0.0604374
\(718\) −10.2900 −0.384020
\(719\) −31.2742 −1.16633 −0.583165 0.812354i \(-0.698186\pi\)
−0.583165 + 0.812354i \(0.698186\pi\)
\(720\) −7.51165 −0.279943
\(721\) −19.9570 −0.743239
\(722\) 40.0661 1.49111
\(723\) −4.30336 −0.160044
\(724\) 2.63311 0.0978589
\(725\) 2.12725 0.0790041
\(726\) 2.72696 0.101207
\(727\) 19.7903 0.733982 0.366991 0.930224i \(-0.380388\pi\)
0.366991 + 0.930224i \(0.380388\pi\)
\(728\) −31.3217 −1.16086
\(729\) −21.8345 −0.808684
\(730\) 1.63771 0.0606143
\(731\) −2.40690 −0.0890223
\(732\) −10.7121 −0.395930
\(733\) −38.5548 −1.42406 −0.712028 0.702151i \(-0.752223\pi\)
−0.712028 + 0.702151i \(0.752223\pi\)
\(734\) −58.0383 −2.14223
\(735\) −0.262598 −0.00968608
\(736\) 8.28529 0.305400
\(737\) −7.08139 −0.260846
\(738\) 1.03891 0.0382427
\(739\) −6.00577 −0.220926 −0.110463 0.993880i \(-0.535233\pi\)
−0.110463 + 0.993880i \(0.535233\pi\)
\(740\) −11.7538 −0.432080
\(741\) 1.31638 0.0483585
\(742\) 39.1613 1.43766
\(743\) 22.9137 0.840622 0.420311 0.907380i \(-0.361921\pi\)
0.420311 + 0.907380i \(0.361921\pi\)
\(744\) 9.67353 0.354649
\(745\) −4.88859 −0.179104
\(746\) 84.6257 3.09837
\(747\) 8.86339 0.324294
\(748\) 93.2575 3.40983
\(749\) −5.04873 −0.184477
\(750\) 3.46606 0.126563
\(751\) −31.4220 −1.14661 −0.573303 0.819343i \(-0.694338\pi\)
−0.573303 + 0.819343i \(0.694338\pi\)
\(752\) 30.3779 1.10777
\(753\) 2.32277 0.0846465
\(754\) −2.68851 −0.0979097
\(755\) 2.24957 0.0818701
\(756\) 17.9515 0.652888
\(757\) −30.1880 −1.09720 −0.548601 0.836084i \(-0.684839\pi\)
−0.548601 + 0.836084i \(0.684839\pi\)
\(758\) 77.9166 2.83006
\(759\) 2.38648 0.0866236
\(760\) 4.46029 0.161792
\(761\) 9.31657 0.337725 0.168863 0.985640i \(-0.445991\pi\)
0.168863 + 0.985640i \(0.445991\pi\)
\(762\) −9.01512 −0.326583
\(763\) −38.7514 −1.40290
\(764\) −75.1226 −2.71784
\(765\) 10.3780 0.375217
\(766\) −75.0447 −2.71147
\(767\) 25.1785 0.909143
\(768\) −10.0792 −0.363703
\(769\) −10.3196 −0.372133 −0.186066 0.982537i \(-0.559574\pi\)
−0.186066 + 0.982537i \(0.559574\pi\)
\(770\) −7.01875 −0.252938
\(771\) 8.86797 0.319372
\(772\) −58.6687 −2.11153
\(773\) −27.4937 −0.988881 −0.494441 0.869211i \(-0.664627\pi\)
−0.494441 + 0.869211i \(0.664627\pi\)
\(774\) 2.20312 0.0791894
\(775\) 25.9202 0.931081
\(776\) 83.2878 2.98986
\(777\) 4.33741 0.155604
\(778\) 83.4981 2.99355
\(779\) −0.247907 −0.00888218
\(780\) −1.46170 −0.0523371
\(781\) 28.7691 1.02944
\(782\) −55.2049 −1.97412
\(783\) 0.820605 0.0293260
\(784\) −10.6934 −0.381908
\(785\) −4.57893 −0.163429
\(786\) 2.18339 0.0778789
\(787\) −39.1479 −1.39547 −0.697736 0.716355i \(-0.745809\pi\)
