Properties

Label 8013.2.a.d.1.7
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

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Newspace parameters

Level: \( N \) = \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9841271397\)
Analytic rank: \(0\)
Dimension: \(129\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.59380 q^{2}\) \(+1.00000 q^{3}\) \(+4.72779 q^{4}\) \(+3.19035 q^{5}\) \(-2.59380 q^{6}\) \(-1.98667 q^{7}\) \(-7.07533 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.59380 q^{2}\) \(+1.00000 q^{3}\) \(+4.72779 q^{4}\) \(+3.19035 q^{5}\) \(-2.59380 q^{6}\) \(-1.98667 q^{7}\) \(-7.07533 q^{8}\) \(+1.00000 q^{9}\) \(-8.27513 q^{10}\) \(+5.06836 q^{11}\) \(+4.72779 q^{12}\) \(+0.245801 q^{13}\) \(+5.15303 q^{14}\) \(+3.19035 q^{15}\) \(+8.89640 q^{16}\) \(+4.87352 q^{17}\) \(-2.59380 q^{18}\) \(+0.823783 q^{19}\) \(+15.0833 q^{20}\) \(-1.98667 q^{21}\) \(-13.1463 q^{22}\) \(+1.93066 q^{23}\) \(-7.07533 q^{24}\) \(+5.17835 q^{25}\) \(-0.637557 q^{26}\) \(+1.00000 q^{27}\) \(-9.39256 q^{28}\) \(-3.16980 q^{29}\) \(-8.27513 q^{30}\) \(-3.64138 q^{31}\) \(-8.92480 q^{32}\) \(+5.06836 q^{33}\) \(-12.6409 q^{34}\) \(-6.33818 q^{35}\) \(+4.72779 q^{36}\) \(-4.19585 q^{37}\) \(-2.13673 q^{38}\) \(+0.245801 q^{39}\) \(-22.5728 q^{40}\) \(+9.38947 q^{41}\) \(+5.15303 q^{42}\) \(+12.9096 q^{43}\) \(+23.9621 q^{44}\) \(+3.19035 q^{45}\) \(-5.00773 q^{46}\) \(+0.500259 q^{47}\) \(+8.89640 q^{48}\) \(-3.05313 q^{49}\) \(-13.4316 q^{50}\) \(+4.87352 q^{51}\) \(+1.16209 q^{52}\) \(+1.17465 q^{53}\) \(-2.59380 q^{54}\) \(+16.1699 q^{55}\) \(+14.0564 q^{56}\) \(+0.823783 q^{57}\) \(+8.22181 q^{58}\) \(-7.13919 q^{59}\) \(+15.0833 q^{60}\) \(-1.40681 q^{61}\) \(+9.44500 q^{62}\) \(-1.98667 q^{63}\) \(+5.35633 q^{64}\) \(+0.784191 q^{65}\) \(-13.1463 q^{66}\) \(+11.2667 q^{67}\) \(+23.0410 q^{68}\) \(+1.93066 q^{69}\) \(+16.4400 q^{70}\) \(+8.14403 q^{71}\) \(-7.07533 q^{72}\) \(+16.1711 q^{73}\) \(+10.8832 q^{74}\) \(+5.17835 q^{75}\) \(+3.89467 q^{76}\) \(-10.0692 q^{77}\) \(-0.637557 q^{78}\) \(-3.53457 q^{79}\) \(+28.3826 q^{80}\) \(+1.00000 q^{81}\) \(-24.3544 q^{82}\) \(-15.2846 q^{83}\) \(-9.39256 q^{84}\) \(+15.5483 q^{85}\) \(-33.4848 q^{86}\) \(-3.16980 q^{87}\) \(-35.8603 q^{88}\) \(-10.1431 q^{89}\) \(-8.27513 q^{90}\) \(-0.488325 q^{91}\) \(+9.12773 q^{92}\) \(-3.64138 q^{93}\) \(-1.29757 q^{94}\) \(+2.62816 q^{95}\) \(-8.92480 q^{96}\) \(+2.80629 q^{97}\) \(+7.91921 q^{98}\) \(+5.06836 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut 41q^{10} \) \(\mathstrut +\mathstrut 51q^{11} \) \(\mathstrut +\mathstrut 151q^{12} \) \(\mathstrut +\mathstrut 56q^{13} \) \(\mathstrut +\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 195q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 15q^{18} \) \(\mathstrut +\mathstrut 93q^{19} \) \(\mathstrut +\mathstrut 44q^{20} \) \(\mathstrut +\mathstrut 61q^{21} \) \(\mathstrut +\mathstrut 46q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 42q^{24} \) \(\mathstrut +\mathstrut 193q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut 129q^{27} \) \(\mathstrut +\mathstrut 145q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 41q^{30} \) \(\mathstrut +\mathstrut 67q^{31} \) \(\mathstrut +\mathstrut 89q^{32} \) \(\mathstrut +\mathstrut 51q^{33} \) \(\mathstrut +\mathstrut 73q^{34} \) \(\mathstrut +\mathstrut 56q^{35} \) \(\mathstrut +\mathstrut 151q^{36} \) \(\mathstrut +\mathstrut 95q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 103q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 5q^{42} \) \(\mathstrut +\mathstrut 150q^{43} \) \(\mathstrut +\mathstrut 69q^{44} \) \(\mathstrut +\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 53q^{47} \) \(\mathstrut +\mathstrut 195q^{48} \) \(\mathstrut +\mathstrut 240q^{49} \) \(\mathstrut +\mathstrut 17q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 124q^{52} \) \(\mathstrut +\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut 15q^{54} \) \(\mathstrut +\mathstrut 66q^{55} \) \(\mathstrut -\mathstrut 17q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 57q^{58} \) \(\mathstrut +\mathstrut 49q^{59} \) \(\mathstrut +\mathstrut 44q^{60} \) \(\mathstrut +\mathstrut 113q^{61} \) \(\mathstrut +\mathstrut 27q^{62} \) \(\mathstrut +\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 262q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 46q^{66} \) \(\mathstrut +\mathstrut 185q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 50q^{69} \) \(\mathstrut +\mathstrut 25q^{70} \) \(\mathstrut +\mathstrut 41q^{71} \) \(\mathstrut +\mathstrut 42q^{72} \) \(\mathstrut +\mathstrut 153q^{73} \) \(\mathstrut -\mathstrut q^{74} \) \(\mathstrut +\mathstrut 193q^{75} \) \(\mathstrut +\mathstrut 190q^{76} \) \(\mathstrut +\mathstrut 39q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 101q^{79} \) \(\mathstrut +\mathstrut 48q^{80} \) \(\mathstrut +\mathstrut 129q^{81} \) \(\mathstrut +\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 162q^{83} \) \(\mathstrut +\mathstrut 145q^{84} \) \(\mathstrut +\mathstrut 99q^{85} \) \(\mathstrut +\mathstrut 13q^{86} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 86q^{88} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 117q^{91} \) \(\mathstrut +\mathstrut 56q^{92} \) \(\mathstrut +\mathstrut 67q^{93} \) \(\mathstrut +\mathstrut 49q^{94} \) \(\mathstrut +\mathstrut 71q^{95} \) \(\mathstrut +\mathstrut 89q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut +\mathstrut 40q^{98} \) \(\mathstrut +\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59380 −1.83409 −0.917046 0.398781i \(-0.869433\pi\)
