Properties

Label 8003.2.a.c.1.10
Level 8003
Weight 2
Character 8003.1
Self dual Yes
Analytic conductor 63.904
Analytic rank 0
Dimension 172
CM No

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Newspace parameters

Level: \( N \) = \( 8003 = 53 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(0\)
Dimension: \(172\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.56961 q^{2}\) \(-1.95716 q^{3}\) \(+4.60287 q^{4}\) \(+1.92681 q^{5}\) \(+5.02912 q^{6}\) \(+3.09633 q^{7}\) \(-6.68835 q^{8}\) \(+0.830463 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.56961 q^{2}\) \(-1.95716 q^{3}\) \(+4.60287 q^{4}\) \(+1.92681 q^{5}\) \(+5.02912 q^{6}\) \(+3.09633 q^{7}\) \(-6.68835 q^{8}\) \(+0.830463 q^{9}\) \(-4.95115 q^{10}\) \(+6.15017 q^{11}\) \(-9.00854 q^{12}\) \(+6.36427 q^{13}\) \(-7.95633 q^{14}\) \(-3.77108 q^{15}\) \(+7.98068 q^{16}\) \(-2.90133 q^{17}\) \(-2.13396 q^{18}\) \(-0.236083 q^{19}\) \(+8.86888 q^{20}\) \(-6.05999 q^{21}\) \(-15.8035 q^{22}\) \(+7.62505 q^{23}\) \(+13.0902 q^{24}\) \(-1.28739 q^{25}\) \(-16.3537 q^{26}\) \(+4.24612 q^{27}\) \(+14.2520 q^{28}\) \(-2.66639 q^{29}\) \(+9.69018 q^{30}\) \(+10.1255 q^{31}\) \(-7.13049 q^{32}\) \(-12.0369 q^{33}\) \(+7.45528 q^{34}\) \(+5.96604 q^{35}\) \(+3.82251 q^{36}\) \(-10.8285 q^{37}\) \(+0.606640 q^{38}\) \(-12.4559 q^{39}\) \(-12.8872 q^{40}\) \(-1.58063 q^{41}\) \(+15.5718 q^{42}\) \(+4.88250 q^{43}\) \(+28.3084 q^{44}\) \(+1.60015 q^{45}\) \(-19.5934 q^{46}\) \(-8.88615 q^{47}\) \(-15.6194 q^{48}\) \(+2.58723 q^{49}\) \(+3.30808 q^{50}\) \(+5.67836 q^{51}\) \(+29.2939 q^{52}\) \(-1.00000 q^{53}\) \(-10.9109 q^{54}\) \(+11.8502 q^{55}\) \(-20.7093 q^{56}\) \(+0.462051 q^{57}\) \(+6.85158 q^{58}\) \(+5.79894 q^{59}\) \(-17.3578 q^{60}\) \(-9.67044 q^{61}\) \(-26.0186 q^{62}\) \(+2.57138 q^{63}\) \(+2.36119 q^{64}\) \(+12.2628 q^{65}\) \(+30.9300 q^{66}\) \(+10.5985 q^{67}\) \(-13.3545 q^{68}\) \(-14.9234 q^{69}\) \(-15.3304 q^{70}\) \(-2.11613 q^{71}\) \(-5.55443 q^{72}\) \(+5.85458 q^{73}\) \(+27.8251 q^{74}\) \(+2.51962 q^{75}\) \(-1.08666 q^{76}\) \(+19.0429 q^{77}\) \(+32.0067 q^{78}\) \(-4.48344 q^{79}\) \(+15.3773 q^{80}\) \(-10.8017 q^{81}\) \(+4.06159 q^{82}\) \(+10.5266 q^{83}\) \(-27.8934 q^{84}\) \(-5.59033 q^{85}\) \(-12.5461 q^{86}\) \(+5.21855 q^{87}\) \(-41.1345 q^{88}\) \(+0.534793 q^{89}\) \(-4.11175 q^{90}\) \(+19.7059 q^{91}\) \(+35.0971 q^{92}\) \(-19.8173 q^{93}\) \(+22.8339 q^{94}\) \(-0.454888 q^{95}\) \(+13.9555 q^{96}\) \(-8.93829 q^{97}\) \(-6.64816 q^{98}\) \(+5.10749 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56961 −1.81699 −0.908493 0.417901i \(-0.862766\pi\)
−0.908493 + 0.417901i \(0.862766\pi\)
\(3\) −1.95716 −1.12997 −0.564983 0.825103i \(-0.691117\pi\)
−0.564983 + 0.825103i \(0.691117\pi\)
\(4\) 4.60287 2.30144
\(5\) 1.92681 0.861697 0.430849 0.902424i \(-0.358214\pi\)
0.430849 + 0.902424i \(0.358214\pi\)
\(6\) 5.02912 2.05313
\(7\) 3.09633 1.17030 0.585150 0.810925i \(-0.301035\pi\)
0.585150 + 0.810925i \(0.301035\pi\)
\(8\) −6.68835 −2.36469
\(9\) 0.830463 0.276821
\(10\) −4.95115 −1.56569
\(11\) 6.15017 1.85435 0.927173 0.374633i \(-0.122231\pi\)
0.927173 + 0.374633i \(0.122231\pi\)
\(12\) −9.00854 −2.60054
\(13\) 6.36427 1.76513 0.882566 0.470189i \(-0.155814\pi\)
0.882566 + 0.470189i \(0.155814\pi\)
\(14\) −7.95633 −2.12642
\(15\) −3.77108 −0.973688
\(16\) 7.98068 1.99517
\(17\) −2.90133 −0.703677 −0.351838 0.936061i \(-0.614443\pi\)
−0.351838 + 0.936061i \(0.614443\pi\)
\(18\) −2.13396 −0.502980
\(19\) −0.236083 −0.0541611 −0.0270806 0.999633i \(-0.508621\pi\)
−0.0270806 + 0.999633i \(0.508621\pi\)
\(20\) 8.86888 1.98314
\(21\) −6.05999 −1.32240
\(22\) −15.8035 −3.36932
\(23\) 7.62505 1.58993 0.794967 0.606653i \(-0.207488\pi\)
0.794967 + 0.606653i \(0.207488\pi\)
\(24\) 13.0902 2.67202
\(25\) −1.28739 −0.257478
\(26\) −16.3537 −3.20722
\(27\) 4.24612 0.817167
\(28\) 14.2520 2.69337
\(29\) −2.66639 −0.495137 −0.247568 0.968870i \(-0.579631\pi\)
−0.247568 + 0.968870i \(0.579631\pi\)
\(30\) 9.69018 1.76918
\(31\) 10.1255 1.81860 0.909300 0.416142i \(-0.136618\pi\)
0.909300 + 0.416142i \(0.136618\pi\)
\(32\) −7.13049 −1.26050
\(33\) −12.0369 −2.09535
\(34\) 7.45528 1.27857
\(35\) 5.96604 1.00845
\(36\) 3.82251 0.637086
\(37\) −10.8285 −1.78020 −0.890101 0.455764i \(-0.849366\pi\)
−0.890101 + 0.455764i \(0.849366\pi\)
\(38\) 0.606640 0.0984100
\(39\) −12.4559 −1.99454
\(40\) −12.8872 −2.03765
\(41\) −1.58063 −0.246852 −0.123426 0.992354i \(-0.539388\pi\)
−0.123426 + 0.992354i \(0.539388\pi\)
\(42\) 15.5718 2.40278
\(43\) 4.88250 0.744574 0.372287 0.928118i \(-0.378574\pi\)
0.372287 + 0.928118i \(0.378574\pi\)
\(44\) 28.3084 4.26766
\(45\) 1.60015 0.238536
\(46\) −19.5934 −2.88889
\(47\) −8.88615 −1.29618 −0.648089 0.761565i \(-0.724431\pi\)
−0.648089 + 0.761565i \(0.724431\pi\)
\(48\) −15.6194 −2.25447
\(49\) 2.58723 0.369604
\(50\) 3.30808 0.467833
\(51\) 5.67836 0.795130
\(52\) 29.2939 4.06234
\(53\) −1.00000 −0.137361
\(54\) −10.9109 −1.48478
\(55\) 11.8502 1.59789
\(56\) −20.7093 −2.76740
\(57\) 0.462051 0.0612002
