Properties

Label 8018.2.a.d.1.4
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.56870 q^{3}\) \(+1.00000 q^{4}\) \(-1.11955 q^{5}\) \(-2.56870 q^{6}\) \(-1.44974 q^{7}\) \(+1.00000 q^{8}\) \(+3.59821 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.56870 q^{3}\) \(+1.00000 q^{4}\) \(-1.11955 q^{5}\) \(-2.56870 q^{6}\) \(-1.44974 q^{7}\) \(+1.00000 q^{8}\) \(+3.59821 q^{9}\) \(-1.11955 q^{10}\) \(-1.59607 q^{11}\) \(-2.56870 q^{12}\) \(+3.12799 q^{13}\) \(-1.44974 q^{14}\) \(+2.87579 q^{15}\) \(+1.00000 q^{16}\) \(-5.27438 q^{17}\) \(+3.59821 q^{18}\) \(+1.00000 q^{19}\) \(-1.11955 q^{20}\) \(+3.72395 q^{21}\) \(-1.59607 q^{22}\) \(-0.783250 q^{23}\) \(-2.56870 q^{24}\) \(-3.74661 q^{25}\) \(+3.12799 q^{26}\) \(-1.53663 q^{27}\) \(-1.44974 q^{28}\) \(+8.48094 q^{29}\) \(+2.87579 q^{30}\) \(+4.24784 q^{31}\) \(+1.00000 q^{32}\) \(+4.09983 q^{33}\) \(-5.27438 q^{34}\) \(+1.62306 q^{35}\) \(+3.59821 q^{36}\) \(-7.23807 q^{37}\) \(+1.00000 q^{38}\) \(-8.03487 q^{39}\) \(-1.11955 q^{40}\) \(-0.308723 q^{41}\) \(+3.72395 q^{42}\) \(+10.5372 q^{43}\) \(-1.59607 q^{44}\) \(-4.02838 q^{45}\) \(-0.783250 q^{46}\) \(+1.70974 q^{47}\) \(-2.56870 q^{48}\) \(-4.89825 q^{49}\) \(-3.74661 q^{50}\) \(+13.5483 q^{51}\) \(+3.12799 q^{52}\) \(+6.97906 q^{53}\) \(-1.53663 q^{54}\) \(+1.78689 q^{55}\) \(-1.44974 q^{56}\) \(-2.56870 q^{57}\) \(+8.48094 q^{58}\) \(-12.0572 q^{59}\) \(+2.87579 q^{60}\) \(-0.529483 q^{61}\) \(+4.24784 q^{62}\) \(-5.21648 q^{63}\) \(+1.00000 q^{64}\) \(-3.50195 q^{65}\) \(+4.09983 q^{66}\) \(+4.61367 q^{67}\) \(-5.27438 q^{68}\) \(+2.01193 q^{69}\) \(+1.62306 q^{70}\) \(-2.79282 q^{71}\) \(+3.59821 q^{72}\) \(+13.8081 q^{73}\) \(-7.23807 q^{74}\) \(+9.62390 q^{75}\) \(+1.00000 q^{76}\) \(+2.31390 q^{77}\) \(-8.03487 q^{78}\) \(-5.27871 q^{79}\) \(-1.11955 q^{80}\) \(-6.84751 q^{81}\) \(-0.308723 q^{82}\) \(+9.23497 q^{83}\) \(+3.72395 q^{84}\) \(+5.90493 q^{85}\) \(+10.5372 q^{86}\) \(-21.7850 q^{87}\) \(-1.59607 q^{88}\) \(-4.76645 q^{89}\) \(-4.02838 q^{90}\) \(-4.53478 q^{91}\) \(-0.783250 q^{92}\) \(-10.9114 q^{93}\) \(+1.70974 q^{94}\) \(-1.11955 q^{95}\) \(-2.56870 q^{96}\) \(-12.8257 q^{97}\) \(-4.89825 q^{98}\) \(-5.74301 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 17q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 19q^{13} \) \(\mathstrut -\mathstrut 15q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 10q^{18} \) \(\mathstrut +\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut -\mathstrut 17q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 10q^{24} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 19q^{26} \) \(\mathstrut -\mathstrut 37q^{27} \) \(\mathstrut -\mathstrut 15q^{28} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 30q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 10q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut +\mathstrut 30q^{38} \) \(\mathstrut -\mathstrut 12q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 14q^{42} \) \(\mathstrut -\mathstrut 61q^{43} \) \(\mathstrut -\mathstrut 17q^{44} \) \(\mathstrut -\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 19q^{52} \) \(\mathstrut -\mathstrut 19q^{53} \) \(\mathstrut -\mathstrut 37q^{54} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 37q^{58} \) \(\mathstrut -\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut -\mathstrut 11q^{62} \) \(\mathstrut -\mathstrut 24q^{63} \) \(\mathstrut +\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 18q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 10q^{72} \) \(\mathstrut -\mathstrut 58q^{73} \) \(\mathstrut -\mathstrut 46q^{74} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut -\mathstrut 32q^{77} \) \(\mathstrut -\mathstrut 42q^{79} \) \(\mathstrut -\mathstrut 12q^{80} \) \(\mathstrut -\mathstrut 38q^{81} \) \(\mathstrut -\mathstrut 28q^{82} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 48q^{85} \) \(\mathstrut -\mathstrut 61q^{86} \) \(\mathstrut -\mathstrut 15q^{87} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 39q^{89} \) \(\mathstrut -\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 45q^{93} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut -\mathstrut 38q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.56870 −1.48304 −0.741519 0.670931i \(-0.765894\pi\)
−0.741519 + 0.670931i \(0.765894\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.11955 −0.500678 −0.250339 0.968158i \(-0.580542\pi\)
−0.250339 + 0.968158i \(0.580542\pi\)
\(6\) −2.56870 −1.04867
\(7\) −1.44974 −0.547951 −0.273975 0.961737i \(-0.588339\pi\)
−0.273975 + 0.961737i \(0.588339\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.59821 1.19940
\(10\) −1.11955 −0.354033
\(11\) −1.59607 −0.481234 −0.240617 0.970620i \(-0.577350\pi\)
−0.240617 + 0.970620i \(0.577350\pi\)
\(12\) −2.56870 −0.741519
\(13\) 3.12799 0.867549 0.433775 0.901021i \(-0.357181\pi\)
0.433775 + 0.901021i \(0.357181\pi\)
\(14\) −1.44974 −0.387460
\(15\) 2.87579 0.742525
\(16\) 1.00000 0.250000
\(17\) −5.27438 −1.27922 −0.639612 0.768698i \(-0.720905\pi\)
−0.639612 + 0.768698i \(0.720905\pi\)
\(18\) 3.59821 0.848107
\(19\) 1.00000 0.229416
\(20\) −1.11955 −0.250339
\(21\) 3.72395 0.812632
\(22\) −1.59607 −0.340284
\(23\) −0.783250 −0.163319 −0.0816594 0.996660i \(-0.526022\pi\)
−0.0816594 + 0.996660i \(0.526022\pi\)
