Properties

Label 6001.2.a.b.1.16
Level 6001
Weight 2
Character 6001.1
Self dual Yes
Analytic conductor 47.918
Analytic rank 1
Dimension 114
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.918226253\)
Analytic rank: \(1\)
Dimension: \(114\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.28982 q^{2}\) \(-3.10307 q^{3}\) \(+3.24328 q^{4}\) \(+2.16467 q^{5}\) \(+7.10548 q^{6}\) \(-1.63956 q^{7}\) \(-2.84688 q^{8}\) \(+6.62906 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.28982 q^{2}\) \(-3.10307 q^{3}\) \(+3.24328 q^{4}\) \(+2.16467 q^{5}\) \(+7.10548 q^{6}\) \(-1.63956 q^{7}\) \(-2.84688 q^{8}\) \(+6.62906 q^{9}\) \(-4.95671 q^{10}\) \(-5.86219 q^{11}\) \(-10.0641 q^{12}\) \(+1.80761 q^{13}\) \(+3.75431 q^{14}\) \(-6.71713 q^{15}\) \(+0.0322975 q^{16}\) \(+1.00000 q^{17}\) \(-15.1794 q^{18}\) \(-2.74943 q^{19}\) \(+7.02063 q^{20}\) \(+5.08769 q^{21}\) \(+13.4234 q^{22}\) \(-3.48732 q^{23}\) \(+8.83409 q^{24}\) \(-0.314198 q^{25}\) \(-4.13911 q^{26}\) \(-11.2612 q^{27}\) \(-5.31756 q^{28}\) \(+5.15263 q^{29}\) \(+15.3810 q^{30}\) \(+3.45994 q^{31}\) \(+5.61981 q^{32}\) \(+18.1908 q^{33}\) \(-2.28982 q^{34}\) \(-3.54912 q^{35}\) \(+21.4999 q^{36}\) \(+5.57495 q^{37}\) \(+6.29570 q^{38}\) \(-5.60916 q^{39}\) \(-6.16257 q^{40}\) \(-4.42454 q^{41}\) \(-11.6499 q^{42}\) \(+3.95099 q^{43}\) \(-19.0127 q^{44}\) \(+14.3497 q^{45}\) \(+7.98534 q^{46}\) \(+1.39132 q^{47}\) \(-0.100222 q^{48}\) \(-4.31183 q^{49}\) \(+0.719456 q^{50}\) \(-3.10307 q^{51}\) \(+5.86259 q^{52}\) \(-4.72508 q^{53}\) \(+25.7862 q^{54}\) \(-12.6897 q^{55}\) \(+4.66765 q^{56}\) \(+8.53168 q^{57}\) \(-11.7986 q^{58}\) \(+5.75199 q^{59}\) \(-21.7855 q^{60}\) \(-5.18024 q^{61}\) \(-7.92265 q^{62}\) \(-10.8688 q^{63}\) \(-12.9330 q^{64}\) \(+3.91289 q^{65}\) \(-41.6537 q^{66}\) \(+14.6590 q^{67}\) \(+3.24328 q^{68}\) \(+10.8214 q^{69}\) \(+8.12684 q^{70}\) \(+7.70835 q^{71}\) \(-18.8722 q^{72}\) \(+11.4341 q^{73}\) \(-12.7656 q^{74}\) \(+0.974978 q^{75}\) \(-8.91717 q^{76}\) \(+9.61144 q^{77}\) \(+12.8440 q^{78}\) \(-2.92339 q^{79}\) \(+0.0699136 q^{80}\) \(+15.0572 q^{81}\) \(+10.1314 q^{82}\) \(-7.63267 q^{83}\) \(+16.5008 q^{84}\) \(+2.16467 q^{85}\) \(-9.04706 q^{86}\) \(-15.9890 q^{87}\) \(+16.6890 q^{88}\) \(-8.20182 q^{89}\) \(-32.8583 q^{90}\) \(-2.96370 q^{91}\) \(-11.3104 q^{92}\) \(-10.7365 q^{93}\) \(-3.18587 q^{94}\) \(-5.95161 q^{95}\) \(-17.4387 q^{96}\) \(-15.6624 q^{97}\) \(+9.87331 q^{98}\) \(-38.8608 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28982 −1.61915 −0.809574 0.587018i \(-0.800302\pi\)
−0.809574 + 0.587018i \(0.800302\pi\)
\(3\) −3.10307 −1.79156 −0.895780 0.444498i \(-0.853382\pi\)
−0.895780 + 0.444498i \(0.853382\pi\)
\(4\) 3.24328 1.62164
\(5\) 2.16467 0.968070 0.484035 0.875049i \(-0.339171\pi\)
0.484035 + 0.875049i \(0.339171\pi\)
\(6\) 7.10548 2.90080
\(7\) −1.63956 −0.619697 −0.309849 0.950786i \(-0.600278\pi\)
−0.309849 + 0.950786i \(0.600278\pi\)
\(8\) −2.84688 −1.00653
\(9\) 6.62906 2.20969
\(10\) −4.95671 −1.56745
\(11\) −5.86219 −1.76752 −0.883759 0.467943i \(-0.844995\pi\)
−0.883759 + 0.467943i \(0.844995\pi\)
\(12\) −10.0641 −2.90526
\(13\) 1.80761 0.501342 0.250671 0.968072i \(-0.419349\pi\)
0.250671 + 0.968072i \(0.419349\pi\)
\(14\) 3.75431 1.00338
\(15\) −6.71713 −1.73436
\(16\) 0.0322975 0.00807439
\(17\) 1.00000 0.242536
\(18\) −15.1794 −3.57781
\(19\) −2.74943 −0.630763 −0.315381 0.948965i \(-0.602132\pi\)
−0.315381 + 0.948965i \(0.602132\pi\)
\(20\) 7.02063 1.56986
\(21\) 5.08769 1.11022
\(22\) 13.4234 2.86187
\(23\) −3.48732 −0.727157 −0.363579 0.931564i \(-0.618445\pi\)
−0.363579 + 0.931564i \(0.618445\pi\)
\(24\) 8.83409 1.80325
\(25\) −0.314198 −0.0628395
\(26\) −4.13911 −0.811746
\(27\) −11.2612 −2.16722
\(28\) −5.31756 −1.00493
\(29\) 5.15263 0.956820 0.478410 0.878137i \(-0.341213\pi\)
0.478410 + 0.878137i \(0.341213\pi\)
\(30\) 15.3810 2.80818
\(31\) 3.45994 0.621424 0.310712 0.950504i \(-0.399432\pi\)
0.310712 + 0.950504i \(0.399432\pi\)
\(32\) 5.61981 0.993452
\(33\) 18.1908 3.16661
\(34\) −2.28982 −0.392701
\(35\) −3.54912 −0.599911
\(36\) 21.4999 3.58331
\(37\) 5.57495 0.916516 0.458258 0.888819i \(-0.348474\pi\)
0.458258 + 0.888819i \(0.348474\pi\)
\(38\) 6.29570 1.02130
\(39\) −5.60916 −0.898184
\(40\) −6.16257 −0.974388
\(41\) −4.42454 −0.690998 −0.345499 0.938419i \(-0.612290\pi\)
−0.345499 + 0.938419i \(0.612290\pi\)
\(42\) −11.6499 −1.79762
\(43\) 3.95099 0.602521 0.301260 0.953542i \(-0.402593\pi\)
0.301260 + 0.953542i \(0.402593\pi\)
\(44\) −19.0127 −2.86628
\(45\) 14.3497 2.13913
\(46\) 7.98534 1.17737
\(47\) 1.39132 0.202945 0.101472 0.994838i \(-0.467645\pi\)
0.101472 + 0.994838i \(0.467645\pi\)
\(48\) −0.100222 −0.0144657
\(49\) −4.31183 −0.615975
\(50\) 0.719456 0.101746
\(51\) −3.10307 −0.434517
\(52\) 5.86259 0.812995
\(53\) −4.72508 −0.649039 −0.324520 0.945879i \(-0.605203\pi\)
−0.324520 + 0.945879i \(0.605203\pi\)
\(54\) 25.7862 3.50906
\(55\) −12.6897 −1.71108
\(56\) 4.66765 0.623741
\(57\) 8.53168 1.13005
\(58\) −11.7986 −1.54923
\(59\) 5.75199 0.748846 0.374423 0.927258i \(-0.377841\pi\)
