Properties

Label 6026.2.a.h.1.10
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 1.10
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-0.785811 q^{3}\) \(+1.00000 q^{4}\) \(-1.42219 q^{5}\) \(+0.785811 q^{6}\) \(+3.87369 q^{7}\) \(-1.00000 q^{8}\) \(-2.38250 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-0.785811 q^{3}\) \(+1.00000 q^{4}\) \(-1.42219 q^{5}\) \(+0.785811 q^{6}\) \(+3.87369 q^{7}\) \(-1.00000 q^{8}\) \(-2.38250 q^{9}\) \(+1.42219 q^{10}\) \(+4.24761 q^{11}\) \(-0.785811 q^{12}\) \(+2.46631 q^{13}\) \(-3.87369 q^{14}\) \(+1.11757 q^{15}\) \(+1.00000 q^{16}\) \(+1.55090 q^{17}\) \(+2.38250 q^{18}\) \(-2.53414 q^{19}\) \(-1.42219 q^{20}\) \(-3.04399 q^{21}\) \(-4.24761 q^{22}\) \(-1.00000 q^{23}\) \(+0.785811 q^{24}\) \(-2.97737 q^{25}\) \(-2.46631 q^{26}\) \(+4.22963 q^{27}\) \(+3.87369 q^{28}\) \(+4.09137 q^{29}\) \(-1.11757 q^{30}\) \(-7.27950 q^{31}\) \(-1.00000 q^{32}\) \(-3.33782 q^{33}\) \(-1.55090 q^{34}\) \(-5.50912 q^{35}\) \(-2.38250 q^{36}\) \(-5.04022 q^{37}\) \(+2.53414 q^{38}\) \(-1.93805 q^{39}\) \(+1.42219 q^{40}\) \(-6.34949 q^{41}\) \(+3.04399 q^{42}\) \(-9.30138 q^{43}\) \(+4.24761 q^{44}\) \(+3.38837 q^{45}\) \(+1.00000 q^{46}\) \(-5.01571 q^{47}\) \(-0.785811 q^{48}\) \(+8.00545 q^{49}\) \(+2.97737 q^{50}\) \(-1.21871 q^{51}\) \(+2.46631 q^{52}\) \(-6.61052 q^{53}\) \(-4.22963 q^{54}\) \(-6.04091 q^{55}\) \(-3.87369 q^{56}\) \(+1.99135 q^{57}\) \(-4.09137 q^{58}\) \(-1.17415 q^{59}\) \(+1.11757 q^{60}\) \(+6.46185 q^{61}\) \(+7.27950 q^{62}\) \(-9.22906 q^{63}\) \(+1.00000 q^{64}\) \(-3.50756 q^{65}\) \(+3.33782 q^{66}\) \(+9.88156 q^{67}\) \(+1.55090 q^{68}\) \(+0.785811 q^{69}\) \(+5.50912 q^{70}\) \(+6.27474 q^{71}\) \(+2.38250 q^{72}\) \(-13.0599 q^{73}\) \(+5.04022 q^{74}\) \(+2.33965 q^{75}\) \(-2.53414 q^{76}\) \(+16.4539 q^{77}\) \(+1.93805 q^{78}\) \(-8.91977 q^{79}\) \(-1.42219 q^{80}\) \(+3.82381 q^{81}\) \(+6.34949 q^{82}\) \(+14.1085 q^{83}\) \(-3.04399 q^{84}\) \(-2.20568 q^{85}\) \(+9.30138 q^{86}\) \(-3.21504 q^{87}\) \(-4.24761 q^{88}\) \(-11.5983 q^{89}\) \(-3.38837 q^{90}\) \(+9.55371 q^{91}\) \(-1.00000 q^{92}\) \(+5.72031 q^{93}\) \(+5.01571 q^{94}\) \(+3.60403 q^{95}\) \(+0.785811 q^{96}\) \(-14.5136 q^{97}\) \(-8.00545 q^{98}\) \(-10.1199 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 27q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 39q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 13q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 21q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut +\mathstrut 7q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut +\mathstrut 23q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 29q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 17q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 36q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 39q^{78} \) \(\mathstrut -\mathstrut 53q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 37q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 7q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut +\mathstrut 13q^{90} \) \(\mathstrut -\mathstrut 44q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 23q^{93} \) \(\mathstrut -\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 13q^{98} \) \(\mathstrut -\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.785811 −0.453688 −0.226844 0.973931i \(-0.572841\pi\)
−0.226844 + 0.973931i \(0.572841\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.42219 −0.636023 −0.318011 0.948087i \(-0.603015\pi\)
−0.318011 + 0.948087i \(0.603015\pi\)
\(6\) 0.785811 0.320806
\(7\) 3.87369 1.46412 0.732058 0.681242i \(-0.238560\pi\)
0.732058 + 0.681242i \(0.238560\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.38250 −0.794167
\(10\) 1.42219 0.449736
\(11\) 4.24761 1.28070 0.640351 0.768082i \(-0.278789\pi\)
0.640351 + 0.768082i \(0.278789\pi\)
\(12\) −0.785811 −0.226844
\(13\) 2.46631 0.684031 0.342016 0.939694i \(-0.388890\pi\)
0.342016 + 0.939694i \(0.388890\pi\)
\(14\) −3.87369 −1.03529
\(15\) 1.11757 0.288556
\(16\) 1.00000 0.250000
\(17\) 1.55090 0.376149 0.188074 0.982155i \(-0.439775\pi\)
0.188074 + 0.982155i \(0.439775\pi\)
\(18\) 2.38250 0.561561
\(19\) −2.53414 −0.581371 −0.290686 0.956819i \(-0.593883\pi\)
−0.290686 + 0.956819i \(0.593883\pi\)
\(20\) −1.42219 −0.318011
\(21\) −3.04399 −0.664252
\(22\) −4.24761 −0.905593
\(23\) −1.00000 −0.208514
\(24\) 0.785811 0.160403
\(25\) −2.97737 −0.595475
\(26\) −2.46631 −0.483683
\(27\) 4.22963 0.813993
\(28\) 3.87369 0.732058
\(29\) 4.09137 0.759748 0.379874 0.925038i \(-0.375967\pi\)
0.379874 + 0.925038i \(0.375967\pi\)
\(30\) −1.11757 −0.204040
\(31\) −7.27950 −1.30744 −0.653719 0.756738i \(-0.726792\pi\)
−0.653719 + 0.756738i \(0.726792\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.33782 −0.581040
\(34\) −1.55090 −0.265977
\(35\) −5.50912 −0.931211
\(36\) −2.38250 −0.397083
\(37\) −5.04022 −0.828606 −0.414303 0.910139i \(-0.635975\pi\)
−0.414303 + 0.910139i \(0.635975\pi\)
\(38\) 2.53414 0.411092
\(39\) −1.93805 −0.310337
\(40\) 1.42219 0.224868
\(41\) −6.34949 −0.991624 −0.495812 0.868430i \(-0.665129\pi\)
−0.495812 + 0.868430i \(0.665129\pi\)
\(42\) 3.04399 0.469697
