Properties

Label 6026.2.a.i.1.8
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.70631 q^{3}\) \(+1.00000 q^{4}\) \(-2.14849 q^{5}\) \(+1.70631 q^{6}\) \(+0.462300 q^{7}\) \(-1.00000 q^{8}\) \(-0.0885110 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.70631 q^{3}\) \(+1.00000 q^{4}\) \(-2.14849 q^{5}\) \(+1.70631 q^{6}\) \(+0.462300 q^{7}\) \(-1.00000 q^{8}\) \(-0.0885110 q^{9}\) \(+2.14849 q^{10}\) \(-3.41002 q^{11}\) \(-1.70631 q^{12}\) \(-6.04792 q^{13}\) \(-0.462300 q^{14}\) \(+3.66598 q^{15}\) \(+1.00000 q^{16}\) \(-2.77403 q^{17}\) \(+0.0885110 q^{18}\) \(+4.36385 q^{19}\) \(-2.14849 q^{20}\) \(-0.788826 q^{21}\) \(+3.41002 q^{22}\) \(+1.00000 q^{23}\) \(+1.70631 q^{24}\) \(-0.384005 q^{25}\) \(+6.04792 q^{26}\) \(+5.26995 q^{27}\) \(+0.462300 q^{28}\) \(+6.57354 q^{29}\) \(-3.66598 q^{30}\) \(+5.44377 q^{31}\) \(-1.00000 q^{32}\) \(+5.81854 q^{33}\) \(+2.77403 q^{34}\) \(-0.993245 q^{35}\) \(-0.0885110 q^{36}\) \(-6.84000 q^{37}\) \(-4.36385 q^{38}\) \(+10.3196 q^{39}\) \(+2.14849 q^{40}\) \(+1.53465 q^{41}\) \(+0.788826 q^{42}\) \(-2.73922 q^{43}\) \(-3.41002 q^{44}\) \(+0.190165 q^{45}\) \(-1.00000 q^{46}\) \(+12.7774 q^{47}\) \(-1.70631 q^{48}\) \(-6.78628 q^{49}\) \(+0.384005 q^{50}\) \(+4.73336 q^{51}\) \(-6.04792 q^{52}\) \(+12.6731 q^{53}\) \(-5.26995 q^{54}\) \(+7.32638 q^{55}\) \(-0.462300 q^{56}\) \(-7.44608 q^{57}\) \(-6.57354 q^{58}\) \(-5.46884 q^{59}\) \(+3.66598 q^{60}\) \(-6.36193 q^{61}\) \(-5.44377 q^{62}\) \(-0.0409186 q^{63}\) \(+1.00000 q^{64}\) \(+12.9939 q^{65}\) \(-5.81854 q^{66}\) \(+8.91040 q^{67}\) \(-2.77403 q^{68}\) \(-1.70631 q^{69}\) \(+0.993245 q^{70}\) \(+4.61001 q^{71}\) \(+0.0885110 q^{72}\) \(+13.6164 q^{73}\) \(+6.84000 q^{74}\) \(+0.655231 q^{75}\) \(+4.36385 q^{76}\) \(-1.57645 q^{77}\) \(-10.3196 q^{78}\) \(+5.62326 q^{79}\) \(-2.14849 q^{80}\) \(-8.72663 q^{81}\) \(-1.53465 q^{82}\) \(+14.2897 q^{83}\) \(-0.788826 q^{84}\) \(+5.95997 q^{85}\) \(+2.73922 q^{86}\) \(-11.2165 q^{87}\) \(+3.41002 q^{88}\) \(-5.27072 q^{89}\) \(-0.190165 q^{90}\) \(-2.79595 q^{91}\) \(+1.00000 q^{92}\) \(-9.28875 q^{93}\) \(-12.7774 q^{94}\) \(-9.37568 q^{95}\) \(+1.70631 q^{96}\) \(-0.514420 q^{97}\) \(+6.78628 q^{98}\) \(+0.301824 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 25q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut -\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut -\mathstrut 7q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 23q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 26q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 47q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 11q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 7q^{58} \) \(\mathstrut -\mathstrut 19q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 25q^{64} \) \(\mathstrut +\mathstrut 13q^{65} \) \(\mathstrut -\mathstrut 3q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 23q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 42q^{85} \) \(\mathstrut +\mathstrut 26q^{86} \) \(\mathstrut -\mathstrut 17q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 27q^{89} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 25q^{92} \) \(\mathstrut -\mathstrut 27q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.70631 −0.985138 −0.492569 0.870273i \(-0.663942\pi\)
−0.492569 + 0.870273i \(0.663942\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.14849 −0.960832 −0.480416 0.877041i \(-0.659514\pi\)
−0.480416 + 0.877041i \(0.659514\pi\)
\(6\) 1.70631 0.696598
\(7\) 0.462300 0.174733 0.0873664 0.996176i \(-0.472155\pi\)
0.0873664 + 0.996176i \(0.472155\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.0885110 −0.0295037
\(10\) 2.14849 0.679411
\(11\) −3.41002 −1.02816 −0.514080 0.857742i \(-0.671866\pi\)
−0.514080 + 0.857742i \(0.671866\pi\)
\(12\) −1.70631 −0.492569
\(13\) −6.04792 −1.67739 −0.838696 0.544600i \(-0.816682\pi\)
−0.838696 + 0.544600i \(0.816682\pi\)
\(14\) −0.462300 −0.123555
\(15\) 3.66598 0.946552
\(16\) 1.00000 0.250000
\(17\) −2.77403 −0.672802 −0.336401 0.941719i \(-0.609210\pi\)
−0.336401 + 0.941719i \(0.609210\pi\)
\(18\) 0.0885110 0.0208623
\(19\) 4.36385 1.00114 0.500568 0.865697i \(-0.333124\pi\)
0.500568 + 0.865697i \(0.333124\pi\)
\(20\) −2.14849 −0.480416
\(21\) −0.788826 −0.172136
\(22\) 3.41002 0.727018
\(23\) 1.00000 0.208514
\(24\) 1.70631 0.348299
\(25\) −0.384005 −0.0768010
\(26\) 6.04792 1.18610
\(27\) 5.26995 1.01420
\(28\) 0.462300 0.0873664
\(29\) 6.57354 1.22068 0.610338 0.792141i \(-0.291034\pi\)
0.610338 + 0.792141i \(0.291034\pi\)
\(30\) −3.66598 −0.669314
\(31\) 5.44377 0.977730 0.488865 0.872359i \(-0.337411\pi\)
0.488865 + 0.872359i \(0.337411\pi\)
\(32\) −1.00000 −0.176777
\(33\) 5.81854 1.01288
\(34\) 2.77403 0.475743
\(35\) −0.993245 −0.167889
\(36\) −0.0885110 −0.0147518
\(37\) −6.84000 −1.12449 −0.562245 0.826971i \(-0.690062\pi\)
−0.562245 + 0.826971i \(0.690062\pi\)
\(38\) −4.36385 −0.707910
\(39\) 10.3196 1.65246
\(40\) 2.14849 0.339706
\(41\) 1.53465 0.239672 0.119836 0.992794i \(-0.461763\pi\)
0.119836 + 0.992794i \(0.461763\pi\)
\(42\) 0.788826 0.121718
\(43\) −2.73922 −0.417727 −0.208864 0.977945i \(-0.566976\pi\)
−0.208864 + 0.977945i \(0.566976\pi\)
\(44\) −3.41002 −0.514080
