Properties

Label 8043.2.a.t.1.17
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(52\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.10272 q^{2}\) \(-1.00000 q^{3}\) \(-0.784010 q^{4}\) \(+0.760743 q^{5}\) \(+1.10272 q^{6}\) \(+1.00000 q^{7}\) \(+3.06998 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.10272 q^{2}\) \(-1.00000 q^{3}\) \(-0.784010 q^{4}\) \(+0.760743 q^{5}\) \(+1.10272 q^{6}\) \(+1.00000 q^{7}\) \(+3.06998 q^{8}\) \(+1.00000 q^{9}\) \(-0.838886 q^{10}\) \(+0.597329 q^{11}\) \(+0.784010 q^{12}\) \(-4.75703 q^{13}\) \(-1.10272 q^{14}\) \(-0.760743 q^{15}\) \(-1.81731 q^{16}\) \(+1.90750 q^{17}\) \(-1.10272 q^{18}\) \(-5.87579 q^{19}\) \(-0.596430 q^{20}\) \(-1.00000 q^{21}\) \(-0.658686 q^{22}\) \(-7.97969 q^{23}\) \(-3.06998 q^{24}\) \(-4.42127 q^{25}\) \(+5.24567 q^{26}\) \(-1.00000 q^{27}\) \(-0.784010 q^{28}\) \(+3.85644 q^{29}\) \(+0.838886 q^{30}\) \(-4.54227 q^{31}\) \(-4.13598 q^{32}\) \(-0.597329 q^{33}\) \(-2.10344 q^{34}\) \(+0.760743 q^{35}\) \(-0.784010 q^{36}\) \(-4.13929 q^{37}\) \(+6.47935 q^{38}\) \(+4.75703 q^{39}\) \(+2.33547 q^{40}\) \(+9.73395 q^{41}\) \(+1.10272 q^{42}\) \(-10.9381 q^{43}\) \(-0.468312 q^{44}\) \(+0.760743 q^{45}\) \(+8.79936 q^{46}\) \(-5.17145 q^{47}\) \(+1.81731 q^{48}\) \(+1.00000 q^{49}\) \(+4.87542 q^{50}\) \(-1.90750 q^{51}\) \(+3.72956 q^{52}\) \(+14.0161 q^{53}\) \(+1.10272 q^{54}\) \(+0.454414 q^{55}\) \(+3.06998 q^{56}\) \(+5.87579 q^{57}\) \(-4.25257 q^{58}\) \(-7.09175 q^{59}\) \(+0.596430 q^{60}\) \(-4.13631 q^{61}\) \(+5.00885 q^{62}\) \(+1.00000 q^{63}\) \(+8.19545 q^{64}\) \(-3.61888 q^{65}\) \(+0.658686 q^{66}\) \(+1.80164 q^{67}\) \(-1.49550 q^{68}\) \(+7.97969 q^{69}\) \(-0.838886 q^{70}\) \(-15.7873 q^{71}\) \(+3.06998 q^{72}\) \(+6.46981 q^{73}\) \(+4.56447 q^{74}\) \(+4.42127 q^{75}\) \(+4.60668 q^{76}\) \(+0.597329 q^{77}\) \(-5.24567 q^{78}\) \(-2.06675 q^{79}\) \(-1.38251 q^{80}\) \(+1.00000 q^{81}\) \(-10.7338 q^{82}\) \(+10.4388 q^{83}\) \(+0.784010 q^{84}\) \(+1.45112 q^{85}\) \(+12.0617 q^{86}\) \(-3.85644 q^{87}\) \(+1.83379 q^{88}\) \(+5.04949 q^{89}\) \(-0.838886 q^{90}\) \(-4.75703 q^{91}\) \(+6.25615 q^{92}\) \(+4.54227 q^{93}\) \(+5.70266 q^{94}\) \(-4.46997 q^{95}\) \(+4.13598 q^{96}\) \(+12.8199 q^{97}\) \(-1.10272 q^{98}\) \(+0.597329 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 61q^{12} \) \(\mathstrut +\mathstrut 44q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 95q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 21q^{20} \) \(\mathstrut -\mathstrut 52q^{21} \) \(\mathstrut +\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 83q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 61q^{28} \) \(\mathstrut +\mathstrut 31q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 71q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 17q^{34} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 61q^{36} \) \(\mathstrut +\mathstrut 71q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 44q^{39} \) \(\mathstrut +\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 25q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut +\mathstrut 75q^{43} \) \(\mathstrut +\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 36q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 95q^{48} \) \(\mathstrut +\mathstrut 52q^{49} \) \(\mathstrut +\mathstrut 26q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 88q^{52} \) \(\mathstrut +\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 7q^{57} \) \(\mathstrut +\mathstrut 48q^{58} \) \(\mathstrut -\mathstrut 27q^{59} \) \(\mathstrut +\mathstrut 21q^{60} \) \(\mathstrut +\mathstrut 59q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 138q^{64} \) \(\mathstrut +\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 65q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut -\mathstrut 83q^{75} \) \(\mathstrut +\mathstrut 31q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 52q^{81} \) \(\mathstrut +\mathstrut 51q^{82} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 61q^{84} \) \(\mathstrut +\mathstrut 70q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 31q^{87} \) \(\mathstrut +\mathstrut 90q^{88} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 34q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 27q^{94} \) \(\mathstrut +\mathstrut 9q^{95} \) \(\mathstrut -\mathstrut 71q^{96} \) \(\mathstrut +\mathstrut 73q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.10272 −0.779740 −0.389870 0.920870i \(-0.627480\pi\)
−0.389870 + 0.920870i \(0.627480\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.784010 −0.392005
\(5\) 0.760743 0.340215 0.170107 0.985426i \(-0.445589\pi\)
0.170107 + 0.985426i \(0.445589\pi\)
\(6\) 1.10272 0.450183
\(7\) 1.00000 0.377964
\(8\) 3.06998 1.08540
\(9\) 1.00000 0.333333
\(10\) −0.838886 −0.265279
\(11\) 0.597329 0.180101 0.0900507 0.995937i \(-0.471297\pi\)
0.0900507 + 0.995937i \(0.471297\pi\)
\(12\) 0.784010 0.226324
\(13\) −4.75703 −1.31936 −0.659681 0.751546i \(-0.729309\pi\)
−0.659681 + 0.751546i \(0.729309\pi\)
\(14\) −1.10272 −0.294714
\(15\) −0.760743 −0.196423
\(16\) −1.81731 −0.454327
\(17\) 1.90750 0.462637 0.231319 0.972878i \(-0.425696\pi\)
0.231319 + 0.972878i \(0.425696\pi\)
\(18\) −1.10272 −0.259913
\(19\) −5.87579 −1.34800 −0.673999 0.738732i \(-0.735425\pi\)
−0.673999 + 0.738732i \(0.735425\pi\)