\(24\) −2.56870 −0.524333
\(25\) −3.74661 −0.749321
\(26\) 3.12799 0.613450
\(27\) −1.53663 −0.295724
\(28\) −1.44974 −0.273975
\(29\) 8.48094 1.57487 0.787435 0.616397i \(-0.211408\pi\)
0.787435 + 0.616397i \(0.211408\pi\)
\(30\) 2.87579 0.525044
\(31\) 4.24784 0.762934 0.381467 0.924382i \(-0.375419\pi\)
0.381467 + 0.924382i \(0.375419\pi\)
\(32\) 1.00000 0.176777
\(33\) 4.09983 0.713689
\(34\) −5.27438 −0.904548
\(35\) 1.62306 0.274347
\(36\) 3.59821 0.599702
\(37\) −7.23807 −1.18993 −0.594966 0.803751i \(-0.702834\pi\)
−0.594966 + 0.803751i \(0.702834\pi\)
\(38\) 1.00000 0.162221
\(39\) −8.03487 −1.28661
\(40\) −1.11955 −0.177016
\(41\) −0.308723 −0.0482144 −0.0241072 0.999709i \(-0.507674\pi\)
−0.0241072 + 0.999709i \(0.507674\pi\)
\(42\) 3.72395 0.574618
\(43\) 10.5372 1.60690 0.803452 0.595370i \(-0.202995\pi\)
0.803452 + 0.595370i \(0.202995\pi\)
\(44\) −1.59607 −0.240617
\(45\) −4.02838 −0.600515
\(46\) −0.783250 −0.115484
\(47\) 1.70974 0.249392 0.124696 0.992195i \(-0.460204\pi\)
0.124696 + 0.992195i \(0.460204\pi\)
\(48\) −2.56870 −0.370760
\(49\) −4.89825 −0.699750
\(50\) −3.74661 −0.529850
\(51\) 13.5483 1.89714
\(52\) 3.12799 0.433775
\(53\) 6.97906 0.958647 0.479324 0.877638i \(-0.340882\pi\)
0.479324 + 0.877638i \(0.340882\pi\)
\(54\) −1.53663 −0.209108
\(55\) 1.78689 0.240944
\(56\) −1.44974 −0.193730
\(57\) −2.56870 −0.340232
\(58\) 8.48094 1.11360
\(59\) −12.0572 −1.56971 −0.784854 0.619681i \(-0.787262\pi\)
−0.784854 + 0.619681i \(0.787262\pi\)
\(60\) 2.87579 0.371262
\(61\) −0.529483 −0.0677934 −0.0338967 0.999425i \(-0.510792\pi\)
−0.0338967 + 0.999425i \(0.510792\pi\)
\(62\) 4.24784 0.539476
\(63\) −5.21648 −0.657215
\(64\) 1.00000 0.125000
\(65\) −3.50195 −0.434363
\(66\) 4.09983 0.504655
\(67\) 4.61367 0.563649 0.281825 0.959466i \(-0.409060\pi\)
0.281825 + 0.959466i \(0.409060\pi\)
\(68\) −5.27438 −0.639612
\(69\) 2.01193 0.242208
\(70\) 1.62306 0.193993
\(71\) −2.79282 −0.331447 −0.165723 0.986172i \(-0.552996\pi\)
−0.165723 + 0.986172i \(0.552996\pi\)
\(72\) 3.59821 0.424053
\(73\) 13.8081 1.61612 0.808058 0.589103i \(-0.200519\pi\)
0.808058 + 0.589103i \(0.200519\pi\)
\(74\) −7.23807 −0.841409
\(75\) 9.62390 1.11127
\(76\) 1.00000 0.114708
\(77\) 2.31390 0.263693
\(78\) −8.03487 −0.909770
\(79\) −5.27871 −0.593901 −0.296951 0.954893i \(-0.595970\pi\)
−0.296951 + 0.954893i \(0.595970\pi\)
\(80\) −1.11955 −0.125170
\(81\) −6.84751 −0.760834
\(82\) −0.308723 −0.0340927
\(83\) 9.23497 1.01367 0.506835 0.862043i \(-0.330815\pi\)
0.506835 + 0.862043i \(0.330815\pi\)
\(84\) 3.72395 0.406316
\(85\) 5.90493 0.640480
\(86\) 10.5372 1.13625
\(87\) −21.7850 −2.33559
\(88\) −1.59607 −0.170142
\(89\) −4.76645 −0.505243 −0.252621 0.967565i \(-0.581293\pi\)
−0.252621 + 0.967565i \(0.581293\pi\)
\(90\) −4.02838 −0.424628
\(91\) −4.53478 −0.475374
\(92\) −0.783250 −0.0816594
\(93\) −10.9114 −1.13146
\(94\) 1.70974 0.176347
\(95\) −1.11955 −0.114863
\(96\) −2.56870 −0.262167
\(97\) −12.8257 −1.30225 −0.651125 0.758970i \(-0.725703\pi\)
−0.651125 + 0.758970i \(0.725703\pi\)
\(98\) −4.89825 −0.494798
\(99\) −5.74301 −0.577195
\(100\) −3.74661 −0.374661
\(101\) 14.1213 1.40512 0.702560 0.711625i \(-0.252040\pi\)
0.702560 + 0.711625i \(0.252040\pi\)
\(102\) 13.5483 1.34148
\(103\) 10.7149 1.05577 0.527884 0.849316i \(-0.322985\pi\)
0.527884 + 0.849316i \(0.322985\pi\)
\(104\) 3.12799 0.306725
\(105\) −4.16915 −0.406867
\(106\) 6.97906 0.677866
\(107\) −10.6703 −1.03154 −0.515770 0.856727i \(-0.672494\pi\)
−0.515770 + 0.856727i \(0.672494\pi\)
\(108\) −1.53663 −0.147862
\(109\) −9.54223 −0.913980 −0.456990 0.889472i \(-0.651072\pi\)
−0.456990 + 0.889472i \(0.651072\pi\)
\(110\) 1.78689 0.170373
\(111\) 18.5924 1.76471
\(112\) −1.44974 −0.136988
\(113\) 3.61727 0.340284 0.170142 0.985420i \(-0.445577\pi\)
0.170142 + 0.985420i \(0.445577\pi\)
\(114\) −2.56870 −0.240581
\(115\) 0.876887 0.0817702
\(116\) 8.48094 0.787435
\(117\) 11.2552 1.04054
\(118\) −12.0572 −1.10995
\(119\) 7.64649 0.700952
\(120\) 2.87579 0.262522
\(121\) −8.45255 −0.768413
\(122\) −0.529483 −0.0479372
\(123\) 0.793016 0.0715038
\(124\) 4.24784 0.381467
\(125\) 9.79227 0.875847
\(126\) −5.21648 −0.464721
\(127\) −8.96922 −0.795890 −0.397945 0.917409i \(-0.630277\pi\)
−0.397945 + 0.917409i \(0.630277\pi\)
\(128\) 1.00000 0.0883883
\(129\) −27.0668 −2.38310
\(130\) −3.50195 −0.307141
\(131\) 19.2311 1.68023 0.840115 0.542408i \(-0.182487\pi\)
0.840115 + 0.542408i \(0.182487\pi\)
\(132\) 4.09983 0.356845
\(133\) −1.44974 −0.125709
\(134\) 4.61367 0.398560
\(135\) 1.72033 0.148062
\(136\) −5.27438 −0.452274
\(137\) 8.29430 0.708630 0.354315 0.935126i \(-0.384714\pi\)
0.354315 + 0.935126i \(0.384714\pi\)
\(138\) 2.01193 0.171267
\(139\) 2.58268 0.219060 0.109530 0.993983i \(-0.465065\pi\)
0.109530 + 0.993983i \(0.465065\pi\)
\(140\) 1.62306 0.137174
\(141\) −4.39182 −0.369858
\(142\) −2.79282 −0.234368
\(143\) −4.99251 −0.417495
\(144\) 3.59821 0.299851
\(145\) −9.49484 −0.788503
\(146\) 13.8081 1.14277
\(147\) 12.5821 1.03776
\(148\) −7.23807 −0.594966
\(149\) −3.79596 −0.310977 −0.155489 0.987838i \(-0.549695\pi\)
−0.155489 + 0.987838i \(0.549695\pi\)
\(150\) 9.62390 0.785789
\(151\) −4.42526 −0.360122 −0.180061 0.983655i \(-0.557630\pi\)
−0.180061 + 0.983655i \(0.557630\pi\)
\(152\) 1.00000 0.0811107
\(153\) −18.9783 −1.53431
