Properties

Label 8018.2.a.d.1.19
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+0.677734 q^{3}\) \(+1.00000 q^{4}\) \(-4.37664 q^{5}\) \(+0.677734 q^{6}\) \(-1.03965 q^{7}\) \(+1.00000 q^{8}\) \(-2.54068 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+0.677734 q^{3}\) \(+1.00000 q^{4}\) \(-4.37664 q^{5}\) \(+0.677734 q^{6}\) \(-1.03965 q^{7}\) \(+1.00000 q^{8}\) \(-2.54068 q^{9}\) \(-4.37664 q^{10}\) \(+1.08793 q^{11}\) \(+0.677734 q^{12}\) \(+1.73790 q^{13}\) \(-1.03965 q^{14}\) \(-2.96620 q^{15}\) \(+1.00000 q^{16}\) \(+3.23599 q^{17}\) \(-2.54068 q^{18}\) \(+1.00000 q^{19}\) \(-4.37664 q^{20}\) \(-0.704609 q^{21}\) \(+1.08793 q^{22}\) \(+0.112769 q^{23}\) \(+0.677734 q^{24}\) \(+14.1550 q^{25}\) \(+1.73790 q^{26}\) \(-3.75510 q^{27}\) \(-1.03965 q^{28}\) \(+3.19669 q^{29}\) \(-2.96620 q^{30}\) \(-0.880743 q^{31}\) \(+1.00000 q^{32}\) \(+0.737328 q^{33}\) \(+3.23599 q^{34}\) \(+4.55020 q^{35}\) \(-2.54068 q^{36}\) \(-5.39162 q^{37}\) \(+1.00000 q^{38}\) \(+1.17783 q^{39}\) \(-4.37664 q^{40}\) \(-3.58857 q^{41}\) \(-0.704609 q^{42}\) \(+4.67245 q^{43}\) \(+1.08793 q^{44}\) \(+11.1196 q^{45}\) \(+0.112769 q^{46}\) \(+11.3703 q^{47}\) \(+0.677734 q^{48}\) \(-5.91912 q^{49}\) \(+14.1550 q^{50}\) \(+2.19314 q^{51}\) \(+1.73790 q^{52}\) \(+6.66703 q^{53}\) \(-3.75510 q^{54}\) \(-4.76149 q^{55}\) \(-1.03965 q^{56}\) \(+0.677734 q^{57}\) \(+3.19669 q^{58}\) \(-6.07647 q^{59}\) \(-2.96620 q^{60}\) \(-3.81434 q^{61}\) \(-0.880743 q^{62}\) \(+2.64142 q^{63}\) \(+1.00000 q^{64}\) \(-7.60617 q^{65}\) \(+0.737328 q^{66}\) \(-11.5399 q^{67}\) \(+3.23599 q^{68}\) \(+0.0764274 q^{69}\) \(+4.55020 q^{70}\) \(-8.52973 q^{71}\) \(-2.54068 q^{72}\) \(-3.18541 q^{73}\) \(-5.39162 q^{74}\) \(+9.59333 q^{75}\) \(+1.00000 q^{76}\) \(-1.13107 q^{77}\) \(+1.17783 q^{78}\) \(-9.57466 q^{79}\) \(-4.37664 q^{80}\) \(+5.07707 q^{81}\) \(-3.58857 q^{82}\) \(+12.4902 q^{83}\) \(-0.704609 q^{84}\) \(-14.1628 q^{85}\) \(+4.67245 q^{86}\) \(+2.16650 q^{87}\) \(+1.08793 q^{88}\) \(-12.6888 q^{89}\) \(+11.1196 q^{90}\) \(-1.80681 q^{91}\) \(+0.112769 q^{92}\) \(-0.596909 q^{93}\) \(+11.3703 q^{94}\) \(-4.37664 q^{95}\) \(+0.677734 q^{96}\) \(+9.17511 q^{97}\) \(-5.91912 q^{98}\) \(-2.76408 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 17q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 19q^{13} \) \(\mathstrut -\mathstrut 15q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 10q^{18} \) \(\mathstrut +\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut -\mathstrut 17q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 10q^{24} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 19q^{26} \) \(\mathstrut -\mathstrut 37q^{27} \) \(\mathstrut -\mathstrut 15q^{28} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 30q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 10q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut +\mathstrut 30q^{38} \) \(\mathstrut -\mathstrut 12q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 14q^{42} \) \(\mathstrut -\mathstrut 61q^{43} \) \(\mathstrut -\mathstrut 17q^{44} \) \(\mathstrut -\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 19q^{52} \) \(\mathstrut -\mathstrut 19q^{53} \) \(\mathstrut -\mathstrut 37q^{54} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 37q^{58} \) \(\mathstrut -\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut -\mathstrut 11q^{62} \) \(\mathstrut -\mathstrut 24q^{63} \) \(\mathstrut +\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 18q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 10q^{72} \) \(\mathstrut -\mathstrut 58q^{73} \) \(\mathstrut -\mathstrut 46q^{74} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut -\mathstrut 32q^{77} \) \(\mathstrut -\mathstrut 42q^{79} \) \(\mathstrut -\mathstrut 12q^{80} \) \(\mathstrut -\mathstrut 38q^{81} \) \(\mathstrut -\mathstrut 28q^{82} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 48q^{85} \) \(\mathstrut -\mathstrut 61q^{86} \) \(\mathstrut -\mathstrut 15q^{87} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 39q^{89} \) \(\mathstrut -\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 45q^{93} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut -\mathstrut 38q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.677734 0.391290 0.195645 0.980675i \(-0.437320\pi\)
0.195645 + 0.980675i \(0.437320\pi\)
\(4\) 1.00000 0.500000
\(5\) −4.37664 −1.95729 −0.978647 0.205546i \(-0.934103\pi\)
−0.978647 + 0.205546i \(0.934103\pi\)
\(6\) 0.677734 0.276684
\(7\) −1.03965 −0.392952 −0.196476 0.980509i \(-0.562950\pi\)
−0.196476 + 0.980509i \(0.562950\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.54068 −0.846892
\(10\) −4.37664 −1.38402
\(11\) 1.08793 0.328024 0.164012 0.986458i \(-0.447556\pi\)
0.164012 + 0.986458i \(0.447556\pi\)
\(12\) 0.677734 0.195645
\(13\) 1.73790 0.482007 0.241003 0.970524i \(-0.422524\pi\)
0.241003 + 0.970524i \(0.422524\pi\)
\(14\) −1.03965 −0.277859
\(15\) −2.96620 −0.765869
\(16\) 1.00000 0.250000
\(17\) 3.23599 0.784844 0.392422 0.919785i \(-0.371637\pi\)
0.392422 + 0.919785i \(0.371637\pi\)
\(18\) −2.54068 −0.598843
\(19\) 1.00000 0.229416
\(20\) −4.37664 −0.978647
\(21\) −0.704609 −0.153758
\(22\) 1.08793 0.231948
\(23\) 0.112769 0.0235140 0.0117570 0.999931i \(-0.496258\pi\)
0.0117570 + 0.999931i \(0.496258\pi\)
\(24\) 0.677734 0.138342
