Properties

Label 8013.2.a.d.1.9
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

Related objects

Downloads

Learn more about

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 1.9
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.52915 q^{2}\) \(+1.00000 q^{3}\) \(+4.39659 q^{4}\) \(+0.815749 q^{5}\) \(-2.52915 q^{6}\) \(+5.25378 q^{7}\) \(-6.06134 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.52915 q^{2}\) \(+1.00000 q^{3}\) \(+4.39659 q^{4}\) \(+0.815749 q^{5}\) \(-2.52915 q^{6}\) \(+5.25378 q^{7}\) \(-6.06134 q^{8}\) \(+1.00000 q^{9}\) \(-2.06315 q^{10}\) \(-6.35997 q^{11}\) \(+4.39659 q^{12}\) \(-5.16695 q^{13}\) \(-13.2876 q^{14}\) \(+0.815749 q^{15}\) \(+6.53685 q^{16}\) \(-6.61161 q^{17}\) \(-2.52915 q^{18}\) \(+4.45699 q^{19}\) \(+3.58651 q^{20}\) \(+5.25378 q^{21}\) \(+16.0853 q^{22}\) \(+5.17552 q^{23}\) \(-6.06134 q^{24}\) \(-4.33455 q^{25}\) \(+13.0680 q^{26}\) \(+1.00000 q^{27}\) \(+23.0988 q^{28}\) \(-4.11231 q^{29}\) \(-2.06315 q^{30}\) \(+3.82973 q^{31}\) \(-4.40998 q^{32}\) \(-6.35997 q^{33}\) \(+16.7217 q^{34}\) \(+4.28577 q^{35}\) \(+4.39659 q^{36}\) \(-0.123346 q^{37}\) \(-11.2724 q^{38}\) \(-5.16695 q^{39}\) \(-4.94453 q^{40}\) \(+3.24200 q^{41}\) \(-13.2876 q^{42}\) \(+1.37385 q^{43}\) \(-27.9622 q^{44}\) \(+0.815749 q^{45}\) \(-13.0897 q^{46}\) \(-2.44058 q^{47}\) \(+6.53685 q^{48}\) \(+20.6022 q^{49}\) \(+10.9627 q^{50}\) \(-6.61161 q^{51}\) \(-22.7170 q^{52}\) \(+8.92718 q^{53}\) \(-2.52915 q^{54}\) \(-5.18813 q^{55}\) \(-31.8450 q^{56}\) \(+4.45699 q^{57}\) \(+10.4006 q^{58}\) \(+1.43964 q^{59}\) \(+3.58651 q^{60}\) \(+0.278119 q^{61}\) \(-9.68597 q^{62}\) \(+5.25378 q^{63}\) \(-1.92021 q^{64}\) \(-4.21494 q^{65}\) \(+16.0853 q^{66}\) \(+4.63116 q^{67}\) \(-29.0686 q^{68}\) \(+5.17552 q^{69}\) \(-10.8393 q^{70}\) \(-2.14340 q^{71}\) \(-6.06134 q^{72}\) \(-9.87479 q^{73}\) \(+0.311961 q^{74}\) \(-4.33455 q^{75}\) \(+19.5956 q^{76}\) \(-33.4139 q^{77}\) \(+13.0680 q^{78}\) \(-4.60528 q^{79}\) \(+5.33242 q^{80}\) \(+1.00000 q^{81}\) \(-8.19950 q^{82}\) \(+4.10619 q^{83}\) \(+23.0988 q^{84}\) \(-5.39341 q^{85}\) \(-3.47468 q^{86}\) \(-4.11231 q^{87}\) \(+38.5499 q^{88}\) \(-14.0465 q^{89}\) \(-2.06315 q^{90}\) \(-27.1461 q^{91}\) \(+22.7547 q^{92}\) \(+3.82973 q^{93}\) \(+6.17258 q^{94}\) \(+3.63578 q^{95}\) \(-4.40998 q^{96}\) \(+10.9796 q^{97}\) \(-52.1062 q^{98}\) \(-6.35997 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut 41q^{10} \) \(\mathstrut +\mathstrut 51q^{11} \) \(\mathstrut +\mathstrut 151q^{12} \) \(\mathstrut +\mathstrut 56q^{13} \) \(\mathstrut +\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 195q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 15q^{18} \) \(\mathstrut +\mathstrut 93q^{19} \) \(\mathstrut +\mathstrut 44q^{20} \) \(\mathstrut +\mathstrut 61q^{21} \) \(\mathstrut +\mathstrut 46q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 42q^{24} \) \(\mathstrut +\mathstrut 193q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut 129q^{27} \) \(\mathstrut +\mathstrut 145q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 41q^{30} \) \(\mathstrut +\mathstrut 67q^{31} \) \(\mathstrut +\mathstrut 89q^{32} \) \(\mathstrut +\mathstrut 51q^{33} \) \(\mathstrut +\mathstrut 73q^{34} \) \(\mathstrut +\mathstrut 56q^{35} \) \(\mathstrut +\mathstrut 151q^{36} \) \(\mathstrut +\mathstrut 95q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 103q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 5q^{42} \) \(\mathstrut +\mathstrut 150q^{43} \) \(\mathstrut +\mathstrut 69q^{44} \) \(\mathstrut +\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 53q^{47} \) \(\mathstrut +\mathstrut 195q^{48} \) \(\mathstrut +\mathstrut 240q^{49} \) \(\mathstrut +\mathstrut 17q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 124q^{52} \) \(\mathstrut +\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut 15q^{54} \) \(\mathstrut +\mathstrut 66q^{55} \) \(\mathstrut -\mathstrut 17q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 57q^{58} \) \(\mathstrut +\mathstrut 49q^{59} \) \(\mathstrut +\mathstrut 44q^{60} \) \(\mathstrut +\mathstrut 113q^{61} \) \(\mathstrut +\mathstrut 27q^{62} \) \(\mathstrut +\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 262q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 46q^{66} \) \(\mathstrut +\mathstrut 185q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 50q^{69} \) \(\mathstrut +\mathstrut 25q^{70} \) \(\mathstrut +\mathstrut 41q^{71} \) \(\mathstrut +\mathstrut 42q^{72} \) \(\mathstrut +\mathstrut 153q^{73} \) \(\mathstrut -\mathstrut q^{74} \) \(\mathstrut +\mathstrut 193q^{75} \) \(\mathstrut +\mathstrut 190q^{76} \) \(\mathstrut +\mathstrut 39q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 101q^{79} \) \(\mathstrut +\mathstrut 48q^{80} \) \(\mathstrut +\mathstrut 129q^{81} \) \(\mathstrut +\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 162q^{83} \) \(\mathstrut +\mathstrut 145q^{84} \) \(\mathstrut +\mathstrut 99q^{85} \) \(\mathstrut +\mathstrut 13q^{86} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 86q^{88} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 117q^{91} \) \(\mathstrut +\mathstrut 56q^{92} \) \(\mathstrut +\mathstrut 67q^{93} \) \(\mathstrut +\mathstrut 49q^{94} \) \(\mathstrut +\mathstrut 71q^{95} \) \(\mathstrut +\mathstrut 89q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut +\mathstrut 40q^{98} \) \(\mathstrut +\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.52915 −1.78838 −0.894189 0.447689i \(-0.852247\pi\)
