Properties

Label 6019.2.a.c.1.4
Level 6019
Weight 2
Character 6019.1
Self dual Yes
Analytic conductor 48.062
Analytic rank 1
Dimension 108
CM No

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Newspace parameters

Level: \( N \) = \( 6019 = 13 \cdot 463 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0619569766\)
Analytic rank: \(1\)
Dimension: \(108\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.62932 q^{2}\) \(+0.928194 q^{3}\) \(+4.91333 q^{4}\) \(+1.81764 q^{5}\) \(-2.44052 q^{6}\) \(+3.79843 q^{7}\) \(-7.66009 q^{8}\) \(-2.13846 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.62932 q^{2}\) \(+0.928194 q^{3}\) \(+4.91333 q^{4}\) \(+1.81764 q^{5}\) \(-2.44052 q^{6}\) \(+3.79843 q^{7}\) \(-7.66009 q^{8}\) \(-2.13846 q^{9}\) \(-4.77917 q^{10}\) \(+0.597155 q^{11}\) \(+4.56053 q^{12}\) \(-1.00000 q^{13}\) \(-9.98729 q^{14}\) \(+1.68713 q^{15}\) \(+10.3142 q^{16}\) \(-6.29148 q^{17}\) \(+5.62269 q^{18}\) \(+3.84371 q^{19}\) \(+8.93068 q^{20}\) \(+3.52568 q^{21}\) \(-1.57011 q^{22}\) \(-1.64780 q^{23}\) \(-7.11005 q^{24}\) \(-1.69618 q^{25}\) \(+2.62932 q^{26}\) \(-4.76948 q^{27}\) \(+18.6629 q^{28}\) \(-7.96027 q^{29}\) \(-4.43600 q^{30}\) \(-2.25637 q^{31}\) \(-11.7991 q^{32}\) \(+0.554275 q^{33}\) \(+16.5423 q^{34}\) \(+6.90418 q^{35}\) \(-10.5069 q^{36}\) \(-3.94507 q^{37}\) \(-10.1064 q^{38}\) \(-0.928194 q^{39}\) \(-13.9233 q^{40}\) \(+2.09558 q^{41}\) \(-9.27014 q^{42}\) \(-2.01409 q^{43}\) \(+2.93402 q^{44}\) \(-3.88695 q^{45}\) \(+4.33259 q^{46}\) \(+1.57582 q^{47}\) \(+9.57355 q^{48}\) \(+7.42805 q^{49}\) \(+4.45979 q^{50}\) \(-5.83972 q^{51}\) \(-4.91333 q^{52}\) \(+4.25474 q^{53}\) \(+12.5405 q^{54}\) \(+1.08541 q^{55}\) \(-29.0963 q^{56}\) \(+3.56771 q^{57}\) \(+20.9301 q^{58}\) \(-3.74510 q^{59}\) \(+8.28941 q^{60}\) \(-2.61101 q^{61}\) \(+5.93272 q^{62}\) \(-8.12277 q^{63}\) \(+10.3953 q^{64}\) \(-1.81764 q^{65}\) \(-1.45737 q^{66}\) \(+7.44967 q^{67}\) \(-30.9121 q^{68}\) \(-1.52948 q^{69}\) \(-18.1533 q^{70}\) \(-5.97636 q^{71}\) \(+16.3808 q^{72}\) \(+5.55999 q^{73}\) \(+10.3729 q^{74}\) \(-1.57438 q^{75}\) \(+18.8854 q^{76}\) \(+2.26825 q^{77}\) \(+2.44052 q^{78}\) \(+4.70309 q^{79}\) \(+18.7475 q^{80}\) \(+1.98836 q^{81}\) \(-5.50995 q^{82}\) \(-7.03268 q^{83}\) \(+17.3228 q^{84}\) \(-11.4357 q^{85}\) \(+5.29568 q^{86}\) \(-7.38868 q^{87}\) \(-4.57426 q^{88}\) \(-11.6459 q^{89}\) \(+10.2200 q^{90}\) \(-3.79843 q^{91}\) \(-8.09619 q^{92}\) \(-2.09435 q^{93}\) \(-4.14334 q^{94}\) \(+6.98650 q^{95}\) \(-10.9519 q^{96}\) \(+16.6462 q^{97}\) \(-19.5307 q^{98}\) \(-1.27699 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62932 −1.85921 −0.929606 0.368556i \(-0.879852\pi\)
−0.929606 + 0.368556i \(0.879852\pi\)
\(3\) 0.928194 0.535893 0.267947 0.963434i \(-0.413655\pi\)
0.267947 + 0.963434i \(0.413655\pi\)
\(4\) 4.91333 2.45667
\(5\) 1.81764 0.812874 0.406437 0.913679i \(-0.366771\pi\)
0.406437 + 0.913679i \(0.366771\pi\)
\(6\) −2.44052 −0.996339
\(7\) 3.79843 1.43567 0.717835 0.696213i \(-0.245133\pi\)
0.717835 + 0.696213i \(0.245133\pi\)
\(8\) −7.66009 −2.70825
\(9\) −2.13846 −0.712818
\(10\) −4.77917 −1.51131
\(11\) 0.597155 0.180049 0.0900244 0.995940i \(-0.471305\pi\)
0.0900244 + 0.995940i \(0.471305\pi\)
\(12\) 4.56053 1.31651
\(13\) −1.00000 −0.277350
\(14\) −9.98729 −2.66921
\(15\) 1.68713 0.435614
\(16\) 10.3142 2.57854
\(17\) −6.29148 −1.52591 −0.762954 0.646452i \(-0.776252\pi\)
−0.762954 + 0.646452i \(0.776252\pi\)
\(18\) 5.62269 1.32528
\(19\) 3.84371 0.881809 0.440904 0.897554i \(-0.354658\pi\)
0.440904 + 0.897554i \(0.354658\pi\)
\(20\) 8.93068 1.99696
\(21\) 3.52568 0.769366
\(22\) −1.57011 −0.334749
\(23\) −1.64780 −0.343590 −0.171795 0.985133i \(-0.554957\pi\)
−0.171795 + 0.985133i \(0.554957\pi\)
\(24\) −7.11005 −1.45133
\(25\) −1.69618 −0.339235
\(26\) 2.62932 0.515652
\(27\) −4.76948 −0.917888
\(28\) 18.6629 3.52696
\(29\) −7.96027 −1.47819 −0.739093 0.673604i \(-0.764746\pi\)
−0.739093 + 0.673604i \(0.764746\pi\)
\(30\) −4.43600 −0.809898
\(31\) −2.25637 −0.405256 −0.202628 0.979256i \(-0.564948\pi\)
−0.202628 + 0.979256i \(0.564948\pi\)
\(32\) −11.7991 −2.08581
\(33\) 0.554275 0.0964870
\(34\) 16.5423 2.83699
\(35\) 6.90418 1.16702
\(36\) −10.5069 −1.75116
\(37\) −3.94507 −0.648565 −0.324283 0.945960i \(-0.605123\pi\)
−0.324283 + 0.945960i \(0.605123\pi\)
\(38\) −10.1064 −1.63947
\(39\) −0.928194 −0.148630
\(40\) −13.9233 −2.20147
\(41\) 2.09558 0.327274 0.163637 0.986521i \(-0.447677\pi\)
0.163637 + 0.986521i \(0.447677\pi\)
\(42\) −9.27014 −1.43041
\(43\) −2.01409 −0.307145 −0.153573 0.988137i \(-0.549078\pi\)
−0.153573 + 0.988137i \(0.549078\pi\)
\(44\) 2.93402 0.442320
\(45\) −3.88695 −0.579432
\(46\) 4.33259 0.638806
\(47\) 1.57582 0.229857 0.114928 0.993374i \(-0.463336\pi\)
0.114928 + 0.993374i \(0.463336\pi\)
\(48\) 9.57355 1.38182
\(49\) 7.42805 1.06115
\(50\) 4.45979 0.630710
\(51\) −5.83972 −0.817724
\(52\) −4.91333 −0.681357
\(53\) 4.25474 0.584433 0.292217 0.956352i \(-0.405607\pi\)
0.292217 + 0.956352i \(0.405607\pi\)
\(54\) 12.5405 1.70655
\(55\) 1.08541 0.146357
\(56\) −29.0963 −3.88816
\(57\) 3.56771 0.472555
