Properties

Label 5077.2.a.c.1.14
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 1.14
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.46114 q^{2} +2.54758 q^{3} +4.05723 q^{4} +0.498025 q^{5} -6.26997 q^{6} -4.84312 q^{7} -5.06313 q^{8} +3.49018 q^{9} +O(q^{10})\) \(q-2.46114 q^{2} +2.54758 q^{3} +4.05723 q^{4} +0.498025 q^{5} -6.26997 q^{6} -4.84312 q^{7} -5.06313 q^{8} +3.49018 q^{9} -1.22571 q^{10} -3.11702 q^{11} +10.3361 q^{12} -3.68171 q^{13} +11.9196 q^{14} +1.26876 q^{15} +4.34664 q^{16} +1.96034 q^{17} -8.58983 q^{18} -2.10999 q^{19} +2.02060 q^{20} -12.3383 q^{21} +7.67144 q^{22} -5.10126 q^{23} -12.8988 q^{24} -4.75197 q^{25} +9.06122 q^{26} +1.24877 q^{27} -19.6497 q^{28} -9.54412 q^{29} -3.12260 q^{30} +5.27605 q^{31} -0.571449 q^{32} -7.94087 q^{33} -4.82469 q^{34} -2.41200 q^{35} +14.1605 q^{36} +10.8609 q^{37} +5.19299 q^{38} -9.37947 q^{39} -2.52157 q^{40} +6.08868 q^{41} +30.3662 q^{42} +6.41401 q^{43} -12.6465 q^{44} +1.73820 q^{45} +12.5549 q^{46} -5.11266 q^{47} +11.0734 q^{48} +16.4559 q^{49} +11.6953 q^{50} +4.99414 q^{51} -14.9375 q^{52} +5.59624 q^{53} -3.07341 q^{54} -1.55236 q^{55} +24.5214 q^{56} -5.37538 q^{57} +23.4894 q^{58} +5.97964 q^{59} +5.14765 q^{60} -10.2278 q^{61} -12.9851 q^{62} -16.9034 q^{63} -7.28687 q^{64} -1.83359 q^{65} +19.5436 q^{66} +4.03308 q^{67} +7.95356 q^{68} -12.9959 q^{69} +5.93627 q^{70} +14.4935 q^{71} -17.6712 q^{72} +0.0705208 q^{73} -26.7302 q^{74} -12.1060 q^{75} -8.56072 q^{76} +15.0961 q^{77} +23.0842 q^{78} +3.20700 q^{79} +2.16474 q^{80} -7.28919 q^{81} -14.9851 q^{82} -3.85529 q^{83} -50.0591 q^{84} +0.976300 q^{85} -15.7858 q^{86} -24.3144 q^{87} +15.7819 q^{88} +1.63395 q^{89} -4.27795 q^{90} +17.8310 q^{91} -20.6970 q^{92} +13.4412 q^{93} +12.5830 q^{94} -1.05083 q^{95} -1.45581 q^{96} +9.03075 q^{97} -40.5002 q^{98} -10.8790 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46114 −1.74029 −0.870146 0.492795i \(-0.835975\pi\)
−0.870146 + 0.492795i \(0.835975\pi\)
\(3\) 2.54758 1.47085 0.735424 0.677607i \(-0.236983\pi\)
0.735424 + 0.677607i \(0.236983\pi\)
\(4\) 4.05723 2.02861
\(5\) 0.498025 0.222724 0.111362 0.993780i \(-0.464479\pi\)
0.111362 + 0.993780i \(0.464479\pi\)
\(6\) −6.26997 −2.55970
\(7\) −4.84312 −1.83053 −0.915264 0.402854i \(-0.868018\pi\)
−0.915264 + 0.402854i \(0.868018\pi\)
\(8\) −5.06313 −1.79009
\(9\) 3.49018 1.16339
\(10\) −1.22571 −0.387604
\(11\) −3.11702 −0.939818 −0.469909 0.882715i \(-0.655713\pi\)
−0.469909 + 0.882715i \(0.655713\pi\)
\(12\) 10.3361 2.98378
\(13\) −3.68171 −1.02112 −0.510562 0.859841i \(-0.670562\pi\)
−0.510562 + 0.859841i \(0.670562\pi\)
\(14\) 11.9196 3.18565
\(15\) 1.26876 0.327593
\(16\) 4.34664 1.08666
\(17\) 1.96034 0.475453 0.237726 0.971332i \(-0.423598\pi\)
0.237726 + 0.971332i \(0.423598\pi\)
\(18\) −8.58983 −2.02464
\(19\) −2.10999 −0.484065 −0.242033 0.970268i \(-0.577814\pi\)
−0.242033 + 0.970268i \(0.577814\pi\)
\(20\) 2.02060 0.451820
\(21\) −12.3383 −2.69243
\(22\) 7.67144 1.63556
\(23\) −5.10126 −1.06369 −0.531844 0.846843i \(-0.678501\pi\)
−0.531844 + 0.846843i \(0.678501\pi\)
\(24\) −12.8988 −2.63295
\(25\) −4.75197 −0.950394
\(26\) 9.06122 1.77705
\(27\) 1.24877 0.240326
\(28\) −19.6497 −3.71344
\(29\) −9.54412 −1.77230 −0.886149 0.463400i \(-0.846629\pi\)
−0.886149 + 0.463400i \(0.846629\pi\)
\(30\) −3.12260 −0.570106
\(31\) 5.27605 0.947607 0.473803 0.880631i \(-0.342881\pi\)
0.473803 + 0.880631i \(0.342881\pi\)
\(32\) −0.571449 −0.101019
\(33\) −7.94087 −1.38233
\(34\) −4.82469 −0.827427
\(35\) −2.41200 −0.407702
\(36\) 14.1605 2.36008
\(37\) 10.8609 1.78552 0.892759 0.450534i \(-0.148767\pi\)
0.892759 + 0.450534i \(0.148767\pi\)
\(38\) 5.19299 0.842415
\(39\) −9.37947 −1.50192
\(40\) −2.52157 −0.398695
\(41\) 6.08868 0.950891 0.475446 0.879745i \(-0.342287\pi\)
0.475446 + 0.879745i \(0.342287\pi\)
\(42\) 30.3662 4.68561
\(43\) 6.41401 0.978128 0.489064 0.872248i \(-0.337338\pi\)
0.489064 + 0.872248i \(0.337338\pi\)
\(44\) −12.6465 −1.90653
\(45\) 1.73820 0.259115
\(46\) 12.5549 1.85113
\(47\) −5.11266 −0.745758 −0.372879 0.927880i \(-0.621629\pi\)
−0.372879 + 0.927880i \(0.621629\pi\)
\(48\) 11.0734 1.59831
\(49\) 16.4559 2.35084
\(50\) 11.6953 1.65396
\(51\) 4.99414 0.699319
\(52\) −14.9375 −2.07147
\(53\) 5.59624 0.768702 0.384351 0.923187i \(-0.374425\pi\)
0.384351 + 0.923187i \(0.374425\pi\)
\(54\) −3.07341 −0.418238
\(55\) −1.55236 −0.209320
\(56\) 24.5214 3.27681
\(57\) −5.37538 −0.711986
\(58\) 23.4894 3.08432
\(59\) 5.97964 0.778483 0.389241 0.921136i \(-0.372737\pi\)
0.389241 + 0.921136i \(0.372737\pi\)
\(60\) 5.14765 0.664559
\(61\) −10.2278 −1.30953 −0.654767 0.755831i \(-0.727233\pi\)
−0.654767 + 0.755831i \(0.727233\pi\)
\(62\) −12.9851 −1.64911
\(63\) −16.9034 −2.12962
\(64\) −7.28687 −0.910859
\(65\) −1.83359 −0.227428
\(66\) 19.5436 2.40565
\(67\) 4.03308 0.492720 0.246360 0.969178i \(-0.420765\pi\)
0.246360 + 0.969178i \(0.420765\pi\)
\(68\) 7.95356 0.964511
\(69\) −12.9959 −1.56452
\(70\) 5.93627 0.709520
