Properties

Label 8002.2.a.d.1.14
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.38948 q^{3}\) \(+1.00000 q^{4}\) \(+1.42184 q^{5}\) \(-2.38948 q^{6}\) \(-5.14183 q^{7}\) \(+1.00000 q^{8}\) \(+2.70964 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.38948 q^{3}\) \(+1.00000 q^{4}\) \(+1.42184 q^{5}\) \(-2.38948 q^{6}\) \(-5.14183 q^{7}\) \(+1.00000 q^{8}\) \(+2.70964 q^{9}\) \(+1.42184 q^{10}\) \(+2.90336 q^{11}\) \(-2.38948 q^{12}\) \(-4.20957 q^{13}\) \(-5.14183 q^{14}\) \(-3.39746 q^{15}\) \(+1.00000 q^{16}\) \(-4.01441 q^{17}\) \(+2.70964 q^{18}\) \(+1.37465 q^{19}\) \(+1.42184 q^{20}\) \(+12.2863 q^{21}\) \(+2.90336 q^{22}\) \(+1.34345 q^{23}\) \(-2.38948 q^{24}\) \(-2.97838 q^{25}\) \(-4.20957 q^{26}\) \(+0.693819 q^{27}\) \(-5.14183 q^{28}\) \(+5.22382 q^{29}\) \(-3.39746 q^{30}\) \(+9.21736 q^{31}\) \(+1.00000 q^{32}\) \(-6.93752 q^{33}\) \(-4.01441 q^{34}\) \(-7.31084 q^{35}\) \(+2.70964 q^{36}\) \(+9.16884 q^{37}\) \(+1.37465 q^{38}\) \(+10.0587 q^{39}\) \(+1.42184 q^{40}\) \(+3.42707 q^{41}\) \(+12.2863 q^{42}\) \(+10.8992 q^{43}\) \(+2.90336 q^{44}\) \(+3.85266 q^{45}\) \(+1.34345 q^{46}\) \(-11.4604 q^{47}\) \(-2.38948 q^{48}\) \(+19.4384 q^{49}\) \(-2.97838 q^{50}\) \(+9.59236 q^{51}\) \(-4.20957 q^{52}\) \(-4.25818 q^{53}\) \(+0.693819 q^{54}\) \(+4.12810 q^{55}\) \(-5.14183 q^{56}\) \(-3.28471 q^{57}\) \(+5.22382 q^{58}\) \(-2.10949 q^{59}\) \(-3.39746 q^{60}\) \(-10.6807 q^{61}\) \(+9.21736 q^{62}\) \(-13.9325 q^{63}\) \(+1.00000 q^{64}\) \(-5.98532 q^{65}\) \(-6.93752 q^{66}\) \(-9.40553 q^{67}\) \(-4.01441 q^{68}\) \(-3.21015 q^{69}\) \(-7.31084 q^{70}\) \(-2.34289 q^{71}\) \(+2.70964 q^{72}\) \(+13.5006 q^{73}\) \(+9.16884 q^{74}\) \(+7.11679 q^{75}\) \(+1.37465 q^{76}\) \(-14.9286 q^{77}\) \(+10.0587 q^{78}\) \(+0.841782 q^{79}\) \(+1.42184 q^{80}\) \(-9.78678 q^{81}\) \(+3.42707 q^{82}\) \(+0.945519 q^{83}\) \(+12.2863 q^{84}\) \(-5.70783 q^{85}\) \(+10.8992 q^{86}\) \(-12.4822 q^{87}\) \(+2.90336 q^{88}\) \(-13.0187 q^{89}\) \(+3.85266 q^{90}\) \(+21.6449 q^{91}\) \(+1.34345 q^{92}\) \(-22.0247 q^{93}\) \(-11.4604 q^{94}\) \(+1.95453 q^{95}\) \(-2.38948 q^{96}\) \(-14.8817 q^{97}\) \(+19.4384 q^{98}\) \(+7.86704 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.38948 −1.37957 −0.689785 0.724014i \(-0.742295\pi\)
−0.689785 + 0.724014i \(0.742295\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.42184 0.635865 0.317933 0.948113i \(-0.397011\pi\)
0.317933 + 0.948113i \(0.397011\pi\)
\(6\) −2.38948 −0.975503
\(7\) −5.14183 −1.94343 −0.971714 0.236161i \(-0.924111\pi\)
−0.971714 + 0.236161i \(0.924111\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.70964 0.903212
\(10\) 1.42184 0.449625
\(11\) 2.90336 0.875395 0.437697 0.899122i \(-0.355794\pi\)
0.437697 + 0.899122i \(0.355794\pi\)
\(12\) −2.38948 −0.689785
\(13\) −4.20957 −1.16752 −0.583762 0.811925i \(-0.698420\pi\)
−0.583762 + 0.811925i \(0.698420\pi\)
\(14\) −5.14183 −1.37421
\(15\) −3.39746 −0.877220
\(16\) 1.00000 0.250000
\(17\) −4.01441 −0.973636 −0.486818 0.873503i \(-0.661843\pi\)
−0.486818 + 0.873503i \(0.661843\pi\)
\(18\) 2.70964 0.638667
\(19\) 1.37465 0.315366 0.157683 0.987490i \(-0.449598\pi\)
0.157683 + 0.987490i \(0.449598\pi\)
\(20\) 1.42184 0.317933
\(21\) 12.2863 2.68109
\(22\) 2.90336 0.618997
\(23\) 1.34345 0.280128 0.140064 0.990142i \(-0.455269\pi\)
0.140064 + 0.990142i \(0.455269\pi\)
\(24\) −2.38948 −0.487751
\(25\) −2.97838 −0.595676
\(26\) −4.20957 −0.825564
\(27\) 0.693819 0.133526
\(28\) −5.14183 −0.971714
\(29\) 5.22382 0.970040 0.485020 0.874503i \(-0.338812\pi\)
0.485020 + 0.874503i \(0.338812\pi\)
\(30\) −3.39746 −0.620288
\(31\) 9.21736 1.65549 0.827743 0.561107i \(-0.189624\pi\)
0.827743 + 0.561107i \(0.189624\pi\)
\(32\) 1.00000 0.176777
\(33\) −6.93752 −1.20767
\(34\) −4.01441 −0.688465
\(35\) −7.31084 −1.23576
\(36\) 2.70964 0.451606
\(37\) 9.16884 1.50735 0.753674 0.657249i \(-0.228280\pi\)
0.753674 + 0.657249i \(0.228280\pi\)
\(38\) 1.37465 0.222998
\(39\) 10.0587 1.61068
\(40\) 1.42184 0.224812
\(41\) 3.42707 0.535218 0.267609 0.963528i \(-0.413766\pi\)
0.267609 + 0.963528i \(0.413766\pi\)
\(42\) 12.2863 1.89582
\(43\) 10.8992 1.66211 0.831056 0.556189i \(-0.187737\pi\)
0.831056 + 0.556189i \(0.187737\pi\)
\(44\) 2.90336 0.437697
\(45\) 3.85266 0.574321
\(46\) 1.34345 0.198081
\(47\) −11.4604 −1.67167 −0.835835 0.548981i \(-0.815016\pi\)
−0.835835 + 0.548981i \(0.815016\pi\)
\(48\) −2.38948 −0.344892
\(49\) 19.4384 2.77691
\(50\) −2.97838 −0.421206
\(51\) 9.59236 1.34320
\(52\) −4.20957 −0.583762
\(53\) −4.25818 −0.584906 −0.292453 0.956280i \(-0.594472\pi\)
−0.292453 + 0.956280i \(0.594472\pi\)
\(54\) 0.693819 0.0944168
\(55\) 4.12810 0.556633
\(56\) −5.14183 −0.687106
\(57\) −3.28471 −0.435070
\(58\) 5.22382 0.685922
\(59\) −2.10949 −0.274632 −0.137316 0.990527i \(-0.543848\pi\)
−0.137316 + 0.990527i \(0.543848\pi\)
\(60\) −3.39746 −0.438610
\(61\) −10.6807 −1.36753 −0.683764 0.729703i \(-0.739658\pi\)
−0.683764 + 0.729703i \(0.739658\pi\)
\(62\) 9.21736 1.17061
\(63\) −13.9325 −1.75533
\(64\) 1.00000 0.125000