\(58\) 6.85158 0.899656
\(59\) 5.79894 0.754958 0.377479 0.926018i \(-0.376791\pi\)
0.377479 + 0.926018i \(0.376791\pi\)
\(60\) −17.3578 −2.24088
\(61\) −9.67044 −1.23817 −0.619086 0.785323i \(-0.712497\pi\)
−0.619086 + 0.785323i \(0.712497\pi\)
\(62\) −26.0186 −3.30437
\(63\) 2.57138 0.323964
\(64\) 2.36119 0.295149
\(65\) 12.2628 1.52101
\(66\) 30.9300 3.80721
\(67\) 10.5985 1.29481 0.647406 0.762146i \(-0.275854\pi\)
0.647406 + 0.762146i \(0.275854\pi\)
\(68\) −13.3545 −1.61947
\(69\) −14.9234 −1.79657
\(70\) −15.3304 −1.83233
\(71\) −2.11613 −0.251138 −0.125569 0.992085i \(-0.540076\pi\)
−0.125569 + 0.992085i \(0.540076\pi\)
\(72\) −5.55443 −0.654596
\(73\) 5.85458 0.685227 0.342614 0.939476i \(-0.388688\pi\)
0.342614 + 0.939476i \(0.388688\pi\)
\(74\) 27.8251 3.23460
\(75\) 2.51962 0.290941
\(76\) −1.08666 −0.124648
\(77\) 19.0429 2.17014
\(78\) 32.0067 3.62404
\(79\) −4.48344 −0.504426 −0.252213 0.967672i \(-0.581158\pi\)
−0.252213 + 0.967672i \(0.581158\pi\)
\(80\) 15.3773 1.71923
\(81\) −10.8017 −1.20019
\(82\) 4.06159 0.448527
\(83\) 10.5266 1.15544 0.577722 0.816233i \(-0.303942\pi\)
0.577722 + 0.816233i \(0.303942\pi\)
\(84\) −27.8934 −3.04342
\(85\) −5.59033 −0.606356
\(86\) −12.5461 −1.35288
\(87\) 5.21855 0.559487
\(88\) −41.1345 −4.38495
\(89\) 0.534793 0.0566879 0.0283440 0.999598i \(-0.490977\pi\)
0.0283440 + 0.999598i \(0.490977\pi\)
\(90\) −4.11175 −0.433416
\(91\) 19.7059 2.06574
\(92\) 35.0971 3.65913
\(93\) −19.8173 −2.05495
\(94\) 22.8339 2.35514
\(95\) −0.454888 −0.0466705
\(96\) 13.9555 1.42433
\(97\) −8.93829 −0.907546 −0.453773 0.891117i \(-0.649922\pi\)
−0.453773 + 0.891117i \(0.649922\pi\)
\(98\) −6.64816 −0.671565
\(99\) 5.10749 0.513322
\(100\) −5.92568 −0.592568
\(101\) −7.12335 −0.708799 −0.354400 0.935094i \(-0.615315\pi\)
−0.354400 + 0.935094i \(0.615315\pi\)
\(102\) −14.5912 −1.44474
\(103\) 6.75786 0.665871 0.332936 0.942950i \(-0.391961\pi\)
0.332936 + 0.942950i \(0.391961\pi\)
\(104\) −42.5665 −4.17399
\(105\) −11.6765 −1.13951
\(106\) 2.56961 0.249582
\(107\) −7.60615 −0.735315 −0.367657 0.929961i \(-0.619840\pi\)
−0.367657 + 0.929961i \(0.619840\pi\)
\(108\) 19.5444 1.88066
\(109\) 17.6098 1.68671 0.843357 0.537354i \(-0.180576\pi\)
0.843357 + 0.537354i \(0.180576\pi\)
\(110\) −30.4504 −2.90333
\(111\) 21.1932 2.01157
\(112\) 24.7108 2.33495
\(113\) 12.0941 1.13772 0.568858 0.822435i \(-0.307385\pi\)
0.568858 + 0.822435i \(0.307385\pi\)
\(114\) −1.18729 −0.111200
\(115\) 14.6921 1.37004
\(116\) −12.2731 −1.13953
\(117\) 5.28529 0.488626
\(118\) −14.9010 −1.37175
\(119\) −8.98347 −0.823513
\(120\) 25.2223 2.30247
\(121\) 26.8246 2.43860
\(122\) 24.8492 2.24974
\(123\) 3.09354 0.278935
\(124\) 46.6065 4.18539
\(125\) −12.1146 −1.08357
\(126\) −6.60744 −0.588638
\(127\) 14.0469 1.24646 0.623229 0.782040i \(-0.285821\pi\)
0.623229 + 0.782040i \(0.285821\pi\)
\(128\) 8.19365 0.724223
\(129\) −9.55582 −0.841343
\(130\) −31.5105 −2.76365
\(131\) −15.3049 −1.33719 −0.668597 0.743625i \(-0.733105\pi\)
−0.668597 + 0.743625i \(0.733105\pi\)
\(132\) −55.4041 −4.82231
\(133\) −0.730989 −0.0633848
\(134\) −27.2339 −2.35265
\(135\) 8.18149 0.704151
\(136\) 19.4051 1.66398
\(137\) 3.90928 0.333992 0.166996 0.985958i \(-0.446593\pi\)
0.166996 + 0.985958i \(0.446593\pi\)
\(138\) 38.3473 3.26434
\(139\) 17.3281 1.46975 0.734873 0.678205i \(-0.237242\pi\)
0.734873 + 0.678205i \(0.237242\pi\)
\(140\) 27.4609 2.32087
\(141\) 17.3916 1.46464
\(142\) 5.43761 0.456314
\(143\) 39.1414 3.27317
\(144\) 6.62766 0.552305
\(145\) −5.13764 −0.426658
\(146\) −15.0440 −1.24505
\(147\) −5.06361 −0.417640
\(148\) −49.8424 −4.09702
\(149\) −17.1782 −1.40729 −0.703646 0.710550i \(-0.748446\pi\)
−0.703646 + 0.710550i \(0.748446\pi\)
\(150\) −6.47443 −0.528635
\(151\) 1.00000 0.0813788
\(152\) 1.57901 0.128074
\(153\) −2.40945 −0.194793
\(154\) −48.9328 −3.94312
\(155\) 19.5100 1.56708
\(156\) −57.3328 −4.59030
\(157\) −9.59457 −0.765730 −0.382865 0.923804i \(-0.625063\pi\)
−0.382865 + 0.923804i \(0.625063\pi\)
\(158\) 11.5207 0.916535
\(159\) 1.95716 0.155213
\(160\) −13.7391 −1.08617
\(161\) 23.6096 1.86070
\(162\) 27.7562 2.18073
\(163\) 13.3034 1.04200 0.521002 0.853556i \(-0.325559\pi\)
0.521002 + 0.853556i \(0.325559\pi\)
\(164\) −7.27542 −0.568115
\(165\) −23.1928 −1.80555
\(166\) −27.0492 −2.09943
\(167\) 10.6748 0.826041 0.413021 0.910722i \(-0.364474\pi\)
0.413021 + 0.910722i \(0.364474\pi\)
\(168\) 40.5314 3.12706
\(169\) 27.5040 2.11569
\(170\) 14.3649 1.10174
\(171\) −0.196058 −0.0149929
\(172\) 22.4735 1.71359
\(173\) 1.63788 0.124526 0.0622628 0.998060i \(-0.480168\pi\)
0.0622628 + 0.998060i \(0.480168\pi\)
\(174\) −13.4096 −1.01658
\(175\) −3.98617 −0.301326
\(176\) 49.0825 3.69974
\(177\) −11.3494 −0.853076
\(178\) −1.37421 −0.103001
\(179\) −5.15232 −0.385102 −0.192551 0.981287i \(-0.561676\pi\)
−0.192551 + 0.981287i \(0.561676\pi\)
\(180\) 7.36527 0.548975
\(181\) 19.3628 1.43923 0.719614 0.694374i \(-0.244319\pi\)
0.719614 + 0.694374i \(0.244319\pi\)
\(182\) −50.6363 −3.75341
\(183\) 18.9266 1.39909
\(184\) −50.9990 −3.75970