\(71\) 14.4935 1.72006 0.860029 0.510245i \(-0.170445\pi\)
0.860029 + 0.510245i \(0.170445\pi\)
\(72\) −17.6712 −2.08258
\(73\) 0.0705208 0.00825384 0.00412692 0.999991i \(-0.498686\pi\)
0.00412692 + 0.999991i \(0.498686\pi\)
\(74\) −26.7302 −3.10732
\(75\) −12.1060 −1.39789
\(76\) −8.56072 −0.981982
\(77\) 15.0961 1.72036
\(78\) 23.0842 2.61377
\(79\) 3.20700 0.360815 0.180408 0.983592i \(-0.442258\pi\)
0.180408 + 0.983592i \(0.442258\pi\)
\(80\) 2.16474 0.242025
\(81\) −7.28919 −0.809910
\(82\) −14.9851 −1.65483
\(83\) −3.85529 −0.423173 −0.211587 0.977359i \(-0.567863\pi\)
−0.211587 + 0.977359i \(0.567863\pi\)
\(84\) −50.0591 −5.46190
\(85\) 0.976300 0.105895
\(86\) −15.7858 −1.70223
\(87\) −24.3144 −2.60678
\(88\) 15.7819 1.68236
\(89\) 1.63395 0.173199 0.0865993 0.996243i \(-0.472400\pi\)
0.0865993 + 0.996243i \(0.472400\pi\)
\(90\) −4.27795 −0.450936
\(91\) 17.8310 1.86920
\(92\) −20.6970 −2.15781
\(93\) 13.4412 1.39379
\(94\) 12.5830 1.29784
\(95\) −1.05083 −0.107813
\(96\) −1.45581 −0.148583
\(97\) 9.03075 0.916934 0.458467 0.888712i \(-0.348399\pi\)
0.458467 + 0.888712i \(0.348399\pi\)
\(98\) −40.5002 −4.09114
\(99\) −10.8790 −1.09338
\(100\) −19.2798 −1.92798
\(101\) 8.75427 0.871083 0.435541 0.900169i \(-0.356557\pi\)
0.435541 + 0.900169i \(0.356557\pi\)
\(102\) −12.2913 −1.21702
\(103\) 4.69400 0.462514 0.231257 0.972893i \(-0.425716\pi\)
0.231257 + 0.972893i \(0.425716\pi\)
\(104\) 18.6410 1.82790
\(105\) −6.14476 −0.599668
\(106\) −13.7731 −1.33777
\(107\) 14.2147 1.37419 0.687095 0.726568i \(-0.258886\pi\)
0.687095 + 0.726568i \(0.258886\pi\)
\(108\) 5.06655 0.487529
\(109\) −10.9113 −1.04511 −0.522555 0.852606i \(-0.675021\pi\)
−0.522555 + 0.852606i \(0.675021\pi\)
\(110\) 3.82057 0.364277
\(111\) 27.6690 2.62623
\(112\) −21.0513 −1.98916
\(113\) 2.90892 0.273648 0.136824 0.990595i \(-0.456310\pi\)
0.136824 + 0.990595i \(0.456310\pi\)
\(114\) 13.2296 1.23906
\(115\) −2.54056 −0.236908
\(116\) −38.7227 −3.59531
\(117\) −12.8498 −1.18797
\(118\) −14.7168 −1.35479
\(119\) −9.49418 −0.870330
\(120\) −6.42390 −0.586420
\(121\) −1.28417 −0.116743
\(122\) 25.1720 2.27897
\(123\) 15.5114 1.39862
\(124\) 21.4061 1.92233
\(125\) −4.85673 −0.434399
\(126\) 41.6016 3.70617
\(127\) 12.9759 1.15143 0.575713 0.817652i \(-0.304725\pi\)
0.575713 + 0.817652i \(0.304725\pi\)
\(128\) 19.0769 1.68618
\(129\) 16.3402 1.43868
\(130\) 4.51272 0.395791
\(131\) −4.12382 −0.360300 −0.180150 0.983639i \(-0.557658\pi\)
−0.180150 + 0.983639i \(0.557658\pi\)
\(132\) −32.2179 −2.80421
\(133\) 10.2190 0.886095
\(134\) −9.92600 −0.857476
\(135\) 0.621920 0.0535263
\(136\) −9.92548 −0.851103
\(137\) 3.38638 0.289318 0.144659 0.989482i \(-0.453792\pi\)
0.144659 + 0.989482i \(0.453792\pi\)
\(138\) 31.9848 2.72272
\(139\) 5.81049 0.492839 0.246420 0.969163i \(-0.420746\pi\)
0.246420 + 0.969163i \(0.420746\pi\)
\(140\) −9.78602 −0.827070
\(141\) −13.0249 −1.09690
\(142\) −35.6705 −2.99340
\(143\) 11.4760 0.959670
\(144\) 15.1706 1.26421
\(145\) −4.75321 −0.394733
\(146\) −0.173562 −0.0143641
\(147\) 41.9227 3.45772
\(148\) 44.0651 3.62213
\(149\) 5.66001 0.463686 0.231843 0.972753i \(-0.425524\pi\)
0.231843 + 0.972753i \(0.425524\pi\)
\(150\) 29.7947 2.43273
\(151\) 4.89829 0.398618 0.199309 0.979937i \(-0.436130\pi\)
0.199309 + 0.979937i \(0.436130\pi\)
\(152\) 10.6832 0.866520
\(153\) 6.84195 0.553139
\(154\) −37.1537 −2.99393
\(155\) 2.62761 0.211054
\(156\) −38.0546 −3.04681
\(157\) −17.0242 −1.35868 −0.679339 0.733825i \(-0.737733\pi\)
−0.679339 + 0.733825i \(0.737733\pi\)
\(158\) −7.89288 −0.627924
\(159\) 14.2569 1.13064
\(160\) −0.284596 −0.0224993
\(161\) 24.7061 1.94711
\(162\) 17.9397 1.40948
\(163\) 8.55783 0.670301 0.335151 0.942165i \(-0.391213\pi\)
0.335151 + 0.942165i \(0.391213\pi\)
\(164\) 24.7031 1.92899
\(165\) −3.95475 −0.307877
\(166\) 9.48843 0.736445
\(167\) −8.77925 −0.679359 −0.339679 0.940541i \(-0.610319\pi\)
−0.339679 + 0.940541i \(0.610319\pi\)
\(168\) 62.4703 4.81969
\(169\) 0.555006 0.0426927
\(170\) −2.40281 −0.184287
\(171\) −7.36425 −0.563158
\(172\) 26.0231 1.98424
\(173\) 9.75543 0.741692 0.370846 0.928694i \(-0.379068\pi\)
0.370846 + 0.928694i \(0.379068\pi\)
\(174\) 59.8413 4.53656
\(175\) 23.0144 1.73972
\(176\) −13.5486 −1.02126
\(177\) 15.2336 1.14503
\(178\) −4.02139 −0.301416
\(179\) 17.1359 1.28080 0.640400 0.768042i \(-0.278769\pi\)
0.640400 + 0.768042i \(0.278769\pi\)
\(180\) 7.05226 0.525645
\(181\) −9.50242 −0.706310 −0.353155 0.935565i \(-0.614891\pi\)
−0.353155 + 0.935565i \(0.614891\pi\)
\(182\) −43.8846 −3.25295
\(183\) −26.0561 −1.92612
\(184\) 25.8284 1.90409
\(185\) 5.40899 0.397677
\(186\) −33.0807 −2.42559
\(187\) −6.11043 −0.446839
\(188\) −20.7432 −1.51285
\(189\) −6.04796 −0.439924
\(190\) 2.58624 0.187626
\(191\) −4.68020 −0.338647 −0.169324 0.985560i \(-0.554158\pi\)
−0.169324 + 0.985560i \(0.554158\pi\)
\(192\) −18.5639 −1.33973
\(193\) 26.0836 1.87754 0.938771 0.344543i \(-0.111966\pi\)
0.938771 + 0.344543i \(0.111966\pi\)
\(194\) −22.2260 −1.59573