\(154\) 2.31390 0.186459
\(155\) −4.75567 −0.381984
\(156\) −8.03487 −0.643305
\(157\) −10.9439 −0.873422 −0.436711 0.899602i \(-0.643857\pi\)
−0.436711 + 0.899602i \(0.643857\pi\)
\(158\) −5.27871 −0.419951
\(159\) −17.9271 −1.42171
\(160\) −1.11955 −0.0885082
\(161\) 1.13551 0.0894907
\(162\) −6.84751 −0.537991
\(163\) −7.68585 −0.602002 −0.301001 0.953624i \(-0.597321\pi\)
−0.301001 + 0.953624i \(0.597321\pi\)
\(164\) −0.308723 −0.0241072
\(165\) −4.58997 −0.357329
\(166\) 9.23497 0.716773
\(167\) 12.0757 0.934447 0.467223 0.884139i \(-0.345254\pi\)
0.467223 + 0.884139i \(0.345254\pi\)
\(168\) 3.72395 0.287309
\(169\) −3.21566 −0.247358
\(170\) 5.90493 0.452887
\(171\) 3.59821 0.275162
\(172\) 10.5372 0.803452
\(173\) −12.7449 −0.968976 −0.484488 0.874798i \(-0.660994\pi\)
−0.484488 + 0.874798i \(0.660994\pi\)
\(174\) −21.7850 −1.65151
\(175\) 5.43161 0.410591
\(176\) −1.59607 −0.120309
\(177\) 30.9712 2.32794
\(178\) −4.76645 −0.357260
\(179\) 20.9073 1.56269 0.781344 0.624101i \(-0.214535\pi\)
0.781344 + 0.624101i \(0.214535\pi\)
\(180\) −4.02838 −0.300258
\(181\) 1.33857 0.0994954 0.0497477 0.998762i \(-0.484158\pi\)
0.0497477 + 0.998762i \(0.484158\pi\)
\(182\) −4.53478 −0.336140
\(183\) 1.36008 0.100540
\(184\) −0.783250 −0.0577419
\(185\) 8.10338 0.595773
\(186\) −10.9114 −0.800063
\(187\) 8.41830 0.615607
\(188\) 1.70974 0.124696
\(189\) 2.22771 0.162042
\(190\) −1.11955 −0.0812207
\(191\) −21.7762 −1.57567 −0.787834 0.615888i \(-0.788797\pi\)
−0.787834 + 0.615888i \(0.788797\pi\)
\(192\) −2.56870 −0.185380
\(193\) −4.51037 −0.324663 −0.162332 0.986736i \(-0.551901\pi\)
−0.162332 + 0.986736i \(0.551901\pi\)
\(194\) −12.8257 −0.920830
\(195\) 8.99544 0.644177
\(196\) −4.89825 −0.349875
\(197\) −6.26163 −0.446122 −0.223061 0.974804i \(-0.571605\pi\)
−0.223061 + 0.974804i \(0.571605\pi\)
\(198\) −5.74301 −0.408138
\(199\) −6.13531 −0.434921 −0.217460 0.976069i \(-0.569777\pi\)
−0.217460 + 0.976069i \(0.569777\pi\)
\(200\) −3.74661 −0.264925
\(201\) −11.8511 −0.835914
\(202\) 14.1213 0.993569
\(203\) −12.2952 −0.862952
\(204\) 13.5483 0.948570
\(205\) 0.345631 0.0241399
\(206\) 10.7149 0.746541
\(207\) −2.81830 −0.195885
\(208\) 3.12799 0.216887
\(209\) −1.59607 −0.110403
\(210\) −4.16915 −0.287699
\(211\) −1.00000 −0.0688428
\(212\) 6.97906 0.479324
\(213\) 7.17391 0.491548
\(214\) −10.6703 −0.729409
\(215\) −11.7969 −0.804541
\(216\) −1.53663 −0.104554
\(217\) −6.15827 −0.418050
\(218\) −9.54223 −0.646281
\(219\) −35.4688 −2.39676
\(220\) 1.78689 0.120472
\(221\) −16.4982 −1.10979
\(222\) 18.5924 1.24784
\(223\) −13.4467 −0.900459 −0.450229 0.892913i \(-0.648658\pi\)
−0.450229 + 0.892913i \(0.648658\pi\)
\(224\) −1.44974 −0.0968650
\(225\) −13.4811 −0.898739
\(226\) 3.61727 0.240617
\(227\) −14.0539 −0.932790 −0.466395 0.884577i \(-0.654447\pi\)
−0.466395 + 0.884577i \(0.654447\pi\)
\(228\) −2.56870 −0.170116
\(229\) 3.54804 0.234461 0.117230 0.993105i \(-0.462598\pi\)
0.117230 + 0.993105i \(0.462598\pi\)
\(230\) 0.876887 0.0578202
\(231\) −5.94370 −0.391067
\(232\) 8.48094 0.556801
\(233\) −26.5635 −1.74024 −0.870118 0.492844i \(-0.835957\pi\)
−0.870118 + 0.492844i \(0.835957\pi\)
\(234\) 11.2552 0.735774
\(235\) −1.91414 −0.124865
\(236\) −12.0572 −0.784854
\(237\) 13.5594 0.880778
\(238\) 7.64649 0.495648
\(239\) −4.33166 −0.280192 −0.140096 0.990138i \(-0.544741\pi\)
−0.140096 + 0.990138i \(0.544741\pi\)
\(240\) 2.87579 0.185631
\(241\) 17.5154 1.12827 0.564135 0.825683i \(-0.309210\pi\)
0.564135 + 0.825683i \(0.309210\pi\)
\(242\) −8.45255 −0.543350
\(243\) 22.1991 1.42407
\(244\) −0.529483 −0.0338967
\(245\) 5.48383 0.350349
\(246\) 0.793016 0.0505608
\(247\) 3.12799 0.199029
\(248\) 4.24784 0.269738
\(249\) −23.7218 −1.50331
\(250\) 9.79227 0.619317
\(251\) 17.9688 1.13418 0.567091 0.823655i \(-0.308069\pi\)
0.567091 + 0.823655i \(0.308069\pi\)
\(252\) −5.21648 −0.328607
\(253\) 1.25012 0.0785947
\(254\) −8.96922 −0.562779
\(255\) −15.1680 −0.949856
\(256\) 1.00000 0.0625000
\(257\) −13.8193 −0.862023 −0.431011 0.902346i \(-0.641843\pi\)
−0.431011 + 0.902346i \(0.641843\pi\)
\(258\) −27.0668 −1.68511
\(259\) 10.4933 0.652024
\(260\) −3.50195 −0.217181
\(261\) 30.5162 1.88891
\(262\) 19.2311 1.18810
\(263\) 19.3564 1.19357 0.596783 0.802402i \(-0.296445\pi\)
0.596783 + 0.802402i \(0.296445\pi\)
\(264\) 4.09983 0.252327
\(265\) −7.81341 −0.479974
\(266\) −1.44974 −0.0888894
\(267\) 12.2436 0.749294
\(268\) 4.61367 0.281825
\(269\) −7.48232 −0.456205 −0.228103 0.973637i \(-0.573252\pi\)
−0.228103 + 0.973637i \(0.573252\pi\)
\(270\) 1.72033 0.104696
\(271\) 22.9387 1.39343 0.696713 0.717350i \(-0.254645\pi\)
0.696713 + 0.717350i \(0.254645\pi\)
\(272\) −5.27438 −0.319806
\(273\) 11.6485 0.704999
\(274\) 8.29430 0.501077
\(275\) 5.97986 0.360599
\(276\) 2.01193 0.121104
\(277\) −22.6938 −1.36354 −0.681770 0.731567i \(-0.738789\pi\)
−0.681770 + 0.731567i \(0.738789\pi\)
\(278\) 2.58268 0.154899
\(279\) 15.2846 0.915066
\(280\) 1.62306 0.0969963
\(281\) 11.2472 0.670951 0.335475 0.942049i \(-0.391103\pi\)
0.335475 + 0.942049i \(0.391103\pi\)
\(282\) −4.39182 −0.261529
\(283\) −33.5810 −1.99618 −0.998091 0.0617538i \(-0.980331\pi\)
−0.998091 + 0.0617538i \(0.980331\pi\)
\(284\) −2.79282 −0.165723
\(285\) 2.87579 0.170347
\(286\) −4.99251 −0.295213
\(287\) 0.447568 0.0264191
\(288\) 3.59821 0.212027
