Properties

Label 8041.2.a.j.1.3
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 82
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(82\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.65190 q^{2}\) \(+1.08303 q^{3}\) \(+5.03256 q^{4}\) \(+0.484312 q^{5}\) \(-2.87208 q^{6}\) \(+1.56821 q^{7}\) \(-8.04203 q^{8}\) \(-1.82705 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.65190 q^{2}\) \(+1.08303 q^{3}\) \(+5.03256 q^{4}\) \(+0.484312 q^{5}\) \(-2.87208 q^{6}\) \(+1.56821 q^{7}\) \(-8.04203 q^{8}\) \(-1.82705 q^{9}\) \(-1.28435 q^{10}\) \(+1.00000 q^{11}\) \(+5.45040 q^{12}\) \(+1.02036 q^{13}\) \(-4.15873 q^{14}\) \(+0.524523 q^{15}\) \(+11.2615 q^{16}\) \(+1.00000 q^{17}\) \(+4.84515 q^{18}\) \(-7.33635 q^{19}\) \(+2.43733 q^{20}\) \(+1.69842 q^{21}\) \(-2.65190 q^{22}\) \(+4.79280 q^{23}\) \(-8.70974 q^{24}\) \(-4.76544 q^{25}\) \(-2.70590 q^{26}\) \(-5.22783 q^{27}\) \(+7.89211 q^{28}\) \(-6.14051 q^{29}\) \(-1.39098 q^{30}\) \(-8.14245 q^{31}\) \(-13.7803 q^{32}\) \(+1.08303 q^{33}\) \(-2.65190 q^{34}\) \(+0.759504 q^{35}\) \(-9.19474 q^{36}\) \(+7.46703 q^{37}\) \(+19.4552 q^{38}\) \(+1.10508 q^{39}\) \(-3.89485 q^{40}\) \(-10.1278 q^{41}\) \(-4.50402 q^{42}\) \(+1.00000 q^{43}\) \(+5.03256 q^{44}\) \(-0.884863 q^{45}\) \(-12.7100 q^{46}\) \(+1.41818 q^{47}\) \(+12.1965 q^{48}\) \(-4.54071 q^{49}\) \(+12.6375 q^{50}\) \(+1.08303 q^{51}\) \(+5.13504 q^{52}\) \(+10.8066 q^{53}\) \(+13.8637 q^{54}\) \(+0.484312 q^{55}\) \(-12.6116 q^{56}\) \(-7.94547 q^{57}\) \(+16.2840 q^{58}\) \(-1.27321 q^{59}\) \(+2.63969 q^{60}\) \(+5.68853 q^{61}\) \(+21.5929 q^{62}\) \(-2.86520 q^{63}\) \(+14.0210 q^{64}\) \(+0.494174 q^{65}\) \(-2.87208 q^{66}\) \(+11.3268 q^{67}\) \(+5.03256 q^{68}\) \(+5.19073 q^{69}\) \(-2.01413 q^{70}\) \(+4.89737 q^{71}\) \(+14.6932 q^{72}\) \(+1.41558 q^{73}\) \(-19.8018 q^{74}\) \(-5.16110 q^{75}\) \(-36.9206 q^{76}\) \(+1.56821 q^{77}\) \(-2.93056 q^{78}\) \(-8.10888 q^{79}\) \(+5.45409 q^{80}\) \(-0.180729 q^{81}\) \(+26.8580 q^{82}\) \(+6.65886 q^{83}\) \(+8.54738 q^{84}\) \(+0.484312 q^{85}\) \(-2.65190 q^{86}\) \(-6.65034 q^{87}\) \(-8.04203 q^{88}\) \(+11.4605 q^{89}\) \(+2.34657 q^{90}\) \(+1.60015 q^{91}\) \(+24.1200 q^{92}\) \(-8.81850 q^{93}\) \(-3.76087 q^{94}\) \(-3.55308 q^{95}\) \(-14.9245 q^{96}\) \(+1.82310 q^{97}\) \(+12.0415 q^{98}\) \(-1.82705 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65190 −1.87517 −0.937587 0.347750i \(-0.886946\pi\)
−0.937587 + 0.347750i \(0.886946\pi\)
\(3\) 1.08303 0.625286 0.312643 0.949871i \(-0.398786\pi\)
0.312643 + 0.949871i \(0.398786\pi\)
\(4\) 5.03256 2.51628
\(5\) 0.484312 0.216591 0.108295 0.994119i \(-0.465461\pi\)
0.108295 + 0.994119i \(0.465461\pi\)
\(6\) −2.87208 −1.17252
\(7\) 1.56821 0.592728 0.296364 0.955075i \(-0.404226\pi\)
0.296364 + 0.955075i \(0.404226\pi\)
\(8\) −8.04203 −2.84329
\(9\) −1.82705 −0.609017
\(10\) −1.28435 −0.406146
\(11\) 1.00000 0.301511
\(12\) 5.45040 1.57339
\(13\) 1.02036 0.282998 0.141499 0.989938i \(-0.454808\pi\)
0.141499 + 0.989938i \(0.454808\pi\)
\(14\) −4.15873 −1.11147
\(15\) 0.524523 0.135431
\(16\) 11.2615 2.81538
\(17\) 1.00000 0.242536
\(18\) 4.84515 1.14201
\(19\) −7.33635 −1.68307 −0.841537 0.540200i \(-0.818349\pi\)
−0.841537 + 0.540200i \(0.818349\pi\)
\(20\) 2.43733 0.545003
\(21\) 1.69842 0.370625
\(22\) −2.65190 −0.565386
\(23\) 4.79280 0.999367 0.499684 0.866208i \(-0.333450\pi\)
0.499684 + 0.866208i \(0.333450\pi\)
\(24\) −8.70974 −1.77787
\(25\) −4.76544 −0.953088
\(26\) −2.70590 −0.530670
\(27\) −5.22783 −1.00610
\(28\) 7.89211 1.49147
\(29\) −6.14051 −1.14026 −0.570132 0.821553i \(-0.693108\pi\)
−0.570132 + 0.821553i \(0.693108\pi\)
\(30\) −1.39098 −0.253957
\(31\) −8.14245 −1.46243 −0.731214 0.682148i \(-0.761046\pi\)
−0.731214 + 0.682148i \(0.761046\pi\)
\(32\) −13.7803 −2.43604
\(33\) 1.08303 0.188531
\(34\) −2.65190 −0.454797
\(35\) 0.759504 0.128380
\(36\) −9.19474 −1.53246
\(37\) 7.46703 1.22757 0.613786 0.789472i \(-0.289646\pi\)
0.613786 + 0.789472i \(0.289646\pi\)
\(38\) 19.4552 3.15606
\(39\) 1.10508 0.176955
\(40\) −3.89485 −0.615830
\(41\) −10.1278 −1.58170 −0.790852 0.612008i \(-0.790362\pi\)
−0.790852 + 0.612008i \(0.790362\pi\)
\(42\) −4.50402 −0.694986
\(43\) 1.00000 0.152499
\(44\) 5.03256 0.758687
\(45\) −0.884863 −0.131908
\(46\) −12.7100 −1.87399
\(47\) 1.41818 0.206863 0.103432 0.994637i \(-0.467018\pi\)
0.103432 + 0.994637i \(0.467018\pi\)
\(48\) 12.1965 1.76042
\(49\) −4.54071 −0.648673
\(50\) 12.6375 1.78721
\(51\) 1.08303 0.151654
\(52\) 5.13504 0.712102
\(53\) 10.8066 1.48441 0.742203 0.670175i \(-0.233781\pi\)
0.742203 + 0.670175i \(0.233781\pi\)
\(54\) 13.8637 1.88661
\(55\) 0.484312 0.0653046
\(56\) −12.6116 −1.68530
\(57\) −7.94547 −1.05240
\(58\) 16.2840 2.13819
\(59\) −1.27321 −0.165758 −0.0828792 0.996560i \(-0.526412\pi\)
−0.0828792 + 0.996560i \(0.526412\pi\)
\(60\) 2.63969 0.340783
\(61\) 5.68853 0.728342 0.364171 0.931332i \(-0.381352\pi\)
0.364171 + 0.931332i \(0.381352\pi\)
\(62\) 21.5929 2.74231
\(63\) −2.86520 −0.360982
\(64\) 14.0210 1.75263