\(65\) −5.98532 −0.742388
\(66\) −6.93752 −0.853950
\(67\) −9.40553 −1.14907 −0.574534 0.818481i \(-0.694817\pi\)
−0.574534 + 0.818481i \(0.694817\pi\)
\(68\) −4.01441 −0.486818
\(69\) −3.21015 −0.386456
\(70\) −7.31084 −0.873813
\(71\) −2.34289 −0.278050 −0.139025 0.990289i \(-0.544397\pi\)
−0.139025 + 0.990289i \(0.544397\pi\)
\(72\) 2.70964 0.319334
\(73\) 13.5006 1.58012 0.790062 0.613026i \(-0.210048\pi\)
0.790062 + 0.613026i \(0.210048\pi\)
\(74\) 9.16884 1.06586
\(75\) 7.11679 0.821776
\(76\) 1.37465 0.157683
\(77\) −14.9286 −1.70127
\(78\) 10.0587 1.13892
\(79\) 0.841782 0.0947078 0.0473539 0.998878i \(-0.484921\pi\)
0.0473539 + 0.998878i \(0.484921\pi\)
\(80\) 1.42184 0.158966
\(81\) −9.78678 −1.08742
\(82\) 3.42707 0.378456
\(83\) 0.945519 0.103784 0.0518921 0.998653i \(-0.483475\pi\)
0.0518921 + 0.998653i \(0.483475\pi\)
\(84\) 12.2863 1.34055
\(85\) −5.70783 −0.619101
\(86\) 10.8992 1.17529
\(87\) −12.4822 −1.33824
\(88\) 2.90336 0.309499
\(89\) −13.0187 −1.37998 −0.689988 0.723821i \(-0.742384\pi\)
−0.689988 + 0.723821i \(0.742384\pi\)
\(90\) 3.85266 0.406106
\(91\) 21.6449 2.26900
\(92\) 1.34345 0.140064
\(93\) −22.0247 −2.28386
\(94\) −11.4604 −1.18205
\(95\) 1.95453 0.200530
\(96\) −2.38948 −0.243876
\(97\) −14.8817 −1.51100 −0.755502 0.655146i \(-0.772607\pi\)
−0.755502 + 0.655146i \(0.772607\pi\)
\(98\) 19.4384 1.96357
\(99\) 7.86704 0.790667
\(100\) −2.97838 −0.297838
\(101\) −7.67362 −0.763553 −0.381777 0.924255i \(-0.624688\pi\)
−0.381777 + 0.924255i \(0.624688\pi\)
\(102\) 9.59236 0.949785
\(103\) −14.9345 −1.47154 −0.735770 0.677231i \(-0.763180\pi\)
−0.735770 + 0.677231i \(0.763180\pi\)
\(104\) −4.20957 −0.412782
\(105\) 17.4691 1.70481
\(106\) −4.25818 −0.413591
\(107\) 14.5995 1.41138 0.705691 0.708519i \(-0.250636\pi\)
0.705691 + 0.708519i \(0.250636\pi\)
\(108\) 0.693819 0.0667628
\(109\) 7.70309 0.737822 0.368911 0.929465i \(-0.379731\pi\)
0.368911 + 0.929465i \(0.379731\pi\)
\(110\) 4.12810 0.393599
\(111\) −21.9088 −2.07949
\(112\) −5.14183 −0.485857
\(113\) −16.4504 −1.54752 −0.773762 0.633477i \(-0.781627\pi\)
−0.773762 + 0.633477i \(0.781627\pi\)
\(114\) −3.28471 −0.307641
\(115\) 1.91016 0.178124
\(116\) 5.22382 0.485020
\(117\) −11.4064 −1.05452
\(118\) −2.10949 −0.194194
\(119\) 20.6414 1.89219
\(120\) −3.39746 −0.310144
\(121\) −2.57053 −0.233684
\(122\) −10.6807 −0.966989
\(123\) −8.18892 −0.738370
\(124\) 9.21736 0.827743
\(125\) −11.3440 −1.01463
\(126\) −13.9325 −1.24120
\(127\) 0.453407 0.0402334 0.0201167 0.999798i \(-0.493596\pi\)
0.0201167 + 0.999798i \(0.493596\pi\)
\(128\) 1.00000 0.0883883
\(129\) −26.0435 −2.29300
\(130\) −5.98532 −0.524947
\(131\) −10.0133 −0.874862 −0.437431 0.899252i \(-0.644112\pi\)
−0.437431 + 0.899252i \(0.644112\pi\)
\(132\) −6.93752 −0.603834
\(133\) −7.06821 −0.612892
\(134\) −9.40553 −0.812514
\(135\) 0.986498 0.0849042
\(136\) −4.01441 −0.344232
\(137\) −11.7423 −1.00321 −0.501605 0.865097i \(-0.667257\pi\)
−0.501605 + 0.865097i \(0.667257\pi\)
\(138\) −3.21015 −0.273266
\(139\) 2.92705 0.248269 0.124134 0.992265i \(-0.460385\pi\)
0.124134 + 0.992265i \(0.460385\pi\)
\(140\) −7.31084 −0.617879
\(141\) 27.3844 2.30618
\(142\) −2.34289 −0.196611
\(143\) −12.2219 −1.02204
\(144\) 2.70964 0.225803
\(145\) 7.42743 0.616814
\(146\) 13.5006 1.11732
\(147\) −46.4477 −3.83094
\(148\) 9.16884 0.753674
\(149\) 15.0761 1.23508 0.617539 0.786540i \(-0.288130\pi\)
0.617539 + 0.786540i \(0.288130\pi\)
\(150\) 7.11679 0.581083
\(151\) 21.2341 1.72801 0.864005 0.503483i \(-0.167948\pi\)
0.864005 + 0.503483i \(0.167948\pi\)
\(152\) 1.37465 0.111499
\(153\) −10.8776 −0.879400
\(154\) −14.9286 −1.20298
\(155\) 13.1056 1.05267
\(156\) 10.0587 0.805340
\(157\) 5.39203 0.430331 0.215165 0.976578i \(-0.430971\pi\)
0.215165 + 0.976578i \(0.430971\pi\)
\(158\) 0.841782 0.0669686
\(159\) 10.1749 0.806919
\(160\) 1.42184 0.112406
\(161\) −6.90778 −0.544409
\(162\) −9.78678 −0.768922
\(163\) −3.59900 −0.281896 −0.140948 0.990017i \(-0.545015\pi\)
−0.140948 + 0.990017i \(0.545015\pi\)
\(164\) 3.42707 0.267609
\(165\) −9.86403 −0.767914
\(166\) 0.945519 0.0733865
\(167\) 10.5908 0.819544 0.409772 0.912188i \(-0.365608\pi\)
0.409772 + 0.912188i \(0.365608\pi\)
\(168\) 12.2863 0.947910
\(169\) 4.72046 0.363112
\(170\) −5.70783 −0.437771
\(171\) 3.72480 0.284843
\(172\) 10.8992 0.831056
\(173\) 0.430848 0.0327568 0.0163784 0.999866i \(-0.494786\pi\)
0.0163784 + 0.999866i \(0.494786\pi\)
\(174\) −12.4822 −0.946277
\(175\) 15.3143 1.15765
\(176\) 2.90336 0.218849
\(177\) 5.04058 0.378873
\(178\) −13.0187 −0.975790
\(179\) 19.1538 1.43162 0.715809 0.698296i \(-0.246058\pi\)
0.715809 + 0.698296i \(0.246058\pi\)
\(180\) 3.85266 0.287161
\(181\) 0.121914 0.00906181 0.00453091 0.999990i \(-0.498558\pi\)
0.00453091 + 0.999990i \(0.498558\pi\)
\(182\) 21.6449 1.60442
\(183\) 25.5215 1.88660
\(184\) 1.34345 0.0990403
\(185\) 13.0366 0.958470
\(186\) −22.0247 −1.61493
\(187\) −11.6552 −0.852316
\(188\) −11.4604 −0.835835
\(189\) −3.56750 −0.259497
\(190\) 1.95453 0.141796
\(191\) 2.34992 0.170034 0.0850170 0.996379i \(-0.472906\pi\)
