Properties

Label 8043.2.a.t.1.10
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(52\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.90192 q^{2}\) \(-1.00000 q^{3}\) \(+1.61732 q^{4}\) \(+0.767188 q^{5}\) \(+1.90192 q^{6}\) \(+1.00000 q^{7}\) \(+0.727834 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.90192 q^{2}\) \(-1.00000 q^{3}\) \(+1.61732 q^{4}\) \(+0.767188 q^{5}\) \(+1.90192 q^{6}\) \(+1.00000 q^{7}\) \(+0.727834 q^{8}\) \(+1.00000 q^{9}\) \(-1.45913 q^{10}\) \(+0.295463 q^{11}\) \(-1.61732 q^{12}\) \(+3.77953 q^{13}\) \(-1.90192 q^{14}\) \(-0.767188 q^{15}\) \(-4.61892 q^{16}\) \(+5.24425 q^{17}\) \(-1.90192 q^{18}\) \(-3.76509 q^{19}\) \(+1.24079 q^{20}\) \(-1.00000 q^{21}\) \(-0.561948 q^{22}\) \(-1.71339 q^{23}\) \(-0.727834 q^{24}\) \(-4.41142 q^{25}\) \(-7.18839 q^{26}\) \(-1.00000 q^{27}\) \(+1.61732 q^{28}\) \(-7.83095 q^{29}\) \(+1.45913 q^{30}\) \(+0.600616 q^{31}\) \(+7.32917 q^{32}\) \(-0.295463 q^{33}\) \(-9.97417 q^{34}\) \(+0.767188 q^{35}\) \(+1.61732 q^{36}\) \(-3.78080 q^{37}\) \(+7.16091 q^{38}\) \(-3.77953 q^{39}\) \(+0.558386 q^{40}\) \(+8.68124 q^{41}\) \(+1.90192 q^{42}\) \(+2.68115 q^{43}\) \(+0.477857 q^{44}\) \(+0.767188 q^{45}\) \(+3.25875 q^{46}\) \(-10.2548 q^{47}\) \(+4.61892 q^{48}\) \(+1.00000 q^{49}\) \(+8.39019 q^{50}\) \(-5.24425 q^{51}\) \(+6.11270 q^{52}\) \(-7.17506 q^{53}\) \(+1.90192 q^{54}\) \(+0.226676 q^{55}\) \(+0.727834 q^{56}\) \(+3.76509 q^{57}\) \(+14.8939 q^{58}\) \(+9.38143 q^{59}\) \(-1.24079 q^{60}\) \(+10.0051 q^{61}\) \(-1.14233 q^{62}\) \(+1.00000 q^{63}\) \(-4.70168 q^{64}\) \(+2.89961 q^{65}\) \(+0.561948 q^{66}\) \(+0.510569 q^{67}\) \(+8.48161 q^{68}\) \(+1.71339 q^{69}\) \(-1.45913 q^{70}\) \(+7.64336 q^{71}\) \(+0.727834 q^{72}\) \(+6.16649 q^{73}\) \(+7.19080 q^{74}\) \(+4.41142 q^{75}\) \(-6.08934 q^{76}\) \(+0.295463 q^{77}\) \(+7.18839 q^{78}\) \(-1.92887 q^{79}\) \(-3.54358 q^{80}\) \(+1.00000 q^{81}\) \(-16.5111 q^{82}\) \(-4.65688 q^{83}\) \(-1.61732 q^{84}\) \(+4.02332 q^{85}\) \(-5.09934 q^{86}\) \(+7.83095 q^{87}\) \(+0.215048 q^{88}\) \(+5.88295 q^{89}\) \(-1.45913 q^{90}\) \(+3.77953 q^{91}\) \(-2.77110 q^{92}\) \(-0.600616 q^{93}\) \(+19.5039 q^{94}\) \(-2.88853 q^{95}\) \(-7.32917 q^{96}\) \(+18.0326 q^{97}\) \(-1.90192 q^{98}\) \(+0.295463 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 61q^{12} \) \(\mathstrut +\mathstrut 44q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 95q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 21q^{20} \) \(\mathstrut -\mathstrut 52q^{21} \) \(\mathstrut +\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 83q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 61q^{28} \) \(\mathstrut +\mathstrut 31q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 71q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 17q^{34} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 61q^{36} \) \(\mathstrut +\mathstrut 71q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 44q^{39} \) \(\mathstrut +\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 25q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut +\mathstrut 75q^{43} \) \(\mathstrut +\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 36q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 95q^{48} \) \(\mathstrut +\mathstrut 52q^{49} \) \(\mathstrut +\mathstrut 26q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 88q^{52} \) \(\mathstrut +\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 