\(58\) 20.9301 2.74826
\(59\) −3.74510 −0.487571 −0.243785 0.969829i \(-0.578389\pi\)
−0.243785 + 0.969829i \(0.578389\pi\)
\(60\) 8.28941 1.07016
\(61\) −2.61101 −0.334306 −0.167153 0.985931i \(-0.553457\pi\)
−0.167153 + 0.985931i \(0.553457\pi\)
\(62\) 5.93272 0.753456
\(63\) −8.12277 −1.02337
\(64\) 10.3953 1.29941
\(65\) −1.81764 −0.225451
\(66\) −1.45737 −0.179390
\(67\) 7.44967 0.910122 0.455061 0.890460i \(-0.349617\pi\)
0.455061 + 0.890460i \(0.349617\pi\)
\(68\) −30.9121 −3.74865
\(69\) −1.52948 −0.184127
\(70\) −18.1533 −2.16974
\(71\) −5.97636 −0.709264 −0.354632 0.935006i \(-0.615394\pi\)
−0.354632 + 0.935006i \(0.615394\pi\)
\(72\) 16.3808 1.93049
\(73\) 5.55999 0.650747 0.325374 0.945586i \(-0.394510\pi\)
0.325374 + 0.945586i \(0.394510\pi\)
\(74\) 10.3729 1.20582
\(75\) −1.57438 −0.181794
\(76\) 18.8854 2.16631
\(77\) 2.26825 0.258491
\(78\) 2.44052 0.276335
\(79\) 4.70309 0.529139 0.264569 0.964367i \(-0.414770\pi\)
0.264569 + 0.964367i \(0.414770\pi\)
\(80\) 18.7475 2.09603
\(81\) 1.98836 0.220929
\(82\) −5.50995 −0.608472
\(83\) −7.03268 −0.771936 −0.385968 0.922512i \(-0.626133\pi\)
−0.385968 + 0.922512i \(0.626133\pi\)
\(84\) 17.3228 1.89008
\(85\) −11.4357 −1.24037
\(86\) 5.29568 0.571048
\(87\) −7.38868 −0.792150
\(88\) −4.57426 −0.487617
\(89\) −11.6459 −1.23446 −0.617230 0.786783i \(-0.711745\pi\)
−0.617230 + 0.786783i \(0.711745\pi\)
\(90\) 10.2200 1.07729
\(91\) −3.79843 −0.398183
\(92\) −8.09619 −0.844086
\(93\) −2.09435 −0.217174
\(94\) −4.14334 −0.427353
\(95\) 6.98650 0.716800
\(96\) −10.9519 −1.11777
\(97\) 16.6462 1.69017 0.845083 0.534636i \(-0.179551\pi\)
0.845083 + 0.534636i \(0.179551\pi\)
\(98\) −19.5307 −1.97290
\(99\) −1.27699 −0.128342
\(100\) −8.33388 −0.833388
\(101\) 14.3705 1.42992 0.714959 0.699166i \(-0.246445\pi\)
0.714959 + 0.699166i \(0.246445\pi\)
\(102\) 15.3545 1.52032
\(103\) −6.51358 −0.641802 −0.320901 0.947113i \(-0.603986\pi\)
−0.320901 + 0.947113i \(0.603986\pi\)
\(104\) 7.66009 0.751133
\(105\) 6.40842 0.625398
\(106\) −11.1871 −1.08658
\(107\) 2.24666 0.217192 0.108596 0.994086i \(-0.465364\pi\)
0.108596 + 0.994086i \(0.465364\pi\)
\(108\) −23.4341 −2.25494
\(109\) −7.82159 −0.749173 −0.374586 0.927192i \(-0.622215\pi\)
−0.374586 + 0.927192i \(0.622215\pi\)
\(110\) −2.85390 −0.272109
\(111\) −3.66179 −0.347562
\(112\) 39.1776 3.70194
\(113\) −7.39754 −0.695902 −0.347951 0.937513i \(-0.613122\pi\)
−0.347951 + 0.937513i \(0.613122\pi\)
\(114\) −9.38067 −0.878580
\(115\) −2.99511 −0.279295
\(116\) −39.1115 −3.63141
\(117\) 2.13846 0.197700
\(118\) 9.84708 0.906497
\(119\) −23.8977 −2.19070
\(120\) −12.9235 −1.17975
\(121\) −10.6434 −0.967582
\(122\) 6.86519 0.621545
\(123\) 1.94510 0.175384
\(124\) −11.0863 −0.995578
\(125\) −12.1713 −1.08863
\(126\) 21.3574 1.90267
\(127\) −6.85015 −0.607852 −0.303926 0.952696i \(-0.598298\pi\)
−0.303926 + 0.952696i \(0.598298\pi\)
\(128\) −3.73434 −0.330072
\(129\) −1.86946 −0.164597
\(130\) 4.77917 0.419161
\(131\) −10.8310 −0.946309 −0.473155 0.880979i \(-0.656885\pi\)
−0.473155 + 0.880979i \(0.656885\pi\)
\(132\) 2.72334 0.237036
\(133\) 14.6001 1.26599
\(134\) −19.5876 −1.69211
\(135\) −8.66922 −0.746128
\(136\) 48.1933 4.13254
\(137\) −13.9910 −1.19533 −0.597666 0.801746i \(-0.703905\pi\)
−0.597666 + 0.801746i \(0.703905\pi\)
\(138\) 4.02149 0.342332
\(139\) −10.7896 −0.915165 −0.457583 0.889167i \(-0.651285\pi\)
−0.457583 + 0.889167i \(0.651285\pi\)
\(140\) 33.9225 2.86698
\(141\) 1.46267 0.123179
\(142\) 15.7138 1.31867
\(143\) −0.597155 −0.0499366
\(144\) −22.0564 −1.83803
\(145\) −14.4689 −1.20158
\(146\) −14.6190 −1.20988
\(147\) 6.89467 0.568663
\(148\) −19.3834 −1.59331
\(149\) −7.58507 −0.621393 −0.310696 0.950509i \(-0.600562\pi\)
−0.310696 + 0.950509i \(0.600562\pi\)
\(150\) 4.13955 0.337993
\(151\) −18.7979 −1.52975 −0.764875 0.644179i \(-0.777199\pi\)
−0.764875 + 0.644179i \(0.777199\pi\)
\(152\) −29.4432 −2.38816
\(153\) 13.4541 1.08770
\(154\) −5.96395 −0.480589
\(155\) −4.10127 −0.329422
\(156\) −4.56053 −0.365134
\(157\) −12.9440 −1.03304 −0.516521 0.856275i \(-0.672773\pi\)
−0.516521 + 0.856275i \(0.672773\pi\)
\(158\) −12.3659 −0.983780
\(159\) 3.94922 0.313194
\(160\) −21.4465 −1.69550
\(161\) −6.25905 −0.493282
\(162\) −5.22803 −0.410753
\(163\) 4.80617 0.376448 0.188224 0.982126i \(-0.439727\pi\)
0.188224 + 0.982126i \(0.439727\pi\)
\(164\) 10.2963 0.804004
\(165\) 1.00747 0.0784318
\(166\) 18.4912 1.43519
\(167\) −0.994647 −0.0769681 −0.0384840 0.999259i \(-0.512253\pi\)
−0.0384840 + 0.999259i \(0.512253\pi\)
\(168\) −27.0070 −2.08364
\(169\) 1.00000 0.0769231
\(170\) 30.0680 2.30611
\(171\) −8.21961 −0.628569
\(172\) −9.89587 −0.754553
\(173\) −14.6709 −1.11541 −0.557705 0.830039i \(-0.688318\pi\)
−0.557705 + 0.830039i \(0.688318\pi\)
\(174\) 19.4272 1.47277
\(175\) −6.44280 −0.487030
\(176\) 6.15915 0.464264
\(177\) −3.47618 −0.261286
\(178\) 30.6208 2.29512
\(179\) −0.555342 −0.0415082 −0.0207541 0.999785i \(-0.506607\pi\)
−0.0207541 + 0.999785i \(0.506607\pi\)
\(180\) −19.0979 −1.42347
\(181\) 24.1279 1.79341 0.896706 0.442626i \(-0.145953\pi\)