0.0850170 + 0.996379i \(0.472906\pi\)
\(192\) −2.38948 −0.172446
\(193\) −20.8041 −1.49751 −0.748755 0.662847i \(-0.769348\pi\)
−0.748755 + 0.662847i \(0.769348\pi\)
\(194\) −14.8817 −1.06844
\(195\) 14.3018 1.02418
\(196\) 19.4384 1.38846
\(197\) −13.6446 −0.972140 −0.486070 0.873920i \(-0.661570\pi\)
−0.486070 + 0.873920i \(0.661570\pi\)
\(198\) 7.86704 0.559086
\(199\) 17.0564 1.20910 0.604549 0.796568i \(-0.293354\pi\)
0.604549 + 0.796568i \(0.293354\pi\)
\(200\) −2.97838 −0.210603
\(201\) 22.4744 1.58522
\(202\) −7.67362 −0.539914
\(203\) −26.8600 −1.88520
\(204\) 9.59236 0.671600
\(205\) 4.87273 0.340326
\(206\) −14.9345 −1.04054
\(207\) 3.64026 0.253015
\(208\) −4.20957 −0.291881
\(209\) 3.99110 0.276070
\(210\) 17.4691 1.20549
\(211\) 2.25313 0.155112 0.0775561 0.996988i \(-0.475288\pi\)
0.0775561 + 0.996988i \(0.475288\pi\)
\(212\) −4.25818 −0.292453
\(213\) 5.59830 0.383589
\(214\) 14.5995 0.997998
\(215\) 15.4969 1.05688
\(216\) 0.693819 0.0472084
\(217\) −47.3941 −3.21732
\(218\) 7.70309 0.521719
\(219\) −32.2595 −2.17989
\(220\) 4.12810 0.278316
\(221\) 16.8989 1.13674
\(222\) −21.9088 −1.47042
\(223\) −19.8645 −1.33023 −0.665113 0.746743i \(-0.731617\pi\)
−0.665113 + 0.746743i \(0.731617\pi\)
\(224\) −5.14183 −0.343553
\(225\) −8.07032 −0.538021
\(226\) −16.4504 −1.09426
\(227\) 3.37445 0.223970 0.111985 0.993710i \(-0.464279\pi\)
0.111985 + 0.993710i \(0.464279\pi\)
\(228\) −3.28471 −0.217535
\(229\) −18.9033 −1.24916 −0.624582 0.780959i \(-0.714731\pi\)
−0.624582 + 0.780959i \(0.714731\pi\)
\(230\) 1.91016 0.125953
\(231\) 35.6715 2.34702
\(232\) 5.22382 0.342961
\(233\) −16.4601 −1.07834 −0.539169 0.842197i \(-0.681262\pi\)
−0.539169 + 0.842197i \(0.681262\pi\)
\(234\) −11.4064 −0.745659
\(235\) −16.2948 −1.06296
\(236\) −2.10949 −0.137316
\(237\) −2.01142 −0.130656
\(238\) 20.6414 1.33798
\(239\) −26.5319 −1.71620 −0.858102 0.513479i \(-0.828356\pi\)
−0.858102 + 0.513479i \(0.828356\pi\)
\(240\) −3.39746 −0.219305
\(241\) −7.44610 −0.479646 −0.239823 0.970817i \(-0.577089\pi\)
−0.239823 + 0.970817i \(0.577089\pi\)
\(242\) −2.57053 −0.165240
\(243\) 21.3039 1.36665
\(244\) −10.6807 −0.683764
\(245\) 27.6382 1.76574
\(246\) −8.18892 −0.522107
\(247\) −5.78668 −0.368198
\(248\) 9.21736 0.585303
\(249\) −2.25930 −0.143177
\(250\) −11.3440 −0.717455
\(251\) −1.86646 −0.117810 −0.0589050 0.998264i \(-0.518761\pi\)
−0.0589050 + 0.998264i \(0.518761\pi\)
\(252\) −13.9325 −0.877664
\(253\) 3.90051 0.245223
\(254\) 0.453407 0.0284493
\(255\) 13.6388 0.854093
\(256\) 1.00000 0.0625000
\(257\) 7.34741 0.458319 0.229159 0.973389i \(-0.426402\pi\)
0.229159 + 0.973389i \(0.426402\pi\)
\(258\) −26.0435 −1.62140
\(259\) −47.1446 −2.92942
\(260\) −5.98532 −0.371194
\(261\) 14.1547 0.876152
\(262\) −10.0133 −0.618621
\(263\) −20.6752 −1.27489 −0.637445 0.770496i \(-0.720009\pi\)
−0.637445 + 0.770496i \(0.720009\pi\)
\(264\) −6.93752 −0.426975
\(265\) −6.05444 −0.371921
\(266\) −7.06821 −0.433380
\(267\) 31.1079 1.90377
\(268\) −9.40553 −0.574534
\(269\) −17.4334 −1.06293 −0.531466 0.847080i \(-0.678359\pi\)
−0.531466 + 0.847080i \(0.678359\pi\)
\(270\) 0.986498 0.0600364
\(271\) −18.9859 −1.15331 −0.576656 0.816987i \(-0.695643\pi\)
−0.576656 + 0.816987i \(0.695643\pi\)
\(272\) −4.01441 −0.243409
\(273\) −51.7201 −3.13024
\(274\) −11.7423 −0.709376
\(275\) −8.64729 −0.521451
\(276\) −3.21015 −0.193228
\(277\) 29.3601 1.76408 0.882040 0.471175i \(-0.156170\pi\)
0.882040 + 0.471175i \(0.156170\pi\)
\(278\) 2.92705 0.175553
\(279\) 24.9757 1.49526
\(280\) −7.31084 −0.436906
\(281\) −15.9187 −0.949630 −0.474815 0.880086i \(-0.657485\pi\)
−0.474815 + 0.880086i \(0.657485\pi\)
\(282\) 27.3844 1.63072
\(283\) 24.5215 1.45765 0.728826 0.684699i \(-0.240066\pi\)
0.728826 + 0.684699i \(0.240066\pi\)
\(284\) −2.34289 −0.139025
\(285\) −4.67032 −0.276646
\(286\) −12.2219 −0.722694
\(287\) −17.6214 −1.04016
\(288\) 2.70964 0.159667
\(289\) −0.884550 −0.0520324
\(290\) 7.42743 0.436154
\(291\) 35.5595 2.08454
\(292\) 13.5006 0.790062
\(293\) −9.15367 −0.534763 −0.267382 0.963591i \(-0.586158\pi\)
−0.267382 + 0.963591i \(0.586158\pi\)
\(294\) −46.4477 −2.70889
\(295\) −2.99935 −0.174629
\(296\) 9.16884 0.532928
\(297\) 2.01440 0.116888
\(298\) 15.0761 0.873333
\(299\) −5.65533 −0.327056
\(300\) 7.11679 0.410888
\(301\) −56.0418 −3.23019
\(302\) 21.2341 1.22189
\(303\) 18.3360 1.05338
\(304\) 1.37465 0.0788416
\(305\) −15.1863 −0.869564
\(306\) −10.8776 −0.621830
\(307\) −1.15471 −0.0659030 −0.0329515 0.999457i \(-0.510491\pi\)
−0.0329515 + 0.999457i \(0.510491\pi\)
\(308\) −14.9286 −0.850633
\(309\) 35.6858 2.03009
\(310\) 13.1056 0.744347
\(311\) 3.08684 0.175039 0.0875194 0.996163i \(-0.472106\pi\)
0.0875194 + 0.996163i \(0.472106\pi\)
\(312\) 10.0587 0.569462
\(313\) −3.44957 −0.194981 −0.0974907 0.995236i \(-0.531082\pi\)
−0.0974907 + 0.995236i \(0.531082\pi\)
\(314\) 5.39203 0.304290
\(315\) −19.8097 −1.11615
\(316\) 0.841782 0.0473539
\(317\) 23.8691 1.34062 0.670311 0.742080i \(-0.266160\pi\)
0.670311 + 0.742080i \(0.266160\pi\)
\(318\) 10.1749 0.570578