\(195\) −4.67121 −0.334512
\(196\) 66.7652 4.76894
\(197\) 3.91475 0.278915 0.139457 0.990228i \(-0.455464\pi\)
0.139457 + 0.990228i \(0.455464\pi\)
\(198\) 26.7747 1.90280
\(199\) −15.1426 −1.07343 −0.536716 0.843763i \(-0.680335\pi\)
−0.536716 + 0.843763i \(0.680335\pi\)
\(200\) 24.0599 1.70129
\(201\) 10.2746 0.724716
\(202\) −21.5455 −1.51594
\(203\) 46.2234 3.24424
\(204\) 20.2623 1.41865
\(205\) 3.03231 0.211786
\(206\) −11.5526 −0.804909
\(207\) −17.8043 −1.23749
\(208\) −16.0031 −1.10962
\(209\) 6.57689 0.454933
\(210\) 15.1231 1.04360
\(211\) −27.8910 −1.92010 −0.960048 0.279834i \(-0.909721\pi\)
−0.960048 + 0.279834i \(0.909721\pi\)
\(212\) 22.7052 1.55940
\(213\) 36.9233 2.52994
\(214\) −34.9845 −2.39149
\(215\) 3.19434 0.217852
\(216\) −6.32270 −0.430205
\(217\) −25.5526 −1.73462
\(218\) 26.8542 1.81879
\(219\) 0.179658 0.0121401
\(220\) −6.29826 −0.424629
\(221\) −7.21742 −0.485496
\(222\) −68.0974 −4.57040
\(223\) −21.3522 −1.42985 −0.714926 0.699201i \(-0.753539\pi\)
−0.714926 + 0.699201i \(0.753539\pi\)
\(224\) 2.76760 0.184918
\(225\) −16.5852 −1.10568
\(226\) −7.15927 −0.476228
\(227\) −1.24150 −0.0824010 −0.0412005 0.999151i \(-0.513118\pi\)
−0.0412005 + 0.999151i \(0.513118\pi\)
\(228\) −21.8091 −1.44435
\(229\) 24.5978 1.62547 0.812734 0.582635i \(-0.197978\pi\)
0.812734 + 0.582635i \(0.197978\pi\)
\(230\) 6.25268 0.412289
\(231\) 38.4586 2.53039
\(232\) 48.3232 3.17257
\(233\) 17.6700 1.15760 0.578801 0.815469i \(-0.303521\pi\)
0.578801 + 0.815469i \(0.303521\pi\)
\(234\) 31.6253 2.06741
\(235\) −2.54623 −0.166098
\(236\) 24.2608 1.57924
\(237\) 8.17009 0.530704
\(238\) 23.3666 1.51463
\(239\) 21.3992 1.38420 0.692101 0.721801i \(-0.256685\pi\)
0.692101 + 0.721801i \(0.256685\pi\)
\(240\) 5.51485 0.355982
\(241\) 17.4458 1.12378 0.561892 0.827211i \(-0.310074\pi\)
0.561892 + 0.827211i \(0.310074\pi\)
\(242\) 3.16053 0.203167
\(243\) −22.3161 −1.43158
\(244\) −41.4965 −2.65654
\(245\) 8.19543 0.523587
\(246\) −38.1758 −2.43400
\(247\) 7.76838 0.494290
\(248\) −26.7134 −1.69630
\(249\) −9.82168 −0.622423
\(250\) 11.9531 0.755981
\(251\) 25.5777 1.61445 0.807224 0.590246i \(-0.200969\pi\)
0.807224 + 0.590246i \(0.200969\pi\)
\(252\) −68.5808 −4.32019
\(253\) 15.9008 0.999672
\(254\) −31.9356 −2.00382
\(255\) 2.48721 0.155755
\(256\) −32.3773 −2.02358
\(257\) −18.8741 −1.17733 −0.588666 0.808376i \(-0.700347\pi\)
−0.588666 + 0.808376i \(0.700347\pi\)
\(258\) −40.2157 −2.50372
\(259\) −52.6006 −3.26844
\(260\) −7.43927 −0.461364
\(261\) −33.3107 −2.06188
\(262\) 10.1493 0.627026
\(263\) −21.8899 −1.34979 −0.674895 0.737914i \(-0.735811\pi\)
−0.674895 + 0.737914i \(0.735811\pi\)
\(264\) 40.2057 2.47449
\(265\) 2.78707 0.171208
\(266\) −25.1503 −1.54206
\(267\) 4.16263 0.254749
\(268\) 16.3631 0.999538
\(269\) −25.5912 −1.56033 −0.780163 0.625576i \(-0.784864\pi\)
−0.780163 + 0.625576i \(0.784864\pi\)
\(270\) −1.53063 −0.0931514
\(271\) 17.2043 1.04509 0.522543 0.852613i \(-0.324984\pi\)
0.522543 + 0.852613i \(0.324984\pi\)
\(272\) 8.52091 0.516656
\(273\) 45.4259 2.74930
\(274\) −8.33436 −0.503497
\(275\) 14.8120 0.893197
\(276\) −52.7273 −3.17381
\(277\) −25.6496 −1.54113 −0.770567 0.637359i \(-0.780027\pi\)
−0.770567 + 0.637359i \(0.780027\pi\)
\(278\) −14.3005 −0.857684
\(279\) 18.4144 1.10244
\(280\) 12.2123 0.729823
\(281\) −19.4675 −1.16134 −0.580668 0.814140i \(-0.697209\pi\)
−0.580668 + 0.814140i \(0.697209\pi\)
\(282\) 32.0562 1.90892
\(283\) −0.968842 −0.0575917 −0.0287958 0.999585i \(-0.509167\pi\)
−0.0287958 + 0.999585i \(0.509167\pi\)
\(284\) 58.8033 3.48934
\(285\) −2.67707 −0.158576
\(286\) −28.2440 −1.67010
\(287\) −29.4882 −1.74063
\(288\) −1.99446 −0.117525
\(289\) −13.1571 −0.773944
\(290\) 11.6983 0.686950
\(291\) 23.0066 1.34867
\(292\) 0.286119 0.0167438
\(293\) 12.1498 0.709800 0.354900 0.934904i \(-0.384515\pi\)
0.354900 + 0.934904i \(0.384515\pi\)
\(294\) −103.178 −6.01744
\(295\) 2.97801 0.173387
\(296\) −54.9901 −3.19624
\(297\) −3.89245 −0.225863
\(298\) −13.9301 −0.806949
\(299\) 18.7814 1.08616
\(300\) −49.1170 −2.83577
\(301\) −31.0639 −1.79049
\(302\) −12.0554 −0.693711
\(303\) 22.3022 1.28123
\(304\) −9.17138 −0.526015
\(305\) −5.09369 −0.291664
\(306\) −16.8390 −0.962622
\(307\) 0.314156 0.0179298 0.00896492 0.999960i \(-0.497146\pi\)
0.00896492 + 0.999960i \(0.497146\pi\)
\(308\) 61.2484 3.48995
\(309\) 11.9584 0.680287
\(310\) −6.46692 −0.367296
\(311\) −1.50810 −0.0855166 −0.0427583 0.999085i \(-0.513615\pi\)
−0.0427583 + 0.999085i \(0.513615\pi\)
\(312\) 47.4895 2.68856
\(313\) 10.4059 0.588176 0.294088 0.955778i \(-0.404984\pi\)
0.294088 + 0.955778i \(0.404984\pi\)
\(314\) 41.8990 2.36450
\(315\) −8.41830 −0.474318
\(316\) 13.0115 0.731955
\(317\) 21.7763 1.22308 0.611538 0.791215i \(-0.290551\pi\)
0.611538 + 0.791215i \(0.290551\pi\)
\(318\) −35.0882 −1.96765
\(319\) 29.7492 1.66564
\(320\) −3.62905 −0.202870
\(321\) 36.2132 2.02122
\(322\) −60.8051 −3.38854
\(323\) −4.13631 −0.230150
\(324\) −29.5739 −1.64299
\(325\) 17.4954 0.970470