\(43\) −9.30138 −1.41845 −0.709223 0.704984i \(-0.750954\pi\)
−0.709223 + 0.704984i \(0.750954\pi\)
\(44\) 4.24761 0.640351
\(45\) 3.38837 0.505108
\(46\) 1.00000 0.147442
\(47\) −5.01571 −0.731617 −0.365808 0.930690i \(-0.619207\pi\)
−0.365808 + 0.930690i \(0.619207\pi\)
\(48\) −0.785811 −0.113422
\(49\) 8.00545 1.14364
\(50\) 2.97737 0.421064
\(51\) −1.21871 −0.170654
\(52\) 2.46631 0.342016
\(53\) −6.61052 −0.908025 −0.454013 0.890995i \(-0.650008\pi\)
−0.454013 + 0.890995i \(0.650008\pi\)
\(54\) −4.22963 −0.575580
\(55\) −6.04091 −0.814556
\(56\) −3.87369 −0.517643
\(57\) 1.99135 0.263761
\(58\) −4.09137 −0.537223
\(59\) −1.17415 −0.152861 −0.0764306 0.997075i \(-0.524352\pi\)
−0.0764306 + 0.997075i \(0.524352\pi\)
\(60\) 1.11757 0.144278
\(61\) 6.46185 0.827355 0.413677 0.910424i \(-0.364244\pi\)
0.413677 + 0.910424i \(0.364244\pi\)
\(62\) 7.27950 0.924498
\(63\) −9.22906 −1.16275
\(64\) 1.00000 0.125000
\(65\) −3.50756 −0.435060
\(66\) 3.33782 0.410857
\(67\) 9.88156 1.20723 0.603613 0.797278i \(-0.293727\pi\)
0.603613 + 0.797278i \(0.293727\pi\)
\(68\) 1.55090 0.188074
\(69\) 0.785811 0.0946006
\(70\) 5.50912 0.658466
\(71\) 6.27474 0.744674 0.372337 0.928098i \(-0.378557\pi\)
0.372337 + 0.928098i \(0.378557\pi\)
\(72\) 2.38250 0.280780
\(73\) −13.0599 −1.52854 −0.764271 0.644895i \(-0.776901\pi\)
−0.764271 + 0.644895i \(0.776901\pi\)
\(74\) 5.04022 0.585913
\(75\) 2.33965 0.270160
\(76\) −2.53414 −0.290686
\(77\) 16.4539 1.87510
\(78\) 1.93805 0.219441
\(79\) −8.91977 −1.00355 −0.501776 0.864998i \(-0.667320\pi\)
−0.501776 + 0.864998i \(0.667320\pi\)
\(80\) −1.42219 −0.159006
\(81\) 3.82381 0.424868
\(82\) 6.34949 0.701184
\(83\) 14.1085 1.54861 0.774307 0.632810i \(-0.218099\pi\)
0.774307 + 0.632810i \(0.218099\pi\)
\(84\) −3.04399 −0.332126
\(85\) −2.20568 −0.239239
\(86\) 9.30138 1.00299
\(87\) −3.21504 −0.344689
\(88\) −4.24761 −0.452797
\(89\) −11.5983 −1.22941 −0.614706 0.788756i \(-0.710725\pi\)
−0.614706 + 0.788756i \(0.710725\pi\)
\(90\) −3.38837 −0.357166
\(91\) 9.55371 1.00150
\(92\) −1.00000 −0.104257
\(93\) 5.72031 0.593169
\(94\) 5.01571 0.517331
\(95\) 3.60403 0.369765
\(96\) 0.785811 0.0802015
\(97\) −14.5136 −1.47363 −0.736817 0.676092i \(-0.763672\pi\)
−0.736817 + 0.676092i \(0.763672\pi\)
\(98\) −8.00545 −0.808673
\(99\) −10.1199 −1.01709
\(100\) −2.97737 −0.297737
\(101\) −1.16747 −0.116168 −0.0580840 0.998312i \(-0.518499\pi\)
−0.0580840 + 0.998312i \(0.518499\pi\)
\(102\) 1.21871 0.120671
\(103\) −3.01876 −0.297447 −0.148724 0.988879i \(-0.547516\pi\)
−0.148724 + 0.988879i \(0.547516\pi\)
\(104\) −2.46631 −0.241842
\(105\) 4.32913 0.422480
\(106\) 6.61052 0.642071
\(107\) −7.17272 −0.693413 −0.346706 0.937974i \(-0.612700\pi\)
−0.346706 + 0.937974i \(0.612700\pi\)
\(108\) 4.22963 0.406996
\(109\) −3.99600 −0.382747 −0.191373 0.981517i \(-0.561294\pi\)
−0.191373 + 0.981517i \(0.561294\pi\)
\(110\) 6.04091 0.575978
\(111\) 3.96066 0.375929
\(112\) 3.87369 0.366029
\(113\) 13.6826 1.28715 0.643574 0.765384i \(-0.277451\pi\)
0.643574 + 0.765384i \(0.277451\pi\)
\(114\) −1.99135 −0.186507
\(115\) 1.42219 0.132620
\(116\) 4.09137 0.379874
\(117\) −5.87599 −0.543235
\(118\) 1.17415 0.108089
\(119\) 6.00770 0.550725
\(120\) −1.11757 −0.102020
\(121\) 7.04218 0.640199
\(122\) −6.46185 −0.585028
\(123\) 4.98950 0.449888
\(124\) −7.27950 −0.653719
\(125\) 11.3453 1.01476
\(126\) 9.22906 0.822190
\(127\) 14.2216 1.26197 0.630983 0.775797i \(-0.282652\pi\)
0.630983 + 0.775797i \(0.282652\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 7.30913 0.643533
\(130\) 3.50756 0.307634
\(131\) −1.00000 −0.0873704
\(132\) −3.33782 −0.290520
\(133\) −9.81646 −0.851195
\(134\) −9.88156 −0.853637
\(135\) −6.01534 −0.517718
\(136\) −1.55090 −0.132989
\(137\) −16.5255 −1.41187 −0.705935 0.708277i \(-0.749473\pi\)
−0.705935 + 0.708277i \(0.749473\pi\)
\(138\) −0.785811 −0.0668927
\(139\) 8.60490 0.729858 0.364929 0.931035i \(-0.381093\pi\)
0.364929 + 0.931035i \(0.381093\pi\)
\(140\) −5.50912 −0.465606
\(141\) 3.94140 0.331926
\(142\) −6.27474 −0.526564
\(143\) 10.4759 0.876041
\(144\) −2.38250 −0.198542
\(145\) −5.81870 −0.483217
\(146\) 13.0599 1.08084
\(147\) −6.29078 −0.518854
\(148\) −5.04022 −0.414303
\(149\) −15.3186 −1.25495 −0.627475 0.778637i \(-0.715911\pi\)
−0.627475 + 0.778637i \(0.715911\pi\)
\(150\) −2.33965 −0.191032
\(151\) −13.1238 −1.06800 −0.534001 0.845484i \(-0.679312\pi\)
−0.534001 + 0.845484i \(0.679312\pi\)
\(152\) 2.53414 0.205546
\(153\) −3.69502 −0.298725
\(154\) −16.4539 −1.32589
\(155\) 10.3528 0.831560
\(156\) −1.93805 −0.155169
\(157\) −0.761128 −0.0607446 −0.0303723 0.999539i \(-0.509669\pi\)
−0.0303723 + 0.999539i \(0.509669\pi\)
\(158\) 8.91977 0.709618
\(159\) 5.19462 0.411960
\(160\) 1.42219 0.112434
\(161\) −3.87369 −0.305289
\(162\) −3.82381 −0.300427
\(163\) 19.8011 1.55094 0.775470 0.631384i \(-0.217513\pi\)
0.775470 + 0.631384i \(0.217513\pi\)
\(164\) −6.34949 −0.495812
\(165\) 4.74701 0.369555
\(166\) −14.1085 −1.09504
\(167\) 4.08020 0.315735 0.157868 0.987460i \(-0.449538\pi\)
0.157868 + 0.987460i \(0.449538\pi\)
\(168\) 3.04399 0.234849
\(169\) −6.91731 −0.532101
\(170\) 2.20568 0.169168
\(171\) 6.03759 0.461706
\(172\) −9.30138 −0.709223