\(319\) 15.1666 0.849167
\(320\) 1.42184 0.0794831
\(321\) −34.8852 −1.94710
\(322\) −6.90778 −0.384955
\(323\) −5.51840 −0.307052
\(324\) −9.78678 −0.543710
\(325\) 12.5377 0.695465
\(326\) −3.59900 −0.199330
\(327\) −18.4064 −1.01788
\(328\) 3.42707 0.189228
\(329\) 58.9273 3.24877
\(330\) −9.86403 −0.542997
\(331\) −29.2312 −1.60669 −0.803346 0.595512i \(-0.796949\pi\)
−0.803346 + 0.595512i \(0.796949\pi\)
\(332\) 0.945519 0.0518921
\(333\) 24.8442 1.36145
\(334\) 10.5908 0.579505
\(335\) −13.3731 −0.730652
\(336\) 12.2863 0.670274
\(337\) −5.93720 −0.323420 −0.161710 0.986838i \(-0.551701\pi\)
−0.161710 + 0.986838i \(0.551701\pi\)
\(338\) 4.72046 0.256759
\(339\) 39.3080 2.13492
\(340\) −5.70783 −0.309551
\(341\) 26.7613 1.44920
\(342\) 3.72480 0.201414
\(343\) −63.9560 −3.45330
\(344\) 10.8992 0.587645
\(345\) −4.56431 −0.245734
\(346\) 0.430848 0.0231625
\(347\) 16.1106 0.864864 0.432432 0.901666i \(-0.357656\pi\)
0.432432 + 0.901666i \(0.357656\pi\)
\(348\) −12.4822 −0.669119
\(349\) −35.1279 −1.88035 −0.940177 0.340687i \(-0.889340\pi\)
−0.940177 + 0.340687i \(0.889340\pi\)
\(350\) 15.3143 0.818584
\(351\) −2.92068 −0.155894
\(352\) 2.90336 0.154749
\(353\) 15.1299 0.805284 0.402642 0.915358i \(-0.368092\pi\)
0.402642 + 0.915358i \(0.368092\pi\)
\(354\) 5.04058 0.267904
\(355\) −3.33121 −0.176802
\(356\) −13.0187 −0.689988
\(357\) −49.3223 −2.61041
\(358\) 19.1538 1.01231
\(359\) −22.5462 −1.18994 −0.594972 0.803746i \(-0.702837\pi\)
−0.594972 + 0.803746i \(0.702837\pi\)
\(360\) 3.85266 0.203053
\(361\) −17.1103 −0.900544
\(362\) 0.121914 0.00640767
\(363\) 6.14224 0.322384
\(364\) 21.6449 1.13450
\(365\) 19.1956 1.00475
\(366\) 25.5215 1.33403
\(367\) 6.83473 0.356770 0.178385 0.983961i \(-0.442913\pi\)
0.178385 + 0.983961i \(0.442913\pi\)
\(368\) 1.34345 0.0700321
\(369\) 9.28611 0.483415
\(370\) 13.0366 0.677740
\(371\) 21.8948 1.13672
\(372\) −22.0247 −1.14193
\(373\) −0.0491684 −0.00254584 −0.00127292 0.999999i \(-0.500405\pi\)
−0.00127292 + 0.999999i \(0.500405\pi\)
\(374\) −11.6552 −0.602678
\(375\) 27.1062 1.39976
\(376\) −11.4604 −0.591024
\(377\) −21.9900 −1.13254
\(378\) −3.56750 −0.183492
\(379\) −1.17398 −0.0603035 −0.0301518 0.999545i \(-0.509599\pi\)
−0.0301518 + 0.999545i \(0.509599\pi\)
\(380\) 1.95453 0.100265
\(381\) −1.08341 −0.0555048
\(382\) 2.34992 0.120232
\(383\) 9.07320 0.463619 0.231810 0.972761i \(-0.425535\pi\)
0.231810 + 0.972761i \(0.425535\pi\)
\(384\) −2.38948 −0.121938
\(385\) −21.2260 −1.08178
\(386\) −20.8041 −1.05890
\(387\) 29.5329 1.50124
\(388\) −14.8817 −0.755502
\(389\) 33.3885 1.69286 0.846432 0.532497i \(-0.178746\pi\)
0.846432 + 0.532497i \(0.178746\pi\)
\(390\) 14.3018 0.724201
\(391\) −5.39315 −0.272743
\(392\) 19.4384 0.981787
\(393\) 23.9265 1.20693
\(394\) −13.6446 −0.687407
\(395\) 1.19688 0.0602214
\(396\) 7.86704 0.395333
\(397\) −9.96264 −0.500010 −0.250005 0.968244i \(-0.580432\pi\)
−0.250005 + 0.968244i \(0.580432\pi\)
\(398\) 17.0564 0.854961
\(399\) 16.8894 0.845527
\(400\) −2.97838 −0.148919
\(401\) 1.14364 0.0571105 0.0285553 0.999592i \(-0.490909\pi\)
0.0285553 + 0.999592i \(0.490909\pi\)
\(402\) 22.4744 1.12092
\(403\) −38.8011 −1.93282
\(404\) −7.67362 −0.381777
\(405\) −13.9152 −0.691452
\(406\) −26.8600 −1.33304
\(407\) 26.6204 1.31952
\(408\) 9.59236 0.474893
\(409\) −19.3315 −0.955880 −0.477940 0.878392i \(-0.658616\pi\)
−0.477940 + 0.878392i \(0.658616\pi\)
\(410\) 4.87273 0.240647
\(411\) 28.0580 1.38400
\(412\) −14.9345 −0.735770
\(413\) 10.8466 0.533727
\(414\) 3.64026 0.178909
\(415\) 1.34437 0.0659927
\(416\) −4.20957 −0.206391
\(417\) −6.99414 −0.342504
\(418\) 3.99110 0.195211
\(419\) 22.2939 1.08913 0.544563 0.838720i \(-0.316695\pi\)
0.544563 + 0.838720i \(0.316695\pi\)
\(420\) 17.4691 0.852407
\(421\) 14.8667 0.724556 0.362278 0.932070i \(-0.381999\pi\)
0.362278 + 0.932070i \(0.381999\pi\)
\(422\) 2.25313 0.109681
\(423\) −31.0535 −1.50987
\(424\) −4.25818 −0.206796
\(425\) 11.9564 0.579971
\(426\) 5.59830 0.271238
\(427\) 54.9185 2.65769
\(428\) 14.5995 0.705691
\(429\) 29.2040 1.40998
\(430\) 15.4969 0.747326
\(431\) −24.4479 −1.17761 −0.588806 0.808274i \(-0.700402\pi\)
−0.588806 + 0.808274i \(0.700402\pi\)
\(432\) 0.693819 0.0333814
\(433\) 10.2369 0.491955 0.245977 0.969276i \(-0.420891\pi\)
0.245977 + 0.969276i \(0.420891\pi\)
\(434\) −47.3941 −2.27499
\(435\) −17.7477 −0.850938
\(436\) 7.70309 0.368911
\(437\) 1.84677 0.0883431
\(438\) −32.2595 −1.54142
\(439\) 21.3360 1.01831 0.509155 0.860675i \(-0.329958\pi\)
0.509155 + 0.860675i \(0.329958\pi\)
\(440\) 4.12810 0.196799
\(441\) 52.6710 2.50814
\(442\) 16.8989 0.803799
\(443\) −22.7643 −1.08156 −0.540782 0.841163i \(-0.681871\pi\)
−0.540782 + 0.841163i \(0.681871\pi\)
\(444\) −21.9088 −1.03975
\(445\) −18.5104 −0.877479
\(446\) −19.8645 −0.940612
\(447\) −36.0240 −1.70388
\(448\) −5.14183 −0.242928
\(449\) −21.7543 −1.02665 −0.513325 0.858194i \(-0.671587\pi\)
−0.513325 + 0.858194i \(0.671587\pi\)
\(450\) −8.07032 −0.380439
\(451\) 9.94999 0.468527
\(452\) −16.4504 −0.773762
\(453\) −50.7387 −2.38391