\(185\) −20.8646 −1.53399
\(186\) 50.9225 3.73382
\(187\) −17.8437 −1.30486
\(188\) −40.9018 −2.98307
\(189\) 13.1474 0.956331
\(190\) 1.16888 0.0847996
\(191\) −5.56546 −0.402702 −0.201351 0.979519i \(-0.564533\pi\)
−0.201351 + 0.979519i \(0.564533\pi\)
\(192\) −4.62122 −0.333508
\(193\) −2.83189 −0.203844 −0.101922 0.994792i \(-0.532499\pi\)
−0.101922 + 0.994792i \(0.532499\pi\)
\(194\) 22.9679 1.64900
\(195\) −24.0002 −1.71869
\(196\) 11.9087 0.850620
\(197\) 17.9925 1.28191 0.640957 0.767576i \(-0.278538\pi\)
0.640957 + 0.767576i \(0.278538\pi\)
\(198\) −13.1242 −0.932699
\(199\) −2.94895 −0.209045 −0.104523 0.994523i \(-0.533331\pi\)
−0.104523 + 0.994523i \(0.533331\pi\)
\(200\) 8.61050 0.608855
\(201\) −20.7429 −1.46309
\(202\) 18.3042 1.28788
\(203\) −8.25602 −0.579459
\(204\) 26.1368 1.82994
\(205\) −3.04557 −0.212712
\(206\) −17.3650 −1.20988
\(207\) 6.33232 0.440127
\(208\) 50.7912 3.52174
\(209\) −1.45195 −0.100434
\(210\) 30.0039 2.07047
\(211\) 25.0992 1.72790 0.863949 0.503580i \(-0.167984\pi\)
0.863949 + 0.503580i \(0.167984\pi\)
\(212\) −4.60287 −0.316126
\(213\) 4.14159 0.283777
\(214\) 19.5448 1.33606
\(215\) 9.40767 0.641598
\(216\) −28.3996 −1.93235
\(217\) 31.3519 2.12831
\(218\) −45.2502 −3.06473
\(219\) −11.4583 −0.774283
\(220\) 54.5451 3.67743
\(221\) −18.4649 −1.24208
\(222\) −54.4580 −3.65498
\(223\) 16.0509 1.07485 0.537425 0.843312i \(-0.319397\pi\)
0.537425 + 0.843312i \(0.319397\pi\)
\(224\) −22.0783 −1.47517
\(225\) −1.06913 −0.0712752
\(226\) −31.0771 −2.06721
\(227\) 1.84432 0.122412 0.0612059 0.998125i \(-0.480505\pi\)
0.0612059 + 0.998125i \(0.480505\pi\)
\(228\) 2.12676 0.140848
\(229\) −3.96237 −0.261841 −0.130920 0.991393i \(-0.541793\pi\)
−0.130920 + 0.991393i \(0.541793\pi\)
\(230\) −37.7528 −2.48934
\(231\) −37.2700 −2.45219
\(232\) 17.8338 1.17084
\(233\) −18.6650 −1.22278 −0.611392 0.791328i \(-0.709390\pi\)
−0.611392 + 0.791328i \(0.709390\pi\)
\(234\) −13.5811 −0.887825
\(235\) −17.1220 −1.11691
\(236\) 26.6918 1.73749
\(237\) 8.77479 0.569984
\(238\) 23.0840 1.49631
\(239\) −29.0092 −1.87645 −0.938225 0.346025i \(-0.887531\pi\)
−0.938225 + 0.346025i \(0.887531\pi\)
\(240\) −30.0958 −1.94267
\(241\) 1.00207 0.0645493 0.0322746 0.999479i \(-0.489725\pi\)
0.0322746 + 0.999479i \(0.489725\pi\)
\(242\) −68.9287 −4.43090
\(243\) 8.40229 0.539007
\(244\) −44.5118 −2.84957
\(245\) 4.98511 0.318487
\(246\) −7.94916 −0.506820
\(247\) −1.50250 −0.0956015
\(248\) −67.7231 −4.30042
\(249\) −20.6022 −1.30561
\(250\) 31.1298 1.96882
\(251\) −21.1688 −1.33616 −0.668081 0.744089i \(-0.732884\pi\)
−0.668081 + 0.744089i \(0.732884\pi\)
\(252\) 11.8357 0.745582
\(253\) 46.8954 2.94829
\(254\) −36.0949 −2.26479
\(255\) 10.9412 0.685161
\(256\) −25.7768 −1.61105
\(257\) 1.63829 0.102194 0.0510969 0.998694i \(-0.483728\pi\)
0.0510969 + 0.998694i \(0.483728\pi\)
\(258\) 24.5547 1.52871
\(259\) −33.5287 −2.08337
\(260\) 56.4439 3.50050
\(261\) −2.21434 −0.137064
\(262\) 39.3275 2.42966
\(263\) −14.6672 −0.904421 −0.452210 0.891911i \(-0.649364\pi\)
−0.452210 + 0.891911i \(0.649364\pi\)
\(264\) 80.5067 4.95484
\(265\) −1.92681 −0.118363
\(266\) 1.87835 0.115169
\(267\) −1.04667 −0.0640554
\(268\) 48.7835 2.97992
\(269\) 11.1480 0.679707 0.339853 0.940478i \(-0.389623\pi\)
0.339853 + 0.940478i \(0.389623\pi\)
\(270\) −21.0232 −1.27943
\(271\) −6.90273 −0.419311 −0.209655 0.977775i \(-0.567234\pi\)
−0.209655 + 0.977775i \(0.567234\pi\)
\(272\) −23.1546 −1.40395
\(273\) −38.5675 −2.33421
\(274\) −10.0453 −0.606859
\(275\) −7.91766 −0.477453
\(276\) −68.6906 −4.13469
\(277\) 10.1010 0.606909 0.303454 0.952846i \(-0.401860\pi\)
0.303454 + 0.952846i \(0.401860\pi\)
\(278\) −44.5263 −2.67051
\(279\) 8.40888 0.503427
\(280\) −39.9030 −2.38466
\(281\) 14.5577 0.868438 0.434219 0.900807i \(-0.357024\pi\)
0.434219 + 0.900807i \(0.357024\pi\)
\(282\) −44.6895 −2.66122
\(283\) −11.3298 −0.673489 −0.336744 0.941596i \(-0.609326\pi\)
−0.336744 + 0.941596i \(0.609326\pi\)
\(284\) −9.74026 −0.577978
\(285\) 0.890287 0.0527360
\(286\) −100.578 −5.94729
\(287\) −4.89414 −0.288892
\(288\) −5.92161 −0.348934
\(289\) −8.58227 −0.504839
\(290\) 13.2017 0.775231
\(291\) 17.4936 1.02550
\(292\) 26.9479 1.57701
\(293\) 26.6184 1.55506 0.777532 0.628844i \(-0.216472\pi\)
0.777532 + 0.628844i \(0.216472\pi\)
\(294\) 13.0115 0.758845
\(295\) 11.1735 0.650546
\(296\) 72.4251 4.20962
\(297\) 26.1144 1.51531
\(298\) 44.1412 2.55703
\(299\) 48.5279 2.80644
\(300\) 11.5975 0.669581
\(301\) 15.1178 0.871376
\(302\) −2.56961 −0.147864
\(303\) 13.9415 0.800919
\(304\) −1.88410 −0.108061
\(305\) −18.6331 −1.06693
\(306\) 6.19134 0.353935
\(307\) −28.8719 −1.64781 −0.823903 0.566731i \(-0.808208\pi\)
−0.823903 + 0.566731i \(0.808208\pi\)
\(308\) 87.6522 4.99444
\(309\) −13.2262 −0.752411
\(310\) −50.1330 −2.84737
\(311\) 14.4098 0.817106 0.408553 0.912735i \(-0.366034\pi\)
0.408553 + 0.912735i \(0.366034\pi\)
\(312\) 83.3093 4.71646
\(313\) 0.0941437 0.00532132 0.00266066 0.999996i \(-0.499153\pi\)
0.00266066 + 0.999996i \(0.499153\pi\)
\(314\) 24.6543 1.39132
\(315\) 4.95458 0.279159