\(25\) 14.1550 2.83100
\(26\) 1.73790 0.340830
\(27\) −3.75510 −0.722670
\(28\) −1.03965 −0.196476
\(29\) 3.19669 0.593610 0.296805 0.954938i \(-0.404079\pi\)
0.296805 + 0.954938i \(0.404079\pi\)
\(30\) −2.96620 −0.541551
\(31\) −0.880743 −0.158186 −0.0790930 0.996867i \(-0.525202\pi\)
−0.0790930 + 0.996867i \(0.525202\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.737328 0.128352
\(34\) 3.23599 0.554969
\(35\) 4.55020 0.769123
\(36\) −2.54068 −0.423446
\(37\) −5.39162 −0.886376 −0.443188 0.896429i \(-0.646153\pi\)
−0.443188 + 0.896429i \(0.646153\pi\)
\(38\) 1.00000 0.162221
\(39\) 1.17783 0.188604
\(40\) −4.37664 −0.692008
\(41\) −3.58857 −0.560440 −0.280220 0.959936i \(-0.590407\pi\)
−0.280220 + 0.959936i \(0.590407\pi\)
\(42\) −0.704609 −0.108723
\(43\) 4.67245 0.712542 0.356271 0.934383i \(-0.384048\pi\)
0.356271 + 0.934383i \(0.384048\pi\)
\(44\) 1.08793 0.164012
\(45\) 11.1196 1.65762
\(46\) 0.112769 0.0166269
\(47\) 11.3703 1.65853 0.829264 0.558856i \(-0.188760\pi\)
0.829264 + 0.558856i \(0.188760\pi\)
\(48\) 0.677734 0.0978225
\(49\) −5.91912 −0.845589
\(50\) 14.1550 2.00182
\(51\) 2.19314 0.307101
\(52\) 1.73790 0.241003
\(53\) 6.66703 0.915786 0.457893 0.889007i \(-0.348604\pi\)
0.457893 + 0.889007i \(0.348604\pi\)
\(54\) −3.75510 −0.511005
\(55\) −4.76149 −0.642039
\(56\) −1.03965 −0.138930
\(57\) 0.677734 0.0897680
\(58\) 3.19669 0.419745
\(59\) −6.07647 −0.791090 −0.395545 0.918447i \(-0.629444\pi\)
−0.395545 + 0.918447i \(0.629444\pi\)
\(60\) −2.96620 −0.382935
\(61\) −3.81434 −0.488376 −0.244188 0.969728i \(-0.578521\pi\)
−0.244188 + 0.969728i \(0.578521\pi\)
\(62\) −0.880743 −0.111854
\(63\) 2.64142 0.332788
\(64\) 1.00000 0.125000
\(65\) −7.60617 −0.943429
\(66\) 0.737328 0.0907588
\(67\) −11.5399 −1.40982 −0.704909 0.709298i \(-0.749012\pi\)
−0.704909 + 0.709298i \(0.749012\pi\)
\(68\) 3.23599 0.392422
\(69\) 0.0764274 0.00920077
\(70\) 4.55020 0.543852
\(71\) −8.52973 −1.01229 −0.506146 0.862448i \(-0.668930\pi\)
−0.506146 + 0.862448i \(0.668930\pi\)
\(72\) −2.54068 −0.299422
\(73\) −3.18541 −0.372824 −0.186412 0.982472i \(-0.559686\pi\)
−0.186412 + 0.982472i \(0.559686\pi\)
\(74\) −5.39162 −0.626763
\(75\) 9.59333 1.10774
\(76\) 1.00000 0.114708
\(77\) −1.13107 −0.128898
\(78\) 1.17783 0.133363
\(79\) −9.57466 −1.07723 −0.538616 0.842551i \(-0.681053\pi\)
−0.538616 + 0.842551i \(0.681053\pi\)
\(80\) −4.37664 −0.489324
\(81\) 5.07707 0.564119
\(82\) −3.58857 −0.396291
\(83\) 12.4902 1.37098 0.685489 0.728083i \(-0.259589\pi\)
0.685489 + 0.728083i \(0.259589\pi\)
\(84\) −0.704609 −0.0768791
\(85\) −14.1628 −1.53617
\(86\) 4.67245 0.503843
\(87\) 2.16650 0.232273
\(88\) 1.08793 0.115974
\(89\) −12.6888 −1.34501 −0.672503 0.740094i \(-0.734781\pi\)
−0.672503 + 0.740094i \(0.734781\pi\)
\(90\) 11.1196 1.17211
\(91\) −1.80681 −0.189406
\(92\) 0.112769 0.0117570
\(93\) −0.596909 −0.0618966
\(94\) 11.3703 1.17276
\(95\) −4.37664 −0.449034
\(96\) 0.677734 0.0691709
\(97\) 9.17511 0.931591 0.465796 0.884892i \(-0.345768\pi\)
0.465796 + 0.884892i \(0.345768\pi\)
\(98\) −5.91912 −0.597921
\(99\) −2.76408 −0.277801
\(100\) 14.1550 1.41550
\(101\) −14.1641 −1.40938 −0.704691 0.709514i \(-0.748914\pi\)
−0.704691 + 0.709514i \(0.748914\pi\)
\(102\) 2.19314 0.217154
\(103\) −3.16377 −0.311736 −0.155868 0.987778i \(-0.549817\pi\)
−0.155868 + 0.987778i \(0.549817\pi\)
\(104\) 1.73790 0.170415
\(105\) 3.08382 0.300950
\(106\) 6.66703 0.647559
\(107\) 2.48968 0.240686 0.120343 0.992732i \(-0.461601\pi\)
0.120343 + 0.992732i \(0.461601\pi\)
\(108\) −3.75510 −0.361335
\(109\) 7.05283 0.675539 0.337769 0.941229i \(-0.390328\pi\)
0.337769 + 0.941229i \(0.390328\pi\)
\(110\) −4.76149 −0.453990
\(111\) −3.65408 −0.346830
\(112\) −1.03965 −0.0982381
\(113\) −16.5892 −1.56058 −0.780291 0.625416i \(-0.784929\pi\)
−0.780291 + 0.625416i \(0.784929\pi\)
\(114\) 0.677734 0.0634756
\(115\) −0.493550 −0.0460237
\(116\) 3.19669 0.296805
\(117\) −4.41544 −0.408208
\(118\) −6.07647 −0.559385
\(119\) −3.36431 −0.308406
\(120\) −2.96620 −0.270776
\(121\) −9.81641 −0.892401
\(122\) −3.81434 −0.345334
\(123\) −2.43209 −0.219295
\(124\) −0.880743 −0.0790930
\(125\) −40.0682 −3.58381
\(126\) 2.64142 0.235317
\(127\) −3.51464 −0.311874 −0.155937 0.987767i \(-0.549840\pi\)
−0.155937 + 0.987767i \(0.549840\pi\)
\(128\) 1.00000 0.0883883
\(129\) 3.16668 0.278810
\(130\) −7.60617 −0.667105
\(131\) −12.9808 −1.13414 −0.567070 0.823669i \(-0.691923\pi\)
−0.567070 + 0.823669i \(0.691923\pi\)
\(132\) 0.737328 0.0641761
\(133\) −1.03965 −0.0901494
\(134\) −11.5399 −0.996892
\(135\) 16.4348 1.41448
\(136\) 3.23599 0.277484
\(137\) 8.38749 0.716592 0.358296 0.933608i \(-0.383358\pi\)
0.358296 + 0.933608i \(0.383358\pi\)
\(138\) 0.0764274 0.00650593
\(139\) −18.9541 −1.60767 −0.803834 0.594854i \(-0.797210\pi\)
−0.803834 + 0.594854i \(0.797210\pi\)
\(140\) 4.55020 0.384562
\(141\) 7.70604 0.648965
\(142\) −8.52973 −0.715799
\(143\) 1.89072 0.158110
\(144\) −2.54068 −0.211723
\(145\) −13.9908 −1.16187
\(146\) −3.18541 −0.263626
\(147\) −4.01159 −0.330870
\(148\) −5.39162 −0.443188
\(149\) −15.3632 −1.25860 −0.629302 0.777161i \(-0.716659\pi\)
−0.629302 + 0.777161i \(0.716659\pi\)
\(150\) 9.59333 0.783292
\(151\) 16.1717 1.31603 0.658016 0.753004i \(-0.271396\pi\)
0.658016 + 0.753004i \(0.271396\pi\)
\(152\) 1.00000 0.0811107
\(153\) −8.22162 −0.664678