−0.697736 + 0.716355i \(0.745809\pi\)
\(788\) 61.4119 2.18771
\(789\) −6.41290 −0.228305
\(790\) 12.7497 0.453613
\(791\) −46.2291 −1.64372
\(792\) −45.4604 −1.61536
\(793\) 19.3192 0.686044
\(794\) −16.3592 −0.580566
\(795\) 0.973280 0.0345187
\(796\) −5.67057 −0.200988
\(797\) 9.64106 0.341504 0.170752 0.985314i \(-0.445380\pi\)
0.170752 + 0.985314i \(0.445380\pi\)
\(798\) −3.09062 −0.109407
\(799\) −41.9697 −1.48478
\(800\) 14.3304 0.506655
\(801\) −5.59116 −0.197554
\(802\) 76.5007 2.70133
\(803\) 3.98308 0.140560
\(804\) 3.46242 0.122110
\(805\) 2.83135 0.0997919
\(806\) −32.7590 −1.15389
\(807\) 4.20579 0.148051
\(808\) −66.7309 −2.34758
\(809\) 52.6848 1.85230 0.926149 0.377158i \(-0.123098\pi\)
0.926149 + 0.377158i \(0.123098\pi\)
\(810\) −9.16654 −0.322079
\(811\) 12.1832 0.427809 0.213905 0.976855i \(-0.431382\pi\)
0.213905 + 0.976855i \(0.431382\pi\)
\(812\) 4.30144 0.150951
\(813\) −3.40479 −0.119411
\(814\) −41.9490 −1.47031
\(815\) 0.439651 0.0154003
\(816\) −14.3205 −0.501318
\(817\) −0.525714 −0.0183924
\(818\) −15.7133 −0.549402
\(819\) −15.9180 −0.556219
\(820\) 0.275273 0.00961296
\(821\) −21.9469 −0.765951 −0.382975 0.923759i \(-0.625101\pi\)
−0.382975 + 0.923759i \(0.625101\pi\)
\(822\) −10.6536 −0.371587
\(823\) −41.9032 −1.46065 −0.730327 0.683098i \(-0.760632\pi\)
−0.730327 + 0.683098i \(0.760632\pi\)
\(824\) −50.2594 −1.75087
\(825\) 4.12769 0.143708
\(826\) −59.1144 −2.05685
\(827\) −7.21165 −0.250774 −0.125387 0.992108i \(-0.540017\pi\)
−0.125387 + 0.992108i \(0.540017\pi\)
\(828\) 34.4348 1.19669
\(829\) 50.0425 1.73805 0.869024 0.494770i \(-0.164748\pi\)
0.869024 + 0.494770i \(0.164748\pi\)
\(830\) 3.44625 0.119621
\(831\) 1.40378 0.0486967
\(832\) 9.71190 0.336700
\(833\) 14.7739 0.511884
\(834\) 0.234217 0.00811027
\(835\) 3.22244 0.111517
\(836\) 20.3693 0.704487
\(837\) 9.99894 0.345614
\(838\) −72.0953 −2.49049
\(839\) 15.1486 0.522989 0.261495 0.965205i \(-0.415785\pi\)
0.261495 + 0.965205i \(0.415785\pi\)
\(840\) 1.82764 0.0630594
\(841\) −28.8034 −0.993220
\(842\) 11.2284 0.386957
\(843\) −7.84391 −0.270159
\(844\) −20.3076 −0.699017
\(845\) −3.21722 −0.110676
\(846\) 38.4164 1.32078
\(847\) 7.86860 0.270368
\(848\) 39.6335 1.36102
\(849\) −3.46016 −0.118752
\(850\) −95.4832 −3.27505
\(851\) 16.9222 0.580084
\(852\) −14.0665 −0.481911
\(853\) −37.8000 −1.29425 −0.647124 0.762385i \(-0.724028\pi\)
−0.647124 + 0.762385i \(0.724028\pi\)
\(854\) −45.3578 −1.55211
\(855\) 2.26676 0.0775215
\(856\) −12.7146 −0.434577
\(857\) −22.4546 −0.767033 −0.383517 0.923534i \(-0.625287\pi\)
−0.383517 + 0.923534i \(0.625287\pi\)
\(858\) −5.21674 −0.178097
