Properties

Label 4031.2.a.c.1.16
Level 4031
Weight 2
Character 4031.1
Self dual Yes
Analytic conductor 32.188
Analytic rank 1
Dimension 61
CM No

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Newspace parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(61\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.50584 q^{2}\) \(-0.996538 q^{3}\) \(+0.267567 q^{4}\) \(+0.533194 q^{5}\) \(+1.50063 q^{6}\) \(+3.56628 q^{7}\) \(+2.60877 q^{8}\) \(-2.00691 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.50584 q^{2}\) \(-0.996538 q^{3}\) \(+0.267567 q^{4}\) \(+0.533194 q^{5}\) \(+1.50063 q^{6}\) \(+3.56628 q^{7}\) \(+2.60877 q^{8}\) \(-2.00691 q^{9}\) \(-0.802908 q^{10}\) \(-1.85590 q^{11}\) \(-0.266641 q^{12}\) \(-0.546756 q^{13}\) \(-5.37026 q^{14}\) \(-0.531348 q^{15}\) \(-4.46354 q^{16}\) \(+3.22596 q^{17}\) \(+3.02210 q^{18}\) \(+0.447533 q^{19}\) \(+0.142665 q^{20}\) \(-3.55393 q^{21}\) \(+2.79470 q^{22}\) \(+4.54791 q^{23}\) \(-2.59974 q^{24}\) \(-4.71570 q^{25}\) \(+0.823330 q^{26}\) \(+4.98958 q^{27}\) \(+0.954220 q^{28}\) \(-1.00000 q^{29}\) \(+0.800128 q^{30}\) \(-1.38386 q^{31}\) \(+1.50385 q^{32}\) \(+1.84948 q^{33}\) \(-4.85779 q^{34}\) \(+1.90152 q^{35}\) \(-0.536984 q^{36}\) \(-1.42959 q^{37}\) \(-0.673915 q^{38}\) \(+0.544863 q^{39}\) \(+1.39098 q^{40}\) \(-4.79477 q^{41}\) \(+5.35167 q^{42}\) \(-1.84240 q^{43}\) \(-0.496579 q^{44}\) \(-1.07007 q^{45}\) \(-6.84844 q^{46}\) \(-11.9403 q^{47}\) \(+4.44809 q^{48}\) \(+5.71835 q^{49}\) \(+7.10112 q^{50}\) \(-3.21479 q^{51}\) \(-0.146294 q^{52}\) \(-8.51261 q^{53}\) \(-7.51353 q^{54}\) \(-0.989557 q^{55}\) \(+9.30362 q^{56}\) \(-0.445983 q^{57}\) \(+1.50584 q^{58}\) \(+0.183189 q^{59}\) \(-0.142171 q^{60}\) \(+10.1235 q^{61}\) \(+2.08387 q^{62}\) \(-7.15721 q^{63}\) \(+6.66252 q^{64}\) \(-0.291527 q^{65}\) \(-2.78502 q^{66}\) \(-0.991572 q^{67}\) \(+0.863161 q^{68}\) \(-4.53216 q^{69}\) \(-2.86339 q^{70}\) \(+6.65460 q^{71}\) \(-5.23558 q^{72}\) \(+5.08255 q^{73}\) \(+2.15273 q^{74}\) \(+4.69938 q^{75}\) \(+0.119745 q^{76}\) \(-6.61867 q^{77}\) \(-0.820479 q^{78}\) \(-16.2374 q^{79}\) \(-2.37994 q^{80}\) \(+1.04844 q^{81}\) \(+7.22018 q^{82}\) \(-17.4016 q^{83}\) \(-0.950916 q^{84}\) \(+1.72006 q^{85}\) \(+2.77437 q^{86}\) \(+0.996538 q^{87}\) \(-4.84163 q^{88}\) \(+8.28978 q^{89}\) \(+1.61137 q^{90}\) \(-1.94988 q^{91}\) \(+1.21687 q^{92}\) \(+1.37906 q^{93}\) \(+17.9802 q^{94}\) \(+0.238622 q^{95}\) \(-1.49865 q^{96}\) \(-12.3705 q^{97}\) \(-8.61094 q^{98}\) \(+3.72463 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50584 −1.06479 −0.532396 0.846495i \(-0.678708\pi\)
−0.532396 + 0.846495i \(0.678708\pi\)
\(3\) −0.996538 −0.575351 −0.287676 0.957728i \(-0.592883\pi\)
−0.287676 + 0.957728i \(0.592883\pi\)
\(4\) 0.267567 0.133784
\(5\) 0.533194 0.238452 0.119226 0.992867i \(-0.461959\pi\)
0.119226 + 0.992867i \(0.461959\pi\)
\(6\) 1.50063 0.612630
\(7\) 3.56628 1.34793 0.673963 0.738765i \(-0.264591\pi\)
0.673963 + 0.738765i \(0.264591\pi\)
\(8\) 2.60877 0.922341
\(9\) −2.00691 −0.668971
\(10\) −0.802908 −0.253902
\(11\) −1.85590 −0.559576 −0.279788 0.960062i \(-0.590264\pi\)
−0.279788 + 0.960062i \(0.590264\pi\)
\(12\) −0.266641 −0.0769726
\(13\) −0.546756 −0.151643 −0.0758214 0.997121i \(-0.524158\pi\)
−0.0758214 + 0.997121i \(0.524158\pi\)
\(14\) −5.37026 −1.43526
\(15\) −0.531348 −0.137194
\(16\) −4.46354 −1.11589
\(17\) 3.22596 0.782410 0.391205 0.920304i \(-0.372058\pi\)
0.391205 + 0.920304i \(0.372058\pi\)
\(18\) 3.02210 0.712315
\(19\) 0.447533 0.102671 0.0513355 0.998681i \(-0.483652\pi\)
0.0513355 + 0.998681i \(0.483652\pi\)
\(20\) 0.142665 0.0319010
\(21\) −3.55393 −0.775531
\(22\) 2.79470 0.595832
\(23\) 4.54791 0.948305 0.474152 0.880443i \(-0.342755\pi\)
0.474152 + 0.880443i \(0.342755\pi\)
\(24\) −2.59974 −0.530670
\(25\) −4.71570 −0.943141
\(26\) 0.823330 0.161468
\(27\) 4.98958 0.960245
\(28\) 0.954220 0.180331
\(29\) −1.00000 −0.185695
\(30\) 0.800128 0.146083
\(31\) −1.38386 −0.248548 −0.124274 0.992248i \(-0.539660\pi\)
−0.124274 + 0.992248i \(0.539660\pi\)
\(32\) 1.50385 0.265846
\(33\) 1.84948 0.321953
\(34\) −4.85779 −0.833104
\(35\) 1.90152 0.321416
\(36\) −0.536984 −0.0894974
\(37\) −1.42959 −0.235022 −0.117511 0.993072i \(-0.537492\pi\)
−0.117511 + 0.993072i \(0.537492\pi\)
\(38\) −0.673915 −0.109323
\(39\) 0.544863 0.0872479
\(40\) 1.39098 0.219934
\(41\) −4.79477 −0.748817 −0.374409 0.927264i \(-0.622154\pi\)
−0.374409 + 0.927264i \(0.622154\pi\)
\(42\) 5.35167 0.825780
\(43\) −1.84240 −0.280963 −0.140482 0.990083i \(-0.544865\pi\)
−0.140482 + 0.990083i \(0.544865\pi\)
\(44\) −0.496579 −0.0748621
\(45\) −1.07007 −0.159517
\(46\) −6.84844 −1.00975
\(47\) −11.9403 −1.74167 −0.870835 0.491576i \(-0.836421\pi\)
−0.870835 + 0.491576i \(0.836421\pi\)
\(48\) 4.44809 0.642026
\(49\) 5.71835 0.816907
\(50\) 7.10112 1.00425
\(51\) −3.21479 −0.450160
\(52\) −0.146294 −0.0202873
\(53\) −8.51261 −1.16930 −0.584649 0.811287i \(-0.698768\pi\)
−0.584649 + 0.811287i \(0.698768\pi\)
\(54\) −7.51353 −1.02246
\(55\) −0.989557 −0.133432
\(56\) 9.30362 1.24325
\(57\) −0.445983 −0.0590719
\(58\) 1.50584 0.197727
\(59\) 0.183189 0.0238492 0.0119246 0.999929i \(-0.496204\pi\)
