Properties

Label 8018.2.a.f.1.15
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
CM No

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(34\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-0.916646 q^{3}\) \(+1.00000 q^{4}\) \(-1.80395 q^{5}\) \(+0.916646 q^{6}\) \(-2.30047 q^{7}\) \(-1.00000 q^{8}\) \(-2.15976 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-0.916646 q^{3}\) \(+1.00000 q^{4}\) \(-1.80395 q^{5}\) \(+0.916646 q^{6}\) \(-2.30047 q^{7}\) \(-1.00000 q^{8}\) \(-2.15976 q^{9}\) \(+1.80395 q^{10}\) \(+5.03734 q^{11}\) \(-0.916646 q^{12}\) \(+3.75894 q^{13}\) \(+2.30047 q^{14}\) \(+1.65359 q^{15}\) \(+1.00000 q^{16}\) \(-1.14389 q^{17}\) \(+2.15976 q^{18}\) \(-1.00000 q^{19}\) \(-1.80395 q^{20}\) \(+2.10872 q^{21}\) \(-5.03734 q^{22}\) \(-3.89553 q^{23}\) \(+0.916646 q^{24}\) \(-1.74576 q^{25}\) \(-3.75894 q^{26}\) \(+4.72967 q^{27}\) \(-2.30047 q^{28}\) \(-6.08127 q^{29}\) \(-1.65359 q^{30}\) \(+2.27780 q^{31}\) \(-1.00000 q^{32}\) \(-4.61746 q^{33}\) \(+1.14389 q^{34}\) \(+4.14994 q^{35}\) \(-2.15976 q^{36}\) \(+6.22253 q^{37}\) \(+1.00000 q^{38}\) \(-3.44562 q^{39}\) \(+1.80395 q^{40}\) \(+11.2605 q^{41}\) \(-2.10872 q^{42}\) \(-10.5371 q^{43}\) \(+5.03734 q^{44}\) \(+3.89610 q^{45}\) \(+3.89553 q^{46}\) \(-7.77272 q^{47}\) \(-0.916646 q^{48}\) \(-1.70784 q^{49}\) \(+1.74576 q^{50}\) \(+1.04855 q^{51}\) \(+3.75894 q^{52}\) \(+4.91807 q^{53}\) \(-4.72967 q^{54}\) \(-9.08712 q^{55}\) \(+2.30047 q^{56}\) \(+0.916646 q^{57}\) \(+6.08127 q^{58}\) \(+0.349209 q^{59}\) \(+1.65359 q^{60}\) \(+1.02372 q^{61}\) \(-2.27780 q^{62}\) \(+4.96846 q^{63}\) \(+1.00000 q^{64}\) \(-6.78096 q^{65}\) \(+4.61746 q^{66}\) \(+2.71873 q^{67}\) \(-1.14389 q^{68}\) \(+3.57082 q^{69}\) \(-4.14994 q^{70}\) \(+7.52431 q^{71}\) \(+2.15976 q^{72}\) \(-5.77390 q^{73}\) \(-6.22253 q^{74}\) \(+1.60024 q^{75}\) \(-1.00000 q^{76}\) \(-11.5882 q^{77}\) \(+3.44562 q^{78}\) \(+1.97978 q^{79}\) \(-1.80395 q^{80}\) \(+2.14384 q^{81}\) \(-11.2605 q^{82}\) \(-7.97117 q^{83}\) \(+2.10872 q^{84}\) \(+2.06353 q^{85}\) \(+10.5371 q^{86}\) \(+5.57437 q^{87}\) \(-5.03734 q^{88}\) \(+8.56375 q^{89}\) \(-3.89610 q^{90}\) \(-8.64734 q^{91}\) \(-3.89553 q^{92}\) \(-2.08793 q^{93}\) \(+7.77272 q^{94}\) \(+1.80395 q^{95}\) \(+0.916646 q^{96}\) \(-8.80542 q^{97}\) \(+1.70784 q^{98}\) \(-10.8794 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut -\mathstrut 7q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 38q^{18} \) \(\mathstrut -\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 31q^{27} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 17q^{30} \) \(\mathstrut -\mathstrut 28q^{31} \) \(\mathstrut -\mathstrut 34q^{32} \) \(\mathstrut -\mathstrut 16q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 36q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 7q^{40} \) \(\mathstrut +\mathstrut 9q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 22q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 29q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 22q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 21q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 9q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 23q^{61} \) \(\mathstrut +\mathstrut 28q^{62} \) \(\mathstrut -\mathstrut 27q^{63} \) \(\mathstrut +\mathstrut 34q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 51q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 17q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut -\mathstrut 38q^{72} \) \(\mathstrut -\mathstrut 26q^{73} \) \(\mathstrut +\mathstrut 36q^{74} \) \(\mathstrut -\mathstrut 109q^{75} \) \(\mathstrut -\mathstrut 34q^{76} \) \(\mathstrut -\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 9q^{78} \) \(\mathstrut -\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 7q^{80} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 9q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 22q^{90} \) \(\mathstrut -\mathstrut 41q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 56q^{97} \) \(\mathstrut -\mathstrut 22q^{98} \) \(\mathstrut -\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.916646 −0.529226 −0.264613 0.964355i \(-0.585244\pi\)
−0.264613 + 0.964355i \(0.585244\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.80395 −0.806752 −0.403376 0.915034i \(-0.632163\pi\)
−0.403376 + 0.915034i \(0.632163\pi\)
\(6\) 0.916646 0.374219
\(7\) −2.30047 −0.869496 −0.434748 0.900552i \(-0.643163\pi\)
−0.434748 + 0.900552i \(0.643163\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.15976 −0.719920
\(10\) 1.80395 0.570460
\(11\) 5.03734 1.51882 0.759408 0.650615i \(-0.225489\pi\)
0.759408 + 0.650615i \(0.225489\pi\)
\(12\) −0.916646 −0.264613
\(13\) 3.75894 1.04254 0.521272 0.853391i \(-0.325458\pi\)
0.521272 + 0.853391i \(0.325458\pi\)
\(14\) 2.30047 0.614826
\(15\) 1.65359 0.426954
\(16\) 1.00000 0.250000
\(17\) −1.14389 −0.277435 −0.138718 0.990332i \(-0.544298\pi\)
−0.138718 + 0.990332i \(0.544298\pi\)
\(18\) 2.15976 0.509060
\(19\) −1.00000 −0.229416
\(20\) −1.80395 −0.403376
\(21\) 2.10872 0.460160
\(22\) −5.03734 −1.07396
\(23\) −3.89553 −0.812273 −0.406137 0.913812i \(-0.633124\pi\)
−0.406137 + 0.913812i \(0.633124\pi\)
\(24\) 0.916646 0.187110
\(25\) −1.74576 −0.349151
\(26\) −3.75894 −0.737190
\(27\) 4.72967 0.910226
\(28\) −2.30047 −0.434748