\(289\) 10.8191 0.636415
\(290\) −9.49484 −0.557556
\(291\) 32.9453 1.93129
\(292\) 13.8081 0.808058
\(293\) −16.6218 −0.971057 −0.485528 0.874221i \(-0.661373\pi\)
−0.485528 + 0.874221i \(0.661373\pi\)
\(294\) 12.5821 0.733804
\(295\) 13.4986 0.785918
\(296\) −7.23807 −0.420704
\(297\) 2.45257 0.142312
\(298\) −3.79596 −0.219894
\(299\) −2.45000 −0.141687
\(300\) 9.62390 0.555636
\(301\) −15.2762 −0.880504
\(302\) −4.42526 −0.254645
\(303\) −36.2733 −2.08385
\(304\) 1.00000 0.0573539
\(305\) 0.592783 0.0339427
\(306\) −18.9783 −1.08492
\(307\) −23.7172 −1.35361 −0.676806 0.736162i \(-0.736636\pi\)
−0.676806 + 0.736162i \(0.736636\pi\)
\(308\) 2.31390 0.131846
\(309\) −27.5233 −1.56575
\(310\) −4.75567 −0.270104
\(311\) −31.4708 −1.78454 −0.892272 0.451498i \(-0.850890\pi\)
−0.892272 + 0.451498i \(0.850890\pi\)
\(312\) −8.03487 −0.454885
\(313\) −20.0011 −1.13053 −0.565265 0.824910i \(-0.691226\pi\)
−0.565265 + 0.824910i \(0.691226\pi\)
\(314\) −10.9439 −0.617603
\(315\) 5.84011 0.329053
\(316\) −5.27871 −0.296951
\(317\) −20.0539 −1.12634 −0.563169 0.826341i \(-0.690418\pi\)
−0.563169 + 0.826341i \(0.690418\pi\)
\(318\) −17.9271 −1.00530
\(319\) −13.5362 −0.757882
\(320\) −1.11955 −0.0625848
\(321\) 27.4089 1.52981
\(322\) 1.13551 0.0632795
\(323\) −5.27438 −0.293474
\(324\) −6.84751 −0.380417
\(325\) −11.7194 −0.650073
\(326\) −7.68585 −0.425680
\(327\) 24.5111 1.35547
\(328\) −0.308723 −0.0170464
\(329\) −2.47869 −0.136654
\(330\) −4.58997 −0.252669
\(331\) 6.26128 0.344151 0.172075 0.985084i \(-0.444953\pi\)
0.172075 + 0.985084i \(0.444953\pi\)
\(332\) 9.23497 0.506835
\(333\) −26.0441 −1.42721
\(334\) 12.0757 0.660754
\(335\) −5.16523 −0.282207
\(336\) 3.72395 0.203158
\(337\) −14.6756 −0.799431 −0.399715 0.916639i \(-0.630891\pi\)
−0.399715 + 0.916639i \(0.630891\pi\)
\(338\) −3.21566 −0.174909
\(339\) −9.29168 −0.504655
\(340\) 5.90493 0.320240
\(341\) −6.77986 −0.367150
\(342\) 3.59821 0.194569
\(343\) 17.2494 0.931380
\(344\) 10.5372 0.568126
\(345\) −2.25246 −0.121268
\(346\) −12.7449 −0.685170
\(347\) −31.6736 −1.70033 −0.850163 0.526520i \(-0.823497\pi\)
−0.850163 + 0.526520i \(0.823497\pi\)
\(348\) −21.7850 −1.16780
\(349\) −4.24754 −0.227366 −0.113683 0.993517i \(-0.536265\pi\)
−0.113683 + 0.993517i \(0.536265\pi\)
\(350\) 5.43161 0.290332
\(351\) −4.80655 −0.256555
\(352\) −1.59607 −0.0850710
\(353\) 24.0277 1.27886 0.639432 0.768848i \(-0.279169\pi\)
0.639432 + 0.768848i \(0.279169\pi\)
\(354\) 30.9712 1.64610
\(355\) 3.12670 0.165948
\(356\) −4.76645 −0.252621
\(357\) −19.6415 −1.03954
\(358\) 20.9073 1.10499
\(359\) 23.1048 1.21943 0.609713 0.792622i \(-0.291285\pi\)
0.609713 + 0.792622i \(0.291285\pi\)
\(360\) −4.02838 −0.212314
\(361\) 1.00000 0.0526316
\(362\) 1.33857 0.0703539
\(363\) 21.7120 1.13959
\(364\) −4.53478 −0.237687
\(365\) −15.4589 −0.809154
\(366\) 1.36008 0.0710927
\(367\) 9.79259 0.511169 0.255584 0.966787i \(-0.417732\pi\)
0.255584 + 0.966787i \(0.417732\pi\)
\(368\) −0.783250 −0.0408297
\(369\) −1.11085 −0.0578285
\(370\) 8.10338 0.421275
\(371\) −10.1178 −0.525292
\(372\) −10.9114 −0.565730
\(373\) −14.7854 −0.765561 −0.382781 0.923839i \(-0.625033\pi\)
−0.382781 + 0.923839i \(0.625033\pi\)
\(374\) 8.41830 0.435300
\(375\) −25.1534 −1.29891
\(376\) 1.70974 0.0881733
\(377\) 26.5283 1.36628
\(378\) 2.22771 0.114581
\(379\) −32.9460 −1.69232 −0.846160 0.532929i \(-0.821091\pi\)
−0.846160 + 0.532929i \(0.821091\pi\)
\(380\) −1.11955 −0.0574317
\(381\) 23.0392 1.18034
\(382\) −21.7762 −1.11416
\(383\) −2.22797 −0.113844 −0.0569220 0.998379i \(-0.518129\pi\)
−0.0569220 + 0.998379i \(0.518129\pi\)
\(384\) −2.56870 −0.131083
\(385\) −2.59052 −0.132025
\(386\) −4.51037 −0.229572
\(387\) 37.9150 1.92733
\(388\) −12.8257 −0.651125
\(389\) −15.9564 −0.809022 −0.404511 0.914533i \(-0.632558\pi\)
−0.404511 + 0.914533i \(0.632558\pi\)
\(390\) 8.99544 0.455502
\(391\) 4.13115 0.208921
\(392\) −4.89825 −0.247399
\(393\) −49.3989 −2.49185
\(394\) −6.26163 −0.315456
\(395\) 5.90978 0.297353
\(396\) −5.74301 −0.288597
\(397\) −16.5148 −0.828855 −0.414427 0.910082i \(-0.636018\pi\)
−0.414427 + 0.910082i \(0.636018\pi\)
\(398\) −6.13531 −0.307535
\(399\) 3.72395 0.186431
\(400\) −3.74661 −0.187330
\(401\) −1.36916 −0.0683726 −0.0341863 0.999415i \(-0.510884\pi\)
−0.0341863 + 0.999415i \(0.510884\pi\)
\(402\) −11.8511 −0.591080
\(403\) 13.2872 0.661883
\(404\) 14.1213 0.702560
\(405\) 7.66613 0.380933
\(406\) −12.2952 −0.610199
\(407\) 11.5525 0.572636
\(408\) 13.5483 0.670740
\(409\) −33.9138 −1.67693 −0.838464 0.544958i \(-0.816546\pi\)
−0.838464 + 0.544958i \(0.816546\pi\)
\(410\) 0.345631 0.0170695
\(411\) −21.3056 −1.05093
\(412\) 10.7149 0.527884
\(413\) 17.4798 0.860123
\(414\) −2.81830 −0.138512
\(415\) −10.3390 −0.507522
\(416\) 3.12799 0.153362
\(417\) −6.63413 −0.324875
\(418\) −1.59607 −0.0780665
\(419\) −4.70812 −0.230007 −0.115003 0.993365i \(-0.536688\pi\)
−0.115003 + 0.993365i \(0.536688\pi\)
\(420\) −4.16915 −0.203434
\(421\) −5.43867 −0.265065 −0.132532 0.991179i \(-0.542311\pi\)
−0.132532 + 0.991179i \(0.542311\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 6.15202 0.299121
\(424\) 6.97906 0.338933
\(425\) 19.7610 0.958550
\(426\) 7.17391 0.347577
\(427\) 0.767614 0.0371474
\(428\) −10.6703 −0.515770
\(429\) 12.8243 0.619161
\(430\) −11.7969 −0.568897
