Properties

Label 8015.2.a.l.1.42
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.42
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.20865 q^{2} -0.0912122 q^{3} -0.539165 q^{4} -1.00000 q^{5} -0.110244 q^{6} -1.00000 q^{7} -3.06896 q^{8} -2.99168 q^{9} +O(q^{10})\) \(q+1.20865 q^{2} -0.0912122 q^{3} -0.539165 q^{4} -1.00000 q^{5} -0.110244 q^{6} -1.00000 q^{7} -3.06896 q^{8} -2.99168 q^{9} -1.20865 q^{10} +1.74455 q^{11} +0.0491785 q^{12} -0.184416 q^{13} -1.20865 q^{14} +0.0912122 q^{15} -2.63097 q^{16} -2.26732 q^{17} -3.61589 q^{18} +2.30496 q^{19} +0.539165 q^{20} +0.0912122 q^{21} +2.10855 q^{22} -5.73212 q^{23} +0.279927 q^{24} +1.00000 q^{25} -0.222894 q^{26} +0.546515 q^{27} +0.539165 q^{28} +5.32663 q^{29} +0.110244 q^{30} -3.10052 q^{31} +2.95800 q^{32} -0.159125 q^{33} -2.74040 q^{34} +1.00000 q^{35} +1.61301 q^{36} -5.98040 q^{37} +2.78589 q^{38} +0.0168209 q^{39} +3.06896 q^{40} +8.60516 q^{41} +0.110244 q^{42} -11.7652 q^{43} -0.940602 q^{44} +2.99168 q^{45} -6.92812 q^{46} -11.7562 q^{47} +0.239977 q^{48} +1.00000 q^{49} +1.20865 q^{50} +0.206808 q^{51} +0.0994305 q^{52} +7.18179 q^{53} +0.660545 q^{54} -1.74455 q^{55} +3.06896 q^{56} -0.210240 q^{57} +6.43802 q^{58} -14.8032 q^{59} -0.0491785 q^{60} -12.3438 q^{61} -3.74744 q^{62} +2.99168 q^{63} +8.83713 q^{64} +0.184416 q^{65} -0.192326 q^{66} +13.4961 q^{67} +1.22246 q^{68} +0.522839 q^{69} +1.20865 q^{70} -11.2242 q^{71} +9.18135 q^{72} +7.58054 q^{73} -7.22821 q^{74} -0.0912122 q^{75} -1.24275 q^{76} -1.74455 q^{77} +0.0203306 q^{78} -9.71372 q^{79} +2.63097 q^{80} +8.92519 q^{81} +10.4006 q^{82} -11.6453 q^{83} -0.0491785 q^{84} +2.26732 q^{85} -14.2200 q^{86} -0.485853 q^{87} -5.35396 q^{88} +13.0871 q^{89} +3.61589 q^{90} +0.184416 q^{91} +3.09056 q^{92} +0.282805 q^{93} -14.2092 q^{94} -2.30496 q^{95} -0.269806 q^{96} +14.4199 q^{97} +1.20865 q^{98} -5.21914 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.20865 0.854645 0.427322 0.904099i \(-0.359457\pi\)
0.427322 + 0.904099i \(0.359457\pi\)
\(3\) −0.0912122 −0.0526614 −0.0263307 0.999653i \(-0.508382\pi\)
−0.0263307 + 0.999653i \(0.508382\pi\)
\(4\) −0.539165 −0.269583
\(5\) −1.00000 −0.447214
\(6\) −0.110244 −0.0450068
\(7\) −1.00000 −0.377964
\(8\) −3.06896 −1.08504
\(9\) −2.99168 −0.997227
\(10\) −1.20865 −0.382209
\(11\) 1.74455 0.526002 0.263001 0.964796i \(-0.415288\pi\)
0.263001 + 0.964796i \(0.415288\pi\)
\(12\) 0.0491785 0.0141966
\(13\) −0.184416 −0.0511477 −0.0255738 0.999673i \(-0.508141\pi\)
−0.0255738 + 0.999673i \(0.508141\pi\)
\(14\) −1.20865 −0.323025
\(15\) 0.0912122 0.0235509
\(16\) −2.63097 −0.657742
\(17\) −2.26732 −0.549907 −0.274953 0.961458i \(-0.588662\pi\)
−0.274953 + 0.961458i \(0.588662\pi\)
\(18\) −3.61589 −0.852274
\(19\) 2.30496 0.528794 0.264397 0.964414i \(-0.414827\pi\)
0.264397 + 0.964414i \(0.414827\pi\)
\(20\) 0.539165 0.120561
\(21\) 0.0912122 0.0199041
\(22\) 2.10855 0.449545
\(23\) −5.73212 −1.19523 −0.597615 0.801783i \(-0.703885\pi\)
−0.597615 + 0.801783i \(0.703885\pi\)
\(24\) 0.279927 0.0571398
\(25\) 1.00000 0.200000
\(26\) −0.222894 −0.0437131
\(27\) 0.546515 0.105177
\(28\) 0.539165 0.101893
\(29\) 5.32663 0.989129 0.494565 0.869141i \(-0.335327\pi\)
0.494565 + 0.869141i \(0.335327\pi\)
\(30\) 0.110244 0.0201276
\(31\) −3.10052 −0.556870 −0.278435 0.960455i \(-0.589816\pi\)
−0.278435 + 0.960455i \(0.589816\pi\)
\(32\) 2.95800 0.522906
\(33\) −0.159125 −0.0277000
\(34\) −2.74040 −0.469975
\(35\) 1.00000 0.169031
\(36\) 1.61301 0.268835
\(37\) −5.98040 −0.983171 −0.491586 0.870829i \(-0.663583\pi\)
−0.491586 + 0.870829i \(0.663583\pi\)
\(38\) 2.78589 0.451931
\(39\) 0.0168209 0.00269351
\(40\) 3.06896 0.485246
\(41\) 8.60516 1.34390 0.671950 0.740596i \(-0.265457\pi\)
0.671950 + 0.740596i \(0.265457\pi\)
\(42\) 0.110244 0.0170110
\(43\) −11.7652 −1.79417 −0.897086 0.441855i \(-0.854321\pi\)
−0.897086 + 0.441855i \(0.854321\pi\)
\(44\) −0.940602 −0.141801
\(45\) 2.99168 0.445973
\(46\) −6.92812 −1.02150
\(47\) −11.7562 −1.71482 −0.857411 0.514632i \(-0.827929\pi\)
−0.857411 + 0.514632i \(0.827929\pi\)
\(48\) 0.239977 0.0346376
\(49\) 1.00000 0.142857
\(50\) 1.20865 0.170929
\(51\) 0.206808 0.0289589
\(52\) 0.0994305 0.0137885
\(53\) 7.18179 0.986495 0.493247 0.869889i \(-0.335810\pi\)
0.493247 + 0.869889i \(0.335810\pi\)
\(54\) 0.660545 0.0898887
\(55\) −1.74455 −0.235235
\(56\) 3.06896 0.410107
\(57\) −0.210240 −0.0278470
\(58\) 6.43802 0.845354
\(59\) −14.8032 −1.92721 −0.963607 0.267323i \(-0.913861\pi\)
−0.963607 + 0.267323i \(0.913861\pi\)
\(60\) −0.0491785 −0.00634891
\(61\) −12.3438 −1.58046 −0.790230 0.612810i \(-0.790039\pi\)
−0.790230 + 0.612810i \(0.790039\pi\)
\(62\) −3.74744 −0.475926
\(63\) 2.99168 0.376916
\(64\) 8.83713 1.10464
\(65\) 0.184416 0.0228739
\(66\) −0.192326 −0.0236737
\(67\) 13.4961 1.64881 0.824407 0.565997i \(-0.191509\pi\)
0.824407 + 0.565997i \(0.191509\pi\)
\(68\) 1.22246 0.148245
\(69\) 0.522839 0.0629425
\(70\) 1.20865 0.144461
\(71\) −11.2242 −1.33206 −0.666031 0.745924i \(-0.732008\pi\)
−0.666031 + 0.745924i \(0.732008\pi\)
\(72\) 9.18135 1.08203
