Properties

Label 6026.2.a.h.1.3
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 24
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: \(24\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.99000 q^{3}\) \(+1.00000 q^{4}\) \(-3.60098 q^{5}\) \(+2.99000 q^{6}\) \(+0.0770196 q^{7}\) \(-1.00000 q^{8}\) \(+5.94012 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.99000 q^{3}\) \(+1.00000 q^{4}\) \(-3.60098 q^{5}\) \(+2.99000 q^{6}\) \(+0.0770196 q^{7}\) \(-1.00000 q^{8}\) \(+5.94012 q^{9}\) \(+3.60098 q^{10}\) \(-3.44726 q^{11}\) \(-2.99000 q^{12}\) \(-1.64024 q^{13}\) \(-0.0770196 q^{14}\) \(+10.7669 q^{15}\) \(+1.00000 q^{16}\) \(+1.47240 q^{17}\) \(-5.94012 q^{18}\) \(-4.21923 q^{19}\) \(-3.60098 q^{20}\) \(-0.230289 q^{21}\) \(+3.44726 q^{22}\) \(-1.00000 q^{23}\) \(+2.99000 q^{24}\) \(+7.96704 q^{25}\) \(+1.64024 q^{26}\) \(-8.79097 q^{27}\) \(+0.0770196 q^{28}\) \(+1.09731 q^{29}\) \(-10.7669 q^{30}\) \(-7.91422 q^{31}\) \(-1.00000 q^{32}\) \(+10.3073 q^{33}\) \(-1.47240 q^{34}\) \(-0.277346 q^{35}\) \(+5.94012 q^{36}\) \(-5.70246 q^{37}\) \(+4.21923 q^{38}\) \(+4.90432 q^{39}\) \(+3.60098 q^{40}\) \(+4.71846 q^{41}\) \(+0.230289 q^{42}\) \(-7.51355 q^{43}\) \(-3.44726 q^{44}\) \(-21.3902 q^{45}\) \(+1.00000 q^{46}\) \(+12.4554 q^{47}\) \(-2.99000 q^{48}\) \(-6.99407 q^{49}\) \(-7.96704 q^{50}\) \(-4.40248 q^{51}\) \(-1.64024 q^{52}\) \(+3.15448 q^{53}\) \(+8.79097 q^{54}\) \(+12.4135 q^{55}\) \(-0.0770196 q^{56}\) \(+12.6155 q^{57}\) \(-1.09731 q^{58}\) \(+6.93982 q^{59}\) \(+10.7669 q^{60}\) \(+1.16148 q^{61}\) \(+7.91422 q^{62}\) \(+0.457506 q^{63}\) \(+1.00000 q^{64}\) \(+5.90646 q^{65}\) \(-10.3073 q^{66}\) \(-7.07056 q^{67}\) \(+1.47240 q^{68}\) \(+2.99000 q^{69}\) \(+0.277346 q^{70}\) \(-11.7341 q^{71}\) \(-5.94012 q^{72}\) \(+11.7419 q^{73}\) \(+5.70246 q^{74}\) \(-23.8215 q^{75}\) \(-4.21923 q^{76}\) \(-0.265506 q^{77}\) \(-4.90432 q^{78}\) \(+9.37314 q^{79}\) \(-3.60098 q^{80}\) \(+8.46468 q^{81}\) \(-4.71846 q^{82}\) \(-1.82659 q^{83}\) \(-0.230289 q^{84}\) \(-5.30207 q^{85}\) \(+7.51355 q^{86}\) \(-3.28097 q^{87}\) \(+3.44726 q^{88}\) \(-5.14553 q^{89}\) \(+21.3902 q^{90}\) \(-0.126330 q^{91}\) \(-1.00000 q^{92}\) \(+23.6635 q^{93}\) \(-12.4554 q^{94}\) \(+15.1933 q^{95}\) \(+2.99000 q^{96}\) \(+9.78642 q^{97}\) \(+6.99407 q^{98}\) \(-20.4771 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 27q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 39q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 13q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 21q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut +\mathstrut 7q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut +\mathstrut 23q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 29q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 17q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 36q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 39q^{78} \) \(\mathstrut -\mathstrut 53q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 37q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 7q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut +\mathstrut 13q^{90} \) \(\mathstrut -\mathstrut 44q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 23q^{93} \) \(\mathstrut -\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 13q^{98} \) \(\mathstrut -\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.99000 −1.72628 −0.863140 0.504965i \(-0.831505\pi\)
−0.863140 + 0.504965i \(0.831505\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.60098 −1.61041 −0.805203 0.592999i \(-0.797944\pi\)
−0.805203 + 0.592999i \(0.797944\pi\)
\(6\) 2.99000 1.22066
\(7\) 0.0770196 0.0291107 0.0145553 0.999894i \(-0.495367\pi\)
0.0145553 + 0.999894i \(0.495367\pi\)
\(8\) −1.00000 −0.353553
\(9\) 5.94012 1.98004
\(10\) 3.60098 1.13873
\(11\) −3.44726 −1.03939 −0.519693 0.854353i \(-0.673954\pi\)
−0.519693 + 0.854353i \(0.673954\pi\)
\(12\) −2.99000 −0.863140
\(13\) −1.64024 −0.454920 −0.227460 0.973787i \(-0.573042\pi\)
−0.227460 + 0.973787i \(0.573042\pi\)
\(14\) −0.0770196 −0.0205844
\(15\) 10.7669 2.78001
\(16\) 1.00000 0.250000
\(17\) 1.47240 0.357109 0.178554 0.983930i \(-0.442858\pi\)
0.178554 + 0.983930i \(0.442858\pi\)
\(18\) −5.94012 −1.40010
\(19\) −4.21923 −0.967957 −0.483978 0.875080i \(-0.660809\pi\)
−0.483978 + 0.875080i \(0.660809\pi\)
\(20\) −3.60098 −0.805203
\(21\) −0.230289 −0.0502531
\(22\) 3.44726 0.734958
\(23\) −1.00000 −0.208514
\(24\) 2.99000 0.610332
\(25\) 7.96704 1.59341
\(26\) 1.64024 0.321677
\(27\) −8.79097 −1.69182
\(28\) 0.0770196 0.0145553
\(29\) 1.09731 0.203766 0.101883 0.994796i \(-0.467513\pi\)
0.101883 + 0.994796i \(0.467513\pi\)
\(30\) −10.7669 −1.96576
\(31\) −7.91422 −1.42144 −0.710718 0.703477i \(-0.751630\pi\)
−0.710718 + 0.703477i \(0.751630\pi\)
\(32\) −1.00000 −0.176777
\(33\) 10.3073 1.79427
\(34\) −1.47240 −0.252514
\(35\) −0.277346 −0.0468800
\(36\) 5.94012 0.990020
\(37\) −5.70246 −0.937479 −0.468740 0.883336i \(-0.655292\pi\)
−0.468740 + 0.883336i \(0.655292\pi\)
\(38\) 4.21923 0.684449
\(39\) 4.90432 0.785319
\(40\) 3.60098 0.569364
\(41\) 4.71846 0.736900 0.368450 0.929648i \(-0.379889\pi\)
0.368450 + 0.929648i \(0.379889\pi\)
\(42\) 0.230289 0.0355343