\(431\) 24.7539 1.19235 0.596177 0.802853i \(-0.296686\pi\)
0.596177 + 0.802853i \(0.296686\pi\)
\(432\) −1.53663 −0.0739309
\(433\) −17.4451 −0.838360 −0.419180 0.907903i \(-0.637682\pi\)
−0.419180 + 0.907903i \(0.637682\pi\)
\(434\) −6.15827 −0.295606
\(435\) 24.3894 1.16938
\(436\) −9.54223 −0.456990
\(437\) −0.783250 −0.0374679
\(438\) −35.4688 −1.69477
\(439\) 27.0520 1.29112 0.645561 0.763708i \(-0.276623\pi\)
0.645561 + 0.763708i \(0.276623\pi\)
\(440\) 1.78689 0.0851864
\(441\) −17.6249 −0.839283
\(442\) −16.4982 −0.784740
\(443\) −11.9016 −0.565460 −0.282730 0.959199i \(-0.591240\pi\)
−0.282730 + 0.959199i \(0.591240\pi\)
\(444\) 18.5924 0.882357
\(445\) 5.33628 0.252964
\(446\) −13.4467 −0.636721
\(447\) 9.75068 0.461191
\(448\) −1.44974 −0.0684939
\(449\) −10.4434 −0.492855 −0.246427 0.969161i \(-0.579257\pi\)
−0.246427 + 0.969161i \(0.579257\pi\)
\(450\) −13.4811 −0.635505
\(451\) 0.492745 0.0232024
\(452\) 3.61727 0.170142
\(453\) 11.3672 0.534075
\(454\) −14.0539 −0.659582
\(455\) 5.07692 0.238010
\(456\) −2.56870 −0.120290
\(457\) −6.79423 −0.317821 −0.158910 0.987293i \(-0.550798\pi\)
−0.158910 + 0.987293i \(0.550798\pi\)
\(458\) 3.54804 0.165789
\(459\) 8.10474 0.378297
\(460\) 0.876887 0.0408851
\(461\) −16.7365 −0.779498 −0.389749 0.920921i \(-0.627438\pi\)
−0.389749 + 0.920921i \(0.627438\pi\)
\(462\) −5.94370 −0.276526
\(463\) 1.46440 0.0680564 0.0340282 0.999421i \(-0.489166\pi\)
0.0340282 + 0.999421i \(0.489166\pi\)
\(464\) 8.48094 0.393718
\(465\) 12.2159 0.566497
\(466\) −26.5635 −1.23053
\(467\) −10.8327 −0.501278 −0.250639 0.968081i \(-0.580641\pi\)
−0.250639 + 0.968081i \(0.580641\pi\)
\(468\) 11.2552 0.520271
\(469\) −6.68863 −0.308852
\(470\) −1.91414 −0.0882929
\(471\) 28.1117 1.29532
\(472\) −12.0572 −0.554975
\(473\) −16.8181 −0.773297
\(474\) 13.5594 0.622804
\(475\) −3.74661 −0.171906
\(476\) 7.64649 0.350476
\(477\) 25.1121 1.14981
\(478\) −4.33166 −0.198125
\(479\) −20.9816 −0.958672 −0.479336 0.877631i \(-0.659123\pi\)
−0.479336 + 0.877631i \(0.659123\pi\)
\(480\) 2.87579 0.131261
\(481\) −22.6406 −1.03232
\(482\) 17.5154 0.797807
\(483\) −2.91678 −0.132718
\(484\) −8.45255 −0.384207
\(485\) 14.3590 0.652008
\(486\) 22.1991 1.00697
\(487\) −19.9002 −0.901764 −0.450882 0.892584i \(-0.648890\pi\)
−0.450882 + 0.892584i \(0.648890\pi\)
\(488\) −0.529483 −0.0239686
\(489\) 19.7426 0.892792
\(490\) 5.48383 0.247734
\(491\) 41.2744 1.86269 0.931345 0.364139i \(-0.118637\pi\)
0.931345 + 0.364139i \(0.118637\pi\)
\(492\) 0.793016 0.0357519
\(493\) −44.7317 −2.01461
\(494\) 3.12799 0.140735
\(495\) 6.42959 0.288989
\(496\) 4.24784 0.190733
\(497\) 4.04887 0.181617
\(498\) −23.7218 −1.06300
\(499\) −21.2431 −0.950972 −0.475486 0.879723i \(-0.657728\pi\)
−0.475486 + 0.879723i \(0.657728\pi\)
\(500\) 9.79227 0.437923
\(501\) −31.0189 −1.38582
\(502\) 17.9688 0.801988
\(503\) 24.6494 1.09906 0.549531 0.835473i \(-0.314806\pi\)
0.549531 + 0.835473i \(0.314806\pi\)
\(504\) −5.21648 −0.232360
\(505\) −15.8095 −0.703512
\(506\) 1.25012 0.0555748
\(507\) 8.26006 0.366842
\(508\) −8.96922 −0.397945
\(509\) −32.1847 −1.42656 −0.713281 0.700878i \(-0.752792\pi\)
−0.713281 + 0.700878i \(0.752792\pi\)
\(510\) −15.1680 −0.671650
\(511\) −20.0182 −0.885552
\(512\) 1.00000 0.0441942
\(513\) −1.53663 −0.0678437
\(514\) −13.8193 −0.609542
\(515\) −11.9958 −0.528600
\(516\) −27.0668 −1.19155
\(517\) −2.72888 −0.120016
\(518\) 10.4933 0.461051
\(519\) 32.7378 1.43703
\(520\) −3.50195 −0.153570
\(521\) 30.9918 1.35777 0.678887 0.734243i \(-0.262463\pi\)
0.678887 + 0.734243i \(0.262463\pi\)
\(522\) 30.5162 1.33566
\(523\) 19.9724 0.873332 0.436666 0.899624i \(-0.356159\pi\)
0.436666 + 0.899624i \(0.356159\pi\)
\(524\) 19.2311 0.840115
\(525\) −13.9522 −0.608923
\(526\) 19.3564 0.843979
\(527\) −22.4047 −0.975963
\(528\) 4.09983 0.178422
\(529\) −22.3865 −0.973327
\(530\) −7.81341 −0.339393
\(531\) −43.3842 −1.88271
\(532\) −1.44974 −0.0628543
\(533\) −0.965683 −0.0418284
\(534\) 12.2436 0.529831
\(535\) 11.9460 0.516470
\(536\) 4.61367 0.199280
\(537\) −53.7046 −2.31753
\(538\) −7.48232 −0.322586
\(539\) 7.81797 0.336744
\(540\) 1.72033 0.0740312
\(541\) −19.8748 −0.854483 −0.427242 0.904137i \(-0.640515\pi\)
−0.427242 + 0.904137i \(0.640515\pi\)
\(542\) 22.9387 0.985300
\(543\) −3.43839 −0.147556
\(544\) −5.27438 −0.226137
\(545\) 10.6830 0.457610
\(546\) 11.6485 0.498509
\(547\) −3.92524 −0.167831 −0.0839156 0.996473i \(-0.526743\pi\)
−0.0839156 + 0.996473i \(0.526743\pi\)
\(548\) 8.29430 0.354315
\(549\) −1.90519 −0.0813116
\(550\) 5.97986 0.254982
\(551\) 8.48094 0.361300
\(552\) 2.01193 0.0856335
\(553\) 7.65277 0.325429
\(554\) −22.6938 −0.964168
\(555\) −20.8151 −0.883554
\(556\) 2.58268 0.109530
\(557\) 16.5212 0.700027 0.350014 0.936745i \(-0.386177\pi\)
0.350014 + 0.936745i \(0.386177\pi\)
\(558\) 15.2846 0.647049
\(559\) 32.9602 1.39407
\(560\) 1.62306 0.0685868
\(561\) −21.6241 −0.912969
\(562\) 11.2472 0.474434
\(563\) −25.7588 −1.08560 −0.542801 0.839861i \(-0.682636\pi\)
−0.542801 + 0.839861i \(0.682636\pi\)
\(564\) −4.39182 −0.184929
\(565\) −4.04972 −0.170373
\(566\) −33.5810 −1.41151
\(567\) 9.92712 0.416900
\(568\) −2.79282 −0.117184
\(569\) 27.8785 1.16873 0.584364 0.811492i \(-0.301344\pi\)
0.584364 + 0.811492i \(0.301344\pi\)
\(570\) 2.87579 0.120453
\(571\) −9.63791 −0.403334 −0.201667 0.979454i \(-0.564636\pi\)