−0.894189 + 0.447689i \(0.852247\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.39659 2.19830
\(5\) 0.815749 0.364814 0.182407 0.983223i \(-0.441611\pi\)
0.182407 + 0.983223i \(0.441611\pi\)
\(6\) −2.52915 −1.03252
\(7\) 5.25378 1.98574 0.992872 0.119187i \(-0.0380286\pi\)
0.992872 + 0.119187i \(0.0380286\pi\)
\(8\) −6.06134 −2.14301
\(9\) 1.00000 0.333333
\(10\) −2.06315 −0.652425
\(11\) −6.35997 −1.91760 −0.958801 0.284079i \(-0.908312\pi\)
−0.958801 + 0.284079i \(0.908312\pi\)
\(12\) 4.39659 1.26919
\(13\) −5.16695 −1.43306 −0.716528 0.697559i \(-0.754270\pi\)
−0.716528 + 0.697559i \(0.754270\pi\)
\(14\) −13.2876 −3.55126
\(15\) 0.815749 0.210625
\(16\) 6.53685 1.63421
\(17\) −6.61161 −1.60355 −0.801775 0.597626i \(-0.796111\pi\)
−0.801775 + 0.597626i \(0.796111\pi\)
\(18\) −2.52915 −0.596126
\(19\) 4.45699 1.02250 0.511252 0.859431i \(-0.329182\pi\)
0.511252 + 0.859431i \(0.329182\pi\)
\(20\) 3.58651 0.801969
\(21\) 5.25378 1.14647
\(22\) 16.0853 3.42940
\(23\) 5.17552 1.07917 0.539585 0.841931i \(-0.318581\pi\)
0.539585 + 0.841931i \(0.318581\pi\)
\(24\) −6.06134 −1.23727
\(25\) −4.33455 −0.866911
\(26\) 13.0680 2.56284
\(27\) 1.00000 0.192450
\(28\) 23.0988 4.36525
\(29\) −4.11231 −0.763636 −0.381818 0.924237i \(-0.624702\pi\)
−0.381818 + 0.924237i \(0.624702\pi\)
\(30\) −2.06315 −0.376678
\(31\) 3.82973 0.687841 0.343920 0.938999i \(-0.388245\pi\)
0.343920 + 0.938999i \(0.388245\pi\)
\(32\) −4.40998 −0.779581
\(33\) −6.35997 −1.10713
\(34\) 16.7217 2.86776
\(35\) 4.28577 0.724427
\(36\) 4.39659 0.732766
\(37\) −0.123346 −0.0202780 −0.0101390 0.999949i \(-0.503227\pi\)
−0.0101390 + 0.999949i \(0.503227\pi\)
\(38\) −11.2724 −1.82862
\(39\) −5.16695 −0.827375
\(40\) −4.94453 −0.781799
\(41\) 3.24200 0.506315 0.253158 0.967425i \(-0.418531\pi\)
0.253158 + 0.967425i \(0.418531\pi\)
\(42\) −13.2876 −2.05032
\(43\) 1.37385 0.209511 0.104755 0.994498i \(-0.466594\pi\)
0.104755 + 0.994498i \(0.466594\pi\)
\(44\) −27.9622 −4.21546
\(45\) 0.815749 0.121605
\(46\) −13.0897 −1.92997
\(47\) −2.44058 −0.355995 −0.177997 0.984031i \(-0.556962\pi\)
−0.177997 + 0.984031i \(0.556962\pi\)
\(48\) 6.53685 0.943513
\(49\) 20.6022 2.94318
\(50\) 10.9627 1.55036
\(51\) −6.61161 −0.925810
\(52\) −22.7170 −3.15028
\(53\) 8.92718 1.22624 0.613121 0.789989i \(-0.289914\pi\)
0.613121 + 0.789989i \(0.289914\pi\)
\(54\) −2.52915 −0.344174
\(55\) −5.18813 −0.699568
\(56\) −31.8450 −4.25546
\(57\) 4.45699 0.590343
\(58\) 10.4006 1.36567
\(59\) 1.43964 0.187426 0.0937128 0.995599i \(-0.470126\pi\)
0.0937128 + 0.995599i \(0.470126\pi\)
\(60\) 3.58651 0.463017
\(61\) 0.278119 0.0356095 0.0178047 0.999841i \(-0.494332\pi\)
0.0178047 + 0.999841i \(0.494332\pi\)
\(62\) −9.68597 −1.23012
\(63\) 5.25378 0.661915
\(64\) −1.92021 −0.240026
\(65\) −4.21494 −0.522798
\(66\) 16.0853 1.97996
\(67\) 4.63116 0.565787 0.282893 0.959151i \(-0.408706\pi\)
0.282893 + 0.959151i \(0.408706\pi\)
\(68\) −29.0686 −3.52508
\(69\) 5.17552 0.623060
\(70\) −10.8393 −1.29555
\(71\) −2.14340 −0.254374 −0.127187 0.991879i \(-0.540595\pi\)
−0.127187 + 0.991879i \(0.540595\pi\)
\(72\) −6.06134 −0.714336
\(73\) −9.87479 −1.15576 −0.577879 0.816123i \(-0.696119\pi\)
−0.577879 + 0.816123i \(0.696119\pi\)
\(74\) 0.311961 0.0362647
\(75\) −4.33455 −0.500511
\(76\) 19.5956 2.24777
\(77\) −33.4139 −3.80787
\(78\) 13.0680 1.47966
\(79\) −4.60528 −0.518134 −0.259067 0.965859i \(-0.583415\pi\)
−0.259067 + 0.965859i \(0.583415\pi\)
\(80\) 5.33242 0.596183
\(81\) 1.00000 0.111111
\(82\) −8.19950 −0.905483
\(83\) 4.10619 0.450713 0.225356 0.974276i \(-0.427645\pi\)
0.225356 + 0.974276i \(0.427645\pi\)
\(84\) 23.0988 2.52028
\(85\) −5.39341 −0.584997
\(86\) −3.47468 −0.374685
\(87\) −4.11231 −0.440886
\(88\) 38.5499 4.10944
\(89\) −14.0465 −1.48893 −0.744463 0.667663i \(-0.767295\pi\)
−0.744463 + 0.667663i \(0.767295\pi\)
\(90\) −2.06315 −0.217475
\(91\) −27.1461 −2.84568
\(92\) 22.7547 2.37234
\(93\) 3.82973 0.397125
\(94\) 6.17258 0.636653
\(95\) 3.63578 0.373023
\(96\) −4.40998 −0.450091
\(97\) 10.9796 1.11481 0.557407 0.830240i \(-0.311796\pi\)
0.557407 + 0.830240i \(0.311796\pi\)
\(98\) −52.1062 −5.26352
\(99\) −6.35997 −0.639201
\(100\) −19.0573 −1.90573
\(101\) 15.0962 1.50213 0.751063 0.660231i \(-0.229542\pi\)
0.751063 + 0.660231i \(0.229542\pi\)
\(102\) 16.7217 1.65570
\(103\) 3.00861 0.296447 0.148223 0.988954i \(-0.452645\pi\)
0.148223 + 0.988954i \(0.452645\pi\)
\(104\) 31.3187 3.07105
\(105\) 4.28577 0.418248
\(106\) −22.5782 −2.19298
\(107\) 12.8733 1.24451 0.622254 0.782815i \(-0.286217\pi\)
0.622254 + 0.782815i \(0.286217\pi\)
\(108\) 4.39659 0.423062
\(109\) 8.97425 0.859577 0.429788 0.902930i \(-0.358588\pi\)
0.429788 + 0.902930i \(0.358588\pi\)
\(110\) 13.1216 1.25109
\(111\) −0.123346 −0.0117075
\(112\) 34.3432 3.24513
\(113\) 10.2325 0.962593 0.481297 0.876558i \(-0.340166\pi\)
0.481297 + 0.876558i \(0.340166\pi\)
\(114\) −11.2724 −1.05576
\(115\) 4.22192 0.393696
\(116\) −18.0801 −1.67870
\(117\) −5.16695 −0.477685
\(118\) −3.64107 −0.335188
\(119\) −34.7360 −3.18424
\(120\) −4.94453 −0.451372
\(121\) 29.4492 2.67720
\(122\) −0.703404 −0.0636832
\(123\) 3.24200 0.292321
\(124\) 16.8378 1.51208
\(125\) −7.61465 −0.681075
\(126\) −13.2876 −1.18375
\(127\) 9.94229 0.882235 0.441118 0.897449i \(-0.354582\pi\)
0.441118 + 0.897449i \(0.354582\pi\)
\(128\) 13.6764 1.20884
\(129\) 1.37385 0.120961