7q^{57} \) \(\mathstrut +\mathstrut 48q^{58} \) \(\mathstrut -\mathstrut 27q^{59} \) \(\mathstrut +\mathstrut 21q^{60} \) \(\mathstrut +\mathstrut 59q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 138q^{64} \) \(\mathstrut +\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 65q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut -\mathstrut 83q^{75} \) \(\mathstrut +\mathstrut 31q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 52q^{81} \) \(\mathstrut +\mathstrut 51q^{82} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 61q^{84} \) \(\mathstrut +\mathstrut 70q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 31q^{87} \) \(\mathstrut +\mathstrut 90q^{88} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 34q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 27q^{94} \) \(\mathstrut +\mathstrut 9q^{95} \) \(\mathstrut -\mathstrut 71q^{96} \) \(\mathstrut +\mathstrut 73q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.90192 −1.34486 −0.672432 0.740159i \(-0.734750\pi\)
−0.672432 + 0.740159i \(0.734750\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.61732 0.808658
\(5\) 0.767188 0.343097 0.171548 0.985176i \(-0.445123\pi\)
0.171548 + 0.985176i \(0.445123\pi\)
\(6\) 1.90192 0.776457
\(7\) 1.00000 0.377964
\(8\) 0.727834 0.257328
\(9\) 1.00000 0.333333
\(10\) −1.45913 −0.461418
\(11\) 0.295463 0.0890855 0.0445427 0.999007i \(-0.485817\pi\)
0.0445427 + 0.999007i \(0.485817\pi\)
\(12\) −1.61732 −0.466879
\(13\) 3.77953 1.04825 0.524127 0.851640i \(-0.324392\pi\)
0.524127 + 0.851640i \(0.324392\pi\)
\(14\) −1.90192 −0.508311
\(15\) −0.767188 −0.198087
\(16\) −4.61892 −1.15473
\(17\) 5.24425 1.27192 0.635959 0.771723i \(-0.280605\pi\)
0.635959 + 0.771723i \(0.280605\pi\)
\(18\) −1.90192 −0.448288
\(19\) −3.76509 −0.863771 −0.431885 0.901929i \(-0.642151\pi\)
−0.431885 + 0.901929i \(0.642151\pi\)
\(20\) 1.24079 0.277448
\(21\) −1.00000 −0.218218
\(22\) −0.561948 −0.119808
\(23\) −1.71339 −0.357267 −0.178634 0.983916i \(-0.557168\pi\)
−0.178634 + 0.983916i \(0.557168\pi\)
\(24\) −0.727834 −0.148569
\(25\) −4.41142 −0.882285
\(26\) −7.18839 −1.40976
\(27\) −1.00000 −0.192450
\(28\) 1.61732 0.305644
\(29\) −7.83095 −1.45417 −0.727086 0.686547i \(-0.759126\pi\)
−0.727086 + 0.686547i \(0.759126\pi\)
\(30\) 1.45913 0.266400
\(31\) 0.600616 0.107874 0.0539369 0.998544i \(-0.482823\pi\)
0.0539369 + 0.998544i \(0.482823\pi\)
\(32\) 7.32917 1.29563
\(33\) −0.295463 −0.0514335
\(34\) −9.97417 −1.71056
\(35\) 0.767188 0.129678
\(36\) 1.61732 0.269553
\(37\) −3.78080 −0.621560 −0.310780 0.950482i \(-0.600590\pi\)
−0.310780 + 0.950482i \(0.600590\pi\)
\(38\) 7.16091 1.16165
\(39\) −3.77953 −0.605210
\(40\) 0.558386 0.0882885
\(41\) 8.68124 1.35578 0.677891 0.735162i \(-0.262894\pi\)
0.677891 + 0.735162i \(0.262894\pi\)
\(42\) 1.90192 0.293473
\(43\) 2.68115 0.408871 0.204435 0.978880i \(-0.434464\pi\)
0.204435 + 0.978880i \(0.434464\pi\)
\(44\) 0.477857 0.0720397
\(45\) 0.767188 0.114366
\(46\) 3.25875 0.480476
\(47\) −10.2548 −1.49582 −0.747910 0.663800i \(-0.768943\pi\)
−0.747910 + 0.663800i \(0.768943\pi\)
\(48\) 4.61892 0.666684
\(49\) 1.00000 0.142857
\(50\) 8.39019 1.18655
\(51\) −5.24425 −0.734342
\(52\) 6.11270 0.847679
\(53\) −7.17506 −0.985570 −0.492785 0.870151i \(-0.664021\pi\)
−0.492785 + 0.870151i \(0.664021\pi\)
\(54\) 1.90192 0.258819
\(55\) 0.226676 0.0305649
\(56\) 0.727834 0.0972610
\(57\) 3.76509 0.498698
\(58\) 14.8939 1.95566