\(29\) −6.08127 −1.12926 −0.564632 0.825343i \(-0.690982\pi\)
−0.564632 + 0.825343i \(0.690982\pi\)
\(30\) −1.65359 −0.301902
\(31\) 2.27780 0.409104 0.204552 0.978856i \(-0.434426\pi\)
0.204552 + 0.978856i \(0.434426\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.61746 −0.803796
\(34\) 1.14389 0.196176
\(35\) 4.14994 0.701467
\(36\) −2.15976 −0.359960
\(37\) 6.22253 1.02298 0.511489 0.859290i \(-0.329094\pi\)
0.511489 + 0.859290i \(0.329094\pi\)
\(38\) 1.00000 0.162221
\(39\) −3.44562 −0.551741
\(40\) 1.80395 0.285230
\(41\) 11.2605 1.75859 0.879294 0.476280i \(-0.158015\pi\)
0.879294 + 0.476280i \(0.158015\pi\)
\(42\) −2.10872 −0.325382
\(43\) −10.5371 −1.60689 −0.803444 0.595381i \(-0.797001\pi\)
−0.803444 + 0.595381i \(0.797001\pi\)
\(44\) 5.03734 0.759408
\(45\) 3.89610 0.580797
\(46\) 3.89553 0.574364
\(47\) −7.77272 −1.13377 −0.566884 0.823798i \(-0.691851\pi\)
−0.566884 + 0.823798i \(0.691851\pi\)
\(48\) −0.916646 −0.132306
\(49\) −1.70784 −0.243977
\(50\) 1.74576 0.246887
\(51\) 1.04855 0.146826
\(52\) 3.75894 0.521272
\(53\) 4.91807 0.675548 0.337774 0.941227i \(-0.390326\pi\)
0.337774 + 0.941227i \(0.390326\pi\)
\(54\) −4.72967 −0.643627
\(55\) −9.08712 −1.22531
\(56\) 2.30047 0.307413
\(57\) 0.916646 0.121413
\(58\) 6.08127 0.798510
\(59\) 0.349209 0.0454631 0.0227316 0.999742i \(-0.492764\pi\)
0.0227316 + 0.999742i \(0.492764\pi\)
\(60\) 1.65359 0.213477
\(61\) 1.02372 0.131073 0.0655367 0.997850i \(-0.479124\pi\)
0.0655367 + 0.997850i \(0.479124\pi\)
\(62\) −2.27780 −0.289280
\(63\) 4.96846 0.625967
\(64\) 1.00000 0.125000
\(65\) −6.78096 −0.841074
\(66\) 4.61746 0.568370
\(67\) 2.71873 0.332146 0.166073 0.986113i \(-0.446891\pi\)
0.166073 + 0.986113i \(0.446891\pi\)
\(68\) −1.14389 −0.138718
\(69\) 3.57082 0.429876
\(70\) −4.14994 −0.496012
\(71\) 7.52431 0.892972 0.446486 0.894791i \(-0.352675\pi\)
0.446486 + 0.894791i \(0.352675\pi\)
\(72\) 2.15976 0.254530
\(73\) −5.77390 −0.675784 −0.337892 0.941185i \(-0.609714\pi\)
−0.337892 + 0.941185i \(0.609714\pi\)
\(74\) −6.22253 −0.723354
\(75\) 1.60024 0.184780
\(76\) −1.00000 −0.114708
\(77\) −11.5882 −1.32060
\(78\) 3.44562 0.390140
\(79\) 1.97978 0.222743 0.111372 0.993779i \(-0.464476\pi\)
0.111372 + 0.993779i \(0.464476\pi\)
\(80\) −1.80395 −0.201688
\(81\) 2.14384 0.238205
\(82\) −11.2605 −1.24351
\(83\) −7.97117 −0.874949 −0.437475 0.899231i \(-0.644127\pi\)
−0.437475 + 0.899231i \(0.644127\pi\)
\(84\) 2.10872 0.230080
\(85\) 2.06353 0.223821
\(86\) 10.5371 1.13624
\(87\) 5.57437 0.597635
\(88\) −5.03734 −0.536982
\(89\) 8.56375 0.907755 0.453878 0.891064i \(-0.350040\pi\)
0.453878 + 0.891064i \(0.350040\pi\)
\(90\) −3.89610 −0.410685
\(91\) −8.64734 −0.906487
\(92\) −3.89553 −0.406137
\(93\) −2.08793 −0.216508
\(94\) 7.77272 0.801695
\(95\) 1.80395 0.185082
\(96\) 0.916646 0.0935548
\(97\) −8.80542 −0.894055 −0.447028 0.894520i \(-0.647517\pi\)
−0.447028 + 0.894520i \(0.647517\pi\)
\(98\) 1.70784 0.172518
\(99\) −10.8794 −1.09343
\(100\) −1.74576 −0.174576
\(101\) −0.929275 −0.0924663 −0.0462332 0.998931i \(-0.514722\pi\)
−0.0462332 + 0.998931i \(0.514722\pi\)
\(102\) −1.04855 −0.103822
\(103\) 6.26961 0.617763 0.308881 0.951101i \(-0.400045\pi\)
0.308881 + 0.951101i \(0.400045\pi\)
\(104\) −3.75894 −0.368595
\(105\) −3.80402 −0.371235
\(106\) −4.91807 −0.477685
\(107\) 9.91391 0.958413 0.479207 0.877702i \(-0.340924\pi\)
0.479207 + 0.877702i \(0.340924\pi\)
\(108\) 4.72967 0.455113
\(109\) 13.5714 1.29991 0.649954 0.759974i \(-0.274788\pi\)
0.649954 + 0.759974i \(0.274788\pi\)
\(110\) 9.08712 0.866423
\(111\) −5.70386 −0.541386
\(112\) −2.30047 −0.217374
\(113\) 1.30944 0.123182 0.0615910 0.998101i \(-0.480383\pi\)
0.0615910 + 0.998101i \(0.480383\pi\)
\(114\) −0.916646 −0.0858518
\(115\) 7.02734 0.655303
\(116\) −6.08127 −0.564632
\(117\) −8.11842 −0.750548
\(118\) −0.349209 −0.0321473
\(119\) 2.63149 0.241229
\(120\) −1.65359 −0.150951
\(121\) 14.3748 1.30680
\(122\) −1.02372 −0.0926829
\(123\) −10.3218 −0.930690
\(124\) 2.27780 0.204552
\(125\) 12.1690 1.08843
\(126\) −4.96846 −0.442626
\(127\) 19.3759 1.71933 0.859666 0.510856i \(-0.170671\pi\)
0.859666 + 0.510856i \(0.170671\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 9.65876 0.850406
\(130\) 6.78096 0.594729
\(131\) 19.6343 1.71546 0.857729 0.514102i \(-0.171875\pi\)
0.857729 + 0.514102i \(0.171875\pi\)
\(132\) −4.61746 −0.401898
\(133\) 2.30047 0.199476
\(134\) −2.71873 −0.234863
\(135\) −8.53210 −0.734327
\(136\) 1.14389 0.0980881
\(137\) 11.8902 1.01585 0.507926 0.861401i \(-0.330412\pi\)
0.507926 + 0.861401i \(0.330412\pi\)
\(138\) −3.57082 −0.303968
\(139\) 7.08368 0.600830 0.300415 0.953809i \(-0.402875\pi\)
0.300415 + 0.953809i \(0.402875\pi\)
\(140\) 4.14994 0.350734
\(141\) 7.12483 0.600019
\(142\) −7.52431 −0.631426
\(143\) 18.9351 1.58343
\(144\) −2.15976 −0.179980
\(145\) 10.9703 0.911036
\(146\) 5.77390 0.477852
\(147\) 1.56548 0.129119
\(148\) 6.22253 0.511489
\(149\) −19.2546 −1.57740 −0.788699 0.614780i \(-0.789245\pi\)
−0.788699 + 0.614780i \(0.789245\pi\)
\(150\) −1.60024 −0.130659
\(151\) 8.28752 0.674429 0.337215 0.941428i \(-0.390515\pi\)
0.337215 + 0.941428i \(0.390515\pi\)
\(152\) 1.00000 0.0811107
\(153\) 2.47054 0.199731
\(154\) 11.5882 0.933808
\(155\) −4.10903 −0.330046
\(156\) −3.44562 −0.275870
