Properties

Label 8018.2.a.j.1.17
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 47
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: \(0\)
Dimension: \(47\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.03614 q^{3}\) \(+1.00000 q^{4}\) \(+0.118794 q^{5}\) \(-1.03614 q^{6}\) \(+2.13406 q^{7}\) \(+1.00000 q^{8}\) \(-1.92642 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.03614 q^{3}\) \(+1.00000 q^{4}\) \(+0.118794 q^{5}\) \(-1.03614 q^{6}\) \(+2.13406 q^{7}\) \(+1.00000 q^{8}\) \(-1.92642 q^{9}\) \(+0.118794 q^{10}\) \(+5.30344 q^{11}\) \(-1.03614 q^{12}\) \(+0.953466 q^{13}\) \(+2.13406 q^{14}\) \(-0.123087 q^{15}\) \(+1.00000 q^{16}\) \(-1.40790 q^{17}\) \(-1.92642 q^{18}\) \(-1.00000 q^{19}\) \(+0.118794 q^{20}\) \(-2.21118 q^{21}\) \(+5.30344 q^{22}\) \(-7.01405 q^{23}\) \(-1.03614 q^{24}\) \(-4.98589 q^{25}\) \(+0.953466 q^{26}\) \(+5.10445 q^{27}\) \(+2.13406 q^{28}\) \(-3.22709 q^{29}\) \(-0.123087 q^{30}\) \(+5.86651 q^{31}\) \(+1.00000 q^{32}\) \(-5.49510 q^{33}\) \(-1.40790 q^{34}\) \(+0.253514 q^{35}\) \(-1.92642 q^{36}\) \(+9.27789 q^{37}\) \(-1.00000 q^{38}\) \(-0.987923 q^{39}\) \(+0.118794 q^{40}\) \(+6.08967 q^{41}\) \(-2.21118 q^{42}\) \(+11.1940 q^{43}\) \(+5.30344 q^{44}\) \(-0.228847 q^{45}\) \(-7.01405 q^{46}\) \(+5.03802 q^{47}\) \(-1.03614 q^{48}\) \(-2.44578 q^{49}\) \(-4.98589 q^{50}\) \(+1.45878 q^{51}\) \(+0.953466 q^{52}\) \(-12.2837 q^{53}\) \(+5.10445 q^{54}\) \(+0.630018 q^{55}\) \(+2.13406 q^{56}\) \(+1.03614 q^{57}\) \(-3.22709 q^{58}\) \(-6.60513 q^{59}\) \(-0.123087 q^{60}\) \(+8.99482 q^{61}\) \(+5.86651 q^{62}\) \(-4.11109 q^{63}\) \(+1.00000 q^{64}\) \(+0.113266 q^{65}\) \(-5.49510 q^{66}\) \(+5.49250 q^{67}\) \(-1.40790 q^{68}\) \(+7.26753 q^{69}\) \(+0.253514 q^{70}\) \(+13.7678 q^{71}\) \(-1.92642 q^{72}\) \(+13.0402 q^{73}\) \(+9.27789 q^{74}\) \(+5.16607 q^{75}\) \(-1.00000 q^{76}\) \(+11.3179 q^{77}\) \(-0.987923 q^{78}\) \(+9.40559 q^{79}\) \(+0.118794 q^{80}\) \(+0.490332 q^{81}\) \(+6.08967 q^{82}\) \(-1.93571 q^{83}\) \(-2.21118 q^{84}\) \(-0.167250 q^{85}\) \(+11.1940 q^{86}\) \(+3.34371 q^{87}\) \(+5.30344 q^{88}\) \(-16.4497 q^{89}\) \(-0.228847 q^{90}\) \(+2.03476 q^{91}\) \(-7.01405 q^{92}\) \(-6.07852 q^{93}\) \(+5.03802 q^{94}\) \(-0.118794 q^{95}\) \(-1.03614 q^{96}\) \(-5.85181 q^{97}\) \(-2.44578 q^{98}\) \(-10.2166 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 27q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 47q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 69q^{18} \) \(\mathstrut -\mathstrut 47q^{19} \) \(\mathstrut +\mathstrut 15q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 86q^{25} \) \(\mathstrut +\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 43q^{27} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut +\mathstrut 78q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 53q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut +\mathstrut 47q^{43} \) \(\mathstrut +\mathstrut 17q^{44} \) \(\mathstrut +\mathstrut 23q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 93q^{49} \) \(\mathstrut +\mathstrut 86q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 27q^{52} \) \(\mathstrut +\mathstrut 43q^{53} \) \(\mathstrut +\mathstrut 43q^{54} \) \(\mathstrut +\mathstrut 23q^{55} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 21q^{62} \) \(\mathstrut -\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 47q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 68q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 69q^{72} \) \(\mathstrut +\mathstrut 35q^{73} \) \(\mathstrut +\mathstrut 78q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 47q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 123q^{81} \) \(\mathstrut +\mathstrut 53q^{82} \) \(\mathstrut +\mathstrut 23q^{83} \) \(\mathstrut +\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 47q^{86} \) \(\mathstrut +\mathstrut 39q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 49q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 91q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 88q^{97} \) \(\mathstrut +\mathstrut 93q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.03614 −0.598215 −0.299107 0.954219i \(-0.596689\pi\)
−0.299107 + 0.954219i \(0.596689\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.118794 0.0531263 0.0265632 0.999647i \(-0.491544\pi\)
0.0265632 + 0.999647i \(0.491544\pi\)
\(6\) −1.03614 −0.423002
\(7\) 2.13406 0.806600 0.403300 0.915068i \(-0.367863\pi\)
0.403300 + 0.915068i \(0.367863\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.92642 −0.642139
\(10\) 0.118794 0.0375660
\(11\) 5.30344 1.59905 0.799524 0.600634i \(-0.205085\pi\)
0.799524 + 0.600634i \(0.205085\pi\)
\(12\) −1.03614 −0.299107
\(13\) 0.953466 0.264444 0.132222 0.991220i \(-0.457789\pi\)
0.132222 + 0.991220i \(0.457789\pi\)
\(14\) 2.13406 0.570352
\(15\) −0.123087 −0.0317810
\(16\) 1.00000 0.250000
\(17\) −1.40790 −0.341466 −0.170733 0.985317i \(-0.554614\pi\)
−0.170733 + 0.985317i \(0.554614\pi\)
\(18\) −1.92642 −0.454061
\(19\) −1.00000 −0.229416
\(20\) 0.118794 0.0265632
\(21\) −2.21118 −0.482520
\(22\) 5.30344 1.13070
\(23\) −7.01405 −1.46253 −0.731265 0.682093i \(-0.761070\pi\)
−0.731265 + 0.682093i \(0.761070\pi\)
\(24\) −1.03614 −0.211501
\(25\) −4.98589 −0.997178
\(26\) 0.953466 0.186990
\(27\) 5.10445 0.982352