\(43\) −7.51355 −1.14581 −0.572903 0.819623i \(-0.694183\pi\)
−0.572903 + 0.819623i \(0.694183\pi\)
\(44\) −3.44726 −0.519693
\(45\) −21.3902 −3.18867
\(46\) 1.00000 0.147442
\(47\) 12.4554 1.81680 0.908401 0.418099i \(-0.137304\pi\)
0.908401 + 0.418099i \(0.137304\pi\)
\(48\) −2.99000 −0.431570
\(49\) −6.99407 −0.999153
\(50\) −7.96704 −1.12671
\(51\) −4.40248 −0.616470
\(52\) −1.64024 −0.227460
\(53\) 3.15448 0.433301 0.216650 0.976249i \(-0.430487\pi\)
0.216650 + 0.976249i \(0.430487\pi\)
\(54\) 8.79097 1.19630
\(55\) 12.4135 1.67383
\(56\) −0.0770196 −0.0102922
\(57\) 12.6155 1.67096
\(58\) −1.09731 −0.144084
\(59\) 6.93982 0.903488 0.451744 0.892148i \(-0.350802\pi\)
0.451744 + 0.892148i \(0.350802\pi\)
\(60\) 10.7669 1.39001
\(61\) 1.16148 0.148712 0.0743562 0.997232i \(-0.476310\pi\)
0.0743562 + 0.997232i \(0.476310\pi\)
\(62\) 7.91422 1.00511
\(63\) 0.457506 0.0576403
\(64\) 1.00000 0.125000
\(65\) 5.90646 0.732606
\(66\) −10.3073 −1.26874
\(67\) −7.07056 −0.863807 −0.431903 0.901920i \(-0.642158\pi\)
−0.431903 + 0.901920i \(0.642158\pi\)
\(68\) 1.47240 0.178554
\(69\) 2.99000 0.359954
\(70\) 0.277346 0.0331492
\(71\) −11.7341 −1.39258 −0.696288 0.717762i \(-0.745166\pi\)
−0.696288 + 0.717762i \(0.745166\pi\)
\(72\) −5.94012 −0.700050
\(73\) 11.7419 1.37428 0.687142 0.726523i \(-0.258865\pi\)
0.687142 + 0.726523i \(0.258865\pi\)
\(74\) 5.70246 0.662898
\(75\) −23.8215 −2.75067
\(76\) −4.21923 −0.483978
\(77\) −0.265506 −0.0302573
\(78\) −4.90432 −0.555304
\(79\) 9.37314 1.05456 0.527280 0.849691i \(-0.323212\pi\)
0.527280 + 0.849691i \(0.323212\pi\)
\(80\) −3.60098 −0.402601
\(81\) 8.46468 0.940520
\(82\) −4.71846 −0.521067
\(83\) −1.82659 −0.200494 −0.100247 0.994963i \(-0.531963\pi\)
−0.100247 + 0.994963i \(0.531963\pi\)
\(84\) −0.230289 −0.0251266
\(85\) −5.30207 −0.575090
\(86\) 7.51355 0.810207
\(87\) −3.28097 −0.351757
\(88\) 3.44726 0.367479
\(89\) −5.14553 −0.545425 −0.272712 0.962096i \(-0.587921\pi\)
−0.272712 + 0.962096i \(0.587921\pi\)
\(90\) 21.3902 2.25473
\(91\) −0.126330 −0.0132430
\(92\) −1.00000 −0.104257
\(93\) 23.6635 2.45379
\(94\) −12.4554 −1.28467
\(95\) 15.1933 1.55880
\(96\) 2.99000 0.305166
\(97\) 9.78642 0.993660 0.496830 0.867848i \(-0.334497\pi\)
0.496830 + 0.867848i \(0.334497\pi\)
\(98\) 6.99407 0.706508
\(99\) −20.4771 −2.05803
\(100\) 7.96704 0.796704
\(101\) 16.9790 1.68947 0.844734 0.535186i \(-0.179758\pi\)
0.844734 + 0.535186i \(0.179758\pi\)
\(102\) 4.40248 0.435910
\(103\) 4.64990 0.458169 0.229084 0.973407i \(-0.426427\pi\)
0.229084 + 0.973407i \(0.426427\pi\)
\(104\) 1.64024 0.160838
\(105\) 0.829265 0.0809280
\(106\) −3.15448 −0.306390
\(107\) 3.22063 0.311350 0.155675 0.987808i \(-0.450245\pi\)
0.155675 + 0.987808i \(0.450245\pi\)
\(108\) −8.79097 −0.845912
\(109\) 13.7492 1.31693 0.658465 0.752611i \(-0.271206\pi\)
0.658465 + 0.752611i \(0.271206\pi\)
\(110\) −12.4135 −1.18358
\(111\) 17.0504 1.61835
\(112\) 0.0770196 0.00727767
\(113\) 12.9767 1.22074 0.610371 0.792116i \(-0.291020\pi\)
0.610371 + 0.792116i \(0.291020\pi\)
\(114\) −12.6155 −1.18155
\(115\) 3.60098 0.335793
\(116\) 1.09731 0.101883
\(117\) −9.74321 −0.900760
\(118\) −6.93982 −0.638862
\(119\) 0.113403 0.0103957
\(120\) −10.7669 −0.982882
\(121\) 0.883578 0.0803253
\(122\) −1.16148 −0.105155
\(123\) −14.1082 −1.27209
\(124\) −7.91422 −0.710718
\(125\) −10.6842 −0.955626
\(126\) −0.457506 −0.0407578
\(127\) −9.74780 −0.864977 −0.432489 0.901639i \(-0.642364\pi\)
−0.432489 + 0.901639i \(0.642364\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 22.4656 1.97798
\(130\) −5.90646 −0.518031
\(131\) −1.00000 −0.0873704
\(132\) 10.3073 0.897136
\(133\) −0.324963 −0.0281779
\(134\) 7.07056 0.610804
\(135\) 31.6561 2.72452
\(136\) −1.47240 −0.126257
\(137\) −1.83693 −0.156939 −0.0784696 0.996917i \(-0.525003\pi\)
−0.0784696 + 0.996917i \(0.525003\pi\)
\(138\) −2.99000 −0.254526
\(139\) 13.1562 1.11590 0.557948 0.829876i \(-0.311589\pi\)
0.557948 + 0.829876i \(0.311589\pi\)
\(140\) −0.277346 −0.0234400
\(141\) −37.2416 −3.13631
\(142\) 11.7341 0.984700
\(143\) 5.65432 0.472838
\(144\) 5.94012 0.495010
\(145\) −3.95140 −0.328146
\(146\) −11.7419 −0.971766
\(147\) 20.9123 1.72482
\(148\) −5.70246 −0.468740
\(149\) −9.49063 −0.777503 −0.388751 0.921343i \(-0.627094\pi\)
−0.388751 + 0.921343i \(0.627094\pi\)
\(150\) 23.8215 1.94501
\(151\) 9.18991 0.747864 0.373932 0.927456i \(-0.378009\pi\)
0.373932 + 0.927456i \(0.378009\pi\)
\(152\) 4.21923 0.342224
\(153\) 8.74622 0.707090
\(154\) 0.265506 0.0213951
\(155\) 28.4989 2.28909
\(156\) 4.90432 0.392659
\(157\) −4.04858 −0.323112 −0.161556 0.986864i \(-0.551651\pi\)
−0.161556 + 0.986864i \(0.551651\pi\)
\(158\) −9.37314 −0.745687
\(159\) −9.43190 −0.747998
\(160\) 3.60098 0.284682
\(161\) −0.0770196 −0.00606999
\(162\) −8.46468 −0.665048
\(163\) 10.8577 0.850439 0.425219 0.905090i \(-0.360197\pi\)
0.425219 + 0.905090i \(0.360197\pi\)
\(164\) 4.71846 0.368450
\(165\) −37.1164 −2.88951
\(166\) 1.82659 0.141771
\(167\) 8.96759 0.693933 0.346966 0.937878i \(-0.387212\pi\)
0.346966 + 0.937878i \(0.387212\pi\)
\(168\) 0.230289 0.0177672
\(169\) −10.3096 −0.793048
\(170\) 5.30207 0.406650
\(171\) −25.0627 −1.91659
\(172\) −7.51355 −0.572903