\(316\) −20.6367 −1.16090
\(317\) 7.16773 0.402580 0.201290 0.979532i \(-0.435487\pi\)
0.201290 + 0.979532i \(0.435487\pi\)
\(318\) −5.02912 −0.282019
\(319\) −16.3988 −0.918155
\(320\) 4.54958 0.254329
\(321\) 14.8864 0.830880
\(322\) −60.6675 −3.38086
\(323\) 0.684955 0.0381119
\(324\) −49.7189 −2.76216
\(325\) −8.19329 −0.454482
\(326\) −34.1845 −1.89330
\(327\) −34.4652 −1.90593
\(328\) 10.5718 0.583729
\(329\) −27.5144 −1.51692
\(330\) 59.5963 3.28067
\(331\) −21.3369 −1.17278 −0.586390 0.810029i \(-0.699451\pi\)
−0.586390 + 0.810029i \(0.699451\pi\)
\(332\) 48.4526 2.65918
\(333\) −8.99270 −0.492797
\(334\) −27.4300 −1.50090
\(335\) 20.4213 1.11574
\(336\) −48.3629 −2.63841
\(337\) −20.7162 −1.12848 −0.564240 0.825611i \(-0.690831\pi\)
−0.564240 + 0.825611i \(0.690831\pi\)
\(338\) −70.6743 −3.84418
\(339\) −23.6700 −1.28558
\(340\) −25.7316 −1.39549
\(341\) 62.2738 3.37231
\(342\) 0.503792 0.0272420
\(343\) −13.6634 −0.737753
\(344\) −32.6559 −1.76069
\(345\) −28.7547 −1.54810
\(346\) −4.20870 −0.226261
\(347\) −26.0475 −1.39830 −0.699152 0.714973i \(-0.746439\pi\)
−0.699152 + 0.714973i \(0.746439\pi\)
\(348\) 24.0203 1.28762
\(349\) 16.9724 0.908514 0.454257 0.890871i \(-0.349905\pi\)
0.454257 + 0.890871i \(0.349905\pi\)
\(350\) 10.2429 0.547505
\(351\) 27.0235 1.44241
\(352\) −43.8537 −2.33741
\(353\) −10.7292 −0.571057 −0.285528 0.958370i \(-0.592169\pi\)
−0.285528 + 0.958370i \(0.592169\pi\)
\(354\) 29.1636 1.55003
\(355\) −4.07738 −0.216405
\(356\) 2.46158 0.130464
\(357\) 17.5821 0.930541
\(358\) 13.2394 0.699725
\(359\) −6.92824 −0.365659 −0.182829 0.983145i \(-0.558526\pi\)
−0.182829 + 0.983145i \(0.558526\pi\)
\(360\) −10.7024 −0.564063
\(361\) −18.9443 −0.997067
\(362\) −49.7548 −2.61506
\(363\) −52.5000 −2.75553
\(364\) 90.7035 4.75416
\(365\) 11.2807 0.590459
\(366\) −48.6338 −2.54213
\(367\) 7.39768 0.386156 0.193078 0.981183i \(-0.438153\pi\)
0.193078 + 0.981183i \(0.438153\pi\)
\(368\) 60.8531 3.17219
\(369\) −1.31265 −0.0683340
\(370\) 53.6137 2.78725
\(371\) −3.09633 −0.160753
\(372\) −91.2163 −4.72934
\(373\) 13.1800 0.682437 0.341218 0.939984i \(-0.389160\pi\)
0.341218 + 0.939984i \(0.389160\pi\)
\(374\) 45.8513 2.37091
\(375\) 23.7102 1.22439
\(376\) 59.4337 3.06506
\(377\) −16.9697 −0.873981
\(378\) −33.7836 −1.73764
\(379\) −14.0861 −0.723552 −0.361776 0.932265i \(-0.617829\pi\)
−0.361776 + 0.932265i \(0.617829\pi\)
\(380\) −2.09379 −0.107409
\(381\) −27.4919 −1.40845
\(382\) 14.3010 0.731704
\(383\) 28.1796 1.43991 0.719955 0.694021i \(-0.244162\pi\)
0.719955 + 0.694021i \(0.244162\pi\)
\(384\) −16.0363 −0.818347
\(385\) 36.6922 1.87001
\(386\) 7.27684 0.370381
\(387\) 4.05474 0.206114
\(388\) −41.1418 −2.08866
\(389\) −21.4230 −1.08619 −0.543095 0.839671i \(-0.682748\pi\)
−0.543095 + 0.839671i \(0.682748\pi\)
\(390\) 61.6709 3.12283
\(391\) −22.1228 −1.11880
\(392\) −17.3043 −0.873999
\(393\) 29.9541 1.51098
\(394\) −46.2337 −2.32922
\(395\) −8.63875 −0.434663
\(396\) 23.5091 1.18138
\(397\) −5.93437 −0.297838 −0.148919 0.988849i \(-0.547579\pi\)
−0.148919 + 0.988849i \(0.547579\pi\)
\(398\) 7.57763 0.379832
\(399\) 1.43066 0.0716226
\(400\) −10.2742 −0.513712
\(401\) −1.51787 −0.0757988 −0.0378994 0.999282i \(-0.512067\pi\)
−0.0378994 + 0.999282i \(0.512067\pi\)
\(402\) 53.3011 2.65842
\(403\) 64.4416 3.21007
\(404\) −32.7878 −1.63126
\(405\) −20.8129 −1.03420
\(406\) 21.2147 1.05287
\(407\) −66.5974 −3.30111
\(408\) −37.9789 −1.88024
\(409\) −4.02674 −0.199109 −0.0995547 0.995032i \(-0.531742\pi\)
−0.0995547 + 0.995032i \(0.531742\pi\)
\(410\) 7.82592 0.386495
\(411\) −7.65107 −0.377400
\(412\) 31.1055 1.53246
\(413\) 17.9554 0.883528
\(414\) −16.2716 −0.799704
\(415\) 20.2828 0.995643
\(416\) −45.3804 −2.22496
\(417\) −33.9137 −1.66076
\(418\) 3.73094 0.182486
\(419\) −15.3243 −0.748641 −0.374320 0.927299i \(-0.622124\pi\)
−0.374320 + 0.927299i \(0.622124\pi\)
\(420\) −53.7453 −2.62250
\(421\) −16.1333 −0.786290 −0.393145 0.919477i \(-0.628613\pi\)
−0.393145 + 0.919477i \(0.628613\pi\)
\(422\) −64.4949 −3.13956
\(423\) −7.37962 −0.358809
\(424\) 6.68835 0.324815
\(425\) 3.73514 0.181181
\(426\) −10.6423 −0.515619
\(427\) −29.9428 −1.44903
\(428\) −35.0101 −1.69228
\(429\) −76.6058 −3.69856
\(430\) −24.1740 −1.16577
\(431\) −28.7911 −1.38682 −0.693410 0.720543i \(-0.743893\pi\)
−0.693410 + 0.720543i \(0.743893\pi\)
\(432\) 33.8869 1.63039
\(433\) −23.7864 −1.14310 −0.571552 0.820566i \(-0.693658\pi\)
−0.571552 + 0.820566i \(0.693658\pi\)
\(434\) −80.5621 −3.86710
\(435\) 10.0552 0.482109
\(436\) 81.0557 3.88186
\(437\) −1.80014 −0.0861126
\(438\) 29.4434 1.40686
\(439\) 1.00425 0.0479301 0.0239650 0.999713i \(-0.492371\pi\)
0.0239650 + 0.999713i \(0.492371\pi\)
\(440\) −79.2585 −3.77850
\(441\) 2.14860 0.102314
\(442\) 47.4474 2.25684
\(443\) 27.3989 1.30176 0.650881 0.759180i \(-0.274400\pi\)
0.650881 + 0.759180i \(0.274400\pi\)
\(444\) 97.5493 4.62949
\(445\) 1.03045 0.0488478
\(446\) −41.2446 −1.95299
\(447\) 33.6204 1.59019
\(448\) 7.31102 0.345413
\(449\) −33.3591 −1.57431 −0.787156 0.616754i \(-0.788447\pi\)