\(154\) −1.13107 −0.0911444
\(155\) 3.85470 0.309617
\(156\) 1.17783 0.0943021
\(157\) 20.0070 1.59673 0.798365 0.602174i \(-0.205699\pi\)
0.798365 + 0.602174i \(0.205699\pi\)
\(158\) −9.57466 −0.761719
\(159\) 4.51847 0.358338
\(160\) −4.37664 −0.346004
\(161\) −0.117241 −0.00923986
\(162\) 5.07707 0.398892
\(163\) 7.50860 0.588119 0.294060 0.955787i \(-0.404994\pi\)
0.294060 + 0.955787i \(0.404994\pi\)
\(164\) −3.58857 −0.280220
\(165\) −3.22702 −0.251223
\(166\) 12.4902 0.969427
\(167\) 10.5744 0.818270 0.409135 0.912474i \(-0.365831\pi\)
0.409135 + 0.912474i \(0.365831\pi\)
\(168\) −0.704609 −0.0543617
\(169\) −9.97971 −0.767670
\(170\) −14.1628 −1.08624
\(171\) −2.54068 −0.194290
\(172\) 4.67245 0.356271
\(173\) 17.9144 1.36201 0.681004 0.732279i \(-0.261543\pi\)
0.681004 + 0.732279i \(0.261543\pi\)
\(174\) 2.16650 0.164242
\(175\) −14.7163 −1.11245
\(176\) 1.08793 0.0820059
\(177\) −4.11823 −0.309545
\(178\) −12.6888 −0.951063
\(179\) −22.4848 −1.68060 −0.840298 0.542124i \(-0.817620\pi\)
−0.840298 + 0.542124i \(0.817620\pi\)
\(180\) 11.1196 0.828809
\(181\) 1.63017 0.121169 0.0605847 0.998163i \(-0.480703\pi\)
0.0605847 + 0.998163i \(0.480703\pi\)
\(182\) −1.80681 −0.133930
\(183\) −2.58511 −0.191097
\(184\) 0.112769 0.00831344
\(185\) 23.5972 1.73490
\(186\) −0.596909 −0.0437675
\(187\) 3.52054 0.257447
\(188\) 11.3703 0.829264
\(189\) 3.90401 0.283975
\(190\) −4.37664 −0.317515
\(191\) −3.20936 −0.232221 −0.116111 0.993236i \(-0.537043\pi\)
−0.116111 + 0.993236i \(0.537043\pi\)
\(192\) 0.677734 0.0489112
\(193\) −13.6373 −0.981636 −0.490818 0.871262i \(-0.663302\pi\)
−0.490818 + 0.871262i \(0.663302\pi\)
\(194\) 9.17511 0.658734
\(195\) −5.15496 −0.369154
\(196\) −5.91912 −0.422794
\(197\) −24.4141 −1.73944 −0.869718 0.493549i \(-0.835699\pi\)
−0.869718 + 0.493549i \(0.835699\pi\)
\(198\) −2.76408 −0.196435
\(199\) 4.83687 0.342877 0.171438 0.985195i \(-0.445159\pi\)
0.171438 + 0.985195i \(0.445159\pi\)
\(200\) 14.1550 1.00091
\(201\) −7.82095 −0.551647
\(202\) −14.1641 −0.996584
\(203\) −3.32345 −0.233260
\(204\) 2.19314 0.153551
\(205\) 15.7059 1.09695
\(206\) −3.16377 −0.220430
\(207\) −0.286510 −0.0199138
\(208\) 1.73790 0.120502
\(209\) 1.08793 0.0752538
\(210\) 3.08382 0.212804
\(211\) −1.00000 −0.0688428
\(212\) 6.66703 0.457893
\(213\) −5.78088 −0.396100
\(214\) 2.48968 0.170191
\(215\) −20.4496 −1.39465
\(216\) −3.75510 −0.255502
\(217\) 0.915668 0.0621596
\(218\) 7.05283 0.477678
\(219\) −2.15886 −0.145882
\(220\) −4.76149 −0.321019
\(221\) 5.62383 0.378300
\(222\) −3.65408 −0.245246
\(223\) 3.93852 0.263743 0.131871 0.991267i \(-0.457901\pi\)
0.131871 + 0.991267i \(0.457901\pi\)
\(224\) −1.03965 −0.0694648
\(225\) −35.9633 −2.39755
\(226\) −16.5892 −1.10350
\(227\) 2.97691 0.197585 0.0987923 0.995108i \(-0.468502\pi\)
0.0987923 + 0.995108i \(0.468502\pi\)
\(228\) 0.677734 0.0448840
\(229\) −24.6325 −1.62776 −0.813882 0.581030i \(-0.802650\pi\)
−0.813882 + 0.581030i \(0.802650\pi\)
\(230\) −0.493550 −0.0325437
\(231\) −0.766566 −0.0504363
\(232\) 3.19669 0.209873
\(233\) 3.21421 0.210570 0.105285 0.994442i \(-0.466424\pi\)
0.105285 + 0.994442i \(0.466424\pi\)
\(234\) −4.41544 −0.288646
\(235\) −49.7638 −3.24623
\(236\) −6.07647 −0.395545
\(237\) −6.48907 −0.421510
\(238\) −3.36431 −0.218076
\(239\) 1.83792 0.118885 0.0594427 0.998232i \(-0.481068\pi\)
0.0594427 + 0.998232i \(0.481068\pi\)
\(240\) −2.96620 −0.191467
\(241\) 2.01575 0.129846 0.0649228 0.997890i \(-0.479320\pi\)
0.0649228 + 0.997890i \(0.479320\pi\)
\(242\) −9.81641 −0.631022
\(243\) 14.7062 0.943404
\(244\) −3.81434 −0.244188
\(245\) 25.9059 1.65507
\(246\) −2.43209 −0.155065
\(247\) 1.73790 0.110580
\(248\) −0.880743 −0.0559272
\(249\) 8.46503 0.536449
\(250\) −40.0682 −2.53414
\(251\) 1.53715 0.0970240 0.0485120 0.998823i \(-0.484552\pi\)
0.0485120 + 0.998823i \(0.484552\pi\)
\(252\) 2.64142 0.166394
\(253\) 0.122685 0.00771313
\(254\) −3.51464 −0.220528
\(255\) −9.59861 −0.601088
\(256\) 1.00000 0.0625000
\(257\) −13.8071 −0.861264 −0.430632 0.902528i \(-0.641709\pi\)
−0.430632 + 0.902528i \(0.641709\pi\)
\(258\) 3.16668 0.197149
\(259\) 5.60542 0.348304
\(260\) −7.60617 −0.471714
\(261\) −8.12174 −0.502723
\(262\) −12.9808 −0.801958
\(263\) −10.5628 −0.651330 −0.325665 0.945485i \(-0.605588\pi\)
−0.325665 + 0.945485i \(0.605588\pi\)
\(264\) 0.737328 0.0453794
\(265\) −29.1792 −1.79246
\(266\) −1.03965 −0.0637453
\(267\) −8.59961 −0.526287
\(268\) −11.5399 −0.704909
\(269\) 16.6982 1.01811 0.509055 0.860734i \(-0.329995\pi\)
0.509055 + 0.860734i \(0.329995\pi\)
\(270\) 16.4348 1.00019
\(271\) −2.72534 −0.165553 −0.0827763 0.996568i \(-0.526379\pi\)
−0.0827763 + 0.996568i \(0.526379\pi\)
\(272\) 3.23599 0.196211
\(273\) −1.22454 −0.0741125
\(274\) 8.38749 0.506707
\(275\) 15.3997 0.928636
\(276\) 0.0764274 0.00460039
\(277\) 29.0179 1.74352 0.871759 0.489935i \(-0.162980\pi\)
0.871759 + 0.489935i \(0.162980\pi\)
\(278\) −18.9541 −1.13679
\(279\) 2.23768 0.133967
\(280\) 4.55020 0.271926
\(281\) 1.00727 0.0600888 0.0300444 0.999549i \(-0.490435\pi\)
0.0300444 + 0.999549i \(0.490435\pi\)
\(282\) 7.70604 0.458888
\(283\) −33.1531 −1.97075 −0.985373 0.170414i \(-0.945490\pi\)
−0.985373 + 0.170414i \(0.945490\pi\)
\(284\) −8.52973 −0.506146
\(285\) −2.96620 −0.175703
\(286\) 1.89072 0.111800
\(287\) 3.73087 0.220226
\(288\) −2.54068 −0.149711
