Properties

Label 6017.2.a.c.1.5
Level 6017
Weight 2
Character 6017.1
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
CM No

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(1\)
Dimension: \(106\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.66450 q^{2}\) \(+0.632884 q^{3}\) \(+5.09957 q^{4}\) \(-0.0737087 q^{5}\) \(-1.68632 q^{6}\) \(+1.42532 q^{7}\) \(-8.25880 q^{8}\) \(-2.59946 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.66450 q^{2}\) \(+0.632884 q^{3}\) \(+5.09957 q^{4}\) \(-0.0737087 q^{5}\) \(-1.68632 q^{6}\) \(+1.42532 q^{7}\) \(-8.25880 q^{8}\) \(-2.59946 q^{9}\) \(+0.196397 q^{10}\) \(+1.00000 q^{11}\) \(+3.22743 q^{12}\) \(-1.48315 q^{13}\) \(-3.79777 q^{14}\) \(-0.0466491 q^{15}\) \(+11.8064 q^{16}\) \(+5.01296 q^{17}\) \(+6.92626 q^{18}\) \(+4.10128 q^{19}\) \(-0.375882 q^{20}\) \(+0.902062 q^{21}\) \(-2.66450 q^{22}\) \(+4.32710 q^{23}\) \(-5.22686 q^{24}\) \(-4.99457 q^{25}\) \(+3.95186 q^{26}\) \(-3.54381 q^{27}\) \(+7.26851 q^{28}\) \(-3.98915 q^{29}\) \(+0.124297 q^{30}\) \(-5.93552 q^{31}\) \(-14.9407 q^{32}\) \(+0.632884 q^{33}\) \(-13.3570 q^{34}\) \(-0.105058 q^{35}\) \(-13.2561 q^{36}\) \(+3.30096 q^{37}\) \(-10.9279 q^{38}\) \(-0.938663 q^{39}\) \(+0.608745 q^{40}\) \(-1.93398 q^{41}\) \(-2.40355 q^{42}\) \(-7.31464 q^{43}\) \(+5.09957 q^{44}\) \(+0.191603 q^{45}\) \(-11.5296 q^{46}\) \(+3.81602 q^{47}\) \(+7.47211 q^{48}\) \(-4.96846 q^{49}\) \(+13.3080 q^{50}\) \(+3.17262 q^{51}\) \(-7.56343 q^{52}\) \(-10.5485 q^{53}\) \(+9.44248 q^{54}\) \(-0.0737087 q^{55}\) \(-11.7714 q^{56}\) \(+2.59563 q^{57}\) \(+10.6291 q^{58}\) \(+8.85659 q^{59}\) \(-0.237890 q^{60}\) \(-14.2965 q^{61}\) \(+15.8152 q^{62}\) \(-3.70506 q^{63}\) \(+16.1966 q^{64}\) \(+0.109321 q^{65}\) \(-1.68632 q^{66}\) \(+0.702432 q^{67}\) \(+25.5639 q^{68}\) \(+2.73855 q^{69}\) \(+0.279928 q^{70}\) \(+10.2267 q^{71}\) \(+21.4684 q^{72}\) \(-1.29592 q^{73}\) \(-8.79541 q^{74}\) \(-3.16098 q^{75}\) \(+20.9147 q^{76}\) \(+1.42532 q^{77}\) \(+2.50107 q^{78}\) \(-1.72792 q^{79}\) \(-0.870237 q^{80}\) \(+5.55555 q^{81}\) \(+5.15310 q^{82}\) \(-1.11795 q^{83}\) \(+4.60013 q^{84}\) \(-0.369499 q^{85}\) \(+19.4899 q^{86}\) \(-2.52467 q^{87}\) \(-8.25880 q^{88}\) \(+12.6518 q^{89}\) \(-0.510525 q^{90}\) \(-2.11397 q^{91}\) \(+22.0663 q^{92}\) \(-3.75650 q^{93}\) \(-10.1678 q^{94}\) \(-0.302300 q^{95}\) \(-9.45572 q^{96}\) \(-12.1613 q^{97}\) \(+13.2385 q^{98}\) \(-2.59946 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66450 −1.88409 −0.942043 0.335491i \(-0.891098\pi\)
−0.942043 + 0.335491i \(0.891098\pi\)
\(3\) 0.632884 0.365396 0.182698 0.983169i \(-0.441517\pi\)
0.182698 + 0.983169i \(0.441517\pi\)
\(4\) 5.09957 2.54978
\(5\) −0.0737087 −0.0329635 −0.0164818 0.999864i \(-0.505247\pi\)
−0.0164818 + 0.999864i \(0.505247\pi\)
\(6\) −1.68632 −0.688437
\(7\) 1.42532 0.538720 0.269360 0.963040i \(-0.413188\pi\)
0.269360 + 0.963040i \(0.413188\pi\)
\(8\) −8.25880 −2.91993
\(9\) −2.59946 −0.866486
\(10\) 0.196397 0.0621062
\(11\) 1.00000 0.301511
\(12\) 3.22743 0.931680
\(13\) −1.48315 −0.411352 −0.205676 0.978620i \(-0.565939\pi\)
−0.205676 + 0.978620i \(0.565939\pi\)
\(14\) −3.79777 −1.01500
\(15\) −0.0466491 −0.0120447
\(16\) 11.8064 2.95161
\(17\) 5.01296 1.21582 0.607911 0.794005i \(-0.292008\pi\)
0.607911 + 0.794005i \(0.292008\pi\)
\(18\) 6.92626 1.63253
\(19\) 4.10128 0.940898 0.470449 0.882427i \(-0.344092\pi\)
0.470449 + 0.882427i \(0.344092\pi\)
\(20\) −0.375882 −0.0840499
\(21\) 0.902062 0.196846
\(22\) −2.66450 −0.568074
\(23\) 4.32710 0.902263 0.451131 0.892458i \(-0.351021\pi\)
0.451131 + 0.892458i \(0.351021\pi\)
\(24\) −5.22686 −1.06693
\(25\) −4.99457 −0.998913
\(26\) 3.95186 0.775023
\(27\) −3.54381 −0.682006
\(28\) 7.26851 1.37362
\(29\) −3.98915 −0.740766 −0.370383 0.928879i \(-0.620774\pi\)
−0.370383 + 0.928879i \(0.620774\pi\)
\(30\) 0.124297 0.0226933
\(31\) −5.93552 −1.06605 −0.533026 0.846099i \(-0.678945\pi\)
−0.533026 + 0.846099i \(0.678945\pi\)
\(32\) −14.9407 −2.64116
\(33\) 0.632884 0.110171
\(34\) −13.3570 −2.29071
\(35\) −0.105058 −0.0177581
\(36\) −13.2561 −2.20935
\(37\) 3.30096 0.542675 0.271337 0.962484i \(-0.412534\pi\)
0.271337 + 0.962484i \(0.412534\pi\)
\(38\) −10.9279 −1.77273
\(39\) −0.938663 −0.150306
\(40\) 0.608745 0.0962511
\(41\) −1.93398 −0.302037 −0.151019 0.988531i \(-0.548255\pi\)
−0.151019 + 0.988531i \(0.548255\pi\)
\(42\) −2.40355 −0.370875
\(43\) −7.31464 −1.11547 −0.557736 0.830019i \(-0.688330\pi\)
−0.557736 + 0.830019i \(0.688330\pi\)
\(44\) 5.09957 0.768788
\(45\) 0.191603 0.0285624
\(46\) −11.5296 −1.69994
\(47\) 3.81602 0.556623 0.278312 0.960491i \(-0.410225\pi\)
0.278312 + 0.960491i \(0.410225\pi\)
\(48\) 7.47211 1.07851
\(49\) −4.96846 −0.709780
\(50\) 13.3080 1.88204
\(51\) 3.17262 0.444256
\(52\) −7.56343 −1.04886
\(53\) −10.5485 −1.44894 −0.724471 0.689305i \(-0.757916\pi\)
−0.724471 + 0.689305i \(0.757916\pi\)
\(54\) 9.44248 1.28496
\(55\) −0.0737087 −0.00993888
\(56\) −11.7714 −1.57302
\(57\) 2.59563 0.343800
\(58\) 10.6291 1.39567
\(59\) 8.85659 1.15303 0.576515 0.817086i \(-0.304412\pi\)
0.576515 + 0.817086i \(0.304412\pi\)
\(60\) −0.237890 −0.0307115