0.0119246 + 0.999929i \(0.496204\pi\)
\(60\) −0.142171 −0.0183543
\(61\) 10.1235 1.29619 0.648093 0.761562i \(-0.275567\pi\)
0.648093 + 0.761562i \(0.275567\pi\)
\(62\) 2.08387 0.264652
\(63\) −7.15721 −0.901724
\(64\) 6.66252 0.832815
\(65\) −0.291527 −0.0361595
\(66\) −2.78502 −0.342813
\(67\) −0.991572 −0.121140 −0.0605699 0.998164i \(-0.519292\pi\)
−0.0605699 + 0.998164i \(0.519292\pi\)
\(68\) 0.863161 0.104674
\(69\) −4.53216 −0.545608
\(70\) −2.86339 −0.342241
\(71\) 6.65460 0.789755 0.394878 0.918734i \(-0.370787\pi\)
0.394878 + 0.918734i \(0.370787\pi\)
\(72\) −5.23558 −0.617019
\(73\) 5.08255 0.594867 0.297434 0.954742i \(-0.403869\pi\)
0.297434 + 0.954742i \(0.403869\pi\)
\(74\) 2.15273 0.250250
\(75\) 4.69938 0.542637
\(76\) 0.119745 0.0137357
\(77\) −6.61867 −0.754267
\(78\) −0.820479 −0.0929009
\(79\) −16.2374 −1.82685 −0.913427 0.407002i \(-0.866574\pi\)
−0.913427 + 0.407002i \(0.866574\pi\)
\(80\) −2.37994 −0.266085
\(81\) 1.04844 0.116493
\(82\) 7.22018 0.797335
\(83\) −17.4016 −1.91007 −0.955035 0.296494i \(-0.904183\pi\)
−0.955035 + 0.296494i \(0.904183\pi\)
\(84\) −0.950916 −0.103753
\(85\) 1.72006 0.186567
\(86\) 2.77437 0.299168
\(87\) 0.996538 0.106840
\(88\) −4.84163 −0.516120
\(89\) 8.28978 0.878715 0.439358 0.898312i \(-0.355206\pi\)
0.439358 + 0.898312i \(0.355206\pi\)
\(90\) 1.61137 0.169853
\(91\) −1.94988 −0.204403
\(92\) 1.21687 0.126868
\(93\) 1.37906 0.143002
\(94\) 17.9802 1.85452
\(95\) 0.238622 0.0244821
\(96\) −1.49865 −0.152955
\(97\) −12.3705 −1.25604 −0.628019 0.778198i \(-0.716134\pi\)
−0.628019 + 0.778198i \(0.716134\pi\)
\(98\) −8.61094 −0.869837
\(99\) 3.72463 0.374340
\(100\) −1.26177 −0.126177
\(101\) 9.80623 0.975756 0.487878 0.872912i \(-0.337771\pi\)
0.487878 + 0.872912i \(0.337771\pi\)
\(102\) 4.84097 0.479328
\(103\) −6.58895 −0.649229 −0.324614 0.945846i \(-0.605235\pi\)
−0.324614 + 0.945846i \(0.605235\pi\)
\(104\) −1.42636 −0.139866
\(105\) −1.89494 −0.184927
\(106\) 12.8187 1.24506
\(107\) 1.77285 0.171387 0.0856937 0.996322i \(-0.472689\pi\)
0.0856937 + 0.996322i \(0.472689\pi\)
\(108\) 1.33505 0.128465
\(109\) 10.6745 1.02243 0.511216 0.859452i \(-0.329195\pi\)
0.511216 + 0.859452i \(0.329195\pi\)
\(110\) 1.49012 0.142077
\(111\) 1.42464 0.135220
\(112\) −15.9182 −1.50413
\(113\) 6.62343 0.623080 0.311540 0.950233i \(-0.399155\pi\)
0.311540 + 0.950233i \(0.399155\pi\)
\(114\) 0.671581 0.0628994
\(115\) 2.42492 0.226125
\(116\) −0.267567 −0.0248430
\(117\) 1.09729 0.101445
\(118\) −0.275854 −0.0253945
\(119\) 11.5047 1.05463
\(120\) −1.38617 −0.126539
\(121\) −7.55563 −0.686875
\(122\) −15.2445 −1.38017
\(123\) 4.77817 0.430833
\(124\) −0.370275 −0.0332517
\(125\) −5.18036 −0.463345
\(126\) 10.7776 0.960149
\(127\) 12.0085 1.06558 0.532792 0.846246i \(-0.321143\pi\)
0.532792 + 0.846246i \(0.321143\pi\)
\(128\) −13.0404 −1.15262
\(129\) 1.83602 0.161653
\(130\) 0.438995 0.0385024
\(131\) 10.4677 0.914565 0.457282 0.889322i \(-0.348823\pi\)
0.457282 + 0.889322i \(0.348823\pi\)
\(132\) 0.494860 0.0430720
\(133\) 1.59603 0.138393
\(134\) 1.49315 0.128989
\(135\) 2.66041 0.228972
\(136\) 8.41579 0.721648
\(137\) 6.77339 0.578690 0.289345 0.957225i \(-0.406563\pi\)
0.289345 + 0.957225i \(0.406563\pi\)
\(138\) 6.82473 0.580960
\(139\) −1.00000 −0.0848189
\(140\) 0.508785 0.0430002
\(141\) 11.8989 1.00207
\(142\) −10.0208 −0.840926
\(143\) 1.01473 0.0848557
\(144\) 8.95794 0.746495
\(145\) −0.533194 −0.0442794
\(146\) −7.65353 −0.633410
\(147\) −5.69855 −0.470008
\(148\) −0.382511 −0.0314422
\(149\) 10.9634 0.898158 0.449079 0.893492i \(-0.351752\pi\)
0.449079 + 0.893492i \(0.351752\pi\)
\(150\) −7.07653 −0.577796
\(151\) 9.24888 0.752663 0.376331 0.926485i \(-0.377185\pi\)
0.376331 + 0.926485i \(0.377185\pi\)
\(152\) 1.16751 0.0946977
\(153\) −6.47422 −0.523409
\(154\) 9.96668 0.803138
\(155\) −0.737864 −0.0592667
\(156\) 0.145788 0.0116723
\(157\) 6.64000 0.529930 0.264965 0.964258i \(-0.414640\pi\)
0.264965 + 0.964258i \(0.414640\pi\)
\(158\) 24.4511 1.94522
\(159\) 8.48314 0.672757
\(160\) 0.801846 0.0633915
\(161\) 16.2191 1.27825
\(162\) −1.57878 −0.124041
\(163\) −9.30139 −0.728541 −0.364271 0.931293i \(-0.618682\pi\)
−0.364271 + 0.931293i \(0.618682\pi\)
\(164\) −1.28292 −0.100180
\(165\) 0.986131 0.0767702
\(166\) 26.2040 2.03383
\(167\) 0.921978 0.0713448 0.0356724 0.999364i \(-0.488643\pi\)
0.0356724 + 0.999364i \(0.488643\pi\)
\(168\) −9.27140 −0.715304
\(169\) −12.7011 −0.977004
\(170\) −2.59015 −0.198655
\(171\) −0.898159 −0.0686840
\(172\) −0.492966 −0.0375883
\(173\) −4.11889 −0.313153 −0.156577 0.987666i \(-0.550046\pi\)
−0.156577 + 0.987666i \(0.550046\pi\)
\(174\) −1.50063 −0.113763
\(175\) −16.8175 −1.27128
\(176\) 8.28390 0.624422
\(177\) −0.182555 −0.0137217
\(178\) −12.4831 −0.935649
\(179\) −1.50370 −0.112392 −0.0561958 0.998420i \(-0.517897\pi\)
−0.0561958 + 0.998420i \(0.517897\pi\)
\(180\) −0.286317 −0.0213408
\(181\) −12.0879 −0.898485 −0.449242 0.893410i \(-0.648306\pi\)
−0.449242 + 0.893410i \(0.648306\pi\)
\(182\) 2.93622 0.217647
\(183\) −10.0885 −0.745762
\(184\) 11.8645 0.874660
\(185\) −0.762247 −0.0560415
\(186\) −2.07666 −0.152268
