Properties

Label 8013.2.a.d.1.17
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

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Newspace parameters

Level: \( N \) = \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9841271397\)
Analytic rank: \(0\)
Dimension: \(129\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.18651 q^{2}\) \(+1.00000 q^{3}\) \(+2.78083 q^{4}\) \(-0.652555 q^{5}\) \(-2.18651 q^{6}\) \(+2.68769 q^{7}\) \(-1.70730 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.18651 q^{2}\) \(+1.00000 q^{3}\) \(+2.78083 q^{4}\) \(-0.652555 q^{5}\) \(-2.18651 q^{6}\) \(+2.68769 q^{7}\) \(-1.70730 q^{8}\) \(+1.00000 q^{9}\) \(+1.42682 q^{10}\) \(+6.13704 q^{11}\) \(+2.78083 q^{12}\) \(+2.00005 q^{13}\) \(-5.87666 q^{14}\) \(-0.652555 q^{15}\) \(-1.82864 q^{16}\) \(-1.92138 q^{17}\) \(-2.18651 q^{18}\) \(+8.00888 q^{19}\) \(-1.81465 q^{20}\) \(+2.68769 q^{21}\) \(-13.4187 q^{22}\) \(+2.70586 q^{23}\) \(-1.70730 q^{24}\) \(-4.57417 q^{25}\) \(-4.37313 q^{26}\) \(+1.00000 q^{27}\) \(+7.47400 q^{28}\) \(+1.12436 q^{29}\) \(+1.42682 q^{30}\) \(+8.03868 q^{31}\) \(+7.41293 q^{32}\) \(+6.13704 q^{33}\) \(+4.20113 q^{34}\) \(-1.75386 q^{35}\) \(+2.78083 q^{36}\) \(-2.79404 q^{37}\) \(-17.5115 q^{38}\) \(+2.00005 q^{39}\) \(+1.11411 q^{40}\) \(+9.02599 q^{41}\) \(-5.87666 q^{42}\) \(+6.61674 q^{43}\) \(+17.0661 q^{44}\) \(-0.652555 q^{45}\) \(-5.91639 q^{46}\) \(-9.77226 q^{47}\) \(-1.82864 q^{48}\) \(+0.223654 q^{49}\) \(+10.0015 q^{50}\) \(-1.92138 q^{51}\) \(+5.56181 q^{52}\) \(-5.24965 q^{53}\) \(-2.18651 q^{54}\) \(-4.00476 q^{55}\) \(-4.58868 q^{56}\) \(+8.00888 q^{57}\) \(-2.45843 q^{58}\) \(+7.44285 q^{59}\) \(-1.81465 q^{60}\) \(+1.98726 q^{61}\) \(-17.5767 q^{62}\) \(+2.68769 q^{63}\) \(-12.5512 q^{64}\) \(-1.30514 q^{65}\) \(-13.4187 q^{66}\) \(+14.8687 q^{67}\) \(-5.34304 q^{68}\) \(+2.70586 q^{69}\) \(+3.83484 q^{70}\) \(-7.12294 q^{71}\) \(-1.70730 q^{72}\) \(+0.801682 q^{73}\) \(+6.10920 q^{74}\) \(-4.57417 q^{75}\) \(+22.2714 q^{76}\) \(+16.4944 q^{77}\) \(-4.37313 q^{78}\) \(-3.41932 q^{79}\) \(+1.19329 q^{80}\) \(+1.00000 q^{81}\) \(-19.7354 q^{82}\) \(+3.13048 q^{83}\) \(+7.47400 q^{84}\) \(+1.25381 q^{85}\) \(-14.4676 q^{86}\) \(+1.12436 q^{87}\) \(-10.4778 q^{88}\) \(-14.3573 q^{89}\) \(+1.42682 q^{90}\) \(+5.37551 q^{91}\) \(+7.52454 q^{92}\) \(+8.03868 q^{93}\) \(+21.3672 q^{94}\) \(-5.22624 q^{95}\) \(+7.41293 q^{96}\) \(+18.0263 q^{97}\) \(-0.489022 q^{98}\) \(+6.13704 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut 41q^{10} \) \(\mathstrut +\mathstrut 51q^{11} \) \(\mathstrut +\mathstrut 151q^{12} \) \(\mathstrut +\mathstrut 56q^{13} \) \(\mathstrut +\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 195q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 15q^{18} \) \(\mathstrut +\mathstrut 93q^{19} \) \(\mathstrut +\mathstrut 44q^{20} \) \(\mathstrut +\mathstrut 61q^{21} \) \(\mathstrut +\mathstrut 46q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 42q^{24} \) \(\mathstrut +\mathstrut 193q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut 129q^{27} \) \(\mathstrut +\mathstrut 145q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 41q^{30} \) \(\mathstrut +\mathstrut 67q^{31} \) \(\mathstrut +\mathstrut 89q^{32} \) \(\mathstrut +\mathstrut 51q^{33} \) \(\mathstrut +\mathstrut 73q^{34} \) \(\mathstrut +\mathstrut 56q^{35} \) \(\mathstrut +\mathstrut 151q^{36} \) \(\mathstrut +\mathstrut 95q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 103q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 5q^{42} \) \(\mathstrut +\mathstrut 150q^{43} \) \(\mathstrut +\mathstrut 69q^{44} \) \(\mathstrut +\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 53q^{47} \) \(\mathstrut +\mathstrut 195q^{48} \) \(\mathstrut +\mathstrut 240q^{49} \) \(\mathstrut +\mathstrut 17q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 124q^{52} \) \(\mathstrut +\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut 15q^{54} \) \(\mathstrut +\mathstrut 66q^{55} \) \(\mathstrut -\mathstrut 17q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 57q^{58} \) \(\mathstrut +\mathstrut 49q^{59} \) \(\mathstrut +\mathstrut 44q^{60} \) \(\mathstrut +\mathstrut 113q^{61} \) \(\mathstrut +\mathstrut 27q^{62} \) \(\mathstrut +\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 262q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 46q^{66} \) \(\mathstrut +\mathstrut 185q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 50q^{69} \) \(\mathstrut +\mathstrut 25q^{70} \) \(\mathstrut +\mathstrut 41q^{71} \) \(\mathstrut +\mathstrut 42q^{72} \) \(\mathstrut +\mathstrut 153q^{73} \) \(\mathstrut -\mathstrut q^{74} \) \(\mathstrut +\mathstrut 193q^{75} \) \(\mathstrut +\mathstrut 190q^{76} \) \(\mathstrut +\mathstrut 39q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 101q^{79} \) \(\mathstrut +\mathstrut 48q^{80} \) \(\mathstrut +\mathstrut 129q^{81} \) \(\mathstrut +\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 162q^{83} \) \(\mathstrut +\mathstrut 145q^{84} \) \(\mathstrut +\mathstrut 99q^{85} \) \(\mathstrut +\mathstrut 13q^{86} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 86q^{88} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 117q^{91} \) \(\mathstrut +\mathstrut 56q^{92} \) \(\mathstrut +\mathstrut 67q^{93} \) \(\mathstrut +\mathstrut 49q^{94} \) \(\mathstrut +\mathstrut 71q^{95} \) \(\mathstrut +\mathstrut 89q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut +\mathstrut 40q^{98} \) \(\mathstrut +\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.18651 −1.54610 −0.773048 0.634347i \(-0.781269\pi\)