\(173\) 2.46367 0.187309 0.0936545 0.995605i \(-0.470145\pi\)
0.0936545 + 0.995605i \(0.470145\pi\)
\(174\) 3.21504 0.243732
\(175\) −11.5334 −0.871845
\(176\) 4.24761 0.320176
\(177\) 0.922660 0.0693513
\(178\) 11.5983 0.869326
\(179\) 10.7958 0.806916 0.403458 0.914998i \(-0.367808\pi\)
0.403458 + 0.914998i \(0.367808\pi\)
\(180\) 3.38837 0.252554
\(181\) 9.47637 0.704373 0.352187 0.935930i \(-0.385438\pi\)
0.352187 + 0.935930i \(0.385438\pi\)
\(182\) −9.55371 −0.708168
\(183\) −5.07779 −0.375361
\(184\) 1.00000 0.0737210
\(185\) 7.16815 0.527013
\(186\) −5.72031 −0.419434
\(187\) 6.58762 0.481734
\(188\) −5.01571 −0.365808
\(189\) 16.3843 1.19178
\(190\) −3.60403 −0.261464
\(191\) 6.80800 0.492610 0.246305 0.969192i \(-0.420784\pi\)
0.246305 + 0.969192i \(0.420784\pi\)
\(192\) −0.785811 −0.0567110
\(193\) −14.7284 −1.06018 −0.530088 0.847943i \(-0.677841\pi\)
−0.530088 + 0.847943i \(0.677841\pi\)
\(194\) 14.5136 1.04202
\(195\) 2.75628 0.197381
\(196\) 8.00545 0.571818
\(197\) −13.0172 −0.927438 −0.463719 0.885982i \(-0.653485\pi\)
−0.463719 + 0.885982i \(0.653485\pi\)
\(198\) 10.1199 0.719192
\(199\) 16.5962 1.17647 0.588236 0.808690i \(-0.299823\pi\)
0.588236 + 0.808690i \(0.299823\pi\)
\(200\) 2.97737 0.210532
\(201\) −7.76504 −0.547704
\(202\) 1.16747 0.0821432
\(203\) 15.8487 1.11236
\(204\) −1.21871 −0.0853271
\(205\) 9.03018 0.630695
\(206\) 3.01876 0.210327
\(207\) 2.38250 0.165595
\(208\) 2.46631 0.171008
\(209\) −10.7640 −0.744564
\(210\) −4.32913 −0.298738
\(211\) −4.82200 −0.331960 −0.165980 0.986129i \(-0.553079\pi\)
−0.165980 + 0.986129i \(0.553079\pi\)
\(212\) −6.61052 −0.454013
\(213\) −4.93076 −0.337850
\(214\) 7.17272 0.490317
\(215\) 13.2283 0.902165
\(216\) −4.22963 −0.287790
\(217\) −28.1985 −1.91424
\(218\) 3.99600 0.270643
\(219\) 10.2626 0.693482
\(220\) −6.04091 −0.407278
\(221\) 3.82500 0.257297
\(222\) −3.96066 −0.265822
\(223\) −23.8010 −1.59383 −0.796915 0.604091i \(-0.793536\pi\)
−0.796915 + 0.604091i \(0.793536\pi\)
\(224\) −3.87369 −0.258822
\(225\) 7.09360 0.472906
\(226\) −13.6826 −0.910151
\(227\) −6.05338 −0.401777 −0.200889 0.979614i \(-0.564383\pi\)
−0.200889 + 0.979614i \(0.564383\pi\)
\(228\) 1.99135 0.131881
\(229\) −25.9038 −1.71177 −0.855885 0.517167i \(-0.826987\pi\)
−0.855885 + 0.517167i \(0.826987\pi\)
\(230\) −1.42219 −0.0937765
\(231\) −12.9297 −0.850710
\(232\) −4.09137 −0.268611
\(233\) 10.7270 0.702746 0.351373 0.936236i \(-0.385715\pi\)
0.351373 + 0.936236i \(0.385715\pi\)
\(234\) 5.87599 0.384125
\(235\) 7.13330 0.465325
\(236\) −1.17415 −0.0764306
\(237\) 7.00925 0.455300
\(238\) −6.00770 −0.389422
\(239\) −24.0030 −1.55263 −0.776314 0.630347i \(-0.782913\pi\)
−0.776314 + 0.630347i \(0.782913\pi\)
\(240\) 1.11757 0.0721390
\(241\) 6.77771 0.436591 0.218295 0.975883i \(-0.429950\pi\)
0.218295 + 0.975883i \(0.429950\pi\)
\(242\) −7.04218 −0.452689
\(243\) −15.6937 −1.00675
\(244\) 6.46185 0.413677
\(245\) −11.3853 −0.727379
\(246\) −4.98950 −0.318119
\(247\) −6.24997 −0.397676
\(248\) 7.27950 0.462249
\(249\) −11.0867 −0.702588
\(250\) −11.3453 −0.717543
\(251\) 11.3933 0.719136 0.359568 0.933119i \(-0.382924\pi\)
0.359568 + 0.933119i \(0.382924\pi\)
\(252\) −9.22906 −0.581376
\(253\) −4.24761 −0.267045
\(254\) −14.2216 −0.892345
\(255\) 1.73324 0.108540
\(256\) 1.00000 0.0625000
\(257\) 9.94455 0.620324 0.310162 0.950684i \(-0.399617\pi\)
0.310162 + 0.950684i \(0.399617\pi\)
\(258\) −7.30913 −0.455046
\(259\) −19.5242 −1.21318
\(260\) −3.50756 −0.217530
\(261\) −9.74768 −0.603366
\(262\) 1.00000 0.0617802
\(263\) 9.89205 0.609970 0.304985 0.952357i \(-0.401349\pi\)
0.304985 + 0.952357i \(0.401349\pi\)
\(264\) 3.33782 0.205429
\(265\) 9.40142 0.577525
\(266\) 9.81646 0.601886
\(267\) 9.11404 0.557770
\(268\) 9.88156 0.603613
\(269\) 4.93260 0.300746 0.150373 0.988629i \(-0.451953\pi\)
0.150373 + 0.988629i \(0.451953\pi\)
\(270\) 6.01534 0.366082
\(271\) 28.7211 1.74468 0.872342 0.488895i \(-0.162600\pi\)
0.872342 + 0.488895i \(0.162600\pi\)
\(272\) 1.55090 0.0940371
\(273\) −7.50742 −0.454370
\(274\) 16.5255 0.998343
\(275\) −12.6467 −0.762626
\(276\) 0.785811 0.0473003
\(277\) −25.9935 −1.56180 −0.780898 0.624658i \(-0.785238\pi\)
−0.780898 + 0.624658i \(0.785238\pi\)
\(278\) −8.60490 −0.516088
\(279\) 17.3434 1.03832
\(280\) 5.50912 0.329233
\(281\) 32.0766 1.91353 0.956763 0.290867i \(-0.0939439\pi\)
0.956763 + 0.290867i \(0.0939439\pi\)
\(282\) −3.94140 −0.234707
\(283\) −30.7274 −1.82655 −0.913277 0.407340i \(-0.866456\pi\)
−0.913277 + 0.407340i \(0.866456\pi\)
\(284\) 6.27474 0.372337
\(285\) −2.83209 −0.167758
\(286\) −10.4759 −0.619454
\(287\) −24.5959 −1.45185
\(288\) 2.38250 0.140390
\(289\) −14.5947 −0.858512
\(290\) 5.81870 0.341686
\(291\) 11.4050 0.668570
\(292\) −13.0599 −0.764271
\(293\) −13.4226 −0.784156 −0.392078 0.919932i \(-0.628244\pi\)
−0.392078 + 0.919932i \(0.628244\pi\)
\(294\) 6.29078 0.366885
\(295\) 1.66986 0.0972232
\(296\) 5.04022 0.292957
\(297\) 17.9658 1.04248
\(298\) 15.3186 0.887383
\(299\) −2.46631 −0.142630
\(300\) 2.33965 0.135080
\(301\) −36.0306 −2.07677
\(302\) 13.1238 0.755192
\(303\) 0.917415 0.0527041
\(304\) −2.53414 −0.145343
\(305\) −9.18998 −0.526217
\(306\) 3.69502 0.211230
\(307\) 13.7714 0.785976 0.392988 0.919544i \(-0.371441\pi\)
