Properties

Label 8013.2.a.d.1.14
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.34305 q^{2}\) \(+1.00000 q^{3}\) \(+3.48991 q^{4}\) \(+4.17579 q^{5}\) \(-2.34305 q^{6}\) \(+2.00162 q^{7}\) \(-3.49093 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.34305 q^{2}\) \(+1.00000 q^{3}\) \(+3.48991 q^{4}\) \(+4.17579 q^{5}\) \(-2.34305 q^{6}\) \(+2.00162 q^{7}\) \(-3.49093 q^{8}\) \(+1.00000 q^{9}\) \(-9.78411 q^{10}\) \(-2.15096 q^{11}\) \(+3.48991 q^{12}\) \(+3.24262 q^{13}\) \(-4.68991 q^{14}\) \(+4.17579 q^{15}\) \(+1.19963 q^{16}\) \(-2.09287 q^{17}\) \(-2.34305 q^{18}\) \(+0.161917 q^{19}\) \(+14.5731 q^{20}\) \(+2.00162 q^{21}\) \(+5.03981 q^{22}\) \(-3.28322 q^{23}\) \(-3.49093 q^{24}\) \(+12.4372 q^{25}\) \(-7.59765 q^{26}\) \(+1.00000 q^{27}\) \(+6.98548 q^{28}\) \(-3.33120 q^{29}\) \(-9.78411 q^{30}\) \(+7.31068 q^{31}\) \(+4.17106 q^{32}\) \(-2.15096 q^{33}\) \(+4.90371 q^{34}\) \(+8.35837 q^{35}\) \(+3.48991 q^{36}\) \(+5.37776 q^{37}\) \(-0.379381 q^{38}\) \(+3.24262 q^{39}\) \(-14.5774 q^{40}\) \(+7.75006 q^{41}\) \(-4.68991 q^{42}\) \(+3.01864 q^{43}\) \(-7.50664 q^{44}\) \(+4.17579 q^{45}\) \(+7.69275 q^{46}\) \(-12.8616 q^{47}\) \(+1.19963 q^{48}\) \(-2.99350 q^{49}\) \(-29.1411 q^{50}\) \(-2.09287 q^{51}\) \(+11.3165 q^{52}\) \(+7.09486 q^{53}\) \(-2.34305 q^{54}\) \(-8.98196 q^{55}\) \(-6.98753 q^{56}\) \(+0.161917 q^{57}\) \(+7.80520 q^{58}\) \(+1.24551 q^{59}\) \(+14.5731 q^{60}\) \(-3.52142 q^{61}\) \(-17.1293 q^{62}\) \(+2.00162 q^{63}\) \(-12.1723 q^{64}\) \(+13.5405 q^{65}\) \(+5.03981 q^{66}\) \(-11.9537 q^{67}\) \(-7.30392 q^{68}\) \(-3.28322 q^{69}\) \(-19.5841 q^{70}\) \(+13.5920 q^{71}\) \(-3.49093 q^{72}\) \(+7.95855 q^{73}\) \(-12.6004 q^{74}\) \(+12.4372 q^{75}\) \(+0.565076 q^{76}\) \(-4.30541 q^{77}\) \(-7.59765 q^{78}\) \(-5.27964 q^{79}\) \(+5.00940 q^{80}\) \(+1.00000 q^{81}\) \(-18.1588 q^{82}\) \(+16.0761 q^{83}\) \(+6.98548 q^{84}\) \(-8.73939 q^{85}\) \(-7.07283 q^{86}\) \(-3.33120 q^{87}\) \(+7.50885 q^{88}\) \(-3.14423 q^{89}\) \(-9.78411 q^{90}\) \(+6.49052 q^{91}\) \(-11.4581 q^{92}\) \(+7.31068 q^{93}\) \(+30.1354 q^{94}\) \(+0.676132 q^{95}\) \(+4.17106 q^{96}\) \(-5.77643 q^{97}\) \(+7.01394 q^{98}\) \(-2.15096 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut 41q^{10} \) \(\mathstrut +\mathstrut 51q^{11} \) \(\mathstrut +\mathstrut 151q^{12} \) \(\mathstrut +\mathstrut 56q^{13} \) \(\mathstrut +\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 195q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 15q^{18} \) \(\mathstrut +\mathstrut 93q^{19} \) \(\mathstrut +\mathstrut 44q^{20} \) \(\mathstrut +\mathstrut 61q^{21} \) \(\mathstrut +\mathstrut 46q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 42q^{24} \) \(\mathstrut +\mathstrut 193q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut 129q^{27} \) \(\mathstrut +\mathstrut 145q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 41q^{30} \) \(\mathstrut +\mathstrut 67q^{31} \) \(\mathstrut +\mathstrut 89q^{32} \) \(\mathstrut +\mathstrut 51q^{33} \) \(\mathstrut +\mathstrut 73q^{34} \) \(\mathstrut +\mathstrut 56q^{35} \) \(\mathstrut +\mathstrut 151q^{36} \) \(\mathstrut +\mathstrut 95q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 103q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 5q^{42} \) \(\mathstrut +\mathstrut 150q^{43} \) \(\mathstrut +\mathstrut 69q^{44} \) \(\mathstrut +\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 53q^{47} \) \(\mathstrut +\mathstrut 195q^{48} \) \(\mathstrut +\mathstrut 240q^{49} \) \(\mathstrut +\mathstrut 17q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 124q^{52} \) \(\mathstrut +\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut 15q^{54} \) \(\mathstrut +\mathstrut 66q^{55} \) \(\mathstrut -\mathstrut 17q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 57q^{58} \) \(\mathstrut +\mathstrut 49q^{59} \) \(\mathstrut +\mathstrut 44q^{60} \) \(\mathstrut +\mathstrut 113q^{61} \) \(\mathstrut +\mathstrut 27q^{62} \) \(\mathstrut +\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 262q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 46q^{66} \) \(\mathstrut +\mathstrut 185q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 50q^{69} \) \(\mathstrut +\mathstrut 25q^{70} \) \(\mathstrut +\mathstrut 41q^{71} \) \(\mathstrut +\mathstrut 42q^{72} \) \(\mathstrut +\mathstrut 153q^{73} \) \(\mathstrut -\mathstrut q^{74} \) \(\mathstrut +\mathstrut 193q^{75} \) \(\mathstrut +\mathstrut 190q^{76} \) \(\mathstrut +\mathstrut 39q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 101q^{79} \) \(\mathstrut +\mathstrut 48q^{80} \) \(\mathstrut +\mathstrut 129q^{81} \) \(\mathstrut +\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 162q^{83} \) \(\mathstrut +\mathstrut 145q^{84} \) \(\mathstrut +\mathstrut 99q^{85} \) \(\mathstrut +\mathstrut 13q^{86} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 86q^{88} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 117q^{91} \) \(\mathstrut +\mathstrut 56q^{92} \) \(\mathstrut +\mathstrut 67q^{93} \) \(\mathstrut +\mathstrut 49q^{94} \) \(\mathstrut +\mathstrut 71q^{95} \) \(\mathstrut +\mathstrut 89q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut +\mathstrut 40q^{98} \) \(\mathstrut +\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34305 −1.65679 −0.828395 0.560144i \(-0.810746\pi\)
−0.828395 + 0.560144i \(0.810746\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.48991 1.74495