\(187\) −5.98706 −0.437817
\(188\) −3.19483 −0.233007
\(189\) 17.7942 1.29434
\(190\) −0.359328 −0.0260684
\(191\) −9.73818 −0.704630 −0.352315 0.935881i \(-0.614605\pi\)
−0.352315 + 0.935881i \(0.614605\pi\)
\(192\) −6.63945 −0.479161
\(193\) −2.99921 −0.215888 −0.107944 0.994157i \(-0.534427\pi\)
−0.107944 + 0.994157i \(0.534427\pi\)
\(194\) 18.6281 1.33742
\(195\) 0.290518 0.0208044
\(196\) 1.53004 0.109289
\(197\) −6.66612 −0.474941 −0.237471 0.971395i \(-0.576318\pi\)
−0.237471 + 0.971395i \(0.576318\pi\)
\(198\) −5.60872 −0.398594
\(199\) 5.54858 0.393329 0.196664 0.980471i \(-0.436989\pi\)
0.196664 + 0.980471i \(0.436989\pi\)
\(200\) −12.3022 −0.869897
\(201\) 0.988138 0.0696979
\(202\) −14.7666 −1.03898
\(203\) −3.56628 −0.250304
\(204\) −0.860173 −0.0602241
\(205\) −2.55654 −0.178557
\(206\) 9.92194 0.691294
\(207\) −9.12726 −0.634388
\(208\) 2.44047 0.169216
\(209\) −0.830577 −0.0574522
\(210\) 2.85348 0.196909
\(211\) −24.1942 −1.66560 −0.832798 0.553576i \(-0.813263\pi\)
−0.832798 + 0.553576i \(0.813263\pi\)
\(212\) −2.27770 −0.156433
\(213\) −6.63156 −0.454387
\(214\) −2.66963 −0.182492
\(215\) −0.982357 −0.0669962
\(216\) 13.0167 0.885673
\(217\) −4.93522 −0.335024
\(218\) −16.0741 −1.08868
\(219\) −5.06495 −0.342258
\(220\) −0.264773 −0.0178510
\(221\) −1.76381 −0.118647
\(222\) −2.14528 −0.143982
\(223\) 9.44158 0.632255 0.316128 0.948717i \(-0.397617\pi\)
0.316128 + 0.948717i \(0.397617\pi\)
\(224\) 5.36316 0.358341
\(225\) 9.46401 0.630934
\(226\) −9.97386 −0.663451
\(227\) 21.5271 1.42881 0.714403 0.699734i \(-0.246698\pi\)
0.714403 + 0.699734i \(0.246698\pi\)
\(228\) −0.119331 −0.00790286
\(229\) −23.9008 −1.57941 −0.789703 0.613489i \(-0.789766\pi\)
−0.789703 + 0.613489i \(0.789766\pi\)
\(230\) −3.65155 −0.240776
\(231\) 6.59575 0.433969
\(232\) −2.60877 −0.171274
\(233\) 6.52276 0.427320 0.213660 0.976908i \(-0.431461\pi\)
0.213660 + 0.976908i \(0.431461\pi\)
\(234\) −1.65235 −0.108018
\(235\) −6.36649 −0.415304
\(236\) 0.0490155 0.00319063
\(237\) 16.1812 1.05108
\(238\) −17.3242 −1.12296
\(239\) −25.0050 −1.61744 −0.808721 0.588193i \(-0.799840\pi\)
−0.808721 + 0.588193i \(0.799840\pi\)
\(240\) 2.37170 0.153092
\(241\) 15.4575 0.995707 0.497854 0.867261i \(-0.334122\pi\)
0.497854 + 0.867261i \(0.334122\pi\)
\(242\) 11.3776 0.731380
\(243\) −16.0135 −1.02727
\(244\) 2.70873 0.173408
\(245\) 3.04899 0.194793
\(246\) −7.19518 −0.458748
\(247\) −0.244691 −0.0155693
\(248\) −3.61017 −0.229246
\(249\) 17.3413 1.09896
\(250\) 7.80081 0.493367
\(251\) 4.60415 0.290612 0.145306 0.989387i \(-0.453583\pi\)
0.145306 + 0.989387i \(0.453583\pi\)
\(252\) −1.91504 −0.120636
\(253\) −8.44048 −0.530648
\(254\) −18.0830 −1.13463
\(255\) −1.71411 −0.107342
\(256\) 6.31181 0.394488
\(257\) −20.0195 −1.24879 −0.624393 0.781111i \(-0.714653\pi\)
−0.624393 + 0.781111i \(0.714653\pi\)
\(258\) −2.76476 −0.172127
\(259\) −5.09830 −0.316793
\(260\) −0.0780032 −0.00483755
\(261\) 2.00691 0.124225
\(262\) −15.7627 −0.973822
\(263\) 6.83942 0.421737 0.210868 0.977514i \(-0.432371\pi\)
0.210868 + 0.977514i \(0.432371\pi\)
\(264\) 4.82487 0.296950
\(265\) −4.53888 −0.278821
\(266\) −2.40337 −0.147360
\(267\) −8.26108 −0.505570
\(268\) −0.265312 −0.0162065
\(269\) 23.4324 1.42870 0.714350 0.699789i \(-0.246723\pi\)
0.714350 + 0.699789i \(0.246723\pi\)
\(270\) −4.00617 −0.243808
\(271\) −20.0439 −1.21758 −0.608790 0.793331i \(-0.708345\pi\)
−0.608790 + 0.793331i \(0.708345\pi\)
\(272\) −14.3992 −0.873080
\(273\) 1.94313 0.117604
\(274\) −10.1997 −0.616185
\(275\) 8.75189 0.527759
\(276\) −1.21266 −0.0729935
\(277\) −11.0581 −0.664419 −0.332210 0.943206i \(-0.607794\pi\)
−0.332210 + 0.943206i \(0.607794\pi\)
\(278\) 1.50584 0.0903145
\(279\) 2.77728 0.166271
\(280\) 4.96064 0.296455
\(281\) −28.0077 −1.67080 −0.835399 0.549643i \(-0.814764\pi\)
−0.835399 + 0.549643i \(0.814764\pi\)
\(282\) −17.9180 −1.06700
\(283\) −15.7444 −0.935908 −0.467954 0.883753i \(-0.655009\pi\)
−0.467954 + 0.883753i \(0.655009\pi\)
\(284\) 1.78055 0.105656
\(285\) −0.237796 −0.0140858
\(286\) −1.52802 −0.0903537
\(287\) −17.0995 −1.00935
\(288\) −3.01810 −0.177843
\(289\) −6.59320 −0.387835
\(290\) 0.802908 0.0471484
\(291\) 12.3277 0.722663
\(292\) 1.35992 0.0795836
\(293\) 11.1312 0.650290 0.325145 0.945664i \(-0.394587\pi\)
0.325145 + 0.945664i \(0.394587\pi\)
\(294\) 8.58113 0.500462
\(295\) 0.0976754 0.00568688
\(296\) −3.72947 −0.216771
\(297\) −9.26017 −0.537329
\(298\) −16.5092 −0.956352
\(299\) −2.48660 −0.143804
\(300\) 1.25740 0.0725960
\(301\) −6.57051 −0.378718
\(302\) −13.9274 −0.801430
\(303\) −9.77227 −0.561402
\(304\) −1.99758 −0.114569
\(305\) 5.39781 0.309078
\(306\) 9.74916 0.557322
\(307\) −15.5498 −0.887474 −0.443737 0.896157i \(-0.646348\pi\)
−0.443737 + 0.896157i \(0.646348\pi\)
\(308\) −1.77094 −0.100909
\(309\) 6.56614 0.373535
\(310\) 1.11111 0.0631067
\(311\) −6.43317 −0.364792 −0.182396 0.983225i \(-0.558385\pi\)
−0.182396 + 0.983225i \(0.558385\pi\)
\(312\) 1.42142 0.0804723
\(313\) −29.9163 −1.69097 −0.845484 0.534001i \(-0.820688\pi\)
−0.845484 + 0.534001i \(0.820688\pi\)
\(314\) −9.99880 −0.564265
\(315\) −3.81618 −0.215018