\(73\) 7.58054 0.887235 0.443617 0.896216i \(-0.353695\pi\)
0.443617 + 0.896216i \(0.353695\pi\)
\(74\) −7.22821 −0.840262
\(75\) −0.0912122 −0.0105323
\(76\) −1.24275 −0.142554
\(77\) −1.74455 −0.198810
\(78\) 0.0203306 0.00230199
\(79\) −9.71372 −1.09288 −0.546439 0.837499i \(-0.684017\pi\)
−0.546439 + 0.837499i \(0.684017\pi\)
\(80\) 2.63097 0.294151
\(81\) 8.92519 0.991688
\(82\) 10.4006 1.14856
\(83\) −11.6453 −1.27823 −0.639117 0.769109i \(-0.720700\pi\)
−0.639117 + 0.769109i \(0.720700\pi\)
\(84\) −0.0491785 −0.00536581
\(85\) 2.26732 0.245926
\(86\) −14.2200 −1.53338
\(87\) −0.485853 −0.0520889
\(88\) −5.35396 −0.570735
\(89\) 13.0871 1.38723 0.693614 0.720347i \(-0.256017\pi\)
0.693614 + 0.720347i \(0.256017\pi\)
\(90\) 3.61589 0.381149
\(91\) 0.184416 0.0193320
\(92\) 3.09056 0.322213
\(93\) 0.282805 0.0293255
\(94\) −14.2092 −1.46556
\(95\) −2.30496 −0.236484
\(96\) −0.269806 −0.0275370
\(97\) 14.4199 1.46412 0.732058 0.681242i \(-0.238560\pi\)
0.732058 + 0.681242i \(0.238560\pi\)
\(98\) 1.20865 0.122092
\(99\) −5.21914 −0.524544
\(100\) −0.539165 −0.0539165
\(101\) 9.18275 0.913718 0.456859 0.889539i \(-0.348974\pi\)
0.456859 + 0.889539i \(0.348974\pi\)
\(102\) 0.249958 0.0247495
\(103\) 15.2143 1.49911 0.749556 0.661941i \(-0.230267\pi\)
0.749556 + 0.661941i \(0.230267\pi\)
\(104\) 0.565964 0.0554974
\(105\) −0.0912122 −0.00890140
\(106\) 8.68027 0.843102
\(107\) 13.9214 1.34583 0.672916 0.739719i \(-0.265042\pi\)
0.672916 + 0.739719i \(0.265042\pi\)
\(108\) −0.294662 −0.0283538
\(109\) −11.2973 −1.08209 −0.541043 0.840995i \(-0.681970\pi\)
−0.541043 + 0.840995i \(0.681970\pi\)
\(110\) −2.10855 −0.201043
\(111\) 0.545485 0.0517752
\(112\) 2.63097 0.248603
\(113\) 18.2639 1.71812 0.859062 0.511871i \(-0.171047\pi\)
0.859062 + 0.511871i \(0.171047\pi\)
\(114\) −0.254107 −0.0237993
\(115\) 5.73212 0.534523
\(116\) −2.87193 −0.266652
\(117\) 0.551712 0.0510058
\(118\) −17.8919 −1.64708
\(119\) 2.26732 0.207845
\(120\) −0.279927 −0.0255537
\(121\) −7.95654 −0.723322
\(122\) −14.9193 −1.35073
\(123\) −0.784896 −0.0707717
\(124\) 1.67169 0.150122
\(125\) −1.00000 −0.0894427
\(126\) 3.61589 0.322129
\(127\) 20.0424 1.77848 0.889239 0.457444i \(-0.151235\pi\)
0.889239 + 0.457444i \(0.151235\pi\)
\(128\) 4.76499 0.421170
\(129\) 1.07313 0.0944837
\(130\) 0.222894 0.0195491
\(131\) 1.70674 0.149118 0.0745591 0.997217i \(-0.476245\pi\)
0.0745591 + 0.997217i \(0.476245\pi\)
\(132\) 0.0857944 0.00746745
\(133\) −2.30496 −0.199865
\(134\) 16.3121 1.40915
\(135\) −0.546515 −0.0470365
\(136\) 6.95833 0.596672
\(137\) 16.4040 1.40149 0.700746 0.713411i \(-0.252851\pi\)
0.700746 + 0.713411i \(0.252851\pi\)
\(138\) 0.631930 0.0537934
\(139\) 3.44041 0.291812 0.145906 0.989298i \(-0.453390\pi\)
0.145906 + 0.989298i \(0.453390\pi\)
\(140\) −0.539165 −0.0455678
\(141\) 1.07231 0.0903050
\(142\) −13.5661 −1.13844
\(143\) −0.321723 −0.0269038
\(144\) 7.87102 0.655918
\(145\) −5.32663 −0.442352
\(146\) 9.16222 0.758270
\(147\) −0.0912122 −0.00752306
\(148\) 3.22442 0.265046
\(149\) 18.7076 1.53259 0.766293 0.642491i \(-0.222099\pi\)
0.766293 + 0.642491i \(0.222099\pi\)
\(150\) −0.110244 −0.00900136
\(151\) 4.03808 0.328614 0.164307 0.986409i \(-0.447461\pi\)
0.164307 + 0.986409i \(0.447461\pi\)
\(152\) −7.07383 −0.573763
\(153\) 6.78311 0.548382
\(154\) −2.10855 −0.169912
\(155\) 3.10052 0.249040
\(156\) −0.00906927 −0.000726123 0
\(157\) 11.8333 0.944398 0.472199 0.881492i \(-0.343460\pi\)
0.472199 + 0.881492i \(0.343460\pi\)
\(158\) −11.7405 −0.934023
\(159\) −0.655067 −0.0519502
\(160\) −2.95800 −0.233851
\(161\) 5.73212 0.451754
\(162\) 10.7874 0.847541
\(163\) 6.69477 0.524375 0.262188 0.965017i \(-0.415556\pi\)
0.262188 + 0.965017i \(0.415556\pi\)
\(164\) −4.63961 −0.362292
\(165\) 0.159125 0.0123878
\(166\) −14.0751 −1.09244
\(167\) 8.70211 0.673390 0.336695 0.941614i \(-0.390691\pi\)
0.336695 + 0.941614i \(0.390691\pi\)
\(168\) −0.279927 −0.0215968
\(169\) −12.9660 −0.997384
\(170\) 2.74040 0.210179
\(171\) −6.89570 −0.527327
\(172\) 6.34338 0.483678
\(173\) −9.87592 −0.750852 −0.375426 0.926852i \(-0.622504\pi\)
−0.375426 + 0.926852i \(0.622504\pi\)
\(174\) −0.587227 −0.0445175
\(175\) −1.00000 −0.0755929
\(176\) −4.58986 −0.345974
\(177\) 1.35023 0.101490
\(178\) 15.8177 1.18559
\(179\) 13.1160 0.980333 0.490167 0.871629i \(-0.336936\pi\)
0.490167 + 0.871629i \(0.336936\pi\)
\(180\) −1.61301 −0.120227
\(181\) 16.7545 1.24535 0.622677 0.782479i \(-0.286045\pi\)
0.622677 + 0.782479i \(0.286045\pi\)
\(182\) 0.222894 0.0165220
\(183\) 1.12590 0.0832292
\(184\) 17.5917 1.29687
\(185\) 5.98040 0.439688
\(186\) 0.341812 0.0250629
\(187\) −3.95546 −0.289252
\(188\) 6.33855 0.462287
\(189\) −0.546515 −0.0397531
\(190\) −2.78589 −0.202109
\(191\) −7.91999 −0.573071 −0.286535 0.958070i \(-0.592504\pi\)
−0.286535 + 0.958070i \(0.592504\pi\)
\(192\) −0.806054 −0.0581720
\(193\) 5.33649 0.384129 0.192064 0.981382i \(-0.438482\pi\)
0.192064 + 0.981382i \(0.438482\pi\)
\(194\) 17.4286 1.25130
\(195\) −0.0168209 −0.00120457
\(196\) −0.539165 −0.0385118
\(197\) 12.4342 0.885900 0.442950 0.896546i \(-0.353932\pi\)