\(5\) 4.17579 1.86747 0.933736 0.357964i \(-0.116529\pi\)
0.933736 + 0.357964i \(0.116529\pi\)
\(6\) −2.34305 −0.956548
\(7\) 2.00162 0.756543 0.378271 0.925695i \(-0.376519\pi\)
0.378271 + 0.925695i \(0.376519\pi\)
\(8\) −3.49093 −1.23423
\(9\) 1.00000 0.333333
\(10\) −9.78411 −3.09401
\(11\) −2.15096 −0.648539 −0.324269 0.945965i \(-0.605118\pi\)
−0.324269 + 0.945965i \(0.605118\pi\)
\(12\) 3.48991 1.00745
\(13\) 3.24262 0.899342 0.449671 0.893194i \(-0.351541\pi\)
0.449671 + 0.893194i \(0.351541\pi\)
\(14\) −4.68991 −1.25343
\(15\) 4.17579 1.07818
\(16\) 1.19963 0.299907
\(17\) −2.09287 −0.507596 −0.253798 0.967257i \(-0.581680\pi\)
−0.253798 + 0.967257i \(0.581680\pi\)
\(18\) −2.34305 −0.552263
\(19\) 0.161917 0.0371463 0.0185732 0.999828i \(-0.494088\pi\)
0.0185732 + 0.999828i \(0.494088\pi\)
\(20\) 14.5731 3.25865
\(21\) 2.00162 0.436790
\(22\) 5.03981 1.07449
\(23\) −3.28322 −0.684598 −0.342299 0.939591i \(-0.611206\pi\)
−0.342299 + 0.939591i \(0.611206\pi\)
\(24\) −3.49093 −0.712583
\(25\) 12.4372 2.48745
\(26\) −7.59765 −1.49002
\(27\) 1.00000 0.192450
\(28\) 6.98548 1.32013
\(29\) −3.33120 −0.618589 −0.309295 0.950966i \(-0.600093\pi\)
−0.309295 + 0.950966i \(0.600093\pi\)
\(30\) −9.78411 −1.78633
\(31\) 7.31068 1.31304 0.656518 0.754310i \(-0.272028\pi\)
0.656518 + 0.754310i \(0.272028\pi\)
\(32\) 4.17106 0.737347
\(33\) −2.15096 −0.374434
\(34\) 4.90371 0.840979
\(35\) 8.35837 1.41282
\(36\) 3.48991 0.581651
\(37\) 5.37776 0.884098 0.442049 0.896991i \(-0.354252\pi\)
0.442049 + 0.896991i \(0.354252\pi\)
\(38\) −0.379381 −0.0615437
\(39\) 3.24262 0.519235
\(40\) −14.5774 −2.30489
\(41\) 7.75006 1.21036 0.605178 0.796090i \(-0.293102\pi\)
0.605178 + 0.796090i \(0.293102\pi\)
\(42\) −4.68991 −0.723670
\(43\) 3.01864 0.460338 0.230169 0.973151i \(-0.426072\pi\)
0.230169 + 0.973151i \(0.426072\pi\)
\(44\) −7.50664 −1.13167
\(45\) 4.17579 0.622490
\(46\) 7.69275 1.13423
\(47\) −12.8616 −1.87606 −0.938028 0.346561i \(-0.887349\pi\)
−0.938028 + 0.346561i \(0.887349\pi\)
\(48\) 1.19963 0.173152
\(49\) −2.99350 −0.427643
\(50\) −29.1411 −4.12118
\(51\) −2.09287 −0.293060
\(52\) 11.3165 1.56931
\(53\) 7.09486 0.974554 0.487277 0.873247i \(-0.337990\pi\)
0.487277 + 0.873247i \(0.337990\pi\)
\(54\) −2.34305 −0.318849
\(55\) −8.98196 −1.21113
\(56\) −6.98753 −0.933748
\(57\) 0.161917 0.0214465
\(58\) 7.80520 1.02487
\(59\) 1.24551 0.162151 0.0810757 0.996708i \(-0.474164\pi\)
0.0810757 + 0.996708i \(0.474164\pi\)
\(60\) 14.5731 1.88138
\(61\) −3.52142 −0.450872 −0.225436 0.974258i \(-0.572381\pi\)
−0.225436 + 0.974258i \(0.572381\pi\)
\(62\) −17.1293 −2.17543
\(63\) 2.00162 0.252181
\(64\) −12.1723 −1.52154
\(65\) 13.5405 1.67950
\(66\) 5.03981 0.620358
\(67\) −11.9537 −1.46037 −0.730187 0.683247i \(-0.760567\pi\)
−0.730187 + 0.683247i \(0.760567\pi\)
\(68\) −7.30392 −0.885730
\(69\) −3.28322 −0.395253
\(70\) −19.5841 −2.34075
\(71\) 13.5920 1.61308 0.806539 0.591180i \(-0.201338\pi\)
0.806539 + 0.591180i \(0.201338\pi\)
\(72\) −3.49093 −0.411410
\(73\) 7.95855 0.931478 0.465739 0.884922i \(-0.345788\pi\)
0.465739 + 0.884922i \(0.345788\pi\)
\(74\) −12.6004 −1.46476
\(75\) 12.4372 1.43613
\(76\) 0.565076 0.0648186
\(77\) −4.30541 −0.490647
\(78\) −7.59765 −0.860264
\(79\) −5.27964 −0.594006 −0.297003 0.954877i \(-0.595987\pi\)
−0.297003 + 0.954877i \(0.595987\pi\)
\(80\) 5.00940 0.560068
\(81\) 1.00000 0.111111
\(82\) −18.1588 −2.00531
\(83\) 16.0761 1.76458 0.882288 0.470710i \(-0.156002\pi\)
0.882288 + 0.470710i \(0.156002\pi\)
\(84\) 6.98548 0.762178
\(85\) −8.73939 −0.947920
\(86\) −7.07283 −0.762683
\(87\) −3.33120 −0.357143
\(88\) 7.50885 0.800446
\(89\) −3.14423 −0.333288 −0.166644 0.986017i \(-0.553293\pi\)
−0.166644 + 0.986017i \(0.553293\pi\)
\(90\) −9.78411 −1.03134
\(91\) 6.49052 0.680391
\(92\) −11.4581 −1.19459
\(93\) 7.31068 0.758082
\(94\) 30.1354 3.10823
\(95\) 0.676132 0.0693697
\(96\) 4.17106 0.425707
\(97\) −5.77643 −0.586507 −0.293254 0.956035i \(-0.594738\pi\)
−0.293254 + 0.956035i \(0.594738\pi\)
\(98\) 7.01394 0.708515
\(99\) −2.15096 −0.216180
\(100\) 43.4048 4.34048
\(101\) −18.0864 −1.79966 −0.899832 0.436236i \(-0.856311\pi\)
−0.899832 + 0.436236i \(0.856311\pi\)
\(102\) 4.90371 0.485540
\(103\) 3.87069 0.381391 0.190695 0.981649i \(-0.438926\pi\)
0.190695 + 0.981649i \(0.438926\pi\)
\(104\) −11.3198 −1.11000
\(105\) 8.35837 0.815693
\(106\) −16.6237 −1.61463
\(107\) −0.907788 −0.0877592 −0.0438796 0.999037i \(-0.513972\pi\)
−0.0438796 + 0.999037i \(0.513972\pi\)
\(108\) 3.48991 0.335816
\(109\) 2.34366 0.224482 0.112241 0.993681i \(-0.464197\pi\)
0.112241 + 0.993681i \(0.464197\pi\)
\(110\) 21.0452 2.00658
\(111\) 5.37776 0.510434
\(112\) 2.40121 0.226893
\(113\) 4.10777 0.386426 0.193213 0.981157i \(-0.438109\pi\)
0.193213 + 0.981157i \(0.438109\pi\)
\(114\) −0.379381 −0.0355323
\(115\) −13.7100 −1.27847
\(116\) −11.6256 −1.07941
\(117\) 3.24262 0.299781
\(118\) −2.91829 −0.268651
\(119\) −4.18914 −0.384018
\(120\) −14.5774 −1.33073
\(121\) −6.37337 −0.579398
\(122\) 8.25088 0.746999
\(123\) 7.75006 0.698799
\(124\) 25.5136 2.29119
\(125\) 31.0564 2.77777
\(126\) −4.68991 −0.417811
\(127\) 7.35002 0.652209 0.326104 0.945334i \(-0.394264\pi\)
0.326104 + 0.945334i \(0.394264\pi\)
\(128\) 20.1782 1.78352
\(129\) 3.01864 0.265776
\(130\) −31.7262 −2.78257
\(131\) 18.9112 1.65228 0.826138 0.563467i \(-0.190533\pi\)
0.826138 + 0.563467i \(0.190533\pi\)