0.392988 + 0.919544i \(0.371441\pi\)
\(308\) 16.4539 0.937549
\(309\) 2.37218 0.134948
\(310\) −10.3528 −0.588002
\(311\) 17.4388 0.988864 0.494432 0.869216i \(-0.335376\pi\)
0.494432 + 0.869216i \(0.335376\pi\)
\(312\) 1.93805 0.109721
\(313\) −14.0667 −0.795099 −0.397549 0.917581i \(-0.630139\pi\)
−0.397549 + 0.917581i \(0.630139\pi\)
\(314\) 0.761128 0.0429529
\(315\) 13.1255 0.739537
\(316\) −8.91977 −0.501776
\(317\) 6.19260 0.347811 0.173905 0.984762i \(-0.444361\pi\)
0.173905 + 0.984762i \(0.444361\pi\)
\(318\) −5.19462 −0.291300
\(319\) 17.3785 0.973011
\(320\) −1.42219 −0.0795029
\(321\) 5.63640 0.314593
\(322\) 3.87369 0.215872
\(323\) −3.93020 −0.218682
\(324\) 3.82381 0.212434
\(325\) −7.34313 −0.407324
\(326\) −19.8011 −1.09668
\(327\) 3.14010 0.173648
\(328\) 6.34949 0.350592
\(329\) −19.4293 −1.07117
\(330\) −4.74701 −0.261315
\(331\) −18.1773 −0.999114 −0.499557 0.866281i \(-0.666504\pi\)
−0.499557 + 0.866281i \(0.666504\pi\)
\(332\) 14.1085 0.774307
\(333\) 12.0083 0.658052
\(334\) −4.08020 −0.223259
\(335\) −14.0535 −0.767823
\(336\) −3.04399 −0.166063
\(337\) 23.9544 1.30488 0.652440 0.757841i \(-0.273745\pi\)
0.652440 + 0.757841i \(0.273745\pi\)
\(338\) 6.91731 0.376252
\(339\) −10.7519 −0.583964
\(340\) −2.20568 −0.119620
\(341\) −30.9205 −1.67444
\(342\) −6.03759 −0.326475
\(343\) 3.89481 0.210300
\(344\) 9.30138 0.501497
\(345\) −1.11757 −0.0601681
\(346\) −2.46367 −0.132448
\(347\) −32.0717 −1.72170 −0.860849 0.508861i \(-0.830067\pi\)
−0.860849 + 0.508861i \(0.830067\pi\)
\(348\) −3.21504 −0.172344
\(349\) 0.128543 0.00688074 0.00344037 0.999994i \(-0.498905\pi\)
0.00344037 + 0.999994i \(0.498905\pi\)
\(350\) 11.5334 0.616487
\(351\) 10.4316 0.556796
\(352\) −4.24761 −0.226398
\(353\) 5.01443 0.266891 0.133446 0.991056i \(-0.457396\pi\)
0.133446 + 0.991056i \(0.457396\pi\)
\(354\) −0.922660 −0.0490388
\(355\) −8.92387 −0.473630
\(356\) −11.5983 −0.614706
\(357\) −4.72092 −0.249858
\(358\) −10.7958 −0.570575
\(359\) −23.3707 −1.23346 −0.616730 0.787175i \(-0.711543\pi\)
−0.616730 + 0.787175i \(0.711543\pi\)
\(360\) −3.38837 −0.178583
\(361\) −12.5781 −0.662007
\(362\) −9.47637 −0.498067
\(363\) −5.53383 −0.290451
\(364\) 9.55371 0.500751
\(365\) 18.5736 0.972188
\(366\) 5.07779 0.265420
\(367\) 25.8392 1.34880 0.674398 0.738368i \(-0.264403\pi\)
0.674398 + 0.738368i \(0.264403\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 15.1277 0.787515
\(370\) −7.16815 −0.372654
\(371\) −25.6071 −1.32945
\(372\) 5.72031 0.296584
\(373\) −2.83438 −0.146758 −0.0733792 0.997304i \(-0.523378\pi\)
−0.0733792 + 0.997304i \(0.523378\pi\)
\(374\) −6.58762 −0.340638
\(375\) −8.91530 −0.460384
\(376\) 5.01571 0.258666
\(377\) 10.0906 0.519691
\(378\) −16.3843 −0.842716
\(379\) −33.9194 −1.74232 −0.871160 0.490999i \(-0.836632\pi\)
−0.871160 + 0.490999i \(0.836632\pi\)
\(380\) 3.60403 0.184883
\(381\) −11.1755 −0.572539
\(382\) −6.80800 −0.348328
\(383\) 29.3851 1.50151 0.750753 0.660583i \(-0.229691\pi\)
0.750753 + 0.660583i \(0.229691\pi\)
\(384\) 0.785811 0.0401008
\(385\) −23.4006 −1.19260
\(386\) 14.7284 0.749657
\(387\) 22.1605 1.12648
\(388\) −14.5136 −0.736817
\(389\) 11.5197 0.584070 0.292035 0.956408i \(-0.405668\pi\)
0.292035 + 0.956408i \(0.405668\pi\)
\(390\) −2.75628 −0.139570
\(391\) −1.55090 −0.0784324
\(392\) −8.00545 −0.404336
\(393\) 0.785811 0.0396389
\(394\) 13.0172 0.655798
\(395\) 12.6856 0.638282
\(396\) −10.1199 −0.508546
\(397\) −30.2065 −1.51602 −0.758010 0.652243i \(-0.773828\pi\)
−0.758010 + 0.652243i \(0.773828\pi\)
\(398\) −16.5962 −0.831891
\(399\) 7.71389 0.386177
\(400\) −2.97737 −0.148869
\(401\) −3.54033 −0.176796 −0.0883978 0.996085i \(-0.528175\pi\)
−0.0883978 + 0.996085i \(0.528175\pi\)
\(402\) 7.76504 0.387285
\(403\) −17.9535 −0.894328
\(404\) −1.16747 −0.0580840
\(405\) −5.43819 −0.270226
\(406\) −15.8487 −0.786556
\(407\) −21.4089 −1.06120
\(408\) 1.21871 0.0603354
\(409\) −24.7495 −1.22378 −0.611891 0.790942i \(-0.709591\pi\)
−0.611891 + 0.790942i \(0.709591\pi\)
\(410\) −9.03018 −0.445969
\(411\) 12.9859 0.640549
\(412\) −3.01876 −0.148724
\(413\) −4.54829 −0.223807
\(414\) −2.38250 −0.117094
\(415\) −20.0650 −0.984954
\(416\) −2.46631 −0.120921
\(417\) −6.76183 −0.331128
\(418\) 10.7640 0.526486
\(419\) 30.3852 1.48441 0.742206 0.670171i \(-0.233779\pi\)
0.742206 + 0.670171i \(0.233779\pi\)
\(420\) 4.32913 0.211240
\(421\) −23.4771 −1.14420 −0.572102 0.820183i \(-0.693872\pi\)
−0.572102 + 0.820183i \(0.693872\pi\)
\(422\) 4.82200 0.234731
\(423\) 11.9499 0.581026
\(424\) 6.61052 0.321035
\(425\) −4.61761 −0.223987
\(426\) 4.93076 0.238896
\(427\) 25.0312 1.21134
\(428\) −7.17272 −0.346706
\(429\) −8.23210 −0.397449
\(430\) −13.2283 −0.637927
\(431\) 16.7750 0.808025 0.404013 0.914753i \(-0.367615\pi\)
0.404013 + 0.914753i \(0.367615\pi\)
\(432\) 4.22963 0.203498
\(433\) 33.2177 1.59634 0.798170 0.602433i \(-0.205802\pi\)
0.798170 + 0.602433i \(0.205802\pi\)
\(434\) 28.1985 1.35357
\(435\) 4.57240 0.219230
\(436\) −3.99600 −0.191373
\(437\) 2.53414 0.121224
\(438\) −10.2626 −0.490366
\(439\) −4.02949 −0.192317 −0.0961585 0.995366i \(-0.530656\pi\)
−0.0961585 + 0.995366i \(0.530656\pi\)
\(440\) 6.04091 0.287989
\(441\) −19.0730 −0.908238