0.442950 + 0.896546i \(0.353932\pi\)
\(198\) −6.30812 −0.448298
\(199\) −14.1842 −1.00549 −0.502747 0.864434i \(-0.667677\pi\)
−0.502747 + 0.864434i \(0.667677\pi\)
\(200\) −3.06896 −0.217008
\(201\) −1.23101 −0.0868289
\(202\) 11.0987 0.780904
\(203\) −5.32663 −0.373856
\(204\) −0.111504 −0.00780681
\(205\) −8.60516 −0.601011
\(206\) 18.3888 1.28121
\(207\) 17.1487 1.19191
\(208\) 0.485192 0.0336420
\(209\) 4.02112 0.278147
\(210\) −0.110244 −0.00760753
\(211\) 1.35383 0.0932018 0.0466009 0.998914i \(-0.485161\pi\)
0.0466009 + 0.998914i \(0.485161\pi\)
\(212\) −3.87217 −0.265942
\(213\) 1.02378 0.0701483
\(214\) 16.8261 1.15021
\(215\) 11.7652 0.802378
\(216\) −1.67723 −0.114121
\(217\) 3.10052 0.210477
\(218\) −13.6545 −0.924799
\(219\) −0.691438 −0.0467230
\(220\) 0.940602 0.0634154
\(221\) 0.418130 0.0281264
\(222\) 0.659301 0.0442494
\(223\) −22.1254 −1.48163 −0.740813 0.671711i \(-0.765559\pi\)
−0.740813 + 0.671711i \(0.765559\pi\)
\(224\) −2.95800 −0.197640
\(225\) −2.99168 −0.199445
\(226\) 22.0747 1.46839
\(227\) 14.2787 0.947712 0.473856 0.880602i \(-0.342862\pi\)
0.473856 + 0.880602i \(0.342862\pi\)
\(228\) 0.113354 0.00750707
\(229\) 1.00000 0.0660819
\(230\) 6.92812 0.456827
\(231\) 0.159125 0.0104696
\(232\) −16.3472 −1.07325
\(233\) −25.3197 −1.65875 −0.829375 0.558692i \(-0.811303\pi\)
−0.829375 + 0.558692i \(0.811303\pi\)
\(234\) 0.666827 0.0435918
\(235\) 11.7562 0.766892
\(236\) 7.98138 0.519544
\(237\) 0.886010 0.0575525
\(238\) 2.74040 0.177634
\(239\) −22.5717 −1.46004 −0.730019 0.683426i \(-0.760489\pi\)
−0.730019 + 0.683426i \(0.760489\pi\)
\(240\) −0.239977 −0.0154904
\(241\) −4.68292 −0.301654 −0.150827 0.988560i \(-0.548194\pi\)
−0.150827 + 0.988560i \(0.548194\pi\)
\(242\) −9.61667 −0.618183
\(243\) −2.45363 −0.157400
\(244\) 6.65534 0.426065
\(245\) −1.00000 −0.0638877
\(246\) −0.948665 −0.0604847
\(247\) −0.425070 −0.0270466
\(248\) 9.51537 0.604227
\(249\) 1.06219 0.0673136
\(250\) −1.20865 −0.0764417
\(251\) 25.5054 1.60989 0.804944 0.593351i \(-0.202195\pi\)
0.804944 + 0.593351i \(0.202195\pi\)
\(252\) −1.61301 −0.101610
\(253\) −9.99998 −0.628693
\(254\) 24.2243 1.51997
\(255\) −0.206808 −0.0129508
\(256\) −11.9151 −0.744691
\(257\) −0.133807 −0.00834665 −0.00417332 0.999991i \(-0.501328\pi\)
−0.00417332 + 0.999991i \(0.501328\pi\)
\(258\) 1.29704 0.0807499
\(259\) 5.98040 0.371604
\(260\) −0.0994305 −0.00616642
\(261\) −15.9356 −0.986386
\(262\) 2.06285 0.127443
\(263\) −0.0837003 −0.00516118 −0.00258059 0.999997i \(-0.500821\pi\)
−0.00258059 + 0.999997i \(0.500821\pi\)
\(264\) 0.488347 0.0300557
\(265\) −7.18179 −0.441174
\(266\) −2.78589 −0.170814
\(267\) −1.19370 −0.0730534
\(268\) −7.27665 −0.444492
\(269\) 14.8327 0.904367 0.452183 0.891925i \(-0.350645\pi\)
0.452183 + 0.891925i \(0.350645\pi\)
\(270\) −0.660545 −0.0401995
\(271\) 7.64694 0.464518 0.232259 0.972654i \(-0.425388\pi\)
0.232259 + 0.972654i \(0.425388\pi\)
\(272\) 5.96526 0.361697
\(273\) −0.0168209 −0.00101805
\(274\) 19.8267 1.19778
\(275\) 1.74455 0.105200
\(276\) −0.281897 −0.0169682
\(277\) 25.0262 1.50368 0.751839 0.659346i \(-0.229167\pi\)
0.751839 + 0.659346i \(0.229167\pi\)
\(278\) 4.15825 0.249395
\(279\) 9.27576 0.555325
\(280\) −3.06896 −0.183406
\(281\) −24.5678 −1.46559 −0.732796 0.680448i \(-0.761785\pi\)
−0.732796 + 0.680448i \(0.761785\pi\)
\(282\) 1.29605 0.0771787
\(283\) −20.1559 −1.19814 −0.599071 0.800696i \(-0.704463\pi\)
−0.599071 + 0.800696i \(0.704463\pi\)
\(284\) 6.05168 0.359101
\(285\) 0.210240 0.0124536
\(286\) −0.388850 −0.0229932
\(287\) −8.60516 −0.507947
\(288\) −8.84940 −0.521456
\(289\) −11.8592 −0.697603
\(290\) −6.43802 −0.378054
\(291\) −1.31527 −0.0771024
\(292\) −4.08716 −0.239183
\(293\) −5.68780 −0.332285 −0.166142 0.986102i \(-0.553131\pi\)
−0.166142 + 0.986102i \(0.553131\pi\)
\(294\) −0.110244 −0.00642954
\(295\) 14.8032 0.861876
\(296\) 18.3536 1.06678
\(297\) 0.953423 0.0553232
\(298\) 22.6109 1.30982
\(299\) 1.05709 0.0611332
\(300\) 0.0491785 0.00283932
\(301\) 11.7652 0.678134
\(302\) 4.88063 0.280849
\(303\) −0.837579 −0.0481177
\(304\) −6.06427 −0.347810
\(305\) 12.3438 0.706803
\(306\) 8.19840 0.468671
\(307\) −3.92243 −0.223865 −0.111932 0.993716i \(-0.535704\pi\)
−0.111932 + 0.993716i \(0.535704\pi\)
\(308\) 0.940602 0.0535958
\(309\) −1.38773 −0.0789453
\(310\) 3.74744 0.212840
\(311\) −18.0632 −1.02427 −0.512135 0.858905i \(-0.671145\pi\)
−0.512135 + 0.858905i \(0.671145\pi\)
\(312\) −0.0516229 −0.00292257
\(313\) 19.2973 1.09075 0.545373 0.838194i \(-0.316388\pi\)
0.545373 + 0.838194i \(0.316388\pi\)
\(314\) 14.3023 0.807124
\(315\) −2.99168 −0.168562
\(316\) 5.23730 0.294621
\(317\) −5.86021 −0.329142 −0.164571 0.986365i \(-0.552624\pi\)
−0.164571 + 0.986365i \(0.552624\pi\)
\(318\) −0.791747 −0.0443989
\(319\) 9.29258 0.520284
\(320\) −8.83713 −0.494011
\(321\) −1.26980 −0.0708734
\(322\) 6.92812 0.386089
\(323\) −5.22608 −0.290787
\(324\) −4.81215 −0.267342
\(325\) −0.184416 −0.0102295
\(326\) 8.09164 0.448154
\(327\) 1.03045 0.0569842
\(328\) −26.4089 −1.45819
\(329\) 11.7562 0.648142
\(330\) 0.192326 0.0105872
\(331\) 19.6138 1.07807 0.539036 0.842283i \(-0.318789\pi\)