\(130\) 10.6602 0.934961
\(131\) 12.5504 1.09653 0.548266 0.836304i \(-0.315288\pi\)
0.548266 + 0.836304i \(0.315288\pi\)
\(132\) −27.9622 −2.43380
\(133\) 23.4161 2.03043
\(134\) −11.7129 −1.01184
\(135\) 0.815749 0.0702085
\(136\) 40.0752 3.43642
\(137\) −9.86060 −0.842448 −0.421224 0.906957i \(-0.638399\pi\)
−0.421224 + 0.906957i \(0.638399\pi\)
\(138\) −13.0897 −1.11427
\(139\) −9.61820 −0.815805 −0.407903 0.913025i \(-0.633740\pi\)
−0.407903 + 0.913025i \(0.633740\pi\)
\(140\) 18.8428 1.59251
\(141\) −2.44058 −0.205534
\(142\) 5.42097 0.454917
\(143\) 32.8617 2.74803
\(144\) 6.53685 0.544737
\(145\) −3.35461 −0.278585
\(146\) 24.9748 2.06693
\(147\) 20.6022 1.69924
\(148\) −0.542303 −0.0445770
\(149\) 13.7117 1.12331 0.561654 0.827372i \(-0.310165\pi\)
0.561654 + 0.827372i \(0.310165\pi\)
\(150\) 10.9627 0.895103
\(151\) 20.7955 1.69232 0.846158 0.532931i \(-0.178910\pi\)
0.846158 + 0.532931i \(0.178910\pi\)
\(152\) −27.0153 −2.19123
\(153\) −6.61161 −0.534517
\(154\) 84.5087 6.80991
\(155\) 3.12410 0.250934
\(156\) −22.7170 −1.81882
\(157\) −15.5407 −1.24028 −0.620140 0.784491i \(-0.712924\pi\)
−0.620140 + 0.784491i \(0.712924\pi\)
\(158\) 11.6474 0.926620
\(159\) 8.92718 0.707971
\(160\) −3.59743 −0.284402
\(161\) 27.1911 2.14296
\(162\) −2.52915 −0.198709
\(163\) 1.04865 0.0821370 0.0410685 0.999156i \(-0.486924\pi\)
0.0410685 + 0.999156i \(0.486924\pi\)
\(164\) 14.2538 1.11303
\(165\) −5.18813 −0.403896
\(166\) −10.3852 −0.806045
\(167\) −3.72886 −0.288548 −0.144274 0.989538i \(-0.546085\pi\)
−0.144274 + 0.989538i \(0.546085\pi\)
\(168\) −31.8450 −2.45689
\(169\) 13.6974 1.05365
\(170\) 13.6407 1.04620
\(171\) 4.45699 0.340834
\(172\) 6.04028 0.460567
\(173\) 16.0712 1.22187 0.610934 0.791682i \(-0.290794\pi\)
0.610934 + 0.791682i \(0.290794\pi\)
\(174\) 10.4006 0.788470
\(175\) −22.7728 −1.72146
\(176\) −41.5741 −3.13377
\(177\) 1.43964 0.108210
\(178\) 35.5257 2.66276
\(179\) 11.0433 0.825416 0.412708 0.910863i \(-0.364583\pi\)
0.412708 + 0.910863i \(0.364583\pi\)
\(180\) 3.58651 0.267323
\(181\) −14.5280 −1.07985 −0.539927 0.841712i \(-0.681548\pi\)
−0.539927 + 0.841712i \(0.681548\pi\)
\(182\) 68.6564 5.08915
\(183\) 0.278119 0.0205591
\(184\) −31.3706 −2.31267
\(185\) −0.100619 −0.00739768
\(186\) −9.68597 −0.710210
\(187\) 42.0496 3.07497
\(188\) −10.7302 −0.782582
\(189\) 5.25378 0.382157
\(190\) −9.19543 −0.667107
\(191\) −24.4500 −1.76914 −0.884571 0.466405i \(-0.845549\pi\)
−0.884571 + 0.466405i \(0.845549\pi\)
\(192\) −1.92021 −0.138579
\(193\) −1.86342 −0.134132 −0.0670659 0.997749i \(-0.521364\pi\)
−0.0670659 + 0.997749i \(0.521364\pi\)
\(194\) −27.7691 −1.99371
\(195\) −4.21494 −0.301838
\(196\) 90.5797 6.46998
\(197\) 24.4286 1.74047 0.870233 0.492640i \(-0.163968\pi\)
0.870233 + 0.492640i \(0.163968\pi\)
\(198\) 16.0853 1.14313
\(199\) −9.71993 −0.689028 −0.344514 0.938781i \(-0.611956\pi\)
−0.344514 + 0.938781i \(0.611956\pi\)
\(200\) 26.2732 1.85780
\(201\) 4.63116 0.326657
\(202\) −38.1805 −2.68637
\(203\) −21.6052 −1.51639
\(204\) −29.0686 −2.03521
\(205\) 2.64466 0.184711
\(206\) −7.60922 −0.530159
\(207\) 5.17552 0.359724
\(208\) −33.7756 −2.34192
\(209\) −28.3463 −1.96075
\(210\) −10.8393 −0.747986
\(211\) 4.43381 0.305236 0.152618 0.988285i \(-0.451230\pi\)
0.152618 + 0.988285i \(0.451230\pi\)
\(212\) 39.2492 2.69564
\(213\) −2.14340 −0.146863
\(214\) −32.5585 −2.22565
\(215\) 1.12072 0.0764325
\(216\) −6.06134 −0.412422
\(217\) 20.1206 1.36588
\(218\) −22.6972 −1.53725
\(219\) −9.87479 −0.667277
\(220\) −22.8101 −1.53786
\(221\) 34.1619 2.29798
\(222\) 0.311961 0.0209374
\(223\) −22.5583 −1.51062 −0.755309 0.655369i \(-0.772513\pi\)
−0.755309 + 0.655369i \(0.772513\pi\)
\(224\) −23.1691 −1.54805
\(225\) −4.33455 −0.288970
\(226\) −25.8795 −1.72148
\(227\) −11.3839 −0.755574 −0.377787 0.925893i \(-0.623315\pi\)
−0.377787 + 0.925893i \(0.623315\pi\)
\(228\) 19.5956 1.29775
\(229\) 26.7214 1.76580 0.882901 0.469560i \(-0.155587\pi\)
0.882901 + 0.469560i \(0.155587\pi\)
\(230\) −10.6779 −0.704078
\(231\) −33.4139 −2.19847
\(232\) 24.9261 1.63648
\(233\) 26.1740 1.71471 0.857357 0.514722i \(-0.172105\pi\)
0.857357 + 0.514722i \(0.172105\pi\)
\(234\) 13.0680 0.854282
\(235\) −1.99090 −0.129872
\(236\) 6.32953 0.412017
\(237\) −4.60528 −0.299145
\(238\) 87.8524 5.69463
\(239\) 24.2993 1.57179 0.785896 0.618359i \(-0.212202\pi\)
0.785896 + 0.618359i \(0.212202\pi\)
\(240\) 5.33242 0.344206
\(241\) 27.6640 1.78200 0.890998 0.454007i \(-0.150006\pi\)
0.890998 + 0.454007i \(0.150006\pi\)
\(242\) −74.4813 −4.78784
\(243\) 1.00000 0.0641500
\(244\) 1.22278 0.0782802
\(245\) 16.8063 1.07371
\(246\) −8.19950 −0.522781
\(247\) −23.0291 −1.46530
\(248\) −23.2133 −1.47405
\(249\) 4.10619 0.260219
\(250\) 19.2586 1.21802
\(251\) −27.1157 −1.71153 −0.855764 0.517366i \(-0.826913\pi\)
−0.855764 + 0.517366i \(0.826913\pi\)
\(252\) 23.0988 1.45508
\(253\) −32.9161 −2.06942
\(254\) −25.1455 −1.57777
\(255\) −5.39341 −0.337748
\(256\) −30.7493 −1.92183
\(257\) −2.14433 −0.133760 −0.0668799 0.997761i \(-0.521304\pi\)
−0.0668799 + 0.997761i \(0.521304\pi\)
\(258\) −3.47468 −0.216324
\(259\) −0.648034 −0.0402669
\(260\) −18.5314 −1.14927
\(261\) −4.11231 −0.254545
\(262\) −31.7418 −1.96101
\(263\) 8.36006 0.515503 0.257752 0.966211i \(-0.417018\pi\)
0.257752 + 0.966211i \(0.417018\pi\)
\(264\) 38.5499 2.37258
\(265\) 7.28233 0.447350
\(266\) −59.2227 −3.63118
\(267\) −14.0465 −0.859632
\(268\) 20.3613 1.24377