\(65\) 0.494174 0.0612948
\(66\) −2.87208 −0.353528
\(67\) 11.3268 1.38379 0.691893 0.722000i \(-0.256777\pi\)
0.691893 + 0.722000i \(0.256777\pi\)
\(68\) 5.03256 0.610287
\(69\) 5.19073 0.624891
\(70\) −2.01413 −0.240734
\(71\) 4.89737 0.581211 0.290605 0.956843i \(-0.406143\pi\)
0.290605 + 0.956843i \(0.406143\pi\)
\(72\) 14.6932 1.73161
\(73\) 1.41558 0.165682 0.0828408 0.996563i \(-0.473601\pi\)
0.0828408 + 0.996563i \(0.473601\pi\)
\(74\) −19.8018 −2.30191
\(75\) −5.16110 −0.595953
\(76\) −36.9206 −4.23508
\(77\) 1.56821 0.178714
\(78\) −2.93056 −0.331821
\(79\) −8.10888 −0.912320 −0.456160 0.889898i \(-0.650775\pi\)
−0.456160 + 0.889898i \(0.650775\pi\)
\(80\) 5.45409 0.609786
\(81\) −0.180729 −0.0200810
\(82\) 26.8580 2.96597
\(83\) 6.65886 0.730905 0.365452 0.930830i \(-0.380914\pi\)
0.365452 + 0.930830i \(0.380914\pi\)
\(84\) 8.54738 0.932595
\(85\) 0.484312 0.0525310
\(86\) −2.65190 −0.285961
\(87\) −6.65034 −0.712991
\(88\) −8.04203 −0.857284
\(89\) 11.4605 1.21481 0.607405 0.794392i \(-0.292210\pi\)
0.607405 + 0.794392i \(0.292210\pi\)
\(90\) 2.34657 0.247350
\(91\) 1.60015 0.167741
\(92\) 24.1200 2.51469
\(93\) −8.81850 −0.914436
\(94\) −3.76087 −0.387905
\(95\) −3.55308 −0.364538
\(96\) −14.9245 −1.52322
\(97\) 1.82310 0.185107 0.0925537 0.995708i \(-0.470497\pi\)
0.0925537 + 0.995708i \(0.470497\pi\)
\(98\) 12.0415 1.21638
\(99\) −1.82705 −0.183626
\(100\) −23.9824 −2.39824
\(101\) 14.2470 1.41763 0.708813 0.705396i \(-0.249231\pi\)
0.708813 + 0.705396i \(0.249231\pi\)
\(102\) −2.87208 −0.284378
\(103\) −3.92423 −0.386666 −0.193333 0.981133i \(-0.561930\pi\)
−0.193333 + 0.981133i \(0.561930\pi\)
\(104\) −8.20580 −0.804645
\(105\) 0.822563 0.0802740
\(106\) −28.6581 −2.78352
\(107\) 6.86098 0.663276 0.331638 0.943407i \(-0.392399\pi\)
0.331638 + 0.943407i \(0.392399\pi\)
\(108\) −26.3094 −2.53162
\(109\) −2.06549 −0.197838 −0.0989188 0.995096i \(-0.531538\pi\)
−0.0989188 + 0.995096i \(0.531538\pi\)
\(110\) −1.28435 −0.122458
\(111\) 8.08700 0.767584
\(112\) 17.6605 1.66876
\(113\) −12.9132 −1.21477 −0.607386 0.794407i \(-0.707782\pi\)
−0.607386 + 0.794407i \(0.707782\pi\)
\(114\) 21.0706 1.97344
\(115\) 2.32121 0.216454
\(116\) −30.9025 −2.86922
\(117\) −1.86426 −0.172351
\(118\) 3.37643 0.310826
\(119\) 1.56821 0.143758
\(120\) −4.21823 −0.385070
\(121\) 1.00000 0.0909091
\(122\) −15.0854 −1.36577
\(123\) −10.9687 −0.989017
\(124\) −40.9774 −3.67988
\(125\) −4.72952 −0.423021
\(126\) 7.59822 0.676903
\(127\) 12.5242 1.11134 0.555672 0.831402i \(-0.312461\pi\)
0.555672 + 0.831402i \(0.312461\pi\)
\(128\) −9.62157 −0.850435
\(129\) 1.08303 0.0953553
\(130\) −1.31050 −0.114938
\(131\) 9.19874 0.803698 0.401849 0.915706i \(-0.368368\pi\)
0.401849 + 0.915706i \(0.368368\pi\)
\(132\) 5.45040 0.474396
\(133\) −11.5049 −0.997605
\(134\) −30.0375 −2.59484
\(135\) −2.53190 −0.217911
\(136\) −8.04203 −0.689599
\(137\) 20.3360 1.73742 0.868710 0.495322i \(-0.164950\pi\)
0.868710 + 0.495322i \(0.164950\pi\)
\(138\) −13.7653 −1.17178
\(139\) 17.2386 1.46216 0.731081 0.682290i \(-0.239016\pi\)
0.731081 + 0.682290i \(0.239016\pi\)
\(140\) 3.82225 0.323039
\(141\) 1.53593 0.129349
\(142\) −12.9873 −1.08987
\(143\) 1.02036 0.0853271
\(144\) −20.5754 −1.71462
\(145\) −2.97392 −0.246971
\(146\) −3.75399 −0.310682
\(147\) −4.91772 −0.405607
\(148\) 37.5783 3.08891
\(149\) −7.08661 −0.580558 −0.290279 0.956942i \(-0.593748\pi\)
−0.290279 + 0.956942i \(0.593748\pi\)
\(150\) 13.6867 1.11752
\(151\) 4.13116 0.336189 0.168095 0.985771i \(-0.446239\pi\)
0.168095 + 0.985771i \(0.446239\pi\)
\(152\) 58.9991 4.78546
\(153\) −1.82705 −0.147708
\(154\) −4.15873 −0.335120
\(155\) −3.94349 −0.316749
\(156\) 5.56139 0.445267
\(157\) 11.0556 0.882333 0.441167 0.897425i \(-0.354565\pi\)
0.441167 + 0.897425i \(0.354565\pi\)
\(158\) 21.5039 1.71076
\(159\) 11.7039 0.928179
\(160\) −6.67399 −0.527625
\(161\) 7.51612 0.592353
\(162\) 0.479274 0.0376553
\(163\) 18.9901 1.48742 0.743708 0.668504i \(-0.233065\pi\)
0.743708 + 0.668504i \(0.233065\pi\)
\(164\) −50.9690 −3.98001
\(165\) 0.524523 0.0408341
\(166\) −17.6586 −1.37057
\(167\) −15.6790 −1.21328 −0.606640 0.794976i \(-0.707483\pi\)
−0.606640 + 0.794976i \(0.707483\pi\)
\(168\) −13.6587 −1.05379
\(169\) −11.9589 −0.919912
\(170\) −1.28435 −0.0985048
\(171\) 13.4039 1.02502
\(172\) 5.03256 0.383729
\(173\) 13.5295 1.02863 0.514316 0.857601i \(-0.328046\pi\)
0.514316 + 0.857601i \(0.328046\pi\)
\(174\) 17.6360 1.33698
\(175\) −7.47322 −0.564922
\(176\) 11.2615 0.848870
\(177\) −1.37893 −0.103646
\(178\) −30.3921 −2.27798
\(179\) 25.8414 1.93148 0.965739 0.259514i \(-0.0835625\pi\)
0.965739 + 0.259514i \(0.0835625\pi\)
\(180\) −4.45313 −0.331916
\(181\) 17.7521 1.31950 0.659750 0.751485i \(-0.270662\pi\)
0.659750 + 0.751485i \(0.270662\pi\)
\(182\) −4.24342 −0.314543
\(183\) 6.16084 0.455422
\(184\) −38.5438 −2.84149
\(185\) 3.61637 0.265881
\(186\) 23.3858 1.71473
\(187\) 1.00000 0.0731272
\(188\) 7.13709 0.520526
\(189\) −8.19834 −0.596342
\(190\) 9.42241 0.683573
\(191\) 12.6545 0.915647 0.457824 0.889043i \(-0.348629\pi\)