0.539036 + 0.842283i \(0.318789\pi\)
\(332\) 6.27873 0.344590
\(333\) 17.8914 0.980445
\(334\) 10.5178 0.575509
\(335\) −13.4961 −0.737372
\(336\) −0.239977 −0.0130918
\(337\) −9.11015 −0.496262 −0.248131 0.968727i \(-0.579816\pi\)
−0.248131 + 0.968727i \(0.579816\pi\)
\(338\) −15.6713 −0.852409
\(339\) −1.66589 −0.0904789
\(340\) −1.22246 −0.0662973
\(341\) −5.40902 −0.292915
\(342\) −8.33448 −0.450677
\(343\) −1.00000 −0.0539949
\(344\) 36.1069 1.94675
\(345\) −0.522839 −0.0281487
\(346\) −11.9365 −0.641712
\(347\) −24.0694 −1.29211 −0.646056 0.763290i \(-0.723583\pi\)
−0.646056 + 0.763290i \(0.723583\pi\)
\(348\) 0.261955 0.0140423
\(349\) −24.8257 −1.32889 −0.664444 0.747338i \(-0.731331\pi\)
−0.664444 + 0.747338i \(0.731331\pi\)
\(350\) −1.20865 −0.0646051
\(351\) −0.100786 −0.00537955
\(352\) 5.16039 0.275050
\(353\) 24.3804 1.29764 0.648818 0.760944i \(-0.275264\pi\)
0.648818 + 0.760944i \(0.275264\pi\)
\(354\) 1.63196 0.0867377
\(355\) 11.2242 0.595716
\(356\) −7.05610 −0.373973
\(357\) −0.206808 −0.0109454
\(358\) 15.8526 0.837837
\(359\) 24.0581 1.26974 0.634868 0.772621i \(-0.281055\pi\)
0.634868 + 0.772621i \(0.281055\pi\)
\(360\) −9.18135 −0.483900
\(361\) −13.6872 −0.720377
\(362\) 20.2504 1.06434
\(363\) 0.725733 0.0380911
\(364\) −0.0994305 −0.00521157
\(365\) −7.58054 −0.396784
\(366\) 1.36082 0.0711314
\(367\) −0.0349649 −0.00182515 −0.000912576 1.00000i \(-0.500290\pi\)
−0.000912576 1.00000i \(0.500290\pi\)
\(368\) 15.0810 0.786153
\(369\) −25.7439 −1.34017
\(370\) 7.22821 0.375777
\(371\) −7.18179 −0.372860
\(372\) −0.152479 −0.00790566
\(373\) 11.5511 0.598094 0.299047 0.954238i \(-0.403331\pi\)
0.299047 + 0.954238i \(0.403331\pi\)
\(374\) −4.78077 −0.247208
\(375\) 0.0912122 0.00471018
\(376\) 36.0794 1.86065
\(377\) −0.982312 −0.0505917
\(378\) −0.660545 −0.0339748
\(379\) 25.3075 1.29996 0.649978 0.759953i \(-0.274778\pi\)
0.649978 + 0.759953i \(0.274778\pi\)
\(380\) 1.24275 0.0637519
\(381\) −1.82811 −0.0936571
\(382\) −9.57250 −0.489772
\(383\) 16.2445 0.830057 0.415029 0.909808i \(-0.363772\pi\)
0.415029 + 0.909808i \(0.363772\pi\)
\(384\) −0.434625 −0.0221794
\(385\) 1.74455 0.0889106
\(386\) 6.44994 0.328293
\(387\) 35.1977 1.78920
\(388\) −7.77469 −0.394700
\(389\) −23.1278 −1.17263 −0.586314 0.810084i \(-0.699421\pi\)
−0.586314 + 0.810084i \(0.699421\pi\)
\(390\) −0.0203306 −0.00102948
\(391\) 12.9966 0.657265
\(392\) −3.06896 −0.155006
\(393\) −0.155675 −0.00785277
\(394\) 15.0286 0.757130
\(395\) 9.71372 0.488750
\(396\) 2.81398 0.141408
\(397\) −19.0740 −0.957295 −0.478648 0.878007i \(-0.658873\pi\)
−0.478648 + 0.878007i \(0.658873\pi\)
\(398\) −17.1438 −0.859340
\(399\) 0.210240 0.0105252
\(400\) −2.63097 −0.131548
\(401\) 10.6948 0.534071 0.267036 0.963687i \(-0.413956\pi\)
0.267036 + 0.963687i \(0.413956\pi\)
\(402\) −1.48786 −0.0742078
\(403\) 0.571784 0.0284826
\(404\) −4.95102 −0.246323
\(405\) −8.92519 −0.443496
\(406\) −6.43802 −0.319514
\(407\) −10.4331 −0.517150
\(408\) −0.634685 −0.0314216
\(409\) 22.0837 1.09197 0.545984 0.837796i \(-0.316156\pi\)
0.545984 + 0.837796i \(0.316156\pi\)
\(410\) −10.4006 −0.513651
\(411\) −1.49625 −0.0738045
\(412\) −8.20304 −0.404135
\(413\) 14.8032 0.728418
\(414\) 20.7267 1.01866
\(415\) 11.6453 0.571644
\(416\) −0.545502 −0.0267454
\(417\) −0.313807 −0.0153672
\(418\) 4.86013 0.237717
\(419\) 16.5758 0.809781 0.404891 0.914365i \(-0.367310\pi\)
0.404891 + 0.914365i \(0.367310\pi\)
\(420\) 0.0491785 0.00239966
\(421\) −16.2118 −0.790113 −0.395057 0.918657i \(-0.629275\pi\)
−0.395057 + 0.918657i \(0.629275\pi\)
\(422\) 1.63631 0.0796544
\(423\) 35.1709 1.71007
\(424\) −22.0406 −1.07039
\(425\) −2.26732 −0.109981
\(426\) 1.23739 0.0599518
\(427\) 12.3438 0.597358
\(428\) −7.50593 −0.362813
\(429\) 0.0293450 0.00141679
\(430\) 14.2200 0.685748
\(431\) −7.54054 −0.363215 −0.181608 0.983371i \(-0.558130\pi\)
−0.181608 + 0.983371i \(0.558130\pi\)
\(432\) −1.43786 −0.0691792
\(433\) 36.1610 1.73779 0.868893 0.495001i \(-0.164832\pi\)
0.868893 + 0.495001i \(0.164832\pi\)
\(434\) 3.74744 0.179883
\(435\) 0.485853 0.0232949
\(436\) 6.09112 0.291712
\(437\) −13.2123 −0.632030
\(438\) −0.835706 −0.0399316
\(439\) −8.70213 −0.415330 −0.207665 0.978200i \(-0.566586\pi\)
−0.207665 + 0.978200i \(0.566586\pi\)
\(440\) 5.35396 0.255240
\(441\) −2.99168 −0.142461
\(442\) 0.505372 0.0240381
\(443\) −28.5661 −1.35722 −0.678609 0.734500i \(-0.737417\pi\)
−0.678609 + 0.734500i \(0.737417\pi\)
\(444\) −0.294107 −0.0139577
\(445\) −13.0871 −0.620387
\(446\) −26.7419 −1.26626
\(447\) −1.70636 −0.0807081
\(448\) −8.83713 −0.417515
\(449\) −14.1671 −0.668585 −0.334293 0.942469i \(-0.608497\pi\)
−0.334293 + 0.942469i \(0.608497\pi\)
\(450\) −3.61589 −0.170455
\(451\) 15.0122 0.706895
\(452\) −9.84727 −0.463177
\(453\) −0.368322 −0.0173053
\(454\) 17.2580 0.809957
\(455\) −0.184416 −0.00864553
\(456\) 0.645220 0.0302152
\(457\) 26.5663 1.24272 0.621359 0.783526i \(-0.286581\pi\)
0.621359 + 0.783526i \(0.286581\pi\)
\(458\) 1.20865 0.0564765
\(459\) −1.23913 −0.0578374
\(460\) −3.09056 −0.144098