−0.917046 + 0.398781i \(0.869433\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.72779 2.36389
\(5\) 3.19035 1.42677 0.713384 0.700773i \(-0.247161\pi\)
0.713384 + 0.700773i \(0.247161\pi\)
\(6\) −2.59380 −1.05891
\(7\) −1.98667 −0.750892 −0.375446 0.926844i \(-0.622510\pi\)
−0.375446 + 0.926844i \(0.622510\pi\)
\(8\) −7.07533 −2.50151
\(9\) 1.00000 0.333333
\(10\) −8.27513 −2.61683
\(11\) 5.06836 1.52817 0.764084 0.645116i \(-0.223191\pi\)
0.764084 + 0.645116i \(0.223191\pi\)
\(12\) 4.72779 1.36479
\(13\) 0.245801 0.0681728 0.0340864 0.999419i \(-0.489148\pi\)
0.0340864 + 0.999419i \(0.489148\pi\)
\(14\) 5.15303 1.37720
\(15\) 3.19035 0.823745
\(16\) 8.89640 2.22410
\(17\) 4.87352 1.18200 0.591001 0.806671i \(-0.298733\pi\)
0.591001 + 0.806671i \(0.298733\pi\)
\(18\) −2.59380 −0.611364
\(19\) 0.823783 0.188989 0.0944944 0.995525i \(-0.469877\pi\)
0.0944944 + 0.995525i \(0.469877\pi\)
\(20\) 15.0833 3.37273
\(21\) −1.98667 −0.433527
\(22\) −13.1463 −2.80280
\(23\) 1.93066 0.402570 0.201285 0.979533i \(-0.435488\pi\)
0.201285 + 0.979533i \(0.435488\pi\)
\(24\) −7.07533 −1.44425
\(25\) 5.17835 1.03567
\(26\) −0.637557 −0.125035
\(27\) 1.00000 0.192450
\(28\) −9.39256 −1.77503
\(29\) −3.16980 −0.588616 −0.294308 0.955711i \(-0.595089\pi\)
−0.294308 + 0.955711i \(0.595089\pi\)
\(30\) −8.27513 −1.51082
\(31\) −3.64138 −0.654011 −0.327006 0.945022i \(-0.606040\pi\)
−0.327006 + 0.945022i \(0.606040\pi\)
\(32\) −8.92480 −1.57770
\(33\) 5.06836 0.882289
\(34\) −12.6409 −2.16790
\(35\) −6.33818 −1.07135
\(36\) 4.72779 0.787965
\(37\) −4.19585 −0.689793 −0.344896 0.938641i \(-0.612086\pi\)
−0.344896 + 0.938641i \(0.612086\pi\)
\(38\) −2.13673 −0.346623
\(39\) 0.245801 0.0393596
\(40\) −22.5728 −3.56907
\(41\) 9.38947 1.46639 0.733194 0.680019i \(-0.238029\pi\)
0.733194 + 0.680019i \(0.238029\pi\)
\(42\) 5.15303 0.795129
\(43\) 12.9096 1.96869 0.984345 0.176254i \(-0.0563981\pi\)
0.984345 + 0.176254i \(0.0563981\pi\)
\(44\) 23.9621 3.61243
\(45\) 3.19035 0.475590
\(46\) −5.00773 −0.738350
\(47\) 0.500259 0.0729702 0.0364851 0.999334i \(-0.488384\pi\)
0.0364851 + 0.999334i \(0.488384\pi\)
\(48\) 8.89640 1.28408
\(49\) −3.05313 −0.436162
\(50\) −13.4316 −1.89951
\(51\) 4.87352 0.682430
\(52\) 1.16209 0.161153
\(53\) 1.17465 0.161351 0.0806756 0.996740i \(-0.474292\pi\)
0.0806756 + 0.996740i \(0.474292\pi\)
\(54\) −2.59380 −0.352971
\(55\) 16.1699 2.18034
\(56\) 14.0564 1.87836
\(57\) 0.823783 0.109113
\(58\) 8.22181 1.07958
\(59\) −7.13919 −0.929444 −0.464722 0.885457i \(-0.653846\pi\)
−0.464722 + 0.885457i \(0.653846\pi\)
\(60\) 15.0833 1.94725
\(61\) −1.40681 −0.180123 −0.0900617 0.995936i \(-0.528706\pi\)
−0.0900617 + 0.995936i \(0.528706\pi\)
\(62\) 9.44500 1.19952
\(63\) −1.98667 −0.250297
\(64\) 5.35633 0.669541
\(65\) 0.784191 0.0972669
\(66\) −13.1463 −1.61820
\(67\) 11.2667 1.37645 0.688223 0.725499i \(-0.258391\pi\)
0.688223 + 0.725499i \(0.258391\pi\)
\(68\) 23.0410 2.79413
\(69\) 1.93066 0.232424
\(70\) 16.4400 1.96495
\(71\) 8.14403 0.966519 0.483259 0.875477i \(-0.339453\pi\)
0.483259 + 0.875477i \(0.339453\pi\)
\(72\) −7.07533 −0.833835
\(73\) 16.1711 1.89269 0.946344 0.323161i \(-0.104745\pi\)
0.946344 + 0.323161i \(0.104745\pi\)
\(74\) 10.8832 1.26514
\(75\) 5.17835 0.597944
\(76\) 3.89467 0.446750
\(77\) −10.0692 −1.14749
\(78\) −0.637557 −0.0721891
\(79\) −3.53457 −0.397671 −0.198835 0.980033i \(-0.563716\pi\)
−0.198835 + 0.980033i \(0.563716\pi\)
\(80\) 28.3826 3.17328
\(81\) 1.00000 0.111111
\(82\) −24.3544 −2.68949
\(83\) −15.2846 −1.67770 −0.838852 0.544360i \(-0.816772\pi\)
−0.838852 + 0.544360i \(0.816772\pi\)
\(84\) −9.39256 −1.02481
\(85\) 15.5483 1.68644
\(86\) −33.4848 −3.61076
\(87\) −3.16980 −0.339838
\(88\) −35.8603 −3.82272
\(89\) −10.1431 −1.07517 −0.537586 0.843209i \(-0.680663\pi\)
−0.537586 + 0.843209i \(0.680663\pi\)
\(90\) −8.27513 −0.872275
\(91\) −0.488325 −0.0511904
\(92\) 9.12773 0.951632
\(93\) −3.64138 −0.377594
\(94\) −1.29757 −0.133834
\(95\) 2.62816 0.269643
\(96\) −8.92480 −0.910883
\(97\) 2.80629 0.284936 0.142468 0.989799i \(-0.454496\pi\)
0.142468 + 0.989799i \(0.454496\pi\)
\(98\) 7.91921 0.799961
\(99\) 5.06836 0.509390
\(100\) 24.4821 2.44821
\(101\) 1.18833 0.118243 0.0591216 0.998251i \(-0.481170\pi\)
0.0591216 + 0.998251i \(0.481170\pi\)
\(102\) −12.6409 −1.25164
\(103\) −3.87228 −0.381547 −0.190773 0.981634i \(-0.561100\pi\)
−0.190773 + 0.981634i \(0.561100\pi\)
\(104\) −1.73912 −0.170535
\(105\) −6.33818 −0.618543
\(106\) −3.04681 −0.295933
\(107\) −3.55642 −0.343812 −0.171906 0.985113i \(-0.554993\pi\)
−0.171906 + 0.985113i \(0.554993\pi\)
\(108\) 4.72779 0.454932
\(109\) −8.09175 −0.775049 −0.387524 0.921859i \(-0.626670\pi\)
−0.387524 + 0.921859i \(0.626670\pi\)
\(110\) −41.9414 −3.99895
\(111\) −4.19585 −0.398252
\(112\) −17.6742 −1.67006
\(113\) −3.85557 −0.362702 −0.181351 0.983418i \(-0.558047\pi\)
−0.181351 + 0.983418i \(0.558047\pi\)
\(114\) −2.13673 −0.200123
\(115\) 6.15947 0.574374
\(116\) −14.9861 −1.39143
\(117\) 0.245801 0.0227243
\(118\) 18.5176 1.70469
\(119\) −9.68209 −0.887556
\(120\) −22.5728 −2.06060
\(121\) 14.6883 1.33530
\(122\) 3.64898 0.330363
\(123\) 9.38947 0.846620
\(124\) −17.2157 −1.54601
\(125\) 0.568991 0.0508921
\(126\) 5.15303 0.459068
\(127\) 13.0579 1.15870 0.579350 0.815079i \(-0.303307\pi\)
0.579350 + 0.815079i \(0.303307\pi\)