\(20\) −0.596430 −0.133366
\(21\) −1.00000 −0.218218
\(22\) −0.658686 −0.140432
\(23\) −7.97969 −1.66388 −0.831940 0.554866i \(-0.812770\pi\)
−0.831940 + 0.554866i \(0.812770\pi\)
\(24\) −3.06998 −0.626657
\(25\) −4.42127 −0.884254
\(26\) 5.24567 1.02876
\(27\) −1.00000 −0.192450
\(28\) −0.784010 −0.148164
\(29\) 3.85644 0.716123 0.358061 0.933698i \(-0.383438\pi\)
0.358061 + 0.933698i \(0.383438\pi\)
\(30\) 0.838886 0.153159
\(31\) −4.54227 −0.815816 −0.407908 0.913023i \(-0.633742\pi\)
−0.407908 + 0.913023i \(0.633742\pi\)
\(32\) −4.13598 −0.731145
\(33\) −0.597329 −0.103982
\(34\) −2.10344 −0.360737
\(35\) 0.760743 0.128589
\(36\) −0.784010 −0.130668
\(37\) −4.13929 −0.680494 −0.340247 0.940336i \(-0.610511\pi\)
−0.340247 + 0.940336i \(0.610511\pi\)
\(38\) 6.47935 1.05109
\(39\) 4.75703 0.761734
\(40\) 2.33547 0.369270
\(41\) 9.73395 1.52019 0.760093 0.649814i \(-0.225153\pi\)
0.760093 + 0.649814i \(0.225153\pi\)
\(42\) 1.10272 0.170153
\(43\) −10.9381 −1.66804 −0.834022 0.551731i \(-0.813967\pi\)
−0.834022 + 0.551731i \(0.813967\pi\)
\(44\) −0.468312 −0.0706006
\(45\) 0.760743 0.113405
\(46\) 8.79936 1.29739
\(47\) −5.17145 −0.754333 −0.377167 0.926145i \(-0.623102\pi\)
−0.377167 + 0.926145i \(0.623102\pi\)
\(48\) 1.81731 0.262306
\(49\) 1.00000 0.142857
\(50\) 4.87542 0.689489
\(51\) −1.90750 −0.267104
\(52\) 3.72956 0.517196
\(53\) 14.0161 1.92526 0.962628 0.270829i \(-0.0872978\pi\)
0.962628 + 0.270829i \(0.0872978\pi\)
\(54\) 1.10272 0.150061
\(55\) 0.454414 0.0612731
\(56\) 3.06998 0.410244
\(57\) 5.87579 0.778267
\(58\) −4.25257 −0.558390
\(59\) −7.09175 −0.923268 −0.461634 0.887071i \(-0.652737\pi\)
−0.461634 + 0.887071i \(0.652737\pi\)
\(60\) 0.596430 0.0769988
\(61\) −4.13631 −0.529600 −0.264800 0.964303i \(-0.585306\pi\)
−0.264800 + 0.964303i \(0.585306\pi\)
\(62\) 5.00885 0.636125
\(63\) 1.00000 0.125988
\(64\) 8.19545 1.02443
\(65\) −3.61888 −0.448866
\(66\) 0.658686 0.0810787
\(67\) 1.80164 0.220105 0.110052 0.993926i \(-0.464898\pi\)
0.110052 + 0.993926i \(0.464898\pi\)
\(68\) −1.49550 −0.181356
\(69\) 7.97969 0.960642
\(70\) −0.838886 −0.100266
\(71\) −15.7873 −1.87361 −0.936805 0.349852i \(-0.886232\pi\)
−0.936805 + 0.349852i \(0.886232\pi\)
\(72\) 3.06998 0.361801
\(73\) 6.46981 0.757234 0.378617 0.925553i \(-0.376400\pi\)
0.378617 + 0.925553i \(0.376400\pi\)
\(74\) 4.56447 0.530609
\(75\) 4.42127 0.510524
\(76\) 4.60668 0.528422
\(77\) 0.597329 0.0680719
\(78\) −5.24567 −0.593955
\(79\) −2.06675 −0.232528 −0.116264 0.993218i \(-0.537092\pi\)
−0.116264 + 0.993218i \(0.537092\pi\)
\(80\) −1.38251 −0.154569
\(81\) 1.00000 0.111111
\(82\) −10.7338 −1.18535
\(83\) 10.4388 1.14581 0.572906 0.819621i \(-0.305816\pi\)
0.572906 + 0.819621i \(0.305816\pi\)
\(84\) 0.784010 0.0855425
\(85\) 1.45112 0.157396
\(86\) 12.0617 1.30064
\(87\) −3.85644 −0.413454
\(88\) 1.83379 0.195483
\(89\) 5.04949 0.535245 0.267623 0.963524i \(-0.413762\pi\)
0.267623 + 0.963524i \(0.413762\pi\)
\(90\) −0.838886 −0.0884264
\(91\) −4.75703 −0.498672
\(92\) 6.25615 0.652249
\(93\) 4.54227 0.471012
\(94\) 5.70266 0.588184
\(95\) −4.46997 −0.458609
\(96\) 4.13598 0.422127
\(97\) 12.8199 1.30167 0.650833 0.759221i \(-0.274420\pi\)
0.650833 + 0.759221i \(0.274420\pi\)
\(98\) −1.10272 −0.111391
\(99\) 0.597329 0.0600338
\(100\) 3.46632 0.346632
\(101\) 12.3187 1.22575 0.612877 0.790178i \(-0.290012\pi\)
0.612877 + 0.790178i \(0.290012\pi\)
\(102\) 2.10344 0.208272
\(103\) 8.63579 0.850909 0.425455 0.904980i \(-0.360114\pi\)
0.425455 + 0.904980i \(0.360114\pi\)
\(104\) −14.6040 −1.43204
\(105\) −0.760743 −0.0742409
\(106\) −15.4558 −1.50120
\(107\) 12.0518 1.16509 0.582544 0.812799i \(-0.302057\pi\)
0.582544 + 0.812799i \(0.302057\pi\)
\(108\) 0.784010 0.0754414
\(109\) 13.3643 1.28006 0.640032 0.768349i \(-0.278921\pi\)
0.640032 + 0.768349i \(0.278921\pi\)
\(110\) −0.501091 −0.0477772
\(111\) 4.13929 0.392884
\(112\) −1.81731 −0.171720
\(113\) −17.2347 −1.62131 −0.810653 0.585527i \(-0.800887\pi\)
−0.810653 + 0.585527i \(0.800887\pi\)
\(114\) −6.47935 −0.606847
\(115\) −6.07049 −0.566076
\(116\) −3.02349 −0.280724
\(117\) −4.75703 −0.439787
\(118\) 7.82021 0.719909
\(119\) 1.90750 0.174861
\(120\) −2.33547 −0.213198
\(121\) −10.6432 −0.967563
\(122\) 4.56119 0.412951
\(123\) −9.73395 −0.877680
\(124\) 3.56118 0.319804
\(125\) −7.16717 −0.641051
\(126\) −1.10272 −0.0982381
\(127\) −10.0255 −0.889616 −0.444808 0.895626i \(-0.646728\pi\)
−0.444808 + 0.895626i \(0.646728\pi\)
\(128\) −0.765317 −0.0676451
\(129\) 10.9381 0.963046
\(130\) 3.99060 0.349999
\(131\) 2.29268 0.200313 0.100156 0.994972i \(-0.468066\pi\)
0.100156 + 0.994972i \(0.468066\pi\)
\(132\) 0.468312 0.0407613
\(133\) −5.87579 −0.509496
\(134\) −1.98670 −0.171625
\(135\) −0.760743 −0.0654743
\(136\) 5.85600 0.502148
\(137\) 14.5342 1.24174 0.620872 0.783912i \(-0.286779\pi\)
0.620872 + 0.783912i \(0.286779\pi\)
\(138\) −8.79936 −0.749051
\(139\) −16.4202 −1.39274 −0.696371 0.717682i \(-0.745203\pi\)
−0.696371 + 0.717682i \(0.745203\pi\)
\(140\) −0.596430 −0.0504075
\(141\) 5.17145 0.435514
\(142\) 17.4090 1.46093
\(143\) −2.84151 −0.237619
\(144\) −1.81731 −0.151442
\(145\) 2.93376 0.243635
\(146\) −7.13439 −0.590446
\(147\) −1.00000 −0.0824786
\(148\) 3.24524 0.266757
\(149\) 17.8458 1.46198 0.730991 0.682387i \(-0.239058\pi\)
0.730991 + 0.682387i \(0.239058\pi\)
\(150\) −4.87542 −0.398076