0.457824 + 0.889043i \(0.348629\pi\)
\(192\) 15.1851 1.09589
\(193\) −6.34203 −0.456509 −0.228255 0.973601i \(-0.573302\pi\)
−0.228255 + 0.973601i \(0.573302\pi\)
\(194\) −4.83466 −0.347109
\(195\) 0.535204 0.0383268
\(196\) −22.8514 −1.63224
\(197\) 21.3012 1.51765 0.758823 0.651297i \(-0.225775\pi\)
0.758823 + 0.651297i \(0.225775\pi\)
\(198\) 4.84515 0.344330
\(199\) −15.1294 −1.07249 −0.536247 0.844061i \(-0.680158\pi\)
−0.536247 + 0.844061i \(0.680158\pi\)
\(200\) 38.3238 2.70990
\(201\) 12.2672 0.865262
\(202\) −37.7815 −2.65830
\(203\) −9.62961 −0.675866
\(204\) 5.45040 0.381604
\(205\) −4.90504 −0.342583
\(206\) 10.4066 0.725065
\(207\) −8.75669 −0.608632
\(208\) 11.4909 0.796747
\(209\) −7.33635 −0.507466
\(210\) −2.18135 −0.150528
\(211\) −17.8984 −1.23218 −0.616090 0.787676i \(-0.711284\pi\)
−0.616090 + 0.787676i \(0.711284\pi\)
\(212\) 54.3851 3.73518
\(213\) 5.30399 0.363423
\(214\) −18.1946 −1.24376
\(215\) 0.484312 0.0330298
\(216\) 42.0424 2.86062
\(217\) −12.7691 −0.866822
\(218\) 5.47745 0.370980
\(219\) 1.53312 0.103598
\(220\) 2.43733 0.164325
\(221\) 1.02036 0.0686371
\(222\) −21.4459 −1.43935
\(223\) 15.5531 1.04151 0.520757 0.853705i \(-0.325650\pi\)
0.520757 + 0.853705i \(0.325650\pi\)
\(224\) −21.6105 −1.44391
\(225\) 8.70671 0.580447
\(226\) 34.2445 2.27791
\(227\) 11.9457 0.792863 0.396431 0.918064i \(-0.370249\pi\)
0.396431 + 0.918064i \(0.370249\pi\)
\(228\) −39.9860 −2.64814
\(229\) 9.02160 0.596164 0.298082 0.954540i \(-0.403653\pi\)
0.298082 + 0.954540i \(0.403653\pi\)
\(230\) −6.15561 −0.405889
\(231\) 1.69842 0.111748
\(232\) 49.3821 3.24210
\(233\) −10.0158 −0.656155 −0.328078 0.944651i \(-0.606401\pi\)
−0.328078 + 0.944651i \(0.606401\pi\)
\(234\) 4.94382 0.323187
\(235\) 0.686843 0.0448047
\(236\) −6.40753 −0.417094
\(237\) −8.78213 −0.570461
\(238\) −4.15873 −0.269571
\(239\) 10.3697 0.670762 0.335381 0.942083i \(-0.391135\pi\)
0.335381 + 0.942083i \(0.391135\pi\)
\(240\) 5.90693 0.381291
\(241\) 7.73951 0.498546 0.249273 0.968433i \(-0.419808\pi\)
0.249273 + 0.968433i \(0.419808\pi\)
\(242\) −2.65190 −0.170470
\(243\) 15.4878 0.993540
\(244\) 28.6279 1.83271
\(245\) −2.19912 −0.140497
\(246\) 29.0879 1.85458
\(247\) −7.48574 −0.476306
\(248\) 65.4819 4.15810
\(249\) 7.21173 0.457025
\(250\) 12.5422 0.793239
\(251\) 0.232469 0.0146733 0.00733665 0.999973i \(-0.497665\pi\)
0.00733665 + 0.999973i \(0.497665\pi\)
\(252\) −14.4193 −0.908330
\(253\) 4.79280 0.301321
\(254\) −33.2129 −2.08396
\(255\) 0.524523 0.0328469
\(256\) −2.52660 −0.157912
\(257\) 16.7108 1.04239 0.521196 0.853437i \(-0.325486\pi\)
0.521196 + 0.853437i \(0.325486\pi\)
\(258\) −2.87208 −0.178808
\(259\) 11.7099 0.727616
\(260\) 2.48696 0.154235
\(261\) 11.2190 0.694440
\(262\) −24.3941 −1.50707
\(263\) −21.4264 −1.32121 −0.660604 0.750734i \(-0.729700\pi\)
−0.660604 + 0.750734i \(0.729700\pi\)
\(264\) −8.70974 −0.536048
\(265\) 5.23379 0.321509
\(266\) 30.5099 1.87068
\(267\) 12.4120 0.759604
\(268\) 57.0027 3.48199
\(269\) 8.20255 0.500118 0.250059 0.968231i \(-0.419550\pi\)
0.250059 + 0.968231i \(0.419550\pi\)
\(270\) 6.71434 0.408622
\(271\) −6.08472 −0.369621 −0.184810 0.982774i \(-0.559167\pi\)
−0.184810 + 0.982774i \(0.559167\pi\)
\(272\) 11.2615 0.682830
\(273\) 1.73300 0.104886
\(274\) −53.9289 −3.25796
\(275\) −4.76544 −0.287367
\(276\) 26.1227 1.57240
\(277\) −24.3509 −1.46310 −0.731552 0.681786i \(-0.761204\pi\)
−0.731552 + 0.681786i \(0.761204\pi\)
\(278\) −45.7151 −2.74181
\(279\) 14.8767 0.890643
\(280\) −6.10795 −0.365020
\(281\) 30.4146 1.81438 0.907191 0.420719i \(-0.138222\pi\)
0.907191 + 0.420719i \(0.138222\pi\)
\(282\) −4.07313 −0.242551
\(283\) −6.60928 −0.392881 −0.196440 0.980516i \(-0.562938\pi\)
−0.196440 + 0.980516i \(0.562938\pi\)
\(284\) 24.6463 1.46249
\(285\) −3.84808 −0.227941
\(286\) −2.70590 −0.160003
\(287\) −15.8826 −0.937520
\(288\) 25.1774 1.48359
\(289\) 1.00000 0.0588235
\(290\) 7.88653 0.463113
\(291\) 1.97446 0.115745
\(292\) 7.12401 0.416901
\(293\) 26.9491 1.57439 0.787193 0.616707i \(-0.211534\pi\)
0.787193 + 0.616707i \(0.211534\pi\)
\(294\) 13.0413 0.760583
\(295\) −0.616633 −0.0359018
\(296\) −60.0501 −3.49034
\(297\) −5.22783 −0.303349
\(298\) 18.7930 1.08865
\(299\) 4.89040 0.282819
\(300\) −25.9736 −1.49958
\(301\) 1.56821 0.0903902
\(302\) −10.9554 −0.630413
\(303\) 15.4299 0.886423
\(304\) −82.6185 −4.73849
\(305\) 2.75502 0.157752
\(306\) 4.84515 0.276979
\(307\) 32.9525 1.88070 0.940349 0.340212i \(-0.110499\pi\)
0.940349 + 0.340212i \(0.110499\pi\)
\(308\) 7.89211 0.449695
\(309\) −4.25005 −0.241777
\(310\) 10.4577 0.593959
\(311\) 5.88050 0.333453 0.166726 0.986003i \(-0.446680\pi\)
0.166726 + 0.986003i \(0.446680\pi\)
\(312\) −8.88710 −0.503133
\(313\) −29.2161 −1.65139 −0.825695 0.564117i \(-0.809217\pi\)
−0.825695 + 0.564117i \(0.809217\pi\)
\(314\) −29.3183 −1.65453
\(315\) −1.38765 −0.0781853
\(316\) −40.8084 −2.29565
\(317\) 25.6428 1.44024 0.720121 0.693848i \(-0.244086\pi\)
0.720121 + 0.693848i \(0.244086\pi\)
\(318\) −31.0375 −1.74050
\(319\) −6.14051 −0.343802
