Properties

Label 6026.2.a.h.1.13
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 1.13
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-0.510961 q^{3}\) \(+1.00000 q^{4}\) \(+2.36930 q^{5}\) \(+0.510961 q^{6}\) \(+2.78886 q^{7}\) \(-1.00000 q^{8}\) \(-2.73892 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-0.510961 q^{3}\) \(+1.00000 q^{4}\) \(+2.36930 q^{5}\) \(+0.510961 q^{6}\) \(+2.78886 q^{7}\) \(-1.00000 q^{8}\) \(-2.73892 q^{9}\) \(-2.36930 q^{10}\) \(+0.898516 q^{11}\) \(-0.510961 q^{12}\) \(+1.36209 q^{13}\) \(-2.78886 q^{14}\) \(-1.21062 q^{15}\) \(+1.00000 q^{16}\) \(-4.57925 q^{17}\) \(+2.73892 q^{18}\) \(+3.53869 q^{19}\) \(+2.36930 q^{20}\) \(-1.42500 q^{21}\) \(-0.898516 q^{22}\) \(-1.00000 q^{23}\) \(+0.510961 q^{24}\) \(+0.613574 q^{25}\) \(-1.36209 q^{26}\) \(+2.93236 q^{27}\) \(+2.78886 q^{28}\) \(-9.50770 q^{29}\) \(+1.21062 q^{30}\) \(-7.83584 q^{31}\) \(-1.00000 q^{32}\) \(-0.459106 q^{33}\) \(+4.57925 q^{34}\) \(+6.60763 q^{35}\) \(-2.73892 q^{36}\) \(-3.08532 q^{37}\) \(-3.53869 q^{38}\) \(-0.695976 q^{39}\) \(-2.36930 q^{40}\) \(+6.50322 q^{41}\) \(+1.42500 q^{42}\) \(-2.06915 q^{43}\) \(+0.898516 q^{44}\) \(-6.48932 q^{45}\) \(+1.00000 q^{46}\) \(+2.55882 q^{47}\) \(-0.510961 q^{48}\) \(+0.777721 q^{49}\) \(-0.613574 q^{50}\) \(+2.33982 q^{51}\) \(+1.36209 q^{52}\) \(-0.0206505 q^{53}\) \(-2.93236 q^{54}\) \(+2.12885 q^{55}\) \(-2.78886 q^{56}\) \(-1.80813 q^{57}\) \(+9.50770 q^{58}\) \(-3.00244 q^{59}\) \(-1.21062 q^{60}\) \(-8.28348 q^{61}\) \(+7.83584 q^{62}\) \(-7.63845 q^{63}\) \(+1.00000 q^{64}\) \(+3.22721 q^{65}\) \(+0.459106 q^{66}\) \(-12.5193 q^{67}\) \(-4.57925 q^{68}\) \(+0.510961 q^{69}\) \(-6.60763 q^{70}\) \(-2.24850 q^{71}\) \(+2.73892 q^{72}\) \(-6.70712 q^{73}\) \(+3.08532 q^{74}\) \(-0.313512 q^{75}\) \(+3.53869 q^{76}\) \(+2.50583 q^{77}\) \(+0.695976 q^{78}\) \(-5.25698 q^{79}\) \(+2.36930 q^{80}\) \(+6.71844 q^{81}\) \(-6.50322 q^{82}\) \(-6.21446 q^{83}\) \(-1.42500 q^{84}\) \(-10.8496 q^{85}\) \(+2.06915 q^{86}\) \(+4.85806 q^{87}\) \(-0.898516 q^{88}\) \(-2.45122 q^{89}\) \(+6.48932 q^{90}\) \(+3.79868 q^{91}\) \(-1.00000 q^{92}\) \(+4.00381 q^{93}\) \(-2.55882 q^{94}\) \(+8.38421 q^{95}\) \(+0.510961 q^{96}\) \(-8.88248 q^{97}\) \(-0.777721 q^{98}\) \(-2.46096 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 27q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 39q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 13q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 21q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut +\mathstrut 7q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut +\mathstrut 23q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 29q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 17q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 36q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 39q^{78} \) \(\mathstrut -\mathstrut 53q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 37q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 7q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut +\mathstrut 13q^{90} \) \(\mathstrut -\mathstrut 44q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 23q^{93} \) \(\mathstrut -\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 13q^{98} \) \(\mathstrut -\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.510961 −0.295003 −0.147502 0.989062i \(-0.547123\pi\)
−0.147502 + 0.989062i \(0.547123\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.36930 1.05958 0.529791 0.848128i \(-0.322270\pi\)
0.529791 + 0.848128i \(0.322270\pi\)
\(6\) 0.510961 0.208599
\(7\) 2.78886 1.05409 0.527044 0.849838i \(-0.323300\pi\)
0.527044 + 0.849838i \(0.323300\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.73892 −0.912973
\(10\) −2.36930 −0.749238
\(11\) 0.898516 0.270913 0.135456 0.990783i \(-0.456750\pi\)
0.135456 + 0.990783i \(0.456750\pi\)
\(12\) −0.510961 −0.147502
\(13\) 1.36209 0.377777 0.188888 0.981999i \(-0.439512\pi\)
0.188888 + 0.981999i \(0.439512\pi\)
\(14\) −2.78886 −0.745353
\(15\) −1.21062 −0.312580
\(16\) 1.00000 0.250000
\(17\) −4.57925 −1.11063 −0.555316 0.831640i \(-0.687403\pi\)
−0.555316 + 0.831640i \(0.687403\pi\)
\(18\) 2.73892 0.645569
\(19\) 3.53869 0.811831 0.405915 0.913911i \(-0.366953\pi\)
0.405915 + 0.913911i \(0.366953\pi\)
\(20\) 2.36930 0.529791
\(21\) −1.42500 −0.310960
\(22\) −0.898516 −0.191564
\(23\) −1.00000 −0.208514
\(24\) 0.510961 0.104299
\(25\) 0.613574 0.122715
\(26\) −1.36209 −0.267129
\(27\) 2.93236 0.564333
\(28\) 2.78886 0.527044
\(29\) −9.50770 −1.76554 −0.882768 0.469809i \(-0.844323\pi\)
−0.882768 + 0.469809i \(0.844323\pi\)
\(30\) 1.21062 0.221028
\(31\) −7.83584 −1.40736 −0.703679 0.710518i \(-0.748461\pi\)
−0.703679 + 0.710518i \(0.748461\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.459106 −0.0799202
\(34\) 4.57925 0.785335
\(35\) 6.60763 1.11689
\(36\) −2.73892 −0.456487
\(37\) −3.08532 −0.507224 −0.253612 0.967306i \(-0.581619\pi\)
−0.253612 + 0.967306i \(0.581619\pi\)
\(38\) −3.53869 −0.574051
\(39\) −0.695976 −0.111445
\(40\) −2.36930 −0.374619
\(41\) 6.50322 1.01563 0.507816 0.861465i \(-0.330453\pi\)
0.507816 + 0.861465i \(0.330453\pi\)
\(42\) 1.42500 0.219882
\(43\) −2.06915 −0.315542 −0.157771 0.987476i \(-0.550431\pi\)