\(173\) 1.81878 0.138279 0.0691395 0.997607i \(-0.477975\pi\)
0.0691395 + 0.997607i \(0.477975\pi\)
\(174\) 3.28097 0.248730
\(175\) 0.613618 0.0463851
\(176\) −3.44726 −0.259847
\(177\) −20.7501 −1.55967
\(178\) 5.14553 0.385674
\(179\) 8.29213 0.619783 0.309892 0.950772i \(-0.399707\pi\)
0.309892 + 0.950772i \(0.399707\pi\)
\(180\) −21.3902 −1.59433
\(181\) 0.918978 0.0683071 0.0341536 0.999417i \(-0.489126\pi\)
0.0341536 + 0.999417i \(0.489126\pi\)
\(182\) 0.126330 0.00936423
\(183\) −3.47283 −0.256719
\(184\) 1.00000 0.0737210
\(185\) 20.5344 1.50972
\(186\) −23.6635 −1.73509
\(187\) −5.07573 −0.371174
\(188\) 12.4554 0.908401
\(189\) −0.677077 −0.0492501
\(190\) −15.1933 −1.10224
\(191\) 0.947662 0.0685704 0.0342852 0.999412i \(-0.489085\pi\)
0.0342852 + 0.999412i \(0.489085\pi\)
\(192\) −2.99000 −0.215785
\(193\) 8.03115 0.578095 0.289047 0.957315i \(-0.406661\pi\)
0.289047 + 0.957315i \(0.406661\pi\)
\(194\) −9.78642 −0.702624
\(195\) −17.6603 −1.26468
\(196\) −6.99407 −0.499576
\(197\) 19.3318 1.37733 0.688666 0.725079i \(-0.258197\pi\)
0.688666 + 0.725079i \(0.258197\pi\)
\(198\) 20.4771 1.45525
\(199\) −8.17427 −0.579459 −0.289729 0.957109i \(-0.593565\pi\)
−0.289729 + 0.957109i \(0.593565\pi\)
\(200\) −7.96704 −0.563355
\(201\) 21.1410 1.49117
\(202\) −16.9790 −1.19463
\(203\) 0.0845147 0.00593177
\(204\) −4.40248 −0.308235
\(205\) −16.9911 −1.18671
\(206\) −4.64990 −0.323974
\(207\) −5.94012 −0.412867
\(208\) −1.64024 −0.113730
\(209\) 14.5448 1.00608
\(210\) −0.829265 −0.0572247
\(211\) 1.06067 0.0730193 0.0365096 0.999333i \(-0.488376\pi\)
0.0365096 + 0.999333i \(0.488376\pi\)
\(212\) 3.15448 0.216650
\(213\) 35.0849 2.40398
\(214\) −3.22063 −0.220158
\(215\) 27.0561 1.84521
\(216\) 8.79097 0.598150
\(217\) −0.609550 −0.0413789
\(218\) −13.7492 −0.931210
\(219\) −35.1083 −2.37240
\(220\) 12.4135 0.836917
\(221\) −2.41508 −0.162456
\(222\) −17.0504 −1.14435
\(223\) 0.663109 0.0444051 0.0222025 0.999753i \(-0.492932\pi\)
0.0222025 + 0.999753i \(0.492932\pi\)
\(224\) −0.0770196 −0.00514609
\(225\) 47.3252 3.15501
\(226\) −12.9767 −0.863195
\(227\) 14.0558 0.932915 0.466457 0.884544i \(-0.345530\pi\)
0.466457 + 0.884544i \(0.345530\pi\)
\(228\) 12.6155 0.835482
\(229\) −24.7782 −1.63739 −0.818696 0.574227i \(-0.805303\pi\)
−0.818696 + 0.574227i \(0.805303\pi\)
\(230\) −3.60098 −0.237441
\(231\) 0.793865 0.0522325
\(232\) −1.09731 −0.0720422
\(233\) 30.1574 1.97568 0.987838 0.155488i \(-0.0496950\pi\)
0.987838 + 0.155488i \(0.0496950\pi\)
\(234\) 9.74321 0.636933
\(235\) −44.8515 −2.92579
\(236\) 6.93982 0.451744
\(237\) −28.0257 −1.82047
\(238\) −0.113403 −0.00735086
\(239\) −19.4110 −1.25560 −0.627798 0.778376i \(-0.716044\pi\)
−0.627798 + 0.778376i \(0.716044\pi\)
\(240\) 10.7669 0.695003
\(241\) −18.3537 −1.18227 −0.591133 0.806574i \(-0.701319\pi\)
−0.591133 + 0.806574i \(0.701319\pi\)
\(242\) −0.883578 −0.0567986
\(243\) 1.06351 0.0682239
\(244\) 1.16148 0.0743562
\(245\) 25.1855 1.60904
\(246\) 14.1082 0.899507
\(247\) 6.92053 0.440343
\(248\) 7.91422 0.502553
\(249\) 5.46151 0.346109
\(250\) 10.6842 0.675730
\(251\) 12.4385 0.785114 0.392557 0.919728i \(-0.371591\pi\)
0.392557 + 0.919728i \(0.371591\pi\)
\(252\) 0.457506 0.0288202
\(253\) 3.44726 0.216727
\(254\) 9.74780 0.611631
\(255\) 15.8532 0.992767
\(256\) 1.00000 0.0625000
\(257\) −2.45137 −0.152913 −0.0764563 0.997073i \(-0.524361\pi\)
−0.0764563 + 0.997073i \(0.524361\pi\)
\(258\) −22.4656 −1.39864
\(259\) −0.439201 −0.0272906
\(260\) 5.90646 0.366303
\(261\) 6.51818 0.403465
\(262\) 1.00000 0.0617802
\(263\) 0.617517 0.0380778 0.0190389 0.999819i \(-0.493939\pi\)
0.0190389 + 0.999819i \(0.493939\pi\)
\(264\) −10.3073 −0.634371
\(265\) −11.3592 −0.697790
\(266\) 0.324963 0.0199248
\(267\) 15.3851 0.941556
\(268\) −7.07056 −0.431903
\(269\) 1.11424 0.0679365 0.0339683 0.999423i \(-0.489185\pi\)
0.0339683 + 0.999423i \(0.489185\pi\)
\(270\) −31.6561 −1.92653
\(271\) 26.6667 1.61989 0.809944 0.586507i \(-0.199497\pi\)
0.809944 + 0.586507i \(0.199497\pi\)
\(272\) 1.47240 0.0892772
\(273\) 0.377728 0.0228612
\(274\) 1.83693 0.110973
\(275\) −27.4644 −1.65617
\(276\) 2.99000 0.179977
\(277\) −11.1258 −0.668482 −0.334241 0.942488i \(-0.608480\pi\)
−0.334241 + 0.942488i \(0.608480\pi\)
\(278\) −13.1562 −0.789058
\(279\) −47.0114 −2.81450
\(280\) 0.277346 0.0165746
\(281\) 16.7834 1.00121 0.500606 0.865675i \(-0.333111\pi\)
0.500606 + 0.865675i \(0.333111\pi\)
\(282\) 37.2416 2.21771
\(283\) −14.3100 −0.850641 −0.425321 0.905043i \(-0.639839\pi\)
−0.425321 + 0.905043i \(0.639839\pi\)
\(284\) −11.7341 −0.696288
\(285\) −45.4281 −2.69093
\(286\) −5.65432 −0.334347
\(287\) 0.363414 0.0214516
\(288\) −5.94012 −0.350025
\(289\) −14.8320 −0.872473
\(290\) 3.95140 0.232034
\(291\) −29.2614 −1.71534
\(292\) 11.7419 0.687142
\(293\) 0.942375 0.0550542 0.0275271 0.999621i \(-0.491237\pi\)
0.0275271 + 0.999621i \(0.491237\pi\)
\(294\) −20.9123 −1.21963
\(295\) −24.9901 −1.45498
\(296\) 5.70246 0.331449
\(297\) 30.3047 1.75846
\(298\) 9.49063 0.549778
\(299\) 1.64024 0.0948574
\(300\) −23.8215 −1.37533
\(301\) −0.578691 −0.0333552
\(302\) −9.18991 −0.528820
\(303\) −50.7671 −2.91649
\(304\) −4.21923 −0.241989
\(305\) −4.18246 −0.239487
\(306\) −8.74622 −0.499988
