Properties

Label 8018.2.a.f.1.6
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(34\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.52151 q^{3}\) \(+1.00000 q^{4}\) \(-1.30481 q^{5}\) \(+2.52151 q^{6}\) \(+0.799571 q^{7}\) \(-1.00000 q^{8}\) \(+3.35801 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.52151 q^{3}\) \(+1.00000 q^{4}\) \(-1.30481 q^{5}\) \(+2.52151 q^{6}\) \(+0.799571 q^{7}\) \(-1.00000 q^{8}\) \(+3.35801 q^{9}\) \(+1.30481 q^{10}\) \(-2.77863 q^{11}\) \(-2.52151 q^{12}\) \(+3.89576 q^{13}\) \(-0.799571 q^{14}\) \(+3.29008 q^{15}\) \(+1.00000 q^{16}\) \(+7.65293 q^{17}\) \(-3.35801 q^{18}\) \(-1.00000 q^{19}\) \(-1.30481 q^{20}\) \(-2.01613 q^{21}\) \(+2.77863 q^{22}\) \(-0.364205 q^{23}\) \(+2.52151 q^{24}\) \(-3.29748 q^{25}\) \(-3.89576 q^{26}\) \(-0.902726 q^{27}\) \(+0.799571 q^{28}\) \(+1.06453 q^{29}\) \(-3.29008 q^{30}\) \(-6.08375 q^{31}\) \(-1.00000 q^{32}\) \(+7.00634 q^{33}\) \(-7.65293 q^{34}\) \(-1.04329 q^{35}\) \(+3.35801 q^{36}\) \(-0.605400 q^{37}\) \(+1.00000 q^{38}\) \(-9.82319 q^{39}\) \(+1.30481 q^{40}\) \(-6.71543 q^{41}\) \(+2.01613 q^{42}\) \(-8.72098 q^{43}\) \(-2.77863 q^{44}\) \(-4.38156 q^{45}\) \(+0.364205 q^{46}\) \(+4.28942 q^{47}\) \(-2.52151 q^{48}\) \(-6.36069 q^{49}\) \(+3.29748 q^{50}\) \(-19.2969 q^{51}\) \(+3.89576 q^{52}\) \(+4.28026 q^{53}\) \(+0.902726 q^{54}\) \(+3.62558 q^{55}\) \(-0.799571 q^{56}\) \(+2.52151 q^{57}\) \(-1.06453 q^{58}\) \(+3.47311 q^{59}\) \(+3.29008 q^{60}\) \(+0.0120131 q^{61}\) \(+6.08375 q^{62}\) \(+2.68497 q^{63}\) \(+1.00000 q^{64}\) \(-5.08322 q^{65}\) \(-7.00634 q^{66}\) \(+7.73505 q^{67}\) \(+7.65293 q^{68}\) \(+0.918346 q^{69}\) \(+1.04329 q^{70}\) \(+1.35383 q^{71}\) \(-3.35801 q^{72}\) \(+14.5653 q^{73}\) \(+0.605400 q^{74}\) \(+8.31462 q^{75}\) \(-1.00000 q^{76}\) \(-2.22171 q^{77}\) \(+9.82319 q^{78}\) \(-5.61430 q^{79}\) \(-1.30481 q^{80}\) \(-7.79780 q^{81}\) \(+6.71543 q^{82}\) \(-11.4959 q^{83}\) \(-2.01613 q^{84}\) \(-9.98560 q^{85}\) \(+8.72098 q^{86}\) \(-2.68422 q^{87}\) \(+2.77863 q^{88}\) \(-14.4300 q^{89}\) \(+4.38156 q^{90}\) \(+3.11493 q^{91}\) \(-0.364205 q^{92}\) \(+15.3402 q^{93}\) \(-4.28942 q^{94}\) \(+1.30481 q^{95}\) \(+2.52151 q^{96}\) \(-5.00978 q^{97}\) \(+6.36069 q^{98}\) \(-9.33067 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut -\mathstrut 7q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 38q^{18} \) \(\mathstrut -\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 31q^{27} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 17q^{30} \) \(\mathstrut -\mathstrut 28q^{31} \) \(\mathstrut -\mathstrut 34q^{32} \) \(\mathstrut -\mathstrut 16q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 36q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 7q^{40} \) \(\mathstrut +\mathstrut 9q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 22q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 29q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 22q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 21q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 9q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 23q^{61} \) \(\mathstrut +\mathstrut 28q^{62} \) \(\mathstrut -\mathstrut 27q^{63} \) \(\mathstrut +\mathstrut 34q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 51q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 17q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut -\mathstrut 38q^{72} \) \(\mathstrut -\mathstrut 26q^{73} \) \(\mathstrut +\mathstrut 36q^{74} \) \(\mathstrut -\mathstrut 109q^{75} \) \(\mathstrut -\mathstrut 34q^{76} \) \(\mathstrut -\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 9q^{78} \) \(\mathstrut -\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 7q^{80} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 9q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 22q^{90} \) \(\mathstrut -\mathstrut 41q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 56q^{97} \) \(\mathstrut -\mathstrut 22q^{98} \) \(\mathstrut -\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.52151 −1.45579 −0.727897 0.685686i \(-0.759502\pi\)
−0.727897 + 0.685686i \(0.759502\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.30481 −0.583528 −0.291764 0.956490i \(-0.594242\pi\)
−0.291764 + 0.956490i \(0.594242\pi\)
\(6\) 2.52151 1.02940
\(7\) 0.799571 0.302209 0.151105 0.988518i \(-0.451717\pi\)
0.151105 + 0.988518i \(0.451717\pi\)
\(8\) −1.00000 −0.353553
\(9\) 3.35801 1.11934
\(10\) 1.30481 0.412616
\(11\) −2.77863 −0.837788 −0.418894 0.908035i \(-0.637582\pi\)
−0.418894 + 0.908035i \(0.637582\pi\)
\(12\) −2.52151 −0.727897
\(13\) 3.89576 1.08049 0.540245 0.841508i \(-0.318332\pi\)
0.540245 + 0.841508i \(0.318332\pi\)
\(14\) −0.799571 −0.213694
\(15\) 3.29008 0.849496
\(16\) 1.00000 0.250000
\(17\) 7.65293 1.85611 0.928054 0.372446i \(-0.121481\pi\)
0.928054 + 0.372446i \(0.121481\pi\)
\(18\) −3.35801 −0.791491
\(19\) −1.00000 −0.229416
\(20\) −1.30481 −0.291764
\(21\) −2.01613 −0.439955
\(22\) 2.77863 0.592406
\(23\) −0.364205 −0.0759420 −0.0379710 0.999279i \(-0.512089\pi\)
−0.0379710 + 0.999279i \(0.512089\pi\)
\(24\) 2.52151 0.514701
\(25\) −3.29748 −0.659495
\(26\) −3.89576 −0.764021
\(27\) −0.902726 −0.173730
\(28\) 0.799571 0.151105
\(29\) 1.06453 0.197678 0.0988391 0.995103i \(-0.468487\pi\)