−0.157771 + 0.987476i \(0.550431\pi\)
\(44\) 0.898516 0.135456
\(45\) −6.48932 −0.967370
\(46\) 1.00000 0.147442
\(47\) 2.55882 0.373243 0.186621 0.982432i \(-0.440246\pi\)
0.186621 + 0.982432i \(0.440246\pi\)
\(48\) −0.510961 −0.0737508
\(49\) 0.777721 0.111103
\(50\) −0.613574 −0.0867724
\(51\) 2.33982 0.327640
\(52\) 1.36209 0.188888
\(53\) −0.0206505 −0.00283657 −0.00141828 0.999999i \(-0.500451\pi\)
−0.00141828 + 0.999999i \(0.500451\pi\)
\(54\) −2.93236 −0.399044
\(55\) 2.12885 0.287054
\(56\) −2.78886 −0.372677
\(57\) −1.80813 −0.239493
\(58\) 9.50770 1.24842
\(59\) −3.00244 −0.390884 −0.195442 0.980715i \(-0.562614\pi\)
−0.195442 + 0.980715i \(0.562614\pi\)
\(60\) −1.21062 −0.156290
\(61\) −8.28348 −1.06059 −0.530295 0.847813i \(-0.677919\pi\)
−0.530295 + 0.847813i \(0.677919\pi\)
\(62\) 7.83584 0.995153
\(63\) −7.63845 −0.962355
\(64\) 1.00000 0.125000
\(65\) 3.22721 0.400286
\(66\) 0.459106 0.0565121
\(67\) −12.5193 −1.52948 −0.764738 0.644342i \(-0.777132\pi\)
−0.764738 + 0.644342i \(0.777132\pi\)
\(68\) −4.57925 −0.555316
\(69\) 0.510961 0.0615124
\(70\) −6.60763 −0.789763
\(71\) −2.24850 −0.266848 −0.133424 0.991059i \(-0.542597\pi\)
−0.133424 + 0.991059i \(0.542597\pi\)
\(72\) 2.73892 0.322785
\(73\) −6.70712 −0.785009 −0.392504 0.919750i \(-0.628391\pi\)
−0.392504 + 0.919750i \(0.628391\pi\)
\(74\) 3.08532 0.358662
\(75\) −0.313512 −0.0362013
\(76\) 3.53869 0.405915
\(77\) 2.50583 0.285566
\(78\) 0.695976 0.0788038
\(79\) −5.25698 −0.591457 −0.295728 0.955272i \(-0.595562\pi\)
−0.295728 + 0.955272i \(0.595562\pi\)
\(80\) 2.36930 0.264896
\(81\) 6.71844 0.746493
\(82\) −6.50322 −0.718161
\(83\) −6.21446 −0.682126 −0.341063 0.940041i \(-0.610787\pi\)
−0.341063 + 0.940041i \(0.610787\pi\)
\(84\) −1.42500 −0.155480
\(85\) −10.8496 −1.17681
\(86\) 2.06915 0.223122
\(87\) 4.85806 0.520839
\(88\) −0.898516 −0.0957821
\(89\) −2.45122 −0.259828 −0.129914 0.991525i \(-0.541470\pi\)
−0.129914 + 0.991525i \(0.541470\pi\)
\(90\) 6.48932 0.684034
\(91\) 3.79868 0.398210
\(92\) −1.00000 −0.104257
\(93\) 4.00381 0.415175
\(94\) −2.55882 −0.263923
\(95\) 8.38421 0.860202
\(96\) 0.510961 0.0521497
\(97\) −8.88248 −0.901879 −0.450940 0.892555i \(-0.648911\pi\)
−0.450940 + 0.892555i \(0.648911\pi\)
\(98\) −0.777721 −0.0785617
\(99\) −2.46096 −0.247336
\(100\) 0.613574 0.0613574
\(101\) 12.4967 1.24347 0.621734 0.783229i \(-0.286429\pi\)
0.621734 + 0.783229i \(0.286429\pi\)
\(102\) −2.33982 −0.231676
\(103\) −8.31273 −0.819078 −0.409539 0.912293i \(-0.634310\pi\)
−0.409539 + 0.912293i \(0.634310\pi\)
\(104\) −1.36209 −0.133564
\(105\) −3.37624 −0.329487
\(106\) 0.0206505 0.00200576
\(107\) 15.8181 1.52919 0.764597 0.644509i \(-0.222938\pi\)
0.764597 + 0.644509i \(0.222938\pi\)
\(108\) 2.93236 0.282167
\(109\) −3.38985 −0.324689 −0.162345 0.986734i \(-0.551906\pi\)
−0.162345 + 0.986734i \(0.551906\pi\)
\(110\) −2.12885 −0.202978
\(111\) 1.57648 0.149633
\(112\) 2.78886 0.263522
\(113\) −12.8122 −1.20527 −0.602635 0.798017i \(-0.705883\pi\)
−0.602635 + 0.798017i \(0.705883\pi\)
\(114\) 1.80813 0.169347
\(115\) −2.36930 −0.220938
\(116\) −9.50770 −0.882768
\(117\) −3.73066 −0.344900
\(118\) 3.00244 0.276397
\(119\) −12.7709 −1.17070
\(120\) 1.21062 0.110514
\(121\) −10.1927 −0.926606
\(122\) 8.28348 0.749951
\(123\) −3.32289 −0.299615
\(124\) −7.83584 −0.703679
\(125\) −10.3928 −0.929556
\(126\) 7.63845 0.680487
\(127\) 10.3367 0.917234 0.458617 0.888634i \(-0.348345\pi\)
0.458617 + 0.888634i \(0.348345\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.05725 0.0930860
\(130\) −3.22721 −0.283045
\(131\) −1.00000 −0.0873704
\(132\) −0.459106 −0.0399601
\(133\) 9.86889 0.855742
\(134\) 12.5193 1.08150
\(135\) 6.94764 0.597958
\(136\) 4.57925 0.392668
\(137\) −6.03988 −0.516022 −0.258011 0.966142i \(-0.583067\pi\)
−0.258011 + 0.966142i \(0.583067\pi\)
\(138\) −0.510961 −0.0434959
\(139\) 7.51656 0.637547 0.318773 0.947831i \(-0.396729\pi\)
0.318773 + 0.947831i \(0.396729\pi\)
\(140\) 6.60763 0.558447
\(141\) −1.30746 −0.110108
\(142\) 2.24850 0.188690
\(143\) 1.22386 0.102345
\(144\) −2.73892 −0.228243
\(145\) −22.5266 −1.87073
\(146\) 6.70712 0.555085
\(147\) −0.397385 −0.0327758
\(148\) −3.08532 −0.253612
\(149\) 9.92371 0.812982 0.406491 0.913655i \(-0.366752\pi\)
0.406491 + 0.913655i \(0.366752\pi\)
\(150\) 0.313512 0.0255982
\(151\) 0.928938 0.0755959 0.0377979 0.999285i \(-0.487966\pi\)
0.0377979 + 0.999285i \(0.487966\pi\)
\(152\) −3.53869 −0.287026
\(153\) 12.5422 1.01398
\(154\) −2.50583 −0.201926
\(155\) −18.5654 −1.49121
\(156\) −0.695976 −0.0557227
\(157\) 6.44044 0.514003 0.257001 0.966411i \(-0.417266\pi\)
0.257001 + 0.966411i \(0.417266\pi\)
\(158\) 5.25698 0.418223
\(159\) 0.0105516 0.000836797 0
\(160\) −2.36930 −0.187309
\(161\) −2.78886 −0.219793
\(162\) −6.71844 −0.527850
\(163\) −21.0988 −1.65258 −0.826291 0.563243i \(-0.809553\pi\)
−0.826291 + 0.563243i \(0.809553\pi\)
\(164\) 6.50322 0.507816
\(165\) −1.08776 −0.0846820
\(166\) 6.21446 0.482336
\(167\) 7.53014 0.582699 0.291350 0.956617i \(-0.405896\pi\)
0.291350 + 0.956617i \(0.405896\pi\)
\(168\) 1.42500 0.109941
\(169\) −11.1447 −0.857285
\(170\) 10.8496 0.832127
\(171\) −9.69218 −0.741180
\(172\) −2.06915 −0.157771