\(859\) 24.8383 0.847471 0.423736 0.905786i \(-0.360719\pi\)
0.423736 + 0.905786i \(0.360719\pi\)
\(860\) 0.583747 0.0199056
\(861\) −0.101582 −0.00346189
\(862\) 22.8578 0.778541
\(863\) 22.1548 0.754158 0.377079 0.926181i \(-0.376929\pi\)
0.377079 + 0.926181i \(0.376929\pi\)
\(864\) 5.52806 0.188069
\(865\) −5.68781 −0.193391
\(866\) 28.0694 0.953837
\(867\) 14.4543 0.490895
\(868\) 52.4124 1.77899
\(869\) 31.0085 1.05189
\(870\) 0.156876 0.00531858
\(871\) −6.24445 −0.211585
\(872\) −97.5908 −3.30484
\(873\) 42.3277 1.43257
\(874\) −12.0578 −0.407863
\(875\) 10.0012 0.338104
\(876\) −1.94751 −0.0658003
\(877\) −34.5612 −1.16705 −0.583525 0.812095i \(-0.698327\pi\)
−0.583525 + 0.812095i \(0.698327\pi\)
\(878\) 40.3775 1.36267
\(879\) 2.44054 0.0823173
\(880\) −7.10338 −0.239455
\(881\) −18.1847 −0.612659 −0.306330 0.951925i \(-0.599101\pi\)
−0.306330 + 0.951925i \(0.599101\pi\)
\(882\) −13.5230 −0.455344
\(883\) −1.51004 −0.0508169 −0.0254084 0.999677i \(-0.508089\pi\)
−0.0254084 + 0.999677i \(0.508089\pi\)
\(884\) 82.2356 2.76588
\(885\) −1.46918 −0.0493858
\(886\) −45.7464 −1.53688
\(887\) 11.8609 0.398251 0.199125 0.979974i \(-0.436190\pi\)
0.199125 + 0.979974i \(0.436190\pi\)
\(888\) 10.9232 0.366560
\(889\) −26.0129 −0.872446
\(890\) −2.17395 −0.0728710
\(891\) −22.2940 −0.746876
\(892\) −35.4094 −1.18559
\(893\) −9.16702 −0.306763
\(894\) 8.53074 0.285311
\(895\) −3.17623 −0.106170
\(896\) −36.3467 −1.21426
\(897\) 2.10442 0.0702647
\(898\) −79.6714 −2.65867
\(899\) 2.39590 0.0799078
\(900\) 59.5589 1.98530
\(901\) −54.7571 −1.82422
\(902\) 0.982441 0.0327117
\(903\) −0.215415 −0.00716857
\(904\) −116.422 −3.87215
\(905\) 0.277095 0.00921095
\(906\) −3.92556 −0.130418
\(907\) 5.84159 0.193967 0.0969835 0.995286i \(-0.469081\pi\)
0.0969835 + 0.995286i \(0.469081\pi\)
\(908\) −70.0547 −2.32485
\(909\) −33.9132 −1.12483
\(910\) −6.18921 −0.205170
\(911\) 49.9718 1.65564 0.827820 0.560993i \(-0.189581\pi\)
0.827820 + 0.560993i \(0.189581\pi\)
\(912\) −3.12788 −0.103575
\(913\) 8.38165 0.277392
\(914\) 85.4899 2.82776
\(915\) −1.12728 −0.0372668
\(916\) 47.9529 1.58441
\(917\) 6.30013 0.208049
\(918\) −36.8335 −1.21569
\(919\) −59.6154 −1.96653 −0.983265 0.182180i \(-0.941685\pi\)
−0.983265 + 0.182180i \(0.941685\pi\)
\(920\) 7.13041 0.235083
\(921\) −8.12375 −0.267687
\(922\) 32.1294 1.05813
\(923\) 25.3689 0.835028
\(924\) 8.34647 0.274579
\(925\) 29.2688 0.962352
\(926\) −57.2889 −1.88263
\(927\) −25.5423 −0.838918
\(928\) 1.32461 0.0434824
\(929\) 29.6554 0.972961 0.486481 0.873691i \(-0.338280\pi\)
0.486481 + 0.873691i \(0.338280\pi\)
\(930\) 1.91150 0.0626807