\(289\) −6.52834 −0.384020
\(290\) −13.9908 −0.821565
\(291\) 6.21828 0.364522
\(292\) −3.18541 −0.186412
\(293\) 11.2238 0.655701 0.327850 0.944730i \(-0.393676\pi\)
0.327850 + 0.944730i \(0.393676\pi\)
\(294\) −4.01159 −0.233961
\(295\) 26.5946 1.54840
\(296\) −5.39162 −0.313381
\(297\) −4.08530 −0.237053
\(298\) −15.3632 −0.889967
\(299\) 0.195981 0.0113339
\(300\) 9.59333 0.553871
\(301\) −4.85773 −0.279995
\(302\) 16.1717 0.930575
\(303\) −9.59950 −0.551477
\(304\) 1.00000 0.0573539
\(305\) 16.6940 0.955896
\(306\) −8.22162 −0.469999
\(307\) −1.17249 −0.0669175 −0.0334588 0.999440i \(-0.510652\pi\)
−0.0334588 + 0.999440i \(0.510652\pi\)
\(308\) −1.13107 −0.0644488
\(309\) −2.14419 −0.121979
\(310\) 3.85470 0.218932
\(311\) −12.4924 −0.708377 −0.354188 0.935174i \(-0.615243\pi\)
−0.354188 + 0.935174i \(0.615243\pi\)
\(312\) 1.17783 0.0666817
\(313\) 6.41799 0.362766 0.181383 0.983412i \(-0.441943\pi\)
0.181383 + 0.983412i \(0.441943\pi\)
\(314\) 20.0070 1.12906
\(315\) −11.5606 −0.651365
\(316\) −9.57466 −0.538616
\(317\) 16.0619 0.902129 0.451064 0.892491i \(-0.351044\pi\)
0.451064 + 0.892491i \(0.351044\pi\)
\(318\) 4.51847 0.253383
\(319\) 3.47777 0.194718
\(320\) −4.37664 −0.244662
\(321\) 1.68734 0.0941780
\(322\) −0.117241 −0.00653357
\(323\) 3.23599 0.180056
\(324\) 5.07707 0.282059
\(325\) 24.6000 1.36456
\(326\) 7.50860 0.415863
\(327\) 4.77994 0.264331
\(328\) −3.58857 −0.198146
\(329\) −11.8212 −0.651723
\(330\) −3.22702 −0.177642
\(331\) −29.6379 −1.62905 −0.814524 0.580130i \(-0.803002\pi\)
−0.814524 + 0.580130i \(0.803002\pi\)
\(332\) 12.4902 0.685489
\(333\) 13.6984 0.750665
\(334\) 10.5744 0.578604
\(335\) 50.5058 2.75943
\(336\) −0.704609 −0.0384396
\(337\) −4.45504 −0.242682 −0.121341 0.992611i \(-0.538719\pi\)
−0.121341 + 0.992611i \(0.538719\pi\)
\(338\) −9.97971 −0.542824
\(339\) −11.2431 −0.610640
\(340\) −14.1628 −0.768086
\(341\) −0.958188 −0.0518888
\(342\) −2.54068 −0.137384
\(343\) 13.4314 0.725228
\(344\) 4.67245 0.251922
\(345\) −0.334495 −0.0180086
\(346\) 17.9144 0.963086
\(347\) 2.94754 0.158232 0.0791162 0.996865i \(-0.474790\pi\)
0.0791162 + 0.996865i \(0.474790\pi\)
\(348\) 2.16650 0.116137
\(349\) 12.1898 0.652504 0.326252 0.945283i \(-0.394214\pi\)
0.326252 + 0.945283i \(0.394214\pi\)
\(350\) −14.7163 −0.786620
\(351\) −6.52599 −0.348332
\(352\) 1.08793 0.0579869
\(353\) 1.80519 0.0960807 0.0480403 0.998845i \(-0.484702\pi\)
0.0480403 + 0.998845i \(0.484702\pi\)
\(354\) −4.11823 −0.218882
\(355\) 37.3316 1.98135
\(356\) −12.6888 −0.672503
\(357\) −2.28011 −0.120676
\(358\) −22.4848 −1.18836
\(359\) 3.38306 0.178551 0.0892754 0.996007i \(-0.471545\pi\)
0.0892754 + 0.996007i \(0.471545\pi\)
\(360\) 11.1196 0.586056
\(361\) 1.00000 0.0526316
\(362\) 1.63017 0.0856798
\(363\) −6.65291 −0.349187
\(364\) −1.80681 −0.0947028
\(365\) 13.9414 0.729726
\(366\) −2.58511 −0.135126
\(367\) −30.5652 −1.59549 −0.797746 0.602993i \(-0.793975\pi\)
−0.797746 + 0.602993i \(0.793975\pi\)
\(368\) 0.112769 0.00587849
\(369\) 9.11739 0.474632
\(370\) 23.5972 1.22676
\(371\) −6.93140 −0.359860
\(372\) −0.596909 −0.0309483
\(373\) −19.5072 −1.01004 −0.505022 0.863106i \(-0.668516\pi\)
−0.505022 + 0.863106i \(0.668516\pi\)
\(374\) 3.52054 0.182043
\(375\) −27.1556 −1.40231
\(376\) 11.3703 0.586378
\(377\) 5.55552 0.286124
\(378\) 3.90401 0.200801
\(379\) −25.9549 −1.33321 −0.666607 0.745409i \(-0.732254\pi\)
−0.666607 + 0.745409i \(0.732254\pi\)
\(380\) −4.37664 −0.224517
\(381\) −2.38199 −0.122033
\(382\) −3.20936 −0.164205
\(383\) 30.3912 1.55292 0.776460 0.630167i \(-0.217013\pi\)
0.776460 + 0.630167i \(0.217013\pi\)
\(384\) 0.677734 0.0345855
\(385\) 4.95030 0.252291
\(386\) −13.6373 −0.694122
\(387\) −11.8712 −0.603446
\(388\) 9.17511 0.465796
\(389\) 10.7419 0.544636 0.272318 0.962207i \(-0.412210\pi\)
0.272318 + 0.962207i \(0.412210\pi\)
\(390\) −5.15496 −0.261031
\(391\) 0.364920 0.0184548
\(392\) −5.91912 −0.298961
\(393\) −8.79755 −0.443778
\(394\) −24.4141 −1.22997
\(395\) 41.9049 2.10846
\(396\) −2.76408 −0.138900
\(397\) −9.73475 −0.488573 −0.244287 0.969703i \(-0.578554\pi\)
−0.244287 + 0.969703i \(0.578554\pi\)
\(398\) 4.83687 0.242451
\(399\) −0.704609 −0.0352746
\(400\) 14.1550 0.707751
\(401\) 8.63370 0.431146 0.215573 0.976488i \(-0.430838\pi\)
0.215573 + 0.976488i \(0.430838\pi\)
\(402\) −7.82095 −0.390074
\(403\) −1.53064 −0.0762467
\(404\) −14.1641 −0.704691
\(405\) −22.2205 −1.10415
\(406\) −3.32345 −0.164940
\(407\) −5.86571 −0.290752
\(408\) 2.19314 0.108577
\(409\) 0.907335 0.0448648 0.0224324 0.999748i \(-0.492859\pi\)
0.0224324 + 0.999748i \(0.492859\pi\)
\(410\) 15.7059 0.775658
\(411\) 5.68449 0.280395
\(412\) −3.16377 −0.155868
\(413\) 6.31743 0.310860
\(414\) −0.286510 −0.0140812
\(415\) −54.6651 −2.68341
\(416\) 1.73790 0.0852075
\(417\) −12.8459 −0.629064
\(418\) 1.08793 0.0532125
\(419\) −19.6319 −0.959080 −0.479540 0.877520i \(-0.659196\pi\)
−0.479540 + 0.877520i \(0.659196\pi\)
\(420\) 3.08382 0.150475
\(421\) −27.2987 −1.33046 −0.665229 0.746640i \(-0.731666\pi\)
−0.665229 + 0.746640i \(0.731666\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −28.8883 −1.40460
\(424\) 6.66703 0.323779
\(425\) 45.8055 2.22190
\(426\) −5.78088 −0.280085
\(427\) 3.96559 0.191908
\(428\) 2.48968 0.120343
\(429\) 1.28140 0.0618667
\(430\) −20.4496 −0.986169