\(132\) −7.50664 −0.653370
\(133\) 0.324097 0.0281028
\(134\) 28.0081 2.41953
\(135\) 4.17579 0.359395
\(136\) 7.30606 0.626490
\(137\) −13.6216 −1.16377 −0.581885 0.813271i \(-0.697685\pi\)
−0.581885 + 0.813271i \(0.697685\pi\)
\(138\) 7.69275 0.654851
\(139\) 16.8766 1.43146 0.715729 0.698378i \(-0.246094\pi\)
0.715729 + 0.698378i \(0.246094\pi\)
\(140\) 29.1699 2.46531
\(141\) −12.8616 −1.08314
\(142\) −31.8469 −2.67253
\(143\) −6.97475 −0.583258
\(144\) 1.19963 0.0999691
\(145\) −13.9104 −1.15520
\(146\) −18.6473 −1.54326
\(147\) −2.99350 −0.246900
\(148\) 18.7679 1.54271
\(149\) −14.1696 −1.16082 −0.580409 0.814325i \(-0.697107\pi\)
−0.580409 + 0.814325i \(0.697107\pi\)
\(150\) −29.1411 −2.37936
\(151\) 22.3910 1.82215 0.911075 0.412241i \(-0.135254\pi\)
0.911075 + 0.412241i \(0.135254\pi\)
\(152\) −0.565241 −0.0458471
\(153\) −2.09287 −0.169199
\(154\) 10.0878 0.812899
\(155\) 30.5279 2.45206
\(156\) 11.3165 0.906041
\(157\) 12.0714 0.963400 0.481700 0.876336i \(-0.340019\pi\)
0.481700 + 0.876336i \(0.340019\pi\)
\(158\) 12.3705 0.984143
\(159\) 7.09486 0.562659
\(160\) 17.4175 1.37697
\(161\) −6.57176 −0.517928
\(162\) −2.34305 −0.184088
\(163\) 2.11896 0.165969 0.0829847 0.996551i \(-0.473555\pi\)
0.0829847 + 0.996551i \(0.473555\pi\)
\(164\) 27.0470 2.11201
\(165\) −8.98196 −0.699244
\(166\) −37.6671 −2.92353
\(167\) −0.323736 −0.0250515 −0.0125257 0.999922i \(-0.503987\pi\)
−0.0125257 + 0.999922i \(0.503987\pi\)
\(168\) −6.98753 −0.539100
\(169\) −2.48539 −0.191184
\(170\) 20.4769 1.57050
\(171\) 0.161917 0.0123821
\(172\) 10.5348 0.803268
\(173\) −19.4735 −1.48054 −0.740271 0.672308i \(-0.765303\pi\)
−0.740271 + 0.672308i \(0.765303\pi\)
\(174\) 7.80520 0.591710
\(175\) 24.8947 1.88186
\(176\) −2.58035 −0.194501
\(177\) 1.24551 0.0936181
\(178\) 7.36711 0.552188
\(179\) −6.22080 −0.464965 −0.232482 0.972601i \(-0.574685\pi\)
−0.232482 + 0.972601i \(0.574685\pi\)
\(180\) 14.5731 1.08622
\(181\) 6.35341 0.472245 0.236123 0.971723i \(-0.424123\pi\)
0.236123 + 0.971723i \(0.424123\pi\)
\(182\) −15.2076 −1.12726
\(183\) −3.52142 −0.260311
\(184\) 11.4615 0.844951
\(185\) 22.4564 1.65103
\(186\) −17.1293 −1.25598
\(187\) 4.50168 0.329195
\(188\) −44.8857 −3.27363
\(189\) 2.00162 0.145597
\(190\) −1.58422 −0.114931
\(191\) 0.741680 0.0536661 0.0268330 0.999640i \(-0.491458\pi\)
0.0268330 + 0.999640i \(0.491458\pi\)
\(192\) −12.1723 −0.878459
\(193\) −14.6653 −1.05563 −0.527817 0.849358i \(-0.676989\pi\)
−0.527817 + 0.849358i \(0.676989\pi\)
\(194\) 13.5345 0.971719
\(195\) 13.5405 0.969657
\(196\) −10.4470 −0.746217
\(197\) −19.7969 −1.41047 −0.705237 0.708972i \(-0.749159\pi\)
−0.705237 + 0.708972i \(0.749159\pi\)
\(198\) 5.03981 0.358164
\(199\) 23.2319 1.64687 0.823435 0.567411i \(-0.192055\pi\)
0.823435 + 0.567411i \(0.192055\pi\)
\(200\) −43.4175 −3.07008
\(201\) −11.9537 −0.843148
\(202\) 42.3774 2.98167
\(203\) −6.66782 −0.467989
\(204\) −7.30392 −0.511377
\(205\) 32.3626 2.26030
\(206\) −9.06925 −0.631885
\(207\) −3.28322 −0.228199
\(208\) 3.88995 0.269719
\(209\) −0.348277 −0.0240908
\(210\) −19.5841 −1.35143
\(211\) 22.4290 1.54408 0.772038 0.635576i \(-0.219237\pi\)
0.772038 + 0.635576i \(0.219237\pi\)
\(212\) 24.7604 1.70055
\(213\) 13.5920 0.931311
\(214\) 2.12700 0.145399
\(215\) 12.6052 0.859668
\(216\) −3.49093 −0.237528
\(217\) 14.6332 0.993368
\(218\) −5.49132 −0.371919
\(219\) 7.95855 0.537789
\(220\) −31.3462 −2.11336
\(221\) −6.78639 −0.456502
\(222\) −12.6004 −0.845682
\(223\) 18.8720 1.26376 0.631882 0.775065i \(-0.282283\pi\)
0.631882 + 0.775065i \(0.282283\pi\)
\(224\) 8.34890 0.557834
\(225\) 12.4372 0.829149
\(226\) −9.62472 −0.640227
\(227\) 20.0458 1.33049 0.665244 0.746626i \(-0.268328\pi\)
0.665244 + 0.746626i \(0.268328\pi\)
\(228\) 0.565076 0.0374230
\(229\) −14.0287 −0.927040 −0.463520 0.886087i \(-0.653414\pi\)
−0.463520 + 0.886087i \(0.653414\pi\)
\(230\) 32.1233 2.11815
\(231\) −4.30541 −0.283275
\(232\) 11.6290 0.763482
\(233\) −6.03502 −0.395368 −0.197684 0.980266i \(-0.563342\pi\)
−0.197684 + 0.980266i \(0.563342\pi\)
\(234\) −7.59765 −0.496674
\(235\) −53.7073 −3.50348
\(236\) 4.34671 0.282946
\(237\) −5.27964 −0.342949
\(238\) 9.81538 0.636237
\(239\) 13.7450 0.889087 0.444544 0.895757i \(-0.353366\pi\)
0.444544 + 0.895757i \(0.353366\pi\)
\(240\) 5.00940 0.323356
\(241\) 17.4079 1.12134 0.560672 0.828038i \(-0.310543\pi\)
0.560672 + 0.828038i \(0.310543\pi\)
\(242\) 14.9332 0.959940
\(243\) 1.00000 0.0641500
\(244\) −12.2894 −0.786750
\(245\) −12.5002 −0.798611
\(246\) −18.1588 −1.15776
\(247\) 0.525037 0.0334073
\(248\) −25.5211 −1.62059
\(249\) 16.0761 1.01878
\(250\) −72.7668 −4.60217
\(251\) 15.0873 0.952301 0.476150 0.879364i \(-0.342032\pi\)
0.476150 + 0.879364i \(0.342032\pi\)
\(252\) 6.98548 0.440044
\(253\) 7.06206 0.443988
\(254\) −17.2215 −1.08057
\(255\) −8.73939 −0.547282
\(256\) −22.9341 −1.43338
\(257\) 18.0086 1.12334 0.561672 0.827360i \(-0.310158\pi\)
0.561672 + 0.827360i \(0.310158\pi\)
\(258\) −7.07283 −0.440335
\(259\) 10.7642 0.668858
\(260\) 47.2552 2.93064
\(261\) −3.33120 −0.206196
\(262\) −44.3099 −2.73748
\(263\) −13.5515 −0.835620 −0.417810 0.908535i \(-0.637202\pi\)
−0.417810 + 0.908535i \(0.637202\pi\)
\(264\) 7.50885 0.462138
\(265\) 29.6267 1.81995
\(266\) −0.759378 −0.0465604
\(267\) −3.14423 −0.192424
\(268\) −41.7172 −2.54828
\(269\) 3.20506 0.195416 0.0977078 0.995215i \(-0.468849\pi\)
0.0977078 + 0.995215i \(0.468849\pi\)
\(270\) −9.78411 −0.595442