\(45\) 0.190165 0.0283481
\(46\) −1.00000 −0.147442
\(47\) 12.7774 1.86377 0.931884 0.362755i \(-0.118164\pi\)
0.931884 + 0.362755i \(0.118164\pi\)
\(48\) −1.70631 −0.246284
\(49\) −6.78628 −0.969468
\(50\) 0.384005 0.0543065
\(51\) 4.73336 0.662803
\(52\) −6.04792 −0.838696
\(53\) 12.6731 1.74078 0.870389 0.492364i \(-0.163867\pi\)
0.870389 + 0.492364i \(0.163867\pi\)
\(54\) −5.26995 −0.717150
\(55\) 7.32638 0.987889
\(56\) −0.462300 −0.0617774
\(57\) −7.44608 −0.986257
\(58\) −6.57354 −0.863148
\(59\) −5.46884 −0.711982 −0.355991 0.934489i \(-0.615857\pi\)
−0.355991 + 0.934489i \(0.615857\pi\)
\(60\) 3.66598 0.473276
\(61\) −6.36193 −0.814562 −0.407281 0.913303i \(-0.633523\pi\)
−0.407281 + 0.913303i \(0.633523\pi\)
\(62\) −5.44377 −0.691360
\(63\) −0.0409186 −0.00515526
\(64\) 1.00000 0.125000
\(65\) 12.9939 1.61169
\(66\) −5.81854 −0.716213
\(67\) 8.91040 1.08858 0.544290 0.838897i \(-0.316799\pi\)
0.544290 + 0.838897i \(0.316799\pi\)
\(68\) −2.77403 −0.336401
\(69\) −1.70631 −0.205415
\(70\) 0.993245 0.118715
\(71\) 4.61001 0.547108 0.273554 0.961857i \(-0.411801\pi\)
0.273554 + 0.961857i \(0.411801\pi\)
\(72\) 0.0885110 0.0104311
\(73\) 13.6164 1.59368 0.796838 0.604193i \(-0.206504\pi\)
0.796838 + 0.604193i \(0.206504\pi\)
\(74\) 6.84000 0.795134
\(75\) 0.655231 0.0756595
\(76\) 4.36385 0.500568
\(77\) −1.57645 −0.179653
\(78\) −10.3196 −1.16847
\(79\) 5.62326 0.632667 0.316333 0.948648i \(-0.397548\pi\)
0.316333 + 0.948648i \(0.397548\pi\)
\(80\) −2.14849 −0.240208
\(81\) −8.72663 −0.969626
\(82\) −1.53465 −0.169474
\(83\) 14.2897 1.56850 0.784251 0.620444i \(-0.213047\pi\)
0.784251 + 0.620444i \(0.213047\pi\)
\(84\) −0.788826 −0.0860680
\(85\) 5.95997 0.646450
\(86\) 2.73922 0.295378
\(87\) −11.2165 −1.20253
\(88\) 3.41002 0.363509
\(89\) −5.27072 −0.558695 −0.279348 0.960190i \(-0.590118\pi\)
−0.279348 + 0.960190i \(0.590118\pi\)
\(90\) −0.190165 −0.0200451
\(91\) −2.79595 −0.293096
\(92\) 1.00000 0.104257
\(93\) −9.28875 −0.963199
\(94\) −12.7774 −1.31788
\(95\) −9.37568 −0.961924
\(96\) 1.70631 0.174149
\(97\) −0.514420 −0.0522315 −0.0261157 0.999659i \(-0.508314\pi\)
−0.0261157 + 0.999659i \(0.508314\pi\)
\(98\) 6.78628 0.685518
\(99\) 0.301824 0.0303345
\(100\) −0.384005 −0.0384005
\(101\) −14.1006 −1.40306 −0.701530 0.712640i \(-0.747499\pi\)
−0.701530 + 0.712640i \(0.747499\pi\)
\(102\) −4.73336 −0.468672
\(103\) −13.0653 −1.28737 −0.643684 0.765292i \(-0.722595\pi\)
−0.643684 + 0.765292i \(0.722595\pi\)
\(104\) 6.04792 0.593048
\(105\) 1.69478 0.165394
\(106\) −12.6731 −1.23092
\(107\) −3.46269 −0.334751 −0.167375 0.985893i \(-0.553529\pi\)
−0.167375 + 0.985893i \(0.553529\pi\)
\(108\) 5.26995 0.507101
\(109\) −16.5604 −1.58619 −0.793097 0.609095i \(-0.791533\pi\)
−0.793097 + 0.609095i \(0.791533\pi\)
\(110\) −7.32638 −0.698543
\(111\) 11.6712 1.10778
\(112\) 0.462300 0.0436832
\(113\) −10.3145 −0.970306 −0.485153 0.874429i \(-0.661236\pi\)
−0.485153 + 0.874429i \(0.661236\pi\)
\(114\) 7.44608 0.697389
\(115\) −2.14849 −0.200347
\(116\) 6.57354 0.610338
\(117\) 0.535308 0.0494892
\(118\) 5.46884 0.503447
\(119\) −1.28243 −0.117561
\(120\) −3.66598 −0.334657
\(121\) 0.628230 0.0571118
\(122\) 6.36193 0.575982
\(123\) −2.61859 −0.236110
\(124\) 5.44377 0.488865
\(125\) 11.5675 1.03463
\(126\) 0.0409186 0.00364532
\(127\) 1.87095 0.166020 0.0830100 0.996549i \(-0.473547\pi\)
0.0830100 + 0.996549i \(0.473547\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.67396 0.411519
\(130\) −12.9939 −1.13964
\(131\) 1.00000 0.0873704
\(132\) 5.81854 0.506439
\(133\) 2.01741 0.174931
\(134\) −8.91040 −0.769742
\(135\) −11.3224 −0.974479
\(136\) 2.77403 0.237871
\(137\) 7.53349 0.643630 0.321815 0.946803i \(-0.395707\pi\)
0.321815 + 0.946803i \(0.395707\pi\)
\(138\) 1.70631 0.145251
\(139\) −21.1310 −1.79230 −0.896152 0.443747i \(-0.853649\pi\)
−0.896152 + 0.443747i \(0.853649\pi\)
\(140\) −0.993245 −0.0839445
\(141\) −21.8021 −1.83607
\(142\) −4.61001 −0.386864
\(143\) 20.6235 1.72463
\(144\) −0.0885110 −0.00737592
\(145\) −14.1232 −1.17286
\(146\) −13.6164 −1.12690
\(147\) 11.5795 0.955060
\(148\) −6.84000 −0.562245
\(149\) 2.30869 0.189135 0.0945675 0.995518i \(-0.469853\pi\)
0.0945675 + 0.995518i \(0.469853\pi\)
\(150\) −0.655231 −0.0534994
\(151\) −10.9526 −0.891311 −0.445655 0.895205i \(-0.647029\pi\)
−0.445655 + 0.895205i \(0.647029\pi\)
\(152\) −4.36385 −0.353955
\(153\) 0.245533 0.0198501
\(154\) 1.57645 0.127034
\(155\) −11.6959 −0.939435
\(156\) 10.3196 0.826231
\(157\) 19.7577 1.57684 0.788418 0.615140i \(-0.210901\pi\)
0.788418 + 0.615140i \(0.210901\pi\)
\(158\) −5.62326 −0.447363
\(159\) −21.6241 −1.71491
\(160\) 2.14849 0.169853
\(161\) 0.462300 0.0364343
\(162\) 8.72663 0.685629
\(163\) 16.7013 1.30815 0.654075 0.756430i \(-0.273058\pi\)
0.654075 + 0.756430i \(0.273058\pi\)
\(164\) 1.53465 0.119836
\(165\) −12.5011 −0.973207
\(166\) −14.2897 −1.10910
\(167\) 6.26009 0.484420 0.242210 0.970224i \(-0.422128\pi\)
0.242210 + 0.970224i \(0.422128\pi\)
\(168\) 0.788826 0.0608592
\(169\) 23.5774 1.81364
\(170\) −5.95997 −0.457109
\(171\) −0.386249 −0.0295372
\(172\) −2.73922 −0.208864
\(173\) 17.3483 1.31896 0.659482 0.751720i \(-0.270776\pi\)
0.659482 + 0.751720i \(0.270776\pi\)