\(431\) 6.94829 0.334687 0.167344 0.985899i \(-0.446481\pi\)
0.167344 + 0.985899i \(0.446481\pi\)
\(432\) −3.75510 −0.180668
\(433\) −28.7277 −1.38056 −0.690282 0.723540i \(-0.742514\pi\)
−0.690282 + 0.723540i \(0.742514\pi\)
\(434\) 0.915668 0.0439535
\(435\) −9.48201 −0.454627
\(436\) 7.05283 0.337769
\(437\) 0.112769 0.00539447
\(438\) −2.15886 −0.103154
\(439\) 22.0835 1.05399 0.526993 0.849870i \(-0.323319\pi\)
0.526993 + 0.849870i \(0.323319\pi\)
\(440\) −4.76149 −0.226995
\(441\) 15.0386 0.716122
\(442\) 5.62383 0.267498
\(443\) 3.42410 0.162684 0.0813420 0.996686i \(-0.474079\pi\)
0.0813420 + 0.996686i \(0.474079\pi\)
\(444\) −3.65408 −0.173415
\(445\) 55.5342 2.63257
\(446\) 3.93852 0.186494
\(447\) −10.4122 −0.492479
\(448\) −1.03965 −0.0491190
\(449\) −6.45014 −0.304401 −0.152200 0.988350i \(-0.548636\pi\)
−0.152200 + 0.988350i \(0.548636\pi\)
\(450\) −35.9633 −1.69533
\(451\) −3.90412 −0.183838
\(452\) −16.5892 −0.780291
\(453\) 10.9601 0.514950
\(454\) 2.97691 0.139713
\(455\) 7.90778 0.370723
\(456\) 0.677734 0.0317378
\(457\) 17.0170 0.796023 0.398012 0.917380i \(-0.369700\pi\)
0.398012 + 0.917380i \(0.369700\pi\)
\(458\) −24.6325 −1.15100
\(459\) −12.1515 −0.567183
\(460\) −0.493550 −0.0230119
\(461\) −6.85354 −0.319201 −0.159601 0.987182i \(-0.551021\pi\)
−0.159601 + 0.987182i \(0.551021\pi\)
\(462\) −0.766566 −0.0356639
\(463\) −13.7414 −0.638615 −0.319308 0.947651i \(-0.603450\pi\)
−0.319308 + 0.947651i \(0.603450\pi\)
\(464\) 3.19669 0.148402
\(465\) 2.61246 0.121150
\(466\) 3.21421 0.148896
\(467\) 33.1199 1.53261 0.766303 0.642480i \(-0.222094\pi\)
0.766303 + 0.642480i \(0.222094\pi\)
\(468\) −4.41544 −0.204104
\(469\) 11.9975 0.553991
\(470\) −49.7638 −2.29543
\(471\) 13.5594 0.624784
\(472\) −6.07647 −0.279692
\(473\) 5.08330 0.233731
\(474\) −6.48907 −0.298053
\(475\) 14.1550 0.649477
\(476\) −3.36431 −0.154203
\(477\) −16.9388 −0.775572
\(478\) 1.83792 0.0840646
\(479\) 10.3502 0.472913 0.236456 0.971642i \(-0.424014\pi\)
0.236456 + 0.971642i \(0.424014\pi\)
\(480\) −2.96620 −0.135388
\(481\) −9.37009 −0.427239
\(482\) 2.01575 0.0918147
\(483\) −0.0794580 −0.00361546
\(484\) −9.81641 −0.446200
\(485\) −40.1562 −1.82340
\(486\) 14.7062 0.667087
\(487\) −8.92066 −0.404234 −0.202117 0.979361i \(-0.564782\pi\)
−0.202117 + 0.979361i \(0.564782\pi\)
\(488\) −3.81434 −0.172667
\(489\) 5.08883 0.230125
\(490\) 25.9059 1.17031
\(491\) 26.0318 1.17480 0.587400 0.809297i \(-0.300152\pi\)
0.587400 + 0.809297i \(0.300152\pi\)
\(492\) −2.43209 −0.109647
\(493\) 10.3445 0.465891
\(494\) 1.73790 0.0781918
\(495\) 12.0974 0.543738
\(496\) −0.880743 −0.0395465
\(497\) 8.86796 0.397783
\(498\) 8.46503 0.379327
\(499\) −4.96533 −0.222279 −0.111139 0.993805i \(-0.535450\pi\)
−0.111139 + 0.993805i \(0.535450\pi\)
\(500\) −40.0682 −1.79191
\(501\) 7.16661 0.320181
\(502\) 1.53715 0.0686063
\(503\) −15.5829 −0.694808 −0.347404 0.937716i \(-0.612937\pi\)
−0.347404 + 0.937716i \(0.612937\pi\)
\(504\) 2.64142 0.117658
\(505\) 61.9913 2.75858
\(506\) 0.122685 0.00545401
\(507\) −6.76358 −0.300381
\(508\) −3.51464 −0.155937
\(509\) −18.7446 −0.830842 −0.415421 0.909629i \(-0.636366\pi\)
−0.415421 + 0.909629i \(0.636366\pi\)
\(510\) −9.59861 −0.425033
\(511\) 3.31172 0.146502
\(512\) 1.00000 0.0441942
\(513\) −3.75510 −0.165792
\(514\) −13.8071 −0.609005
\(515\) 13.8467 0.610159
\(516\) 3.16668 0.139405
\(517\) 12.3701 0.544037
\(518\) 5.60542 0.246288
\(519\) 12.1412 0.532940
\(520\) −7.60617 −0.333553
\(521\) 4.43158 0.194151 0.0970755 0.995277i \(-0.469051\pi\)
0.0970755 + 0.995277i \(0.469051\pi\)
\(522\) −8.12174 −0.355479
\(523\) −0.307784 −0.0134585 −0.00672923 0.999977i \(-0.502142\pi\)
−0.00672923 + 0.999977i \(0.502142\pi\)
\(524\) −12.9808 −0.567070
\(525\) −9.97374 −0.435290
\(526\) −10.5628 −0.460560
\(527\) −2.85008 −0.124151
\(528\) 0.737328 0.0320881
\(529\) −22.9873 −0.999447
\(530\) −29.1792 −1.26746
\(531\) 15.4384 0.669968
\(532\) −1.03965 −0.0450747
\(533\) −6.23657 −0.270136
\(534\) −8.59961 −0.372141
\(535\) −10.8964 −0.471094
\(536\) −11.5399 −0.498446
\(537\) −15.2387 −0.657600
\(538\) 16.6982 0.719912
\(539\) −6.43960 −0.277373
\(540\) 16.4348 0.707239
\(541\) 4.14272 0.178109 0.0890546 0.996027i \(-0.471615\pi\)
0.0890546 + 0.996027i \(0.471615\pi\)
\(542\) −2.72534 −0.117063
\(543\) 1.10482 0.0474124
\(544\) 3.23599 0.138742
\(545\) −30.8677 −1.32223
\(546\) −1.22454 −0.0524054
\(547\) −29.3319 −1.25414 −0.627070 0.778963i \(-0.715746\pi\)
−0.627070 + 0.778963i \(0.715746\pi\)
\(548\) 8.38749 0.358296
\(549\) 9.69100 0.413602
\(550\) 15.3997 0.656645
\(551\) 3.19669 0.136183
\(552\) 0.0764274 0.00325296
\(553\) 9.95433 0.423301
\(554\) 29.0179 1.23285
\(555\) 15.9926 0.678849
\(556\) −18.9541 −0.803834
\(557\) 11.4328 0.484422 0.242211 0.970224i \(-0.422127\pi\)
0.242211 + 0.970224i \(0.422127\pi\)
\(558\) 2.23768 0.0947287
\(559\) 8.12025 0.343450
\(560\) 4.55020 0.192281
\(561\) 2.38599 0.100737
\(562\) 1.00727 0.0424892
\(563\) −43.2521 −1.82286 −0.911430 0.411455i \(-0.865021\pi\)
−0.911430 + 0.411455i \(0.865021\pi\)
\(564\) 7.70604 0.324483
\(565\) 72.6051 3.05452
\(566\) −33.1531 −1.39353
\(567\) −5.27840 −0.221672
\(568\) −8.52973 −0.357899
\(569\) −24.0639 −1.00881 −0.504406 0.863466i \(-0.668289\pi\)
−0.504406 + 0.863466i \(0.668289\pi\)
\(570\) −2.96620 −0.124240
\(571\) 8.73645 0.365609 0.182805 0.983149i \(-0.441482\pi\)