0.896706 + 0.442626i \(0.145953\pi\)
\(182\) 9.98729 0.740307
\(183\) −2.42353 −0.179152
\(184\) 12.6223 0.930527
\(185\) −7.17073 −0.527202
\(186\) 5.50672 0.403772
\(187\) −3.75699 −0.274738
\(188\) 7.74253 0.564682
\(189\) −18.1165 −1.31778
\(190\) −18.3698 −1.33268
\(191\) 13.5152 0.977922 0.488961 0.872306i \(-0.337376\pi\)
0.488961 + 0.872306i \(0.337376\pi\)
\(192\) 9.64884 0.696345
\(193\) 19.7479 1.42148 0.710742 0.703453i \(-0.248359\pi\)
0.710742 + 0.703453i \(0.248359\pi\)
\(194\) −43.7682 −3.14237
\(195\) −1.68713 −0.120818
\(196\) 36.4965 2.60689
\(197\) −6.46596 −0.460681 −0.230340 0.973110i \(-0.573984\pi\)
−0.230340 + 0.973110i \(0.573984\pi\)
\(198\) 3.35761 0.238615
\(199\) −8.21724 −0.582505 −0.291252 0.956646i \(-0.594072\pi\)
−0.291252 + 0.956646i \(0.594072\pi\)
\(200\) 12.9929 0.918734
\(201\) 6.91474 0.487728
\(202\) −37.7847 −2.65852
\(203\) −30.2365 −2.12219
\(204\) −28.6925 −2.00888
\(205\) 3.80901 0.266033
\(206\) 17.1263 1.19325
\(207\) 3.52374 0.244917
\(208\) −10.3142 −0.715159
\(209\) 2.29529 0.158769
\(210\) −16.8498 −1.16275
\(211\) −1.12780 −0.0776410 −0.0388205 0.999246i \(-0.512360\pi\)
−0.0388205 + 0.999246i \(0.512360\pi\)
\(212\) 20.9049 1.43576
\(213\) −5.54723 −0.380090
\(214\) −5.90718 −0.403806
\(215\) −3.66089 −0.249670
\(216\) 36.5347 2.48587
\(217\) −8.57065 −0.581814
\(218\) 20.5655 1.39287
\(219\) 5.16075 0.348731
\(220\) 5.33300 0.359551
\(221\) 6.29148 0.423211
\(222\) 9.62803 0.646191
\(223\) −25.6995 −1.72097 −0.860484 0.509478i \(-0.829838\pi\)
−0.860484 + 0.509478i \(0.829838\pi\)
\(224\) −44.8180 −2.99453
\(225\) 3.62720 0.241813
\(226\) 19.4505 1.29383
\(227\) 8.19413 0.543863 0.271932 0.962317i \(-0.412338\pi\)
0.271932 + 0.962317i \(0.412338\pi\)
\(228\) 17.5294 1.16091
\(229\) −16.0732 −1.06215 −0.531073 0.847326i \(-0.678211\pi\)
−0.531073 + 0.847326i \(0.678211\pi\)
\(230\) 7.87511 0.519269
\(231\) 2.10537 0.138524
\(232\) 60.9764 4.00330
\(233\) −15.4720 −1.01361 −0.506803 0.862062i \(-0.669173\pi\)
−0.506803 + 0.862062i \(0.669173\pi\)
\(234\) −5.62269 −0.367567
\(235\) 2.86428 0.186845
\(236\) −18.4009 −1.19780
\(237\) 4.36538 0.283562
\(238\) 62.8348 4.07298
\(239\) −10.4146 −0.673665 −0.336833 0.941565i \(-0.609356\pi\)
−0.336833 + 0.941565i \(0.609356\pi\)
\(240\) 17.4013 1.12325
\(241\) −4.52938 −0.291763 −0.145881 0.989302i \(-0.546602\pi\)
−0.145881 + 0.989302i \(0.546602\pi\)
\(242\) 27.9849 1.79894
\(243\) 16.1540 1.03628
\(244\) −12.8288 −0.821278
\(245\) 13.5015 0.862582
\(246\) −5.11430 −0.326076
\(247\) −3.84371 −0.244570
\(248\) 17.2840 1.09753
\(249\) −6.52769 −0.413676
\(250\) 32.0021 2.02399
\(251\) −6.90516 −0.435850 −0.217925 0.975966i \(-0.569929\pi\)
−0.217925 + 0.975966i \(0.569929\pi\)
\(252\) −39.9099 −2.51408
\(253\) −0.983991 −0.0618630
\(254\) 18.0112 1.13013
\(255\) −10.6145 −0.664707
\(256\) −10.9718 −0.685736
\(257\) 28.2197 1.76030 0.880150 0.474696i \(-0.157442\pi\)
0.880150 + 0.474696i \(0.157442\pi\)
\(258\) 4.91542 0.306021
\(259\) −14.9851 −0.931126
\(260\) −8.93068 −0.553857
\(261\) 17.0227 1.05368
\(262\) 28.4782 1.75939
\(263\) −12.4078 −0.765097 −0.382549 0.923935i \(-0.624954\pi\)
−0.382549 + 0.923935i \(0.624954\pi\)
\(264\) −4.24580 −0.261311
\(265\) 7.73359 0.475071
\(266\) −38.3883 −2.35374
\(267\) −10.8096 −0.661539
\(268\) 36.6027 2.23587
\(269\) 6.06078 0.369532 0.184766 0.982783i \(-0.440847\pi\)
0.184766 + 0.982783i \(0.440847\pi\)
\(270\) 22.7942 1.38721
\(271\) 7.27201 0.441743 0.220872 0.975303i \(-0.429110\pi\)
0.220872 + 0.975303i \(0.429110\pi\)
\(272\) −64.8914 −3.93462
\(273\) −3.52568 −0.213384
\(274\) 36.7868 2.22237
\(275\) −1.01288 −0.0610789
\(276\) −7.51483 −0.452340
\(277\) 21.1748 1.27227 0.636135 0.771578i \(-0.280532\pi\)
0.636135 + 0.771578i \(0.280532\pi\)
\(278\) 28.3694 1.70149
\(279\) 4.82514 0.288874
\(280\) −52.8867 −3.16058
\(281\) 21.8837 1.30547 0.652736 0.757585i \(-0.273621\pi\)
0.652736 + 0.757585i \(0.273621\pi\)
\(282\) −3.84582 −0.229015
\(283\) 24.2867 1.44369 0.721846 0.692054i \(-0.243294\pi\)
0.721846 + 0.692054i \(0.243294\pi\)
\(284\) −29.3639 −1.74242
\(285\) 6.48483 0.384128
\(286\) 1.57011 0.0928426
\(287\) 7.95990 0.469858
\(288\) 25.2318 1.48680
\(289\) 22.5828 1.32840
\(290\) 38.0435 2.23399
\(291\) 15.4509 0.905748
\(292\) 27.3181 1.59867
\(293\) 3.82656 0.223550 0.111775 0.993734i \(-0.464346\pi\)
0.111775 + 0.993734i \(0.464346\pi\)
\(294\) −18.1283 −1.05726
\(295\) −6.80726 −0.396334
\(296\) 30.2196 1.75648
\(297\) −2.84812 −0.165265
\(298\) 19.9436 1.15530
\(299\) 1.64780 0.0952947
\(300\) −7.73546 −0.446607
\(301\) −7.65036 −0.440959
\(302\) 49.4257 2.84413
\(303\) 13.3386 0.766283
\(304\) 39.6447 2.27378
\(305\) −4.74589 −0.271749
\(306\) −35.3750 −2.02226
\(307\) −4.14652 −0.236654 −0.118327 0.992975i \(-0.537753\pi\)
−0.118327 + 0.992975i \(0.537753\pi\)
\(308\) 11.1447 0.635026
\(309\) −6.04587 −0.343938
\(310\) 10.7836 0.612465
\(311\) −19.7040 −1.11731 −0.558654 0.829401i \(-0.688682\pi\)
−0.558654 + 0.829401i \(0.688682\pi\)
\(312\) 7.11005 0.402527
\(313\) −11.6856 −0.660511 −0.330255 0.943892i \(-0.607135\pi\)