\(173\) 5.61427 0.426845 0.213423 0.976960i \(-0.431539\pi\)
0.213423 + 0.976960i \(0.431539\pi\)
\(174\) −4.85806 −0.368289
\(175\) 1.71117 0.129352
\(176\) 0.898516 0.0677282
\(177\) 1.53413 0.115312
\(178\) 2.45122 0.183726
\(179\) 23.9003 1.78639 0.893196 0.449667i \(-0.148458\pi\)
0.893196 + 0.449667i \(0.148458\pi\)
\(180\) −6.48932 −0.483685
\(181\) −16.2641 −1.20890 −0.604450 0.796643i \(-0.706607\pi\)
−0.604450 + 0.796643i \(0.706607\pi\)
\(182\) −3.79868 −0.281577
\(183\) 4.23253 0.312878
\(184\) 1.00000 0.0737210
\(185\) −7.31005 −0.537446
\(186\) −4.00381 −0.293573
\(187\) −4.11453 −0.300884
\(188\) 2.55882 0.186621
\(189\) 8.17794 0.594857
\(190\) −8.38421 −0.608254
\(191\) 12.0462 0.871633 0.435816 0.900036i \(-0.356460\pi\)
0.435816 + 0.900036i \(0.356460\pi\)
\(192\) −0.510961 −0.0368754
\(193\) −1.94869 −0.140270 −0.0701350 0.997538i \(-0.522343\pi\)
−0.0701350 + 0.997538i \(0.522343\pi\)
\(194\) 8.88248 0.637725
\(195\) −1.64898 −0.118086
\(196\) 0.777721 0.0555515
\(197\) −21.5515 −1.53548 −0.767740 0.640761i \(-0.778619\pi\)
−0.767740 + 0.640761i \(0.778619\pi\)
\(198\) 2.46096 0.174893
\(199\) −8.18967 −0.580550 −0.290275 0.956943i \(-0.593747\pi\)
−0.290275 + 0.956943i \(0.593747\pi\)
\(200\) −0.613574 −0.0433862
\(201\) 6.39687 0.451200
\(202\) −12.4967 −0.879264
\(203\) −26.5156 −1.86103
\(204\) 2.33982 0.163820
\(205\) 15.4081 1.07615
\(206\) 8.31273 0.579176
\(207\) 2.73892 0.190368
\(208\) 1.36209 0.0944442
\(209\) 3.17957 0.219935
\(210\) 3.37624 0.232983
\(211\) 3.83262 0.263849 0.131924 0.991260i \(-0.457884\pi\)
0.131924 + 0.991260i \(0.457884\pi\)
\(212\) −0.0206505 −0.00141828
\(213\) 1.14890 0.0787211
\(214\) −15.8181 −1.08130
\(215\) −4.90243 −0.334343
\(216\) −2.93236 −0.199522
\(217\) −21.8530 −1.48348
\(218\) 3.38985 0.229590
\(219\) 3.42707 0.231580
\(220\) 2.12885 0.143527
\(221\) −6.23737 −0.419571
\(222\) −1.57648 −0.105806
\(223\) 18.0304 1.20741 0.603704 0.797209i \(-0.293691\pi\)
0.603704 + 0.797209i \(0.293691\pi\)
\(224\) −2.78886 −0.186338
\(225\) −1.68053 −0.112035
\(226\) 12.8122 0.852255
\(227\) 19.8771 1.31929 0.659643 0.751579i \(-0.270707\pi\)
0.659643 + 0.751579i \(0.270707\pi\)
\(228\) −1.80813 −0.119746
\(229\) 12.8990 0.852387 0.426193 0.904632i \(-0.359854\pi\)
0.426193 + 0.904632i \(0.359854\pi\)
\(230\) 2.36930 0.156227
\(231\) −1.28038 −0.0842430
\(232\) 9.50770 0.624211
\(233\) 13.4158 0.878898 0.439449 0.898268i \(-0.355174\pi\)
0.439449 + 0.898268i \(0.355174\pi\)
\(234\) 3.73066 0.243881
\(235\) 6.06262 0.395482
\(236\) −3.00244 −0.195442
\(237\) 2.68611 0.174482
\(238\) 12.7709 0.827813
\(239\) −4.38008 −0.283324 −0.141662 0.989915i \(-0.545245\pi\)
−0.141662 + 0.989915i \(0.545245\pi\)
\(240\) −1.21062 −0.0781451
\(241\) 3.61274 0.232717 0.116359 0.993207i \(-0.462878\pi\)
0.116359 + 0.993207i \(0.462878\pi\)
\(242\) 10.1927 0.655210
\(243\) −12.2299 −0.784551
\(244\) −8.28348 −0.530295
\(245\) 1.84265 0.117723
\(246\) 3.32289 0.211860
\(247\) 4.82002 0.306691
\(248\) 7.83584 0.497576
\(249\) 3.17534 0.201229
\(250\) 10.3928 0.657295
\(251\) −7.04420 −0.444626 −0.222313 0.974975i \(-0.571361\pi\)
−0.222313 + 0.974975i \(0.571361\pi\)
\(252\) −7.63845 −0.481177
\(253\) −0.898516 −0.0564892
\(254\) −10.3367 −0.648583
\(255\) 5.54372 0.347162
\(256\) 1.00000 0.0625000
\(257\) −3.26883 −0.203904 −0.101952 0.994789i \(-0.532509\pi\)
−0.101952 + 0.994789i \(0.532509\pi\)
\(258\) −1.05725 −0.0658218
\(259\) −8.60452 −0.534659
\(260\) 3.22721 0.200143
\(261\) 26.0408 1.61189
\(262\) 1.00000 0.0617802
\(263\) 19.8540 1.22425 0.612126 0.790760i \(-0.290314\pi\)
0.612126 + 0.790760i \(0.290314\pi\)
\(264\) 0.459106 0.0282560
\(265\) −0.0489273 −0.00300558
\(266\) −9.86889 −0.605101
\(267\) 1.25248 0.0766502
\(268\) −12.5193 −0.764738
\(269\) 19.6024 1.19518 0.597591 0.801801i \(-0.296125\pi\)
0.597591 + 0.801801i \(0.296125\pi\)
\(270\) −6.94764 −0.422820
\(271\) −3.63275 −0.220674 −0.110337 0.993894i \(-0.535193\pi\)
−0.110337 + 0.993894i \(0.535193\pi\)
\(272\) −4.57925 −0.277658
\(273\) −1.94098 −0.117473
\(274\) 6.03988 0.364883
\(275\) 0.551306 0.0332450
\(276\) 0.510961 0.0307562
\(277\) 20.3699 1.22391 0.611956 0.790892i \(-0.290383\pi\)
0.611956 + 0.790892i \(0.290383\pi\)
\(278\) −7.51656 −0.450813
\(279\) 21.4617 1.28488
\(280\) −6.60763 −0.394882
\(281\) −0.960400 −0.0572927 −0.0286463 0.999590i \(-0.509120\pi\)
−0.0286463 + 0.999590i \(0.509120\pi\)
\(282\) 1.30746 0.0778580
\(283\) −7.94276 −0.472148 −0.236074 0.971735i \(-0.575861\pi\)
−0.236074 + 0.971735i \(0.575861\pi\)
\(284\) −2.24850 −0.133424
\(285\) −4.28400 −0.253762
\(286\) −1.22386 −0.0723686
\(287\) 18.1366 1.07057
\(288\) 2.73892 0.161392
\(289\) 3.96954 0.233502
\(290\) 22.5266 1.32281
\(291\) 4.53860 0.266057
\(292\) −6.70712 −0.392504
\(293\) 20.7207 1.21052 0.605259 0.796029i \(-0.293070\pi\)
0.605259 + 0.796029i \(0.293070\pi\)
\(294\) 0.397385 0.0231760
\(295\) −7.11367 −0.414174
\(296\) 3.08532 0.179331
\(297\) 2.63477 0.152885
\(298\) −9.92371 −0.574865
\(299\) −1.36209 −0.0787719
\(300\) −0.313512 −0.0181006
\(301\) −5.77056 −0.332610
\(302\) −0.928938 −0.0534544
\(303\) −6.38532 −0.366827
\(304\) 3.53869 0.202958
\(305\) −19.6260 −1.12378
\(306\) −12.5422 −0.716990
\(307\) −6.56579 −0.374730 −0.187365 0.982290i \(-0.559995\pi\)