\(271\) 11.9387 0.725224 0.362612 0.931940i \(-0.381885\pi\)
0.362612 + 0.931940i \(0.381885\pi\)
\(272\) −2.51067 −0.152232
\(273\) 6.49052 0.392824
\(274\) 31.9161 1.92812
\(275\) −26.7520 −1.61321
\(276\) −11.4581 −0.689697
\(277\) 19.9194 1.19684 0.598420 0.801182i \(-0.295795\pi\)
0.598420 + 0.801182i \(0.295795\pi\)
\(278\) −39.5429 −2.37163
\(279\) 7.31068 0.437679
\(280\) −29.1785 −1.74375
\(281\) −13.9582 −0.832679 −0.416339 0.909209i \(-0.636687\pi\)
−0.416339 + 0.909209i \(0.636687\pi\)
\(282\) 30.1354 1.79454
\(283\) 26.5983 1.58110 0.790551 0.612396i \(-0.209794\pi\)
0.790551 + 0.612396i \(0.209794\pi\)
\(284\) 47.4349 2.81475
\(285\) 0.676132 0.0400506
\(286\) 16.3422 0.966336
\(287\) 15.5127 0.915686
\(288\) 4.17106 0.245782
\(289\) −12.6199 −0.742347
\(290\) 32.5929 1.91392
\(291\) −5.77643 −0.338620
\(292\) 27.7746 1.62539
\(293\) −28.1611 −1.64519 −0.822594 0.568630i \(-0.807474\pi\)
−0.822594 + 0.568630i \(0.807474\pi\)
\(294\) 7.01394 0.409061
\(295\) 5.20098 0.302813
\(296\) −18.7734 −1.09118
\(297\) −2.15096 −0.124811
\(298\) 33.2001 1.92323
\(299\) −10.6462 −0.615688
\(300\) 43.4048 2.50598
\(301\) 6.04218 0.348265
\(302\) −52.4632 −3.01892
\(303\) −18.0864 −1.03904
\(304\) 0.194241 0.0111405
\(305\) −14.7047 −0.841990
\(306\) 4.90371 0.280326
\(307\) −8.94615 −0.510584 −0.255292 0.966864i \(-0.582172\pi\)
−0.255292 + 0.966864i \(0.582172\pi\)
\(308\) −15.0255 −0.856156
\(309\) 3.87069 0.220196
\(310\) −71.5285 −4.06254
\(311\) 2.30852 0.130904 0.0654521 0.997856i \(-0.479151\pi\)
0.0654521 + 0.997856i \(0.479151\pi\)
\(312\) −11.3198 −0.640856
\(313\) −3.94664 −0.223077 −0.111539 0.993760i \(-0.535578\pi\)
−0.111539 + 0.993760i \(0.535578\pi\)
\(314\) −28.2839 −1.59615
\(315\) 8.35837 0.470941
\(316\) −18.4254 −1.03651
\(317\) −3.70170 −0.207908 −0.103954 0.994582i \(-0.533150\pi\)
−0.103954 + 0.994582i \(0.533150\pi\)
\(318\) −16.6237 −0.932208
\(319\) 7.16529 0.401179
\(320\) −50.8289 −2.84142
\(321\) −0.907788 −0.0506678
\(322\) 15.3980 0.858097
\(323\) −0.338872 −0.0188553
\(324\) 3.48991 0.193884
\(325\) 40.3293 2.23707
\(326\) −4.96483 −0.274976
\(327\) 2.34366 0.129605
\(328\) −27.0549 −1.49386
\(329\) −25.7441 −1.41932
\(330\) 21.0452 1.15850
\(331\) −0.559387 −0.0307467 −0.0153733 0.999882i \(-0.504894\pi\)
−0.0153733 + 0.999882i \(0.504894\pi\)
\(332\) 56.1039 3.07910
\(333\) 5.37776 0.294699
\(334\) 0.758532 0.0415050
\(335\) −49.9161 −2.72721
\(336\) 2.40121 0.130997
\(337\) 5.06501 0.275909 0.137954 0.990439i \(-0.455947\pi\)
0.137954 + 0.990439i \(0.455947\pi\)
\(338\) 5.82340 0.316751
\(339\) 4.10777 0.223103
\(340\) −30.4997 −1.65408
\(341\) −15.7250 −0.851555
\(342\) −0.379381 −0.0205146
\(343\) −20.0032 −1.08007
\(344\) −10.5379 −0.568163
\(345\) −13.7100 −0.738123
\(346\) 45.6275 2.45295
\(347\) 21.4984 1.15409 0.577047 0.816711i \(-0.304205\pi\)
0.577047 + 0.816711i \(0.304205\pi\)
\(348\) −11.6256 −0.623197
\(349\) −31.4413 −1.68301 −0.841507 0.540247i \(-0.818331\pi\)
−0.841507 + 0.540247i \(0.818331\pi\)
\(350\) −58.3296 −3.11785
\(351\) 3.24262 0.173078
\(352\) −8.97179 −0.478198
\(353\) 18.2528 0.971499 0.485749 0.874098i \(-0.338547\pi\)
0.485749 + 0.874098i \(0.338547\pi\)
\(354\) −2.91829 −0.155106
\(355\) 56.7575 3.01238
\(356\) −10.9731 −0.581572
\(357\) −4.18914 −0.221713
\(358\) 14.5757 0.770349
\(359\) −33.2525 −1.75500 −0.877500 0.479576i \(-0.840790\pi\)
−0.877500 + 0.479576i \(0.840790\pi\)
\(360\) −14.5774 −0.768296
\(361\) −18.9738 −0.998620
\(362\) −14.8864 −0.782411
\(363\) −6.37337 −0.334515
\(364\) 22.6513 1.18725
\(365\) 33.2333 1.73951
\(366\) 8.25088 0.431280
\(367\) −7.34009 −0.383149 −0.191575 0.981478i \(-0.561359\pi\)
−0.191575 + 0.981478i \(0.561359\pi\)
\(368\) −3.93864 −0.205316
\(369\) 7.75006 0.403452
\(370\) −52.6165 −2.73540
\(371\) 14.2012 0.737292
\(372\) 25.5136 1.32282
\(373\) 13.4933 0.698654 0.349327 0.937001i \(-0.386410\pi\)
0.349327 + 0.937001i \(0.386410\pi\)
\(374\) −10.5477 −0.545408
\(375\) 31.0564 1.60374
\(376\) 44.8989 2.31548
\(377\) −10.8018 −0.556323
\(378\) −4.68991 −0.241223
\(379\) 11.1621 0.573360 0.286680 0.958026i \(-0.407448\pi\)
0.286680 + 0.958026i \(0.407448\pi\)
\(380\) 2.35964 0.121047
\(381\) 7.35002 0.376553
\(382\) −1.73780 −0.0889134
\(383\) −25.6713 −1.31174 −0.655872 0.754872i \(-0.727699\pi\)
−0.655872 + 0.754872i \(0.727699\pi\)
\(384\) 20.1782 1.02971
\(385\) −17.9785 −0.916269
\(386\) 34.3617 1.74896
\(387\) 3.01864 0.153446
\(388\) −20.1592 −1.02343
\(389\) −23.9597 −1.21481 −0.607403 0.794394i \(-0.707789\pi\)
−0.607403 + 0.794394i \(0.707789\pi\)
\(390\) −31.7262 −1.60652
\(391\) 6.87135 0.347499
\(392\) 10.4501 0.527810
\(393\) 18.9112 0.953942
\(394\) 46.3853 2.33686
\(395\) −22.0467 −1.10929
\(396\) −7.50664 −0.377223
\(397\) −8.35155 −0.419152 −0.209576 0.977792i \(-0.567208\pi\)
−0.209576 + 0.977792i \(0.567208\pi\)
\(398\) −54.4337 −2.72852
\(399\) 0.324097 0.0162252
\(400\) 14.9201 0.746004
\(401\) 11.8812 0.593319 0.296660 0.954983i \(-0.404127\pi\)
0.296660 + 0.954983i \(0.404127\pi\)
\(402\) 28.0081 1.39692
\(403\) 23.7058 1.18087
\(404\) −63.1199 −3.14033
\(405\) 4.17579 0.207497
\(406\) 15.6231 0.775360
\(407\) −11.5673 −0.573371
\(408\) 7.30606 0.361704
\(409\) 13.6833 0.676595 0.338297 0.941039i \(-0.390149\pi\)
0.338297 + 0.941039i \(0.390149\pi\)
\(410\) −75.8274 −3.74485
\(411\) −13.6216 −0.671903
\(412\) 13.5084 0.665509
\(413\) 2.49304 0.122674
\(414\) 7.69275 0.378078