−0.330255 + 0.943892i \(0.607135\pi\)
\(314\) 34.0339 1.92064
\(315\) −14.7643 −0.831873
\(316\) 23.1078 1.29992
\(317\) −15.0907 −0.847576 −0.423788 0.905761i \(-0.639300\pi\)
−0.423788 + 0.905761i \(0.639300\pi\)
\(318\) −10.3838 −0.582293
\(319\) −4.75351 −0.266146
\(320\) 18.8949 1.05626
\(321\) 2.08533 0.116392
\(322\) 16.4570 0.917115
\(323\) −24.1827 −1.34556
\(324\) 9.76946 0.542748
\(325\) 1.69618 0.0940869
\(326\) −12.6370 −0.699897
\(327\) −7.25996 −0.401477
\(328\) −16.0523 −0.886341
\(329\) 5.98564 0.329999
\(330\) −2.64897 −0.145821
\(331\) −12.0351 −0.661508 −0.330754 0.943717i \(-0.607303\pi\)
−0.330754 + 0.943717i \(0.607303\pi\)
\(332\) −34.5539 −1.89639
\(333\) 8.43635 0.462309
\(334\) 2.61525 0.143100
\(335\) 13.5408 0.739815
\(336\) 36.3645 1.98384
\(337\) −15.0586 −0.820296 −0.410148 0.912019i \(-0.634523\pi\)
−0.410148 + 0.912019i \(0.634523\pi\)
\(338\) −2.62932 −0.143016
\(339\) −6.86635 −0.372929
\(340\) −56.1872 −3.04718
\(341\) −1.34740 −0.0729658
\(342\) 21.6120 1.16864
\(343\) 1.62592 0.0877914
\(344\) 15.4281 0.831826
\(345\) −2.78004 −0.149673
\(346\) 38.5746 2.07378
\(347\) −22.9679 −1.23298 −0.616492 0.787361i \(-0.711447\pi\)
−0.616492 + 0.787361i \(0.711447\pi\)
\(348\) −36.3030 −1.94605
\(349\) −2.01351 −0.107781 −0.0538904 0.998547i \(-0.517162\pi\)
−0.0538904 + 0.998547i \(0.517162\pi\)
\(350\) 16.9402 0.905492
\(351\) 4.76948 0.254576
\(352\) −7.04588 −0.375547
\(353\) 3.70839 0.197378 0.0986888 0.995118i \(-0.468535\pi\)
0.0986888 + 0.995118i \(0.468535\pi\)
\(354\) 9.14000 0.485786
\(355\) −10.8629 −0.576542
\(356\) −57.2201 −3.03266
\(357\) −22.1817 −1.17398
\(358\) 1.46017 0.0771725
\(359\) 4.67697 0.246841 0.123420 0.992354i \(-0.460614\pi\)
0.123420 + 0.992354i \(0.460614\pi\)
\(360\) 29.7744 1.56925
\(361\) −4.22586 −0.222414
\(362\) −63.4400 −3.33433
\(363\) −9.87915 −0.518521
\(364\) −18.6629 −0.978204
\(365\) 10.1061 0.528976
\(366\) 6.37223 0.333082
\(367\) −2.88746 −0.150724 −0.0753622 0.997156i \(-0.524011\pi\)
−0.0753622 + 0.997156i \(0.524011\pi\)
\(368\) −16.9957 −0.885961
\(369\) −4.48130 −0.233287
\(370\) 18.8541 0.980180
\(371\) 16.1613 0.839053
\(372\) −10.2902 −0.533524
\(373\) 31.0683 1.60866 0.804329 0.594184i \(-0.202525\pi\)
0.804329 + 0.594184i \(0.202525\pi\)
\(374\) 9.87833 0.510796
\(375\) −11.2973 −0.583389
\(376\) −12.0709 −0.622510
\(377\) 7.96027 0.409975
\(378\) 47.6342 2.45004
\(379\) 4.11997 0.211628 0.105814 0.994386i \(-0.466255\pi\)
0.105814 + 0.994386i \(0.466255\pi\)
\(380\) 34.3270 1.76094
\(381\) −6.35827 −0.325744
\(382\) −35.5357 −1.81816
\(383\) −0.560735 −0.0286522 −0.0143261 0.999897i \(-0.504560\pi\)
−0.0143261 + 0.999897i \(0.504560\pi\)
\(384\) −3.46619 −0.176883
\(385\) 4.12286 0.210121
\(386\) −51.9236 −2.64284
\(387\) 4.30703 0.218939
\(388\) 81.7883 4.15217
\(389\) 19.8640 1.00714 0.503572 0.863953i \(-0.332019\pi\)
0.503572 + 0.863953i \(0.332019\pi\)
\(390\) 4.43600 0.224625
\(391\) 10.3671 0.524287
\(392\) −56.8995 −2.87386
\(393\) −10.0533 −0.507121
\(394\) 17.0011 0.856502
\(395\) 8.54853 0.430123
\(396\) −6.27427 −0.315294
\(397\) 1.71307 0.0859766 0.0429883 0.999076i \(-0.486312\pi\)
0.0429883 + 0.999076i \(0.486312\pi\)
\(398\) 21.6058 1.08300
\(399\) 13.5517 0.678434
\(400\) −17.4946 −0.874732
\(401\) 26.2570 1.31121 0.655606 0.755103i \(-0.272413\pi\)
0.655606 + 0.755103i \(0.272413\pi\)
\(402\) −18.1811 −0.906790
\(403\) 2.25637 0.112398
\(404\) 70.6070 3.51283
\(405\) 3.61412 0.179587
\(406\) 79.5015 3.94560
\(407\) −2.35582 −0.116773
\(408\) 44.7328 2.21460
\(409\) 15.0583 0.744584 0.372292 0.928116i \(-0.378572\pi\)
0.372292 + 0.928116i \(0.378572\pi\)
\(410\) −10.0151 −0.494611
\(411\) −12.9864 −0.640570
\(412\) −32.0034 −1.57669
\(413\) −14.2255 −0.699991
\(414\) −9.26506 −0.455353
\(415\) −12.7829 −0.627487
\(416\) 11.7991 0.578498
\(417\) −10.0149 −0.490431
\(418\) −6.03506 −0.295184
\(419\) −8.08717 −0.395084 −0.197542 0.980294i \(-0.563296\pi\)
−0.197542 + 0.980294i \(0.563296\pi\)
\(420\) 31.4867 1.53639
\(421\) −24.7564 −1.20655 −0.603276 0.797532i \(-0.706138\pi\)
−0.603276 + 0.797532i \(0.706138\pi\)
\(422\) 2.96535 0.144351
\(423\) −3.36982 −0.163846
\(424\) −32.5917 −1.58279
\(425\) 10.6715 0.517642
\(426\) 14.5854 0.706667
\(427\) −9.91774 −0.479953
\(428\) 11.0386 0.533569
\(429\) −0.554275 −0.0267607
\(430\) 9.62565 0.464190
\(431\) 28.6227 1.37871 0.689354 0.724425i \(-0.257895\pi\)
0.689354 + 0.724425i \(0.257895\pi\)
\(432\) −49.1933 −2.36681
\(433\) −2.93982 −0.141279 −0.0706394 0.997502i \(-0.522504\pi\)
−0.0706394 + 0.997502i \(0.522504\pi\)
\(434\) 22.5350 1.08171
\(435\) −13.4300 −0.643918
\(436\) −38.4301 −1.84047
\(437\) −6.33367 −0.302981
\(438\) −13.5693 −0.648365
\(439\) 3.26546 0.155852 0.0779260 0.996959i \(-0.475170\pi\)
0.0779260 + 0.996959i \(0.475170\pi\)
\(440\) −8.31436 −0.396372
\(441\) −15.8846 −0.756407
\(442\) −16.5423 −0.786838
\(443\) −11.3376 −0.538668 −0.269334 0.963047i \(-0.586803\pi\)
−0.269334 + 0.963047i \(0.586803\pi\)
\(444\) −17.9916 −0.853843
\(445\) −21.1680 −1.00346
\(446\) 67.5723 3.19964
\(447\) −7.04042 −0.333000