\(128\) 3.95636 0.349697
\(129\) 12.9096 1.13662
\(130\) −2.03403 −0.178396
\(131\) −1.51727 −0.132564 −0.0662820 0.997801i \(-0.521114\pi\)
−0.0662820 + 0.997801i \(0.521114\pi\)
\(132\) 23.9621 2.08564
\(133\) −1.63659 −0.141910
\(134\) −29.2235 −2.52453
\(135\) 3.19035 0.274582
\(136\) −34.4818 −2.95679
\(137\) −5.24947 −0.448492 −0.224246 0.974533i \(-0.571992\pi\)
−0.224246 + 0.974533i \(0.571992\pi\)
\(138\) −5.00773 −0.426286
\(139\) 9.48475 0.804486 0.402243 0.915533i \(-0.368231\pi\)
0.402243 + 0.915533i \(0.368231\pi\)
\(140\) −29.9656 −2.53255
\(141\) 0.500259 0.0421294
\(142\) −21.1240 −1.77268
\(143\) 1.24581 0.104180
\(144\) 8.89640 0.741366
\(145\) −10.1128 −0.839819
\(146\) −41.9447 −3.47136
\(147\) −3.05313 −0.251818
\(148\) −19.8371 −1.63060
\(149\) 8.08300 0.662185 0.331093 0.943598i \(-0.392583\pi\)
0.331093 + 0.943598i \(0.392583\pi\)
\(150\) −13.4316 −1.09668
\(151\) 3.82291 0.311104 0.155552 0.987828i \(-0.450284\pi\)
0.155552 + 0.987828i \(0.450284\pi\)
\(152\) −5.82854 −0.472757
\(153\) 4.87352 0.394001
\(154\) 26.1174 2.10460
\(155\) −11.6173 −0.933123
\(156\) 1.16209 0.0930419
\(157\) 7.71216 0.615497 0.307749 0.951468i \(-0.400424\pi\)
0.307749 + 0.951468i \(0.400424\pi\)
\(158\) 9.16797 0.729364
\(159\) 1.17465 0.0931561
\(160\) −28.4732 −2.25101
\(161\) −3.83558 −0.302286
\(162\) −2.59380 −0.203788
\(163\) −4.49641 −0.352186 −0.176093 0.984374i \(-0.556346\pi\)
−0.176093 + 0.984374i \(0.556346\pi\)
\(164\) 44.3914 3.46639
\(165\) 16.1699 1.25882
\(166\) 39.6452 3.07706
\(167\) −1.82265 −0.141041 −0.0705205 0.997510i \(-0.522466\pi\)
−0.0705205 + 0.997510i \(0.522466\pi\)
\(168\) 14.0564 1.08447
\(169\) −12.9396 −0.995352
\(170\) −40.3290 −3.09309
\(171\) 0.823783 0.0629963
\(172\) 61.0336 4.65377
\(173\) −23.5027 −1.78688 −0.893440 0.449183i \(-0.851715\pi\)
−0.893440 + 0.449183i \(0.851715\pi\)
\(174\) 8.22181 0.623294
\(175\) −10.2877 −0.777675
\(176\) 45.0902 3.39880
\(177\) −7.13919 −0.536615
\(178\) 26.3093 1.97196
\(179\) 8.88872 0.664374 0.332187 0.943213i \(-0.392213\pi\)
0.332187 + 0.943213i \(0.392213\pi\)
\(180\) 15.0833 1.12424
\(181\) −7.96963 −0.592378 −0.296189 0.955129i \(-0.595716\pi\)
−0.296189 + 0.955129i \(0.595716\pi\)
\(182\) 1.26662 0.0938879
\(183\) −1.40681 −0.103994
\(184\) −13.6600 −1.00703
\(185\) −13.3862 −0.984175
\(186\) 9.44500 0.692541
\(187\) 24.7008 1.80630
\(188\) 2.36512 0.172494
\(189\) −1.98667 −0.144509
\(190\) −6.81691 −0.494551
\(191\) 10.9738 0.794036 0.397018 0.917811i \(-0.370045\pi\)
0.397018 + 0.917811i \(0.370045\pi\)
\(192\) 5.35633 0.386560
\(193\) 14.2303 1.02432 0.512160 0.858890i \(-0.328845\pi\)
0.512160 + 0.858890i \(0.328845\pi\)
\(194\) −7.27895 −0.522598
\(195\) 0.784191 0.0561571
\(196\) −14.4346 −1.03104
\(197\) 26.3142 1.87481 0.937406 0.348239i \(-0.113220\pi\)
0.937406 + 0.348239i \(0.113220\pi\)
\(198\) −13.1463 −0.934267
\(199\) −11.8744 −0.841755 −0.420878 0.907117i \(-0.638278\pi\)
−0.420878 + 0.907117i \(0.638278\pi\)
\(200\) −36.6385 −2.59073
\(201\) 11.2667 0.794691
\(202\) −3.08229 −0.216869
\(203\) 6.29735 0.441987
\(204\) 23.0410 1.61319
\(205\) 29.9557 2.09220
\(206\) 10.0439 0.699792
\(207\) 1.93066 0.134190
\(208\) 2.18674 0.151623
\(209\) 4.17523 0.288807
\(210\) 16.4400 1.13447
\(211\) −4.95086 −0.340831 −0.170416 0.985372i \(-0.554511\pi\)
−0.170416 + 0.985372i \(0.554511\pi\)
\(212\) 5.55351 0.381417
\(213\) 8.14403 0.558020
\(214\) 9.22464 0.630583
\(215\) 41.1860 2.80886
\(216\) −7.07533 −0.481415
\(217\) 7.23423 0.491091
\(218\) 20.9884 1.42151
\(219\) 16.1711 1.09274
\(220\) 76.4477 5.15410
\(221\) 1.19791 0.0805805
\(222\) 10.8832 0.730431
\(223\) −1.59303 −0.106677 −0.0533386 0.998576i \(-0.516986\pi\)
−0.0533386 + 0.998576i \(0.516986\pi\)
\(224\) 17.7306 1.18468
\(225\) 5.17835 0.345223
\(226\) 10.0006 0.665229
\(227\) −25.9749 −1.72401 −0.862007 0.506896i \(-0.830793\pi\)
−0.862007 + 0.506896i \(0.830793\pi\)
\(228\) 3.89467 0.257931
\(229\) 20.9223 1.38259 0.691293 0.722575i \(-0.257041\pi\)
0.691293 + 0.722575i \(0.257041\pi\)
\(230\) −15.9764 −1.05345
\(231\) −10.0692 −0.662503
\(232\) 22.4273 1.47243
\(233\) 29.5122 1.93341 0.966703 0.255901i \(-0.0823720\pi\)
0.966703 + 0.255901i \(0.0823720\pi\)
\(234\) −0.637557 −0.0416784
\(235\) 1.59600 0.104112
\(236\) −33.7526 −2.19711
\(237\) −3.53457 −0.229595
\(238\) 25.1134 1.62786
\(239\) 17.1530 1.10954 0.554769 0.832005i \(-0.312807\pi\)
0.554769 + 0.832005i \(0.312807\pi\)
\(240\) 28.3826 1.83209
\(241\) 2.52599 0.162713 0.0813565 0.996685i \(-0.474075\pi\)
0.0813565 + 0.996685i \(0.474075\pi\)
\(242\) −38.0985 −2.44906
\(243\) 1.00000 0.0641500
\(244\) −6.65109 −0.425793
\(245\) −9.74057 −0.622302
\(246\) −24.3544 −1.55278
\(247\) 0.202486 0.0128839
\(248\) 25.7640 1.63601
\(249\) −15.2846 −0.968622
\(250\) −1.47585 −0.0933409
\(251\) −14.5430 −0.917945 −0.458973 0.888450i \(-0.651782\pi\)
−0.458973 + 0.888450i \(0.651782\pi\)
\(252\) −9.39256 −0.591676
\(253\) 9.78526 0.615194
\(254\) −33.8695 −2.12516
\(255\) 15.5483 0.973669
\(256\) −20.9747 −1.31092
\(257\) −8.04735 −0.501980 −0.250990 0.967990i \(-0.580756\pi\)
−0.250990 + 0.967990i \(0.580756\pi\)
\(258\) −33.4848 −2.08467
\(259\) 8.33577 0.517960
\(260\) 3.70749 0.229929
\(261\) −3.16980 −0.196205
\(262\) 3.93548 0.243135
\(263\) −3.75214 −0.231367 −0.115683 0.993286i \(-0.536906\pi\)
−0.115683 + 0.993286i \(0.536906\pi\)
\(264\) −35.8603 −2.20705
\(265\) 3.74756 0.230211
\(266\) 4.24498 0.260276