\(174\) 11.2165 0.850320
\(175\) −0.177525 −0.0134197
\(176\) −3.41002 −0.257040
\(177\) 9.33152 0.701400
\(178\) 5.27072 0.395057
\(179\) 11.0069 0.822696 0.411348 0.911478i \(-0.365058\pi\)
0.411348 + 0.911478i \(0.365058\pi\)
\(180\) 0.190165 0.0141740
\(181\) −14.9898 −1.11418 −0.557091 0.830452i \(-0.688082\pi\)
−0.557091 + 0.830452i \(0.688082\pi\)
\(182\) 2.79595 0.207250
\(183\) 10.8554 0.802455
\(184\) −1.00000 −0.0737210
\(185\) 14.6957 1.08045
\(186\) 9.28875 0.681085
\(187\) 9.45951 0.691748
\(188\) 12.7774 0.931884
\(189\) 2.43630 0.177215
\(190\) 9.37568 0.680183
\(191\) 24.7370 1.78991 0.894953 0.446160i \(-0.147209\pi\)
0.894953 + 0.446160i \(0.147209\pi\)
\(192\) −1.70631 −0.123142
\(193\) 8.12329 0.584728 0.292364 0.956307i \(-0.405558\pi\)
0.292364 + 0.956307i \(0.405558\pi\)
\(194\) 0.514420 0.0369332
\(195\) −22.1716 −1.58774
\(196\) −6.78628 −0.484734
\(197\) −25.8609 −1.84251 −0.921255 0.388959i \(-0.872835\pi\)
−0.921255 + 0.388959i \(0.872835\pi\)
\(198\) −0.301824 −0.0214497
\(199\) 0.322025 0.0228278 0.0114139 0.999935i \(-0.496367\pi\)
0.0114139 + 0.999935i \(0.496367\pi\)
\(200\) 0.384005 0.0271532
\(201\) −15.2039 −1.07240
\(202\) 14.1006 0.992114
\(203\) 3.03894 0.213292
\(204\) 4.73336 0.331401
\(205\) −3.29717 −0.230285
\(206\) 13.0653 0.910306
\(207\) −0.0885110 −0.00615194
\(208\) −6.04792 −0.419348
\(209\) −14.8808 −1.02933
\(210\) −1.69478 −0.116951
\(211\) −14.7965 −1.01863 −0.509317 0.860579i \(-0.670102\pi\)
−0.509317 + 0.860579i \(0.670102\pi\)
\(212\) 12.6731 0.870389
\(213\) −7.86611 −0.538977
\(214\) 3.46269 0.236704
\(215\) 5.88518 0.401366
\(216\) −5.26995 −0.358575
\(217\) 2.51665 0.170842
\(218\) 16.5604 1.12161
\(219\) −23.2337 −1.56999
\(220\) 7.32638 0.493944
\(221\) 16.7771 1.12855
\(222\) −11.6712 −0.783317
\(223\) −5.48830 −0.367524 −0.183762 0.982971i \(-0.558828\pi\)
−0.183762 + 0.982971i \(0.558828\pi\)
\(224\) −0.462300 −0.0308887
\(225\) 0.0339887 0.00226591
\(226\) 10.3145 0.686110
\(227\) 27.4766 1.82369 0.911844 0.410537i \(-0.134659\pi\)
0.911844 + 0.410537i \(0.134659\pi\)
\(228\) −7.44608 −0.493128
\(229\) −5.61360 −0.370957 −0.185479 0.982648i \(-0.559384\pi\)
−0.185479 + 0.982648i \(0.559384\pi\)
\(230\) 2.14849 0.141667
\(231\) 2.68991 0.176983
\(232\) −6.57354 −0.431574
\(233\) 21.9038 1.43496 0.717482 0.696577i \(-0.245294\pi\)
0.717482 + 0.696577i \(0.245294\pi\)
\(234\) −0.535308 −0.0349942
\(235\) −27.4520 −1.79077
\(236\) −5.46884 −0.355991
\(237\) −9.59502 −0.623264
\(238\) 1.28243 0.0831279
\(239\) 13.5102 0.873903 0.436952 0.899485i \(-0.356058\pi\)
0.436952 + 0.899485i \(0.356058\pi\)
\(240\) 3.66598 0.236638
\(241\) 23.2160 1.49547 0.747736 0.663996i \(-0.231141\pi\)
0.747736 + 0.663996i \(0.231141\pi\)
\(242\) −0.628230 −0.0403841
\(243\) −0.919531 −0.0589879
\(244\) −6.36193 −0.407281
\(245\) 14.5802 0.931497
\(246\) 2.61859 0.166955
\(247\) −26.3922 −1.67930
\(248\) −5.44377 −0.345680
\(249\) −24.3827 −1.54519
\(250\) −11.5675 −0.731591
\(251\) −7.37930 −0.465777 −0.232889 0.972503i \(-0.574818\pi\)
−0.232889 + 0.972503i \(0.574818\pi\)
\(252\) −0.0409186 −0.00257763
\(253\) −3.41002 −0.214386
\(254\) −1.87095 −0.117394
\(255\) −10.1696 −0.636842
\(256\) 1.00000 0.0625000
\(257\) −17.6353 −1.10006 −0.550029 0.835146i \(-0.685383\pi\)
−0.550029 + 0.835146i \(0.685383\pi\)
\(258\) −4.67396 −0.290988
\(259\) −3.16213 −0.196485
\(260\) 12.9939 0.805846
\(261\) −0.581831 −0.0360144
\(262\) −1.00000 −0.0617802
\(263\) −15.6169 −0.962980 −0.481490 0.876452i \(-0.659904\pi\)
−0.481490 + 0.876452i \(0.659904\pi\)
\(264\) −5.81854 −0.358107
\(265\) −27.2279 −1.67260
\(266\) −2.01741 −0.123695
\(267\) 8.99348 0.550392
\(268\) 8.91040 0.544290
\(269\) −28.1772 −1.71799 −0.858997 0.511981i \(-0.828912\pi\)
−0.858997 + 0.511981i \(0.828912\pi\)
\(270\) 11.3224 0.689061
\(271\) −13.4336 −0.816034 −0.408017 0.912974i \(-0.633780\pi\)
−0.408017 + 0.912974i \(0.633780\pi\)
\(272\) −2.77403 −0.168200
\(273\) 4.77076 0.288739
\(274\) −7.53349 −0.455115
\(275\) 1.30946 0.0789637
\(276\) −1.70631 −0.102708
\(277\) 20.9388 1.25809 0.629045 0.777369i \(-0.283446\pi\)
0.629045 + 0.777369i \(0.283446\pi\)
\(278\) 21.1310 1.26735
\(279\) −0.481834 −0.0288466
\(280\) 0.993245 0.0593577
\(281\) 27.1495 1.61960 0.809802 0.586703i \(-0.199574\pi\)
0.809802 + 0.586703i \(0.199574\pi\)
\(282\) 21.8021 1.29830
\(283\) −9.23249 −0.548814 −0.274407 0.961614i \(-0.588482\pi\)
−0.274407 + 0.961614i \(0.588482\pi\)
\(284\) 4.61001 0.273554
\(285\) 15.9978 0.947628
\(286\) −20.6235 −1.21950
\(287\) 0.709468 0.0418786
\(288\) 0.0885110 0.00521556
\(289\) −9.30474 −0.547338
\(290\) 14.1232 0.829341
\(291\) 0.877760 0.0514552
\(292\) 13.6164 0.796838
\(293\) −1.06545 −0.0622445 −0.0311222 0.999516i \(-0.509908\pi\)
−0.0311222 + 0.999516i \(0.509908\pi\)
\(294\) −11.5795 −0.675329
\(295\) 11.7497 0.684095
\(296\) 6.84000 0.397567
\(297\) −17.9706 −1.04276
\(298\) −2.30869 −0.133739
\(299\) −6.04792 −0.349760
\(300\) 0.655231 0.0378298
\(301\) −1.26634 −0.0729907
\(302\) 10.9526 0.630252
\(303\) 24.0599 1.38221
\(304\) 4.36385 0.250284
\(305\) 13.6685 0.782657
\(306\) −0.245533 −0.0140362
\(307\) −6.98196 −0.398481 −0.199241 0.979951i \(-0.563848\pi\)