0.0988391 + 0.995103i \(0.468487\pi\)
\(30\) −3.29008 −0.600685
\(31\) −6.08375 −1.09267 −0.546337 0.837565i \(-0.683978\pi\)
−0.546337 + 0.837565i \(0.683978\pi\)
\(32\) −1.00000 −0.176777
\(33\) 7.00634 1.21965
\(34\) −7.65293 −1.31247
\(35\) −1.04329 −0.176348
\(36\) 3.35801 0.559668
\(37\) −0.605400 −0.0995272 −0.0497636 0.998761i \(-0.515847\pi\)
−0.0497636 + 0.998761i \(0.515847\pi\)
\(38\) 1.00000 0.162221
\(39\) −9.82319 −1.57297
\(40\) 1.30481 0.206308
\(41\) −6.71543 −1.04877 −0.524387 0.851480i \(-0.675706\pi\)
−0.524387 + 0.851480i \(0.675706\pi\)
\(42\) 2.01613 0.311095
\(43\) −8.72098 −1.32994 −0.664968 0.746872i \(-0.731555\pi\)
−0.664968 + 0.746872i \(0.731555\pi\)
\(44\) −2.77863 −0.418894
\(45\) −4.38156 −0.653164
\(46\) 0.364205 0.0536991
\(47\) 4.28942 0.625677 0.312838 0.949806i \(-0.398720\pi\)
0.312838 + 0.949806i \(0.398720\pi\)
\(48\) −2.52151 −0.363949
\(49\) −6.36069 −0.908670
\(50\) 3.29748 0.466334
\(51\) −19.2969 −2.70211
\(52\) 3.89576 0.540245
\(53\) 4.28026 0.587938 0.293969 0.955815i \(-0.405024\pi\)
0.293969 + 0.955815i \(0.405024\pi\)
\(54\) 0.902726 0.122845
\(55\) 3.62558 0.488873
\(56\) −0.799571 −0.106847
\(57\) 2.52151 0.333982
\(58\) −1.06453 −0.139780
\(59\) 3.47311 0.452160 0.226080 0.974109i \(-0.427409\pi\)
0.226080 + 0.974109i \(0.427409\pi\)
\(60\) 3.29008 0.424748
\(61\) 0.0120131 0.00153812 0.000769059 1.00000i \(-0.499755\pi\)
0.000769059 1.00000i \(0.499755\pi\)
\(62\) 6.08375 0.772637
\(63\) 2.68497 0.338274
\(64\) 1.00000 0.125000
\(65\) −5.08322 −0.630495
\(66\) −7.00634 −0.862421
\(67\) 7.73505 0.944987 0.472494 0.881334i \(-0.343354\pi\)
0.472494 + 0.881334i \(0.343354\pi\)
\(68\) 7.65293 0.928054
\(69\) 0.918346 0.110556
\(70\) 1.04329 0.124697
\(71\) 1.35383 0.160671 0.0803353 0.996768i \(-0.474401\pi\)
0.0803353 + 0.996768i \(0.474401\pi\)
\(72\) −3.35801 −0.395745
\(73\) 14.5653 1.70474 0.852368 0.522943i \(-0.175166\pi\)
0.852368 + 0.522943i \(0.175166\pi\)
\(74\) 0.605400 0.0703763
\(75\) 8.31462 0.960090
\(76\) −1.00000 −0.114708
\(77\) −2.22171 −0.253187
\(78\) 9.82319 1.11226
\(79\) −5.61430 −0.631659 −0.315829 0.948816i \(-0.602283\pi\)
−0.315829 + 0.948816i \(0.602283\pi\)
\(80\) −1.30481 −0.145882
\(81\) −7.79780 −0.866422
\(82\) 6.71543 0.741595
\(83\) −11.4959 −1.26184 −0.630919 0.775848i \(-0.717322\pi\)
−0.630919 + 0.775848i \(0.717322\pi\)
\(84\) −2.01613 −0.219977
\(85\) −9.98560 −1.08309
\(86\) 8.72098 0.940407
\(87\) −2.68422 −0.287779
\(88\) 2.77863 0.296203
\(89\) −14.4300 −1.52958 −0.764791 0.644279i \(-0.777158\pi\)
−0.764791 + 0.644279i \(0.777158\pi\)
\(90\) 4.38156 0.461857
\(91\) 3.11493 0.326534
\(92\) −0.364205 −0.0379710
\(93\) 15.3402 1.59071
\(94\) −4.28942 −0.442420
\(95\) 1.30481 0.133870
\(96\) 2.52151 0.257350
\(97\) −5.00978 −0.508666 −0.254333 0.967117i \(-0.581856\pi\)
−0.254333 + 0.967117i \(0.581856\pi\)
\(98\) 6.36069 0.642526
\(99\) −9.33067 −0.937767
\(100\) −3.29748 −0.329748
\(101\) 9.81176 0.976306 0.488153 0.872758i \(-0.337671\pi\)
0.488153 + 0.872758i \(0.337671\pi\)
\(102\) 19.2969 1.91068
\(103\) −7.28866 −0.718173 −0.359087 0.933304i \(-0.616912\pi\)
−0.359087 + 0.933304i \(0.616912\pi\)
\(104\) −3.89576 −0.382011
\(105\) 2.63066 0.256726
\(106\) −4.28026 −0.415735
\(107\) 2.44780 0.236637 0.118319 0.992976i \(-0.462250\pi\)
0.118319 + 0.992976i \(0.462250\pi\)
\(108\) −0.902726 −0.0868649
\(109\) 19.9143 1.90745 0.953724 0.300682i \(-0.0972144\pi\)
0.953724 + 0.300682i \(0.0972144\pi\)
\(110\) −3.62558 −0.345685
\(111\) 1.52652 0.144891
\(112\) 0.799571 0.0755523
\(113\) 7.64216 0.718913 0.359457 0.933162i \(-0.382962\pi\)
0.359457 + 0.933162i \(0.382962\pi\)
\(114\) −2.52151 −0.236161
\(115\) 0.475217 0.0443142
\(116\) 1.06453 0.0988391
\(117\) 13.0820 1.20943
\(118\) −3.47311 −0.319726
\(119\) 6.11906 0.560933
\(120\) −3.29008 −0.300342
\(121\) −3.27922 −0.298111
\(122\) −0.0120131 −0.00108761
\(123\) 16.9330 1.52680
\(124\) −6.08375 −0.546337
\(125\) 10.8266 0.968362
\(126\) −2.68497 −0.239196
\(127\) 5.82058 0.516493 0.258247 0.966079i \(-0.416855\pi\)
0.258247 + 0.966079i \(0.416855\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 21.9900 1.93611
\(130\) 5.08322 0.445827
\(131\) 12.9111 1.12805 0.564025 0.825757i \(-0.309252\pi\)
0.564025 + 0.825757i \(0.309252\pi\)
\(132\) 7.00634 0.609824
\(133\) −0.799571 −0.0693316
\(134\) −7.73505 −0.668207
\(135\) 1.17788 0.101376
\(136\) −7.65293 −0.656233
\(137\) 7.54807 0.644875 0.322438 0.946591i \(-0.395498\pi\)
0.322438 + 0.946591i \(0.395498\pi\)
\(138\) −0.918346 −0.0781748
\(139\) −7.83970 −0.664955 −0.332477 0.943111i \(-0.607885\pi\)
−0.332477 + 0.943111i \(0.607885\pi\)
\(140\) −1.04329 −0.0881738
\(141\) −10.8158 −0.910856
\(142\) −1.35383 −0.113611
\(143\) −10.8249 −0.905221
\(144\) 3.35801 0.279834
\(145\) −1.38901 −0.115351
\(146\) −14.5653 −1.20543
\(147\) 16.0385 1.32284
\(148\) −0.605400 −0.0497636
\(149\) 19.3930 1.58874 0.794368 0.607437i \(-0.207802\pi\)
0.794368 + 0.607437i \(0.207802\pi\)
\(150\) −8.31462 −0.678886
\(151\) 3.42356 0.278605 0.139303 0.990250i \(-0.455514\pi\)
0.139303 + 0.990250i \(0.455514\pi\)
\(152\) 1.00000 0.0811107
\(153\) 25.6986 2.07761
\(154\) 2.22171 0.179031
\(155\) 7.93813 0.637606
\(156\) −9.82319 −0.786485
\(157\) −11.5698 −0.923371 −0.461686 0.887044i \(-0.652755\pi\)
−0.461686 + 0.887044i \(0.652755\pi\)