0.374423 + 0.927258i \(0.377841\pi\)
\(60\) −21.7855 −2.81250
\(61\) −5.18024 −0.663261 −0.331631 0.943409i \(-0.607599\pi\)
−0.331631 + 0.943409i \(0.607599\pi\)
\(62\) −7.92265 −1.00618
\(63\) −10.8688 −1.36934
\(64\) −12.9330 −1.61662
\(65\) 3.91289 0.485334
\(66\) −41.6537 −5.12721
\(67\) 14.6590 1.79088 0.895440 0.445182i \(-0.146861\pi\)
0.895440 + 0.445182i \(0.146861\pi\)
\(68\) 3.24328 0.393305
\(69\) 10.8214 1.30275
\(70\) 8.12684 0.971344
\(71\) 7.70835 0.914812 0.457406 0.889258i \(-0.348779\pi\)
0.457406 + 0.889258i \(0.348779\pi\)
\(72\) −18.8722 −2.22411
\(73\) 11.4341 1.33826 0.669130 0.743146i \(-0.266667\pi\)
0.669130 + 0.743146i \(0.266667\pi\)
\(74\) −12.7656 −1.48398
\(75\) 0.974978 0.112581
\(76\) −8.91717 −1.02287
\(77\) 9.61144 1.09533
\(78\) 12.8440 1.45429
\(79\) −2.92339 −0.328907 −0.164453 0.986385i \(-0.552586\pi\)
−0.164453 + 0.986385i \(0.552586\pi\)
\(80\) 0.0699136 0.00781658
\(81\) 15.0572 1.67303
\(82\) 10.1314 1.11883
\(83\) −7.63267 −0.837794 −0.418897 0.908034i \(-0.637583\pi\)
−0.418897 + 0.908034i \(0.637583\pi\)
\(84\) 16.5008 1.80038
\(85\) 2.16467 0.234792
\(86\) −9.04706 −0.975570
\(87\) −15.9890 −1.71420
\(88\) 16.6890 1.77905
\(89\) −8.20182 −0.869391 −0.434695 0.900578i \(-0.643144\pi\)
−0.434695 + 0.900578i \(0.643144\pi\)
\(90\) −32.8583 −3.46357
\(91\) −2.96370 −0.310680
\(92\) −11.3104 −1.17919
\(93\) −10.7365 −1.11332
\(94\) −3.18587 −0.328598
\(95\) −5.95161 −0.610623
\(96\) −17.4387 −1.77983
\(97\) −15.6624 −1.59027 −0.795136 0.606431i \(-0.792601\pi\)
−0.795136 + 0.606431i \(0.792601\pi\)
\(98\) 9.87331 0.997355
\(99\) −38.8608 −3.90566
\(100\) −1.01903 −0.101903
\(101\) 3.90949 0.389009 0.194504 0.980902i \(-0.437690\pi\)
0.194504 + 0.980902i \(0.437690\pi\)
\(102\) 7.10548 0.703547
\(103\) −9.67545 −0.953351 −0.476675 0.879079i \(-0.658158\pi\)
−0.476675 + 0.879079i \(0.658158\pi\)
\(104\) −5.14607 −0.504613
\(105\) 11.0132 1.07478
\(106\) 10.8196 1.05089
\(107\) −12.4229 −1.20097 −0.600486 0.799636i \(-0.705026\pi\)
−0.600486 + 0.799636i \(0.705026\pi\)
\(108\) −36.5233 −3.51446
\(109\) −11.9630 −1.14585 −0.572925 0.819608i \(-0.694191\pi\)
−0.572925 + 0.819608i \(0.694191\pi\)
\(110\) 29.0572 2.77049
\(111\) −17.2995 −1.64199
\(112\) −0.0529539 −0.00500367
\(113\) 15.3475 1.44377 0.721885 0.692013i \(-0.243276\pi\)
0.721885 + 0.692013i \(0.243276\pi\)
\(114\) −19.5360 −1.82972
\(115\) −7.54891 −0.703939
\(116\) 16.7114 1.55162
\(117\) 11.9828 1.10781
\(118\) −13.1710 −1.21249
\(119\) −1.63956 −0.150299
\(120\) 19.1229 1.74567
\(121\) 23.3653 2.12412
\(122\) 11.8618 1.07392
\(123\) 13.7297 1.23796
\(124\) 11.2216 1.00773
\(125\) −11.5035 −1.02890
\(126\) 24.8875 2.21716
\(127\) 18.1190 1.60780 0.803900 0.594765i \(-0.202755\pi\)
0.803900 + 0.594765i \(0.202755\pi\)
\(128\) 18.3745 1.62409
\(129\) −12.2602 −1.07945
\(130\) −8.95981 −0.785828
\(131\) −14.3850 −1.25682 −0.628410 0.777883i \(-0.716294\pi\)
−0.628410 + 0.777883i \(0.716294\pi\)
\(132\) 58.9978 5.13510
\(133\) 4.50787 0.390882
\(134\) −33.5665 −2.89970
\(135\) −24.3769 −2.09803
\(136\) −2.84688 −0.244118
\(137\) 3.19856 0.273272 0.136636 0.990621i \(-0.456371\pi\)
0.136636 + 0.990621i \(0.456371\pi\)
\(138\) −24.7791 −2.10934
\(139\) 7.68335 0.651693 0.325847 0.945423i \(-0.394351\pi\)
0.325847 + 0.945423i \(0.394351\pi\)
\(140\) −11.5108 −0.972838
\(141\) −4.31737 −0.363588
\(142\) −17.6507 −1.48122
\(143\) −10.5966 −0.886130
\(144\) 0.214102 0.0178419
\(145\) 11.1538 0.926269
\(146\) −26.1820 −2.16684
\(147\) 13.3799 1.10356
\(148\) 18.0811 1.48626
\(149\) 6.25294 0.512261 0.256131 0.966642i \(-0.417552\pi\)
0.256131 + 0.966642i \(0.417552\pi\)
\(150\) −2.23253 −0.182285
\(151\) −7.95551 −0.647410 −0.323705 0.946158i \(-0.604929\pi\)
−0.323705 + 0.946158i \(0.604929\pi\)
\(152\) 7.82731 0.634879
\(153\) 6.62906 0.535928
\(154\) −22.0085 −1.77349
\(155\) 7.48964 0.601583
\(156\) −18.1921 −1.45653
\(157\) 14.2546 1.13764 0.568821 0.822462i \(-0.307400\pi\)
0.568821 + 0.822462i \(0.307400\pi\)
\(158\) 6.69403 0.532548
\(159\) 14.6623 1.16279
\(160\) 12.1650 0.961732
\(161\) 5.71769 0.450617
\(162\) −34.4784 −2.70888
\(163\) 1.93799 0.151795 0.0758977 0.997116i \(-0.475818\pi\)
0.0758977 + 0.997116i \(0.475818\pi\)
\(164\) −14.3500 −1.12055
\(165\) 39.3771 3.06550
\(166\) 17.4774 1.35651
\(167\) 0.380152 0.0294170 0.0147085 0.999892i \(-0.495318\pi\)
0.0147085 + 0.999892i \(0.495318\pi\)
\(168\) −14.4841 −1.11747
\(169\) −9.73253 −0.748656
\(170\) −4.95671 −0.380162
\(171\) −18.2261 −1.39379
\(172\) 12.8142 0.977071
\(173\) 6.39594 0.486274 0.243137 0.969992i \(-0.421823\pi\)
0.243137 + 0.969992i \(0.421823\pi\)
\(174\) 36.6119 2.77554
\(175\) 0.515147 0.0389415
\(176\) −0.189334 −0.0142716
\(177\) −17.8489 −1.34160
\(178\) 18.7807 1.40767
\(179\) 19.2048 1.43543 0.717715 0.696337i \(-0.245188\pi\)
0.717715 + 0.696337i \(0.245188\pi\)
\(180\) 46.5402 3.46890
\(181\) 12.3052 0.914641 0.457321 0.889302i \(-0.348809\pi\)
0.457321 + 0.889302i \(0.348809\pi\)
\(182\) 6.78634 0.503037
\(183\) 16.0746 1.18827
\(184\) 9.92800 0.731902