−0.773048 + 0.634347i \(0.781269\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.78083 1.39042
\(5\) −0.652555 −0.291832 −0.145916 0.989297i \(-0.546613\pi\)
−0.145916 + 0.989297i \(0.546613\pi\)
\(6\) −2.18651 −0.892640
\(7\) 2.68769 1.01585 0.507925 0.861401i \(-0.330413\pi\)
0.507925 + 0.861401i \(0.330413\pi\)
\(8\) −1.70730 −0.603621
\(9\) 1.00000 0.333333
\(10\) 1.42682 0.451200
\(11\) 6.13704 1.85039 0.925194 0.379495i \(-0.123902\pi\)
0.925194 + 0.379495i \(0.123902\pi\)
\(12\) 2.78083 0.802757
\(13\) 2.00005 0.554714 0.277357 0.960767i \(-0.410541\pi\)
0.277357 + 0.960767i \(0.410541\pi\)
\(14\) −5.87666 −1.57060
\(15\) −0.652555 −0.168489
\(16\) −1.82864 −0.457159
\(17\) −1.92138 −0.466004 −0.233002 0.972476i \(-0.574855\pi\)
−0.233002 + 0.972476i \(0.574855\pi\)
\(18\) −2.18651 −0.515366
\(19\) 8.00888 1.83736 0.918682 0.394998i \(-0.129255\pi\)
0.918682 + 0.394998i \(0.129255\pi\)
\(20\) −1.81465 −0.405767
\(21\) 2.68769 0.586501
\(22\) −13.4187 −2.86088
\(23\) 2.70586 0.564210 0.282105 0.959383i \(-0.408967\pi\)
0.282105 + 0.959383i \(0.408967\pi\)
\(24\) −1.70730 −0.348501
\(25\) −4.57417 −0.914834
\(26\) −4.37313 −0.857642
\(27\) 1.00000 0.192450
\(28\) 7.47400 1.41245
\(29\) 1.12436 0.208788 0.104394 0.994536i \(-0.466710\pi\)
0.104394 + 0.994536i \(0.466710\pi\)
\(30\) 1.42682 0.260500
\(31\) 8.03868 1.44379 0.721895 0.692003i \(-0.243272\pi\)
0.721895 + 0.692003i \(0.243272\pi\)
\(32\) 7.41293 1.31043
\(33\) 6.13704 1.06832
\(34\) 4.20113 0.720487
\(35\) −1.75386 −0.296457
\(36\) 2.78083 0.463472
\(37\) −2.79404 −0.459337 −0.229669 0.973269i \(-0.573764\pi\)
−0.229669 + 0.973269i \(0.573764\pi\)
\(38\) −17.5115 −2.84074
\(39\) 2.00005 0.320265
\(40\) 1.11411 0.176156
\(41\) 9.02599 1.40962 0.704811 0.709395i \(-0.251032\pi\)
0.704811 + 0.709395i \(0.251032\pi\)
\(42\) −5.87666 −0.906788
\(43\) 6.61674 1.00904 0.504521 0.863399i \(-0.331669\pi\)
0.504521 + 0.863399i \(0.331669\pi\)
\(44\) 17.0661 2.57281
\(45\) −0.652555 −0.0972772
\(46\) −5.91639 −0.872324
\(47\) −9.77226 −1.42543 −0.712715 0.701453i \(-0.752535\pi\)
−0.712715 + 0.701453i \(0.752535\pi\)
\(48\) −1.82864 −0.263941
\(49\) 0.223654 0.0319506
\(50\) 10.0015 1.41442
\(51\) −1.92138 −0.269047
\(52\) 5.56181 0.771284
\(53\) −5.24965 −0.721095 −0.360547 0.932741i \(-0.617410\pi\)
−0.360547 + 0.932741i \(0.617410\pi\)
\(54\) −2.18651 −0.297547
\(55\) −4.00476 −0.540001
\(56\) −4.58868 −0.613188
\(57\) 8.00888 1.06080
\(58\) −2.45843 −0.322807
\(59\) 7.44285 0.968977 0.484488 0.874798i \(-0.339006\pi\)
0.484488 + 0.874798i \(0.339006\pi\)
\(60\) −1.81465 −0.234270
\(61\) 1.98726 0.254442 0.127221 0.991874i \(-0.459394\pi\)
0.127221 + 0.991874i \(0.459394\pi\)
\(62\) −17.5767 −2.23224
\(63\) 2.68769 0.338617
\(64\) −12.5512 −1.56890
\(65\) −1.30514 −0.161883
\(66\) −13.4187 −1.65173
\(67\) 14.8687 1.81649 0.908247 0.418433i \(-0.137421\pi\)
0.908247 + 0.418433i \(0.137421\pi\)
\(68\) −5.34304 −0.647939
\(69\) 2.70586 0.325747
\(70\) 3.83484 0.458351
\(71\) −7.12294 −0.845338 −0.422669 0.906284i \(-0.638907\pi\)
−0.422669 + 0.906284i \(0.638907\pi\)
\(72\) −1.70730 −0.201207
\(73\) 0.801682 0.0938297 0.0469149 0.998899i \(-0.485061\pi\)
0.0469149 + 0.998899i \(0.485061\pi\)
\(74\) 6.10920 0.710180
\(75\) −4.57417 −0.528180
\(76\) 22.2714 2.55470
\(77\) 16.4944 1.87972
\(78\) −4.37313 −0.495160
\(79\) −3.41932 −0.384704 −0.192352 0.981326i \(-0.561611\pi\)
−0.192352 + 0.981326i \(0.561611\pi\)
\(80\) 1.19329 0.133414
\(81\) 1.00000 0.111111
\(82\) −19.7354 −2.17941
\(83\) 3.13048 0.343615 0.171808 0.985131i \(-0.445039\pi\)
0.171808 + 0.985131i \(0.445039\pi\)
\(84\) 7.47400 0.815480
\(85\) 1.25381 0.135995
\(86\) −14.4676 −1.56008
\(87\) 1.12436 0.120544
\(88\) −10.4778 −1.11693
\(89\) −14.3573 −1.52187 −0.760936 0.648826i \(-0.775260\pi\)
−0.760936 + 0.648826i \(0.775260\pi\)
\(90\) 1.42682 0.150400
\(91\) 5.37551 0.563506
\(92\) 7.52454 0.784487
\(93\) 8.03868 0.833572
\(94\) 21.3672 2.20385
\(95\) −5.22624 −0.536201
\(96\) 7.41293 0.756579
\(97\) 18.0263 1.83029 0.915146 0.403123i \(-0.132075\pi\)
0.915146 + 0.403123i \(0.132075\pi\)
\(98\) −0.489022 −0.0493987
\(99\) 6.13704 0.616796
\(100\) −12.7200 −1.27200
\(101\) −10.2115 −1.01608 −0.508040 0.861333i \(-0.669630\pi\)
−0.508040 + 0.861333i \(0.669630\pi\)
\(102\) 4.20113 0.415973
\(103\) 14.8657 1.46476 0.732380 0.680896i \(-0.238409\pi\)
0.732380 + 0.680896i \(0.238409\pi\)
\(104\) −3.41468 −0.334837
\(105\) −1.75386 −0.171160
\(106\) 11.4784 1.11488
\(107\) 3.90660 0.377665 0.188832 0.982009i \(-0.439530\pi\)
0.188832 + 0.982009i \(0.439530\pi\)
\(108\) 2.78083 0.267586
\(109\) −3.91532 −0.375020 −0.187510 0.982263i \(-0.560042\pi\)
−0.187510 + 0.982263i \(0.560042\pi\)
\(110\) 8.75645 0.834895
\(111\) −2.79404 −0.265198
\(112\) −4.91480 −0.464405
\(113\) 6.95742 0.654499 0.327250 0.944938i \(-0.393878\pi\)
0.327250 + 0.944938i \(0.393878\pi\)
\(114\) −17.5115 −1.64010
\(115\) −1.76572 −0.164654
\(116\) 3.12666 0.290303
\(117\) 2.00005 0.184905
\(118\) −16.2739 −1.49813
\(119\) −5.16407 −0.473390
\(120\) 1.11411 0.101703
\(121\) 26.6633 2.42393
\(122\) −4.34516 −0.393392
\(123\) 9.02599 0.813846
\(124\) 22.3542 2.00747
\(125\) 6.24768 0.558809
\(126\) −5.87666 −0.523534
\(127\) 1.39821 0.124071 0.0620355 0.998074i \(-0.480241\pi\)
0.0620355 + 0.998074i \(0.480241\pi\)
\(128\) 12.6174 1.11524