−0.201667 + 0.979454i \(0.564636\pi\)
\(572\) −4.99251 −0.208747
\(573\) 55.9364 2.33678
\(574\) 0.447568 0.0186811
\(575\) 2.93453 0.122378
\(576\) 3.59821 0.149925
\(577\) −10.3302 −0.430052 −0.215026 0.976608i \(-0.568984\pi\)
−0.215026 + 0.976608i \(0.568984\pi\)
\(578\) 10.8191 0.450013
\(579\) 11.5858 0.481488
\(580\) −9.49484 −0.394252
\(581\) −13.3883 −0.555441
\(582\) 32.9453 1.36563
\(583\) −11.1391 −0.461334
\(584\) 13.8081 0.571383
\(585\) −12.6007 −0.520977
\(586\) −16.6218 −0.686641
\(587\) 42.4384 1.75162 0.875810 0.482655i \(-0.160328\pi\)
0.875810 + 0.482655i \(0.160328\pi\)
\(588\) 12.5821 0.518878
\(589\) 4.24784 0.175029
\(590\) 13.4986 0.555728
\(591\) 16.0842 0.661617
\(592\) −7.23807 −0.297483
\(593\) −13.3131 −0.546702 −0.273351 0.961914i \(-0.588132\pi\)
−0.273351 + 0.961914i \(0.588132\pi\)
\(594\) 2.45257 0.100630
\(595\) −8.56062 −0.350951
\(596\) −3.79596 −0.155489
\(597\) 15.7598 0.645004
\(598\) −2.45000 −0.100188
\(599\) 7.22746 0.295306 0.147653 0.989039i \(-0.452828\pi\)
0.147653 + 0.989039i \(0.452828\pi\)
\(600\) 9.62390 0.392894
\(601\) 11.0629 0.451264 0.225632 0.974213i \(-0.427555\pi\)
0.225632 + 0.974213i \(0.427555\pi\)
\(602\) −15.2762 −0.622610
\(603\) 16.6010 0.676043
\(604\) −4.42526 −0.180061
\(605\) 9.46305 0.384728
\(606\) −36.2733 −1.47350
\(607\) −18.4308 −0.748083 −0.374041 0.927412i \(-0.622028\pi\)
−0.374041 + 0.927412i \(0.622028\pi\)
\(608\) 1.00000 0.0405554
\(609\) 31.5826 1.27979
\(610\) 0.592783 0.0240011
\(611\) 5.34807 0.216360
\(612\) −18.9783 −0.767153
\(613\) −6.26812 −0.253167 −0.126583 0.991956i \(-0.540401\pi\)
−0.126583 + 0.991956i \(0.540401\pi\)
\(614\) −23.7172 −0.957148
\(615\) −0.887821 −0.0358004
\(616\) 2.31390 0.0932295
\(617\) −7.67738 −0.309080 −0.154540 0.987987i \(-0.549390\pi\)
−0.154540 + 0.987987i \(0.549390\pi\)
\(618\) −27.5233 −1.10715
\(619\) 20.6025 0.828086 0.414043 0.910257i \(-0.364116\pi\)
0.414043 + 0.910257i \(0.364116\pi\)
\(620\) −4.75567 −0.190992
\(621\) 1.20356 0.0482973
\(622\) −31.4708 −1.26186
\(623\) 6.91012 0.276848
\(624\) −8.03487 −0.321652
\(625\) 7.77010 0.310804
\(626\) −20.0011 −0.799405
\(627\) 4.09983 0.163732
\(628\) −10.9439 −0.436711
\(629\) 38.1763 1.52219
\(630\) 5.84011 0.232676
\(631\) −20.8444 −0.829803 −0.414901 0.909866i \(-0.636184\pi\)
−0.414901 + 0.909866i \(0.636184\pi\)
\(632\) −5.27871 −0.209976
\(633\) 2.56870 0.102097
\(634\) −20.0539 −0.796442
\(635\) 10.0415 0.398485
\(636\) −17.9271 −0.710856
\(637\) −15.3217 −0.607067
\(638\) −13.5362 −0.535904
\(639\) −10.0492 −0.397538
\(640\) −1.11955 −0.0442541
\(641\) 13.9591 0.551350 0.275675 0.961251i \(-0.411099\pi\)
0.275675 + 0.961251i \(0.411099\pi\)
\(642\) 27.4089 1.08174
\(643\) 15.3604 0.605756 0.302878 0.953029i \(-0.402052\pi\)
0.302878 + 0.953029i \(0.402052\pi\)
\(644\) 1.13551 0.0447454
\(645\) 30.3027 1.19317
\(646\) −5.27438 −0.207518
\(647\) −27.6543 −1.08720 −0.543602 0.839343i \(-0.682940\pi\)
−0.543602 + 0.839343i \(0.682940\pi\)
\(648\) −6.84751 −0.268996
\(649\) 19.2441 0.755397
\(650\) −11.7194 −0.459671
\(651\) 15.8187 0.619985
\(652\) −7.68585 −0.301001
\(653\) 1.42887 0.0559159 0.0279580 0.999609i \(-0.491100\pi\)
0.0279580 + 0.999609i \(0.491100\pi\)
\(654\) 24.5111 0.958460
\(655\) −21.5302 −0.841255
\(656\) −0.308723 −0.0120536
\(657\) 49.6845 1.93838
\(658\) −2.47869 −0.0966293
\(659\) −11.5309 −0.449180 −0.224590 0.974453i \(-0.572104\pi\)
−0.224590 + 0.974453i \(0.572104\pi\)
\(660\) −4.58997 −0.178664
\(661\) 19.5495 0.760386 0.380193 0.924907i \(-0.375858\pi\)
0.380193 + 0.924907i \(0.375858\pi\)
\(662\) 6.26128 0.243351
\(663\) 42.3789 1.64586
\(664\) 9.23497 0.358386
\(665\) 1.62306 0.0629395
\(666\) −26.0441 −1.00919
\(667\) −6.64269 −0.257206
\(668\) 12.0757 0.467223
\(669\) 34.5406 1.33542
\(670\) −5.16523 −0.199550
\(671\) 0.845094 0.0326245
\(672\) 3.72395 0.143654
\(673\) 27.2522 1.05050 0.525248 0.850949i \(-0.323972\pi\)
0.525248 + 0.850949i \(0.323972\pi\)
\(674\) −14.6756 −0.565283
\(675\) 5.75713 0.221592
\(676\) −3.21566 −0.123679
\(677\) −22.8576 −0.878489 −0.439245 0.898367i \(-0.644754\pi\)
−0.439245 + 0.898367i \(0.644754\pi\)
\(678\) −9.29168 −0.356845
\(679\) 18.5939 0.713569
\(680\) 5.90493 0.226444
\(681\) 36.1002 1.38336
\(682\) −6.77986 −0.259614
\(683\) 1.86134 0.0712221 0.0356111 0.999366i \(-0.488662\pi\)
0.0356111 + 0.999366i \(0.488662\pi\)
\(684\) 3.59821 0.137581
\(685\) −9.28589 −0.354796
\(686\) 17.2494 0.658585
\(687\) −9.11384 −0.347715
\(688\) 10.5372 0.401726
\(689\) 21.8304 0.831674
\(690\) −2.25246 −0.0857497
\(691\) 40.4717 1.53962 0.769808 0.638276i \(-0.220352\pi\)
0.769808 + 0.638276i \(0.220352\pi\)
\(692\) −12.7449 −0.484488
\(693\) 8.32589 0.316274
\(694\) −31.6736 −1.20231
\(695\) −2.89144 −0.109679
\(696\) −21.7850 −0.825757
\(697\) 1.62832 0.0616770
\(698\) −4.24754 −0.160772
\(699\) 68.2337 2.58084
\(700\) 5.43161 0.205296
\(701\) −6.54368 −0.247151 −0.123576 0.992335i \(-0.539436\pi\)
−0.123576 + 0.992335i \(0.539436\pi\)
\(702\) −4.80655 −0.181412
\(703\) −7.23807 −0.272989
\(704\) −1.59607 −0.0601543
\(705\) 4.91686 0.185180
\(706\) 24.0277 0.904294
\(707\) −20.4722 −0.769936
\(708\) 30.9712 1.16397
\(709\) −37.5896 −1.41171 −0.705854 0.708358i \(-0.749436\pi\)
−0.705854 + 0.708358i \(0.749436\pi\)
\(710\) 3.12670 0.117343
\(711\) −18.9939 −0.712327