\(307\) −8.75562 −0.499710 −0.249855 0.968283i \(-0.580383\pi\)
−0.249855 + 0.968283i \(0.580383\pi\)
\(308\) −0.265506 −0.0151286
\(309\) −13.9032 −0.790927
\(310\) −28.4989 −1.61863
\(311\) −9.14464 −0.518545 −0.259272 0.965804i \(-0.583483\pi\)
−0.259272 + 0.965804i \(0.583483\pi\)
\(312\) −4.90432 −0.277652
\(313\) −12.0482 −0.681004 −0.340502 0.940244i \(-0.610597\pi\)
−0.340502 + 0.940244i \(0.610597\pi\)
\(314\) 4.04858 0.228475
\(315\) −1.64747 −0.0928243
\(316\) 9.37314 0.527280
\(317\) −12.7793 −0.717756 −0.358878 0.933384i \(-0.616841\pi\)
−0.358878 + 0.933384i \(0.616841\pi\)
\(318\) 9.43190 0.528915
\(319\) −3.78272 −0.211792
\(320\) −3.60098 −0.201301
\(321\) −9.62970 −0.537478
\(322\) 0.0770196 0.00429213
\(323\) −6.21238 −0.345666
\(324\) 8.46468 0.470260
\(325\) −13.0678 −0.724873
\(326\) −10.8577 −0.601351
\(327\) −41.1100 −2.27339
\(328\) −4.71846 −0.260533
\(329\) 0.959308 0.0528883
\(330\) 37.1164 2.04319
\(331\) −34.6205 −1.90291 −0.951456 0.307784i \(-0.900412\pi\)
−0.951456 + 0.307784i \(0.900412\pi\)
\(332\) −1.82659 −0.100247
\(333\) −33.8733 −1.85625
\(334\) −8.96759 −0.490685
\(335\) 25.4609 1.39108
\(336\) −0.230289 −0.0125633
\(337\) 15.6335 0.851614 0.425807 0.904814i \(-0.359990\pi\)
0.425807 + 0.904814i \(0.359990\pi\)
\(338\) 10.3096 0.560770
\(339\) −38.8003 −2.10734
\(340\) −5.30207 −0.287545
\(341\) 27.2823 1.47742
\(342\) 25.0627 1.35524
\(343\) −1.07782 −0.0581967
\(344\) 7.51355 0.405104
\(345\) −10.7669 −0.579672
\(346\) −1.81878 −0.0977780
\(347\) −7.02646 −0.377200 −0.188600 0.982054i \(-0.560395\pi\)
−0.188600 + 0.982054i \(0.560395\pi\)
\(348\) −3.28097 −0.175879
\(349\) 12.5396 0.671232 0.335616 0.941999i \(-0.391056\pi\)
0.335616 + 0.941999i \(0.391056\pi\)
\(350\) −0.613618 −0.0327993
\(351\) 14.4193 0.769644
\(352\) 3.44726 0.183739
\(353\) 10.6415 0.566392 0.283196 0.959062i \(-0.408605\pi\)
0.283196 + 0.959062i \(0.408605\pi\)
\(354\) 20.7501 1.10285
\(355\) 42.2541 2.24261
\(356\) −5.14553 −0.272712
\(357\) −0.339077 −0.0179459
\(358\) −8.29213 −0.438253
\(359\) 7.40017 0.390566 0.195283 0.980747i \(-0.437437\pi\)
0.195283 + 0.980747i \(0.437437\pi\)
\(360\) 21.3902 1.12736
\(361\) −1.19813 −0.0630596
\(362\) −0.918978 −0.0483004
\(363\) −2.64190 −0.138664
\(364\) −0.126330 −0.00662151
\(365\) −42.2823 −2.21316
\(366\) 3.47283 0.181528
\(367\) 22.4962 1.17429 0.587146 0.809481i \(-0.300252\pi\)
0.587146 + 0.809481i \(0.300252\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 28.0282 1.45909
\(370\) −20.5344 −1.06753
\(371\) 0.242957 0.0126137
\(372\) 23.6635 1.22690
\(373\) 26.6507 1.37992 0.689960 0.723847i \(-0.257628\pi\)
0.689960 + 0.723847i \(0.257628\pi\)
\(374\) 5.07573 0.262460
\(375\) 31.9459 1.64968
\(376\) −12.4554 −0.642337
\(377\) −1.79986 −0.0926973
\(378\) 0.677077 0.0348251
\(379\) −28.1563 −1.44629 −0.723145 0.690696i \(-0.757304\pi\)
−0.723145 + 0.690696i \(0.757304\pi\)
\(380\) 15.1933 0.779402
\(381\) 29.1460 1.49319
\(382\) −0.947662 −0.0484866
\(383\) −27.0559 −1.38249 −0.691245 0.722621i \(-0.742937\pi\)
−0.691245 + 0.722621i \(0.742937\pi\)
\(384\) 2.99000 0.152583
\(385\) 0.956082 0.0487265
\(386\) −8.03115 −0.408775
\(387\) −44.6314 −2.26874
\(388\) 9.78642 0.496830
\(389\) 19.6655 0.997081 0.498540 0.866867i \(-0.333870\pi\)
0.498540 + 0.866867i \(0.333870\pi\)
\(390\) 17.6603 0.894265
\(391\) −1.47240 −0.0744624
\(392\) 6.99407 0.353254
\(393\) 2.99000 0.150826
\(394\) −19.3318 −0.973920
\(395\) −33.7525 −1.69827
\(396\) −20.4771 −1.02901
\(397\) 22.1898 1.11367 0.556836 0.830622i \(-0.312015\pi\)
0.556836 + 0.830622i \(0.312015\pi\)
\(398\) 8.17427 0.409739
\(399\) 0.971641 0.0486429
\(400\) 7.96704 0.398352
\(401\) −9.10238 −0.454551 −0.227276 0.973830i \(-0.572982\pi\)
−0.227276 + 0.973830i \(0.572982\pi\)
\(402\) −21.1410 −1.05442
\(403\) 12.9812 0.646639
\(404\) 16.9790 0.844734
\(405\) −30.4811 −1.51462
\(406\) −0.0845147 −0.00419439
\(407\) 19.6579 0.974404
\(408\) 4.40248 0.217955
\(409\) 6.54110 0.323437 0.161718 0.986837i \(-0.448296\pi\)
0.161718 + 0.986837i \(0.448296\pi\)
\(410\) 16.9911 0.839129
\(411\) 5.49242 0.270921
\(412\) 4.64990 0.229084
\(413\) 0.534502 0.0263011
\(414\) 5.94012 0.291941
\(415\) 6.57751 0.322877
\(416\) 1.64024 0.0804192
\(417\) −39.3371 −1.92635
\(418\) −14.5448 −0.711407
\(419\) −28.3613 −1.38554 −0.692770 0.721158i \(-0.743610\pi\)
−0.692770 + 0.721158i \(0.743610\pi\)
\(420\) 0.829265 0.0404640
\(421\) −36.7888 −1.79298 −0.896489 0.443066i \(-0.853891\pi\)
−0.896489 + 0.443066i \(0.853891\pi\)
\(422\) −1.06067 −0.0516324
\(423\) 73.9864 3.59734
\(424\) −3.15448 −0.153195
\(425\) 11.7306 0.569020
\(426\) −35.0849 −1.69987
\(427\) 0.0894567 0.00432912
\(428\) 3.22063 0.155675
\(429\) −16.9064 −0.816250
\(430\) −27.0561 −1.30476
\(431\) −14.3946 −0.693363 −0.346681 0.937983i \(-0.612691\pi\)
−0.346681 + 0.937983i \(0.612691\pi\)
\(432\) −8.79097 −0.422956
\(433\) −28.1237 −1.35154 −0.675770 0.737113i \(-0.736189\pi\)
−0.675770 + 0.737113i \(0.736189\pi\)
\(434\) 0.609550 0.0292593
\(435\) 11.8147 0.566472
\(436\) 13.7492 0.658465
\(437\) 4.21923 0.201833
\(438\) 35.1083 1.67754
\(439\) 10.9517 0.522698 0.261349 0.965244i \(-0.415833\pi\)
0.261349 + 0.965244i \(0.415833\pi\)
\(440\) −12.4135 −0.591790