\(129\) 6.61674 0.582571
\(130\) 2.85371 0.250287
\(131\) −8.78537 −0.767582 −0.383791 0.923420i \(-0.625382\pi\)
−0.383791 + 0.923420i \(0.625382\pi\)
\(132\) 17.0661 1.48541
\(133\) 21.5254 1.86649
\(134\) −32.5105 −2.80848
\(135\) −0.652555 −0.0561630
\(136\) 3.28037 0.281290
\(137\) −13.5144 −1.15462 −0.577308 0.816527i \(-0.695897\pi\)
−0.577308 + 0.816527i \(0.695897\pi\)
\(138\) −5.91639 −0.503637
\(139\) −9.85284 −0.835707 −0.417854 0.908514i \(-0.637218\pi\)
−0.417854 + 0.908514i \(0.637218\pi\)
\(140\) −4.87720 −0.412199
\(141\) −9.77226 −0.822973
\(142\) 15.5744 1.30697
\(143\) 12.2744 1.02644
\(144\) −1.82864 −0.152386
\(145\) −0.733707 −0.0609310
\(146\) −1.75289 −0.145070
\(147\) 0.223654 0.0184467
\(148\) −7.76975 −0.638670
\(149\) −17.0386 −1.39585 −0.697927 0.716169i \(-0.745894\pi\)
−0.697927 + 0.716169i \(0.745894\pi\)
\(150\) 10.0015 0.816617
\(151\) −18.1673 −1.47844 −0.739218 0.673466i \(-0.764805\pi\)
−0.739218 + 0.673466i \(0.764805\pi\)
\(152\) −13.6735 −1.10907
\(153\) −1.92138 −0.155335
\(154\) −36.0653 −2.90622
\(155\) −5.24568 −0.421343
\(156\) 5.56181 0.445301
\(157\) 12.7630 1.01860 0.509299 0.860590i \(-0.329905\pi\)
0.509299 + 0.860590i \(0.329905\pi\)
\(158\) 7.47638 0.594789
\(159\) −5.24965 −0.416324
\(160\) −4.83735 −0.382426
\(161\) 7.27250 0.573153
\(162\) −2.18651 −0.171789
\(163\) −7.50977 −0.588211 −0.294105 0.955773i \(-0.595022\pi\)
−0.294105 + 0.955773i \(0.595022\pi\)
\(164\) 25.0998 1.95996
\(165\) −4.00476 −0.311770
\(166\) −6.84483 −0.531262
\(167\) −13.0431 −1.00931 −0.504654 0.863322i \(-0.668380\pi\)
−0.504654 + 0.863322i \(0.668380\pi\)
\(168\) −4.58868 −0.354024
\(169\) −8.99980 −0.692292
\(170\) −2.74147 −0.210261
\(171\) 8.00888 0.612455
\(172\) 18.4000 1.40299
\(173\) 19.8639 1.51022 0.755111 0.655596i \(-0.227583\pi\)
0.755111 + 0.655596i \(0.227583\pi\)
\(174\) −2.45843 −0.186373
\(175\) −12.2939 −0.929334
\(176\) −11.2224 −0.845922
\(177\) 7.44285 0.559439
\(178\) 31.3924 2.35296
\(179\) −13.2540 −0.990647 −0.495324 0.868709i \(-0.664950\pi\)
−0.495324 + 0.868709i \(0.664950\pi\)
\(180\) −1.81465 −0.135256
\(181\) 20.0835 1.49279 0.746397 0.665501i \(-0.231782\pi\)
0.746397 + 0.665501i \(0.231782\pi\)
\(182\) −11.7536 −0.871236
\(183\) 1.98726 0.146902
\(184\) −4.61971 −0.340569
\(185\) 1.82326 0.134049
\(186\) −17.5767 −1.28878
\(187\) −11.7916 −0.862287
\(188\) −27.1750 −1.98194
\(189\) 2.68769 0.195500
\(190\) 11.4272 0.829018
\(191\) −6.87606 −0.497534 −0.248767 0.968563i \(-0.580025\pi\)
−0.248767 + 0.968563i \(0.580025\pi\)
\(192\) −12.5512 −0.905804
\(193\) −10.9795 −0.790322 −0.395161 0.918612i \(-0.629311\pi\)
−0.395161 + 0.918612i \(0.629311\pi\)
\(194\) −39.4147 −2.82981
\(195\) −1.30514 −0.0934633
\(196\) 0.621944 0.0444246
\(197\) −4.66023 −0.332027 −0.166014 0.986123i \(-0.553090\pi\)
−0.166014 + 0.986123i \(0.553090\pi\)
\(198\) −13.4187 −0.953626
\(199\) 3.82920 0.271445 0.135723 0.990747i \(-0.456664\pi\)
0.135723 + 0.990747i \(0.456664\pi\)
\(200\) 7.80947 0.552213
\(201\) 14.8687 1.04875
\(202\) 22.3275 1.57096
\(203\) 3.02193 0.212098
\(204\) −5.34304 −0.374088
\(205\) −5.88995 −0.411372
\(206\) −32.5040 −2.26466
\(207\) 2.70586 0.188070
\(208\) −3.65737 −0.253593
\(209\) 49.1508 3.39983
\(210\) 3.83484 0.264629
\(211\) −18.5482 −1.27691 −0.638455 0.769659i \(-0.720426\pi\)
−0.638455 + 0.769659i \(0.720426\pi\)
\(212\) −14.5984 −1.00262
\(213\) −7.12294 −0.488056
\(214\) −8.54182 −0.583907
\(215\) −4.31778 −0.294470
\(216\) −1.70730 −0.116167
\(217\) 21.6054 1.46667
\(218\) 8.56089 0.579817
\(219\) 0.801682 0.0541726
\(220\) −11.1366 −0.750827
\(221\) −3.84286 −0.258499
\(222\) 6.10920 0.410023
\(223\) 1.92216 0.128717 0.0643586 0.997927i \(-0.479500\pi\)
0.0643586 + 0.997927i \(0.479500\pi\)
\(224\) 19.9236 1.33120
\(225\) −4.57417 −0.304945
\(226\) −15.2125 −1.01192
\(227\) 16.8012 1.11513 0.557567 0.830132i \(-0.311735\pi\)
0.557567 + 0.830132i \(0.311735\pi\)
\(228\) 22.2714 1.47496
\(229\) −24.5007 −1.61905 −0.809525 0.587085i \(-0.800275\pi\)
−0.809525 + 0.587085i \(0.800275\pi\)
\(230\) 3.86077 0.254572
\(231\) 16.4944 1.08525
\(232\) −1.91962 −0.126029
\(233\) −17.0879 −1.11946 −0.559732 0.828674i \(-0.689096\pi\)
−0.559732 + 0.828674i \(0.689096\pi\)
\(234\) −4.37313 −0.285881
\(235\) 6.37694 0.415986
\(236\) 20.6973 1.34728
\(237\) −3.41932 −0.222109
\(238\) 11.2913 0.731907
\(239\) −15.4605 −1.00006 −0.500028 0.866009i \(-0.666677\pi\)
−0.500028 + 0.866009i \(0.666677\pi\)
\(240\) 1.19329 0.0770264
\(241\) −18.8038 −1.21126 −0.605631 0.795746i \(-0.707079\pi\)
−0.605631 + 0.795746i \(0.707079\pi\)
\(242\) −58.2995 −3.74764
\(243\) 1.00000 0.0641500
\(244\) 5.52623 0.353780
\(245\) −0.145946 −0.00932418
\(246\) −19.7354 −1.25828
\(247\) 16.0182 1.01921
\(248\) −13.7244 −0.871501
\(249\) 3.13048 0.198386
\(250\) −13.6606 −0.863973
\(251\) −3.37724 −0.213170 −0.106585 0.994304i \(-0.533992\pi\)
−0.106585 + 0.994304i \(0.533992\pi\)
\(252\) 7.47400 0.470818
\(253\) 16.6060 1.04401
\(254\) −3.05720 −0.191826
\(255\) 1.25381 0.0785165
\(256\) −2.48581 −0.155363
\(257\) 19.3182 1.20503 0.602517 0.798106i \(-0.294165\pi\)
0.602517 + 0.798106i \(0.294165\pi\)
\(258\) −14.4676 −0.900711
\(259\) −7.50950 −0.466618
\(260\) −3.62939 −0.225085
\(261\) 1.12436 0.0695961
\(262\) 19.2093 1.18676
\(263\) 0.619074 0.0381737 0.0190869 0.999818i \(-0.493924\pi\)
0.0190869 + 0.999818i \(0.493924\pi\)
\(264\) −10.4778 −0.644861
\(265\) 3.42569 0.210438
\(266\) −47.0654 −2.88577