\(326\) −21.0621 −1.16652
\(327\) −27.7973 −1.53720
\(328\) −30.8278 −1.70218
\(329\) 24.7612 1.36513
\(330\) 9.73322 0.535796
\(331\) 2.69039 0.147877 0.0739386 0.997263i \(-0.476443\pi\)
0.0739386 + 0.997263i \(0.476443\pi\)
\(332\) −15.6418 −0.858455
\(333\) 37.9064 2.07726
\(334\) 21.6070 1.18228
\(335\) 2.00858 0.109740
\(336\) −53.6300 −2.92576
\(337\) −14.7306 −0.802424 −0.401212 0.915985i \(-0.631411\pi\)
−0.401212 + 0.915985i \(0.631411\pi\)
\(338\) −1.36595 −0.0742978
\(339\) 7.41072 0.402495
\(340\) 3.96107 0.214819
\(341\) −16.4456 −0.890577
\(342\) 18.1245 0.980059
\(343\) −45.7959 −2.47274
\(344\) −32.4750 −1.75094
\(345\) −6.47228 −0.348456
\(346\) −24.0095 −1.29076
\(347\) −9.84756 −0.528645 −0.264322 0.964434i \(-0.585148\pi\)
−0.264322 + 0.964434i \(0.585148\pi\)
\(348\) −98.6492 −5.28815
\(349\) −27.9788 −1.49767 −0.748836 0.662755i \(-0.769387\pi\)
−0.748836 + 0.662755i \(0.769387\pi\)
\(350\) −56.6417 −3.02763
\(351\) −4.59762 −0.245403
\(352\) 1.78122 0.0949392
\(353\) 23.5344 1.25261 0.626306 0.779577i \(-0.284566\pi\)
0.626306 + 0.779577i \(0.284566\pi\)
\(354\) −37.4922 −1.99269
\(355\) 7.21811 0.383098
\(356\) 6.62932 0.351353
\(357\) −24.1872 −1.28012
\(358\) −42.1740 −2.22896
\(359\) −0.0937245 −0.00494659 −0.00247329 0.999997i \(-0.500787\pi\)
−0.00247329 + 0.999997i \(0.500787\pi\)
\(360\) −8.80072 −0.463839
\(361\) −14.5479 −0.765681
\(362\) 23.3868 1.22918
\(363\) −3.27153 −0.171711
\(364\) 72.3444 3.79188
\(365\) 0.0351211 0.00183832
\(366\) 64.1279 3.35202
\(367\) 30.6013 1.59737 0.798687 0.601747i \(-0.205528\pi\)
0.798687 + 0.601747i \(0.205528\pi\)
\(368\) −22.1734 −1.15587
\(369\) 21.2506 1.10626
\(370\) −13.3123 −0.692074
\(371\) −27.1033 −1.40713
\(372\) 54.5339 2.82745
\(373\) −17.9035 −0.927009 −0.463504 0.886095i \(-0.653408\pi\)
−0.463504 + 0.886095i \(0.653408\pi\)
\(374\) 15.0387 0.777630
\(375\) −12.3729 −0.638935
\(376\) 25.8861 1.33497
\(377\) 35.1387 1.80974
\(378\) 14.8849 0.765596
\(379\) −15.5647 −0.799503 −0.399752 0.916624i \(-0.630904\pi\)
−0.399752 + 0.916624i \(0.630904\pi\)
\(380\) −4.26345 −0.218710
\(381\) 33.0572 1.69357
\(382\) 11.5186 0.589345
\(383\) 6.51278 0.332788 0.166394 0.986059i \(-0.446788\pi\)
0.166394 + 0.986059i \(0.446788\pi\)
\(384\) 48.6001 2.48011
\(385\) 7.51825 0.383166
\(386\) −64.1956 −3.26747
\(387\) 22.3861 1.13795
\(388\) 36.6398 1.86010
\(389\) 21.7179 1.10114 0.550571 0.834789i \(-0.314410\pi\)
0.550571 + 0.834789i \(0.314410\pi\)
\(390\) 11.4965 0.582149
\(391\) −10.0002 −0.505733
\(392\) −83.3182 −4.20820
\(393\) −10.5058 −0.529946
\(394\) −9.63477 −0.485393
\(395\) 1.59716 0.0803621
\(396\) −44.1384 −2.21804
\(397\) −9.37765 −0.470651 −0.235326 0.971917i \(-0.575616\pi\)
−0.235326 + 0.971917i \(0.575616\pi\)
\(398\) 37.2681 1.86808
\(399\) 26.0336 1.30331
\(400\) −20.6551 −1.03276
\(401\) −4.99848 −0.249612 −0.124806 0.992181i \(-0.539831\pi\)
−0.124806 + 0.992181i \(0.539831\pi\)
\(402\) −25.2873 −1.26122
\(403\) −19.4249 −0.967623
\(404\) 35.5181 1.76709
\(405\) −3.63020 −0.180386
\(406\) −113.762 −5.64593
\(407\) −33.8536 −1.67806
\(408\) −25.2860 −1.25184
\(409\) −37.0960 −1.83428 −0.917138 0.398569i \(-0.869507\pi\)
−0.917138 + 0.398569i \(0.869507\pi\)
\(410\) −7.46296 −0.368569
\(411\) 8.62708 0.425542
\(412\) 19.0446 0.938262
\(413\) −28.9601 −1.42504
\(414\) 43.8190 2.15359
\(415\) −1.92003 −0.0942507
\(416\) 2.10391 0.103153
\(417\) 14.8027 0.724892
\(418\) −16.1867 −0.791716
\(419\) 34.8618 1.70311 0.851555 0.524266i \(-0.175660\pi\)
0.851555 + 0.524266i \(0.175660\pi\)
\(420\) −24.9307 −1.21649
\(421\) −32.8749 −1.60223 −0.801113 0.598513i \(-0.795758\pi\)
−0.801113 + 0.598513i \(0.795758\pi\)
\(422\) 68.6438 3.34153
\(423\) −17.8441 −0.867609
\(424\) −28.3345 −1.37604
\(425\) −9.31549 −0.451868
\(426\) −90.8736 −4.40284
\(427\) 49.5344 2.39714
\(428\) 57.6724 2.78770
\(429\) 29.2360 1.41153
\(430\) −7.86173 −0.379126
\(431\) −38.9186 −1.87464 −0.937320 0.348469i \(-0.886702\pi\)
−0.937320 + 0.348469i \(0.886702\pi\)
\(432\) 5.42797 0.261153
\(433\) −5.96585 −0.286700 −0.143350 0.989672i \(-0.545788\pi\)
−0.143350 + 0.989672i \(0.545788\pi\)
\(434\) 62.8885 3.01875
\(435\) −12.1092 −0.580592
\(436\) −44.2695 −2.12012
\(437\) 10.7636 0.514894
\(438\) −0.442163 −0.0211274
\(439\) 8.26299 0.394371 0.197185 0.980366i \(-0.436820\pi\)
0.197185 + 0.980366i \(0.436820\pi\)
\(440\) 7.85978 0.374701
\(441\) 57.4339 2.73495
\(442\) 17.7631 0.844905
\(443\) 2.38384 0.113260 0.0566299 0.998395i \(-0.481964\pi\)
0.0566299 + 0.998395i \(0.481964\pi\)
\(444\) 112.259 5.32760
\(445\) 0.813749 0.0385754
\(446\) 52.5509 2.48836
\(447\) 14.4193 0.682011
\(448\) 35.2912 1.66735
\(449\) −20.6263 −0.973417 −0.486709 0.873564i \(-0.661803\pi\)
−0.486709 + 0.873564i \(0.661803\pi\)
\(450\) 40.8186 1.92421
\(451\) −18.9785 −0.893665
\(452\) 11.8022 0.555127
\(453\) 12.4788 0.586306
\(454\) 3.05550 0.143402
\(455\) 8.88028 0.416314
\(456\) 27.2163 1.27452
\(457\) −2.56153 −0.119823 −0.0599116 0.998204i \(-0.519082\pi\)