\(454\) 3.37445 0.158371
\(455\) 30.7755 1.44278
\(456\) −3.28471 −0.153820
\(457\) 1.50675 0.0704830 0.0352415 0.999379i \(-0.488780\pi\)
0.0352415 + 0.999379i \(0.488780\pi\)
\(458\) −18.9033 −0.883293
\(459\) −2.78527 −0.130005
\(460\) 1.91016 0.0890619
\(461\) −37.9320 −1.76667 −0.883336 0.468741i \(-0.844708\pi\)
−0.883336 + 0.468741i \(0.844708\pi\)
\(462\) 35.6715 1.65959
\(463\) 6.51234 0.302654 0.151327 0.988484i \(-0.451645\pi\)
0.151327 + 0.988484i \(0.451645\pi\)
\(464\) 5.22382 0.242510
\(465\) −31.3156 −1.45223
\(466\) −16.4601 −0.762501
\(467\) 12.8750 0.595785 0.297892 0.954599i \(-0.403716\pi\)
0.297892 + 0.954599i \(0.403716\pi\)
\(468\) −11.4064 −0.527261
\(469\) 48.3616 2.23313
\(470\) −16.2948 −0.751623
\(471\) −12.8842 −0.593671
\(472\) −2.10949 −0.0970969
\(473\) 31.6442 1.45500
\(474\) −2.01142 −0.0923878
\(475\) −4.09423 −0.187856
\(476\) 20.6414 0.946096
\(477\) −11.5381 −0.528294
\(478\) −26.5319 −1.21354
\(479\) −14.7058 −0.671925 −0.335963 0.941875i \(-0.609062\pi\)
−0.335963 + 0.941875i \(0.609062\pi\)
\(480\) −3.39746 −0.155072
\(481\) −38.5968 −1.75986
\(482\) −7.44610 −0.339161
\(483\) 16.5060 0.751050
\(484\) −2.57053 −0.116842
\(485\) −21.1593 −0.960795
\(486\) 21.3039 0.966365
\(487\) −3.07533 −0.139357 −0.0696784 0.997570i \(-0.522197\pi\)
−0.0696784 + 0.997570i \(0.522197\pi\)
\(488\) −10.6807 −0.483494
\(489\) 8.59976 0.388895
\(490\) 27.6382 1.24857
\(491\) 14.4147 0.650525 0.325263 0.945624i \(-0.394547\pi\)
0.325263 + 0.945624i \(0.394547\pi\)
\(492\) −8.18892 −0.369185
\(493\) −20.9705 −0.944466
\(494\) −5.78668 −0.260355
\(495\) 11.1856 0.502758
\(496\) 9.21736 0.413872
\(497\) 12.0467 0.540370
\(498\) −2.25930 −0.101242
\(499\) 25.0040 1.11933 0.559667 0.828718i \(-0.310929\pi\)
0.559667 + 0.828718i \(0.310929\pi\)
\(500\) −11.3440 −0.507317
\(501\) −25.3067 −1.13062
\(502\) −1.86646 −0.0833043
\(503\) 18.6060 0.829601 0.414801 0.909912i \(-0.363851\pi\)
0.414801 + 0.909912i \(0.363851\pi\)
\(504\) −13.9325 −0.620602
\(505\) −10.9106 −0.485517
\(506\) 3.90051 0.173399
\(507\) −11.2795 −0.500938
\(508\) 0.453407 0.0201167
\(509\) 44.4767 1.97139 0.985697 0.168526i \(-0.0539008\pi\)
0.985697 + 0.168526i \(0.0539008\pi\)
\(510\) 13.6388 0.603935
\(511\) −69.4177 −3.07086
\(512\) 1.00000 0.0441942
\(513\) 0.953759 0.0421095
\(514\) 7.34741 0.324080
\(515\) −21.2344 −0.935701
\(516\) −26.0435 −1.14650
\(517\) −33.2736 −1.46337
\(518\) −47.1446 −2.07141
\(519\) −1.02950 −0.0451902
\(520\) −5.98532 −0.262474
\(521\) −29.5541 −1.29479 −0.647395 0.762155i \(-0.724141\pi\)
−0.647395 + 0.762155i \(0.724141\pi\)
\(522\) 14.1547 0.619533
\(523\) 4.11148 0.179782 0.0898911 0.995952i \(-0.471348\pi\)
0.0898911 + 0.995952i \(0.471348\pi\)
\(524\) −10.0133 −0.437431
\(525\) −36.5933 −1.59706
\(526\) −20.6752 −0.901483
\(527\) −37.0022 −1.61184
\(528\) −6.93752 −0.301917
\(529\) −21.1951 −0.921528
\(530\) −6.05444 −0.262988
\(531\) −5.71594 −0.248051
\(532\) −7.06821 −0.306446
\(533\) −14.4265 −0.624880
\(534\) 31.1079 1.34617
\(535\) 20.7581 0.897449
\(536\) −9.40553 −0.406257
\(537\) −45.7676 −1.97502
\(538\) −17.4334 −0.751607
\(539\) 56.4365 2.43089
\(540\) 0.986498 0.0424521
\(541\) 38.5446 1.65716 0.828582 0.559868i \(-0.189148\pi\)
0.828582 + 0.559868i \(0.189148\pi\)
\(542\) −18.9859 −0.815514
\(543\) −0.291312 −0.0125014
\(544\) −4.01441 −0.172116
\(545\) 10.9525 0.469155
\(546\) −51.7201 −2.21341
\(547\) −33.7371 −1.44249 −0.721246 0.692679i \(-0.756430\pi\)
−0.721246 + 0.692679i \(0.756430\pi\)
\(548\) −11.7423 −0.501605
\(549\) −28.9409 −1.23517
\(550\) −8.64729 −0.368722
\(551\) 7.18093 0.305918
\(552\) −3.21015 −0.136633
\(553\) −4.32830 −0.184058
\(554\) 29.3601 1.24739
\(555\) −31.1507 −1.32228
\(556\) 2.92705 0.124134
\(557\) 18.6700 0.791072 0.395536 0.918450i \(-0.370559\pi\)
0.395536 + 0.918450i \(0.370559\pi\)
\(558\) 24.9757 1.05731
\(559\) −45.8809 −1.94056
\(560\) −7.31084 −0.308940
\(561\) 27.8500 1.17583
\(562\) −15.9187 −0.671490
\(563\) −44.7862 −1.88751 −0.943756 0.330643i \(-0.892734\pi\)
−0.943756 + 0.330643i \(0.892734\pi\)
\(564\) 27.3844 1.15309
\(565\) −23.3898 −0.984016
\(566\) 24.5215 1.03072
\(567\) 50.3219 2.11332
\(568\) −2.34289 −0.0983054
\(569\) −1.74341 −0.0730874 −0.0365437 0.999332i \(-0.511635\pi\)
−0.0365437 + 0.999332i \(0.511635\pi\)
\(570\) −4.67032 −0.195618
\(571\) −23.9500 −1.00227 −0.501137 0.865368i \(-0.667085\pi\)
−0.501137 + 0.865368i \(0.667085\pi\)
\(572\) −12.2219 −0.511022
\(573\) −5.61509 −0.234574
\(574\) −17.6214 −0.735503
\(575\) −4.00130 −0.166866
\(576\) 2.70964 0.112902
\(577\) −36.6678 −1.52650 −0.763251 0.646102i \(-0.776398\pi\)
−0.763251 + 0.646102i \(0.776398\pi\)
\(578\) −0.884550 −0.0367924
\(579\) 49.7110 2.06592
\(580\) 7.42743 0.308407
\(581\) −4.86169 −0.201697
\(582\) 35.5595 1.47399
\(583\) −12.3630 −0.512024
\(584\) 13.5006 0.558658
\(585\) −16.2180 −0.670534
\(586\) −9.15367 −0.378135
\(587\) −5.97899 −0.246779 −0.123390 0.992358i \(-0.539376\pi\)
−0.123390 + 0.992358i \(0.539376\pi\)
\(588\) −46.4477 −1.91547
\(589\) 12.6706 0.522085
\(590\) −2.99935 −0.123481