\(267\) −14.3573 −0.878654
\(268\) 41.3472 2.52568
\(269\) 7.64782 0.466296 0.233148 0.972441i \(-0.425097\pi\)
0.233148 + 0.972441i \(0.425097\pi\)
\(270\) 1.42682 0.0868335
\(271\) 1.12885 0.0685729 0.0342864 0.999412i \(-0.489084\pi\)
0.0342864 + 0.999412i \(0.489084\pi\)
\(272\) 3.51351 0.213038
\(273\) 5.37551 0.325341
\(274\) 29.5494 1.78515
\(275\) −28.0719 −1.69280
\(276\) 7.52454 0.452924
\(277\) −31.2374 −1.87687 −0.938437 0.345452i \(-0.887726\pi\)
−0.938437 + 0.345452i \(0.887726\pi\)
\(278\) 21.5434 1.29208
\(279\) 8.03868 0.481263
\(280\) 2.99437 0.178948
\(281\) 17.8540 1.06508 0.532539 0.846405i \(-0.321238\pi\)
0.532539 + 0.846405i \(0.321238\pi\)
\(282\) 21.3672 1.27240
\(283\) −0.972284 −0.0577963 −0.0288982 0.999582i \(-0.509200\pi\)
−0.0288982 + 0.999582i \(0.509200\pi\)
\(284\) −19.8077 −1.17537
\(285\) −5.22624 −0.309576
\(286\) −26.8381 −1.58697
\(287\) 24.2590 1.43196
\(288\) 7.41293 0.436811
\(289\) −13.3083 −0.782840
\(290\) 1.60426 0.0942053
\(291\) 18.0263 1.05672
\(292\) 2.22934 0.130462
\(293\) −26.8200 −1.56684 −0.783420 0.621492i \(-0.786527\pi\)
−0.783420 + 0.621492i \(0.786527\pi\)
\(294\) −0.489022 −0.0285203
\(295\) −4.85687 −0.282778
\(296\) 4.77026 0.277266
\(297\) 6.13704 0.356107
\(298\) 37.2550 2.15813
\(299\) 5.41186 0.312976
\(300\) −12.7200 −0.734390
\(301\) 17.7837 1.02504
\(302\) 39.7231 2.28581
\(303\) −10.2115 −0.586634
\(304\) −14.6453 −0.839968
\(305\) −1.29679 −0.0742543
\(306\) 4.20113 0.240162
\(307\) 0.676932 0.0386345 0.0193173 0.999813i \(-0.493851\pi\)
0.0193173 + 0.999813i \(0.493851\pi\)
\(308\) 45.8682 2.61359
\(309\) 14.8657 0.845680
\(310\) 11.4697 0.651437
\(311\) −21.1307 −1.19821 −0.599107 0.800669i \(-0.704478\pi\)
−0.599107 + 0.800669i \(0.704478\pi\)
\(312\) −3.41468 −0.193318
\(313\) 27.7779 1.57010 0.785049 0.619433i \(-0.212638\pi\)
0.785049 + 0.619433i \(0.212638\pi\)
\(314\) −27.9064 −1.57485
\(315\) −1.75386 −0.0988190
\(316\) −9.50855 −0.534898
\(317\) −33.5260 −1.88301 −0.941503 0.337004i \(-0.890587\pi\)
−0.941503 + 0.337004i \(0.890587\pi\)
\(318\) 11.4784 0.643678
\(319\) 6.90024 0.386339
\(320\) 8.19034 0.457854
\(321\) 3.90660 0.218045
\(322\) −15.9014 −0.886150
\(323\) −15.3881 −0.856219
\(324\) 2.78083 0.154491
\(325\) −9.14858 −0.507472
\(326\) 16.4202 0.909431
\(327\) −3.91532 −0.216518
\(328\) −15.4100 −0.850877
\(329\) −26.2648 −1.44802
\(330\) 8.75645 0.482027
\(331\) 14.2425 0.782838 0.391419 0.920213i \(-0.371984\pi\)
0.391419 + 0.920213i \(0.371984\pi\)
\(332\) 8.70534 0.477768
\(333\) −2.79404 −0.153112
\(334\) 28.5190 1.56049
\(335\) −9.70262 −0.530111
\(336\) −4.91480 −0.268125
\(337\) 24.8892 1.35580 0.677901 0.735153i \(-0.262890\pi\)
0.677901 + 0.735153i \(0.262890\pi\)
\(338\) 19.6782 1.07035
\(339\) 6.95742 0.377875
\(340\) 3.48663 0.189089
\(341\) 49.3337 2.67157
\(342\) −17.5115 −0.946914
\(343\) −18.2127 −0.983393
\(344\) −11.2967 −0.609079
\(345\) −1.76572 −0.0950633
\(346\) −43.4326 −2.33495
\(347\) −25.7231 −1.38089 −0.690443 0.723387i \(-0.742584\pi\)
−0.690443 + 0.723387i \(0.742584\pi\)
\(348\) 3.12666 0.167606
\(349\) 10.5942 0.567094 0.283547 0.958958i \(-0.408489\pi\)
0.283547 + 0.958958i \(0.408489\pi\)
\(350\) 26.8808 1.43684
\(351\) 2.00005 0.106755
\(352\) 45.4935 2.42481
\(353\) 12.4870 0.664616 0.332308 0.943171i \(-0.392173\pi\)
0.332308 + 0.943171i \(0.392173\pi\)
\(354\) −16.2739 −0.864947
\(355\) 4.64811 0.246696
\(356\) −39.9253 −2.11604
\(357\) −5.16407 −0.273312
\(358\) 28.9799 1.53164
\(359\) 11.2207 0.592203 0.296102 0.955156i \(-0.404313\pi\)
0.296102 + 0.955156i \(0.404313\pi\)
\(360\) 1.11411 0.0587185
\(361\) 45.1422 2.37591
\(362\) −43.9128 −2.30800
\(363\) 26.6633 1.39946
\(364\) 14.9484 0.783508
\(365\) −0.523141 −0.0273825
\(366\) −4.34516 −0.227125
\(367\) −5.64357 −0.294592 −0.147296 0.989092i \(-0.547057\pi\)
−0.147296 + 0.989092i \(0.547057\pi\)
\(368\) −4.94804 −0.257934
\(369\) 9.02599 0.469874
\(370\) −3.98659 −0.207253
\(371\) −14.1094 −0.732524
\(372\) 22.3542 1.15901
\(373\) −11.9364 −0.618043 −0.309021 0.951055i \(-0.600001\pi\)
−0.309021 + 0.951055i \(0.600001\pi\)
\(374\) 25.7825 1.33318
\(375\) 6.24768 0.322629
\(376\) 16.6842 0.860420
\(377\) 2.24878 0.115818
\(378\) −5.87666 −0.302263
\(379\) −14.7330 −0.756785 −0.378392 0.925645i \(-0.623523\pi\)
−0.378392 + 0.925645i \(0.623523\pi\)
\(380\) −14.5333 −0.745542
\(381\) 1.39821 0.0716324
\(382\) 15.0346 0.769236
\(383\) 14.4450 0.738103 0.369051 0.929409i \(-0.379683\pi\)
0.369051 + 0.929409i \(0.379683\pi\)
\(384\) 12.6174 0.643881
\(385\) −10.7635 −0.548560
\(386\) 24.0068 1.22191
\(387\) 6.61674 0.336348
\(388\) 50.1281 2.54487
\(389\) −23.9944 −1.21657 −0.608283 0.793721i \(-0.708141\pi\)
−0.608283 + 0.793721i \(0.708141\pi\)
\(390\) 2.85371 0.144503
\(391\) −5.19899 −0.262924
\(392\) −0.381844 −0.0192860
\(393\) −8.78537 −0.443163
\(394\) 10.1896 0.513347
\(395\) 2.23129 0.112269
\(396\) 17.0661 0.857603
\(397\) −30.2401 −1.51771 −0.758854 0.651261i \(-0.774240\pi\)
−0.758854 + 0.651261i \(0.774240\pi\)
\(398\) −8.37260 −0.419680
\(399\) 21.5254 1.07762
\(400\) 8.36450 0.418225
\(401\) 21.9369 1.09548 0.547738 0.836650i \(-0.315489\pi\)
0.547738 + 0.836650i \(0.315489\pi\)
\(402\) −32.5105 −1.62148
\(403\) 16.0778 0.800891
\(404\) −28.3964 −1.41277
\(405\) −0.652555 −0.0324257
\(406\) −6.60747 −0.327923
\(407\) −17.1471 −0.849952
\(408\) 3.28037 0.162403
\(409\) −21.5971 −1.06791 −0.533954 0.845514i \(-0.679294\pi\)
−0.533954 + 0.845514i \(0.679294\pi\)