\(28\) 2.13406 0.403300
\(29\) −3.22709 −0.599255 −0.299628 0.954056i \(-0.596862\pi\)
−0.299628 + 0.954056i \(0.596862\pi\)
\(30\) −0.123087 −0.0224725
\(31\) 5.86651 1.05366 0.526829 0.849972i \(-0.323381\pi\)
0.526829 + 0.849972i \(0.323381\pi\)
\(32\) 1.00000 0.176777
\(33\) −5.49510 −0.956575
\(34\) −1.40790 −0.241453
\(35\) 0.253514 0.0428517
\(36\) −1.92642 −0.321069
\(37\) 9.27789 1.52528 0.762638 0.646825i \(-0.223904\pi\)
0.762638 + 0.646825i \(0.223904\pi\)
\(38\) −1.00000 −0.162221
\(39\) −0.987923 −0.158194
\(40\) 0.118794 0.0187830
\(41\) 6.08967 0.951046 0.475523 0.879703i \(-0.342259\pi\)
0.475523 + 0.879703i \(0.342259\pi\)
\(42\) −2.21118 −0.341193
\(43\) 11.1940 1.70707 0.853537 0.521032i \(-0.174453\pi\)
0.853537 + 0.521032i \(0.174453\pi\)
\(44\) 5.30344 0.799524
\(45\) −0.228847 −0.0341145
\(46\) −7.01405 −1.03417
\(47\) 5.03802 0.734871 0.367435 0.930049i \(-0.380236\pi\)
0.367435 + 0.930049i \(0.380236\pi\)
\(48\) −1.03614 −0.149554
\(49\) −2.44578 −0.349397
\(50\) −4.98589 −0.705111
\(51\) 1.45878 0.204270
\(52\) 0.953466 0.132222
\(53\) −12.2837 −1.68729 −0.843647 0.536898i \(-0.819596\pi\)
−0.843647 + 0.536898i \(0.819596\pi\)
\(54\) 5.10445 0.694628
\(55\) 0.630018 0.0849516
\(56\) 2.13406 0.285176
\(57\) 1.03614 0.137240
\(58\) −3.22709 −0.423737
\(59\) −6.60513 −0.859914 −0.429957 0.902849i \(-0.641471\pi\)
−0.429957 + 0.902849i \(0.641471\pi\)
\(60\) −0.123087 −0.0158905
\(61\) 8.99482 1.15167 0.575834 0.817566i \(-0.304677\pi\)
0.575834 + 0.817566i \(0.304677\pi\)
\(62\) 5.86651 0.745048
\(63\) −4.11109 −0.517949
\(64\) 1.00000 0.125000
\(65\) 0.113266 0.0140489
\(66\) −5.49510 −0.676400
\(67\) 5.49250 0.671015 0.335508 0.942037i \(-0.391092\pi\)
0.335508 + 0.942037i \(0.391092\pi\)
\(68\) −1.40790 −0.170733
\(69\) 7.26753 0.874908
\(70\) 0.253514 0.0303007
\(71\) 13.7678 1.63394 0.816970 0.576681i \(-0.195652\pi\)
0.816970 + 0.576681i \(0.195652\pi\)
\(72\) −1.92642 −0.227030
\(73\) 13.0402 1.52624 0.763119 0.646258i \(-0.223667\pi\)
0.763119 + 0.646258i \(0.223667\pi\)
\(74\) 9.27789 1.07853
\(75\) 5.16607 0.596526
\(76\) −1.00000 −0.114708
\(77\) 11.3179 1.28979
\(78\) −0.987923 −0.111860
\(79\) 9.40559 1.05821 0.529106 0.848556i \(-0.322527\pi\)
0.529106 + 0.848556i \(0.322527\pi\)
\(80\) 0.118794 0.0132816
\(81\) 0.490332 0.0544814
\(82\) 6.08967 0.672491
\(83\) −1.93571 −0.212472 −0.106236 0.994341i \(-0.533880\pi\)
−0.106236 + 0.994341i \(0.533880\pi\)
\(84\) −2.21118 −0.241260
\(85\) −0.167250 −0.0181408
\(86\) 11.1940 1.20708
\(87\) 3.34371 0.358483
\(88\) 5.30344 0.565349
\(89\) −16.4497 −1.74367 −0.871833 0.489802i \(-0.837069\pi\)
−0.871833 + 0.489802i \(0.837069\pi\)
\(90\) −0.228847 −0.0241226
\(91\) 2.03476 0.213300
\(92\) −7.01405 −0.731265
\(93\) −6.07852 −0.630313
\(94\) 5.03802 0.519632
\(95\) −0.118794 −0.0121880
\(96\) −1.03614 −0.105750
\(97\) −5.85181 −0.594161 −0.297080 0.954852i \(-0.596013\pi\)
−0.297080 + 0.954852i \(0.596013\pi\)
\(98\) −2.44578 −0.247061
\(99\) −10.2166 −1.02681
\(100\) −4.98589 −0.498589
\(101\) −9.55441 −0.950699 −0.475350 0.879797i \(-0.657678\pi\)
−0.475350 + 0.879797i \(0.657678\pi\)
\(102\) 1.45878 0.144441
\(103\) 2.27475 0.224137 0.112069 0.993700i \(-0.464252\pi\)
0.112069 + 0.993700i \(0.464252\pi\)
\(104\) 0.953466 0.0934950
\(105\) −0.262676 −0.0256345
\(106\) −12.2837 −1.19310
\(107\) −6.34312 −0.613212 −0.306606 0.951837i \(-0.599193\pi\)
−0.306606 + 0.951837i \(0.599193\pi\)
\(108\) 5.10445 0.491176
\(109\) −1.82964 −0.175248 −0.0876240 0.996154i \(-0.527927\pi\)
−0.0876240 + 0.996154i \(0.527927\pi\)
\(110\) 0.630018 0.0600698
\(111\) −9.61318 −0.912443
\(112\) 2.13406 0.201650
\(113\) −1.20232 −0.113105 −0.0565526 0.998400i \(-0.518011\pi\)
−0.0565526 + 0.998400i \(0.518011\pi\)
\(114\) 1.03614 0.0970433
\(115\) −0.833228 −0.0776989
\(116\) −3.22709 −0.299628
\(117\) −1.83677 −0.169810
\(118\) −6.60513 −0.608051
\(119\) −3.00455 −0.275426
\(120\) −0.123087 −0.0112363
\(121\) 17.1265 1.55696
\(122\) 8.99482 0.814353
\(123\) −6.30974 −0.568930
\(124\) 5.86651 0.526829
\(125\) −1.18626 −0.106103
\(126\) −4.11109 −0.366245
\(127\) −0.441724 −0.0391966 −0.0195983 0.999808i \(-0.506239\pi\)
−0.0195983 + 0.999808i \(0.506239\pi\)
\(128\) 1.00000 0.0883883
\(129\) −11.5986 −1.02120
\(130\) 0.113266 0.00993410
\(131\) −2.39368 −0.209137 −0.104568 0.994518i \(-0.533346\pi\)
−0.104568 + 0.994518i \(0.533346\pi\)
\(132\) −5.49510 −0.478287
\(133\) −2.13406 −0.185047
\(134\) 5.49250 0.474480
\(135\) 0.606379 0.0521888
\(136\) −1.40790 −0.120726
\(137\) 19.6296 1.67707 0.838536 0.544847i \(-0.183412\pi\)
0.838536 + 0.544847i \(0.183412\pi\)
\(138\) 7.26753 0.618653
\(139\) 2.21189 0.187610 0.0938048 0.995591i \(-0.470097\pi\)
0.0938048 + 0.995591i \(0.470097\pi\)
\(140\) 0.253514 0.0214258
\(141\) −5.22009 −0.439611
\(142\) 13.7678 1.15537
\(143\) 5.05665 0.422859
\(144\) −1.92642 −0.160535
\(145\) −0.383359 −0.0318362
\(146\) 13.0402 1.07921
\(147\) 2.53417 0.209014
\(148\) 9.27789 0.762638
\(149\) −2.85546 −0.233928 −0.116964 0.993136i \(-0.537316\pi\)
−0.116964 + 0.993136i \(0.537316\pi\)
\(150\) 5.16607 0.421808
\(151\) 2.63738 0.214627 0.107313 0.994225i \(-0.465775\pi\)
0.107313 + 0.994225i \(0.465775\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 2.71220 0.219269
\(154\) 11.3179 0.912021
\(155\) 0.696907 0.0559769
\(156\) −0.987923 −0.0790971
