Properties

Label 8042.2.a.c.1.8
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.58298 q^{3}\) \(+1.00000 q^{4}\) \(+0.255702 q^{5}\) \(+2.58298 q^{6}\) \(-2.29966 q^{7}\) \(-1.00000 q^{8}\) \(+3.67181 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.58298 q^{3}\) \(+1.00000 q^{4}\) \(+0.255702 q^{5}\) \(+2.58298 q^{6}\) \(-2.29966 q^{7}\) \(-1.00000 q^{8}\) \(+3.67181 q^{9}\) \(-0.255702 q^{10}\) \(+4.75397 q^{11}\) \(-2.58298 q^{12}\) \(+0.531542 q^{13}\) \(+2.29966 q^{14}\) \(-0.660474 q^{15}\) \(+1.00000 q^{16}\) \(-3.54643 q^{17}\) \(-3.67181 q^{18}\) \(-4.26077 q^{19}\) \(+0.255702 q^{20}\) \(+5.93998 q^{21}\) \(-4.75397 q^{22}\) \(+2.75131 q^{23}\) \(+2.58298 q^{24}\) \(-4.93462 q^{25}\) \(-0.531542 q^{26}\) \(-1.73528 q^{27}\) \(-2.29966 q^{28}\) \(-5.42753 q^{29}\) \(+0.660474 q^{30}\) \(-9.45140 q^{31}\) \(-1.00000 q^{32}\) \(-12.2794 q^{33}\) \(+3.54643 q^{34}\) \(-0.588027 q^{35}\) \(+3.67181 q^{36}\) \(+4.06786 q^{37}\) \(+4.26077 q^{38}\) \(-1.37297 q^{39}\) \(-0.255702 q^{40}\) \(+8.17919 q^{41}\) \(-5.93998 q^{42}\) \(+2.34699 q^{43}\) \(+4.75397 q^{44}\) \(+0.938889 q^{45}\) \(-2.75131 q^{46}\) \(+5.42015 q^{47}\) \(-2.58298 q^{48}\) \(-1.71157 q^{49}\) \(+4.93462 q^{50}\) \(+9.16037 q^{51}\) \(+0.531542 q^{52}\) \(+7.32698 q^{53}\) \(+1.73528 q^{54}\) \(+1.21560 q^{55}\) \(+2.29966 q^{56}\) \(+11.0055 q^{57}\) \(+5.42753 q^{58}\) \(-4.92228 q^{59}\) \(-0.660474 q^{60}\) \(-8.97884 q^{61}\) \(+9.45140 q^{62}\) \(-8.44391 q^{63}\) \(+1.00000 q^{64}\) \(+0.135916 q^{65}\) \(+12.2794 q^{66}\) \(-2.67472 q^{67}\) \(-3.54643 q^{68}\) \(-7.10659 q^{69}\) \(+0.588027 q^{70}\) \(+9.63127 q^{71}\) \(-3.67181 q^{72}\) \(+11.6776 q^{73}\) \(-4.06786 q^{74}\) \(+12.7460 q^{75}\) \(-4.26077 q^{76}\) \(-10.9325 q^{77}\) \(+1.37297 q^{78}\) \(+8.60030 q^{79}\) \(+0.255702 q^{80}\) \(-6.53324 q^{81}\) \(-8.17919 q^{82}\) \(+4.68449 q^{83}\) \(+5.93998 q^{84}\) \(-0.906828 q^{85}\) \(-2.34699 q^{86}\) \(+14.0192 q^{87}\) \(-4.75397 q^{88}\) \(-10.3194 q^{89}\) \(-0.938889 q^{90}\) \(-1.22236 q^{91}\) \(+2.75131 q^{92}\) \(+24.4128 q^{93}\) \(-5.42015 q^{94}\) \(-1.08949 q^{95}\) \(+2.58298 q^{96}\) \(-0.192932 q^{97}\) \(+1.71157 q^{98}\) \(+17.4557 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 45q^{13} \) \(\mathstrut -\mathstrut 35q^{14} \) \(\mathstrut +\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 86q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 72q^{18} \) \(\mathstrut +\mathstrut 47q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 112q^{25} \) \(\mathstrut -\mathstrut 45q^{26} \) \(\mathstrut +\mathstrut 51q^{27} \) \(\mathstrut +\mathstrut 35q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 86q^{32} \) \(\mathstrut +\mathstrut 43q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 42q^{35} \) \(\mathstrut +\mathstrut 72q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 15q^{42} \) \(\mathstrut +\mathstrut 72q^{43} \) \(\mathstrut +\mathstrut 13q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 89q^{49} \) \(\mathstrut -\mathstrut 112q^{50} \) \(\mathstrut +\mathstrut 56q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut -\mathstrut 7q^{53} \) \(\mathstrut -\mathstrut 51q^{54} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut -\mathstrut 35q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 31q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 98q^{63} \) \(\mathstrut +\mathstrut 86q^{64} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut -\mathstrut 43q^{66} \) \(\mathstrut +\mathstrut 157q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 42q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 74q^{73} \) \(\mathstrut -\mathstrut 61q^{74} \) \(\mathstrut +\mathstrut 76q^{75} \) \(\mathstrut +\mathstrut 47q^{76} \) \(\mathstrut -\mathstrut 13q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 57q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 34q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 65q^{83} \) \(\mathstrut +\mathstrut 15q^{84} \) \(\mathstrut +\mathstrut 102q^{85} \) \(\mathstrut -\mathstrut 72q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 91q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 57q^{93} \) \(\mathstrut -\mathstrut 11q^{94} \) \(\mathstrut -\mathstrut 13q^{95} \) \(\mathstrut -\mathstrut 12q^{96} \) \(\mathstrut +\mathstrut 64q^{97} \) \(\mathstrut -\mathstrut 89q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.58298 −1.49129 −0.745644 0.666345i \(-0.767858\pi\)
−0.745644 + 0.666345i \(0.767858\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.255702 0.114353 0.0571767 0.998364i \(-0.481790\pi\)
0.0571767 + 0.998364i \(0.481790\pi\)
\(6\) 2.58298 1.05450
\(7\) −2.29966 −0.869189 −0.434595 0.900626i \(-0.643108\pi\)
−0.434595 + 0.900626i \(0.643108\pi\)
\(8\) −1.00000 −0.353553
\(9\) 3.67181 1.22394
\(10\) −0.255702 −0.0808601
\(11\) 4.75397 1.43337 0.716687 0.697395i \(-0.245657\pi\)
0.716687 + 0.697395i \(0.245657\pi\)
\(12\) −2.58298 −0.745644
\(13\) 0.531542 0.147423 0.0737116 0.997280i \(-0.476516\pi\)
0.0737116 + 0.997280i \(0.476516\pi\)
\(14\) 2.29966 0.614609
\(15\) −0.660474 −0.170534
\(16\) 1.00000 0.250000
\(17\) −3.54643 −0.860135 −0.430067 0.902797i \(-0.641510\pi\)
−0.430067 + 0.902797i \(0.641510\pi\)
\(18\) −3.67181 −0.865454
\(19\) −4.26077 −0.977488 −0.488744 0.872427i \(-0.662545\pi\)