\(185\) 12.0679 0.887252
\(186\) 24.5846 1.80263
\(187\) −5.86219 −0.428686
\(188\) 4.51244 0.329104
\(189\) 18.4635 1.34302
\(190\) 13.6281 0.988688
\(191\) 5.24140 0.379254 0.189627 0.981856i \(-0.439272\pi\)
0.189627 + 0.981856i \(0.439272\pi\)
\(192\) 40.1319 2.89627
\(193\) 21.9020 1.57654 0.788268 0.615331i \(-0.210978\pi\)
0.788268 + 0.615331i \(0.210978\pi\)
\(194\) 35.8640 2.57489
\(195\) −12.1420 −0.869505
\(196\) −13.9845 −0.998890
\(197\) −1.49958 −0.106841 −0.0534205 0.998572i \(-0.517012\pi\)
−0.0534205 + 0.998572i \(0.517012\pi\)
\(198\) 88.9843 6.32384
\(199\) 4.14343 0.293720 0.146860 0.989157i \(-0.453083\pi\)
0.146860 + 0.989157i \(0.453083\pi\)
\(200\) 0.894485 0.0632496
\(201\) −45.4879 −3.20847
\(202\) −8.95203 −0.629863
\(203\) −8.44807 −0.592939
\(204\) −10.0641 −0.704630
\(205\) −9.57768 −0.668934
\(206\) 22.1551 1.54362
\(207\) −23.1177 −1.60679
\(208\) 0.0583815 0.00404803
\(209\) 16.1177 1.11488
\(210\) −25.2182 −1.74022
\(211\) −6.44986 −0.444027 −0.222013 0.975044i \(-0.571263\pi\)
−0.222013 + 0.975044i \(0.571263\pi\)
\(212\) −15.3247 −1.05251
\(213\) −23.9196 −1.63894
\(214\) 28.4463 1.94455
\(215\) 8.55260 0.583282
\(216\) 32.0594 2.18137
\(217\) −5.67280 −0.385095
\(218\) 27.3932 1.85530
\(219\) −35.4808 −2.39757
\(220\) −41.1563 −2.77476
\(221\) 1.80761 0.121593
\(222\) 39.6127 2.65863
\(223\) 14.7174 0.985553 0.492777 0.870156i \(-0.335982\pi\)
0.492777 + 0.870156i \(0.335982\pi\)
\(224\) −9.21405 −0.615639
\(225\) −2.08283 −0.138856
\(226\) −35.1430 −2.33768
\(227\) −14.6991 −0.975614 −0.487807 0.872952i \(-0.662203\pi\)
−0.487807 + 0.872952i \(0.662203\pi\)
\(228\) 27.6706 1.83253
\(229\) −7.14899 −0.472418 −0.236209 0.971702i \(-0.575905\pi\)
−0.236209 + 0.971702i \(0.575905\pi\)
\(230\) 17.2856 1.13978
\(231\) −29.8250 −1.96234
\(232\) −14.6689 −0.963064
\(233\) 4.61616 0.302415 0.151207 0.988502i \(-0.451684\pi\)
0.151207 + 0.988502i \(0.451684\pi\)
\(234\) −27.4384 −1.79370
\(235\) 3.01175 0.196465
\(236\) 18.6553 1.21436
\(237\) 9.07148 0.589256
\(238\) 3.75431 0.243356
\(239\) 7.50613 0.485531 0.242766 0.970085i \(-0.421945\pi\)
0.242766 + 0.970085i \(0.421945\pi\)
\(240\) −0.216947 −0.0140039
\(241\) 23.5152 1.51474 0.757372 0.652983i \(-0.226483\pi\)
0.757372 + 0.652983i \(0.226483\pi\)
\(242\) −53.5023 −3.43926
\(243\) −12.9400 −0.830102
\(244\) −16.8009 −1.07557
\(245\) −9.33369 −0.596308
\(246\) −31.4385 −2.00445
\(247\) −4.96991 −0.316228
\(248\) −9.85006 −0.625479
\(249\) 23.6847 1.50096
\(250\) 26.3409 1.66595
\(251\) 12.8679 0.812216 0.406108 0.913825i \(-0.366886\pi\)
0.406108 + 0.913825i \(0.366886\pi\)
\(252\) −35.2504 −2.22057
\(253\) 20.4434 1.28526
\(254\) −41.4892 −2.60326
\(255\) −6.71713 −0.420643
\(256\) −16.2085 −1.01303
\(257\) 8.19234 0.511024 0.255512 0.966806i \(-0.417756\pi\)
0.255512 + 0.966806i \(0.417756\pi\)
\(258\) 28.0737 1.74779
\(259\) −9.14049 −0.567963
\(260\) 12.6906 0.787037
\(261\) 34.1571 2.11427
\(262\) 32.9390 2.03498
\(263\) −26.0121 −1.60397 −0.801987 0.597342i \(-0.796223\pi\)
−0.801987 + 0.597342i \(0.796223\pi\)
\(264\) −51.7871 −3.18728
\(265\) −10.2282 −0.628316
\(266\) −10.3222 −0.632895
\(267\) 25.4508 1.55757
\(268\) 47.5432 2.90416
\(269\) −24.5396 −1.49620 −0.748102 0.663584i \(-0.769034\pi\)
−0.748102 + 0.663584i \(0.769034\pi\)
\(270\) 55.8186 3.39701
\(271\) −16.1897 −0.983455 −0.491728 0.870749i \(-0.663634\pi\)
−0.491728 + 0.870749i \(0.663634\pi\)
\(272\) 0.0322975 0.00195833
\(273\) 9.19657 0.556602
\(274\) −7.32414 −0.442467
\(275\) 1.84189 0.111070
\(276\) 35.0969 2.11258
\(277\) −10.8813 −0.653792 −0.326896 0.945060i \(-0.606003\pi\)
−0.326896 + 0.945060i \(0.606003\pi\)
\(278\) −17.5935 −1.05519
\(279\) 22.9362 1.37315
\(280\) 10.1039 0.603825
\(281\) −3.39666 −0.202628 −0.101314 0.994855i \(-0.532305\pi\)
−0.101314 + 0.994855i \(0.532305\pi\)
\(282\) 9.88600 0.588703
\(283\) 26.5397 1.57762 0.788809 0.614638i \(-0.210698\pi\)
0.788809 + 0.614638i \(0.210698\pi\)
\(284\) 25.0003 1.48350
\(285\) 18.4683 1.09397
\(286\) 24.2643 1.43478
\(287\) 7.25432 0.428209
\(288\) 37.2541 2.19522
\(289\) 1.00000 0.0588235
\(290\) −25.5401 −1.49977
\(291\) 48.6015 2.84907
\(292\) 37.0839 2.17017
\(293\) −13.2203 −0.772340 −0.386170 0.922428i \(-0.626202\pi\)
−0.386170 + 0.922428i \(0.626202\pi\)
\(294\) −30.6376 −1.78682
\(295\) 12.4512 0.724935
\(296\) −15.8712 −0.922497
\(297\) 66.0155 3.83061
\(298\) −14.3181 −0.829426
\(299\) −6.30373 −0.364554
\(300\) 3.16213 0.182565
\(301\) −6.47791 −0.373380
\(302\) 18.2167 1.04825
\(303\) −12.1314 −0.696933
\(304\) −0.0887999 −0.00509302
\(305\) −11.2135 −0.642084
\(306\) −15.1794 −0.867746
\(307\) 12.8149 0.731384 0.365692 0.930736i \(-0.380832\pi\)
0.365692 + 0.930736i \(0.380832\pi\)
\(308\) 31.1726 1.77622
\(309\) 30.0236 1.70798
\(310\) −17.1499 −0.974051
\(311\) −27.3211 −1.54924 −0.774620 0.632427i \(-0.782059\pi\)
−0.774620 + 0.632427i \(0.782059\pi\)
\(312\) 15.9686 0.904045
\(313\) −19.6826 −1.11252 −0.556262 0.831007i \(-0.687765\pi\)
−0.556262 + 0.831007i \(0.687765\pi\)
\(314\) −32.6405 −1.84201