\(316\) −4.34461 −0.244403
\(317\) −6.34686 −0.356475 −0.178238 0.983987i \(-0.557040\pi\)
−0.178238 + 0.983987i \(0.557040\pi\)
\(318\) −12.7743 −0.716347
\(319\) 1.85590 0.103911
\(320\) 3.55242 0.198586
\(321\) −1.76671 −0.0986080
\(322\) −24.4235 −1.36107
\(323\) 1.44372 0.0803308
\(324\) 0.280528 0.0155849
\(325\) 2.57834 0.143021
\(326\) 14.0064 0.775745
\(327\) −10.6375 −0.588258
\(328\) −12.5085 −0.690665
\(329\) −42.5824 −2.34764
\(330\) −1.48496 −0.0817443
\(331\) 5.15247 0.283205 0.141603 0.989924i \(-0.454774\pi\)
0.141603 + 0.989924i \(0.454774\pi\)
\(332\) −4.65609 −0.255536
\(333\) 2.86905 0.157223
\(334\) −1.38836 −0.0759674
\(335\) −0.528700 −0.0288860
\(336\) 15.8631 0.865404
\(337\) 11.7453 0.639809 0.319905 0.947450i \(-0.396349\pi\)
0.319905 + 0.947450i \(0.396349\pi\)
\(338\) 19.1258 1.04031
\(339\) −6.60050 −0.358490
\(340\) 0.460233 0.0249596
\(341\) 2.56830 0.139081
\(342\) 1.35249 0.0731342
\(343\) −4.57073 −0.246796
\(344\) −4.80640 −0.259144
\(345\) −2.41652 −0.130101
\(346\) 6.20240 0.333443
\(347\) −11.9719 −0.642687 −0.321344 0.946963i \(-0.604134\pi\)
−0.321344 + 0.946963i \(0.604134\pi\)
\(348\) 0.266641 0.0142935
\(349\) −31.8967 −1.70739 −0.853695 0.520774i \(-0.825643\pi\)
−0.853695 + 0.520774i \(0.825643\pi\)
\(350\) 25.3246 1.35365
\(351\) −2.72808 −0.145614
\(352\) −2.79100 −0.148761
\(353\) −4.04102 −0.215082 −0.107541 0.994201i \(-0.534298\pi\)
−0.107541 + 0.994201i \(0.534298\pi\)
\(354\) 0.274899 0.0146107
\(355\) 3.54819 0.188319
\(356\) 2.21808 0.117558
\(357\) −11.4648 −0.606783
\(358\) 2.26433 0.119674
\(359\) 9.42565 0.497467 0.248733 0.968572i \(-0.419986\pi\)
0.248733 + 0.968572i \(0.419986\pi\)
\(360\) −2.79158 −0.147129
\(361\) −18.7997 −0.989459
\(362\) 18.2025 0.956700
\(363\) 7.52947 0.395194
\(364\) −0.521726 −0.0273459
\(365\) 2.70999 0.141847
\(366\) 15.1917 0.794082
\(367\) −8.95622 −0.467511 −0.233756 0.972295i \(-0.575102\pi\)
−0.233756 + 0.972295i \(0.575102\pi\)
\(368\) −20.2998 −1.05820
\(369\) 9.62268 0.500937
\(370\) 1.14783 0.0596726
\(371\) −30.3584 −1.57613
\(372\) 0.368993 0.0191314
\(373\) −20.5670 −1.06492 −0.532459 0.846456i \(-0.678732\pi\)
−0.532459 + 0.846456i \(0.678732\pi\)
\(374\) 9.01559 0.466185
\(375\) 5.16242 0.266586
\(376\) −31.1495 −1.60641
\(377\) 0.546756 0.0281594
\(378\) −26.7953 −1.37820
\(379\) 8.03308 0.412632 0.206316 0.978485i \(-0.433853\pi\)
0.206316 + 0.978485i \(0.433853\pi\)
\(380\) 0.0638475 0.00327531
\(381\) −11.9670 −0.613086
\(382\) 14.6642 0.750285
\(383\) 2.22058 0.113466 0.0567332 0.998389i \(-0.481932\pi\)
0.0567332 + 0.998389i \(0.481932\pi\)
\(384\) 12.9953 0.663162
\(385\) −3.52904 −0.179856
\(386\) 4.51634 0.229876
\(387\) 3.69754 0.187956
\(388\) −3.30995 −0.168037
\(389\) 19.2054 0.973752 0.486876 0.873471i \(-0.338136\pi\)
0.486876 + 0.873471i \(0.338136\pi\)
\(390\) −0.437475 −0.0221524
\(391\) 14.6714 0.741963
\(392\) 14.9179 0.753467
\(393\) −10.4314 −0.526196
\(394\) 10.0381 0.505714
\(395\) −8.65771 −0.435617
\(396\) 0.996591 0.0500806
\(397\) −9.61856 −0.482742 −0.241371 0.970433i \(-0.577597\pi\)
−0.241371 + 0.970433i \(0.577597\pi\)
\(398\) −8.35530 −0.418813
\(399\) −1.59050 −0.0796246
\(400\) 21.0487 1.05244
\(401\) 19.9900 0.998253 0.499126 0.866529i \(-0.333654\pi\)
0.499126 + 0.866529i \(0.333654\pi\)
\(402\) −1.48798 −0.0742138
\(403\) 0.756632 0.0376905
\(404\) 2.62383 0.130540
\(405\) 0.559021 0.0277780
\(406\) 5.37026 0.266522
\(407\) 2.65317 0.131513
\(408\) −8.38666 −0.415201
\(409\) −14.6149 −0.722659 −0.361329 0.932438i \(-0.617677\pi\)
−0.361329 + 0.932438i \(0.617677\pi\)
\(410\) 3.84976 0.190126
\(411\) −6.74994 −0.332950
\(412\) −1.76299 −0.0868562
\(413\) 0.653304 0.0321470
\(414\) 13.7442 0.675492
\(415\) −9.27841 −0.455459
\(416\) −0.822241 −0.0403137
\(417\) 0.996538 0.0488007
\(418\) 1.25072 0.0611747
\(419\) 4.76640 0.232854 0.116427 0.993199i \(-0.462856\pi\)
0.116427 + 0.993199i \(0.462856\pi\)
\(420\) −0.507023 −0.0247402
\(421\) −20.7279 −1.01022 −0.505108 0.863056i \(-0.668547\pi\)
−0.505108 + 0.863056i \(0.668547\pi\)
\(422\) 36.4327 1.77352
\(423\) 23.9631 1.16513
\(424\) −22.2075 −1.07849
\(425\) −15.2127 −0.737922
\(426\) 9.98609 0.483828
\(427\) 36.1033 1.74716
\(428\) 0.474356 0.0229288
\(429\) −1.01121 −0.0488218
\(430\) 1.47928 0.0713371
\(431\) 25.5315 1.22981 0.614903 0.788602i \(-0.289195\pi\)
0.614903 + 0.788602i \(0.289195\pi\)
\(432\) −22.2712 −1.07152
\(433\) −4.93800 −0.237305 −0.118652 0.992936i \(-0.537857\pi\)
−0.118652 + 0.992936i \(0.537857\pi\)
\(434\) 7.43167 0.356732
\(435\) 0.531348 0.0254762
\(436\) 2.85615 0.136785
\(437\) 2.03534 0.0973634
\(438\) 7.62703 0.364433
\(439\) −31.7313 −1.51445 −0.757226 0.653153i \(-0.773446\pi\)
−0.757226 + 0.653153i \(0.773446\pi\)
\(440\) −2.58153 −0.123070
\(441\) −11.4762 −0.546487
\(442\) 2.65603 0.126334
\(443\) −6.75497 −0.320938 −0.160469 0.987041i \(-0.551301\pi\)
−0.160469 + 0.987041i \(0.551301\pi\)
\(444\) 0.381186 0.0180903
\(445\) 4.42006 0.209531
\(446\) −14.2176 −0.673221
\(447\) −10.9255 −0.516756
\(448\) 23.7604 1.12257
\(449\) −28.5970 −1.34958 −0.674788 0.738012i \(-0.735765\pi\)
−0.674788 + 0.738012i \(0.735765\pi\)