\(157\) −9.56476 −0.763351 −0.381676 0.924296i \(-0.624653\pi\)
−0.381676 + 0.924296i \(0.624653\pi\)
\(158\) −1.97978 −0.157503
\(159\) −4.50813 −0.357518
\(160\) 1.80395 0.142615
\(161\) 8.96154 0.706268
\(162\) −2.14384 −0.168436
\(163\) −8.95337 −0.701282 −0.350641 0.936510i \(-0.614036\pi\)
−0.350641 + 0.936510i \(0.614036\pi\)
\(164\) 11.2605 0.879294
\(165\) 8.32967 0.648464
\(166\) 7.97117 0.618682
\(167\) −13.8531 −1.07198 −0.535992 0.844223i \(-0.680062\pi\)
−0.535992 + 0.844223i \(0.680062\pi\)
\(168\) −2.10872 −0.162691
\(169\) 1.12966 0.0868970
\(170\) −2.06353 −0.158266
\(171\) 2.15976 0.165161
\(172\) −10.5371 −0.803444
\(173\) −6.26054 −0.475980 −0.237990 0.971268i \(-0.576488\pi\)
−0.237990 + 0.971268i \(0.576488\pi\)
\(174\) −5.57437 −0.422592
\(175\) 4.01606 0.303586
\(176\) 5.03734 0.379704
\(177\) −0.320101 −0.0240603
\(178\) −8.56375 −0.641880
\(179\) −10.0094 −0.748139 −0.374069 0.927401i \(-0.622038\pi\)
−0.374069 + 0.927401i \(0.622038\pi\)
\(180\) 3.89610 0.290398
\(181\) 3.46958 0.257892 0.128946 0.991652i \(-0.458841\pi\)
0.128946 + 0.991652i \(0.458841\pi\)
\(182\) 8.64734 0.640983
\(183\) −0.938385 −0.0693674
\(184\) 3.89553 0.287182
\(185\) −11.2251 −0.825289
\(186\) 2.08793 0.153095
\(187\) −5.76218 −0.421373
\(188\) −7.77272 −0.566884
\(189\) −10.8805 −0.791438
\(190\) −1.80395 −0.130872
\(191\) −10.8516 −0.785197 −0.392599 0.919710i \(-0.628424\pi\)
−0.392599 + 0.919710i \(0.628424\pi\)
\(192\) −0.916646 −0.0661532
\(193\) −21.2725 −1.53123 −0.765614 0.643300i \(-0.777565\pi\)
−0.765614 + 0.643300i \(0.777565\pi\)
\(194\) 8.80542 0.632192
\(195\) 6.21574 0.445118
\(196\) −1.70784 −0.121989
\(197\) 13.9011 0.990416 0.495208 0.868775i \(-0.335092\pi\)
0.495208 + 0.868775i \(0.335092\pi\)
\(198\) 10.8794 0.773169
\(199\) −4.74177 −0.336135 −0.168067 0.985775i \(-0.553753\pi\)
−0.168067 + 0.985775i \(0.553753\pi\)
\(200\) 1.74576 0.123444
\(201\) −2.49211 −0.175780
\(202\) 0.929275 0.0653836
\(203\) 13.9898 0.981890
\(204\) 1.04855 0.0734129
\(205\) −20.3133 −1.41874
\(206\) −6.26961 −0.436824
\(207\) 8.41340 0.584772
\(208\) 3.75894 0.260636
\(209\) −5.03734 −0.348440
\(210\) 3.80402 0.262503
\(211\) −1.00000 −0.0688428
\(212\) 4.91807 0.337774
\(213\) −6.89713 −0.472584
\(214\) −9.91391 −0.677701
\(215\) 19.0084 1.29636
\(216\) −4.72967 −0.321814
\(217\) −5.24000 −0.355714
\(218\) −13.5714 −0.919173
\(219\) 5.29263 0.357642
\(220\) −9.08712 −0.612654
\(221\) −4.29983 −0.289238
\(222\) 5.70386 0.382818
\(223\) 19.4130 1.29999 0.649996 0.759937i \(-0.274770\pi\)
0.649996 + 0.759937i \(0.274770\pi\)
\(224\) 2.30047 0.153707
\(225\) 3.77041 0.251361
\(226\) −1.30944 −0.0871028
\(227\) 0.405414 0.0269083 0.0134541 0.999909i \(-0.495717\pi\)
0.0134541 + 0.999909i \(0.495717\pi\)
\(228\) 0.916646 0.0607064
\(229\) −11.0518 −0.730321 −0.365160 0.930945i \(-0.618986\pi\)
−0.365160 + 0.930945i \(0.618986\pi\)
\(230\) −7.02734 −0.463369
\(231\) 10.6223 0.698898
\(232\) 6.08127 0.399255
\(233\) 26.9676 1.76670 0.883352 0.468711i \(-0.155281\pi\)
0.883352 + 0.468711i \(0.155281\pi\)
\(234\) 8.11842 0.530718
\(235\) 14.0216 0.914669
\(236\) 0.349209 0.0227316
\(237\) −1.81476 −0.117881
\(238\) −2.63149 −0.170574
\(239\) −5.99193 −0.387586 −0.193793 0.981042i \(-0.562079\pi\)
−0.193793 + 0.981042i \(0.562079\pi\)
\(240\) 1.65359 0.106738
\(241\) −13.9854 −0.900880 −0.450440 0.892807i \(-0.648733\pi\)
−0.450440 + 0.892807i \(0.648733\pi\)
\(242\) −14.3748 −0.924047
\(243\) −16.1542 −1.03629
\(244\) 1.02372 0.0655367
\(245\) 3.08086 0.196829
\(246\) 10.3218 0.658097
\(247\) −3.75894 −0.239176
\(248\) −2.27780 −0.144640
\(249\) 7.30674 0.463046
\(250\) −12.1690 −0.769637
\(251\) −3.43023 −0.216514 −0.108257 0.994123i \(-0.534527\pi\)
−0.108257 + 0.994123i \(0.534527\pi\)
\(252\) 4.96846 0.312984
\(253\) −19.6231 −1.23369
\(254\) −19.3759 −1.21575
\(255\) −1.89153 −0.118452
\(256\) 1.00000 0.0625000
\(257\) −29.4124 −1.83469 −0.917347 0.398090i \(-0.869673\pi\)
−0.917347 + 0.398090i \(0.869673\pi\)
\(258\) −9.65876 −0.601328
\(259\) −14.3147 −0.889475
\(260\) −6.78096 −0.420537
\(261\) 13.1341 0.812979
\(262\) −19.6343 −1.21301
\(263\) 3.88200 0.239374 0.119687 0.992812i \(-0.461811\pi\)
0.119687 + 0.992812i \(0.461811\pi\)
\(264\) 4.61746 0.284185
\(265\) −8.87196 −0.545000
\(266\) −2.30047 −0.141051
\(267\) −7.84993 −0.480408
\(268\) 2.71873 0.166073
\(269\) 29.0181 1.76926 0.884631 0.466292i \(-0.154410\pi\)
0.884631 + 0.466292i \(0.154410\pi\)
\(270\) 8.53210 0.519247
\(271\) −18.6560 −1.13327 −0.566635 0.823969i \(-0.691755\pi\)
−0.566635 + 0.823969i \(0.691755\pi\)
\(272\) −1.14389 −0.0693588
\(273\) 7.92655 0.479736
\(274\) −11.8902 −0.718316
\(275\) −8.79397 −0.530296
\(276\) 3.57082 0.214938
\(277\) −10.7555 −0.646235 −0.323118 0.946359i \(-0.604731\pi\)
−0.323118 + 0.946359i \(0.604731\pi\)
\(278\) −7.08368 −0.424851
\(279\) −4.91949 −0.294522
\(280\) −4.14994 −0.248006
\(281\) 3.44052 0.205244 0.102622 0.994720i \(-0.467277\pi\)
0.102622 + 0.994720i \(0.467277\pi\)
\(282\) −7.12483 −0.424278
\(283\) 12.3736 0.735532 0.367766 0.929918i \(-0.380123\pi\)
0.367766 + 0.929918i \(0.380123\pi\)
\(284\) 7.52431 0.446486
\(285\) −1.65359 −0.0979500
\(286\) −18.9351 −1.11965
\(287\) −25.9043 −1.52908
\(288\) 2.15976 0.127265
\(289\) −15.6915 −0.923030
\(290\) −10.9703 −0.644199
\(291\) 8.07145 0.473157