\(151\) −7.76863 −0.632202 −0.316101 0.948726i \(-0.602374\pi\)
−0.316101 + 0.948726i \(0.602374\pi\)
\(152\) −18.0386 −1.46312
\(153\) 1.90750 0.154212
\(154\) −0.658686 −0.0530784
\(155\) −3.45550 −0.277553
\(156\) −3.72956 −0.298603
\(157\) 7.79929 0.622451 0.311226 0.950336i \(-0.399261\pi\)
0.311226 + 0.950336i \(0.399261\pi\)
\(158\) 2.27905 0.181312
\(159\) −14.0161 −1.11155
\(160\) −3.14642 −0.248746
\(161\) −7.97969 −0.628887
\(162\) −1.10272 −0.0866378
\(163\) 18.1935 1.42503 0.712514 0.701658i \(-0.247556\pi\)
0.712514 + 0.701658i \(0.247556\pi\)
\(164\) −7.63151 −0.595921
\(165\) −0.454414 −0.0353761
\(166\) −11.5111 −0.893436
\(167\) −15.8635 −1.22755 −0.613776 0.789480i \(-0.710350\pi\)
−0.613776 + 0.789480i \(0.710350\pi\)
\(168\) −3.06998 −0.236854
\(169\) 9.62931 0.740716
\(170\) −1.60018 −0.122728
\(171\) −5.87579 −0.449333
\(172\) 8.57557 0.653881
\(173\) −21.0753 −1.60232 −0.801162 0.598447i \(-0.795785\pi\)
−0.801162 + 0.598447i \(0.795785\pi\)
\(174\) 4.25257 0.322387
\(175\) −4.42127 −0.334217
\(176\) −1.08553 −0.0818250
\(177\) 7.09175 0.533049
\(178\) −5.56818 −0.417352
\(179\) 0.843371 0.0630365 0.0315182 0.999503i \(-0.489966\pi\)
0.0315182 + 0.999503i \(0.489966\pi\)
\(180\) −0.596430 −0.0444553
\(181\) −5.23412 −0.389049 −0.194525 0.980898i \(-0.562316\pi\)
−0.194525 + 0.980898i \(0.562316\pi\)
\(182\) 5.24567 0.388835
\(183\) 4.13631 0.305765
\(184\) −24.4975 −1.80598
\(185\) −3.14893 −0.231514
\(186\) −5.00885 −0.367267
\(187\) 1.13941 0.0833217
\(188\) 4.05446 0.295702
\(189\) −1.00000 −0.0727393
\(190\) 4.92912 0.357596
\(191\) 20.0268 1.44909 0.724544 0.689229i \(-0.242051\pi\)
0.724544 + 0.689229i \(0.242051\pi\)
\(192\) −8.19545 −0.591455
\(193\) 1.87046 0.134638 0.0673192 0.997731i \(-0.478555\pi\)
0.0673192 + 0.997731i \(0.478555\pi\)
\(194\) −14.1368 −1.01496
\(195\) 3.61888 0.259153
\(196\) −0.784010 −0.0560007
\(197\) −8.97502 −0.639444 −0.319722 0.947511i \(-0.603589\pi\)
−0.319722 + 0.947511i \(0.603589\pi\)
\(198\) −0.658686 −0.0468108
\(199\) −0.936829 −0.0664100 −0.0332050 0.999449i \(-0.510571\pi\)
−0.0332050 + 0.999449i \(0.510571\pi\)
\(200\) −13.5732 −0.959771
\(201\) −1.80164 −0.127078
\(202\) −13.5840 −0.955770
\(203\) 3.85644 0.270669
\(204\) 1.49550 0.104706
\(205\) 7.40503 0.517190
\(206\) −9.52285 −0.663488
\(207\) −7.97969 −0.554627
\(208\) 8.64499 0.599422
\(209\) −3.50978 −0.242777
\(210\) 0.838886 0.0578886
\(211\) −22.8895 −1.57578 −0.787890 0.615815i \(-0.788827\pi\)
−0.787890 + 0.615815i \(0.788827\pi\)
\(212\) −10.9887 −0.754709
\(213\) 15.7873 1.08173
\(214\) −13.2897 −0.908466
\(215\) −8.32108 −0.567493
\(216\) −3.06998 −0.208886
\(217\) −4.54227 −0.308349
\(218\) −14.7370 −0.998117
\(219\) −6.46981 −0.437189
\(220\) −0.356265 −0.0240194
\(221\) −9.07404 −0.610386
\(222\) −4.56447 −0.306347
\(223\) 27.8810 1.86705 0.933526 0.358511i \(-0.116715\pi\)
0.933526 + 0.358511i \(0.116715\pi\)
\(224\) −4.13598 −0.276347
\(225\) −4.42127 −0.294751
\(226\) 19.0051 1.26420
\(227\) −5.06112 −0.335918 −0.167959 0.985794i \(-0.553718\pi\)
−0.167959 + 0.985794i \(0.553718\pi\)
\(228\) −4.60668 −0.305085
\(229\) −18.5129 −1.22337 −0.611683 0.791103i \(-0.709507\pi\)
−0.611683 + 0.791103i \(0.709507\pi\)
\(230\) 6.69405 0.441393
\(231\) −0.597329 −0.0393014
\(232\) 11.8392 0.777281
\(233\) −5.29665 −0.346995 −0.173497 0.984834i \(-0.555507\pi\)
−0.173497 + 0.984834i \(0.555507\pi\)
\(234\) 5.24567 0.342920
\(235\) −3.93414 −0.256635
\(236\) 5.56000 0.361925
\(237\) 2.06675 0.134250
\(238\) −2.10344 −0.136346
\(239\) 25.2222 1.63149 0.815744 0.578413i \(-0.196328\pi\)
0.815744 + 0.578413i \(0.196328\pi\)
\(240\) 1.38251 0.0892404
\(241\) 27.6212 1.77924 0.889618 0.456706i \(-0.150971\pi\)
0.889618 + 0.456706i \(0.150971\pi\)
\(242\) 11.7365 0.754448
\(243\) −1.00000 −0.0641500
\(244\) 3.24291 0.207606
\(245\) 0.760743 0.0486021
\(246\) 10.7338 0.684363
\(247\) 27.9513 1.77850
\(248\) −13.9447 −0.885489
\(249\) −10.4388 −0.661535
\(250\) 7.90337 0.499853
\(251\) −7.27590 −0.459251 −0.229625 0.973279i \(-0.573750\pi\)
−0.229625 + 0.973279i \(0.573750\pi\)
\(252\) −0.784010 −0.0493880
\(253\) −4.76650 −0.299667
\(254\) 11.0553 0.693669
\(255\) −1.45112 −0.0908726
\(256\) −15.5470 −0.971685
\(257\) 21.9250 1.36764 0.683821 0.729649i \(-0.260317\pi\)
0.683821 + 0.729649i \(0.260317\pi\)
\(258\) −12.0617 −0.750926
\(259\) −4.13929 −0.257203
\(260\) 2.83723 0.175958
\(261\) 3.85644 0.238708
\(262\) −2.52819 −0.156192
\(263\) 16.9826 1.04719 0.523595 0.851967i \(-0.324591\pi\)
0.523595 + 0.851967i \(0.324591\pi\)
\(264\) −1.83379 −0.112862
\(265\) 10.6626 0.655000
\(266\) 6.47935 0.397274
\(267\) −5.04949 −0.309024
\(268\) −1.41250 −0.0862822
\(269\) −27.0483 −1.64916 −0.824581 0.565744i \(-0.808589\pi\)
−0.824581 + 0.565744i \(0.808589\pi\)
\(270\) 0.838886 0.0510530
\(271\) 8.39077 0.509703 0.254851 0.966980i \(-0.417973\pi\)
0.254851 + 0.966980i \(0.417973\pi\)
\(272\) −3.46652 −0.210189
\(273\) 4.75703 0.287908
\(274\) −16.0272 −0.968237
\(275\) −2.64095 −0.159255
\(276\) −6.25615 −0.376576
\(277\) 18.3355 1.10167 0.550836 0.834614i \(-0.314309\pi\)
0.550836 + 0.834614i \(0.314309\pi\)
\(278\) 18.1069 1.08598
\(279\) −4.54227 −0.271939
\(280\) 2.33547 0.139571
\(281\) −21.9017 −1.30655 −0.653273 0.757123i \(-0.726605\pi\)
−0.653273 + 0.757123i \(0.726605\pi\)
\(282\) −5.70266 −0.339588