\(712\) −4.76645 −0.178630
\(713\) −3.32712 −0.124601
\(714\) −19.6415 −0.735065
\(715\) 5.58936 0.209030
\(716\) 20.9073 0.781344
\(717\) 11.1267 0.415535
\(718\) 23.1048 0.862264
\(719\) 41.8677 1.56140 0.780702 0.624904i \(-0.214862\pi\)
0.780702 + 0.624904i \(0.214862\pi\)
\(720\) −4.02838 −0.150129
\(721\) −15.5338 −0.578509
\(722\) 1.00000 0.0372161
\(723\) −44.9919 −1.67327
\(724\) 1.33857 0.0497477
\(725\) −31.7747 −1.18008
\(726\) 21.7120 0.805810
\(727\) −31.8289 −1.18047 −0.590234 0.807232i \(-0.700965\pi\)
−0.590234 + 0.807232i \(0.700965\pi\)
\(728\) −4.53478 −0.168070
\(729\) −36.4802 −1.35112
\(730\) −15.4589 −0.572158
\(731\) −55.5770 −2.05559
\(732\) 1.36008 0.0502701
\(733\) 0.782883 0.0289164 0.0144582 0.999895i \(-0.495398\pi\)
0.0144582 + 0.999895i \(0.495398\pi\)
\(734\) 9.79259 0.361451
\(735\) −14.0863 −0.519582
\(736\) −0.783250 −0.0288710
\(737\) −7.36376 −0.271247
\(738\) −1.11085 −0.0408910
\(739\) −12.9409 −0.476038 −0.238019 0.971260i \(-0.576498\pi\)
−0.238019 + 0.971260i \(0.576498\pi\)
\(740\) 8.10338 0.297886
\(741\) −8.03487 −0.295168
\(742\) −10.1178 −0.371437
\(743\) −21.3676 −0.783901 −0.391950 0.919986i \(-0.628199\pi\)
−0.391950 + 0.919986i \(0.628199\pi\)
\(744\) −10.9114 −0.400032
\(745\) 4.24977 0.155699
\(746\) −14.7854 −0.541333
\(747\) 33.2294 1.21580
\(748\) 8.41830 0.307803
\(749\) 15.4692 0.565233
\(750\) −25.1534 −0.918472
\(751\) 17.7401 0.647345 0.323673 0.946169i \(-0.395082\pi\)
0.323673 + 0.946169i \(0.395082\pi\)
\(752\) 1.70974 0.0623479
\(753\) −46.1565 −1.68204
\(754\) 26.5283 0.966104
\(755\) 4.95430 0.180305
\(756\) 2.22771 0.0810210
\(757\) 7.83074 0.284613 0.142307 0.989823i \(-0.454548\pi\)
0.142307 + 0.989823i \(0.454548\pi\)
\(758\) −32.9460 −1.19665
\(759\) −3.21119 −0.116559
\(760\) −1.11955 −0.0406104
\(761\) 24.5923 0.891469 0.445735 0.895165i \(-0.352943\pi\)
0.445735 + 0.895165i \(0.352943\pi\)
\(762\) 23.0392 0.834623
\(763\) 13.8338 0.500816
\(764\) −21.7762 −0.787834
\(765\) 21.2472 0.768194
\(766\) −2.22797 −0.0804999
\(767\) −37.7147 −1.36180
\(768\) −2.56870 −0.0926899
\(769\) 47.8044 1.72387 0.861936 0.507017i \(-0.169252\pi\)
0.861936 + 0.507017i \(0.169252\pi\)
\(770\) −2.59052 −0.0933560
\(771\) 35.4976 1.27841
\(772\) −4.51037 −0.162332
\(773\) −27.1576 −0.976789 −0.488395 0.872623i \(-0.662417\pi\)
−0.488395 + 0.872623i \(0.662417\pi\)
\(774\) 37.9150 1.36283
\(775\) −15.9150 −0.571683
\(776\) −12.8257 −0.460415
\(777\) −26.9542 −0.966977
\(778\) −15.9564 −0.572065
\(779\) −0.308723 −0.0110611
\(780\) 8.99544 0.322088
\(781\) 4.45755 0.159504
\(782\) 4.13115 0.147730
\(783\) −13.0320 −0.465727
\(784\) −4.89825 −0.174937
\(785\) 12.2523 0.437303
\(786\) −49.3989 −1.76200
\(787\) −31.5415 −1.12433 −0.562167 0.827024i \(-0.690032\pi\)
−0.562167 + 0.827024i \(0.690032\pi\)
\(788\) −6.26163 −0.223061
\(789\) −49.7208 −1.77011
\(790\) 5.90978 0.210261
\(791\) −5.24411 −0.186459
\(792\) −5.74301 −0.204069
\(793\) −1.65622 −0.0588141
\(794\) −16.5148 −0.586089
\(795\) 20.0703 0.711820
\(796\) −6.13531 −0.217460
\(797\) 23.5790 0.835210 0.417605 0.908629i \(-0.362870\pi\)
0.417605 + 0.908629i \(0.362870\pi\)
\(798\) 3.72395 0.131826
\(799\) −9.01783 −0.319028
\(800\) −3.74661 −0.132463
\(801\) −17.1507 −0.605990
\(802\) −1.36916 −0.0483467
\(803\) −22.0387 −0.777731
\(804\) −11.8511 −0.417957
\(805\) −1.27126 −0.0448060
\(806\) 13.2872 0.468022
\(807\) 19.2198 0.676570
\(808\) 14.1213 0.496785
\(809\) −15.7494 −0.553721 −0.276861 0.960910i \(-0.589294\pi\)
−0.276861 + 0.960910i \(0.589294\pi\)
\(810\) 7.66613 0.269360
\(811\) 1.28089 0.0449780 0.0224890 0.999747i \(-0.492841\pi\)
0.0224890 + 0.999747i \(0.492841\pi\)
\(812\) −12.2952 −0.431476
\(813\) −58.9225 −2.06650
\(814\) 11.5525 0.404915
\(815\) 8.60469 0.301409
\(816\) 13.5483 0.474285
\(817\) 10.5372 0.368649
\(818\) −33.9138 −1.18577
\(819\) −16.3171 −0.570166
\(820\) 0.345631 0.0120699
\(821\) 5.21179 0.181893 0.0909464 0.995856i \(-0.471011\pi\)
0.0909464 + 0.995856i \(0.471011\pi\)
\(822\) −21.3056 −0.743117
\(823\) 5.52758 0.192679 0.0963396 0.995349i \(-0.469287\pi\)
0.0963396 + 0.995349i \(0.469287\pi\)
\(824\) 10.7149 0.373271
\(825\) −15.3605 −0.534783
\(826\) 17.4798 0.608199
\(827\) 7.72995 0.268797 0.134398 0.990927i \(-0.457090\pi\)
0.134398 + 0.990927i \(0.457090\pi\)
\(828\) −2.81830 −0.0979426
\(829\) −24.6254 −0.855277 −0.427638 0.903950i \(-0.640654\pi\)
−0.427638 + 0.903950i \(0.640654\pi\)
\(830\) −10.3390 −0.358872
\(831\) 58.2936 2.02218
\(832\) 3.12799 0.108444
\(833\) 25.8352 0.895137
\(834\) −6.63413 −0.229721
\(835\) −13.5194 −0.467857
\(836\) −1.59607 −0.0552014
\(837\) −6.52733 −0.225618
\(838\) −4.70812 −0.162639
\(839\) 41.7298 1.44067 0.720337 0.693624i \(-0.243987\pi\)
0.720337 + 0.693624i \(0.243987\pi\)
\(840\) −4.16915 −0.143849
\(841\) 42.9263 1.48022
\(842\) −5.43867 −0.187429
\(843\) −28.8906 −0.995046
\(844\) −1.00000 −0.0344214
\(845\) 3.60009 0.123847
\(846\) 6.15202 0.211511
\(847\) 12.2540 0.421053
\(848\) 6.97906 0.239662
\(849\) 86.2594 2.96042
\(850\) 19.7610 0.677797
\(851\) 5.66922 0.194338
\(852\) 7.17391 0.245774
\(853\) −38.6648 −1.32386 −0.661929 0.749566i \(-0.730262\pi\)
−0.661929 + 0.749566i \(0.730262\pi\)
\(854\) 0.767614 0.0262672
\(855\) −4.02838 −0.137768
\(856\) −10.6703 −0.364705