\(267\) −10.1431 −0.620750
\(268\) 53.2665 3.25377
\(269\) 4.71612 0.287547 0.143773 0.989611i \(-0.454076\pi\)
0.143773 + 0.989611i \(0.454076\pi\)
\(270\) −8.27513 −0.503608
\(271\) −25.8057 −1.56759 −0.783794 0.621021i \(-0.786718\pi\)
−0.783794 + 0.621021i \(0.786718\pi\)
\(272\) 43.3568 2.62889
\(273\) −0.488325 −0.0295548
\(274\) 13.6161 0.822576
\(275\) 26.2457 1.58268
\(276\) 9.12773 0.549425
\(277\) −17.4050 −1.04577 −0.522883 0.852404i \(-0.675144\pi\)
−0.522883 + 0.852404i \(0.675144\pi\)
\(278\) −24.6015 −1.47550
\(279\) −3.64138 −0.218004
\(280\) 44.8447 2.67999
\(281\) −18.8805 −1.12631 −0.563157 0.826350i \(-0.690413\pi\)
−0.563157 + 0.826350i \(0.690413\pi\)
\(282\) −1.29757 −0.0772691
\(283\) 13.8879 0.825549 0.412775 0.910833i \(-0.364560\pi\)
0.412775 + 0.910833i \(0.364560\pi\)
\(284\) 38.5032 2.28475
\(285\) 2.62816 0.155679
\(286\) −3.23137 −0.191075
\(287\) −18.6538 −1.10110
\(288\) −8.92480 −0.525899
\(289\) 6.75122 0.397130
\(290\) 26.2305 1.54031
\(291\) 2.80629 0.164508
\(292\) 76.4537 4.47411
\(293\) −3.75980 −0.219650 −0.109825 0.993951i \(-0.535029\pi\)
−0.109825 + 0.993951i \(0.535029\pi\)
\(294\) 7.91921 0.461858
\(295\) −22.7765 −1.32610
\(296\) 29.6870 1.72552
\(297\) 5.06836 0.294096
\(298\) −20.9657 −1.21451
\(299\) 0.474556 0.0274443
\(300\) 24.4821 1.41348
\(301\) −25.6471 −1.47827
\(302\) −9.91585 −0.570593
\(303\) 1.18833 0.0682678
\(304\) 7.32870 0.420330
\(305\) −4.48822 −0.256995
\(306\) −12.6409 −0.722634
\(307\) 30.5207 1.74191 0.870955 0.491363i \(-0.163501\pi\)
0.870955 + 0.491363i \(0.163501\pi\)
\(308\) −47.6049 −2.71254
\(309\) −3.87228 −0.220286
\(310\) 30.1329 1.71143
\(311\) 2.13835 0.121254 0.0606272 0.998160i \(-0.480690\pi\)
0.0606272 + 0.998160i \(0.480690\pi\)
\(312\) −1.73912 −0.0984583
\(313\) −18.0403 −1.01970 −0.509850 0.860263i \(-0.670299\pi\)
−0.509850 + 0.860263i \(0.670299\pi\)
\(314\) −20.0038 −1.12888
\(315\) −6.33818 −0.357116
\(316\) −16.7107 −0.940051
\(317\) −5.53079 −0.310640 −0.155320 0.987864i \(-0.549641\pi\)
−0.155320 + 0.987864i \(0.549641\pi\)
\(318\) −3.04681 −0.170857
\(319\) −16.0657 −0.899505
\(320\) 17.0886 0.955280
\(321\) −3.55642 −0.198500
\(322\) 9.94872 0.554420
\(323\) 4.01473 0.223385
\(324\) 4.72779 0.262655
\(325\) 1.27284 0.0706045
\(326\) 11.6628 0.645942
\(327\) −8.09175 −0.447475
\(328\) −66.4336 −3.66818
\(329\) −0.993850 −0.0547927
\(330\) −41.9414 −2.30880
\(331\) 11.8230 0.649851 0.324926 0.945740i \(-0.394661\pi\)
0.324926 + 0.945740i \(0.394661\pi\)
\(332\) −72.2623 −3.96591
\(333\) −4.19585 −0.229931
\(334\) 4.72759 0.258682
\(335\) 35.9447 1.96387
\(336\) −17.6742 −0.964208
\(337\) 2.77650 0.151246 0.0756229 0.997136i \(-0.475905\pi\)
0.0756229 + 0.997136i \(0.475905\pi\)
\(338\) 33.5627 1.82557
\(339\) −3.85557 −0.209406
\(340\) 73.5088 3.98658
\(341\) −18.4558 −0.999440
\(342\) −2.13673 −0.115541
\(343\) 19.9723 1.07840
\(344\) −91.3394 −4.92469
\(345\) 6.15947 0.331615
\(346\) 60.9613 3.27730
\(347\) −1.62885 −0.0874413 −0.0437207 0.999044i \(-0.513921\pi\)
−0.0437207 + 0.999044i \(0.513921\pi\)
\(348\) −14.9861 −0.803340
\(349\) −14.8821 −0.796620 −0.398310 0.917251i \(-0.630403\pi\)
−0.398310 + 0.917251i \(0.630403\pi\)
\(350\) 26.6842 1.42633
\(351\) 0.245801 0.0131199
\(352\) −45.2341 −2.41099
\(353\) 10.2288 0.544426 0.272213 0.962237i \(-0.412245\pi\)
0.272213 + 0.962237i \(0.412245\pi\)
\(354\) 18.5176 0.984201
\(355\) 25.9823 1.37900
\(356\) −47.9546 −2.54159
\(357\) −9.68209 −0.512431
\(358\) −23.0555 −1.21852
\(359\) 19.8878 1.04964 0.524820 0.851213i \(-0.324133\pi\)
0.524820 + 0.851213i \(0.324133\pi\)
\(360\) −22.5728 −1.18969
\(361\) −18.3214 −0.964283
\(362\) 20.6716 1.08648
\(363\) 14.6883 0.770936
\(364\) −2.30870 −0.121009
\(365\) 51.5916 2.70043
\(366\) 3.64898 0.190735
\(367\) 22.7948 1.18988 0.594941 0.803770i \(-0.297176\pi\)
0.594941 + 0.803770i \(0.297176\pi\)
\(368\) 17.1759 0.895355
\(369\) 9.38947 0.488796
\(370\) 34.7212 1.80507
\(371\) −2.33365 −0.121157
\(372\) −17.2157 −0.892591
\(373\) 31.6897 1.64083 0.820414 0.571770i \(-0.193743\pi\)
0.820414 + 0.571770i \(0.193743\pi\)
\(374\) −64.0688 −3.31292
\(375\) 0.568991 0.0293826
\(376\) −3.53949 −0.182535
\(377\) −0.779138 −0.0401276
\(378\) 5.15303 0.265043
\(379\) 24.9493 1.28156 0.640779 0.767725i \(-0.278611\pi\)
0.640779 + 0.767725i \(0.278611\pi\)
\(380\) 12.4254 0.637408
\(381\) 13.0579 0.668975
\(382\) −28.4638 −1.45633
\(383\) −31.0206 −1.58508 −0.792539 0.609821i \(-0.791241\pi\)
−0.792539 + 0.609821i \(0.791241\pi\)
\(384\) 3.95636 0.201897
\(385\) −32.1242 −1.63720
\(386\) −36.9106 −1.87870
\(387\) 12.9096 0.656230
\(388\) 13.2675 0.673557
\(389\) 8.75417 0.443854 0.221927 0.975063i \(-0.428765\pi\)
0.221927 + 0.975063i \(0.428765\pi\)
\(390\) −2.03403 −0.102997
\(391\) 9.40909 0.475838
\(392\) 21.6019 1.09106
\(393\) −1.51727 −0.0765359
\(394\) −68.2538 −3.43858
\(395\) −11.2765 −0.567384
\(396\) 23.9621 1.20414
\(397\) −18.7909 −0.943089 −0.471544 0.881842i \(-0.656303\pi\)
−0.471544 + 0.881842i \(0.656303\pi\)
\(398\) 30.7998 1.54386
\(399\) −1.63659 −0.0819319
\(400\) 46.0686 2.30343
\(401\) −2.82244 −0.140946 −0.0704730 0.997514i \(-0.522451\pi\)
−0.0704730 + 0.997514i \(0.522451\pi\)
\(402\) −29.2235 −1.45754
\(403\) −0.895054 −0.0445858
\(404\) 5.61817 0.279514
\(405\) 3.19035 0.158530
\(406\) −16.3340 −0.810645
\(407\) −21.2661 −1.05412
\(408\) −34.4818 −1.70710
\(409\) −29.8231 −1.47466 −0.737329 0.675534i \(-0.763913\pi\)
−0.737329 + 0.675534i \(0.763913\pi\)