\(448\) 39.4857 1.86552
\(449\) 25.4093 1.19914 0.599570 0.800322i \(-0.295338\pi\)
0.599570 + 0.800322i \(0.295338\pi\)
\(450\) −9.53707 −0.449582
\(451\) 1.25138 0.0589254
\(452\) −36.3466 −1.70960
\(453\) −17.4481 −0.819782
\(454\) −21.5450 −1.01116
\(455\) −6.90418 −0.323673
\(456\) −27.3290 −1.27980
\(457\) 18.5014 0.865461 0.432730 0.901523i \(-0.357550\pi\)
0.432730 + 0.901523i \(0.357550\pi\)
\(458\) 42.2616 1.97475
\(459\) 30.0071 1.40061
\(460\) −14.7160 −0.686136
\(461\) −30.3524 −1.41365 −0.706826 0.707388i \(-0.749874\pi\)
−0.706826 + 0.707388i \(0.749874\pi\)
\(462\) −5.53571 −0.257544
\(463\) −1.00000 −0.0464739
\(464\) −82.1036 −3.81156
\(465\) −3.80678 −0.176535
\(466\) 40.6809 1.88451
\(467\) 17.7439 0.821088 0.410544 0.911841i \(-0.365339\pi\)
0.410544 + 0.911841i \(0.365339\pi\)
\(468\) 10.5069 0.485684
\(469\) 28.2970 1.30664
\(470\) −7.53111 −0.347384
\(471\) −12.0145 −0.553600
\(472\) 28.6878 1.32046
\(473\) −1.20272 −0.0553011
\(474\) −11.4780 −0.527201
\(475\) −6.51962 −0.299140
\(476\) −117.418 −5.38182
\(477\) −9.09857 −0.416595
\(478\) 27.3834 1.25249
\(479\) 19.0719 0.871417 0.435709 0.900088i \(-0.356498\pi\)
0.435709 + 0.900088i \(0.356498\pi\)
\(480\) −19.9066 −0.908606
\(481\) 3.94507 0.179880
\(482\) 11.9092 0.542449
\(483\) −5.80961 −0.264346
\(484\) −52.2946 −2.37703
\(485\) 30.2568 1.37389
\(486\) −42.4742 −1.92667
\(487\) −22.2951 −1.01029 −0.505143 0.863036i \(-0.668560\pi\)
−0.505143 + 0.863036i \(0.668560\pi\)
\(488\) 20.0006 0.905384
\(489\) 4.46106 0.201736
\(490\) −35.4999 −1.60372
\(491\) 24.7232 1.11574 0.557871 0.829927i \(-0.311618\pi\)
0.557871 + 0.829927i \(0.311618\pi\)
\(492\) 9.55694 0.430860
\(493\) 50.0819 2.25558
\(494\) 10.1064 0.454707
\(495\) −2.32111 −0.104326
\(496\) −23.2726 −1.04497
\(497\) −22.7008 −1.01827
\(498\) 17.1634 0.769110
\(499\) 28.3063 1.26717 0.633583 0.773675i \(-0.281583\pi\)
0.633583 + 0.773675i \(0.281583\pi\)
\(500\) −59.8014 −2.67440
\(501\) −0.923225 −0.0412467
\(502\) 18.1559 0.810337
\(503\) −9.48245 −0.422802 −0.211401 0.977399i \(-0.567803\pi\)
−0.211401 + 0.977399i \(0.567803\pi\)
\(504\) 62.2211 2.77155
\(505\) 26.1204 1.16234
\(506\) 2.58723 0.115016
\(507\) 0.928194 0.0412226
\(508\) −33.6570 −1.49329
\(509\) −10.0831 −0.446926 −0.223463 0.974712i \(-0.571736\pi\)
−0.223463 + 0.974712i \(0.571736\pi\)
\(510\) 27.9090 1.23583
\(511\) 21.1192 0.934258
\(512\) 36.3170 1.60500
\(513\) −18.3325 −0.809401
\(514\) −74.1988 −3.27277
\(515\) −11.8394 −0.521705
\(516\) −9.18529 −0.404360
\(517\) 0.941008 0.0413855
\(518\) 39.4005 1.73116
\(519\) −13.6175 −0.597741
\(520\) 13.9233 0.610577
\(521\) 20.7233 0.907902 0.453951 0.891027i \(-0.350014\pi\)
0.453951 + 0.891027i \(0.350014\pi\)
\(522\) −44.7581 −1.95901
\(523\) 14.9854 0.655264 0.327632 0.944805i \(-0.393749\pi\)
0.327632 + 0.944805i \(0.393749\pi\)
\(524\) −53.2163 −2.32477
\(525\) −5.98017 −0.260996
\(526\) 32.6241 1.42248
\(527\) 14.1959 0.618383
\(528\) 5.71689 0.248796
\(529\) −20.2848 −0.881946
\(530\) −20.3341 −0.883257
\(531\) 8.00874 0.347550
\(532\) 71.7350 3.11011
\(533\) −2.09558 −0.0907696
\(534\) 28.4220 1.22994
\(535\) 4.08362 0.176550
\(536\) −57.0651 −2.46484
\(537\) −0.515465 −0.0222440
\(538\) −15.9357 −0.687039
\(539\) 4.43569 0.191059
\(540\) −42.5948 −1.83299
\(541\) 13.6275 0.585893 0.292946 0.956129i \(-0.405364\pi\)
0.292946 + 0.956129i \(0.405364\pi\)
\(542\) −19.1205 −0.821294
\(543\) 22.3954 0.961078
\(544\) 74.2338 3.18275
\(545\) −14.2169 −0.608983
\(546\) 9.27014 0.396726
\(547\) −25.9183 −1.10819 −0.554094 0.832454i \(-0.686935\pi\)
−0.554094 + 0.832454i \(0.686935\pi\)
\(548\) −68.7424 −2.93653
\(549\) 5.58353 0.238299
\(550\) 2.66318 0.113559
\(551\) −30.5970 −1.30348
\(552\) 11.7159 0.498663
\(553\) 17.8643 0.759669
\(554\) −55.6753 −2.36542
\(555\) −6.65583 −0.282524
\(556\) −53.0131 −2.24826
\(557\) 0.345068 0.0146210 0.00731050 0.999973i \(-0.497673\pi\)
0.00731050 + 0.999973i \(0.497673\pi\)
\(558\) −12.6869 −0.537077
\(559\) 2.01409 0.0851867
\(560\) 71.2109 3.00921
\(561\) −3.48721 −0.147230
\(562\) −57.5393 −2.42715
\(563\) 7.18860 0.302963 0.151482 0.988460i \(-0.451596\pi\)
0.151482 + 0.988460i \(0.451596\pi\)
\(564\) 7.18657 0.302609
\(565\) −13.4461 −0.565681
\(566\) −63.8574 −2.68413
\(567\) 7.55263 0.317181
\(568\) 45.7795 1.92086
\(569\) −12.0933 −0.506977 −0.253489 0.967338i \(-0.581578\pi\)
−0.253489 + 0.967338i \(0.581578\pi\)
\(570\) −17.0507 −0.714175
\(571\) −7.81091 −0.326876 −0.163438 0.986554i \(-0.552258\pi\)
−0.163438 + 0.986554i \(0.552258\pi\)
\(572\) −2.93402 −0.122677
\(573\) 12.5447 0.524062
\(574\) −20.9291 −0.873565
\(575\) 2.79496 0.116558
\(576\) −22.2298 −0.926243
\(577\) −26.7558 −1.11386 −0.556929 0.830560i \(-0.688021\pi\)
−0.556929 + 0.830560i \(0.688021\pi\)
\(578\) −59.3773 −2.46977
\(579\) 18.3299 0.761764
\(580\) −71.0907 −2.95188
\(581\) −26.7131 −1.10825
\(582\) −40.6254 −1.68398
\(583\) 2.54074 0.105227
\(584\) −42.5900 −1.76239
\(585\) 3.88695 0.160705
\(586\) −10.0613 −0.415626
\(587\) −2.66043 −0.109808 −0.0549039 0.998492i \(-0.517485\pi\)
−0.0549039 + 0.998492i \(0.517485\pi\)