\(320\) 6.79054 0.379603
\(321\) 7.43063 0.414737
\(322\) −19.9320 −1.11077
\(323\) −7.33635 −0.408205
\(324\) −0.909527 −0.0505293
\(325\) −4.86248 −0.269722
\(326\) −50.3597 −2.78917
\(327\) −2.23698 −0.123705
\(328\) 81.4484 4.49724
\(329\) 2.22401 0.122614
\(330\) −1.39098 −0.0765710
\(331\) 31.2118 1.71556 0.857779 0.514019i \(-0.171844\pi\)
0.857779 + 0.514019i \(0.171844\pi\)
\(332\) 33.5111 1.83916
\(333\) −13.6426 −0.747612
\(334\) 41.5792 2.27511
\(335\) 5.48570 0.299716
\(336\) 19.1268 1.04345
\(337\) −31.9453 −1.74017 −0.870087 0.492899i \(-0.835937\pi\)
−0.870087 + 0.492899i \(0.835937\pi\)
\(338\) 31.7137 1.72500
\(339\) −13.9853 −0.759580
\(340\) 2.43733 0.132183
\(341\) −8.14245 −0.440938
\(342\) −35.5457 −1.92209
\(343\) −18.0983 −0.977215
\(344\) −8.04203 −0.433597
\(345\) 2.51393 0.135346
\(346\) −35.8790 −1.92887
\(347\) −0.821024 −0.0440749 −0.0220374 0.999757i \(-0.507015\pi\)
−0.0220374 + 0.999757i \(0.507015\pi\)
\(348\) −33.4682 −1.79408
\(349\) −25.0895 −1.34301 −0.671505 0.741000i \(-0.734352\pi\)
−0.671505 + 0.741000i \(0.734352\pi\)
\(350\) 19.8182 1.05933
\(351\) −5.33429 −0.284723
\(352\) −13.7803 −0.734495
\(353\) −8.68853 −0.462444 −0.231222 0.972901i \(-0.574272\pi\)
−0.231222 + 0.972901i \(0.574272\pi\)
\(354\) 3.65677 0.194355
\(355\) 2.37185 0.125885
\(356\) 57.6756 3.05680
\(357\) 1.69842 0.0898897
\(358\) −68.5288 −3.62186
\(359\) 12.1388 0.640660 0.320330 0.947306i \(-0.396206\pi\)
0.320330 + 0.947306i \(0.396206\pi\)
\(360\) 7.11610 0.375051
\(361\) 34.8220 1.83274
\(362\) −47.0766 −2.47429
\(363\) 1.08303 0.0568442
\(364\) 8.05283 0.422083
\(365\) 0.685585 0.0358851
\(366\) −16.3379 −0.853996
\(367\) −11.1331 −0.581141 −0.290571 0.956854i \(-0.593845\pi\)
−0.290571 + 0.956854i \(0.593845\pi\)
\(368\) 53.9742 2.81360
\(369\) 18.5041 0.963284
\(370\) −9.59025 −0.498573
\(371\) 16.9471 0.879850
\(372\) −44.3796 −2.30098
\(373\) −14.6057 −0.756255 −0.378127 0.925754i \(-0.623432\pi\)
−0.378127 + 0.925754i \(0.623432\pi\)
\(374\) −2.65190 −0.137126
\(375\) −5.12220 −0.264509
\(376\) −11.4051 −0.588172
\(377\) −6.26555 −0.322692
\(378\) 21.7412 1.11824
\(379\) 3.50121 0.179845 0.0899226 0.995949i \(-0.471338\pi\)
0.0899226 + 0.995949i \(0.471338\pi\)
\(380\) −17.8811 −0.917281
\(381\) 13.5641 0.694908
\(382\) −33.5584 −1.71700
\(383\) −22.2719 −1.13804 −0.569019 0.822324i \(-0.692677\pi\)
−0.569019 + 0.822324i \(0.692677\pi\)
\(384\) −10.4204 −0.531765
\(385\) 0.759504 0.0387079
\(386\) 16.8184 0.856034
\(387\) −1.82705 −0.0928742
\(388\) 9.17484 0.465782
\(389\) −4.82631 −0.244704 −0.122352 0.992487i \(-0.539044\pi\)
−0.122352 + 0.992487i \(0.539044\pi\)
\(390\) −1.41931 −0.0718694
\(391\) 4.79280 0.242382
\(392\) 36.5166 1.84437
\(393\) 9.96249 0.502541
\(394\) −56.4885 −2.84585
\(395\) −3.92723 −0.197600
\(396\) −9.19474 −0.462053
\(397\) −5.16985 −0.259468 −0.129734 0.991549i \(-0.541412\pi\)
−0.129734 + 0.991549i \(0.541412\pi\)
\(398\) 40.1216 2.01111
\(399\) −12.4602 −0.623789
\(400\) −53.6661 −2.68331
\(401\) 11.5195 0.575256 0.287628 0.957742i \(-0.407133\pi\)
0.287628 + 0.957742i \(0.407133\pi\)
\(402\) −32.5314 −1.62252
\(403\) −8.30826 −0.413864
\(404\) 71.6987 3.56715
\(405\) −0.0875291 −0.00434935
\(406\) 25.5367 1.26737
\(407\) 7.46703 0.370127
\(408\) −8.70974 −0.431197
\(409\) −13.5590 −0.670449 −0.335224 0.942138i \(-0.608812\pi\)
−0.335224 + 0.942138i \(0.608812\pi\)
\(410\) 13.0077 0.642402
\(411\) 22.0244 1.08638
\(412\) −19.7489 −0.972958
\(413\) −1.99667 −0.0982497
\(414\) 23.2218 1.14129
\(415\) 3.22497 0.158307
\(416\) −14.0610 −0.689395
\(417\) 18.6699 0.914270
\(418\) 19.4552 0.951587
\(419\) 1.91395 0.0935028 0.0467514 0.998907i \(-0.485113\pi\)
0.0467514 + 0.998907i \(0.485113\pi\)
\(420\) 4.13960 0.201992
\(421\) 10.6250 0.517832 0.258916 0.965900i \(-0.416635\pi\)
0.258916 + 0.965900i \(0.416635\pi\)
\(422\) 47.4648 2.31055
\(423\) −2.59109 −0.125983
\(424\) −86.9074 −4.22060
\(425\) −4.76544 −0.231158
\(426\) −14.0656 −0.681482
\(427\) 8.92082 0.431709
\(428\) 34.5283 1.66899
\(429\) 1.10508 0.0533538
\(430\) −1.28435 −0.0619367
\(431\) −36.9115 −1.77797 −0.888983 0.457940i \(-0.848588\pi\)
−0.888983 + 0.457940i \(0.848588\pi\)
\(432\) −58.8733 −2.83254
\(433\) 7.31761 0.351662 0.175831 0.984420i \(-0.443739\pi\)
0.175831 + 0.984420i \(0.443739\pi\)
\(434\) 33.8623 1.62544
\(435\) −3.22084 −0.154427
\(436\) −10.3947 −0.497815
\(437\) −35.1616 −1.68201
\(438\) −4.06567 −0.194265
\(439\) −10.9146 −0.520924 −0.260462 0.965484i \(-0.583875\pi\)
−0.260462 + 0.965484i \(0.583875\pi\)
\(440\) −3.89485 −0.185680
\(441\) 8.29612 0.395053
\(442\) −2.70590 −0.128706
\(443\) 22.9347 1.08966 0.544831 0.838546i \(-0.316594\pi\)
0.544831 + 0.838546i \(0.316594\pi\)
\(444\) 40.6983 1.93146
\(445\) 5.55046 0.263117
\(446\) −41.2453 −1.95302
\(447\) −7.67499 −0.363015
\(448\) 21.9879 1.03883
\(449\) 14.4872 0.683693 0.341846 0.939756i \(-0.388948\pi\)
0.341846 + 0.939756i \(0.388948\pi\)
\(450\) −23.0893 −1.08844
\(451\) −10.1278 −0.476902
\(452\) −64.9864 −3.05670
\(453\) 4.47416 0.210214