−0.787156 + 0.616754i \(0.788447\pi\)
\(450\) 2.74724 0.129506
\(451\) −9.72113 −0.457750
\(452\) 55.6676 2.61838
\(453\) −1.95716 −0.0919553
\(454\) −4.73917 −0.222420
\(455\) 37.9695 1.78004
\(456\) −3.09036 −0.144719
\(457\) −1.82851 −0.0855339 −0.0427669 0.999085i \(-0.513617\pi\)
−0.0427669 + 0.999085i \(0.513617\pi\)
\(458\) 10.1817 0.475761
\(459\) −12.3194 −0.575021
\(460\) 67.6256 3.15306
\(461\) −20.1952 −0.940584 −0.470292 0.882511i \(-0.655851\pi\)
−0.470292 + 0.882511i \(0.655851\pi\)
\(462\) 95.7692 4.45559
\(463\) 39.4200 1.83200 0.916002 0.401174i \(-0.131398\pi\)
0.916002 + 0.401174i \(0.131398\pi\)
\(464\) −21.2796 −0.987882
\(465\) −38.1842 −1.77075
\(466\) 47.9617 2.22178
\(467\) 0.938522 0.0434296 0.0217148 0.999764i \(-0.493087\pi\)
0.0217148 + 0.999764i \(0.493087\pi\)
\(468\) 24.3275 1.12454
\(469\) 32.8164 1.51532
\(470\) 43.9967 2.02941
\(471\) 18.7781 0.865248
\(472\) −38.7854 −1.78524
\(473\) 30.0282 1.38070
\(474\) −22.5478 −1.03565
\(475\) 0.303930 0.0139453
\(476\) −41.3498 −1.89526
\(477\) −0.830463 −0.0380243
\(478\) 74.5422 3.40948
\(479\) 35.8664 1.63878 0.819390 0.573237i \(-0.194313\pi\)
0.819390 + 0.573237i \(0.194313\pi\)
\(480\) 26.8896 1.22734
\(481\) −68.9158 −3.14229
\(482\) −2.57494 −0.117285
\(483\) −46.2078 −2.10253
\(484\) 123.470 5.61228
\(485\) −17.2224 −0.782030
\(486\) −21.5906 −0.979368
\(487\) 34.2292 1.55107 0.775537 0.631302i \(-0.217479\pi\)
0.775537 + 0.631302i \(0.217479\pi\)
\(488\) 64.6793 2.92789
\(489\) −26.0369 −1.17743
\(490\) −12.8098 −0.578686
\(491\) 5.62962 0.254061 0.127031 0.991899i \(-0.459455\pi\)
0.127031 + 0.991899i \(0.459455\pi\)
\(492\) 14.2391 0.641950
\(493\) 7.73609 0.348416
\(494\) 3.86082 0.173707
\(495\) 9.84118 0.442328
\(496\) 80.8086 3.62841
\(497\) −6.55222 −0.293907
\(498\) 52.9395 2.37228
\(499\) −17.9921 −0.805436 −0.402718 0.915324i \(-0.631935\pi\)
−0.402718 + 0.915324i \(0.631935\pi\)
\(500\) −55.7621 −2.49376
\(501\) −20.8923 −0.933397
\(502\) 54.3954 2.42779
\(503\) −21.8662 −0.974965 −0.487483 0.873133i \(-0.662085\pi\)
−0.487483 + 0.873133i \(0.662085\pi\)
\(504\) −17.1983 −0.766074
\(505\) −13.7254 −0.610771
\(506\) −120.503 −5.35699
\(507\) −53.8296 −2.39066
\(508\) 64.6559 2.86864
\(509\) 7.98458 0.353910 0.176955 0.984219i \(-0.443375\pi\)
0.176955 + 0.984219i \(0.443375\pi\)
\(510\) −28.1144 −1.24493
\(511\) 18.1277 0.801922
\(512\) 49.8490 2.20303
\(513\) −1.00244 −0.0442587
\(514\) −4.20976 −0.185685
\(515\) 13.0211 0.573780
\(516\) −43.9842 −1.93630
\(517\) −54.6513 −2.40356
\(518\) 86.1555 3.78545
\(519\) −3.20559 −0.140710
\(520\) −82.0177 −3.59671
\(521\) −10.3063 −0.451527 −0.225763 0.974182i \(-0.572488\pi\)
−0.225763 + 0.974182i \(0.572488\pi\)
\(522\) 5.68998 0.249044
\(523\) 5.41422 0.236748 0.118374 0.992969i \(-0.462232\pi\)
0.118374 + 0.992969i \(0.462232\pi\)
\(524\) −70.4464 −3.07747
\(525\) 7.80157 0.340488
\(526\) 37.6890 1.64332
\(527\) −29.3775 −1.27971
\(528\) −96.0622 −4.18057
\(529\) 35.1414 1.52789
\(530\) 4.95115 0.215064
\(531\) 4.81581 0.208988
\(532\) −3.36465 −0.145876
\(533\) −10.0595 −0.435727
\(534\) 2.68954 0.116388
\(535\) −14.6556 −0.633619
\(536\) −70.8864 −3.06183
\(537\) 10.0839 0.435152
\(538\) −28.6460 −1.23502
\(539\) 15.9119 0.685374
\(540\) 37.6583 1.62056
\(541\) 6.20288 0.266682 0.133341 0.991070i \(-0.457429\pi\)
0.133341 + 0.991070i \(0.457429\pi\)
\(542\) 17.7373 0.761882
\(543\) −37.8961 −1.62628
\(544\) 20.6879 0.886988
\(545\) 33.9308 1.45344
\(546\) 99.1031 4.24122
\(547\) −24.9925 −1.06860 −0.534301 0.845294i \(-0.679425\pi\)
−0.534301 + 0.845294i \(0.679425\pi\)
\(548\) 17.9939 0.768662
\(549\) −8.03094 −0.342752
\(550\) 20.3453 0.867525
\(551\) 0.629490 0.0268172
\(552\) 99.8131 4.24833
\(553\) −13.8822 −0.590330
\(554\) −25.9555 −1.10274
\(555\) 40.8353 1.73336
\(556\) 79.7588 3.38253
\(557\) −1.40811 −0.0596636 −0.0298318 0.999555i \(-0.509497\pi\)
−0.0298318 + 0.999555i \(0.509497\pi\)
\(558\) −21.6075 −0.914719
\(559\) 31.0736 1.31427
\(560\) 47.6131 2.01202
\(561\) 34.9229 1.47445
\(562\) −37.4075 −1.57794
\(563\) −20.7359 −0.873913 −0.436956 0.899483i \(-0.643944\pi\)
−0.436956 + 0.899483i \(0.643944\pi\)
\(564\) 80.0512 3.37076
\(565\) 23.3031 0.980368
\(566\) 29.1132 1.22372
\(567\) −33.4456 −1.40458
\(568\) 14.1534 0.593863
\(569\) 32.3798 1.35743 0.678716 0.734400i \(-0.262537\pi\)
0.678716 + 0.734400i \(0.262537\pi\)
\(570\) −2.28769 −0.0958206
\(571\) −2.25737 −0.0944682 −0.0472341 0.998884i \(-0.515041\pi\)
−0.0472341 + 0.998884i \(0.515041\pi\)
\(572\) 180.163 7.53298
\(573\) 10.8925 0.455040
\(574\) 12.5760 0.524912
\(575\) −9.81640 −0.409372
\(576\) 1.96088 0.0817034
\(577\) 46.0912 1.91880 0.959402 0.282044i \(-0.0910123\pi\)
0.959402 + 0.282044i \(0.0910123\pi\)
\(578\) 22.0530 0.917285
\(579\) 5.54245 0.230336
\(580\) −23.6479 −0.981926
\(581\) 32.5938 1.35222
\(582\) −44.9518 −1.86331
\(583\) −6.15017 −0.254714
\(584\) −39.1575 −1.62035
\(585\) 10.1838 0.421047
\(586\) −68.3988 −2.82553
\(587\) −32.3043 −1.33334 −0.666670 0.745353i \(-0.732281\pi\)
−0.666670 + 0.745353i \(0.732281\pi\)