\(591\) 32.6036 1.34113
\(592\) 9.16884 0.376837
\(593\) −38.4295 −1.57811 −0.789055 0.614322i \(-0.789430\pi\)
−0.789055 + 0.614322i \(0.789430\pi\)
\(594\) 2.01440 0.0826520
\(595\) 29.3487 1.20318
\(596\) 15.0761 0.617539
\(597\) −40.7560 −1.66803
\(598\) −5.65533 −0.231264
\(599\) −17.1038 −0.698842 −0.349421 0.936966i \(-0.613622\pi\)
−0.349421 + 0.936966i \(0.613622\pi\)
\(600\) 7.11679 0.290542
\(601\) 16.8252 0.686316 0.343158 0.939278i \(-0.388503\pi\)
0.343158 + 0.939278i \(0.388503\pi\)
\(602\) −56.0418 −2.28409
\(603\) −25.4856 −1.03785
\(604\) 21.2341 0.864005
\(605\) −3.65487 −0.148592
\(606\) 18.3360 0.744849
\(607\) −8.43571 −0.342395 −0.171197 0.985237i \(-0.554764\pi\)
−0.171197 + 0.985237i \(0.554764\pi\)
\(608\) 1.37465 0.0557494
\(609\) 64.1815 2.60077
\(610\) −15.1863 −0.614874
\(611\) 48.2433 1.95171
\(612\) −10.8776 −0.439700
\(613\) −40.1922 −1.62335 −0.811674 0.584111i \(-0.801443\pi\)
−0.811674 + 0.584111i \(0.801443\pi\)
\(614\) −1.15471 −0.0466005
\(615\) −11.6433 −0.469504
\(616\) −14.9286 −0.601488
\(617\) 11.7673 0.473734 0.236867 0.971542i \(-0.423879\pi\)
0.236867 + 0.971542i \(0.423879\pi\)
\(618\) 35.6858 1.43549
\(619\) 8.17547 0.328600 0.164300 0.986410i \(-0.447464\pi\)
0.164300 + 0.986410i \(0.447464\pi\)
\(620\) 13.1056 0.526333
\(621\) 0.932110 0.0374043
\(622\) 3.08684 0.123771
\(623\) 66.9397 2.68188
\(624\) 10.0587 0.402670
\(625\) −1.23738 −0.0494950
\(626\) −3.44957 −0.137873
\(627\) −9.53667 −0.380858
\(628\) 5.39203 0.215165
\(629\) −36.8074 −1.46761
\(630\) −19.8097 −0.789238
\(631\) 10.6052 0.422187 0.211093 0.977466i \(-0.432298\pi\)
0.211093 + 0.977466i \(0.432298\pi\)
\(632\) 0.841782 0.0334843
\(633\) −5.38383 −0.213988
\(634\) 23.8691 0.947964
\(635\) 0.644672 0.0255830
\(636\) 10.1749 0.403459
\(637\) −81.8272 −3.24211
\(638\) 15.1666 0.600452
\(639\) −6.34838 −0.251138
\(640\) 1.42184 0.0562031
\(641\) −10.4993 −0.414698 −0.207349 0.978267i \(-0.566484\pi\)
−0.207349 + 0.978267i \(0.566484\pi\)
\(642\) −34.8852 −1.37681
\(643\) 44.5720 1.75775 0.878875 0.477053i \(-0.158295\pi\)
0.878875 + 0.477053i \(0.158295\pi\)
\(644\) −6.90778 −0.272205
\(645\) −37.0296 −1.45804
\(646\) −5.51840 −0.217119
\(647\) 37.3445 1.46816 0.734082 0.679061i \(-0.237613\pi\)
0.734082 + 0.679061i \(0.237613\pi\)
\(648\) −9.78678 −0.384461
\(649\) −6.12459 −0.240411
\(650\) 12.5377 0.491768
\(651\) 113.247 4.43852
\(652\) −3.59900 −0.140948
\(653\) 13.2176 0.517243 0.258622 0.965979i \(-0.416732\pi\)
0.258622 + 0.965979i \(0.416732\pi\)
\(654\) −18.4064 −0.719748
\(655\) −14.2372 −0.556294
\(656\) 3.42707 0.133804
\(657\) 36.5817 1.42719
\(658\) 58.9273 2.29723
\(659\) 36.9145 1.43798 0.718992 0.695019i \(-0.244604\pi\)
0.718992 + 0.695019i \(0.244604\pi\)
\(660\) −9.86403 −0.383957
\(661\) 22.0881 0.859129 0.429565 0.903036i \(-0.358667\pi\)
0.429565 + 0.903036i \(0.358667\pi\)
\(662\) −29.2312 −1.13610
\(663\) −40.3797 −1.56822
\(664\) 0.945519 0.0366932
\(665\) −10.0499 −0.389717
\(666\) 24.8442 0.962694
\(667\) 7.01794 0.271736
\(668\) 10.5908 0.409772
\(669\) 47.4659 1.83514
\(670\) −13.3731 −0.516649
\(671\) −31.0100 −1.19713
\(672\) 12.2863 0.473955
\(673\) 22.6873 0.874531 0.437266 0.899332i \(-0.355947\pi\)
0.437266 + 0.899332i \(0.355947\pi\)
\(674\) −5.93720 −0.228692
\(675\) −2.06646 −0.0795379
\(676\) 4.72046 0.181556
\(677\) −27.6032 −1.06088 −0.530439 0.847723i \(-0.677973\pi\)
−0.530439 + 0.847723i \(0.677973\pi\)
\(678\) 39.3080 1.50961
\(679\) 76.5190 2.93653
\(680\) −5.70783 −0.218885
\(681\) −8.06319 −0.308982
\(682\) 26.7613 1.02474
\(683\) −14.1438 −0.541196 −0.270598 0.962692i \(-0.587221\pi\)
−0.270598 + 0.962692i \(0.587221\pi\)
\(684\) 3.72480 0.142421
\(685\) −16.6956 −0.637906
\(686\) −63.9560 −2.44185
\(687\) 45.1691 1.72331
\(688\) 10.8992 0.415528
\(689\) 17.9251 0.682892
\(690\) −4.56431 −0.173760
\(691\) −23.2651 −0.885047 −0.442523 0.896757i \(-0.645917\pi\)
−0.442523 + 0.896757i \(0.645917\pi\)
\(692\) 0.430848 0.0163784
\(693\) −40.4509 −1.53660
\(694\) 16.1106 0.611551
\(695\) 4.16179 0.157866
\(696\) −12.4822 −0.473138
\(697\) −13.7576 −0.521108
\(698\) −35.1279 −1.32961
\(699\) 39.3312 1.48764
\(700\) 15.3143 0.578826
\(701\) −13.7469 −0.519215 −0.259607 0.965714i \(-0.583593\pi\)
−0.259607 + 0.965714i \(0.583593\pi\)
\(702\) −2.92068 −0.110234
\(703\) 12.6039 0.475367
\(704\) 2.90336 0.109424
\(705\) 38.9362 1.46642
\(706\) 15.1299 0.569421
\(707\) 39.4564 1.48391
\(708\) 5.04058 0.189437
\(709\) −43.8140 −1.64547 −0.822734 0.568427i \(-0.807552\pi\)
−0.822734 + 0.568427i \(0.807552\pi\)
\(710\) −3.33121 −0.125018
\(711\) 2.28092 0.0855413
\(712\) −13.0187 −0.487895
\(713\) 12.3830 0.463749
\(714\) −49.3223 −1.84584
\(715\) −17.3775 −0.649882
\(716\) 19.1538 0.715809
\(717\) 63.3975 2.36762
\(718\) −22.5462 −0.841418
\(719\) −3.99758 −0.149084 −0.0745422 0.997218i \(-0.523750\pi\)
−0.0745422 + 0.997218i \(0.523750\pi\)
\(720\) 3.85266 0.143580
\(721\) 76.7906 2.85983
\(722\) −17.1103 −0.636781
\(723\) 17.7923 0.661704
\(724\) 0.121914 0.00453091
\(725\) −15.5585 −0.577829