\(442\) −3.82500 −0.181937
\(443\) −23.2202 −1.10323 −0.551613 0.834100i \(-0.685988\pi\)
−0.551613 + 0.834100i \(0.685988\pi\)
\(444\) 3.96066 0.187965
\(445\) 16.4949 0.781934
\(446\) 23.8010 1.12701
\(447\) 12.0375 0.569356
\(448\) 3.87369 0.183015
\(449\) 15.7458 0.743092 0.371546 0.928415i \(-0.378828\pi\)
0.371546 + 0.928415i \(0.378828\pi\)
\(450\) −7.09360 −0.334395
\(451\) −26.9702 −1.26998
\(452\) 13.6826 0.643574
\(453\) 10.3129 0.484540
\(454\) 6.05338 0.284099
\(455\) −13.5872 −0.636978
\(456\) −1.99135 −0.0932537
\(457\) 22.8637 1.06952 0.534760 0.845004i \(-0.320402\pi\)
0.534760 + 0.845004i \(0.320402\pi\)
\(458\) 25.9038 1.21040
\(459\) 6.55973 0.306182
\(460\) 1.42219 0.0663100
\(461\) −1.40109 −0.0652555 −0.0326277 0.999468i \(-0.510388\pi\)
−0.0326277 + 0.999468i \(0.510388\pi\)
\(462\) 12.9297 0.601543
\(463\) −38.6071 −1.79423 −0.897113 0.441802i \(-0.854339\pi\)
−0.897113 + 0.441802i \(0.854339\pi\)
\(464\) 4.09137 0.189937
\(465\) −8.13537 −0.377269
\(466\) −10.7270 −0.496916
\(467\) −33.5864 −1.55420 −0.777098 0.629380i \(-0.783309\pi\)
−0.777098 + 0.629380i \(0.783309\pi\)
\(468\) −5.87599 −0.271618
\(469\) 38.2781 1.76752
\(470\) −7.13330 −0.329034
\(471\) 0.598103 0.0275591
\(472\) 1.17415 0.0540446
\(473\) −39.5086 −1.81661
\(474\) −7.00925 −0.321946
\(475\) 7.54508 0.346192
\(476\) 6.00770 0.275363
\(477\) 15.7496 0.721124
\(478\) 24.0030 1.09787
\(479\) 16.2242 0.741304 0.370652 0.928772i \(-0.379134\pi\)
0.370652 + 0.928772i \(0.379134\pi\)
\(480\) −1.11757 −0.0510100
\(481\) −12.4307 −0.566793
\(482\) −6.77771 −0.308716
\(483\) 3.04399 0.138506
\(484\) 7.04218 0.320099
\(485\) 20.6411 0.937265
\(486\) 15.6937 0.711880
\(487\) −1.66642 −0.0755125 −0.0377562 0.999287i \(-0.512021\pi\)
−0.0377562 + 0.999287i \(0.512021\pi\)
\(488\) −6.46185 −0.292514
\(489\) −15.5599 −0.703644
\(490\) 11.3853 0.514334
\(491\) 5.78439 0.261046 0.130523 0.991445i \(-0.458334\pi\)
0.130523 + 0.991445i \(0.458334\pi\)
\(492\) 4.98950 0.224944
\(493\) 6.34530 0.285778
\(494\) 6.24997 0.281200
\(495\) 14.3925 0.646893
\(496\) −7.27950 −0.326859
\(497\) 24.3064 1.09029
\(498\) 11.0867 0.496805
\(499\) −26.4914 −1.18592 −0.592959 0.805232i \(-0.702041\pi\)
−0.592959 + 0.805232i \(0.702041\pi\)
\(500\) 11.3453 0.507379
\(501\) −3.20627 −0.143245
\(502\) −11.3933 −0.508506
\(503\) −16.6310 −0.741539 −0.370769 0.928725i \(-0.620906\pi\)
−0.370769 + 0.928725i \(0.620906\pi\)
\(504\) 9.22906 0.411095
\(505\) 1.66037 0.0738855
\(506\) 4.24761 0.188829
\(507\) 5.43570 0.241408
\(508\) 14.2216 0.630983
\(509\) −12.7565 −0.565422 −0.282711 0.959205i \(-0.591234\pi\)
−0.282711 + 0.959205i \(0.591234\pi\)
\(510\) −1.73324 −0.0767493
\(511\) −50.5899 −2.23796
\(512\) −1.00000 −0.0441942
\(513\) −10.7185 −0.473232
\(514\) −9.94455 −0.438635
\(515\) 4.29325 0.189183
\(516\) 7.30913 0.321766
\(517\) −21.3048 −0.936983
\(518\) 19.5242 0.857845
\(519\) −1.93598 −0.0849799
\(520\) 3.50756 0.153817
\(521\) −12.7609 −0.559063 −0.279532 0.960137i \(-0.590179\pi\)
−0.279532 + 0.960137i \(0.590179\pi\)
\(522\) 9.74768 0.426644
\(523\) −6.25629 −0.273569 −0.136784 0.990601i \(-0.543677\pi\)
−0.136784 + 0.990601i \(0.543677\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 9.06309 0.395546
\(526\) −9.89205 −0.431314
\(527\) −11.2898 −0.491791
\(528\) −3.33782 −0.145260
\(529\) 1.00000 0.0434783
\(530\) −9.40142 −0.408372
\(531\) 2.79741 0.121397
\(532\) −9.81646 −0.425598
\(533\) −15.6598 −0.678302
\(534\) −9.11404 −0.394403
\(535\) 10.2010 0.441026
\(536\) −9.88156 −0.426819
\(537\) −8.48346 −0.366088
\(538\) −4.93260 −0.212659
\(539\) 34.0040 1.46466
\(540\) −6.01534 −0.258859
\(541\) −3.89662 −0.167529 −0.0837643 0.996486i \(-0.526694\pi\)
−0.0837643 + 0.996486i \(0.526694\pi\)
\(542\) −28.7211 −1.23368
\(543\) −7.44664 −0.319566
\(544\) −1.55090 −0.0664943
\(545\) 5.68307 0.243436
\(546\) 7.50742 0.321288
\(547\) 4.45583 0.190517 0.0952587 0.995453i \(-0.469632\pi\)
0.0952587 + 0.995453i \(0.469632\pi\)
\(548\) −16.5255 −0.705935
\(549\) −15.3954 −0.657058
\(550\) 12.6467 0.539258
\(551\) −10.3681 −0.441695
\(552\) −0.785811 −0.0334463
\(553\) −34.5524 −1.46932
\(554\) 25.9935 1.10436
\(555\) −5.63281 −0.239099
\(556\) 8.60490 0.364929
\(557\) 43.4169 1.83963 0.919817 0.392348i \(-0.128337\pi\)
0.919817 + 0.392348i \(0.128337\pi\)
\(558\) −17.3434 −0.734205
\(559\) −22.9401 −0.970262
\(560\) −5.50912 −0.232803
\(561\) −5.17662 −0.218557
\(562\) −32.0766 −1.35307
\(563\) −16.3347 −0.688424 −0.344212 0.938892i \(-0.611854\pi\)
−0.344212 + 0.938892i \(0.611854\pi\)
\(564\) 3.94140 0.165963
\(565\) −19.4592 −0.818655
\(566\) 30.7274 1.29157
\(567\) 14.8123 0.622056
\(568\) −6.27474 −0.263282
\(569\) 23.3598 0.979293 0.489647 0.871921i \(-0.337126\pi\)
0.489647 + 0.871921i \(0.337126\pi\)
\(570\) 2.83209 0.118623
\(571\) −4.00674 −0.167677 −0.0838384 0.996479i \(-0.526718\pi\)
−0.0838384 + 0.996479i \(0.526718\pi\)
\(572\) 10.4759 0.438020
\(573\) −5.34980 −0.223491
\(574\) 24.5959 1.02661
\(575\) 2.97737 0.124165
\(576\) −2.38250 −0.0992709
\(577\) −0.942727 −0.0392463 −0.0196231 0.999807i \(-0.506247\pi\)
−0.0196231 + 0.999807i \(0.506247\pi\)
\(578\) 14.5947 0.607060
\(579\) 11.5738 0.480989
\(580\) −5.81870 −0.241608