\(61\) −14.2965 −1.83048 −0.915242 0.402904i \(-0.868001\pi\)
−0.915242 + 0.402904i \(0.868001\pi\)
\(62\) 15.8152 2.00853
\(63\) −3.70506 −0.466794
\(64\) 16.1966 2.02457
\(65\) 0.109321 0.0135596
\(66\) −1.68632 −0.207572
\(67\) 0.702432 0.0858157 0.0429079 0.999079i \(-0.486338\pi\)
0.0429079 + 0.999079i \(0.486338\pi\)
\(68\) 25.5639 3.10008
\(69\) 2.73855 0.329683
\(70\) 0.279928 0.0334578
\(71\) 10.2267 1.21369 0.606846 0.794820i \(-0.292435\pi\)
0.606846 + 0.794820i \(0.292435\pi\)
\(72\) 21.4684 2.53007
\(73\) −1.29592 −0.151676 −0.0758379 0.997120i \(-0.524163\pi\)
−0.0758379 + 0.997120i \(0.524163\pi\)
\(74\) −8.79541 −1.02245
\(75\) −3.16098 −0.364999
\(76\) 20.9147 2.39909
\(77\) 1.42532 0.162430
\(78\) 2.50107 0.283190
\(79\) −1.72792 −0.194407 −0.0972033 0.995265i \(-0.530990\pi\)
−0.0972033 + 0.995265i \(0.530990\pi\)
\(80\) −0.870237 −0.0972955
\(81\) 5.55555 0.617284
\(82\) 5.15310 0.569065
\(83\) −1.11795 −0.122711 −0.0613553 0.998116i \(-0.519542\pi\)
−0.0613553 + 0.998116i \(0.519542\pi\)
\(84\) 4.60013 0.501915
\(85\) −0.369499 −0.0400778
\(86\) 19.4899 2.10164
\(87\) −2.52467 −0.270673
\(88\) −8.25880 −0.880391
\(89\) 12.6518 1.34109 0.670545 0.741869i \(-0.266060\pi\)
0.670545 + 0.741869i \(0.266060\pi\)
\(90\) −0.510525 −0.0538141
\(91\) −2.11397 −0.221604
\(92\) 22.0663 2.30057
\(93\) −3.75650 −0.389531
\(94\) −10.1678 −1.04873
\(95\) −0.302300 −0.0310153
\(96\) −9.45572 −0.965070
\(97\) −12.1613 −1.23479 −0.617395 0.786653i \(-0.711812\pi\)
−0.617395 + 0.786653i \(0.711812\pi\)
\(98\) 13.2385 1.33729
\(99\) −2.59946 −0.261255
\(100\) −25.4701 −2.54701
\(101\) −16.6250 −1.65425 −0.827123 0.562021i \(-0.810024\pi\)
−0.827123 + 0.562021i \(0.810024\pi\)
\(102\) −8.45346 −0.837017
\(103\) 6.84176 0.674139 0.337069 0.941480i \(-0.390564\pi\)
0.337069 + 0.941480i \(0.390564\pi\)
\(104\) 12.2490 1.20112
\(105\) −0.0664899 −0.00648875
\(106\) 28.1064 2.72993
\(107\) −0.816300 −0.0789147 −0.0394573 0.999221i \(-0.512563\pi\)
−0.0394573 + 0.999221i \(0.512563\pi\)
\(108\) −18.0719 −1.73897
\(109\) 0.997247 0.0955189 0.0477595 0.998859i \(-0.484792\pi\)
0.0477595 + 0.998859i \(0.484792\pi\)
\(110\) 0.196397 0.0187257
\(111\) 2.08913 0.198291
\(112\) 16.8280 1.59009
\(113\) 6.86549 0.645851 0.322925 0.946424i \(-0.395334\pi\)
0.322925 + 0.946424i \(0.395334\pi\)
\(114\) −6.91607 −0.647749
\(115\) −0.318945 −0.0297418
\(116\) −20.3429 −1.88879
\(117\) 3.85539 0.356431
\(118\) −23.5984 −2.17241
\(119\) 7.14507 0.654988
\(120\) 0.385265 0.0351697
\(121\) 1.00000 0.0909091
\(122\) 38.0932 3.44879
\(123\) −1.22399 −0.110363
\(124\) −30.2686 −2.71820
\(125\) 0.736687 0.0658913
\(126\) 9.87213 0.879480
\(127\) −5.14407 −0.456462 −0.228231 0.973607i \(-0.573294\pi\)
−0.228231 + 0.973607i \(0.573294\pi\)
\(128\) −13.2744 −1.17330
\(129\) −4.62932 −0.407589
\(130\) −0.291286 −0.0255475
\(131\) 3.36131 0.293679 0.146839 0.989160i \(-0.453090\pi\)
0.146839 + 0.989160i \(0.453090\pi\)
\(132\) 3.22743 0.280912
\(133\) 5.84563 0.506881
\(134\) −1.87163 −0.161684
\(135\) 0.261210 0.0224813
\(136\) −41.4010 −3.55011
\(137\) −22.9521 −1.96093 −0.980465 0.196695i \(-0.936979\pi\)
−0.980465 + 0.196695i \(0.936979\pi\)
\(138\) −7.29688 −0.621151
\(139\) −8.64393 −0.733168 −0.366584 0.930385i \(-0.619473\pi\)
−0.366584 + 0.930385i \(0.619473\pi\)
\(140\) −0.535753 −0.0452794
\(141\) 2.41510 0.203388
\(142\) −27.2492 −2.28670
\(143\) −1.48315 −0.124027
\(144\) −30.6903 −2.55753
\(145\) 0.294035 0.0244183
\(146\) 3.45297 0.285770
\(147\) −3.14446 −0.259351
\(148\) 16.8335 1.38370
\(149\) 5.62480 0.460802 0.230401 0.973096i \(-0.425996\pi\)
0.230401 + 0.973096i \(0.425996\pi\)
\(150\) 8.42244 0.687689
\(151\) −14.3512 −1.16788 −0.583942 0.811795i \(-0.698491\pi\)
−0.583942 + 0.811795i \(0.698491\pi\)
\(152\) −33.8716 −2.74735
\(153\) −13.0310 −1.05349
\(154\) −3.79777 −0.306033
\(155\) 0.437500 0.0351408
\(156\) −4.78677 −0.383249
\(157\) −1.93703 −0.154592 −0.0772958 0.997008i \(-0.524629\pi\)
−0.0772958 + 0.997008i \(0.524629\pi\)
\(158\) 4.60406 0.366279
\(159\) −6.67595 −0.529438
\(160\) 1.10126 0.0870621
\(161\) 6.16750 0.486067
\(162\) −14.8028 −1.16302
\(163\) 18.3161 1.43463 0.717313 0.696751i \(-0.245372\pi\)
0.717313 + 0.696751i \(0.245372\pi\)
\(164\) −9.86247 −0.770130
\(165\) −0.0466491 −0.00363163
\(166\) 2.97877 0.231198
\(167\) 6.41727 0.496583 0.248291 0.968685i \(-0.420131\pi\)
0.248291 + 0.968685i \(0.420131\pi\)
\(168\) −7.44995 −0.574776
\(169\) −10.8003 −0.830789
\(170\) 0.984530 0.0755100
\(171\) −10.6611 −0.815275
\(172\) −37.3015 −2.84421
\(173\) −24.4133 −1.85611 −0.928054 0.372445i \(-0.878520\pi\)
−0.928054 + 0.372445i \(0.878520\pi\)
\(174\) 6.72698 0.509971
\(175\) −7.11886 −0.538135
\(176\) 11.8064 0.889944
\(177\) 5.60520 0.421312
\(178\) −33.7108 −2.52673
\(179\) 22.9508 1.71543 0.857713 0.514129i \(-0.171885\pi\)
0.857713 + 0.514129i \(0.171885\pi\)
\(180\) 0.977090 0.0728280
\(181\) 9.26210 0.688447 0.344223 0.938888i \(-0.388142\pi\)
0.344223 + 0.938888i \(0.388142\pi\)
\(182\) 5.63266 0.417521
\(183\) −9.04806 −0.668852
\(184\) −35.7366 −2.63454
\(185\) −0.243310 −0.0178885