\(454\) −31.6787 −1.48676
\(455\) 0.774970 0.0363311
\(456\) 63.8977 2.99228
\(457\) −9.74970 −0.456072 −0.228036 0.973653i \(-0.573230\pi\)
−0.228036 + 0.973653i \(0.573230\pi\)
\(458\) −23.9244 −1.11791
\(459\) −5.22783 −0.244014
\(460\) 11.6816 0.544659
\(461\) −6.42711 −0.299340 −0.149670 0.988736i \(-0.547821\pi\)
−0.149670 + 0.988736i \(0.547821\pi\)
\(462\) −4.50402 −0.209546
\(463\) −25.6703 −1.19300 −0.596501 0.802612i \(-0.703443\pi\)
−0.596501 + 0.802612i \(0.703443\pi\)
\(464\) −69.1515 −3.21028
\(465\) −4.27091 −0.198059
\(466\) 26.5608 1.23041
\(467\) −13.8491 −0.640858 −0.320429 0.947272i \(-0.603827\pi\)
−0.320429 + 0.947272i \(0.603827\pi\)
\(468\) −9.38198 −0.433682
\(469\) 17.7628 0.820209
\(470\) −1.82144 −0.0840166
\(471\) 11.9735 0.551711
\(472\) 10.2392 0.471299
\(473\) 1.00000 0.0459800
\(474\) 23.2893 1.06971
\(475\) 34.9609 1.60412
\(476\) 7.89211 0.361734
\(477\) −19.7443 −0.904029
\(478\) −27.4995 −1.25780
\(479\) −23.6330 −1.07982 −0.539910 0.841723i \(-0.681542\pi\)
−0.539910 + 0.841723i \(0.681542\pi\)
\(480\) −7.22811 −0.329917
\(481\) 7.61908 0.347400
\(482\) −20.5244 −0.934860
\(483\) 8.14016 0.370390
\(484\) 5.03256 0.228753
\(485\) 0.882948 0.0400926
\(486\) −41.0719 −1.86306
\(487\) −18.1556 −0.822710 −0.411355 0.911475i \(-0.634944\pi\)
−0.411355 + 0.911475i \(0.634944\pi\)
\(488\) −45.7474 −2.07089
\(489\) 20.5668 0.930061
\(490\) 5.83185 0.263456
\(491\) −23.5022 −1.06064 −0.530321 0.847797i \(-0.677928\pi\)
−0.530321 + 0.847797i \(0.677928\pi\)
\(492\) −55.2008 −2.48864
\(493\) −6.14051 −0.276554
\(494\) 19.8514 0.893157
\(495\) −0.884863 −0.0397716
\(496\) −91.6964 −4.11729
\(497\) 7.68011 0.344500
\(498\) −19.1248 −0.857001
\(499\) −30.8475 −1.38093 −0.690463 0.723368i \(-0.742593\pi\)
−0.690463 + 0.723368i \(0.742593\pi\)
\(500\) −23.8016 −1.06444
\(501\) −16.9808 −0.758648
\(502\) −0.616483 −0.0275150
\(503\) 8.04226 0.358587 0.179293 0.983796i \(-0.442619\pi\)
0.179293 + 0.983796i \(0.442619\pi\)
\(504\) 23.0421 1.02637
\(505\) 6.89998 0.307045
\(506\) −12.7100 −0.565029
\(507\) −12.9518 −0.575208
\(508\) 63.0288 2.79645
\(509\) 9.35402 0.414610 0.207305 0.978276i \(-0.433531\pi\)
0.207305 + 0.978276i \(0.433531\pi\)
\(510\) −1.39098 −0.0615937
\(511\) 2.21994 0.0982042
\(512\) 25.9434 1.14655
\(513\) 38.3532 1.69333
\(514\) −44.3154 −1.95467
\(515\) −1.90055 −0.0837483
\(516\) 5.45040 0.239940
\(517\) 1.41818 0.0623716
\(518\) −31.0534 −1.36441
\(519\) 14.6529 0.643190
\(520\) −3.97417 −0.174279
\(521\) −5.30658 −0.232486 −0.116243 0.993221i \(-0.537085\pi\)
−0.116243 + 0.993221i \(0.537085\pi\)
\(522\) −29.7517 −1.30220
\(523\) 1.93256 0.0845048 0.0422524 0.999107i \(-0.486547\pi\)
0.0422524 + 0.999107i \(0.486547\pi\)
\(524\) 46.2932 2.02233
\(525\) −8.09370 −0.353238
\(526\) 56.8206 2.47750
\(527\) −8.14245 −0.354691
\(528\) 12.1965 0.530786
\(529\) −0.0290886 −0.00126472
\(530\) −13.8795 −0.602886
\(531\) 2.32623 0.100950
\(532\) −57.8993 −2.51025
\(533\) −10.3341 −0.447619
\(534\) −32.9154 −1.42439
\(535\) 3.32286 0.143660
\(536\) −91.0903 −3.93450
\(537\) 27.9870 1.20773
\(538\) −21.7523 −0.937809
\(539\) −4.54071 −0.195582
\(540\) −12.7419 −0.548326
\(541\) −36.2145 −1.55698 −0.778491 0.627656i \(-0.784015\pi\)
−0.778491 + 0.627656i \(0.784015\pi\)
\(542\) 16.1361 0.693103
\(543\) 19.2260 0.825065
\(544\) −13.7803 −0.590827
\(545\) −1.00034 −0.0428498
\(546\) −4.59574 −0.196680
\(547\) 17.5984 0.752454 0.376227 0.926528i \(-0.377221\pi\)
0.376227 + 0.926528i \(0.377221\pi\)
\(548\) 102.342 4.37183
\(549\) −10.3932 −0.443573
\(550\) 12.6375 0.538863
\(551\) 45.0489 1.91915
\(552\) −41.7440 −1.77674
\(553\) −12.7164 −0.540758
\(554\) 64.5761 2.74357
\(555\) 3.91663 0.166252
\(556\) 86.7545 3.67921
\(557\) −27.6812 −1.17289 −0.586444 0.809990i \(-0.699473\pi\)
−0.586444 + 0.809990i \(0.699473\pi\)
\(558\) −39.4514 −1.67011
\(559\) 1.02036 0.0431568
\(560\) 8.55317 0.361437
\(561\) 1.08303 0.0457255
\(562\) −80.6563 −3.40228
\(563\) 27.8477 1.17364 0.586820 0.809718i \(-0.300380\pi\)
0.586820 + 0.809718i \(0.300380\pi\)
\(564\) 7.72966 0.325477
\(565\) −6.25402 −0.263108
\(566\) 17.5271 0.736720
\(567\) −0.283421 −0.0119025
\(568\) −39.3848 −1.65255
\(569\) −13.4866 −0.565386 −0.282693 0.959210i \(-0.591228\pi\)
−0.282693 + 0.959210i \(0.591228\pi\)
\(570\) 10.2047 0.427429
\(571\) −29.9641 −1.25396 −0.626979 0.779036i \(-0.715709\pi\)
−0.626979 + 0.779036i \(0.715709\pi\)
\(572\) 5.13504 0.214707
\(573\) 13.7052 0.572542
\(574\) 42.1190 1.75801
\(575\) −22.8398 −0.952485
\(576\) −25.6171 −1.06738
\(577\) 37.3022 1.55291 0.776456 0.630171i \(-0.217015\pi\)
0.776456 + 0.630171i \(0.217015\pi\)
\(578\) −2.65190 −0.110304
\(579\) −6.86859 −0.285449
\(580\) −14.9664 −0.621447
\(581\) 10.4425 0.433228
\(582\) −5.23607 −0.217042
\(583\) 10.8066 0.447565
\(584\) −11.3842 −0.471081
\(585\) −0.902882 −0.0373296
\(586\) −71.4664 −2.95225
\(587\) −28.8806 −1.19203 −0.596016 0.802973i \(-0.703250\pi\)
−0.596016 + 0.802973i \(0.703250\pi\)
\(588\) −24.7487 −1.02062
\(589\) 59.7359 2.46137