−0.199241 + 0.979951i \(0.563848\pi\)
\(308\) −1.57645 −0.0898266
\(309\) 22.2935 1.26823
\(310\) 11.6959 0.664281
\(311\) 13.5109 0.766134 0.383067 0.923721i \(-0.374868\pi\)
0.383067 + 0.923721i \(0.374868\pi\)
\(312\) −10.3196 −0.584234
\(313\) −12.8271 −0.725031 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(314\) −19.7577 −1.11499
\(315\) 0.0879131 0.00495334
\(316\) 5.62326 0.316333
\(317\) −13.1491 −0.738528 −0.369264 0.929325i \(-0.620390\pi\)
−0.369264 + 0.929325i \(0.620390\pi\)
\(318\) 21.6241 1.21262
\(319\) −22.4159 −1.25505
\(320\) −2.14849 −0.120104
\(321\) 5.90841 0.329775
\(322\) −0.462300 −0.0257630
\(323\) −12.1055 −0.673566
\(324\) −8.72663 −0.484813
\(325\) 2.32243 0.128825
\(326\) −16.7013 −0.925002
\(327\) 28.2571 1.56262
\(328\) −1.53465 −0.0847369
\(329\) 5.90697 0.325662
\(330\) 12.5011 0.688161
\(331\) 3.02991 0.166539 0.0832695 0.996527i \(-0.473464\pi\)
0.0832695 + 0.996527i \(0.473464\pi\)
\(332\) 14.2897 0.784251
\(333\) 0.605416 0.0331766
\(334\) −6.26009 −0.342537
\(335\) −19.1439 −1.04594
\(336\) −0.788826 −0.0430340
\(337\) 19.6583 1.07085 0.535427 0.844581i \(-0.320151\pi\)
0.535427 + 0.844581i \(0.320151\pi\)
\(338\) −23.5774 −1.28244
\(339\) 17.5997 0.955885
\(340\) 5.95997 0.323225
\(341\) −18.5634 −1.00526
\(342\) 0.386249 0.0208860
\(343\) −6.37339 −0.344131
\(344\) 2.73922 0.147689
\(345\) 3.66598 0.197370
\(346\) −17.3483 −0.932649
\(347\) −34.2420 −1.83821 −0.919104 0.394014i \(-0.871086\pi\)
−0.919104 + 0.394014i \(0.871086\pi\)
\(348\) −11.2165 −0.601267
\(349\) −18.6430 −0.997939 −0.498970 0.866619i \(-0.666288\pi\)
−0.498970 + 0.866619i \(0.666288\pi\)
\(350\) 0.177525 0.00948913
\(351\) −31.8723 −1.70122
\(352\) 3.41002 0.181755
\(353\) 12.9701 0.690327 0.345164 0.938543i \(-0.387823\pi\)
0.345164 + 0.938543i \(0.387823\pi\)
\(354\) −9.33152 −0.495965
\(355\) −9.90456 −0.525679
\(356\) −5.27072 −0.279348
\(357\) 2.18823 0.115813
\(358\) −11.0069 −0.581734
\(359\) −23.2322 −1.22615 −0.613073 0.790026i \(-0.710067\pi\)
−0.613073 + 0.790026i \(0.710067\pi\)
\(360\) −0.190165 −0.0100226
\(361\) 0.0431978 0.00227357
\(362\) 14.9898 0.787845
\(363\) −1.07195 −0.0562630
\(364\) −2.79595 −0.146548
\(365\) −29.2546 −1.53126
\(366\) −10.8554 −0.567422
\(367\) 1.96667 0.102659 0.0513296 0.998682i \(-0.483654\pi\)
0.0513296 + 0.998682i \(0.483654\pi\)
\(368\) 1.00000 0.0521286
\(369\) −0.135833 −0.00707121
\(370\) −14.6957 −0.763991
\(371\) 5.85875 0.304171
\(372\) −9.28875 −0.481599
\(373\) −23.5961 −1.22176 −0.610879 0.791724i \(-0.709184\pi\)
−0.610879 + 0.791724i \(0.709184\pi\)
\(374\) −9.45951 −0.489139
\(375\) −19.7377 −1.01925
\(376\) −12.7774 −0.658942
\(377\) −39.7563 −2.04755
\(378\) −2.43630 −0.125310
\(379\) 13.1391 0.674910 0.337455 0.941342i \(-0.390434\pi\)
0.337455 + 0.941342i \(0.390434\pi\)
\(380\) −9.37568 −0.480962
\(381\) −3.19242 −0.163553
\(382\) −24.7370 −1.26566
\(383\) 24.1222 1.23259 0.616294 0.787516i \(-0.288633\pi\)
0.616294 + 0.787516i \(0.288633\pi\)
\(384\) 1.70631 0.0870747
\(385\) 3.38698 0.172617
\(386\) −8.12329 −0.413465
\(387\) 0.242451 0.0123245
\(388\) −0.514420 −0.0261157
\(389\) 0.405394 0.0205543 0.0102771 0.999947i \(-0.496729\pi\)
0.0102771 + 0.999947i \(0.496729\pi\)
\(390\) 22.1716 1.12270
\(391\) −2.77403 −0.140289
\(392\) 6.78628 0.342759
\(393\) −1.70631 −0.0860719
\(394\) 25.8609 1.30285
\(395\) −12.0815 −0.607887
\(396\) 0.301824 0.0151672
\(397\) −30.3848 −1.52497 −0.762485 0.647006i \(-0.776021\pi\)
−0.762485 + 0.647006i \(0.776021\pi\)
\(398\) −0.322025 −0.0161417
\(399\) −3.44232 −0.172332
\(400\) −0.384005 −0.0192002
\(401\) 12.9185 0.645119 0.322559 0.946549i \(-0.395457\pi\)
0.322559 + 0.946549i \(0.395457\pi\)
\(402\) 15.2039 0.758302
\(403\) −32.9235 −1.64004
\(404\) −14.1006 −0.701530
\(405\) 18.7491 0.931648
\(406\) −3.03894 −0.150820
\(407\) 23.3245 1.15615
\(408\) −4.73336 −0.234336
\(409\) −4.15444 −0.205424 −0.102712 0.994711i \(-0.532752\pi\)
−0.102712 + 0.994711i \(0.532752\pi\)
\(410\) 3.29717 0.162836
\(411\) −12.8545 −0.634064
\(412\) −13.0653 −0.643684
\(413\) −2.52824 −0.124407
\(414\) 0.0885110 0.00435008
\(415\) −30.7013 −1.50707
\(416\) 6.04792 0.296524
\(417\) 36.0559 1.76567
\(418\) 14.8808 0.727844
\(419\) 37.1244 1.81365 0.906823 0.421511i \(-0.138500\pi\)
0.906823 + 0.421511i \(0.138500\pi\)
\(420\) 1.69478 0.0826969
\(421\) −13.1832 −0.642508 −0.321254 0.946993i \(-0.604104\pi\)
−0.321254 + 0.946993i \(0.604104\pi\)
\(422\) 14.7965 0.720282
\(423\) −1.13094 −0.0549880
\(424\) −12.6731 −0.615458
\(425\) 1.06524 0.0516718
\(426\) 7.86611 0.381114
\(427\) −2.94112 −0.142331
\(428\) −3.46269 −0.167375
\(429\) −35.1901 −1.69899
\(430\) −5.88518 −0.283809
\(431\) −8.36675 −0.403012 −0.201506 0.979487i \(-0.564584\pi\)
−0.201506 + 0.979487i \(0.564584\pi\)
\(432\) 5.26995 0.253551
\(433\) 14.8705 0.714632 0.357316 0.933984i \(-0.383692\pi\)
0.357316 + 0.933984i \(0.383692\pi\)
\(434\) −2.51665 −0.120803
\(435\) 24.0985 1.15543
\(436\) −16.5604 −0.793097
\(437\) 4.36385 0.208751
\(438\) 23.2337 1.11015
\(439\) −1.02009 −0.0486862 −0.0243431 0.999704i \(-0.507749\pi\)
−0.0243431 + 0.999704i \(0.507749\pi\)
\(440\) −7.32638 −0.349271
\(441\) 0.600661 0.0286029
\(442\) −16.7771 −0.798007