\(186\) 10.0092 0.733910
\(187\) 5.01296 0.366584
\(188\) 19.4600 1.41927
\(189\) −5.05106 −0.367411
\(190\) 0.805478 0.0584356
\(191\) 2.72613 0.197256 0.0986278 0.995124i \(-0.468555\pi\)
0.0986278 + 0.995124i \(0.468555\pi\)
\(192\) 10.2505 0.739770
\(193\) 17.6743 1.27222 0.636111 0.771598i \(-0.280542\pi\)
0.636111 + 0.771598i \(0.280542\pi\)
\(194\) 32.4037 2.32645
\(195\) 0.0691876 0.00495463
\(196\) −25.3370 −1.80979
\(197\) −7.36795 −0.524944 −0.262472 0.964940i \(-0.584538\pi\)
−0.262472 + 0.964940i \(0.584538\pi\)
\(198\) 6.92626 0.492228
\(199\) −9.09351 −0.644622 −0.322311 0.946634i \(-0.604460\pi\)
−0.322311 + 0.946634i \(0.604460\pi\)
\(200\) 41.2491 2.91675
\(201\) 0.444558 0.0313567
\(202\) 44.2972 3.11674
\(203\) −5.68581 −0.399066
\(204\) 16.1790 1.13276
\(205\) 0.142551 0.00995622
\(206\) −18.2299 −1.27014
\(207\) −11.2481 −0.781798
\(208\) −17.5107 −1.21415
\(209\) 4.10128 0.283691
\(210\) 0.177162 0.0122254
\(211\) −5.69835 −0.392290 −0.196145 0.980575i \(-0.562842\pi\)
−0.196145 + 0.980575i \(0.562842\pi\)
\(212\) −53.7926 −3.69449
\(213\) 6.47235 0.443478
\(214\) 2.17503 0.148682
\(215\) 0.539152 0.0367699
\(216\) 29.2676 1.99141
\(217\) −8.46002 −0.574303
\(218\) −2.65717 −0.179966
\(219\) −0.820166 −0.0554217
\(220\) −0.375882 −0.0253420
\(221\) −7.43498 −0.500131
\(222\) −5.56648 −0.373598
\(223\) −9.88994 −0.662280 −0.331140 0.943582i \(-0.607433\pi\)
−0.331140 + 0.943582i \(0.607433\pi\)
\(224\) −21.2952 −1.42285
\(225\) 12.9832 0.865544
\(226\) −18.2931 −1.21684
\(227\) 6.49674 0.431204 0.215602 0.976481i \(-0.430829\pi\)
0.215602 + 0.976481i \(0.430829\pi\)
\(228\) 13.2366 0.876616
\(229\) 5.44877 0.360065 0.180032 0.983661i \(-0.442380\pi\)
0.180032 + 0.983661i \(0.442380\pi\)
\(230\) 0.849829 0.0560361
\(231\) 0.902062 0.0593514
\(232\) 32.9456 2.16298
\(233\) −4.12902 −0.270501 −0.135250 0.990811i \(-0.543184\pi\)
−0.135250 + 0.990811i \(0.543184\pi\)
\(234\) −10.2727 −0.671547
\(235\) −0.281274 −0.0183483
\(236\) 45.1648 2.93998
\(237\) −1.09358 −0.0710354
\(238\) −19.0381 −1.23405
\(239\) −3.38666 −0.219065 −0.109532 0.993983i \(-0.534935\pi\)
−0.109532 + 0.993983i \(0.534935\pi\)
\(240\) −0.550759 −0.0355514
\(241\) −16.3868 −1.05557 −0.527784 0.849379i \(-0.676977\pi\)
−0.527784 + 0.849379i \(0.676977\pi\)
\(242\) −2.66450 −0.171281
\(243\) 14.1474 0.907559
\(244\) −72.9062 −4.66734
\(245\) 0.366219 0.0233969
\(246\) 3.26132 0.207934
\(247\) −6.08282 −0.387040
\(248\) 49.0203 3.11279
\(249\) −0.707531 −0.0448380
\(250\) −1.96290 −0.124145
\(251\) 20.5627 1.29791 0.648954 0.760828i \(-0.275207\pi\)
0.648954 + 0.760828i \(0.275207\pi\)
\(252\) −18.8942 −1.19022
\(253\) 4.32710 0.272042
\(254\) 13.7064 0.860015
\(255\) −0.233850 −0.0146443
\(256\) 2.97656 0.186035
\(257\) −11.7115 −0.730545 −0.365273 0.930901i \(-0.619024\pi\)
−0.365273 + 0.930901i \(0.619024\pi\)
\(258\) 12.3348 0.767932
\(259\) 4.70493 0.292350
\(260\) 0.557491 0.0345741
\(261\) 10.3696 0.641864
\(262\) −8.95621 −0.553316
\(263\) −12.7110 −0.783796 −0.391898 0.920009i \(-0.628181\pi\)
−0.391898 + 0.920009i \(0.628181\pi\)
\(264\) −5.22686 −0.321691
\(265\) 0.777513 0.0477623
\(266\) −15.5757 −0.955007
\(267\) 8.00713 0.490029
\(268\) 3.58210 0.218811
\(269\) −10.9319 −0.666531 −0.333266 0.942833i \(-0.608151\pi\)
−0.333266 + 0.942833i \(0.608151\pi\)
\(270\) −0.695993 −0.0423568
\(271\) 2.49191 0.151373 0.0756864 0.997132i \(-0.475885\pi\)
0.0756864 + 0.997132i \(0.475885\pi\)
\(272\) 59.1852 3.58863
\(273\) −1.33790 −0.0809731
\(274\) 61.1559 3.69456
\(275\) −4.99457 −0.301184
\(276\) 13.9654 0.840620
\(277\) 14.9585 0.898767 0.449384 0.893339i \(-0.351644\pi\)
0.449384 + 0.893339i \(0.351644\pi\)
\(278\) 23.0318 1.38135
\(279\) 15.4291 0.923718
\(280\) 0.867657 0.0518524
\(281\) −3.28602 −0.196027 −0.0980137 0.995185i \(-0.531249\pi\)
−0.0980137 + 0.995185i \(0.531249\pi\)
\(282\) −6.43502 −0.383200
\(283\) −8.94873 −0.531947 −0.265973 0.963980i \(-0.585693\pi\)
−0.265973 + 0.963980i \(0.585693\pi\)
\(284\) 52.1520 3.09465
\(285\) −0.191321 −0.0113329
\(286\) 3.95186 0.233678
\(287\) −2.75655 −0.162714
\(288\) 38.8376 2.28853
\(289\) 8.12977 0.478222
\(290\) −0.783457 −0.0460062
\(291\) −7.69668 −0.451187
\(292\) −6.60862 −0.386740
\(293\) −17.2043 −1.00509 −0.502544 0.864552i \(-0.667602\pi\)
−0.502544 + 0.864552i \(0.667602\pi\)
\(294\) 8.37842 0.488639
\(295\) −0.652808 −0.0380080
\(296\) −27.2620 −1.58457
\(297\) −3.54381 −0.205633
\(298\) −14.9873 −0.868190
\(299\) −6.41774 −0.371148
\(300\) −16.1196 −0.930668
\(301\) −10.4257 −0.600927
\(302\) 38.2388 2.20040
\(303\) −10.5217 −0.604455
\(304\) 48.4215 2.77716
\(305\) 1.05378 0.0603392
\(306\) 34.7211 1.98487
\(307\) −26.5302 −1.51416 −0.757078 0.653324i \(-0.773374\pi\)
−0.757078 + 0.653324i \(0.773374\pi\)
\(308\) 7.26851 0.414162
\(309\) 4.33004 0.246328
\(310\) −1.16572 −0.0662083
\(311\) −0.827063 −0.0468984 −0.0234492 0.999725i \(-0.507465\pi\)
−0.0234492 + 0.999725i \(0.507465\pi\)
\(312\) 7.75223 0.438883
\(313\) 12.6170 0.713152 0.356576 0.934266i \(-0.383944\pi\)
0.356576 + 0.934266i \(0.383944\pi\)
\(314\) 5.16121 0.291264
\(315\) 0.273095 0.0153872