\(857\) 10.7384 0.366815 0.183408 0.983037i \(-0.441287\pi\)
0.183408 + 0.983037i \(0.441287\pi\)
\(858\) 12.8243 0.437813
\(859\) 43.6837 1.49047 0.745235 0.666802i \(-0.232337\pi\)
0.745235 + 0.666802i \(0.232337\pi\)
\(860\) −11.7969 −0.402271
\(861\) −1.14967 −0.0391806
\(862\) 24.7539 0.843121
\(863\) −31.2451 −1.06360 −0.531798 0.846871i \(-0.678483\pi\)
−0.531798 + 0.846871i \(0.678483\pi\)
\(864\) −1.53663 −0.0522771
\(865\) 14.2685 0.485145
\(866\) −17.4451 −0.592810
\(867\) −27.7909 −0.943828
\(868\) −6.15827 −0.209025
\(869\) 8.42521 0.285806
\(870\) 24.3894 0.826877
\(871\) 14.4315 0.488993
\(872\) −9.54223 −0.323141
\(873\) −46.1495 −1.56192
\(874\) −0.783250 −0.0264938
\(875\) −14.1963 −0.479921
\(876\) −35.4688 −1.19838
\(877\) 21.0182 0.709733 0.354866 0.934917i \(-0.384526\pi\)
0.354866 + 0.934917i \(0.384526\pi\)
\(878\) 27.0520 0.912962
\(879\) 42.6964 1.44011
\(880\) 1.78689 0.0602359
\(881\) 50.9134 1.71532 0.857658 0.514220i \(-0.171919\pi\)
0.857658 + 0.514220i \(0.171919\pi\)
\(882\) −17.6249 −0.593462
\(883\) 48.8130 1.64269 0.821344 0.570434i \(-0.193225\pi\)
0.821344 + 0.570434i \(0.193225\pi\)
\(884\) −16.4982 −0.554895
\(885\) −34.6738 −1.16555
\(886\) −11.9016 −0.399841
\(887\) −3.52130 −0.118234 −0.0591168 0.998251i \(-0.518828\pi\)
−0.0591168 + 0.998251i \(0.518828\pi\)
\(888\) 18.5924 0.623921
\(889\) 13.0031 0.436109
\(890\) 5.33628 0.178872
\(891\) 10.9291 0.366140
\(892\) −13.4467 −0.450229
\(893\) 1.70974 0.0572144
\(894\) 9.75068 0.326111
\(895\) −23.4068 −0.782403
\(896\) −1.44974 −0.0484325
\(897\) 6.29331 0.210128
\(898\) −10.4434 −0.348501
\(899\) 36.0256 1.20152
\(900\) −13.4811 −0.449370
\(901\) −36.8102 −1.22633
\(902\) 0.492745 0.0164066
\(903\) 39.2399 1.30582
\(904\) 3.61727 0.120309
\(905\) −1.49860 −0.0498152
\(906\) 11.3672 0.377648
\(907\) 48.9809 1.62639 0.813193 0.581994i \(-0.197727\pi\)
0.813193 + 0.581994i \(0.197727\pi\)
\(908\) −14.0539 −0.466395
\(909\) 50.8113 1.68531
\(910\) 5.07692 0.168298
\(911\) −22.5447 −0.746939 −0.373470 0.927642i \(-0.621832\pi\)
−0.373470 + 0.927642i \(0.621832\pi\)
\(912\) −2.56870 −0.0850581
\(913\) −14.7397 −0.487813
\(914\) −6.79423 −0.224733
\(915\) −1.52268 −0.0503383
\(916\) 3.54804 0.117230
\(917\) −27.8802 −0.920684
\(918\) 8.10474 0.267496
\(919\) −40.3174 −1.32995 −0.664975 0.746866i \(-0.731558\pi\)
−0.664975 + 0.746866i \(0.731558\pi\)
\(920\) 0.876887 0.0289101
\(921\) 60.9223 2.00746
\(922\) −16.7365 −0.551188
\(923\) −8.73592 −0.287546
\(924\) −5.94370 −0.195533
\(925\) 27.1182 0.891641
\(926\) 1.46440 0.0481231
\(927\) 38.5544 1.26629
\(928\) 8.48094 0.278400
\(929\) −19.3473 −0.634764 −0.317382 0.948298i \(-0.602804\pi\)
−0.317382 + 0.948298i \(0.602804\pi\)
\(930\) 12.2159 0.400574
\(931\) −4.89825 −0.160534
\(932\) −26.5635 −0.870118
\(933\) 80.8390 2.64655
\(934\) −10.8327 −0.354457
\(935\) −9.42471 −0.308221
\(936\) 11.2552 0.367887
\(937\) 19.3382 0.631752 0.315876 0.948800i \(-0.397702\pi\)
0.315876 + 0.948800i \(0.397702\pi\)
\(938\) −6.68863 −0.218391
\(939\) 51.3768 1.67662
\(940\) −1.91414 −0.0624325
\(941\) 22.1728 0.722811 0.361406 0.932409i \(-0.382297\pi\)
0.361406 + 0.932409i \(0.382297\pi\)
\(942\) 28.1117 0.915929
\(943\) 0.241807 0.00787432
\(944\) −12.0572 −0.392427
\(945\) −2.49403 −0.0811309
\(946\) −16.8181 −0.546804
\(947\) 49.7447 1.61648 0.808242 0.588850i \(-0.200419\pi\)
0.808242 + 0.588850i \(0.200419\pi\)
\(948\) 13.5594 0.440389
\(949\) 43.1916 1.40206
\(950\) −3.74661 −0.121556
\(951\) 51.5124 1.67040
\(952\) 7.64649 0.247824
\(953\) −43.1522 −1.39784 −0.698918 0.715202i \(-0.746335\pi\)
−0.698918 + 0.715202i \(0.746335\pi\)
\(954\) 25.1121 0.813035
\(955\) 24.3795 0.788902
\(956\) −4.33166 −0.140096
\(957\) 34.7704 1.12397
\(958\) −20.9816 −0.677884
\(959\) −12.0246 −0.388295
\(960\) 2.87579 0.0928156
\(961\) −12.9559 −0.417932
\(962\) −22.6406 −0.729963
\(963\) −38.3941 −1.23723
\(964\) 17.5154 0.564135
\(965\) 5.04958 0.162552
\(966\) −2.91678 −0.0938459
\(967\) −10.6831 −0.343546 −0.171773 0.985137i \(-0.554950\pi\)
−0.171773 + 0.985137i \(0.554950\pi\)
\(968\) −8.45255 −0.271675
\(969\) 13.5483 0.435234
\(970\) 14.3590 0.461039
\(971\) −12.6516 −0.406010 −0.203005 0.979178i \(-0.565071\pi\)
−0.203005 + 0.979178i \(0.565071\pi\)
\(972\) 22.1991 0.712035
\(973\) −3.74422 −0.120034
\(974\) −19.9002 −0.637643
\(975\) 30.1035 0.964084
\(976\) −0.529483 −0.0169483
\(977\) −17.7318 −0.567291 −0.283646 0.958929i \(-0.591544\pi\)
−0.283646 + 0.958929i \(0.591544\pi\)
\(978\) 19.7426 0.631299
\(979\) 7.60761 0.243140
\(980\) 5.48383 0.175175
\(981\) −34.3350 −1.09623
\(982\) 41.2744 1.31712
\(983\) 25.9136 0.826516 0.413258 0.910614i \(-0.364391\pi\)
0.413258 + 0.910614i \(0.364391\pi\)
\(984\) 0.793016 0.0252804
\(985\) 7.01020 0.223364
\(986\) −44.7317 −1.42455
\(987\) 6.36700 0.202664
\(988\) 3.12799 0.0995147
\(989\) −8.25324 −0.262438
\(990\) 6.42959 0.204346
\(991\) −23.8788 −0.758535 −0.379267 0.925287i \(-0.623824\pi\)
−0.379267 + 0.925287i \(0.623824\pi\)
\(992\) 4.24784 0.134869
\(993\) −16.0833 −0.510389
\(994\) 4.04887 0.128422
\(995\) 6.86879 0.217755
\(996\) −23.7218 −0.751656
\(997\) −36.2352 −1.14758 −0.573790 0.819003i \(-0.694527\pi\)
−0.573790 + 0.819003i \(0.694527\pi\)
\(998\) −21.2431 −0.672439
\(999\) 11.1222 0.351891
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 \(a_p\))