\(590\) 1.63525 0.0673221
\(591\) 23.0698 0.948963
\(592\) 84.0901 3.45608
\(593\) −21.6510 −0.889100 −0.444550 0.895754i \(-0.646636\pi\)
−0.444550 + 0.895754i \(0.646636\pi\)
\(594\) 13.8637 0.568833
\(595\) 0.759504 0.0311366
\(596\) −35.6638 −1.46085
\(597\) −16.3855 −0.670615
\(598\) −12.9688 −0.530335
\(599\) 23.0256 0.940802 0.470401 0.882453i \(-0.344109\pi\)
0.470401 + 0.882453i \(0.344109\pi\)
\(600\) 41.5058 1.69447
\(601\) 0.612719 0.0249933 0.0124967 0.999922i \(-0.496022\pi\)
0.0124967 + 0.999922i \(0.496022\pi\)
\(602\) −4.15873 −0.169497
\(603\) −20.6946 −0.842750
\(604\) 20.7903 0.845946
\(605\) 0.484312 0.0196901
\(606\) −40.9184 −1.66220
\(607\) 5.55922 0.225642 0.112821 0.993615i \(-0.464011\pi\)
0.112821 + 0.993615i \(0.464011\pi\)
\(608\) 101.097 4.10004
\(609\) −10.4291 −0.422610
\(610\) −7.30604 −0.295813
\(611\) 1.44706 0.0585419
\(612\) −9.19474 −0.371675
\(613\) 18.0912 0.730695 0.365347 0.930871i \(-0.380950\pi\)
0.365347 + 0.930871i \(0.380950\pi\)
\(614\) −87.3866 −3.52664
\(615\) −5.31229 −0.214212
\(616\) −12.6116 −0.508136
\(617\) −36.5000 −1.46943 −0.734717 0.678374i \(-0.762685\pi\)
−0.734717 + 0.678374i \(0.762685\pi\)
\(618\) 11.2707 0.453373
\(619\) 39.7950 1.59950 0.799748 0.600336i \(-0.204967\pi\)
0.799748 + 0.600336i \(0.204967\pi\)
\(620\) −19.8458 −0.797028
\(621\) −25.0559 −1.00546
\(622\) −15.5945 −0.625282
\(623\) 17.9725 0.720052
\(624\) 12.4449 0.498195
\(625\) 21.5366 0.861466
\(626\) 77.4780 3.09664
\(627\) −7.94547 −0.317311
\(628\) 55.6380 2.22020
\(629\) 7.46703 0.297730
\(630\) 3.67991 0.146611
\(631\) −13.1475 −0.523394 −0.261697 0.965150i \(-0.584282\pi\)
−0.261697 + 0.965150i \(0.584282\pi\)
\(632\) 65.2118 2.59399
\(633\) −19.3845 −0.770465
\(634\) −68.0020 −2.70071
\(635\) 6.06563 0.240707
\(636\) 58.9005 2.33556
\(637\) −4.63318 −0.183573
\(638\) 16.2840 0.644689
\(639\) −8.94775 −0.353967
\(640\) −4.65984 −0.184196
\(641\) 19.1939 0.758113 0.379056 0.925374i \(-0.376249\pi\)
0.379056 + 0.925374i \(0.376249\pi\)
\(642\) −19.7053 −0.777705
\(643\) −40.2102 −1.58573 −0.792867 0.609395i \(-0.791413\pi\)
−0.792867 + 0.609395i \(0.791413\pi\)
\(644\) 37.8253 1.49053
\(645\) 0.524523 0.0206531
\(646\) 19.4552 0.765456
\(647\) 4.58287 0.180171 0.0900855 0.995934i \(-0.471286\pi\)
0.0900855 + 0.995934i \(0.471286\pi\)
\(648\) 1.45343 0.0570959
\(649\) −1.27321 −0.0499780
\(650\) 12.8948 0.505776
\(651\) −13.8293 −0.542012
\(652\) 95.5686 3.74276
\(653\) 12.2990 0.481298 0.240649 0.970612i \(-0.422640\pi\)
0.240649 + 0.970612i \(0.422640\pi\)
\(654\) 5.93223 0.231969
\(655\) 4.45506 0.174074
\(656\) −114.055 −4.45310
\(657\) −2.58635 −0.100903
\(658\) −5.89785 −0.229922
\(659\) 13.4355 0.523371 0.261686 0.965153i \(-0.415722\pi\)
0.261686 + 0.965153i \(0.415722\pi\)
\(660\) 2.63969 0.102750
\(661\) 17.7966 0.692206 0.346103 0.938196i \(-0.387505\pi\)
0.346103 + 0.938196i \(0.387505\pi\)
\(662\) −82.7706 −3.21697
\(663\) 1.10508 0.0429178
\(664\) −53.5508 −2.07817
\(665\) −5.57198 −0.216072
\(666\) 36.1789 1.40190
\(667\) −29.4302 −1.13954
\(668\) −78.9057 −3.05295
\(669\) 16.8445 0.651245
\(670\) −14.5475 −0.562019
\(671\) 5.68853 0.219603
\(672\) −23.4048 −0.902858
\(673\) 26.6423 1.02699 0.513493 0.858094i \(-0.328351\pi\)
0.513493 + 0.858094i \(0.328351\pi\)
\(674\) 84.7157 3.26313
\(675\) 24.9129 0.958899
\(676\) −60.1837 −2.31476
\(677\) 23.2799 0.894720 0.447360 0.894354i \(-0.352364\pi\)
0.447360 + 0.894354i \(0.352364\pi\)
\(678\) 37.0877 1.42434
\(679\) 2.85900 0.109718
\(680\) −3.89485 −0.149361
\(681\) 12.9375 0.495766
\(682\) 21.5929 0.826837
\(683\) 12.8161 0.490396 0.245198 0.969473i \(-0.421147\pi\)
0.245198 + 0.969473i \(0.421147\pi\)
\(684\) 67.4558 2.57924
\(685\) 9.84895 0.376309
\(686\) 47.9948 1.83245
\(687\) 9.77065 0.372773
\(688\) 11.2615 0.429342
\(689\) 11.0267 0.420084
\(690\) −6.66669 −0.253797
\(691\) 31.9623 1.21590 0.607951 0.793974i \(-0.291992\pi\)
0.607951 + 0.793974i \(0.291992\pi\)
\(692\) 68.0882 2.58833
\(693\) −2.86520 −0.108840
\(694\) 2.17727 0.0826481
\(695\) 8.34888 0.316691
\(696\) 53.4822 2.02724
\(697\) −10.1278 −0.383619
\(698\) 66.5348 2.51838
\(699\) −10.8474 −0.410285
\(700\) −37.6094 −1.42150
\(701\) −36.7874 −1.38944 −0.694720 0.719280i \(-0.744472\pi\)
−0.694720 + 0.719280i \(0.744472\pi\)
\(702\) 14.1460 0.533906
\(703\) −54.7807 −2.06609
\(704\) 14.0210 0.528436
\(705\) 0.743870 0.0280158
\(706\) 23.0411 0.867163
\(707\) 22.3423 0.840267
\(708\) −6.93953 −0.260803
\(709\) 17.7689 0.667324 0.333662 0.942693i \(-0.391716\pi\)
0.333662 + 0.942693i \(0.391716\pi\)
\(710\) −6.28992 −0.236056
\(711\) 14.8153 0.555618
\(712\) −92.1657 −3.45406
\(713\) −39.0251 −1.46150
\(714\) −4.50402 −0.168559
\(715\) 0.494174 0.0184811
\(716\) 130.048 4.86014
\(717\) 11.2307 0.419418
\(718\) −32.1908 −1.20135
\(719\) −18.0141 −0.671811 −0.335906 0.941896i \(-0.609042\pi\)
−0.335906 + 0.941896i \(0.609042\pi\)
\(720\) −9.96491 −0.371370
\(721\) −6.15402 −0.229188
\(722\) −92.3443 −3.43670
\(723\) 8.38210 0.311734
\(724\) 89.3383 3.32023
\(725\) 29.2622 1.08677