\(59\) 9.38143 1.22136 0.610679 0.791878i \(-0.290897\pi\)
0.610679 + 0.791878i \(0.290897\pi\)
\(60\) −1.24079 −0.160185
\(61\) 10.0051 1.28103 0.640514 0.767947i \(-0.278721\pi\)
0.640514 + 0.767947i \(0.278721\pi\)
\(62\) −1.14233 −0.145075
\(63\) 1.00000 0.125988
\(64\) −4.70168 −0.587711
\(65\) 2.89961 0.359653
\(66\) 0.561948 0.0691711
\(67\) 0.510569 0.0623759 0.0311880 0.999514i \(-0.490071\pi\)
0.0311880 + 0.999514i \(0.490071\pi\)
\(68\) 8.48161 1.02855
\(69\) 1.71339 0.206268
\(70\) −1.45913 −0.174400
\(71\) 7.64336 0.907100 0.453550 0.891231i \(-0.350157\pi\)
0.453550 + 0.891231i \(0.350157\pi\)
\(72\) 0.727834 0.0857761
\(73\) 6.16649 0.721734 0.360867 0.932617i \(-0.382481\pi\)
0.360867 + 0.932617i \(0.382481\pi\)
\(74\) 7.19080 0.835914
\(75\) 4.41142 0.509387
\(76\) −6.08934 −0.698495
\(77\) 0.295463 0.0336711
\(78\) 7.18839 0.813925
\(79\) −1.92887 −0.217015 −0.108507 0.994096i \(-0.534607\pi\)
−0.108507 + 0.994096i \(0.534607\pi\)
\(80\) −3.54358 −0.396184
\(81\) 1.00000 0.111111
\(82\) −16.5111 −1.82334
\(83\) −4.65688 −0.511159 −0.255580 0.966788i \(-0.582266\pi\)
−0.255580 + 0.966788i \(0.582266\pi\)
\(84\) −1.61732 −0.176464
\(85\) 4.02332 0.436391
\(86\) −5.09934 −0.549876
\(87\) 7.83095 0.839566
\(88\) 0.215048 0.0229242
\(89\) 5.88295 0.623591 0.311796 0.950149i \(-0.399070\pi\)
0.311796 + 0.950149i \(0.399070\pi\)
\(90\) −1.45913 −0.153806
\(91\) 3.77953 0.396203
\(92\) −2.77110 −0.288907
\(93\) −0.600616 −0.0622809
\(94\) 19.5039 2.01167
\(95\) −2.88853 −0.296357
\(96\) −7.32917 −0.748030
\(97\) 18.0326 1.83094 0.915468 0.402390i \(-0.131820\pi\)
0.915468 + 0.402390i \(0.131820\pi\)
\(98\) −1.90192 −0.192123
\(99\) 0.295463 0.0296952
\(100\) −7.13467 −0.713467
\(101\) −14.1510 −1.40807 −0.704037 0.710163i \(-0.748621\pi\)
−0.704037 + 0.710163i \(0.748621\pi\)
\(102\) 9.97417 0.987590
\(103\) −1.46581 −0.144430 −0.0722151 0.997389i \(-0.523007\pi\)
−0.0722151 + 0.997389i \(0.523007\pi\)
\(104\) 2.75087 0.269745
\(105\) −0.767188 −0.0748699
\(106\) 13.6464 1.32546
\(107\) −7.15713 −0.691906 −0.345953 0.938252i \(-0.612444\pi\)
−0.345953 + 0.938252i \(0.612444\pi\)
\(108\) −1.61732 −0.155626
\(109\) 9.55398 0.915106 0.457553 0.889182i \(-0.348726\pi\)
0.457553 + 0.889182i \(0.348726\pi\)
\(110\) −0.431120 −0.0411057
\(111\) 3.78080 0.358858
\(112\) −4.61892 −0.436447
\(113\) 3.35560 0.315668 0.157834 0.987466i \(-0.449549\pi\)
0.157834 + 0.987466i \(0.449549\pi\)
\(114\) −7.16091 −0.670681
\(115\) −1.31449 −0.122577
\(116\) −12.6651 −1.17593
\(117\) 3.77953 0.349418
\(118\) −17.8428 −1.64256
\(119\) 5.24425 0.480740
\(120\) −0.558386 −0.0509734
\(121\) −10.9127 −0.992064
\(122\) −19.0290 −1.72281
\(123\) −8.68124 −0.782761
\(124\) 0.971386 0.0872330
\(125\) −7.22033 −0.645806
\(126\) −1.90192 −0.169437
\(127\) −13.4223 −1.19104 −0.595518 0.803342i \(-0.703053\pi\)
−0.595518 + 0.803342i \(0.703053\pi\)
\(128\) −5.71609 −0.505235
\(129\) −2.68115 −0.236062
\(130\) −5.51484 −0.483684
\(131\) 8.26951 0.722510 0.361255 0.932467i \(-0.382348\pi\)
0.361255 + 0.932467i \(0.382348\pi\)
\(132\) −0.477857 −0.0415921
\(133\) −3.76509 −0.326475
\(134\) −0.971064 −0.0838871
\(135\) −0.767188 −0.0660290
\(136\) 3.81695 0.327300
\(137\) 3.75976 0.321218 0.160609 0.987018i \(-0.448654\pi\)
0.160609 + 0.987018i \(0.448654\pi\)
\(138\) −3.25875 −0.277403
\(139\) 19.7004 1.67096 0.835482 0.549518i \(-0.185189\pi\)
0.835482 + 0.549518i \(0.185189\pi\)
\(140\) 1.24079 0.104866
\(141\) 10.2548 0.863612