\(292\) −5.77390 −0.337892
\(293\) −26.9137 −1.57232 −0.786159 0.618024i \(-0.787933\pi\)
−0.786159 + 0.618024i \(0.787933\pi\)
\(294\) −1.56548 −0.0913009
\(295\) −0.629956 −0.0366775
\(296\) −6.22253 −0.361677
\(297\) 23.8250 1.38247
\(298\) 19.2546 1.11539
\(299\) −14.6431 −0.846830
\(300\) 1.60024 0.0923899
\(301\) 24.2402 1.39718
\(302\) −8.28752 −0.476893
\(303\) 0.851816 0.0489356
\(304\) −1.00000 −0.0573539
\(305\) −1.84673 −0.105744
\(306\) −2.47054 −0.141231
\(307\) −6.75633 −0.385604 −0.192802 0.981238i \(-0.561758\pi\)
−0.192802 + 0.981238i \(0.561758\pi\)
\(308\) −11.5882 −0.660302
\(309\) −5.74701 −0.326936
\(310\) 4.10903 0.233377
\(311\) 12.3349 0.699447 0.349723 0.936853i \(-0.386276\pi\)
0.349723 + 0.936853i \(0.386276\pi\)
\(312\) 3.44562 0.195070
\(313\) −24.5621 −1.38833 −0.694165 0.719816i \(-0.744226\pi\)
−0.694165 + 0.719816i \(0.744226\pi\)
\(314\) 9.56476 0.539771
\(315\) −8.96287 −0.505000
\(316\) 1.97978 0.111372
\(317\) −0.769189 −0.0432020 −0.0216010 0.999767i \(-0.506876\pi\)
−0.0216010 + 0.999767i \(0.506876\pi\)
\(318\) 4.50813 0.252803
\(319\) −30.6334 −1.71514
\(320\) −1.80395 −0.100844
\(321\) −9.08754 −0.507217
\(322\) −8.96154 −0.499407
\(323\) 1.14389 0.0636480
\(324\) 2.14384 0.119102
\(325\) −6.56220 −0.364005
\(326\) 8.95337 0.495882
\(327\) −12.4402 −0.687945
\(328\) −11.2605 −0.621755
\(329\) 17.8809 0.985806
\(330\) −8.32967 −0.458533
\(331\) −12.0282 −0.661129 −0.330565 0.943783i \(-0.607239\pi\)
−0.330565 + 0.943783i \(0.607239\pi\)
\(332\) −7.97117 −0.437475
\(333\) −13.4392 −0.736462
\(334\) 13.8531 0.758007
\(335\) −4.90446 −0.267959
\(336\) 2.10872 0.115040
\(337\) 1.51714 0.0826441 0.0413220 0.999146i \(-0.486843\pi\)
0.0413220 + 0.999146i \(0.486843\pi\)
\(338\) −1.12966 −0.0614455
\(339\) −1.20029 −0.0651911
\(340\) 2.06353 0.111911
\(341\) 11.4740 0.621354
\(342\) −2.15976 −0.116786
\(343\) 20.0321 1.08163
\(344\) 10.5371 0.568120
\(345\) −6.44159 −0.346803
\(346\) 6.26054 0.336568
\(347\) −8.02304 −0.430699 −0.215350 0.976537i \(-0.569089\pi\)
−0.215350 + 0.976537i \(0.569089\pi\)
\(348\) 5.57437 0.298818
\(349\) −32.8943 −1.76079 −0.880394 0.474242i \(-0.842722\pi\)
−0.880394 + 0.474242i \(0.842722\pi\)
\(350\) −4.01606 −0.214667
\(351\) 17.7786 0.948950
\(352\) −5.03734 −0.268491
\(353\) −2.29128 −0.121952 −0.0609761 0.998139i \(-0.519421\pi\)
−0.0609761 + 0.998139i \(0.519421\pi\)
\(354\) 0.320101 0.0170132
\(355\) −13.5735 −0.720407
\(356\) 8.56375 0.453878
\(357\) −2.41215 −0.127664
\(358\) 10.0094 0.529014
\(359\) −14.9524 −0.789157 −0.394579 0.918862i \(-0.629109\pi\)
−0.394579 + 0.918862i \(0.629109\pi\)
\(360\) −3.89610 −0.205343
\(361\) 1.00000 0.0526316
\(362\) −3.46958 −0.182357
\(363\) −13.1766 −0.691593
\(364\) −8.64734 −0.453244
\(365\) 10.4158 0.545190
\(366\) 0.938385 0.0490502
\(367\) 7.59164 0.396281 0.198140 0.980174i \(-0.436510\pi\)
0.198140 + 0.980174i \(0.436510\pi\)
\(368\) −3.89553 −0.203068
\(369\) −24.3199 −1.26604
\(370\) 11.2251 0.583568
\(371\) −11.3139 −0.587386
\(372\) −2.08793 −0.108254
\(373\) −15.0313 −0.778292 −0.389146 0.921176i \(-0.627230\pi\)
−0.389146 + 0.921176i \(0.627230\pi\)
\(374\) 5.76218 0.297955
\(375\) −11.1547 −0.576025
\(376\) 7.77272 0.400847
\(377\) −22.8592 −1.17731
\(378\) 10.8805 0.559631
\(379\) −16.5727 −0.851282 −0.425641 0.904892i \(-0.639951\pi\)
−0.425641 + 0.904892i \(0.639951\pi\)
\(380\) 1.80395 0.0925408
\(381\) −17.7608 −0.909915
\(382\) 10.8516 0.555218
\(383\) −12.1259 −0.619603 −0.309801 0.950801i \(-0.600263\pi\)
−0.309801 + 0.950801i \(0.600263\pi\)
\(384\) 0.916646 0.0467774
\(385\) 20.9046 1.06540
\(386\) 21.2725 1.08274
\(387\) 22.7575 1.15683
\(388\) −8.80542 −0.447028
\(389\) −0.291108 −0.0147597 −0.00737987 0.999973i \(-0.502349\pi\)
−0.00737987 + 0.999973i \(0.502349\pi\)
\(390\) −6.21574 −0.314746
\(391\) 4.45607 0.225353
\(392\) 1.70784 0.0862589
\(393\) −17.9977 −0.907864
\(394\) −13.9011 −0.700330
\(395\) −3.57144 −0.179698
\(396\) −10.8794 −0.546713
\(397\) −32.4759 −1.62992 −0.814960 0.579518i \(-0.803241\pi\)
−0.814960 + 0.579518i \(0.803241\pi\)
\(398\) 4.74177 0.237683
\(399\) −2.10872 −0.105568
\(400\) −1.74576 −0.0872878
\(401\) 17.3177 0.864804 0.432402 0.901681i \(-0.357666\pi\)
0.432402 + 0.901681i \(0.357666\pi\)
\(402\) 2.49211 0.124295
\(403\) 8.56211 0.426509
\(404\) −0.929275 −0.0462332
\(405\) −3.86739 −0.192172
\(406\) −13.9898 −0.694301
\(407\) 31.3450 1.55371
\(408\) −1.04855 −0.0519108
\(409\) 19.0537 0.942143 0.471071 0.882095i \(-0.343867\pi\)
0.471071 + 0.882095i \(0.343867\pi\)
\(410\) 20.3133 1.00320
\(411\) −10.8991 −0.537615
\(412\) 6.26961 0.308881
\(413\) −0.803345 −0.0395300
\(414\) −8.41340 −0.413496
\(415\) 14.3796 0.705867
\(416\) −3.75894 −0.184297
\(417\) −6.49322 −0.317975
\(418\) 5.03734 0.246384
\(419\) 8.34101 0.407485 0.203743 0.979024i \(-0.434689\pi\)
0.203743 + 0.979024i \(0.434689\pi\)
\(420\) −3.80402 −0.185617
\(421\) −11.4766 −0.559336 −0.279668 0.960097i \(-0.590224\pi\)
−0.279668 + 0.960097i \(0.590224\pi\)
\(422\) 1.00000 0.0486792
\(423\) 16.7872 0.816222
\(424\) −4.91807 −0.238842
\(425\) 1.99696 0.0968668
\(426\) 6.89713 0.334167
\(427\) −2.35503 −0.113968
\(428\) 9.91391 0.479207
\(429\) −17.3568 −0.837993
\(430\) −19.0084 −0.916664
\(431\) −8.54311 −0.411507 −0.205754 0.978604i \(-0.565965\pi\)