\(410\) 12.8785 0.636021
\(411\) −13.5144 −0.666617
\(412\) 41.3390 2.03663
\(413\) 20.0040 0.984335
\(414\) −5.91639 −0.290775
\(415\) −2.04281 −0.100278
\(416\) 14.8262 0.726916
\(417\) −9.85284 −0.482496
\(418\) −107.469 −5.25647
\(419\) −10.6821 −0.521855 −0.260927 0.965358i \(-0.584028\pi\)
−0.260927 + 0.965358i \(0.584028\pi\)
\(420\) −4.87720 −0.237983
\(421\) −7.04420 −0.343314 −0.171657 0.985157i \(-0.554912\pi\)
−0.171657 + 0.985157i \(0.554912\pi\)
\(422\) 40.5558 1.97423
\(423\) −9.77226 −0.475144
\(424\) 8.96271 0.435268
\(425\) 8.78873 0.426316
\(426\) 15.5744 0.754582
\(427\) 5.34112 0.258475
\(428\) 10.8636 0.525111
\(429\) 12.2744 0.592613
\(430\) 9.44089 0.455280
\(431\) −34.8480 −1.67857 −0.839285 0.543691i \(-0.817026\pi\)
−0.839285 + 0.543691i \(0.817026\pi\)
\(432\) −1.82864 −0.0879804
\(433\) 20.7170 0.995598 0.497799 0.867292i \(-0.334142\pi\)
0.497799 + 0.867292i \(0.334142\pi\)
\(434\) −47.2405 −2.26762
\(435\) −0.733707 −0.0351786
\(436\) −10.8878 −0.521433
\(437\) 21.6709 1.03666
\(438\) −1.75289 −0.0837561
\(439\) 5.80589 0.277100 0.138550 0.990355i \(-0.455756\pi\)
0.138550 + 0.990355i \(0.455756\pi\)
\(440\) 6.83731 0.325956
\(441\) 0.223654 0.0106502
\(442\) 8.40247 0.399665
\(443\) −37.5687 −1.78494 −0.892470 0.451106i \(-0.851030\pi\)
−0.892470 + 0.451106i \(0.851030\pi\)
\(444\) −7.76975 −0.368736
\(445\) 9.36894 0.444130
\(446\) −4.20282 −0.199009
\(447\) −17.0386 −0.805897
\(448\) −33.7336 −1.59376
\(449\) −0.143300 −0.00676274 −0.00338137 0.999994i \(-0.501076\pi\)
−0.00338137 + 0.999994i \(0.501076\pi\)
\(450\) 10.0015 0.471474
\(451\) 55.3928 2.60835
\(452\) 19.3474 0.910026
\(453\) −18.1673 −0.853576
\(454\) −36.7360 −1.72411
\(455\) −3.50782 −0.164449
\(456\) −13.6735 −0.640323
\(457\) 9.71023 0.454225 0.227113 0.973868i \(-0.427071\pi\)
0.227113 + 0.973868i \(0.427071\pi\)
\(458\) 53.5710 2.50321
\(459\) −1.92138 −0.0896825
\(460\) −4.91018 −0.228938
\(461\) −0.134998 −0.00628749 −0.00314374 0.999995i \(-0.501001\pi\)
−0.00314374 + 0.999995i \(0.501001\pi\)
\(462\) −36.0653 −1.67791
\(463\) 28.2002 1.31057 0.655287 0.755380i \(-0.272548\pi\)
0.655287 + 0.755380i \(0.272548\pi\)
\(464\) −2.05605 −0.0954496
\(465\) −5.24568 −0.243263
\(466\) 37.3629 1.73080
\(467\) −19.1322 −0.885331 −0.442665 0.896687i \(-0.645967\pi\)
−0.442665 + 0.896687i \(0.645967\pi\)
\(468\) 5.56181 0.257095
\(469\) 39.9623 1.84529
\(470\) −13.9433 −0.643154
\(471\) 12.7630 0.588088
\(472\) −12.7072 −0.584895
\(473\) 40.6072 1.86712
\(474\) 7.47638 0.343402
\(475\) −36.6340 −1.68088
\(476\) −14.3604 −0.658209
\(477\) −5.24965 −0.240365
\(478\) 33.8045 1.54618
\(479\) 23.4978 1.07364 0.536821 0.843696i \(-0.319625\pi\)
0.536821 + 0.843696i \(0.319625\pi\)
\(480\) −4.83735 −0.220794
\(481\) −5.58822 −0.254801
\(482\) 41.1148 1.87273
\(483\) 7.27250 0.330910
\(484\) 74.1461 3.37028
\(485\) −11.7631 −0.534137
\(486\) −2.18651 −0.0991822
\(487\) 21.9006 0.992411 0.496206 0.868205i \(-0.334726\pi\)
0.496206 + 0.868205i \(0.334726\pi\)
\(488\) −3.39284 −0.153587
\(489\) −7.50977 −0.339604
\(490\) 0.319114 0.0144161
\(491\) 18.6524 0.841772 0.420886 0.907114i \(-0.361719\pi\)
0.420886 + 0.907114i \(0.361719\pi\)
\(492\) 25.0998 1.13158
\(493\) −2.16033 −0.0972962
\(494\) −35.0239 −1.57580
\(495\) −4.00476 −0.180000
\(496\) −14.6998 −0.660042
\(497\) −19.1442 −0.858736
\(498\) −6.84483 −0.306724
\(499\) 25.0170 1.11991 0.559957 0.828522i \(-0.310818\pi\)
0.559957 + 0.828522i \(0.310818\pi\)
\(500\) 17.3737 0.776977
\(501\) −13.0431 −0.582724
\(502\) 7.38438 0.329581
\(503\) −0.146721 −0.00654198 −0.00327099 0.999995i \(-0.501041\pi\)
−0.00327099 + 0.999995i \(0.501041\pi\)
\(504\) −4.58868 −0.204396
\(505\) 6.66356 0.296524
\(506\) −36.3091 −1.61414
\(507\) −8.99980 −0.399695
\(508\) 3.88818 0.172510
\(509\) −7.09949 −0.314679 −0.157340 0.987545i \(-0.550292\pi\)
−0.157340 + 0.987545i \(0.550292\pi\)
\(510\) −2.74147 −0.121394
\(511\) 2.15467 0.0953169
\(512\) −19.7996 −0.875028
\(513\) 8.00888 0.353601
\(514\) −42.2394 −1.86310
\(515\) −9.70069 −0.427463
\(516\) 18.4000 0.810016
\(517\) −59.9728 −2.63760
\(518\) 16.4196 0.721436
\(519\) 19.8639 0.871928
\(520\) 2.22827 0.0977161
\(521\) 8.65426 0.379150 0.189575 0.981866i \(-0.439289\pi\)
0.189575 + 0.981866i \(0.439289\pi\)
\(522\) −2.45843 −0.107602
\(523\) −2.51679 −0.110052 −0.0550258 0.998485i \(-0.517524\pi\)
−0.0550258 + 0.998485i \(0.517524\pi\)
\(524\) −24.4306 −1.06726
\(525\) −12.2939 −0.536551
\(526\) −1.35361 −0.0590203
\(527\) −15.4454 −0.672811
\(528\) −11.2224 −0.488393
\(529\) −15.6783 −0.681667
\(530\) −7.49030 −0.325358
\(531\) 7.44285 0.322992
\(532\) 59.8584 2.59519
\(533\) 18.0524 0.781938
\(534\) 31.3924 1.35848
\(535\) −2.54927 −0.110215
\(536\) −25.3852 −1.09647
\(537\) −13.2540 −0.571950
\(538\) −16.7220 −0.720938
\(539\) 1.37257 0.0591209
\(540\) −1.81465 −0.0780899
\(541\) 23.8170 1.02397 0.511987 0.858993i \(-0.328910\pi\)
0.511987 + 0.858993i \(0.328910\pi\)
\(542\) −2.46825 −0.106020
\(543\) 20.0835 0.861865
\(544\) −14.2431 −0.610667
\(545\) 2.55496 0.109443
\(546\) −11.7536 −0.503008
\(547\) −32.0708 −1.37125 −0.685624 0.727956i \(-0.740471\pi\)
−0.685624 + 0.727956i \(0.740471\pi\)
\(548\) −37.5813 −1.60540
\(549\) 1.98726 0.0848141
\(550\) 61.3795 2.61723
\(551\) 9.00487 0.383620
\(552\) −4.61971 −0.196628
\(553\) −9.19006 −0.390801
\(554\) 68.3009 2.90183
\(555\) 1.82326 0.0773933
\(556\) −27.3991 −1.16198
\(557\) −40.7966 −1.72861 −0.864303 0.502971i \(-0.832240\pi\)