\(410\) −77.6991 −3.83728
\(411\) −5.24947 −0.258937
\(412\) −18.3073 −0.901936
\(413\) 14.1832 0.697911
\(414\) −5.00773 −0.246117
\(415\) −48.7633 −2.39369
\(416\) −2.19372 −0.107556
\(417\) 9.48475 0.464470
\(418\) −10.8297 −0.529698
\(419\) −29.3549 −1.43408 −0.717042 0.697030i \(-0.754504\pi\)
−0.717042 + 0.697030i \(0.754504\pi\)
\(420\) −29.9656 −1.46217
\(421\) −22.8494 −1.11361 −0.556806 0.830642i \(-0.687973\pi\)
−0.556806 + 0.830642i \(0.687973\pi\)
\(422\) 12.8415 0.625115
\(423\) 0.500259 0.0243234
\(424\) −8.31106 −0.403621
\(425\) 25.2368 1.22416
\(426\) −21.1240 −1.02346
\(427\) 2.79487 0.135253
\(428\) −16.8140 −0.812736
\(429\) 1.24581 0.0601481
\(430\) −106.828 −5.15172
\(431\) −14.2715 −0.687436 −0.343718 0.939073i \(-0.611686\pi\)
−0.343718 + 0.939073i \(0.611686\pi\)
\(432\) 8.89640 0.428028
\(433\) 7.11365 0.341860 0.170930 0.985283i \(-0.445323\pi\)
0.170930 + 0.985283i \(0.445323\pi\)
\(434\) −18.7641 −0.900707
\(435\) −10.1128 −0.484870
\(436\) −38.2561 −1.83213
\(437\) 1.59044 0.0760812
\(438\) −41.9447 −2.00419
\(439\) −32.7073 −1.56103 −0.780516 0.625136i \(-0.785044\pi\)
−0.780516 + 0.625136i \(0.785044\pi\)
\(440\) −114.407 −5.45414
\(441\) −3.05313 −0.145387
\(442\) −3.10715 −0.147792
\(443\) 17.8792 0.849468 0.424734 0.905318i \(-0.360368\pi\)
0.424734 + 0.905318i \(0.360368\pi\)
\(444\) −19.8371 −0.941426
\(445\) −32.3602 −1.53402
\(446\) 4.13200 0.195656
\(447\) 8.08300 0.382313
\(448\) −10.6413 −0.502753
\(449\) −20.7607 −0.979758 −0.489879 0.871790i \(-0.662959\pi\)
−0.489879 + 0.871790i \(0.662959\pi\)
\(450\) −13.4316 −0.633171
\(451\) 47.5892 2.24089
\(452\) −18.2283 −0.857389
\(453\) 3.82291 0.179616
\(454\) 67.3736 3.16200
\(455\) −1.55793 −0.0730369
\(456\) −5.82854 −0.272946
\(457\) 18.6577 0.872772 0.436386 0.899760i \(-0.356258\pi\)
0.436386 + 0.899760i \(0.356258\pi\)
\(458\) −54.2683 −2.53579
\(459\) 4.87352 0.227477
\(460\) 29.1207 1.35776
\(461\) 3.77911 0.176011 0.0880053 0.996120i \(-0.471951\pi\)
0.0880053 + 0.996120i \(0.471951\pi\)
\(462\) 26.1174 1.21509
\(463\) 33.6188 1.56240 0.781198 0.624283i \(-0.214609\pi\)
0.781198 + 0.624283i \(0.214609\pi\)
\(464\) −28.1998 −1.30914
\(465\) −11.6173 −0.538739
\(466\) −76.5486 −3.54604
\(467\) −8.47037 −0.391962 −0.195981 0.980608i \(-0.562789\pi\)
−0.195981 + 0.980608i \(0.562789\pi\)
\(468\) 1.16209 0.0537178
\(469\) −22.3832 −1.03356
\(470\) −4.13970 −0.190950
\(471\) 7.71216 0.355358
\(472\) 50.5121 2.32501
\(473\) 65.4303 3.00849
\(474\) 9.16797 0.421099
\(475\) 4.26584 0.195730
\(476\) −45.7749 −2.09809
\(477\) 1.17465 0.0537837
\(478\) −44.4915 −2.03499
\(479\) −17.4170 −0.795802 −0.397901 0.917428i \(-0.630261\pi\)
−0.397901 + 0.917428i \(0.630261\pi\)
\(480\) −28.4732 −1.29962
\(481\) −1.03134 −0.0470251
\(482\) −6.55190 −0.298431
\(483\) −3.83558 −0.174525
\(484\) 69.4432 3.15651
\(485\) 8.95305 0.406537
\(486\) −2.59380 −0.117657
\(487\) −22.1569 −1.00402 −0.502012 0.864861i \(-0.667407\pi\)
−0.502012 + 0.864861i \(0.667407\pi\)
\(488\) 9.95364 0.450580
\(489\) −4.49641 −0.203335
\(490\) 25.2651 1.14136
\(491\) 28.9121 1.30479 0.652393 0.757881i \(-0.273765\pi\)
0.652393 + 0.757881i \(0.273765\pi\)
\(492\) 44.3914 2.00132
\(493\) −15.4481 −0.695746
\(494\) −0.525209 −0.0236303
\(495\) 16.1699 0.726781
\(496\) −32.3952 −1.45459
\(497\) −16.1795 −0.725751
\(498\) 39.6452 1.77654
\(499\) 30.3108 1.35690 0.678448 0.734649i \(-0.262653\pi\)
0.678448 + 0.734649i \(0.262653\pi\)
\(500\) 2.69007 0.120304
\(501\) −1.82265 −0.0814300
\(502\) 37.7216 1.68360
\(503\) −3.63230 −0.161956 −0.0809782 0.996716i \(-0.525804\pi\)
−0.0809782 + 0.996716i \(0.525804\pi\)
\(504\) 14.0564 0.626120
\(505\) 3.79119 0.168706
\(506\) −25.3810 −1.12832
\(507\) −12.9396 −0.574667
\(508\) 61.7349 2.73904
\(509\) −17.1381 −0.759632 −0.379816 0.925062i \(-0.624013\pi\)
−0.379816 + 0.925062i \(0.624013\pi\)
\(510\) −40.3290 −1.78580
\(511\) −32.1267 −1.42120
\(512\) 46.4913 2.05465
\(513\) 0.823783 0.0363709
\(514\) 20.8732 0.920677
\(515\) −12.3539 −0.544379
\(516\) 61.0336 2.68686
\(517\) 2.53549 0.111511
\(518\) −21.6213 −0.949986
\(519\) −23.5027 −1.03166
\(520\) −5.54841 −0.243314
\(521\) −11.1236 −0.487334 −0.243667 0.969859i \(-0.578350\pi\)
−0.243667 + 0.969859i \(0.578350\pi\)
\(522\) 8.22181 0.359859
\(523\) 6.50848 0.284596 0.142298 0.989824i \(-0.454551\pi\)
0.142298 + 0.989824i \(0.454551\pi\)
\(524\) −7.17331 −0.313367
\(525\) −10.2877 −0.448991
\(526\) 9.73229 0.424348
\(527\) −17.7463 −0.773043
\(528\) 45.0902 1.96230
\(529\) −19.2726 −0.837938
\(530\) −9.72041 −0.422228
\(531\) −7.13919 −0.309815
\(532\) −7.73744 −0.335460
\(533\) 2.30794 0.0999679
\(534\) 26.3093 1.13851
\(535\) −11.3462 −0.490541
\(536\) −79.7156 −3.44319
\(537\) 8.88872 0.383577
\(538\) −12.2327 −0.527388
\(539\) −15.4744 −0.666529
\(540\) 15.0833 0.649082
\(541\) −12.3854 −0.532491 −0.266245 0.963905i \(-0.585783\pi\)
−0.266245 + 0.963905i \(0.585783\pi\)
\(542\) 66.9349 2.87510
\(543\) −7.96963 −0.342009
\(544\) −43.4952 −1.86484
\(545\) −25.8155 −1.10582
\(546\) 1.26662 0.0542062
\(547\) 28.6251 1.22392 0.611960 0.790889i \(-0.290381\pi\)
0.611960 + 0.790889i \(0.290381\pi\)
\(548\) −24.8184 −1.06019
\(549\) −1.40681 −0.0600412
\(550\) −68.0762 −2.90278
\(551\) −2.61123 −0.111242
\(552\) −13.6600 −0.581409
\(553\) 7.02204 0.298607
\(554\) 45.1451 1.91803
\(555\) −13.3862 −0.568214
\(556\) 44.8419 1.90172
\(557\) −30.5013 −1.29238 −0.646191 0.763176i \(-0.723639\pi\)