\(581\) 54.6521 2.26735
\(582\) −11.4050 −0.472751
\(583\) −28.0789 −1.16291
\(584\) 13.0599 0.540421
\(585\) 8.35677 0.345510
\(586\) 13.4226 0.554482
\(587\) −1.48796 −0.0614145 −0.0307073 0.999528i \(-0.509776\pi\)
−0.0307073 + 0.999528i \(0.509776\pi\)
\(588\) −6.29078 −0.259427
\(589\) 18.4473 0.760106
\(590\) −1.66986 −0.0687472
\(591\) 10.2291 0.420768
\(592\) −5.04022 −0.207152
\(593\) 1.86374 0.0765345 0.0382673 0.999268i \(-0.487816\pi\)
0.0382673 + 0.999268i \(0.487816\pi\)
\(594\) −17.9658 −0.737146
\(595\) −8.54410 −0.350274
\(596\) −15.3186 −0.627475
\(597\) −13.0415 −0.533751
\(598\) 2.46631 0.100855
\(599\) −11.8117 −0.482614 −0.241307 0.970449i \(-0.577576\pi\)
−0.241307 + 0.970449i \(0.577576\pi\)
\(600\) −2.33965 −0.0955160
\(601\) 41.3786 1.68787 0.843934 0.536447i \(-0.180234\pi\)
0.843934 + 0.536447i \(0.180234\pi\)
\(602\) 36.0306 1.46850
\(603\) −23.5428 −0.958738
\(604\) −13.1238 −0.534001
\(605\) −10.0153 −0.407181
\(606\) −0.917415 −0.0372674
\(607\) −2.96436 −0.120320 −0.0601598 0.998189i \(-0.519161\pi\)
−0.0601598 + 0.998189i \(0.519161\pi\)
\(608\) 2.53414 0.102773
\(609\) −12.4541 −0.504664
\(610\) 9.18998 0.372091
\(611\) −12.3703 −0.500449
\(612\) −3.69502 −0.149362
\(613\) −46.7489 −1.88817 −0.944086 0.329700i \(-0.893052\pi\)
−0.944086 + 0.329700i \(0.893052\pi\)
\(614\) −13.7714 −0.555769
\(615\) −7.09602 −0.286139
\(616\) −16.4539 −0.662947
\(617\) −7.73953 −0.311582 −0.155791 0.987790i \(-0.549793\pi\)
−0.155791 + 0.987790i \(0.549793\pi\)
\(618\) −2.37218 −0.0954229
\(619\) −1.07015 −0.0430131 −0.0215066 0.999769i \(-0.506846\pi\)
−0.0215066 + 0.999769i \(0.506846\pi\)
\(620\) 10.3528 0.415780
\(621\) −4.22963 −0.169729
\(622\) −17.4388 −0.699233
\(623\) −44.9280 −1.80000
\(624\) −1.93805 −0.0775843
\(625\) −1.24837 −0.0499346
\(626\) 14.0667 0.562220
\(627\) 8.45850 0.337800
\(628\) −0.761128 −0.0303723
\(629\) −7.81687 −0.311679
\(630\) −13.1255 −0.522932
\(631\) −8.86536 −0.352924 −0.176462 0.984307i \(-0.556465\pi\)
−0.176462 + 0.984307i \(0.556465\pi\)
\(632\) 8.91977 0.354809
\(633\) 3.78918 0.150607
\(634\) −6.19260 −0.245939
\(635\) −20.2259 −0.802639
\(636\) 5.19462 0.205980
\(637\) 19.7439 0.782283
\(638\) −17.3785 −0.688022
\(639\) −14.9496 −0.591395
\(640\) 1.42219 0.0562170
\(641\) −21.3470 −0.843157 −0.421578 0.906792i \(-0.638524\pi\)
−0.421578 + 0.906792i \(0.638524\pi\)
\(642\) −5.63640 −0.222451
\(643\) −24.2440 −0.956092 −0.478046 0.878335i \(-0.658655\pi\)
−0.478046 + 0.878335i \(0.658655\pi\)
\(644\) −3.87369 −0.152645
\(645\) −10.3950 −0.409302
\(646\) 3.93020 0.154632
\(647\) −40.1279 −1.57759 −0.788796 0.614656i \(-0.789295\pi\)
−0.788796 + 0.614656i \(0.789295\pi\)
\(648\) −3.82381 −0.150214
\(649\) −4.98733 −0.195770
\(650\) 7.34313 0.288021
\(651\) 22.1587 0.868468
\(652\) 19.8011 0.775470
\(653\) 42.4364 1.66066 0.830331 0.557270i \(-0.188151\pi\)
0.830331 + 0.557270i \(0.188151\pi\)
\(654\) −3.14010 −0.122788
\(655\) 1.42219 0.0555696
\(656\) −6.34949 −0.247906
\(657\) 31.1152 1.21392
\(658\) 19.4293 0.757433
\(659\) 37.0603 1.44366 0.721832 0.692068i \(-0.243300\pi\)
0.721832 + 0.692068i \(0.243300\pi\)
\(660\) 4.74701 0.184777
\(661\) −47.4400 −1.84520 −0.922601 0.385755i \(-0.873941\pi\)
−0.922601 + 0.385755i \(0.873941\pi\)
\(662\) 18.1773 0.706480
\(663\) −3.00573 −0.116733
\(664\) −14.1085 −0.547518
\(665\) 13.9609 0.541380
\(666\) −12.0083 −0.465313
\(667\) −4.09137 −0.158418
\(668\) 4.08020 0.157868
\(669\) 18.7031 0.723102
\(670\) 14.0535 0.542933
\(671\) 27.4474 1.05960
\(672\) 3.04399 0.117424
\(673\) −10.1492 −0.391223 −0.195612 0.980681i \(-0.562669\pi\)
−0.195612 + 0.980681i \(0.562669\pi\)
\(674\) −23.9544 −0.922689
\(675\) −12.5932 −0.484712
\(676\) −6.91731 −0.266051
\(677\) −6.88451 −0.264593 −0.132297 0.991210i \(-0.542235\pi\)
−0.132297 + 0.991210i \(0.542235\pi\)
\(678\) 10.7519 0.412925
\(679\) −56.2212 −2.15757
\(680\) 2.20568 0.0845838
\(681\) 4.75682 0.182282
\(682\) 30.9205 1.18401
\(683\) −43.2779 −1.65598 −0.827991 0.560741i \(-0.810516\pi\)
−0.827991 + 0.560741i \(0.810516\pi\)
\(684\) 6.03759 0.230853
\(685\) 23.5024 0.897981
\(686\) −3.89481 −0.148705
\(687\) 20.3555 0.776610
\(688\) −9.30138 −0.354612
\(689\) −16.3036 −0.621118
\(690\) 1.11757 0.0425453
\(691\) −10.0098 −0.380792 −0.190396 0.981707i \(-0.560977\pi\)
−0.190396 + 0.981707i \(0.560977\pi\)
\(692\) 2.46367 0.0936545
\(693\) −39.2015 −1.48914
\(694\) 32.0717 1.21742
\(695\) −12.2378 −0.464206
\(696\) 3.21504 0.121866
\(697\) −9.84743 −0.372998
\(698\) −0.128543 −0.00486542
\(699\) −8.42936 −0.318828
\(700\) −11.5334 −0.435922
\(701\) −22.1761 −0.837581 −0.418790 0.908083i \(-0.637546\pi\)
−0.418790 + 0.908083i \(0.637546\pi\)
\(702\) −10.4316 −0.393715
\(703\) 12.7726 0.481728
\(704\) 4.24761 0.160088
\(705\) −5.60543 −0.211113
\(706\) −5.01443 −0.188721
\(707\) −4.52243 −0.170084
\(708\) 0.922660 0.0346757
\(709\) −49.8074 −1.87056 −0.935278 0.353915i \(-0.884850\pi\)
−0.935278 + 0.353915i \(0.884850\pi\)
\(710\) 8.92387 0.334907
\(711\) 21.2513 0.796988
\(712\) 11.5983 0.434663
\(713\) 7.27950 0.272619
\(714\) 4.72092 0.176676
\(715\) −14.8988 −0.557182
\(716\) 10.7958 0.403458
\(717\) 18.8619 0.704409
\(718\) 23.3707 0.872187