−0.205754 + 0.978604i \(0.565965\pi\)
\(432\) 4.72967 0.227557
\(433\) 28.9936 1.39334 0.696671 0.717391i \(-0.254664\pi\)
0.696671 + 0.717391i \(0.254664\pi\)
\(434\) 5.24000 0.251528
\(435\) −10.0559 −0.482144
\(436\) 13.5714 0.649954
\(437\) 3.89553 0.186348
\(438\) −5.29263 −0.252891
\(439\) −29.5292 −1.40935 −0.704676 0.709530i \(-0.748907\pi\)
−0.704676 + 0.709530i \(0.748907\pi\)
\(440\) 9.08712 0.433212
\(441\) 3.68852 0.175644
\(442\) 4.29983 0.204522
\(443\) −25.1195 −1.19346 −0.596732 0.802440i \(-0.703535\pi\)
−0.596732 + 0.802440i \(0.703535\pi\)
\(444\) −5.70386 −0.270693
\(445\) −15.4486 −0.732334
\(446\) −19.4130 −0.919234
\(447\) 17.6496 0.834800
\(448\) −2.30047 −0.108687
\(449\) 22.6595 1.06937 0.534683 0.845053i \(-0.320431\pi\)
0.534683 + 0.845053i \(0.320431\pi\)
\(450\) −3.77041 −0.177739
\(451\) 56.7227 2.67097
\(452\) 1.30944 0.0615910
\(453\) −7.59673 −0.356925
\(454\) −0.405414 −0.0190270
\(455\) 15.5994 0.731310
\(456\) −0.916646 −0.0429259
\(457\) 29.8646 1.39701 0.698503 0.715607i \(-0.253850\pi\)
0.698503 + 0.715607i \(0.253850\pi\)
\(458\) 11.0518 0.516415
\(459\) −5.41024 −0.252529
\(460\) 7.02734 0.327652
\(461\) −19.8220 −0.923204 −0.461602 0.887087i \(-0.652725\pi\)
−0.461602 + 0.887087i \(0.652725\pi\)
\(462\) −10.6223 −0.494195
\(463\) 19.5899 0.910418 0.455209 0.890385i \(-0.349565\pi\)
0.455209 + 0.890385i \(0.349565\pi\)
\(464\) −6.08127 −0.282316
\(465\) 3.76653 0.174669
\(466\) −26.9676 −1.24925
\(467\) 31.7186 1.46776 0.733881 0.679278i \(-0.237707\pi\)
0.733881 + 0.679278i \(0.237707\pi\)
\(468\) −8.11842 −0.375274
\(469\) −6.25436 −0.288799
\(470\) −14.0216 −0.646769
\(471\) 8.76750 0.403985
\(472\) −0.349209 −0.0160736
\(473\) −53.0788 −2.44056
\(474\) 1.81476 0.0833547
\(475\) 1.74576 0.0801008
\(476\) 2.63149 0.120614
\(477\) −10.6218 −0.486341
\(478\) 5.99193 0.274064
\(479\) 22.0025 1.00532 0.502661 0.864484i \(-0.332354\pi\)
0.502661 + 0.864484i \(0.332354\pi\)
\(480\) −1.65359 −0.0754755
\(481\) 23.3901 1.06650
\(482\) 13.9854 0.637018
\(483\) −8.21456 −0.373775
\(484\) 14.3748 0.653400
\(485\) 15.8846 0.721281
\(486\) 16.1542 0.732768
\(487\) −13.3471 −0.604814 −0.302407 0.953179i \(-0.597790\pi\)
−0.302407 + 0.953179i \(0.597790\pi\)
\(488\) −1.02372 −0.0463415
\(489\) 8.20707 0.371137
\(490\) −3.08086 −0.139179
\(491\) −31.5431 −1.42352 −0.711759 0.702424i \(-0.752101\pi\)
−0.711759 + 0.702424i \(0.752101\pi\)
\(492\) −10.3218 −0.465345
\(493\) 6.95633 0.313297
\(494\) 3.75894 0.169123
\(495\) 19.6260 0.882123
\(496\) 2.27780 0.102276
\(497\) −17.3095 −0.776435
\(498\) −7.30674 −0.327423
\(499\) 14.3523 0.642497 0.321248 0.946995i \(-0.395898\pi\)
0.321248 + 0.946995i \(0.395898\pi\)
\(500\) 12.1690 0.544215
\(501\) 12.6984 0.567322
\(502\) 3.43023 0.153099
\(503\) −33.9717 −1.51472 −0.757362 0.652996i \(-0.773512\pi\)
−0.757362 + 0.652996i \(0.773512\pi\)
\(504\) −4.96846 −0.221313
\(505\) 1.67637 0.0745974
\(506\) 19.6231 0.872353
\(507\) −1.03550 −0.0459881
\(508\) 19.3759 0.859666
\(509\) −12.1682 −0.539348 −0.269674 0.962952i \(-0.586916\pi\)
−0.269674 + 0.962952i \(0.586916\pi\)
\(510\) 1.89153 0.0837582
\(511\) 13.2827 0.587592
\(512\) −1.00000 −0.0441942
\(513\) −4.72967 −0.208820
\(514\) 29.4124 1.29732
\(515\) −11.3101 −0.498381
\(516\) 9.65876 0.425203
\(517\) −39.1538 −1.72198
\(518\) 14.3147 0.628954
\(519\) 5.73869 0.251901
\(520\) 6.78096 0.297365
\(521\) 30.0526 1.31663 0.658314 0.752744i \(-0.271270\pi\)
0.658314 + 0.752744i \(0.271270\pi\)
\(522\) −13.1341 −0.574863
\(523\) 11.1640 0.488169 0.244084 0.969754i \(-0.421513\pi\)
0.244084 + 0.969754i \(0.421513\pi\)
\(524\) 19.6343 0.857729
\(525\) −3.68130 −0.160665
\(526\) −3.88200 −0.169263
\(527\) −2.60556 −0.113500
\(528\) −4.61746 −0.200949
\(529\) −7.82487 −0.340212
\(530\) 8.87196 0.385373
\(531\) −0.754208 −0.0327298
\(532\) 2.30047 0.0997380
\(533\) 42.3274 1.83340
\(534\) 7.84993 0.339699
\(535\) −17.8842 −0.773202
\(536\) −2.71873 −0.117431
\(537\) 9.17509 0.395934
\(538\) −29.0181 −1.25106
\(539\) −8.60297 −0.370556
\(540\) −8.53210 −0.367163
\(541\) −25.0047 −1.07504 −0.537519 0.843252i \(-0.680638\pi\)
−0.537519 + 0.843252i \(0.680638\pi\)
\(542\) 18.6560 0.801343
\(543\) −3.18038 −0.136483
\(544\) 1.14389 0.0490440
\(545\) −24.4822 −1.04870
\(546\) −7.92655 −0.339225
\(547\) −27.0033 −1.15458 −0.577289 0.816540i \(-0.695889\pi\)
−0.577289 + 0.816540i \(0.695889\pi\)
\(548\) 11.8902 0.507926
\(549\) −2.21098 −0.0943624
\(550\) 8.79397 0.374976
\(551\) 6.08127 0.259071
\(552\) −3.57082 −0.151984
\(553\) −4.55443 −0.193674
\(554\) 10.7555 0.456957
\(555\) 10.2895 0.436764
\(556\) 7.08368 0.300415
\(557\) 29.5619 1.25258 0.626290 0.779590i \(-0.284573\pi\)
0.626290 + 0.779590i \(0.284573\pi\)
\(558\) 4.91949 0.208259
\(559\) −39.6082 −1.67525
\(560\) 4.14994 0.175367
\(561\) 5.28188 0.223001
\(562\) −3.44052 −0.145130
\(563\) −31.8337 −1.34163 −0.670816 0.741624i \(-0.734056\pi\)
−0.670816 + 0.741624i \(0.734056\pi\)
\(564\) 7.12483 0.300010
\(565\) −2.36217 −0.0993773
\(566\) −12.3736 −0.520099
\(567\) −4.93185 −0.207118
\(568\) −7.52431 −0.315713
\(569\) 38.0016 1.59311 0.796555 0.604566i \(-0.206654\pi\)
0.796555 + 0.604566i \(0.206654\pi\)
\(570\) 1.65359 0.0692611
\(571\) −23.6507 −0.989752 −0.494876 0.868964i \(-0.664786\pi\)
−0.494876 + 0.868964i \(0.664786\pi\)