\(316\) −8.81166 −0.495695
\(317\) 17.4785 0.981689 0.490844 0.871247i \(-0.336688\pi\)
0.490844 + 0.871247i \(0.336688\pi\)
\(318\) 17.7881 0.997506
\(319\) −3.98915 −0.223349
\(320\) −1.19383 −0.0667370
\(321\) −0.516623 −0.0288351
\(322\) −16.4333 −0.915793
\(323\) 20.5595 1.14396
\(324\) 28.3309 1.57394
\(325\) 7.40770 0.410905
\(326\) −48.8032 −2.70296
\(327\) 0.631142 0.0349022
\(328\) 15.9724 0.881927
\(329\) 5.43904 0.299864
\(330\) 0.124297 0.00684230
\(331\) 2.34040 0.128640 0.0643201 0.997929i \(-0.479512\pi\)
0.0643201 + 0.997929i \(0.479512\pi\)
\(332\) −5.70105 −0.312886
\(333\) −8.58071 −0.470220
\(334\) −17.0988 −0.935605
\(335\) −0.0517753 −0.00282879
\(336\) 10.6501 0.581013
\(337\) −24.2515 −1.32107 −0.660533 0.750797i \(-0.729670\pi\)
−0.660533 + 0.750797i \(0.729670\pi\)
\(338\) 28.7773 1.56528
\(339\) 4.34506 0.235991
\(340\) −1.88428 −0.102190
\(341\) −5.93552 −0.321427
\(342\) 28.4065 1.53605
\(343\) −17.0589 −0.921093
\(344\) 60.4101 3.25709
\(345\) −0.201855 −0.0108675
\(346\) 65.0493 3.49707
\(347\) 19.1649 1.02882 0.514412 0.857543i \(-0.328010\pi\)
0.514412 + 0.857543i \(0.328010\pi\)
\(348\) −12.8747 −0.690157
\(349\) 31.6119 1.69214 0.846072 0.533068i \(-0.178961\pi\)
0.846072 + 0.533068i \(0.178961\pi\)
\(350\) 18.9682 1.01389
\(351\) 5.25600 0.280545
\(352\) −14.9407 −0.796341
\(353\) −31.9416 −1.70008 −0.850040 0.526718i \(-0.823423\pi\)
−0.850040 + 0.526718i \(0.823423\pi\)
\(354\) −14.9351 −0.793789
\(355\) −0.753800 −0.0400076
\(356\) 64.5187 3.41949
\(357\) 4.52200 0.239330
\(358\) −61.1525 −3.23201
\(359\) −5.76982 −0.304519 −0.152260 0.988341i \(-0.548655\pi\)
−0.152260 + 0.988341i \(0.548655\pi\)
\(360\) −1.58241 −0.0834002
\(361\) −2.17951 −0.114711
\(362\) −24.6789 −1.29709
\(363\) 0.632884 0.0332178
\(364\) −10.7803 −0.565042
\(365\) 0.0955204 0.00499977
\(366\) 24.1086 1.26017
\(367\) 2.26015 0.117979 0.0589894 0.998259i \(-0.481212\pi\)
0.0589894 + 0.998259i \(0.481212\pi\)
\(368\) 51.0876 2.66313
\(369\) 5.02731 0.261711
\(370\) 0.648299 0.0337034
\(371\) −15.0349 −0.780575
\(372\) −19.1565 −0.993219
\(373\) 5.91416 0.306223 0.153112 0.988209i \(-0.451071\pi\)
0.153112 + 0.988209i \(0.451071\pi\)
\(374\) −13.3570 −0.690676
\(375\) 0.466237 0.0240764
\(376\) −31.5157 −1.62530
\(377\) 5.91651 0.304716
\(378\) 13.4586 0.692233
\(379\) 0.892182 0.0458283 0.0229142 0.999737i \(-0.492706\pi\)
0.0229142 + 0.999737i \(0.492706\pi\)
\(380\) −1.54160 −0.0790823
\(381\) −3.25560 −0.166789
\(382\) −7.26377 −0.371647
\(383\) −18.5655 −0.948652 −0.474326 0.880349i \(-0.657308\pi\)
−0.474326 + 0.880349i \(0.657308\pi\)
\(384\) −8.40117 −0.428720
\(385\) −0.105058 −0.00535428
\(386\) −47.0931 −2.39698
\(387\) 19.0141 0.966540
\(388\) −62.0172 −3.14845
\(389\) 9.19885 0.466400 0.233200 0.972429i \(-0.425080\pi\)
0.233200 + 0.972429i \(0.425080\pi\)
\(390\) −0.184351 −0.00933495
\(391\) 21.6916 1.09699
\(392\) 41.0335 2.07251
\(393\) 2.12732 0.107309
\(394\) 19.6319 0.989041
\(395\) 0.127363 0.00640833
\(396\) −13.2561 −0.666144
\(397\) −25.8396 −1.29685 −0.648426 0.761278i \(-0.724572\pi\)
−0.648426 + 0.761278i \(0.724572\pi\)
\(398\) 24.2297 1.21452
\(399\) 3.69961 0.185212
\(400\) −58.9680 −2.94840
\(401\) −34.4979 −1.72274 −0.861372 0.507975i \(-0.830394\pi\)
−0.861372 + 0.507975i \(0.830394\pi\)
\(402\) −1.18453 −0.0590787
\(403\) 8.80328 0.438523
\(404\) −84.7801 −4.21797
\(405\) −0.409493 −0.0203479
\(406\) 15.1499 0.751875
\(407\) 3.30096 0.163623
\(408\) −26.2020 −1.29719
\(409\) −6.49690 −0.321251 −0.160625 0.987015i \(-0.551351\pi\)
−0.160625 + 0.987015i \(0.551351\pi\)
\(410\) −0.379828 −0.0187584
\(411\) −14.5260 −0.716516
\(412\) 34.8900 1.71891
\(413\) 12.6235 0.621161
\(414\) 29.9706 1.47297
\(415\) 0.0824025 0.00404498
\(416\) 22.1593 1.08645
\(417\) −5.47061 −0.267897
\(418\) −10.9279 −0.534499
\(419\) 27.3348 1.33539 0.667697 0.744433i \(-0.267280\pi\)
0.667697 + 0.744433i \(0.267280\pi\)
\(420\) −0.339069 −0.0165449
\(421\) 3.02611 0.147484 0.0737419 0.997277i \(-0.476506\pi\)
0.0737419 + 0.997277i \(0.476506\pi\)
\(422\) 15.1832 0.739109
\(423\) −9.91957 −0.482306
\(424\) 87.1176 4.23080
\(425\) −25.0376 −1.21450
\(426\) −17.2456 −0.835551
\(427\) −20.3771 −0.986119
\(428\) −4.16277 −0.201215
\(429\) −0.938663 −0.0453191
\(430\) −1.43657 −0.0692776
\(431\) 18.1136 0.872502 0.436251 0.899825i \(-0.356306\pi\)
0.436251 + 0.899825i \(0.356306\pi\)
\(432\) −41.8397 −2.01302
\(433\) 23.3076 1.12009 0.560046 0.828461i \(-0.310783\pi\)
0.560046 + 0.828461i \(0.310783\pi\)
\(434\) 22.5417 1.08204
\(435\) 0.186090 0.00892234
\(436\) 5.08553 0.243553
\(437\) 17.7466 0.848937
\(438\) 2.18533 0.104419
\(439\) −6.63189 −0.316523 −0.158261 0.987397i \(-0.550589\pi\)
−0.158261 + 0.987397i \(0.550589\pi\)
\(440\) 0.608745 0.0290208
\(441\) 12.9153 0.615015
\(442\) 19.8105 0.942290
\(443\) −8.47135 −0.402486 −0.201243 0.979541i \(-0.564498\pi\)
−0.201243 + 0.979541i \(0.564498\pi\)
\(444\) 10.6536 0.505599
\(445\) −0.932549 −0.0442070
\(446\) 26.3518 1.24779
\(447\) 3.55985 0.168375
\(448\) 23.0853 1.09068
\(449\) −29.2118 −1.37859 −0.689296 0.724480i \(-0.742080\pi\)