\(588\) −23.3072 −0.961171
\(589\) −2.39047 −0.0984974
\(590\) −28.7115 −1.18203
\(591\) −35.2142 −1.44852
\(592\) −86.4191 −3.55180
\(593\) −6.44386 −0.264618 −0.132309 0.991209i \(-0.542239\pi\)
−0.132309 + 0.991209i \(0.542239\pi\)
\(594\) −67.1037 −2.75330
\(595\) −17.3095 −0.709619
\(596\) −79.0690 −3.23879
\(597\) 5.77155 0.236214
\(598\) −124.698 −5.09926
\(599\) −1.11296 −0.0454741 −0.0227371 0.999741i \(-0.507238\pi\)
−0.0227371 + 0.999741i \(0.507238\pi\)
\(600\) −16.8521 −0.687984
\(601\) −21.9545 −0.895542 −0.447771 0.894148i \(-0.647782\pi\)
−0.447771 + 0.894148i \(0.647782\pi\)
\(602\) −38.8468 −1.58328
\(603\) 8.80165 0.358431
\(604\) 4.60287 0.187288
\(605\) 51.6860 2.10134
\(606\) −35.8242 −1.45526
\(607\) 2.54798 0.103419 0.0517097 0.998662i \(-0.483533\pi\)
0.0517097 + 0.998662i \(0.483533\pi\)
\(608\) 1.68339 0.0682704
\(609\) 16.1583 0.654768
\(610\) 47.8798 1.93860
\(611\) −56.5539 −2.28792
\(612\) −11.0904 −0.448302
\(613\) 12.3377 0.498316 0.249158 0.968463i \(-0.419846\pi\)
0.249158 + 0.968463i \(0.419846\pi\)
\(614\) 74.1893 2.99404
\(615\) 5.96067 0.240357
\(616\) −127.366 −5.13171
\(617\) 13.5676 0.546212 0.273106 0.961984i \(-0.411949\pi\)
0.273106 + 0.961984i \(0.411949\pi\)
\(618\) 33.9861 1.36712
\(619\) 0.945242 0.0379925 0.0189962 0.999820i \(-0.493953\pi\)
0.0189962 + 0.999820i \(0.493953\pi\)
\(620\) 89.8021 3.60654
\(621\) 32.3769 1.29924
\(622\) −37.0275 −1.48467
\(623\) 1.65589 0.0663419
\(624\) −99.4064 −3.97944
\(625\) −16.9057 −0.676228
\(626\) −0.241912 −0.00966875
\(627\) 2.84169 0.113486
\(628\) −44.1626 −1.76228
\(629\) 31.4172 1.25269
\(630\) −12.7313 −0.507228
\(631\) −24.8837 −0.990605 −0.495303 0.868721i \(-0.664943\pi\)
−0.495303 + 0.868721i \(0.664943\pi\)
\(632\) 29.9868 1.19281
\(633\) −49.1230 −1.95246
\(634\) −18.4182 −0.731482
\(635\) 27.0657 1.07407
\(636\) 9.00854 0.357212
\(637\) 16.4658 0.652400
\(638\) 42.1384 1.66827
\(639\) −1.75737 −0.0695203
\(640\) 15.7876 0.624061
\(641\) 18.5341 0.732054 0.366027 0.930604i \(-0.380718\pi\)
0.366027 + 0.930604i \(0.380718\pi\)
\(642\) −38.2523 −1.50970
\(643\) 13.5133 0.532911 0.266455 0.963847i \(-0.414147\pi\)
0.266455 + 0.963847i \(0.414147\pi\)
\(644\) 108.672 4.28228
\(645\) −18.4123 −0.724983
\(646\) −1.76006 −0.0692488
\(647\) −7.52570 −0.295866 −0.147933 0.988997i \(-0.547262\pi\)
−0.147933 + 0.988997i \(0.547262\pi\)
\(648\) 72.2457 2.83808
\(649\) 35.6645 1.39995
\(650\) 21.0535 0.825787
\(651\) −61.3607 −2.40491
\(652\) 61.2339 2.39810
\(653\) 6.81586 0.266725 0.133363 0.991067i \(-0.457423\pi\)
0.133363 + 0.991067i \(0.457423\pi\)
\(654\) 88.5618 3.46304
\(655\) −29.4897 −1.15226
\(656\) −12.6145 −0.492513
\(657\) 4.86202 0.189685
\(658\) 70.7011 2.75622
\(659\) 1.03706 0.0403982 0.0201991 0.999796i \(-0.493570\pi\)
0.0201991 + 0.999796i \(0.493570\pi\)
\(660\) −106.753 −4.15537
\(661\) −18.4538 −0.717770 −0.358885 0.933382i \(-0.616843\pi\)
−0.358885 + 0.933382i \(0.616843\pi\)
\(662\) 54.8273 2.13092
\(663\) 36.1387 1.40351
\(664\) −70.4056 −2.73227
\(665\) −1.40848 −0.0546185
\(666\) 23.1077 0.895405
\(667\) −20.3314 −0.787234
\(668\) 49.1347 1.90108
\(669\) −31.4142 −1.21454
\(670\) −52.4747 −2.02727
\(671\) −59.4749 −2.29600
\(672\) 43.2107 1.66689
\(673\) 47.3958 1.82697 0.913487 0.406868i \(-0.133379\pi\)
0.913487 + 0.406868i \(0.133379\pi\)
\(674\) 53.2323 2.05043
\(675\) −5.46641 −0.210402
\(676\) 126.597 4.86912
\(677\) −30.2052 −1.16088 −0.580441 0.814303i \(-0.697120\pi\)
−0.580441 + 0.814303i \(0.697120\pi\)
\(678\) 60.8227 2.33588
\(679\) −27.6759 −1.06210
\(680\) 37.3901 1.43384
\(681\) −3.60962 −0.138321
\(682\) −160.019 −6.12744
\(683\) 7.78364 0.297833 0.148916 0.988850i \(-0.452421\pi\)
0.148916 + 0.988850i \(0.452421\pi\)
\(684\) −0.902430 −0.0345053
\(685\) 7.53245 0.287800
\(686\) 35.1095 1.34049
\(687\) 7.75498 0.295871
\(688\) 38.9657 1.48555
\(689\) −6.36427 −0.242459
\(690\) 73.8881 2.81287
\(691\) 25.3481 0.964287 0.482144 0.876092i \(-0.339858\pi\)
0.482144 + 0.876092i \(0.339858\pi\)
\(692\) 7.53895 0.286588
\(693\) 15.8145 0.600741
\(694\) 66.9318 2.54070
\(695\) 33.3879 1.26648
\(696\) −34.9035 −1.32301
\(697\) 4.58593 0.173704
\(698\) −43.6125 −1.65076
\(699\) 36.5303 1.38170
\(700\) −18.3478 −0.693483
\(701\) −30.1439 −1.13852 −0.569260 0.822158i \(-0.692770\pi\)
−0.569260 + 0.822158i \(0.692770\pi\)
\(702\) −69.4397 −2.62083
\(703\) 2.55643 0.0964177
\(704\) 14.5217 0.547308
\(705\) 33.5103 1.26207
\(706\) 27.5698 1.03760
\(707\) −22.0562 −0.829509
\(708\) −52.2400 −1.96330
\(709\) −42.6602 −1.60214 −0.801069 0.598572i \(-0.795735\pi\)
−0.801069 + 0.598572i \(0.795735\pi\)
\(710\) 10.4773 0.393205
\(711\) −3.72333 −0.139636
\(712\) −3.57688 −0.134049
\(713\) 77.2077 2.89145
\(714\) −45.1790 −1.69078
\(715\) 75.4181 2.82048
\(716\) −23.7154 −0.886288
\(717\) 56.7756 2.12032
\(718\) 17.8028 0.664396
\(719\) 38.5686 1.43837 0.719183 0.694820i \(-0.244516\pi\)
0.719183 + 0.694820i \(0.244516\pi\)
\(720\) 12.7703 0.475920
\(721\) 20.9245 0.779270
\(722\) 48.6793 1.81166
\(723\) −1.96122 −0.0729384