\(450\) −14.2513 −0.671814
\(451\) 8.89862 0.419020
\(452\) 1.77221 0.0833579
\(453\) −9.21685 −0.433046
\(454\) −32.4165 −1.52138
\(455\) −1.03967 −0.0487404
\(456\) −1.16347 −0.0544845
\(457\) 21.6677 1.01357 0.506786 0.862072i \(-0.330833\pi\)
0.506786 + 0.862072i \(0.330833\pi\)
\(458\) 35.9908 1.68174
\(459\) 16.0962 0.751305
\(460\) 0.648829 0.0302518
\(461\) −20.0139 −0.932141 −0.466070 0.884748i \(-0.654331\pi\)
−0.466070 + 0.884748i \(0.654331\pi\)
\(462\) −9.93217 −0.462087
\(463\) 15.5175 0.721159 0.360579 0.932729i \(-0.382579\pi\)
0.360579 + 0.932729i \(0.382579\pi\)
\(464\) 4.46354 0.207215
\(465\) 0.735309 0.0340992
\(466\) −9.82226 −0.455008
\(467\) 18.2714 0.845499 0.422750 0.906246i \(-0.361065\pi\)
0.422750 + 0.906246i \(0.361065\pi\)
\(468\) 0.293600 0.0135716
\(469\) −3.53622 −0.163288
\(470\) 9.58694 0.442213
\(471\) −6.61701 −0.304896
\(472\) 0.477899 0.0219971
\(473\) 3.41931 0.157220
\(474\) −24.3664 −1.11919
\(475\) −2.11043 −0.0968333
\(476\) 3.07827 0.141092
\(477\) 17.0841 0.782226
\(478\) 37.6537 1.72224
\(479\) 18.2613 0.834378 0.417189 0.908820i \(-0.363015\pi\)
0.417189 + 0.908820i \(0.363015\pi\)
\(480\) −0.799070 −0.0364724
\(481\) 0.781635 0.0356395
\(482\) −23.2766 −1.06022
\(483\) −16.1630 −0.735440
\(484\) −2.02164 −0.0918927
\(485\) −6.59590 −0.299505
\(486\) 24.1139 1.09383
\(487\) −28.7130 −1.30111 −0.650555 0.759459i \(-0.725464\pi\)
−0.650555 + 0.759459i \(0.725464\pi\)
\(488\) 26.4100 1.19552
\(489\) 9.26919 0.419167
\(490\) −4.59131 −0.207414
\(491\) −7.83568 −0.353619 −0.176810 0.984245i \(-0.556578\pi\)
−0.176810 + 0.984245i \(0.556578\pi\)
\(492\) 1.27848 0.0576384
\(493\) −3.22596 −0.145290
\(494\) 0.368467 0.0165781
\(495\) 1.98595 0.0892620
\(496\) 6.17690 0.277351
\(497\) 23.7322 1.06453
\(498\) −26.1133 −1.17017
\(499\) 32.7557 1.46635 0.733174 0.680042i \(-0.238038\pi\)
0.733174 + 0.680042i \(0.238038\pi\)
\(500\) −1.38610 −0.0619881
\(501\) −0.918786 −0.0410483
\(502\) −6.93314 −0.309441
\(503\) 31.2587 1.39375 0.696877 0.717190i \(-0.254572\pi\)
0.696877 + 0.717190i \(0.254572\pi\)
\(504\) −18.6715 −0.831697
\(505\) 5.22862 0.232671
\(506\) 12.7100 0.565030
\(507\) 12.6571 0.562121
\(508\) 3.21309 0.142558
\(509\) −13.7101 −0.607690 −0.303845 0.952721i \(-0.598271\pi\)
−0.303845 + 0.952721i \(0.598271\pi\)
\(510\) 2.58118 0.114296
\(511\) 18.1258 0.801838
\(512\) 16.5762 0.732573
\(513\) 2.23300 0.0985893
\(514\) 30.1463 1.32970
\(515\) −3.51319 −0.154810
\(516\) 0.491259 0.0216265
\(517\) 22.1600 0.974596
\(518\) 7.67725 0.337319
\(519\) 4.10462 0.180173
\(520\) −0.760529 −0.0333514
\(521\) −35.4471 −1.55296 −0.776482 0.630139i \(-0.782998\pi\)
−0.776482 + 0.630139i \(0.782998\pi\)
\(522\) −3.02210 −0.132274
\(523\) −23.7853 −1.04006 −0.520030 0.854148i \(-0.674079\pi\)
−0.520030 + 0.854148i \(0.674079\pi\)
\(524\) 2.80081 0.122354
\(525\) 16.7593 0.731435
\(526\) −10.2991 −0.449062
\(527\) −4.46426 −0.194466
\(528\) −8.25522 −0.359262
\(529\) −2.31653 −0.100719
\(530\) 6.83484 0.296887
\(531\) −0.367645 −0.0159544
\(532\) 0.427045 0.0185147
\(533\) 2.62157 0.113553
\(534\) 12.4399 0.538327
\(535\) 0.945271 0.0408676
\(536\) −2.58679 −0.111732
\(537\) 1.49849 0.0646646
\(538\) −35.2856 −1.52127
\(539\) −10.6127 −0.457121
\(540\) 0.711840 0.0306327
\(541\) 12.1302 0.521517 0.260758 0.965404i \(-0.416027\pi\)
0.260758 + 0.965404i \(0.416027\pi\)
\(542\) 30.1830 1.29647
\(543\) 12.0460 0.516944
\(544\) 4.85137 0.208001
\(545\) 5.69158 0.243801
\(546\) −2.92606 −0.125224
\(547\) 22.5418 0.963818 0.481909 0.876221i \(-0.339943\pi\)
0.481909 + 0.876221i \(0.339943\pi\)
\(548\) 1.81234 0.0774193
\(549\) −20.3170 −0.867110
\(550\) −13.1790 −0.561954
\(551\) −0.447533 −0.0190655
\(552\) −11.8234 −0.503237
\(553\) −57.9073 −2.46247
\(554\) 16.6518 0.707469
\(555\) 0.759608 0.0322436
\(556\) −0.267567 −0.0113474
\(557\) 30.5722 1.29539 0.647693 0.761901i \(-0.275734\pi\)
0.647693 + 0.761901i \(0.275734\pi\)
\(558\) −4.18215 −0.177044
\(559\) 1.00734 0.0426061
\(560\) −8.48752 −0.358663
\(561\) 5.96633 0.251899
\(562\) 42.1752 1.77905
\(563\) −5.87437 −0.247575 −0.123788 0.992309i \(-0.539504\pi\)
−0.123788 + 0.992309i \(0.539504\pi\)
\(564\) 3.18377 0.134061
\(565\) 3.53158 0.148575
\(566\) 23.7086 0.996548
\(567\) 3.73902 0.157024
\(568\) 17.3603 0.728424
\(569\) −16.8377 −0.705875 −0.352938 0.935647i \(-0.614817\pi\)
−0.352938 + 0.935647i \(0.614817\pi\)
\(570\) 0.358083 0.0149985
\(571\) 18.3488 0.767874 0.383937 0.923359i \(-0.374568\pi\)
0.383937 + 0.923359i \(0.374568\pi\)
\(572\) 0.271508 0.0113523
\(573\) 9.70446 0.405410
\(574\) 25.7492 1.07475
\(575\) −21.4466 −0.894385
\(576\) −13.3711 −0.557129
\(577\) −2.79171 −0.116220 −0.0581102 0.998310i \(-0.518507\pi\)
−0.0581102 + 0.998310i \(0.518507\pi\)
\(578\) 9.92833 0.412964
\(579\) 2.98882 0.124211
\(580\) −0.142665 −0.00592386
\(581\) −62.0588 −2.57463
\(582\) −18.5636 −0.769487
\(583\) 15.7986 0.654310
\(584\) 13.2592 0.548670
\(585\) 0.585070 0.0241897
\(586\) −16.7618 −0.692425
\(587\) 19.3686 0.799427 0.399713 0.916640i \(-0.369110\pi\)
0.399713 + 0.916640i \(0.369110\pi\)
\(588\) −1.52475 −0.0628795