−0.488744 + 0.872427i \(0.662545\pi\)
\(20\) 0.255702 0.0571767
\(21\) 5.93998 1.29621
\(22\) −4.75397 −1.01355
\(23\) 2.75131 0.573688 0.286844 0.957977i \(-0.407394\pi\)
0.286844 + 0.957977i \(0.407394\pi\)
\(24\) 2.58298 0.527250
\(25\) −4.93462 −0.986923
\(26\) −0.531542 −0.104244
\(27\) −1.73528 −0.333954
\(28\) −2.29966 −0.434595
\(29\) −5.42753 −1.00787 −0.503934 0.863742i \(-0.668114\pi\)
−0.503934 + 0.863742i \(0.668114\pi\)
\(30\) 0.660474 0.120586
\(31\) −9.45140 −1.69752 −0.848761 0.528777i \(-0.822651\pi\)
−0.848761 + 0.528777i \(0.822651\pi\)
\(32\) −1.00000 −0.176777
\(33\) −12.2794 −2.13757
\(34\) 3.54643 0.608207
\(35\) −0.588027 −0.0993947
\(36\) 3.67181 0.611968
\(37\) 4.06786 0.668752 0.334376 0.942440i \(-0.391474\pi\)
0.334376 + 0.942440i \(0.391474\pi\)
\(38\) 4.26077 0.691188
\(39\) −1.37297 −0.219850
\(40\) −0.255702 −0.0404300
\(41\) 8.17919 1.27738 0.638688 0.769466i \(-0.279478\pi\)
0.638688 + 0.769466i \(0.279478\pi\)
\(42\) −5.93998 −0.916559
\(43\) 2.34699 0.357912 0.178956 0.983857i \(-0.442728\pi\)
0.178956 + 0.983857i \(0.442728\pi\)
\(44\) 4.75397 0.716687
\(45\) 0.938889 0.139961
\(46\) −2.75131 −0.405659
\(47\) 5.42015 0.790611 0.395305 0.918550i \(-0.370639\pi\)
0.395305 + 0.918550i \(0.370639\pi\)
\(48\) −2.58298 −0.372822
\(49\) −1.71157 −0.244510
\(50\) 4.93462 0.697860
\(51\) 9.16037 1.28271
\(52\) 0.531542 0.0737116
\(53\) 7.32698 1.00644 0.503219 0.864159i \(-0.332149\pi\)
0.503219 + 0.864159i \(0.332149\pi\)
\(54\) 1.73528 0.236141
\(55\) 1.21560 0.163911
\(56\) 2.29966 0.307305
\(57\) 11.0055 1.45772
\(58\) 5.42753 0.712670
\(59\) −4.92228 −0.640827 −0.320413 0.947278i \(-0.603822\pi\)
−0.320413 + 0.947278i \(0.603822\pi\)
\(60\) −0.660474 −0.0852669
\(61\) −8.97884 −1.14962 −0.574812 0.818286i \(-0.694925\pi\)
−0.574812 + 0.818286i \(0.694925\pi\)
\(62\) 9.45140 1.20033
\(63\) −8.44391 −1.06383
\(64\) 1.00000 0.125000
\(65\) 0.135916 0.0168583
\(66\) 12.2794 1.51149
\(67\) −2.67472 −0.326769 −0.163385 0.986562i \(-0.552241\pi\)
−0.163385 + 0.986562i \(0.552241\pi\)
\(68\) −3.54643 −0.430067
\(69\) −7.10659 −0.855533
\(70\) 0.588027 0.0702827
\(71\) 9.63127 1.14302 0.571511 0.820594i \(-0.306357\pi\)
0.571511 + 0.820594i \(0.306357\pi\)
\(72\) −3.67181 −0.432727
\(73\) 11.6776 1.36676 0.683380 0.730063i \(-0.260509\pi\)
0.683380 + 0.730063i \(0.260509\pi\)
\(74\) −4.06786 −0.472879
\(75\) 12.7460 1.47179
\(76\) −4.26077 −0.488744
\(77\) −10.9325 −1.24587
\(78\) 1.37297 0.155458
\(79\) 8.60030 0.967610 0.483805 0.875176i \(-0.339254\pi\)
0.483805 + 0.875176i \(0.339254\pi\)
\(80\) 0.255702 0.0285883
\(81\) −6.53324 −0.725915
\(82\) −8.17919 −0.903241
\(83\) 4.68449 0.514189 0.257095 0.966386i \(-0.417235\pi\)
0.257095 + 0.966386i \(0.417235\pi\)
\(84\) 5.93998 0.648105
\(85\) −0.906828 −0.0983593
\(86\) −2.34699 −0.253082
\(87\) 14.0192 1.50302
\(88\) −4.75397 −0.506774
\(89\) −10.3194 −1.09386 −0.546929 0.837179i \(-0.684203\pi\)
−0.546929 + 0.837179i \(0.684203\pi\)
\(90\) −0.938889 −0.0989676
\(91\) −1.22236 −0.128139
\(92\) 2.75131 0.286844
\(93\) 24.4128 2.53149
\(94\) −5.42015 −0.559046
\(95\) −1.08949 −0.111779
\(96\) 2.58298 0.263625
\(97\) −0.192932 −0.0195893 −0.00979464 0.999952i \(-0.503118\pi\)
−0.00979464 + 0.999952i \(0.503118\pi\)
\(98\) 1.71157 0.172895
\(99\) 17.4557 1.75436
\(100\) −4.93462 −0.493462
\(101\) −18.4028 −1.83115 −0.915574 0.402150i \(-0.868263\pi\)
−0.915574 + 0.402150i \(0.868263\pi\)
\(102\) −9.16037 −0.907012
\(103\) −14.8940 −1.46755 −0.733777 0.679391i \(-0.762244\pi\)
−0.733777 + 0.679391i \(0.762244\pi\)
\(104\) −0.531542 −0.0521220
\(105\) 1.51886 0.148226
\(106\) −7.32698 −0.711660
\(107\) 9.96286 0.963146 0.481573 0.876406i \(-0.340066\pi\)
0.481573 + 0.876406i \(0.340066\pi\)
\(108\) −1.73528 −0.166977
\(109\) −3.23819 −0.310162 −0.155081 0.987902i \(-0.549564\pi\)
−0.155081 + 0.987902i \(0.549564\pi\)
\(110\) −1.21560 −0.115903
\(111\) −10.5072 −0.997301
\(112\) −2.29966 −0.217297
\(113\) 12.6432 1.18937 0.594687 0.803958i \(-0.297276\pi\)
0.594687 + 0.803958i \(0.297276\pi\)
\(114\) −11.0055 −1.03076
\(115\) 0.703515 0.0656032
\(116\) −5.42753 −0.503934
\(117\) 1.95172 0.180437
\(118\) 4.92228 0.453133
\(119\) 8.15557 0.747620
\(120\) 0.660474 0.0602928
\(121\) 11.6002 1.05456
\(122\) 8.97884 0.812906
\(123\) −21.1267 −1.90493
\(124\) −9.45140 −0.848761
\(125\) −2.54030 −0.227211
\(126\) 8.44391 0.752243
\(127\) −6.10413 −0.541654 −0.270827 0.962628i \(-0.587297\pi\)
−0.270827 + 0.962628i \(0.587297\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −6.06223 −0.533750
\(130\) −0.135916 −0.0119207
\(131\) −9.12062 −0.796873 −0.398436 0.917196i \(-0.630447\pi\)
−0.398436 + 0.917196i \(0.630447\pi\)
\(132\) −12.2794 −1.06879
\(133\) 9.79832 0.849622
\(134\) 2.67472 0.231061
\(135\) −0.443714 −0.0381888
\(136\) 3.54643 0.304104
\(137\) −7.38745 −0.631153 −0.315576 0.948900i \(-0.602198\pi\)
−0.315576 + 0.948900i \(0.602198\pi\)
\(138\) 7.10659 0.604953
\(139\) 1.21366 0.102942 0.0514708 0.998675i \(-0.483609\pi\)
0.0514708 + 0.998675i \(0.483609\pi\)
\(140\) −0.588027 −0.0496974
\(141\) −14.0002 −1.17903
\(142\) −9.63127 −0.808239
\(143\) 2.52693 0.211313
\(144\) 3.67181 0.305984
\(145\) −1.38783 −0.115253
\(146\) −11.6776 −0.966446
\(147\) 4.42097 0.364635
\(148\) 4.06786 0.334376
\(149\) −4.77978 −0.391575 −0.195788 0.980646i \(-0.562726\pi\)