\(724\) 89.1246 3.31229
\(725\) 3.43268 0.127487
\(726\) 134.904 5.00676
\(727\) 22.9505 0.851189 0.425594 0.904914i \(-0.360065\pi\)
0.425594 + 0.904914i \(0.360065\pi\)
\(728\) −131.800 −4.88482
\(729\) 15.9606 0.591132
\(730\) −28.9869 −1.07285
\(731\) −14.1658 −0.523940
\(732\) 87.1165 3.21992
\(733\) −20.8831 −0.771336 −0.385668 0.922638i \(-0.626029\pi\)
−0.385668 + 0.922638i \(0.626029\pi\)
\(734\) −19.0091 −0.701639
\(735\) −9.75664 −0.359879
\(736\) −54.3704 −2.00412
\(737\) 65.1825 2.40103
\(738\) 3.37300 0.124162
\(739\) 22.4207 0.824760 0.412380 0.911012i \(-0.364698\pi\)
0.412380 + 0.911012i \(0.364698\pi\)
\(740\) −96.0370 −3.53039
\(741\) 2.94062 0.108026
\(742\) 7.95633 0.292086
\(743\) −6.87486 −0.252214 −0.126107 0.992017i \(-0.540248\pi\)
−0.126107 + 0.992017i \(0.540248\pi\)
\(744\) 132.545 4.85933
\(745\) −33.0992 −1.21266
\(746\) −33.8675 −1.23998
\(747\) 8.74195 0.319851
\(748\) −82.1322 −3.00305
\(749\) −23.5511 −0.860539
\(750\) −60.9259 −2.22470
\(751\) −3.98480 −0.145408 −0.0727038 0.997354i \(-0.523163\pi\)
−0.0727038 + 0.997354i \(0.523163\pi\)
\(752\) −70.9175 −2.58609
\(753\) 41.4306 1.50982
\(754\) 43.6053 1.58801
\(755\) 1.92681 0.0701239
\(756\) 60.5157 2.20093
\(757\) 26.9694 0.980219 0.490110 0.871661i \(-0.336957\pi\)
0.490110 + 0.871661i \(0.336957\pi\)
\(758\) 36.1956 1.31468
\(759\) −91.7816 −3.33146
\(760\) 3.04245 0.110361
\(761\) 36.7973 1.33390 0.666950 0.745103i \(-0.267600\pi\)
0.666950 + 0.745103i \(0.267600\pi\)
\(762\) 70.6434 2.55914
\(763\) 54.5257 1.97396
\(764\) −25.6171 −0.926794
\(765\) −4.64256 −0.167852
\(766\) −72.4104 −2.61629
\(767\) 36.9061 1.33260
\(768\) 50.4493 1.82043
\(769\) 0.0864354 0.00311694 0.00155847 0.999999i \(-0.499504\pi\)
0.00155847 + 0.999999i \(0.499504\pi\)
\(770\) −94.2844 −3.39777
\(771\) −3.20639 −0.115475
\(772\) −13.0348 −0.469133
\(773\) −44.3466 −1.59504 −0.797518 0.603295i \(-0.793854\pi\)
−0.797518 + 0.603295i \(0.793854\pi\)
\(774\) −10.4191 −0.374506
\(775\) −13.0355 −0.468249
\(776\) 59.7824 2.14606
\(777\) 65.6209 2.35414
\(778\) 55.0487 1.97359
\(779\) 0.373159 0.0133698
\(780\) −110.470 −3.95545
\(781\) −13.0145 −0.465697
\(782\) 56.8469 2.03284
\(783\) −11.3218 −0.404609
\(784\) 20.6478 0.737423
\(785\) −18.4870 −0.659828
\(786\) −76.9701 −2.74543
\(787\) 27.7727 0.989989 0.494995 0.868896i \(-0.335170\pi\)
0.494995 + 0.868896i \(0.335170\pi\)
\(788\) 82.8173 2.95024
\(789\) 28.7061 1.02196
\(790\) 22.1982 0.789776
\(791\) 37.4473 1.33147
\(792\) −34.1607 −1.21385
\(793\) −61.5453 −2.18554
\(794\) 15.2490 0.541167
\(795\) 3.77108 0.133746
\(796\) −13.5736 −0.481104
\(797\) 11.8945 0.421323 0.210662 0.977559i \(-0.432438\pi\)
0.210662 + 0.977559i \(0.432438\pi\)
\(798\) −3.67623 −0.130137
\(799\) 25.7817 0.912090
\(800\) 9.17971 0.324552
\(801\) 0.444126 0.0156924
\(802\) 3.90033 0.137725
\(803\) 36.0067 1.27065
\(804\) −95.4769 −3.36721
\(805\) 45.4914 1.60336
\(806\) −165.590 −5.83264
\(807\) −21.8184 −0.768045
\(808\) 47.6434 1.67609
\(809\) 4.14679 0.145794 0.0728968 0.997339i \(-0.476776\pi\)
0.0728968 + 0.997339i \(0.476776\pi\)
\(810\) 53.4809 1.87913
\(811\) 17.1220 0.601235 0.300617 0.953745i \(-0.402807\pi\)
0.300617 + 0.953745i \(0.402807\pi\)
\(812\) −38.0014 −1.33359
\(813\) 13.5097 0.473807
\(814\) 171.129 5.99807
\(815\) 25.6332 0.897891
\(816\) 45.3172 1.58642
\(817\) −1.15267 −0.0403270
\(818\) 10.3471 0.361779
\(819\) 16.3650 0.571839
\(820\) −14.0184 −0.489543
\(821\) −7.96579 −0.278008 −0.139004 0.990292i \(-0.544390\pi\)
−0.139004 + 0.990292i \(0.544390\pi\)
\(822\) 19.6602 0.685729
\(823\) 7.28353 0.253888 0.126944 0.991910i \(-0.459483\pi\)
0.126944 + 0.991910i \(0.459483\pi\)
\(824\) −45.1989 −1.57458
\(825\) 15.4961 0.539505
\(826\) −46.1383 −1.60536
\(827\) 40.7437 1.41680 0.708399 0.705812i \(-0.249418\pi\)
0.708399 + 0.705812i \(0.249418\pi\)
\(828\) 29.1469 1.01292
\(829\) −18.6694 −0.648414 −0.324207 0.945986i \(-0.605097\pi\)
−0.324207 + 0.945986i \(0.605097\pi\)
\(830\) −52.1188 −1.80907
\(831\) −19.7692 −0.685786
\(832\) 15.0273 0.520977
\(833\) −7.50642 −0.260082
\(834\) 87.1449 3.01758
\(835\) 20.5684 0.711797
\(836\) −6.68314 −0.231141
\(837\) 42.9943 1.48610
\(838\) 39.3774 1.36027
\(839\) 10.6419 0.367399 0.183700 0.982982i \(-0.441193\pi\)
0.183700 + 0.982982i \(0.441193\pi\)
\(840\) 78.0964 2.69458
\(841\) −21.8903 −0.754840
\(842\) 41.4563 1.42868
\(843\) −28.4917 −0.981305
\(844\) 115.528 3.97664
\(845\) 52.9950 1.82308
\(846\) 18.9627 0.651951
\(847\) 83.0577 2.85390
\(848\) −7.98068 −0.274058
\(849\) 22.1743 0.761019
\(850\) −9.59784 −0.329203
\(851\) −82.5682 −2.83040
\(852\) 19.0632 0.653095
\(853\) 16.8532 0.577041 0.288520 0.957474i \(-0.406837\pi\)
0.288520 + 0.957474i \(0.406837\pi\)
\(854\) 76.9412 2.63287
\(855\) −0.377768 −0.0129194
\(856\) 50.8726 1.73879
\(857\) 23.0230 0.786449 0.393225 0.919442i \(-0.371360\pi\)
0.393225 + 0.919442i \(0.371360\pi\)
\(858\) 196.847 6.72023
\(859\) 43.1268 1.47147 0.735733 0.677271i \(-0.236838\pi\)
0.735733 + 0.677271i \(0.236838\pi\)
\(860\) 43.3023 1.47660