\(588\) 33.8758 1.39702
\(589\) −8.67284 −0.357358
\(590\) 17.8985 0.736868
\(591\) −6.00167 −0.246876
\(592\) −40.6901 −1.67235
\(593\) 43.4373 1.78375 0.891877 0.452277i \(-0.149388\pi\)
0.891877 + 0.452277i \(0.149388\pi\)
\(594\) 7.48862 0.307262
\(595\) −43.4375 −1.78077
\(596\) −37.2680 −1.52656
\(597\) −7.62719 −0.312160
\(598\) −4.33259 −0.177173
\(599\) −21.3712 −0.873205 −0.436602 0.899655i \(-0.643818\pi\)
−0.436602 + 0.899655i \(0.643818\pi\)
\(600\) 12.0599 0.492343
\(601\) −16.5101 −0.673461 −0.336731 0.941601i \(-0.609321\pi\)
−0.336731 + 0.941601i \(0.609321\pi\)
\(602\) 20.1152 0.819836
\(603\) −15.9308 −0.648752
\(604\) −92.3602 −3.75808
\(605\) −19.3459 −0.786523
\(606\) −35.0715 −1.42468
\(607\) 41.0526 1.66627 0.833136 0.553068i \(-0.186543\pi\)
0.833136 + 0.553068i \(0.186543\pi\)
\(608\) −45.3524 −1.83928
\(609\) −28.0654 −1.13727
\(610\) 12.4785 0.505238
\(611\) −1.57582 −0.0637509
\(612\) 66.1042 2.67211
\(613\) 26.8724 1.08536 0.542682 0.839938i \(-0.317409\pi\)
0.542682 + 0.839938i \(0.317409\pi\)
\(614\) 10.9025 0.439990
\(615\) 3.53550 0.142565
\(616\) −17.3750 −0.700058
\(617\) −35.3571 −1.42342 −0.711712 0.702471i \(-0.752080\pi\)
−0.711712 + 0.702471i \(0.752080\pi\)
\(618\) 15.8965 0.639453
\(619\) −20.1091 −0.808252 −0.404126 0.914703i \(-0.632424\pi\)
−0.404126 + 0.914703i \(0.632424\pi\)
\(620\) −20.1509 −0.809280
\(621\) 7.85915 0.315377
\(622\) 51.8080 2.07731
\(623\) −44.2360 −1.77228
\(624\) −9.57355 −0.383249
\(625\) −13.6421 −0.545684
\(626\) 30.7253 1.22803
\(627\) 2.13048 0.0850830
\(628\) −63.5980 −2.53784
\(629\) 24.8203 0.989652
\(630\) 38.8201 1.54663
\(631\) 1.90161 0.0757020 0.0378510 0.999283i \(-0.487949\pi\)
0.0378510 + 0.999283i \(0.487949\pi\)
\(632\) −36.0261 −1.43304
\(633\) −1.04682 −0.0416073
\(634\) 39.6782 1.57582
\(635\) −12.4511 −0.494107
\(636\) 19.4038 0.769413
\(637\) −7.42805 −0.294310
\(638\) 12.4985 0.494821
\(639\) 12.7802 0.505576
\(640\) −6.78769 −0.268307
\(641\) −31.4869 −1.24366 −0.621830 0.783153i \(-0.713610\pi\)
−0.621830 + 0.783153i \(0.713610\pi\)
\(642\) −5.48301 −0.216397
\(643\) 9.04150 0.356562 0.178281 0.983980i \(-0.442946\pi\)
0.178281 + 0.983980i \(0.442946\pi\)
\(644\) −30.7528 −1.21183
\(645\) −3.39801 −0.133797
\(646\) 63.5840 2.50168
\(647\) 23.4677 0.922609 0.461304 0.887242i \(-0.347382\pi\)
0.461304 + 0.887242i \(0.347382\pi\)
\(648\) −15.2310 −0.598330
\(649\) −2.23641 −0.0877866
\(650\) −4.45979 −0.174927
\(651\) −7.95523 −0.311790
\(652\) 23.6143 0.924808
\(653\) −46.6335 −1.82491 −0.912455 0.409178i \(-0.865816\pi\)
−0.912455 + 0.409178i \(0.865816\pi\)
\(654\) 19.0888 0.746430
\(655\) −19.6869 −0.769230
\(656\) 21.6141 0.843891
\(657\) −11.8898 −0.463865
\(658\) −15.7382 −0.613538
\(659\) −26.9078 −1.04818 −0.524089 0.851663i \(-0.675594\pi\)
−0.524089 + 0.851663i \(0.675594\pi\)
\(660\) 4.95006 0.192681
\(661\) −34.2933 −1.33385 −0.666927 0.745123i \(-0.732391\pi\)
−0.666927 + 0.745123i \(0.732391\pi\)
\(662\) 31.6441 1.22988
\(663\) 5.83972 0.226796
\(664\) 53.8709 2.09060
\(665\) 26.5377 1.02909
\(666\) −22.1819 −0.859531
\(667\) 13.1169 0.507890
\(668\) −4.88703 −0.189085
\(669\) −23.8541 −0.922255
\(670\) −35.6032 −1.37547
\(671\) −1.55918 −0.0601914
\(672\) −41.5998 −1.60475
\(673\) 41.5895 1.60316 0.801579 0.597889i \(-0.203994\pi\)
0.801579 + 0.597889i \(0.203994\pi\)
\(674\) 39.5940 1.52510
\(675\) 8.08988 0.311380
\(676\) 4.91333 0.188974
\(677\) 39.5259 1.51910 0.759552 0.650446i \(-0.225418\pi\)
0.759552 + 0.650446i \(0.225418\pi\)
\(678\) 18.0538 0.693354
\(679\) 63.2294 2.42652
\(680\) 87.5982 3.35924
\(681\) 7.60574 0.291453
\(682\) 3.54275 0.135659
\(683\) 4.80529 0.183869 0.0919347 0.995765i \(-0.470695\pi\)
0.0919347 + 0.995765i \(0.470695\pi\)
\(684\) −40.3857 −1.54419
\(685\) −25.4306 −0.971654
\(686\) −4.27507 −0.163223
\(687\) −14.9190 −0.569197
\(688\) −20.7736 −0.791987
\(689\) −4.25474 −0.162093
\(690\) 7.30963 0.278273
\(691\) −32.9368 −1.25298 −0.626488 0.779431i \(-0.715508\pi\)
−0.626488 + 0.779431i \(0.715508\pi\)
\(692\) −72.0831 −2.74019
\(693\) −4.85055 −0.184257
\(694\) 60.3901 2.29238
\(695\) −19.6117 −0.743914
\(696\) 56.5979 2.14534
\(697\) −13.1843 −0.499391
\(698\) 5.29417 0.200387
\(699\) −14.3610 −0.543184
\(700\) −31.6556 −1.19647
\(701\) −6.83127 −0.258014 −0.129007 0.991644i \(-0.541179\pi\)
−0.129007 + 0.991644i \(0.541179\pi\)
\(702\) −12.5405 −0.473311
\(703\) −15.1637 −0.571911
\(704\) 6.20759 0.233957
\(705\) 2.65861 0.100129
\(706\) −9.75054 −0.366967
\(707\) 54.5853 2.05289
\(708\) −17.0796 −0.641892
\(709\) 7.35350 0.276167 0.138083 0.990421i \(-0.455906\pi\)
0.138083 + 0.990421i \(0.455906\pi\)
\(710\) 28.5620 1.07191
\(711\) −10.0573 −0.377180
\(712\) 89.2084 3.34323
\(713\) 3.71804 0.139242
\(714\) 58.3229 2.18268
\(715\) −1.08541 −0.0405922
\(716\) −2.72858 −0.101972
\(717\) −9.66678 −0.361013
\(718\) −12.2973 −0.458929
\(719\) −47.2443 −1.76191 −0.880957 0.473196i \(-0.843100\pi\)
−0.880957 + 0.473196i \(0.843100\pi\)
\(720\) −40.0906 −1.49409
\(721\) −24.7414 −0.921417
\(722\) 11.1111 0.413514
\(723\) −4.20414 −0.156354