\(415\) 67.1302 3.29529
\(416\) 13.5252 0.663127
\(417\) 16.8766 0.826453
\(418\) 0.816032 0.0399135
\(419\) −9.88295 −0.482813 −0.241407 0.970424i \(-0.577609\pi\)
−0.241407 + 0.970424i \(0.577609\pi\)
\(420\) 29.1699 1.42335
\(421\) −21.4740 −1.04658 −0.523288 0.852156i \(-0.675295\pi\)
−0.523288 + 0.852156i \(0.675295\pi\)
\(422\) −52.5524 −2.55821
\(423\) −12.8616 −0.625352
\(424\) −24.7677 −1.20282
\(425\) −26.0295 −1.26262
\(426\) −31.8469 −1.54299
\(427\) −7.04856 −0.341104
\(428\) −3.16810 −0.153136
\(429\) −6.97475 −0.336744
\(430\) −29.5347 −1.42429
\(431\) 26.3445 1.26897 0.634486 0.772934i \(-0.281212\pi\)
0.634486 + 0.772934i \(0.281212\pi\)
\(432\) 1.19963 0.0577172
\(433\) −1.08572 −0.0521763 −0.0260882 0.999660i \(-0.508305\pi\)
−0.0260882 + 0.999660i \(0.508305\pi\)
\(434\) −34.2865 −1.64580
\(435\) −13.9104 −0.666954
\(436\) 8.17915 0.391710
\(437\) −0.531609 −0.0254303
\(438\) −18.6473 −0.891004
\(439\) −26.3362 −1.25696 −0.628479 0.777826i \(-0.716322\pi\)
−0.628479 + 0.777826i \(0.716322\pi\)
\(440\) 31.3554 1.49481
\(441\) −2.99350 −0.142548
\(442\) 15.9009 0.756328
\(443\) −34.4193 −1.63531 −0.817656 0.575707i \(-0.804727\pi\)
−0.817656 + 0.575707i \(0.804727\pi\)
\(444\) 18.7679 0.890683
\(445\) −13.1297 −0.622405
\(446\) −44.2182 −2.09379
\(447\) −14.1696 −0.670198
\(448\) −24.3643 −1.15111
\(449\) 3.15913 0.149089 0.0745443 0.997218i \(-0.476250\pi\)
0.0745443 + 0.997218i \(0.476250\pi\)
\(450\) −29.1411 −1.37373
\(451\) −16.6701 −0.784962
\(452\) 14.3357 0.674296
\(453\) 22.3910 1.05202
\(454\) −46.9684 −2.20434
\(455\) 27.1030 1.27061
\(456\) −0.565241 −0.0264699
\(457\) 27.3636 1.28002 0.640008 0.768368i \(-0.278931\pi\)
0.640008 + 0.768368i \(0.278931\pi\)
\(458\) 32.8699 1.53591
\(459\) −2.09287 −0.0976868
\(460\) −47.8467 −2.23086
\(461\) −0.796407 −0.0370924 −0.0185462 0.999828i \(-0.505904\pi\)
−0.0185462 + 0.999828i \(0.505904\pi\)
\(462\) 10.0878 0.469328
\(463\) −34.1285 −1.58609 −0.793043 0.609166i \(-0.791504\pi\)
−0.793043 + 0.609166i \(0.791504\pi\)
\(464\) −3.99621 −0.185519
\(465\) 30.5279 1.41570
\(466\) 14.1404 0.655041
\(467\) −28.9324 −1.33883 −0.669416 0.742888i \(-0.733456\pi\)
−0.669416 + 0.742888i \(0.733456\pi\)
\(468\) 11.3165 0.523103
\(469\) −23.9268 −1.10484
\(470\) 125.839 5.80453
\(471\) 12.0714 0.556219
\(472\) −4.34798 −0.200132
\(473\) −6.49297 −0.298547
\(474\) 12.3705 0.568195
\(475\) 2.01380 0.0923996
\(476\) −14.6197 −0.670093
\(477\) 7.09486 0.324851
\(478\) −32.2052 −1.47303
\(479\) −33.8314 −1.54580 −0.772899 0.634529i \(-0.781194\pi\)
−0.772899 + 0.634529i \(0.781194\pi\)
\(480\) 17.4175 0.794996
\(481\) 17.4380 0.795106
\(482\) −40.7877 −1.85783
\(483\) −6.57176 −0.299026
\(484\) −22.2425 −1.01102
\(485\) −24.1212 −1.09529
\(486\) −2.34305 −0.106283
\(487\) −27.0276 −1.22474 −0.612369 0.790572i \(-0.709783\pi\)
−0.612369 + 0.790572i \(0.709783\pi\)
\(488\) 12.2930 0.556479
\(489\) 2.11896 0.0958225
\(490\) 29.2887 1.32313
\(491\) 6.09357 0.274999 0.137500 0.990502i \(-0.456093\pi\)
0.137500 + 0.990502i \(0.456093\pi\)
\(492\) 27.0470 1.21937
\(493\) 6.97178 0.313993
\(494\) −1.23019 −0.0553488
\(495\) −8.98196 −0.403709
\(496\) 8.77010 0.393789
\(497\) 27.2062 1.22036
\(498\) −37.6671 −1.68790
\(499\) −17.9123 −0.801867 −0.400933 0.916107i \(-0.631314\pi\)
−0.400933 + 0.916107i \(0.631314\pi\)
\(500\) 108.384 4.84707
\(501\) −0.323736 −0.0144635
\(502\) −35.3503 −1.57776
\(503\) 8.24823 0.367770 0.183885 0.982948i \(-0.441133\pi\)
0.183885 + 0.982948i \(0.441133\pi\)
\(504\) −6.98753 −0.311249
\(505\) −75.5251 −3.36082
\(506\) −16.5468 −0.735595
\(507\) −2.48539 −0.110380
\(508\) 25.6509 1.13807
\(509\) 2.35771 0.104504 0.0522518 0.998634i \(-0.483360\pi\)
0.0522518 + 0.998634i \(0.483360\pi\)
\(510\) 20.4769 0.906731
\(511\) 15.9300 0.704703
\(512\) 13.3794 0.591290
\(513\) 0.161917 0.00714882
\(514\) −42.1951 −1.86115
\(515\) 16.1632 0.712236
\(516\) 10.5348 0.463767
\(517\) 27.6647 1.21669
\(518\) −25.2212 −1.10816
\(519\) −19.4735 −0.854792
\(520\) −47.2690 −2.07288
\(521\) −24.4351 −1.07052 −0.535260 0.844687i \(-0.679786\pi\)
−0.535260 + 0.844687i \(0.679786\pi\)
\(522\) 7.80520 0.341624
\(523\) −25.2942 −1.10604 −0.553019 0.833169i \(-0.686524\pi\)
−0.553019 + 0.833169i \(0.686524\pi\)
\(524\) 65.9982 2.88314
\(525\) 24.8947 1.08649
\(526\) 31.7518 1.38445
\(527\) −15.3003 −0.666492
\(528\) −2.58035 −0.112295
\(529\) −12.2205 −0.531326
\(530\) −69.4169 −3.01528
\(531\) 1.24551 0.0540504
\(532\) 1.13107 0.0490381
\(533\) 25.1305 1.08852
\(534\) 7.36711 0.318806
\(535\) −3.79074 −0.163888
\(536\) 41.7295 1.80244
\(537\) −6.22080 −0.268447
\(538\) −7.50962 −0.323763
\(539\) 6.43890 0.277343
\(540\) 14.5731 0.627127
\(541\) −14.8992 −0.640566 −0.320283 0.947322i \(-0.603778\pi\)
−0.320283 + 0.947322i \(0.603778\pi\)
\(542\) −27.9730 −1.20154
\(543\) 6.35341 0.272651
\(544\) −8.72949 −0.374274
\(545\) 9.78663 0.419213
\(546\) −15.2076 −0.650827
\(547\) −32.7616 −1.40078 −0.700392 0.713759i \(-0.746991\pi\)
−0.700392 + 0.713759i \(0.746991\pi\)
\(548\) −47.5380 −2.03072
\(549\) −3.52142 −0.150291
\(550\) 62.6814 2.67274
\(551\) −0.539379 −0.0229783
\(552\) 11.4615 0.487833
\(553\) −10.5679 −0.449391
\(554\) −46.6722 −1.98291
\(555\) 22.4564 0.953221
\(556\) 58.8979 2.49783
\(557\) −3.69567 −0.156591 −0.0782953 0.996930i \(-0.524948\pi\)
−0.0782953 + 0.996930i \(0.524948\pi\)
\(558\) −17.1293 −0.725142
\(559\) 9.78831 0.414001
\(560\) 10.0269 0.423716