\(572\) 18.9351 0.791716
\(573\) 9.94711 0.415547
\(574\) 25.9043 1.08123
\(575\) 6.80064 0.283606
\(576\) −2.15976 −0.0899900
\(577\) 39.7472 1.65470 0.827349 0.561689i \(-0.189848\pi\)
0.827349 + 0.561689i \(0.189848\pi\)
\(578\) 15.6915 0.652681
\(579\) 19.4994 0.810366
\(580\) 10.9703 0.455518
\(581\) 18.3374 0.760765
\(582\) −8.07145 −0.334573
\(583\) 24.7740 1.02603
\(584\) 5.77390 0.238926
\(585\) 14.6452 0.605506
\(586\) 26.9137 1.11180
\(587\) −34.1703 −1.41036 −0.705179 0.709029i \(-0.749133\pi\)
−0.705179 + 0.709029i \(0.749133\pi\)
\(588\) 1.56548 0.0645595
\(589\) −2.27780 −0.0938549
\(590\) 0.629956 0.0259349
\(591\) −12.7424 −0.524153
\(592\) 6.22253 0.255744
\(593\) 5.27597 0.216658 0.108329 0.994115i \(-0.465450\pi\)
0.108329 + 0.994115i \(0.465450\pi\)
\(594\) −23.8250 −0.977551
\(595\) −4.74709 −0.194612
\(596\) −19.2546 −0.788699
\(597\) 4.34652 0.177891
\(598\) 14.6431 0.598800
\(599\) −30.3111 −1.23848 −0.619239 0.785203i \(-0.712559\pi\)
−0.619239 + 0.785203i \(0.712559\pi\)
\(600\) −1.60024 −0.0653295
\(601\) −1.51024 −0.0616038 −0.0308019 0.999526i \(-0.509806\pi\)
−0.0308019 + 0.999526i \(0.509806\pi\)
\(602\) −24.2402 −0.987957
\(603\) −5.87181 −0.239118
\(604\) 8.28752 0.337215
\(605\) −25.9315 −1.05426
\(606\) −0.851816 −0.0346027
\(607\) 14.9361 0.606238 0.303119 0.952953i \(-0.401972\pi\)
0.303119 + 0.952953i \(0.401972\pi\)
\(608\) 1.00000 0.0405554
\(609\) −12.8237 −0.519641
\(610\) 1.84673 0.0747721
\(611\) −29.2172 −1.18200
\(612\) 2.47054 0.0998655
\(613\) −4.57905 −0.184946 −0.0924730 0.995715i \(-0.529477\pi\)
−0.0924730 + 0.995715i \(0.529477\pi\)
\(614\) 6.75633 0.272663
\(615\) 18.6201 0.750836
\(616\) 11.5882 0.466904
\(617\) −41.9578 −1.68916 −0.844579 0.535430i \(-0.820149\pi\)
−0.844579 + 0.535430i \(0.820149\pi\)
\(618\) 5.74701 0.231179
\(619\) −11.7878 −0.473793 −0.236896 0.971535i \(-0.576130\pi\)
−0.236896 + 0.971535i \(0.576130\pi\)
\(620\) −4.10903 −0.165023
\(621\) −18.4246 −0.739352
\(622\) −12.3349 −0.494584
\(623\) −19.7006 −0.789290
\(624\) −3.44562 −0.137935
\(625\) −13.2236 −0.528942
\(626\) 24.5621 0.981698
\(627\) 4.61746 0.184404
\(628\) −9.56476 −0.381676
\(629\) −7.11791 −0.283810
\(630\) 8.96287 0.357089
\(631\) −31.5924 −1.25767 −0.628837 0.777537i \(-0.716469\pi\)
−0.628837 + 0.777537i \(0.716469\pi\)
\(632\) −1.97978 −0.0787516
\(633\) 0.916646 0.0364334
\(634\) 0.769189 0.0305484
\(635\) −34.9532 −1.38708
\(636\) −4.50813 −0.178759
\(637\) −6.41967 −0.254357
\(638\) 30.6334 1.21279
\(639\) −16.2507 −0.642868
\(640\) 1.80395 0.0713075
\(641\) 12.2690 0.484597 0.242298 0.970202i \(-0.422099\pi\)
0.242298 + 0.970202i \(0.422099\pi\)
\(642\) 9.08754 0.358657
\(643\) −33.0276 −1.30248 −0.651241 0.758871i \(-0.725751\pi\)
−0.651241 + 0.758871i \(0.725751\pi\)
\(644\) 8.96154 0.353134
\(645\) −17.4239 −0.686067
\(646\) −1.14389 −0.0450059
\(647\) −10.2503 −0.402982 −0.201491 0.979490i \(-0.564579\pi\)
−0.201491 + 0.979490i \(0.564579\pi\)
\(648\) −2.14384 −0.0842182
\(649\) 1.75908 0.0690501
\(650\) 6.56220 0.257391
\(651\) 4.80322 0.188253
\(652\) −8.95337 −0.350641
\(653\) 36.6172 1.43294 0.716471 0.697617i \(-0.245756\pi\)
0.716471 + 0.697617i \(0.245756\pi\)
\(654\) 12.4402 0.486450
\(655\) −35.4194 −1.38395
\(656\) 11.2605 0.439647
\(657\) 12.4702 0.486511
\(658\) −17.8809 −0.697070
\(659\) −9.86508 −0.384289 −0.192145 0.981367i \(-0.561544\pi\)
−0.192145 + 0.981367i \(0.561544\pi\)
\(660\) 8.32967 0.324232
\(661\) 31.3352 1.21880 0.609398 0.792864i \(-0.291411\pi\)
0.609398 + 0.792864i \(0.291411\pi\)
\(662\) 12.0282 0.467489
\(663\) 3.94143 0.153072
\(664\) 7.97117 0.309341
\(665\) −4.14994 −0.160928
\(666\) 13.4392 0.520757
\(667\) 23.6897 0.917271
\(668\) −13.8531 −0.535992
\(669\) −17.7949 −0.687990
\(670\) 4.90446 0.189476
\(671\) 5.15681 0.199076
\(672\) −2.10872 −0.0813455
\(673\) −3.11963 −0.120253 −0.0601264 0.998191i \(-0.519150\pi\)
−0.0601264 + 0.998191i \(0.519150\pi\)
\(674\) −1.51714 −0.0584382
\(675\) −8.25686 −0.317807
\(676\) 1.12966 0.0434485
\(677\) 28.6072 1.09946 0.549732 0.835341i \(-0.314730\pi\)
0.549732 + 0.835341i \(0.314730\pi\)
\(678\) 1.20029 0.0460971
\(679\) 20.2566 0.777377
\(680\) −2.06353 −0.0791328
\(681\) −0.371621 −0.0142406
\(682\) −11.4740 −0.439363
\(683\) −3.83116 −0.146595 −0.0732976 0.997310i \(-0.523352\pi\)
−0.0732976 + 0.997310i \(0.523352\pi\)
\(684\) 2.15976 0.0825805
\(685\) −21.4494 −0.819541
\(686\) −20.0321 −0.764830
\(687\) 10.1305 0.386504
\(688\) −10.5371 −0.401722
\(689\) 18.4867 0.704289
\(690\) 6.44159 0.245227
\(691\) 13.4824 0.512893 0.256447 0.966558i \(-0.417448\pi\)
0.256447 + 0.966558i \(0.417448\pi\)
\(692\) −6.26054 −0.237990
\(693\) 25.0278 0.950729
\(694\) 8.02304 0.304550
\(695\) −12.7786 −0.484721
\(696\) −5.57437 −0.211296
\(697\) −12.8808 −0.487894
\(698\) 32.8943 1.24507
\(699\) −24.7197 −0.934985
\(700\) 4.01606 0.151793
\(701\) 1.49666 0.0565281 0.0282640 0.999600i \(-0.491002\pi\)
0.0282640 + 0.999600i \(0.491002\pi\)
\(702\) −17.7786 −0.671009
\(703\) −6.22253 −0.234687
\(704\) 5.03734 0.189852
\(705\) −12.8529 −0.484067
\(706\) 2.29128 0.0862333
\(707\) 2.13777 0.0803991
\(708\) −0.320101 −0.0120301
\(709\) −12.8767 −0.483595 −0.241797 0.970327i \(-0.577737\pi\)
−0.241797 + 0.970327i \(0.577737\pi\)
\(710\) 13.5735 0.509404
\(711\) −4.27586 −0.160357