\(142\) −14.5371 −1.21993
\(143\) 1.11671 0.0933842
\(144\) −4.61892 −0.384910
\(145\) −6.00781 −0.498922
\(146\) −11.7282 −0.970633
\(147\) −1.00000 −0.0824786
\(148\) −6.11476 −0.502630
\(149\) 17.0164 1.39404 0.697019 0.717053i \(-0.254510\pi\)
0.697019 + 0.717053i \(0.254510\pi\)
\(150\) −8.39019 −0.685056
\(151\) 22.3002 1.81476 0.907382 0.420307i \(-0.138078\pi\)
0.907382 + 0.420307i \(0.138078\pi\)
\(152\) −2.74036 −0.222273
\(153\) 5.24425 0.423972
\(154\) −0.561948 −0.0452831
\(155\) 0.460785 0.0370111
\(156\) −6.11270 −0.489408
\(157\) 5.94616 0.474555 0.237277 0.971442i \(-0.423745\pi\)
0.237277 + 0.971442i \(0.423745\pi\)
\(158\) 3.66857 0.291855
\(159\) 7.17506 0.569019
\(160\) 5.62285 0.444525
\(161\) −1.71339 −0.135034
\(162\) −1.90192 −0.149429
\(163\) 8.03189 0.629106 0.314553 0.949240i \(-0.398145\pi\)
0.314553 + 0.949240i \(0.398145\pi\)
\(164\) 14.0403 1.09636
\(165\) −0.226676 −0.0176467
\(166\) 8.85704 0.687440
\(167\) −3.00437 −0.232486 −0.116243 0.993221i \(-0.537085\pi\)
−0.116243 + 0.993221i \(0.537085\pi\)
\(168\) −0.727834 −0.0561536
\(169\) 1.28487 0.0988363
\(170\) −7.65206 −0.586886
\(171\) −3.76509 −0.287924
\(172\) 4.33626 0.330637
\(173\) 14.1731 1.07756 0.538779 0.842447i \(-0.318886\pi\)
0.538779 + 0.842447i \(0.318886\pi\)
\(174\) −14.8939 −1.12910
\(175\) −4.41142 −0.333472
\(176\) −1.36472 −0.102870
\(177\) −9.38143 −0.705152
\(178\) −11.1889 −0.838645
\(179\) −16.6373 −1.24353 −0.621764 0.783205i \(-0.713583\pi\)
−0.621764 + 0.783205i \(0.713583\pi\)
\(180\) 1.24079 0.0924827
\(181\) 3.39381 0.252260 0.126130 0.992014i \(-0.459744\pi\)
0.126130 + 0.992014i \(0.459744\pi\)
\(182\) −7.18839 −0.532839
\(183\) −10.0051 −0.739602
\(184\) −1.24707 −0.0919350
\(185\) −2.90059 −0.213255
\(186\) 1.14233 0.0837594
\(187\) 1.54948 0.113309
\(188\) −16.5853 −1.20961
\(189\) −1.00000 −0.0727393
\(190\) 5.49377 0.398560
\(191\) −24.8240 −1.79620 −0.898101 0.439789i \(-0.855053\pi\)
−0.898101 + 0.439789i \(0.855053\pi\)
\(192\) 4.70168 0.339315
\(193\) 1.89762 0.136594 0.0682969 0.997665i \(-0.478243\pi\)
0.0682969 + 0.997665i \(0.478243\pi\)
\(194\) −34.2967 −2.46236
\(195\) −2.89961 −0.207645
\(196\) 1.61732 0.115523
\(197\) −15.6176 −1.11271 −0.556353 0.830946i \(-0.687800\pi\)
−0.556353 + 0.830946i \(0.687800\pi\)
\(198\) −0.561948 −0.0399359
\(199\) 6.07308 0.430509 0.215254 0.976558i \(-0.430942\pi\)
0.215254 + 0.976558i \(0.430942\pi\)
\(200\) −3.21079 −0.227037
\(201\) −0.510569 −0.0360128
\(202\) 26.9141 1.89367
\(203\) −7.83095 −0.549625
\(204\) −8.48161 −0.593832
\(205\) 6.66014 0.465164
\(206\) 2.78785 0.194239
\(207\) −1.71339 −0.119089
\(208\) −17.4574 −1.21045
\(209\) −1.11244 −0.0769494
\(210\) 1.45913 0.100690
\(211\) −0.221019 −0.0152156 −0.00760779 0.999971i \(-0.502422\pi\)
−0.00760779 + 0.999971i \(0.502422\pi\)
\(212\) −11.6043 −0.796990
\(213\) −7.64336 −0.523714
\(214\) 13.6123 0.930519
\(215\) 2.05694 0.140282
\(216\) −0.727834 −0.0495229
\(217\) 0.600616 0.0407724
\(218\) −18.1710 −1.23069
\(219\) −6.16649 −0.416693
\(220\) 0.366606 0.0247166
\(221\) 19.8208 1.33329
\(222\) −7.19080 −0.482615
\(223\) 2.40462 0.161025 0.0805125 0.996754i \(-0.474344\pi\)
0.0805125 + 0.996754i \(0.474344\pi\)
\(224\) 7.32917 0.489701
\(225\) −4.41142 −0.294095
\(226\) −6.38210 −0.424531
\(227\) 19.0248 1.26272 0.631361 0.775489i \(-0.282497\pi\)
0.631361 + 0.775489i \(0.282497\pi\)
\(228\) 6.08934 0.403277
\(229\) 23.2092 1.53371 0.766855 0.641821i \(-0.221821\pi\)