\(443\) 4.92802 0.234137 0.117069 0.993124i \(-0.462650\pi\)
0.117069 + 0.993124i \(0.462650\pi\)
\(444\) 11.6712 0.553889
\(445\) 11.3241 0.536813
\(446\) 5.48830 0.259879
\(447\) −3.93933 −0.186324
\(448\) 0.462300 0.0218416
\(449\) −21.7847 −1.02808 −0.514041 0.857765i \(-0.671852\pi\)
−0.514041 + 0.857765i \(0.671852\pi\)
\(450\) −0.0339887 −0.00160224
\(451\) −5.23318 −0.246421
\(452\) −10.3145 −0.485153
\(453\) 18.6885 0.878064
\(454\) −27.4766 −1.28954
\(455\) 6.00707 0.281616
\(456\) 7.44608 0.348694
\(457\) 4.26096 0.199319 0.0996597 0.995022i \(-0.468225\pi\)
0.0996597 + 0.995022i \(0.468225\pi\)
\(458\) 5.61360 0.262307
\(459\) −14.6190 −0.682358
\(460\) −2.14849 −0.100174
\(461\) −13.9234 −0.648476 −0.324238 0.945976i \(-0.605108\pi\)
−0.324238 + 0.945976i \(0.605108\pi\)
\(462\) −2.68991 −0.125146
\(463\) −9.03717 −0.419993 −0.209997 0.977702i \(-0.567345\pi\)
−0.209997 + 0.977702i \(0.567345\pi\)
\(464\) 6.57354 0.305169
\(465\) 19.9568 0.925473
\(466\) −21.9038 −1.01467
\(467\) −13.7982 −0.638506 −0.319253 0.947670i \(-0.603432\pi\)
−0.319253 + 0.947670i \(0.603432\pi\)
\(468\) 0.535308 0.0247446
\(469\) 4.11928 0.190211
\(470\) 27.4520 1.26627
\(471\) −33.7127 −1.55340
\(472\) 5.46884 0.251724
\(473\) 9.34080 0.429490
\(474\) 9.59502 0.440714
\(475\) −1.67574 −0.0768882
\(476\) −1.28243 −0.0587803
\(477\) −1.12171 −0.0513594
\(478\) −13.5102 −0.617943
\(479\) −24.2577 −1.10836 −0.554181 0.832396i \(-0.686969\pi\)
−0.554181 + 0.832396i \(0.686969\pi\)
\(480\) −3.66598 −0.167328
\(481\) 41.3678 1.88621
\(482\) −23.2160 −1.05746
\(483\) −0.788826 −0.0358928
\(484\) 0.628230 0.0285559
\(485\) 1.10523 0.0501857
\(486\) 0.919531 0.0417108
\(487\) −6.63383 −0.300608 −0.150304 0.988640i \(-0.548025\pi\)
−0.150304 + 0.988640i \(0.548025\pi\)
\(488\) 6.36193 0.287991
\(489\) −28.4976 −1.28871
\(490\) −14.5802 −0.658668
\(491\) −11.9218 −0.538021 −0.269011 0.963137i \(-0.586697\pi\)
−0.269011 + 0.963137i \(0.586697\pi\)
\(492\) −2.61859 −0.118055
\(493\) −18.2352 −0.821273
\(494\) 26.3922 1.18744
\(495\) −0.648466 −0.0291464
\(496\) 5.44377 0.244433
\(497\) 2.13121 0.0955978
\(498\) 24.3827 1.09261
\(499\) −17.6929 −0.792042 −0.396021 0.918241i \(-0.629609\pi\)
−0.396021 + 0.918241i \(0.629609\pi\)
\(500\) 11.5675 0.517313
\(501\) −10.6816 −0.477221
\(502\) 7.37930 0.329354
\(503\) −31.2734 −1.39441 −0.697206 0.716870i \(-0.745574\pi\)
−0.697206 + 0.716870i \(0.745574\pi\)
\(504\) 0.0409186 0.00182266
\(505\) 30.2949 1.34811
\(506\) 3.41002 0.151594
\(507\) −40.2303 −1.78669
\(508\) 1.87095 0.0830100
\(509\) 3.09527 0.137195 0.0685976 0.997644i \(-0.478148\pi\)
0.0685976 + 0.997644i \(0.478148\pi\)
\(510\) 10.1696 0.450315
\(511\) 6.29485 0.278468
\(512\) −1.00000 −0.0441942
\(513\) 22.9973 1.01536
\(514\) 17.6353 0.777858
\(515\) 28.0707 1.23694
\(516\) 4.67396 0.205759
\(517\) −43.5710 −1.91625
\(518\) 3.16213 0.138936
\(519\) −29.6015 −1.29936
\(520\) −12.9939 −0.569819
\(521\) −16.2798 −0.713233 −0.356616 0.934251i \(-0.616070\pi\)
−0.356616 + 0.934251i \(0.616070\pi\)
\(522\) 0.581831 0.0254660
\(523\) 7.68937 0.336233 0.168116 0.985767i \(-0.446232\pi\)
0.168116 + 0.985767i \(0.446232\pi\)
\(524\) 1.00000 0.0436852
\(525\) 0.302913 0.0132202
\(526\) 15.6169 0.680930
\(527\) −15.1012 −0.657819
\(528\) 5.81854 0.253220
\(529\) 1.00000 0.0434783
\(530\) 27.2279 1.18270
\(531\) 0.484052 0.0210061
\(532\) 2.01741 0.0874657
\(533\) −9.28144 −0.402024
\(534\) −8.99348 −0.389186
\(535\) 7.43954 0.321639
\(536\) −8.91040 −0.384871
\(537\) −18.7812 −0.810469
\(538\) 28.1772 1.21481
\(539\) 23.1413 0.996768
\(540\) −11.3224 −0.487240
\(541\) 36.4870 1.56870 0.784349 0.620319i \(-0.212997\pi\)
0.784349 + 0.620319i \(0.212997\pi\)
\(542\) 13.4336 0.577023
\(543\) 25.5772 1.09762
\(544\) 2.77403 0.118936
\(545\) 35.5797 1.52407
\(546\) −4.77076 −0.204170
\(547\) −30.5126 −1.30462 −0.652312 0.757950i \(-0.726201\pi\)
−0.652312 + 0.757950i \(0.726201\pi\)
\(548\) 7.53349 0.321815
\(549\) 0.563101 0.0240326
\(550\) −1.30946 −0.0558357
\(551\) 28.6859 1.22206
\(552\) 1.70631 0.0726253
\(553\) 2.59963 0.110548
\(554\) −20.9388 −0.889604
\(555\) −25.0753 −1.06439
\(556\) −21.1310 −0.896152
\(557\) −32.6063 −1.38157 −0.690787 0.723058i \(-0.742736\pi\)
−0.690787 + 0.723058i \(0.742736\pi\)
\(558\) 0.481834 0.0203977
\(559\) 16.5666 0.700693
\(560\) −0.993245 −0.0419723
\(561\) −16.1408 −0.681467
\(562\) −27.1495 −1.14523
\(563\) 3.23426 0.136308 0.0681540 0.997675i \(-0.478289\pi\)
0.0681540 + 0.997675i \(0.478289\pi\)
\(564\) −21.8021 −0.918035
\(565\) 22.1605 0.932301
\(566\) 9.23249 0.388070
\(567\) −4.03432 −0.169425
\(568\) −4.61001 −0.193432
\(569\) −16.0167 −0.671457 −0.335728 0.941959i \(-0.608982\pi\)
−0.335728 + 0.941959i \(0.608982\pi\)
\(570\) −15.9978 −0.670074
\(571\) −38.5320 −1.61252 −0.806258 0.591564i \(-0.798511\pi\)
−0.806258 + 0.591564i \(0.798511\pi\)
\(572\) 20.6235 0.862313
\(573\) −42.2090 −1.76330
\(574\) −0.709468 −0.0296126
\(575\) −0.384005 −0.0160141
\(576\) −0.0885110 −0.00368796
\(577\) 8.56120 0.356408 0.178204 0.983994i \(-0.442971\pi\)
0.178204 + 0.983994i \(0.442971\pi\)
\(578\) 9.30474 0.387026
\(579\) −13.8608 −0.576037
\(580\) −14.1232 −0.586432
\(581\) 6.60614 0.274069