\(589\) −0.619321 −0.0255187
\(590\) −0.147084 −0.00605535
\(591\) 6.64304 0.273258
\(592\) 6.38102 0.262258
\(593\) 13.0609 0.536346 0.268173 0.963371i \(-0.413580\pi\)
0.268173 + 0.963371i \(0.413580\pi\)
\(594\) 13.9444 0.572145
\(595\) 6.13422 0.251479
\(596\) 2.93345 0.120159
\(597\) −5.52937 −0.226302
\(598\) 3.74443 0.153121
\(599\) −23.6567 −0.966586 −0.483293 0.875459i \(-0.660559\pi\)
−0.483293 + 0.875459i \(0.660559\pi\)
\(600\) 12.2596 0.500496
\(601\) 6.94308 0.283214 0.141607 0.989923i \(-0.454773\pi\)
0.141607 + 0.989923i \(0.454773\pi\)
\(602\) 9.89417 0.403256
\(603\) 1.99000 0.0810390
\(604\) 2.47470 0.100694
\(605\) −4.02862 −0.163787
\(606\) 14.7155 0.597777
\(607\) −6.80474 −0.276196 −0.138098 0.990419i \(-0.544099\pi\)
−0.138098 + 0.990419i \(0.544099\pi\)
\(608\) 0.673023 0.0272947
\(609\) 3.55393 0.144013
\(610\) −8.12826 −0.329104
\(611\) 6.52842 0.264112
\(612\) −1.73229 −0.0700236
\(613\) −31.3901 −1.26784 −0.633918 0.773400i \(-0.718554\pi\)
−0.633918 + 0.773400i \(0.718554\pi\)
\(614\) 23.4156 0.944976
\(615\) 2.54769 0.102733
\(616\) −17.2666 −0.695691
\(617\) −13.9366 −0.561068 −0.280534 0.959844i \(-0.590512\pi\)
−0.280534 + 0.959844i \(0.590512\pi\)
\(618\) −9.88758 −0.397737
\(619\) −40.0631 −1.61027 −0.805136 0.593091i \(-0.797908\pi\)
−0.805136 + 0.593091i \(0.797908\pi\)
\(620\) −0.197428 −0.00792892
\(621\) 22.6921 0.910604
\(622\) 9.68735 0.388427
\(623\) 29.5637 1.18444
\(624\) −2.43202 −0.0973587
\(625\) 20.8164 0.832655
\(626\) 45.0492 1.80053
\(627\) 0.827702 0.0330552
\(628\) 1.77665 0.0708959
\(629\) −4.61178 −0.183884
\(630\) 5.74658 0.228949
\(631\) 27.7324 1.10401 0.552004 0.833841i \(-0.313863\pi\)
0.552004 + 0.833841i \(0.313863\pi\)
\(632\) −42.3598 −1.68498
\(633\) 24.1104 0.958303
\(634\) 9.55738 0.379572
\(635\) 6.40288 0.254091
\(636\) 2.26981 0.0900039
\(637\) −3.12654 −0.123878
\(638\) −2.79470 −0.110643
\(639\) −13.3552 −0.528323
\(640\) −6.95308 −0.274845
\(641\) 4.78975 0.189184 0.0945918 0.995516i \(-0.469845\pi\)
0.0945918 + 0.995516i \(0.469845\pi\)
\(642\) 2.66039 0.104997
\(643\) 17.0621 0.672863 0.336432 0.941708i \(-0.390780\pi\)
0.336432 + 0.941708i \(0.390780\pi\)
\(644\) 4.33971 0.171008
\(645\) 0.978956 0.0385463
\(646\) −2.17402 −0.0855357
\(647\) −41.9943 −1.65097 −0.825483 0.564427i \(-0.809097\pi\)
−0.825483 + 0.564427i \(0.809097\pi\)
\(648\) 2.73514 0.107446
\(649\) −0.339981 −0.0133454
\(650\) −3.88258 −0.152287
\(651\) 4.91813 0.192757
\(652\) −2.48875 −0.0974670
\(653\) −23.4678 −0.918366 −0.459183 0.888342i \(-0.651858\pi\)
−0.459183 + 0.888342i \(0.651858\pi\)
\(654\) 16.0185 0.626372
\(655\) 5.58130 0.218080
\(656\) 21.4017 0.835594
\(657\) −10.2002 −0.397949
\(658\) 64.1224 2.49975
\(659\) 43.8175 1.70689 0.853445 0.521184i \(-0.174509\pi\)
0.853445 + 0.521184i \(0.174509\pi\)
\(660\) 0.263856 0.0102706
\(661\) 29.4636 1.14600 0.573000 0.819555i \(-0.305780\pi\)
0.573000 + 0.819555i \(0.305780\pi\)
\(662\) −7.75881 −0.301555
\(663\) 1.75770 0.0682636
\(664\) −45.3967 −1.76174
\(665\) 0.850993 0.0330001
\(666\) −4.32035 −0.167410
\(667\) −4.54791 −0.176096
\(668\) 0.246691 0.00954477
\(669\) −9.40889 −0.363769
\(670\) 0.796140 0.0307576
\(671\) −18.7883 −0.725314
\(672\) −5.34459 −0.206172
\(673\) −35.7137 −1.37666 −0.688330 0.725397i \(-0.741656\pi\)
−0.688330 + 0.725397i \(0.741656\pi\)
\(674\) −17.6866 −0.681264
\(675\) −23.5294 −0.905646
\(676\) −3.39839 −0.130707
\(677\) 8.09211 0.311005 0.155502 0.987836i \(-0.450300\pi\)
0.155502 + 0.987836i \(0.450300\pi\)
\(678\) 9.93932 0.381717
\(679\) −44.1168 −1.69305
\(680\) 4.48725 0.172078
\(681\) −21.4526 −0.822066
\(682\) −3.86746 −0.148093
\(683\) −41.2516 −1.57845 −0.789224 0.614105i \(-0.789517\pi\)
−0.789224 + 0.614105i \(0.789517\pi\)
\(684\) −0.240318 −0.00918879
\(685\) 3.61153 0.137990
\(686\) 6.88281 0.262787
\(687\) 23.8180 0.908714
\(688\) 8.22363 0.313523
\(689\) 4.65432 0.177316
\(690\) 3.63891 0.138531
\(691\) 3.20874 0.122066 0.0610331 0.998136i \(-0.480560\pi\)
0.0610331 + 0.998136i \(0.480560\pi\)
\(692\) −1.10208 −0.0418948
\(693\) 13.2831 0.504583
\(694\) 18.0279 0.684329
\(695\) −0.533194 −0.0202252
\(696\) 2.59974 0.0985429
\(697\) −15.4677 −0.585882
\(698\) 48.0314 1.81802
\(699\) −6.50018 −0.245859
\(700\) −4.49982 −0.170077
\(701\) −16.7741 −0.633549 −0.316774 0.948501i \(-0.602600\pi\)
−0.316774 + 0.948501i \(0.602600\pi\)
\(702\) 4.10807 0.155049
\(703\) −0.639787 −0.0241300
\(704\) −12.3650 −0.466023
\(705\) 6.34445 0.238946
\(706\) 6.08515 0.229017
\(707\) 34.9717 1.31525
\(708\) −0.0488457 −0.00183574
\(709\) −20.2346 −0.759927 −0.379963 0.925001i \(-0.624063\pi\)
−0.379963 + 0.925001i \(0.624063\pi\)
\(710\) −5.34303 −0.200520
\(711\) 32.5871 1.22211
\(712\) 21.6262 0.810475
\(713\) −6.29365 −0.235699
\(714\) 17.2643 0.646098
\(715\) 0.541046 0.0202340
\(716\) −0.402340 −0.0150362
\(717\) 24.9185 0.930597
\(718\) −14.1936 −0.529699
\(719\) −49.3467 −1.84032 −0.920160 0.391542i \(-0.871942\pi\)
−0.920160 + 0.391542i \(0.871942\pi\)
\(720\) 4.77632 0.178003
\(721\) −23.4980 −0.875113
\(722\) 28.3094 1.05357
\(723\) −15.4040 −0.572882
\(724\) −3.23432 −0.120203
\(725\) 4.71570 0.175137