−0.195788 + 0.980646i \(0.562726\pi\)
\(150\) −12.7460 −1.04071
\(151\) −17.5057 −1.42459 −0.712296 0.701879i \(-0.752345\pi\)
−0.712296 + 0.701879i \(0.752345\pi\)
\(152\) 4.26077 0.345594
\(153\) −13.0218 −1.05275
\(154\) 10.9325 0.880966
\(155\) −2.41674 −0.194117
\(156\) −1.37297 −0.109925
\(157\) 6.56075 0.523605 0.261802 0.965122i \(-0.415683\pi\)
0.261802 + 0.965122i \(0.415683\pi\)
\(158\) −8.60030 −0.684203
\(159\) −18.9255 −1.50089
\(160\) −0.255702 −0.0202150
\(161\) −6.32707 −0.498643
\(162\) 6.53324 0.513300
\(163\) −11.2432 −0.880638 −0.440319 0.897841i \(-0.645135\pi\)
−0.440319 + 0.897841i \(0.645135\pi\)
\(164\) 8.17919 0.638688
\(165\) −3.13987 −0.244439
\(166\) −4.68449 −0.363587
\(167\) 4.60273 0.356170 0.178085 0.984015i \(-0.443010\pi\)
0.178085 + 0.984015i \(0.443010\pi\)
\(168\) −5.93998 −0.458280
\(169\) −12.7175 −0.978266
\(170\) 0.906828 0.0695506
\(171\) −15.6447 −1.19638
\(172\) 2.34699 0.178956
\(173\) −12.4098 −0.943503 −0.471751 0.881732i \(-0.656378\pi\)
−0.471751 + 0.881732i \(0.656378\pi\)
\(174\) −14.0192 −1.06280
\(175\) 11.3479 0.857823
\(176\) 4.75397 0.358344
\(177\) 12.7142 0.955656
\(178\) 10.3194 0.773474
\(179\) 3.64873 0.272719 0.136360 0.990659i \(-0.456460\pi\)
0.136360 + 0.990659i \(0.456460\pi\)
\(180\) 0.938889 0.0699807
\(181\) −10.9963 −0.817346 −0.408673 0.912681i \(-0.634008\pi\)
−0.408673 + 0.912681i \(0.634008\pi\)
\(182\) 1.22236 0.0906077
\(183\) 23.1922 1.71442
\(184\) −2.75131 −0.202829
\(185\) 1.04016 0.0764740
\(186\) −24.4128 −1.79004
\(187\) −16.8596 −1.23290
\(188\) 5.42015 0.395305
\(189\) 3.99054 0.290269
\(190\) 1.08949 0.0790397
\(191\) 18.1965 1.31666 0.658328 0.752732i \(-0.271264\pi\)
0.658328 + 0.752732i \(0.271264\pi\)
\(192\) −2.58298 −0.186411
\(193\) −2.80343 −0.201795 −0.100898 0.994897i \(-0.532171\pi\)
−0.100898 + 0.994897i \(0.532171\pi\)
\(194\) 0.192932 0.0138517
\(195\) −0.351070 −0.0251406
\(196\) −1.71157 −0.122255
\(197\) 4.29682 0.306135 0.153068 0.988216i \(-0.451085\pi\)
0.153068 + 0.988216i \(0.451085\pi\)
\(198\) −17.4557 −1.24052
\(199\) −7.31217 −0.518346 −0.259173 0.965831i \(-0.583450\pi\)
−0.259173 + 0.965831i \(0.583450\pi\)
\(200\) 4.93462 0.348930
\(201\) 6.90877 0.487307
\(202\) 18.4028 1.29482
\(203\) 12.4815 0.876027
\(204\) 9.16037 0.641354
\(205\) 2.09144 0.146072
\(206\) 14.8940 1.03772
\(207\) 10.1023 0.702158
\(208\) 0.531542 0.0368558
\(209\) −20.2556 −1.40111
\(210\) −1.51886 −0.104812
\(211\) 15.3743 1.05841 0.529204 0.848494i \(-0.322490\pi\)
0.529204 + 0.848494i \(0.322490\pi\)
\(212\) 7.32698 0.503219
\(213\) −24.8774 −1.70457
\(214\) −9.96286 −0.681047
\(215\) 0.600129 0.0409285
\(216\) 1.73528 0.118071
\(217\) 21.7350 1.47547
\(218\) 3.23819 0.219318
\(219\) −30.1631 −2.03823
\(220\) 1.21560 0.0819556
\(221\) −1.88508 −0.126804
\(222\) 10.5072 0.705198
\(223\) 1.80779 0.121059 0.0605294 0.998166i \(-0.480721\pi\)
0.0605294 + 0.998166i \(0.480721\pi\)
\(224\) 2.29966 0.153652
\(225\) −18.1190 −1.20793
\(226\) −12.6432 −0.841014
\(227\) 11.3254 0.751695 0.375847 0.926682i \(-0.377352\pi\)
0.375847 + 0.926682i \(0.377352\pi\)
\(228\) 11.0055 0.728858
\(229\) −17.0130 −1.12425 −0.562125 0.827052i \(-0.690016\pi\)
−0.562125 + 0.827052i \(0.690016\pi\)
\(230\) −0.703515 −0.0463884
\(231\) 28.2385 1.85796
\(232\) 5.42753 0.356335
\(233\) −6.58144 −0.431164 −0.215582 0.976486i \(-0.569165\pi\)
−0.215582 + 0.976486i \(0.569165\pi\)
\(234\) −1.95172 −0.127588
\(235\) 1.38594 0.0904090
\(236\) −4.92228 −0.320413
\(237\) −22.2145 −1.44298
\(238\) −8.15557 −0.528647
\(239\) 5.75546 0.372290 0.186145 0.982522i \(-0.440401\pi\)
0.186145 + 0.982522i \(0.440401\pi\)
\(240\) −0.660474 −0.0426334
\(241\) 1.37750 0.0887326 0.0443663 0.999015i \(-0.485873\pi\)
0.0443663 + 0.999015i \(0.485873\pi\)
\(242\) −11.6002 −0.745689
\(243\) 22.0811 1.41650
\(244\) −8.97884 −0.574812
\(245\) −0.437653 −0.0279606
\(246\) 21.1267 1.34699
\(247\) −2.26478 −0.144104
\(248\) 9.45140 0.600165
\(249\) −12.1000 −0.766804
\(250\) 2.54030 0.160663
\(251\) 29.5871 1.86752 0.933761 0.357896i \(-0.116506\pi\)
0.933761 + 0.357896i \(0.116506\pi\)
\(252\) −8.44391 −0.531916
\(253\) 13.0796 0.822310
\(254\) 6.10413 0.383007
\(255\) 2.34232 0.146682
\(256\) 1.00000 0.0625000
\(257\) 1.01590 0.0633699 0.0316849 0.999498i \(-0.489913\pi\)
0.0316849 + 0.999498i \(0.489913\pi\)
\(258\) 6.06223 0.377418
\(259\) −9.35468 −0.581272
\(260\) 0.135916 0.00842917
\(261\) −19.9289 −1.23357
\(262\) 9.12062 0.563474
\(263\) 6.08254 0.375065 0.187533 0.982258i \(-0.439951\pi\)
0.187533 + 0.982258i \(0.439951\pi\)
\(264\) 12.2794 0.755746
\(265\) 1.87352 0.115090
\(266\) −9.79832 −0.600773
\(267\) 26.6549 1.63126
\(268\) −2.67472 −0.163385
\(269\) 0.519321 0.0316635 0.0158318 0.999875i \(-0.494960\pi\)
0.0158318 + 0.999875i \(0.494960\pi\)
\(270\) 0.443714 0.0270036
\(271\) 13.3601 0.811566 0.405783 0.913970i \(-0.366999\pi\)
0.405783 + 0.913970i \(0.366999\pi\)
\(272\) −3.54643 −0.215034
\(273\) 3.15735 0.191092
\(274\) 7.38745 0.446292
\(275\) −23.4590 −1.41463
\(276\) −7.10659 −0.427767
\(277\) 22.9534 1.37913 0.689567 0.724222i \(-0.257801\pi\)
0.689567 + 0.724222i \(0.257801\pi\)
\(278\) −1.21366 −0.0727906
\(279\) −34.7038 −2.07766
\(280\) 0.588027 0.0351413
\(281\) 12.8812 0.768426 0.384213 0.923245i \(-0.374473\pi\)
0.384213 + 0.923245i \(0.374473\pi\)
\(282\) 14.0002 0.833698
\(283\) −6.13463 −0.364666 −0.182333 0.983237i \(-0.558365\pi\)