−0.689296 + 0.724480i \(0.742080\pi\)
\(450\) −34.5937 −1.63076
\(451\) −1.93398 −0.0910677
\(452\) 35.0110 1.64678
\(453\) −9.08265 −0.426740
\(454\) −17.3106 −0.812425
\(455\) 0.155818 0.00730484
\(456\) −21.4368 −1.00387
\(457\) −36.6579 −1.71479 −0.857393 0.514663i \(-0.827917\pi\)
−0.857393 + 0.514663i \(0.827917\pi\)
\(458\) −14.5183 −0.678394
\(459\) −17.7650 −0.829198
\(460\) −1.62648 −0.0758350
\(461\) −17.4414 −0.812325 −0.406163 0.913801i \(-0.633133\pi\)
−0.406163 + 0.913801i \(0.633133\pi\)
\(462\) −2.40355 −0.111823
\(463\) 23.6602 1.09958 0.549791 0.835302i \(-0.314707\pi\)
0.549791 + 0.835302i \(0.314707\pi\)
\(464\) −47.0976 −2.18645
\(465\) 0.276887 0.0128403
\(466\) 11.0018 0.509647
\(467\) −11.5532 −0.534617 −0.267308 0.963611i \(-0.586134\pi\)
−0.267308 + 0.963611i \(0.586134\pi\)
\(468\) 19.6608 0.908821
\(469\) 1.00119 0.0462307
\(470\) 0.749454 0.0345697
\(471\) −1.22591 −0.0564871
\(472\) −73.1448 −3.36676
\(473\) −7.31464 −0.336327
\(474\) 2.91383 0.133837
\(475\) −20.4841 −0.939875
\(476\) 36.4368 1.67008
\(477\) 27.4203 1.25549
\(478\) 9.02377 0.412737
\(479\) 34.4319 1.57324 0.786618 0.617440i \(-0.211830\pi\)
0.786618 + 0.617440i \(0.211830\pi\)
\(480\) 0.696969 0.0318121
\(481\) −4.89583 −0.223230
\(482\) 43.6627 1.98878
\(483\) 3.90331 0.177607
\(484\) 5.09957 0.231798
\(485\) 0.896392 0.0407031
\(486\) −37.6959 −1.70992
\(487\) −0.998586 −0.0452503 −0.0226251 0.999744i \(-0.507202\pi\)
−0.0226251 + 0.999744i \(0.507202\pi\)
\(488\) 118.072 5.34488
\(489\) 11.5920 0.524206
\(490\) −0.975791 −0.0440817
\(491\) −25.1720 −1.13600 −0.567998 0.823030i \(-0.692282\pi\)
−0.567998 + 0.823030i \(0.692282\pi\)
\(492\) −6.24180 −0.281402
\(493\) −19.9974 −0.900640
\(494\) 16.2077 0.729218
\(495\) 0.191603 0.00861190
\(496\) −70.0774 −3.14657
\(497\) 14.5764 0.653840
\(498\) 1.88522 0.0844786
\(499\) 24.3572 1.09038 0.545188 0.838314i \(-0.316458\pi\)
0.545188 + 0.838314i \(0.316458\pi\)
\(500\) 3.75678 0.168008
\(501\) 4.06139 0.181449
\(502\) −54.7894 −2.44537
\(503\) −34.9289 −1.55740 −0.778702 0.627395i \(-0.784121\pi\)
−0.778702 + 0.627395i \(0.784121\pi\)
\(504\) 30.5993 1.36300
\(505\) 1.22540 0.0545298
\(506\) −11.5296 −0.512551
\(507\) −6.83531 −0.303567
\(508\) −26.2325 −1.16388
\(509\) 7.02214 0.311251 0.155625 0.987816i \(-0.450261\pi\)
0.155625 + 0.987816i \(0.450261\pi\)
\(510\) 0.623093 0.0275910
\(511\) −1.84710 −0.0817108
\(512\) 18.6178 0.822797
\(513\) −14.5341 −0.641698
\(514\) 31.2054 1.37641
\(515\) −0.504298 −0.0222220
\(516\) −23.6075 −1.03926
\(517\) 3.81602 0.167828
\(518\) −12.5363 −0.550812
\(519\) −15.4508 −0.678214
\(520\) −0.902861 −0.0395931
\(521\) 37.7258 1.65280 0.826399 0.563084i \(-0.190385\pi\)
0.826399 + 0.563084i \(0.190385\pi\)
\(522\) −27.6299 −1.20933
\(523\) −0.695267 −0.0304019 −0.0152010 0.999884i \(-0.504839\pi\)
−0.0152010 + 0.999884i \(0.504839\pi\)
\(524\) 17.1412 0.748817
\(525\) −4.50541 −0.196632
\(526\) 33.8686 1.47674
\(527\) −29.7545 −1.29613
\(528\) 7.47211 0.325182
\(529\) −4.27621 −0.185922
\(530\) −2.07168 −0.0899882
\(531\) −23.0223 −0.999084
\(532\) 29.8102 1.29244
\(533\) 2.86839 0.124244
\(534\) −21.3350 −0.923256
\(535\) 0.0601684 0.00260131
\(536\) −5.80124 −0.250575
\(537\) 14.5252 0.626809
\(538\) 29.1281 1.25580
\(539\) −4.96846 −0.214007
\(540\) 1.33206 0.0573225
\(541\) −26.7494 −1.15005 −0.575024 0.818136i \(-0.695007\pi\)
−0.575024 + 0.818136i \(0.695007\pi\)
\(542\) −6.63970 −0.285200
\(543\) 5.86184 0.251556
\(544\) −74.8970 −3.21118
\(545\) −0.0735058 −0.00314864
\(546\) 3.56482 0.152560
\(547\) 1.00000 0.0427569
\(548\) −117.046 −4.99994
\(549\) 37.1633 1.58609
\(550\) 13.3080 0.567456
\(551\) −16.3606 −0.696986
\(552\) −22.6171 −0.962650
\(553\) −2.46284 −0.104731
\(554\) −39.8568 −1.69336
\(555\) −0.153987 −0.00653637
\(556\) −44.0803 −1.86942
\(557\) −22.4930 −0.953058 −0.476529 0.879159i \(-0.658105\pi\)
−0.476529 + 0.879159i \(0.658105\pi\)
\(558\) −41.1110 −1.74037
\(559\) 10.8487 0.458852
\(560\) −1.24037 −0.0524150
\(561\) 3.17262 0.133948
\(562\) 8.75560 0.369333
\(563\) 23.3165 0.982672 0.491336 0.870970i \(-0.336509\pi\)
0.491336 + 0.870970i \(0.336509\pi\)
\(564\) 12.3159 0.518595
\(565\) −0.506046 −0.0212895
\(566\) 23.8439 1.00223
\(567\) 7.91844 0.332543
\(568\) −84.4606 −3.54389
\(569\) 26.8930 1.12742 0.563708 0.825974i \(-0.309375\pi\)
0.563708 + 0.825974i \(0.309375\pi\)
\(570\) 0.509775 0.0213521
\(571\) 20.0685 0.839839 0.419920 0.907561i \(-0.362058\pi\)
0.419920 + 0.907561i \(0.362058\pi\)
\(572\) −7.56343 −0.316243
\(573\) 1.72532 0.0720764
\(574\) 7.34482 0.306567
\(575\) −21.6120 −0.901282
\(576\) −42.1023 −1.75426
\(577\) −9.28955 −0.386729 −0.193365 0.981127i \(-0.561940\pi\)
−0.193365 + 0.981127i \(0.561940\pi\)
\(578\) −21.6618 −0.901011
\(579\) 11.1858 0.464865
\(580\) 1.49945 0.0622613
\(581\) −1.59343 −0.0661067
\(582\) 20.5078 0.850076
\(583\) −10.5485 −0.436873
\(584\) 10.7027 0.442882
\(585\) −0.284176 −0.0117492
\(586\) 45.8409 1.89367
\(587\) 4.50672 0.186012 0.0930062 0.995666i \(-0.470352\pi\)
0.0930062 + 0.995666i \(0.470352\pi\)
\(588\) −16.0354 −0.661288
\(589\) −24.3432 −1.00305