−0.864303 + 0.502971i \(0.832240\pi\)
\(558\) −17.5767 −0.744079
\(559\) 13.2338 0.559730
\(560\) 3.20718 0.135528
\(561\) −11.7916 −0.497842
\(562\) −39.0379 −1.64672
\(563\) −28.4638 −1.19960 −0.599802 0.800148i \(-0.704754\pi\)
−0.599802 + 0.800148i \(0.704754\pi\)
\(564\) −27.1750 −1.14427
\(565\) −4.54010 −0.191003
\(566\) 2.12591 0.0893587
\(567\) 2.68769 0.112872
\(568\) 12.1610 0.510263
\(569\) −23.4160 −0.981650 −0.490825 0.871258i \(-0.663305\pi\)
−0.490825 + 0.871258i \(0.663305\pi\)
\(570\) 11.4272 0.478634
\(571\) −27.7694 −1.16211 −0.581056 0.813864i \(-0.697360\pi\)
−0.581056 + 0.813864i \(0.697360\pi\)
\(572\) 34.1330 1.42717
\(573\) −6.87606 −0.287251
\(574\) −53.0426 −2.21396
\(575\) −12.3771 −0.516159
\(576\) −12.5512 −0.522966
\(577\) −21.3672 −0.889528 −0.444764 0.895648i \(-0.646712\pi\)
−0.444764 + 0.895648i \(0.646712\pi\)
\(578\) 29.0987 1.21035
\(579\) −10.9795 −0.456292
\(580\) −2.04032 −0.0847195
\(581\) 8.41375 0.349061
\(582\) −39.4147 −1.63379
\(583\) −32.2173 −1.33430
\(584\) −1.36871 −0.0566376
\(585\) −1.30514 −0.0539611
\(586\) 58.6422 2.42249
\(587\) 23.8070 0.982619 0.491309 0.870985i \(-0.336518\pi\)
0.491309 + 0.870985i \(0.336518\pi\)
\(588\) 0.621944 0.0256485
\(589\) 64.3808 2.65277
\(590\) 10.6196 0.437202
\(591\) −4.66023 −0.191696
\(592\) 5.10929 0.209990
\(593\) 14.3937 0.591078 0.295539 0.955331i \(-0.404501\pi\)
0.295539 + 0.955331i \(0.404501\pi\)
\(594\) −13.4187 −0.550576
\(595\) 3.36984 0.138150
\(596\) −47.3814 −1.94082
\(597\) 3.82920 0.156719
\(598\) −11.8331 −0.483891
\(599\) −27.3054 −1.11567 −0.557835 0.829952i \(-0.688368\pi\)
−0.557835 + 0.829952i \(0.688368\pi\)
\(600\) 7.80947 0.318820
\(601\) −25.4834 −1.03949 −0.519745 0.854322i \(-0.673973\pi\)
−0.519745 + 0.854322i \(0.673973\pi\)
\(602\) −38.8843 −1.58480
\(603\) 14.8687 0.605498
\(604\) −50.5203 −2.05564
\(605\) −17.3993 −0.707380
\(606\) 22.3275 0.906994
\(607\) 23.4614 0.952269 0.476134 0.879372i \(-0.342038\pi\)
0.476134 + 0.879372i \(0.342038\pi\)
\(608\) 59.3693 2.40774
\(609\) 3.02193 0.122455
\(610\) 2.83546 0.114804
\(611\) −19.5450 −0.790707
\(612\) −5.34304 −0.215980
\(613\) −26.1108 −1.05461 −0.527303 0.849677i \(-0.676797\pi\)
−0.527303 + 0.849677i \(0.676797\pi\)
\(614\) −1.48012 −0.0597328
\(615\) −5.88995 −0.237506
\(616\) −28.1609 −1.13464
\(617\) 41.7210 1.67962 0.839811 0.542879i \(-0.182666\pi\)
0.839811 + 0.542879i \(0.182666\pi\)
\(618\) −32.5040 −1.30750
\(619\) 4.44877 0.178811 0.0894055 0.995995i \(-0.471503\pi\)
0.0894055 + 0.995995i \(0.471503\pi\)
\(620\) −14.5874 −0.585842
\(621\) 2.70586 0.108582
\(622\) 46.2026 1.85256
\(623\) −38.5880 −1.54599
\(624\) −3.65737 −0.146412
\(625\) 18.7939 0.751756
\(626\) −60.7367 −2.42753
\(627\) 49.1508 1.96290
\(628\) 35.4917 1.41627
\(629\) 5.36842 0.214053
\(630\) 3.83484 0.152784
\(631\) −21.3634 −0.850464 −0.425232 0.905084i \(-0.639807\pi\)
−0.425232 + 0.905084i \(0.639807\pi\)
\(632\) 5.83780 0.232215
\(633\) −18.5482 −0.737224
\(634\) 73.3049 2.91131
\(635\) −0.912408 −0.0362078
\(636\) −14.5984 −0.578864
\(637\) 0.447319 0.0177234
\(638\) −15.0875 −0.597318
\(639\) −7.12294 −0.281779
\(640\) −8.23358 −0.325461
\(641\) 21.8440 0.862785 0.431393 0.902164i \(-0.358022\pi\)
0.431393 + 0.902164i \(0.358022\pi\)
\(642\) −8.54182 −0.337119
\(643\) −22.9196 −0.903860 −0.451930 0.892053i \(-0.649264\pi\)
−0.451930 + 0.892053i \(0.649264\pi\)
\(644\) 20.2236 0.796921
\(645\) −4.31778 −0.170013
\(646\) 33.6463 1.32380
\(647\) 6.73789 0.264894 0.132447 0.991190i \(-0.457717\pi\)
0.132447 + 0.991190i \(0.457717\pi\)
\(648\) −1.70730 −0.0670690
\(649\) 45.6771 1.79298
\(650\) 20.0035 0.784601
\(651\) 21.6054 0.846784
\(652\) −20.8834 −0.817857
\(653\) 26.3951 1.03292 0.516461 0.856311i \(-0.327249\pi\)
0.516461 + 0.856311i \(0.327249\pi\)
\(654\) 8.56089 0.334757
\(655\) 5.73294 0.224005
\(656\) −16.5053 −0.644422
\(657\) 0.801682 0.0312766
\(658\) 57.4282 2.23878
\(659\) 29.4785 1.14832 0.574159 0.818744i \(-0.305329\pi\)
0.574159 + 0.818744i \(0.305329\pi\)
\(660\) −11.1366 −0.433490
\(661\) −44.0953 −1.71511 −0.857554 0.514394i \(-0.828017\pi\)
−0.857554 + 0.514394i \(0.828017\pi\)
\(662\) −31.1414 −1.21034
\(663\) −3.84286 −0.149244
\(664\) −5.34466 −0.207413
\(665\) −14.0465 −0.544699
\(666\) 6.10920 0.236727
\(667\) 3.04236 0.117801
\(668\) −36.2708 −1.40336
\(669\) 1.92216 0.0743149
\(670\) 21.2149 0.819602
\(671\) 12.1959 0.470817
\(672\) 19.9236 0.768571
\(673\) 40.6645 1.56750 0.783752 0.621074i \(-0.213304\pi\)
0.783752 + 0.621074i \(0.213304\pi\)
\(674\) −54.4206 −2.09620
\(675\) −4.57417 −0.176060
\(676\) −25.0269 −0.962574
\(677\) 40.2436 1.54669 0.773344 0.633987i \(-0.218583\pi\)
0.773344 + 0.633987i \(0.218583\pi\)
\(678\) −15.2125 −0.584232
\(679\) 48.4490 1.85930
\(680\) −2.14062 −0.0820892
\(681\) 16.8012 0.643823
\(682\) −107.869 −4.13050
\(683\) 13.1245 0.502196 0.251098 0.967962i \(-0.419208\pi\)
0.251098 + 0.967962i \(0.419208\pi\)
\(684\) 22.2714 0.851567
\(685\) 8.81891 0.336953
\(686\) 39.8222 1.52042
\(687\) −24.5007 −0.934759
\(688\) −12.0996 −0.461293
\(689\) −10.4996 −0.400002
\(690\) 3.86077 0.146977
\(691\) −49.2232 −1.87254 −0.936269 0.351285i \(-0.885745\pi\)
−0.936269 + 0.351285i \(0.885745\pi\)
\(692\) 55.2381 2.09984
\(693\) 16.4944 0.626572
\(694\) 56.2438 2.13498
\(695\) 6.42952 0.243886
\(696\) −1.91962 −0.0727629
\(697\) −17.3424 −0.656889
\(698\) −23.1643 −0.876782
\(699\) −17.0879 −0.646323
\(700\) −34.1874 −1.29216