\(441\) −41.5456 −1.97836
\(442\) 2.41508 0.114874
\(443\) −31.2553 −1.48498 −0.742492 0.669855i \(-0.766356\pi\)
−0.742492 + 0.669855i \(0.766356\pi\)
\(444\) 17.0504 0.809175
\(445\) 18.5289 0.878355
\(446\) −0.663109 −0.0313991
\(447\) 28.3770 1.34219
\(448\) 0.0770196 0.00363883
\(449\) −1.86012 −0.0877846 −0.0438923 0.999036i \(-0.513976\pi\)
−0.0438923 + 0.999036i \(0.513976\pi\)
\(450\) −47.3252 −2.23093
\(451\) −16.2657 −0.765924
\(452\) 12.9767 0.610371
\(453\) −27.4779 −1.29102
\(454\) −14.0558 −0.659670
\(455\) 0.454913 0.0213266
\(456\) −12.6155 −0.590775
\(457\) −23.3474 −1.09214 −0.546072 0.837738i \(-0.683878\pi\)
−0.546072 + 0.837738i \(0.683878\pi\)
\(458\) 24.7782 1.15781
\(459\) −12.9438 −0.604165
\(460\) 3.60098 0.167896
\(461\) −34.9380 −1.62722 −0.813612 0.581408i \(-0.802502\pi\)
−0.813612 + 0.581408i \(0.802502\pi\)
\(462\) −0.793865 −0.0369339
\(463\) −14.4155 −0.669947 −0.334973 0.942228i \(-0.608727\pi\)
−0.334973 + 0.942228i \(0.608727\pi\)
\(464\) 1.09731 0.0509415
\(465\) −85.2119 −3.95161
\(466\) −30.1574 −1.39701
\(467\) −4.75470 −0.220021 −0.110011 0.993930i \(-0.535088\pi\)
−0.110011 + 0.993930i \(0.535088\pi\)
\(468\) −9.74321 −0.450380
\(469\) −0.544572 −0.0251460
\(470\) 44.8515 2.06885
\(471\) 12.1053 0.557782
\(472\) −6.93982 −0.319431
\(473\) 25.9012 1.19094
\(474\) 28.0257 1.28726
\(475\) −33.6147 −1.54235
\(476\) 0.113403 0.00519784
\(477\) 18.7380 0.857953
\(478\) 19.4110 0.887841
\(479\) 26.2639 1.20003 0.600015 0.799989i \(-0.295161\pi\)
0.600015 + 0.799989i \(0.295161\pi\)
\(480\) −10.7669 −0.491441
\(481\) 9.35339 0.426478
\(482\) 18.3537 0.835988
\(483\) 0.230289 0.0104785
\(484\) 0.883578 0.0401627
\(485\) −35.2407 −1.60020
\(486\) −1.06351 −0.0482416
\(487\) 5.11045 0.231576 0.115788 0.993274i \(-0.463061\pi\)
0.115788 + 0.993274i \(0.463061\pi\)
\(488\) −1.16148 −0.0525777
\(489\) −32.4645 −1.46809
\(490\) −25.1855 −1.13776
\(491\) −9.56913 −0.431849 −0.215924 0.976410i \(-0.569276\pi\)
−0.215924 + 0.976410i \(0.569276\pi\)
\(492\) −14.1082 −0.636047
\(493\) 1.61568 0.0727667
\(494\) −6.92053 −0.311369
\(495\) 73.7376 3.31426
\(496\) −7.91422 −0.355359
\(497\) −0.903752 −0.0405388
\(498\) −5.46151 −0.244736
\(499\) −32.1300 −1.43834 −0.719169 0.694835i \(-0.755477\pi\)
−0.719169 + 0.694835i \(0.755477\pi\)
\(500\) −10.6842 −0.477813
\(501\) −26.8131 −1.19792
\(502\) −12.4385 −0.555160
\(503\) −11.6372 −0.518878 −0.259439 0.965759i \(-0.583538\pi\)
−0.259439 + 0.965759i \(0.583538\pi\)
\(504\) −0.457506 −0.0203789
\(505\) −61.1408 −2.72073
\(506\) −3.44726 −0.153249
\(507\) 30.8258 1.36902
\(508\) −9.74780 −0.432489
\(509\) 12.6193 0.559339 0.279670 0.960096i \(-0.409775\pi\)
0.279670 + 0.960096i \(0.409775\pi\)
\(510\) −15.8532 −0.701992
\(511\) 0.904355 0.0400063
\(512\) −1.00000 −0.0441942
\(513\) 37.0911 1.63761
\(514\) 2.45137 0.108126
\(515\) −16.7442 −0.737837
\(516\) 22.4656 0.988991
\(517\) −42.9369 −1.88836
\(518\) 0.439201 0.0192974
\(519\) −5.43815 −0.238708
\(520\) −5.90646 −0.259015
\(521\) −18.3199 −0.802611 −0.401306 0.915944i \(-0.631443\pi\)
−0.401306 + 0.915944i \(0.631443\pi\)
\(522\) −6.51818 −0.285293
\(523\) 35.4819 1.55151 0.775757 0.631032i \(-0.217368\pi\)
0.775757 + 0.631032i \(0.217368\pi\)
\(524\) −1.00000 −0.0436852
\(525\) −1.83472 −0.0800737
\(526\) −0.617517 −0.0269250
\(527\) −11.6529 −0.507607
\(528\) 10.3073 0.448568
\(529\) 1.00000 0.0434783
\(530\) 11.3592 0.493412
\(531\) 41.2234 1.78894
\(532\) −0.324963 −0.0140889
\(533\) −7.73939 −0.335230
\(534\) −15.3851 −0.665780
\(535\) −11.5974 −0.501400
\(536\) 7.07056 0.305402
\(537\) −24.7935 −1.06992
\(538\) −1.11424 −0.0480384
\(539\) 24.1103 1.03851
\(540\) 31.6561 1.36226
\(541\) −6.96693 −0.299532 −0.149766 0.988722i \(-0.547852\pi\)
−0.149766 + 0.988722i \(0.547852\pi\)
\(542\) −26.6667 −1.14543
\(543\) −2.74775 −0.117917
\(544\) −1.47240 −0.0631285
\(545\) −49.5104 −2.12079
\(546\) −0.377728 −0.0161653
\(547\) 3.85875 0.164988 0.0824941 0.996592i \(-0.473711\pi\)
0.0824941 + 0.996592i \(0.473711\pi\)
\(548\) −1.83693 −0.0784696
\(549\) 6.89933 0.294456
\(550\) 27.4644 1.17109
\(551\) −4.62982 −0.197237
\(552\) −2.99000 −0.127263
\(553\) 0.721915 0.0306990
\(554\) 11.1258 0.472688
\(555\) −61.3980 −2.60620
\(556\) 13.1562 0.557948
\(557\) −38.1197 −1.61518 −0.807592 0.589742i \(-0.799230\pi\)
−0.807592 + 0.589742i \(0.799230\pi\)
\(558\) 47.0114 1.99015
\(559\) 12.3240 0.521250
\(560\) −0.277346 −0.0117200
\(561\) 15.1765 0.640751
\(562\) −16.7834 −0.707963
\(563\) 28.4896 1.20069 0.600346 0.799740i \(-0.295029\pi\)
0.600346 + 0.799740i \(0.295029\pi\)
\(564\) −37.2416 −1.56815
\(565\) −46.7287 −1.96589
\(566\) 14.3100 0.601494
\(567\) 0.651946 0.0273792
\(568\) 11.7341 0.492350
\(569\) 7.59471 0.318387 0.159193 0.987247i \(-0.449111\pi\)
0.159193 + 0.987247i \(0.449111\pi\)
\(570\) 45.4281 1.90277
\(571\) 30.2555 1.26615 0.633076 0.774090i \(-0.281792\pi\)
0.633076 + 0.774090i \(0.281792\pi\)
\(572\) 5.65432 0.236419
\(573\) −2.83351 −0.118372
\(574\) −0.363414 −0.0151686
\(575\) −7.96704 −0.332248
\(576\) 5.94012 0.247505
\(577\) 11.3262 0.471514 0.235757 0.971812i \(-0.424243\pi\)
0.235757 + 0.971812i \(0.424243\pi\)
\(578\) 14.8320 0.616932
\(579\) −24.0132 −0.997953