−0.0599116 + 0.998204i \(0.519082\pi\)
\(458\) −60.5387 −2.82879
\(459\) 2.44802 0.114264
\(460\) −10.3076 −0.480595
\(461\) 15.9974 0.745073 0.372536 0.928018i \(-0.378488\pi\)
0.372536 + 0.928018i \(0.378488\pi\)
\(462\) −94.6522 −4.40362
\(463\) 14.4785 0.672873 0.336437 0.941706i \(-0.390778\pi\)
0.336437 + 0.941706i \(0.390778\pi\)
\(464\) −41.4849 −1.92589
\(465\) 6.69404 0.310429
\(466\) −43.4885 −2.01456
\(467\) 18.7824 0.869144 0.434572 0.900637i \(-0.356900\pi\)
0.434572 + 0.900637i \(0.356900\pi\)
\(468\) −52.1347 −2.40993
\(469\) −19.5327 −0.901938
\(470\) 6.26664 0.289059
\(471\) −43.3705 −1.99841
\(472\) −30.2757 −1.39355
\(473\) −19.9926 −0.919262
\(474\) −20.1078 −0.923580
\(475\) 10.0266 0.460053
\(476\) −38.5201 −1.76556
\(477\) 19.5319 0.894303
\(478\) −52.6666 −2.40891
\(479\) 14.0936 0.643955 0.321977 0.946747i \(-0.395653\pi\)
0.321977 + 0.946747i \(0.395653\pi\)
\(480\) −0.725031 −0.0330930
\(481\) −39.9866 −1.82323
\(482\) −42.9366 −1.95571
\(483\) 62.9407 2.86390
\(484\) −5.21018 −0.236826
\(485\) 4.49754 0.204223
\(486\) 54.9232 2.49137
\(487\) −2.21478 −0.100361 −0.0501806 0.998740i \(-0.515980\pi\)
−0.0501806 + 0.998740i \(0.515980\pi\)
\(488\) 51.7846 2.34418
\(489\) 21.8018 0.985911
\(490\) −20.1701 −0.911193
\(491\) −38.2578 −1.72655 −0.863275 0.504733i \(-0.831591\pi\)
−0.863275 + 0.504733i \(0.831591\pi\)
\(492\) 62.9333 2.83725
\(493\) −18.7097 −0.842645
\(494\) −19.1191 −0.860209
\(495\) −5.41800 −0.243521
\(496\) 22.9331 1.02973
\(497\) −70.1937 −3.14862
\(498\) 24.1726 1.08320
\(499\) 29.4056 1.31638 0.658188 0.752853i \(-0.271323\pi\)
0.658188 + 0.752853i \(0.271323\pi\)
\(500\) −19.7048 −0.881228
\(501\) −22.3659 −0.999233
\(502\) −62.9503 −2.80961
\(503\) 37.8702 1.68855 0.844275 0.535910i \(-0.180031\pi\)
0.844275 + 0.535910i \(0.180031\pi\)
\(504\) 85.5840 3.81222
\(505\) 4.35985 0.194011
\(506\) −39.1340 −1.73972
\(507\) 1.41392 0.0627945
\(508\) 52.6462 2.33580
\(509\) −24.2543 −1.07505 −0.537527 0.843247i \(-0.680641\pi\)
−0.537527 + 0.843247i \(0.680641\pi\)
\(510\) −6.12137 −0.271059
\(511\) −0.341541 −0.0151089
\(512\) 41.5314 1.83545
\(513\) −2.63490 −0.116334
\(514\) 46.4518 2.04890
\(515\) 2.33773 0.103013
\(516\) 66.2960 2.91852
\(517\) 15.9363 0.700876
\(518\) 129.458 5.68804
\(519\) 24.8528 1.09092
\(520\) 9.28369 0.407117
\(521\) −1.09893 −0.0481452 −0.0240726 0.999710i \(-0.507663\pi\)
−0.0240726 + 0.999710i \(0.507663\pi\)
\(522\) 81.9824 3.58827
\(523\) −40.2783 −1.76125 −0.880623 0.473818i \(-0.842875\pi\)
−0.880623 + 0.473818i \(0.842875\pi\)
\(524\) −16.7313 −0.730909
\(525\) 58.6311 2.55887
\(526\) 53.8742 2.34903
\(527\) 10.3429 0.450542
\(528\) −34.5162 −1.50212
\(529\) 3.02289 0.131430
\(530\) −6.85937 −0.297952
\(531\) 20.8700 0.905682
\(532\) 41.4606 1.79755
\(533\) −22.4168 −0.970977
\(534\) −10.2448 −0.443337
\(535\) 7.07929 0.306064
\(536\) −20.4201 −0.882012
\(537\) 43.6552 1.88386
\(538\) 62.9837 2.71542
\(539\) −51.2933 −2.20936
\(540\) 2.52327 0.108584
\(541\) −15.6569 −0.673143 −0.336572 0.941658i \(-0.609267\pi\)
−0.336572 + 0.941658i \(0.609267\pi\)
\(542\) −42.3422 −1.81875
\(543\) −24.2082 −1.03887
\(544\) −1.12024 −0.0480297
\(545\) −5.43408 −0.232770
\(546\) −111.800 −4.78459
\(547\) 26.3164 1.12521 0.562604 0.826727i \(-0.309800\pi\)
0.562604 + 0.826727i \(0.309800\pi\)
\(548\) 13.7393 0.586914
\(549\) −35.6968 −1.52350
\(550\) −36.4545 −1.55442
\(551\) 20.1380 0.857908
\(552\) 65.8000 2.80063
\(553\) −15.5319 −0.660483
\(554\) 63.1273 2.68202
\(555\) 13.7799 0.584922
\(556\) 23.5745 0.999781
\(557\) −10.2631 −0.434860 −0.217430 0.976076i \(-0.569767\pi\)
−0.217430 + 0.976076i \(0.569767\pi\)
\(558\) −45.3204 −1.91857
\(559\) −23.6146 −0.998789
\(560\) −10.4841 −0.443034
\(561\) −15.5668 −0.657232
\(562\) 47.9124 2.02106
\(563\) 13.9941 0.589782 0.294891 0.955531i \(-0.404717\pi\)
0.294891 + 0.955531i \(0.404717\pi\)
\(564\) −52.8451 −2.22518
\(565\) 1.44872 0.0609479
\(566\) 2.38446 0.100226
\(567\) 35.3024 1.48256
\(568\) −73.3824 −3.07906
\(569\) −4.63507 −0.194312 −0.0971561 0.995269i \(-0.530975\pi\)
−0.0971561 + 0.995269i \(0.530975\pi\)
\(570\) 6.58866 0.275969
\(571\) −18.6791 −0.781696 −0.390848 0.920455i \(-0.627818\pi\)
−0.390848 + 0.920455i \(0.627818\pi\)
\(572\) 46.5607 1.94680
\(573\) −11.9232 −0.498099
\(574\) 72.5747 3.02921
\(575\) 24.2411 1.01092
\(576\) −25.4325 −1.05969
\(577\) 4.43894 0.184796 0.0923978 0.995722i \(-0.470547\pi\)
0.0923978 + 0.995722i \(0.470547\pi\)
\(578\) 32.3814 1.34689
\(579\) 66.4502 2.76158
\(580\) −19.2849 −0.800760
\(581\) 18.6717 0.774631
\(582\) −56.6225 −2.34708
\(583\) −17.4436 −0.722440
\(584\) −0.357056 −0.0147751
\(585\) −6.39954 −0.264588
\(586\) −29.9025 −1.23526
\(587\) 24.8269 1.02471 0.512357 0.858772i \(-0.328772\pi\)
0.512357 + 0.858772i \(0.328772\pi\)
\(588\) 170.090 7.01438
\(589\) −11.1324 −0.458703
\(590\) −7.32931 −0.301743
\(591\) 9.97316 0.410241
\(592\) 47.2084 1.94025
\(593\) 29.5417 1.21313 0.606566 0.795033i \(-0.292546\pi\)