\(701\) 48.4682 1.83062 0.915310 0.402749i \(-0.131945\pi\)
0.915310 + 0.402749i \(0.131945\pi\)
\(702\) −4.37313 −0.165053
\(703\) −22.3771 −0.843970
\(704\) −77.0271 −2.90307
\(705\) 6.37694 0.240169
\(706\) −27.3030 −1.02756
\(707\) −27.4453 −1.03219
\(708\) 20.6973 0.777853
\(709\) −1.36550 −0.0512825 −0.0256413 0.999671i \(-0.508163\pi\)
−0.0256413 + 0.999671i \(0.508163\pi\)
\(710\) −10.1631 −0.381416
\(711\) −3.41932 −0.128235
\(712\) 24.5122 0.918634
\(713\) 21.7515 0.814601
\(714\) 11.2913 0.422566
\(715\) −8.00972 −0.299547
\(716\) −36.8570 −1.37741
\(717\) −15.4605 −0.577382
\(718\) −24.5341 −0.915604
\(719\) −14.8131 −0.552437 −0.276218 0.961095i \(-0.589081\pi\)
−0.276218 + 0.961095i \(0.589081\pi\)
\(720\) 1.19329 0.0444712
\(721\) 39.9543 1.48798
\(722\) −98.7040 −3.67338
\(723\) −18.8038 −0.699322
\(724\) 55.8488 2.07561
\(725\) −5.14301 −0.191007
\(726\) −58.2995 −2.16370
\(727\) 30.5074 1.13146 0.565729 0.824591i \(-0.308595\pi\)
0.565729 + 0.824591i \(0.308595\pi\)
\(728\) −9.17759 −0.340144
\(729\) 1.00000 0.0370370
\(730\) 1.14385 0.0423360
\(731\) −12.7133 −0.470218
\(732\) 5.52623 0.204255
\(733\) −3.44415 −0.127212 −0.0636062 0.997975i \(-0.520260\pi\)
−0.0636062 + 0.997975i \(0.520260\pi\)
\(734\) 12.3397 0.455468
\(735\) −0.145946 −0.00538332
\(736\) 20.0583 0.739361
\(737\) 91.2495 3.36122
\(738\) −19.7354 −0.726471
\(739\) 13.8353 0.508940 0.254470 0.967081i \(-0.418099\pi\)
0.254470 + 0.967081i \(0.418099\pi\)
\(740\) 5.07019 0.186384
\(741\) 16.0182 0.588442
\(742\) 30.8504 1.13255
\(743\) −32.7485 −1.20143 −0.600713 0.799465i \(-0.705116\pi\)
−0.600713 + 0.799465i \(0.705116\pi\)
\(744\) −13.7244 −0.503161
\(745\) 11.1186 0.407354
\(746\) 26.0990 0.955554
\(747\) 3.13048 0.114538
\(748\) −32.7905 −1.19894
\(749\) 10.4997 0.383651
\(750\) −13.6606 −0.498815
\(751\) −47.7375 −1.74197 −0.870983 0.491314i \(-0.836517\pi\)
−0.870983 + 0.491314i \(0.836517\pi\)
\(752\) 17.8699 0.651649
\(753\) −3.37724 −0.123074
\(754\) −4.91698 −0.179066
\(755\) 11.8552 0.431454
\(756\) 7.47400 0.271827
\(757\) 6.55990 0.238423 0.119212 0.992869i \(-0.461963\pi\)
0.119212 + 0.992869i \(0.461963\pi\)
\(758\) 32.2139 1.17006
\(759\) 16.6060 0.602758
\(760\) 8.92274 0.323662
\(761\) 10.7896 0.391123 0.195561 0.980691i \(-0.437347\pi\)
0.195561 + 0.980691i \(0.437347\pi\)
\(762\) −3.05720 −0.110751
\(763\) −10.5232 −0.380964
\(764\) −19.1212 −0.691779
\(765\) 1.25381 0.0453315
\(766\) −31.5841 −1.14118
\(767\) 14.8861 0.537505
\(768\) −2.48581 −0.0896991
\(769\) −18.7574 −0.676408 −0.338204 0.941073i \(-0.609819\pi\)
−0.338204 + 0.941073i \(0.609819\pi\)
\(770\) 23.5346 0.848127
\(771\) 19.3182 0.695727
\(772\) −30.5321 −1.09888
\(773\) 16.7113 0.601062 0.300531 0.953772i \(-0.402836\pi\)
0.300531 + 0.953772i \(0.402836\pi\)
\(774\) −14.4676 −0.520026
\(775\) −36.7703 −1.32083
\(776\) −30.7762 −1.10480
\(777\) −7.50950 −0.269402
\(778\) 52.4641 1.88093
\(779\) 72.2881 2.58999
\(780\) −3.62939 −0.129953
\(781\) −43.7138 −1.56420
\(782\) 11.3677 0.406506
\(783\) 1.12436 0.0401813
\(784\) −0.408982 −0.0146065
\(785\) −8.32856 −0.297259
\(786\) 19.2093 0.685174
\(787\) 34.2776 1.22186 0.610932 0.791683i \(-0.290795\pi\)
0.610932 + 0.791683i \(0.290795\pi\)
\(788\) −12.9593 −0.461656
\(789\) 0.619074 0.0220396
\(790\) −4.87875 −0.173578
\(791\) 18.6994 0.664873
\(792\) −10.4778 −0.372311
\(793\) 3.97462 0.141143
\(794\) 66.1203 2.34652
\(795\) 3.42569 0.121497
\(796\) 10.6484 0.377422
\(797\) 28.1692 0.997804 0.498902 0.866658i \(-0.333737\pi\)
0.498902 + 0.866658i \(0.333737\pi\)
\(798\) −47.0654 −1.66610
\(799\) 18.7763 0.664256
\(800\) −33.9080 −1.19883
\(801\) −14.3573 −0.507291
\(802\) −47.9652 −1.69371
\(803\) 4.91995 0.173621
\(804\) 41.3472 1.45820
\(805\) −4.74571 −0.167264
\(806\) −35.1542 −1.23825
\(807\) 7.64782 0.269216
\(808\) 17.4340 0.613327
\(809\) 52.6841 1.85228 0.926138 0.377186i \(-0.123108\pi\)
0.926138 + 0.377186i \(0.123108\pi\)
\(810\) 1.42682 0.0501333
\(811\) 39.2479 1.37818 0.689090 0.724676i \(-0.258011\pi\)
0.689090 + 0.724676i \(0.258011\pi\)
\(812\) 8.40347 0.294904
\(813\) 1.12885 0.0395906
\(814\) 37.4924 1.31411
\(815\) 4.90054 0.171658
\(816\) 3.51351 0.122998
\(817\) 52.9927 1.85398
\(818\) 47.2223 1.65109
\(819\) 5.37551 0.187835
\(820\) −16.3790 −0.571979
\(821\) 41.0399 1.43230 0.716152 0.697944i \(-0.245902\pi\)
0.716152 + 0.697944i \(0.245902\pi\)
\(822\) 29.5494 1.03066
\(823\) −34.5116 −1.20300 −0.601499 0.798873i \(-0.705430\pi\)
−0.601499 + 0.798873i \(0.705430\pi\)
\(824\) −25.3802 −0.884160
\(825\) −28.0719 −0.977337
\(826\) −43.7391 −1.52188
\(827\) 8.41939 0.292771 0.146386 0.989228i \(-0.453236\pi\)
0.146386 + 0.989228i \(0.453236\pi\)
\(828\) 7.52454 0.261496
\(829\) 40.6329 1.41124 0.705620 0.708590i \(-0.250669\pi\)
0.705620 + 0.708590i \(0.250669\pi\)
\(830\) 4.46663 0.155039
\(831\) −31.2374 −1.08361
\(832\) −25.1030 −0.870290
\(833\) −0.429725 −0.0148891
\(834\) 21.5434 0.745985
\(835\) 8.51136 0.294548
\(836\) 136.680 4.72718
\(837\) 8.03868 0.277857
\(838\) 23.3565 0.806838
\(839\) 34.5638 1.19327 0.596637 0.802511i \(-0.296503\pi\)
0.596637 + 0.802511i \(0.296503\pi\)
\(840\) 2.99437 0.103315
\(841\) −27.7358 −0.956407
\(842\) 15.4022 0.530796
\(843\) 17.8540 0.614924
\(844\) −51.5794 −1.77544
\(845\) 5.87286 0.202033
\(846\) 21.3672 0.734618
\(847\) 71.6625 2.46235
\(848\) 9.59971 0.329655
\(849\) −0.972284 −0.0333687
\(850\) −19.2167 −0.659126
\(851\) −7.56028 −0.259163
\(852\) −19.8077 −0.678601