\(726\) −2.87208 −0.106593
\(727\) 3.40152 0.126155 0.0630776 0.998009i \(-0.479908\pi\)
0.0630776 + 0.998009i \(0.479908\pi\)
\(728\) −12.8684 −0.476935
\(729\) 17.3158 0.641328
\(730\) −1.81810 −0.0672909
\(731\) 1.00000 0.0369863
\(732\) 31.0048 1.14597
\(733\) 23.0184 0.850205 0.425102 0.905145i \(-0.360238\pi\)
0.425102 + 0.905145i \(0.360238\pi\)
\(734\) 29.5237 1.08974
\(735\) −2.38171 −0.0878507
\(736\) −66.0464 −2.43450
\(737\) 11.3268 0.417227
\(738\) −49.0709 −1.80633
\(739\) −40.3901 −1.48578 −0.742888 0.669416i \(-0.766544\pi\)
−0.742888 + 0.669416i \(0.766544\pi\)
\(740\) 18.1996 0.669031
\(741\) −8.10726 −0.297828
\(742\) −44.9420 −1.64987
\(743\) −15.2934 −0.561059 −0.280530 0.959845i \(-0.590510\pi\)
−0.280530 + 0.959845i \(0.590510\pi\)
\(744\) 70.9187 2.60000
\(745\) −3.43213 −0.125744
\(746\) 38.7328 1.41811
\(747\) −12.1661 −0.445134
\(748\) 5.03256 0.184009
\(749\) 10.7595 0.393142
\(750\) 13.5836 0.496001
\(751\) 12.6008 0.459808 0.229904 0.973213i \(-0.426159\pi\)
0.229904 + 0.973213i \(0.426159\pi\)
\(752\) 15.9709 0.582399
\(753\) 0.251770 0.00917501
\(754\) 16.6156 0.605104
\(755\) 2.00077 0.0728155
\(756\) −41.2586 −1.50056
\(757\) 1.42839 0.0519157 0.0259579 0.999663i \(-0.491736\pi\)
0.0259579 + 0.999663i \(0.491736\pi\)
\(758\) −9.28486 −0.337241
\(759\) 5.19073 0.188412
\(760\) 28.5740 1.03649
\(761\) −29.8787 −1.08310 −0.541550 0.840668i \(-0.682162\pi\)
−0.541550 + 0.840668i \(0.682162\pi\)
\(762\) −35.9705 −1.30307
\(763\) −3.23912 −0.117264
\(764\) 63.6845 2.30402
\(765\) −0.884863 −0.0319923
\(766\) 59.0627 2.13402
\(767\) −1.29914 −0.0469093
\(768\) −2.73637 −0.0987404
\(769\) 27.3343 0.985700 0.492850 0.870114i \(-0.335955\pi\)
0.492850 + 0.870114i \(0.335955\pi\)
\(770\) −2.01413 −0.0725840
\(771\) 18.0983 0.651793
\(772\) −31.9166 −1.14870
\(773\) 16.4424 0.591393 0.295696 0.955282i \(-0.404448\pi\)
0.295696 + 0.955282i \(0.404448\pi\)
\(774\) 4.84515 0.174155
\(775\) 38.8024 1.39382
\(776\) −14.6614 −0.526314
\(777\) 12.6821 0.454969
\(778\) 12.7989 0.458862
\(779\) 74.3014 2.66212
\(780\) 2.69345 0.0964409
\(781\) 4.89737 0.175242
\(782\) −12.7100 −0.454509
\(783\) 32.1015 1.14721
\(784\) −51.1354 −1.82626
\(785\) 5.35436 0.191105
\(786\) −26.4195 −0.942352
\(787\) −33.9183 −1.20906 −0.604528 0.796584i \(-0.706638\pi\)
−0.604528 + 0.796584i \(0.706638\pi\)
\(788\) 107.199 3.81882
\(789\) −23.2054 −0.826134
\(790\) 10.4146 0.370535
\(791\) −20.2506 −0.720029
\(792\) 14.6932 0.522100
\(793\) 5.80437 0.206119
\(794\) 13.7099 0.486547
\(795\) 5.66834 0.201035
\(796\) −76.1395 −2.69869
\(797\) 34.9331 1.23739 0.618697 0.785629i \(-0.287661\pi\)
0.618697 + 0.785629i \(0.287661\pi\)
\(798\) 33.0431 1.16971
\(799\) 1.41818 0.0501717
\(800\) 65.6694 2.32176
\(801\) −20.9389 −0.739840
\(802\) −30.5485 −1.07871
\(803\) 1.41558 0.0499549
\(804\) 61.7355 2.17724
\(805\) 3.64015 0.128298
\(806\) 22.0327 0.776067
\(807\) 8.88359 0.312717
\(808\) −114.575 −4.03072
\(809\) −52.0232 −1.82904 −0.914518 0.404544i \(-0.867430\pi\)
−0.914518 + 0.404544i \(0.867430\pi\)
\(810\) 0.232118 0.00815580
\(811\) −46.4867 −1.63237 −0.816184 0.577792i \(-0.803915\pi\)
−0.816184 + 0.577792i \(0.803915\pi\)
\(812\) −48.4616 −1.70067
\(813\) −6.58992 −0.231119
\(814\) −19.8018 −0.694052
\(815\) 9.19712 0.322161
\(816\) 12.1965 0.426964
\(817\) −7.33635 −0.256666
\(818\) 35.9570 1.25721
\(819\) −2.92355 −0.102157
\(820\) −24.6849 −0.862034
\(821\) 13.2659 0.462982 0.231491 0.972837i \(-0.425640\pi\)
0.231491 + 0.972837i \(0.425640\pi\)
\(822\) −58.4065 −2.03716
\(823\) −47.4929 −1.65550 −0.827748 0.561099i \(-0.810379\pi\)
−0.827748 + 0.561099i \(0.810379\pi\)
\(824\) 31.5588 1.09940
\(825\) −5.16110 −0.179687
\(826\) 5.29496 0.184235
\(827\) 38.7721 1.34824 0.674119 0.738623i \(-0.264524\pi\)
0.674119 + 0.738623i \(0.264524\pi\)
\(828\) −44.0685 −1.53149
\(829\) −43.9338 −1.52588 −0.762942 0.646467i \(-0.776246\pi\)
−0.762942 + 0.646467i \(0.776246\pi\)
\(830\) −8.55228 −0.296854
\(831\) −26.3727 −0.914859
\(832\) 14.3065 0.495989
\(833\) −4.54071 −0.157326
\(834\) −49.5107 −1.71442
\(835\) −7.59355 −0.262786
\(836\) −36.9206 −1.27693
\(837\) 42.5673 1.47134
\(838\) −5.07561 −0.175334
\(839\) 12.1994 0.421170 0.210585 0.977576i \(-0.432463\pi\)
0.210585 + 0.977576i \(0.432463\pi\)
\(840\) −6.61508 −0.228242
\(841\) 8.70581 0.300200
\(842\) −28.1765 −0.971026
\(843\) 32.9398 1.13451
\(844\) −90.0749 −3.10051
\(845\) −5.79182 −0.199245
\(846\) 6.87131 0.236241
\(847\) 1.56821 0.0538844
\(848\) 121.699 4.17917
\(849\) −7.15803 −0.245663
\(850\) 12.6375 0.433461
\(851\) 35.7880 1.22680
\(852\) 26.6926 0.914474
\(853\) −31.2174 −1.06886 −0.534432 0.845211i \(-0.679475\pi\)
−0.534432 + 0.845211i \(0.679475\pi\)
\(854\) −23.6571 −0.809529
\(855\) 6.49166 0.222010
\(856\) −55.1762 −1.88588
\(857\) −30.7427 −1.05015 −0.525075 0.851056i \(-0.675963\pi\)
−0.525075 + 0.851056i \(0.675963\pi\)
\(858\) −2.93056 −0.100048
\(859\) 42.7205 1.45760 0.728802 0.684725i \(-0.240078\pi\)
0.728802 + 0.684725i \(0.240078\pi\)
\(860\) 2.43733 0.0831122