0.182805 + 0.983149i \(0.441482\pi\)
\(572\) 1.89072 0.0790548
\(573\) −2.17509 −0.0908658
\(574\) 3.73087 0.155723
\(575\) 1.59625 0.0665681
\(576\) −2.54068 −0.105862
\(577\) 34.3770 1.43113 0.715567 0.698544i \(-0.246169\pi\)
0.715567 + 0.698544i \(0.246169\pi\)
\(578\) −6.52834 −0.271543
\(579\) −9.24248 −0.384104
\(580\) −13.9908 −0.580934
\(581\) −12.9855 −0.538729
\(582\) 6.21828 0.257756
\(583\) 7.25327 0.300400
\(584\) −3.18541 −0.131813
\(585\) 19.3248 0.798983
\(586\) 11.2238 0.463650
\(587\) 22.1454 0.914039 0.457020 0.889457i \(-0.348917\pi\)
0.457020 + 0.889457i \(0.348917\pi\)
\(588\) −4.01159 −0.165435
\(589\) −0.880743 −0.0362904
\(590\) 26.5946 1.09488
\(591\) −16.5463 −0.680624
\(592\) −5.39162 −0.221594
\(593\) 27.9209 1.14657 0.573287 0.819355i \(-0.305668\pi\)
0.573287 + 0.819355i \(0.305668\pi\)
\(594\) −4.08530 −0.167622
\(595\) 14.7244 0.603642
\(596\) −15.3632 −0.629302
\(597\) 3.27811 0.134164
\(598\) 0.195981 0.00801427
\(599\) 1.89628 0.0774798 0.0387399 0.999249i \(-0.487666\pi\)
0.0387399 + 0.999249i \(0.487666\pi\)
\(600\) 9.59333 0.391646
\(601\) −20.6199 −0.841102 −0.420551 0.907269i \(-0.638163\pi\)
−0.420551 + 0.907269i \(0.638163\pi\)
\(602\) −4.85773 −0.197986
\(603\) 29.3190 1.19396
\(604\) 16.1717 0.658016
\(605\) 42.9629 1.74669
\(606\) −9.59950 −0.389953
\(607\) −28.1411 −1.14221 −0.571107 0.820876i \(-0.693486\pi\)
−0.571107 + 0.820876i \(0.693486\pi\)
\(608\) 1.00000 0.0405554
\(609\) −2.25241 −0.0912723
\(610\) 16.6940 0.675920
\(611\) 19.7604 0.799422
\(612\) −8.22162 −0.332339
\(613\) 1.60168 0.0646911 0.0323455 0.999477i \(-0.489702\pi\)
0.0323455 + 0.999477i \(0.489702\pi\)
\(614\) −1.17249 −0.0473178
\(615\) 10.6444 0.429224
\(616\) −1.13107 −0.0455722
\(617\) −22.0485 −0.887640 −0.443820 0.896116i \(-0.646377\pi\)
−0.443820 + 0.896116i \(0.646377\pi\)
\(618\) −2.14419 −0.0862522
\(619\) −29.7628 −1.19627 −0.598135 0.801396i \(-0.704091\pi\)
−0.598135 + 0.801396i \(0.704091\pi\)
\(620\) 3.85470 0.154808
\(621\) −0.423459 −0.0169928
\(622\) −12.4924 −0.500898
\(623\) 13.1919 0.528523
\(624\) 1.17783 0.0471511
\(625\) 104.589 4.18357
\(626\) 6.41799 0.256515
\(627\) 0.737328 0.0294460
\(628\) 20.0070 0.798365
\(629\) −17.4472 −0.695667
\(630\) −11.5606 −0.460584
\(631\) −9.89467 −0.393901 −0.196950 0.980413i \(-0.563104\pi\)
−0.196950 + 0.980413i \(0.563104\pi\)
\(632\) −9.57466 −0.380859
\(633\) −0.677734 −0.0269375
\(634\) 16.0619 0.637901
\(635\) 15.3823 0.610429
\(636\) 4.51847 0.179169
\(637\) −10.2868 −0.407579
\(638\) 3.47777 0.137686
\(639\) 21.6713 0.857303
\(640\) −4.37664 −0.173002
\(641\) 37.3617 1.47570 0.737849 0.674965i \(-0.235841\pi\)
0.737849 + 0.674965i \(0.235841\pi\)
\(642\) 1.68734 0.0665939
\(643\) −27.7726 −1.09524 −0.547622 0.836726i \(-0.684467\pi\)
−0.547622 + 0.836726i \(0.684467\pi\)
\(644\) −0.117241 −0.00461993
\(645\) −13.8594 −0.545714
\(646\) 3.23599 0.127319
\(647\) −29.6180 −1.16440 −0.582202 0.813044i \(-0.697809\pi\)
−0.582202 + 0.813044i \(0.697809\pi\)
\(648\) 5.07707 0.199446
\(649\) −6.61079 −0.259496
\(650\) 24.6000 0.964891
\(651\) 0.620579 0.0243224
\(652\) 7.50860 0.294060
\(653\) 17.4693 0.683626 0.341813 0.939768i \(-0.388959\pi\)
0.341813 + 0.939768i \(0.388959\pi\)
\(654\) 4.77994 0.186911
\(655\) 56.8125 2.21985
\(656\) −3.58857 −0.140110
\(657\) 8.09309 0.315741
\(658\) −11.8212 −0.460838
\(659\) 13.7271 0.534733 0.267367 0.963595i \(-0.413847\pi\)
0.267367 + 0.963595i \(0.413847\pi\)
\(660\) −3.22702 −0.125612
\(661\) 31.9960 1.24450 0.622249 0.782819i \(-0.286219\pi\)
0.622249 + 0.782819i \(0.286219\pi\)
\(662\) −29.6379 −1.15191
\(663\) 3.81146 0.148025
\(664\) 12.4902 0.484714
\(665\) 4.55020 0.176449
\(666\) 13.6984 0.530800
\(667\) 0.360487 0.0139581
\(668\) 10.5744 0.409135
\(669\) 2.66927 0.103200
\(670\) 50.5058 1.95121
\(671\) −4.14974 −0.160199
\(672\) −0.704609 −0.0271809
\(673\) 4.33516 0.167108 0.0835541 0.996503i \(-0.473373\pi\)
0.0835541 + 0.996503i \(0.473373\pi\)
\(674\) −4.45504 −0.171602
\(675\) −53.1535 −2.04588
\(676\) −9.97971 −0.383835
\(677\) 30.9367 1.18899 0.594497 0.804098i \(-0.297351\pi\)
0.594497 + 0.804098i \(0.297351\pi\)
\(678\) −11.2431 −0.431788
\(679\) −9.53894 −0.366071
\(680\) −14.1628 −0.543118
\(681\) 2.01755 0.0773128
\(682\) −0.958188 −0.0366909
\(683\) 14.5295 0.555957 0.277978 0.960587i \(-0.410336\pi\)
0.277978 + 0.960587i \(0.410336\pi\)
\(684\) −2.54068 −0.0971452
\(685\) −36.7091 −1.40258
\(686\) 13.4314 0.512814
\(687\) −16.6943 −0.636927
\(688\) 4.67245 0.178135
\(689\) 11.5866 0.441415
\(690\) −0.334495 −0.0127340
\(691\) −14.3955 −0.547632 −0.273816 0.961782i \(-0.588286\pi\)
−0.273816 + 0.961782i \(0.588286\pi\)
\(692\) 17.9144 0.681004
\(693\) 2.87369 0.109162
\(694\) 2.94754 0.111887
\(695\) 82.9554 3.14668
\(696\) 2.16650 0.0821210
\(697\) −11.6126 −0.439858
\(698\) 12.1898 0.461390
\(699\) 2.17838 0.0823940
\(700\) −14.7163 −0.556224
\(701\) 5.95449 0.224898 0.112449 0.993657i \(-0.464131\pi\)
0.112449 + 0.993657i \(0.464131\pi\)
\(702\) −6.52599 −0.246308
\(703\) −5.39162 −0.203349
\(704\) 1.08793 0.0410030
\(705\) −33.7266 −1.27022
\(706\) 1.80519 0.0679393
\(707\) 14.7258 0.553820
\(708\) −4.11823 −0.154773
\(709\) −18.9234 −0.710682 −0.355341 0.934737i \(-0.615635\pi\)
−0.355341 + 0.934737i \(0.615635\pi\)
\(710\) 37.3316 1.40103
\(711\) 24.3261 0.912300