\(461\) −31.6583 −1.47447 −0.737237 0.675634i \(-0.763870\pi\)
−0.737237 + 0.675634i \(0.763870\pi\)
\(462\) 0.192326 0.00894781
\(463\) 28.6513 1.33154 0.665769 0.746158i \(-0.268103\pi\)
0.665769 + 0.746158i \(0.268103\pi\)
\(464\) −14.0142 −0.650592
\(465\) −0.282805 −0.0131148
\(466\) −30.6027 −1.41764
\(467\) 23.1155 1.06966 0.534830 0.844960i \(-0.320376\pi\)
0.534830 + 0.844960i \(0.320376\pi\)
\(468\) −0.297464 −0.0137503
\(469\) −13.4961 −0.623193
\(470\) 14.2092 0.655420
\(471\) −1.07934 −0.0497333
\(472\) 45.4305 2.09111
\(473\) −20.5250 −0.943739
\(474\) 1.07088 0.0491870
\(475\) 2.30496 0.105759
\(476\) −1.22246 −0.0560315
\(477\) −21.4856 −0.983759
\(478\) −27.2812 −1.24781
\(479\) −0.544574 −0.0248822 −0.0124411 0.999923i \(-0.503960\pi\)
−0.0124411 + 0.999923i \(0.503960\pi\)
\(480\) 0.269806 0.0123149
\(481\) 1.10288 0.0502869
\(482\) −5.66002 −0.257807
\(483\) −0.522839 −0.0237900
\(484\) 4.28989 0.194995
\(485\) −14.4199 −0.654772
\(486\) −2.96558 −0.134521
\(487\) −3.00389 −0.136119 −0.0680596 0.997681i \(-0.521681\pi\)
−0.0680596 + 0.997681i \(0.521681\pi\)
\(488\) 37.8826 1.71487
\(489\) −0.610645 −0.0276143
\(490\) −1.20865 −0.0546012
\(491\) −39.3483 −1.77576 −0.887882 0.460071i \(-0.847824\pi\)
−0.887882 + 0.460071i \(0.847824\pi\)
\(492\) 0.423189 0.0190788
\(493\) −12.0772 −0.543929
\(494\) −0.513761 −0.0231152
\(495\) 5.21914 0.234583
\(496\) 8.15737 0.366277
\(497\) 11.2242 0.503472
\(498\) 1.28382 0.0575292
\(499\) −3.83123 −0.171509 −0.0857546 0.996316i \(-0.527330\pi\)
−0.0857546 + 0.996316i \(0.527330\pi\)
\(500\) 0.539165 0.0241122
\(501\) −0.793739 −0.0354617
\(502\) 30.8271 1.37588
\(503\) −28.5272 −1.27197 −0.635983 0.771703i \(-0.719405\pi\)
−0.635983 + 0.771703i \(0.719405\pi\)
\(504\) −9.18135 −0.408970
\(505\) −9.18275 −0.408627
\(506\) −12.0865 −0.537309
\(507\) 1.18266 0.0525236
\(508\) −10.8062 −0.479447
\(509\) −14.2012 −0.629458 −0.314729 0.949181i \(-0.601914\pi\)
−0.314729 + 0.949181i \(0.601914\pi\)
\(510\) −0.249958 −0.0110683
\(511\) −7.58054 −0.335343
\(512\) −23.9311 −1.05762
\(513\) 1.25969 0.0556168
\(514\) −0.161726 −0.00713342
\(515\) −15.2143 −0.670423
\(516\) −0.578594 −0.0254712
\(517\) −20.5094 −0.902001
\(518\) 7.22821 0.317589
\(519\) 0.900804 0.0395409
\(520\) −0.565964 −0.0248192
\(521\) 1.00728 0.0441299 0.0220650 0.999757i \(-0.492976\pi\)
0.0220650 + 0.999757i \(0.492976\pi\)
\(522\) −19.2605 −0.843010
\(523\) −13.7063 −0.599333 −0.299667 0.954044i \(-0.596875\pi\)
−0.299667 + 0.954044i \(0.596875\pi\)
\(524\) −0.920213 −0.0401997
\(525\) 0.0912122 0.00398083
\(526\) −0.101164 −0.00441098
\(527\) 7.02988 0.306226
\(528\) 0.418652 0.0182195
\(529\) 9.85718 0.428573
\(530\) −8.68027 −0.377047
\(531\) 44.2865 1.92187
\(532\) 1.24275 0.0538802
\(533\) −1.58693 −0.0687374
\(534\) −1.44277 −0.0624347
\(535\) −13.9214 −0.601874
\(536\) −41.4191 −1.78903
\(537\) −1.19634 −0.0516257
\(538\) 17.9276 0.772912
\(539\) 1.74455 0.0751432
\(540\) 0.294662 0.0126802
\(541\) −20.8515 −0.896475 −0.448238 0.893914i \(-0.647948\pi\)
−0.448238 + 0.893914i \(0.647948\pi\)
\(542\) 9.24247 0.396998
\(543\) −1.52822 −0.0655821
\(544\) −6.70675 −0.287549
\(545\) 11.2973 0.483924
\(546\) −0.0203306 −0.000870071 0
\(547\) 26.9356 1.15168 0.575842 0.817561i \(-0.304674\pi\)
0.575842 + 0.817561i \(0.304674\pi\)
\(548\) −8.84449 −0.377818
\(549\) 36.9287 1.57608
\(550\) 2.10855 0.0899090
\(551\) 12.2776 0.523045
\(552\) −1.60457 −0.0682952
\(553\) 9.71372 0.413069
\(554\) 30.2479 1.28511
\(555\) −0.545485 −0.0231546
\(556\) −1.85495 −0.0786674
\(557\) −19.6483 −0.832526 −0.416263 0.909244i \(-0.636660\pi\)
−0.416263 + 0.909244i \(0.636660\pi\)
\(558\) 11.2111 0.474606
\(559\) 2.16968 0.0917677
\(560\) −2.63097 −0.111179
\(561\) 0.360787 0.0152324
\(562\) −29.6939 −1.25256
\(563\) 17.2534 0.727142 0.363571 0.931566i \(-0.381557\pi\)
0.363571 + 0.931566i \(0.381557\pi\)
\(564\) −0.578154 −0.0243447
\(565\) −18.2639 −0.768369
\(566\) −24.3614 −1.02399
\(567\) −8.92519 −0.374823
\(568\) 34.4465 1.44534
\(569\) 42.5671 1.78450 0.892252 0.451537i \(-0.149124\pi\)
0.892252 + 0.451537i \(0.149124\pi\)
\(570\) 0.254107 0.0106434
\(571\) 32.4227 1.35685 0.678424 0.734670i \(-0.262663\pi\)
0.678424 + 0.734670i \(0.262663\pi\)
\(572\) 0.173462 0.00725280
\(573\) 0.722400 0.0301787
\(574\) −10.4006 −0.434114
\(575\) −5.73212 −0.239046
\(576\) −26.4379 −1.10158
\(577\) 33.0469 1.37576 0.687880 0.725824i \(-0.258541\pi\)
0.687880 + 0.725824i \(0.258541\pi\)
\(578\) −14.3337 −0.596202
\(579\) −0.486753 −0.0202288
\(580\) 2.87193 0.119250
\(581\) 11.6453 0.483127
\(582\) −1.58970 −0.0658951
\(583\) 12.5290 0.518898
\(584\) −23.2644 −0.962687
\(585\) −0.551712 −0.0228105
\(586\) −6.87456 −0.283985
\(587\) 45.7224 1.88717 0.943584 0.331135i \(-0.107431\pi\)
0.943584 + 0.331135i \(0.107431\pi\)
\(588\) 0.0491785 0.00202809
\(589\) −7.14656 −0.294469
\(590\) 17.8919 0.736598
\(591\) −1.13415 −0.0466528
\(592\) 15.7342 0.646673
\(593\) −23.0752 −0.947584 −0.473792 0.880637i \(-0.657115\pi\)
−0.473792 + 0.880637i \(0.657115\pi\)
\(594\) 1.15235 0.0472817
\(595\) −2.26732 −0.0929512
\(596\) −10.0865 −0.413159