\(853\) 37.9728 1.30016 0.650082 0.759864i \(-0.274735\pi\)
0.650082 + 0.759864i \(0.274735\pi\)
\(854\) −11.6784 −0.399627
\(855\) −5.22624 −0.178734
\(856\) −6.66972 −0.227966
\(857\) −41.7626 −1.42658 −0.713291 0.700868i \(-0.752796\pi\)
−0.713291 + 0.700868i \(0.752796\pi\)
\(858\) −26.8381 −0.916238
\(859\) 0.450663 0.0153764 0.00768822 0.999970i \(-0.497553\pi\)
0.00768822 + 0.999970i \(0.497553\pi\)
\(860\) −12.0070 −0.409436
\(861\) 24.2590 0.826745
\(862\) 76.1956 2.59523
\(863\) −39.0769 −1.33019 −0.665097 0.746757i \(-0.731610\pi\)
−0.665097 + 0.746757i \(0.731610\pi\)
\(864\) 7.41293 0.252193
\(865\) −12.9623 −0.440731
\(866\) −45.2981 −1.53929
\(867\) −13.3083 −0.451973
\(868\) 60.0811 2.03929
\(869\) −20.9845 −0.711850
\(870\) 1.60426 0.0543895
\(871\) 29.7381 1.00764
\(872\) 6.68462 0.226370
\(873\) 18.0263 0.610097
\(874\) −47.3837 −1.60278
\(875\) 16.7918 0.567666
\(876\) 2.22934 0.0753225
\(877\) 6.02916 0.203590 0.101795 0.994805i \(-0.467541\pi\)
0.101795 + 0.994805i \(0.467541\pi\)
\(878\) −12.6946 −0.428423
\(879\) −26.8200 −0.904616
\(880\) 7.32325 0.246867
\(881\) 8.76369 0.295256 0.147628 0.989043i \(-0.452836\pi\)
0.147628 + 0.989043i \(0.452836\pi\)
\(882\) −0.489022 −0.0164662
\(883\) 55.2541 1.85945 0.929725 0.368255i \(-0.120045\pi\)
0.929725 + 0.368255i \(0.120045\pi\)
\(884\) −10.6864 −0.359421
\(885\) −4.85687 −0.163262
\(886\) 82.1443 2.75969
\(887\) 0.260653 0.00875187 0.00437594 0.999990i \(-0.498607\pi\)
0.00437594 + 0.999990i \(0.498607\pi\)
\(888\) 4.77026 0.160079
\(889\) 3.75794 0.126037
\(890\) −20.4853 −0.686669
\(891\) 6.13704 0.205599
\(892\) 5.34519 0.178970
\(893\) −78.2649 −2.61904
\(894\) 37.2550 1.24599
\(895\) 8.64894 0.289102
\(896\) 33.9117 1.13291
\(897\) 5.41186 0.180697
\(898\) 0.313327 0.0104558
\(899\) 9.03837 0.301446
\(900\) −12.7200 −0.424000
\(901\) 10.0866 0.336033
\(902\) −121.117 −4.03276
\(903\) 17.7837 0.591805
\(904\) −11.8784 −0.395069
\(905\) −13.1056 −0.435645
\(906\) 39.7231 1.31971
\(907\) −42.6676 −1.41675 −0.708377 0.705834i \(-0.750572\pi\)
−0.708377 + 0.705834i \(0.750572\pi\)
\(908\) 46.7213 1.55050
\(909\) −10.2115 −0.338694
\(910\) 7.66988 0.254254
\(911\) 41.5197 1.37561 0.687804 0.725896i \(-0.258575\pi\)
0.687804 + 0.725896i \(0.258575\pi\)
\(912\) −14.6453 −0.484956
\(913\) 19.2119 0.635821
\(914\) −21.2315 −0.702277
\(915\) −1.29679 −0.0428707
\(916\) −68.1323 −2.25115
\(917\) −23.6123 −0.779747
\(918\) 4.20113 0.138658
\(919\) −35.2159 −1.16167 −0.580833 0.814023i \(-0.697273\pi\)
−0.580833 + 0.814023i \(0.697273\pi\)
\(920\) 3.01461 0.0993888
\(921\) 0.676932 0.0223057
\(922\) 0.295175 0.00972107
\(923\) −14.2462 −0.468921
\(924\) 45.8682 1.50895
\(925\) 12.7804 0.420217
\(926\) −61.6600 −2.02627
\(927\) 14.8657 0.488253
\(928\) 8.33480 0.273603
\(929\) −18.3817 −0.603083 −0.301542 0.953453i \(-0.597501\pi\)
−0.301542 + 0.953453i \(0.597501\pi\)
\(930\) 11.4697 0.376108
\(931\) 1.79122 0.0587048
\(932\) −47.5185 −1.55652
\(933\) −21.1307 −0.691789
\(934\) 41.8327 1.36881
\(935\) 7.69467 0.251643
\(936\) −3.41468 −0.111612
\(937\) −32.7210 −1.06895 −0.534474 0.845185i \(-0.679490\pi\)
−0.534474 + 0.845185i \(0.679490\pi\)
\(938\) −87.3779 −2.85299
\(939\) 27.7779 0.906497
\(940\) 17.7332 0.578393
\(941\) −21.7375 −0.708623 −0.354311 0.935128i \(-0.615285\pi\)
−0.354311 + 0.935128i \(0.615285\pi\)
\(942\) −27.9064 −0.909241
\(943\) 24.4230 0.795324
\(944\) −13.6103 −0.442977
\(945\) −1.75386 −0.0570532
\(946\) −88.7880 −2.88675
\(947\) 10.0913 0.327923 0.163962 0.986467i \(-0.447573\pi\)
0.163962 + 0.986467i \(0.447573\pi\)
\(948\) −9.50855 −0.308823
\(949\) 1.60340 0.0520487
\(950\) 80.1007 2.59881
\(951\) −33.5260 −1.08715
\(952\) 8.81661 0.285748
\(953\) 20.2619 0.656349 0.328174 0.944617i \(-0.393567\pi\)
0.328174 + 0.944617i \(0.393567\pi\)
\(954\) 11.4784 0.371627
\(955\) 4.48701 0.145196
\(956\) −42.9930 −1.39049
\(957\) 6.90024 0.223053
\(958\) −51.3783 −1.65996
\(959\) −36.3225 −1.17292
\(960\) 8.19034 0.264342
\(961\) 33.6203 1.08453
\(962\) 12.2187 0.393947
\(963\) 3.90660 0.125888
\(964\) −52.2903 −1.68416
\(965\) 7.16473 0.230641
\(966\) −15.9014 −0.511619
\(967\) 49.8507 1.60309 0.801546 0.597933i \(-0.204011\pi\)
0.801546 + 0.597933i \(0.204011\pi\)
\(968\) −45.5221 −1.46314
\(969\) −15.3881 −0.494338
\(970\) 25.7203 0.825828
\(971\) 10.2722 0.329650 0.164825 0.986323i \(-0.447294\pi\)
0.164825 + 0.986323i \(0.447294\pi\)
\(972\) 2.78083 0.0891952
\(973\) −26.4813 −0.848953
\(974\) −47.8859 −1.53436
\(975\) −9.14858 −0.292989
\(976\) −3.63397 −0.116321
\(977\) −15.7281 −0.503187 −0.251593 0.967833i \(-0.580955\pi\)
−0.251593 + 0.967833i \(0.580955\pi\)
\(978\) 16.4202 0.525060
\(979\) −88.1114 −2.81605
\(980\) −0.405853 −0.0129645
\(981\) −3.91532 −0.125007
\(982\) −40.7837 −1.30146
\(983\) 9.91869 0.316357 0.158179 0.987411i \(-0.449438\pi\)
0.158179 + 0.987411i \(0.449438\pi\)
\(984\) −15.4100 −0.491254
\(985\) 3.04105 0.0968961
\(986\) 4.72358 0.150429
\(987\) −26.2648 −0.836017
\(988\) 44.5439 1.41713
\(989\) 17.9039 0.569312
\(990\) 8.75645 0.278298
\(991\) 45.9476 1.45957 0.729786 0.683675i \(-0.239619\pi\)
0.729786 + 0.683675i \(0.239619\pi\)
\(992\) 59.5902 1.89199
\(993\) 14.2425 0.451972
\(994\) 41.8591 1.32769
\(995\) −2.49877 −0.0792163
\(996\) 8.70534 0.275839
\(997\) −7.02739 −0.222560 −0.111280 0.993789i \(-0.535495\pi\)
−0.111280 + 0.993789i \(0.535495\pi\)
\(998\) −54.6999 −1.73150
\(999\) −2.79404 −0.0883995
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 \(a_p\))