\(283\) 2.35374 0.139915 0.0699577 0.997550i \(-0.477714\pi\)
0.0699577 + 0.997550i \(0.477714\pi\)
\(284\) 12.3774 0.734464
\(285\) 4.46997 0.264778
\(286\) 3.13339 0.185281
\(287\) 9.73395 0.574577
\(288\) −4.13598 −0.243715
\(289\) −13.3614 −0.785967
\(290\) −3.23511 −0.189972
\(291\) −12.8199 −0.751517
\(292\) −5.07239 −0.296839
\(293\) −6.44889 −0.376748 −0.188374 0.982097i \(-0.560322\pi\)
−0.188374 + 0.982097i \(0.560322\pi\)
\(294\) 1.10272 0.0643119
\(295\) −5.39500 −0.314109
\(296\) −12.7075 −0.738610
\(297\) −0.597329 −0.0346605
\(298\) −19.6789 −1.13997
\(299\) 37.9596 2.19526
\(300\) −3.46632 −0.200128
\(301\) −10.9381 −0.630461
\(302\) 8.56662 0.492954
\(303\) −12.3187 −0.707689
\(304\) 10.6781 0.612433
\(305\) −3.14667 −0.180178
\(306\) −2.10344 −0.120246
\(307\) −0.105629 −0.00602858 −0.00301429 0.999995i \(-0.500959\pi\)
−0.00301429 + 0.999995i \(0.500959\pi\)
\(308\) −0.468312 −0.0266845
\(309\) −8.63579 −0.491273
\(310\) 3.81045 0.216419
\(311\) −3.41558 −0.193680 −0.0968399 0.995300i \(-0.530873\pi\)
−0.0968399 + 0.995300i \(0.530873\pi\)
\(312\) 14.6040 0.826788
\(313\) −18.3685 −1.03825 −0.519124 0.854699i \(-0.673742\pi\)
−0.519124 + 0.854699i \(0.673742\pi\)
\(314\) −8.60043 −0.485350
\(315\) 0.760743 0.0428630
\(316\) 1.62036 0.0911521
\(317\) 29.2567 1.64322 0.821610 0.570051i \(-0.193076\pi\)
0.821610 + 0.570051i \(0.193076\pi\)
\(318\) 15.4558 0.866718
\(319\) 2.30356 0.128975
\(320\) 6.23463 0.348526
\(321\) −12.0518 −0.672664
\(322\) 8.79936 0.490369
\(323\) −11.2081 −0.623635
\(324\) −0.784010 −0.0435561
\(325\) 21.0321 1.16665
\(326\) −20.0624 −1.11115
\(327\) −13.3643 −0.739045
\(328\) 29.8830 1.65001
\(329\) −5.17145 −0.285111
\(330\) 0.501091 0.0275842
\(331\) −0.175156 −0.00962742 −0.00481371 0.999988i \(-0.501532\pi\)
−0.00481371 + 0.999988i \(0.501532\pi\)
\(332\) −8.18416 −0.449164
\(333\) −4.13929 −0.226831
\(334\) 17.4930 0.957172
\(335\) 1.37058 0.0748829
\(336\) 1.81731 0.0991424
\(337\) −1.14949 −0.0626167 −0.0313084 0.999510i \(-0.509967\pi\)
−0.0313084 + 0.999510i \(0.509967\pi\)
\(338\) −10.6184 −0.577566
\(339\) 17.2347 0.936061
\(340\) −1.13769 −0.0617000
\(341\) −2.71323 −0.146930
\(342\) 6.47935 0.350363
\(343\) 1.00000 0.0539949
\(344\) −33.5798 −1.81050
\(345\) 6.07049 0.326824
\(346\) 23.2401 1.24940
\(347\) 12.9858 0.697115 0.348557 0.937287i \(-0.386672\pi\)
0.348557 + 0.937287i \(0.386672\pi\)
\(348\) 3.02349 0.162076
\(349\) −4.50375 −0.241080 −0.120540 0.992708i \(-0.538463\pi\)
−0.120540 + 0.992708i \(0.538463\pi\)
\(350\) 4.87542 0.260602
\(351\) 4.75703 0.253911
\(352\) −2.47054 −0.131680
\(353\) −34.4305 −1.83255 −0.916274 0.400551i \(-0.868819\pi\)
−0.916274 + 0.400551i \(0.868819\pi\)
\(354\) −7.82021 −0.415640
\(355\) −12.0101 −0.637430
\(356\) −3.95885 −0.209819
\(357\) −1.90750 −0.100956
\(358\) −0.930001 −0.0491521
\(359\) 13.7260 0.724429 0.362215 0.932095i \(-0.382021\pi\)
0.362215 + 0.932095i \(0.382021\pi\)
\(360\) 2.33547 0.123090
\(361\) 15.5249 0.817101
\(362\) 5.77177 0.303357
\(363\) 10.6432 0.558623
\(364\) 3.72956 0.195482
\(365\) 4.92186 0.257622
\(366\) −4.56119 −0.238417
\(367\) −21.1634 −1.10472 −0.552361 0.833605i \(-0.686273\pi\)
−0.552361 + 0.833605i \(0.686273\pi\)
\(368\) 14.5016 0.755946
\(369\) 9.73395 0.506729
\(370\) 3.47239 0.180521
\(371\) 14.0161 0.727678
\(372\) −3.56118 −0.184639
\(373\) 15.9716 0.826976 0.413488 0.910510i \(-0.364310\pi\)
0.413488 + 0.910510i \(0.364310\pi\)
\(374\) −1.25645 −0.0649693
\(375\) 7.16717 0.370111
\(376\) −15.8763 −0.818755
\(377\) −18.3452 −0.944825
\(378\) 1.10272 0.0567178
\(379\) −3.78560 −0.194453 −0.0972265 0.995262i \(-0.530997\pi\)
−0.0972265 + 0.995262i \(0.530997\pi\)
\(380\) 3.50450 0.179777
\(381\) 10.0255 0.513620
\(382\) −22.0839 −1.12991
\(383\) −1.00000 −0.0510976
\(384\) 0.765317 0.0390549
\(385\) 0.454414 0.0231591
\(386\) −2.06259 −0.104983
\(387\) −10.9381 −0.556015
\(388\) −10.0509 −0.510259
\(389\) 28.6332 1.45176 0.725881 0.687820i \(-0.241432\pi\)
0.725881 + 0.687820i \(0.241432\pi\)
\(390\) −3.99060 −0.202072
\(391\) −15.2213 −0.769773
\(392\) 3.06998 0.155057
\(393\) −2.29268 −0.115651
\(394\) 9.89693 0.498600
\(395\) −1.57227 −0.0791094
\(396\) −0.468312 −0.0235335
\(397\) 3.98827 0.200165 0.100083 0.994979i \(-0.468089\pi\)
0.100083 + 0.994979i \(0.468089\pi\)
\(398\) 1.03306 0.0517826
\(399\) 5.87579 0.294157
\(400\) 8.03482 0.401741
\(401\) −17.4610 −0.871961 −0.435980 0.899956i \(-0.643598\pi\)
−0.435980 + 0.899956i \(0.643598\pi\)
\(402\) 1.98670 0.0990875
\(403\) 21.6077 1.07636
\(404\) −9.65796 −0.480501
\(405\) 0.760743 0.0378016
\(406\) −4.25257 −0.211052
\(407\) −2.47251 −0.122558
\(408\) −5.85600 −0.289915
\(409\) 31.4462 1.55491 0.777457 0.628937i \(-0.216509\pi\)
0.777457 + 0.628937i \(0.216509\pi\)
\(410\) −8.16567 −0.403274
\(411\) −14.5342 −0.716921
\(412\) −6.77054 −0.333561
\(413\) −7.09175 −0.348962
\(414\) 8.79936 0.432465
\(415\) 7.94128 0.389822
\(416\) 19.6750 0.964645
\(417\) 16.4202 0.804100
\(418\) 3.87030 0.189303
\(419\) 25.9974 1.27006 0.635028 0.772489i \(-0.280988\pi\)
0.635028 + 0.772489i \(0.280988\pi\)
\(420\) 0.596430 0.0291028
\(421\) 33.0449 1.61051 0.805256 0.592927i \(-0.202028\pi\)
0.805256 + 0.592927i \(0.202028\pi\)
\(422\) 25.2407 1.22870
\(423\) −5.17145 −0.251444
\(424\) 43.0291 2.08968
\(425\) −8.43359 −0.409089
\(426\) −17.4090 −0.843468