\(597\) 1.29378 0.0529507
\(598\) 1.27765 0.0522471
\(599\) −31.3047 −1.27907 −0.639537 0.768761i \(-0.720874\pi\)
−0.639537 + 0.768761i \(0.720874\pi\)
\(600\) 0.279927 0.0114280
\(601\) −25.1488 −1.02584 −0.512921 0.858436i \(-0.671437\pi\)
−0.512921 + 0.858436i \(0.671437\pi\)
\(602\) 14.2200 0.579563
\(603\) −40.3761 −1.64424
\(604\) −2.17719 −0.0885888
\(605\) 7.95654 0.323479
\(606\) −1.01234 −0.0411235
\(607\) 21.6562 0.879000 0.439500 0.898243i \(-0.355156\pi\)
0.439500 + 0.898243i \(0.355156\pi\)
\(608\) 6.81807 0.276509
\(609\) 0.485853 0.0196878
\(610\) 14.9193 0.604066
\(611\) 2.16803 0.0877092
\(612\) −3.65722 −0.147834
\(613\) −37.0958 −1.49828 −0.749142 0.662409i \(-0.769534\pi\)
−0.749142 + 0.662409i \(0.769534\pi\)
\(614\) −4.74085 −0.191325
\(615\) 0.784896 0.0316501
\(616\) 5.35396 0.215717
\(617\) 1.95146 0.0785628 0.0392814 0.999228i \(-0.487493\pi\)
0.0392814 + 0.999228i \(0.487493\pi\)
\(618\) −1.67728 −0.0674702
\(619\) −0.396705 −0.0159449 −0.00797245 0.999968i \(-0.502538\pi\)
−0.00797245 + 0.999968i \(0.502538\pi\)
\(620\) −1.67169 −0.0671368
\(621\) −3.13269 −0.125710
\(622\) −21.8321 −0.875387
\(623\) −13.0871 −0.524323
\(624\) −0.0442554 −0.00177163
\(625\) 1.00000 0.0400000
\(626\) 23.3236 0.932200
\(627\) −0.366775 −0.0146476
\(628\) −6.38009 −0.254593
\(629\) 13.5595 0.540652
\(630\) −3.61589 −0.144061
\(631\) 7.56559 0.301181 0.150591 0.988596i \(-0.451882\pi\)
0.150591 + 0.988596i \(0.451882\pi\)
\(632\) 29.8110 1.18582
\(633\) −0.123486 −0.00490814
\(634\) −7.08294 −0.281299
\(635\) −20.0424 −0.795359
\(636\) 0.353189 0.0140049
\(637\) −0.184416 −0.00730681
\(638\) 11.2315 0.444658
\(639\) 33.5791 1.32837
\(640\) −4.76499 −0.188353
\(641\) −0.689964 −0.0272519 −0.0136260 0.999907i \(-0.504337\pi\)
−0.0136260 + 0.999907i \(0.504337\pi\)
\(642\) −1.53475 −0.0605716
\(643\) −5.28631 −0.208472 −0.104236 0.994553i \(-0.533240\pi\)
−0.104236 + 0.994553i \(0.533240\pi\)
\(644\) −3.09056 −0.121785
\(645\) −1.07313 −0.0422544
\(646\) −6.31651 −0.248520
\(647\) 10.9490 0.430451 0.215226 0.976564i \(-0.430951\pi\)
0.215226 + 0.976564i \(0.430951\pi\)
\(648\) −27.3911 −1.07602
\(649\) −25.8250 −1.01372
\(650\) −0.222894 −0.00874261
\(651\) −0.282805 −0.0110840
\(652\) −3.60959 −0.141362
\(653\) −41.3961 −1.61996 −0.809978 0.586461i \(-0.800521\pi\)
−0.809978 + 0.586461i \(0.800521\pi\)
\(654\) 1.24546 0.0487012
\(655\) −1.70674 −0.0666877
\(656\) −22.6399 −0.883941
\(657\) −22.6785 −0.884774
\(658\) 14.2092 0.553931
\(659\) −20.0152 −0.779682 −0.389841 0.920882i \(-0.627470\pi\)
−0.389841 + 0.920882i \(0.627470\pi\)
\(660\) −0.0857944 −0.00333954
\(661\) 41.5881 1.61759 0.808795 0.588091i \(-0.200120\pi\)
0.808795 + 0.588091i \(0.200120\pi\)
\(662\) 23.7062 0.921368
\(663\) −0.0381385 −0.00148118
\(664\) 35.7389 1.38694
\(665\) 2.30496 0.0893824
\(666\) 21.6245 0.837932
\(667\) −30.5328 −1.18224
\(668\) −4.69188 −0.181534
\(669\) 2.01811 0.0780245
\(670\) −16.3121 −0.630191
\(671\) −21.5344 −0.831326
\(672\) 0.269806 0.0104080
\(673\) −15.0916 −0.581739 −0.290869 0.956763i \(-0.593944\pi\)
−0.290869 + 0.956763i \(0.593944\pi\)
\(674\) −11.0110 −0.424127
\(675\) 0.546515 0.0210354
\(676\) 6.99081 0.268877
\(677\) −3.24684 −0.124786 −0.0623930 0.998052i \(-0.519873\pi\)
−0.0623930 + 0.998052i \(0.519873\pi\)
\(678\) −2.01348 −0.0773273
\(679\) −14.4199 −0.553384
\(680\) −6.95833 −0.266840
\(681\) −1.30239 −0.0499078
\(682\) −6.53761 −0.250338
\(683\) −42.7632 −1.63629 −0.818145 0.575012i \(-0.804997\pi\)
−0.818145 + 0.575012i \(0.804997\pi\)
\(684\) 3.71792 0.142158
\(685\) −16.4040 −0.626766
\(686\) −1.20865 −0.0461465
\(687\) −0.0912122 −0.00347996
\(688\) 30.9538 1.18010
\(689\) −1.32443 −0.0504569
\(690\) −0.631930 −0.0240572
\(691\) 3.18493 0.121160 0.0605802 0.998163i \(-0.480705\pi\)
0.0605802 + 0.998163i \(0.480705\pi\)
\(692\) 5.32475 0.202417
\(693\) 5.21914 0.198259
\(694\) −29.0915 −1.10430
\(695\) −3.44041 −0.130502
\(696\) 1.49107 0.0565187
\(697\) −19.5107 −0.739020
\(698\) −30.0055 −1.13573
\(699\) 2.30947 0.0873521
\(700\) 0.539165 0.0203785
\(701\) 19.1500 0.723285 0.361643 0.932317i \(-0.382216\pi\)
0.361643 + 0.932317i \(0.382216\pi\)
\(702\) −0.121815 −0.00459760
\(703\) −13.7846 −0.519895
\(704\) 15.4168 0.581044
\(705\) −1.07231 −0.0403856
\(706\) 29.4673 1.10902
\(707\) −9.18275 −0.345353
\(708\) −0.727999 −0.0273599
\(709\) 8.71879 0.327441 0.163721 0.986507i \(-0.447650\pi\)
0.163721 + 0.986507i \(0.447650\pi\)
\(710\) 13.5661 0.509126
\(711\) 29.0603 1.08985
\(712\) −40.1638 −1.50520
\(713\) 17.7725 0.665587
\(714\) −0.249958 −0.00935444
\(715\) 0.321723 0.0120317
\(716\) −7.07168 −0.264281
\(717\) 2.05881 0.0768877
\(718\) 29.0778 1.08517
\(719\) −18.5144 −0.690469 −0.345234 0.938516i \(-0.612201\pi\)
−0.345234 + 0.938516i \(0.612201\pi\)
\(720\) −7.87102 −0.293336
\(721\) −15.2143 −0.566611
\(722\) −16.5430 −0.615667
\(723\) 0.427140 0.0158855
\(724\) −9.03346 −0.335726
\(725\) 5.32663 0.197826
\(726\) 0.877158 0.0325544
\(727\) 16.3623 0.606843 0.303422 0.952856i \(-0.401871\pi\)
0.303422 + 0.952856i \(0.401871\pi\)