\(157\) −12.5380 −1.00064 −0.500319 0.865841i \(-0.666784\pi\)
−0.500319 + 0.865841i \(0.666784\pi\)
\(158\) 9.40559 0.748269
\(159\) 12.7276 1.00936
\(160\) 0.118794 0.00939150
\(161\) −14.9684 −1.17968
\(162\) 0.490332 0.0385241
\(163\) 10.7906 0.845185 0.422593 0.906320i \(-0.361120\pi\)
0.422593 + 0.906320i \(0.361120\pi\)
\(164\) 6.08967 0.475523
\(165\) −0.652786 −0.0508193
\(166\) −1.93571 −0.150241
\(167\) 3.91981 0.303324 0.151662 0.988432i \(-0.451537\pi\)
0.151662 + 0.988432i \(0.451537\pi\)
\(168\) −2.21118 −0.170597
\(169\) −12.0909 −0.930069
\(170\) −0.167250 −0.0128275
\(171\) 1.92642 0.147317
\(172\) 11.1940 0.853537
\(173\) −11.5395 −0.877331 −0.438666 0.898650i \(-0.644549\pi\)
−0.438666 + 0.898650i \(0.644549\pi\)
\(174\) 3.34371 0.253486
\(175\) −10.6402 −0.804323
\(176\) 5.30344 0.399762
\(177\) 6.84383 0.514413
\(178\) −16.4497 −1.23296
\(179\) 23.6668 1.76894 0.884469 0.466598i \(-0.154521\pi\)
0.884469 + 0.466598i \(0.154521\pi\)
\(180\) −0.228847 −0.0170572
\(181\) 10.4171 0.774295 0.387147 0.922018i \(-0.373460\pi\)
0.387147 + 0.922018i \(0.373460\pi\)
\(182\) 2.03476 0.150826
\(183\) −9.31988 −0.688945
\(184\) −7.01405 −0.517083
\(185\) 1.10216 0.0810323
\(186\) −6.07852 −0.445699
\(187\) −7.46672 −0.546021
\(188\) 5.03802 0.367435
\(189\) 10.8932 0.792365
\(190\) −0.118794 −0.00861823
\(191\) 13.9644 1.01043 0.505214 0.862994i \(-0.331414\pi\)
0.505214 + 0.862994i \(0.331414\pi\)
\(192\) −1.03614 −0.0747769
\(193\) −9.29956 −0.669397 −0.334699 0.942325i \(-0.608635\pi\)
−0.334699 + 0.942325i \(0.608635\pi\)
\(194\) −5.85181 −0.420135
\(195\) −0.117359 −0.00840428
\(196\) −2.44578 −0.174698
\(197\) −24.1737 −1.72231 −0.861154 0.508344i \(-0.830258\pi\)
−0.861154 + 0.508344i \(0.830258\pi\)
\(198\) −10.2166 −0.726065
\(199\) 11.3541 0.804872 0.402436 0.915448i \(-0.368164\pi\)
0.402436 + 0.915448i \(0.368164\pi\)
\(200\) −4.98589 −0.352556
\(201\) −5.69099 −0.401411
\(202\) −9.55441 −0.672246
\(203\) −6.88680 −0.483359
\(204\) 1.45878 0.102135
\(205\) 0.723417 0.0505256
\(206\) 2.27475 0.158489
\(207\) 13.5120 0.939148
\(208\) 0.953466 0.0661110
\(209\) −5.30344 −0.366847
\(210\) −0.262676 −0.0181263
\(211\) −1.00000 −0.0688428
\(212\) −12.2837 −0.843647
\(213\) −14.2654 −0.977447
\(214\) −6.34312 −0.433606
\(215\) 1.32978 0.0906906
\(216\) 5.10445 0.347314
\(217\) 12.5195 0.849880
\(218\) −1.82964 −0.123919
\(219\) −13.5114 −0.913018
\(220\) 0.630018 0.0424758
\(221\) −1.34238 −0.0902986
\(222\) −9.61318 −0.645195
\(223\) −3.96485 −0.265506 −0.132753 0.991149i \(-0.542382\pi\)
−0.132753 + 0.991149i \(0.542382\pi\)
\(224\) 2.13406 0.142588
\(225\) 9.60490 0.640327
\(226\) −1.20232 −0.0799774
\(227\) −0.200978 −0.0133394 −0.00666969 0.999978i \(-0.502123\pi\)
−0.00666969 + 0.999978i \(0.502123\pi\)
\(228\) 1.03614 0.0686200
\(229\) 18.2921 1.20877 0.604387 0.796691i \(-0.293418\pi\)
0.604387 + 0.796691i \(0.293418\pi\)
\(230\) −0.833228 −0.0549414
\(231\) −11.7269 −0.771573
\(232\) −3.22709 −0.211869
\(233\) 2.10683 0.138023 0.0690115 0.997616i \(-0.478015\pi\)
0.0690115 + 0.997616i \(0.478015\pi\)
\(234\) −1.83677 −0.120074
\(235\) 0.598487 0.0390410
\(236\) −6.60513 −0.429957
\(237\) −9.74549 −0.633038
\(238\) −3.00455 −0.194756
\(239\) −14.8788 −0.962430 −0.481215 0.876603i \(-0.659804\pi\)
−0.481215 + 0.876603i \(0.659804\pi\)
\(240\) −0.123087 −0.00794524
\(241\) −23.1676 −1.49236 −0.746179 0.665745i \(-0.768114\pi\)
−0.746179 + 0.665745i \(0.768114\pi\)
\(242\) 17.1265 1.10093
\(243\) −15.8214 −1.01494
\(244\) 8.99482 0.575834
\(245\) −0.290544 −0.0185622
\(246\) −6.30974 −0.402294
\(247\) −0.953466 −0.0606676
\(248\) 5.86651 0.372524
\(249\) 2.00567 0.127104
\(250\) −1.18626 −0.0750260
\(251\) 9.62081 0.607260 0.303630 0.952790i \(-0.401801\pi\)
0.303630 + 0.952790i \(0.401801\pi\)
\(252\) −4.11109 −0.258975
\(253\) −37.1986 −2.33866
\(254\) −0.441724 −0.0277162
\(255\) 0.173294 0.0108521
\(256\) 1.00000 0.0625000
\(257\) 25.3603 1.58193 0.790965 0.611862i \(-0.209579\pi\)
0.790965 + 0.611862i \(0.209579\pi\)
\(258\) −11.5986 −0.722095
\(259\) 19.7996 1.23029
\(260\) 0.113266 0.00702447
\(261\) 6.21672 0.384805
\(262\) −2.39368 −0.147882
\(263\) 3.19578 0.197060 0.0985300 0.995134i \(-0.468586\pi\)
0.0985300 + 0.995134i \(0.468586\pi\)
\(264\) −5.49510 −0.338200
\(265\) −1.45923 −0.0896398
\(266\) −2.13406 −0.130848
\(267\) 17.0442 1.04309
\(268\) 5.49250 0.335508
\(269\) 14.4034 0.878192 0.439096 0.898440i \(-0.355299\pi\)
0.439096 + 0.898440i \(0.355299\pi\)
\(270\) 0.606379 0.0369030
\(271\) 18.6847 1.13501 0.567507 0.823369i \(-0.307908\pi\)
0.567507 + 0.823369i \(0.307908\pi\)
\(272\) −1.40790 −0.0853665
\(273\) −2.10829 −0.127599
\(274\) 19.6296 1.18587
\(275\) −26.4424 −1.59454
\(276\) 7.26753 0.437454
\(277\) 25.3666 1.52413 0.762064 0.647501i \(-0.224186\pi\)
0.762064 + 0.647501i \(0.224186\pi\)
\(278\) 2.21189 0.132660
\(279\) −11.3014 −0.676594
\(280\) 0.253514 0.0151504
\(281\) 13.8266 0.824824 0.412412 0.910997i \(-0.364686\pi\)
0.412412 + 0.910997i \(0.364686\pi\)
\(282\) −5.22009 −0.310852
\(283\) 9.96315 0.592248 0.296124 0.955150i \(-0.404306\pi\)
0.296124 + 0.955150i \(0.404306\pi\)
\(284\) 13.7678 0.816970
\(285\) 0.123087 0.00729105
\(286\) 5.05665 0.299006
\(287\) 12.9957 0.767114
\(288\) −1.92642 −0.113515
\(289\) −15.0178 −0.883401
\(290\) −0.383359 −0.0225116
\(291\) 6.06328 0.355436