\(712\) −8.56375 −0.320940
\(713\) −8.87321 −0.332304
\(714\) 2.41215 0.0902724
\(715\) −34.1580 −1.27744
\(716\) −10.0094 −0.374069
\(717\) 5.49248 0.205120
\(718\) 14.9524 0.558018
\(719\) 8.83064 0.329327 0.164664 0.986350i \(-0.447346\pi\)
0.164664 + 0.986350i \(0.447346\pi\)
\(720\) 3.89610 0.145199
\(721\) −14.4230 −0.537142
\(722\) −1.00000 −0.0372161
\(723\) 12.8197 0.476769
\(724\) 3.46958 0.128946
\(725\) 10.6164 0.394284
\(726\) 13.1766 0.489030
\(727\) −48.4962 −1.79862 −0.899312 0.437308i \(-0.855932\pi\)
−0.899312 + 0.437308i \(0.855932\pi\)
\(728\) 8.64734 0.320492
\(729\) 8.37612 0.310227
\(730\) −10.4158 −0.385508
\(731\) 12.0533 0.445807
\(732\) −0.938385 −0.0346837
\(733\) −8.35967 −0.308771 −0.154386 0.988011i \(-0.549340\pi\)
−0.154386 + 0.988011i \(0.549340\pi\)
\(734\) −7.59164 −0.280213
\(735\) −2.82406 −0.104167
\(736\) 3.89553 0.143591
\(737\) 13.6952 0.504468
\(738\) 24.3199 0.895227
\(739\) −15.1413 −0.556983 −0.278491 0.960439i \(-0.589834\pi\)
−0.278491 + 0.960439i \(0.589834\pi\)
\(740\) −11.2251 −0.412645
\(741\) 3.44562 0.126578
\(742\) 11.3139 0.415345
\(743\) −27.4040 −1.00536 −0.502678 0.864474i \(-0.667652\pi\)
−0.502678 + 0.864474i \(0.667652\pi\)
\(744\) 2.08793 0.0765473
\(745\) 34.7344 1.27257
\(746\) 15.0313 0.550335
\(747\) 17.2158 0.629893
\(748\) −5.76218 −0.210686
\(749\) −22.8066 −0.833336
\(750\) 11.1547 0.407312
\(751\) −3.93228 −0.143491 −0.0717454 0.997423i \(-0.522857\pi\)
−0.0717454 + 0.997423i \(0.522857\pi\)
\(752\) −7.77272 −0.283442
\(753\) 3.14431 0.114585
\(754\) 22.8592 0.832481
\(755\) −14.9503 −0.544097
\(756\) −10.8805 −0.395719
\(757\) −22.4832 −0.817166 −0.408583 0.912721i \(-0.633977\pi\)
−0.408583 + 0.912721i \(0.633977\pi\)
\(758\) 16.5727 0.601947
\(759\) 17.9874 0.652902
\(760\) −1.80395 −0.0654362
\(761\) 16.6118 0.602178 0.301089 0.953596i \(-0.402650\pi\)
0.301089 + 0.953596i \(0.402650\pi\)
\(762\) 17.7608 0.643407
\(763\) −31.2207 −1.13026
\(764\) −10.8516 −0.392599
\(765\) −4.45673 −0.161133
\(766\) 12.1259 0.438125
\(767\) 1.31266 0.0473973
\(768\) −0.916646 −0.0330766
\(769\) −40.5577 −1.46255 −0.731274 0.682084i \(-0.761074\pi\)
−0.731274 + 0.682084i \(0.761074\pi\)
\(770\) −20.9046 −0.753351
\(771\) 26.9607 0.970967
\(772\) −21.2725 −0.765614
\(773\) −28.5300 −1.02615 −0.513077 0.858343i \(-0.671495\pi\)
−0.513077 + 0.858343i \(0.671495\pi\)
\(774\) −22.7575 −0.818002
\(775\) −3.97648 −0.142839
\(776\) 8.80542 0.316096
\(777\) 13.1215 0.470733
\(778\) 0.291108 0.0104367
\(779\) −11.2605 −0.403448
\(780\) 6.21574 0.222559
\(781\) 37.9025 1.35626
\(782\) −4.45607 −0.159349
\(783\) −28.7624 −1.02789
\(784\) −1.70784 −0.0609943
\(785\) 17.2544 0.615835
\(786\) 17.9977 0.641957
\(787\) −21.7389 −0.774908 −0.387454 0.921889i \(-0.626645\pi\)
−0.387454 + 0.921889i \(0.626645\pi\)
\(788\) 13.9011 0.495208
\(789\) −3.55842 −0.126683
\(790\) 3.57144 0.127066
\(791\) −3.01233 −0.107106
\(792\) 10.8794 0.386584
\(793\) 3.84809 0.136650
\(794\) 32.4759 1.15253
\(795\) 8.13244 0.288428
\(796\) −4.74177 −0.168067
\(797\) −8.16785 −0.289320 −0.144660 0.989481i \(-0.546209\pi\)
−0.144660 + 0.989481i \(0.546209\pi\)
\(798\) 2.10872 0.0746477
\(799\) 8.89117 0.314547
\(800\) 1.74576 0.0617218
\(801\) −18.4956 −0.653511
\(802\) −17.3177 −0.611509
\(803\) −29.0851 −1.02639
\(804\) −2.49211 −0.0878901
\(805\) −16.1662 −0.569783
\(806\) −8.56211 −0.301587
\(807\) −26.5993 −0.936339
\(808\) 0.929275 0.0326918
\(809\) 56.0399 1.97026 0.985129 0.171814i \(-0.0549628\pi\)
0.985129 + 0.171814i \(0.0549628\pi\)
\(810\) 3.86739 0.135886
\(811\) 24.5101 0.860665 0.430332 0.902671i \(-0.358396\pi\)
0.430332 + 0.902671i \(0.358396\pi\)
\(812\) 13.9898 0.490945
\(813\) 17.1009 0.599756
\(814\) −31.3450 −1.09864
\(815\) 16.1515 0.565761
\(816\) 1.04855 0.0367064
\(817\) 10.5371 0.368645
\(818\) −19.0537 −0.666196
\(819\) 18.6762 0.652598
\(820\) −20.3133 −0.709372
\(821\) −37.7694 −1.31816 −0.659081 0.752072i \(-0.729055\pi\)
−0.659081 + 0.752072i \(0.729055\pi\)
\(822\) 10.8991 0.380151
\(823\) −40.6626 −1.41741 −0.708704 0.705506i \(-0.750720\pi\)
−0.708704 + 0.705506i \(0.750720\pi\)
\(824\) −6.26961 −0.218412
\(825\) 8.06096 0.280647
\(826\) 0.803345 0.0279519
\(827\) 15.1717 0.527573 0.263786 0.964581i \(-0.415029\pi\)
0.263786 + 0.964581i \(0.415029\pi\)
\(828\) 8.41340 0.292386
\(829\) −13.2935 −0.461702 −0.230851 0.972989i \(-0.574151\pi\)
−0.230851 + 0.972989i \(0.574151\pi\)
\(830\) −14.3796 −0.499123
\(831\) 9.85898 0.342004
\(832\) 3.75894 0.130318
\(833\) 1.95359 0.0676878
\(834\) 6.49322 0.224842
\(835\) 24.9903 0.864825
\(836\) −5.03734 −0.174220
\(837\) 10.7732 0.372377
\(838\) −8.34101 −0.288136
\(839\) −42.0679 −1.45235 −0.726173 0.687512i \(-0.758703\pi\)
−0.726173 + 0.687512i \(0.758703\pi\)
\(840\) 3.80402 0.131251
\(841\) 7.98185 0.275236
\(842\) 11.4766 0.395510
\(843\) −3.15374 −0.108621
\(844\) −1.00000 −0.0344214
\(845\) −2.03785 −0.0701043
\(846\) −16.7872 −0.577156
\(847\) −33.0688 −1.13626
\(848\) 4.91807 0.168887
\(849\) −11.3422 −0.389262
\(850\) −1.99696 −0.0684952
\(851\) −24.2400 −0.830937
\(852\) −6.89713 −0.236292
\(853\) −38.7786 −1.32775 −0.663877 0.747842i \(-0.731090\pi\)
−0.663877 + 0.747842i \(0.731090\pi\)
\(854\) 2.35503 0.0805874
\(855\) −3.89610 −0.133244
\(856\) −9.91391 −0.338850
\(857\) 41.5158 1.41815 0.709077 0.705131i \(-0.249112\pi\)