\(719\) −7.28751 −0.271778 −0.135889 0.990724i \(-0.543389\pi\)
−0.135889 + 0.990724i \(0.543389\pi\)
\(720\) 3.38837 0.126277
\(721\) −11.6937 −0.435498
\(722\) 12.5781 0.468110
\(723\) −5.32600 −0.198076
\(724\) 9.47637 0.352187
\(725\) −12.1815 −0.452411
\(726\) 5.53383 0.205380
\(727\) −0.170838 −0.00633602 −0.00316801 0.999995i \(-0.501008\pi\)
−0.00316801 + 0.999995i \(0.501008\pi\)
\(728\) −9.55371 −0.354084
\(729\) 0.860836 0.0318828
\(730\) −18.5736 −0.687441
\(731\) −14.4255 −0.533547
\(732\) −5.07779 −0.187681
\(733\) −43.1216 −1.59273 −0.796367 0.604814i \(-0.793247\pi\)
−0.796367 + 0.604814i \(0.793247\pi\)
\(734\) −25.8392 −0.953743
\(735\) 8.94668 0.330003
\(736\) 1.00000 0.0368605
\(737\) 41.9730 1.54610
\(738\) −15.1277 −0.556857
\(739\) 9.57554 0.352242 0.176121 0.984369i \(-0.443645\pi\)
0.176121 + 0.984369i \(0.443645\pi\)
\(740\) 7.16815 0.263506
\(741\) 4.91130 0.180421
\(742\) 25.6071 0.940066
\(743\) 13.1943 0.484053 0.242027 0.970270i \(-0.422188\pi\)
0.242027 + 0.970270i \(0.422188\pi\)
\(744\) −5.72031 −0.209717
\(745\) 21.7860 0.798176
\(746\) 2.83438 0.103774
\(747\) −33.6136 −1.22986
\(748\) 6.58762 0.240867
\(749\) −27.7849 −1.01524
\(750\) 8.91530 0.325541
\(751\) 10.1773 0.371374 0.185687 0.982609i \(-0.440549\pi\)
0.185687 + 0.982609i \(0.440549\pi\)
\(752\) −5.01571 −0.182904
\(753\) −8.95295 −0.326264
\(754\) −10.0906 −0.367477
\(755\) 18.6646 0.679274
\(756\) 16.3843 0.595890
\(757\) 41.7124 1.51606 0.758031 0.652218i \(-0.226161\pi\)
0.758031 + 0.652218i \(0.226161\pi\)
\(758\) 33.9194 1.23201
\(759\) 3.33782 0.121155
\(760\) −3.60403 −0.130732
\(761\) 25.8827 0.938246 0.469123 0.883133i \(-0.344570\pi\)
0.469123 + 0.883133i \(0.344570\pi\)
\(762\) 11.1755 0.404846
\(763\) −15.4792 −0.560386
\(764\) 6.80800 0.246305
\(765\) 5.25502 0.189996
\(766\) −29.3851 −1.06173
\(767\) −2.89582 −0.104562
\(768\) −0.785811 −0.0283555
\(769\) −11.2893 −0.407101 −0.203551 0.979064i \(-0.565248\pi\)
−0.203551 + 0.979064i \(0.565248\pi\)
\(770\) 23.4006 0.843299
\(771\) −7.81454 −0.281434
\(772\) −14.7284 −0.530088
\(773\) 15.5274 0.558483 0.279242 0.960221i \(-0.409917\pi\)
0.279242 + 0.960221i \(0.409917\pi\)
\(774\) −22.1605 −0.796544
\(775\) 21.6738 0.778546
\(776\) 14.5136 0.521008
\(777\) 15.3424 0.550404
\(778\) −11.5197 −0.413000
\(779\) 16.0905 0.576502
\(780\) 2.75628 0.0986907
\(781\) 26.6526 0.953706
\(782\) 1.55090 0.0554601
\(783\) 17.3050 0.618429
\(784\) 8.00545 0.285909
\(785\) 1.08247 0.0386350
\(786\) −0.785811 −0.0280290
\(787\) 34.8319 1.24162 0.620811 0.783960i \(-0.286803\pi\)
0.620811 + 0.783960i \(0.286803\pi\)
\(788\) −13.0172 −0.463719
\(789\) −7.77328 −0.276736
\(790\) −12.6856 −0.451334
\(791\) 53.0020 1.88453
\(792\) 10.1199 0.359596
\(793\) 15.9369 0.565937
\(794\) 30.2065 1.07199
\(795\) −7.38774 −0.262016
\(796\) 16.5962 0.588236
\(797\) −3.51665 −0.124566 −0.0622830 0.998059i \(-0.519838\pi\)
−0.0622830 + 0.998059i \(0.519838\pi\)
\(798\) −7.71389 −0.273069
\(799\) −7.77887 −0.275197
\(800\) 2.97737 0.105266
\(801\) 27.6328 0.976359
\(802\) 3.54033 0.125013
\(803\) −55.4732 −1.95761
\(804\) −7.76504 −0.273852
\(805\) 5.50912 0.194171
\(806\) 17.9535 0.632385
\(807\) −3.87609 −0.136445
\(808\) 1.16747 0.0410716
\(809\) −11.4465 −0.402437 −0.201218 0.979546i \(-0.564490\pi\)
−0.201218 + 0.979546i \(0.564490\pi\)
\(810\) 5.43819 0.191078
\(811\) 12.3087 0.432217 0.216109 0.976369i \(-0.430663\pi\)
0.216109 + 0.976369i \(0.430663\pi\)
\(812\) 15.8487 0.556179
\(813\) −22.5694 −0.791543
\(814\) 21.4089 0.750380
\(815\) −28.1609 −0.986434
\(816\) −1.21871 −0.0426635
\(817\) 23.5710 0.824644
\(818\) 24.7495 0.865345
\(819\) −22.7617 −0.795359
\(820\) 9.03018 0.315348
\(821\) 39.0355 1.36235 0.681174 0.732122i \(-0.261470\pi\)
0.681174 + 0.732122i \(0.261470\pi\)
\(822\) −12.9859 −0.452936
\(823\) −3.40609 −0.118729 −0.0593644 0.998236i \(-0.518907\pi\)
−0.0593644 + 0.998236i \(0.518907\pi\)
\(824\) 3.01876 0.105164
\(825\) 9.93794 0.345995
\(826\) 4.54829 0.158255
\(827\) 40.6519 1.41361 0.706803 0.707411i \(-0.250137\pi\)
0.706803 + 0.707411i \(0.250137\pi\)
\(828\) 2.38250 0.0827976
\(829\) −30.8370 −1.07101 −0.535507 0.844530i \(-0.679880\pi\)
−0.535507 + 0.844530i \(0.679880\pi\)
\(830\) 20.0650 0.696468
\(831\) 20.4260 0.708569
\(832\) 2.46631 0.0855039
\(833\) 12.4157 0.430177
\(834\) 6.76183 0.234143
\(835\) −5.80282 −0.200815
\(836\) −10.7640 −0.372282
\(837\) −30.7896 −1.06424
\(838\) −30.3852 −1.04964
\(839\) 39.4504 1.36198 0.680989 0.732294i \(-0.261550\pi\)
0.680989 + 0.732294i \(0.261550\pi\)
\(840\) −4.32913 −0.149369
\(841\) −12.2607 −0.422784
\(842\) 23.4771 0.809074
\(843\) −25.2061 −0.868145
\(844\) −4.82200 −0.165980
\(845\) 9.83774 0.338428
\(846\) −11.9499 −0.410847
\(847\) 27.2792 0.937325
\(848\) −6.61052 −0.227006
\(849\) 24.1459 0.828686
\(850\) 4.61761 0.158383
\(851\) 5.04022 0.172776
\(852\) −4.93076 −0.168925
\(853\) 24.7081 0.845988 0.422994 0.906132i \(-0.360979\pi\)
0.422994 + 0.906132i \(0.360979\pi\)
\(854\) −25.0312 −0.856549
\(855\) −8.58660 −0.293655
\(856\) 7.17272 0.245158
\(857\) 34.1846 1.16772 0.583861 0.811854i \(-0.301541\pi\)
0.583861 + 0.811854i \(0.301541\pi\)
\(858\) 8.23210 0.281039