−0.182333 + 0.983237i \(0.558365\pi\)
\(284\) 9.63127 0.571511
\(285\) 2.81413 0.166695
\(286\) −2.52693 −0.149421
\(287\) −18.8093 −1.11028
\(288\) −3.67181 −0.216364
\(289\) −4.42285 −0.260168
\(290\) 1.38783 0.0814962
\(291\) 0.498340 0.0292132
\(292\) 11.6776 0.683380
\(293\) −19.8943 −1.16223 −0.581117 0.813820i \(-0.697384\pi\)
−0.581117 + 0.813820i \(0.697384\pi\)
\(294\) −4.42097 −0.257836
\(295\) −1.25864 −0.0732807
\(296\) −4.06786 −0.236439
\(297\) −8.24945 −0.478682
\(298\) 4.77978 0.276885
\(299\) 1.46244 0.0845749
\(300\) 12.7460 0.735893
\(301\) −5.39727 −0.311093
\(302\) 17.5057 1.00734
\(303\) 47.5342 2.73077
\(304\) −4.26077 −0.244372
\(305\) −2.29591 −0.131463
\(306\) 13.0218 0.744407
\(307\) 3.79527 0.216607 0.108304 0.994118i \(-0.465458\pi\)
0.108304 + 0.994118i \(0.465458\pi\)
\(308\) −10.9325 −0.622937
\(309\) 38.4711 2.18854
\(310\) 2.41674 0.137262
\(311\) −10.9816 −0.622708 −0.311354 0.950294i \(-0.600782\pi\)
−0.311354 + 0.950294i \(0.600782\pi\)
\(312\) 1.37297 0.0777288
\(313\) 19.8895 1.12422 0.562110 0.827062i \(-0.309990\pi\)
0.562110 + 0.827062i \(0.309990\pi\)
\(314\) −6.56075 −0.370244
\(315\) −2.15912 −0.121653
\(316\) 8.60030 0.483805
\(317\) −17.8387 −1.00192 −0.500962 0.865469i \(-0.667020\pi\)
−0.500962 + 0.865469i \(0.667020\pi\)
\(318\) 18.9255 1.06129
\(319\) −25.8023 −1.44465
\(320\) 0.255702 0.0142942
\(321\) −25.7339 −1.43633
\(322\) 6.32707 0.352594
\(323\) 15.1105 0.840772
\(324\) −6.53324 −0.362958
\(325\) −2.62296 −0.145495
\(326\) 11.2432 0.622705
\(327\) 8.36420 0.462541
\(328\) −8.17919 −0.451620
\(329\) −12.4645 −0.687190
\(330\) 3.13987 0.172844
\(331\) 20.8272 1.14477 0.572383 0.819987i \(-0.306019\pi\)
0.572383 + 0.819987i \(0.306019\pi\)
\(332\) 4.68449 0.257095
\(333\) 14.9364 0.818510
\(334\) −4.60273 −0.251850
\(335\) −0.683932 −0.0373672
\(336\) 5.93998 0.324053
\(337\) −12.4668 −0.679109 −0.339555 0.940586i \(-0.610276\pi\)
−0.339555 + 0.940586i \(0.610276\pi\)
\(338\) 12.7175 0.691739
\(339\) −32.6572 −1.77370
\(340\) −0.906828 −0.0491797
\(341\) −44.9316 −2.43318
\(342\) 15.6447 0.845971
\(343\) 20.0336 1.08171
\(344\) −2.34699 −0.126541
\(345\) −1.81717 −0.0978331
\(346\) 12.4098 0.667157
\(347\) −1.21299 −0.0651169 −0.0325585 0.999470i \(-0.510366\pi\)
−0.0325585 + 0.999470i \(0.510366\pi\)
\(348\) 14.0192 0.751510
\(349\) 21.3604 1.14339 0.571697 0.820465i \(-0.306285\pi\)
0.571697 + 0.820465i \(0.306285\pi\)
\(350\) −11.3479 −0.606572
\(351\) −0.922373 −0.0492326
\(352\) −4.75397 −0.253387
\(353\) −11.5593 −0.615242 −0.307621 0.951509i \(-0.599533\pi\)
−0.307621 + 0.951509i \(0.599533\pi\)
\(354\) −12.7142 −0.675751
\(355\) 2.46274 0.130708
\(356\) −10.3194 −0.546929
\(357\) −21.0657 −1.11492
\(358\) −3.64873 −0.192841
\(359\) −1.36694 −0.0721443 −0.0360721 0.999349i \(-0.511485\pi\)
−0.0360721 + 0.999349i \(0.511485\pi\)
\(360\) −0.938889 −0.0494838
\(361\) −0.845829 −0.0445173
\(362\) 10.9963 0.577951
\(363\) −29.9631 −1.57266
\(364\) −1.22236 −0.0640693
\(365\) 2.98599 0.156294
\(366\) −23.1922 −1.21228
\(367\) 19.4295 1.01421 0.507106 0.861884i \(-0.330715\pi\)
0.507106 + 0.861884i \(0.330715\pi\)
\(368\) 2.75131 0.143422
\(369\) 30.0324 1.56343
\(370\) −1.04016 −0.0540753
\(371\) −16.8496 −0.874785
\(372\) 24.4128 1.26575
\(373\) −7.76266 −0.401935 −0.200968 0.979598i \(-0.564409\pi\)
−0.200968 + 0.979598i \(0.564409\pi\)
\(374\) 16.8596 0.871789
\(375\) 6.56156 0.338837
\(376\) −5.42015 −0.279523
\(377\) −2.88496 −0.148583
\(378\) −3.99054 −0.205251
\(379\) −6.97878 −0.358476 −0.179238 0.983806i \(-0.557363\pi\)
−0.179238 + 0.983806i \(0.557363\pi\)
\(380\) −1.08949 −0.0558895
\(381\) 15.7669 0.807761
\(382\) −18.1965 −0.931016
\(383\) −27.7128 −1.41606 −0.708029 0.706183i \(-0.750416\pi\)
−0.708029 + 0.706183i \(0.750416\pi\)
\(384\) 2.58298 0.131812
\(385\) −2.79546 −0.142470
\(386\) 2.80343 0.142691
\(387\) 8.61770 0.438062
\(388\) −0.192932 −0.00979464
\(389\) −31.3993 −1.59201 −0.796003 0.605293i \(-0.793056\pi\)
−0.796003 + 0.605293i \(0.793056\pi\)
\(390\) 0.351070 0.0177771
\(391\) −9.75732 −0.493449
\(392\) 1.71157 0.0864475
\(393\) 23.5584 1.18837
\(394\) −4.29682 −0.216470
\(395\) 2.19911 0.110649
\(396\) 17.4557 0.877180
\(397\) 11.9343 0.598966 0.299483 0.954102i \(-0.403186\pi\)
0.299483 + 0.954102i \(0.403186\pi\)
\(398\) 7.31217 0.366526
\(399\) −25.3089 −1.26703
\(400\) −4.93462 −0.246731
\(401\) 37.1352 1.85444 0.927221 0.374515i \(-0.122191\pi\)
0.927221 + 0.374515i \(0.122191\pi\)
\(402\) −6.90877 −0.344578
\(403\) −5.02382 −0.250254
\(404\) −18.4028 −0.915574
\(405\) −1.67056 −0.0830109
\(406\) −12.4815 −0.619445
\(407\) 19.3385 0.958572
\(408\) −9.16037 −0.453506
\(409\) 17.2827 0.854573 0.427286 0.904116i \(-0.359470\pi\)
0.427286 + 0.904116i \(0.359470\pi\)
\(410\) −2.09144 −0.103289
\(411\) 19.0817 0.941230
\(412\) −14.8940 −0.733777
\(413\) 11.3196 0.556999
\(414\) −10.1023 −0.496501
\(415\) 1.19783 0.0587993
\(416\) −0.531542 −0.0260610
\(417\) −3.13487 −0.153515
\(418\) 20.2556 0.990732
\(419\) −19.2029 −0.938125 −0.469062 0.883165i \(-0.655408\pi\)
−0.469062 + 0.883165i \(0.655408\pi\)
\(420\) 1.51886 0.0741130
\(421\) −15.1998 −0.740792 −0.370396 0.928874i \(-0.620778\pi\)
−0.370396 + 0.928874i \(0.620778\pi\)
\(422\) −15.3743 −0.748408
\(423\) 19.9018 0.967657
\(424\) −7.32698 −0.355830
\(425\) 17.5003 0.848887