0.709077 + 0.705131i \(0.249112\pi\)
\(858\) 17.3568 0.592550
\(859\) 17.4319 0.594770 0.297385 0.954758i \(-0.403885\pi\)
0.297385 + 0.954758i \(0.403885\pi\)
\(860\) 19.0084 0.648180
\(861\) 23.7451 0.809231
\(862\) 8.54311 0.290979
\(863\) 1.79213 0.0610048 0.0305024 0.999535i \(-0.490289\pi\)
0.0305024 + 0.999535i \(0.490289\pi\)
\(864\) −4.72967 −0.160907
\(865\) 11.2937 0.383998
\(866\) −28.9936 −0.985241
\(867\) 14.3836 0.488491
\(868\) −5.24000 −0.177857
\(869\) 9.97285 0.338306
\(870\) 10.0559 0.340927
\(871\) 10.2196 0.346276
\(872\) −13.5714 −0.459587
\(873\) 19.0176 0.643648
\(874\) −3.89553 −0.131768
\(875\) −27.9945 −0.946386
\(876\) 5.29263 0.178821
\(877\) −8.55332 −0.288825 −0.144413 0.989518i \(-0.546129\pi\)
−0.144413 + 0.989518i \(0.546129\pi\)
\(878\) 29.5292 0.996562
\(879\) 24.6704 0.832111
\(880\) −9.08712 −0.306327
\(881\) −3.67238 −0.123726 −0.0618628 0.998085i \(-0.519704\pi\)
−0.0618628 + 0.998085i \(0.519704\pi\)
\(882\) −3.68852 −0.124199
\(883\) 8.32051 0.280007 0.140004 0.990151i \(-0.455289\pi\)
0.140004 + 0.990151i \(0.455289\pi\)
\(884\) −4.29983 −0.144619
\(885\) 0.577447 0.0194107
\(886\) 25.1195 0.843907
\(887\) 20.9799 0.704437 0.352218 0.935918i \(-0.385427\pi\)
0.352218 + 0.935918i \(0.385427\pi\)
\(888\) 5.70386 0.191409
\(889\) −44.5737 −1.49495
\(890\) 15.4486 0.517838
\(891\) 10.7993 0.361789
\(892\) 19.4130 0.649996
\(893\) 7.77272 0.260104
\(894\) −17.6496 −0.590292
\(895\) 18.0565 0.603562
\(896\) 2.30047 0.0768533
\(897\) 13.4225 0.448165
\(898\) −22.6595 −0.756156
\(899\) −13.8519 −0.461986
\(900\) 3.77041 0.125680
\(901\) −5.62575 −0.187421
\(902\) −56.7227 −1.88866
\(903\) −22.2197 −0.739425
\(904\) −1.30944 −0.0435514
\(905\) −6.25896 −0.208055
\(906\) 7.59673 0.252384
\(907\) −27.8852 −0.925913 −0.462957 0.886381i \(-0.653211\pi\)
−0.462957 + 0.886381i \(0.653211\pi\)
\(908\) 0.405414 0.0134541
\(909\) 2.00701 0.0665684
\(910\) −15.5994 −0.517114
\(911\) −15.8265 −0.524356 −0.262178 0.965020i \(-0.584441\pi\)
−0.262178 + 0.965020i \(0.584441\pi\)
\(912\) 0.916646 0.0303532
\(913\) −40.1535 −1.32889
\(914\) −29.8646 −0.987833
\(915\) 1.69280 0.0559623
\(916\) −11.0518 −0.365160
\(917\) −45.1681 −1.49158
\(918\) 5.41024 0.178565
\(919\) −48.3342 −1.59440 −0.797199 0.603717i \(-0.793686\pi\)
−0.797199 + 0.603717i \(0.793686\pi\)
\(920\) −7.02734 −0.231685
\(921\) 6.19316 0.204072
\(922\) 19.8220 0.652804
\(923\) 28.2835 0.930962
\(924\) 10.6223 0.349449
\(925\) −10.8630 −0.357174
\(926\) −19.5899 −0.643763
\(927\) −13.5408 −0.444740
\(928\) 6.08127 0.199627
\(929\) 3.54595 0.116339 0.0581694 0.998307i \(-0.481474\pi\)
0.0581694 + 0.998307i \(0.481474\pi\)
\(930\) −3.76653 −0.123509
\(931\) 1.70784 0.0559722
\(932\) 26.9676 0.883352
\(933\) −11.3067 −0.370165
\(934\) −31.7186 −1.03787
\(935\) 10.3947 0.339943
\(936\) 8.11842 0.265359
\(937\) 15.1613 0.495299 0.247649 0.968850i \(-0.420342\pi\)
0.247649 + 0.968850i \(0.420342\pi\)
\(938\) 6.25436 0.204212
\(939\) 22.5147 0.734740
\(940\) 14.0216 0.457335
\(941\) 4.94062 0.161060 0.0805299 0.996752i \(-0.474339\pi\)
0.0805299 + 0.996752i \(0.474339\pi\)
\(942\) −8.76750 −0.285661
\(943\) −43.8654 −1.42845
\(944\) 0.349209 0.0113658
\(945\) 19.6278 0.638494
\(946\) 53.0788 1.72574
\(947\) −26.7617 −0.869639 −0.434819 0.900518i \(-0.643188\pi\)
−0.434819 + 0.900518i \(0.643188\pi\)
\(948\) −1.81476 −0.0589407
\(949\) −21.7038 −0.704535
\(950\) −1.74576 −0.0566398
\(951\) 0.705074 0.0228636
\(952\) −2.63149 −0.0852872
\(953\) −52.7036 −1.70724 −0.853619 0.520898i \(-0.825597\pi\)
−0.853619 + 0.520898i \(0.825597\pi\)
\(954\) 10.6218 0.343895
\(955\) 19.5758 0.633459
\(956\) −5.99193 −0.193793
\(957\) 28.0800 0.907698
\(958\) −22.0025 −0.710870
\(959\) −27.3531 −0.883279
\(960\) 1.65359 0.0533692
\(961\) −25.8116 −0.832634
\(962\) −23.3901 −0.754128
\(963\) −21.4117 −0.689981
\(964\) −13.9854 −0.450440
\(965\) 38.3746 1.23532
\(966\) 8.21456 0.264299
\(967\) 3.40608 0.109532 0.0547661 0.998499i \(-0.482559\pi\)
0.0547661 + 0.998499i \(0.482559\pi\)
\(968\) −14.3748 −0.462024
\(969\) −1.04855 −0.0336841
\(970\) −15.8846 −0.510022
\(971\) 15.8162 0.507566 0.253783 0.967261i \(-0.418325\pi\)
0.253783 + 0.967261i \(0.418325\pi\)
\(972\) −16.1542 −0.518145
\(973\) −16.2958 −0.522419
\(974\) 13.3471 0.427668
\(975\) 6.01521 0.192641
\(976\) 1.02372 0.0327684
\(977\) 6.22552 0.199172 0.0995860 0.995029i \(-0.468248\pi\)
0.0995860 + 0.995029i \(0.468248\pi\)
\(978\) −8.20707 −0.262433
\(979\) 43.1385 1.37871
\(980\) 3.08086 0.0984145
\(981\) −29.3110 −0.935829
\(982\) 31.5431 1.00658
\(983\) −9.10856 −0.290518 −0.145259 0.989394i \(-0.546402\pi\)
−0.145259 + 0.989394i \(0.546402\pi\)
\(984\) 10.3218 0.329049
\(985\) −25.0770 −0.799020
\(986\) −6.95633 −0.221535
\(987\) −16.3905 −0.521714
\(988\) −3.75894 −0.119588
\(989\) 41.0474 1.30523
\(990\) −19.6260 −0.623755
\(991\) 34.9823 1.11125 0.555625 0.831433i \(-0.312479\pi\)
0.555625 + 0.831433i \(0.312479\pi\)
\(992\) −2.27780 −0.0723201
\(993\) 11.0256 0.349887
\(994\) 17.3095 0.549022
\(995\) 8.55392 0.271178
\(996\) 7.30674 0.231523
\(997\) 46.6233 1.47657 0.738287 0.674487i \(-0.235635\pi\)
0.738287 + 0.674487i \(0.235635\pi\)
\(998\) −14.3523 −0.454314
\(999\) 29.4305 0.931141
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 \(a_p\))