\(158\) 5.61430 0.446650
\(159\) −10.7927 −0.855917
\(160\) 1.30481 0.103154
\(161\) −0.291208 −0.0229504
\(162\) 7.79780 0.612653
\(163\) −1.05270 −0.0824536 −0.0412268 0.999150i \(-0.513127\pi\)
−0.0412268 + 0.999150i \(0.513127\pi\)
\(164\) −6.71543 −0.524387
\(165\) −9.14193 −0.711698
\(166\) 11.4959 0.892255
\(167\) −20.7095 −1.60255 −0.801275 0.598297i \(-0.795844\pi\)
−0.801275 + 0.598297i \(0.795844\pi\)
\(168\) 2.01613 0.155547
\(169\) 2.17694 0.167457
\(170\) 9.98560 0.765861
\(171\) −3.35801 −0.256793
\(172\) −8.72098 −0.664968
\(173\) −11.1231 −0.845677 −0.422839 0.906205i \(-0.638966\pi\)
−0.422839 + 0.906205i \(0.638966\pi\)
\(174\) 2.68422 0.203490
\(175\) −2.63657 −0.199306
\(176\) −2.77863 −0.209447
\(177\) −8.75748 −0.658252
\(178\) 14.4300 1.08158
\(179\) −18.2322 −1.36274 −0.681371 0.731939i \(-0.738616\pi\)
−0.681371 + 0.731939i \(0.738616\pi\)
\(180\) −4.38156 −0.326582
\(181\) 2.80685 0.208631 0.104316 0.994544i \(-0.466735\pi\)
0.104316 + 0.994544i \(0.466735\pi\)
\(182\) −3.11493 −0.230894
\(183\) −0.0302911 −0.00223918
\(184\) 0.364205 0.0268495
\(185\) 0.789931 0.0580768
\(186\) −15.3402 −1.12480
\(187\) −21.2647 −1.55503
\(188\) 4.28942 0.312838
\(189\) −0.721793 −0.0525027
\(190\) −1.30481 −0.0946607
\(191\) −7.64346 −0.553061 −0.276531 0.961005i \(-0.589185\pi\)
−0.276531 + 0.961005i \(0.589185\pi\)
\(192\) −2.52151 −0.181974
\(193\) 16.5009 1.18776 0.593879 0.804554i \(-0.297596\pi\)
0.593879 + 0.804554i \(0.297596\pi\)
\(194\) 5.00978 0.359681
\(195\) 12.8174 0.917871
\(196\) −6.36069 −0.454335
\(197\) 3.98120 0.283648 0.141824 0.989892i \(-0.454703\pi\)
0.141824 + 0.989892i \(0.454703\pi\)
\(198\) 9.33067 0.663102
\(199\) 5.48861 0.389077 0.194538 0.980895i \(-0.437679\pi\)
0.194538 + 0.980895i \(0.437679\pi\)
\(200\) 3.29748 0.233167
\(201\) −19.5040 −1.37571
\(202\) −9.81176 −0.690353
\(203\) 0.851167 0.0597402
\(204\) −19.2969 −1.35106
\(205\) 8.76235 0.611989
\(206\) 7.28866 0.507825
\(207\) −1.22300 −0.0850046
\(208\) 3.89576 0.270122
\(209\) 2.77863 0.192202
\(210\) −2.63066 −0.181532
\(211\) −1.00000 −0.0688428
\(212\) 4.28026 0.293969
\(213\) −3.41371 −0.233903
\(214\) −2.44780 −0.167328
\(215\) 11.3792 0.776055
\(216\) 0.902726 0.0614227
\(217\) −4.86439 −0.330216
\(218\) −19.9143 −1.34877
\(219\) −36.7265 −2.48174
\(220\) 3.62558 0.244436
\(221\) 29.8140 2.00550
\(222\) −1.52652 −0.102453
\(223\) −6.84314 −0.458251 −0.229125 0.973397i \(-0.573587\pi\)
−0.229125 + 0.973397i \(0.573587\pi\)
\(224\) −0.799571 −0.0534236
\(225\) −11.0730 −0.738198
\(226\) −7.64216 −0.508349
\(227\) 3.01964 0.200421 0.100210 0.994966i \(-0.468048\pi\)
0.100210 + 0.994966i \(0.468048\pi\)
\(228\) 2.52151 0.166991
\(229\) 17.5925 1.16255 0.581273 0.813709i \(-0.302555\pi\)
0.581273 + 0.813709i \(0.302555\pi\)
\(230\) −0.475217 −0.0313349
\(231\) 5.60207 0.368589
\(232\) −1.06453 −0.0698898
\(233\) 18.3348 1.20115 0.600576 0.799568i \(-0.294938\pi\)
0.600576 + 0.799568i \(0.294938\pi\)
\(234\) −13.0820 −0.855197
\(235\) −5.59687 −0.365100
\(236\) 3.47311 0.226080
\(237\) 14.1565 0.919565
\(238\) −6.11906 −0.396640
\(239\) 22.9250 1.48290 0.741449 0.671010i \(-0.234139\pi\)
0.741449 + 0.671010i \(0.234139\pi\)
\(240\) 3.29008 0.212374
\(241\) −28.4679 −1.83378 −0.916890 0.399141i \(-0.869308\pi\)
−0.916890 + 0.399141i \(0.869308\pi\)
\(242\) 3.27922 0.210796
\(243\) 22.3704 1.43506
\(244\) 0.0120131 0.000769059 0
\(245\) 8.29947 0.530234
\(246\) −16.9330 −1.07961
\(247\) −3.89576 −0.247881
\(248\) 6.08375 0.386319
\(249\) 28.9870 1.83698
\(250\) −10.8266 −0.684735
\(251\) 1.11181 0.0701770 0.0350885 0.999384i \(-0.488829\pi\)
0.0350885 + 0.999384i \(0.488829\pi\)
\(252\) 2.68497 0.169137
\(253\) 1.01199 0.0636233
\(254\) −5.82058 −0.365216
\(255\) 25.1788 1.57676
\(256\) 1.00000 0.0625000
\(257\) 2.54796 0.158937 0.0794686 0.996837i \(-0.474678\pi\)
0.0794686 + 0.996837i \(0.474678\pi\)
\(258\) −21.9900 −1.36904
\(259\) −0.484060 −0.0300780
\(260\) −5.08322 −0.315248
\(261\) 3.57470 0.221268
\(262\) −12.9111 −0.797652
\(263\) −8.20479 −0.505929 −0.252964 0.967476i \(-0.581406\pi\)
−0.252964 + 0.967476i \(0.581406\pi\)
\(264\) −7.00634 −0.431211
\(265\) −5.58491 −0.343078
\(266\) 0.799571 0.0490248
\(267\) 36.3855 2.22676
\(268\) 7.73505 0.472494
\(269\) −4.08601 −0.249129 −0.124564 0.992212i \(-0.539753\pi\)
−0.124564 + 0.992212i \(0.539753\pi\)
\(270\) −1.17788 −0.0716837
\(271\) 10.9546 0.665442 0.332721 0.943025i \(-0.392033\pi\)
0.332721 + 0.943025i \(0.392033\pi\)
\(272\) 7.65293 0.464027
\(273\) −7.85434 −0.475366
\(274\) −7.54807 −0.455996
\(275\) 9.16247 0.552518
\(276\) 0.918346 0.0552779
\(277\) −12.7817 −0.767979 −0.383990 0.923337i \(-0.625450\pi\)
−0.383990 + 0.923337i \(0.625450\pi\)
\(278\) 7.83970 0.470194
\(279\) −20.4293 −1.22307
\(280\) 1.04329 0.0623483
\(281\) −11.1853 −0.667261 −0.333631 0.942704i \(-0.608274\pi\)
−0.333631 + 0.942704i \(0.608274\pi\)
\(282\) 10.8158 0.644073
\(283\) −23.3188 −1.38616 −0.693080 0.720861i \(-0.743747\pi\)
−0.693080 + 0.720861i \(0.743747\pi\)
\(284\) 1.35383 0.0803353
\(285\) −3.29008 −0.194888
\(286\) 10.8249 0.640088
\(287\) −5.36946 −0.316949
\(288\) −3.35801 −0.197873
\(289\) 41.5673 2.44514
\(290\) 1.38901 0.0815653
\(291\) 12.6322 0.740513
\(292\) 14.5653 0.852368
\(293\) 31.1003 1.81690 0.908448 0.417997i \(-0.137268\pi\)