\(582\) −0.877760 −0.0363843
\(583\) −43.2154 −1.78980
\(584\) −13.6164 −0.563450
\(585\) −1.15010 −0.0475509
\(586\) 1.06545 0.0440135
\(587\) −7.19518 −0.296977 −0.148488 0.988914i \(-0.547441\pi\)
−0.148488 + 0.988914i \(0.547441\pi\)
\(588\) 11.5795 0.477530
\(589\) 23.7558 0.978841
\(590\) −11.7497 −0.483728
\(591\) 44.1266 1.81513
\(592\) −6.84000 −0.281122
\(593\) −10.3517 −0.425092 −0.212546 0.977151i \(-0.568176\pi\)
−0.212546 + 0.977151i \(0.568176\pi\)
\(594\) 17.9706 0.737344
\(595\) 2.75529 0.112956
\(596\) 2.30869 0.0945675
\(597\) −0.549474 −0.0224885
\(598\) 6.04792 0.247318
\(599\) 21.5432 0.880233 0.440116 0.897941i \(-0.354937\pi\)
0.440116 + 0.897941i \(0.354937\pi\)
\(600\) −0.655231 −0.0267497
\(601\) 26.8115 1.09366 0.546832 0.837243i \(-0.315834\pi\)
0.546832 + 0.837243i \(0.315834\pi\)
\(602\) 1.26634 0.0516122
\(603\) −0.788669 −0.0321171
\(604\) −10.9526 −0.445655
\(605\) −1.34974 −0.0548749
\(606\) −24.0599 −0.977369
\(607\) 7.35188 0.298404 0.149202 0.988807i \(-0.452330\pi\)
0.149202 + 0.988807i \(0.452330\pi\)
\(608\) −4.36385 −0.176978
\(609\) −5.18538 −0.210122
\(610\) −13.6685 −0.553422
\(611\) −77.2765 −3.12627
\(612\) 0.245533 0.00992507
\(613\) −15.3073 −0.618255 −0.309127 0.951021i \(-0.600037\pi\)
−0.309127 + 0.951021i \(0.600037\pi\)
\(614\) 6.98196 0.281769
\(615\) 5.62600 0.226862
\(616\) 1.57645 0.0635170
\(617\) −22.0896 −0.889294 −0.444647 0.895706i \(-0.646671\pi\)
−0.444647 + 0.895706i \(0.646671\pi\)
\(618\) −22.2935 −0.896777
\(619\) −18.9036 −0.759800 −0.379900 0.925028i \(-0.624042\pi\)
−0.379900 + 0.925028i \(0.624042\pi\)
\(620\) −11.6959 −0.469717
\(621\) 5.26995 0.211476
\(622\) −13.5109 −0.541738
\(623\) −2.43665 −0.0976225
\(624\) 10.3196 0.413116
\(625\) −22.9325 −0.917301
\(626\) 12.8271 0.512674
\(627\) 25.3913 1.01403
\(628\) 19.7577 0.788418
\(629\) 18.9744 0.756559
\(630\) −0.0879131 −0.00350254
\(631\) 42.0394 1.67356 0.836782 0.547536i \(-0.184434\pi\)
0.836782 + 0.547536i \(0.184434\pi\)
\(632\) −5.62326 −0.223681
\(633\) 25.2474 1.00349
\(634\) 13.1491 0.522218
\(635\) −4.01971 −0.159517
\(636\) −21.6241 −0.857453
\(637\) 41.0429 1.62618
\(638\) 22.4159 0.887454
\(639\) −0.408037 −0.0161417
\(640\) 2.14849 0.0849264
\(641\) −36.2289 −1.43096 −0.715479 0.698635i \(-0.753791\pi\)
−0.715479 + 0.698635i \(0.753791\pi\)
\(642\) −5.90841 −0.233186
\(643\) 39.4152 1.55438 0.777192 0.629263i \(-0.216643\pi\)
0.777192 + 0.629263i \(0.216643\pi\)
\(644\) 0.462300 0.0182172
\(645\) −10.0419 −0.395401
\(646\) 12.1055 0.476283
\(647\) 25.0242 0.983803 0.491902 0.870651i \(-0.336302\pi\)
0.491902 + 0.870651i \(0.336302\pi\)
\(648\) 8.72663 0.342815
\(649\) 18.6488 0.732031
\(650\) −2.32243 −0.0910933
\(651\) −4.29419 −0.168303
\(652\) 16.7013 0.654075
\(653\) 19.4028 0.759292 0.379646 0.925132i \(-0.376046\pi\)
0.379646 + 0.925132i \(0.376046\pi\)
\(654\) −28.2571 −1.10494
\(655\) −2.14849 −0.0839483
\(656\) 1.53465 0.0599180
\(657\) −1.20520 −0.0470193
\(658\) −5.90697 −0.230278
\(659\) −50.9499 −1.98473 −0.992363 0.123350i \(-0.960636\pi\)
−0.992363 + 0.123350i \(0.960636\pi\)
\(660\) −12.5011 −0.486603
\(661\) 15.1861 0.590672 0.295336 0.955393i \(-0.404568\pi\)
0.295336 + 0.955393i \(0.404568\pi\)
\(662\) −3.02991 −0.117761
\(663\) −28.6270 −1.11178
\(664\) −14.2897 −0.554549
\(665\) −4.33437 −0.168080
\(666\) −0.605416 −0.0234594
\(667\) 6.57354 0.254528
\(668\) 6.26009 0.242210
\(669\) 9.36473 0.362062
\(670\) 19.1439 0.739593
\(671\) 21.6943 0.837499
\(672\) 0.788826 0.0304296
\(673\) 10.8830 0.419510 0.209755 0.977754i \(-0.432733\pi\)
0.209755 + 0.977754i \(0.432733\pi\)
\(674\) −19.6583 −0.757208
\(675\) −2.02369 −0.0778918
\(676\) 23.5774 0.906822
\(677\) −22.5225 −0.865611 −0.432805 0.901487i \(-0.642476\pi\)
−0.432805 + 0.901487i \(0.642476\pi\)
\(678\) −17.5997 −0.675913
\(679\) −0.237816 −0.00912655
\(680\) −5.95997 −0.228555
\(681\) −46.8836 −1.79658
\(682\) 18.5634 0.710828
\(683\) −8.55318 −0.327278 −0.163639 0.986520i \(-0.552323\pi\)
−0.163639 + 0.986520i \(0.552323\pi\)
\(684\) −0.386249 −0.0147686
\(685\) −16.1856 −0.618421
\(686\) 6.37339 0.243337
\(687\) 9.57854 0.365444
\(688\) −2.73922 −0.104432
\(689\) −76.6457 −2.91997
\(690\) −3.66598 −0.139562
\(691\) −8.79318 −0.334508 −0.167254 0.985914i \(-0.553490\pi\)
−0.167254 + 0.985914i \(0.553490\pi\)
\(692\) 17.3483 0.659482
\(693\) 0.139533 0.00530043
\(694\) 34.2420 1.29981
\(695\) 45.3996 1.72210
\(696\) 11.2165 0.425160
\(697\) −4.25717 −0.161252
\(698\) 18.6430 0.705650
\(699\) −37.3746 −1.41364
\(700\) −0.177525 −0.00670983
\(701\) 24.4337 0.922847 0.461424 0.887180i \(-0.347339\pi\)
0.461424 + 0.887180i \(0.347339\pi\)
\(702\) 31.8723 1.20294
\(703\) −29.8488 −1.12577
\(704\) −3.41002 −0.128520
\(705\) 46.8415 1.76415
\(706\) −12.9701 −0.488135
\(707\) −6.51870 −0.245161
\(708\) 9.33152 0.350700
\(709\) 8.36034 0.313979 0.156990 0.987600i \(-0.449821\pi\)
0.156990 + 0.987600i \(0.449821\pi\)
\(710\) 9.90456 0.371711
\(711\) −0.497721 −0.0186660
\(712\) 5.27072 0.197529
\(713\) 5.44377 0.203871
\(714\) −2.18823 −0.0818924
\(715\) −44.3094 −1.65708
\(716\) 11.0069 0.411348
\(717\) −23.0526 −0.860915
\(718\) 23.2322 0.867016
\(719\) −2.58641 −0.0964568 −0.0482284 0.998836i \(-0.515358\pi\)