\(427\) −4.13631 −0.200170
\(428\) −9.44870 −0.456720
\(429\) 2.84151 0.137189
\(430\) 9.17582 0.442497
\(431\) 35.1244 1.69188 0.845942 0.533274i \(-0.179039\pi\)
0.845942 + 0.533274i \(0.179039\pi\)
\(432\) 1.81731 0.0874354
\(433\) −14.3613 −0.690162 −0.345081 0.938573i \(-0.612149\pi\)
−0.345081 + 0.938573i \(0.612149\pi\)
\(434\) 5.00885 0.240433
\(435\) −2.93376 −0.140663
\(436\) −10.4777 −0.501791
\(437\) 46.8870 2.24291
\(438\) 7.13439 0.340894
\(439\) −10.5230 −0.502233 −0.251117 0.967957i \(-0.580798\pi\)
−0.251117 + 0.967957i \(0.580798\pi\)
\(440\) 1.39504 0.0665060
\(441\) 1.00000 0.0476190
\(442\) 10.0061 0.475943
\(443\) −19.5076 −0.926833 −0.463417 0.886141i \(-0.653377\pi\)
−0.463417 + 0.886141i \(0.653377\pi\)
\(444\) −3.24524 −0.154012
\(445\) 3.84137 0.182098
\(446\) −30.7449 −1.45582
\(447\) −17.8458 −0.844076
\(448\) 8.19545 0.387198
\(449\) 15.8730 0.749095 0.374547 0.927208i \(-0.377798\pi\)
0.374547 + 0.927208i \(0.377798\pi\)
\(450\) 4.87542 0.229830
\(451\) 5.81437 0.273788
\(452\) 13.5122 0.635560
\(453\) 7.76863 0.365002
\(454\) 5.58099 0.261929
\(455\) −3.61888 −0.169655
\(456\) 18.0386 0.844733
\(457\) 20.0067 0.935875 0.467938 0.883762i \(-0.344997\pi\)
0.467938 + 0.883762i \(0.344997\pi\)
\(458\) 20.4145 0.953908
\(459\) −1.90750 −0.0890346
\(460\) 4.75932 0.221905
\(461\) −11.9005 −0.554261 −0.277130 0.960832i \(-0.589383\pi\)
−0.277130 + 0.960832i \(0.589383\pi\)
\(462\) 0.658686 0.0306449
\(463\) 22.9536 1.06674 0.533372 0.845881i \(-0.320924\pi\)
0.533372 + 0.845881i \(0.320924\pi\)
\(464\) −7.00834 −0.325354
\(465\) 3.45550 0.160245
\(466\) 5.84072 0.270566
\(467\) 38.0405 1.76031 0.880153 0.474690i \(-0.157440\pi\)
0.880153 + 0.474690i \(0.157440\pi\)
\(468\) 3.72956 0.172399
\(469\) 1.80164 0.0831918
\(470\) 4.33826 0.200109
\(471\) −7.79929 −0.359372
\(472\) −21.7716 −1.00212
\(473\) −6.53364 −0.300417
\(474\) −2.27905 −0.104680
\(475\) 25.9785 1.19197
\(476\) −1.49550 −0.0685462
\(477\) 14.0161 0.641752
\(478\) −27.8130 −1.27214
\(479\) −19.2390 −0.879054 −0.439527 0.898229i \(-0.644854\pi\)
−0.439527 + 0.898229i \(0.644854\pi\)
\(480\) 3.14642 0.143614
\(481\) 19.6907 0.897818
\(482\) −30.4584 −1.38734
\(483\) 7.97969 0.363088
\(484\) 8.34437 0.379290
\(485\) 9.75266 0.442846
\(486\) 1.10272 0.0500204
\(487\) −9.78468 −0.443386 −0.221693 0.975116i \(-0.571158\pi\)
−0.221693 + 0.975116i \(0.571158\pi\)
\(488\) −12.6984 −0.574829
\(489\) −18.1935 −0.822740
\(490\) −0.838886 −0.0378970
\(491\) −27.6834 −1.24934 −0.624668 0.780891i \(-0.714766\pi\)
−0.624668 + 0.780891i \(0.714766\pi\)
\(492\) 7.63151 0.344055
\(493\) 7.35617 0.331305
\(494\) −30.8224 −1.38677
\(495\) 0.454414 0.0204244
\(496\) 8.25471 0.370648
\(497\) −15.7873 −0.708158
\(498\) 11.5111 0.515826
\(499\) 6.30431 0.282220 0.141110 0.989994i \(-0.454933\pi\)
0.141110 + 0.989994i \(0.454933\pi\)
\(500\) 5.61913 0.251295
\(501\) 15.8635 0.708728
\(502\) 8.02328 0.358097
\(503\) 1.27932 0.0570419 0.0285210 0.999593i \(-0.490920\pi\)
0.0285210 + 0.999593i \(0.490920\pi\)
\(504\) 3.06998 0.136748
\(505\) 9.37135 0.417019
\(506\) 5.25611 0.233663
\(507\) −9.62931 −0.427652
\(508\) 7.86006 0.348734
\(509\) −12.4422 −0.551490 −0.275745 0.961231i \(-0.588924\pi\)
−0.275745 + 0.961231i \(0.588924\pi\)
\(510\) 1.60018 0.0708571
\(511\) 6.46981 0.286208
\(512\) 18.6746 0.825307
\(513\) 5.87579 0.259422
\(514\) −24.1771 −1.06641
\(515\) 6.56961 0.289492
\(516\) −8.57557 −0.377518
\(517\) −3.08906 −0.135856
\(518\) 4.56447 0.200551
\(519\) 21.0753 0.925102
\(520\) −11.1099 −0.487201
\(521\) −23.2942 −1.02054 −0.510269 0.860015i \(-0.670454\pi\)
−0.510269 + 0.860015i \(0.670454\pi\)
\(522\) −4.25257 −0.186130
\(523\) 35.5096 1.55272 0.776362 0.630287i \(-0.217063\pi\)
0.776362 + 0.630287i \(0.217063\pi\)
\(524\) −1.79749 −0.0785236
\(525\) 4.42127 0.192960
\(526\) −18.7270 −0.816536
\(527\) −8.66440 −0.377427
\(528\) 1.08553 0.0472417
\(529\) 40.6754 1.76850
\(530\) −11.7579 −0.510730
\(531\) −7.09175 −0.307756
\(532\) 4.60668 0.199725
\(533\) −46.3046 −2.00568
\(534\) 5.56818 0.240959
\(535\) 9.16829 0.396380
\(536\) 5.53099 0.238902
\(537\) −0.843371 −0.0363941
\(538\) 29.8266 1.28592
\(539\) 0.597329 0.0257288
\(540\) 0.596430 0.0256663
\(541\) −40.0860 −1.72343 −0.861715 0.507392i \(-0.830610\pi\)
−0.861715 + 0.507392i \(0.830610\pi\)
\(542\) −9.25266 −0.397436
\(543\) 5.23412 0.224618
\(544\) −7.88940 −0.338255
\(545\) 10.1668 0.435496
\(546\) −5.24567 −0.224494
\(547\) 11.8844 0.508139 0.254069 0.967186i \(-0.418231\pi\)
0.254069 + 0.967186i \(0.418231\pi\)
\(548\) −11.3950 −0.486769
\(549\) −4.13631 −0.176533
\(550\) 2.91223 0.124178
\(551\) −22.6596 −0.965333
\(552\) 24.4975 1.04268
\(553\) −2.06675 −0.0878873
\(554\) −20.2189 −0.859018
\(555\) 3.14893 0.133665
\(556\) 12.8736 0.545962
\(557\) 41.3572 1.75236 0.876180 0.481985i \(-0.160084\pi\)
0.876180 + 0.481985i \(0.160084\pi\)
\(558\) 5.00885 0.212042
\(559\) 52.0328 2.20075
\(560\) −1.38251 −0.0584215
\(561\) −1.13941 −0.0481058
\(562\) 24.1514 1.01877
\(563\) −26.3268 −1.10954 −0.554772 0.832002i \(-0.687195\pi\)
−0.554772 + 0.832002i \(0.687195\pi\)
\(564\) −4.05446 −0.170724
\(565\) −13.1112 −0.551592
\(566\) −2.59552 −0.109098
\(567\) 1.00000 0.0419961
\(568\) −48.4668 −2.03362
\(569\) 38.4293 1.61104 0.805520 0.592569i \(-0.201886\pi\)
0.805520 + 0.592569i \(0.201886\pi\)
\(570\) −4.92912 −0.206458