\(315\) −23.5273 −1.32561
\(316\) −9.48135 −0.533368
\(317\) −12.4788 −0.700879 −0.350439 0.936585i \(-0.613968\pi\)
−0.350439 + 0.936585i \(0.613968\pi\)
\(318\) −33.5739 −1.88273
\(319\) −30.2057 −1.69120
\(320\) −27.9956 −1.56500
\(321\) 38.5493 2.15161
\(322\) −13.0925 −0.729616
\(323\) −2.74943 −0.152982
\(324\) 48.8348 2.71305
\(325\) −0.567948 −0.0315041
\(326\) −4.43766 −0.245779
\(327\) 37.1221 2.05286
\(328\) 12.5962 0.695507
\(329\) −2.28116 −0.125764
\(330\) −90.1665 −4.96350
\(331\) −35.1738 −1.93333 −0.966663 0.256051i \(-0.917579\pi\)
−0.966663 + 0.256051i \(0.917579\pi\)
\(332\) −24.7549 −1.35860
\(333\) 36.9567 2.02521
\(334\) −0.870479 −0.0476305
\(335\) 31.7319 1.73370
\(336\) 0.164320 0.00896438
\(337\) 22.2053 1.20960 0.604801 0.796376i \(-0.293253\pi\)
0.604801 + 0.796376i \(0.293253\pi\)
\(338\) 22.2858 1.21219
\(339\) −47.6244 −2.58660
\(340\) 7.02063 0.380747
\(341\) −20.2829 −1.09838
\(342\) 41.7346 2.25675
\(343\) 18.5465 1.00142
\(344\) −11.2480 −0.606452
\(345\) 23.4248 1.26115
\(346\) −14.6456 −0.787350
\(347\) 19.3508 1.03880 0.519402 0.854530i \(-0.326155\pi\)
0.519402 + 0.854530i \(0.326155\pi\)
\(348\) −51.8567 −2.77981
\(349\) 29.0833 1.55679 0.778397 0.627772i \(-0.216033\pi\)
0.778397 + 0.627772i \(0.216033\pi\)
\(350\) −1.17960 −0.0630520
\(351\) −20.3560 −1.08652
\(352\) −32.9444 −1.75594
\(353\) 1.00000 0.0532246
\(354\) 40.8707 2.17225
\(355\) 16.6860 0.885603
\(356\) −26.6008 −1.40984
\(357\) 5.08769 0.269269
\(358\) −43.9754 −2.32417
\(359\) 19.5261 1.03055 0.515275 0.857025i \(-0.327690\pi\)
0.515275 + 0.857025i \(0.327690\pi\)
\(360\) −40.8520 −2.15309
\(361\) −11.4406 −0.602139
\(362\) −28.1768 −1.48094
\(363\) −72.5042 −3.80548
\(364\) −9.61210 −0.503811
\(365\) 24.7510 1.29553
\(366\) −36.8081 −1.92399
\(367\) −12.1543 −0.634449 −0.317224 0.948351i \(-0.602751\pi\)
−0.317224 + 0.948351i \(0.602751\pi\)
\(368\) −0.112632 −0.00587135
\(369\) −29.3306 −1.52689
\(370\) −27.6334 −1.43659
\(371\) 7.74707 0.402208
\(372\) −34.8213 −1.80540
\(373\) 32.6220 1.68910 0.844552 0.535474i \(-0.179867\pi\)
0.844552 + 0.535474i \(0.179867\pi\)
\(374\) 13.4234 0.694106
\(375\) 35.6962 1.84334
\(376\) −3.96093 −0.204269
\(377\) 9.31397 0.479694
\(378\) −42.2781 −2.17455
\(379\) −29.0424 −1.49181 −0.745904 0.666053i \(-0.767982\pi\)
−0.745904 + 0.666053i \(0.767982\pi\)
\(380\) −19.3027 −0.990210
\(381\) −56.2245 −2.88047
\(382\) −12.0019 −0.614069
\(383\) 25.1560 1.28541 0.642705 0.766114i \(-0.277812\pi\)
0.642705 + 0.766114i \(0.277812\pi\)
\(384\) −57.0175 −2.90966
\(385\) 20.8056 1.06035
\(386\) −50.1515 −2.55265
\(387\) 26.1914 1.33138
\(388\) −50.7974 −2.57885
\(389\) −7.50894 −0.380718 −0.190359 0.981715i \(-0.560965\pi\)
−0.190359 + 0.981715i \(0.560965\pi\)
\(390\) 27.8030 1.40786
\(391\) −3.48732 −0.176361
\(392\) 12.2753 0.619995
\(393\) 44.6375 2.25167
\(394\) 3.43378 0.172991
\(395\) −6.32817 −0.318405
\(396\) −126.036 −6.33357
\(397\) 2.44727 0.122825 0.0614124 0.998112i \(-0.480440\pi\)
0.0614124 + 0.998112i \(0.480440\pi\)
\(398\) −9.48770 −0.475576
\(399\) −13.9882 −0.700288
\(400\) −0.0101478 −0.000507391 0
\(401\) 30.4357 1.51989 0.759944 0.649989i \(-0.225226\pi\)
0.759944 + 0.649989i \(0.225226\pi\)
\(402\) 104.159 5.19499
\(403\) 6.25424 0.311546
\(404\) 12.6796 0.630832
\(405\) 32.5940 1.61961
\(406\) 19.3446 0.960055
\(407\) −32.6814 −1.61996
\(408\) 8.83409 0.437353
\(409\) −9.48210 −0.468860 −0.234430 0.972133i \(-0.575322\pi\)
−0.234430 + 0.972133i \(0.575322\pi\)
\(410\) 21.9312 1.08310
\(411\) −9.92537 −0.489583
\(412\) −31.3802 −1.54599
\(413\) −9.43076 −0.464058
\(414\) 52.9353 2.60163
\(415\) −16.5222 −0.811044
\(416\) 10.1584 0.498059
\(417\) −23.8420 −1.16755
\(418\) −36.9066 −1.80516
\(419\) 16.9282 0.826999 0.413499 0.910504i \(-0.364306\pi\)
0.413499 + 0.910504i \(0.364306\pi\)
\(420\) 35.7188 1.74290
\(421\) −8.23088 −0.401148 −0.200574 0.979679i \(-0.564281\pi\)
−0.200574 + 0.979679i \(0.564281\pi\)
\(422\) 14.7690 0.718945
\(423\) 9.22315 0.448445
\(424\) 13.4517 0.653275
\(425\) −0.314198 −0.0152408
\(426\) 54.7715 2.65369
\(427\) 8.49333 0.411021
\(428\) −40.2911 −1.94754
\(429\) 32.8819 1.58756
\(430\) −19.5839 −0.944420
\(431\) −30.8601 −1.48648 −0.743240 0.669024i \(-0.766712\pi\)
−0.743240 + 0.669024i \(0.766712\pi\)
\(432\) −0.363710 −0.0174990
\(433\) 20.8714 1.00301 0.501507 0.865154i \(-0.332779\pi\)
0.501507 + 0.865154i \(0.332779\pi\)
\(434\) 12.9897 0.623525
\(435\) −34.6109 −1.65947
\(436\) −38.7994 −1.85816
\(437\) 9.58815 0.458663
\(438\) 81.2447 3.88202
\(439\) −34.6886 −1.65560 −0.827798 0.561026i \(-0.810407\pi\)
−0.827798 + 0.561026i \(0.810407\pi\)
\(440\) 36.1262 1.72225
\(441\) −28.5834 −1.36111
\(442\) −4.13911 −0.196877
\(443\) 1.00722 0.0478547 0.0239273 0.999714i \(-0.492383\pi\)
0.0239273 + 0.999714i \(0.492383\pi\)
\(444\) −56.1070 −2.66272
\(445\) −17.7542 −0.841632
\(446\) −33.7003 −1.59576
\(447\) −19.4033 −0.917746
\(448\) 21.2044 1.00181
\(449\) −21.5134 −1.01528 −0.507639 0.861570i \(-0.669482\pi\)
−0.507639 + 0.861570i \(0.669482\pi\)
\(450\) 4.76932 0.224828