\(292\) 13.0402 0.763119
\(293\) 17.2137 1.00563 0.502817 0.864393i \(-0.332297\pi\)
0.502817 + 0.864393i \(0.332297\pi\)
\(294\) 2.53417 0.147796
\(295\) −0.784650 −0.0456841
\(296\) 9.27789 0.539267
\(297\) 27.0712 1.57083
\(298\) −2.85546 −0.165412
\(299\) −6.68766 −0.386757
\(300\) 5.16607 0.298263
\(301\) 23.8888 1.37693
\(302\) 2.63738 0.151764
\(303\) 9.89969 0.568722
\(304\) −1.00000 −0.0573539
\(305\) 1.06853 0.0611839
\(306\) 2.71220 0.155046
\(307\) 25.4629 1.45324 0.726622 0.687038i \(-0.241089\pi\)
0.726622 + 0.687038i \(0.241089\pi\)
\(308\) 11.3179 0.644896
\(309\) −2.35695 −0.134082
\(310\) 0.696907 0.0395817
\(311\) 20.4253 1.15821 0.579107 0.815252i \(-0.303401\pi\)
0.579107 + 0.815252i \(0.303401\pi\)
\(312\) −0.987923 −0.0559301
\(313\) 4.53190 0.256158 0.128079 0.991764i \(-0.459119\pi\)
0.128079 + 0.991764i \(0.459119\pi\)
\(314\) −12.5380 −0.707558
\(315\) −0.488374 −0.0275167
\(316\) 9.40559 0.529106
\(317\) 11.5322 0.647714 0.323857 0.946106i \(-0.395020\pi\)
0.323857 + 0.946106i \(0.395020\pi\)
\(318\) 12.7276 0.713729
\(319\) −17.1147 −0.958238
\(320\) 0.118794 0.00664079
\(321\) 6.57235 0.366833
\(322\) −14.9684 −0.834157
\(323\) 1.40790 0.0783377
\(324\) 0.490332 0.0272407
\(325\) −4.75387 −0.263697
\(326\) 10.7906 0.597636
\(327\) 1.89576 0.104836
\(328\) 6.08967 0.336246
\(329\) 10.7515 0.592747
\(330\) −0.652786 −0.0359347
\(331\) −19.4723 −1.07029 −0.535146 0.844759i \(-0.679743\pi\)
−0.535146 + 0.844759i \(0.679743\pi\)
\(332\) −1.93571 −0.106236
\(333\) −17.8731 −0.979439
\(334\) 3.91981 0.214482
\(335\) 0.652476 0.0356486
\(336\) −2.21118 −0.120630
\(337\) 26.9628 1.46876 0.734379 0.678740i \(-0.237474\pi\)
0.734379 + 0.678740i \(0.237474\pi\)
\(338\) −12.0909 −0.657658
\(339\) 1.24577 0.0676612
\(340\) −0.167250 −0.00907042
\(341\) 31.1127 1.68485
\(342\) 1.92642 0.104169
\(343\) −20.1579 −1.08842
\(344\) 11.1940 0.603542
\(345\) 0.863339 0.0464806
\(346\) −11.5395 −0.620367
\(347\) −2.47186 −0.132696 −0.0663482 0.997797i \(-0.521135\pi\)
−0.0663482 + 0.997797i \(0.521135\pi\)
\(348\) 3.34371 0.179242
\(349\) 4.59571 0.246003 0.123001 0.992407i \(-0.460748\pi\)
0.123001 + 0.992407i \(0.460748\pi\)
\(350\) −10.6402 −0.568742
\(351\) 4.86692 0.259777
\(352\) 5.30344 0.282675
\(353\) −0.751216 −0.0399832 −0.0199916 0.999800i \(-0.506364\pi\)
−0.0199916 + 0.999800i \(0.506364\pi\)
\(354\) 6.84383 0.363745
\(355\) 1.63554 0.0868052
\(356\) −16.4497 −0.871833
\(357\) 3.11313 0.164764
\(358\) 23.6668 1.25083
\(359\) 32.4002 1.71002 0.855008 0.518614i \(-0.173552\pi\)
0.855008 + 0.518614i \(0.173552\pi\)
\(360\) −0.228847 −0.0120613
\(361\) 1.00000 0.0526316
\(362\) 10.4171 0.547509
\(363\) −17.7454 −0.931394
\(364\) 2.03476 0.106650
\(365\) 1.54910 0.0810834
\(366\) −9.31988 −0.487158
\(367\) 33.2882 1.73763 0.868814 0.495138i \(-0.164882\pi\)
0.868814 + 0.495138i \(0.164882\pi\)
\(368\) −7.01405 −0.365633
\(369\) −11.7312 −0.610704
\(370\) 1.10216 0.0572985
\(371\) −26.2142 −1.36097
\(372\) −6.07852 −0.315157
\(373\) 12.4366 0.643942 0.321971 0.946749i \(-0.395655\pi\)
0.321971 + 0.946749i \(0.395655\pi\)
\(374\) −7.46672 −0.386095
\(375\) 1.22913 0.0634722
\(376\) 5.03802 0.259816
\(377\) −3.07692 −0.158469
\(378\) 10.8932 0.560287
\(379\) 9.39836 0.482762 0.241381 0.970430i \(-0.422400\pi\)
0.241381 + 0.970430i \(0.422400\pi\)
\(380\) −0.118794 −0.00609401
\(381\) 0.457687 0.0234480
\(382\) 13.9644 0.714480
\(383\) −14.2944 −0.730407 −0.365204 0.930928i \(-0.619001\pi\)
−0.365204 + 0.930928i \(0.619001\pi\)
\(384\) −1.03614 −0.0528752
\(385\) 1.34450 0.0685219
\(386\) −9.29956 −0.473335
\(387\) −21.5644 −1.09618
\(388\) −5.85181 −0.297080
\(389\) 36.3439 1.84271 0.921355 0.388723i \(-0.127084\pi\)
0.921355 + 0.388723i \(0.127084\pi\)
\(390\) −0.117359 −0.00594272
\(391\) 9.87508 0.499404
\(392\) −2.44578 −0.123530
\(393\) 2.48019 0.125109
\(394\) −24.1737 −1.21786
\(395\) 1.11733 0.0562189
\(396\) −10.2166 −0.513406
\(397\) −27.1138 −1.36080 −0.680401 0.732840i \(-0.738195\pi\)
−0.680401 + 0.732840i \(0.738195\pi\)
\(398\) 11.3541 0.569130
\(399\) 2.21118 0.110698
\(400\) −4.98589 −0.249294
\(401\) 20.5133 1.02439 0.512193 0.858870i \(-0.328833\pi\)
0.512193 + 0.858870i \(0.328833\pi\)
\(402\) −5.69099 −0.283841
\(403\) 5.59352 0.278633
\(404\) −9.55441 −0.475350
\(405\) 0.0582486 0.00289439
\(406\) −6.88680 −0.341786
\(407\) 49.2048 2.43899
\(408\) 1.45878 0.0722204
\(409\) 3.77530 0.186677 0.0933383 0.995634i \(-0.470246\pi\)
0.0933383 + 0.995634i \(0.470246\pi\)
\(410\) 0.723417 0.0357270
\(411\) −20.3390 −1.00325
\(412\) 2.27475 0.112069
\(413\) −14.0957 −0.693606
\(414\) 13.5120 0.664078
\(415\) −0.229951 −0.0112879
\(416\) 0.953466 0.0467475
\(417\) −2.29182 −0.112231
\(418\) −5.30344 −0.259400
\(419\) −24.8611 −1.21455 −0.607273 0.794494i \(-0.707736\pi\)
−0.607273 + 0.794494i \(0.707736\pi\)
\(420\) −0.262676 −0.0128173
\(421\) −14.2065 −0.692380 −0.346190 0.938164i \(-0.612525\pi\)
−0.346190 + 0.938164i \(0.612525\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −9.70533 −0.471889
\(424\) −12.2837 −0.596549
\(425\) 7.01963 0.340502
\(426\) −14.2654 −0.691159
\(427\) 19.1955 0.928936
\(428\) −6.34312 −0.306606
\(429\) −5.23939 −0.252960
\(430\) 1.32978 0.0641279
\(431\) −31.1315 −1.49955 −0.749776 0.661692i \(-0.769839\pi\)
−0.749776 + 0.661692i \(0.769839\pi\)
\(432\) 5.10445 0.245588