\(726\) 6.14224 0.227960
\(727\) 23.4184 0.868542 0.434271 0.900782i \(-0.357006\pi\)
0.434271 + 0.900782i \(0.357006\pi\)
\(728\) 21.6449 0.802212
\(729\) −21.5450 −0.797963
\(730\) 19.1956 0.710463
\(731\) −43.7538 −1.61829
\(732\) 25.5215 0.943301
\(733\) −27.7628 −1.02544 −0.512721 0.858555i \(-0.671363\pi\)
−0.512721 + 0.858555i \(0.671363\pi\)
\(734\) 6.83473 0.252274
\(735\) −66.0411 −2.43596
\(736\) 1.34345 0.0495202
\(737\) −27.3076 −1.00589
\(738\) 9.28611 0.341826
\(739\) 24.4177 0.898219 0.449110 0.893477i \(-0.351741\pi\)
0.449110 + 0.893477i \(0.351741\pi\)
\(740\) 13.0366 0.479235
\(741\) 13.8272 0.507954
\(742\) 21.8948 0.803785
\(743\) −33.0279 −1.21168 −0.605839 0.795588i \(-0.707162\pi\)
−0.605839 + 0.795588i \(0.707162\pi\)
\(744\) −22.0247 −0.807466
\(745\) 21.4357 0.785344
\(746\) −0.0491684 −0.00180018
\(747\) 2.56201 0.0937391
\(748\) −11.6552 −0.426158
\(749\) −75.0679 −2.74292
\(750\) 27.1062 0.989779
\(751\) −46.3488 −1.69129 −0.845647 0.533743i \(-0.820785\pi\)
−0.845647 + 0.533743i \(0.820785\pi\)
\(752\) −11.4604 −0.417917
\(753\) 4.45988 0.162527
\(754\) −21.9900 −0.800830
\(755\) 30.1915 1.09878
\(756\) −3.56750 −0.129749
\(757\) 52.5408 1.90963 0.954814 0.297204i \(-0.0960540\pi\)
0.954814 + 0.297204i \(0.0960540\pi\)
\(758\) −1.17398 −0.0426410
\(759\) −9.32020 −0.338302
\(760\) 1.95453 0.0708982
\(761\) 36.9872 1.34078 0.670392 0.742007i \(-0.266126\pi\)
0.670392 + 0.742007i \(0.266126\pi\)
\(762\) −1.08341 −0.0392478
\(763\) −39.6080 −1.43390
\(764\) 2.34992 0.0850170
\(765\) −15.4662 −0.559180
\(766\) 9.07320 0.327828
\(767\) 8.88002 0.320639
\(768\) −2.38948 −0.0862231
\(769\) −26.9105 −0.970417 −0.485208 0.874399i \(-0.661256\pi\)
−0.485208 + 0.874399i \(0.661256\pi\)
\(770\) −21.2260 −0.764931
\(771\) −17.5565 −0.632283
\(772\) −20.8041 −0.748755
\(773\) −27.2374 −0.979661 −0.489831 0.871818i \(-0.662941\pi\)
−0.489831 + 0.871818i \(0.662941\pi\)
\(774\) 29.5329 1.06154
\(775\) −27.4528 −0.986133
\(776\) −14.8817 −0.534221
\(777\) 112.651 4.04134
\(778\) 33.3885 1.19704
\(779\) 4.71102 0.168790
\(780\) 14.3018 0.512088
\(781\) −6.80224 −0.243403
\(782\) −5.39315 −0.192858
\(783\) 3.62439 0.129525
\(784\) 19.4384 0.694228
\(785\) 7.66659 0.273632
\(786\) 23.9265 0.853431
\(787\) −30.0060 −1.06960 −0.534800 0.844979i \(-0.679613\pi\)
−0.534800 + 0.844979i \(0.679613\pi\)
\(788\) −13.6446 −0.486070
\(789\) 49.4031 1.75880
\(790\) 1.19688 0.0425830
\(791\) 84.5851 3.00750
\(792\) 7.86704 0.279543
\(793\) 44.9613 1.59662
\(794\) −9.96264 −0.353561
\(795\) 14.4670 0.513092
\(796\) 17.0564 0.604549
\(797\) −39.2211 −1.38928 −0.694641 0.719356i \(-0.744437\pi\)
−0.694641 + 0.719356i \(0.744437\pi\)
\(798\) 16.8894 0.597878
\(799\) 46.0066 1.62760
\(800\) −2.97838 −0.105302
\(801\) −35.2759 −1.24641
\(802\) 1.14364 0.0403832
\(803\) 39.1970 1.38323
\(804\) 22.4744 0.792609
\(805\) −9.82174 −0.346171
\(806\) −38.8011 −1.36671
\(807\) 41.6568 1.46639
\(808\) −7.67362 −0.269957
\(809\) −44.4862 −1.56405 −0.782026 0.623246i \(-0.785813\pi\)
−0.782026 + 0.623246i \(0.785813\pi\)
\(810\) −13.9152 −0.488931
\(811\) 14.8183 0.520341 0.260171 0.965563i \(-0.416221\pi\)
0.260171 + 0.965563i \(0.416221\pi\)
\(812\) −26.8600 −0.942601
\(813\) 45.3665 1.59107
\(814\) 26.6204 0.933044
\(815\) −5.11720 −0.179248
\(816\) 9.59236 0.335800
\(817\) 14.9826 0.524174
\(818\) −19.3315 −0.675909
\(819\) 58.6497 2.04939
\(820\) 4.87273 0.170163
\(821\) 36.7861 1.28384 0.641921 0.766771i \(-0.278138\pi\)
0.641921 + 0.766771i \(0.278138\pi\)
\(822\) 28.0580 0.978634
\(823\) 3.11744 0.108667 0.0543335 0.998523i \(-0.482697\pi\)
0.0543335 + 0.998523i \(0.482697\pi\)
\(824\) −14.9345 −0.520268
\(825\) 20.6626 0.719378
\(826\) 10.8466 0.377402
\(827\) 19.8669 0.690838 0.345419 0.938448i \(-0.387737\pi\)
0.345419 + 0.938448i \(0.387737\pi\)
\(828\) 3.64026 0.126508
\(829\) −16.7153 −0.580547 −0.290274 0.956944i \(-0.593746\pi\)
−0.290274 + 0.956944i \(0.593746\pi\)
\(830\) 1.34437 0.0466639
\(831\) −70.1556 −2.43367
\(832\) −4.20957 −0.145940
\(833\) −78.0336 −2.70370
\(834\) −6.99414 −0.242187
\(835\) 15.0585 0.521120
\(836\) 3.99110 0.138035
\(837\) 6.39518 0.221050
\(838\) 22.2939 0.770129
\(839\) −51.2827 −1.77048 −0.885238 0.465138i \(-0.846005\pi\)
−0.885238 + 0.465138i \(0.846005\pi\)
\(840\) 17.4691 0.602743
\(841\) −1.71167 −0.0590232
\(842\) 14.8667 0.512339
\(843\) 38.0375 1.31008
\(844\) 2.25313 0.0775561
\(845\) 6.71172 0.230890
\(846\) −31.0535 −1.06764
\(847\) 13.2172 0.454149
\(848\) −4.25818 −0.146227
\(849\) −58.5938 −2.01093
\(850\) 11.9564 0.410102
\(851\) 12.3179 0.422251
\(852\) 5.59830 0.191794
\(853\) 22.7006 0.777255 0.388628 0.921395i \(-0.372949\pi\)
0.388628 + 0.921395i \(0.372949\pi\)
\(854\) 54.9185 1.87927
\(855\) 5.29606 0.181122
\(856\) 14.5995 0.498999
\(857\) −27.1963 −0.929009 −0.464505 0.885571i \(-0.653768\pi\)
−0.464505 + 0.885571i \(0.653768\pi\)
\(858\) 29.2040 0.997007
\(859\) 24.3669 0.831386 0.415693 0.909505i \(-0.363539\pi\)
0.415693 + 0.909505i \(0.363539\pi\)
\(860\) 15.4969 0.528439
\(861\) 42.1060 1.43497