\(451\) 25.9375 1.22135
\(452\) 49.7762 2.34127
\(453\) 24.6865 1.15987
\(454\) 33.6583 1.57966
\(455\) −6.41543 −0.300760
\(456\) −24.2887 −1.13742
\(457\) −3.93775 −0.184200 −0.0921001 0.995750i \(-0.529358\pi\)
−0.0921001 + 0.995750i \(0.529358\pi\)
\(458\) 16.3699 0.764915
\(459\) −11.2612 −0.525629
\(460\) −24.4832 −1.14154
\(461\) 10.4642 0.487368 0.243684 0.969855i \(-0.421644\pi\)
0.243684 + 0.969855i \(0.421644\pi\)
\(462\) 68.2939 3.17732
\(463\) 31.1162 1.44609 0.723046 0.690800i \(-0.242742\pi\)
0.723046 + 0.690800i \(0.242742\pi\)
\(464\) 0.166417 0.00772573
\(465\) −23.2409 −1.07777
\(466\) −10.5702 −0.489654
\(467\) −36.1286 −1.67183 −0.835916 0.548857i \(-0.815063\pi\)
−0.835916 + 0.548857i \(0.815063\pi\)
\(468\) 38.8635 1.79646
\(469\) −24.0344 −1.10980
\(470\) −6.89637 −0.318106
\(471\) −44.2331 −2.03815
\(472\) −16.3753 −0.753732
\(473\) −23.1615 −1.06497
\(474\) −20.7721 −0.954092
\(475\) 0.863865 0.0396368
\(476\) −5.31756 −0.243730
\(477\) −31.3228 −1.43417
\(478\) −17.1877 −0.786147
\(479\) −37.9593 −1.73440 −0.867202 0.497957i \(-0.834084\pi\)
−0.867202 + 0.497957i \(0.834084\pi\)
\(480\) −37.7490 −1.72300
\(481\) 10.0774 0.459488
\(482\) −53.8455 −2.45260
\(483\) −17.7424 −0.807307
\(484\) 75.7801 3.44455
\(485\) −33.9039 −1.53950
\(486\) 29.6303 1.34406
\(487\) 0.521664 0.0236388 0.0118194 0.999930i \(-0.496238\pi\)
0.0118194 + 0.999930i \(0.496238\pi\)
\(488\) 14.7475 0.667590
\(489\) −6.01374 −0.271951
\(490\) 21.3725 0.965510
\(491\) −5.88766 −0.265707 −0.132853 0.991136i \(-0.542414\pi\)
−0.132853 + 0.991136i \(0.542414\pi\)
\(492\) 44.5292 2.00753
\(493\) 5.15263 0.232063
\(494\) 11.3802 0.512019
\(495\) −84.1209 −3.78095
\(496\) 0.111748 0.00501762
\(497\) −12.6383 −0.566907
\(498\) −54.2338 −2.43027
\(499\) −28.2572 −1.26497 −0.632483 0.774574i \(-0.717964\pi\)
−0.632483 + 0.774574i \(0.717964\pi\)
\(500\) −37.3090 −1.66851
\(501\) −1.17964 −0.0527023
\(502\) −29.4652 −1.31510
\(503\) −9.16788 −0.408776 −0.204388 0.978890i \(-0.565520\pi\)
−0.204388 + 0.978890i \(0.565520\pi\)
\(504\) 30.9421 1.37827
\(505\) 8.46276 0.376588
\(506\) −46.8116 −2.08103
\(507\) 30.2008 1.34126
\(508\) 58.7649 2.60727
\(509\) −15.4289 −0.683872 −0.341936 0.939723i \(-0.611083\pi\)
−0.341936 + 0.939723i \(0.611083\pi\)
\(510\) 15.3810 0.681083
\(511\) −18.7469 −0.829315
\(512\) 0.365401 0.0161486
\(513\) 30.9620 1.36700
\(514\) −18.7590 −0.827423
\(515\) −20.9442 −0.922911
\(516\) −39.7633 −1.75048
\(517\) −8.15619 −0.358709
\(518\) 20.9301 0.919615
\(519\) −19.8471 −0.871190
\(520\) −11.1395 −0.488501
\(521\) 8.81733 0.386294 0.193147 0.981170i \(-0.438131\pi\)
0.193147 + 0.981170i \(0.438131\pi\)
\(522\) −78.2136 −3.42332
\(523\) 11.0698 0.484047 0.242024 0.970270i \(-0.422189\pi\)
0.242024 + 0.970270i \(0.422189\pi\)
\(524\) −46.6544 −2.03811
\(525\) −1.59854 −0.0697660
\(526\) 59.5630 2.59707
\(527\) 3.45994 0.150718
\(528\) 0.587518 0.0255685
\(529\) −10.8386 −0.471243
\(530\) 23.4208 1.01734
\(531\) 38.1303 1.65471
\(532\) 14.6203 0.633869
\(533\) −7.99786 −0.346426
\(534\) −58.2778 −2.52193
\(535\) −26.8916 −1.16262
\(536\) −41.7324 −1.80257
\(537\) −59.5937 −2.57166
\(538\) 56.1912 2.42257
\(539\) 25.2768 1.08875
\(540\) −79.0610 −3.40224
\(541\) 7.71937 0.331881 0.165941 0.986136i \(-0.446934\pi\)
0.165941 + 0.986136i \(0.446934\pi\)
\(542\) 37.0716 1.59236
\(543\) −38.1840 −1.63863
\(544\) 5.61981 0.240947
\(545\) −25.8960 −1.10926
\(546\) −21.0585 −0.901221
\(547\) 9.14422 0.390979 0.195489 0.980706i \(-0.437370\pi\)
0.195489 + 0.980706i \(0.437370\pi\)
\(548\) 10.3738 0.443148
\(549\) −34.3401 −1.46560
\(550\) −4.21759 −0.179839
\(551\) −14.1668 −0.603526
\(552\) −30.8073 −1.31125
\(553\) 4.79308 0.203822
\(554\) 24.9161 1.05859
\(555\) −37.4477 −1.58957
\(556\) 24.9192 1.05681
\(557\) −18.1052 −0.767143 −0.383572 0.923511i \(-0.625306\pi\)
−0.383572 + 0.923511i \(0.625306\pi\)
\(558\) −52.5197 −2.22334
\(559\) 7.14187 0.302069
\(560\) −0.114628 −0.00484391
\(561\) 18.1908 0.768016
\(562\) 7.77775 0.328084
\(563\) −7.17913 −0.302564 −0.151282 0.988491i \(-0.548340\pi\)
−0.151282 + 0.988491i \(0.548340\pi\)
\(564\) −14.0024 −0.589609
\(565\) 33.2223 1.39767
\(566\) −60.7711 −2.55440
\(567\) −24.6873 −1.03677
\(568\) −21.9448 −0.920782
\(569\) −6.48243 −0.271757 −0.135879 0.990725i \(-0.543386\pi\)
−0.135879 + 0.990725i \(0.543386\pi\)
\(570\) −42.2891 −1.77129
\(571\) −23.7470 −0.993782 −0.496891 0.867813i \(-0.665525\pi\)
−0.496891 + 0.867813i \(0.665525\pi\)
\(572\) −34.3676 −1.43698
\(573\) −16.2644 −0.679457
\(574\) −16.6111 −0.693334
\(575\) 1.09571 0.0456942
\(576\) −85.7333 −3.57222
\(577\) −12.8455 −0.534767 −0.267384 0.963590i \(-0.586159\pi\)
−0.267384 + 0.963590i \(0.586159\pi\)
\(578\) −2.28982 −0.0952440
\(579\) −67.9633 −2.82446
\(580\) 36.1747 1.50207
\(581\) 12.5143 0.519179
\(582\) −111.289 −4.61306
\(583\) 27.6993 1.14719
\(584\) −32.5515 −1.34699
\(585\) 25.9388 1.07244
\(586\) 30.2722 1.25053
\(587\) 5.58519 0.230525 0.115263 0.993335i \(-0.463229\pi\)
0.115263 + 0.993335i \(0.463229\pi\)