\(561\) 4.50168 0.190061
\(562\) 32.7049 1.37957
\(563\) 42.8868 1.80746 0.903732 0.428098i \(-0.140816\pi\)
0.903732 + 0.428098i \(0.140816\pi\)
\(564\) −44.8857 −1.89003
\(565\) 17.1532 0.721640
\(566\) −62.3212 −2.61955
\(567\) 2.00162 0.0840603
\(568\) −47.4489 −1.99091
\(569\) 10.6331 0.445762 0.222881 0.974846i \(-0.428454\pi\)
0.222881 + 0.974846i \(0.428454\pi\)
\(570\) −1.58422 −0.0663555
\(571\) 28.8545 1.20752 0.603762 0.797165i \(-0.293668\pi\)
0.603762 + 0.797165i \(0.293668\pi\)
\(572\) −24.3412 −1.01776
\(573\) 0.741680 0.0309841
\(574\) −36.3471 −1.51710
\(575\) −40.8341 −1.70290
\(576\) −12.1723 −0.507179
\(577\) 32.2098 1.34091 0.670456 0.741949i \(-0.266098\pi\)
0.670456 + 0.741949i \(0.266098\pi\)
\(578\) 29.5691 1.22991
\(579\) −14.6653 −0.609471
\(580\) −48.5460 −2.01576
\(581\) 32.1782 1.33498
\(582\) 13.5345 0.561022
\(583\) −15.2608 −0.632036
\(584\) −27.7828 −1.14966
\(585\) 13.5405 0.559832
\(586\) 65.9829 2.72573
\(587\) 16.7189 0.690061 0.345031 0.938591i \(-0.387869\pi\)
0.345031 + 0.938591i \(0.387869\pi\)
\(588\) −10.4470 −0.430829
\(589\) 1.18372 0.0487745
\(590\) −12.1862 −0.501697
\(591\) −19.7969 −0.814337
\(592\) 6.45131 0.265147
\(593\) −11.7508 −0.482547 −0.241274 0.970457i \(-0.577565\pi\)
−0.241274 + 0.970457i \(0.577565\pi\)
\(594\) 5.03981 0.206786
\(595\) −17.4930 −0.717142
\(596\) −49.4505 −2.02557
\(597\) 23.2319 0.950820
\(598\) 24.9447 1.02007
\(599\) 23.1536 0.946030 0.473015 0.881054i \(-0.343166\pi\)
0.473015 + 0.881054i \(0.343166\pi\)
\(600\) −43.4175 −1.77251
\(601\) 24.3645 0.993850 0.496925 0.867793i \(-0.334462\pi\)
0.496925 + 0.867793i \(0.334462\pi\)
\(602\) −14.1572 −0.577002
\(603\) −11.9537 −0.486791
\(604\) 78.1423 3.17957
\(605\) −26.6139 −1.08201
\(606\) 42.3774 1.72147
\(607\) 39.5590 1.60565 0.802825 0.596215i \(-0.203329\pi\)
0.802825 + 0.596215i \(0.203329\pi\)
\(608\) 0.675367 0.0273897
\(609\) −6.66782 −0.270194
\(610\) 34.4540 1.39500
\(611\) −41.7053 −1.68722
\(612\) −7.30392 −0.295243
\(613\) −17.4831 −0.706137 −0.353068 0.935598i \(-0.614862\pi\)
−0.353068 + 0.935598i \(0.614862\pi\)
\(614\) 20.9613 0.845930
\(615\) 32.3626 1.30499
\(616\) 15.0299 0.605572
\(617\) −7.74839 −0.311939 −0.155969 0.987762i \(-0.549850\pi\)
−0.155969 + 0.987762i \(0.549850\pi\)
\(618\) −9.06925 −0.364819
\(619\) 10.2141 0.410541 0.205271 0.978705i \(-0.434193\pi\)
0.205271 + 0.978705i \(0.434193\pi\)
\(620\) 106.539 4.27872
\(621\) −3.28322 −0.131751
\(622\) −5.40899 −0.216881
\(623\) −6.29357 −0.252147
\(624\) 3.88995 0.155723
\(625\) 67.4987 2.69995
\(626\) 9.24720 0.369592
\(627\) −0.348277 −0.0139089
\(628\) 42.1279 1.68109
\(629\) −11.2549 −0.448764
\(630\) −19.5841 −0.780250
\(631\) 13.9349 0.554739 0.277369 0.960763i \(-0.410537\pi\)
0.277369 + 0.960763i \(0.410537\pi\)
\(632\) 18.4309 0.733140
\(633\) 22.4290 0.891473
\(634\) 8.67329 0.344460
\(635\) 30.6922 1.21798
\(636\) 24.7604 0.981814
\(637\) −9.70680 −0.384597
\(638\) −16.7887 −0.664669
\(639\) 13.5920 0.537693
\(640\) 84.2600 3.33067
\(641\) −14.7325 −0.581898 −0.290949 0.956739i \(-0.593971\pi\)
−0.290949 + 0.956739i \(0.593971\pi\)
\(642\) 2.12700 0.0839459
\(643\) 3.80579 0.150086 0.0750428 0.997180i \(-0.476091\pi\)
0.0750428 + 0.997180i \(0.476091\pi\)
\(644\) −22.9348 −0.903759
\(645\) 12.6052 0.496329
\(646\) 0.793995 0.0312393
\(647\) 38.2517 1.50383 0.751914 0.659261i \(-0.229131\pi\)
0.751914 + 0.659261i \(0.229131\pi\)
\(648\) −3.49093 −0.137137
\(649\) −2.67904 −0.105161
\(650\) −94.4938 −3.70635
\(651\) 14.6332 0.573521
\(652\) 7.39495 0.289609
\(653\) −7.48727 −0.293000 −0.146500 0.989211i \(-0.546801\pi\)
−0.146500 + 0.989211i \(0.546801\pi\)
\(654\) −5.49132 −0.214728
\(655\) 78.9691 3.08558
\(656\) 9.29720 0.362995
\(657\) 7.95855 0.310493
\(658\) 60.3197 2.35151
\(659\) 25.1510 0.979745 0.489873 0.871794i \(-0.337043\pi\)
0.489873 + 0.871794i \(0.337043\pi\)
\(660\) −31.3462 −1.22015
\(661\) −11.2670 −0.438237 −0.219119 0.975698i \(-0.570318\pi\)
−0.219119 + 0.975698i \(0.570318\pi\)
\(662\) 1.31067 0.0509408
\(663\) −6.78639 −0.263562
\(664\) −56.1204 −2.17789
\(665\) 1.35336 0.0524812
\(666\) −12.6004 −0.488255
\(667\) 10.9371 0.423485
\(668\) −1.12981 −0.0437136
\(669\) 18.8720 0.729634
\(670\) 116.956 4.51841
\(671\) 7.57443 0.292408
\(672\) 8.34890 0.322066
\(673\) 4.64165 0.178923 0.0894613 0.995990i \(-0.471485\pi\)
0.0894613 + 0.995990i \(0.471485\pi\)
\(674\) −11.8676 −0.457123
\(675\) 12.4372 0.478710
\(676\) −8.67376 −0.333606
\(677\) −8.03659 −0.308871 −0.154436 0.988003i \(-0.549356\pi\)
−0.154436 + 0.988003i \(0.549356\pi\)
\(678\) −9.62472 −0.369635
\(679\) −11.5622 −0.443718
\(680\) 30.5086 1.16995
\(681\) 20.0458 0.768157
\(682\) 36.8445 1.41085
\(683\) 25.7364 0.984775 0.492387 0.870376i \(-0.336124\pi\)
0.492387 + 0.870376i \(0.336124\pi\)
\(684\) 0.565076 0.0216062
\(685\) −56.8809 −2.17331
\(686\) 46.8687 1.78945
\(687\) −14.0287 −0.535227
\(688\) 3.62125 0.138059
\(689\) 23.0060 0.876458
\(690\) 32.1233 1.22291
\(691\) 29.2401 1.11234 0.556172 0.831067i \(-0.312269\pi\)
0.556172 + 0.831067i \(0.312269\pi\)
\(692\) −67.9607 −2.58348
\(693\) −4.30541 −0.163549
\(694\) −50.3719 −1.91209
\(695\) 70.4734 2.67321
\(696\) 11.6290 0.440796
\(697\) −16.2199 −0.614371
\(698\) 73.6687 2.78840
\(699\) −6.03502 −0.228266
\(700\) 86.8801 3.28376
\(701\) 35.0950 1.32552 0.662760 0.748832i \(-0.269385\pi\)
0.662760 + 0.748832i \(0.269385\pi\)
\(702\) −7.59765 −0.286755