−0.646191 + 0.763176i \(0.723639\pi\)
\(558\) 9.44500 0.399839
\(559\) 3.17318 0.134211
\(560\) −56.3870 −2.38279
\(561\) 24.7008 1.04287
\(562\) 48.9721 2.06576
\(563\) 3.96459 0.167088 0.0835438 0.996504i \(-0.473376\pi\)
0.0835438 + 0.996504i \(0.473376\pi\)
\(564\) 2.36512 0.0995893
\(565\) −12.3006 −0.517492
\(566\) −36.0224 −1.51413
\(567\) −1.98667 −0.0834324
\(568\) −57.6217 −2.41775
\(569\) −4.85702 −0.203617 −0.101809 0.994804i \(-0.532463\pi\)
−0.101809 + 0.994804i \(0.532463\pi\)
\(570\) −6.81691 −0.285529
\(571\) 16.2021 0.678037 0.339018 0.940780i \(-0.389905\pi\)
0.339018 + 0.940780i \(0.389905\pi\)
\(572\) 5.88991 0.246270
\(573\) 10.9738 0.458437
\(574\) 48.3842 2.01952
\(575\) 9.99761 0.416929
\(576\) 5.35633 0.223180
\(577\) 24.5844 1.02346 0.511731 0.859146i \(-0.329005\pi\)
0.511731 + 0.859146i \(0.329005\pi\)
\(578\) −17.5113 −0.728374
\(579\) 14.2303 0.591392
\(580\) −47.8110 −1.98524
\(581\) 30.3655 1.25977
\(582\) −7.27895 −0.301722
\(583\) 5.95357 0.246572
\(584\) −114.416 −4.73457
\(585\) 0.784191 0.0324223
\(586\) 9.75217 0.402858
\(587\) −11.3682 −0.469214 −0.234607 0.972090i \(-0.575380\pi\)
−0.234607 + 0.972090i \(0.575380\pi\)
\(588\) −14.4346 −0.595271
\(589\) −2.99971 −0.123601
\(590\) 59.0777 2.43219
\(591\) 26.3142 1.08242
\(592\) −37.3279 −1.53417
\(593\) −28.7410 −1.18025 −0.590126 0.807311i \(-0.700922\pi\)
−0.590126 + 0.807311i \(0.700922\pi\)
\(594\) −13.1463 −0.539400
\(595\) −30.8893 −1.26634
\(596\) 38.2147 1.56534
\(597\) −11.8744 −0.485988
\(598\) −1.23090 −0.0503354
\(599\) −26.5938 −1.08659 −0.543297 0.839541i \(-0.682824\pi\)
−0.543297 + 0.839541i \(0.682824\pi\)
\(600\) −36.6385 −1.49576
\(601\) 45.0413 1.83727 0.918636 0.395104i \(-0.129292\pi\)
0.918636 + 0.395104i \(0.129292\pi\)
\(602\) 66.5233 2.71129
\(603\) 11.2667 0.458815
\(604\) 18.0739 0.735416
\(605\) 46.8609 1.90517
\(606\) −3.08229 −0.125209
\(607\) −12.2879 −0.498752 −0.249376 0.968407i \(-0.580226\pi\)
−0.249376 + 0.968407i \(0.580226\pi\)
\(608\) −7.35210 −0.298167
\(609\) 6.29735 0.255181
\(610\) 11.6415 0.471352
\(611\) 0.122964 0.00497459
\(612\) 23.0410 0.931376
\(613\) 1.74580 0.0705123 0.0352562 0.999378i \(-0.488775\pi\)
0.0352562 + 0.999378i \(0.488775\pi\)
\(614\) −79.1646 −3.19482
\(615\) 29.9557 1.20793
\(616\) 71.2427 2.87045
\(617\) 28.2058 1.13552 0.567761 0.823193i \(-0.307810\pi\)
0.567761 + 0.823193i \(0.307810\pi\)
\(618\) 10.0439 0.404025
\(619\) −19.6488 −0.789751 −0.394876 0.918735i \(-0.629212\pi\)
−0.394876 + 0.918735i \(0.629212\pi\)
\(620\) −54.9241 −2.20580
\(621\) 1.93066 0.0774745
\(622\) −5.54644 −0.222392
\(623\) 20.1511 0.807337
\(624\) 2.18674 0.0875397
\(625\) −24.0765 −0.963058
\(626\) 46.7930 1.87022
\(627\) 4.17523 0.166743
\(628\) 36.4615 1.45497
\(629\) −20.4486 −0.815337
\(630\) 16.4400 0.654984
\(631\) 22.9566 0.913888 0.456944 0.889496i \(-0.348944\pi\)
0.456944 + 0.889496i \(0.348944\pi\)
\(632\) 25.0083 0.994775
\(633\) −4.95086 −0.196779
\(634\) 14.3458 0.569743
\(635\) 41.6592 1.65320
\(636\) 5.55351 0.220211
\(637\) −0.750462 −0.0297344
\(638\) 41.6711 1.64978
\(639\) 8.14403 0.322173
\(640\) 12.6222 0.498936
\(641\) 24.4519 0.965791 0.482895 0.875678i \(-0.339585\pi\)
0.482895 + 0.875678i \(0.339585\pi\)
\(642\) 9.22464 0.364068
\(643\) 0.843444 0.0332622 0.0166311 0.999862i \(-0.494706\pi\)
0.0166311 + 0.999862i \(0.494706\pi\)
\(644\) −18.1338 −0.714572
\(645\) 41.1860 1.62170
\(646\) −10.4134 −0.409709
\(647\) −3.98889 −0.156820 −0.0784098 0.996921i \(-0.524984\pi\)
−0.0784098 + 0.996921i \(0.524984\pi\)
\(648\) −7.07533 −0.277945
\(649\) −36.1840 −1.42035
\(650\) −3.30149 −0.129495
\(651\) 7.23423 0.283532
\(652\) −21.2581 −0.832531
\(653\) −27.2412 −1.06603 −0.533015 0.846106i \(-0.678941\pi\)
−0.533015 + 0.846106i \(0.678941\pi\)
\(654\) 20.9884 0.820710
\(655\) −4.84061 −0.189138
\(656\) 83.5324 3.26139
\(657\) 16.1711 0.630896
\(658\) 2.57785 0.100495
\(659\) 22.8314 0.889384 0.444692 0.895684i \(-0.353313\pi\)
0.444692 + 0.895684i \(0.353313\pi\)
\(660\) 76.4477 2.97572
\(661\) 12.2464 0.476328 0.238164 0.971225i \(-0.423454\pi\)
0.238164 + 0.971225i \(0.423454\pi\)
\(662\) −30.6665 −1.19189
\(663\) 1.19791 0.0465232
\(664\) 108.144 4.19678
\(665\) −5.22129 −0.202473
\(666\) 10.8832 0.421715
\(667\) −6.11979 −0.236959
\(668\) −8.61711 −0.333406
\(669\) −1.59303 −0.0615901
\(670\) −93.2333 −3.60192
\(671\) −7.13022 −0.275259
\(672\) 17.7306 0.683975
\(673\) −11.3608 −0.437925 −0.218963 0.975733i \(-0.570267\pi\)
−0.218963 + 0.975733i \(0.570267\pi\)
\(674\) −7.20169 −0.277399
\(675\) 5.17835 0.199315
\(676\) −61.1756 −2.35291
\(677\) 0.568463 0.0218478 0.0109239 0.999940i \(-0.496523\pi\)
0.0109239 + 0.999940i \(0.496523\pi\)
\(678\) 10.0006 0.384070
\(679\) −5.57518 −0.213956
\(680\) −110.009 −4.21865
\(681\) −25.9749 −0.995360
\(682\) 47.8707 1.83306
\(683\) −30.5439 −1.16873 −0.584366 0.811490i \(-0.698657\pi\)
−0.584366 + 0.811490i \(0.698657\pi\)
\(684\) 3.89467 0.148917
\(685\) −16.7477 −0.639895
\(686\) −51.8041 −1.97789
\(687\) 20.9223 0.798236
\(688\) 114.849 4.37856
\(689\) 0.288731 0.0109998
\(690\) −15.9764 −0.608212
\(691\) −4.35824 −0.165795 −0.0828977 0.996558i \(-0.526417\pi\)
−0.0828977 + 0.996558i \(0.526417\pi\)
\(692\) −111.116 −4.22399
\(693\) −10.0692 −0.382496
\(694\) 4.22491 0.160375
\(695\) 30.2597 1.14782
\(696\) 22.4273 0.850106
\(697\) 45.7598 1.73328
\(698\) 38.6011 1.46107
\(699\) 29.5122 1.11625
\(700\) −48.6380 −1.83834
\(701\) −47.8527 −1.80737 −0.903685 0.428198i \(-0.859149\pi\)