\(426\) 24.8774 1.20532
\(427\) 20.6483 0.999240
\(428\) 9.96286 0.481573
\(429\) −6.52703 −0.315128
\(430\) −0.600129 −0.0289408
\(431\) 20.5384 0.989299 0.494650 0.869092i \(-0.335296\pi\)
0.494650 + 0.869092i \(0.335296\pi\)
\(432\) −1.73528 −0.0834886
\(433\) 17.2265 0.827851 0.413925 0.910311i \(-0.364157\pi\)
0.413925 + 0.910311i \(0.364157\pi\)
\(434\) −21.7350 −1.04331
\(435\) 3.58474 0.171875
\(436\) −3.23819 −0.155081
\(437\) −11.7227 −0.560773
\(438\) 30.1631 1.44125
\(439\) −16.1789 −0.772176 −0.386088 0.922462i \(-0.626174\pi\)
−0.386088 + 0.922462i \(0.626174\pi\)
\(440\) −1.21560 −0.0579514
\(441\) −6.28457 −0.299265
\(442\) 1.88508 0.0896639
\(443\) 18.6495 0.886063 0.443032 0.896506i \(-0.353903\pi\)
0.443032 + 0.896506i \(0.353903\pi\)
\(444\) −10.5072 −0.498650
\(445\) −2.63870 −0.125086
\(446\) −1.80779 −0.0856015
\(447\) 12.3461 0.583951
\(448\) −2.29966 −0.108649
\(449\) 5.64613 0.266457 0.133229 0.991085i \(-0.457466\pi\)
0.133229 + 0.991085i \(0.457466\pi\)
\(450\) 18.1190 0.854137
\(451\) 38.8836 1.83096
\(452\) 12.6432 0.594687
\(453\) 45.2169 2.12448
\(454\) −11.3254 −0.531529
\(455\) −0.312561 −0.0146531
\(456\) −11.0055 −0.515380
\(457\) −13.8930 −0.649889 −0.324944 0.945733i \(-0.605346\pi\)
−0.324944 + 0.945733i \(0.605346\pi\)
\(458\) 17.0130 0.794965
\(459\) 6.15404 0.287246
\(460\) 0.703515 0.0328016
\(461\) −3.85963 −0.179761 −0.0898805 0.995953i \(-0.528649\pi\)
−0.0898805 + 0.995953i \(0.528649\pi\)
\(462\) −28.2385 −1.31377
\(463\) 24.0415 1.11730 0.558651 0.829403i \(-0.311319\pi\)
0.558651 + 0.829403i \(0.311319\pi\)
\(464\) −5.42753 −0.251967
\(465\) 6.24241 0.289485
\(466\) 6.58144 0.304879
\(467\) −25.9190 −1.19939 −0.599695 0.800229i \(-0.704711\pi\)
−0.599695 + 0.800229i \(0.704711\pi\)
\(468\) 1.95172 0.0902184
\(469\) 6.15095 0.284024
\(470\) −1.38594 −0.0639288
\(471\) −16.9463 −0.780845
\(472\) 4.92228 0.226566
\(473\) 11.1575 0.513022
\(474\) 22.2145 1.02034
\(475\) 21.0253 0.964706
\(476\) 8.15557 0.373810
\(477\) 26.9033 1.23182
\(478\) −5.75546 −0.263249
\(479\) −4.75090 −0.217074 −0.108537 0.994092i \(-0.534617\pi\)
−0.108537 + 0.994092i \(0.534617\pi\)
\(480\) 0.660474 0.0301464
\(481\) 2.16224 0.0985896
\(482\) −1.37750 −0.0627434
\(483\) 16.3427 0.743620
\(484\) 11.6002 0.527281
\(485\) −0.0493331 −0.00224010
\(486\) −22.0811 −1.00162
\(487\) −2.52316 −0.114335 −0.0571677 0.998365i \(-0.518207\pi\)
−0.0571677 + 0.998365i \(0.518207\pi\)
\(488\) 8.97884 0.406453
\(489\) 29.0411 1.31328
\(490\) 0.437653 0.0197711
\(491\) −28.9562 −1.30677 −0.653387 0.757024i \(-0.726652\pi\)
−0.653387 + 0.757024i \(0.726652\pi\)
\(492\) −21.1267 −0.952467
\(493\) 19.2483 0.866902
\(494\) 2.26478 0.101897
\(495\) 4.46345 0.200617
\(496\) −9.45140 −0.424380
\(497\) −22.1486 −0.993502
\(498\) 12.1000 0.542212
\(499\) −1.73702 −0.0777598 −0.0388799 0.999244i \(-0.512379\pi\)
−0.0388799 + 0.999244i \(0.512379\pi\)
\(500\) −2.54030 −0.113606
\(501\) −11.8888 −0.531152
\(502\) −29.5871 −1.32054
\(503\) 30.5444 1.36191 0.680954 0.732327i \(-0.261566\pi\)
0.680954 + 0.732327i \(0.261566\pi\)
\(504\) 8.44391 0.376122
\(505\) −4.70563 −0.209398
\(506\) −13.0796 −0.581461
\(507\) 32.8490 1.45888
\(508\) −6.10413 −0.270827
\(509\) 28.3632 1.25718 0.628588 0.777739i \(-0.283633\pi\)
0.628588 + 0.777739i \(0.283633\pi\)
\(510\) −2.34232 −0.103720
\(511\) −26.8545 −1.18797
\(512\) −1.00000 −0.0441942
\(513\) 7.39362 0.326436
\(514\) −1.01590 −0.0448093
\(515\) −3.80844 −0.167820
\(516\) −6.06223 −0.266875
\(517\) 25.7672 1.13324
\(518\) 9.35468 0.411021
\(519\) 32.0544 1.40703
\(520\) −0.135916 −0.00596033
\(521\) 0.00673097 0.000294889 0 0.000147445 1.00000i \(-0.499953\pi\)
0.000147445 1.00000i \(0.499953\pi\)
\(522\) 19.9289 0.872263
\(523\) −4.00317 −0.175046 −0.0875232 0.996162i \(-0.527895\pi\)
−0.0875232 + 0.996162i \(0.527895\pi\)
\(524\) −9.12062 −0.398436
\(525\) −29.3115 −1.27926
\(526\) −6.08254 −0.265211
\(527\) 33.5187 1.46010
\(528\) −12.2794 −0.534393
\(529\) −15.4303 −0.670882
\(530\) −1.87352 −0.0813807
\(531\) −18.0737 −0.784331
\(532\) 9.79832 0.424811
\(533\) 4.34758 0.188315
\(534\) −26.6549 −1.15347
\(535\) 2.54752 0.110139
\(536\) 2.67472 0.115530
\(537\) −9.42462 −0.406702
\(538\) −0.519321 −0.0223895
\(539\) −8.13676 −0.350475
\(540\) −0.443714 −0.0190944
\(541\) 32.0008 1.37582 0.687910 0.725796i \(-0.258528\pi\)
0.687910 + 0.725796i \(0.258528\pi\)
\(542\) −13.3601 −0.573864
\(543\) 28.4032 1.21890
\(544\) 3.54643 0.152052
\(545\) −0.828011 −0.0354681
\(546\) −3.15735 −0.135122
\(547\) 4.36019 0.186428 0.0932142 0.995646i \(-0.470286\pi\)
0.0932142 + 0.995646i \(0.470286\pi\)
\(548\) −7.38745 −0.315576
\(549\) −32.9686 −1.40707
\(550\) 23.4590 1.00030
\(551\) 23.1255 0.985178
\(552\) 7.10659 0.302477
\(553\) −19.7778 −0.841036
\(554\) −22.9534 −0.975194
\(555\) −2.68672 −0.114045
\(556\) 1.21366 0.0514708
\(557\) 30.6946 1.30057 0.650286 0.759690i \(-0.274649\pi\)
0.650286 + 0.759690i \(0.274649\pi\)
\(558\) 34.7038 1.46913
\(559\) 1.24752 0.0527646
\(560\) −0.588027 −0.0248487
\(561\) 43.5481 1.83860
\(562\) −12.8812 −0.543359
\(563\) 33.4323 1.40900 0.704502 0.709702i \(-0.251170\pi\)
0.704502 + 0.709702i \(0.251170\pi\)
\(564\) −14.0002 −0.589514
\(565\) 3.23289 0.136009
\(566\) 6.13463 0.257858
\(567\) 15.0242 0.630958
\(568\) −9.63127 −0.404119
\(569\) 21.9206 0.918960 0.459480 0.888188i \(-0.348036\pi\)