\(571\) −0.163185 −0.00682909 −0.00341454 0.999994i \(-0.501087\pi\)
−0.00341454 + 0.999994i \(0.501087\pi\)
\(572\) 2.22777 0.0931478
\(573\) −20.0268 −0.836631
\(574\) −10.7338 −0.448021
\(575\) 35.2804 1.47129
\(576\) 8.19545 0.341477
\(577\) 34.5119 1.43675 0.718374 0.695657i \(-0.244887\pi\)
0.718374 + 0.695657i \(0.244887\pi\)
\(578\) 14.7339 0.612850
\(579\) −1.87046 −0.0777336
\(580\) −2.30010 −0.0955063
\(581\) 10.4388 0.433076
\(582\) 14.1368 0.585988
\(583\) 8.37220 0.346741
\(584\) 19.8622 0.821904
\(585\) −3.61888 −0.149622
\(586\) 7.11132 0.293766
\(587\) −16.8268 −0.694518 −0.347259 0.937769i \(-0.612887\pi\)
−0.347259 + 0.937769i \(0.612887\pi\)
\(588\) 0.784010 0.0323320
\(589\) 26.6894 1.09972
\(590\) 5.94917 0.244924
\(591\) 8.97502 0.369183
\(592\) 7.52236 0.309167
\(593\) −12.8591 −0.528059 −0.264029 0.964515i \(-0.585052\pi\)
−0.264029 + 0.964515i \(0.585052\pi\)
\(594\) 0.658686 0.0270262
\(595\) 1.45112 0.0594901
\(596\) −13.9913 −0.573104
\(597\) 0.936829 0.0383418
\(598\) −41.8588 −1.71173
\(599\) 30.0650 1.22842 0.614212 0.789141i \(-0.289474\pi\)
0.614212 + 0.789141i \(0.289474\pi\)
\(600\) 13.5732 0.554124
\(601\) 21.9451 0.895160 0.447580 0.894244i \(-0.352286\pi\)
0.447580 + 0.894244i \(0.352286\pi\)
\(602\) 12.0617 0.491596
\(603\) 1.80164 0.0733683
\(604\) 6.09068 0.247826
\(605\) −8.09674 −0.329179
\(606\) 13.5840 0.551814
\(607\) −1.14101 −0.0463120 −0.0231560 0.999732i \(-0.507371\pi\)
−0.0231560 + 0.999732i \(0.507371\pi\)
\(608\) 24.3022 0.985583
\(609\) −3.85644 −0.156271
\(610\) 3.46989 0.140492
\(611\) 24.6007 0.995238
\(612\) −1.49550 −0.0604520
\(613\) 34.5707 1.39630 0.698149 0.715953i \(-0.254007\pi\)
0.698149 + 0.715953i \(0.254007\pi\)
\(614\) 0.116479 0.00470073
\(615\) −7.40503 −0.298600
\(616\) 1.83379 0.0738855
\(617\) −31.3212 −1.26094 −0.630472 0.776212i \(-0.717139\pi\)
−0.630472 + 0.776212i \(0.717139\pi\)
\(618\) 9.52285 0.383065
\(619\) 19.7289 0.792972 0.396486 0.918041i \(-0.370230\pi\)
0.396486 + 0.918041i \(0.370230\pi\)
\(620\) 2.70915 0.108802
\(621\) 7.97969 0.320214
\(622\) 3.76643 0.151020
\(623\) 5.04949 0.202304
\(624\) −8.64499 −0.346077
\(625\) 16.6540 0.666159
\(626\) 20.2553 0.809564
\(627\) 3.50978 0.140167
\(628\) −6.11472 −0.244004
\(629\) −7.89570 −0.314822
\(630\) −0.838886 −0.0334220
\(631\) 17.5508 0.698688 0.349344 0.936995i \(-0.386404\pi\)
0.349344 + 0.936995i \(0.386404\pi\)
\(632\) −6.34490 −0.252387
\(633\) 22.8895 0.909777
\(634\) −32.2619 −1.28128
\(635\) −7.62680 −0.302660
\(636\) 10.9887 0.435732
\(637\) −4.75703 −0.188480
\(638\) −2.54018 −0.100567
\(639\) −15.7873 −0.624537
\(640\) −0.582209 −0.0230139
\(641\) −17.8880 −0.706532 −0.353266 0.935523i \(-0.614929\pi\)
−0.353266 + 0.935523i \(0.614929\pi\)
\(642\) 13.2897 0.524503
\(643\) −1.94088 −0.0765408 −0.0382704 0.999267i \(-0.512185\pi\)
−0.0382704 + 0.999267i \(0.512185\pi\)
\(644\) 6.25615 0.246527
\(645\) 8.32108 0.327642
\(646\) 12.3594 0.486273
\(647\) 4.33765 0.170530 0.0852652 0.996358i \(-0.472826\pi\)
0.0852652 + 0.996358i \(0.472826\pi\)
\(648\) 3.06998 0.120600
\(649\) −4.23611 −0.166282
\(650\) −23.1925 −0.909685
\(651\) 4.54227 0.178026
\(652\) −14.2639 −0.558618
\(653\) −26.0061 −1.01770 −0.508849 0.860856i \(-0.669929\pi\)
−0.508849 + 0.860856i \(0.669929\pi\)
\(654\) 14.7370 0.576263
\(655\) 1.74414 0.0681493
\(656\) −17.6896 −0.690663
\(657\) 6.46981 0.252411
\(658\) 5.70266 0.222313
\(659\) 0.167395 0.00652078 0.00326039 0.999995i \(-0.498962\pi\)
0.00326039 + 0.999995i \(0.498962\pi\)
\(660\) 0.356265 0.0138676
\(661\) −29.3022 −1.13972 −0.569862 0.821741i \(-0.693003\pi\)
−0.569862 + 0.821741i \(0.693003\pi\)
\(662\) 0.193148 0.00750689
\(663\) 9.07404 0.352407
\(664\) 32.0471 1.24367
\(665\) −4.46997 −0.173338
\(666\) 4.56447 0.176870
\(667\) −30.7732 −1.19154
\(668\) 12.4371 0.481207
\(669\) −27.8810 −1.07794
\(670\) −1.51137 −0.0583892
\(671\) −2.47074 −0.0953817
\(672\) 4.13598 0.159549
\(673\) 0.640099 0.0246740 0.0123370 0.999924i \(-0.496073\pi\)
0.0123370 + 0.999924i \(0.496073\pi\)
\(674\) 1.26757 0.0488248
\(675\) 4.42127 0.170175
\(676\) −7.54947 −0.290364
\(677\) −30.8481 −1.18559 −0.592794 0.805354i \(-0.701975\pi\)
−0.592794 + 0.805354i \(0.701975\pi\)
\(678\) −19.0051 −0.729885
\(679\) 12.8199 0.491983
\(680\) 4.45491 0.170838
\(681\) 5.06112 0.193942
\(682\) 2.99193 0.114567
\(683\) 7.68670 0.294123 0.147062 0.989127i \(-0.453018\pi\)
0.147062 + 0.989127i \(0.453018\pi\)
\(684\) 4.60668 0.176141
\(685\) 11.0568 0.422459
\(686\) −1.10272 −0.0421020
\(687\) 18.5129 0.706311
\(688\) 19.8779 0.757838
\(689\) −66.6748 −2.54011
\(690\) −6.69405 −0.254838
\(691\) 1.47368 0.0560613 0.0280306 0.999607i \(-0.491076\pi\)
0.0280306 + 0.999607i \(0.491076\pi\)
\(692\) 16.5232 0.628119
\(693\) 0.597329 0.0226906
\(694\) −14.3197 −0.543569
\(695\) −12.4915 −0.473831
\(696\) −11.8392 −0.448764
\(697\) 18.5675 0.703295
\(698\) 4.96638 0.187980
\(699\) 5.29665 0.200338
\(700\) 3.46632 0.131015
\(701\) 33.5155 1.26586 0.632932 0.774207i \(-0.281851\pi\)
0.632932 + 0.774207i \(0.281851\pi\)
\(702\) −5.24567 −0.197985
\(703\) 24.3216 0.917306
\(704\) 4.89538 0.184501
\(705\) 3.93414 0.148168
\(706\) 37.9672 1.42891
\(707\) 12.3187 0.463291
\(708\) −5.56000 −0.208958
\(709\) −37.3801 −1.40384 −0.701919 0.712257i \(-0.747673\pi\)
−0.701919 + 0.712257i \(0.747673\pi\)