−0.187365 + 0.982290i \(0.559995\pi\)
\(308\) 2.50583 0.142783
\(309\) 4.24748 0.241631
\(310\) 18.5654 1.05445
\(311\) −4.91478 −0.278691 −0.139346 0.990244i \(-0.544500\pi\)
−0.139346 + 0.990244i \(0.544500\pi\)
\(312\) 0.695976 0.0394019
\(313\) 5.15580 0.291423 0.145711 0.989327i \(-0.453453\pi\)
0.145711 + 0.989327i \(0.453453\pi\)
\(314\) −6.44044 −0.363455
\(315\) −18.0978 −1.01969
\(316\) −5.25698 −0.295728
\(317\) −1.06135 −0.0596112 −0.0298056 0.999556i \(-0.509489\pi\)
−0.0298056 + 0.999556i \(0.509489\pi\)
\(318\) −0.0105516 −0.000591705 0
\(319\) −8.54283 −0.478306
\(320\) 2.36930 0.132448
\(321\) −8.08242 −0.451117
\(322\) 2.78886 0.155417
\(323\) −16.2045 −0.901645
\(324\) 6.71844 0.373246
\(325\) 0.835745 0.0463588
\(326\) 21.0988 1.16855
\(327\) 1.73208 0.0957844
\(328\) −6.50322 −0.359080
\(329\) 7.13619 0.393431
\(330\) 1.08776 0.0598792
\(331\) 15.7680 0.866690 0.433345 0.901228i \(-0.357333\pi\)
0.433345 + 0.901228i \(0.357333\pi\)
\(332\) −6.21446 −0.341063
\(333\) 8.45045 0.463082
\(334\) −7.53014 −0.412031
\(335\) −29.6620 −1.62061
\(336\) −1.42500 −0.0777399
\(337\) 24.4343 1.33102 0.665510 0.746389i \(-0.268214\pi\)
0.665510 + 0.746389i \(0.268214\pi\)
\(338\) 11.1447 0.606192
\(339\) 6.54653 0.355559
\(340\) −10.8496 −0.588403
\(341\) −7.04063 −0.381271
\(342\) 9.69218 0.524093
\(343\) −17.3530 −0.936976
\(344\) 2.06915 0.111561
\(345\) 1.21062 0.0651775
\(346\) −5.61427 −0.301825
\(347\) −9.11262 −0.489191 −0.244596 0.969625i \(-0.578655\pi\)
−0.244596 + 0.969625i \(0.578655\pi\)
\(348\) 4.85806 0.260419
\(349\) −12.3863 −0.663021 −0.331511 0.943451i \(-0.607558\pi\)
−0.331511 + 0.943451i \(0.607558\pi\)
\(350\) −1.71117 −0.0914659
\(351\) 3.99415 0.213192
\(352\) −0.898516 −0.0478911
\(353\) −5.10072 −0.271484 −0.135742 0.990744i \(-0.543342\pi\)
−0.135742 + 0.990744i \(0.543342\pi\)
\(354\) −1.53413 −0.0815379
\(355\) −5.32737 −0.282748
\(356\) −2.45122 −0.129914
\(357\) 6.52541 0.345362
\(358\) −23.9003 −1.26317
\(359\) −14.3929 −0.759627 −0.379814 0.925063i \(-0.624012\pi\)
−0.379814 + 0.925063i \(0.624012\pi\)
\(360\) 6.48932 0.342017
\(361\) −6.47769 −0.340931
\(362\) 16.2641 0.854822
\(363\) 5.20805 0.273352
\(364\) 3.79868 0.199105
\(365\) −15.8912 −0.831781
\(366\) −4.23253 −0.221238
\(367\) 4.65866 0.243180 0.121590 0.992580i \(-0.461201\pi\)
0.121590 + 0.992580i \(0.461201\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −17.8118 −0.927245
\(370\) 7.31005 0.380031
\(371\) −0.0575914 −0.00299000
\(372\) 4.00381 0.207588
\(373\) 2.02497 0.104849 0.0524246 0.998625i \(-0.483305\pi\)
0.0524246 + 0.998625i \(0.483305\pi\)
\(374\) 4.11453 0.212757
\(375\) 5.31029 0.274222
\(376\) −2.55882 −0.131961
\(377\) −12.9504 −0.666979
\(378\) −8.17794 −0.420628
\(379\) 13.2463 0.680418 0.340209 0.940350i \(-0.389502\pi\)
0.340209 + 0.940350i \(0.389502\pi\)
\(380\) 8.38421 0.430101
\(381\) −5.28165 −0.270587
\(382\) −12.0462 −0.616337
\(383\) −19.7135 −1.00731 −0.503657 0.863904i \(-0.668012\pi\)
−0.503657 + 0.863904i \(0.668012\pi\)
\(384\) 0.510961 0.0260749
\(385\) 5.93707 0.302581
\(386\) 1.94869 0.0991858
\(387\) 5.66723 0.288082
\(388\) −8.88248 −0.450940
\(389\) 22.6822 1.15003 0.575016 0.818142i \(-0.304996\pi\)
0.575016 + 0.818142i \(0.304996\pi\)
\(390\) 1.64898 0.0834991
\(391\) 4.57925 0.231583
\(392\) −0.777721 −0.0392809
\(393\) 0.510961 0.0257746
\(394\) 21.5515 1.08575
\(395\) −12.4554 −0.626697
\(396\) −2.46096 −0.123668
\(397\) 11.7673 0.590584 0.295292 0.955407i \(-0.404583\pi\)
0.295292 + 0.955407i \(0.404583\pi\)
\(398\) 8.18967 0.410511
\(399\) −5.04262 −0.252447
\(400\) 0.613574 0.0306787
\(401\) −16.1699 −0.807484 −0.403742 0.914873i \(-0.632291\pi\)
−0.403742 + 0.914873i \(0.632291\pi\)
\(402\) −6.39687 −0.319047
\(403\) −10.6731 −0.531667
\(404\) 12.4967 0.621734
\(405\) 15.9180 0.790971
\(406\) 26.5156 1.31595
\(407\) −2.77221 −0.137413
\(408\) −2.33982 −0.115838
\(409\) 39.9690 1.97634 0.988169 0.153367i \(-0.0490116\pi\)
0.988169 + 0.153367i \(0.0490116\pi\)
\(410\) −15.4081 −0.760951
\(411\) 3.08614 0.152228
\(412\) −8.31273 −0.409539
\(413\) −8.37336 −0.412026
\(414\) −2.73892 −0.134611
\(415\) −14.7239 −0.722768
\(416\) −1.36209 −0.0667821
\(417\) −3.84067 −0.188078
\(418\) −3.17957 −0.155518
\(419\) −30.0864 −1.46982 −0.734908 0.678167i \(-0.762775\pi\)
−0.734908 + 0.678167i \(0.762775\pi\)
\(420\) −3.37624 −0.164744
\(421\) −31.6647 −1.54324 −0.771622 0.636082i \(-0.780554\pi\)
−0.771622 + 0.636082i \(0.780554\pi\)
\(422\) −3.83262 −0.186569
\(423\) −7.00841 −0.340761
\(424\) 0.0206505 0.00100288
\(425\) −2.80971 −0.136291
\(426\) −1.14890 −0.0556642
\(427\) −23.1014 −1.11796
\(428\) 15.8181 0.764597
\(429\) −0.625346 −0.0301920
\(430\) 4.90243 0.236416
\(431\) −20.4046 −0.982853 −0.491426 0.870919i \(-0.663524\pi\)
−0.491426 + 0.870919i \(0.663524\pi\)
\(432\) 2.93236 0.141083
\(433\) −8.53681 −0.410253 −0.205126 0.978735i \(-0.565761\pi\)
−0.205126 + 0.978735i \(0.565761\pi\)
\(434\) 21.8530 1.04898
\(435\) 11.5102 0.551872
\(436\) −3.38985 −0.162345
\(437\) −3.53869 −0.169278
\(438\) −3.42707 −0.163752
\(439\) −19.1651 −0.914700 −0.457350 0.889287i \(-0.651201\pi\)
−0.457350 + 0.889287i \(0.651201\pi\)
\(440\) −2.12885 −0.101489