\(712\) −12.6888 −0.475532
\(713\) −0.0993205 −0.00371958
\(714\) −2.28011 −0.0853310
\(715\) −8.27499 −0.309467
\(716\) −22.4848 −0.840298
\(717\) 1.24562 0.0465186
\(718\) 3.38306 0.126255
\(719\) −9.62073 −0.358793 −0.179396 0.983777i \(-0.557414\pi\)
−0.179396 + 0.983777i \(0.557414\pi\)
\(720\) 11.1196 0.414404
\(721\) 3.28923 0.122497
\(722\) 1.00000 0.0372161
\(723\) 1.36614 0.0508073
\(724\) 1.63017 0.0605847
\(725\) 45.2491 1.68051
\(726\) −6.65291 −0.246913
\(727\) −43.6033 −1.61716 −0.808579 0.588387i \(-0.799763\pi\)
−0.808579 + 0.588387i \(0.799763\pi\)
\(728\) −1.80681 −0.0669650
\(729\) −5.26431 −0.194974
\(730\) 13.9414 0.515994
\(731\) 15.1200 0.559234
\(732\) −2.58511 −0.0955483
\(733\) 26.9647 0.995964 0.497982 0.867187i \(-0.334075\pi\)
0.497982 + 0.867187i \(0.334075\pi\)
\(734\) −30.5652 −1.12818
\(735\) 17.5573 0.647610
\(736\) 0.112769 0.00415672
\(737\) −12.5546 −0.462454
\(738\) 9.11739 0.335616
\(739\) −13.8465 −0.509353 −0.254677 0.967026i \(-0.581969\pi\)
−0.254677 + 0.967026i \(0.581969\pi\)
\(740\) 23.5972 0.867450
\(741\) 1.17783 0.0432688
\(742\) −6.93140 −0.254460
\(743\) 17.1248 0.628248 0.314124 0.949382i \(-0.398289\pi\)
0.314124 + 0.949382i \(0.398289\pi\)
\(744\) −0.596909 −0.0218838
\(745\) 67.2393 2.46346
\(746\) −19.5072 −0.714210
\(747\) −31.7336 −1.16107
\(748\) 3.52054 0.128724
\(749\) −2.58840 −0.0945782
\(750\) −27.1556 −0.991582
\(751\) 32.5624 1.18822 0.594109 0.804384i \(-0.297505\pi\)
0.594109 + 0.804384i \(0.297505\pi\)
\(752\) 11.3703 0.414632
\(753\) 1.04178 0.0379645
\(754\) 5.55552 0.202320
\(755\) −70.7776 −2.57586
\(756\) 3.90401 0.141987
\(757\) −25.7400 −0.935535 −0.467767 0.883852i \(-0.654942\pi\)
−0.467767 + 0.883852i \(0.654942\pi\)
\(758\) −25.9549 −0.942725
\(759\) 0.0831477 0.00301807
\(760\) −4.37664 −0.158758
\(761\) 11.3198 0.410344 0.205172 0.978726i \(-0.434225\pi\)
0.205172 + 0.978726i \(0.434225\pi\)
\(762\) −2.38199 −0.0862904
\(763\) −7.33250 −0.265454
\(764\) −3.20936 −0.116111
\(765\) 35.9831 1.30097
\(766\) 30.3912 1.09808
\(767\) −10.5603 −0.381310
\(768\) 0.677734 0.0244556
\(769\) 35.1897 1.26897 0.634487 0.772933i \(-0.281211\pi\)
0.634487 + 0.772933i \(0.281211\pi\)
\(770\) 4.95030 0.178396
\(771\) −9.35754 −0.337004
\(772\) −13.6373 −0.490818
\(773\) 15.8358 0.569576 0.284788 0.958591i \(-0.408077\pi\)
0.284788 + 0.958591i \(0.408077\pi\)
\(774\) −11.8712 −0.426701
\(775\) −12.4669 −0.447825
\(776\) 9.17511 0.329367
\(777\) 3.79898 0.136288
\(778\) 10.7419 0.385116
\(779\) −3.58857 −0.128574
\(780\) −5.15496 −0.184577
\(781\) −9.27976 −0.332056
\(782\) 0.364920 0.0130495
\(783\) −12.0039 −0.428984
\(784\) −5.91912 −0.211397
\(785\) −87.5634 −3.12527
\(786\) −8.79755 −0.313798
\(787\) −34.6096 −1.23370 −0.616849 0.787081i \(-0.711591\pi\)
−0.616849 + 0.787081i \(0.711591\pi\)
\(788\) −24.4141 −0.869718
\(789\) −7.15876 −0.254859
\(790\) 41.9049 1.49091
\(791\) 17.2470 0.613234
\(792\) −2.76408 −0.0982174
\(793\) −6.62894 −0.235400
\(794\) −9.73475 −0.345473
\(795\) −19.7757 −0.701373
\(796\) 4.83687 0.171438
\(797\) 22.2230 0.787179 0.393589 0.919286i \(-0.371233\pi\)
0.393589 + 0.919286i \(0.371233\pi\)
\(798\) −0.704609 −0.0249429
\(799\) 36.7942 1.30169
\(800\) 14.1550 0.500455
\(801\) 32.2381 1.13908
\(802\) 8.63370 0.304867
\(803\) −3.46550 −0.122295
\(804\) −7.82095 −0.275824
\(805\) 0.513121 0.0180851
\(806\) −1.53064 −0.0539146
\(807\) 11.3170 0.398376
\(808\) −14.1641 −0.498292
\(809\) 14.4195 0.506962 0.253481 0.967340i \(-0.418424\pi\)
0.253481 + 0.967340i \(0.418424\pi\)
\(810\) −22.2205 −0.780750
\(811\) 55.7753 1.95854 0.979268 0.202569i \(-0.0649291\pi\)
0.979268 + 0.202569i \(0.0649291\pi\)
\(812\) −3.32345 −0.116630
\(813\) −1.84706 −0.0647791
\(814\) −5.86571 −0.205593
\(815\) −32.8625 −1.15112
\(816\) 2.19314 0.0767754
\(817\) 4.67245 0.163468
\(818\) 0.907335 0.0317242
\(819\) 4.59053 0.160406
\(820\) 15.7059 0.548473
\(821\) −52.6843 −1.83870 −0.919348 0.393446i \(-0.871283\pi\)
−0.919348 + 0.393446i \(0.871283\pi\)
\(822\) 5.68449 0.198269
\(823\) −10.9292 −0.380969 −0.190484 0.981690i \(-0.561006\pi\)
−0.190484 + 0.981690i \(0.561006\pi\)
\(824\) −3.16377 −0.110215
\(825\) 10.4369 0.363366
\(826\) 6.31743 0.219812
\(827\) −28.5567 −0.993012 −0.496506 0.868033i \(-0.665384\pi\)
−0.496506 + 0.868033i \(0.665384\pi\)
\(828\) −0.286510 −0.00995690
\(829\) 31.2443 1.08516 0.542580 0.840004i \(-0.317448\pi\)
0.542580 + 0.840004i \(0.317448\pi\)
\(830\) −54.6651 −1.89745
\(831\) 19.6664 0.682221
\(832\) 1.73790 0.0602508
\(833\) −19.1542 −0.663655
\(834\) −12.8459 −0.444815
\(835\) −46.2803 −1.60159
\(836\) 1.08793 0.0376269
\(837\) 3.30728 0.114316
\(838\) −19.6319 −0.678172
\(839\) −25.6234 −0.884616 −0.442308 0.896863i \(-0.645840\pi\)
−0.442308 + 0.896863i \(0.645840\pi\)
\(840\) 3.08382 0.106402
\(841\) −18.7812 −0.647628
\(842\) −27.2987 −0.940775
\(843\) 0.682662 0.0235121
\(844\) −1.00000 −0.0344214
\(845\) 43.6776 1.50256
\(846\) −28.8883 −0.993199
\(847\) 10.2057 0.350671
\(848\) 6.66703 0.228947
\(849\) −22.4690 −0.771132
\(850\) 45.8055 1.57112
\(851\) −0.608007 −0.0208422
\(852\) −5.78088 −0.198050
\(853\) 22.0570 0.755219 0.377609 0.925965i \(-0.376746\pi\)
0.377609 + 0.925965i \(0.376746\pi\)
\(854\) 3.96559 0.135700
\(855\) 11.1196 0.380284
\(856\) 2.48968 0.0850954
\(857\) 24.5272 0.837834 0.418917 0.908024i \(-0.362410\pi\)