\(580\) −3.95140 −0.164073
\(581\) −0.140683 −0.00583652
\(582\) 29.2614 1.21293
\(583\) −10.8743 −0.450367
\(584\) −11.7419 −0.485883
\(585\) 35.0851 1.45059
\(586\) −0.942375 −0.0389292
\(587\) 11.5012 0.474705 0.237353 0.971424i \(-0.423720\pi\)
0.237353 + 0.971424i \(0.423720\pi\)
\(588\) 20.9123 0.862408
\(589\) 33.3919 1.37589
\(590\) 24.9901 1.02883
\(591\) −57.8020 −2.37766
\(592\) −5.70246 −0.234370
\(593\) 16.7957 0.689715 0.344858 0.938655i \(-0.387927\pi\)
0.344858 + 0.938655i \(0.387927\pi\)
\(594\) −30.3047 −1.24342
\(595\) −0.408363 −0.0167413
\(596\) −9.49063 −0.388751
\(597\) 24.4411 1.00031
\(598\) −1.64024 −0.0670743
\(599\) −8.67551 −0.354472 −0.177236 0.984168i \(-0.556716\pi\)
−0.177236 + 0.984168i \(0.556716\pi\)
\(600\) 23.8215 0.972507
\(601\) 43.6184 1.77923 0.889616 0.456710i \(-0.150972\pi\)
0.889616 + 0.456710i \(0.150972\pi\)
\(602\) 0.578691 0.0235857
\(603\) −42.0000 −1.71037
\(604\) 9.18991 0.373932
\(605\) −3.18175 −0.129356
\(606\) 50.7671 2.06227
\(607\) −28.0310 −1.13774 −0.568872 0.822426i \(-0.692620\pi\)
−0.568872 + 0.822426i \(0.692620\pi\)
\(608\) 4.21923 0.171112
\(609\) −0.252699 −0.0102399
\(610\) 4.18246 0.169343
\(611\) −20.4298 −0.826500
\(612\) 8.74622 0.353545
\(613\) 40.9667 1.65463 0.827315 0.561738i \(-0.189867\pi\)
0.827315 + 0.561738i \(0.189867\pi\)
\(614\) 8.75562 0.353348
\(615\) 50.8033 2.04859
\(616\) 0.265506 0.0106976
\(617\) 5.54719 0.223321 0.111661 0.993746i \(-0.464383\pi\)
0.111661 + 0.993746i \(0.464383\pi\)
\(618\) 13.9032 0.559270
\(619\) 23.8468 0.958485 0.479243 0.877682i \(-0.340911\pi\)
0.479243 + 0.877682i \(0.340911\pi\)
\(620\) 28.4989 1.14454
\(621\) 8.79097 0.352770
\(622\) 9.14464 0.366667
\(623\) −0.396306 −0.0158777
\(624\) 4.90432 0.196330
\(625\) −1.36152 −0.0544607
\(626\) 12.0482 0.481543
\(627\) −43.4889 −1.73678
\(628\) −4.04858 −0.161556
\(629\) −8.39630 −0.334782
\(630\) 1.64747 0.0656367
\(631\) −24.8882 −0.990783 −0.495392 0.868670i \(-0.664975\pi\)
−0.495392 + 0.868670i \(0.664975\pi\)
\(632\) −9.37314 −0.372844
\(633\) −3.17140 −0.126052
\(634\) 12.7793 0.507530
\(635\) 35.1016 1.39296
\(636\) −9.43190 −0.373999
\(637\) 11.4719 0.454534
\(638\) 3.78272 0.149759
\(639\) −69.7017 −2.75736
\(640\) 3.60098 0.142341
\(641\) 33.3289 1.31641 0.658206 0.752838i \(-0.271316\pi\)
0.658206 + 0.752838i \(0.271316\pi\)
\(642\) 9.62970 0.380054
\(643\) −5.29873 −0.208961 −0.104481 0.994527i \(-0.533318\pi\)
−0.104481 + 0.994527i \(0.533318\pi\)
\(644\) −0.0770196 −0.00303500
\(645\) −80.8979 −3.18535
\(646\) 6.21238 0.244423
\(647\) 24.4003 0.959276 0.479638 0.877466i \(-0.340768\pi\)
0.479638 + 0.877466i \(0.340768\pi\)
\(648\) −8.46468 −0.332524
\(649\) −23.9233 −0.939073
\(650\) 13.0678 0.512562
\(651\) 1.82256 0.0714316
\(652\) 10.8577 0.425219
\(653\) −1.86903 −0.0731407 −0.0365703 0.999331i \(-0.511643\pi\)
−0.0365703 + 0.999331i \(0.511643\pi\)
\(654\) 41.1100 1.60753
\(655\) 3.60098 0.140702
\(656\) 4.71846 0.184225
\(657\) 69.7482 2.72114
\(658\) −0.959308 −0.0373977
\(659\) −16.4831 −0.642089 −0.321044 0.947064i \(-0.604034\pi\)
−0.321044 + 0.947064i \(0.604034\pi\)
\(660\) −37.1164 −1.44475
\(661\) −10.2400 −0.398291 −0.199145 0.979970i \(-0.563817\pi\)
−0.199145 + 0.979970i \(0.563817\pi\)
\(662\) 34.6205 1.34556
\(663\) 7.22110 0.280444
\(664\) 1.82659 0.0708854
\(665\) 1.17018 0.0453778
\(666\) 33.8733 1.31256
\(667\) −1.09731 −0.0424882
\(668\) 8.96759 0.346966
\(669\) −1.98270 −0.0766555
\(670\) −25.4609 −0.983642
\(671\) −4.00392 −0.154570
\(672\) 0.230289 0.00888359
\(673\) 34.9902 1.34877 0.674387 0.738378i \(-0.264408\pi\)
0.674387 + 0.738378i \(0.264408\pi\)
\(674\) −15.6335 −0.602182
\(675\) −70.0380 −2.69576
\(676\) −10.3096 −0.396524
\(677\) 15.8005 0.607263 0.303632 0.952789i \(-0.401801\pi\)
0.303632 + 0.952789i \(0.401801\pi\)
\(678\) 38.8003 1.49012
\(679\) 0.753746 0.0289261
\(680\) 5.30207 0.203325
\(681\) −42.0268 −1.61047
\(682\) −27.2823 −1.04469
\(683\) 23.6768 0.905968 0.452984 0.891519i \(-0.350360\pi\)
0.452984 + 0.891519i \(0.350360\pi\)
\(684\) −25.0627 −0.958297
\(685\) 6.61473 0.252736
\(686\) 1.07782 0.0411513
\(687\) 74.0870 2.82660
\(688\) −7.51355 −0.286452
\(689\) −5.17409 −0.197117
\(690\) 10.7669 0.409890
\(691\) 23.0648 0.877426 0.438713 0.898627i \(-0.355435\pi\)
0.438713 + 0.898627i \(0.355435\pi\)
\(692\) 1.81878 0.0691395
\(693\) −1.57714 −0.0599106
\(694\) 7.02646 0.266721
\(695\) −47.3752 −1.79705
\(696\) 3.28097 0.124365
\(697\) 6.94745 0.263153
\(698\) −12.5396 −0.474633
\(699\) −90.1707 −3.41057
\(700\) 0.613618 0.0231926
\(701\) 39.0006 1.47303 0.736516 0.676420i \(-0.236469\pi\)
0.736516 + 0.676420i \(0.236469\pi\)
\(702\) −14.4193 −0.544221
\(703\) 24.0600 0.907439
\(704\) −3.44726 −0.129923
\(705\) 134.106 5.05073
\(706\) −10.6415 −0.400500
\(707\) 1.30771 0.0491816
\(708\) −20.7501 −0.779836
\(709\) −33.5908 −1.26153 −0.630764 0.775975i \(-0.717258\pi\)
−0.630764 + 0.775975i \(0.717258\pi\)
\(710\) −42.2541 −1.58577
\(711\) 55.6776 2.08807
\(712\) 5.14553 0.192837
\(713\) 7.91422 0.296390
\(714\) 0.339077 0.0126896
\(715\) −20.3611 −0.761461
\(716\) 8.29213 0.309892
\(717\) 58.0391 2.16751
\(718\) −7.40017 −0.276172
\(719\) −21.0588 −0.785361 −0.392681 0.919675i \(-0.628452\pi\)