\(590\) 1.73941 0.0716103
\(591\) −4.66306 −0.191813
\(592\) 38.9726 1.60176
\(593\) −7.86527 −0.322988 −0.161494 0.986874i \(-0.551631\pi\)
−0.161494 + 0.986874i \(0.551631\pi\)
\(594\) 9.44248 0.387430
\(595\) −0.526654 −0.0215907
\(596\) 28.6840 1.17494
\(597\) −5.75514 −0.235542
\(598\) 17.1001 0.699274
\(599\) 13.2632 0.541921 0.270961 0.962590i \(-0.412659\pi\)
0.270961 + 0.962590i \(0.412659\pi\)
\(600\) 26.1059 1.06577
\(601\) 13.6816 0.558083 0.279041 0.960279i \(-0.409983\pi\)
0.279041 + 0.960279i \(0.409983\pi\)
\(602\) 27.7793 1.13220
\(603\) −1.82594 −0.0743581
\(604\) −73.1849 −2.97785
\(605\) −0.0737087 −0.00299668
\(606\) 28.0350 1.13884
\(607\) −13.0997 −0.531701 −0.265850 0.964014i \(-0.585653\pi\)
−0.265850 + 0.964014i \(0.585653\pi\)
\(608\) −61.2759 −2.48506
\(609\) −3.59846 −0.145817
\(610\) −2.80780 −0.113684
\(611\) −5.65973 −0.228968
\(612\) −66.4523 −2.68618
\(613\) −20.4335 −0.825302 −0.412651 0.910889i \(-0.635397\pi\)
−0.412651 + 0.910889i \(0.635397\pi\)
\(614\) 70.6896 2.85280
\(615\) 0.0902185 0.00363796
\(616\) −11.7714 −0.474284
\(617\) −44.7323 −1.80085 −0.900427 0.435007i \(-0.856746\pi\)
−0.900427 + 0.435007i \(0.856746\pi\)
\(618\) −11.5374 −0.464103
\(619\) −0.997640 −0.0400985 −0.0200493 0.999799i \(-0.506382\pi\)
−0.0200493 + 0.999799i \(0.506382\pi\)
\(620\) 2.23106 0.0896014
\(621\) −15.3344 −0.615349
\(622\) 2.20371 0.0883607
\(623\) 18.0329 0.722472
\(624\) −11.0823 −0.443646
\(625\) 24.9185 0.996741
\(626\) −33.6179 −1.34364
\(627\) 2.59563 0.103660
\(628\) −9.87800 −0.394175
\(629\) 16.5476 0.659795
\(630\) −0.727662 −0.0289908
\(631\) 20.0025 0.796286 0.398143 0.917323i \(-0.369655\pi\)
0.398143 + 0.917323i \(0.369655\pi\)
\(632\) 14.2706 0.567653
\(633\) −3.60639 −0.143341
\(634\) −46.5714 −1.84959
\(635\) 0.379163 0.0150466
\(636\) −34.0445 −1.34995
\(637\) 7.36898 0.291970
\(638\) 10.6291 0.420810
\(639\) −26.5840 −1.05165
\(640\) 0.978440 0.0386762
\(641\) −5.17111 −0.204247 −0.102123 0.994772i \(-0.532564\pi\)
−0.102123 + 0.994772i \(0.532564\pi\)
\(642\) 1.37654 0.0543278
\(643\) 0.247247 0.00975046 0.00487523 0.999988i \(-0.498448\pi\)
0.00487523 + 0.999988i \(0.498448\pi\)
\(644\) 31.4516 1.23937
\(645\) 0.341221 0.0134356
\(646\) −54.7809 −2.15533
\(647\) 27.7771 1.09203 0.546016 0.837775i \(-0.316144\pi\)
0.546016 + 0.837775i \(0.316144\pi\)
\(648\) −45.8822 −1.80242
\(649\) 8.85659 0.347652
\(650\) −19.7378 −0.774181
\(651\) −5.35421 −0.209848
\(652\) 93.4040 3.65798
\(653\) −33.2479 −1.30109 −0.650545 0.759467i \(-0.725460\pi\)
−0.650545 + 0.759467i \(0.725460\pi\)
\(654\) −1.68168 −0.0657588
\(655\) −0.247758 −0.00968069
\(656\) −22.8335 −0.891497
\(657\) 3.36868 0.131425
\(658\) −14.4923 −0.564970
\(659\) 15.7010 0.611624 0.305812 0.952092i \(-0.401072\pi\)
0.305812 + 0.952092i \(0.401072\pi\)
\(660\) −0.237890 −0.00925986
\(661\) −43.9460 −1.70930 −0.854651 0.519202i \(-0.826229\pi\)
−0.854651 + 0.519202i \(0.826229\pi\)
\(662\) −6.23601 −0.242369
\(663\) −4.70548 −0.182746
\(664\) 9.23290 0.358306
\(665\) −0.430874 −0.0167086
\(666\) 22.8633 0.885935
\(667\) −17.2614 −0.668366
\(668\) 32.7253 1.26618
\(669\) −6.25919 −0.241994
\(670\) 0.137955 0.00532968
\(671\) −14.2965 −0.551912
\(672\) −13.4774 −0.519903
\(673\) −29.2848 −1.12885 −0.564424 0.825485i \(-0.690902\pi\)
−0.564424 + 0.825485i \(0.690902\pi\)
\(674\) 64.6183 2.48900
\(675\) 17.6998 0.681265
\(676\) −55.0766 −2.11833
\(677\) −23.4703 −0.902036 −0.451018 0.892515i \(-0.648939\pi\)
−0.451018 + 0.892515i \(0.648939\pi\)
\(678\) −11.5774 −0.444628
\(679\) −17.3337 −0.665207
\(680\) 3.05161 0.117024
\(681\) 4.11168 0.157560
\(682\) 15.8152 0.605595
\(683\) −13.2782 −0.508076 −0.254038 0.967194i \(-0.581759\pi\)
−0.254038 + 0.967194i \(0.581759\pi\)
\(684\) −54.3670 −2.07877
\(685\) 1.69177 0.0646392
\(686\) 45.4534 1.73542
\(687\) 3.44844 0.131566
\(688\) −86.3598 −3.29244
\(689\) 15.6450 0.596026
\(690\) 0.537843 0.0204753
\(691\) −31.3622 −1.19307 −0.596537 0.802586i \(-0.703457\pi\)
−0.596537 + 0.802586i \(0.703457\pi\)
\(692\) −124.497 −4.73267
\(693\) −3.70506 −0.140744
\(694\) −51.0648 −1.93839
\(695\) 0.637133 0.0241678
\(696\) 20.8507 0.790345
\(697\) −9.69498 −0.367224
\(698\) −84.2298 −3.18815
\(699\) −2.61319 −0.0988399
\(700\) −36.3031 −1.37213
\(701\) 8.56870 0.323635 0.161818 0.986821i \(-0.448264\pi\)
0.161818 + 0.986821i \(0.448264\pi\)
\(702\) −14.0046 −0.528571
\(703\) 13.5382 0.510601
\(704\) 16.1966 0.610431
\(705\) −0.178014 −0.00670438
\(706\) 85.1085 3.20310
\(707\) −23.6959 −0.891176
\(708\) 28.5841 1.07426
\(709\) −31.8833 −1.19740 −0.598700 0.800973i \(-0.704316\pi\)
−0.598700 + 0.800973i \(0.704316\pi\)
\(710\) 2.00850 0.0753777
\(711\) 4.49167 0.168451
\(712\) −104.489 −3.91588
\(713\) −25.6836 −0.961858
\(714\) −12.0489 −0.450918
\(715\) 0.109321 0.00408838
\(716\) 117.039 4.37396
\(717\) −2.14337 −0.0800454
\(718\) 15.3737 0.573741
\(719\) −13.7014 −0.510975 −0.255487 0.966812i \(-0.582236\pi\)
−0.255487 + 0.966812i \(0.582236\pi\)
\(720\) 2.26214 0.0843052
\(721\) 9.75170 0.363172
\(722\) 5.80731 0.216126
\(723\) −10.3710 −0.385700
\(724\) 47.2327 1.75539