\(861\) 9.57859 0.326438
\(862\) 73.9819 2.51983
\(863\) 39.5391 1.34593 0.672963 0.739676i \(-0.265021\pi\)
0.672963 + 0.739676i \(0.265021\pi\)
\(864\) −30.2770 −1.03004
\(865\) 3.15589 0.107303
\(866\) 61.1218 2.07700
\(867\) 16.7968 0.570451
\(868\) 144.309 4.89816
\(869\) −27.5739 −0.935381
\(870\) −25.8378 −0.875984
\(871\) 67.4516 2.28551
\(872\) −117.781 −3.98855
\(873\) −7.42292 −0.251228
\(874\) 4.62566 0.156465
\(875\) −37.5108 −1.26810
\(876\) −52.7413 −1.78196
\(877\) −46.6303 −1.57459 −0.787297 0.616574i \(-0.788520\pi\)
−0.787297 + 0.616574i \(0.788520\pi\)
\(878\) −2.58052 −0.0870882
\(879\) −52.0964 −1.75717
\(880\) 94.5729 3.18805
\(881\) 10.0041 0.337045 0.168523 0.985698i \(-0.446100\pi\)
0.168523 + 0.985698i \(0.446100\pi\)
\(882\) −5.52105 −0.185903
\(883\) −0.433467 −0.0145873 −0.00729366 0.999973i \(-0.502322\pi\)
−0.00729366 + 0.999973i \(0.502322\pi\)
\(884\) −84.9914 −2.85857
\(885\) −21.8683 −0.735094
\(886\) −70.4044 −2.36528
\(887\) 37.3796 1.25508 0.627541 0.778583i \(-0.284061\pi\)
0.627541 + 0.778583i \(0.284061\pi\)
\(888\) −141.747 −4.75673
\(889\) 43.4936 1.45873
\(890\) −2.64784 −0.0887558
\(891\) −66.4324 −2.22557
\(892\) 73.8804 2.47370
\(893\) 2.09787 0.0702025
\(894\) −86.3912 −2.88935
\(895\) −9.92755 −0.331841
\(896\) 25.3702 0.847559
\(897\) −94.9767 −3.17118
\(898\) 85.7196 2.86050
\(899\) −26.9986 −0.900455
\(900\) −4.92106 −0.164035
\(901\) 2.90133 0.0966574
\(902\) 24.9795 0.831725
\(903\) −29.5879 −0.984624
\(904\) −80.8896 −2.69035
\(905\) 37.3086 1.24018
\(906\) 5.02912 0.167081
\(907\) −22.6439 −0.751879 −0.375940 0.926644i \(-0.622680\pi\)
−0.375940 + 0.926644i \(0.622680\pi\)
\(908\) 8.48916 0.281723
\(909\) −5.91568 −0.196211
\(910\) −97.5667 −3.23430
\(911\) 31.0427 1.02849 0.514246 0.857643i \(-0.328072\pi\)
0.514246 + 0.857643i \(0.328072\pi\)
\(912\) 3.68748 0.122105
\(913\) 64.7404 2.14259
\(914\) 4.69854 0.155414
\(915\) 36.4680 1.20559
\(916\) −18.2383 −0.602610
\(917\) −47.3889 −1.56492
\(918\) 31.6560 1.04481
\(919\) 53.4816 1.76420 0.882098 0.471066i \(-0.156130\pi\)
0.882098 + 0.471066i \(0.156130\pi\)
\(920\) −98.2656 −3.23972
\(921\) 56.5068 1.86196
\(922\) 51.8937 1.70903
\(923\) −13.4676 −0.443292
\(924\) −171.549 −5.64355
\(925\) 13.9405 0.458362
\(926\) −101.294 −3.32872
\(927\) 5.61215 0.184327
\(928\) 19.0127 0.624122
\(929\) −43.2319 −1.41839 −0.709196 0.705011i \(-0.750942\pi\)
−0.709196 + 0.705011i \(0.750942\pi\)
\(930\) 98.1182 3.21742
\(931\) −0.610801 −0.0200182
\(932\) −85.9125 −2.81416
\(933\) −28.2023 −0.923301
\(934\) −2.41163 −0.0789110
\(935\) −34.3815 −1.12439
\(936\) −35.3499 −1.15545
\(937\) 8.45574 0.276237 0.138119 0.990416i \(-0.455895\pi\)
0.138119 + 0.990416i \(0.455895\pi\)
\(938\) −84.3251 −2.75331
\(939\) −0.184254 −0.00601290
\(940\) −78.8101 −2.57050
\(941\) −27.3643 −0.892050 −0.446025 0.895020i \(-0.647161\pi\)
−0.446025 + 0.895020i \(0.647161\pi\)
\(942\) −48.2522 −1.57214
\(943\) −12.0524 −0.392479
\(944\) 46.2795 1.50627
\(945\) 25.3326 0.824068
\(946\) −77.1607 −2.50871
\(947\) −24.4766 −0.795382 −0.397691 0.917520i \(-0.630188\pi\)
−0.397691 + 0.917520i \(0.630188\pi\)
\(948\) 40.3892 1.31178
\(949\) 37.2602 1.20952
\(950\) −0.780981 −0.0253384
\(951\) −14.0284 −0.454901
\(952\) 60.0846 1.94735
\(953\) 19.2937 0.624984 0.312492 0.949920i \(-0.398836\pi\)
0.312492 + 0.949920i \(0.398836\pi\)
\(954\) 2.13396 0.0690896
\(955\) −10.7236 −0.347008
\(956\) −133.526 −4.31853
\(957\) 32.0950 1.03748
\(958\) −92.1626 −2.97764
\(959\) 12.1044 0.390871
\(960\) −8.90424 −0.287383
\(961\) 71.5264 2.30730
\(962\) 177.086 5.70949
\(963\) −6.31663 −0.203551
\(964\) 4.61242 0.148556
\(965\) −5.45652 −0.175652
\(966\) 118.736 3.82026
\(967\) −2.54289 −0.0817739 −0.0408870 0.999164i \(-0.513018\pi\)
−0.0408870 + 0.999164i \(0.513018\pi\)
\(968\) −179.412 −5.76653
\(969\) −1.34056 −0.0430651
\(970\) 44.2548 1.42094
\(971\) −48.9246 −1.57006 −0.785032 0.619455i \(-0.787353\pi\)
−0.785032 + 0.619455i \(0.787353\pi\)
\(972\) 38.6747 1.24049
\(973\) 53.6533 1.72005
\(974\) −87.9556 −2.81828
\(975\) 16.0356 0.513549
\(976\) −77.1767 −2.47036
\(977\) 2.22069 0.0710461 0.0355230 0.999369i \(-0.488690\pi\)
0.0355230 + 0.999369i \(0.488690\pi\)
\(978\) 66.9044 2.13937
\(979\) 3.28907 0.105119
\(980\) 22.9458 0.732977
\(981\) 14.6243 0.466918
\(982\) −14.4659 −0.461625
\(983\) −0.529805 −0.0168981 −0.00844907 0.999964i \(-0.502689\pi\)
−0.00844907 + 0.999964i \(0.502689\pi\)
\(984\) −20.6906 −0.659594
\(985\) 34.6683 1.10462
\(986\) −19.8787 −0.633067
\(987\) 53.8500 1.71406
\(988\) −6.91579 −0.220021
\(989\) 37.2293 1.18382
\(990\) −25.2880 −0.803704
\(991\) −24.2643 −0.770780 −0.385390 0.922754i \(-0.625933\pi\)
−0.385390 + 0.922754i \(0.625933\pi\)
\(992\) −72.2000 −2.29235
\(993\) 41.7596 1.32520
\(994\) 16.8366 0.534025
\(995\) −5.68207 −0.180134
\(996\) −94.8293 −3.00478
\(997\) 48.2040 1.52664 0.763318 0.646023i \(-0.223569\pi\)
0.763318 + 0.646023i \(0.223569\pi\)
\(998\) 46.2326 1.46347
\(999\) −45.9793 −1.45472
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 \(a_p\))