\(269\) 21.4114 1.30548 0.652739 0.757583i \(-0.273620\pi\)
0.652739 + 0.757583i \(0.273620\pi\)
\(270\) −2.06315 −0.125559
\(271\) −20.5066 −1.24569 −0.622844 0.782346i \(-0.714023\pi\)
−0.622844 + 0.782346i \(0.714023\pi\)
\(272\) −43.2191 −2.62054
\(273\) −27.1461 −1.64295
\(274\) 24.9389 1.50662
\(275\) 27.5676 1.66239
\(276\) 22.7547 1.36967
\(277\) 2.65236 0.159365 0.0796824 0.996820i \(-0.474609\pi\)
0.0796824 + 0.996820i \(0.474609\pi\)
\(278\) 24.3259 1.45897
\(279\) 3.82973 0.229280
\(280\) −25.9775 −1.55245
\(281\) −15.8422 −0.945069 −0.472534 0.881312i \(-0.656661\pi\)
−0.472534 + 0.881312i \(0.656661\pi\)
\(282\) 6.17258 0.367572
\(283\) 20.9307 1.24420 0.622102 0.782936i \(-0.286279\pi\)
0.622102 + 0.782936i \(0.286279\pi\)
\(284\) −9.42364 −0.559190
\(285\) 3.63578 0.215365
\(286\) −83.1120 −4.91452
\(287\) 17.0328 1.00541
\(288\) −4.40998 −0.259860
\(289\) 26.7134 1.57138
\(290\) 8.48430 0.498215
\(291\) 10.9796 0.643638
\(292\) −43.4154 −2.54070
\(293\) 0.141149 0.00824600 0.00412300 0.999992i \(-0.498688\pi\)
0.00412300 + 0.999992i \(0.498688\pi\)
\(294\) −52.1062 −3.03889
\(295\) 1.17439 0.0683754
\(296\) 0.747643 0.0434558
\(297\) −6.35997 −0.369043
\(298\) −34.6790 −2.00890
\(299\) −26.7417 −1.54651
\(300\) −19.0573 −1.10027
\(301\) 7.21794 0.416035
\(302\) −52.5950 −3.02650
\(303\) 15.0962 0.867252
\(304\) 29.1347 1.67099
\(305\) 0.226875 0.0129908
\(306\) 16.7217 0.955918
\(307\) −22.5600 −1.28757 −0.643784 0.765207i \(-0.722636\pi\)
−0.643784 + 0.765207i \(0.722636\pi\)
\(308\) −146.907 −8.37082
\(309\) 3.00861 0.171154
\(310\) −7.90131 −0.448764
\(311\) 15.5859 0.883797 0.441898 0.897065i \(-0.354305\pi\)
0.441898 + 0.897065i \(0.354305\pi\)
\(312\) 31.3187 1.77307
\(313\) −16.0266 −0.905879 −0.452939 0.891541i \(-0.649625\pi\)
−0.452939 + 0.891541i \(0.649625\pi\)
\(314\) 39.3046 2.21809
\(315\) 4.28577 0.241476
\(316\) −20.2475 −1.13901
\(317\) 7.79954 0.438066 0.219033 0.975717i \(-0.429710\pi\)
0.219033 + 0.975717i \(0.429710\pi\)
\(318\) −22.5782 −1.26612
\(319\) 26.1541 1.46435
\(320\) −1.56641 −0.0875648
\(321\) 12.8733 0.718517
\(322\) −68.7703 −3.83242
\(323\) −29.4679 −1.63964
\(324\) 4.39659 0.244255
\(325\) 22.3964 1.24233
\(326\) −2.65220 −0.146892
\(327\) 8.97425 0.496277
\(328\) −19.6509 −1.08504
\(329\) −12.8223 −0.706914
\(330\) 13.1216 0.722318
\(331\) 11.3588 0.624335 0.312168 0.950027i \(-0.398945\pi\)
0.312168 + 0.950027i \(0.398945\pi\)
\(332\) 18.0532 0.990800
\(333\) −0.123346 −0.00675932
\(334\) 9.43085 0.516033
\(335\) 3.77787 0.206407
\(336\) 34.3432 1.87357
\(337\) −8.73318 −0.475726 −0.237863 0.971299i \(-0.576447\pi\)
−0.237863 + 0.971299i \(0.576447\pi\)
\(338\) −34.6428 −1.88432
\(339\) 10.2325 0.555753
\(340\) −23.7126 −1.28600
\(341\) −24.3570 −1.31900
\(342\) −11.2724 −0.609541
\(343\) 71.4633 3.85865
\(344\) −8.32740 −0.448983
\(345\) 4.22192 0.227301
\(346\) −40.6464 −2.18516
\(347\) 26.1661 1.40467 0.702336 0.711846i \(-0.252141\pi\)
0.702336 + 0.711846i \(0.252141\pi\)
\(348\) −18.0801 −0.969197
\(349\) 21.8890 1.17169 0.585847 0.810422i \(-0.300762\pi\)
0.585847 + 0.810422i \(0.300762\pi\)
\(350\) 57.5958 3.07863
\(351\) −5.16695 −0.275792
\(352\) 28.0473 1.49493
\(353\) −10.9351 −0.582015 −0.291008 0.956721i \(-0.593991\pi\)
−0.291008 + 0.956721i \(0.593991\pi\)
\(354\) −3.64107 −0.193521
\(355\) −1.74847 −0.0927992
\(356\) −61.7568 −3.27310
\(357\) −34.7360 −1.83842
\(358\) −27.9302 −1.47616
\(359\) 24.1220 1.27311 0.636556 0.771230i \(-0.280358\pi\)
0.636556 + 0.771230i \(0.280358\pi\)
\(360\) −4.94453 −0.260600
\(361\) 0.864745 0.0455129
\(362\) 36.7434 1.93119
\(363\) 29.4492 1.54568
\(364\) −119.350 −6.25565
\(365\) −8.05535 −0.421636
\(366\) −0.703404 −0.0367675
\(367\) 8.09849 0.422738 0.211369 0.977406i \(-0.432208\pi\)
0.211369 + 0.977406i \(0.432208\pi\)
\(368\) 33.8316 1.76359
\(369\) 3.24200 0.168772
\(370\) 0.254481 0.0132299
\(371\) 46.9015 2.43500
\(372\) 16.8378 0.872998
\(373\) −30.1993 −1.56366 −0.781831 0.623490i \(-0.785714\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(374\) −106.350 −5.49921
\(375\) −7.61465 −0.393219
\(376\) 14.7932 0.762899
\(377\) 21.2481 1.09433
\(378\) −13.2876 −0.683440
\(379\) −0.885968 −0.0455091 −0.0227546 0.999741i \(-0.507244\pi\)
−0.0227546 + 0.999741i \(0.507244\pi\)
\(380\) 15.9851 0.820016
\(381\) 9.94229 0.509359
\(382\) 61.8378 3.16390
\(383\) −17.5225 −0.895360 −0.447680 0.894194i \(-0.647750\pi\)
−0.447680 + 0.894194i \(0.647750\pi\)
\(384\) 13.6764 0.697923
\(385\) −27.2573 −1.38916
\(386\) 4.71286 0.239878
\(387\) 1.37385 0.0698370
\(388\) 48.2730 2.45069
\(389\) −12.4351 −0.630486 −0.315243 0.949011i \(-0.602086\pi\)
−0.315243 + 0.949011i \(0.602086\pi\)
\(390\) 10.6602 0.539800
\(391\) −34.2185 −1.73051
\(392\) −124.877 −6.30725
\(393\) 12.5504 0.633083
\(394\) −61.7836 −3.11261
\(395\) −3.75675 −0.189022
\(396\) −27.9622 −1.40515
\(397\) 3.10596 0.155884 0.0779419 0.996958i \(-0.475165\pi\)
0.0779419 + 0.996958i \(0.475165\pi\)
\(398\) 24.5832 1.23224
\(399\) 23.4161 1.17227
\(400\) −28.3343 −1.41672
\(401\) 15.7484 0.786437 0.393219 0.919445i \(-0.371362\pi\)
0.393219 + 0.919445i \(0.371362\pi\)
\(402\) −11.7129 −0.584187
\(403\) −19.7881 −0.985714
\(404\) 66.3717 3.30212
\(405\) 0.815749 0.0405349
\(406\) 54.6427 2.71187
\(407\) 0.784477 0.0388851
\(408\) 40.0752 1.98402
\(409\) 18.3891 0.909280 0.454640 0.890675i \(-0.349768\pi\)
0.454640 + 0.890675i \(0.349768\pi\)
\(410\) −6.68873 −0.330333
\(411\) −9.86060 −0.486388