\(703\) 0.870751 0.0328410
\(704\) 26.1821 0.986775
\(705\) −53.7073 −2.02273
\(706\) −42.7673 −1.60957
\(707\) −36.2022 −1.36152
\(708\) 4.34671 0.163359
\(709\) 25.7782 0.968119 0.484059 0.875035i \(-0.339162\pi\)
0.484059 + 0.875035i \(0.339162\pi\)
\(710\) −132.986 −4.99088
\(711\) −5.27964 −0.198002
\(712\) 10.9763 0.411354
\(713\) −24.0025 −0.898902
\(714\) 9.81538 0.367331
\(715\) −29.1251 −1.08922
\(716\) −21.7100 −0.811341
\(717\) 13.7450 0.513315
\(718\) 77.9124 2.90767
\(719\) −40.9383 −1.52674 −0.763371 0.645960i \(-0.776457\pi\)
−0.763371 + 0.645960i \(0.776457\pi\)
\(720\) 5.00940 0.186689
\(721\) 7.74768 0.288539
\(722\) 44.4566 1.65450
\(723\) 17.4079 0.647408
\(724\) 22.1728 0.824045
\(725\) −41.4310 −1.53871
\(726\) 14.9332 0.554222
\(727\) −48.2040 −1.78779 −0.893894 0.448278i \(-0.852038\pi\)
−0.893894 + 0.448278i \(0.852038\pi\)
\(728\) −22.6579 −0.839759
\(729\) 1.00000 0.0370370
\(730\) −77.8674 −2.88200
\(731\) −6.31762 −0.233666
\(732\) −12.2894 −0.454230
\(733\) 14.2607 0.526729 0.263365 0.964696i \(-0.415168\pi\)
0.263365 + 0.964696i \(0.415168\pi\)
\(734\) 17.1982 0.634798
\(735\) −12.5002 −0.461078
\(736\) −13.6945 −0.504786
\(737\) 25.7119 0.947109
\(738\) −18.1588 −0.668435
\(739\) −30.8515 −1.13489 −0.567446 0.823411i \(-0.692068\pi\)
−0.567446 + 0.823411i \(0.692068\pi\)
\(740\) 78.3707 2.88096
\(741\) 0.525037 0.0192877
\(742\) −33.2743 −1.22154
\(743\) 0.347632 0.0127534 0.00637670 0.999980i \(-0.497970\pi\)
0.00637670 + 0.999980i \(0.497970\pi\)
\(744\) −25.5211 −0.935648
\(745\) −59.1692 −2.16779
\(746\) −31.6154 −1.15752
\(747\) 16.0761 0.588192
\(748\) 15.7104 0.574430
\(749\) −1.81705 −0.0663936
\(750\) −72.7668 −2.65707
\(751\) 34.6914 1.26591 0.632954 0.774189i \(-0.281842\pi\)
0.632954 + 0.774189i \(0.281842\pi\)
\(752\) −15.4291 −0.562643
\(753\) 15.0873 0.549811
\(754\) 25.3093 0.921711
\(755\) 93.5000 3.40281
\(756\) 6.98548 0.254059
\(757\) 14.3258 0.520681 0.260341 0.965517i \(-0.416165\pi\)
0.260341 + 0.965517i \(0.416165\pi\)
\(758\) −26.1535 −0.949937
\(759\) 7.06206 0.256337
\(760\) −2.36033 −0.0856182
\(761\) −4.56190 −0.165369 −0.0826843 0.996576i \(-0.526349\pi\)
−0.0826843 + 0.996576i \(0.526349\pi\)
\(762\) −17.2215 −0.623869
\(763\) 4.69112 0.169830
\(764\) 2.58839 0.0936448
\(765\) −8.73939 −0.315973
\(766\) 60.1494 2.17329
\(767\) 4.03871 0.145830
\(768\) −22.9341 −0.827562
\(769\) −8.83896 −0.318741 −0.159371 0.987219i \(-0.550946\pi\)
−0.159371 + 0.987219i \(0.550946\pi\)
\(770\) 42.1246 1.51807
\(771\) 18.0086 0.648563
\(772\) −51.1807 −1.84203
\(773\) −7.30977 −0.262914 −0.131457 0.991322i \(-0.541966\pi\)
−0.131457 + 0.991322i \(0.541966\pi\)
\(774\) −7.07283 −0.254228
\(775\) 90.9247 3.26611
\(776\) 20.1651 0.723885
\(777\) 10.7642 0.386165
\(778\) 56.1390 2.01268
\(779\) 1.25487 0.0449603
\(780\) 47.2552 1.69201
\(781\) −29.2359 −1.04614
\(782\) −16.0999 −0.575733
\(783\) −3.33120 −0.119048
\(784\) −3.59109 −0.128253
\(785\) 50.4075 1.79912
\(786\) −44.3099 −1.58048
\(787\) 10.1260 0.360953 0.180477 0.983579i \(-0.442236\pi\)
0.180477 + 0.983579i \(0.442236\pi\)
\(788\) −69.0894 −2.46121
\(789\) −13.5515 −0.482445
\(790\) 51.6566 1.83786
\(791\) 8.22221 0.292348
\(792\) 7.50885 0.266815
\(793\) −11.4186 −0.405488
\(794\) 19.5681 0.694447
\(795\) 29.6267 1.05075
\(796\) 81.0773 2.87371
\(797\) −27.1299 −0.960991 −0.480496 0.876997i \(-0.659543\pi\)
−0.480496 + 0.876997i \(0.659543\pi\)
\(798\) −0.759378 −0.0268817
\(799\) 26.9176 0.952277
\(800\) 51.8765 1.83411
\(801\) −3.14423 −0.111096
\(802\) −27.8383 −0.983005
\(803\) −17.1185 −0.604100
\(804\) −41.7172 −1.47125
\(805\) −27.4423 −0.967215
\(806\) −55.5439 −1.95645
\(807\) 3.20506 0.112823
\(808\) 63.1384 2.22120
\(809\) 8.66266 0.304563 0.152281 0.988337i \(-0.451338\pi\)
0.152281 + 0.988337i \(0.451338\pi\)
\(810\) −9.78411 −0.343779
\(811\) −45.8484 −1.60996 −0.804978 0.593305i \(-0.797823\pi\)
−0.804978 + 0.593305i \(0.797823\pi\)
\(812\) −23.2701 −0.816619
\(813\) 11.9387 0.418708
\(814\) 27.1029 0.949956
\(815\) 8.84832 0.309943
\(816\) −2.51067 −0.0878910
\(817\) 0.488769 0.0170999
\(818\) −32.0607 −1.12098
\(819\) 6.49052 0.226797
\(820\) 112.943 3.94412
\(821\) 12.8012 0.446764 0.223382 0.974731i \(-0.428290\pi\)
0.223382 + 0.974731i \(0.428290\pi\)
\(822\) 31.9161 1.11320
\(823\) −29.0836 −1.01379 −0.506895 0.862008i \(-0.669207\pi\)
−0.506895 + 0.862008i \(0.669207\pi\)
\(824\) −13.5123 −0.470724
\(825\) −26.7520 −0.931385
\(826\) −5.84133 −0.203246
\(827\) 29.7931 1.03601 0.518004 0.855378i \(-0.326675\pi\)
0.518004 + 0.855378i \(0.326675\pi\)
\(828\) −11.4581 −0.398197
\(829\) −44.2010 −1.53516 −0.767582 0.640950i \(-0.778540\pi\)
−0.767582 + 0.640950i \(0.778540\pi\)
\(830\) −157.290 −5.45961
\(831\) 19.9194 0.690996
\(832\) −39.4702 −1.36838
\(833\) 6.26501 0.217070
\(834\) −39.5429 −1.36926
\(835\) −1.35186 −0.0467829
\(836\) −1.21545 −0.0420374
\(837\) 7.31068 0.252694
\(838\) 23.1563 0.799920
\(839\) −44.8866 −1.54966 −0.774829 0.632171i \(-0.782164\pi\)
−0.774829 + 0.632171i \(0.782164\pi\)
\(840\) −29.1785 −1.00675
\(841\) −17.9031 −0.617347
\(842\) 50.3147 1.73396
\(843\) −13.9582 −0.480747
\(844\) 78.2751 2.69434
\(845\) −10.3785 −0.357030
\(846\) 30.1354 1.03608
\(847\) −12.7571 −0.438339
\(848\) 8.51121 0.292276
\(849\) 26.5983 0.912850
\(850\) 60.9886 2.09189
\(851\) −17.6563 −0.605251
\(852\) 47.4349 1.62509
\(853\) 53.1256 1.81899 0.909493 0.415719i \(-0.136470\pi\)