0.908448 + 0.417997i \(0.137268\pi\)
\(294\) −16.0385 −0.935386
\(295\) −4.53174 −0.263848
\(296\) 0.605400 0.0351882
\(297\) 2.50834 0.145549
\(298\) −19.3930 −1.12341
\(299\) −1.41885 −0.0820545
\(300\) 8.31462 0.480045
\(301\) −6.97304 −0.401919
\(302\) −3.42356 −0.197004
\(303\) −24.7404 −1.42130
\(304\) −1.00000 −0.0573539
\(305\) −0.0156748 −0.000897534 0
\(306\) −25.6986 −1.46909
\(307\) −0.0218889 −0.00124927 −0.000624634 1.00000i \(-0.500199\pi\)
−0.000624634 1.00000i \(0.500199\pi\)
\(308\) −2.22171 −0.126594
\(309\) 18.3784 1.04551
\(310\) −7.93813 −0.450855
\(311\) 13.2602 0.751915 0.375958 0.926637i \(-0.377314\pi\)
0.375958 + 0.926637i \(0.377314\pi\)
\(312\) 9.82319 0.556129
\(313\) 10.0382 0.567395 0.283697 0.958914i \(-0.408439\pi\)
0.283697 + 0.958914i \(0.408439\pi\)
\(314\) 11.5698 0.652922
\(315\) −3.50336 −0.197392
\(316\) −5.61430 −0.315829
\(317\) −4.97697 −0.279534 −0.139767 0.990184i \(-0.544635\pi\)
−0.139767 + 0.990184i \(0.544635\pi\)
\(318\) 10.7927 0.605225
\(319\) −2.95793 −0.165613
\(320\) −1.30481 −0.0729410
\(321\) −6.17214 −0.344495
\(322\) 0.291208 0.0162284
\(323\) −7.65293 −0.425820
\(324\) −7.79780 −0.433211
\(325\) −12.8462 −0.712578
\(326\) 1.05270 0.0583035
\(327\) −50.2142 −2.77685
\(328\) 6.71543 0.370798
\(329\) 3.42970 0.189085
\(330\) 9.14193 0.503247
\(331\) −7.36237 −0.404672 −0.202336 0.979316i \(-0.564853\pi\)
−0.202336 + 0.979316i \(0.564853\pi\)
\(332\) −11.4959 −0.630919
\(333\) −2.03294 −0.111404
\(334\) 20.7095 1.13317
\(335\) −10.0928 −0.551426
\(336\) −2.01613 −0.109989
\(337\) −32.7350 −1.78319 −0.891594 0.452836i \(-0.850412\pi\)
−0.891594 + 0.452836i \(0.850412\pi\)
\(338\) −2.17694 −0.118410
\(339\) −19.2698 −1.04659
\(340\) −9.98560 −0.541545
\(341\) 16.9045 0.915430
\(342\) 3.35801 0.181580
\(343\) −10.6828 −0.576818
\(344\) 8.72098 0.470204
\(345\) −1.19826 −0.0645124
\(346\) 11.1231 0.597984
\(347\) −5.23535 −0.281048 −0.140524 0.990077i \(-0.544879\pi\)
−0.140524 + 0.990077i \(0.544879\pi\)
\(348\) −2.68422 −0.143889
\(349\) 4.59594 0.246015 0.123008 0.992406i \(-0.460746\pi\)
0.123008 + 0.992406i \(0.460746\pi\)
\(350\) 2.63657 0.140930
\(351\) −3.51680 −0.187713
\(352\) 2.77863 0.148101
\(353\) −12.7713 −0.679749 −0.339874 0.940471i \(-0.610385\pi\)
−0.339874 + 0.940471i \(0.610385\pi\)
\(354\) 8.75748 0.465455
\(355\) −1.76649 −0.0937557
\(356\) −14.4300 −0.764791
\(357\) −15.4293 −0.816603
\(358\) 18.2322 0.963604
\(359\) 26.1923 1.38238 0.691189 0.722674i \(-0.257087\pi\)
0.691189 + 0.722674i \(0.257087\pi\)
\(360\) 4.38156 0.230928
\(361\) 1.00000 0.0526316
\(362\) −2.80685 −0.147525
\(363\) 8.26857 0.433988
\(364\) 3.11493 0.163267
\(365\) −19.0049 −0.994761
\(366\) 0.0302911 0.00158334
\(367\) −2.59280 −0.135343 −0.0676715 0.997708i \(-0.521557\pi\)
−0.0676715 + 0.997708i \(0.521557\pi\)
\(368\) −0.364205 −0.0189855
\(369\) −22.5505 −1.17393
\(370\) −0.789931 −0.0410665
\(371\) 3.42237 0.177680
\(372\) 15.3402 0.795354
\(373\) −14.7986 −0.766242 −0.383121 0.923698i \(-0.625151\pi\)
−0.383121 + 0.923698i \(0.625151\pi\)
\(374\) 21.2647 1.09957
\(375\) −27.2994 −1.40974
\(376\) −4.28942 −0.221210
\(377\) 4.14715 0.213589
\(378\) 0.721793 0.0371250
\(379\) −1.85860 −0.0954697 −0.0477348 0.998860i \(-0.515200\pi\)
−0.0477348 + 0.998860i \(0.515200\pi\)
\(380\) 1.30481 0.0669352
\(381\) −14.6767 −0.751908
\(382\) 7.64346 0.391073
\(383\) 4.34636 0.222089 0.111044 0.993815i \(-0.464580\pi\)
0.111044 + 0.993815i \(0.464580\pi\)
\(384\) 2.52151 0.128675
\(385\) 2.89891 0.147742
\(386\) −16.5009 −0.839872
\(387\) −29.2851 −1.48865
\(388\) −5.00978 −0.254333
\(389\) 17.5666 0.890664 0.445332 0.895366i \(-0.353086\pi\)
0.445332 + 0.895366i \(0.353086\pi\)
\(390\) −12.8174 −0.649033
\(391\) −2.78723 −0.140957
\(392\) 6.36069 0.321263
\(393\) −32.5555 −1.64221
\(394\) −3.98120 −0.200570
\(395\) 7.32559 0.368590
\(396\) −9.33067 −0.468884
\(397\) −19.4283 −0.975080 −0.487540 0.873101i \(-0.662106\pi\)
−0.487540 + 0.873101i \(0.662106\pi\)
\(398\) −5.48861 −0.275119
\(399\) 2.01613 0.100933
\(400\) −3.29748 −0.164874
\(401\) 0.725569 0.0362332 0.0181166 0.999836i \(-0.494233\pi\)
0.0181166 + 0.999836i \(0.494233\pi\)
\(402\) 19.5040 0.972772
\(403\) −23.7008 −1.18062
\(404\) 9.81176 0.488153
\(405\) 10.1746 0.505581
\(406\) −0.851167 −0.0422427
\(407\) 1.68218 0.0833827
\(408\) 19.2969 0.955341
\(409\) −31.2019 −1.54283 −0.771417 0.636330i \(-0.780452\pi\)
−0.771417 + 0.636330i \(0.780452\pi\)
\(410\) −8.76235 −0.432741
\(411\) −19.0325 −0.938806
\(412\) −7.28866 −0.359087
\(413\) 2.77700 0.136647
\(414\) 1.22300 0.0601074
\(415\) 14.9999 0.736318
\(416\) −3.89576 −0.191005
\(417\) 19.7679 0.968037
\(418\) −2.77863 −0.135907
\(419\) 25.3211 1.23702 0.618508 0.785778i \(-0.287737\pi\)
0.618508 + 0.785778i \(0.287737\pi\)
\(420\) 2.63066 0.128363
\(421\) 0.00367721 0.000179216 0 8.96081e−5 1.00000i \(-0.499971\pi\)
8.96081e−5 1.00000i \(0.499971\pi\)
\(422\) 1.00000 0.0486792
\(423\) 14.4039 0.700343
\(424\) −4.28026 −0.207868
\(425\) −25.2354 −1.22409
\(426\) 3.41371 0.165395
\(427\) 0.00960531 0.000464834 0
\(428\) 2.44780 0.118319
\(429\) 27.2950 1.31782
\(430\) −11.3792 −0.548754
\(431\) 0.218352 0.0105177 0.00525883 0.999986i \(-0.498326\pi\)
0.00525883 + 0.999986i \(0.498326\pi\)
\(432\) −0.902726 −0.0434324