0.766855 + 0.641821i \(0.221821\pi\)
\(230\) 2.50007 0.164850
\(231\) −0.295463 −0.0194400
\(232\) −5.69964 −0.374200
\(233\) 5.31731 0.348349 0.174174 0.984715i \(-0.444274\pi\)
0.174174 + 0.984715i \(0.444274\pi\)
\(234\) −7.18839 −0.469920
\(235\) −7.86738 −0.513211
\(236\) 15.1727 0.987662
\(237\) 1.92887 0.125294
\(238\) −9.97417 −0.646529
\(239\) 9.26093 0.599039 0.299520 0.954090i \(-0.403174\pi\)
0.299520 + 0.954090i \(0.403174\pi\)
\(240\) 3.54358 0.228737
\(241\) −22.2302 −1.43198 −0.715988 0.698113i \(-0.754023\pi\)
−0.715988 + 0.698113i \(0.754023\pi\)
\(242\) 20.7551 1.33419
\(243\) −1.00000 −0.0641500
\(244\) 16.1815 1.03591
\(245\) 0.767188 0.0490138
\(246\) 16.5111 1.05271
\(247\) −14.2303 −0.905451
\(248\) 0.437149 0.0277590
\(249\) 4.65688 0.295118
\(250\) 13.7325 0.868521
\(251\) −27.8959 −1.76078 −0.880388 0.474255i \(-0.842717\pi\)
−0.880388 + 0.474255i \(0.842717\pi\)
\(252\) 1.61732 0.101881
\(253\) −0.506245 −0.0318273
\(254\) 25.5282 1.60178
\(255\) −4.02332 −0.251950
\(256\) 20.2749 1.26718
\(257\) −7.42797 −0.463344 −0.231672 0.972794i \(-0.574420\pi\)
−0.231672 + 0.972794i \(0.574420\pi\)
\(258\) 5.09934 0.317471
\(259\) −3.78080 −0.234928
\(260\) 4.68959 0.290836
\(261\) −7.83095 −0.484724
\(262\) −15.7280 −0.971678
\(263\) 17.8180 1.09871 0.549354 0.835590i \(-0.314874\pi\)
0.549354 + 0.835590i \(0.314874\pi\)
\(264\) −0.215048 −0.0132353
\(265\) −5.50462 −0.338146
\(266\) 7.16091 0.439064
\(267\) −5.88295 −0.360031
\(268\) 0.825752 0.0504408
\(269\) 12.2074 0.744298 0.372149 0.928173i \(-0.378621\pi\)
0.372149 + 0.928173i \(0.378621\pi\)
\(270\) 1.45913 0.0888000
\(271\) 6.36680 0.386755 0.193378 0.981124i \(-0.438056\pi\)
0.193378 + 0.981124i \(0.438056\pi\)
\(272\) −24.2228 −1.46872
\(273\) −3.77953 −0.228748
\(274\) −7.15077 −0.431994
\(275\) −1.30341 −0.0785987
\(276\) 2.77110 0.166801
\(277\) 23.3907 1.40541 0.702706 0.711481i \(-0.251975\pi\)
0.702706 + 0.711481i \(0.251975\pi\)
\(278\) −37.4686 −2.24722
\(279\) 0.600616 0.0359579
\(280\) 0.558386 0.0333699
\(281\) −13.8862 −0.828381 −0.414191 0.910190i \(-0.635935\pi\)
−0.414191 + 0.910190i \(0.635935\pi\)
\(282\) −19.5039 −1.16144
\(283\) 15.0386 0.893954 0.446977 0.894546i \(-0.352501\pi\)
0.446977 + 0.894546i \(0.352501\pi\)
\(284\) 12.3617 0.733534
\(285\) 2.88853 0.171102
\(286\) −2.12390 −0.125589
\(287\) 8.68124 0.512438
\(288\) 7.32917 0.431875
\(289\) 10.5022 0.617774
\(290\) 11.4264 0.670982
\(291\) −18.0326 −1.05709
\(292\) 9.97317 0.583636
\(293\) 7.98940 0.466746 0.233373 0.972387i \(-0.425024\pi\)
0.233373 + 0.972387i \(0.425024\pi\)
\(294\) 1.90192 0.110922
\(295\) 7.19732 0.419044
\(296\) −2.75180 −0.159945
\(297\) −0.295463 −0.0171445
\(298\) −32.3639 −1.87479
\(299\) −6.47583 −0.374507
\(300\) 7.13467 0.411920
\(301\) 2.68115 0.154539
\(302\) −42.4133 −2.44061
\(303\) 14.1510 0.812952
\(304\) 17.3906 0.997422
\(305\) 7.67582 0.439516
\(306\) −9.97417 −0.570185
\(307\) 7.17730 0.409630 0.204815 0.978801i \(-0.434341\pi\)
0.204815 + 0.978801i \(0.434341\pi\)
\(308\) 0.477857 0.0272285
\(309\) 1.46581 0.0833869
\(310\) −0.876378 −0.0497749
\(311\) −9.33978 −0.529611 −0.264805 0.964302i \(-0.585308\pi\)
−0.264805 + 0.964302i \(0.585308\pi\)
\(312\) −2.75087 −0.155738
\(313\) 8.57535 0.484707 0.242354 0.970188i \(-0.422081\pi\)
0.242354 + 0.970188i \(0.422081\pi\)
\(314\) −11.3091 −0.638212
\(315\) 0.767188 0.0432261
\(316\) −3.11959 −0.175491
\(317\) −21.1175 −1.18608 −0.593039 0.805174i \(-0.702072\pi\)