0.459480 + 0.888188i \(0.348036\pi\)
\(570\) −2.81413 −0.117871
\(571\) 38.7483 1.62157 0.810783 0.585347i \(-0.199042\pi\)
0.810783 + 0.585347i \(0.199042\pi\)
\(572\) 2.52693 0.105656
\(573\) −47.0014 −1.96351
\(574\) 18.8093 0.785087
\(575\) −13.5767 −0.566186
\(576\) 3.67181 0.152992
\(577\) −12.7225 −0.529643 −0.264821 0.964298i \(-0.585313\pi\)
−0.264821 + 0.964298i \(0.585313\pi\)
\(578\) 4.42285 0.183966
\(579\) 7.24121 0.300934
\(580\) −1.38783 −0.0576265
\(581\) −10.7727 −0.446928
\(582\) −0.498340 −0.0206569
\(583\) 34.8322 1.44260
\(584\) −11.6776 −0.483223
\(585\) 0.499059 0.0206336
\(586\) 19.8943 0.821824
\(587\) 11.2868 0.465857 0.232928 0.972494i \(-0.425169\pi\)
0.232928 + 0.972494i \(0.425169\pi\)
\(588\) 4.42097 0.182318
\(589\) 40.2703 1.65931
\(590\) 1.25864 0.0518173
\(591\) −11.0986 −0.456536
\(592\) 4.06786 0.167188
\(593\) −41.8544 −1.71876 −0.859378 0.511341i \(-0.829149\pi\)
−0.859378 + 0.511341i \(0.829149\pi\)
\(594\) 8.24945 0.338479
\(595\) 2.08540 0.0854929
\(596\) −4.77978 −0.195788
\(597\) 18.8872 0.773003
\(598\) −1.46244 −0.0598035
\(599\) 16.3718 0.668934 0.334467 0.942407i \(-0.391444\pi\)
0.334467 + 0.942407i \(0.391444\pi\)
\(600\) −12.7460 −0.520355
\(601\) −4.07972 −0.166415 −0.0832076 0.996532i \(-0.526516\pi\)
−0.0832076 + 0.996532i \(0.526516\pi\)
\(602\) 5.39727 0.219976
\(603\) −9.82108 −0.399945
\(604\) −17.5057 −0.712296
\(605\) 2.96619 0.120593
\(606\) −47.5342 −1.93094
\(607\) −0.0803433 −0.00326103 −0.00163052 0.999999i \(-0.500519\pi\)
−0.00163052 + 0.999999i \(0.500519\pi\)
\(608\) 4.26077 0.172797
\(609\) −32.2394 −1.30641
\(610\) 2.29591 0.0929586
\(611\) 2.88104 0.116554
\(612\) −13.0218 −0.526375
\(613\) −9.45182 −0.381755 −0.190878 0.981614i \(-0.561133\pi\)
−0.190878 + 0.981614i \(0.561133\pi\)
\(614\) −3.79527 −0.153165
\(615\) −5.40215 −0.217836
\(616\) 10.9325 0.440483
\(617\) 4.30842 0.173451 0.0867253 0.996232i \(-0.472360\pi\)
0.0867253 + 0.996232i \(0.472360\pi\)
\(618\) −38.4711 −1.54753
\(619\) 8.85654 0.355974 0.177987 0.984033i \(-0.443041\pi\)
0.177987 + 0.984033i \(0.443041\pi\)
\(620\) −2.41674 −0.0970587
\(621\) −4.77429 −0.191586
\(622\) 10.9816 0.440321
\(623\) 23.7312 0.950769
\(624\) −1.37297 −0.0549626
\(625\) 24.0235 0.960941
\(626\) −19.8895 −0.794944
\(627\) 52.3198 2.08945
\(628\) 6.56075 0.261802
\(629\) −14.4264 −0.575217
\(630\) 2.15912 0.0860216
\(631\) 36.2875 1.44458 0.722292 0.691588i \(-0.243089\pi\)
0.722292 + 0.691588i \(0.243089\pi\)
\(632\) −8.60030 −0.342102
\(633\) −39.7115 −1.57839
\(634\) 17.8387 0.708467
\(635\) −1.56084 −0.0619399
\(636\) −18.9255 −0.750444
\(637\) −0.909773 −0.0360465
\(638\) 25.8023 1.02152
\(639\) 35.3642 1.39899
\(640\) −0.255702 −0.0101075
\(641\) −14.7369 −0.582072 −0.291036 0.956712i \(-0.594000\pi\)
−0.291036 + 0.956712i \(0.594000\pi\)
\(642\) 25.7339 1.01564
\(643\) −14.3162 −0.564577 −0.282289 0.959330i \(-0.591094\pi\)
−0.282289 + 0.959330i \(0.591094\pi\)
\(644\) −6.32707 −0.249322
\(645\) −1.55013 −0.0610361
\(646\) −15.1105 −0.594515
\(647\) 43.7432 1.71972 0.859861 0.510529i \(-0.170550\pi\)
0.859861 + 0.510529i \(0.170550\pi\)
\(648\) 6.53324 0.256650
\(649\) −23.4004 −0.918545
\(650\) 2.62296 0.102881
\(651\) −56.1411 −2.20035
\(652\) −11.2432 −0.440319
\(653\) 43.5572 1.70452 0.852262 0.523116i \(-0.175230\pi\)
0.852262 + 0.523116i \(0.175230\pi\)
\(654\) −8.36420 −0.327066
\(655\) −2.33216 −0.0911251
\(656\) 8.17919 0.319344
\(657\) 42.8780 1.67283
\(658\) 12.4645 0.485917
\(659\) −36.1525 −1.40830 −0.704151 0.710050i \(-0.748672\pi\)
−0.704151 + 0.710050i \(0.748672\pi\)
\(660\) −3.13987 −0.122219
\(661\) 17.4547 0.678911 0.339455 0.940622i \(-0.389757\pi\)
0.339455 + 0.940622i \(0.389757\pi\)
\(662\) −20.8272 −0.809471
\(663\) 4.86912 0.189101
\(664\) −4.68449 −0.181793
\(665\) 2.50545 0.0971571
\(666\) −14.9364 −0.578774
\(667\) −14.9328 −0.578201
\(668\) 4.60273 0.178085
\(669\) −4.66950 −0.180533
\(670\) 0.683932 0.0264226
\(671\) −42.6851 −1.64784
\(672\) −5.93998 −0.229140
\(673\) 32.5652 1.25530 0.627649 0.778497i \(-0.284017\pi\)
0.627649 + 0.778497i \(0.284017\pi\)
\(674\) 12.4668 0.480203
\(675\) 8.56293 0.329587
\(676\) −12.7175 −0.489133
\(677\) 18.7680 0.721314 0.360657 0.932699i \(-0.382553\pi\)
0.360657 + 0.932699i \(0.382553\pi\)
\(678\) 32.6572 1.25419
\(679\) 0.443677 0.0170268
\(680\) 0.906828 0.0347753
\(681\) −29.2534 −1.12099
\(682\) 44.9316 1.72052
\(683\) −6.68495 −0.255793 −0.127896 0.991788i \(-0.540822\pi\)
−0.127896 + 0.991788i \(0.540822\pi\)
\(684\) −15.6447 −0.598192
\(685\) −1.88899 −0.0721744
\(686\) −20.0336 −0.764888
\(687\) 43.9443 1.67658
\(688\) 2.34699 0.0894781
\(689\) 3.89460 0.148372
\(690\) 1.81717 0.0691785
\(691\) 25.2257 0.959631 0.479815 0.877369i \(-0.340704\pi\)
0.479815 + 0.877369i \(0.340704\pi\)
\(692\) −12.4098 −0.471751
\(693\) −40.1421 −1.52487
\(694\) 1.21299 0.0460446
\(695\) 0.310336 0.0117717
\(696\) −14.0192 −0.531398
\(697\) −29.0069 −1.09872
\(698\) −21.3604 −0.808502
\(699\) 16.9998 0.642990
\(700\) 11.3479 0.428911
\(701\) 5.00180 0.188915 0.0944577 0.995529i \(-0.469888\pi\)
0.0944577 + 0.995529i \(0.469888\pi\)
\(702\) 0.922373 0.0348127
\(703\) −17.3322 −0.653697
\(704\) 4.75397 0.179172
\(705\) −3.57987 −0.134826
\(706\) 11.5593 0.435042
\(707\) 42.3202 1.59161
\(708\) 12.7142 0.477828
\(709\) −21.0843 −0.791836 −0.395918 0.918286i \(-0.629574\pi\)