0.606566 + 0.795033i \(0.292546\pi\)
\(594\) 9.57988 0.393067
\(595\) −4.72834 −0.193843
\(596\) 22.9639 0.940640
\(597\) −38.5771 −1.57885
\(598\) −46.2237 −1.89023
\(599\) 20.8607 0.852345 0.426173 0.904642i \(-0.359862\pi\)
0.426173 + 0.904642i \(0.359862\pi\)
\(600\) 61.2945 2.50234
\(601\) 26.1219 1.06553 0.532767 0.846262i \(-0.321152\pi\)
0.532767 + 0.846262i \(0.321152\pi\)
\(602\) 76.4526 3.11598
\(603\) 14.0762 0.573227
\(604\) 19.8735 0.808641
\(605\) −0.639550 −0.0260014
\(606\) −54.8890 −2.22971
\(607\) 14.7912 0.600355 0.300178 0.953883i \(-0.402954\pi\)
0.300178 + 0.953883i \(0.402954\pi\)
\(608\) 1.20575 0.0488997
\(609\) 117.758 4.77179
\(610\) 12.5363 0.507580
\(611\) 18.8233 0.761511
\(612\) 27.7593 1.12210
\(613\) 0.585736 0.0236577 0.0118288 0.999930i \(-0.496235\pi\)
0.0118288 + 0.999930i \(0.496235\pi\)
\(614\) −0.773184 −0.0312032
\(615\) 7.72507 0.311505
\(616\) −76.4337 −3.07960
\(617\) −11.1345 −0.448258 −0.224129 0.974560i \(-0.571954\pi\)
−0.224129 + 0.974560i \(0.571954\pi\)
\(618\) −29.4312 −1.18390
\(619\) 26.6873 1.07265 0.536326 0.844011i \(-0.319812\pi\)
0.536326 + 0.844011i \(0.319812\pi\)
\(620\) 10.6608 0.428148
\(621\) −6.37031 −0.255632
\(622\) 3.71165 0.148824
\(623\) −7.91343 −0.317045
\(624\) −40.7692 −1.63207
\(625\) 21.3411 0.853643
\(626\) −25.6104 −1.02360
\(627\) 16.7552 0.669137
\(628\) −69.0710 −2.75623
\(629\) 21.2911 0.848930
\(630\) 20.7187 0.825451
\(631\) 3.13409 0.124766 0.0623831 0.998052i \(-0.480130\pi\)
0.0623831 + 0.998052i \(0.480130\pi\)
\(632\) −16.2375 −0.645891
\(633\) −71.0547 −2.82417
\(634\) −53.5945 −2.12851
\(635\) 6.46233 0.256450
\(636\) 57.8434 2.29364
\(637\) −60.5857 −2.40049
\(638\) −73.2171 −2.89869
\(639\) 50.5848 2.00110
\(640\) 9.50079 0.375552
\(641\) −24.7216 −0.976444 −0.488222 0.872719i \(-0.662354\pi\)
−0.488222 + 0.872719i \(0.662354\pi\)
\(642\) −89.1259 −3.51752
\(643\) 29.5599 1.16573 0.582864 0.812570i \(-0.301932\pi\)
0.582864 + 0.812570i \(0.301932\pi\)
\(644\) 100.238 3.94993
\(645\) 8.13785 0.320427
\(646\) 10.1800 0.400529
\(647\) 35.7825 1.40675 0.703377 0.710817i \(-0.251675\pi\)
0.703377 + 0.710817i \(0.251675\pi\)
\(648\) 36.9061 1.44981
\(649\) −18.6387 −0.731632
\(650\) −43.0587 −1.68890
\(651\) −65.0973 −2.55136
\(652\) 34.7211 1.35978
\(653\) 36.1882 1.41615 0.708076 0.706136i \(-0.249563\pi\)
0.708076 + 0.706136i \(0.249563\pi\)
\(654\) 68.4133 2.67517
\(655\) −2.05377 −0.0802472
\(656\) 26.4653 1.03330
\(657\) 0.246130 0.00960246
\(658\) −60.9410 −2.37573
\(659\) 30.5084 1.18844 0.594219 0.804304i \(-0.297461\pi\)
0.594219 + 0.804304i \(0.297461\pi\)
\(660\) −16.0453 −0.624564
\(661\) −8.13789 −0.316527 −0.158264 0.987397i \(-0.550590\pi\)
−0.158264 + 0.987397i \(0.550590\pi\)
\(662\) −6.62144 −0.257350
\(663\) −18.3870 −0.714091
\(664\) 19.5199 0.757518
\(665\) 5.08929 0.197354
\(666\) −93.2932 −3.61504
\(667\) 48.6871 1.88517
\(668\) −35.6194 −1.37816
\(669\) −54.3966 −2.10309
\(670\) −4.94340 −0.190980
\(671\) 31.8802 1.23072
\(672\) 7.05068 0.271986
\(673\) −3.18796 −0.122887 −0.0614435 0.998111i \(-0.519570\pi\)
−0.0614435 + 0.998111i \(0.519570\pi\)
\(674\) 36.2540 1.39645
\(675\) −5.93413 −0.228405
\(676\) 2.25178 0.0866071
\(677\) 48.7601 1.87400 0.937002 0.349324i \(-0.113589\pi\)
0.937002 + 0.349324i \(0.113589\pi\)
\(678\) −18.2388 −0.700459
\(679\) −43.7370 −1.67847
\(680\) −4.94314 −0.189561
\(681\) −3.16281 −0.121199
\(682\) 40.4749 1.54986
\(683\) 37.0621 1.41814 0.709071 0.705137i \(-0.249114\pi\)
0.709071 + 0.705137i \(0.249114\pi\)
\(684\) −29.8784 −1.14243
\(685\) 1.68650 0.0644379
\(686\) 112.710 4.30330
\(687\) 62.6649 2.39082
\(688\) 27.8794 1.06289
\(689\) −20.6037 −0.784940
\(690\) 15.9292 0.606415
\(691\) −6.91861 −0.263196 −0.131598 0.991303i \(-0.542011\pi\)
−0.131598 + 0.991303i \(0.542011\pi\)
\(692\) 39.5800 1.50461
\(693\) 52.6882 2.00146
\(694\) 24.2363 0.919996
\(695\) 2.89377 0.109767
\(696\) 123.107 4.66637
\(697\) 11.9359 0.452104
\(698\) 68.8599 2.60639
\(699\) 45.0158 1.70266
\(700\) 93.3746 3.52923
\(701\) 16.9589 0.640527 0.320264 0.947328i \(-0.396229\pi\)
0.320264 + 0.947328i \(0.396229\pi\)
\(702\) 11.3154 0.427072
\(703\) −22.9164 −0.864307
\(704\) 22.7133 0.856041
\(705\) −6.48674 −0.244305
\(706\) −57.9217 −2.17991
\(707\) −42.3980 −1.59454
\(708\) 61.8063 2.32282
\(709\) −11.5856 −0.435106 −0.217553 0.976048i \(-0.569808\pi\)
−0.217553 + 0.976048i \(0.569808\pi\)
\(710\) −17.7648 −0.666702
\(711\) 11.1930 0.419770
\(712\) −8.27292 −0.310041
\(713\) −26.9145 −1.00796
\(714\) 59.5282 2.22779
\(715\) 5.71533 0.213741
\(716\) 69.5244 2.59825
\(717\) 54.5163 2.03595
\(718\) 0.230669 0.00860851
\(719\) 10.6469 0.397062 0.198531 0.980095i \(-0.436383\pi\)
0.198531 + 0.980095i \(0.436383\pi\)
\(720\) 7.55532 0.281570
\(721\) −22.7336 −0.846645
\(722\) 35.8046 1.33251
\(723\) 44.4446 1.65291
\(724\) −38.5535 −1.43283
\(725\) 45.3534 1.68438
\(726\) 8.05171 0.298827
\(727\) −36.5695 −1.35629 −0.678144 0.734929i \(-0.737215\pi\)