\(433\) −4.43807 −0.213280 −0.106640 0.994298i \(-0.534009\pi\)
−0.106640 + 0.994298i \(0.534009\pi\)
\(434\) 4.86439 0.233498
\(435\) 3.50239 0.167927
\(436\) 19.9143 0.953724
\(437\) 0.364205 0.0174223
\(438\) 36.7265 1.75486
\(439\) 21.9720 1.04867 0.524333 0.851513i \(-0.324315\pi\)
0.524333 + 0.851513i \(0.324315\pi\)
\(440\) −3.62558 −0.172843
\(441\) −21.3593 −1.01711
\(442\) −29.8140 −1.41811
\(443\) 12.8136 0.608794 0.304397 0.952545i \(-0.401545\pi\)
0.304397 + 0.952545i \(0.401545\pi\)
\(444\) 1.52652 0.0724455
\(445\) 18.8284 0.892553
\(446\) 6.84314 0.324032
\(447\) −48.8996 −2.31287
\(448\) 0.799571 0.0377762
\(449\) −18.5901 −0.877321 −0.438660 0.898653i \(-0.644547\pi\)
−0.438660 + 0.898653i \(0.644547\pi\)
\(450\) 11.0730 0.521984
\(451\) 18.6597 0.878651
\(452\) 7.64216 0.359457
\(453\) −8.63253 −0.405592
\(454\) −3.01964 −0.141719
\(455\) −4.06439 −0.190542
\(456\) −2.52151 −0.118081
\(457\) −1.73739 −0.0812718 −0.0406359 0.999174i \(-0.512938\pi\)
−0.0406359 + 0.999174i \(0.512938\pi\)
\(458\) −17.5925 −0.822044
\(459\) −6.90850 −0.322461
\(460\) 0.475217 0.0221571
\(461\) −7.11700 −0.331472 −0.165736 0.986170i \(-0.553000\pi\)
−0.165736 + 0.986170i \(0.553000\pi\)
\(462\) −5.60207 −0.260632
\(463\) −13.3969 −0.622605 −0.311302 0.950311i \(-0.600765\pi\)
−0.311302 + 0.950311i \(0.600765\pi\)
\(464\) 1.06453 0.0494196
\(465\) −20.0161 −0.928222
\(466\) −18.3348 −0.849342
\(467\) 39.7771 1.84067 0.920333 0.391136i \(-0.127918\pi\)
0.920333 + 0.391136i \(0.127918\pi\)
\(468\) 13.0820 0.604716
\(469\) 6.18472 0.285584
\(470\) 5.59687 0.258164
\(471\) 29.1734 1.34424
\(472\) −3.47311 −0.159863
\(473\) 24.2324 1.11421
\(474\) −14.1565 −0.650231
\(475\) 3.29748 0.151299
\(476\) 6.11906 0.280467
\(477\) 14.3731 0.658101
\(478\) −22.9250 −1.04857
\(479\) −38.3005 −1.74999 −0.874997 0.484128i \(-0.839137\pi\)
−0.874997 + 0.484128i \(0.839137\pi\)
\(480\) −3.29008 −0.150171
\(481\) −2.35849 −0.107538
\(482\) 28.4679 1.29668
\(483\) 0.734283 0.0334110
\(484\) −3.27922 −0.149055
\(485\) 6.53679 0.296821
\(486\) −22.3704 −1.01474
\(487\) −7.61033 −0.344857 −0.172429 0.985022i \(-0.555161\pi\)
−0.172429 + 0.985022i \(0.555161\pi\)
\(488\) −0.0120131 −0.000543807 0
\(489\) 2.65438 0.120035
\(490\) −8.29947 −0.374932
\(491\) −19.0040 −0.857637 −0.428819 0.903391i \(-0.641070\pi\)
−0.428819 + 0.903391i \(0.641070\pi\)
\(492\) 16.9330 0.763400
\(493\) 8.14677 0.366912
\(494\) 3.89576 0.175278
\(495\) 12.1747 0.547213
\(496\) −6.08375 −0.273169
\(497\) 1.08249 0.0485562
\(498\) −28.9870 −1.29894
\(499\) −21.3594 −0.956179 −0.478089 0.878311i \(-0.658671\pi\)
−0.478089 + 0.878311i \(0.658671\pi\)
\(500\) 10.8266 0.484181
\(501\) 52.2192 2.33298
\(502\) −1.11181 −0.0496226
\(503\) 2.46112 0.109736 0.0548680 0.998494i \(-0.482526\pi\)
0.0548680 + 0.998494i \(0.482526\pi\)
\(504\) −2.68497 −0.119598
\(505\) −12.8025 −0.569702
\(506\) −1.01199 −0.0449885
\(507\) −5.48917 −0.243782
\(508\) 5.82058 0.258247
\(509\) 12.1939 0.540486 0.270243 0.962792i \(-0.412896\pi\)
0.270243 + 0.962792i \(0.412896\pi\)
\(510\) −25.1788 −1.11494
\(511\) 11.6460 0.515187
\(512\) −1.00000 −0.0441942
\(513\) 0.902726 0.0398563
\(514\) −2.54796 −0.112386
\(515\) 9.51030 0.419074
\(516\) 21.9900 0.968057
\(517\) −11.9187 −0.524185
\(518\) 0.484060 0.0212684
\(519\) 28.0471 1.23113
\(520\) 5.08322 0.222914
\(521\) −42.8254 −1.87622 −0.938108 0.346343i \(-0.887423\pi\)
−0.938108 + 0.346343i \(0.887423\pi\)
\(522\) −3.57470 −0.156460
\(523\) −31.0624 −1.35826 −0.679131 0.734017i \(-0.737643\pi\)
−0.679131 + 0.734017i \(0.737643\pi\)
\(524\) 12.9111 0.564025
\(525\) 6.64813 0.290148
\(526\) 8.20479 0.357746
\(527\) −46.5585 −2.02812
\(528\) 7.00634 0.304912
\(529\) −22.8674 −0.994233
\(530\) 5.58491 0.242593
\(531\) 11.6627 0.506120
\(532\) −0.799571 −0.0346658
\(533\) −26.1617 −1.13319
\(534\) −36.3855 −1.57455
\(535\) −3.19390 −0.138084
\(536\) −7.73505 −0.334103
\(537\) 45.9728 1.98387
\(538\) 4.08601 0.176161
\(539\) 17.6740 0.761273
\(540\) 1.17788 0.0506880
\(541\) −17.4481 −0.750152 −0.375076 0.926994i \(-0.622383\pi\)
−0.375076 + 0.926994i \(0.622383\pi\)
\(542\) −10.9546 −0.470539
\(543\) −7.07750 −0.303724
\(544\) −7.65293 −0.328117
\(545\) −25.9844 −1.11305
\(546\) 7.85434 0.336135
\(547\) −4.97551 −0.212737 −0.106369 0.994327i \(-0.533922\pi\)
−0.106369 + 0.994327i \(0.533922\pi\)
\(548\) 7.54807 0.322438
\(549\) 0.0403401 0.00172167
\(550\) −9.16247 −0.390689
\(551\) −1.06453 −0.0453505
\(552\) −0.918346 −0.0390874
\(553\) −4.48903 −0.190893
\(554\) 12.7817 0.543043
\(555\) −1.99182 −0.0845479
\(556\) −7.83970 −0.332477
\(557\) −15.1663 −0.642618 −0.321309 0.946974i \(-0.604123\pi\)
−0.321309 + 0.946974i \(0.604123\pi\)
\(558\) 20.4293 0.864841
\(559\) −33.9748 −1.43698
\(560\) −1.04329 −0.0440869
\(561\) 53.6190 2.26380
\(562\) 11.1853 0.471825
\(563\) 16.6395 0.701273 0.350636 0.936512i \(-0.385965\pi\)
0.350636 + 0.936512i \(0.385965\pi\)
\(564\) −10.8158 −0.455428
\(565\) −9.97154 −0.419506
\(566\) 23.3188 0.980163
\(567\) −6.23489 −0.261841
\(568\) −1.35383 −0.0568056
\(569\) 38.3381 1.60722 0.803609 0.595158i \(-0.202911\pi\)
0.803609 + 0.595158i \(0.202911\pi\)
\(570\) 3.29008 0.137806
\(571\) 11.3271 0.474024 0.237012 0.971507i \(-0.423832\pi\)
0.237012 + 0.971507i \(0.423832\pi\)
\(572\) −10.8249 −0.452611
\(573\) 19.2730 0.805143