−0.395918 + 0.918286i \(0.629574\pi\)
\(710\) −2.46274 −0.0924248
\(711\) 31.5787 1.18429
\(712\) 10.3194 0.386737
\(713\) −26.0037 −0.973848
\(714\) 21.0657 0.788364
\(715\) 0.646142 0.0241643
\(716\) 3.64873 0.136360
\(717\) −14.8663 −0.555191
\(718\) 1.36694 0.0510137
\(719\) 10.8353 0.404088 0.202044 0.979376i \(-0.435242\pi\)
0.202044 + 0.979376i \(0.435242\pi\)
\(720\) 0.938889 0.0349903
\(721\) 34.2512 1.27558
\(722\) 0.845829 0.0314785
\(723\) −3.55806 −0.132326
\(724\) −10.9963 −0.408673
\(725\) 26.7828 0.994688
\(726\) 29.9631 1.11204
\(727\) 30.5210 1.13196 0.565981 0.824418i \(-0.308497\pi\)
0.565981 + 0.824418i \(0.308497\pi\)
\(728\) 1.22236 0.0453039
\(729\) −37.4354 −1.38650
\(730\) −2.98599 −0.110516
\(731\) −8.32342 −0.307853
\(732\) 23.1922 0.857209
\(733\) −24.1276 −0.891174 −0.445587 0.895239i \(-0.647005\pi\)
−0.445587 + 0.895239i \(0.647005\pi\)
\(734\) −19.4295 −0.717157
\(735\) 1.13045 0.0416973
\(736\) −2.75131 −0.101415
\(737\) −12.7155 −0.468383
\(738\) −30.0324 −1.10551
\(739\) 37.1991 1.36839 0.684195 0.729299i \(-0.260154\pi\)
0.684195 + 0.729299i \(0.260154\pi\)
\(740\) 1.04016 0.0382370
\(741\) 5.84989 0.214901
\(742\) 16.8496 0.618567
\(743\) 1.62668 0.0596772 0.0298386 0.999555i \(-0.490501\pi\)
0.0298386 + 0.999555i \(0.490501\pi\)
\(744\) −24.4128 −0.895018
\(745\) −1.22220 −0.0447779
\(746\) 7.76266 0.284211
\(747\) 17.2006 0.629335
\(748\) −16.8596 −0.616448
\(749\) −22.9112 −0.837156
\(750\) −6.56156 −0.239594
\(751\) 13.2496 0.483485 0.241743 0.970340i \(-0.422281\pi\)
0.241743 + 0.970340i \(0.422281\pi\)
\(752\) 5.42015 0.197653
\(753\) −76.4231 −2.78501
\(754\) 2.88496 0.105064
\(755\) −4.47624 −0.162907
\(756\) 3.99054 0.145135
\(757\) −41.4521 −1.50660 −0.753301 0.657675i \(-0.771540\pi\)
−0.753301 + 0.657675i \(0.771540\pi\)
\(758\) 6.97878 0.253481
\(759\) −33.7845 −1.22630
\(760\) 1.08949 0.0395199
\(761\) −9.70505 −0.351808 −0.175904 0.984407i \(-0.556285\pi\)
−0.175904 + 0.984407i \(0.556285\pi\)
\(762\) −15.7669 −0.571173
\(763\) 7.44673 0.269590
\(764\) 18.1965 0.658328
\(765\) −3.32970 −0.120386
\(766\) 27.7128 1.00130
\(767\) −2.61640 −0.0944727
\(768\) −2.58298 −0.0932054
\(769\) −3.80266 −0.137127 −0.0685637 0.997647i \(-0.521842\pi\)
−0.0685637 + 0.997647i \(0.521842\pi\)
\(770\) 2.79546 0.100741
\(771\) −2.62404 −0.0945027
\(772\) −2.80343 −0.100898
\(773\) −52.5078 −1.88857 −0.944287 0.329123i \(-0.893247\pi\)
−0.944287 + 0.329123i \(0.893247\pi\)
\(774\) −8.61770 −0.309757
\(775\) 46.6390 1.67532
\(776\) 0.192932 0.00692585
\(777\) 24.1630 0.866843
\(778\) 31.3993 1.12572
\(779\) −34.8497 −1.24862
\(780\) −0.351070 −0.0125703
\(781\) 45.7867 1.63838
\(782\) 9.75732 0.348921
\(783\) 9.41827 0.336582
\(784\) −1.71157 −0.0611276
\(785\) 1.67760 0.0598760
\(786\) −23.5584 −0.840302
\(787\) −30.2766 −1.07924 −0.539621 0.841908i \(-0.681433\pi\)
−0.539621 + 0.841908i \(0.681433\pi\)
\(788\) 4.29682 0.153068
\(789\) −15.7111 −0.559330
\(790\) −2.19911 −0.0782410
\(791\) −29.0751 −1.03379
\(792\) −17.4557 −0.620260
\(793\) −4.77263 −0.169481
\(794\) −11.9343 −0.423533
\(795\) −4.83928 −0.171632
\(796\) −7.31217 −0.259173
\(797\) 16.8208 0.595822 0.297911 0.954594i \(-0.403710\pi\)
0.297911 + 0.954594i \(0.403710\pi\)
\(798\) 25.3089 0.895925
\(799\) −19.2222 −0.680032
\(800\) 4.93462 0.174465
\(801\) −37.8910 −1.33881
\(802\) −37.1352 −1.31129
\(803\) 55.5149 1.95908
\(804\) 6.90877 0.243653
\(805\) −1.61784 −0.0570215
\(806\) 5.02382 0.176956
\(807\) −1.34140 −0.0472194
\(808\) 18.4028 0.647408
\(809\) −1.63854 −0.0576080 −0.0288040 0.999585i \(-0.509170\pi\)
−0.0288040 + 0.999585i \(0.509170\pi\)
\(810\) 1.67056 0.0586975
\(811\) −25.6862 −0.901964 −0.450982 0.892533i \(-0.648926\pi\)
−0.450982 + 0.892533i \(0.648926\pi\)
\(812\) 12.4815 0.438014
\(813\) −34.5088 −1.21028
\(814\) −19.3385 −0.677813
\(815\) −2.87492 −0.100704
\(816\) 9.16037 0.320677
\(817\) −9.99998 −0.349855
\(818\) −17.2827 −0.604274
\(819\) −4.48829 −0.156834
\(820\) 2.09144 0.0730361
\(821\) −42.6847 −1.48971 −0.744853 0.667229i \(-0.767480\pi\)
−0.744853 + 0.667229i \(0.767480\pi\)
\(822\) −19.0817 −0.665550
\(823\) 40.5864 1.41475 0.707377 0.706836i \(-0.249878\pi\)
0.707377 + 0.706836i \(0.249878\pi\)
\(824\) 14.8940 0.518859
\(825\) 60.5942 2.10962
\(826\) −11.3196 −0.393858
\(827\) 44.6760 1.55354 0.776768 0.629787i \(-0.216858\pi\)
0.776768 + 0.629787i \(0.216858\pi\)
\(828\) 10.1023 0.351079
\(829\) 10.8787 0.377833 0.188916 0.981993i \(-0.439502\pi\)
0.188916 + 0.981993i \(0.439502\pi\)
\(830\) −1.19783 −0.0415774
\(831\) −59.2882 −2.05668
\(832\) 0.531542 0.0184279
\(833\) 6.06997 0.210312
\(834\) 3.13487 0.108552
\(835\) 1.17693 0.0407293
\(836\) −20.2556 −0.700553
\(837\) 16.4008 0.566895
\(838\) 19.2029 0.663354
\(839\) 18.9961 0.655817 0.327909 0.944709i \(-0.393656\pi\)
0.327909 + 0.944709i \(0.393656\pi\)
\(840\) −1.51886 −0.0524058
\(841\) 0.458096 0.0157964
\(842\) 15.1998 0.523819
\(843\) −33.2718 −1.14594
\(844\) 15.3743 0.529204
\(845\) −3.25188 −0.111868
\(846\) −19.9018 −0.684237
\(847\) −26.6765 −0.916615
\(848\) 7.32698 0.251610
\(849\) 15.8457 0.543822
\(850\) −17.5003 −0.600254
\(851\) 11.1919 0.383655
\(852\) −24.8774 −0.852287
\(853\) 51.7180 1.77079 0.885395 0.464840i \(-0.153888\pi\)
0.885395 + 0.464840i \(0.153888\pi\)
\(854\) −20.6483 −0.706569
\(855\) −4.00039 −0.136811