\(724\) 118.548 4.40582
\(725\) 13.5020 0.501453
\(726\) 25.9755 0.964040
\(727\) 33.1859 1.23080 0.615398 0.788217i \(-0.288995\pi\)
0.615398 + 0.788217i \(0.288995\pi\)
\(728\) 29.0963 1.07838
\(729\) 9.02901 0.334408
\(730\) −26.5721 −0.983477
\(731\) 12.6716 0.468675
\(732\) −11.9076 −0.440117
\(733\) 22.3900 0.826993 0.413496 0.910506i \(-0.364307\pi\)
0.413496 + 0.910506i \(0.364307\pi\)
\(734\) 7.59207 0.280228
\(735\) 12.5321 0.462252
\(736\) 19.4425 0.716662
\(737\) 4.44860 0.163866
\(738\) 11.7828 0.433730
\(739\) −21.4240 −0.788095 −0.394047 0.919090i \(-0.628925\pi\)
−0.394047 + 0.919090i \(0.628925\pi\)
\(740\) −35.2322 −1.29516
\(741\) −3.56771 −0.131063
\(742\) −42.4933 −1.55998
\(743\) −45.8313 −1.68139 −0.840695 0.541510i \(-0.817853\pi\)
−0.840695 + 0.541510i \(0.817853\pi\)
\(744\) 16.0429 0.588161
\(745\) −13.7869 −0.505114
\(746\) −81.6887 −2.99083
\(747\) 15.0391 0.550251
\(748\) −18.4593 −0.674940
\(749\) 8.53376 0.311817
\(750\) 29.7042 1.08464
\(751\) 17.4634 0.637247 0.318623 0.947881i \(-0.396779\pi\)
0.318623 + 0.947881i \(0.396779\pi\)
\(752\) 16.2533 0.592696
\(753\) −6.40933 −0.233569
\(754\) −20.9301 −0.762230
\(755\) −34.1678 −1.24349
\(756\) −89.0126 −3.23736
\(757\) 25.3201 0.920274 0.460137 0.887848i \(-0.347800\pi\)
0.460137 + 0.887848i \(0.347800\pi\)
\(758\) −10.8327 −0.393462
\(759\) −0.913335 −0.0331519
\(760\) −53.5172 −1.94127
\(761\) −14.8624 −0.538763 −0.269382 0.963034i \(-0.586819\pi\)
−0.269382 + 0.963034i \(0.586819\pi\)
\(762\) 16.7179 0.605627
\(763\) −29.7098 −1.07557
\(764\) 66.4044 2.40243
\(765\) 24.4547 0.884160
\(766\) 1.47435 0.0532705
\(767\) 3.74510 0.135228
\(768\) −10.1839 −0.367481
\(769\) −0.317481 −0.0114487 −0.00572433 0.999984i \(-0.501822\pi\)
−0.00572433 + 0.999984i \(0.501822\pi\)
\(770\) −10.8403 −0.390659
\(771\) 26.1934 0.943333
\(772\) 97.0279 3.49211
\(773\) −6.87615 −0.247318 −0.123659 0.992325i \(-0.539463\pi\)
−0.123659 + 0.992325i \(0.539463\pi\)
\(774\) −11.3246 −0.407053
\(775\) 3.82720 0.137477
\(776\) −127.511 −4.57739
\(777\) −13.9090 −0.498984
\(778\) −52.2288 −1.87249
\(779\) 8.05480 0.288593
\(780\) −8.28941 −0.296808
\(781\) −3.56881 −0.127702
\(782\) −27.2584 −0.974760
\(783\) 37.9664 1.35681
\(784\) 76.6142 2.73622
\(785\) −23.5275 −0.839733
\(786\) 26.4333 0.942844
\(787\) −23.2841 −0.829989 −0.414995 0.909824i \(-0.636217\pi\)
−0.414995 + 0.909824i \(0.636217\pi\)
\(788\) −31.7694 −1.13174
\(789\) −11.5168 −0.410010
\(790\) −22.4768 −0.799690
\(791\) −28.0990 −0.999085
\(792\) 9.78184 0.347583
\(793\) 2.61101 0.0927197
\(794\) −4.50422 −0.159849
\(795\) 7.17828 0.254587
\(796\) −40.3740 −1.43102
\(797\) −4.86891 −0.172466 −0.0862328 0.996275i \(-0.527483\pi\)
−0.0862328 + 0.996275i \(0.527483\pi\)
\(798\) −35.6318 −1.26135
\(799\) −9.91425 −0.350741
\(800\) 20.0133 0.707578
\(801\) 24.9042 0.879946
\(802\) −69.0381 −2.43782
\(803\) 3.32017 0.117166
\(804\) 33.9744 1.19819
\(805\) −11.3767 −0.400976
\(806\) −5.93272 −0.208971
\(807\) 5.62558 0.198030
\(808\) −110.079 −3.87258
\(809\) −6.82863 −0.240082 −0.120041 0.992769i \(-0.538303\pi\)
−0.120041 + 0.992769i \(0.538303\pi\)
\(810\) −9.50269 −0.333891
\(811\) −55.7435 −1.95742 −0.978710 0.205248i \(-0.934200\pi\)
−0.978710 + 0.205248i \(0.934200\pi\)
\(812\) −148.562 −5.21351
\(813\) 6.74984 0.236727
\(814\) 6.19420 0.217107
\(815\) 8.73590 0.306005
\(816\) −60.2319 −2.10854
\(817\) −7.74157 −0.270843
\(818\) −39.5931 −1.38434
\(819\) 8.12277 0.283832
\(820\) 18.7149 0.653554
\(821\) −5.97522 −0.208537 −0.104268 0.994549i \(-0.533250\pi\)
−0.104268 + 0.994549i \(0.533250\pi\)
\(822\) 34.1453 1.19095
\(823\) −6.90000 −0.240519 −0.120259 0.992743i \(-0.538373\pi\)
−0.120259 + 0.992743i \(0.538373\pi\)
\(824\) 49.8946 1.73816
\(825\) −0.940149 −0.0327318
\(826\) 37.4034 1.30143
\(827\) 4.63798 0.161278 0.0806392 0.996743i \(-0.474304\pi\)
0.0806392 + 0.996743i \(0.474304\pi\)
\(828\) 17.3133 0.601680
\(829\) −4.60847 −0.160059 −0.0800294 0.996793i \(-0.525501\pi\)
−0.0800294 + 0.996793i \(0.525501\pi\)
\(830\) 33.6103 1.16663
\(831\) 19.6543 0.681801
\(832\) −10.3953 −0.360391
\(833\) −46.7335 −1.61922
\(834\) 26.3323 0.911814
\(835\) −1.80791 −0.0625654
\(836\) 11.2775 0.390042
\(837\) 10.7617 0.371979
\(838\) 21.2638 0.734545
\(839\) 23.7001 0.818219 0.409110 0.912485i \(-0.365839\pi\)
0.409110 + 0.912485i \(0.365839\pi\)
\(840\) −49.0891 −1.69373
\(841\) 34.3660 1.18503
\(842\) 65.0925 2.24324
\(843\) 20.3123 0.699594
\(844\) −5.54126 −0.190738
\(845\) 1.81764 0.0625288
\(846\) 8.86034 0.304625
\(847\) −40.4282 −1.38913
\(848\) 43.8841 1.50699
\(849\) 22.5427 0.773665
\(850\) −28.0587 −0.962406
\(851\) 6.50068 0.222841
\(852\) −27.2554 −0.933753
\(853\) 1.58740 0.0543515 0.0271757 0.999631i \(-0.491349\pi\)
0.0271757 + 0.999631i \(0.491349\pi\)
\(854\) 26.0769 0.892334
\(855\) −14.9403 −0.510948
\(856\) −17.2096 −0.588211
\(857\) −20.5758 −0.702857 −0.351428 0.936215i \(-0.614304\pi\)
−0.351428 + 0.936215i \(0.614304\pi\)
\(858\) 1.45737 0.0497537
\(859\) −17.8949 −0.610564 −0.305282 0.952262i \(-0.598751\pi\)
−0.305282 + 0.952262i \(0.598751\pi\)