\(588\) 43.3948 1.78957
\(589\) −9.51288 −0.391971
\(590\) −28.5110 −1.17378
\(591\) 4.65332 0.191412
\(592\) 0.180057 0.00740031
\(593\) 8.88240 0.364757 0.182378 0.983228i \(-0.441620\pi\)
0.182378 + 0.983228i \(0.441620\pi\)
\(594\) −151.164 −6.20232
\(595\) −3.54912 −0.145500
\(596\) 20.2800 0.830703
\(597\) −12.8574 −0.526216
\(598\) 14.4344 0.590267
\(599\) 10.1605 0.415145 0.207573 0.978220i \(-0.433444\pi\)
0.207573 + 0.978220i \(0.433444\pi\)
\(600\) −2.77565 −0.113315
\(601\) 45.5495 1.85800 0.929002 0.370075i \(-0.120668\pi\)
0.929002 + 0.370075i \(0.120668\pi\)
\(602\) 14.8332 0.604558
\(603\) 97.1753 3.95728
\(604\) −25.8019 −1.04987
\(605\) 50.5782 2.05630
\(606\) 27.7788 1.12844
\(607\) −31.9655 −1.29744 −0.648719 0.761028i \(-0.724695\pi\)
−0.648719 + 0.761028i \(0.724695\pi\)
\(608\) −15.4513 −0.626632
\(609\) 26.2150 1.06228
\(610\) 25.6769 1.03963
\(611\) 2.51497 0.101745
\(612\) 21.4999 0.869081
\(613\) 25.5826 1.03327 0.516636 0.856205i \(-0.327184\pi\)
0.516636 + 0.856205i \(0.327184\pi\)
\(614\) −29.3438 −1.18422
\(615\) 29.7202 1.19844
\(616\) −27.3627 −1.10247
\(617\) −7.30124 −0.293937 −0.146968 0.989141i \(-0.546952\pi\)
−0.146968 + 0.989141i \(0.546952\pi\)
\(618\) −68.7487 −2.76548
\(619\) −9.01014 −0.362148 −0.181074 0.983469i \(-0.557957\pi\)
−0.181074 + 0.983469i \(0.557957\pi\)
\(620\) 24.2910 0.975550
\(621\) 39.2715 1.57591
\(622\) 62.5605 2.50845
\(623\) 13.4474 0.538759
\(624\) −0.181162 −0.00725228
\(625\) −23.3303 −0.933212
\(626\) 45.0695 1.80134
\(627\) −50.0144 −1.99738
\(628\) 46.2317 1.84484
\(629\) 5.57495 0.222288
\(630\) 53.8733 2.14636
\(631\) 24.1078 0.959714 0.479857 0.877347i \(-0.340688\pi\)
0.479857 + 0.877347i \(0.340688\pi\)
\(632\) 8.32254 0.331053
\(633\) 20.0144 0.795501
\(634\) 28.5742 1.13483
\(635\) 39.2216 1.55646
\(636\) 47.5538 1.88563
\(637\) −7.79412 −0.308814
\(638\) 69.1657 2.73830
\(639\) 51.0991 2.02145
\(640\) 39.7748 1.57224
\(641\) −44.4722 −1.75655 −0.878273 0.478160i \(-0.841304\pi\)
−0.878273 + 0.478160i \(0.841304\pi\)
\(642\) −88.2710 −3.48378
\(643\) 6.46535 0.254968 0.127484 0.991841i \(-0.459310\pi\)
0.127484 + 0.991841i \(0.459310\pi\)
\(644\) 18.5441 0.730738
\(645\) −26.5393 −1.04499
\(646\) 6.29570 0.247701
\(647\) −24.9539 −0.981039 −0.490520 0.871430i \(-0.663193\pi\)
−0.490520 + 0.871430i \(0.663193\pi\)
\(648\) −42.8662 −1.68394
\(649\) −33.7193 −1.32360
\(650\) 1.30050 0.0510098
\(651\) 17.6031 0.689920
\(652\) 6.28546 0.246157
\(653\) −11.5147 −0.450606 −0.225303 0.974289i \(-0.572337\pi\)
−0.225303 + 0.974289i \(0.572337\pi\)
\(654\) −85.0030 −3.32388
\(655\) −31.1387 −1.21669
\(656\) −0.142902 −0.00557938
\(657\) 75.7973 2.95713
\(658\) 5.22345 0.203631
\(659\) −24.8784 −0.969124 −0.484562 0.874757i \(-0.661021\pi\)
−0.484562 + 0.874757i \(0.661021\pi\)
\(660\) 127.711 4.97114
\(661\) 33.2052 1.29153 0.645766 0.763535i \(-0.276538\pi\)
0.645766 + 0.763535i \(0.276538\pi\)
\(662\) 80.5417 3.13034
\(663\) −5.60916 −0.217842
\(664\) 21.7293 0.843261
\(665\) 9.75805 0.378401
\(666\) −84.6242 −3.27912
\(667\) −17.9689 −0.695758
\(668\) 1.23294 0.0477038
\(669\) −45.6693 −1.76568
\(670\) −72.6603 −2.80711
\(671\) 30.3675 1.17233
\(672\) 28.5919 1.10295
\(673\) −43.4556 −1.67509 −0.837546 0.546367i \(-0.816010\pi\)
−0.837546 + 0.546367i \(0.816010\pi\)
\(674\) −50.8463 −1.95852
\(675\) 3.53825 0.136187
\(676\) −31.5653 −1.21405
\(677\) −2.59030 −0.0995535 −0.0497767 0.998760i \(-0.515851\pi\)
−0.0497767 + 0.998760i \(0.515851\pi\)
\(678\) 109.051 4.18809
\(679\) 25.6795 0.985487
\(680\) −6.16257 −0.236324
\(681\) 45.6124 1.74787
\(682\) 46.4441 1.77844
\(683\) 18.4685 0.706678 0.353339 0.935495i \(-0.385046\pi\)
0.353339 + 0.935495i \(0.385046\pi\)
\(684\) −59.1124 −2.26022
\(685\) 6.92384 0.264546
\(686\) −42.4681 −1.62144
\(687\) 22.1838 0.846366
\(688\) 0.127607 0.00486499
\(689\) −8.54111 −0.325390
\(690\) −53.6386 −2.04199
\(691\) −21.9046 −0.833291 −0.416645 0.909069i \(-0.636794\pi\)
−0.416645 + 0.909069i \(0.636794\pi\)
\(692\) 20.7438 0.788562
\(693\) 63.7148 2.42033
\(694\) −44.3098 −1.68198
\(695\) 16.6319 0.630885
\(696\) 45.5188 1.72539
\(697\) −4.42454 −0.167592
\(698\) −66.5956 −2.52068
\(699\) −14.3243 −0.541794
\(700\) 1.67077 0.0631490
\(701\) −14.8084 −0.559305 −0.279652 0.960101i \(-0.590219\pi\)
−0.279652 + 0.960101i \(0.590219\pi\)
\(702\) 46.6115 1.75924
\(703\) −15.3279 −0.578104
\(704\) 75.8155 2.85740
\(705\) −9.34569 −0.351979
\(706\) −2.28982 −0.0861785
\(707\) −6.40986 −0.241068
\(708\) −57.8888 −2.17559
\(709\) 17.9391 0.673718 0.336859 0.941555i \(-0.390635\pi\)
0.336859 + 0.941555i \(0.390635\pi\)
\(710\) −38.2080 −1.43392
\(711\) −19.3793 −0.726780
\(712\) 23.3496 0.875064
\(713\) −12.0659 −0.451873
\(714\) −11.6499 −0.435986
\(715\) −22.9381 −0.857837
\(716\) 62.2864 2.32775
\(717\) −23.2921 −0.869858
\(718\) −44.7113 −1.66861
\(719\) 26.8367 1.00084 0.500420 0.865783i \(-0.333179\pi\)
0.500420 + 0.865783i \(0.333179\pi\)
\(720\) 0.463461 0.0172722
\(721\) 15.8635 0.590789
\(722\) 26.1970 0.974951
\(723\) −72.9692 −2.71376
\(724\) 39.9093 1.48322