\(861\) −17.2013 −0.586218
\(862\) 97.8856 3.33400
\(863\) 11.2589 0.383259 0.191629 0.981467i \(-0.438623\pi\)
0.191629 + 0.981467i \(0.438623\pi\)
\(864\) 72.0413 2.45089
\(865\) 6.55252 0.222792
\(866\) −19.4055 −0.659427
\(867\) 1.08303 0.0367815
\(868\) −64.2612 −2.18117
\(869\) −8.10888 −0.275075
\(870\) 8.54133 0.289578
\(871\) 11.5574 0.391609
\(872\) 16.6107 0.562509
\(873\) −3.33089 −0.112734
\(874\) 93.2450 3.15406
\(875\) −7.41689 −0.250737
\(876\) 7.71550 0.260683
\(877\) 3.08997 0.104341 0.0521704 0.998638i \(-0.483386\pi\)
0.0521704 + 0.998638i \(0.483386\pi\)
\(878\) 28.9443 0.976824
\(879\) 29.1867 0.984442
\(880\) 5.45409 0.183857
\(881\) −36.8348 −1.24100 −0.620498 0.784208i \(-0.713070\pi\)
−0.620498 + 0.784208i \(0.713070\pi\)
\(882\) −22.0004 −0.740794
\(883\) 1.84452 0.0620730 0.0310365 0.999518i \(-0.490119\pi\)
0.0310365 + 0.999518i \(0.490119\pi\)
\(884\) 5.13504 0.172710
\(885\) −0.667831 −0.0224489
\(886\) −60.8206 −2.04331
\(887\) −10.8252 −0.363476 −0.181738 0.983347i \(-0.558172\pi\)
−0.181738 + 0.983347i \(0.558172\pi\)
\(888\) −65.0359 −2.18246
\(889\) 19.6406 0.658725
\(890\) −14.7192 −0.493390
\(891\) −0.180729 −0.00605464
\(892\) 78.2720 2.62074
\(893\) −10.4043 −0.348166
\(894\) 20.3533 0.680716
\(895\) 12.5153 0.418341
\(896\) −15.0887 −0.504076
\(897\) 5.29643 0.176843
\(898\) −38.4185 −1.28204
\(899\) 49.9988 1.66755
\(900\) 43.8170 1.46057
\(901\) 10.8066 0.360022
\(902\) 26.8580 0.894274
\(903\) 1.69842 0.0565197
\(904\) 103.848 3.45394
\(905\) 8.59753 0.285792
\(906\) −11.8650 −0.394189
\(907\) 25.7796 0.855998 0.427999 0.903779i \(-0.359219\pi\)
0.427999 + 0.903779i \(0.359219\pi\)
\(908\) 60.1173 1.99506
\(909\) −26.0300 −0.863359
\(910\) −2.05514 −0.0681272
\(911\) 27.2784 0.903774 0.451887 0.892075i \(-0.350751\pi\)
0.451887 + 0.892075i \(0.350751\pi\)
\(912\) −89.4781 −2.96291
\(913\) 6.65886 0.220376
\(914\) 25.8552 0.855214
\(915\) 2.98377 0.0986403
\(916\) 45.4017 1.50012
\(917\) 14.4256 0.476374
\(918\) 13.8637 0.457569
\(919\) 33.1425 1.09327 0.546635 0.837371i \(-0.315909\pi\)
0.546635 + 0.837371i \(0.315909\pi\)
\(920\) −18.6672 −0.615441
\(921\) 35.6884 1.17597
\(922\) 17.0440 0.561315
\(923\) 4.99710 0.164481
\(924\) 8.54738 0.281188
\(925\) −35.5837 −1.16998
\(926\) 68.0751 2.23709
\(927\) 7.16976 0.235486
\(928\) 84.6183 2.77773
\(929\) −0.0748777 −0.00245666 −0.00122833 0.999999i \(-0.500391\pi\)
−0.00122833 + 0.999999i \(0.500391\pi\)
\(930\) 11.3260 0.371394
\(931\) 33.3123 1.09176
\(932\) −50.4050 −1.65107
\(933\) 6.36875 0.208503
\(934\) 36.7263 1.20172
\(935\) 0.484312 0.0158387
\(936\) 14.9924 0.490042
\(937\) 60.6074 1.97996 0.989979 0.141214i \(-0.0451007\pi\)
0.989979 + 0.141214i \(0.0451007\pi\)
\(938\) −47.1051 −1.53804
\(939\) −31.6418 −1.03259
\(940\) 3.45658 0.112741
\(941\) 31.7439 1.03482 0.517410 0.855737i \(-0.326896\pi\)
0.517410 + 0.855737i \(0.326896\pi\)
\(942\) −31.7525 −1.03455
\(943\) −48.5407 −1.58070
\(944\) −14.3383 −0.466673
\(945\) −3.97056 −0.129162
\(946\) −2.65190 −0.0862206
\(947\) 43.7339 1.42116 0.710581 0.703616i \(-0.248432\pi\)
0.710581 + 0.703616i \(0.248432\pi\)
\(948\) −44.1966 −1.43544
\(949\) 1.44441 0.0468876
\(950\) −92.7128 −3.00800
\(951\) 27.7718 0.900564
\(952\) −12.6116 −0.408744
\(953\) −38.8015 −1.25690 −0.628452 0.777848i \(-0.716311\pi\)
−0.628452 + 0.777848i \(0.716311\pi\)
\(954\) 52.3598 1.69521
\(955\) 6.12873 0.198321
\(956\) 52.1863 1.68783
\(957\) −6.65034 −0.214975
\(958\) 62.6723 2.02485
\(959\) 31.8911 1.02982
\(960\) 7.35434 0.237360
\(961\) 35.2995 1.13869
\(962\) −20.2050 −0.651436
\(963\) −12.5354 −0.403947
\(964\) 38.9495 1.25448
\(965\) −3.07152 −0.0988758
\(966\) −21.5869 −0.694546
\(967\) 55.5641 1.78682 0.893411 0.449240i \(-0.148305\pi\)
0.893411 + 0.449240i \(0.148305\pi\)
\(968\) −8.04203 −0.258481
\(969\) −7.94547 −0.255245
\(970\) −2.34149 −0.0751806
\(971\) −34.5549 −1.10892 −0.554459 0.832211i \(-0.687075\pi\)
−0.554459 + 0.832211i \(0.687075\pi\)
\(972\) 77.9430 2.50002
\(973\) 27.0338 0.866665
\(974\) 48.1469 1.54273
\(975\) −5.26620 −0.168653
\(976\) 64.0615 2.05056
\(977\) 34.5407 1.10506 0.552528 0.833495i \(-0.313663\pi\)
0.552528 + 0.833495i \(0.313663\pi\)
\(978\) −54.5409 −1.74403
\(979\) 11.4605 0.366279
\(980\) −11.0672 −0.353529
\(981\) 3.77375 0.120487
\(982\) 62.3255 1.98889
\(983\) −30.1136 −0.960476 −0.480238 0.877138i \(-0.659450\pi\)
−0.480238 + 0.877138i \(0.659450\pi\)
\(984\) 88.2109 2.81206
\(985\) 10.3164 0.328708
\(986\) 16.2840 0.518588
\(987\) 2.40866 0.0766686
\(988\) −37.6724 −1.19852
\(989\) 4.79280 0.152402
\(990\) 2.34657 0.0745788
\(991\) −53.3869 −1.69589 −0.847946 0.530083i \(-0.822161\pi\)
−0.847946 + 0.530083i \(0.822161\pi\)
\(992\) 112.206 3.56254
\(993\) 33.8033 1.07271
\(994\) −20.3669 −0.645998
\(995\) −7.32734 −0.232292
\(996\) 36.2934 1.15000
\(997\) 7.11891 0.225458 0.112729 0.993626i \(-0.464041\pi\)
0.112729 + 0.993626i \(0.464041\pi\)
\(998\) 81.8045 2.58948
\(999\) −39.0364 −1.23506
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 \(a_p\))