0.909493 + 0.415719i \(0.136470\pi\)
\(854\) 16.5152 0.565137
\(855\) 0.676132 0.0231232
\(856\) 3.16903 0.108315
\(857\) −7.15186 −0.244303 −0.122151 0.992511i \(-0.538979\pi\)
−0.122151 + 0.992511i \(0.538979\pi\)
\(858\) 16.3422 0.557914
\(859\) 7.91071 0.269910 0.134955 0.990852i \(-0.456911\pi\)
0.134955 + 0.990852i \(0.456911\pi\)
\(860\) 43.9910 1.50008
\(861\) 15.5127 0.528672
\(862\) −61.7267 −2.10242
\(863\) 5.88977 0.200490 0.100245 0.994963i \(-0.468037\pi\)
0.100245 + 0.994963i \(0.468037\pi\)
\(864\) 4.17106 0.141902
\(865\) −81.3173 −2.76487
\(866\) 2.54390 0.0864452
\(867\) −12.6199 −0.428594
\(868\) 51.0686 1.73338
\(869\) 11.3563 0.385236
\(870\) 32.5929 1.10500
\(871\) −38.7613 −1.31338
\(872\) −8.18155 −0.277062
\(873\) −5.77643 −0.195502
\(874\) 1.24559 0.0421327
\(875\) 62.1632 2.10150
\(876\) 27.7746 0.938417
\(877\) −11.0507 −0.373157 −0.186578 0.982440i \(-0.559740\pi\)
−0.186578 + 0.982440i \(0.559740\pi\)
\(878\) 61.7072 2.08252
\(879\) −28.1611 −0.949849
\(880\) −10.7750 −0.363226
\(881\) 3.42535 0.115403 0.0577015 0.998334i \(-0.481623\pi\)
0.0577015 + 0.998334i \(0.481623\pi\)
\(882\) 7.01394 0.236172
\(883\) −30.7828 −1.03592 −0.517962 0.855404i \(-0.673309\pi\)
−0.517962 + 0.855404i \(0.673309\pi\)
\(884\) −23.6839 −0.796575
\(885\) 5.20098 0.174829
\(886\) 80.6464 2.70937
\(887\) 24.2927 0.815670 0.407835 0.913056i \(-0.366284\pi\)
0.407835 + 0.913056i \(0.366284\pi\)
\(888\) −18.7734 −0.629993
\(889\) 14.7120 0.493424
\(890\) 30.7635 1.03120
\(891\) −2.15096 −0.0720598
\(892\) 65.8616 2.20521
\(893\) −2.08251 −0.0696886
\(894\) 33.2001 1.11038
\(895\) −25.9768 −0.868308
\(896\) 40.3892 1.34931
\(897\) −10.6462 −0.355468
\(898\) −7.40201 −0.247008
\(899\) −24.3534 −0.812230
\(900\) 43.4048 1.44683
\(901\) −14.8486 −0.494680
\(902\) 39.0589 1.30052
\(903\) 6.04218 0.201071
\(904\) −14.3399 −0.476939
\(905\) 26.5305 0.881904
\(906\) −52.4632 −1.74297
\(907\) −49.4068 −1.64053 −0.820263 0.571986i \(-0.806173\pi\)
−0.820263 + 0.571986i \(0.806173\pi\)
\(908\) 69.9580 2.32164
\(909\) −18.0864 −0.599888
\(910\) −63.5039 −2.10513
\(911\) 25.2011 0.834951 0.417475 0.908688i \(-0.362915\pi\)
0.417475 + 0.908688i \(0.362915\pi\)
\(912\) 0.194241 0.00643195
\(913\) −34.5789 −1.14440
\(914\) −64.1144 −2.12072
\(915\) −14.7047 −0.486123
\(916\) −48.9587 −1.61764
\(917\) 37.8531 1.25002
\(918\) 4.90371 0.161847
\(919\) −26.7094 −0.881062 −0.440531 0.897737i \(-0.645210\pi\)
−0.440531 + 0.897737i \(0.645210\pi\)
\(920\) 47.8607 1.57792
\(921\) −8.94615 −0.294786
\(922\) 1.86603 0.0614543
\(923\) 44.0739 1.45071
\(924\) −15.0255 −0.494302
\(925\) 66.8844 2.19915
\(926\) 79.9649 2.62781
\(927\) 3.87069 0.127130
\(928\) −13.8947 −0.456115
\(929\) −2.52027 −0.0826873 −0.0413436 0.999145i \(-0.513164\pi\)
−0.0413436 + 0.999145i \(0.513164\pi\)
\(930\) −71.5285 −2.34551
\(931\) −0.484699 −0.0158854
\(932\) −21.0617 −0.689898
\(933\) 2.30852 0.0755776
\(934\) 67.7902 2.21816
\(935\) 18.7981 0.614763
\(936\) −11.3198 −0.369998
\(937\) 24.5539 0.802140 0.401070 0.916047i \(-0.368638\pi\)
0.401070 + 0.916047i \(0.368638\pi\)
\(938\) 56.0617 1.83048
\(939\) −3.94664 −0.128794
\(940\) −187.433 −6.11340
\(941\) −10.2010 −0.332544 −0.166272 0.986080i \(-0.553173\pi\)
−0.166272 + 0.986080i \(0.553173\pi\)
\(942\) −28.2839 −0.921539
\(943\) −25.4451 −0.828607
\(944\) 1.49415 0.0486304
\(945\) 8.35837 0.271898
\(946\) 15.2134 0.494629
\(947\) −24.1383 −0.784389 −0.392194 0.919882i \(-0.628284\pi\)
−0.392194 + 0.919882i \(0.628284\pi\)
\(948\) −18.4254 −0.598430
\(949\) 25.8066 0.837718
\(950\) −4.71845 −0.153087
\(951\) −3.70170 −0.120036
\(952\) 14.6240 0.473966
\(953\) −52.8188 −1.71097 −0.855485 0.517828i \(-0.826741\pi\)
−0.855485 + 0.517828i \(0.826741\pi\)
\(954\) −16.6237 −0.538211
\(955\) 3.09710 0.100220
\(956\) 47.9686 1.55142
\(957\) 7.16529 0.231621
\(958\) 79.2689 2.56106
\(959\) −27.2653 −0.880442
\(960\) −50.8289 −1.64050
\(961\) 22.4460 0.724065
\(962\) −40.8583 −1.31732
\(963\) −0.907788 −0.0292531
\(964\) 60.7520 1.95669
\(965\) −61.2394 −1.97137
\(966\) 15.3980 0.495423
\(967\) 55.0774 1.77117 0.885584 0.464479i \(-0.153758\pi\)
0.885584 + 0.464479i \(0.153758\pi\)
\(968\) 22.2490 0.715110
\(969\) −0.338872 −0.0108861
\(970\) 56.5172 1.81466
\(971\) 31.3003 1.00447 0.502237 0.864730i \(-0.332510\pi\)
0.502237 + 0.864730i \(0.332510\pi\)
\(972\) 3.48991 0.111939
\(973\) 33.7807 1.08296
\(974\) 63.3271 2.02913
\(975\) 40.3293 1.29157
\(976\) −4.22440 −0.135220
\(977\) 13.2080 0.422563 0.211281 0.977425i \(-0.432236\pi\)
0.211281 + 0.977425i \(0.432236\pi\)
\(978\) −4.96483 −0.158758
\(979\) 6.76311 0.216150
\(980\) −43.6247 −1.39354
\(981\) 2.34366 0.0748273
\(982\) −14.2776 −0.455616
\(983\) −58.8611 −1.87738 −0.938689 0.344765i \(-0.887959\pi\)
−0.938689 + 0.344765i \(0.887959\pi\)
\(984\) −27.0549 −0.862479
\(985\) −82.6679 −2.63402
\(986\) −16.3353 −0.520221
\(987\) −25.7441 −0.819442
\(988\) 1.83233 0.0582941
\(989\) −9.91084 −0.315146
\(990\) 21.0452 0.668861
\(991\) −36.5107 −1.15980 −0.579901 0.814687i \(-0.696909\pi\)
−0.579901 + 0.814687i \(0.696909\pi\)
\(992\) 30.4933 0.968163
\(993\) −0.559387 −0.0177516
\(994\) −63.7455 −2.02189
\(995\) 97.0118 3.07548
\(996\) 56.1039 1.77772
\(997\) −14.6469 −0.463872 −0.231936 0.972731i \(-0.574506\pi\)
−0.231936 + 0.972731i \(0.574506\pi\)
\(998\) 41.9696 1.32852
\(999\) 5.37776 0.170145
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 \(a_p\))