\(441\) −2.13012 −0.101434
\(442\) 6.23737 0.296681
\(443\) 23.9265 1.13678 0.568392 0.822758i \(-0.307566\pi\)
0.568392 + 0.822758i \(0.307566\pi\)
\(444\) 1.57648 0.0748164
\(445\) −5.80766 −0.275310
\(446\) −18.0304 −0.853766
\(447\) −5.07063 −0.239832
\(448\) 2.78886 0.131761
\(449\) 23.2056 1.09514 0.547571 0.836759i \(-0.315553\pi\)
0.547571 + 0.836759i \(0.315553\pi\)
\(450\) 1.68053 0.0792209
\(451\) 5.84325 0.275148
\(452\) −12.8122 −0.602635
\(453\) −0.474651 −0.0223010
\(454\) −19.8771 −0.932876
\(455\) 9.00022 0.421937
\(456\) 1.80813 0.0846735
\(457\) −4.56956 −0.213755 −0.106877 0.994272i \(-0.534085\pi\)
−0.106877 + 0.994272i \(0.534085\pi\)
\(458\) −12.8990 −0.602728
\(459\) −13.4280 −0.626766
\(460\) −2.36930 −0.110469
\(461\) −22.1990 −1.03391 −0.516955 0.856012i \(-0.672935\pi\)
−0.516955 + 0.856012i \(0.672935\pi\)
\(462\) 1.28038 0.0595688
\(463\) −21.1625 −0.983507 −0.491753 0.870735i \(-0.663644\pi\)
−0.491753 + 0.870735i \(0.663644\pi\)
\(464\) −9.50770 −0.441384
\(465\) 9.48621 0.439913
\(466\) −13.4158 −0.621475
\(467\) −1.89152 −0.0875292 −0.0437646 0.999042i \(-0.513935\pi\)
−0.0437646 + 0.999042i \(0.513935\pi\)
\(468\) −3.73066 −0.172450
\(469\) −34.9145 −1.61220
\(470\) −6.06262 −0.279648
\(471\) −3.29081 −0.151633
\(472\) 3.00244 0.138198
\(473\) −1.85916 −0.0854845
\(474\) −2.68611 −0.123377
\(475\) 2.17125 0.0996236
\(476\) −12.7709 −0.585352
\(477\) 0.0565601 0.00258971
\(478\) 4.38008 0.200340
\(479\) −9.85969 −0.450501 −0.225250 0.974301i \(-0.572320\pi\)
−0.225250 + 0.974301i \(0.572320\pi\)
\(480\) 1.21062 0.0552569
\(481\) −4.20250 −0.191617
\(482\) −3.61274 −0.164556
\(483\) 1.42500 0.0648396
\(484\) −10.1927 −0.463303
\(485\) −21.0452 −0.955615
\(486\) 12.2299 0.554761
\(487\) −32.8919 −1.49047 −0.745237 0.666799i \(-0.767664\pi\)
−0.745237 + 0.666799i \(0.767664\pi\)
\(488\) 8.28348 0.374976
\(489\) 10.7806 0.487517
\(490\) −1.84265 −0.0832426
\(491\) −21.7901 −0.983372 −0.491686 0.870773i \(-0.663619\pi\)
−0.491686 + 0.870773i \(0.663619\pi\)
\(492\) −3.32289 −0.149808
\(493\) 43.5382 1.96086
\(494\) −4.82002 −0.216863
\(495\) −5.83076 −0.262073
\(496\) −7.83584 −0.351840
\(497\) −6.27075 −0.281282
\(498\) −3.17534 −0.142291
\(499\) 11.1791 0.500443 0.250222 0.968189i \(-0.419497\pi\)
0.250222 + 0.968189i \(0.419497\pi\)
\(500\) −10.3928 −0.464778
\(501\) −3.84760 −0.171898
\(502\) 7.04420 0.314398
\(503\) −38.2699 −1.70637 −0.853185 0.521609i \(-0.825332\pi\)
−0.853185 + 0.521609i \(0.825332\pi\)
\(504\) 7.63845 0.340244
\(505\) 29.6084 1.31756
\(506\) 0.898516 0.0399439
\(507\) 5.69450 0.252902
\(508\) 10.3367 0.458617
\(509\) 13.0436 0.578148 0.289074 0.957307i \(-0.406653\pi\)
0.289074 + 0.957307i \(0.406653\pi\)
\(510\) −5.54372 −0.245480
\(511\) −18.7052 −0.827469
\(512\) −1.00000 −0.0441942
\(513\) 10.3767 0.458143
\(514\) 3.26883 0.144182
\(515\) −19.6953 −0.867881
\(516\) 1.05725 0.0465430
\(517\) 2.29915 0.101116
\(518\) 8.60452 0.378061
\(519\) −2.86867 −0.125921
\(520\) −3.22721 −0.141522
\(521\) 12.1415 0.531927 0.265963 0.963983i \(-0.414310\pi\)
0.265963 + 0.963983i \(0.414310\pi\)
\(522\) −26.0408 −1.13978
\(523\) −5.14171 −0.224831 −0.112416 0.993661i \(-0.535859\pi\)
−0.112416 + 0.993661i \(0.535859\pi\)
\(524\) −1.00000 −0.0436852
\(525\) −0.874340 −0.0381593
\(526\) −19.8540 −0.865677
\(527\) 35.8823 1.56306
\(528\) −0.459106 −0.0199800
\(529\) 1.00000 0.0434783
\(530\) 0.0489273 0.00212526
\(531\) 8.22343 0.356866
\(532\) 9.86889 0.427871
\(533\) 8.85800 0.383683
\(534\) −1.25248 −0.0541999
\(535\) 37.4778 1.62031
\(536\) 12.5193 0.540751
\(537\) −12.2121 −0.526992
\(538\) −19.6024 −0.845121
\(539\) 0.698795 0.0300992
\(540\) 6.94764 0.298979
\(541\) 1.01304 0.0435539 0.0217769 0.999763i \(-0.493068\pi\)
0.0217769 + 0.999763i \(0.493068\pi\)
\(542\) 3.63275 0.156040
\(543\) 8.31032 0.356630
\(544\) 4.57925 0.196334
\(545\) −8.03157 −0.344035
\(546\) 1.94098 0.0830662
\(547\) −27.2628 −1.16567 −0.582837 0.812589i \(-0.698057\pi\)
−0.582837 + 0.812589i \(0.698057\pi\)
\(548\) −6.03988 −0.258011
\(549\) 22.6878 0.968291
\(550\) −0.551306 −0.0235078
\(551\) −33.6448 −1.43332
\(552\) −0.510961 −0.0217479
\(553\) −14.6610 −0.623448
\(554\) −20.3699 −0.865436
\(555\) 3.73515 0.158548
\(556\) 7.51656 0.318773
\(557\) 3.16273 0.134009 0.0670046 0.997753i \(-0.478656\pi\)
0.0670046 + 0.997753i \(0.478656\pi\)
\(558\) −21.4617 −0.908548
\(559\) −2.81838 −0.119205
\(560\) 6.60763 0.279223
\(561\) 2.10236 0.0887619
\(562\) 0.960400 0.0405120
\(563\) −19.7409 −0.831978 −0.415989 0.909370i \(-0.636565\pi\)
−0.415989 + 0.909370i \(0.636565\pi\)
\(564\) −1.30746 −0.0550539
\(565\) −30.3559 −1.27708
\(566\) 7.94276 0.333859
\(567\) 18.7368 0.786870
\(568\) 2.24850 0.0943451
\(569\) 9.48894 0.397797 0.198898 0.980020i \(-0.436264\pi\)
0.198898 + 0.980020i \(0.436264\pi\)
\(570\) 4.28400 0.179437
\(571\) 45.8540 1.91893 0.959465 0.281826i \(-0.0909402\pi\)
0.959465 + 0.281826i \(0.0909402\pi\)
\(572\) 1.22386 0.0511723
\(573\) −6.15514 −0.257135
\(574\) −18.1366 −0.757005
\(575\) −0.613574 −0.0255878
\(576\) −2.73892 −0.114122
\(577\) 10.6861 0.444870 0.222435 0.974948i \(-0.428599\pi\)
0.222435 + 0.974948i \(0.428599\pi\)
\(578\) −3.96954 −0.165111
\(579\) 0.995705 0.0413801