−0.903685 + 0.428198i \(0.859149\pi\)
\(702\) −0.637557 −0.0240630
\(703\) −3.45647 −0.130363
\(704\) 27.1478 1.02317
\(705\) 1.59600 0.0601089
\(706\) −26.5315 −0.998527
\(707\) −2.36082 −0.0887879
\(708\) −33.7526 −1.26850
\(709\) −11.7029 −0.439511 −0.219755 0.975555i \(-0.570526\pi\)
−0.219755 + 0.975555i \(0.570526\pi\)
\(710\) −67.3929 −2.52921
\(711\) −3.53457 −0.132557
\(712\) 71.7661 2.68955
\(713\) −7.03025 −0.263285
\(714\) 25.1134 0.939845
\(715\) 3.97456 0.148640
\(716\) 42.0240 1.57051
\(717\) 17.1530 0.640592
\(718\) −51.5850 −1.92513
\(719\) −26.3660 −0.983287 −0.491644 0.870797i \(-0.663604\pi\)
−0.491644 + 0.870797i \(0.663604\pi\)
\(720\) 28.3826 1.05776
\(721\) 7.69294 0.286500
\(722\) 47.5220 1.76858
\(723\) 2.52599 0.0939424
\(724\) −37.6787 −1.40032
\(725\) −16.4143 −0.609612
\(726\) −38.0985 −1.41397
\(727\) −16.9348 −0.628078 −0.314039 0.949410i \(-0.601682\pi\)
−0.314039 + 0.949410i \(0.601682\pi\)
\(728\) 3.45506 0.128053
\(729\) 1.00000 0.0370370
\(730\) −133.818 −4.95283
\(731\) 62.9150 2.32700
\(732\) −6.65109 −0.245832
\(733\) −15.8156 −0.584163 −0.292082 0.956393i \(-0.594348\pi\)
−0.292082 + 0.956393i \(0.594348\pi\)
\(734\) −59.1252 −2.18235
\(735\) −9.74057 −0.359286
\(736\) −17.2307 −0.635132
\(737\) 57.1037 2.10344
\(738\) −24.3544 −0.896497
\(739\) −30.0321 −1.10475 −0.552375 0.833596i \(-0.686278\pi\)
−0.552375 + 0.833596i \(0.686278\pi\)
\(740\) −63.2872 −2.32649
\(741\) 0.202486 0.00743853
\(742\) 6.05302 0.222213
\(743\) 3.39514 0.124555 0.0622777 0.998059i \(-0.480164\pi\)
0.0622777 + 0.998059i \(0.480164\pi\)
\(744\) 25.7640 0.944553
\(745\) 25.7876 0.944786
\(746\) −82.1965 −3.00943
\(747\) −15.2846 −0.559234
\(748\) 116.780 4.26990
\(749\) 7.06545 0.258166
\(750\) −1.47585 −0.0538904
\(751\) −13.0174 −0.475010 −0.237505 0.971386i \(-0.576330\pi\)
−0.237505 + 0.971386i \(0.576330\pi\)
\(752\) 4.45050 0.162293
\(753\) −14.5430 −0.529976
\(754\) 2.02093 0.0735978
\(755\) 12.1964 0.443873
\(756\) −9.39256 −0.341604
\(757\) 41.2008 1.49747 0.748735 0.662869i \(-0.230662\pi\)
0.748735 + 0.662869i \(0.230662\pi\)
\(758\) −64.7134 −2.35050
\(759\) 9.78526 0.355183
\(760\) −18.5951 −0.674515
\(761\) 36.4020 1.31957 0.659785 0.751454i \(-0.270647\pi\)
0.659785 + 0.751454i \(0.270647\pi\)
\(762\) −33.8695 −1.22696
\(763\) 16.0757 0.581978
\(764\) 51.8818 1.87702
\(765\) 15.5483 0.562148
\(766\) 80.4612 2.90718
\(767\) −1.75482 −0.0633628
\(768\) −20.9747 −0.756858
\(769\) 34.1171 1.23029 0.615147 0.788412i \(-0.289097\pi\)
0.615147 + 0.788412i \(0.289097\pi\)
\(770\) 83.3237 3.00278
\(771\) −8.04735 −0.289818
\(772\) 67.2779 2.42139
\(773\) 33.7241 1.21297 0.606486 0.795095i \(-0.292579\pi\)
0.606486 + 0.795095i \(0.292579\pi\)
\(774\) −33.4848 −1.20359
\(775\) −18.8563 −0.677339
\(776\) −19.8554 −0.712768
\(777\) 8.33577 0.299044
\(778\) −22.7065 −0.814069
\(779\) 7.73489 0.277131
\(780\) 3.70749 0.132749
\(781\) 41.2769 1.47700
\(782\) −24.4053 −0.872731
\(783\) −3.16980 −0.113279
\(784\) −27.1619 −0.970067
\(785\) 24.6045 0.878173
\(786\) 3.93548 0.140374
\(787\) −29.6566 −1.05714 −0.528572 0.848889i \(-0.677272\pi\)
−0.528572 + 0.848889i \(0.677272\pi\)
\(788\) 124.408 4.43185
\(789\) −3.75214 −0.133580
\(790\) 29.2490 1.04063
\(791\) 7.65976 0.272350
\(792\) −35.8603 −1.27424
\(793\) −0.345795 −0.0122795
\(794\) 48.7398 1.72971
\(795\) 3.74756 0.132912
\(796\) −56.1397 −1.98982
\(797\) −32.7636 −1.16055 −0.580273 0.814422i \(-0.697054\pi\)
−0.580273 + 0.814422i \(0.697054\pi\)
\(798\) 4.24498 0.150271
\(799\) 2.43802 0.0862510
\(800\) −46.2157 −1.63397
\(801\) −10.1431 −0.358390
\(802\) 7.32084 0.258508
\(803\) 81.9612 2.89235
\(804\) 53.2665 1.87857
\(805\) −12.2369 −0.431292
\(806\) 2.32159 0.0817745
\(807\) 4.71612 0.166015
\(808\) −8.40782 −0.295786
\(809\) −25.4596 −0.895112 −0.447556 0.894256i \(-0.647705\pi\)
−0.447556 + 0.894256i \(0.647705\pi\)
\(810\) −8.27513 −0.290758
\(811\) 49.0358 1.72188 0.860941 0.508705i \(-0.169876\pi\)
0.860941 + 0.508705i \(0.169876\pi\)
\(812\) 29.7725 1.04481
\(813\) −25.8057 −0.905047
\(814\) 55.1599 1.93335
\(815\) −14.3451 −0.502489
\(816\) 43.3568 1.51779
\(817\) 10.6347 0.372060
\(818\) 77.3551 2.70466
\(819\) −0.488325 −0.0170635
\(820\) 141.624 4.94573
\(821\) −12.3424 −0.430753 −0.215377 0.976531i \(-0.569098\pi\)
−0.215377 + 0.976531i \(0.569098\pi\)
\(822\) 13.6161 0.474915
\(823\) 24.0480 0.838261 0.419130 0.907926i \(-0.362335\pi\)
0.419130 + 0.907926i \(0.362335\pi\)
\(824\) 27.3976 0.954441
\(825\) 26.2457 0.913760
\(826\) −36.7884 −1.28003
\(827\) 50.9901 1.77310 0.886550 0.462632i \(-0.153095\pi\)
0.886550 + 0.462632i \(0.153095\pi\)
\(828\) 9.12773 0.317211
\(829\) −25.6581 −0.891141 −0.445571 0.895247i \(-0.646999\pi\)
−0.445571 + 0.895247i \(0.646999\pi\)
\(830\) 126.482 4.39026
\(831\) −17.4050 −0.603774
\(832\) 1.31659 0.0456445
\(833\) −14.8795 −0.515545
\(834\) −24.6015 −0.851881
\(835\) −5.81490 −0.201233
\(836\) 19.7396 0.682709
\(837\) −3.64138 −0.125865
\(838\) 76.1408 2.63024
\(839\) 22.3736 0.772423 0.386212 0.922410i \(-0.373783\pi\)
0.386212 + 0.922410i \(0.373783\pi\)
\(840\) 44.8447 1.54729
\(841\) −18.9524 −0.653531
\(842\) 59.2668 2.04247
\(843\) −18.8805 −0.650278
\(844\) −23.4066 −0.805688
\(845\) −41.2818 −1.42014
\(846\) −1.29757 −0.0446114
\(847\) −29.1808 −1.00267
\(848\) 10.4502 0.358861
\(849\) 13.8879 0.476631
\(850\) −65.4591 −2.24523
\(851\) −8.10074 −0.277690
\(852\) 38.5032 1.31910