\(412\) 13.2276 0.651678
\(413\) 7.56357 0.372179
\(414\) −13.0897 −0.643322
\(415\) 3.34962 0.164426
\(416\) 22.7861 1.11718
\(417\) −9.61820 −0.471005
\(418\) 71.6920 3.50657
\(419\) −14.1577 −0.691649 −0.345824 0.938299i \(-0.612401\pi\)
−0.345824 + 0.938299i \(0.612401\pi\)
\(420\) 18.8428 0.919433
\(421\) 38.0572 1.85479 0.927396 0.374080i \(-0.122042\pi\)
0.927396 + 0.374080i \(0.122042\pi\)
\(422\) −11.2138 −0.545878
\(423\) −2.44058 −0.118665
\(424\) −54.1107 −2.62785
\(425\) 28.6584 1.39014
\(426\) 5.42097 0.262647
\(427\) 1.46118 0.0707113
\(428\) 56.5987 2.73580
\(429\) 32.8617 1.58658
\(430\) −2.83447 −0.136690
\(431\) 2.06300 0.0993714 0.0496857 0.998765i \(-0.484178\pi\)
0.0496857 + 0.998765i \(0.484178\pi\)
\(432\) 6.53685 0.314504
\(433\) 4.77277 0.229365 0.114682 0.993402i \(-0.463415\pi\)
0.114682 + 0.993402i \(0.463415\pi\)
\(434\) −50.8880 −2.44270
\(435\) −3.35461 −0.160841
\(436\) 39.4561 1.88960
\(437\) 23.0672 1.10346
\(438\) 24.9748 1.19334
\(439\) −0.398314 −0.0190105 −0.00950524 0.999955i \(-0.503026\pi\)
−0.00950524 + 0.999955i \(0.503026\pi\)
\(440\) 31.4470 1.49918
\(441\) 20.6022 0.981059
\(442\) −86.4005 −4.10965
\(443\) 12.6519 0.601108 0.300554 0.953765i \(-0.402828\pi\)
0.300554 + 0.953765i \(0.402828\pi\)
\(444\) −0.542303 −0.0257365
\(445\) −11.4584 −0.543181
\(446\) 57.0534 2.70155
\(447\) 13.7117 0.648542
\(448\) −10.0884 −0.476630
\(449\) −4.27997 −0.201984 −0.100992 0.994887i \(-0.532202\pi\)
−0.100992 + 0.994887i \(0.532202\pi\)
\(450\) 10.9627 0.516788
\(451\) −20.6190 −0.970911
\(452\) 44.9882 2.11607
\(453\) 20.7955 0.977060
\(454\) 28.7915 1.35125
\(455\) −22.1444 −1.03814
\(456\) −27.0153 −1.26511
\(457\) 33.3571 1.56038 0.780189 0.625544i \(-0.215123\pi\)
0.780189 + 0.625544i \(0.215123\pi\)
\(458\) −67.5824 −3.15792
\(459\) −6.61161 −0.308603
\(460\) 18.5621 0.865462
\(461\) −15.4471 −0.719443 −0.359722 0.933060i \(-0.617128\pi\)
−0.359722 + 0.933060i \(0.617128\pi\)
\(462\) 84.5087 3.93170
\(463\) −30.5723 −1.42082 −0.710408 0.703791i \(-0.751489\pi\)
−0.710408 + 0.703791i \(0.751489\pi\)
\(464\) −26.8815 −1.24794
\(465\) 3.12410 0.144877
\(466\) −66.1979 −3.06656
\(467\) 1.35551 0.0627256 0.0313628 0.999508i \(-0.490015\pi\)
0.0313628 + 0.999508i \(0.490015\pi\)
\(468\) −22.7170 −1.05009
\(469\) 24.3311 1.12351
\(470\) 5.03527 0.232260
\(471\) −15.5407 −0.716076
\(472\) −8.72617 −0.401654
\(473\) −8.73767 −0.401758
\(474\) 11.6474 0.534984
\(475\) −19.3191 −0.886419
\(476\) −152.720 −6.99991
\(477\) 8.92718 0.408747
\(478\) −61.4566 −2.81096
\(479\) −32.2503 −1.47355 −0.736777 0.676136i \(-0.763653\pi\)
−0.736777 + 0.676136i \(0.763653\pi\)
\(480\) −3.59743 −0.164200
\(481\) 0.637324 0.0290595
\(482\) −69.9664 −3.18688
\(483\) 27.1911 1.23724
\(484\) 129.476 5.88527
\(485\) 8.95662 0.406699
\(486\) −2.52915 −0.114725
\(487\) 18.6700 0.846018 0.423009 0.906126i \(-0.360974\pi\)
0.423009 + 0.906126i \(0.360974\pi\)
\(488\) −1.68577 −0.0763114
\(489\) 1.04865 0.0474218
\(490\) −42.5055 −1.92020
\(491\) 21.8665 0.986820 0.493410 0.869797i \(-0.335750\pi\)
0.493410 + 0.869797i \(0.335750\pi\)
\(492\) 14.2538 0.642609
\(493\) 27.1890 1.22453
\(494\) 58.2439 2.62052
\(495\) −5.18813 −0.233189
\(496\) 25.0344 1.12408
\(497\) −11.2609 −0.505122
\(498\) −10.3852 −0.465370
\(499\) 1.31331 0.0587918 0.0293959 0.999568i \(-0.490642\pi\)
0.0293959 + 0.999568i \(0.490642\pi\)
\(500\) −33.4785 −1.49720
\(501\) −3.72886 −0.166593
\(502\) 68.5797 3.06086
\(503\) −18.0579 −0.805162 −0.402581 0.915384i \(-0.631887\pi\)
−0.402581 + 0.915384i \(0.631887\pi\)
\(504\) −31.8450 −1.41849
\(505\) 12.3147 0.547996
\(506\) 83.2498 3.70091
\(507\) 13.6974 0.608324
\(508\) 43.7122 1.93941
\(509\) −22.4330 −0.994325 −0.497162 0.867658i \(-0.665625\pi\)
−0.497162 + 0.867658i \(0.665625\pi\)
\(510\) 13.6407 0.604022
\(511\) −51.8800 −2.29504
\(512\) 50.4168 2.22813
\(513\) 4.45699 0.196781
\(514\) 5.42334 0.239213
\(515\) 2.45427 0.108148
\(516\) 6.04028 0.265909
\(517\) 15.5220 0.682656
\(518\) 1.63897 0.0720124
\(519\) 16.0712 0.705446
\(520\) 25.5482 1.12036
\(521\) 1.48960 0.0652605 0.0326302 0.999467i \(-0.489612\pi\)
0.0326302 + 0.999467i \(0.489612\pi\)
\(522\) 10.4006 0.455223
\(523\) 6.78485 0.296681 0.148340 0.988936i \(-0.452607\pi\)
0.148340 + 0.988936i \(0.452607\pi\)
\(524\) 55.1789 2.41050
\(525\) −22.7728 −0.993887
\(526\) −21.1438 −0.921915
\(527\) −25.3207 −1.10299
\(528\) −41.5741 −1.80928
\(529\) 3.78603 0.164610
\(530\) −18.4181 −0.800031
\(531\) 1.43964 0.0624752
\(532\) 102.951 4.46349
\(533\) −16.7513 −0.725578
\(534\) 35.5257 1.53735
\(535\) 10.5014 0.454014
\(536\) −28.0711 −1.21249
\(537\) 11.0433 0.476554
\(538\) −54.1527 −2.33469
\(539\) −131.030 −5.64384
\(540\) 3.58651 0.154339
\(541\) 4.27699 0.183882 0.0919411 0.995764i \(-0.470693\pi\)
0.0919411 + 0.995764i \(0.470693\pi\)
\(542\) 51.8643 2.22776
\(543\) −14.5280 −0.623454
\(544\) 29.1570 1.25010
\(545\) 7.32073 0.313585
\(546\) 68.6564 2.93822
\(547\) 4.83449 0.206708 0.103354 0.994645i \(-0.467043\pi\)
0.103354 + 0.994645i \(0.467043\pi\)
\(548\) −43.3531 −1.85195
\(549\) 0.278119 0.0118698
\(550\) −69.7226 −2.97298
\(551\) −18.3285 −0.780820
\(552\) −31.3706 −1.33522
\(553\) −24.1951 −1.02888
\(554\) −6.70821 −0.285005
\(555\) −0.100619 −0.00427105
\(556\) −42.2873 −1.79338
\(557\) 18.0229 0.763656 0.381828 0.924233i \(-0.375295\pi\)
0.381828 + 0.924233i \(0.375295\pi\)
\(558\) −9.68597 −0.410040
\(559\) −7.09864 −0.300241