−0.593039 + 0.805174i \(0.702072\pi\)
\(318\) −13.6464 −0.765253
\(319\) −2.31376 −0.129546
\(320\) −3.60707 −0.201642
\(321\) 7.15713 0.399472
\(322\) 3.25875 0.181603
\(323\) −19.7451 −1.09864
\(324\) 1.61732 0.0898509
\(325\) −16.6731 −0.924858
\(326\) −15.2761 −0.846062
\(327\) −9.55398 −0.528337
\(328\) 6.31851 0.348881
\(329\) −10.2548 −0.565367
\(330\) 0.431120 0.0237324
\(331\) −11.9243 −0.655419 −0.327709 0.944779i \(-0.606277\pi\)
−0.327709 + 0.944779i \(0.606277\pi\)
\(332\) −7.53166 −0.413353
\(333\) −3.78080 −0.207187
\(334\) 5.71409 0.312661
\(335\) 0.391702 0.0214010
\(336\) 4.61892 0.251983
\(337\) −20.7509 −1.13037 −0.565186 0.824964i \(-0.691195\pi\)
−0.565186 + 0.824964i \(0.691195\pi\)
\(338\) −2.44373 −0.132921
\(339\) −3.35560 −0.182251
\(340\) 6.50699 0.352891
\(341\) 0.177460 0.00960998
\(342\) 7.16091 0.387218
\(343\) 1.00000 0.0539949
\(344\) 1.95143 0.105214
\(345\) 1.31449 0.0707700
\(346\) −26.9561 −1.44917
\(347\) 23.7950 1.27738 0.638691 0.769463i \(-0.279476\pi\)
0.638691 + 0.769463i \(0.279476\pi\)
\(348\) 12.6651 0.678922
\(349\) 27.5842 1.47655 0.738274 0.674501i \(-0.235641\pi\)
0.738274 + 0.674501i \(0.235641\pi\)
\(350\) 8.39019 0.448475
\(351\) −3.77953 −0.201737
\(352\) 2.16550 0.115421
\(353\) 21.1141 1.12379 0.561895 0.827208i \(-0.310072\pi\)
0.561895 + 0.827208i \(0.310072\pi\)
\(354\) 17.8428 0.948333
\(355\) 5.86389 0.311223
\(356\) 9.51459 0.504272
\(357\) −5.24425 −0.277555
\(358\) 31.6428 1.67237
\(359\) −5.18095 −0.273440 −0.136720 0.990610i \(-0.543656\pi\)
−0.136720 + 0.990610i \(0.543656\pi\)
\(360\) 0.558386 0.0294295
\(361\) −4.82411 −0.253900
\(362\) −6.45476 −0.339255
\(363\) 10.9127 0.572768
\(364\) 6.11270 0.320393
\(365\) 4.73086 0.247624
\(366\) 19.0290 0.994663
\(367\) −32.1695 −1.67923 −0.839616 0.543180i \(-0.817220\pi\)
−0.839616 + 0.543180i \(0.817220\pi\)
\(368\) 7.91403 0.412547
\(369\) 8.68124 0.451927
\(370\) 5.51670 0.286799
\(371\) −7.17506 −0.372511
\(372\) −0.971386 −0.0503640
\(373\) −13.6941 −0.709055 −0.354527 0.935046i \(-0.615358\pi\)
−0.354527 + 0.935046i \(0.615358\pi\)
\(374\) −2.94700 −0.152386
\(375\) 7.22033 0.372856
\(376\) −7.46382 −0.384917
\(377\) −29.5974 −1.52434
\(378\) 1.90192 0.0978244
\(379\) 13.6856 0.702981 0.351490 0.936191i \(-0.385675\pi\)
0.351490 + 0.936191i \(0.385675\pi\)
\(380\) −4.67167 −0.239652
\(381\) 13.4223 0.687645
\(382\) 47.2134 2.41565
\(383\) −1.00000 −0.0510976
\(384\) 5.71609 0.291698
\(385\) 0.226676 0.0115525
\(386\) −3.60913 −0.183700
\(387\) 2.68115 0.136290
\(388\) 29.1645 1.48060
\(389\) 7.83762 0.397383 0.198692 0.980062i \(-0.436331\pi\)
0.198692 + 0.980062i \(0.436331\pi\)
\(390\) 5.51484 0.279255
\(391\) −8.98547 −0.454415
\(392\) 0.727834 0.0367612
\(393\) −8.26951 −0.417142
\(394\) 29.7035 1.49644
\(395\) −1.47981 −0.0744571
\(396\) 0.477857 0.0240132
\(397\) 25.5653 1.28309 0.641543 0.767087i \(-0.278294\pi\)
0.641543 + 0.767087i \(0.278294\pi\)
\(398\) −11.5505 −0.578976
\(399\) 3.76509 0.188490
\(400\) 20.3760 1.01880
\(401\) −5.32713 −0.266024 −0.133012 0.991114i \(-0.542465\pi\)
−0.133012 + 0.991114i \(0.542465\pi\)
\(402\) 0.971064 0.0484323
\(403\) 2.27005 0.113079
\(404\) −22.8866 −1.13865
\(405\) 0.767188 0.0381219
\(406\) 14.8939 0.739171
\(407\) −1.11709 −0.0553720
\(408\) −3.81695 −0.188967
\(409\) 1.46525 0.0724517 0.0362259 0.999344i \(-0.488466\pi\)
0.0362259 + 0.999344i \(0.488466\pi\)
\(410\) −12.6671 −0.625583
\(411\) −3.75976 −0.185455