−0.0482284 + 0.998836i \(0.515358\pi\)
\(720\) 0.190165 0.00708702
\(721\) −6.04011 −0.224945
\(722\) −0.0431978 −0.00160766
\(723\) −39.6136 −1.47325
\(724\) −14.9898 −0.557091
\(725\) −2.52427 −0.0937491
\(726\) 1.07195 0.0397839
\(727\) −43.8900 −1.62779 −0.813895 0.581012i \(-0.802657\pi\)
−0.813895 + 0.581012i \(0.802657\pi\)
\(728\) 2.79595 0.103625
\(729\) 27.7489 1.02774
\(730\) 29.2546 1.08276
\(731\) 7.59869 0.281048
\(732\) 10.8554 0.401228
\(733\) 34.3440 1.26853 0.634263 0.773118i \(-0.281304\pi\)
0.634263 + 0.773118i \(0.281304\pi\)
\(734\) −1.96667 −0.0725910
\(735\) −24.8784 −0.917653
\(736\) −1.00000 −0.0368605
\(737\) −30.3846 −1.11923
\(738\) 0.135833 0.00500010
\(739\) −36.2714 −1.33427 −0.667133 0.744939i \(-0.732479\pi\)
−0.667133 + 0.744939i \(0.732479\pi\)
\(740\) 14.6957 0.540223
\(741\) 45.0333 1.65434
\(742\) −5.85875 −0.215082
\(743\) 32.8892 1.20659 0.603294 0.797519i \(-0.293855\pi\)
0.603294 + 0.797519i \(0.293855\pi\)
\(744\) 9.28875 0.340542
\(745\) −4.96018 −0.181727
\(746\) 23.5961 0.863913
\(747\) −1.26480 −0.0462766
\(748\) 9.45951 0.345874
\(749\) −1.60080 −0.0584919
\(750\) 19.7377 0.720717
\(751\) 13.0252 0.475297 0.237648 0.971351i \(-0.423623\pi\)
0.237648 + 0.971351i \(0.423623\pi\)
\(752\) 12.7774 0.465942
\(753\) 12.5914 0.458855
\(754\) 39.7563 1.44784
\(755\) 23.5315 0.856400
\(756\) 2.43630 0.0886073
\(757\) 15.5324 0.564535 0.282268 0.959336i \(-0.408913\pi\)
0.282268 + 0.959336i \(0.408913\pi\)
\(758\) −13.1391 −0.477233
\(759\) 5.81854 0.211200
\(760\) 9.37568 0.340092
\(761\) 20.2717 0.734850 0.367425 0.930053i \(-0.380240\pi\)
0.367425 + 0.930053i \(0.380240\pi\)
\(762\) 3.19242 0.115649
\(763\) −7.65585 −0.277160
\(764\) 24.7370 0.894953
\(765\) −0.527524 −0.0190727
\(766\) −24.1222 −0.871572
\(767\) 33.0751 1.19427
\(768\) −1.70631 −0.0615711
\(769\) −36.0118 −1.29862 −0.649309 0.760525i \(-0.724942\pi\)
−0.649309 + 0.760525i \(0.724942\pi\)
\(770\) −3.38698 −0.122058
\(771\) 30.0912 1.08371
\(772\) 8.12329 0.292364
\(773\) 20.6523 0.742811 0.371406 0.928471i \(-0.378876\pi\)
0.371406 + 0.928471i \(0.378876\pi\)
\(774\) −0.242451 −0.00871473
\(775\) −2.09043 −0.0750906
\(776\) 0.514420 0.0184666
\(777\) 5.39557 0.193565
\(778\) −0.405394 −0.0145341
\(779\) 6.69698 0.239944
\(780\) −22.1716 −0.793870
\(781\) −15.7202 −0.562514
\(782\) 2.77403 0.0991992
\(783\) 34.6422 1.23801
\(784\) −6.78628 −0.242367
\(785\) −42.4491 −1.51507
\(786\) 1.70631 0.0608620
\(787\) 35.5465 1.26709 0.633547 0.773704i \(-0.281598\pi\)
0.633547 + 0.773704i \(0.281598\pi\)
\(788\) −25.8609 −0.921255
\(789\) 26.6473 0.948668
\(790\) 12.0815 0.429841
\(791\) −4.76839 −0.169544
\(792\) −0.301824 −0.0107249
\(793\) 38.4765 1.36634
\(794\) 30.3848 1.07832
\(795\) 46.4592 1.64774
\(796\) 0.322025 0.0114139
\(797\) −30.3283 −1.07428 −0.537142 0.843492i \(-0.680496\pi\)
−0.537142 + 0.843492i \(0.680496\pi\)
\(798\) 3.44232 0.121857
\(799\) −35.4448 −1.25395
\(800\) 0.384005 0.0135766
\(801\) 0.466517 0.0164836
\(802\) −12.9185 −0.456168
\(803\) −46.4321 −1.63855
\(804\) −15.2039 −0.536200
\(805\) −0.993245 −0.0350073
\(806\) 32.9235 1.15968
\(807\) 48.0790 1.69246
\(808\) 14.1006 0.496057
\(809\) 55.2012 1.94077 0.970386 0.241561i \(-0.0776593\pi\)
0.970386 + 0.241561i \(0.0776593\pi\)
\(810\) −18.7491 −0.658775
\(811\) 24.9677 0.876736 0.438368 0.898796i \(-0.355557\pi\)
0.438368 + 0.898796i \(0.355557\pi\)
\(812\) 3.03894 0.106646
\(813\) 22.9219 0.803905
\(814\) −23.3245 −0.817525
\(815\) −35.8826 −1.25691
\(816\) 4.73336 0.165701
\(817\) −11.9536 −0.418202
\(818\) 4.15444 0.145256
\(819\) 0.247473 0.00864740
\(820\) −3.29717 −0.115142
\(821\) −7.94429 −0.277258 −0.138629 0.990344i \(-0.544270\pi\)
−0.138629 + 0.990344i \(0.544270\pi\)
\(822\) 12.8545 0.448351
\(823\) 16.2890 0.567798 0.283899 0.958854i \(-0.408372\pi\)
0.283899 + 0.958854i \(0.408372\pi\)
\(824\) 13.0653 0.455153
\(825\) −2.23435 −0.0777901
\(826\) 2.52824 0.0879688
\(827\) 30.8604 1.07312 0.536561 0.843862i \(-0.319723\pi\)
0.536561 + 0.843862i \(0.319723\pi\)
\(828\) −0.0885110 −0.00307597
\(829\) 25.2951 0.878535 0.439268 0.898356i \(-0.355238\pi\)
0.439268 + 0.898356i \(0.355238\pi\)
\(830\) 30.7013 1.06566
\(831\) −35.7280 −1.23939
\(832\) −6.04792 −0.209674
\(833\) 18.8254 0.652260
\(834\) −36.0559 −1.24851
\(835\) −13.4497 −0.465447
\(836\) −14.8808 −0.514664
\(837\) 28.6884 0.991617
\(838\) −37.1244 −1.28244
\(839\) −16.7549 −0.578445 −0.289222 0.957262i \(-0.593397\pi\)
−0.289222 + 0.957262i \(0.593397\pi\)
\(840\) −1.69478 −0.0584755
\(841\) 14.2114 0.490049
\(842\) 13.1832 0.454322
\(843\) −46.3255 −1.59553
\(844\) −14.7965 −0.509317
\(845\) −50.6557 −1.74261
\(846\) 1.13094 0.0388824
\(847\) 0.290430 0.00997931
\(848\) 12.6731 0.435195
\(849\) 15.7535 0.540658
\(850\) −1.06524 −0.0365375
\(851\) −6.84000 −0.234472
\(852\) −7.86611 −0.269488
\(853\) 0.667979 0.0228712 0.0114356 0.999935i \(-0.496360\pi\)
0.0114356 + 0.999935i \(0.496360\pi\)
\(854\) 2.94112 0.100643
\(855\) 0.829851 0.0283803
\(856\) 3.46269 0.118352
\(857\) 43.0535 1.47068 0.735340 0.677699i \(-0.237023\pi\)
0.735340 + 0.677699i \(0.237023\pi\)
\(858\) 35.1901 1.20137
\(859\) 38.7041 1.32057 0.660283 0.751016i \(-0.270436\pi\)