\(728\) −0.565964 −0.0209760
\(729\) −26.5518 −0.983399
\(730\) −9.16222 −0.339109
\(731\) 26.6755 0.986628
\(732\) −0.607049 −0.0224372
\(733\) 11.7799 0.435102 0.217551 0.976049i \(-0.430193\pi\)
0.217551 + 0.976049i \(0.430193\pi\)
\(734\) −0.0422603 −0.00155986
\(735\) 0.0912122 0.00336441
\(736\) −16.9556 −0.624993
\(737\) 23.5447 0.867280
\(738\) −31.1154 −1.14537
\(739\) −19.0277 −0.699946 −0.349973 0.936760i \(-0.613809\pi\)
−0.349973 + 0.936760i \(0.613809\pi\)
\(740\) −3.22442 −0.118532
\(741\) 0.0387716 0.00142431
\(742\) −8.68027 −0.318663
\(743\) −24.4100 −0.895517 −0.447759 0.894154i \(-0.647778\pi\)
−0.447759 + 0.894154i \(0.647778\pi\)
\(744\) −0.867918 −0.0318194
\(745\) −18.7076 −0.685393
\(746\) 13.9612 0.511158
\(747\) 34.8389 1.27469
\(748\) 2.13265 0.0779774
\(749\) −13.9214 −0.508677
\(750\) 0.110244 0.00402553
\(751\) −2.49103 −0.0908989 −0.0454494 0.998967i \(-0.514472\pi\)
−0.0454494 + 0.998967i \(0.514472\pi\)
\(752\) 30.9303 1.12791
\(753\) −2.32641 −0.0847790
\(754\) −1.18727 −0.0432379
\(755\) −4.03808 −0.146961
\(756\) 0.294662 0.0107167
\(757\) −30.1700 −1.09655 −0.548273 0.836299i \(-0.684715\pi\)
−0.548273 + 0.836299i \(0.684715\pi\)
\(758\) 30.5878 1.11100
\(759\) 0.912121 0.0331079
\(760\) 7.07383 0.256595
\(761\) 32.7666 1.18779 0.593895 0.804543i \(-0.297589\pi\)
0.593895 + 0.804543i \(0.297589\pi\)
\(762\) −2.20955 −0.0800435
\(763\) 11.2973 0.408990
\(764\) 4.27019 0.154490
\(765\) −6.78311 −0.245244
\(766\) 19.6340 0.709404
\(767\) 2.72994 0.0985725
\(768\) 1.08680 0.0392165
\(769\) −37.5626 −1.35454 −0.677271 0.735733i \(-0.736838\pi\)
−0.677271 + 0.735733i \(0.736838\pi\)
\(770\) 2.10855 0.0759870
\(771\) 0.0122048 0.000439546 0
\(772\) −2.87725 −0.103554
\(773\) 26.7818 0.963276 0.481638 0.876370i \(-0.340042\pi\)
0.481638 + 0.876370i \(0.340042\pi\)
\(774\) 42.5416 1.52913
\(775\) −3.10052 −0.111374
\(776\) −44.2540 −1.58863
\(777\) −0.545485 −0.0195692
\(778\) −27.9535 −1.00218
\(779\) 19.8345 0.710646
\(780\) 0.00906927 0.000324732 0
\(781\) −19.5811 −0.700668
\(782\) 15.7083 0.561728
\(783\) 2.91108 0.104033
\(784\) −2.63097 −0.0939632
\(785\) −11.8333 −0.422347
\(786\) −0.188157 −0.00671133
\(787\) 2.66319 0.0949325 0.0474662 0.998873i \(-0.484885\pi\)
0.0474662 + 0.998873i \(0.484885\pi\)
\(788\) −6.70409 −0.238823
\(789\) 0.00763449 0.000271795 0
\(790\) 11.7405 0.417708
\(791\) −18.2639 −0.649390
\(792\) 16.0174 0.569152
\(793\) 2.27639 0.0808368
\(794\) −23.0538 −0.818147
\(795\) 0.655067 0.0232328
\(796\) 7.64765 0.271064
\(797\) 27.1363 0.961217 0.480608 0.876935i \(-0.340416\pi\)
0.480608 + 0.876935i \(0.340416\pi\)
\(798\) 0.254107 0.00899529
\(799\) 26.6552 0.942993
\(800\) 2.95800 0.104581
\(801\) −39.1524 −1.38338
\(802\) 12.9262 0.456441
\(803\) 13.2246 0.466688
\(804\) 0.663719 0.0234076
\(805\) −5.73212 −0.202031
\(806\) 0.691086 0.0243425
\(807\) −1.35293 −0.0476252
\(808\) −28.1815 −0.991422
\(809\) 41.7824 1.46899 0.734496 0.678613i \(-0.237419\pi\)
0.734496 + 0.678613i \(0.237419\pi\)
\(810\) −10.7874 −0.379032
\(811\) 8.93514 0.313755 0.156878 0.987618i \(-0.449857\pi\)
0.156878 + 0.987618i \(0.449857\pi\)
\(812\) 2.87193 0.100785
\(813\) −0.697494 −0.0244622
\(814\) −12.6100 −0.441980
\(815\) −6.69477 −0.234508
\(816\) −0.544105 −0.0190475
\(817\) −27.1182 −0.948747
\(818\) 26.6914 0.933244
\(819\) −0.551712 −0.0192784
\(820\) 4.63961 0.162022
\(821\) 50.6233 1.76677 0.883384 0.468651i \(-0.155260\pi\)
0.883384 + 0.468651i \(0.155260\pi\)
\(822\) −1.80844 −0.0630766
\(823\) 10.2355 0.356785 0.178393 0.983959i \(-0.442910\pi\)
0.178393 + 0.983959i \(0.442910\pi\)
\(824\) −46.6922 −1.62660
\(825\) −0.159125 −0.00554000
\(826\) 17.8919 0.622539
\(827\) 15.4448 0.537068 0.268534 0.963270i \(-0.413461\pi\)
0.268534 + 0.963270i \(0.413461\pi\)
\(828\) −9.24597 −0.321320
\(829\) 16.9725 0.589480 0.294740 0.955577i \(-0.404767\pi\)
0.294740 + 0.955577i \(0.404767\pi\)
\(830\) 14.0751 0.488552
\(831\) −2.28270 −0.0791858
\(832\) −1.62970 −0.0564998
\(833\) −2.26732 −0.0785581
\(834\) −0.379283 −0.0131335
\(835\) −8.70211 −0.301149
\(836\) −2.16805 −0.0749835
\(837\) −1.69448 −0.0585697
\(838\) 20.0344 0.692075
\(839\) −32.0498 −1.10648 −0.553241 0.833022i \(-0.686609\pi\)
−0.553241 + 0.833022i \(0.686609\pi\)
\(840\) 0.279927 0.00965839
\(841\) −0.627064 −0.0216229
\(842\) −19.5944 −0.675266
\(843\) 2.24088 0.0771802
\(844\) −0.729941 −0.0251256
\(845\) 12.9660 0.446044
\(846\) 42.5093 1.46150
\(847\) 7.95654 0.273390
\(848\) −18.8951 −0.648859
\(849\) 1.83846 0.0630958
\(850\) −2.74040 −0.0939949
\(851\) 34.2803 1.17512
\(852\) −0.551987 −0.0189108
\(853\) 10.6268 0.363855 0.181928 0.983312i \(-0.441766\pi\)
0.181928 + 0.983312i \(0.441766\pi\)
\(854\) 14.9193 0.510529
\(855\) 6.89570 0.235828
\(856\) −42.7242 −1.46028
\(857\) 4.15965 0.142091 0.0710455 0.997473i \(-0.477366\pi\)
0.0710455 + 0.997473i \(0.477366\pi\)
\(858\) 0.0354679 0.00121085
\(859\) 25.4422 0.868075 0.434038 0.900895i \(-0.357088\pi\)
0.434038 + 0.900895i \(0.357088\pi\)
\(860\) −6.34338 −0.216307
\(861\) 0.784896 0.0267492
\(862\) −9.11387 −0.310420