\(725\) 19.9241 0.739962
\(726\) −1.68632 −0.0625852
\(727\) 28.0737 1.04119 0.520597 0.853802i \(-0.325709\pi\)
0.520597 + 0.853802i \(0.325709\pi\)
\(728\) 17.4588 0.647067
\(729\) −7.71296 −0.285665
\(730\) −0.254514 −0.00942000
\(731\) −36.6680 −1.35621
\(732\) −46.1412 −1.70543
\(733\) −39.2716 −1.45053 −0.725264 0.688470i \(-0.758283\pi\)
−0.725264 + 0.688470i \(0.758283\pi\)
\(734\) −6.02217 −0.222282
\(735\) 0.231774 0.00854912
\(736\) −64.6498 −2.38302
\(737\) 0.702432 0.0258744
\(738\) −13.3953 −0.493087
\(739\) 8.47942 0.311920 0.155960 0.987763i \(-0.450153\pi\)
0.155960 + 0.987763i \(0.450153\pi\)
\(740\) −1.24077 −0.0456117
\(741\) −3.84972 −0.141423
\(742\) 40.0606 1.47067
\(743\) −46.0670 −1.69003 −0.845017 0.534740i \(-0.820410\pi\)
−0.845017 + 0.534740i \(0.820410\pi\)
\(744\) 31.0241 1.13740
\(745\) −0.414597 −0.0151897
\(746\) −15.7583 −0.576952
\(747\) 2.90606 0.106327
\(748\) 25.5639 0.934709
\(749\) −1.16349 −0.0425129
\(750\) −1.24229 −0.0453620
\(751\) 48.6755 1.77620 0.888098 0.459655i \(-0.152027\pi\)
0.888098 + 0.459655i \(0.152027\pi\)
\(752\) 45.0535 1.64293
\(753\) 13.0138 0.474250
\(754\) −15.7646 −0.574111
\(755\) 1.05781 0.0384976
\(756\) −25.7582 −0.936817
\(757\) −10.6471 −0.386974 −0.193487 0.981103i \(-0.561980\pi\)
−0.193487 + 0.981103i \(0.561980\pi\)
\(758\) −2.37722 −0.0863445
\(759\) 2.73855 0.0994032
\(760\) 2.49663 0.0905624
\(761\) 20.0648 0.727349 0.363675 0.931526i \(-0.381522\pi\)
0.363675 + 0.931526i \(0.381522\pi\)
\(762\) 8.67455 0.314246
\(763\) 1.42140 0.0514580
\(764\) 13.9021 0.502959
\(765\) 0.960496 0.0347268
\(766\) 49.4678 1.78734
\(767\) −13.1357 −0.474302
\(768\) 1.88382 0.0679764
\(769\) −28.3409 −1.02200 −0.510999 0.859581i \(-0.670724\pi\)
−0.510999 + 0.859581i \(0.670724\pi\)
\(770\) 0.279928 0.0100879
\(771\) −7.41204 −0.266938
\(772\) 90.1311 3.24389
\(773\) 21.5459 0.774953 0.387476 0.921880i \(-0.373347\pi\)
0.387476 + 0.921880i \(0.373347\pi\)
\(774\) −50.6630 −1.82105
\(775\) 29.6454 1.06489
\(776\) 100.438 3.60550
\(777\) 2.97767 0.106823
\(778\) −24.5103 −0.878738
\(779\) −7.93180 −0.284186
\(780\) 0.352827 0.0126332
\(781\) 10.2267 0.365942
\(782\) −57.7972 −2.06682
\(783\) 14.1368 0.505207
\(784\) −58.6598 −2.09499
\(785\) 0.142776 0.00509589
\(786\) −5.66824 −0.202179
\(787\) 2.42272 0.0863606 0.0431803 0.999067i \(-0.486251\pi\)
0.0431803 + 0.999067i \(0.486251\pi\)
\(788\) −37.5733 −1.33849
\(789\) −8.04462 −0.286396
\(790\) −0.339359 −0.0120739
\(791\) 9.78552 0.347933
\(792\) 21.4684 0.762846
\(793\) 21.2039 0.752974
\(794\) 68.8496 2.44338
\(795\) 0.492076 0.0174521
\(796\) −46.3729 −1.64365
\(797\) −20.9072 −0.740571 −0.370285 0.928918i \(-0.620740\pi\)
−0.370285 + 0.928918i \(0.620740\pi\)
\(798\) −9.85761 −0.348956
\(799\) 19.1295 0.676754
\(800\) 74.6222 2.63829
\(801\) −32.8878 −1.16203
\(802\) 91.9197 3.24580
\(803\) −1.29592 −0.0457320
\(804\) 2.26705 0.0799528
\(805\) −0.454599 −0.0160225
\(806\) −23.4563 −0.826214
\(807\) −6.91864 −0.243548
\(808\) 137.302 4.83027
\(809\) −41.8001 −1.46961 −0.734806 0.678278i \(-0.762727\pi\)
−0.734806 + 0.678278i \(0.762727\pi\)
\(810\) 1.09109 0.0383371
\(811\) −9.15876 −0.321608 −0.160804 0.986986i \(-0.551409\pi\)
−0.160804 + 0.986986i \(0.551409\pi\)
\(812\) −28.9952 −1.01753
\(813\) 1.57709 0.0553110
\(814\) −8.79541 −0.308279
\(815\) −1.35005 −0.0472903
\(816\) 37.4574 1.31127
\(817\) −29.9994 −1.04954
\(818\) 17.3110 0.605265
\(819\) 5.49516 0.192017
\(820\) 0.726950 0.0253862
\(821\) 36.4528 1.27221 0.636106 0.771601i \(-0.280544\pi\)
0.636106 + 0.771601i \(0.280544\pi\)
\(822\) 38.7046 1.34998
\(823\) −18.4350 −0.642604 −0.321302 0.946977i \(-0.604120\pi\)
−0.321302 + 0.946977i \(0.604120\pi\)
\(824\) −56.5047 −1.96844
\(825\) −3.16098 −0.110051
\(826\) −33.6353 −1.17032
\(827\) 20.9533 0.728617 0.364308 0.931278i \(-0.381305\pi\)
0.364308 + 0.931278i \(0.381305\pi\)
\(828\) −57.3605 −1.99341
\(829\) −31.2352 −1.08484 −0.542421 0.840107i \(-0.682492\pi\)
−0.542421 + 0.840107i \(0.682492\pi\)
\(830\) −0.219561 −0.00762109
\(831\) 9.46698 0.328406
\(832\) −24.0220 −0.832812
\(833\) −24.9067 −0.862966
\(834\) 14.5764 0.504741
\(835\) −0.473008 −0.0163691
\(836\) 20.9147 0.723351
\(837\) 21.0344 0.727054
\(838\) −72.8337 −2.51600
\(839\) −45.6398 −1.57566 −0.787830 0.615893i \(-0.788795\pi\)
−0.787830 + 0.615893i \(0.788795\pi\)
\(840\) 0.549126 0.0189467
\(841\) −13.0867 −0.451265
\(842\) −8.06308 −0.277872
\(843\) −2.07967 −0.0716276
\(844\) −29.0591 −1.00026
\(845\) 0.796073 0.0273858
\(846\) 26.4307 0.908706
\(847\) 1.42532 0.0489746
\(848\) −124.540 −4.27671
\(849\) −5.66351 −0.194371
\(850\) 66.7126 2.28822
\(851\) 14.2836 0.489635
\(852\) 33.0061 1.13077
\(853\) 13.6100 0.465997 0.232999 0.972477i \(-0.425146\pi\)
0.232999 + 0.972477i \(0.425146\pi\)
\(854\) 54.2949 1.85793
\(855\) 0.785816 0.0268743
\(856\) 6.74165 0.230425
\(857\) 5.37825 0.183718 0.0918588 0.995772i \(-0.470719\pi\)
0.0918588 + 0.995772i \(0.470719\pi\)
\(858\) 2.50107 0.0853851
\(859\) −21.5537 −0.735403 −0.367701 0.929944i \(-0.619855\pi\)
−0.367701 + 0.929944i \(0.619855\pi\)
\(860\) 2.74944 0.0937552