\(580\) −22.5266 −0.935365
\(581\) −17.3312 −0.719021
\(582\) −4.53860 −0.188131
\(583\) −0.0185548 −0.000768463 0
\(584\) 6.70712 0.277543
\(585\) −8.83906 −0.365450
\(586\) −20.7207 −0.855965
\(587\) −2.26704 −0.0935706 −0.0467853 0.998905i \(-0.514898\pi\)
−0.0467853 + 0.998905i \(0.514898\pi\)
\(588\) −0.397385 −0.0163879
\(589\) −27.7286 −1.14254
\(590\) 7.11367 0.292865
\(591\) 11.0120 0.452972
\(592\) −3.08532 −0.126806
\(593\) −19.8737 −0.816115 −0.408057 0.912956i \(-0.633794\pi\)
−0.408057 + 0.912956i \(0.633794\pi\)
\(594\) −2.63477 −0.108106
\(595\) −30.2580 −1.24046
\(596\) 9.92371 0.406491
\(597\) 4.18460 0.171264
\(598\) 1.36209 0.0557002
\(599\) −30.7323 −1.25569 −0.627843 0.778340i \(-0.716062\pi\)
−0.627843 + 0.778340i \(0.716062\pi\)
\(600\) 0.313512 0.0127991
\(601\) −22.8624 −0.932576 −0.466288 0.884633i \(-0.654409\pi\)
−0.466288 + 0.884633i \(0.654409\pi\)
\(602\) 5.77056 0.235191
\(603\) 34.2893 1.39637
\(604\) 0.928938 0.0377979
\(605\) −24.1495 −0.981816
\(606\) 6.38532 0.259386
\(607\) −24.2688 −0.985042 −0.492521 0.870301i \(-0.663925\pi\)
−0.492521 + 0.870301i \(0.663925\pi\)
\(608\) −3.53869 −0.143513
\(609\) 13.5484 0.549010
\(610\) 19.6260 0.794635
\(611\) 3.48536 0.141003
\(612\) 12.5422 0.506988
\(613\) −27.8346 −1.12423 −0.562115 0.827059i \(-0.690012\pi\)
−0.562115 + 0.827059i \(0.690012\pi\)
\(614\) 6.56579 0.264974
\(615\) −7.87292 −0.317467
\(616\) −2.50583 −0.100963
\(617\) −18.6085 −0.749150 −0.374575 0.927197i \(-0.622211\pi\)
−0.374575 + 0.927197i \(0.622211\pi\)
\(618\) −4.24748 −0.170859
\(619\) −43.8186 −1.76122 −0.880610 0.473842i \(-0.842867\pi\)
−0.880610 + 0.473842i \(0.842867\pi\)
\(620\) −18.5654 −0.745606
\(621\) −2.93236 −0.117672
\(622\) 4.91478 0.197065
\(623\) −6.83609 −0.273882
\(624\) −0.695976 −0.0278614
\(625\) −27.6914 −1.10766
\(626\) −5.15580 −0.206067
\(627\) −1.62463 −0.0648817
\(628\) 6.44044 0.257001
\(629\) 14.1285 0.563339
\(630\) 18.0978 0.721033
\(631\) 36.3020 1.44516 0.722579 0.691288i \(-0.242956\pi\)
0.722579 + 0.691288i \(0.242956\pi\)
\(632\) 5.25698 0.209112
\(633\) −1.95832 −0.0778362
\(634\) 1.06135 0.0421515
\(635\) 24.4907 0.971885
\(636\) 0.0105516 0.000418399 0
\(637\) 1.05933 0.0419722
\(638\) 8.54283 0.338214
\(639\) 6.15847 0.243625
\(640\) −2.36930 −0.0936547
\(641\) 5.87055 0.231873 0.115936 0.993257i \(-0.463013\pi\)
0.115936 + 0.993257i \(0.463013\pi\)
\(642\) 8.08242 0.318988
\(643\) 24.4460 0.964057 0.482028 0.876156i \(-0.339900\pi\)
0.482028 + 0.876156i \(0.339900\pi\)
\(644\) −2.78886 −0.109896
\(645\) 2.50495 0.0986323
\(646\) 16.2045 0.637559
\(647\) −6.93673 −0.272711 −0.136356 0.990660i \(-0.543539\pi\)
−0.136356 + 0.990660i \(0.543539\pi\)
\(648\) −6.71844 −0.263925
\(649\) −2.69774 −0.105895
\(650\) −0.835745 −0.0327806
\(651\) 11.1660 0.437632
\(652\) −21.0988 −0.826291
\(653\) 38.2599 1.49723 0.748613 0.663008i \(-0.230720\pi\)
0.748613 + 0.663008i \(0.230720\pi\)
\(654\) −1.73208 −0.0677298
\(655\) −2.36930 −0.0925761
\(656\) 6.50322 0.253908
\(657\) 18.3703 0.716692
\(658\) −7.13619 −0.278198
\(659\) −35.4568 −1.38120 −0.690599 0.723237i \(-0.742653\pi\)
−0.690599 + 0.723237i \(0.742653\pi\)
\(660\) −1.08776 −0.0423410
\(661\) 33.2645 1.29384 0.646920 0.762558i \(-0.276057\pi\)
0.646920 + 0.762558i \(0.276057\pi\)
\(662\) −15.7680 −0.612842
\(663\) 3.18705 0.123775
\(664\) 6.21446 0.241168
\(665\) 23.3824 0.906729
\(666\) −8.45045 −0.327448
\(667\) 9.50770 0.368140
\(668\) 7.53014 0.291350
\(669\) −9.21285 −0.356189
\(670\) 29.6620 1.14594
\(671\) −7.44284 −0.287328
\(672\) 1.42500 0.0549704
\(673\) −17.5508 −0.676535 −0.338267 0.941050i \(-0.609841\pi\)
−0.338267 + 0.941050i \(0.609841\pi\)
\(674\) −24.4343 −0.941174
\(675\) 1.79922 0.0692520
\(676\) −11.1447 −0.428642
\(677\) 42.2559 1.62403 0.812013 0.583639i \(-0.198372\pi\)
0.812013 + 0.583639i \(0.198372\pi\)
\(678\) −6.54653 −0.251418
\(679\) −24.7720 −0.950661
\(680\) 10.8496 0.416064
\(681\) −10.1564 −0.389194
\(682\) 7.04063 0.269600
\(683\) −21.5436 −0.824344 −0.412172 0.911106i \(-0.635230\pi\)
−0.412172 + 0.911106i \(0.635230\pi\)
\(684\) −9.69218 −0.370590
\(685\) −14.3103 −0.546768
\(686\) 17.3530 0.662542
\(687\) −6.59086 −0.251457
\(688\) −2.06915 −0.0788856
\(689\) −0.0281280 −0.00107159
\(690\) −1.21062 −0.0460874
\(691\) −16.9878 −0.646248 −0.323124 0.946357i \(-0.604733\pi\)
−0.323124 + 0.946357i \(0.604733\pi\)
\(692\) 5.61427 0.213423
\(693\) −6.86327 −0.260714
\(694\) 9.11262 0.345910
\(695\) 17.8090 0.675533
\(696\) −4.85806 −0.184144
\(697\) −29.7799 −1.12799
\(698\) 12.3863 0.468827
\(699\) −6.85494 −0.259278
\(700\) 1.71117 0.0646761
\(701\) 2.96122 0.111844 0.0559218 0.998435i \(-0.482190\pi\)
0.0559218 + 0.998435i \(0.482190\pi\)
\(702\) −3.99415 −0.150750
\(703\) −10.9180 −0.411780
\(704\) 0.898516 0.0338641
\(705\) −3.09776 −0.116668
\(706\) 5.10072 0.191968
\(707\) 34.8515 1.31072
\(708\) 1.53413 0.0576560
\(709\) 0.271298 0.0101888 0.00509440 0.999987i \(-0.498378\pi\)
0.00509440 + 0.999987i \(0.498378\pi\)
\(710\) 5.32737 0.199933
\(711\) 14.3985 0.539984
\(712\) 2.45122 0.0918632
\(713\) 7.83584 0.293455
\(714\) −6.52541 −0.244208
\(715\) 2.89970 0.108443
\(716\) 23.9003 0.893196
\(717\) 2.23805 0.0835815
\(718\) 14.3929 0.537138