−0.678144 + 0.734929i \(0.737215\pi\)
\(728\) −90.2807 −3.34603
\(729\) −34.9846 −1.29573
\(730\) −0.0864382 −0.00319922
\(731\) 12.5737 0.465054
\(732\) −105.716 −3.90736
\(733\) −17.8068 −0.657709 −0.328855 0.944381i \(-0.606663\pi\)
−0.328855 + 0.944381i \(0.606663\pi\)
\(734\) −75.3141 −2.77990
\(735\) 20.8785 0.770116
\(736\) 2.91511 0.107452
\(737\) −12.5712 −0.463067
\(738\) −52.3007 −1.92522
\(739\) 41.6790 1.53319 0.766594 0.642132i \(-0.221950\pi\)
0.766594 + 0.642132i \(0.221950\pi\)
\(740\) 21.9455 0.806733
\(741\) 19.7906 0.727026
\(742\) 66.7050 2.44882
\(743\) −20.7703 −0.761987 −0.380994 0.924578i \(-0.624418\pi\)
−0.380994 + 0.924578i \(0.624418\pi\)
\(744\) −68.0545 −2.49500
\(745\) 2.81883 0.103274
\(746\) 44.0631 1.61327
\(747\) −13.4557 −0.492317
\(748\) −24.7914 −0.906464
\(749\) −68.8437 −2.51549
\(750\) 30.4515 1.11193
\(751\) 9.65977 0.352490 0.176245 0.984346i \(-0.443605\pi\)
0.176245 + 0.984346i \(0.443605\pi\)
\(752\) −22.2229 −0.810386
\(753\) 65.1612 2.37461
\(754\) −86.4814 −3.14947
\(755\) 2.43947 0.0887815
\(756\) −24.5379 −0.892436
\(757\) 6.28118 0.228293 0.114147 0.993464i \(-0.463587\pi\)
0.114147 + 0.993464i \(0.463587\pi\)
\(758\) 38.3069 1.39137
\(759\) 40.5085 1.47036
\(760\) 5.32049 0.192994
\(761\) 6.56520 0.237988 0.118994 0.992895i \(-0.462033\pi\)
0.118994 + 0.992895i \(0.462033\pi\)
\(762\) −81.3586 −2.94731
\(763\) 52.8446 1.91310
\(764\) −18.9886 −0.686985
\(765\) 3.40746 0.123197
\(766\) −16.0289 −0.579147
\(767\) −22.0153 −0.794927
\(768\) −82.4840 −2.97638
\(769\) 5.63828 0.203321 0.101661 0.994819i \(-0.467584\pi\)
0.101661 + 0.994819i \(0.467584\pi\)
\(770\) −18.5035 −0.666820
\(771\) −48.0833 −1.73168
\(772\) 105.827 3.80881
\(773\) 4.65494 0.167427 0.0837133 0.996490i \(-0.473322\pi\)
0.0837133 + 0.996490i \(0.473322\pi\)
\(774\) −55.0953 −1.98036
\(775\) −25.0716 −0.900600
\(776\) −45.7239 −1.64139
\(777\) −134.004 −4.80738
\(778\) −53.4509 −1.91631
\(779\) −12.8471 −0.460293
\(780\) −18.9522 −0.678596
\(781\) −45.1765 −1.61654
\(782\) 24.6120 0.880123
\(783\) −11.9184 −0.425930
\(784\) 71.5277 2.55456
\(785\) −8.47847 −0.302610
\(786\) 25.8562 0.922260
\(787\) −40.5724 −1.44625 −0.723124 0.690718i \(-0.757295\pi\)
−0.723124 + 0.690718i \(0.757295\pi\)
\(788\) 15.8830 0.565810
\(789\) −55.7664 −1.98533
\(790\) −3.93085 −0.139853
\(791\) −14.0883 −0.500921
\(792\) 55.0817 1.95724
\(793\) 37.6558 1.33720
\(794\) 23.0798 0.819070
\(795\) 7.10028 0.251821
\(796\) −61.4370 −2.17758
\(797\) 44.0804 1.56141 0.780704 0.624901i \(-0.214861\pi\)
0.780704 + 0.624901i \(0.214861\pi\)
\(798\) −64.0725 −2.26814
\(799\) −10.0226 −0.354573
\(800\) 2.71551 0.0960077
\(801\) 5.70278 0.201498
\(802\) 12.3020 0.434398
\(803\) −0.219815 −0.00775710
\(804\) 41.6865 1.47017
\(805\) 12.3042 0.433667
\(806\) 47.8075 1.68395
\(807\) −65.1958 −2.29500
\(808\) −44.3241 −1.55931
\(809\) −30.2995 −1.06527 −0.532637 0.846344i \(-0.678799\pi\)
−0.532637 + 0.846344i \(0.678799\pi\)
\(810\) 8.93444 0.313924
\(811\) 14.6943 0.515986 0.257993 0.966147i \(-0.416939\pi\)
0.257993 + 0.966147i \(0.416939\pi\)
\(812\) 187.539 6.58132
\(813\) 43.8293 1.53716
\(814\) 83.3186 2.92032
\(815\) 4.26202 0.149292
\(816\) 21.7077 0.759923
\(817\) −13.5335 −0.473478
\(818\) 91.2985 3.19218
\(819\) 62.2333 2.17461
\(820\) 12.3028 0.429632
\(821\) 6.23239 0.217512 0.108756 0.994068i \(-0.465313\pi\)
0.108756 + 0.994068i \(0.465313\pi\)
\(822\) −21.2325 −0.740568
\(823\) −40.2644 −1.40353 −0.701765 0.712409i \(-0.747604\pi\)
−0.701765 + 0.712409i \(0.747604\pi\)
\(824\) −23.7664 −0.827940
\(825\) 37.7348 1.31376
\(826\) 71.2751 2.47998
\(827\) 23.4708 0.816159 0.408080 0.912946i \(-0.366199\pi\)
0.408080 + 0.912946i \(0.366199\pi\)
\(828\) −72.2362 −2.51038
\(829\) −43.1027 −1.49702 −0.748509 0.663124i \(-0.769230\pi\)
−0.748509 + 0.663124i \(0.769230\pi\)
\(830\) 4.72548 0.164024
\(831\) −65.3445 −2.26677
\(832\) 26.8282 0.930099
\(833\) 32.2591 1.11771
\(834\) −36.4316 −1.26152
\(835\) −4.37229 −0.151309
\(836\) 26.6839 0.922884
\(837\) 6.58858 0.227735
\(838\) −85.7998 −2.96391
\(839\) −18.2383 −0.629657 −0.314828 0.949149i \(-0.601947\pi\)
−0.314828 + 0.949149i \(0.601947\pi\)
\(840\) 31.1118 1.07346
\(841\) 62.0902 2.14104
\(842\) 80.9099 2.78834
\(843\) −49.5952 −1.70815
\(844\) −113.160 −3.89514
\(845\) 0.276407 0.00950868
\(846\) 43.9169 1.50989
\(847\) 6.21940 0.213701
\(848\) 24.3249 0.835319
\(849\) −2.46821 −0.0847086
\(850\) 22.9268 0.786382
\(851\) −55.4042 −1.89923
\(852\) 149.806 5.13228
\(853\) −6.43860 −0.220453 −0.110227 0.993906i \(-0.535158\pi\)
−0.110227 + 0.993906i \(0.535158\pi\)
\(854\) −121.911 −4.17172
\(855\) −3.66758 −0.125429
\(856\) −71.9711 −2.45992
\(857\) 0.451812 0.0154336 0.00771680 0.999970i \(-0.497544\pi\)
0.00771680 + 0.999970i \(0.497544\pi\)
\(858\) −71.9540 −2.45647
\(859\) −0.702645 −0.0239739 −0.0119870 0.999928i \(-0.503816\pi\)
−0.0119870 + 0.999928i \(0.503816\pi\)
\(860\) 12.9602 0.441938
\(861\) −75.1237 −2.56021
\(862\) 95.7842 3.26242