−0.392681 + 0.919675i \(0.628452\pi\)
\(720\) −21.3902 −0.797167
\(721\) 0.358134 0.0133376
\(722\) 1.19813 0.0445899
\(723\) 54.8776 2.04092
\(724\) 0.918978 0.0341536
\(725\) 8.74234 0.324682
\(726\) 2.64190 0.0980502
\(727\) −27.3263 −1.01348 −0.506738 0.862100i \(-0.669149\pi\)
−0.506738 + 0.862100i \(0.669149\pi\)
\(728\) 0.126330 0.00468212
\(729\) −28.5739 −1.05829
\(730\) 42.2823 1.56494
\(731\) −11.0629 −0.409178
\(732\) −3.47283 −0.128360
\(733\) 19.9590 0.737202 0.368601 0.929588i \(-0.379837\pi\)
0.368601 + 0.929588i \(0.379837\pi\)
\(734\) −22.4962 −0.830349
\(735\) −75.3047 −2.77765
\(736\) 1.00000 0.0368605
\(737\) 24.3740 0.897829
\(738\) −28.0282 −1.03173
\(739\) −13.4618 −0.495200 −0.247600 0.968862i \(-0.579642\pi\)
−0.247600 + 0.968862i \(0.579642\pi\)
\(740\) 20.5344 0.754861
\(741\) −20.6924 −0.760155
\(742\) −0.242957 −0.00891921
\(743\) −6.99538 −0.256635 −0.128318 0.991733i \(-0.540958\pi\)
−0.128318 + 0.991733i \(0.540958\pi\)
\(744\) −23.6635 −0.867547
\(745\) 34.1755 1.25210
\(746\) −26.6507 −0.975751
\(747\) −10.8502 −0.396987
\(748\) −5.07573 −0.185587
\(749\) 0.248052 0.00906361
\(750\) −31.9459 −1.16650
\(751\) −35.7870 −1.30589 −0.652943 0.757407i \(-0.726466\pi\)
−0.652943 + 0.757407i \(0.726466\pi\)
\(752\) 12.4554 0.454201
\(753\) −37.1913 −1.35533
\(754\) 1.79986 0.0655469
\(755\) −33.0927 −1.20437
\(756\) −0.677077 −0.0246251
\(757\) −9.06855 −0.329602 −0.164801 0.986327i \(-0.552698\pi\)
−0.164801 + 0.986327i \(0.552698\pi\)
\(758\) 28.1563 1.02268
\(759\) −10.3073 −0.374132
\(760\) −15.1933 −0.551120
\(761\) −4.50028 −0.163135 −0.0815675 0.996668i \(-0.525993\pi\)
−0.0815675 + 0.996668i \(0.525993\pi\)
\(762\) −29.1460 −1.05585
\(763\) 1.05895 0.0383367
\(764\) 0.947662 0.0342852
\(765\) −31.4949 −1.13870
\(766\) 27.0559 0.977568
\(767\) −11.3830 −0.411015
\(768\) −2.99000 −0.107892
\(769\) −12.6478 −0.456090 −0.228045 0.973651i \(-0.573233\pi\)
−0.228045 + 0.973651i \(0.573233\pi\)
\(770\) −0.956082 −0.0344548
\(771\) 7.32962 0.263970
\(772\) 8.03115 0.289047
\(773\) −2.83952 −0.102131 −0.0510653 0.998695i \(-0.516262\pi\)
−0.0510653 + 0.998695i \(0.516262\pi\)
\(774\) 44.6314 1.60424
\(775\) −63.0529 −2.26493
\(776\) −9.78642 −0.351312
\(777\) 1.31321 0.0471113
\(778\) −19.6655 −0.705042
\(779\) −19.9082 −0.713287
\(780\) −17.6603 −0.632341
\(781\) 40.4503 1.44743
\(782\) 1.47240 0.0526528
\(783\) −9.64646 −0.344736
\(784\) −6.99407 −0.249788
\(785\) 14.5789 0.520342
\(786\) −2.99000 −0.106650
\(787\) 48.6368 1.73371 0.866857 0.498558i \(-0.166137\pi\)
0.866857 + 0.498558i \(0.166137\pi\)
\(788\) 19.3318 0.688666
\(789\) −1.84638 −0.0657328
\(790\) 33.7525 1.20086
\(791\) 0.999457 0.0355366
\(792\) 20.4771 0.727623
\(793\) −1.90510 −0.0676522
\(794\) −22.1898 −0.787485
\(795\) 33.9640 1.20458
\(796\) −8.17427 −0.289729
\(797\) −7.94293 −0.281353 −0.140676 0.990056i \(-0.544928\pi\)
−0.140676 + 0.990056i \(0.544928\pi\)
\(798\) −0.971641 −0.0343957
\(799\) 18.3393 0.648797
\(800\) −7.96704 −0.281677
\(801\) −30.5651 −1.07996
\(802\) 9.10238 0.321416
\(803\) −40.4773 −1.42841
\(804\) 21.1410 0.745586
\(805\) 0.277346 0.00977515
\(806\) −12.9812 −0.457243
\(807\) −3.33159 −0.117277
\(808\) −16.9790 −0.597317
\(809\) 34.3262 1.20685 0.603423 0.797421i \(-0.293803\pi\)
0.603423 + 0.797421i \(0.293803\pi\)
\(810\) 30.4811 1.07100
\(811\) −30.6912 −1.07771 −0.538856 0.842398i \(-0.681143\pi\)
−0.538856 + 0.842398i \(0.681143\pi\)
\(812\) 0.0845147 0.00296588
\(813\) −79.7336 −2.79638
\(814\) −19.6579 −0.689007
\(815\) −39.0982 −1.36955
\(816\) −4.40248 −0.154117
\(817\) 31.7014 1.10909
\(818\) −6.54110 −0.228704
\(819\) −0.750418 −0.0262217
\(820\) −16.9911 −0.593354
\(821\) 24.8130 0.865978 0.432989 0.901399i \(-0.357459\pi\)
0.432989 + 0.901399i \(0.357459\pi\)
\(822\) −5.49242 −0.191570
\(823\) 53.0040 1.84760 0.923802 0.382870i \(-0.125064\pi\)
0.923802 + 0.382870i \(0.125064\pi\)
\(824\) −4.64990 −0.161987
\(825\) 82.1187 2.85901
\(826\) −0.534502 −0.0185977
\(827\) −41.3980 −1.43955 −0.719775 0.694207i \(-0.755755\pi\)
−0.719775 + 0.694207i \(0.755755\pi\)
\(828\) −5.94012 −0.206433
\(829\) −3.08786 −0.107246 −0.0536230 0.998561i \(-0.517077\pi\)
−0.0536230 + 0.998561i \(0.517077\pi\)
\(830\) −6.57751 −0.228309
\(831\) 33.2661 1.15399
\(832\) −1.64024 −0.0568650
\(833\) −10.2981 −0.356806
\(834\) 39.3371 1.36213
\(835\) −32.2921 −1.11751
\(836\) 14.5448 0.503041
\(837\) 69.5737 2.40482
\(838\) 28.3613 0.979725
\(839\) −35.6258 −1.22994 −0.614970 0.788551i \(-0.710832\pi\)
−0.614970 + 0.788551i \(0.710832\pi\)
\(840\) −0.829265 −0.0286124
\(841\) −27.7959 −0.958479
\(842\) 36.7888 1.26783
\(843\) −50.1823 −1.72837
\(844\) 1.06067 0.0365096
\(845\) 37.1247 1.27713
\(846\) −73.9864 −2.54371
\(847\) 0.0680528 0.00233832
\(848\) 3.15448 0.108325
\(849\) 42.7870 1.46844
\(850\) −11.7306 −0.402358
\(851\) 5.70246 0.195478
\(852\) 35.0849 1.20199
\(853\) 56.2474 1.92587 0.962937 0.269725i \(-0.0869329\pi\)
0.962937 + 0.269725i \(0.0869329\pi\)
\(854\) −0.0894567 −0.00306115
\(855\) 90.2503 3.08649
\(856\) −3.22063 −0.110079
\(857\) −36.1413 −1.23456 −0.617282 0.786742i \(-0.711766\pi\)
−0.617282 + 0.786742i \(0.711766\pi\)
\(858\) 16.9064 0.577176