\(433\) −14.0770 −0.676500 −0.338250 0.941056i \(-0.609835\pi\)
−0.338250 + 0.941056i \(0.609835\pi\)
\(434\) 12.5195 0.600956
\(435\) 0.397213 0.0190449
\(436\) −1.82964 −0.0876240
\(437\) 7.01405 0.335528
\(438\) −13.5114 −0.645601
\(439\) 15.2653 0.728573 0.364287 0.931287i \(-0.381313\pi\)
0.364287 + 0.931287i \(0.381313\pi\)
\(440\) 0.630018 0.0300349
\(441\) 4.71159 0.224361
\(442\) −1.34238 −0.0638507
\(443\) 6.44080 0.306012 0.153006 0.988225i \(-0.451105\pi\)
0.153006 + 0.988225i \(0.451105\pi\)
\(444\) −9.61318 −0.456222
\(445\) −1.95413 −0.0926346
\(446\) −3.96485 −0.187741
\(447\) 2.95865 0.139939
\(448\) 2.13406 0.100825
\(449\) −33.6440 −1.58776 −0.793880 0.608074i \(-0.791942\pi\)
−0.793880 + 0.608074i \(0.791942\pi\)
\(450\) 9.60490 0.452779
\(451\) 32.2962 1.52077
\(452\) −1.20232 −0.0565526
\(453\) −2.73269 −0.128393
\(454\) −0.200978 −0.00943236
\(455\) 0.241717 0.0113319
\(456\) 1.03614 0.0485216
\(457\) −23.7652 −1.11169 −0.555844 0.831286i \(-0.687605\pi\)
−0.555844 + 0.831286i \(0.687605\pi\)
\(458\) 18.2921 0.854733
\(459\) −7.18656 −0.335440
\(460\) −0.833228 −0.0388494
\(461\) −33.2389 −1.54809 −0.774045 0.633130i \(-0.781770\pi\)
−0.774045 + 0.633130i \(0.781770\pi\)
\(462\) −11.7269 −0.545584
\(463\) −4.13838 −0.192327 −0.0961635 0.995366i \(-0.530657\pi\)
−0.0961635 + 0.995366i \(0.530657\pi\)
\(464\) −3.22709 −0.149814
\(465\) −0.722093 −0.0334862
\(466\) 2.10683 0.0975970
\(467\) 28.7669 1.33117 0.665586 0.746321i \(-0.268182\pi\)
0.665586 + 0.746321i \(0.268182\pi\)
\(468\) −1.83677 −0.0849048
\(469\) 11.7213 0.541241
\(470\) 0.598487 0.0276062
\(471\) 12.9911 0.598597
\(472\) −6.60513 −0.304026
\(473\) 59.3669 2.72969
\(474\) −9.74549 −0.447625
\(475\) 4.98589 0.228768
\(476\) −3.00455 −0.137713
\(477\) 23.6635 1.08348
\(478\) −14.8788 −0.680541
\(479\) −9.34694 −0.427073 −0.213536 0.976935i \(-0.568498\pi\)
−0.213536 + 0.976935i \(0.568498\pi\)
\(480\) −0.123087 −0.00561813
\(481\) 8.84615 0.403350
\(482\) −23.1676 −1.05526
\(483\) 15.5094 0.705700
\(484\) 17.1265 0.778478
\(485\) −0.695160 −0.0315656
\(486\) −15.8214 −0.717673
\(487\) 3.81019 0.172656 0.0863280 0.996267i \(-0.472487\pi\)
0.0863280 + 0.996267i \(0.472487\pi\)
\(488\) 8.99482 0.407176
\(489\) −11.1806 −0.505602
\(490\) −0.290544 −0.0131254
\(491\) 3.90927 0.176423 0.0882113 0.996102i \(-0.471885\pi\)
0.0882113 + 0.996102i \(0.471885\pi\)
\(492\) −6.30974 −0.284465
\(493\) 4.54342 0.204625
\(494\) −0.953466 −0.0428985
\(495\) −1.21368 −0.0545507
\(496\) 5.86651 0.263414
\(497\) 29.3814 1.31793
\(498\) 2.00567 0.0898761
\(499\) −25.8060 −1.15524 −0.577618 0.816307i \(-0.696018\pi\)
−0.577618 + 0.816307i \(0.696018\pi\)
\(500\) −1.18626 −0.0530514
\(501\) −4.06147 −0.181453
\(502\) 9.62081 0.429398
\(503\) −4.32665 −0.192916 −0.0964580 0.995337i \(-0.530751\pi\)
−0.0964580 + 0.995337i \(0.530751\pi\)
\(504\) −4.11109 −0.183123
\(505\) −1.13501 −0.0505072
\(506\) −37.1986 −1.65368
\(507\) 12.5279 0.556381
\(508\) −0.441724 −0.0195983
\(509\) −21.4576 −0.951093 −0.475547 0.879690i \(-0.657750\pi\)
−0.475547 + 0.879690i \(0.657750\pi\)
\(510\) 0.173294 0.00767361
\(511\) 27.8286 1.23106
\(512\) 1.00000 0.0441942
\(513\) −5.10445 −0.225367
\(514\) 25.3603 1.11859
\(515\) 0.270226 0.0119076
\(516\) −11.5986 −0.510599
\(517\) 26.7189 1.17509
\(518\) 19.7996 0.869945
\(519\) 11.9565 0.524832
\(520\) 0.113266 0.00496705
\(521\) 25.3942 1.11254 0.556269 0.831002i \(-0.312232\pi\)
0.556269 + 0.831002i \(0.312232\pi\)
\(522\) 6.21672 0.272098
\(523\) −21.0553 −0.920684 −0.460342 0.887742i \(-0.652273\pi\)
−0.460342 + 0.887742i \(0.652273\pi\)
\(524\) −2.39368 −0.104568
\(525\) 11.0247 0.481158
\(526\) 3.19578 0.139342
\(527\) −8.25947 −0.359788
\(528\) −5.49510 −0.239144
\(529\) 26.1969 1.13900
\(530\) −1.45923 −0.0633849
\(531\) 12.7242 0.552184
\(532\) −2.13406 −0.0925233
\(533\) 5.80629 0.251498
\(534\) 17.0442 0.737574
\(535\) −0.753525 −0.0325777
\(536\) 5.49250 0.237240
\(537\) −24.5221 −1.05821
\(538\) 14.4034 0.620975
\(539\) −12.9711 −0.558703
\(540\) 0.606379 0.0260944
\(541\) −26.6048 −1.14383 −0.571914 0.820313i \(-0.693799\pi\)
−0.571914 + 0.820313i \(0.693799\pi\)
\(542\) 18.6847 0.802575
\(543\) −10.7935 −0.463195
\(544\) −1.40790 −0.0603632
\(545\) −0.217351 −0.00931028
\(546\) −2.10829 −0.0902264
\(547\) −29.3789 −1.25615 −0.628075 0.778152i \(-0.716157\pi\)
−0.628075 + 0.778152i \(0.716157\pi\)
\(548\) 19.6296 0.838536
\(549\) −17.3278 −0.739531
\(550\) −26.4424 −1.12751
\(551\) 3.22709 0.137479
\(552\) 7.26753 0.309327
\(553\) 20.0721 0.853553
\(554\) 25.3666 1.07772
\(555\) −1.14199 −0.0484748
\(556\) 2.21189 0.0938048
\(557\) −20.7385 −0.878719 −0.439359 0.898311i \(-0.644794\pi\)
−0.439359 + 0.898311i \(0.644794\pi\)
\(558\) −11.3014 −0.478424
\(559\) 10.6731 0.451425
\(560\) 0.253514 0.0107129
\(561\) 7.73656 0.326638
\(562\) 13.8266 0.583239
\(563\) 35.4515 1.49410 0.747051 0.664767i \(-0.231469\pi\)
0.747051 + 0.664767i \(0.231469\pi\)
\(564\) −5.22009 −0.219805
\(565\) −0.142829 −0.00600886
\(566\) 9.96315 0.418782
\(567\) 1.04640 0.0439446
\(568\) 13.7678 0.577685
\(569\) −41.3306 −1.73267 −0.866335 0.499463i \(-0.833531\pi\)
−0.866335 + 0.499463i \(0.833531\pi\)
\(570\) 0.123087 0.00515555
\(571\) −44.1532 −1.84775 −0.923876 0.382691i \(-0.874997\pi\)
−0.923876 + 0.382691i \(0.874997\pi\)
\(572\) 5.05665 0.211429