\(859\) −27.2217 −0.928793 −0.464396 0.885628i \(-0.653729\pi\)
−0.464396 + 0.885628i \(0.653729\pi\)
\(860\) 13.2283 0.451082
\(861\) 19.3278 0.658689
\(862\) −16.7750 −0.571360
\(863\) −21.5808 −0.734618 −0.367309 0.930099i \(-0.619721\pi\)
−0.367309 + 0.930099i \(0.619721\pi\)
\(864\) −4.22963 −0.143895
\(865\) −3.50380 −0.119133
\(866\) −33.2177 −1.12878
\(867\) 11.4687 0.389497
\(868\) −28.1985 −0.957120
\(869\) −37.8877 −1.28525
\(870\) −4.57240 −0.155019
\(871\) 24.3710 0.825780
\(872\) 3.99600 0.135321
\(873\) 34.5787 1.17031
\(874\) −2.53414 −0.0857185
\(875\) 43.9483 1.48572
\(876\) 10.2626 0.346741
\(877\) −18.4620 −0.623416 −0.311708 0.950178i \(-0.600901\pi\)
−0.311708 + 0.950178i \(0.600901\pi\)
\(878\) 4.02949 0.135989
\(879\) 10.5476 0.355763
\(880\) −6.04091 −0.203639
\(881\) −31.8132 −1.07181 −0.535907 0.844277i \(-0.680030\pi\)
−0.535907 + 0.844277i \(0.680030\pi\)
\(882\) 19.0730 0.642221
\(883\) 15.6302 0.526000 0.263000 0.964796i \(-0.415288\pi\)
0.263000 + 0.964796i \(0.415288\pi\)
\(884\) 3.82500 0.128649
\(885\) −1.31220 −0.0441090
\(886\) 23.2202 0.780099
\(887\) 6.66364 0.223743 0.111872 0.993723i \(-0.464315\pi\)
0.111872 + 0.993723i \(0.464315\pi\)
\(888\) −3.96066 −0.132911
\(889\) 55.0902 1.84767
\(890\) −16.4949 −0.552911
\(891\) 16.2421 0.544129
\(892\) −23.8010 −0.796915
\(893\) 12.7105 0.425341
\(894\) −12.0375 −0.402595
\(895\) −15.3537 −0.513217
\(896\) −3.87369 −0.129411
\(897\) 1.93805 0.0647097
\(898\) −15.7458 −0.525445
\(899\) −29.7831 −0.993322
\(900\) 7.09360 0.236453
\(901\) −10.2523 −0.341552
\(902\) 26.9702 0.898008
\(903\) 28.3133 0.942207
\(904\) −13.6826 −0.455075
\(905\) −13.4772 −0.447997
\(906\) −10.3129 −0.342622
\(907\) 50.1996 1.66685 0.833425 0.552633i \(-0.186377\pi\)
0.833425 + 0.552633i \(0.186377\pi\)
\(908\) −6.05338 −0.200889
\(909\) 2.78151 0.0922568
\(910\) 13.5872 0.450411
\(911\) −0.523949 −0.0173592 −0.00867960 0.999962i \(-0.502763\pi\)
−0.00867960 + 0.999962i \(0.502763\pi\)
\(912\) 1.99135 0.0659403
\(913\) 59.9276 1.98331
\(914\) −22.8637 −0.756265
\(915\) 7.22159 0.238738
\(916\) −25.9038 −0.855885
\(917\) −3.87369 −0.127920
\(918\) −6.55973 −0.216503
\(919\) 5.86338 0.193415 0.0967076 0.995313i \(-0.469169\pi\)
0.0967076 + 0.995313i \(0.469169\pi\)
\(920\) −1.42219 −0.0468882
\(921\) −10.8217 −0.356588
\(922\) 1.40109 0.0461426
\(923\) 15.4754 0.509380
\(924\) −12.9297 −0.425355
\(925\) 15.0066 0.493414
\(926\) 38.6071 1.26871
\(927\) 7.19220 0.236223
\(928\) −4.09137 −0.134306
\(929\) −31.0110 −1.01744 −0.508719 0.860933i \(-0.669881\pi\)
−0.508719 + 0.860933i \(0.669881\pi\)
\(930\) 8.13537 0.266769
\(931\) −20.2869 −0.664877
\(932\) 10.7270 0.351373
\(933\) −13.7036 −0.448636
\(934\) 33.5864 1.09898
\(935\) −9.36885 −0.306394
\(936\) 5.87599 0.192063
\(937\) 39.6895 1.29660 0.648300 0.761385i \(-0.275480\pi\)
0.648300 + 0.761385i \(0.275480\pi\)
\(938\) −38.2781 −1.24982
\(939\) 11.0538 0.360727
\(940\) 7.13330 0.232663
\(941\) −39.2170 −1.27844 −0.639219 0.769025i \(-0.720742\pi\)
−0.639219 + 0.769025i \(0.720742\pi\)
\(942\) −0.598103 −0.0194872
\(943\) 6.34949 0.206768
\(944\) −1.17415 −0.0382153
\(945\) −23.3015 −0.757999
\(946\) 39.5086 1.28454
\(947\) 39.1458 1.27207 0.636033 0.771662i \(-0.280574\pi\)
0.636033 + 0.771662i \(0.280574\pi\)
\(948\) 7.00925 0.227650
\(949\) −32.2097 −1.04557
\(950\) −7.54508 −0.244795
\(951\) −4.86621 −0.157798
\(952\) −6.00770 −0.194711
\(953\) −16.8460 −0.545694 −0.272847 0.962057i \(-0.587965\pi\)
−0.272847 + 0.962057i \(0.587965\pi\)
\(954\) −15.7496 −0.509911
\(955\) −9.68228 −0.313311
\(956\) −24.0030 −0.776314
\(957\) −13.6562 −0.441444
\(958\) −16.2242 −0.524181
\(959\) −64.0147 −2.06714
\(960\) 1.11757 0.0360695
\(961\) 21.9911 0.709392
\(962\) 12.4307 0.400783
\(963\) 17.0890 0.550686
\(964\) 6.77771 0.218295
\(965\) 20.9466 0.674296
\(966\) −3.04399 −0.0979387
\(967\) 10.1989 0.327973 0.163987 0.986463i \(-0.447565\pi\)
0.163987 + 0.986463i \(0.447565\pi\)
\(968\) −7.04218 −0.226344
\(969\) 3.08839 0.0992135
\(970\) −20.6411 −0.662746
\(971\) 4.67632 0.150070 0.0750351 0.997181i \(-0.476093\pi\)
0.0750351 + 0.997181i \(0.476093\pi\)
\(972\) −15.6937 −0.503375
\(973\) 33.3327 1.06860
\(974\) 1.66642 0.0533954
\(975\) 5.77031 0.184798
\(976\) 6.46185 0.206839
\(977\) −38.5977 −1.23485 −0.617425 0.786630i \(-0.711824\pi\)
−0.617425 + 0.786630i \(0.711824\pi\)
\(978\) 15.5599 0.497551
\(979\) −49.2649 −1.57451
\(980\) −11.3853 −0.363689
\(981\) 9.52046 0.303965
\(982\) −5.78439 −0.184587
\(983\) −20.1571 −0.642910 −0.321455 0.946925i \(-0.604172\pi\)
−0.321455 + 0.946925i \(0.604172\pi\)
\(984\) −4.98950 −0.159059
\(985\) 18.5130 0.589872
\(986\) −6.34530 −0.202076
\(987\) 15.2678 0.485978
\(988\) −6.24997 −0.198838
\(989\) 9.30138 0.295767
\(990\) −14.3925 −0.457423
\(991\) 33.4154 1.06148 0.530738 0.847536i \(-0.321915\pi\)
0.530738 + 0.847536i \(0.321915\pi\)
\(992\) 7.27950 0.231124
\(993\) 14.2839 0.453286
\(994\) −24.3064 −0.770951
\(995\) −23.6029 −0.748263
\(996\) −11.0867 −0.351294
\(997\) −17.8866 −0.566474 −0.283237 0.959050i \(-0.591408\pi\)
−0.283237 + 0.959050i \(0.591408\pi\)
\(998\) 26.4914 0.838571
\(999\) −21.3182 −0.674479
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 \(a_p\))