\(862\) −24.4479 −0.832698
\(863\) 15.6830 0.533856 0.266928 0.963717i \(-0.413991\pi\)
0.266928 + 0.963717i \(0.413991\pi\)
\(864\) 0.693819 0.0236042
\(865\) 0.612596 0.0208289
\(866\) 10.2369 0.347865
\(867\) 2.11362 0.0717823
\(868\) −47.3941 −1.60866
\(869\) 2.44399 0.0829067
\(870\) −17.7477 −0.601704
\(871\) 39.5932 1.34156
\(872\) 7.70309 0.260860
\(873\) −40.3239 −1.36476
\(874\) 1.84677 0.0624680
\(875\) 58.3287 1.97187
\(876\) −32.2595 −1.08995
\(877\) −4.09764 −0.138367 −0.0691837 0.997604i \(-0.522039\pi\)
−0.0691837 + 0.997604i \(0.522039\pi\)
\(878\) 21.3360 0.720054
\(879\) 21.8726 0.737743
\(880\) 4.12810 0.139158
\(881\) 45.9598 1.54842 0.774212 0.632926i \(-0.218146\pi\)
0.774212 + 0.632926i \(0.218146\pi\)
\(882\) 52.6710 1.77352
\(883\) −23.1347 −0.778544 −0.389272 0.921123i \(-0.627273\pi\)
−0.389272 + 0.921123i \(0.627273\pi\)
\(884\) 16.8989 0.568372
\(885\) 7.16689 0.240912
\(886\) −22.7643 −0.764781
\(887\) −41.2367 −1.38459 −0.692297 0.721613i \(-0.743401\pi\)
−0.692297 + 0.721613i \(0.743401\pi\)
\(888\) −21.9088 −0.735211
\(889\) −2.33134 −0.0781907
\(890\) −18.5104 −0.620471
\(891\) −28.4145 −0.951921
\(892\) −19.8645 −0.665113
\(893\) −15.7540 −0.527188
\(894\) −36.0240 −1.20482
\(895\) 27.2335 0.910316
\(896\) −5.14183 −0.171776
\(897\) 13.5133 0.451197
\(898\) −21.7543 −0.725952
\(899\) 48.1499 1.60589
\(900\) −8.07032 −0.269011
\(901\) 17.0941 0.569486
\(902\) 9.94999 0.331299
\(903\) 133.911 4.45628
\(904\) −16.4504 −0.547132
\(905\) 0.173342 0.00576209
\(906\) −50.7387 −1.68568
\(907\) 13.1698 0.437296 0.218648 0.975804i \(-0.429835\pi\)
0.218648 + 0.975804i \(0.429835\pi\)
\(908\) 3.37445 0.111985
\(909\) −20.7927 −0.689651
\(910\) 30.7755 1.02020
\(911\) 42.1216 1.39555 0.697776 0.716316i \(-0.254173\pi\)
0.697776 + 0.716316i \(0.254173\pi\)
\(912\) −3.28471 −0.108767
\(913\) 2.74518 0.0908521
\(914\) 1.50675 0.0498390
\(915\) 36.2874 1.19962
\(916\) −18.9033 −0.624582
\(917\) 51.4864 1.70023
\(918\) −2.78527 −0.0919276
\(919\) −25.9396 −0.855669 −0.427835 0.903857i \(-0.640723\pi\)
−0.427835 + 0.903857i \(0.640723\pi\)
\(920\) 1.91016 0.0629763
\(921\) 2.75917 0.0909178
\(922\) −37.9320 −1.24923
\(923\) 9.86255 0.324630
\(924\) 35.6715 1.17351
\(925\) −27.3083 −0.897890
\(926\) 6.51234 0.214009
\(927\) −40.4671 −1.32911
\(928\) 5.22382 0.171480
\(929\) 51.6682 1.69518 0.847590 0.530652i \(-0.178053\pi\)
0.847590 + 0.530652i \(0.178053\pi\)
\(930\) −31.3156 −1.02688
\(931\) 26.7210 0.875745
\(932\) −16.4601 −0.539169
\(933\) −7.37596 −0.241478
\(934\) 12.8750 0.421284
\(935\) −16.5719 −0.541958
\(936\) −11.4064 −0.372830
\(937\) 37.0522 1.21044 0.605221 0.796057i \(-0.293085\pi\)
0.605221 + 0.796057i \(0.293085\pi\)
\(938\) 48.3616 1.57906
\(939\) 8.24271 0.268991
\(940\) −16.2948 −0.531478
\(941\) 18.6478 0.607901 0.303950 0.952688i \(-0.401694\pi\)
0.303950 + 0.952688i \(0.401694\pi\)
\(942\) −12.8842 −0.419789
\(943\) 4.60409 0.149930
\(944\) −2.10949 −0.0686579
\(945\) −5.07240 −0.165005
\(946\) 31.6442 1.02884
\(947\) −33.9415 −1.10295 −0.551475 0.834191i \(-0.685935\pi\)
−0.551475 + 0.834191i \(0.685935\pi\)
\(948\) −2.01142 −0.0653280
\(949\) −56.8316 −1.84483
\(950\) −4.09423 −0.132834
\(951\) −57.0349 −1.84948
\(952\) 20.6414 0.668991
\(953\) −8.99410 −0.291347 −0.145674 0.989333i \(-0.546535\pi\)
−0.145674 + 0.989333i \(0.546535\pi\)
\(954\) −11.5381 −0.373561
\(955\) 3.34120 0.108119
\(956\) −26.5319 −0.858102
\(957\) −36.2404 −1.17149
\(958\) −14.7058 −0.475123
\(959\) 60.3767 1.94966
\(960\) −3.39746 −0.109653
\(961\) 53.9597 1.74064
\(962\) −38.5968 −1.24441
\(963\) 39.5592 1.27478
\(964\) −7.44610 −0.239823
\(965\) −29.5800 −0.952214
\(966\) 16.5060 0.531073
\(967\) 4.86864 0.156565 0.0782824 0.996931i \(-0.475056\pi\)
0.0782824 + 0.996931i \(0.475056\pi\)
\(968\) −2.57053 −0.0826199
\(969\) 13.1861 0.423600
\(970\) −21.1593 −0.679385
\(971\) 10.6197 0.340802 0.170401 0.985375i \(-0.445494\pi\)
0.170401 + 0.985375i \(0.445494\pi\)
\(972\) 21.3039 0.683323
\(973\) −15.0504 −0.482493
\(974\) −3.07533 −0.0985401
\(975\) −29.9586 −0.959443
\(976\) −10.6807 −0.341882
\(977\) −43.8560 −1.40308 −0.701538 0.712632i \(-0.747503\pi\)
−0.701538 + 0.712632i \(0.747503\pi\)
\(978\) 8.59976 0.274990
\(979\) −37.7978 −1.20802
\(980\) 27.6382 0.882871
\(981\) 20.8726 0.666410
\(982\) 14.4147 0.459991
\(983\) −38.4462 −1.22624 −0.613122 0.789988i \(-0.710087\pi\)
−0.613122 + 0.789988i \(0.710087\pi\)
\(984\) −8.18892 −0.261053
\(985\) −19.4005 −0.618150
\(986\) −20.9705 −0.667838
\(987\) −140.806 −4.48190
\(988\) −5.78668 −0.184099
\(989\) 14.6425 0.465605
\(990\) 11.1856 0.355503
\(991\) −25.1973 −0.800418 −0.400209 0.916424i \(-0.631062\pi\)
−0.400209 + 0.916424i \(0.631062\pi\)
\(992\) 9.21736 0.292651
\(993\) 69.8475 2.21654
\(994\) 12.0467 0.382099
\(995\) 24.2514 0.768823
\(996\) −2.25930 −0.0715887
\(997\) 1.07065 0.0339078 0.0169539 0.999856i \(-0.494603\pi\)
0.0169539 + 0.999856i \(0.494603\pi\)
\(998\) 25.0040 0.791488
\(999\) 6.36151 0.201269
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 \(a_p\))