\(573\) −14.4690 −0.604453
\(574\) 12.9957 0.542431
\(575\) 34.9713 1.45840
\(576\) −1.92642 −0.0802674
\(577\) 14.7346 0.613410 0.306705 0.951805i \(-0.400773\pi\)
0.306705 + 0.951805i \(0.400773\pi\)
\(578\) −15.0178 −0.624659
\(579\) 9.63564 0.400443
\(580\) −0.383359 −0.0159181
\(581\) −4.13093 −0.171380
\(582\) 6.06328 0.251331
\(583\) −65.1459 −2.69807
\(584\) 13.0402 0.539607
\(585\) −0.218198 −0.00902137
\(586\) 17.2137 0.711091
\(587\) −42.7940 −1.76630 −0.883148 0.469095i \(-0.844580\pi\)
−0.883148 + 0.469095i \(0.844580\pi\)
\(588\) 2.53417 0.104507
\(589\) −5.86651 −0.241726
\(590\) −0.784650 −0.0323035
\(591\) 25.0474 1.03031
\(592\) 9.27789 0.381319
\(593\) 27.9183 1.14647 0.573234 0.819392i \(-0.305689\pi\)
0.573234 + 0.819392i \(0.305689\pi\)
\(594\) 27.0712 1.11074
\(595\) −0.356922 −0.0146324
\(596\) −2.85546 −0.116964
\(597\) −11.7644 −0.481486
\(598\) −6.68766 −0.273479
\(599\) −14.4316 −0.589658 −0.294829 0.955550i \(-0.595263\pi\)
−0.294829 + 0.955550i \(0.595263\pi\)
\(600\) 5.16607 0.210904
\(601\) −3.58400 −0.146195 −0.0730973 0.997325i \(-0.523288\pi\)
−0.0730973 + 0.997325i \(0.523288\pi\)
\(602\) 23.8888 0.973633
\(603\) −10.5808 −0.430885
\(604\) 2.63738 0.107313
\(605\) 2.03453 0.0827154
\(606\) 9.89969 0.402147
\(607\) −33.7077 −1.36815 −0.684077 0.729410i \(-0.739795\pi\)
−0.684077 + 0.729410i \(0.739795\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 7.13568 0.289153
\(610\) 1.06853 0.0432636
\(611\) 4.80358 0.194332
\(612\) 2.71220 0.109634
\(613\) −12.5034 −0.505008 −0.252504 0.967596i \(-0.581254\pi\)
−0.252504 + 0.967596i \(0.581254\pi\)
\(614\) 25.4629 1.02760
\(615\) −0.749560 −0.0302252
\(616\) 11.3179 0.456010
\(617\) 8.04213 0.323764 0.161882 0.986810i \(-0.448244\pi\)
0.161882 + 0.986810i \(0.448244\pi\)
\(618\) −2.35695 −0.0948105
\(619\) −30.5719 −1.22879 −0.614393 0.789000i \(-0.710599\pi\)
−0.614393 + 0.789000i \(0.710599\pi\)
\(620\) 0.696907 0.0279885
\(621\) −35.8029 −1.43672
\(622\) 20.4253 0.818981
\(623\) −35.1047 −1.40644
\(624\) −0.987923 −0.0395486
\(625\) 24.7885 0.991541
\(626\) 4.53190 0.181131
\(627\) 5.49510 0.219453
\(628\) −12.5380 −0.500319
\(629\) −13.0623 −0.520830
\(630\) −0.488374 −0.0194573
\(631\) 17.9056 0.712811 0.356405 0.934331i \(-0.384002\pi\)
0.356405 + 0.934331i \(0.384002\pi\)
\(632\) 9.40559 0.374134
\(633\) 1.03614 0.0411828
\(634\) 11.5322 0.458003
\(635\) −0.0524742 −0.00208237
\(636\) 12.7276 0.504682
\(637\) −2.33197 −0.0923959
\(638\) −17.1147 −0.677577
\(639\) −26.5226 −1.04922
\(640\) 0.118794 0.00469575
\(641\) 19.3598 0.764667 0.382334 0.924024i \(-0.375121\pi\)
0.382334 + 0.924024i \(0.375121\pi\)
\(642\) 6.57235 0.259390
\(643\) −26.3700 −1.03993 −0.519965 0.854187i \(-0.674055\pi\)
−0.519965 + 0.854187i \(0.674055\pi\)
\(644\) −14.9684 −0.589838
\(645\) −1.37784 −0.0542525
\(646\) 1.40790 0.0553931
\(647\) −39.8331 −1.56600 −0.783001 0.622021i \(-0.786312\pi\)
−0.783001 + 0.622021i \(0.786312\pi\)
\(648\) 0.490332 0.0192621
\(649\) −35.0299 −1.37504
\(650\) −4.75387 −0.186462
\(651\) −12.9719 −0.508411
\(652\) 10.7906 0.422593
\(653\) −0.632296 −0.0247437 −0.0123718 0.999923i \(-0.503938\pi\)
−0.0123718 + 0.999923i \(0.503938\pi\)
\(654\) 1.89576 0.0741302
\(655\) −0.284355 −0.0111107
\(656\) 6.08967 0.237762
\(657\) −25.1208 −0.980057
\(658\) 10.7515 0.419135
\(659\) 5.01220 0.195248 0.0976239 0.995223i \(-0.468876\pi\)
0.0976239 + 0.995223i \(0.468876\pi\)
\(660\) −0.652786 −0.0254097
\(661\) −3.04793 −0.118551 −0.0592753 0.998242i \(-0.518879\pi\)
−0.0592753 + 0.998242i \(0.518879\pi\)
\(662\) −19.4723 −0.756811
\(663\) 1.39090 0.0540179
\(664\) −1.93571 −0.0751203
\(665\) −0.253514 −0.00983085
\(666\) −17.8731 −0.692568
\(667\) 22.6350 0.876429
\(668\) 3.91981 0.151662
\(669\) 4.10814 0.158830
\(670\) 0.652476 0.0252074
\(671\) 47.7035 1.84157
\(672\) −2.21118 −0.0852983
\(673\) −0.735886 −0.0283663 −0.0141832 0.999899i \(-0.504515\pi\)
−0.0141832 + 0.999899i \(0.504515\pi\)
\(674\) 26.9628 1.03857
\(675\) −25.4502 −0.979579
\(676\) −12.0909 −0.465035
\(677\) −21.9886 −0.845090 −0.422545 0.906342i \(-0.638863\pi\)
−0.422545 + 0.906342i \(0.638863\pi\)
\(678\) 1.24577 0.0478437
\(679\) −12.4881 −0.479250
\(680\) −0.167250 −0.00641375
\(681\) 0.208241 0.00797981
\(682\) 31.1127 1.19137
\(683\) 42.4553 1.62451 0.812254 0.583304i \(-0.198240\pi\)
0.812254 + 0.583304i \(0.198240\pi\)
\(684\) 1.92642 0.0736584
\(685\) 2.33188 0.0890966
\(686\) −20.1579 −0.769631
\(687\) −18.9531 −0.723107
\(688\) 11.1940 0.426768
\(689\) −11.7121 −0.446195
\(690\) 0.863339 0.0328668
\(691\) 18.9771 0.721921 0.360961 0.932581i \(-0.382449\pi\)
0.360961 + 0.932581i \(0.382449\pi\)
\(692\) −11.5395 −0.438666
\(693\) −21.8030 −0.828226
\(694\) −2.47186 −0.0938305
\(695\) 0.262759 0.00996701
\(696\) 3.34371 0.126743
\(697\) −8.57364 −0.324750
\(698\) 4.59571 0.173950
\(699\) −2.18297 −0.0825674
\(700\) −10.6402 −0.402162
\(701\) −19.1532 −0.723405 −0.361703 0.932294i \(-0.617804\pi\)
−0.361703 + 0.932294i \(0.617804\pi\)
\(702\) 4.86692 0.183690
\(703\) −9.27789 −0.349922
\(704\) 5.30344 0.199881
\(705\) −0.620116 −0.0233549
\(706\) −0.751216 −0.0282724
\(707\) −20.3897 −0.766834
\(708\) 6.84383 0.257207
\(709\) −30.8487 −1.15855 −0.579274 0.815133i \(-0.696664\pi\)
−0.579274 + 0.815133i \(0.696664\pi\)
\(710\) 1.63554 0.0613806
\(711\) −18.1191 −0.679519