\(726\) −11.3382 −0.420800
\(727\) −21.3409 −0.791492 −0.395746 0.918360i \(-0.629514\pi\)
−0.395746 + 0.918360i \(0.629514\pi\)
\(728\) −5.08681 −0.188530
\(729\) 12.8128 0.474547
\(730\) −4.08082 −0.151038
\(731\) −5.94350 −0.219828
\(732\) −2.69935 −0.0997708
\(733\) −10.8299 −0.400010 −0.200005 0.979795i \(-0.564096\pi\)
−0.200005 + 0.979795i \(0.564096\pi\)
\(734\) 13.4867 0.497802
\(735\) −3.03843 −0.112074
\(736\) 6.83939 0.252103
\(737\) 1.84026 0.0677869
\(738\) −14.4903 −0.533394
\(739\) 20.4680 0.752926 0.376463 0.926432i \(-0.377140\pi\)
0.376463 + 0.926432i \(0.377140\pi\)
\(740\) −0.203952 −0.00749744
\(741\) 0.243844 0.00895784
\(742\) 45.7150 1.67825
\(743\) −7.06376 −0.259144 −0.129572 0.991570i \(-0.541360\pi\)
−0.129572 + 0.991570i \(0.541360\pi\)
\(744\) 3.59767 0.131897
\(745\) 5.84563 0.214167
\(746\) 30.9707 1.13392
\(747\) 34.9234 1.27778
\(748\) −1.60194 −0.0585728
\(749\) 6.32246 0.231018
\(750\) −7.77380 −0.283859
\(751\) −2.76001 −0.100714 −0.0503571 0.998731i \(-0.516036\pi\)
−0.0503571 + 0.998731i \(0.516036\pi\)
\(752\) 53.2960 1.94350
\(753\) −4.58821 −0.167204
\(754\) −0.823330 −0.0299839
\(755\) 4.93145 0.179474
\(756\) 4.76116 0.173162
\(757\) 28.6303 1.04059 0.520293 0.853988i \(-0.325823\pi\)
0.520293 + 0.853988i \(0.325823\pi\)
\(758\) −12.0966 −0.439367
\(759\) 8.41125 0.305309
\(760\) 0.622511 0.0225808
\(761\) −12.7362 −0.461685 −0.230843 0.972991i \(-0.574148\pi\)
−0.230843 + 0.972991i \(0.574148\pi\)
\(762\) 18.0204 0.652809
\(763\) 38.0683 1.37816
\(764\) −2.60562 −0.0942680
\(765\) −3.45201 −0.124808
\(766\) −3.34385 −0.120818
\(767\) −0.100160 −0.00361656
\(768\) −6.28996 −0.226969
\(769\) 11.1633 0.402560 0.201280 0.979534i \(-0.435490\pi\)
0.201280 + 0.979534i \(0.435490\pi\)
\(770\) 5.31418 0.191510
\(771\) 19.9502 0.718490
\(772\) −0.802490 −0.0288822
\(773\) 26.1489 0.940512 0.470256 0.882530i \(-0.344162\pi\)
0.470256 + 0.882530i \(0.344162\pi\)
\(774\) −5.56791 −0.200134
\(775\) 6.52586 0.234416
\(776\) −32.2720 −1.15850
\(777\) 5.08065 0.182267
\(778\) −28.9203 −1.03684
\(779\) −2.14582 −0.0768819
\(780\) 0.0777331 0.00278329
\(781\) −12.3503 −0.441928
\(782\) −22.0928 −0.790036
\(783\) −4.98958 −0.178313
\(784\) −25.5241 −0.911575
\(785\) 3.54041 0.126363
\(786\) 15.7081 0.560290
\(787\) −5.84644 −0.208403 −0.104202 0.994556i \(-0.533229\pi\)
−0.104202 + 0.994556i \(0.533229\pi\)
\(788\) −1.78364 −0.0635394
\(789\) −6.81574 −0.242647
\(790\) 13.0372 0.463842
\(791\) 23.6210 0.839866
\(792\) 9.71673 0.345269
\(793\) −5.53510 −0.196557
\(794\) 14.4841 0.514020
\(795\) 4.52316 0.160420
\(796\) 1.48462 0.0526210
\(797\) −32.1562 −1.13903 −0.569516 0.821980i \(-0.692869\pi\)
−0.569516 + 0.821980i \(0.692869\pi\)
\(798\) 2.39505 0.0847837
\(799\) −38.5188 −1.36270
\(800\) −7.09172 −0.250730
\(801\) −16.6369 −0.587835
\(802\) −30.1018 −1.06293
\(803\) −9.43271 −0.332873
\(804\) 0.264394 0.00932445
\(805\) 8.64794 0.304800
\(806\) −1.13937 −0.0401326
\(807\) −23.3513 −0.822004
\(808\) 25.5822 0.899980
\(809\) −22.5870 −0.794117 −0.397059 0.917793i \(-0.629969\pi\)
−0.397059 + 0.917793i \(0.629969\pi\)
\(810\) −0.841798 −0.0295778
\(811\) −3.88764 −0.136513 −0.0682567 0.997668i \(-0.521744\pi\)
−0.0682567 + 0.997668i \(0.521744\pi\)
\(812\) −0.954220 −0.0334866
\(813\) 19.9745 0.700536
\(814\) −3.99526 −0.140034
\(815\) −4.95945 −0.173722
\(816\) 14.3493 0.502327
\(817\) −0.824534 −0.0288468
\(818\) 22.0077 0.769482
\(819\) 3.91325 0.136740
\(820\) −0.684048 −0.0238880
\(821\) −12.4384 −0.434104 −0.217052 0.976160i \(-0.569644\pi\)
−0.217052 + 0.976160i \(0.569644\pi\)
\(822\) 10.1644 0.354523
\(823\) −3.11605 −0.108619 −0.0543094 0.998524i \(-0.517296\pi\)
−0.0543094 + 0.998524i \(0.517296\pi\)
\(824\) −17.1891 −0.598810
\(825\) −8.72158 −0.303647
\(826\) −0.983774 −0.0342299
\(827\) 27.9296 0.971206 0.485603 0.874179i \(-0.338600\pi\)
0.485603 + 0.874179i \(0.338600\pi\)
\(828\) −2.44216 −0.0848708
\(829\) 1.89086 0.0656724 0.0328362 0.999461i \(-0.489546\pi\)
0.0328362 + 0.999461i \(0.489546\pi\)
\(830\) 13.9718 0.484970
\(831\) 11.0199 0.382274
\(832\) −3.64277 −0.126290
\(833\) 18.4471 0.639156
\(834\) −1.50063 −0.0519626
\(835\) 0.491593 0.0170123
\(836\) −0.222235 −0.00768617
\(837\) −6.90486 −0.238667
\(838\) −7.17746 −0.247941
\(839\) −11.6256 −0.401360 −0.200680 0.979657i \(-0.564315\pi\)
−0.200680 + 0.979657i \(0.564315\pi\)
\(840\) −4.94346 −0.170566
\(841\) 1.00000 0.0344828
\(842\) 31.2130 1.07567
\(843\) 27.9107 0.961296
\(844\) −6.47358 −0.222830
\(845\) −6.77213 −0.232968
\(846\) −36.0847 −1.24062
\(847\) −26.9455 −0.925857
\(848\) 37.9964 1.30480
\(849\) 15.6899 0.538476
\(850\) 22.9079 0.785734
\(851\) −6.50163 −0.222873
\(852\) −1.77439 −0.0607896
\(853\) 0.954917 0.0326957 0.0163479 0.999866i \(-0.494796\pi\)
0.0163479 + 0.999866i \(0.494796\pi\)
\(854\) −54.3660 −1.86037
\(855\) −0.478893 −0.0163778
\(856\) 4.62495 0.158078
\(857\) 52.1614 1.78180 0.890900 0.454200i \(-0.150075\pi\)
0.890900 + 0.454200i \(0.150075\pi\)
\(858\) 1.52273 0.0519851
\(859\) 27.5919 0.941423 0.470712 0.882287i \(-0.343997\pi\)
0.470712 + 0.882287i \(0.343997\pi\)
\(860\) −0.262847 −0.00896300