\(574\) 5.36946 0.224117
\(575\) 1.20096 0.0500834
\(576\) 3.35801 0.139917
\(577\) −31.4533 −1.30942 −0.654709 0.755881i \(-0.727209\pi\)
−0.654709 + 0.755881i \(0.727209\pi\)
\(578\) −41.5673 −1.72897
\(579\) −41.6071 −1.72913
\(580\) −1.38901 −0.0576754
\(581\) −9.19178 −0.381339
\(582\) −12.6322 −0.523621
\(583\) −11.8932 −0.492568
\(584\) −14.5653 −0.602715
\(585\) −17.0695 −0.705737
\(586\) −31.1003 −1.28474
\(587\) 24.4135 1.00765 0.503827 0.863804i \(-0.331925\pi\)
0.503827 + 0.863804i \(0.331925\pi\)
\(588\) 16.0385 0.661418
\(589\) 6.08375 0.250677
\(590\) 4.53174 0.186569
\(591\) −10.0386 −0.412934
\(592\) −0.605400 −0.0248818
\(593\) −8.45840 −0.347345 −0.173672 0.984803i \(-0.555563\pi\)
−0.173672 + 0.984803i \(0.555563\pi\)
\(594\) −2.50834 −0.102919
\(595\) −7.98419 −0.327320
\(596\) 19.3930 0.794368
\(597\) −13.8396 −0.566416
\(598\) 1.41885 0.0580213
\(599\) −30.2801 −1.23721 −0.618606 0.785701i \(-0.712302\pi\)
−0.618606 + 0.785701i \(0.712302\pi\)
\(600\) −8.31462 −0.339443
\(601\) −40.5590 −1.65444 −0.827219 0.561880i \(-0.810078\pi\)
−0.827219 + 0.561880i \(0.810078\pi\)
\(602\) 6.97304 0.284200
\(603\) 25.9744 1.05776
\(604\) 3.42356 0.139303
\(605\) 4.27875 0.173956
\(606\) 24.7404 1.00501
\(607\) −2.93615 −0.119175 −0.0595873 0.998223i \(-0.518978\pi\)
−0.0595873 + 0.998223i \(0.518978\pi\)
\(608\) 1.00000 0.0405554
\(609\) −2.14623 −0.0869694
\(610\) 0.0156748 0.000634652 0
\(611\) 16.7106 0.676037
\(612\) 25.6986 1.03880
\(613\) −47.2433 −1.90814 −0.954070 0.299585i \(-0.903152\pi\)
−0.954070 + 0.299585i \(0.903152\pi\)
\(614\) 0.0218889 0.000883366 0
\(615\) −22.0943 −0.890930
\(616\) 2.22171 0.0895153
\(617\) −27.4424 −1.10479 −0.552395 0.833582i \(-0.686286\pi\)
−0.552395 + 0.833582i \(0.686286\pi\)
\(618\) −18.3784 −0.739289
\(619\) −6.34495 −0.255025 −0.127513 0.991837i \(-0.540699\pi\)
−0.127513 + 0.991837i \(0.540699\pi\)
\(620\) 7.93813 0.318803
\(621\) 0.328777 0.0131934
\(622\) −13.2602 −0.531684
\(623\) −11.5378 −0.462254
\(624\) −9.82319 −0.393242
\(625\) 2.36074 0.0944297
\(626\) −10.0382 −0.401209
\(627\) −7.00634 −0.279806
\(628\) −11.5698 −0.461686
\(629\) −4.63308 −0.184733
\(630\) 3.50336 0.139577
\(631\) −19.8874 −0.791704 −0.395852 0.918314i \(-0.629551\pi\)
−0.395852 + 0.918314i \(0.629551\pi\)
\(632\) 5.61430 0.223325
\(633\) 2.52151 0.100221
\(634\) 4.97697 0.197661
\(635\) −7.59474 −0.301388
\(636\) −10.7927 −0.427959
\(637\) −24.7797 −0.981807
\(638\) 2.95793 0.117106
\(639\) 4.54619 0.179844
\(640\) 1.30481 0.0515770
\(641\) 7.16636 0.283054 0.141527 0.989934i \(-0.454799\pi\)
0.141527 + 0.989934i \(0.454799\pi\)
\(642\) 6.17214 0.243595
\(643\) −3.07420 −0.121235 −0.0606174 0.998161i \(-0.519307\pi\)
−0.0606174 + 0.998161i \(0.519307\pi\)
\(644\) −0.291208 −0.0114752
\(645\) −28.6928 −1.12978
\(646\) 7.65293 0.301100
\(647\) −1.15299 −0.0453288 −0.0226644 0.999743i \(-0.507215\pi\)
−0.0226644 + 0.999743i \(0.507215\pi\)
\(648\) 7.79780 0.306326
\(649\) −9.65048 −0.378815
\(650\) 12.8462 0.503868
\(651\) 12.2656 0.480727
\(652\) −1.05270 −0.0412268
\(653\) 31.1948 1.22075 0.610373 0.792114i \(-0.291019\pi\)
0.610373 + 0.792114i \(0.291019\pi\)
\(654\) 50.2142 1.96353
\(655\) −16.8465 −0.658249
\(656\) −6.71543 −0.262194
\(657\) 48.9103 1.90817
\(658\) −3.42970 −0.133704
\(659\) 5.82510 0.226914 0.113457 0.993543i \(-0.463808\pi\)
0.113457 + 0.993543i \(0.463808\pi\)
\(660\) −9.14193 −0.355849
\(661\) −22.7631 −0.885382 −0.442691 0.896674i \(-0.645976\pi\)
−0.442691 + 0.896674i \(0.645976\pi\)
\(662\) 7.36237 0.286146
\(663\) −75.1762 −2.91960
\(664\) 11.4959 0.446127
\(665\) 1.04329 0.0404569
\(666\) 2.03294 0.0787748
\(667\) −0.387707 −0.0150121
\(668\) −20.7095 −0.801275
\(669\) 17.2550 0.667119
\(670\) 10.0928 0.389917
\(671\) −0.0333799 −0.00128862
\(672\) 2.01613 0.0777737
\(673\) 8.63759 0.332954 0.166477 0.986045i \(-0.446761\pi\)
0.166477 + 0.986045i \(0.446761\pi\)
\(674\) 32.7350 1.26090
\(675\) 2.97672 0.114574
\(676\) 2.17694 0.0837283
\(677\) −6.76957 −0.260176 −0.130088 0.991502i \(-0.541526\pi\)
−0.130088 + 0.991502i \(0.541526\pi\)
\(678\) 19.2698 0.740051
\(679\) −4.00567 −0.153724
\(680\) 9.98560 0.382930
\(681\) −7.61405 −0.291771
\(682\) −16.9045 −0.647307
\(683\) −43.9246 −1.68073 −0.840365 0.542022i \(-0.817659\pi\)
−0.840365 + 0.542022i \(0.817659\pi\)
\(684\) −3.35801 −0.128397
\(685\) −9.84878 −0.376303
\(686\) 10.6828 0.407872
\(687\) −44.3597 −1.69243
\(688\) −8.72098 −0.332484
\(689\) 16.6748 0.635261
\(690\) 1.19826 0.0456172
\(691\) −5.49773 −0.209144 −0.104572 0.994517i \(-0.533347\pi\)
−0.104572 + 0.994517i \(0.533347\pi\)
\(692\) −11.1231 −0.422839
\(693\) −7.46053 −0.283402
\(694\) 5.23535 0.198731
\(695\) 10.2293 0.388020
\(696\) 2.68422 0.101745
\(697\) −51.3927 −1.94664
\(698\) −4.59594 −0.173959
\(699\) −46.2313 −1.74863
\(700\) −2.63657 −0.0996528
\(701\) 25.6821 0.969998 0.484999 0.874515i \(-0.338820\pi\)
0.484999 + 0.874515i \(0.338820\pi\)
\(702\) 3.51680 0.132733
\(703\) 0.605400 0.0228331
\(704\) −2.77863 −0.104724
\(705\) 14.1126 0.531510
\(706\) 12.7713 0.480655
\(707\) 7.84519 0.295049
\(708\) −8.75748 −0.329126
\(709\) 29.3132 1.10088 0.550441 0.834874i \(-0.314460\pi\)
0.550441 + 0.834874i \(0.314460\pi\)
\(710\) 1.76649 0.0662953
\(711\) −18.8529 −0.707039
\(712\) 14.4300 0.540789
\(713\) 2.21573 0.0829798