\(560\) 28.0154 1.18387
\(561\) 42.0496 1.77534
\(562\) 40.0674 1.69014
\(563\) −10.5577 −0.444954 −0.222477 0.974938i \(-0.571414\pi\)
−0.222477 + 0.974938i \(0.571414\pi\)
\(564\) −10.7302 −0.451824
\(565\) 8.34715 0.351167
\(566\) −52.9370 −2.22511
\(567\) 5.25378 0.220638
\(568\) 12.9919 0.545126
\(569\) −18.2849 −0.766541 −0.383270 0.923636i \(-0.625202\pi\)
−0.383270 + 0.923636i \(0.625202\pi\)
\(570\) −9.19543 −0.385154
\(571\) 2.09919 0.0878482 0.0439241 0.999035i \(-0.486014\pi\)
0.0439241 + 0.999035i \(0.486014\pi\)
\(572\) 144.479 6.04098
\(573\) −24.4500 −1.02141
\(574\) −43.0784 −1.79806
\(575\) −22.4336 −0.935545
\(576\) −1.92021 −0.0800087
\(577\) −14.3889 −0.599017 −0.299508 0.954094i \(-0.596823\pi\)
−0.299508 + 0.954094i \(0.596823\pi\)
\(578\) −67.5621 −2.81021
\(579\) −1.86342 −0.0774410
\(580\) −14.7488 −0.612413
\(581\) 21.5730 0.895000
\(582\) −27.7691 −1.15107
\(583\) −56.7765 −2.35144
\(584\) 59.8545 2.47680
\(585\) −4.21494 −0.174266
\(586\) −0.356986 −0.0147470
\(587\) −18.8266 −0.777056 −0.388528 0.921437i \(-0.627016\pi\)
−0.388528 + 0.921437i \(0.627016\pi\)
\(588\) 90.5797 3.73544
\(589\) 17.0691 0.703319
\(590\) −2.97020 −0.122281
\(591\) 24.4286 1.00486
\(592\) −0.806294 −0.0331385
\(593\) −32.0628 −1.31666 −0.658330 0.752730i \(-0.728737\pi\)
−0.658330 + 0.752730i \(0.728737\pi\)
\(594\) 16.0853 0.659988
\(595\) −28.3358 −1.16166
\(596\) 60.2849 2.46937
\(597\) −9.71993 −0.397810
\(598\) 67.6337 2.76575
\(599\) 27.6103 1.12813 0.564064 0.825731i \(-0.309237\pi\)
0.564064 + 0.825731i \(0.309237\pi\)
\(600\) 26.2732 1.07260
\(601\) −37.9500 −1.54801 −0.774006 0.633178i \(-0.781750\pi\)
−0.774006 + 0.633178i \(0.781750\pi\)
\(602\) −18.2552 −0.744028
\(603\) 4.63116 0.188596
\(604\) 91.4295 3.72021
\(605\) 24.0231 0.976679
\(606\) −38.1805 −1.55098
\(607\) 9.06645 0.367996 0.183998 0.982927i \(-0.441096\pi\)
0.183998 + 0.982927i \(0.441096\pi\)
\(608\) −19.6552 −0.797124
\(609\) −21.6052 −0.875486
\(610\) −0.573801 −0.0232325
\(611\) 12.6103 0.510160
\(612\) −29.0686 −1.17503
\(613\) 25.0983 1.01371 0.506855 0.862031i \(-0.330808\pi\)
0.506855 + 0.862031i \(0.330808\pi\)
\(614\) 57.0576 2.30266
\(615\) 2.64466 0.106643
\(616\) 202.533 8.16029
\(617\) 34.9807 1.40827 0.704134 0.710067i \(-0.251335\pi\)
0.704134 + 0.710067i \(0.251335\pi\)
\(618\) −7.60922 −0.306088
\(619\) −3.48882 −0.140227 −0.0701137 0.997539i \(-0.522336\pi\)
−0.0701137 + 0.997539i \(0.522336\pi\)
\(620\) 13.7354 0.551627
\(621\) 5.17552 0.207687
\(622\) −39.4191 −1.58056
\(623\) −73.7973 −2.95663
\(624\) −33.7756 −1.35211
\(625\) 15.4611 0.618445
\(626\) 40.5337 1.62005
\(627\) −28.3463 −1.13204
\(628\) −68.3260 −2.72650
\(629\) 0.815516 0.0325168
\(630\) −10.8393 −0.431850
\(631\) −35.3004 −1.40529 −0.702644 0.711541i \(-0.747997\pi\)
−0.702644 + 0.711541i \(0.747997\pi\)
\(632\) 27.9141 1.11037
\(633\) 4.43381 0.176228
\(634\) −19.7262 −0.783428
\(635\) 8.11040 0.321852
\(636\) 39.2492 1.55633
\(637\) −106.451 −4.21774
\(638\) −66.1477 −2.61881
\(639\) −2.14340 −0.0847914
\(640\) 11.1565 0.441001
\(641\) −7.60745 −0.300476 −0.150238 0.988650i \(-0.548004\pi\)
−0.150238 + 0.988650i \(0.548004\pi\)
\(642\) −32.5585 −1.28498
\(643\) −33.0934 −1.30508 −0.652538 0.757756i \(-0.726296\pi\)
−0.652538 + 0.757756i \(0.726296\pi\)
\(644\) 119.548 4.71086
\(645\) 1.12072 0.0441283
\(646\) 74.5286 2.93229
\(647\) −18.0506 −0.709642 −0.354821 0.934934i \(-0.615458\pi\)
−0.354821 + 0.934934i \(0.615458\pi\)
\(648\) −6.06134 −0.238112
\(649\) −9.15608 −0.359408
\(650\) −56.6439 −2.22176
\(651\) 20.1206 0.788588
\(652\) 4.61051 0.180561
\(653\) 3.10820 0.121633 0.0608166 0.998149i \(-0.480630\pi\)
0.0608166 + 0.998149i \(0.480630\pi\)
\(654\) −22.6972 −0.887531
\(655\) 10.2380 0.400030
\(656\) 21.1925 0.827426
\(657\) −9.87479 −0.385252
\(658\) 32.4294 1.26423
\(659\) −13.0131 −0.506918 −0.253459 0.967346i \(-0.581568\pi\)
−0.253459 + 0.967346i \(0.581568\pi\)
\(660\) −22.8101 −0.887882
\(661\) −2.40314 −0.0934712 −0.0467356 0.998907i \(-0.514882\pi\)
−0.0467356 + 0.998907i \(0.514882\pi\)
\(662\) −28.7281 −1.11655
\(663\) 34.1619 1.32674
\(664\) −24.8890 −0.965881
\(665\) 19.1016 0.740729
\(666\) 0.311961 0.0120882
\(667\) −21.2833 −0.824094
\(668\) −16.3943 −0.634314
\(669\) −22.5583 −0.872155
\(670\) −9.55478 −0.369133
\(671\) −1.76883 −0.0682848
\(672\) −23.1691 −0.893766
\(673\) −41.2556 −1.59029 −0.795143 0.606422i \(-0.792604\pi\)
−0.795143 + 0.606422i \(0.792604\pi\)
\(674\) 22.0875 0.850779
\(675\) −4.33455 −0.166837
\(676\) 60.2220 2.31623
\(677\) 33.8765 1.30198 0.650990 0.759086i \(-0.274354\pi\)
0.650990 + 0.759086i \(0.274354\pi\)
\(678\) −25.8795 −0.993897
\(679\) 57.6846 2.21373
\(680\) 32.6913 1.25365
\(681\) −11.3839 −0.436231
\(682\) 61.6024 2.35888
\(683\) −30.4773 −1.16618 −0.583091 0.812407i \(-0.698157\pi\)
−0.583091 + 0.812407i \(0.698157\pi\)
\(684\) 19.5956 0.749255
\(685\) −8.04377 −0.307337
\(686\) −180.741 −6.90073
\(687\) 26.7214 1.01949
\(688\) 8.98068 0.342385
\(689\) −46.1263 −1.75727
\(690\) −10.6779 −0.406500
\(691\) 4.74001 0.180318 0.0901592 0.995927i \(-0.471262\pi\)
0.0901592 + 0.995927i \(0.471262\pi\)
\(692\) 70.6584 2.68603
\(693\) −33.4139 −1.26929
\(694\) −66.1780 −2.51208
\(695\) −7.84604 −0.297617
\(696\) 24.9261 0.944821
\(697\) −21.4348 −0.811902
\(698\) −55.3606 −2.09543
\(699\) 26.1740 0.989991
\(700\) −100.123 −3.78429
\(701\) 42.7459 1.61449 0.807244 0.590217i \(-0.200958\pi\)