\(712\) −16.4497 −0.616479
\(713\) −41.1480 −1.54101
\(714\) 3.11313 0.116506
\(715\) 0.600700 0.0224649
\(716\) 23.6668 0.884469
\(717\) 15.4165 0.575740
\(718\) 32.4002 1.20916
\(719\) −34.7621 −1.29641 −0.648203 0.761467i \(-0.724479\pi\)
−0.648203 + 0.761467i \(0.724479\pi\)
\(720\) −0.228847 −0.00852862
\(721\) 4.85445 0.180789
\(722\) 1.00000 0.0372161
\(723\) 24.0049 0.892751
\(724\) 10.4171 0.387147
\(725\) 16.0899 0.597564
\(726\) −17.7454 −0.658595
\(727\) −6.96965 −0.258490 −0.129245 0.991613i \(-0.541255\pi\)
−0.129245 + 0.991613i \(0.541255\pi\)
\(728\) 2.03476 0.0754130
\(729\) 14.9222 0.552673
\(730\) 1.54910 0.0573346
\(731\) −15.7601 −0.582908
\(732\) −9.31988 −0.344473
\(733\) 7.43849 0.274747 0.137374 0.990519i \(-0.456134\pi\)
0.137374 + 0.990519i \(0.456134\pi\)
\(734\) 33.2882 1.22869
\(735\) 0.301044 0.0111042
\(736\) −7.01405 −0.258541
\(737\) 29.1292 1.07299
\(738\) −11.7312 −0.431833
\(739\) 48.3900 1.78006 0.890028 0.455907i \(-0.150685\pi\)
0.890028 + 0.455907i \(0.150685\pi\)
\(740\) 1.10216 0.0405162
\(741\) 0.987923 0.0362922
\(742\) −26.2142 −0.962352
\(743\) 10.7258 0.393491 0.196746 0.980455i \(-0.436963\pi\)
0.196746 + 0.980455i \(0.436963\pi\)
\(744\) −6.07852 −0.222849
\(745\) −0.339211 −0.0124277
\(746\) 12.4366 0.455336
\(747\) 3.72899 0.136437
\(748\) −7.46672 −0.273010
\(749\) −13.5366 −0.494617
\(750\) 1.22913 0.0448816
\(751\) −52.5013 −1.91580 −0.957900 0.287102i \(-0.907308\pi\)
−0.957900 + 0.287102i \(0.907308\pi\)
\(752\) 5.03802 0.183718
\(753\) −9.96850 −0.363272
\(754\) −3.07692 −0.112055
\(755\) 0.313305 0.0114023
\(756\) 10.8932 0.396182
\(757\) −35.8842 −1.30423 −0.652116 0.758119i \(-0.726118\pi\)
−0.652116 + 0.758119i \(0.726118\pi\)
\(758\) 9.39836 0.341364
\(759\) 38.5429 1.39902
\(760\) −0.118794 −0.00430911
\(761\) 35.6762 1.29326 0.646631 0.762803i \(-0.276178\pi\)
0.646631 + 0.762803i \(0.276178\pi\)
\(762\) 0.457687 0.0165803
\(763\) −3.90457 −0.141355
\(764\) 13.9644 0.505214
\(765\) 0.322194 0.0116489
\(766\) −14.2944 −0.516476
\(767\) −6.29776 −0.227399
\(768\) −1.03614 −0.0373884
\(769\) 39.4352 1.42207 0.711034 0.703157i \(-0.248227\pi\)
0.711034 + 0.703157i \(0.248227\pi\)
\(770\) 1.34450 0.0484523
\(771\) −26.2767 −0.946334
\(772\) −9.29956 −0.334699
\(773\) 24.5772 0.883980 0.441990 0.897020i \(-0.354273\pi\)
0.441990 + 0.897020i \(0.354273\pi\)
\(774\) −21.5644 −0.775115
\(775\) −29.2498 −1.05068
\(776\) −5.85181 −0.210068
\(777\) −20.5151 −0.735976
\(778\) 36.3439 1.30299
\(779\) −6.08967 −0.218185
\(780\) −0.117359 −0.00420214
\(781\) 73.0169 2.61275
\(782\) 9.87508 0.353132
\(783\) −16.4725 −0.588679
\(784\) −2.44578 −0.0873492
\(785\) −1.48944 −0.0531602
\(786\) 2.48019 0.0884653
\(787\) −29.1101 −1.03766 −0.518832 0.854877i \(-0.673633\pi\)
−0.518832 + 0.854877i \(0.673633\pi\)
\(788\) −24.1737 −0.861154
\(789\) −3.31127 −0.117884
\(790\) 1.11733 0.0397528
\(791\) −2.56583 −0.0912306
\(792\) −10.2166 −0.363033
\(793\) 8.57625 0.304552
\(794\) −27.1138 −0.962233
\(795\) 1.51196 0.0536239
\(796\) 11.3541 0.402436
\(797\) 22.2340 0.787570 0.393785 0.919203i \(-0.371165\pi\)
0.393785 + 0.919203i \(0.371165\pi\)
\(798\) 2.21118 0.0782751
\(799\) −7.09303 −0.250933
\(800\) −4.98589 −0.176278
\(801\) 31.6890 1.11968
\(802\) 20.5133 0.724350
\(803\) 69.1579 2.44053
\(804\) −5.69099 −0.200706
\(805\) −1.77816 −0.0626719
\(806\) 5.59352 0.197023
\(807\) −14.9239 −0.525347
\(808\) −9.55441 −0.336123
\(809\) −29.2975 −1.03004 −0.515022 0.857177i \(-0.672216\pi\)
−0.515022 + 0.857177i \(0.672216\pi\)
\(810\) 0.0582486 0.00204665
\(811\) 47.2019 1.65748 0.828741 0.559632i \(-0.189057\pi\)
0.828741 + 0.559632i \(0.189057\pi\)
\(812\) −6.88680 −0.241679
\(813\) −19.3599 −0.678982
\(814\) 49.2048 1.72463
\(815\) 1.28186 0.0449016
\(816\) 1.45878 0.0510675
\(817\) −11.1940 −0.391630
\(818\) 3.77530 0.132000
\(819\) −3.91979 −0.136968
\(820\) 0.723417 0.0252628
\(821\) −0.369387 −0.0128917 −0.00644584 0.999979i \(-0.502052\pi\)
−0.00644584 + 0.999979i \(0.502052\pi\)
\(822\) −20.3390 −0.709404
\(823\) −4.59959 −0.160332 −0.0801658 0.996782i \(-0.525545\pi\)
−0.0801658 + 0.996782i \(0.525545\pi\)
\(824\) 2.27475 0.0792445
\(825\) 27.3980 0.953875
\(826\) −14.0957 −0.490454
\(827\) −43.8348 −1.52429 −0.762143 0.647409i \(-0.775852\pi\)
−0.762143 + 0.647409i \(0.775852\pi\)
\(828\) 13.5120 0.469574
\(829\) 43.5645 1.51306 0.756528 0.653961i \(-0.226894\pi\)
0.756528 + 0.653961i \(0.226894\pi\)
\(830\) −0.229951 −0.00798173
\(831\) −26.2833 −0.911756
\(832\) 0.953466 0.0330555
\(833\) 3.44341 0.119307
\(834\) −2.29182 −0.0793592
\(835\) 0.465650 0.0161145
\(836\) −5.30344 −0.183423
\(837\) 29.9453 1.03506
\(838\) −24.8611 −0.858813
\(839\) 12.8343 0.443088 0.221544 0.975150i \(-0.428890\pi\)
0.221544 + 0.975150i \(0.428890\pi\)
\(840\) −0.262676 −0.00906317
\(841\) −18.5859 −0.640893
\(842\) −14.2065 −0.489587
\(843\) −14.3262 −0.493422
\(844\) −1.00000 −0.0344214
\(845\) −1.43633 −0.0494112
\(846\) −9.70533 −0.333676
\(847\) 36.5491 1.25584
\(848\) −12.2837 −0.421824
\(849\) −10.3232 −0.354291
\(850\) 7.01963 0.240771
\(851\) −65.0756 −2.23076
\(852\) −14.2654 −0.488723
\(853\) 4.62872 0.158484 0.0792421 0.996855i \(-0.474750\pi\)
0.0792421 + 0.996855i \(0.474750\pi\)
\(854\) 19.1955 0.656857
\(855\) 0.228847 0.00782640
\(856\) −6.34312 −0.216803
\(857\) −31.3069 −1.06942 −0.534712 0.845034i \(-0.679580\pi\)