\(719\) −27.9379 −1.04191 −0.520953 0.853585i \(-0.674423\pi\)
−0.520953 + 0.853585i \(0.674423\pi\)
\(720\) −6.48932 −0.241843
\(721\) −23.1830 −0.863381
\(722\) 6.47769 0.241074
\(723\) −1.84597 −0.0686524
\(724\) −16.2641 −0.604450
\(725\) −5.83368 −0.216657
\(726\) −5.20805 −0.193289
\(727\) −22.5350 −0.835778 −0.417889 0.908498i \(-0.637230\pi\)
−0.417889 + 0.908498i \(0.637230\pi\)
\(728\) −3.79868 −0.140789
\(729\) −13.9063 −0.515048
\(730\) 15.8912 0.588158
\(731\) 9.47515 0.350451
\(732\) 4.23253 0.156439
\(733\) −48.9736 −1.80888 −0.904440 0.426600i \(-0.859711\pi\)
−0.904440 + 0.426600i \(0.859711\pi\)
\(734\) −4.65866 −0.171954
\(735\) −0.941524 −0.0347286
\(736\) 1.00000 0.0368605
\(737\) −11.2488 −0.414355
\(738\) 17.8118 0.655662
\(739\) −3.91778 −0.144118 −0.0720589 0.997400i \(-0.522957\pi\)
−0.0720589 + 0.997400i \(0.522957\pi\)
\(740\) −7.31005 −0.268723
\(741\) −2.46284 −0.0904748
\(742\) 0.0575914 0.00211425
\(743\) 1.74544 0.0640340 0.0320170 0.999487i \(-0.489807\pi\)
0.0320170 + 0.999487i \(0.489807\pi\)
\(744\) −4.00381 −0.146787
\(745\) 23.5122 0.861421
\(746\) −2.02497 −0.0741395
\(747\) 17.0209 0.622762
\(748\) −4.11453 −0.150442
\(749\) 44.1144 1.61191
\(750\) −5.31029 −0.193904
\(751\) 17.7952 0.649355 0.324677 0.945825i \(-0.394744\pi\)
0.324677 + 0.945825i \(0.394744\pi\)
\(752\) 2.55882 0.0933107
\(753\) 3.59931 0.131166
\(754\) 12.9504 0.471625
\(755\) 2.20093 0.0801001
\(756\) 8.17794 0.297429
\(757\) 42.4155 1.54162 0.770809 0.637067i \(-0.219852\pi\)
0.770809 + 0.637067i \(0.219852\pi\)
\(758\) −13.2463 −0.481128
\(759\) 0.459106 0.0166645
\(760\) −8.38421 −0.304127
\(761\) −8.81019 −0.319369 −0.159685 0.987168i \(-0.551048\pi\)
−0.159685 + 0.987168i \(0.551048\pi\)
\(762\) 5.28165 0.191334
\(763\) −9.45382 −0.342251
\(764\) 12.0462 0.435816
\(765\) 29.7162 1.07439
\(766\) 19.7135 0.712278
\(767\) −4.08960 −0.147667
\(768\) −0.510961 −0.0184377
\(769\) −44.1256 −1.59121 −0.795604 0.605817i \(-0.792846\pi\)
−0.795604 + 0.605817i \(0.792846\pi\)
\(770\) −5.93707 −0.213957
\(771\) 1.67024 0.0601523
\(772\) −1.94869 −0.0701350
\(773\) 13.3700 0.480885 0.240443 0.970663i \(-0.422707\pi\)
0.240443 + 0.970663i \(0.422707\pi\)
\(774\) −5.66723 −0.203704
\(775\) −4.80787 −0.172704
\(776\) 8.88248 0.318862
\(777\) 4.39657 0.157726
\(778\) −22.6822 −0.813195
\(779\) 23.0129 0.824522
\(780\) −1.64898 −0.0590428
\(781\) −2.02032 −0.0722926
\(782\) −4.57925 −0.163754
\(783\) −27.8800 −0.996351
\(784\) 0.777721 0.0277758
\(785\) 15.2593 0.544628
\(786\) −0.510961 −0.0182254
\(787\) −26.7837 −0.954734 −0.477367 0.878704i \(-0.658409\pi\)
−0.477367 + 0.878704i \(0.658409\pi\)
\(788\) −21.5515 −0.767740
\(789\) −10.1446 −0.361159
\(790\) 12.4554 0.443142
\(791\) −35.7314 −1.27046
\(792\) 2.46096 0.0874465
\(793\) −11.2829 −0.400667
\(794\) −11.7673 −0.417606
\(795\) 0.0249999 0.000886655 0
\(796\) −8.18967 −0.290275
\(797\) −23.4686 −0.831299 −0.415650 0.909525i \(-0.636446\pi\)
−0.415650 + 0.909525i \(0.636446\pi\)
\(798\) 5.04262 0.178507
\(799\) −11.7175 −0.414535
\(800\) −0.613574 −0.0216931
\(801\) 6.71368 0.237216
\(802\) 16.1699 0.570977
\(803\) −6.02645 −0.212669
\(804\) 6.39687 0.225600
\(805\) −6.60763 −0.232888
\(806\) 10.6731 0.375946
\(807\) −10.0161 −0.352583
\(808\) −12.4967 −0.439632
\(809\) 30.1944 1.06158 0.530789 0.847504i \(-0.321895\pi\)
0.530789 + 0.847504i \(0.321895\pi\)
\(810\) −15.9180 −0.559301
\(811\) 34.2559 1.20289 0.601443 0.798916i \(-0.294593\pi\)
0.601443 + 0.798916i \(0.294593\pi\)
\(812\) −26.5156 −0.930516
\(813\) 1.85619 0.0650995
\(814\) 2.77221 0.0971660
\(815\) −49.9893 −1.75105
\(816\) 2.33982 0.0819100
\(817\) −7.32207 −0.256167
\(818\) −39.9690 −1.39748
\(819\) −10.4043 −0.363555
\(820\) 15.4081 0.538073
\(821\) −25.4104 −0.886829 −0.443415 0.896317i \(-0.646233\pi\)
−0.443415 + 0.896317i \(0.646233\pi\)
\(822\) −3.08614 −0.107642
\(823\) −18.8329 −0.656474 −0.328237 0.944595i \(-0.606454\pi\)
−0.328237 + 0.944595i \(0.606454\pi\)
\(824\) 8.31273 0.289588
\(825\) −0.281696 −0.00980739
\(826\) 8.37336 0.291347
\(827\) 55.5970 1.93330 0.966649 0.256105i \(-0.0824391\pi\)
0.966649 + 0.256105i \(0.0824391\pi\)
\(828\) 2.73892 0.0951840
\(829\) −26.6216 −0.924607 −0.462304 0.886722i \(-0.652977\pi\)
−0.462304 + 0.886722i \(0.652977\pi\)
\(830\) 14.7239 0.511074
\(831\) −10.4082 −0.361058
\(832\) 1.36209 0.0472221
\(833\) −3.56138 −0.123395
\(834\) 3.84067 0.132991
\(835\) 17.8411 0.617418
\(836\) 3.17957 0.109968
\(837\) −22.9775 −0.794219
\(838\) 30.0864 1.03932
\(839\) −40.8399 −1.40995 −0.704975 0.709232i \(-0.749042\pi\)
−0.704975 + 0.709232i \(0.749042\pi\)
\(840\) 3.37624 0.116491
\(841\) 61.3964 2.11712
\(842\) 31.6647 1.09124
\(843\) 0.490727 0.0169015
\(844\) 3.83262 0.131924
\(845\) −26.4051 −0.908364
\(846\) 7.00841 0.240954
\(847\) −28.4259 −0.976725
\(848\) −0.0206505 −0.000709142 0
\(849\) 4.05844 0.139285
\(850\) 2.80971 0.0963722
\(851\) 3.08532 0.105764
\(852\) 1.14890 0.0393606
\(853\) 35.7169 1.22292 0.611461 0.791275i \(-0.290582\pi\)
0.611461 + 0.791275i \(0.290582\pi\)
\(854\) 23.1014 0.790515
\(855\) −22.9637 −0.785341
\(856\) −15.8181 −0.540651
\(857\) 7.36730 0.251662 0.125831 0.992052i \(-0.459840\pi\)
0.125831 + 0.992052i \(0.459840\pi\)
\(858\) 0.625346 0.0213490