\(859\) −35.3588 −1.20643 −0.603213 0.797580i \(-0.706113\pi\)
−0.603213 + 0.797580i \(0.706113\pi\)
\(860\) 27.0561 0.922607
\(861\) −1.08661 −0.0370315
\(862\) 14.3946 0.490281
\(863\) 26.4199 0.899345 0.449672 0.893194i \(-0.351541\pi\)
0.449672 + 0.893194i \(0.351541\pi\)
\(864\) 8.79097 0.299075
\(865\) −6.54937 −0.222685
\(866\) 28.1237 0.955682
\(867\) 44.3479 1.50613
\(868\) −0.609550 −0.0206895
\(869\) −32.3116 −1.09610
\(870\) −11.8147 −0.400556
\(871\) 11.5974 0.392963
\(872\) −13.7492 −0.465605
\(873\) 58.1325 1.96749
\(874\) −4.21923 −0.142717
\(875\) −0.822895 −0.0278189
\(876\) −35.1083 −1.18620
\(877\) −26.8776 −0.907592 −0.453796 0.891106i \(-0.649930\pi\)
−0.453796 + 0.891106i \(0.649930\pi\)
\(878\) −10.9517 −0.369603
\(879\) −2.81771 −0.0950389
\(880\) 12.4135 0.418459
\(881\) −58.4284 −1.96850 −0.984252 0.176771i \(-0.943435\pi\)
−0.984252 + 0.176771i \(0.943435\pi\)
\(882\) 41.5456 1.39891
\(883\) −0.132011 −0.00444252 −0.00222126 0.999998i \(-0.500707\pi\)
−0.00222126 + 0.999998i \(0.500707\pi\)
\(884\) −2.41508 −0.0812280
\(885\) 74.7206 2.51171
\(886\) 31.2553 1.05004
\(887\) −21.1491 −0.710118 −0.355059 0.934844i \(-0.615539\pi\)
−0.355059 + 0.934844i \(0.615539\pi\)
\(888\) −17.0504 −0.572173
\(889\) −0.750772 −0.0251801
\(890\) −18.5289 −0.621091
\(891\) −29.1799 −0.977564
\(892\) 0.663109 0.0222025
\(893\) −52.5520 −1.75859
\(894\) −28.3770 −0.949070
\(895\) −29.8598 −0.998102
\(896\) −0.0770196 −0.00257304
\(897\) −4.90432 −0.163750
\(898\) 1.86012 0.0620731
\(899\) −8.68438 −0.289640
\(900\) 47.3252 1.57751
\(901\) 4.64465 0.154736
\(902\) 16.2657 0.541590
\(903\) 1.73029 0.0575804
\(904\) −12.9767 −0.431597
\(905\) −3.30922 −0.110002
\(906\) 27.4779 0.912891
\(907\) 25.4662 0.845592 0.422796 0.906225i \(-0.361049\pi\)
0.422796 + 0.906225i \(0.361049\pi\)
\(908\) 14.0558 0.466457
\(909\) 100.857 3.34522
\(910\) −0.454913 −0.0150802
\(911\) 51.7433 1.71433 0.857167 0.515039i \(-0.172223\pi\)
0.857167 + 0.515039i \(0.172223\pi\)
\(912\) 12.6155 0.417741
\(913\) 6.29672 0.208391
\(914\) 23.3474 0.772263
\(915\) 12.5056 0.413422
\(916\) −24.7782 −0.818696
\(917\) −0.0770196 −0.00254341
\(918\) 12.9438 0.427209
\(919\) −42.5960 −1.40511 −0.702556 0.711629i \(-0.747958\pi\)
−0.702556 + 0.711629i \(0.747958\pi\)
\(920\) −3.60098 −0.118721
\(921\) 26.1793 0.862638
\(922\) 34.9380 1.15062
\(923\) 19.2466 0.633511
\(924\) 0.793865 0.0261162
\(925\) −45.4317 −1.49379
\(926\) 14.4155 0.473724
\(927\) 27.6210 0.907192
\(928\) −1.09731 −0.0360211
\(929\) −5.47417 −0.179602 −0.0898008 0.995960i \(-0.528623\pi\)
−0.0898008 + 0.995960i \(0.528623\pi\)
\(930\) 85.2119 2.79421
\(931\) 29.5096 0.967137
\(932\) 30.1574 0.987838
\(933\) 27.3425 0.895153
\(934\) 4.75470 0.155578
\(935\) 18.2776 0.597742
\(936\) 9.74321 0.318467
\(937\) 10.3028 0.336578 0.168289 0.985738i \(-0.446176\pi\)
0.168289 + 0.985738i \(0.446176\pi\)
\(938\) 0.544572 0.0177809
\(939\) 36.0241 1.17560
\(940\) −44.8515 −1.46289
\(941\) 28.0391 0.914048 0.457024 0.889454i \(-0.348915\pi\)
0.457024 + 0.889454i \(0.348915\pi\)
\(942\) −12.1053 −0.394411
\(943\) −4.71846 −0.153654
\(944\) 6.93982 0.225872
\(945\) 2.43814 0.0793127
\(946\) −25.9012 −0.842119
\(947\) 0.280483 0.00911446 0.00455723 0.999990i \(-0.498549\pi\)
0.00455723 + 0.999990i \(0.498549\pi\)
\(948\) −28.0257 −0.910233
\(949\) −19.2595 −0.625189
\(950\) 33.6147 1.09061
\(951\) 38.2101 1.23905
\(952\) −0.113403 −0.00367543
\(953\) 16.1361 0.522699 0.261350 0.965244i \(-0.415832\pi\)
0.261350 + 0.965244i \(0.415832\pi\)
\(954\) −18.7380 −0.606664
\(955\) −3.41251 −0.110426
\(956\) −19.4110 −0.627798
\(957\) 11.3104 0.365612
\(958\) −26.2639 −0.848550
\(959\) −0.141479 −0.00456861
\(960\) 10.7669 0.347501
\(961\) 31.6348 1.02048
\(962\) −9.35339 −0.301565
\(963\) 19.1309 0.616486
\(964\) −18.3537 −0.591133
\(965\) −28.9200 −0.930968
\(966\) −0.230289 −0.00740942
\(967\) −48.2859 −1.55277 −0.776384 0.630260i \(-0.782948\pi\)
−0.776384 + 0.630260i \(0.782948\pi\)
\(968\) −0.883578 −0.0283993
\(969\) 18.5750 0.596716
\(970\) 35.2407 1.13151
\(971\) −16.2830 −0.522547 −0.261274 0.965265i \(-0.584143\pi\)
−0.261274 + 0.965265i \(0.584143\pi\)
\(972\) 1.06351 0.0341119
\(973\) 1.01329 0.0324845
\(974\) −5.11045 −0.163749
\(975\) 39.0729 1.25133
\(976\) 1.16148 0.0371781
\(977\) −47.2643 −1.51212 −0.756060 0.654502i \(-0.772878\pi\)
−0.756060 + 0.654502i \(0.772878\pi\)
\(978\) 32.4645 1.03810
\(979\) 17.7380 0.566908
\(980\) 25.1855 0.804521
\(981\) 81.6717 2.60758
\(982\) 9.56913 0.305363
\(983\) 5.79810 0.184931 0.0924653 0.995716i \(-0.470525\pi\)
0.0924653 + 0.995716i \(0.470525\pi\)
\(984\) 14.1082 0.449753
\(985\) −69.6132 −2.21806
\(986\) −1.61568 −0.0514538
\(987\) −2.86833 −0.0913001
\(988\) 6.92053 0.220171
\(989\) 7.51355 0.238917
\(990\) −73.7376 −2.34354
\(991\) 7.60217 0.241491 0.120745 0.992684i \(-0.461472\pi\)
0.120745 + 0.992684i \(0.461472\pi\)
\(992\) 7.91422 0.251277
\(993\) 103.515 3.28496
\(994\) 0.903752 0.0286653
\(995\) 29.4354 0.933163
\(996\) 5.46151 0.173055
\(997\) −16.5320 −0.523575 −0.261787 0.965126i \(-0.584312\pi\)
−0.261787 + 0.965126i \(0.584312\pi\)
\(998\) 32.1300 1.01706
\(999\) 50.1302 1.58605
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 \(a_p\))