\(861\) −1.74457 −0.0594549
\(862\) −48.2637 −1.64387
\(863\) −29.2307 −0.995025 −0.497513 0.867457i \(-0.665753\pi\)
−0.497513 + 0.867457i \(0.665753\pi\)
\(864\) 52.9469 1.80129
\(865\) 1.79947 0.0611839
\(866\) −62.1032 −2.11035
\(867\) 5.14520 0.174740
\(868\) −43.1424 −1.46435
\(869\) −1.72792 −0.0586158
\(870\) −0.495837 −0.0168105
\(871\) −1.04181 −0.0353005
\(872\) −8.23606 −0.278908
\(873\) 31.6127 1.06993
\(874\) −47.2859 −1.59947
\(875\) 1.05001 0.0354970
\(876\) −4.18249 −0.141313
\(877\) 25.4835 0.860517 0.430258 0.902706i \(-0.358422\pi\)
0.430258 + 0.902706i \(0.358422\pi\)
\(878\) 17.6707 0.596357
\(879\) −10.8883 −0.367255
\(880\) −0.870237 −0.0293357
\(881\) 40.4006 1.36113 0.680566 0.732687i \(-0.261734\pi\)
0.680566 + 0.732687i \(0.261734\pi\)
\(882\) −34.4129 −1.15874
\(883\) −7.61709 −0.256336 −0.128168 0.991753i \(-0.540910\pi\)
−0.128168 + 0.991753i \(0.540910\pi\)
\(884\) −37.9152 −1.27523
\(885\) −0.413152 −0.0138879
\(886\) 22.5719 0.758318
\(887\) 0.335598 0.0112683 0.00563414 0.999984i \(-0.498207\pi\)
0.00563414 + 0.999984i \(0.498207\pi\)
\(888\) −17.2537 −0.578995
\(889\) −7.33194 −0.245906
\(890\) 2.48478 0.0832899
\(891\) 5.55555 0.186118
\(892\) −50.4344 −1.68867
\(893\) 15.6505 0.523725
\(894\) −9.48522 −0.317233
\(895\) −1.69168 −0.0565465
\(896\) −18.9203 −0.632082
\(897\) −4.06169 −0.135616
\(898\) 77.8349 2.59739
\(899\) 23.6777 0.789695
\(900\) 66.2085 2.20695
\(901\) −52.8790 −1.76166
\(902\) 5.15310 0.171579
\(903\) −6.59826 −0.219576
\(904\) −56.7007 −1.88584
\(905\) −0.682697 −0.0226936
\(906\) 24.2007 0.804015
\(907\) −22.2108 −0.737499 −0.368749 0.929529i \(-0.620214\pi\)
−0.368749 + 0.929529i \(0.620214\pi\)
\(908\) 33.1306 1.09948
\(909\) 43.2159 1.43338
\(910\) −0.415176 −0.0137630
\(911\) 6.48869 0.214980 0.107490 0.994206i \(-0.465719\pi\)
0.107490 + 0.994206i \(0.465719\pi\)
\(912\) 30.6452 1.01476
\(913\) −1.11795 −0.0369987
\(914\) 97.6751 3.23080
\(915\) 0.666920 0.0220477
\(916\) 27.7864 0.918088
\(917\) 4.79094 0.158211
\(918\) 47.3348 1.56228
\(919\) −10.8674 −0.358484 −0.179242 0.983805i \(-0.557364\pi\)
−0.179242 + 0.983805i \(0.557364\pi\)
\(920\) 2.63410 0.0868437
\(921\) −16.7905 −0.553266
\(922\) 46.4725 1.53049
\(923\) −15.1678 −0.499255
\(924\) 4.60013 0.151333
\(925\) −16.4869 −0.542085
\(926\) −63.0426 −2.07171
\(927\) −17.7849 −0.584132
\(928\) 59.6006 1.95648
\(929\) 5.06818 0.166282 0.0831408 0.996538i \(-0.473505\pi\)
0.0831408 + 0.996538i \(0.473505\pi\)
\(930\) −0.737765 −0.0241923
\(931\) −20.3771 −0.667831
\(932\) −21.0562 −0.689719
\(933\) −0.523435 −0.0171365
\(934\) 30.7834 1.00726
\(935\) −0.369499 −0.0120839
\(936\) −31.8409 −1.04075
\(937\) 20.0779 0.655916 0.327958 0.944692i \(-0.393640\pi\)
0.327958 + 0.944692i \(0.393640\pi\)
\(938\) −2.66767 −0.0871026
\(939\) 7.98507 0.260583
\(940\) −1.43437 −0.0467841
\(941\) −48.0898 −1.56768 −0.783842 0.620961i \(-0.786743\pi\)
−0.783842 + 0.620961i \(0.786743\pi\)
\(942\) 3.26645 0.106427
\(943\) −8.36854 −0.272517
\(944\) 104.565 3.40329
\(945\) 0.372307 0.0121112
\(946\) 19.4899 0.633670
\(947\) −46.2933 −1.50433 −0.752165 0.658975i \(-0.770990\pi\)
−0.752165 + 0.658975i \(0.770990\pi\)
\(948\) −5.57676 −0.181125
\(949\) 1.92204 0.0623922
\(950\) 54.5799 1.77081
\(951\) 11.0619 0.358705
\(952\) −59.0097 −1.91252
\(953\) 7.46186 0.241713 0.120857 0.992670i \(-0.461436\pi\)
0.120857 + 0.992670i \(0.461436\pi\)
\(954\) −73.0613 −2.36545
\(955\) −0.200939 −0.00650224
\(956\) −17.2705 −0.558568
\(957\) −2.52467 −0.0816110
\(958\) −91.7439 −2.96411
\(959\) −32.7141 −1.05639
\(960\) −0.755555 −0.0243854
\(961\) 4.23042 0.136465
\(962\) 13.0449 0.420585
\(963\) 2.12194 0.0683784
\(964\) −83.5657 −2.69147
\(965\) −1.30275 −0.0419369
\(966\) −10.4004 −0.334627
\(967\) −54.0095 −1.73683 −0.868415 0.495839i \(-0.834861\pi\)
−0.868415 + 0.495839i \(0.834861\pi\)
\(968\) −8.25880 −0.265448
\(969\) 13.0118 0.418000
\(970\) −2.38844 −0.0766881
\(971\) 51.6797 1.65848 0.829240 0.558892i \(-0.188773\pi\)
0.829240 + 0.558892i \(0.188773\pi\)
\(972\) 72.1458 2.31408
\(973\) −12.3204 −0.394973
\(974\) 2.66073 0.0852554
\(975\) 4.68822 0.150143
\(976\) −168.791 −5.40288
\(977\) −30.9531 −0.990278 −0.495139 0.868814i \(-0.664883\pi\)
−0.495139 + 0.868814i \(0.664883\pi\)
\(978\) −30.8868 −0.987650
\(979\) 12.6518 0.404354
\(980\) 1.86756 0.0596569
\(981\) −2.59230 −0.0827658
\(982\) 67.0708 2.14032
\(983\) −6.75251 −0.215372 −0.107686 0.994185i \(-0.534344\pi\)
−0.107686 + 0.994185i \(0.534344\pi\)
\(984\) 10.1087 0.322252
\(985\) 0.543082 0.0173040
\(986\) 53.2832 1.69688
\(987\) 3.44228 0.109569
\(988\) −31.0197 −0.986869
\(989\) −31.6512 −1.00645
\(990\) −0.510525 −0.0162256
\(991\) −11.0228 −0.350151 −0.175076 0.984555i \(-0.556017\pi\)
−0.175076 + 0.984555i \(0.556017\pi\)
\(992\) 88.6807 2.81561
\(993\) 1.48120 0.0470046
\(994\) −38.8388 −1.23189
\(995\) 0.670271 0.0212490
\(996\) −3.60810 −0.114327
\(997\) −16.1456 −0.511336 −0.255668 0.966765i \(-0.582295\pi\)
−0.255668 + 0.966765i \(0.582295\pi\)
\(998\) −64.8997 −2.05436
\(999\) −11.6980 −0.370107
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 \(a_p\))