\(725\) −1.61895 −0.0601261
\(726\) 166.022 6.16164
\(727\) 46.7658 1.73445 0.867223 0.497919i \(-0.165902\pi\)
0.867223 + 0.497919i \(0.165902\pi\)
\(728\) 8.43731 0.312707
\(729\) −5.01792 −0.185849
\(730\) −56.6755 −2.09765
\(731\) 3.95099 0.146133
\(732\) 52.1346 1.92695
\(733\) 23.1772 0.856068 0.428034 0.903763i \(-0.359206\pi\)
0.428034 + 0.903763i \(0.359206\pi\)
\(734\) 27.8311 1.02727
\(735\) 28.9631 1.06832
\(736\) −19.5981 −0.722396
\(737\) −85.9338 −3.16541
\(738\) 67.1617 2.47226
\(739\) 31.8635 1.17212 0.586060 0.810268i \(-0.300678\pi\)
0.586060 + 0.810268i \(0.300678\pi\)
\(740\) 39.1397 1.43880
\(741\) 15.4220 0.566541
\(742\) −17.7394 −0.651234
\(743\) −13.1801 −0.483531 −0.241765 0.970335i \(-0.577726\pi\)
−0.241765 + 0.970335i \(0.577726\pi\)
\(744\) 30.5655 1.12058
\(745\) 13.5356 0.495905
\(746\) −74.6985 −2.73491
\(747\) −50.5974 −1.85126
\(748\) −19.0127 −0.695174
\(749\) 20.3682 0.744238
\(750\) −81.7378 −2.98464
\(751\) −18.4561 −0.673474 −0.336737 0.941599i \(-0.609323\pi\)
−0.336737 + 0.941599i \(0.609323\pi\)
\(752\) 0.0449363 0.00163866
\(753\) −39.9301 −1.45513
\(754\) −21.3273 −0.776695
\(755\) −17.2211 −0.626739
\(756\) 59.8823 2.17790
\(757\) 40.4243 1.46925 0.734623 0.678475i \(-0.237359\pi\)
0.734623 + 0.678475i \(0.237359\pi\)
\(758\) 66.5019 2.41546
\(759\) −63.4372 −2.30262
\(760\) 16.9436 0.614607
\(761\) 2.22807 0.0807673 0.0403837 0.999184i \(-0.487142\pi\)
0.0403837 + 0.999184i \(0.487142\pi\)
\(762\) 128.744 4.66390
\(763\) 19.6142 0.710080
\(764\) 16.9993 0.615014
\(765\) 14.3497 0.518816
\(766\) −57.6027 −2.08127
\(767\) 10.3974 0.375428
\(768\) 50.2960 1.81490
\(769\) −36.6919 −1.32315 −0.661573 0.749881i \(-0.730111\pi\)
−0.661573 + 0.749881i \(0.730111\pi\)
\(770\) −47.6411 −1.71687
\(771\) −25.4214 −0.915530
\(772\) 71.0341 2.55657
\(773\) −39.3543 −1.41548 −0.707738 0.706475i \(-0.750284\pi\)
−0.707738 + 0.706475i \(0.750284\pi\)
\(774\) −59.9735 −2.15570
\(775\) −1.08711 −0.0390500
\(776\) 44.5889 1.60065
\(777\) 28.3636 1.01754
\(778\) 17.1941 0.616439
\(779\) 12.1650 0.435855
\(780\) −39.3798 −1.41002
\(781\) −45.1878 −1.61695
\(782\) 7.98534 0.285555
\(783\) −58.0250 −2.07364
\(784\) −0.139261 −0.00497362
\(785\) 30.8565 1.10132
\(786\) −102.212 −3.64578
\(787\) 29.5706 1.05408 0.527040 0.849841i \(-0.323302\pi\)
0.527040 + 0.849841i \(0.323302\pi\)
\(788\) −4.86357 −0.173257
\(789\) 80.7173 2.87361
\(790\) 14.4904 0.515544
\(791\) −25.1632 −0.894700
\(792\) 110.632 3.93115
\(793\) −9.36387 −0.332521
\(794\) −5.60381 −0.198872
\(795\) 31.7390 1.12567
\(796\) 13.4383 0.476307
\(797\) −43.2642 −1.53250 −0.766249 0.642544i \(-0.777879\pi\)
−0.766249 + 0.642544i \(0.777879\pi\)
\(798\) 32.0306 1.13387
\(799\) 1.39132 0.0492214
\(800\) −1.76573 −0.0624281
\(801\) −54.3703 −1.92108
\(802\) −69.6924 −2.46092
\(803\) −67.0288 −2.36540
\(804\) −147.530 −5.20298
\(805\) 12.3769 0.436229
\(806\) −14.3211 −0.504439
\(807\) 76.1480 2.68054
\(808\) −11.1299 −0.391547
\(809\) −17.6419 −0.620257 −0.310128 0.950695i \(-0.600372\pi\)
−0.310128 + 0.950695i \(0.600372\pi\)
\(810\) −74.6344 −2.62238
\(811\) 35.9134 1.26109 0.630545 0.776153i \(-0.282831\pi\)
0.630545 + 0.776153i \(0.282831\pi\)
\(812\) −27.3995 −0.961532
\(813\) 50.2379 1.76192
\(814\) 74.8346 2.62295
\(815\) 4.19512 0.146949
\(816\) −0.100222 −0.00350846
\(817\) −10.8630 −0.380047
\(818\) 21.7123 0.759153
\(819\) −19.6465 −0.686505
\(820\) −31.0631 −1.08477
\(821\) −5.58470 −0.194907 −0.0974537 0.995240i \(-0.531070\pi\)
−0.0974537 + 0.995240i \(0.531070\pi\)
\(822\) 22.7273 0.792706
\(823\) −15.1723 −0.528874 −0.264437 0.964403i \(-0.585186\pi\)
−0.264437 + 0.964403i \(0.585186\pi\)
\(824\) 27.5449 0.959572
\(825\) −5.71551 −0.198989
\(826\) 21.5948 0.751378
\(827\) −44.5791 −1.55017 −0.775084 0.631859i \(-0.782292\pi\)
−0.775084 + 0.631859i \(0.782292\pi\)
\(828\) −74.9770 −2.60563
\(829\) 8.86584 0.307923 0.153962 0.988077i \(-0.450797\pi\)
0.153962 + 0.988077i \(0.450797\pi\)
\(830\) 37.8329 1.31320
\(831\) 33.7653 1.17131
\(832\) −23.3778 −0.810479
\(833\) −4.31183 −0.149396
\(834\) 54.5939 1.89043
\(835\) 0.822903 0.0284777
\(836\) 52.2741 1.80794
\(837\) −38.9632 −1.34677
\(838\) −38.7626 −1.33903
\(839\) 15.7591 0.544066 0.272033 0.962288i \(-0.412304\pi\)
0.272033 + 0.962288i \(0.412304\pi\)
\(840\) −31.3532 −1.08179
\(841\) −2.45038 −0.0844958
\(842\) 18.8472 0.649519
\(843\) 10.5401 0.363020
\(844\) −20.9187 −0.720051
\(845\) −21.0677 −0.724752
\(846\) −21.1194 −0.726098
\(847\) −38.3089 −1.31631
\(848\) −0.152608 −0.00524059
\(849\) −82.3545 −2.82640
\(850\) 0.719456 0.0246772
\(851\) −19.4417 −0.666451
\(852\) −77.5778 −2.65777
\(853\) −15.0212 −0.514316 −0.257158 0.966369i \(-0.582786\pi\)
−0.257158 + 0.966369i \(0.582786\pi\)
\(854\) −19.4482 −0.665504
\(855\) −39.4536 −1.34928
\(856\) 35.3667 1.20881
\(857\) 0.675325 0.0230687 0.0115343 0.999933i \(-0.496328\pi\)
0.0115343 + 0.999933i \(0.496328\pi\)
\(858\) −75.2938 −2.57049
\(859\) 29.4941 1.00632 0.503162 0.864192i \(-0.332170\pi\)
0.503162 + 0.864192i \(0.332170\pi\)