0.807244 + 0.590217i \(0.200958\pi\)
\(702\) 13.0680 0.493220
\(703\) −0.549752 −0.0207343
\(704\) 12.2125 0.460274
\(705\) −1.99090 −0.0749815
\(706\) 27.6564 1.04086
\(707\) 79.3120 2.98284
\(708\) 6.32953 0.237878
\(709\) −7.14601 −0.268374 −0.134187 0.990956i \(-0.542842\pi\)
−0.134187 + 0.990956i \(0.542842\pi\)
\(710\) 4.42214 0.165960
\(711\) −4.60528 −0.172711
\(712\) 85.1407 3.19078
\(713\) 19.8209 0.742298
\(714\) 87.8524 3.28779
\(715\) 26.8068 1.00252
\(716\) 48.5530 1.81451
\(717\) 24.2993 0.907474
\(718\) −61.0082 −2.27681
\(719\) 34.8129 1.29830 0.649151 0.760660i \(-0.275124\pi\)
0.649151 + 0.760660i \(0.275124\pi\)
\(720\) 5.33242 0.198728
\(721\) 15.8066 0.588668
\(722\) −2.18707 −0.0813943
\(723\) 27.6640 1.02884
\(724\) −63.8735 −2.37384
\(725\) 17.8250 0.662004
\(726\) −74.4813 −2.76426
\(727\) 38.0102 1.40972 0.704861 0.709346i \(-0.251010\pi\)
0.704861 + 0.709346i \(0.251010\pi\)
\(728\) 164.542 6.09832
\(729\) 1.00000 0.0370370
\(730\) 20.3732 0.754045
\(731\) −9.08339 −0.335961
\(732\) 1.22278 0.0451951
\(733\) 14.8430 0.548240 0.274120 0.961695i \(-0.411613\pi\)
0.274120 + 0.961695i \(0.411613\pi\)
\(734\) −20.4823 −0.756015
\(735\) 16.8063 0.619908
\(736\) −22.8239 −0.841301
\(737\) −29.4540 −1.08495
\(738\) −8.19950 −0.301828
\(739\) 23.9987 0.882805 0.441403 0.897309i \(-0.354481\pi\)
0.441403 + 0.897309i \(0.354481\pi\)
\(740\) −0.442383 −0.0162623
\(741\) −23.0291 −0.845993
\(742\) −118.621 −4.35470
\(743\) −26.5385 −0.973604 −0.486802 0.873512i \(-0.661837\pi\)
−0.486802 + 0.873512i \(0.661837\pi\)
\(744\) −23.2133 −0.851042
\(745\) 11.1853 0.409798
\(746\) 76.3786 2.79642
\(747\) 4.10619 0.150238
\(748\) 184.875 6.75970
\(749\) 67.6335 2.47128
\(750\) 19.2586 0.703224
\(751\) −18.6788 −0.681598 −0.340799 0.940136i \(-0.610698\pi\)
−0.340799 + 0.940136i \(0.610698\pi\)
\(752\) −15.9537 −0.581771
\(753\) −27.1157 −0.988152
\(754\) −53.7396 −1.95708
\(755\) 16.9639 0.617381
\(756\) 23.0988 0.840094
\(757\) 25.2476 0.917639 0.458820 0.888529i \(-0.348272\pi\)
0.458820 + 0.888529i \(0.348272\pi\)
\(758\) 2.24075 0.0813876
\(759\) −32.9161 −1.19478
\(760\) −22.0377 −0.799392
\(761\) 29.1007 1.05490 0.527450 0.849586i \(-0.323148\pi\)
0.527450 + 0.849586i \(0.323148\pi\)
\(762\) −25.1455 −0.910926
\(763\) 47.1487 1.70690
\(764\) −107.497 −3.88910
\(765\) −5.39341 −0.194999
\(766\) 44.3171 1.60124
\(767\) −7.43857 −0.268591
\(768\) −30.7493 −1.10957
\(769\) −14.3068 −0.515918 −0.257959 0.966156i \(-0.583050\pi\)
−0.257959 + 0.966156i \(0.583050\pi\)
\(770\) 68.9378 2.48435
\(771\) −2.14433 −0.0772263
\(772\) −8.19269 −0.294861
\(773\) −15.0572 −0.541570 −0.270785 0.962640i \(-0.587283\pi\)
−0.270785 + 0.962640i \(0.587283\pi\)
\(774\) −3.47468 −0.124895
\(775\) −16.6002 −0.596296
\(776\) −66.5513 −2.38905
\(777\) −0.648034 −0.0232481
\(778\) 31.4503 1.12755
\(779\) 14.4496 0.517709
\(780\) −18.5314 −0.663529
\(781\) 13.6319 0.487789
\(782\) 86.5437 3.09480
\(783\) −4.11231 −0.146962
\(784\) 134.674 4.80978
\(785\) −12.6773 −0.452471
\(786\) −31.7418 −1.13219
\(787\) 27.9012 0.994570 0.497285 0.867587i \(-0.334330\pi\)
0.497285 + 0.867587i \(0.334330\pi\)
\(788\) 107.403 3.82606
\(789\) 8.36006 0.297626
\(790\) 9.50137 0.338044
\(791\) 53.7594 1.91146
\(792\) 38.5499 1.36981
\(793\) −1.43703 −0.0510303
\(794\) −7.85545 −0.278779
\(795\) 7.28233 0.258278
\(796\) −42.7346 −1.51469
\(797\) 46.4009 1.64360 0.821802 0.569773i \(-0.192969\pi\)
0.821802 + 0.569773i \(0.192969\pi\)
\(798\) −59.2227 −2.09646
\(799\) 16.1361 0.570855
\(800\) 19.1153 0.675827
\(801\) −14.0465 −0.496309
\(802\) −39.8300 −1.40645
\(803\) 62.8033 2.21628
\(804\) 20.3613 0.718089
\(805\) 22.1811 0.781780
\(806\) 50.0470 1.76283
\(807\) 21.4114 0.753718
\(808\) −91.5031 −3.21907
\(809\) −37.0751 −1.30349 −0.651746 0.758437i \(-0.725963\pi\)
−0.651746 + 0.758437i \(0.725963\pi\)
\(810\) −2.06315 −0.0724917
\(811\) −38.1341 −1.33907 −0.669534 0.742782i \(-0.733506\pi\)
−0.669534 + 0.742782i \(0.733506\pi\)
\(812\) −94.9892 −3.33347
\(813\) −20.5066 −0.719199
\(814\) −1.98406 −0.0695412
\(815\) 0.855438 0.0299647
\(816\) −43.2191 −1.51297
\(817\) 6.12325 0.214226
\(818\) −46.5087 −1.62614
\(819\) −27.1461 −0.948560
\(820\) 11.6275 0.406049
\(821\) 8.85943 0.309196 0.154598 0.987977i \(-0.450592\pi\)
0.154598 + 0.987977i \(0.450592\pi\)
\(822\) 24.9389 0.869845
\(823\) 41.4618 1.44527 0.722634 0.691231i \(-0.242931\pi\)
0.722634 + 0.691231i \(0.242931\pi\)
\(824\) −18.2362 −0.635288
\(825\) 27.5676 0.959781
\(826\) −19.1294 −0.665597
\(827\) −20.2918 −0.705614 −0.352807 0.935696i \(-0.614773\pi\)
−0.352807 + 0.935696i \(0.614773\pi\)
\(828\) 22.7547 0.790779
\(829\) −14.3053 −0.496842 −0.248421 0.968652i \(-0.579912\pi\)
−0.248421 + 0.968652i \(0.579912\pi\)
\(830\) −8.47168 −0.294056
\(831\) 2.65236 0.0920094
\(832\) 9.92163 0.343971
\(833\) −136.214 −4.71954
\(834\) 24.3259 0.842336
\(835\) −3.04181 −0.105266
\(836\) −124.627 −4.31032
\(837\) 3.82973 0.132375
\(838\) 35.8069 1.23693
\(839\) 2.58469 0.0892336 0.0446168 0.999004i \(-0.485793\pi\)
0.0446168 + 0.999004i \(0.485793\pi\)
\(840\) −25.9775 −0.896309
\(841\) −12.0889 −0.416860
\(842\) −96.2522 −3.31707
\(843\) −15.8422 −0.545636
\(844\) 19.4937 0.671000
\(845\) 11.1736 0.384385
\(846\) 6.17258 0.212218
\(847\) 154.720 5.31623
\(848\) 58.3556 2.00394
\(849\) 20.9307 0.718341
\(850\) −72.4813 −2.48609
\(851\) −0.638380 −0.0218834
\(852\) −9.42364 −0.322849
\(853\) −15.3580 −0.525848 −0.262924 0.964817i \(-0.584687\pi\)