−0.534712 + 0.845034i \(0.679580\pi\)
\(858\) −5.23939 −0.178870
\(859\) −44.5647 −1.52053 −0.760263 0.649615i \(-0.774930\pi\)
−0.760263 + 0.649615i \(0.774930\pi\)
\(860\) 1.32978 0.0453453
\(861\) −13.4654 −0.458899
\(862\) −31.1315 −1.06034
\(863\) 35.0485 1.19307 0.596533 0.802589i \(-0.296544\pi\)
0.596533 + 0.802589i \(0.296544\pi\)
\(864\) 5.10445 0.173657
\(865\) −1.37082 −0.0466094
\(866\) −14.0770 −0.478357
\(867\) 15.5605 0.528464
\(868\) 12.5195 0.424940
\(869\) 49.8820 1.69213
\(870\) 0.397213 0.0134668
\(871\) 5.23691 0.177446
\(872\) −1.82964 −0.0619595
\(873\) 11.2730 0.381534
\(874\) 7.01405 0.237254
\(875\) −2.53156 −0.0855824
\(876\) −13.5114 −0.456509
\(877\) 36.4438 1.23062 0.615310 0.788285i \(-0.289031\pi\)
0.615310 + 0.788285i \(0.289031\pi\)
\(878\) 15.2653 0.515179
\(879\) −17.8358 −0.601586
\(880\) 0.630018 0.0212379
\(881\) −6.93642 −0.233694 −0.116847 0.993150i \(-0.537279\pi\)
−0.116847 + 0.993150i \(0.537279\pi\)
\(882\) 4.71159 0.158647
\(883\) 41.5904 1.39963 0.699814 0.714325i \(-0.253266\pi\)
0.699814 + 0.714325i \(0.253266\pi\)
\(884\) −1.34238 −0.0451493
\(885\) 0.813006 0.0273289
\(886\) 6.44080 0.216383
\(887\) 33.7553 1.13339 0.566696 0.823927i \(-0.308221\pi\)
0.566696 + 0.823927i \(0.308221\pi\)
\(888\) −9.61318 −0.322597
\(889\) −0.942666 −0.0316160
\(890\) −1.95413 −0.0655026
\(891\) 2.60045 0.0871183
\(892\) −3.96485 −0.132753
\(893\) −5.03802 −0.168591
\(894\) 2.95865 0.0989520
\(895\) 2.81147 0.0939772
\(896\) 2.13406 0.0712940
\(897\) 6.92934 0.231364
\(898\) −33.6440 −1.12272
\(899\) −18.9318 −0.631409
\(900\) 9.60490 0.320163
\(901\) 17.2942 0.576154
\(902\) 32.2962 1.07535
\(903\) −24.7521 −0.823697
\(904\) −1.20232 −0.0399887
\(905\) 1.23749 0.0411354
\(906\) −2.73269 −0.0907875
\(907\) −14.0894 −0.467832 −0.233916 0.972257i \(-0.575154\pi\)
−0.233916 + 0.972257i \(0.575154\pi\)
\(908\) −0.200978 −0.00666969
\(909\) 18.4058 0.610481
\(910\) 0.241717 0.00801284
\(911\) −14.5143 −0.480881 −0.240440 0.970664i \(-0.577292\pi\)
−0.240440 + 0.970664i \(0.577292\pi\)
\(912\) 1.03614 0.0343100
\(913\) −10.2660 −0.339753
\(914\) −23.7652 −0.786082
\(915\) −1.10715 −0.0366011
\(916\) 18.2921 0.604387
\(917\) −5.10827 −0.168690
\(918\) −7.18656 −0.237192
\(919\) 11.8884 0.392163 0.196081 0.980588i \(-0.437178\pi\)
0.196081 + 0.980588i \(0.437178\pi\)
\(920\) −0.833228 −0.0274707
\(921\) −26.3831 −0.869352
\(922\) −33.2389 −1.09467
\(923\) 13.1271 0.432085
\(924\) −11.7269 −0.385786
\(925\) −46.2585 −1.52097
\(926\) −4.13838 −0.135996
\(927\) −4.38211 −0.143927
\(928\) −3.22709 −0.105934
\(929\) −19.8014 −0.649663 −0.324832 0.945772i \(-0.605308\pi\)
−0.324832 + 0.945772i \(0.605308\pi\)
\(930\) −0.722093 −0.0236783
\(931\) 2.44578 0.0801572
\(932\) 2.10683 0.0690115
\(933\) −21.1635 −0.692860
\(934\) 28.7669 0.941281
\(935\) −0.887002 −0.0290081
\(936\) −1.83677 −0.0600368
\(937\) 34.2583 1.11917 0.559585 0.828773i \(-0.310961\pi\)
0.559585 + 0.828773i \(0.310961\pi\)
\(938\) 11.7213 0.382715
\(939\) −4.69567 −0.153237
\(940\) 0.598487 0.0195205
\(941\) −0.766759 −0.0249956 −0.0124978 0.999922i \(-0.503978\pi\)
−0.0124978 + 0.999922i \(0.503978\pi\)
\(942\) 12.9911 0.423272
\(943\) −42.7132 −1.39093
\(944\) −6.60513 −0.214979
\(945\) 1.29405 0.0420954
\(946\) 59.3669 1.93019
\(947\) 20.4260 0.663757 0.331878 0.943322i \(-0.392318\pi\)
0.331878 + 0.943322i \(0.392318\pi\)
\(948\) −9.74549 −0.316519
\(949\) 12.4334 0.403604
\(950\) 4.98589 0.161764
\(951\) −11.9490 −0.387472
\(952\) −3.00455 −0.0973779
\(953\) −2.85501 −0.0924829 −0.0462414 0.998930i \(-0.514724\pi\)
−0.0462414 + 0.998930i \(0.514724\pi\)
\(954\) 23.6635 0.766134
\(955\) 1.65889 0.0536803
\(956\) −14.8788 −0.481215
\(957\) 17.7332 0.573232
\(958\) −9.34694 −0.301986
\(959\) 41.8908 1.35273
\(960\) −0.123087 −0.00397262
\(961\) 3.41600 0.110193
\(962\) 8.84615 0.285211
\(963\) 12.2195 0.393767
\(964\) −23.1676 −0.746179
\(965\) −1.10473 −0.0355626
\(966\) 15.5094 0.499005
\(967\) 60.1612 1.93466 0.967328 0.253530i \(-0.0815916\pi\)
0.967328 + 0.253530i \(0.0815916\pi\)
\(968\) 17.1265 0.550467
\(969\) −1.45878 −0.0468628
\(970\) −0.695160 −0.0223202
\(971\) −45.6797 −1.46593 −0.732965 0.680266i \(-0.761864\pi\)
−0.732965 + 0.680266i \(0.761864\pi\)
\(972\) −15.8214 −0.507472
\(973\) 4.72030 0.151326
\(974\) 3.81019 0.122086
\(975\) 4.92567 0.157748
\(976\) 8.99482 0.287917
\(977\) 46.3154 1.48176 0.740880 0.671638i \(-0.234409\pi\)
0.740880 + 0.671638i \(0.234409\pi\)
\(978\) −11.1806 −0.357515
\(979\) −87.2402 −2.78821
\(980\) −0.290544 −0.00928109
\(981\) 3.52465 0.112534
\(982\) 3.90927 0.124750
\(983\) −28.6791 −0.914722 −0.457361 0.889281i \(-0.651205\pi\)
−0.457361 + 0.889281i \(0.651205\pi\)
\(984\) −6.30974 −0.201147
\(985\) −2.87170 −0.0914999
\(986\) 4.54342 0.144692
\(987\) −11.1400 −0.354590
\(988\) −0.953466 −0.0303338
\(989\) −78.5155 −2.49665
\(990\) −1.21368 −0.0385732
\(991\) 39.1355 1.24318 0.621590 0.783343i \(-0.286487\pi\)
0.621590 + 0.783343i \(0.286487\pi\)
\(992\) 5.86651 0.186262
\(993\) 20.1760 0.640265
\(994\) 29.3814 0.931921
\(995\) 1.34880 0.0427599
\(996\) 2.00567 0.0635520
\(997\) 26.3862 0.835660 0.417830 0.908525i \(-0.362791\pi\)
0.417830 + 0.908525i \(0.362791\pi\)
\(998\) −25.8060 −0.816875
\(999\) 47.3585 1.49836
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 \(a_p\))