\(860\) 27.7385 0.945874
\(861\) −22.5107 −0.767162
\(862\) 70.6642 2.40683
\(863\) −39.3274 −1.33872 −0.669360 0.742938i \(-0.733432\pi\)
−0.669360 + 0.742938i \(0.733432\pi\)
\(864\) −63.2860 −2.15303
\(865\) 13.8451 0.470748
\(866\) −47.7917 −1.62403
\(867\) −3.10307 −0.105386
\(868\) −18.3985 −0.624485
\(869\) 17.1374 0.581348
\(870\) 79.2528 2.68692
\(871\) 26.4978 0.897843
\(872\) 34.0573 1.15333
\(873\) −103.827 −3.51400
\(874\) −21.9551 −0.742644
\(875\) 18.8607 0.637609
\(876\) −115.074 −3.88800
\(877\) −38.1546 −1.28839 −0.644195 0.764862i \(-0.722807\pi\)
−0.644195 + 0.764862i \(0.722807\pi\)
\(878\) 79.4306 2.68065
\(879\) 41.0236 1.38369
\(880\) −0.409847 −0.0138159
\(881\) −29.7310 −1.00166 −0.500832 0.865545i \(-0.666973\pi\)
−0.500832 + 0.865545i \(0.666973\pi\)
\(882\) 65.4508 2.20384
\(883\) 49.5281 1.66675 0.833376 0.552707i \(-0.186405\pi\)
0.833376 + 0.552707i \(0.186405\pi\)
\(884\) 5.86259 0.197180
\(885\) −38.6369 −1.29877
\(886\) −2.30636 −0.0774838
\(887\) −36.2354 −1.21667 −0.608333 0.793682i \(-0.708161\pi\)
−0.608333 + 0.793682i \(0.708161\pi\)
\(888\) 49.2496 1.65271
\(889\) −29.7072 −0.996349
\(890\) 40.6540 1.36273
\(891\) −88.2684 −2.95710
\(892\) 47.7328 1.59821
\(893\) −3.82534 −0.128010
\(894\) 44.4302 1.48597
\(895\) 41.5720 1.38960
\(896\) −30.1262 −1.00645
\(897\) 19.5609 0.653121
\(898\) 49.2617 1.64389
\(899\) 17.8278 0.594591
\(900\) −6.75521 −0.225174
\(901\) −4.72508 −0.157415
\(902\) −59.3923 −1.97755
\(903\) 20.1014 0.668933
\(904\) −43.6925 −1.45319
\(905\) 26.6368 0.885437
\(906\) −56.5277 −1.87801
\(907\) −44.8820 −1.49028 −0.745141 0.666907i \(-0.767618\pi\)
−0.745141 + 0.666907i \(0.767618\pi\)
\(908\) −47.6733 −1.58209
\(909\) 25.9162 0.859588
\(910\) 14.6902 0.486975
\(911\) −10.9670 −0.363353 −0.181676 0.983358i \(-0.558152\pi\)
−0.181676 + 0.983358i \(0.558152\pi\)
\(912\) 0.275552 0.00912445
\(913\) 44.7442 1.48082
\(914\) 9.01674 0.298247
\(915\) 34.7963 1.15033
\(916\) −23.1862 −0.766092
\(917\) 23.5851 0.778847
\(918\) 25.7862 0.851071
\(919\) −26.8394 −0.885350 −0.442675 0.896682i \(-0.645970\pi\)
−0.442675 + 0.896682i \(0.645970\pi\)
\(920\) 21.4909 0.708533
\(921\) −39.7655 −1.31032
\(922\) −23.9612 −0.789121
\(923\) 13.9337 0.458634
\(924\) −96.7308 −3.18221
\(925\) −1.75164 −0.0575935
\(926\) −71.2504 −2.34143
\(927\) −64.1391 −2.10661
\(928\) 28.9568 0.950555
\(929\) −28.4767 −0.934290 −0.467145 0.884181i \(-0.654717\pi\)
−0.467145 + 0.884181i \(0.654717\pi\)
\(930\) 53.2175 1.74507
\(931\) 11.8551 0.388534
\(932\) 14.9715 0.490408
\(933\) 84.7795 2.77556
\(934\) 82.7280 2.70694
\(935\) −12.6897 −0.414998
\(936\) −34.1136 −1.11504
\(937\) −45.5528 −1.48815 −0.744073 0.668098i \(-0.767109\pi\)
−0.744073 + 0.668098i \(0.767109\pi\)
\(938\) 55.0344 1.79694
\(939\) 61.0764 1.99315
\(940\) 9.76795 0.318595
\(941\) 25.2451 0.822966 0.411483 0.911417i \(-0.365011\pi\)
0.411483 + 0.911417i \(0.365011\pi\)
\(942\) 101.286 3.30007
\(943\) 15.4298 0.502464
\(944\) 0.185775 0.00604647
\(945\) 39.9674 1.30014
\(946\) 53.0356 1.72434
\(947\) −10.3089 −0.334995 −0.167497 0.985873i \(-0.553569\pi\)
−0.167497 + 0.985873i \(0.553569\pi\)
\(948\) 29.4213 0.955560
\(949\) 20.6684 0.670925
\(950\) −1.97810 −0.0641779
\(951\) 38.7226 1.25567
\(952\) 4.66765 0.151279
\(953\) −40.8731 −1.32401 −0.662005 0.749499i \(-0.730294\pi\)
−0.662005 + 0.749499i \(0.730294\pi\)
\(954\) 71.7236 2.32214
\(955\) 11.3459 0.367145
\(956\) 24.3445 0.787356
\(957\) 93.7305 3.02988
\(958\) 86.9199 2.80825
\(959\) −5.24425 −0.169346
\(960\) 86.8724 2.80379
\(961\) −19.0288 −0.613832
\(962\) −23.0753 −0.743979
\(963\) −82.3524 −2.65377
\(964\) 76.2662 2.45637
\(965\) 47.4105 1.52620
\(966\) 40.6269 1.30715
\(967\) 6.84739 0.220197 0.110099 0.993921i \(-0.464883\pi\)
0.110099 + 0.993921i \(0.464883\pi\)
\(968\) −66.5183 −2.13798
\(969\) 8.53168 0.274077
\(970\) 77.6338 2.49267
\(971\) −1.16064 −0.0372467 −0.0186234 0.999827i \(-0.505928\pi\)
−0.0186234 + 0.999827i \(0.505928\pi\)
\(972\) −41.9681 −1.34613
\(973\) −12.5974 −0.403853
\(974\) −1.19452 −0.0382748
\(975\) 1.76238 0.0564415
\(976\) −0.167309 −0.00535543
\(977\) 11.1284 0.356030 0.178015 0.984028i \(-0.443033\pi\)
0.178015 + 0.984028i \(0.443033\pi\)
\(978\) 13.7704 0.440328
\(979\) 48.0806 1.53666
\(980\) −30.2718 −0.966996
\(981\) −79.3036 −2.53197
\(982\) 13.4817 0.430218
\(983\) −19.2942 −0.615388 −0.307694 0.951485i \(-0.599557\pi\)
−0.307694 + 0.951485i \(0.599557\pi\)
\(984\) −39.0868 −1.24604
\(985\) −3.24611 −0.103430
\(986\) −11.7986 −0.375744
\(987\) 7.07861 0.225314
\(988\) −16.1188 −0.512807
\(989\) −13.7784 −0.438127
\(990\) 192.622 6.12192
\(991\) 55.0091 1.74742 0.873710 0.486447i \(-0.161707\pi\)
0.873710 + 0.486447i \(0.161707\pi\)
\(992\) 19.4442 0.617355
\(993\) 109.147 3.46367
\(994\) 28.9395 0.917906
\(995\) 8.96916 0.284341
\(996\) 76.8162 2.43401
\(997\) 13.4964 0.427436 0.213718 0.976895i \(-0.431443\pi\)
0.213718 + 0.976895i \(0.431443\pi\)
\(998\) 64.7039 2.04817
\(999\) −62.7808 −1.98630
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 \(a_p\))