\(412\) −2.37067 −0.116795
\(413\) 9.38143 0.461630
\(414\) 3.25875 0.160159
\(415\) −3.57270 −0.175377
\(416\) 27.7008 1.35815
\(417\) −19.7004 −0.964731
\(418\) 2.11579 0.103486
\(419\) −23.1847 −1.13265 −0.566325 0.824182i \(-0.691635\pi\)
−0.566325 + 0.824182i \(0.691635\pi\)
\(420\) −1.24079 −0.0605441
\(421\) 33.2782 1.62188 0.810941 0.585128i \(-0.198956\pi\)
0.810941 + 0.585128i \(0.198956\pi\)
\(422\) 0.420361 0.0204629
\(423\) −10.2548 −0.498607
\(424\) −5.22226 −0.253615
\(425\) −23.1346 −1.12219
\(426\) 14.5371 0.704324
\(427\) 10.0051 0.484183
\(428\) −11.5753 −0.559516
\(429\) −1.11671 −0.0539154
\(430\) −3.91215 −0.188661
\(431\) −3.59405 −0.173119 −0.0865596 0.996247i \(-0.527587\pi\)
−0.0865596 + 0.996247i \(0.527587\pi\)
\(432\) 4.61892 0.222228
\(433\) −11.5775 −0.556379 −0.278190 0.960526i \(-0.589734\pi\)
−0.278190 + 0.960526i \(0.589734\pi\)
\(434\) −1.14233 −0.0548334
\(435\) 6.00781 0.288053
\(436\) 15.4518 0.740008
\(437\) 6.45108 0.308597
\(438\) 11.7282 0.560395
\(439\) −17.9531 −0.856853 −0.428426 0.903577i \(-0.640932\pi\)
−0.428426 + 0.903577i \(0.640932\pi\)
\(440\) 0.164982 0.00786522
\(441\) 1.00000 0.0476190
\(442\) −37.6977 −1.79310
\(443\) −16.7634 −0.796454 −0.398227 0.917287i \(-0.630374\pi\)
−0.398227 + 0.917287i \(0.630374\pi\)
\(444\) 6.11476 0.290194
\(445\) 4.51333 0.213952
\(446\) −4.57340 −0.216557
\(447\) −17.0164 −0.804848
\(448\) −4.70168 −0.222134
\(449\) −27.0944 −1.27866 −0.639332 0.768931i \(-0.720789\pi\)
−0.639332 + 0.768931i \(0.720789\pi\)
\(450\) 8.39019 0.395518
\(451\) 2.56499 0.120780
\(452\) 5.42707 0.255268
\(453\) −22.3002 −1.04775
\(454\) −36.1838 −1.69819
\(455\) 2.89961 0.135936
\(456\) 2.74036 0.128329
\(457\) 6.62146 0.309739 0.154869 0.987935i \(-0.450504\pi\)
0.154869 + 0.987935i \(0.450504\pi\)
\(458\) −44.1422 −2.06263
\(459\) −5.24425 −0.244781
\(460\) −2.12595 −0.0991231
\(461\) 32.5390 1.51549 0.757747 0.652549i \(-0.226300\pi\)
0.757747 + 0.652549i \(0.226300\pi\)
\(462\) 0.561948 0.0261442
\(463\) −19.9036 −0.924997 −0.462498 0.886620i \(-0.653047\pi\)
−0.462498 + 0.886620i \(0.653047\pi\)
\(464\) 36.1706 1.67918
\(465\) −0.460785 −0.0213684
\(466\) −10.1131 −0.468481
\(467\) −19.0186 −0.880074 −0.440037 0.897980i \(-0.645035\pi\)
−0.440037 + 0.897980i \(0.645035\pi\)
\(468\) 6.11270 0.282560
\(469\) 0.510569 0.0235759
\(470\) 14.9632 0.690199
\(471\) −5.94616 −0.273984
\(472\) 6.82813 0.314290
\(473\) 0.792179 0.0364245
\(474\) −3.66857 −0.168503
\(475\) 16.6094 0.762092
\(476\) 8.48161 0.388754
\(477\) −7.17506 −0.328523
\(478\) −17.6136 −0.805626
\(479\) 31.6118 1.44438 0.722191 0.691694i \(-0.243135\pi\)
0.722191 + 0.691694i \(0.243135\pi\)
\(480\) −5.62285 −0.256647
\(481\) −14.2897 −0.651553
\(482\) 42.2802 1.92581
\(483\) 1.71339 0.0779621
\(484\) −17.6493 −0.802241
\(485\) 13.8344 0.628188
\(486\) 1.90192 0.0862730
\(487\) 12.0818 0.547479 0.273740 0.961804i \(-0.411739\pi\)
0.273740 + 0.961804i \(0.411739\pi\)
\(488\) 7.28209 0.329645
\(489\) −8.03189 −0.363215
\(490\) −1.45913 −0.0659169
\(491\) −5.55174 −0.250547 −0.125273 0.992122i \(-0.539981\pi\)
−0.125273 + 0.992122i \(0.539981\pi\)
\(492\) −14.0403 −0.632986
\(493\) −41.0675 −1.84959
\(494\) 27.0649 1.21771
\(495\) 0.226676 0.0101883
\(496\) −2.77420 −0.124565
\(497\) 7.64336 0.342851
\(498\) −8.85704 −0.396893
\(499\) −18.8268 −0.842804 −0.421402 0.906874i \(-0.638462\pi\)
−0.421402 + 0.906874i \(0.638462\pi\)
\(500\) −11.6776 −0.522236
\(501\) 3.00437 0.134226