\(863\) 3.86126 0.131439 0.0657193 0.997838i \(-0.479066\pi\)
0.0657193 + 0.997838i \(0.479066\pi\)
\(864\) −0.713609 −0.0242775
\(865\) 4.85845 0.165192
\(866\) 14.6828 0.498942
\(867\) −33.5187 −1.13835
\(868\) −103.673 −3.51888
\(869\) −9.99628 −0.339100
\(870\) 29.8025 1.01040
\(871\) −14.8487 −0.503128
\(872\) 55.2452 1.87084
\(873\) 31.5189 1.06675
\(874\) −26.4908 −0.896065
\(875\) 23.5217 0.795180
\(876\) 0.728912 0.0246277
\(877\) 19.6597 0.663861 0.331930 0.943304i \(-0.392300\pi\)
0.331930 + 0.943304i \(0.392300\pi\)
\(878\) −20.3364 −0.686320
\(879\) 30.9527 1.04401
\(880\) −6.74754 −0.227459
\(881\) 22.1688 0.746885 0.373442 0.927653i \(-0.378177\pi\)
0.373442 + 0.927653i \(0.378177\pi\)
\(882\) −141.353 −4.75960
\(883\) 30.1890 1.01594 0.507970 0.861375i \(-0.330396\pi\)
0.507970 + 0.861375i \(0.330396\pi\)
\(884\) −29.2827 −0.984884
\(885\) 7.58673 0.255025
\(886\) −5.86698 −0.197105
\(887\) 1.25332 0.0420822 0.0210411 0.999779i \(-0.493302\pi\)
0.0210411 + 0.999779i \(0.493302\pi\)
\(888\) −140.092 −4.70118
\(889\) −62.8440 −2.10772
\(890\) −2.00275 −0.0671324
\(891\) 22.7206 0.761167
\(892\) −86.6309 −2.90062
\(893\) 10.7877 0.360995
\(894\) −35.4881 −1.18690
\(895\) 8.53412 0.285264
\(896\) −92.3920 −3.08660
\(897\) 47.8471 1.59757
\(898\) 50.7644 1.69403
\(899\) −50.3553 −1.67944
\(900\) −67.2901 −2.24300
\(901\) 10.9705 0.365482
\(902\) 46.7089 1.55524
\(903\) −79.1378 −2.63354
\(904\) −14.7283 −0.489855
\(905\) −4.73245 −0.157312
\(906\) −30.7121 −1.02034
\(907\) 11.7446 0.389973 0.194986 0.980806i \(-0.437534\pi\)
0.194986 + 0.980806i \(0.437534\pi\)
\(908\) −5.03703 −0.167160
\(909\) 30.5540 1.01341
\(910\) −21.8556 −0.724508
\(911\) −57.3044 −1.89858 −0.949290 0.314400i \(-0.898197\pi\)
−0.949290 + 0.314400i \(0.898197\pi\)
\(912\) −23.3649 −0.773688
\(913\) 12.0170 0.397706
\(914\) 6.30429 0.208527
\(915\) −12.9766 −0.428993
\(916\) 99.7988 3.29745
\(917\) 19.9722 0.659539
\(918\) −6.02493 −0.198852
\(919\) 37.2022 1.22719 0.613594 0.789621i \(-0.289723\pi\)
0.613594 + 0.789621i \(0.289723\pi\)
\(920\) 12.8632 0.424087
\(921\) 0.800339 0.0263721
\(922\) −39.3719 −1.29664
\(923\) −53.3608 −1.75639
\(924\) 156.035 5.13319
\(925\) −51.6106 −1.69695
\(926\) −35.6337 −1.17100
\(927\) 16.3829 0.538085
\(928\) 5.45397 0.179035
\(929\) 5.10800 0.167588 0.0837941 0.996483i \(-0.473296\pi\)
0.0837941 + 0.996483i \(0.473296\pi\)
\(930\) −16.4750 −0.540237
\(931\) −34.7217 −1.13796
\(932\) 71.6913 2.34833
\(933\) −3.84201 −0.125782
\(934\) −46.2261 −1.51256
\(935\) −3.04315 −0.0995216
\(936\) 65.0604 2.12657
\(937\) 7.37990 0.241091 0.120545 0.992708i \(-0.461536\pi\)
0.120545 + 0.992708i \(0.461536\pi\)
\(938\) 48.0729 1.56963
\(939\) 26.5099 0.865117
\(940\) −10.3306 −0.336948
\(941\) −20.6212 −0.672231 −0.336115 0.941821i \(-0.609113\pi\)
−0.336115 + 0.941821i \(0.609113\pi\)
\(942\) 106.741 3.47781
\(943\) −31.0599 −1.01145
\(944\) 25.9914 0.845947
\(945\) −3.01203 −0.0979815
\(946\) 49.2047 1.59978
\(947\) −20.2395 −0.657696 −0.328848 0.944383i \(-0.606660\pi\)
−0.328848 + 0.944383i \(0.606660\pi\)
\(948\) 33.1479 1.07659
\(949\) −0.259637 −0.00842818
\(950\) −24.6769 −0.800626
\(951\) 55.4768 1.79896
\(952\) 48.0703 1.55797
\(953\) 28.5283 0.924122 0.462061 0.886848i \(-0.347110\pi\)
0.462061 + 0.886848i \(0.347110\pi\)
\(954\) −48.0707 −1.55635
\(955\) −2.33086 −0.0754248
\(956\) 86.8216 2.80801
\(957\) 75.7886 2.44990
\(958\) −34.6865 −1.12067
\(959\) −16.4006 −0.529605
\(960\) −9.24529 −0.298391
\(961\) −3.16329 −0.102042
\(962\) 98.4129 3.17296
\(963\) 49.6119 1.59872
\(964\) 70.7816 2.27972
\(965\) 12.9903 0.418173
\(966\) −154.906 −4.98402
\(967\) 34.5664 1.11158 0.555790 0.831323i \(-0.312416\pi\)
0.555790 + 0.831323i \(0.312416\pi\)
\(968\) 6.50193 0.208980
\(969\) −10.5376 −0.338516
\(970\) −11.0691 −0.355407
\(971\) 43.3283 1.39047 0.695236 0.718781i \(-0.255300\pi\)
0.695236 + 0.718781i \(0.255300\pi\)
\(972\) −90.5416 −2.90412
\(973\) −28.1409 −0.902157
\(974\) 5.45088 0.174658
\(975\) 44.5710 1.42741
\(976\) −44.4565 −1.42302
\(977\) −27.3148 −0.873879 −0.436940 0.899491i \(-0.643938\pi\)
−0.436940 + 0.899491i \(0.643938\pi\)
\(978\) −53.6573 −1.71577
\(979\) −5.09306 −0.162775
\(980\) 33.2507 1.06216
\(981\) −38.0823 −1.21587
\(982\) 94.1580 3.00470
\(983\) 21.7810 0.694706 0.347353 0.937734i \(-0.387080\pi\)
0.347353 + 0.937734i \(0.387080\pi\)
\(984\) −78.5363 −2.50365
\(985\) 1.94964 0.0621209
\(986\) 46.0474 1.46645
\(987\) 63.0813 2.00790
\(988\) 31.5181 1.00272
\(989\) −32.7196 −1.04042
\(990\) 13.3345 0.423797
\(991\) −14.0850 −0.447423 −0.223712 0.974655i \(-0.571817\pi\)
−0.223712 + 0.974655i \(0.571817\pi\)
\(992\) −3.01499 −0.0957261
\(993\) 6.85399 0.217505
\(994\) 172.757 5.47951
\(995\) −7.54140 −0.239078
\(996\) −39.8488 −1.26266
\(997\) −32.1257 −1.01743 −0.508716 0.860934i \(-0.669880\pi\)
−0.508716 + 0.860934i \(0.669880\pi\)
\(998\) −72.3715 −2.29088
\(999\) 13.5628 0.429107
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 \(a_p\))