\(710\) 13.2438 0.497030
\(711\) −2.06675 −0.0775093
\(712\) 15.5019 0.580957
\(713\) 36.2459 1.35742
\(714\) 2.10344 0.0787193
\(715\) −2.16166 −0.0808415
\(716\) −0.661211 −0.0247106
\(717\) −25.2222 −0.941940
\(718\) −15.1359 −0.564867
\(719\) 14.6873 0.547742 0.273871 0.961766i \(-0.411696\pi\)
0.273871 + 0.961766i \(0.411696\pi\)
\(720\) −1.38251 −0.0515229
\(721\) 8.63579 0.321613
\(722\) −17.1196 −0.637126
\(723\) −27.6212 −1.02724
\(724\) 4.10360 0.152509
\(725\) −17.0504 −0.633234
\(726\) −11.7365 −0.435581
\(727\) −37.8324 −1.40312 −0.701562 0.712608i \(-0.747514\pi\)
−0.701562 + 0.712608i \(0.747514\pi\)
\(728\) −14.6040 −0.541260
\(729\) 1.00000 0.0370370
\(730\) −5.42743 −0.200878
\(731\) −20.8644 −0.771700
\(732\) −3.24291 −0.119861
\(733\) 19.3959 0.716403 0.358202 0.933644i \(-0.383390\pi\)
0.358202 + 0.933644i \(0.383390\pi\)
\(734\) 23.3373 0.861396
\(735\) −0.760743 −0.0280604
\(736\) 33.0038 1.21654
\(737\) 1.07617 0.0396412
\(738\) −10.7338 −0.395117
\(739\) 33.3894 1.22825 0.614124 0.789210i \(-0.289510\pi\)
0.614124 + 0.789210i \(0.289510\pi\)
\(740\) 2.46879 0.0907547
\(741\) −27.9513 −1.02682
\(742\) −15.4558 −0.567400
\(743\) −18.9989 −0.697003 −0.348501 0.937308i \(-0.613309\pi\)
−0.348501 + 0.937308i \(0.613309\pi\)
\(744\) 13.9447 0.511237
\(745\) 13.5760 0.497388
\(746\) −17.6121 −0.644826
\(747\) 10.4388 0.381938
\(748\) −0.893306 −0.0326625
\(749\) 12.0518 0.440362
\(750\) −7.90337 −0.288590
\(751\) 46.0114 1.67898 0.839490 0.543375i \(-0.182854\pi\)
0.839490 + 0.543375i \(0.182854\pi\)
\(752\) 9.39812 0.342714
\(753\) 7.27590 0.265149
\(754\) 20.2296 0.736718
\(755\) −5.90993 −0.215084
\(756\) 0.784010 0.0285142
\(757\) −0.926254 −0.0336653 −0.0168326 0.999858i \(-0.505358\pi\)
−0.0168326 + 0.999858i \(0.505358\pi\)
\(758\) 4.17445 0.151623
\(759\) 4.76650 0.173013
\(760\) −13.7227 −0.497775
\(761\) 12.3953 0.449330 0.224665 0.974436i \(-0.427871\pi\)
0.224665 + 0.974436i \(0.427871\pi\)
\(762\) −11.0553 −0.400490
\(763\) 13.3643 0.483818
\(764\) −15.7012 −0.568049
\(765\) 1.45112 0.0524653
\(766\) 1.10272 0.0398429
\(767\) 33.7357 1.21812
\(768\) 15.5470 0.561003
\(769\) −11.6725 −0.420920 −0.210460 0.977602i \(-0.567496\pi\)
−0.210460 + 0.977602i \(0.567496\pi\)
\(770\) −0.501091 −0.0180581
\(771\) −21.9250 −0.789609
\(772\) −1.46646 −0.0527789
\(773\) 24.9741 0.898256 0.449128 0.893467i \(-0.351735\pi\)
0.449128 + 0.893467i \(0.351735\pi\)
\(774\) 12.0617 0.433547
\(775\) 20.0826 0.721389
\(776\) 39.3569 1.41283
\(777\) 4.13929 0.148496
\(778\) −31.5744 −1.13200
\(779\) −57.1946 −2.04921
\(780\) −2.83723 −0.101589
\(781\) −9.43022 −0.337440
\(782\) 16.7848 0.600223
\(783\) −3.85644 −0.137818
\(784\) −1.81731 −0.0649039
\(785\) 5.93326 0.211767
\(786\) 2.52819 0.0901775
\(787\) 17.8922 0.637787 0.318894 0.947790i \(-0.396689\pi\)
0.318894 + 0.947790i \(0.396689\pi\)
\(788\) 7.03650 0.250665
\(789\) −16.9826 −0.604595
\(790\) 1.73377 0.0616848
\(791\) −17.2347 −0.612796
\(792\) 1.83379 0.0651608
\(793\) 19.6765 0.698734
\(794\) −4.39794 −0.156077
\(795\) −10.6626 −0.378164
\(796\) 0.734483 0.0260331
\(797\) 15.1144 0.535378 0.267689 0.963505i \(-0.413740\pi\)
0.267689 + 0.963505i \(0.413740\pi\)
\(798\) −6.47935 −0.229366
\(799\) −9.86455 −0.348983
\(800\) 18.2863 0.646518
\(801\) 5.04949 0.178415
\(802\) 19.2546 0.679903
\(803\) 3.86460 0.136379
\(804\) 1.41250 0.0498150
\(805\) −6.07049 −0.213957
\(806\) −23.8272 −0.839279
\(807\) 27.0483 0.952144
\(808\) 37.8181 1.33044
\(809\) −35.2847 −1.24054 −0.620272 0.784386i \(-0.712978\pi\)
−0.620272 + 0.784386i \(0.712978\pi\)
\(810\) −0.838886 −0.0294755
\(811\) −20.8477 −0.732060 −0.366030 0.930603i \(-0.619283\pi\)
−0.366030 + 0.930603i \(0.619283\pi\)
\(812\) −3.02349 −0.106104
\(813\) −8.39077 −0.294277
\(814\) 2.72649 0.0955634
\(815\) 13.8406 0.484815
\(816\) 3.46652 0.121353
\(817\) 64.2699 2.24852
\(818\) −34.6763 −1.21243
\(819\) −4.75703 −0.166224
\(820\) −5.80562 −0.202741
\(821\) −37.1517 −1.29660 −0.648301 0.761384i \(-0.724520\pi\)
−0.648301 + 0.761384i \(0.724520\pi\)
\(822\) 16.0272 0.559012
\(823\) −43.0417 −1.50034 −0.750169 0.661246i \(-0.770028\pi\)
−0.750169 + 0.661246i \(0.770028\pi\)
\(824\) 26.5117 0.923579
\(825\) 2.64095 0.0919462
\(826\) 7.82021 0.272100
\(827\) 37.1593 1.29215 0.646077 0.763272i \(-0.276408\pi\)
0.646077 + 0.763272i \(0.276408\pi\)
\(828\) 6.25615 0.217416
\(829\) 19.2244 0.667690 0.333845 0.942628i \(-0.391654\pi\)
0.333845 + 0.942628i \(0.391654\pi\)
\(830\) −8.75701 −0.303960
\(831\) −18.3355 −0.636050
\(832\) −38.9860 −1.35159
\(833\) 1.90750 0.0660911
\(834\) −18.1069 −0.626989
\(835\) −12.0680 −0.417631
\(836\) 2.75170 0.0951696
\(837\) 4.54227 0.157004
\(838\) −28.6678 −0.990314
\(839\) 38.2179 1.31943 0.659714 0.751517i \(-0.270678\pi\)
0.659714 + 0.751517i \(0.270678\pi\)
\(840\) −2.33547 −0.0805813
\(841\) −14.1279 −0.487168
\(842\) −36.4393 −1.25578
\(843\) 21.9017 0.754335
\(844\) 17.9456 0.617714
\(845\) 7.32543 0.252002
\(846\) 5.70266 0.196061
\(847\) −10.6432 −0.365705
\(848\) −25.4715 −0.874696
\(849\) −2.35374 −0.0807802
\(850\) 9.29988 0.318983
\(851\) 33.0302 1.13226
\(852\) −12.3774 −0.424043
\(853\) −3.38498 −0.115899 −0.0579497 0.998320i \(-0.518456\pi\)
−0.0579497 + 0.998320i \(0.518456\pi\)
\(854\) 4.56119 0.156081
\(855\) −4.46997 −0.152870
\(856\) 36.9987 1.26459