\(863\) −15.3455 −0.522367 −0.261183 0.965289i \(-0.584113\pi\)
−0.261183 + 0.965289i \(0.584113\pi\)
\(864\) 1.61659 0.0549976
\(865\) 9.87592 0.335791
\(866\) 43.7059 1.48519
\(867\) 1.08171 0.0367367
\(868\) −1.67169 −0.0567409
\(869\) −16.9461 −0.574857
\(870\) 0.587227 0.0199088
\(871\) −2.48890 −0.0843330
\(872\) 34.6710 1.17411
\(873\) −43.1396 −1.46006
\(874\) −15.9690 −0.540161
\(875\) 1.00000 0.0338062
\(876\) 0.372799 0.0125957
\(877\) 42.0001 1.41824 0.709122 0.705086i \(-0.249092\pi\)
0.709122 + 0.705086i \(0.249092\pi\)
\(878\) −10.5178 −0.354959
\(879\) 0.518797 0.0174986
\(880\) 4.58986 0.154724
\(881\) 5.84699 0.196990 0.0984950 0.995138i \(-0.468597\pi\)
0.0984950 + 0.995138i \(0.468597\pi\)
\(882\) −3.61589 −0.121753
\(883\) 56.1037 1.88804 0.944021 0.329887i \(-0.107011\pi\)
0.944021 + 0.329887i \(0.107011\pi\)
\(884\) −0.225441 −0.00758240
\(885\) −1.35023 −0.0453876
\(886\) −34.5264 −1.15994
\(887\) 1.49418 0.0501696 0.0250848 0.999685i \(-0.492014\pi\)
0.0250848 + 0.999685i \(0.492014\pi\)
\(888\) −1.67407 −0.0561782
\(889\) −20.0424 −0.672201
\(890\) −15.8177 −0.530211
\(891\) 15.5705 0.521630
\(892\) 11.9292 0.399421
\(893\) −27.0976 −0.906787
\(894\) −2.06239 −0.0689767
\(895\) −13.1160 −0.438418
\(896\) −4.76499 −0.159187
\(897\) −0.0964197 −0.00321936
\(898\) −17.1230 −0.571403
\(899\) −16.5153 −0.550816
\(900\) 1.61301 0.0537670
\(901\) −16.2834 −0.542480
\(902\) 18.1444 0.604144
\(903\) −1.07313 −0.0357115
\(904\) −56.0513 −1.86424
\(905\) −16.7545 −0.556939
\(906\) −0.445173 −0.0147899
\(907\) −17.7902 −0.590715 −0.295358 0.955387i \(-0.595439\pi\)
−0.295358 + 0.955387i \(0.595439\pi\)
\(908\) −7.69859 −0.255487
\(909\) −27.4719 −0.911184
\(910\) −0.222894 −0.00738886
\(911\) −16.6492 −0.551613 −0.275806 0.961213i \(-0.588945\pi\)
−0.275806 + 0.961213i \(0.588945\pi\)
\(912\) 0.553136 0.0183162
\(913\) −20.3158 −0.672354
\(914\) 32.1093 1.06208
\(915\) −1.12590 −0.0372213
\(916\) −0.539165 −0.0178145
\(917\) −1.70674 −0.0563614
\(918\) −1.49767 −0.0494304
\(919\) −47.9100 −1.58041 −0.790203 0.612846i \(-0.790025\pi\)
−0.790203 + 0.612846i \(0.790025\pi\)
\(920\) −17.5917 −0.579980
\(921\) 0.357774 0.0117890
\(922\) −38.2638 −1.26015
\(923\) 2.06991 0.0681319
\(924\) −0.0857944 −0.00282243
\(925\) −5.98040 −0.196634
\(926\) 34.6294 1.13799
\(927\) −45.5164 −1.49495
\(928\) 15.7562 0.517222
\(929\) 24.2836 0.796719 0.398359 0.917229i \(-0.369580\pi\)
0.398359 + 0.917229i \(0.369580\pi\)
\(930\) −0.341812 −0.0112085
\(931\) 2.30496 0.0755419
\(932\) 13.6515 0.447170
\(933\) 1.64758 0.0539395
\(934\) 27.9386 0.914178
\(935\) 3.95546 0.129358
\(936\) −1.69318 −0.0553434
\(937\) −29.5485 −0.965308 −0.482654 0.875811i \(-0.660327\pi\)
−0.482654 + 0.875811i \(0.660327\pi\)
\(938\) −16.3121 −0.532609
\(939\) −1.76015 −0.0574402
\(940\) −6.33855 −0.206741
\(941\) 39.3715 1.28347 0.641737 0.766924i \(-0.278214\pi\)
0.641737 + 0.766924i \(0.278214\pi\)
\(942\) −1.30454 −0.0425043
\(943\) −49.3258 −1.60627
\(944\) 38.9468 1.26761
\(945\) 0.546515 0.0177781
\(946\) −24.8075 −0.806561
\(947\) 26.0578 0.846766 0.423383 0.905951i \(-0.360843\pi\)
0.423383 + 0.905951i \(0.360843\pi\)
\(948\) −0.477706 −0.0155152
\(949\) −1.39797 −0.0453800
\(950\) 2.78589 0.0903861
\(951\) 0.534523 0.0173331
\(952\) −6.95833 −0.225521
\(953\) 34.6991 1.12401 0.562006 0.827133i \(-0.310030\pi\)
0.562006 + 0.827133i \(0.310030\pi\)
\(954\) −25.9686 −0.840764
\(955\) 7.91999 0.256285
\(956\) 12.1699 0.393601
\(957\) −0.847597 −0.0273989
\(958\) −0.658199 −0.0212655
\(959\) −16.4040 −0.529714
\(960\) 0.806054 0.0260153
\(961\) −21.3868 −0.689896
\(962\) 1.33299 0.0429774
\(963\) −41.6484 −1.34210
\(964\) 2.52487 0.0813206
\(965\) −5.33649 −0.171788
\(966\) −0.631930 −0.0203320
\(967\) 17.3195 0.556956 0.278478 0.960443i \(-0.410170\pi\)
0.278478 + 0.960443i \(0.410170\pi\)
\(968\) 24.4183 0.784834
\(969\) 0.476683 0.0153133
\(970\) −17.4286 −0.559598
\(971\) 10.7631 0.345404 0.172702 0.984974i \(-0.444750\pi\)
0.172702 + 0.984974i \(0.444750\pi\)
\(972\) 1.32291 0.0424324
\(973\) −3.44041 −0.110294
\(974\) −3.63065 −0.116334
\(975\) 0.0168209 0.000538702 0
\(976\) 32.4761 1.03954
\(977\) 6.09114 0.194873 0.0974364 0.995242i \(-0.468936\pi\)
0.0974364 + 0.995242i \(0.468936\pi\)
\(978\) −0.738056 −0.0236004
\(979\) 22.8311 0.729685
\(980\) 0.539165 0.0172230
\(981\) 33.7979 1.07909
\(982\) −47.5583 −1.51765
\(983\) 42.6438 1.36013 0.680063 0.733153i \(-0.261952\pi\)
0.680063 + 0.733153i \(0.261952\pi\)
\(984\) 2.40882 0.0767903
\(985\) −12.4342 −0.396187
\(986\) −14.5971 −0.464866
\(987\) −1.07231 −0.0341321
\(988\) 0.229183 0.00729128
\(989\) 67.4394 2.14445
\(990\) 6.30812 0.200485
\(991\) 3.59121 0.114079 0.0570393 0.998372i \(-0.481834\pi\)
0.0570393 + 0.998372i \(0.481834\pi\)
\(992\) −9.17134 −0.291190
\(993\) −1.78902 −0.0567728
\(994\) 13.5661 0.430290
\(995\) 14.1842 0.449670
\(996\) −0.572697 −0.0181466
\(997\) 16.8430 0.533423 0.266711 0.963776i \(-0.414063\pi\)
0.266711 + 0.963776i \(0.414063\pi\)
\(998\) −4.63061 −0.146579
\(999\) −3.26837 −0.103407
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 \(a_p\))