\(714\) 15.4293 0.577426
\(715\) 14.1244 0.528222
\(716\) −18.2322 −0.681371
\(717\) −57.8057 −2.15879
\(718\) −26.1923 −0.977489
\(719\) 7.09606 0.264639 0.132319 0.991207i \(-0.457758\pi\)
0.132319 + 0.991207i \(0.457758\pi\)
\(720\) −4.38156 −0.163291
\(721\) −5.82780 −0.217039
\(722\) −1.00000 −0.0372161
\(723\) 71.7821 2.66961
\(724\) 2.80685 0.104316
\(725\) −3.51026 −0.130368
\(726\) −8.26857 −0.306876
\(727\) −53.0524 −1.96760 −0.983802 0.179260i \(-0.942630\pi\)
−0.983802 + 0.179260i \(0.942630\pi\)
\(728\) −3.11493 −0.115447
\(729\) −33.0138 −1.22273
\(730\) 19.0049 0.703402
\(731\) −66.7410 −2.46851
\(732\) −0.0302911 −0.00111959
\(733\) 2.07510 0.0766455 0.0383228 0.999265i \(-0.487798\pi\)
0.0383228 + 0.999265i \(0.487798\pi\)
\(734\) 2.59280 0.0957019
\(735\) −20.9272 −0.771911
\(736\) 0.364205 0.0134248
\(737\) −21.4929 −0.791699
\(738\) 22.5505 0.830095
\(739\) 5.31092 0.195365 0.0976826 0.995218i \(-0.468857\pi\)
0.0976826 + 0.995218i \(0.468857\pi\)
\(740\) 0.789931 0.0290384
\(741\) 9.82319 0.360864
\(742\) −3.42237 −0.125639
\(743\) −38.3062 −1.40532 −0.702658 0.711527i \(-0.748004\pi\)
−0.702658 + 0.711527i \(0.748004\pi\)
\(744\) −15.3402 −0.562400
\(745\) −25.3041 −0.927072
\(746\) 14.7986 0.541815
\(747\) −38.6033 −1.41242
\(748\) −21.2647 −0.777513
\(749\) 1.95719 0.0715141
\(750\) 27.2994 0.996833
\(751\) −27.6236 −1.00800 −0.504000 0.863704i \(-0.668139\pi\)
−0.504000 + 0.863704i \(0.668139\pi\)
\(752\) 4.28942 0.156419
\(753\) −2.80344 −0.102163
\(754\) −4.14715 −0.151030
\(755\) −4.46708 −0.162574
\(756\) −0.721793 −0.0262514
\(757\) 21.0354 0.764545 0.382272 0.924050i \(-0.375142\pi\)
0.382272 + 0.924050i \(0.375142\pi\)
\(758\) 1.85860 0.0675073
\(759\) −2.55174 −0.0926224
\(760\) −1.30481 −0.0473303
\(761\) 2.24554 0.0814009 0.0407005 0.999171i \(-0.487041\pi\)
0.0407005 + 0.999171i \(0.487041\pi\)
\(762\) 14.6767 0.531679
\(763\) 15.9229 0.576449
\(764\) −7.64346 −0.276531
\(765\) −33.5317 −1.21234
\(766\) −4.34636 −0.157040
\(767\) 13.5304 0.488554
\(768\) −2.52151 −0.0909871
\(769\) 1.21029 0.0436443 0.0218222 0.999762i \(-0.493053\pi\)
0.0218222 + 0.999762i \(0.493053\pi\)
\(770\) −2.89891 −0.104469
\(771\) −6.42470 −0.231380
\(772\) 16.5009 0.593879
\(773\) −26.0181 −0.935805 −0.467902 0.883780i \(-0.654990\pi\)
−0.467902 + 0.883780i \(0.654990\pi\)
\(774\) 29.2851 1.05263
\(775\) 20.0610 0.720614
\(776\) 5.00978 0.179840
\(777\) 1.22056 0.0437874
\(778\) −17.5666 −0.629794
\(779\) 6.71543 0.240605
\(780\) 12.8174 0.458936
\(781\) −3.76180 −0.134608
\(782\) 2.78723 0.0996713
\(783\) −0.960979 −0.0343426
\(784\) −6.36069 −0.227167
\(785\) 15.0964 0.538813
\(786\) 32.5555 1.16122
\(787\) 46.2025 1.64694 0.823471 0.567358i \(-0.192034\pi\)
0.823471 + 0.567358i \(0.192034\pi\)
\(788\) 3.98120 0.141824
\(789\) 20.6885 0.736528
\(790\) −7.32559 −0.260633
\(791\) 6.11044 0.217262
\(792\) 9.33067 0.331551
\(793\) 0.0468001 0.00166192
\(794\) 19.4283 0.689486
\(795\) 14.0824 0.499451
\(796\) 5.48861 0.194538
\(797\) 23.9577 0.848626 0.424313 0.905515i \(-0.360516\pi\)
0.424313 + 0.905515i \(0.360516\pi\)
\(798\) −2.01613 −0.0713701
\(799\) 32.8267 1.16132
\(800\) 3.29748 0.116583
\(801\) −48.4562 −1.71212
\(802\) −0.725569 −0.0256207
\(803\) −40.4715 −1.42821
\(804\) −19.5040 −0.687853
\(805\) 0.379970 0.0133922
\(806\) 23.7008 0.834826
\(807\) 10.3029 0.362680
\(808\) −9.81176 −0.345176
\(809\) 8.90368 0.313037 0.156518 0.987675i \(-0.449973\pi\)
0.156518 + 0.987675i \(0.449973\pi\)
\(810\) −10.1746 −0.357500
\(811\) 23.9080 0.839524 0.419762 0.907634i \(-0.362113\pi\)
0.419762 + 0.907634i \(0.362113\pi\)
\(812\) 0.851167 0.0298701
\(813\) −27.6220 −0.968747
\(814\) −1.68218 −0.0589605
\(815\) 1.37357 0.0481139
\(816\) −19.2969 −0.675528
\(817\) 8.72098 0.305108
\(818\) 31.2019 1.09095
\(819\) 10.4600 0.365501
\(820\) 8.76235 0.305994
\(821\) −10.6105 −0.370308 −0.185154 0.982710i \(-0.559278\pi\)
−0.185154 + 0.982710i \(0.559278\pi\)
\(822\) 19.0325 0.663836
\(823\) −13.9862 −0.487528 −0.243764 0.969835i \(-0.578382\pi\)
−0.243764 + 0.969835i \(0.578382\pi\)
\(824\) 7.28866 0.253913
\(825\) −23.1033 −0.804352
\(826\) −2.77700 −0.0966241
\(827\) −18.1663 −0.631706 −0.315853 0.948808i \(-0.602291\pi\)
−0.315853 + 0.948808i \(0.602291\pi\)
\(828\) −1.22300 −0.0425023
\(829\) −13.3080 −0.462205 −0.231103 0.972929i \(-0.574233\pi\)
−0.231103 + 0.972929i \(0.574233\pi\)
\(830\) −14.9999 −0.520655
\(831\) 32.2292 1.11802
\(832\) 3.89576 0.135061
\(833\) −48.6779 −1.68659
\(834\) −19.7679 −0.684506
\(835\) 27.0219 0.935132
\(836\) 2.77863 0.0961009
\(837\) 5.49196 0.189830
\(838\) −25.3211 −0.874702
\(839\) 27.2650 0.941291 0.470646 0.882322i \(-0.344021\pi\)
0.470646 + 0.882322i \(0.344021\pi\)
\(840\) −2.63066 −0.0907662
\(841\) −27.8668 −0.960923
\(842\) −0.00367721 −0.000126725 0
\(843\) 28.2039 0.971395
\(844\) −1.00000 −0.0344214
\(845\) −2.84048 −0.0977156
\(846\) −14.4039 −0.495217
\(847\) −2.62197 −0.0900918
\(848\) 4.28026 0.146985
\(849\) 58.7986 2.01796
\(850\) 25.2354 0.865566
\(851\) 0.220490 0.00755829
\(852\) −3.41371 −0.116952
\(853\) 16.2075 0.554934 0.277467 0.960735i \(-0.410505\pi\)
0.277467 + 0.960735i \(0.410505\pi\)
\(854\) −0.00960531 −0.000328687 0
\(855\) 4.38156 0.149846
\(856\) −2.44780 −0.0836640
\(857\) −50.3412 −1.71962 −0.859811 0.510613i \(-0.829419\pi\)