\(857\) 28.5458 0.975107 0.487554 0.873093i \(-0.337889\pi\)
0.487554 + 0.873093i \(0.337889\pi\)
\(858\) −3.13339 −0.106972
\(859\) −12.6058 −0.430105 −0.215053 0.976602i \(-0.568992\pi\)
−0.215053 + 0.976602i \(0.568992\pi\)
\(860\) 6.52381 0.222460
\(861\) −9.73395 −0.331732
\(862\) −38.7324 −1.31923
\(863\) −19.5526 −0.665578 −0.332789 0.943001i \(-0.607990\pi\)
−0.332789 + 0.943001i \(0.607990\pi\)
\(864\) 4.13598 0.140709
\(865\) −16.0329 −0.545134
\(866\) 15.8365 0.538147
\(867\) 13.3614 0.453778
\(868\) 3.56118 0.120874
\(869\) −1.23453 −0.0418786
\(870\) 3.23511 0.109681
\(871\) −8.57043 −0.290398
\(872\) 41.0280 1.38938
\(873\) 12.8199 0.433889
\(874\) −51.7032 −1.74889
\(875\) −7.16717 −0.242294
\(876\) 5.07239 0.171380
\(877\) 7.00669 0.236599 0.118300 0.992978i \(-0.462256\pi\)
0.118300 + 0.992978i \(0.462256\pi\)
\(878\) 11.6039 0.391612
\(879\) 6.44889 0.217516
\(880\) −0.825811 −0.0278381
\(881\) −24.3305 −0.819716 −0.409858 0.912149i \(-0.634422\pi\)
−0.409858 + 0.912149i \(0.634422\pi\)
\(882\) −1.10272 −0.0371305
\(883\) −22.3996 −0.753808 −0.376904 0.926252i \(-0.623011\pi\)
−0.376904 + 0.926252i \(0.623011\pi\)
\(884\) 7.11414 0.239274
\(885\) 5.39500 0.181351
\(886\) 21.5114 0.722689
\(887\) −5.42126 −0.182028 −0.0910141 0.995850i \(-0.529011\pi\)
−0.0910141 + 0.995850i \(0.529011\pi\)
\(888\) 12.7075 0.426437
\(889\) −10.0255 −0.336243
\(890\) −4.23595 −0.141989
\(891\) 0.597329 0.0200113
\(892\) −21.8590 −0.731893
\(893\) 30.3863 1.01684
\(894\) 19.6789 0.658160
\(895\) 0.641588 0.0214459
\(896\) −0.765317 −0.0255674
\(897\) −37.9596 −1.26743
\(898\) −17.5035 −0.584100
\(899\) −17.5170 −0.584224
\(900\) 3.46632 0.115544
\(901\) 26.7357 0.890695
\(902\) −6.41162 −0.213483
\(903\) 10.9381 0.363997
\(904\) −52.9103 −1.75977
\(905\) −3.98182 −0.132360
\(906\) −8.56662 −0.284607
\(907\) −26.4779 −0.879184 −0.439592 0.898198i \(-0.644877\pi\)
−0.439592 + 0.898198i \(0.644877\pi\)
\(908\) 3.96796 0.131682
\(909\) 12.3187 0.408585
\(910\) 3.99060 0.132287
\(911\) −11.0624 −0.366513 −0.183257 0.983065i \(-0.558664\pi\)
−0.183257 + 0.983065i \(0.558664\pi\)
\(912\) −10.6781 −0.353588
\(913\) 6.23543 0.206362
\(914\) −22.0618 −0.729740
\(915\) 3.14667 0.104026
\(916\) 14.5143 0.479566
\(917\) 2.29268 0.0757111
\(918\) 2.10344 0.0694239
\(919\) 56.2859 1.85670 0.928349 0.371709i \(-0.121228\pi\)
0.928349 + 0.371709i \(0.121228\pi\)
\(920\) −18.6363 −0.614421
\(921\) 0.105629 0.00348060
\(922\) 13.1229 0.432179
\(923\) 75.1007 2.47197
\(924\) 0.468312 0.0154063
\(925\) 18.3009 0.601730
\(926\) −25.3114 −0.831784
\(927\) 8.63579 0.283636
\(928\) −15.9502 −0.523590
\(929\) −31.0098 −1.01740 −0.508700 0.860944i \(-0.669874\pi\)
−0.508700 + 0.860944i \(0.669874\pi\)
\(930\) −3.81045 −0.124950
\(931\) −5.87579 −0.192571
\(932\) 4.15262 0.136024
\(933\) 3.41558 0.111821
\(934\) −41.9480 −1.37258
\(935\) 0.866796 0.0283473
\(936\) −14.6040 −0.477346
\(937\) −3.19862 −0.104494 −0.0522472 0.998634i \(-0.516638\pi\)
−0.0522472 + 0.998634i \(0.516638\pi\)
\(938\) −1.98670 −0.0648680
\(939\) 18.3685 0.599433
\(940\) 3.08441 0.100602
\(941\) 47.3661 1.54409 0.772045 0.635568i \(-0.219234\pi\)
0.772045 + 0.635568i \(0.219234\pi\)
\(942\) 8.60043 0.280217
\(943\) −77.6739 −2.52941
\(944\) 12.8879 0.419466
\(945\) −0.760743 −0.0247470
\(946\) 7.20477 0.234247
\(947\) 34.3134 1.11504 0.557518 0.830165i \(-0.311754\pi\)
0.557518 + 0.830165i \(0.311754\pi\)
\(948\) −1.62036 −0.0526267
\(949\) −30.7771 −0.999066
\(950\) −28.6469 −0.929430
\(951\) −29.2567 −0.948713
\(952\) 5.85600 0.189794
\(953\) −5.56951 −0.180414 −0.0902070 0.995923i \(-0.528753\pi\)
−0.0902070 + 0.995923i \(0.528753\pi\)
\(954\) −15.4558 −0.500400
\(955\) 15.2352 0.493001
\(956\) −19.7744 −0.639551
\(957\) −2.30356 −0.0744636
\(958\) 21.2153 0.685434
\(959\) 14.5342 0.469335
\(960\) −6.23463 −0.201222
\(961\) −10.3678 −0.334444
\(962\) −21.7133 −0.700065
\(963\) 12.0518 0.388363
\(964\) −21.6553 −0.697469
\(965\) 1.42294 0.0458060
\(966\) −8.79936 −0.283115
\(967\) 41.6661 1.33989 0.669946 0.742410i \(-0.266317\pi\)
0.669946 + 0.742410i \(0.266317\pi\)
\(968\) −32.6744 −1.05020
\(969\) 11.2081 0.360056
\(970\) −10.7545 −0.345305
\(971\) −40.3016 −1.29334 −0.646669 0.762771i \(-0.723839\pi\)
−0.646669 + 0.762771i \(0.723839\pi\)
\(972\) 0.784010 0.0251471
\(973\) −16.4202 −0.526407
\(974\) 10.7898 0.345726
\(975\) −21.0321 −0.673566
\(976\) 7.51695 0.240612
\(977\) −24.3168 −0.777964 −0.388982 0.921245i \(-0.627173\pi\)
−0.388982 + 0.921245i \(0.627173\pi\)
\(978\) 20.0624 0.641524
\(979\) 3.01621 0.0963985
\(980\) −0.596430 −0.0190523
\(981\) 13.3643 0.426688
\(982\) 30.5271 0.974158
\(983\) −49.8535 −1.59008 −0.795040 0.606558i \(-0.792550\pi\)
−0.795040 + 0.606558i \(0.792550\pi\)
\(984\) −29.8830 −0.952636
\(985\) −6.82768 −0.217548
\(986\) −8.11179 −0.258332
\(987\) 5.17145 0.164609
\(988\) −21.9141 −0.697180
\(989\) 87.2826 2.77542
\(990\) −0.501091 −0.0159257
\(991\) 14.2609 0.453013 0.226507 0.974010i \(-0.427270\pi\)
0.226507 + 0.974010i \(0.427270\pi\)
\(992\) 18.7867 0.596480
\(993\) 0.175156 0.00555840
\(994\) 17.4090 0.552179
\(995\) −0.712686 −0.0225937
\(996\) 8.18416 0.259325
\(997\) 33.4217 1.05848 0.529238 0.848473i \(-0.322478\pi\)
0.529238 + 0.848473i \(0.322478\pi\)
\(998\) −6.95188 −0.220058
\(999\) 4.13929 0.130961
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 \(a_p\))