\(859\) −3.24579 −0.110745 −0.0553724 0.998466i \(-0.517635\pi\)
−0.0553724 + 0.998466i \(0.517635\pi\)
\(860\) −4.90243 −0.167172
\(861\) −9.26707 −0.315821
\(862\) 20.4046 0.694982
\(863\) 16.0169 0.545222 0.272611 0.962124i \(-0.412113\pi\)
0.272611 + 0.962124i \(0.412113\pi\)
\(864\) −2.93236 −0.0997610
\(865\) 13.3019 0.452277
\(866\) 8.53681 0.290093
\(867\) −2.02828 −0.0688840
\(868\) −21.8530 −0.741740
\(869\) −4.72348 −0.160233
\(870\) −11.5102 −0.390232
\(871\) −17.0525 −0.577800
\(872\) 3.38985 0.114795
\(873\) 24.3284 0.823391
\(874\) 3.53869 0.119698
\(875\) −28.9839 −0.979834
\(876\) 3.42707 0.115790
\(877\) 47.0961 1.59032 0.795161 0.606399i \(-0.207387\pi\)
0.795161 + 0.606399i \(0.207387\pi\)
\(878\) 19.1651 0.646791
\(879\) −10.5875 −0.357107
\(880\) 2.12885 0.0717636
\(881\) 30.9668 1.04330 0.521649 0.853160i \(-0.325317\pi\)
0.521649 + 0.853160i \(0.325317\pi\)
\(882\) 2.13012 0.0717247
\(883\) 4.05885 0.136591 0.0682955 0.997665i \(-0.478244\pi\)
0.0682955 + 0.997665i \(0.478244\pi\)
\(884\) −6.23737 −0.209785
\(885\) 3.63480 0.122183
\(886\) −23.9265 −0.803827
\(887\) −33.6774 −1.13078 −0.565388 0.824825i \(-0.691273\pi\)
−0.565388 + 0.824825i \(0.691273\pi\)
\(888\) −1.57648 −0.0529032
\(889\) 28.8276 0.966846
\(890\) 5.80766 0.194673
\(891\) 6.03662 0.202234
\(892\) 18.0304 0.603704
\(893\) 9.05488 0.303010
\(894\) 5.07063 0.169587
\(895\) 56.6269 1.89283
\(896\) −2.78886 −0.0931692
\(897\) 0.695976 0.0232380
\(898\) −23.2056 −0.774382
\(899\) 74.5008 2.48474
\(900\) −1.68053 −0.0560176
\(901\) 0.0945640 0.00315038
\(902\) −5.84325 −0.194559
\(903\) 2.94853 0.0981209
\(904\) 12.8122 0.426128
\(905\) −38.5345 −1.28093
\(906\) 0.474651 0.0157692
\(907\) 22.6180 0.751020 0.375510 0.926818i \(-0.377468\pi\)
0.375510 + 0.926818i \(0.377468\pi\)
\(908\) 19.8771 0.659643
\(909\) −34.2274 −1.13525
\(910\) −9.00022 −0.298354
\(911\) −36.0075 −1.19298 −0.596490 0.802620i \(-0.703439\pi\)
−0.596490 + 0.802620i \(0.703439\pi\)
\(912\) −1.80813 −0.0598732
\(913\) −5.58379 −0.184797
\(914\) 4.56956 0.151148
\(915\) 10.0281 0.331520
\(916\) 12.8990 0.426193
\(917\) −2.78886 −0.0920962
\(918\) 13.4280 0.443191
\(919\) −34.7315 −1.14569 −0.572843 0.819665i \(-0.694159\pi\)
−0.572843 + 0.819665i \(0.694159\pi\)
\(920\) 2.36930 0.0781134
\(921\) 3.35486 0.110546
\(922\) 22.1990 0.731085
\(923\) −3.06267 −0.100809
\(924\) −1.28038 −0.0421215
\(925\) −1.89307 −0.0622439
\(926\) 21.1625 0.695444
\(927\) 22.7679 0.747796
\(928\) 9.50770 0.312106
\(929\) 15.8472 0.519930 0.259965 0.965618i \(-0.416289\pi\)
0.259965 + 0.965618i \(0.416289\pi\)
\(930\) −9.48621 −0.311065
\(931\) 2.75211 0.0901969
\(932\) 13.4158 0.439449
\(933\) 2.51126 0.0822149
\(934\) 1.89152 0.0618925
\(935\) −9.74855 −0.318812
\(936\) 3.73066 0.121941
\(937\) −6.50109 −0.212381 −0.106191 0.994346i \(-0.533865\pi\)
−0.106191 + 0.994346i \(0.533865\pi\)
\(938\) 34.9145 1.14000
\(939\) −2.63441 −0.0859707
\(940\) 6.06262 0.197741
\(941\) −30.9520 −1.00901 −0.504503 0.863410i \(-0.668324\pi\)
−0.504503 + 0.863410i \(0.668324\pi\)
\(942\) 3.29081 0.107220
\(943\) −6.50322 −0.211774
\(944\) −3.00244 −0.0977210
\(945\) 19.3760 0.630300
\(946\) 1.85916 0.0604466
\(947\) −3.25183 −0.105670 −0.0528351 0.998603i \(-0.516826\pi\)
−0.0528351 + 0.998603i \(0.516826\pi\)
\(948\) 2.68611 0.0872408
\(949\) −9.13572 −0.296558
\(950\) −2.17125 −0.0704445
\(951\) 0.542307 0.0175855
\(952\) 12.7709 0.413906
\(953\) 36.9112 1.19567 0.597836 0.801618i \(-0.296027\pi\)
0.597836 + 0.801618i \(0.296027\pi\)
\(954\) −0.0565601 −0.00183120
\(955\) 28.5410 0.923567
\(956\) −4.38008 −0.141662
\(957\) 4.36505 0.141102
\(958\) 9.85969 0.318552
\(959\) −16.8444 −0.543933
\(960\) −1.21062 −0.0390725
\(961\) 30.4004 0.980658
\(962\) 4.20250 0.135494
\(963\) −43.3245 −1.39611
\(964\) 3.61274 0.116359
\(965\) −4.61703 −0.148628
\(966\) −1.42500 −0.0458485
\(967\) 41.6289 1.33870 0.669348 0.742949i \(-0.266574\pi\)
0.669348 + 0.742949i \(0.266574\pi\)
\(968\) 10.1927 0.327605
\(969\) 8.27988 0.265988
\(970\) 21.0452 0.675722
\(971\) 42.7414 1.37164 0.685819 0.727773i \(-0.259444\pi\)
0.685819 + 0.727773i \(0.259444\pi\)
\(972\) −12.2299 −0.392276
\(973\) 20.9626 0.672031
\(974\) 32.8919 1.05392
\(975\) −0.427033 −0.0136760
\(976\) −8.28348 −0.265148
\(977\) 21.1898 0.677921 0.338960 0.940801i \(-0.389925\pi\)
0.338960 + 0.940801i \(0.389925\pi\)
\(978\) −10.7806 −0.344727
\(979\) −2.20246 −0.0703908
\(980\) 1.84265 0.0588614
\(981\) 9.28454 0.296432
\(982\) 21.7901 0.695349
\(983\) −3.06058 −0.0976173 −0.0488087 0.998808i \(-0.515542\pi\)
−0.0488087 + 0.998808i \(0.515542\pi\)
\(984\) 3.32289 0.105930
\(985\) −51.0619 −1.62697
\(986\) −43.5382 −1.38654
\(987\) −3.64631 −0.116063
\(988\) 4.82002 0.153345
\(989\) 2.06915 0.0657951
\(990\) 5.83076 0.185314
\(991\) −29.5613 −0.939044 −0.469522 0.882921i \(-0.655574\pi\)
−0.469522 + 0.882921i \(0.655574\pi\)
\(992\) 7.83584 0.248788
\(993\) −8.05685 −0.255676
\(994\) 6.27075 0.198896
\(995\) −19.4038 −0.615141
\(996\) 3.17534 0.100615
\(997\) 35.0113 1.10882 0.554410 0.832244i \(-0.312944\pi\)
0.554410 + 0.832244i \(0.312944\pi\)
\(998\) −11.1791 −0.353867
\(999\) −9.04728 −0.286243
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 \(a_p\))