0.660283 + 0.751016i \(0.270436\pi\)
\(860\) 5.88518 0.200683
\(861\) −1.21057 −0.0412562
\(862\) 8.36675 0.284973
\(863\) −41.7791 −1.42218 −0.711089 0.703102i \(-0.751798\pi\)
−0.711089 + 0.703102i \(0.751798\pi\)
\(864\) −5.26995 −0.179287
\(865\) −37.2725 −1.26730
\(866\) −14.8705 −0.505321
\(867\) 15.8768 0.539203
\(868\) 2.51665 0.0854208
\(869\) −19.1754 −0.650482
\(870\) −24.0985 −0.817015
\(871\) −53.8894 −1.82597
\(872\) 16.5604 0.560805
\(873\) 0.0455319 0.00154102
\(874\) −4.36385 −0.147609
\(875\) 5.34763 0.180783
\(876\) −23.2337 −0.784995
\(877\) −10.0493 −0.339341 −0.169670 0.985501i \(-0.554270\pi\)
−0.169670 + 0.985501i \(0.554270\pi\)
\(878\) 1.02009 0.0344263
\(879\) 1.81799 0.0613194
\(880\) 7.32638 0.246972
\(881\) 19.6995 0.663693 0.331846 0.943333i \(-0.392328\pi\)
0.331846 + 0.943333i \(0.392328\pi\)
\(882\) −0.600661 −0.0202253
\(883\) −0.205036 −0.00690000 −0.00345000 0.999994i \(-0.501098\pi\)
−0.00345000 + 0.999994i \(0.501098\pi\)
\(884\) 16.7771 0.564276
\(885\) −20.0486 −0.673928
\(886\) −4.92802 −0.165560
\(887\) 3.07636 0.103294 0.0516471 0.998665i \(-0.483553\pi\)
0.0516471 + 0.998665i \(0.483553\pi\)
\(888\) −11.6712 −0.391658
\(889\) 0.864940 0.0290092
\(890\) −11.3241 −0.379584
\(891\) 29.7580 0.996930
\(892\) −5.48830 −0.183762
\(893\) 55.7585 1.86589
\(894\) 3.93933 0.131751
\(895\) −23.6482 −0.790473
\(896\) −0.462300 −0.0154443
\(897\) 10.3196 0.344562
\(898\) 21.7847 0.726964
\(899\) 35.7848 1.19349
\(900\) 0.0339887 0.00113296
\(901\) −35.1555 −1.17120
\(902\) 5.23318 0.174246
\(903\) 2.16077 0.0719059
\(904\) 10.3145 0.343055
\(905\) 32.2053 1.07054
\(906\) −18.6885 −0.620885
\(907\) −11.5866 −0.384726 −0.192363 0.981324i \(-0.561615\pi\)
−0.192363 + 0.981324i \(0.561615\pi\)
\(908\) 27.4766 0.911844
\(909\) 1.24806 0.0413955
\(910\) −6.00707 −0.199132
\(911\) 11.1449 0.369247 0.184623 0.982809i \(-0.440893\pi\)
0.184623 + 0.982809i \(0.440893\pi\)
\(912\) −7.44608 −0.246564
\(913\) −48.7283 −1.61267
\(914\) −4.26096 −0.140940
\(915\) −23.3227 −0.771025
\(916\) −5.61360 −0.185479
\(917\) 0.462300 0.0152665
\(918\) 14.6190 0.482500
\(919\) −20.5781 −0.678808 −0.339404 0.940641i \(-0.610225\pi\)
−0.339404 + 0.940641i \(0.610225\pi\)
\(920\) 2.14849 0.0708335
\(921\) 11.9134 0.392559
\(922\) 13.9234 0.458542
\(923\) −27.8810 −0.917715
\(924\) 2.68991 0.0884916
\(925\) 2.62659 0.0863619
\(926\) 9.03717 0.296980
\(927\) 1.15643 0.0379821
\(928\) −6.57354 −0.215787
\(929\) 14.4253 0.473278 0.236639 0.971598i \(-0.423954\pi\)
0.236639 + 0.971598i \(0.423954\pi\)
\(930\) −19.9568 −0.654408
\(931\) −29.6143 −0.970570
\(932\) 21.9038 0.717482
\(933\) −23.0538 −0.754747
\(934\) 13.7982 0.451492
\(935\) −20.3236 −0.664654
\(936\) −0.535308 −0.0174971
\(937\) 50.8524 1.66127 0.830637 0.556814i \(-0.187976\pi\)
0.830637 + 0.556814i \(0.187976\pi\)
\(938\) −4.11928 −0.134499
\(939\) 21.8870 0.714255
\(940\) −27.4520 −0.895385
\(941\) 47.1642 1.53751 0.768754 0.639544i \(-0.220877\pi\)
0.768754 + 0.639544i \(0.220877\pi\)
\(942\) 33.7127 1.09842
\(943\) 1.53465 0.0499751
\(944\) −5.46884 −0.177995
\(945\) −5.23435 −0.170274
\(946\) −9.34080 −0.303696
\(947\) 15.6230 0.507680 0.253840 0.967246i \(-0.418306\pi\)
0.253840 + 0.967246i \(0.418306\pi\)
\(948\) −9.59502 −0.311632
\(949\) −82.3508 −2.67322
\(950\) 1.67574 0.0543682
\(951\) 22.4365 0.727552
\(952\) 1.28243 0.0415640
\(953\) −0.546248 −0.0176947 −0.00884735 0.999961i \(-0.502816\pi\)
−0.00884735 + 0.999961i \(0.502816\pi\)
\(954\) 1.12171 0.0363166
\(955\) −53.1471 −1.71980
\(956\) 13.5102 0.436952
\(957\) 38.2484 1.23640
\(958\) 24.2577 0.783731
\(959\) 3.48273 0.112463
\(960\) 3.66598 0.118319
\(961\) −1.36535 −0.0440436
\(962\) −41.3678 −1.33375
\(963\) 0.306486 0.00987637
\(964\) 23.2160 0.747736
\(965\) −17.4528 −0.561825
\(966\) 0.788826 0.0253801
\(967\) 48.5887 1.56251 0.781254 0.624213i \(-0.214580\pi\)
0.781254 + 0.624213i \(0.214580\pi\)
\(968\) −0.628230 −0.0201921
\(969\) 20.6557 0.663556
\(970\) −1.10523 −0.0354866
\(971\) −36.5919 −1.17429 −0.587145 0.809482i \(-0.699748\pi\)
−0.587145 + 0.809482i \(0.699748\pi\)
\(972\) −0.919531 −0.0294940
\(973\) −9.76883 −0.313174
\(974\) 6.63383 0.212562
\(975\) −3.96279 −0.126911
\(976\) −6.36193 −0.203640
\(977\) −8.29052 −0.265237 −0.132619 0.991167i \(-0.542339\pi\)
−0.132619 + 0.991167i \(0.542339\pi\)
\(978\) 28.4976 0.911254
\(979\) 17.9733 0.574428
\(980\) 14.5802 0.465748
\(981\) 1.46577 0.0467986
\(982\) 11.9218 0.380438
\(983\) −38.9560 −1.24250 −0.621252 0.783610i \(-0.713376\pi\)
−0.621252 + 0.783610i \(0.713376\pi\)
\(984\) 2.61859 0.0834775
\(985\) 55.5617 1.77034
\(986\) 18.2352 0.580728
\(987\) −10.0791 −0.320822
\(988\) −26.3922 −0.839649
\(989\) −2.73922 −0.0871022
\(990\) 0.648466 0.0206096
\(991\) 9.54943 0.303348 0.151674 0.988431i \(-0.451534\pi\)
0.151674 + 0.988431i \(0.451534\pi\)
\(992\) −5.44377 −0.172840
\(993\) −5.16996 −0.164064
\(994\) −2.13121 −0.0675978
\(995\) −0.691867 −0.0219337
\(996\) −24.3827 −0.772595
\(997\) 34.2305 1.08409 0.542045 0.840349i \(-0.317650\pi\)
0.542045 + 0.840349i \(0.317650\pi\)
\(998\) 17.6929 0.560058
\(999\) −36.0465 −1.14046
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 \(a_p\))