\(860\) −17.9872 −0.613357
\(861\) 7.38833 0.251794
\(862\) −75.2583 −2.56331
\(863\) 47.6149 1.62083 0.810415 0.585856i \(-0.199241\pi\)
0.810415 + 0.585856i \(0.199241\pi\)
\(864\) 56.2756 1.91454
\(865\) −26.6665 −0.906688
\(866\) 7.72973 0.262667
\(867\) 20.9612 0.711879
\(868\) −42.1105 −1.42932
\(869\) 2.80847 0.0952708
\(870\) 35.3117 1.19718
\(871\) −7.44967 −0.252422
\(872\) 59.9141 2.02895
\(873\) −35.5971 −1.20478
\(874\) 16.6533 0.563305
\(875\) −46.2316 −1.56291
\(876\) 25.3565 0.856716
\(877\) 6.33667 0.213974 0.106987 0.994260i \(-0.465880\pi\)
0.106987 + 0.994260i \(0.465880\pi\)
\(878\) −8.58595 −0.289762
\(879\) 3.55179 0.119799
\(880\) 11.1951 0.377388
\(881\) 19.7425 0.665143 0.332572 0.943078i \(-0.392084\pi\)
0.332572 + 0.943078i \(0.392084\pi\)
\(882\) 41.7656 1.40632
\(883\) −49.3588 −1.66106 −0.830528 0.556978i \(-0.811961\pi\)
−0.830528 + 0.556978i \(0.811961\pi\)
\(884\) 30.9121 1.03969
\(885\) −6.31846 −0.212393
\(886\) 29.8103 1.00150
\(887\) −49.0977 −1.64854 −0.824269 0.566198i \(-0.808414\pi\)
−0.824269 + 0.566198i \(0.808414\pi\)
\(888\) 28.0496 0.941284
\(889\) −26.0198 −0.872675
\(890\) 55.6576 1.86565
\(891\) 1.18736 0.0397779
\(892\) −126.270 −4.22784
\(893\) 6.05700 0.202690
\(894\) 18.5115 0.619118
\(895\) −1.00941 −0.0337409
\(896\) −14.1846 −0.473875
\(897\) 1.52948 0.0510678
\(898\) −66.8093 −2.22946
\(899\) 17.9613 0.599043
\(900\) 17.8216 0.594054
\(901\) −26.7686 −0.891792
\(902\) −3.29029 −0.109555
\(903\) −7.10102 −0.236307
\(904\) 56.6658 1.88468
\(905\) 43.8559 1.45782
\(906\) 45.8766 1.52415
\(907\) 52.4797 1.74256 0.871279 0.490787i \(-0.163291\pi\)
0.871279 + 0.490787i \(0.163291\pi\)
\(908\) 40.2605 1.33609
\(909\) −30.7307 −1.01927
\(910\) 18.1533 0.601777
\(911\) 14.5061 0.480607 0.240304 0.970698i \(-0.422753\pi\)
0.240304 + 0.970698i \(0.422753\pi\)
\(912\) 36.7980 1.21850
\(913\) −4.19959 −0.138986
\(914\) −48.6462 −1.60907
\(915\) −4.40510 −0.145628
\(916\) −78.9729 −2.60934
\(917\) −41.1408 −1.35859
\(918\) −78.8984 −2.60404
\(919\) −26.6560 −0.879299 −0.439649 0.898169i \(-0.644897\pi\)
−0.439649 + 0.898169i \(0.644897\pi\)
\(920\) 22.9428 0.756402
\(921\) −3.84877 −0.126821
\(922\) 79.8062 2.62828
\(923\) 5.97636 0.196714
\(924\) 10.3444 0.340306
\(925\) 6.69153 0.220016
\(926\) 2.62932 0.0864049
\(927\) 13.9290 0.457489
\(928\) 93.9240 3.08321
\(929\) −16.7601 −0.549880 −0.274940 0.961461i \(-0.588658\pi\)
−0.274940 + 0.961461i \(0.588658\pi\)
\(930\) 10.0092 0.328216
\(931\) 28.5513 0.935731
\(932\) −76.0192 −2.49009
\(933\) −18.2891 −0.598758
\(934\) −46.6543 −1.52658
\(935\) −6.82886 −0.223328
\(936\) −16.3808 −0.535422
\(937\) 8.12095 0.265300 0.132650 0.991163i \(-0.457651\pi\)
0.132650 + 0.991163i \(0.457651\pi\)
\(938\) −74.4020 −2.42931
\(939\) −10.8465 −0.353963
\(940\) 14.0731 0.459015
\(941\) −30.7369 −1.00200 −0.500998 0.865448i \(-0.667034\pi\)
−0.500998 + 0.865448i \(0.667034\pi\)
\(942\) 31.5900 1.02926
\(943\) −3.45309 −0.112448
\(944\) −38.6276 −1.25722
\(945\) −32.9294 −1.07119
\(946\) 3.16234 0.102816
\(947\) 21.6274 0.702797 0.351399 0.936226i \(-0.385706\pi\)
0.351399 + 0.936226i \(0.385706\pi\)
\(948\) 21.4486 0.696617
\(949\) −5.55999 −0.180485
\(950\) 17.1422 0.556165
\(951\) −14.0071 −0.454210
\(952\) 183.059 5.93297
\(953\) −25.8796 −0.838323 −0.419161 0.907912i \(-0.637676\pi\)
−0.419161 + 0.907912i \(0.637676\pi\)
\(954\) 23.9231 0.774538
\(955\) 24.5657 0.794928
\(956\) −51.1705 −1.65497
\(957\) −4.41218 −0.142626
\(958\) −50.1462 −1.62015
\(959\) −53.1438 −1.71610
\(960\) 17.5381 0.566041
\(961\) −25.9088 −0.835768
\(962\) −10.3729 −0.334434
\(963\) −4.80437 −0.154819
\(964\) −22.2543 −0.716764
\(965\) 35.8946 1.15549
\(966\) 15.2753 0.491476
\(967\) 51.1530 1.64497 0.822484 0.568788i \(-0.192587\pi\)
0.822484 + 0.568788i \(0.192587\pi\)
\(968\) 81.5294 2.62046
\(969\) −22.4462 −0.721076
\(970\) −79.5549 −2.55436
\(971\) −23.5987 −0.757320 −0.378660 0.925536i \(-0.623615\pi\)
−0.378660 + 0.925536i \(0.623615\pi\)
\(972\) 79.3702 2.54580
\(973\) −40.9837 −1.31388
\(974\) 58.6209 1.87834
\(975\) 1.57438 0.0504205
\(976\) −26.9304 −0.862022
\(977\) 61.9423 1.98171 0.990855 0.134930i \(-0.0430809\pi\)
0.990855 + 0.134930i \(0.0430809\pi\)
\(978\) −11.7296 −0.375070
\(979\) −6.95439 −0.222263
\(980\) 66.3376 2.11908
\(981\) 16.7261 0.534024
\(982\) −65.0053 −2.07440
\(983\) −18.7550 −0.598193 −0.299097 0.954223i \(-0.596685\pi\)
−0.299097 + 0.954223i \(0.596685\pi\)
\(984\) −14.8997 −0.474984
\(985\) −11.7528 −0.374475
\(986\) −131.681 −4.19359
\(987\) 5.55584 0.176844
\(988\) −18.8854 −0.600826
\(989\) 3.31881 0.105532
\(990\) 6.10294 0.193964
\(991\) −34.1265 −1.08406 −0.542032 0.840358i \(-0.682345\pi\)
−0.542032 + 0.840358i \(0.682345\pi\)
\(992\) 26.6231 0.845284
\(993\) −11.1709 −0.354498
\(994\) 59.6876 1.89318
\(995\) −14.9360 −0.473503
\(996\) −32.0727 −1.01626
\(997\) −28.2205 −0.893754 −0.446877 0.894596i \(-0.647464\pi\)
−0.446877 + 0.894596i \(0.647464\pi\)
\(998\) −74.4265 −2.35593
\(999\) 18.8159 0.595310
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 \(a_p\))