\(861\) 17.0403 0.580731
\(862\) −38.4464 −1.30949
\(863\) −4.97719 −0.169426 −0.0847128 0.996405i \(-0.526997\pi\)
−0.0847128 + 0.996405i \(0.526997\pi\)
\(864\) 7.50359 0.255277
\(865\) −2.19617 −0.0746719
\(866\) 7.43585 0.252681
\(867\) 6.57037 0.223141
\(868\) −1.32050 −0.0448208
\(869\) 30.1351 1.02226
\(870\) −0.800128 −0.0271269
\(871\) 0.542148 0.0183700
\(872\) 27.8474 0.943031
\(873\) 24.8266 0.840253
\(874\) −3.06490 −0.103672
\(875\) −18.4746 −0.624556
\(876\) −1.35522 −0.0457885
\(877\) 5.00166 0.168894 0.0844470 0.996428i \(-0.473088\pi\)
0.0844470 + 0.996428i \(0.473088\pi\)
\(878\) 47.7824 1.61258
\(879\) −11.0926 −0.374145
\(880\) 4.41693 0.148895
\(881\) 6.24092 0.210262 0.105131 0.994458i \(-0.466474\pi\)
0.105131 + 0.994458i \(0.466474\pi\)
\(882\) 17.2814 0.581895
\(883\) −14.1974 −0.477780 −0.238890 0.971047i \(-0.576784\pi\)
−0.238890 + 0.971047i \(0.576784\pi\)
\(884\) −0.471939 −0.0158730
\(885\) −0.0973372 −0.00327196
\(886\) 10.1719 0.341733
\(887\) 55.6545 1.86869 0.934347 0.356365i \(-0.115984\pi\)
0.934347 + 0.356365i \(0.115984\pi\)
\(888\) 3.71655 0.124719
\(889\) 42.8258 1.43633
\(890\) −6.65593 −0.223107
\(891\) −1.94580 −0.0651866
\(892\) 2.52626 0.0845854
\(893\) −5.34367 −0.178819
\(894\) 16.4520 0.550238
\(895\) −0.801763 −0.0268000
\(896\) −46.5058 −1.55365
\(897\) 2.47799 0.0827376
\(898\) 43.0626 1.43702
\(899\) 1.38386 0.0461542
\(900\) 2.53226 0.0844087
\(901\) −27.4613 −0.914869
\(902\) −13.3999 −0.446169
\(903\) 6.54776 0.217896
\(904\) 17.2790 0.574692
\(905\) −6.44519 −0.214245
\(906\) 13.8791 0.461104
\(907\) 5.68503 0.188768 0.0943842 0.995536i \(-0.469912\pi\)
0.0943842 + 0.995536i \(0.469912\pi\)
\(908\) 5.75996 0.191151
\(909\) −19.6802 −0.652752
\(910\) 1.56558 0.0518984
\(911\) 30.2169 1.00113 0.500565 0.865699i \(-0.333126\pi\)
0.500565 + 0.865699i \(0.333126\pi\)
\(912\) 1.99067 0.0659175
\(913\) 32.2956 1.06883
\(914\) −32.6282 −1.07924
\(915\) −5.37912 −0.177828
\(916\) −6.39507 −0.211299
\(917\) 37.3306 1.23277
\(918\) −24.2383 −0.799984
\(919\) −37.4121 −1.23411 −0.617055 0.786920i \(-0.711674\pi\)
−0.617055 + 0.786920i \(0.711674\pi\)
\(920\) 6.32607 0.208564
\(921\) 15.4960 0.510609
\(922\) 30.1378 0.992537
\(923\) −3.63844 −0.119761
\(924\) 1.76481 0.0580579
\(925\) 6.74150 0.221659
\(926\) −23.3669 −0.767885
\(927\) 13.2235 0.434315
\(928\) −1.50385 −0.0493664
\(929\) −46.3491 −1.52067 −0.760333 0.649534i \(-0.774964\pi\)
−0.760333 + 0.649534i \(0.774964\pi\)
\(930\) −1.10726 −0.0363085
\(931\) 2.55915 0.0838727
\(932\) 1.74528 0.0571685
\(933\) 6.41090 0.209883
\(934\) −27.5139 −0.900282
\(935\) −3.19227 −0.104398
\(936\) 2.86259 0.0935666
\(937\) 0.919669 0.0300443 0.0150221 0.999887i \(-0.495218\pi\)
0.0150221 + 0.999887i \(0.495218\pi\)
\(938\) 5.32500 0.173867
\(939\) 29.8127 0.972900
\(940\) −1.70347 −0.0555609
\(941\) 24.4052 0.795586 0.397793 0.917475i \(-0.369776\pi\)
0.397793 + 0.917475i \(0.369776\pi\)
\(942\) 9.96418 0.324651
\(943\) −21.8062 −0.710107
\(944\) −0.817673 −0.0266130
\(945\) 9.48778 0.308638
\(946\) −5.14896 −0.167407
\(947\) 11.0230 0.358199 0.179099 0.983831i \(-0.442682\pi\)
0.179099 + 0.983831i \(0.442682\pi\)
\(948\) 4.32957 0.140618
\(949\) −2.77891 −0.0902074
\(950\) 3.17798 0.103107
\(951\) 6.32488 0.205098
\(952\) 30.0131 0.972729
\(953\) −15.7100 −0.508898 −0.254449 0.967086i \(-0.581894\pi\)
−0.254449 + 0.967086i \(0.581894\pi\)
\(954\) −25.7260 −0.832909
\(955\) −5.19234 −0.168020
\(956\) −6.69053 −0.216387
\(957\) −1.84948 −0.0597851
\(958\) −27.4986 −0.888440
\(959\) 24.1558 0.780032
\(960\) −3.54012 −0.114257
\(961\) −29.0849 −0.938224
\(962\) −1.17702 −0.0379487
\(963\) −3.55795 −0.114653
\(964\) 4.13593 0.133209
\(965\) −1.59916 −0.0514788
\(966\) 24.3389 0.783091
\(967\) 30.3705 0.976651 0.488325 0.872662i \(-0.337608\pi\)
0.488325 + 0.872662i \(0.337608\pi\)
\(968\) −19.7109 −0.633533
\(969\) −1.43872 −0.0462184
\(970\) 9.93240 0.318910
\(971\) 9.66019 0.310010 0.155005 0.987914i \(-0.450461\pi\)
0.155005 + 0.987914i \(0.450461\pi\)
\(972\) −4.28470 −0.137432
\(973\) −3.56628 −0.114330
\(974\) 43.2373 1.38541
\(975\) −2.56941 −0.0822871
\(976\) −45.1868 −1.44639
\(977\) −58.1945 −1.86181 −0.930904 0.365264i \(-0.880979\pi\)
−0.930904 + 0.365264i \(0.880979\pi\)
\(978\) −13.9580 −0.446326
\(979\) −15.3850 −0.491708
\(980\) 0.815811 0.0260601
\(981\) −21.4228 −0.683977
\(982\) 11.7993 0.376531
\(983\) −40.7163 −1.29865 −0.649324 0.760512i \(-0.724948\pi\)
−0.649324 + 0.760512i \(0.724948\pi\)
\(984\) 12.4652 0.397375
\(985\) −3.55434 −0.113251
\(986\) 4.85779 0.154704
\(987\) 42.4349 1.35072
\(988\) −0.0654714 −0.00208292
\(989\) −8.37906 −0.266439
\(990\) −2.99054 −0.0950455
\(991\) 3.01736 0.0958495 0.0479248 0.998851i \(-0.484739\pi\)
0.0479248 + 0.998851i \(0.484739\pi\)
\(992\) −2.08112 −0.0660755
\(993\) −5.13463 −0.162942
\(994\) −35.7369 −1.13351
\(995\) 2.95847 0.0937899
\(996\) 4.63997 0.147023
\(997\) −32.4003 −1.02613 −0.513064 0.858350i \(-0.671490\pi\)
−0.513064 + 0.858350i \(0.671490\pi\)
\(998\) −49.3250 −1.56136
\(999\) −7.13303 −0.225679
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 \(a_p\))