\(856\) −9.96286 −0.340524
\(857\) 6.16112 0.210460 0.105230 0.994448i \(-0.466442\pi\)
0.105230 + 0.994448i \(0.466442\pi\)
\(858\) 6.52703 0.222829
\(859\) 38.8222 1.32459 0.662297 0.749241i \(-0.269582\pi\)
0.662297 + 0.749241i \(0.269582\pi\)
\(860\) 0.600129 0.0204642
\(861\) 48.5843 1.65575
\(862\) −20.5384 −0.699540
\(863\) −8.12238 −0.276489 −0.138245 0.990398i \(-0.544146\pi\)
−0.138245 + 0.990398i \(0.544146\pi\)
\(864\) 1.73528 0.0590353
\(865\) −3.17322 −0.107893
\(866\) −17.2265 −0.585379
\(867\) 11.4242 0.387985
\(868\) 21.7350 0.737734
\(869\) 40.8856 1.38695
\(870\) −3.58474 −0.121534
\(871\) −1.42173 −0.0481734
\(872\) 3.23819 0.109659
\(873\) −0.708410 −0.0239760
\(874\) 11.7227 0.396526
\(875\) 5.84182 0.197490
\(876\) −30.1631 −1.01912
\(877\) −6.79906 −0.229588 −0.114794 0.993389i \(-0.536621\pi\)
−0.114794 + 0.993389i \(0.536621\pi\)
\(878\) 16.1789 0.546011
\(879\) 51.3866 1.73323
\(880\) 1.21560 0.0409778
\(881\) 38.6729 1.30292 0.651462 0.758681i \(-0.274156\pi\)
0.651462 + 0.758681i \(0.274156\pi\)
\(882\) 6.28457 0.211613
\(883\) 17.4252 0.586406 0.293203 0.956050i \(-0.405279\pi\)
0.293203 + 0.956050i \(0.405279\pi\)
\(884\) −1.88508 −0.0634019
\(885\) 3.25104 0.109283
\(886\) −18.6495 −0.626541
\(887\) 17.4779 0.586851 0.293425 0.955982i \(-0.405205\pi\)
0.293425 + 0.955982i \(0.405205\pi\)
\(888\) 10.5072 0.352599
\(889\) 14.0374 0.470800
\(890\) 2.63870 0.0884494
\(891\) −31.0588 −1.04051
\(892\) 1.80779 0.0605294
\(893\) −23.0940 −0.772812
\(894\) −12.3461 −0.412916
\(895\) 0.932988 0.0311863
\(896\) 2.29966 0.0768262
\(897\) −3.77745 −0.126125
\(898\) −5.64613 −0.188414
\(899\) 51.2978 1.71088
\(900\) −18.1190 −0.603966
\(901\) −25.9846 −0.865673
\(902\) −38.8836 −1.29468
\(903\) 13.9411 0.463930
\(904\) −12.6432 −0.420507
\(905\) −2.81177 −0.0934663
\(906\) −45.2169 −1.50223
\(907\) 7.99327 0.265412 0.132706 0.991155i \(-0.457633\pi\)
0.132706 + 0.991155i \(0.457633\pi\)
\(908\) 11.3254 0.375847
\(909\) −67.5716 −2.24121
\(910\) 0.312561 0.0103613
\(911\) −13.5268 −0.448161 −0.224081 0.974571i \(-0.571938\pi\)
−0.224081 + 0.974571i \(0.571938\pi\)
\(912\) 11.0055 0.364429
\(913\) 22.2699 0.737026
\(914\) 13.8930 0.459541
\(915\) 5.93030 0.196050
\(916\) −17.0130 −0.562125
\(917\) 20.9743 0.692633
\(918\) −6.15404 −0.203113
\(919\) −3.70903 −0.122350 −0.0611748 0.998127i \(-0.519485\pi\)
−0.0611748 + 0.998127i \(0.519485\pi\)
\(920\) −0.703515 −0.0231942
\(921\) −9.80312 −0.323024
\(922\) 3.85963 0.127110
\(923\) 5.11943 0.168508
\(924\) 28.2385 0.928978
\(925\) −20.0733 −0.660007
\(926\) −24.0415 −0.790052
\(927\) −54.6881 −1.79619
\(928\) 5.42753 0.178167
\(929\) 11.3952 0.373863 0.186931 0.982373i \(-0.440146\pi\)
0.186931 + 0.982373i \(0.440146\pi\)
\(930\) −6.24241 −0.204697
\(931\) 7.29262 0.239006
\(932\) −6.58144 −0.215582
\(933\) 28.3652 0.928636
\(934\) 25.9190 0.848097
\(935\) −4.31103 −0.140986
\(936\) −1.95172 −0.0637940
\(937\) 42.6986 1.39490 0.697451 0.716632i \(-0.254317\pi\)
0.697451 + 0.716632i \(0.254317\pi\)
\(938\) −6.15095 −0.200836
\(939\) −51.3743 −1.67654
\(940\) 1.38594 0.0452045
\(941\) 52.0091 1.69545 0.847724 0.530438i \(-0.177973\pi\)
0.847724 + 0.530438i \(0.177973\pi\)
\(942\) 16.9463 0.552141
\(943\) 22.5035 0.732815
\(944\) −4.92228 −0.160207
\(945\) 1.02039 0.0331933
\(946\) −11.1575 −0.362762
\(947\) 20.8192 0.676533 0.338266 0.941050i \(-0.390159\pi\)
0.338266 + 0.941050i \(0.390159\pi\)
\(948\) −22.2145 −0.721492
\(949\) 6.20714 0.201492
\(950\) −21.0253 −0.682150
\(951\) 46.0772 1.49416
\(952\) −8.15557 −0.264324
\(953\) 9.93499 0.321826 0.160913 0.986969i \(-0.448556\pi\)
0.160913 + 0.986969i \(0.448556\pi\)
\(954\) −26.9033 −0.871027
\(955\) 4.65289 0.150564
\(956\) 5.75546 0.186145
\(957\) 66.6469 2.15439
\(958\) 4.75090 0.153495
\(959\) 16.9886 0.548591
\(960\) −0.660474 −0.0213167
\(961\) 58.3290 1.88158
\(962\) −2.16224 −0.0697133
\(963\) 36.5817 1.17883
\(964\) 1.37750 0.0443663
\(965\) −0.716842 −0.0230760
\(966\) −16.3427 −0.525819
\(967\) 31.7654 1.02151 0.510753 0.859728i \(-0.329367\pi\)
0.510753 + 0.859728i \(0.329367\pi\)
\(968\) −11.6002 −0.372844
\(969\) −39.0302 −1.25383
\(970\) 0.0493331 0.00158399
\(971\) 0.510723 0.0163899 0.00819495 0.999966i \(-0.497391\pi\)
0.00819495 + 0.999966i \(0.497391\pi\)
\(972\) 22.0811 0.708251
\(973\) −2.79101 −0.0894756
\(974\) 2.52316 0.0808474
\(975\) 6.77506 0.216975
\(976\) −8.97884 −0.287406
\(977\) 19.6854 0.629793 0.314896 0.949126i \(-0.398030\pi\)
0.314896 + 0.949126i \(0.398030\pi\)
\(978\) −29.0411 −0.928632
\(979\) −49.0582 −1.56791
\(980\) −0.437653 −0.0139803
\(981\) −11.8900 −0.379619
\(982\) 28.9562 0.924028
\(983\) 1.32746 0.0423395 0.0211698 0.999776i \(-0.493261\pi\)
0.0211698 + 0.999776i \(0.493261\pi\)
\(984\) 21.1267 0.673496
\(985\) 1.09870 0.0350076
\(986\) −19.2483 −0.612992
\(987\) 32.1956 1.02480
\(988\) −2.26478 −0.0720522
\(989\) 6.45729 0.205330
\(990\) −4.46345 −0.141858
\(991\) 16.3980 0.520900 0.260450 0.965487i \(-0.416129\pi\)
0.260450 + 0.965487i \(0.416129\pi\)
\(992\) 9.45140 0.300082
\(993\) −53.7963 −1.70717
\(994\) 22.1486 0.702512
\(995\) −1.86974 −0.0592746
\(996\) −12.1000 −0.383402
\(997\) −7.87930 −0.249540 −0.124770 0.992186i \(-0.539819\pi\)
−0.124770 + 0.992186i \(0.539819\pi\)
\(998\) 1.73702 0.0549845
\(999\) −7.05886 −0.223333
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 \(a_p\))