\(853\) −8.89687 −0.304623 −0.152312 0.988333i \(-0.548672\pi\)
−0.152312 + 0.988333i \(0.548672\pi\)
\(854\) −7.24932 −0.248067
\(855\) 2.62816 0.0898811
\(856\) 25.1629 0.860049
\(857\) −28.7920 −0.983516 −0.491758 0.870732i \(-0.663646\pi\)
−0.491758 + 0.870732i \(0.663646\pi\)
\(858\) −3.23137 −0.110317
\(859\) −24.9081 −0.849854 −0.424927 0.905228i \(-0.639700\pi\)
−0.424927 + 0.905228i \(0.639700\pi\)
\(860\) 194.719 6.63986
\(861\) −18.6538 −0.635720
\(862\) 37.0175 1.26082
\(863\) 40.0451 1.36315 0.681575 0.731748i \(-0.261295\pi\)
0.681575 + 0.731748i \(0.261295\pi\)
\(864\) −8.92480 −0.303628
\(865\) −74.9820 −2.54946
\(866\) −18.4514 −0.627003
\(867\) 6.75122 0.229283
\(868\) 34.2019 1.16089
\(869\) −17.9145 −0.607708
\(870\) 26.2305 0.889296
\(871\) 2.76936 0.0938362
\(872\) 57.2518 1.93879
\(873\) 2.80629 0.0949785
\(874\) −4.12529 −0.139540
\(875\) −1.13040 −0.0382145
\(876\) 76.4537 2.58313
\(877\) 50.4087 1.70218 0.851090 0.525020i \(-0.175942\pi\)
0.851090 + 0.525020i \(0.175942\pi\)
\(878\) 84.8360 2.86308
\(879\) −3.75980 −0.126815
\(880\) 143.854 4.84930
\(881\) 27.3603 0.921793 0.460897 0.887454i \(-0.347528\pi\)
0.460897 + 0.887454i \(0.347528\pi\)
\(882\) 7.91921 0.266654
\(883\) 14.7610 0.496746 0.248373 0.968664i \(-0.420104\pi\)
0.248373 + 0.968664i \(0.420104\pi\)
\(884\) 5.66349 0.190484
\(885\) −22.7765 −0.765625
\(886\) −46.3751 −1.55800
\(887\) 28.3115 0.950606 0.475303 0.879822i \(-0.342338\pi\)
0.475303 + 0.879822i \(0.342338\pi\)
\(888\) 29.6870 0.996230
\(889\) −25.9417 −0.870057
\(890\) 83.9358 2.81353
\(891\) 5.06836 0.169797
\(892\) −7.53150 −0.252173
\(893\) 0.412105 0.0137906
\(894\) −20.9657 −0.701197
\(895\) 28.3582 0.947909
\(896\) −7.86000 −0.262584
\(897\) 0.474556 0.0158450
\(898\) 53.8491 1.79697
\(899\) 11.5424 0.384962
\(900\) 24.4821 0.816071
\(901\) 5.72470 0.190717
\(902\) −123.437 −4.11000
\(903\) −25.6471 −0.853481
\(904\) 27.2795 0.907301
\(905\) −25.4259 −0.845186
\(906\) −9.91585 −0.329432
\(907\) 29.8761 0.992021 0.496011 0.868317i \(-0.334798\pi\)
0.496011 + 0.868317i \(0.334798\pi\)
\(908\) −122.804 −4.07539
\(909\) 1.18833 0.0394144
\(910\) 4.04096 0.133956
\(911\) 50.0393 1.65788 0.828938 0.559341i \(-0.188946\pi\)
0.828938 + 0.559341i \(0.188946\pi\)
\(912\) 7.32870 0.242678
\(913\) −77.4679 −2.56381
\(914\) −48.3944 −1.60074
\(915\) −4.48822 −0.148376
\(916\) 98.9163 3.26829
\(917\) 3.01431 0.0995413
\(918\) −12.6409 −0.417213
\(919\) 21.2316 0.700366 0.350183 0.936681i \(-0.386119\pi\)
0.350183 + 0.936681i \(0.386119\pi\)
\(920\) −43.5803 −1.43680
\(921\) 30.5207 1.00569
\(922\) −9.80224 −0.322820
\(923\) 2.00181 0.0658903
\(924\) −47.6049 −1.56609
\(925\) −21.7276 −0.714397
\(926\) −87.2003 −2.86558
\(927\) −3.87228 −0.127182
\(928\) 28.2898 0.928658
\(929\) −0.435512 −0.0142887 −0.00714435 0.999974i \(-0.502274\pi\)
−0.00714435 + 0.999974i \(0.502274\pi\)
\(930\) 30.1329 0.988096
\(931\) −2.51512 −0.0824297
\(932\) 139.527 4.57037
\(933\) 2.13835 0.0700063
\(934\) 21.9704 0.718894
\(935\) 78.8042 2.57717
\(936\) −1.73912 −0.0568449
\(937\) 11.5193 0.376320 0.188160 0.982138i \(-0.439748\pi\)
0.188160 + 0.982138i \(0.439748\pi\)
\(938\) 58.0576 1.89565
\(939\) −18.0403 −0.588724
\(940\) 7.54555 0.246109
\(941\) 35.5870 1.16010 0.580051 0.814580i \(-0.303033\pi\)
0.580051 + 0.814580i \(0.303033\pi\)
\(942\) −20.0038 −0.651759
\(943\) 18.1278 0.590323
\(944\) −63.5131 −2.06717
\(945\) −6.33818 −0.206181
\(946\) −169.713 −5.51785
\(947\) 13.7279 0.446097 0.223048 0.974807i \(-0.428399\pi\)
0.223048 + 0.974807i \(0.428399\pi\)
\(948\) −16.7107 −0.542739
\(949\) 3.97488 0.129030
\(950\) −11.0647 −0.358987
\(951\) −5.53079 −0.179348
\(952\) 68.5040 2.22023
\(953\) 24.9459 0.808076 0.404038 0.914742i \(-0.367606\pi\)
0.404038 + 0.914742i \(0.367606\pi\)
\(954\) −3.04681 −0.0986443
\(955\) 35.0103 1.13291
\(956\) 81.0959 2.62283
\(957\) −16.0657 −0.519330
\(958\) 45.1761 1.45957
\(959\) 10.4290 0.336769
\(960\) 17.0886 0.551531
\(961\) −17.7404 −0.572269
\(962\) 2.67509 0.0862484
\(963\) −3.55642 −0.114604
\(964\) 11.9423 0.384636
\(965\) 45.3997 1.46147
\(966\) 9.94872 0.320095
\(967\) 0.820836 0.0263963 0.0131981 0.999913i \(-0.495799\pi\)
0.0131981 + 0.999913i \(0.495799\pi\)
\(968\) −103.925 −3.34026
\(969\) 4.01473 0.128972
\(970\) −23.2224 −0.745626
\(971\) 6.06879 0.194757 0.0973784 0.995247i \(-0.468954\pi\)
0.0973784 + 0.995247i \(0.468954\pi\)
\(972\) 4.72779 0.151644
\(973\) −18.8431 −0.604082
\(974\) 57.4705 1.84147
\(975\) 1.27284 0.0407635
\(976\) −12.5155 −0.400612
\(977\) −43.8991 −1.40446 −0.702228 0.711952i \(-0.747811\pi\)
−0.702228 + 0.711952i \(0.747811\pi\)
\(978\) 11.6628 0.372935
\(979\) −51.4091 −1.64304
\(980\) −46.0513 −1.47106
\(981\) −8.09175 −0.258350
\(982\) −74.9923 −2.39310
\(983\) −32.7990 −1.04613 −0.523063 0.852294i \(-0.675211\pi\)
−0.523063 + 0.852294i \(0.675211\pi\)
\(984\) −66.4336 −2.11782
\(985\) 83.9517 2.67492
\(986\) 40.0692 1.27606
\(987\) −0.993850 −0.0316346
\(988\) 0.957313 0.0304562
\(989\) 24.9239 0.792534
\(990\) −41.9414 −1.33298
\(991\) −41.3737 −1.31428 −0.657139 0.753769i \(-0.728234\pi\)
−0.657139 + 0.753769i \(0.728234\pi\)
\(992\) 32.4986 1.03183
\(993\) 11.8230 0.375192
\(994\) 41.9664 1.33109
\(995\) −37.8836 −1.20099
\(996\) −72.2623 −2.28972
\(997\) 3.39197 0.107425 0.0537124 0.998556i \(-0.482895\pi\)
0.0537124 + 0.998556i \(0.482895\pi\)
\(998\) −78.6200 −2.48867
\(999\) −4.19585 −0.132751
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 \(a_p\))