0.418917 + 0.908024i \(0.362410\pi\)
\(858\) 1.28140 0.0437463
\(859\) −28.2679 −0.964489 −0.482244 0.876037i \(-0.660178\pi\)
−0.482244 + 0.876037i \(0.660178\pi\)
\(860\) −20.4496 −0.697327
\(861\) 2.52854 0.0861723
\(862\) 6.94829 0.236660
\(863\) 28.0607 0.955198 0.477599 0.878578i \(-0.341507\pi\)
0.477599 + 0.878578i \(0.341507\pi\)
\(864\) −3.75510 −0.127751
\(865\) −78.4051 −2.66585
\(866\) −28.7277 −0.976207
\(867\) −4.42448 −0.150263
\(868\) 0.915668 0.0310798
\(869\) −10.4166 −0.353358
\(870\) −9.48201 −0.321470
\(871\) −20.0551 −0.679541
\(872\) 7.05283 0.238839
\(873\) −23.3110 −0.788957
\(874\) 0.112769 0.00381447
\(875\) 41.6571 1.40827
\(876\) −2.15886 −0.0729410
\(877\) −25.9774 −0.877195 −0.438597 0.898684i \(-0.644525\pi\)
−0.438597 + 0.898684i \(0.644525\pi\)
\(878\) 22.0835 0.745281
\(879\) 7.60674 0.256569
\(880\) −4.76149 −0.160510
\(881\) 50.2449 1.69279 0.846397 0.532553i \(-0.178767\pi\)
0.846397 + 0.532553i \(0.178767\pi\)
\(882\) 15.0386 0.506375
\(883\) 11.2831 0.379707 0.189854 0.981812i \(-0.439199\pi\)
0.189854 + 0.981812i \(0.439199\pi\)
\(884\) 5.62383 0.189150
\(885\) 18.0240 0.605871
\(886\) 3.42410 0.115035
\(887\) −44.7976 −1.50416 −0.752078 0.659074i \(-0.770948\pi\)
−0.752078 + 0.659074i \(0.770948\pi\)
\(888\) −3.65408 −0.122623
\(889\) 3.65401 0.122552
\(890\) 55.5342 1.86151
\(891\) 5.52350 0.185044
\(892\) 3.93852 0.131871
\(893\) 11.3703 0.380493
\(894\) −10.4122 −0.348235
\(895\) 98.4082 3.28942
\(896\) −1.03965 −0.0347324
\(897\) 0.132823 0.00443483
\(898\) −6.45014 −0.215244
\(899\) −2.81546 −0.0939008
\(900\) −35.9633 −1.19878
\(901\) 21.5745 0.718749
\(902\) −3.90412 −0.129993
\(903\) −3.29225 −0.109559
\(904\) −16.5892 −0.551749
\(905\) −7.13467 −0.237164
\(906\) 10.9601 0.364124
\(907\) 5.01363 0.166475 0.0832374 0.996530i \(-0.473474\pi\)
0.0832374 + 0.996530i \(0.473474\pi\)
\(908\) 2.97691 0.0987923
\(909\) 35.9864 1.19359
\(910\) 7.90778 0.262140
\(911\) −55.3502 −1.83384 −0.916918 0.399077i \(-0.869331\pi\)
−0.916918 + 0.399077i \(0.869331\pi\)
\(912\) 0.677734 0.0224420
\(913\) 13.5885 0.449713
\(914\) 17.0170 0.562873
\(915\) 11.3141 0.374032
\(916\) −24.6325 −0.813882
\(917\) 13.4956 0.445663
\(918\) −12.1515 −0.401059
\(919\) −15.0345 −0.495943 −0.247971 0.968767i \(-0.579764\pi\)
−0.247971 + 0.968767i \(0.579764\pi\)
\(920\) −0.493550 −0.0162719
\(921\) −0.794636 −0.0261841
\(922\) −6.85354 −0.225709
\(923\) −14.8238 −0.487932
\(924\) −0.766566 −0.0252182
\(925\) −76.3184 −2.50933
\(926\) −13.7414 −0.451569
\(927\) 8.03812 0.264007
\(928\) 3.19669 0.104936
\(929\) 56.2773 1.84640 0.923198 0.384324i \(-0.125565\pi\)
0.923198 + 0.384324i \(0.125565\pi\)
\(930\) 2.61246 0.0856659
\(931\) −5.91912 −0.193991
\(932\) 3.21421 0.105285
\(933\) −8.46650 −0.277181
\(934\) 33.1199 1.08372
\(935\) −15.4081 −0.503900
\(936\) −4.41544 −0.144323
\(937\) −28.8804 −0.943481 −0.471740 0.881737i \(-0.656374\pi\)
−0.471740 + 0.881737i \(0.656374\pi\)
\(938\) 11.9975 0.391731
\(939\) 4.34969 0.141947
\(940\) −49.7638 −1.62311
\(941\) −0.483464 −0.0157605 −0.00788024 0.999969i \(-0.502508\pi\)
−0.00788024 + 0.999969i \(0.502508\pi\)
\(942\) 13.5594 0.441789
\(943\) −0.404679 −0.0131782
\(944\) −6.07647 −0.197772
\(945\) −17.0865 −0.555823
\(946\) 5.08330 0.165272
\(947\) 4.38320 0.142435 0.0712174 0.997461i \(-0.477312\pi\)
0.0712174 + 0.997461i \(0.477312\pi\)
\(948\) −6.48907 −0.210755
\(949\) −5.53592 −0.179703
\(950\) 14.1550 0.459249
\(951\) 10.8857 0.352994
\(952\) −3.36431 −0.109038
\(953\) 40.0977 1.29889 0.649446 0.760408i \(-0.275001\pi\)
0.649446 + 0.760408i \(0.275001\pi\)
\(954\) −16.9388 −0.548413
\(955\) 14.0462 0.454525
\(956\) 1.83792 0.0594427
\(957\) 2.35700 0.0761911
\(958\) 10.3502 0.334400
\(959\) −8.72009 −0.281586
\(960\) −2.96620 −0.0957337
\(961\) −30.2243 −0.974977
\(962\) −9.37009 −0.302104
\(963\) −6.32546 −0.203835
\(964\) 2.01575 0.0649228
\(965\) 59.6857 1.92135
\(966\) −0.0794580 −0.00255652
\(967\) 33.0590 1.06311 0.531553 0.847025i \(-0.321608\pi\)
0.531553 + 0.847025i \(0.321608\pi\)
\(968\) −9.81641 −0.315511
\(969\) 2.19314 0.0704539
\(970\) −40.1562 −1.28934
\(971\) −0.210526 −0.00675609 −0.00337804 0.999994i \(-0.501075\pi\)
−0.00337804 + 0.999994i \(0.501075\pi\)
\(972\) 14.7062 0.471702
\(973\) 19.7057 0.631737
\(974\) −8.92066 −0.285836
\(975\) 16.6722 0.533939
\(976\) −3.81434 −0.122094
\(977\) 5.30124 0.169602 0.0848009 0.996398i \(-0.472975\pi\)
0.0848009 + 0.996398i \(0.472975\pi\)
\(978\) 5.08883 0.162723
\(979\) −13.8045 −0.441194
\(980\) 25.9059 0.827533
\(981\) −17.9190 −0.572109
\(982\) 26.0318 0.830709
\(983\) 39.0136 1.24434 0.622170 0.782882i \(-0.286251\pi\)
0.622170 + 0.782882i \(0.286251\pi\)
\(984\) −2.43209 −0.0775323
\(985\) 106.852 3.40459
\(986\) 10.3445 0.329435
\(987\) −8.01161 −0.255012
\(988\) 1.73790 0.0552899
\(989\) 0.526907 0.0167547
\(990\) 12.0974 0.384481
\(991\) 7.95223 0.252611 0.126305 0.991991i \(-0.459688\pi\)
0.126305 + 0.991991i \(0.459688\pi\)
\(992\) −0.880743 −0.0279636
\(993\) −20.0866 −0.637430
\(994\) 8.86796 0.281275
\(995\) −21.1693 −0.671111
\(996\) 8.46503 0.268225
\(997\) −43.0933 −1.36478 −0.682389 0.730989i \(-0.739059\pi\)
−0.682389 + 0.730989i \(0.739059\pi\)
\(998\) −4.96533 −0.157175
\(999\) 20.2461 0.640558
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 \(a_p\))