−0.262924 + 0.964817i \(0.584687\pi\)
\(854\) −3.69553 −0.126459
\(855\) 3.63578 0.124341
\(856\) −78.0295 −2.66699
\(857\) −17.6342 −0.602373 −0.301186 0.953565i \(-0.597383\pi\)
−0.301186 + 0.953565i \(0.597383\pi\)
\(858\) −83.1120 −2.83740
\(859\) 13.2189 0.451022 0.225511 0.974241i \(-0.427595\pi\)
0.225511 + 0.974241i \(0.427595\pi\)
\(860\) 4.92735 0.168021
\(861\) 17.0328 0.580475
\(862\) −5.21764 −0.177714
\(863\) −38.0378 −1.29482 −0.647410 0.762142i \(-0.724148\pi\)
−0.647410 + 0.762142i \(0.724148\pi\)
\(864\) −4.40998 −0.150030
\(865\) 13.1100 0.445754
\(866\) −12.0711 −0.410191
\(867\) 26.7134 0.907234
\(868\) 88.4621 3.00260
\(869\) 29.2894 0.993575
\(870\) 8.48430 0.287645
\(871\) −23.9290 −0.810804
\(872\) −54.3960 −1.84208
\(873\) 10.9796 0.371604
\(874\) −58.3405 −1.97340
\(875\) −40.0057 −1.35244
\(876\) −43.4154 −1.46687
\(877\) −54.4413 −1.83835 −0.919176 0.393846i \(-0.871144\pi\)
−0.919176 + 0.393846i \(0.871144\pi\)
\(878\) 1.00739 0.0339979
\(879\) 0.141149 0.00476083
\(880\) −33.9140 −1.14324
\(881\) 1.82979 0.0616473 0.0308236 0.999525i \(-0.490187\pi\)
0.0308236 + 0.999525i \(0.490187\pi\)
\(882\) −52.1062 −1.75451
\(883\) 46.3766 1.56070 0.780349 0.625344i \(-0.215041\pi\)
0.780349 + 0.625344i \(0.215041\pi\)
\(884\) 150.196 5.05163
\(885\) 1.17439 0.0394766
\(886\) −31.9984 −1.07501
\(887\) −13.3258 −0.447437 −0.223719 0.974654i \(-0.571820\pi\)
−0.223719 + 0.974654i \(0.571820\pi\)
\(888\) 0.747643 0.0250892
\(889\) 52.2346 1.75189
\(890\) 28.9800 0.971413
\(891\) −6.35997 −0.213067
\(892\) −99.1798 −3.32078
\(893\) −10.8776 −0.364006
\(894\) −34.6790 −1.15984
\(895\) 9.00857 0.301123
\(896\) 71.8531 2.40044
\(897\) −26.7417 −0.892879
\(898\) 10.8247 0.361224
\(899\) −15.7490 −0.525260
\(900\) −19.0573 −0.635242
\(901\) −59.0230 −1.96634
\(902\) 52.1485 1.73636
\(903\) 7.21794 0.240198
\(904\) −62.0227 −2.06284
\(905\) −11.8512 −0.393946
\(906\) −52.5950 −1.74735
\(907\) −11.4921 −0.381588 −0.190794 0.981630i \(-0.561106\pi\)
−0.190794 + 0.981630i \(0.561106\pi\)
\(908\) −50.0502 −1.66097
\(909\) 15.0962 0.500708
\(910\) 56.0064 1.85659
\(911\) 50.1767 1.66243 0.831214 0.555952i \(-0.187646\pi\)
0.831214 + 0.555952i \(0.187646\pi\)
\(912\) 29.1347 0.964745
\(913\) −26.1152 −0.864287
\(914\) −84.3650 −2.79054
\(915\) 0.226875 0.00750026
\(916\) 117.483 3.88175
\(917\) 65.9370 2.17743
\(918\) 16.7217 0.551900
\(919\) 47.2338 1.55810 0.779049 0.626963i \(-0.215702\pi\)
0.779049 + 0.626963i \(0.215702\pi\)
\(920\) −25.5905 −0.843695
\(921\) −22.5600 −0.743378
\(922\) 39.0680 1.28664
\(923\) 11.0748 0.364532
\(924\) −146.907 −4.83290
\(925\) 0.534650 0.0175792
\(926\) 77.3219 2.54095
\(927\) 3.00861 0.0988156
\(928\) 18.1352 0.595316
\(929\) −50.2828 −1.64973 −0.824863 0.565333i \(-0.808748\pi\)
−0.824863 + 0.565333i \(0.808748\pi\)
\(930\) −7.90131 −0.259094
\(931\) 91.8240 3.00941
\(932\) 115.076 3.76945
\(933\) 15.5859 0.510260
\(934\) −3.42829 −0.112177
\(935\) 34.3019 1.12179
\(936\) 31.3187 1.02368
\(937\) 28.7647 0.939700 0.469850 0.882746i \(-0.344308\pi\)
0.469850 + 0.882746i \(0.344308\pi\)
\(938\) −61.5371 −2.00926
\(939\) −16.0266 −0.523009
\(940\) −8.75316 −0.285497
\(941\) 3.14472 0.102515 0.0512574 0.998685i \(-0.483677\pi\)
0.0512574 + 0.998685i \(0.483677\pi\)
\(942\) 39.3046 1.28061
\(943\) 16.7790 0.546401
\(944\) 9.41073 0.306293
\(945\) 4.28577 0.139416
\(946\) 22.0989 0.718496
\(947\) −36.4896 −1.18575 −0.592876 0.805294i \(-0.702008\pi\)
−0.592876 + 0.805294i \(0.702008\pi\)
\(948\) −20.2475 −0.657609
\(949\) 51.0226 1.65626
\(950\) 48.8608 1.58525
\(951\) 7.79954 0.252917
\(952\) 210.547 6.82385
\(953\) 8.92112 0.288984 0.144492 0.989506i \(-0.453845\pi\)
0.144492 + 0.989506i \(0.453845\pi\)
\(954\) −22.5782 −0.730995
\(955\) −19.9451 −0.645408
\(956\) 106.834 3.45526
\(957\) 26.1541 0.845443
\(958\) 81.5658 2.63527
\(959\) −51.8055 −1.67289
\(960\) −1.56641 −0.0505556
\(961\) −16.3331 −0.526875
\(962\) −1.61189 −0.0519693
\(963\) 12.8733 0.414836
\(964\) 121.627 3.91736
\(965\) −1.52008 −0.0489331
\(966\) −68.7703 −2.21265
\(967\) 35.8043 1.15139 0.575694 0.817665i \(-0.304732\pi\)
0.575694 + 0.817665i \(0.304732\pi\)
\(968\) −178.501 −5.73726
\(969\) −29.4679 −0.946644
\(970\) −22.6526 −0.727332
\(971\) −39.7923 −1.27700 −0.638498 0.769623i \(-0.720444\pi\)
−0.638498 + 0.769623i \(0.720444\pi\)
\(972\) 4.39659 0.141021
\(973\) −50.5320 −1.61998
\(974\) −47.2192 −1.51300
\(975\) 22.3964 0.717260
\(976\) 1.81802 0.0581934
\(977\) 0.229643 0.00734693 0.00367346 0.999993i \(-0.498831\pi\)
0.00367346 + 0.999993i \(0.498831\pi\)
\(978\) −2.65220 −0.0848081
\(979\) 89.3353 2.85517
\(980\) 73.8903 2.36034
\(981\) 8.97425 0.286526
\(982\) −55.3036 −1.76481
\(983\) 15.3595 0.489891 0.244946 0.969537i \(-0.421230\pi\)
0.244946 + 0.969537i \(0.421230\pi\)
\(984\) −19.6509 −0.626447
\(985\) 19.9276 0.634946
\(986\) −68.7649 −2.18992
\(987\) −12.8223 −0.408137
\(988\) −101.249 −3.22117
\(989\) 7.11041 0.226098
\(990\) 13.1216 0.417031
\(991\) 38.8354 1.23365 0.616824 0.787101i \(-0.288419\pi\)
0.616824 + 0.787101i \(0.288419\pi\)
\(992\) −16.8890 −0.536227
\(993\) 11.3588 0.360460
\(994\) 28.4806 0.903349
\(995\) −7.92902 −0.251367
\(996\) 18.0532 0.572039
\(997\) −9.02718 −0.285894 −0.142947 0.989730i \(-0.545658\pi\)
−0.142947 + 0.989730i \(0.545658\pi\)
\(998\) −3.32156 −0.105142
\(999\) −0.123346 −0.00390250
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 \(a_p\))