\(931\) 3.22690 0.105758
\(932\) −69.1385 −2.26471
\(933\) −5.21382 −0.170693
\(934\) 50.1615 1.64133
\(935\) 9.81393 0.320950
\(936\) −40.0875 −1.31030
\(937\) 40.4045 1.31996 0.659978 0.751285i \(-0.270566\pi\)
0.659978 + 0.751285i \(0.270566\pi\)
\(938\) 14.6608 0.478692
\(939\) −3.87515 −0.126461
\(940\) 10.1790 0.332001
\(941\) −15.8654 −0.517196 −0.258598 0.965985i \(-0.583260\pi\)
−0.258598 + 0.965985i \(0.583260\pi\)
\(942\) 7.99038 0.260341
\(943\) −0.396315 −0.0129058
\(944\) −59.8272 −1.94721
\(945\) 1.88912 0.0614530
\(946\) 2.08337 0.0677363
\(947\) 35.6003 1.15685 0.578427 0.815734i \(-0.303667\pi\)
0.578427 + 0.815734i \(0.303667\pi\)
\(948\) −15.1615 −0.492423
\(949\) 3.51232 0.114015
\(950\) −20.8554 −0.676639
\(951\) −0.889933 −0.0288581
\(952\) −102.823 −3.33253
\(953\) −26.6967 −0.864792 −0.432396 0.901684i \(-0.642332\pi\)
−0.432396 + 0.901684i \(0.642332\pi\)
\(954\) 50.1211 1.62273
\(955\) −7.90551 −0.255816
\(956\) −22.0818 −0.714178
\(957\) 0.381538 0.0123334
\(958\) −45.6316 −1.47429
\(959\) −30.7408 −0.992671
\(960\) −0.566694 −0.0182900
\(961\) −1.80633 −0.0582687
\(962\) −36.9911 −1.19264
\(963\) −6.46169 −0.208225
\(964\) −58.7188 −1.89121
\(965\) −6.17399 −0.198748
\(966\) −4.94079 −0.158967
\(967\) 43.2358 1.39037 0.695185 0.718831i \(-0.255322\pi\)
0.695185 + 0.718831i \(0.255322\pi\)
\(968\) 19.8161 0.636914
\(969\) 4.32144 0.138825
\(970\) 16.4578 0.528428
\(971\) −35.7737 −1.14803 −0.574017 0.818844i \(-0.694616\pi\)
−0.574017 + 0.818844i \(0.694616\pi\)
\(972\) 34.6545 1.11154
\(973\) 0.675829 0.0216661
\(974\) −35.0606 −1.12341
\(975\) 3.63984 0.116568
\(976\) −45.9047 −1.46937
\(977\) −25.7365 −0.823385 −0.411693 0.911323i \(-0.635062\pi\)
−0.411693 + 0.911323i \(0.635062\pi\)
\(978\) −0.767204 −0.0245325
\(979\) −5.28727 −0.168982
\(980\) −3.58312 −0.114459
\(981\) −49.5965 −1.58350
\(982\) −38.0886 −1.21546
\(983\) 11.4551 0.365361 0.182681 0.983172i \(-0.441523\pi\)
0.182681 + 0.983172i \(0.441523\pi\)
\(984\) −0.255821 −0.00815528
\(985\) 6.46267 0.205918
\(986\) −8.82588 −0.281073
\(987\) −3.75625 −0.119563
\(988\) 17.9619 0.571443
\(989\) −0.840429 −0.0267241
\(990\) −8.98304 −0.285500
\(991\) −26.7326 −0.849188 −0.424594 0.905384i \(-0.639583\pi\)
−0.424594 + 0.905384i \(0.639583\pi\)
\(992\) 16.1402 0.512450
\(993\) −4.61753 −0.146533
\(994\) −59.5614 −1.88917
\(995\) −0.596741 −0.0189180
\(996\) −4.09817 −0.129856
\(997\) 36.2075 1.14670 0.573351 0.819310i \(-0.305643\pi\)
0.573351 + 0.819310i \(0.305643\pi\)
\(998\) −10.9825 −0.347644
\(999\) 11.2907 0.357222
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 \(a_p\))