−0.859811 + 0.510613i \(0.829419\pi\)
\(858\) −27.2950 −0.931837
\(859\) −19.5488 −0.666996 −0.333498 0.942751i \(-0.608229\pi\)
−0.333498 + 0.942751i \(0.608229\pi\)
\(860\) 11.3792 0.388027
\(861\) 13.5392 0.461413
\(862\) −0.218352 −0.00743711
\(863\) −15.3137 −0.521283 −0.260642 0.965436i \(-0.583934\pi\)
−0.260642 + 0.965436i \(0.583934\pi\)
\(864\) 0.902726 0.0307114
\(865\) 14.5136 0.493476
\(866\) 4.43807 0.150812
\(867\) −104.812 −3.55962
\(868\) −4.86439 −0.165108
\(869\) 15.6001 0.529196
\(870\) −3.50239 −0.118742
\(871\) 30.1339 1.02105
\(872\) −19.9143 −0.674385
\(873\) −16.8229 −0.569368
\(874\) −0.364205 −0.0123194
\(875\) 8.65664 0.292648
\(876\) −36.7265 −1.24087
\(877\) 48.7290 1.64546 0.822731 0.568431i \(-0.192450\pi\)
0.822731 + 0.568431i \(0.192450\pi\)
\(878\) −21.9720 −0.741519
\(879\) −78.4196 −2.64503
\(880\) 3.62558 0.122218
\(881\) −0.668036 −0.0225067 −0.0112533 0.999937i \(-0.503582\pi\)
−0.0112533 + 0.999937i \(0.503582\pi\)
\(882\) 21.3593 0.719203
\(883\) −10.2464 −0.344819 −0.172410 0.985025i \(-0.555155\pi\)
−0.172410 + 0.985025i \(0.555155\pi\)
\(884\) 29.8140 1.00275
\(885\) 11.4268 0.384108
\(886\) −12.8136 −0.430482
\(887\) −34.8610 −1.17052 −0.585259 0.810846i \(-0.699007\pi\)
−0.585259 + 0.810846i \(0.699007\pi\)
\(888\) −1.52652 −0.0512267
\(889\) 4.65397 0.156089
\(890\) −18.8284 −0.631130
\(891\) 21.6672 0.725878
\(892\) −6.84314 −0.229125
\(893\) −4.28942 −0.143540
\(894\) 48.8996 1.63545
\(895\) 23.7896 0.795197
\(896\) −0.799571 −0.0267118
\(897\) 3.57766 0.119454
\(898\) 18.5901 0.620359
\(899\) −6.47634 −0.215998
\(900\) −11.0730 −0.369099
\(901\) 32.7565 1.09128
\(902\) −18.6597 −0.621300
\(903\) 17.5826 0.585112
\(904\) −7.64216 −0.254174
\(905\) −3.66240 −0.121742
\(906\) 8.63253 0.286797
\(907\) −54.8683 −1.82187 −0.910937 0.412546i \(-0.864639\pi\)
−0.910937 + 0.412546i \(0.864639\pi\)
\(908\) 3.01964 0.100210
\(909\) 32.9480 1.09282
\(910\) 4.06439 0.134733
\(911\) −27.5250 −0.911943 −0.455971 0.889994i \(-0.650708\pi\)
−0.455971 + 0.889994i \(0.650708\pi\)
\(912\) 2.52151 0.0834955
\(913\) 31.9428 1.05715
\(914\) 1.73739 0.0574679
\(915\) 0.0395241 0.00130663
\(916\) 17.5925 0.581273
\(917\) 10.3234 0.340907
\(918\) 6.90850 0.228014
\(919\) 9.70911 0.320274 0.160137 0.987095i \(-0.448806\pi\)
0.160137 + 0.987095i \(0.448806\pi\)
\(920\) −0.475217 −0.0156675
\(921\) 0.0551932 0.00181868
\(922\) 7.11700 0.234386
\(923\) 5.27421 0.173603
\(924\) 5.60207 0.184294
\(925\) 1.99629 0.0656377
\(926\) 13.3969 0.440248
\(927\) −24.4754 −0.803878
\(928\) −1.06453 −0.0349449
\(929\) 19.0467 0.624901 0.312450 0.949934i \(-0.398850\pi\)
0.312450 + 0.949934i \(0.398850\pi\)
\(930\) 20.0161 0.656352
\(931\) 6.36069 0.208463
\(932\) 18.3348 0.600576
\(933\) −33.4356 −1.09463
\(934\) −39.7771 −1.30155
\(935\) 27.7463 0.907401
\(936\) −13.0820 −0.427598
\(937\) 33.5339 1.09550 0.547752 0.836641i \(-0.315484\pi\)
0.547752 + 0.836641i \(0.315484\pi\)
\(938\) −6.18472 −0.201938
\(939\) −25.3115 −0.826010
\(940\) −5.59687 −0.182550
\(941\) 10.4020 0.339095 0.169548 0.985522i \(-0.445769\pi\)
0.169548 + 0.985522i \(0.445769\pi\)
\(942\) −29.1734 −0.950520
\(943\) 2.44579 0.0796460
\(944\) 3.47311 0.113040
\(945\) 0.941801 0.0306368
\(946\) −24.2324 −0.787862
\(947\) −41.5978 −1.35175 −0.675873 0.737018i \(-0.736233\pi\)
−0.675873 + 0.737018i \(0.736233\pi\)
\(948\) 14.1565 0.459782
\(949\) 56.7428 1.84195
\(950\) −3.29748 −0.106984
\(951\) 12.5495 0.406944
\(952\) −6.11906 −0.198320
\(953\) −2.75552 −0.0892601 −0.0446300 0.999004i \(-0.514211\pi\)
−0.0446300 + 0.999004i \(0.514211\pi\)
\(954\) −14.3731 −0.465348
\(955\) 9.97324 0.322726
\(956\) 22.9250 0.741449
\(957\) 7.45846 0.241098
\(958\) 38.3005 1.23743
\(959\) 6.03522 0.194887
\(960\) 3.29008 0.106187
\(961\) 6.01204 0.193937
\(962\) 2.35849 0.0760409
\(963\) 8.21973 0.264877
\(964\) −28.4679 −0.916890
\(965\) −21.5304 −0.693090
\(966\) −0.734283 −0.0236252
\(967\) −27.2955 −0.877765 −0.438883 0.898544i \(-0.644626\pi\)
−0.438883 + 0.898544i \(0.644626\pi\)
\(968\) 3.27922 0.105398
\(969\) 19.2969 0.619907
\(970\) −6.53679 −0.209884
\(971\) −1.20939 −0.0388112 −0.0194056 0.999812i \(-0.506177\pi\)
−0.0194056 + 0.999812i \(0.506177\pi\)
\(972\) 22.3704 0.717531
\(973\) −6.26840 −0.200956
\(974\) 7.61033 0.243851
\(975\) 32.3918 1.03737
\(976\) 0.0120131 0.000384529 0
\(977\) 27.2591 0.872095 0.436047 0.899924i \(-0.356378\pi\)
0.436047 + 0.899924i \(0.356378\pi\)
\(978\) −2.65438 −0.0848779
\(979\) 40.0957 1.28147
\(980\) 8.29947 0.265117
\(981\) 66.8726 2.13508
\(982\) 19.0040 0.606441
\(983\) −44.2827 −1.41240 −0.706199 0.708013i \(-0.749592\pi\)
−0.706199 + 0.708013i \(0.749592\pi\)
\(984\) −16.9330 −0.539805
\(985\) −5.19469 −0.165517
\(986\) −8.14677 −0.259446
\(987\) −8.64801 −0.275269
\(988\) −3.89576 −0.123941
\(989\) 3.17622 0.100998
\(990\) −12.1747 −0.386938
\(991\) −23.6487 −0.751224 −0.375612 0.926777i \(-0.622568\pi\)
−0.375612 + 0.926777i \(0.622568\pi\)
\(992\) 6.08375 0.193159
\(993\) 18.5643 0.589119
\(994\) −1.08249 −0.0343344
\(995\) −7.16157 −0.227037
\(996\) 28.9870 0.918489
\(997\) −25.7276 −0.814802 −0.407401 0.913249i \(-0.633565\pi\)
−0.407401 + 0.913249i \(0.633565\pi\)
\(998\) 21.3594 0.676120
\(999\) 0.546510 0.0172908
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 \(a_p\))