\(502\) 53.0559 2.36800
\(503\) 2.85168 0.127150 0.0635751 0.997977i \(-0.479750\pi\)
0.0635751 + 0.997977i \(0.479750\pi\)
\(504\) 0.727834 0.0324203
\(505\) −10.8564 −0.483106
\(506\) 0.962839 0.0428034
\(507\) −1.28487 −0.0570632
\(508\) −21.7081 −0.963141
\(509\) 1.44698 0.0641361 0.0320681 0.999486i \(-0.489791\pi\)
0.0320681 + 0.999486i \(0.489791\pi\)
\(510\) 7.65206 0.338839
\(511\) 6.16649 0.272790
\(512\) −27.1292 −1.19895
\(513\) 3.76509 0.166233
\(514\) 14.1274 0.623135
\(515\) −1.12455 −0.0495536
\(516\) −4.33626 −0.190893
\(517\) −3.02992 −0.133256
\(518\) 7.19080 0.315946
\(519\) −14.1731 −0.622128
\(520\) 2.11044 0.0925488
\(521\) −13.0860 −0.573309 −0.286654 0.958034i \(-0.592543\pi\)
−0.286654 + 0.958034i \(0.592543\pi\)
\(522\) 14.8939 0.651888
\(523\) 11.6582 0.509777 0.254888 0.966971i \(-0.417961\pi\)
0.254888 + 0.966971i \(0.417961\pi\)
\(524\) 13.3744 0.584264
\(525\) 4.41142 0.192530
\(526\) −33.8886 −1.47761
\(527\) 3.14978 0.137206
\(528\) 1.36472 0.0593918
\(529\) −20.0643 −0.872360
\(530\) 10.4694 0.454760
\(531\) 9.38143 0.407119
\(532\) −6.08934 −0.264006
\(533\) 32.8110 1.42120
\(534\) 11.1889 0.484192
\(535\) −5.49086 −0.237391
\(536\) 0.371610 0.0160511
\(537\) 16.6373 0.717951
\(538\) −23.2175 −1.00098
\(539\) 0.295463 0.0127265
\(540\) −1.24079 −0.0533949
\(541\) 10.5262 0.452556 0.226278 0.974063i \(-0.427344\pi\)
0.226278 + 0.974063i \(0.427344\pi\)
\(542\) −12.1092 −0.520133
\(543\) −3.39381 −0.145642
\(544\) 38.4360 1.64793
\(545\) 7.32970 0.313970
\(546\) 7.18839 0.307635
\(547\) 15.0590 0.643877 0.321938 0.946761i \(-0.395666\pi\)
0.321938 + 0.946761i \(0.395666\pi\)
\(548\) 6.08072 0.259755
\(549\) 10.0051 0.427009
\(550\) 2.47899 0.105705
\(551\) 29.4842 1.25607
\(552\) 1.24707 0.0530787
\(553\) −1.92887 −0.0820239
\(554\) −44.4874 −1.89009
\(555\) 2.90059 0.123123
\(556\) 31.8617 1.35124
\(557\) 12.1681 0.515579 0.257790 0.966201i \(-0.417006\pi\)
0.257790 + 0.966201i \(0.417006\pi\)
\(558\) −1.14233 −0.0483585
\(559\) 10.1335 0.428600
\(560\) −3.54358 −0.149744
\(561\) −1.54948 −0.0654192
\(562\) 26.4105 1.11406
\(563\) −9.57859 −0.403689 −0.201845 0.979418i \(-0.564694\pi\)
−0.201845 + 0.979418i \(0.564694\pi\)
\(564\) 16.5853 0.698367
\(565\) 2.57438 0.108305
\(566\) −28.6023 −1.20225
\(567\) 1.00000 0.0419961
\(568\) 5.56310 0.233422
\(569\) 12.8056 0.536840 0.268420 0.963302i \(-0.413498\pi\)
0.268420 + 0.963302i \(0.413498\pi\)
\(570\) −5.49377 −0.230109
\(571\) 14.6512 0.613134 0.306567 0.951849i \(-0.400820\pi\)
0.306567 + 0.951849i \(0.400820\pi\)
\(572\) 1.80608 0.0755159
\(573\) 24.8240 1.03704
\(574\) −16.5111 −0.689159
\(575\) 7.55851 0.315211
\(576\) −4.70168 −0.195904
\(577\) 38.7768 1.61430 0.807150 0.590346i \(-0.201009\pi\)
0.807150 + 0.590346i \(0.201009\pi\)
\(578\) −19.9743 −0.830821
\(579\) −1.89762 −0.0788625
\(580\) −9.71654 −0.403457
\(581\) −4.65688 −0.193200
\(582\) 34.2967 1.42164
\(583\) −2.11997 −0.0878000
\(584\) 4.48819 0.185722
\(585\) 2.89961 0.119884
\(586\) −15.1952 −0.627709
\(587\) −14.9209 −0.615853 −0.307926 0.951410i \(-0.599635\pi\)
−0.307926 + 0.951410i \(0.599635\pi\)
\(588\) −1.61732 −0.0666970
\(589\) −2.26137 −0.0931782
\(590\) −13.6888 −0.563557
\(591\) 15.6176 0.642421
\(592\) 17.4632 0.717734
\(593\) 9.73014 0.399569 0.199784 0.979840i \(-0.435976\pi\)
0.199784 + 0.979840i \(0.435976\pi\)
\(594\) 0.561948 0.0230570
\(595\) 4.02332 0.164940
\(596\) 27.5209 1.12730
\(597\) −6.07308 −0.248554
\(598\) 12.3165 0.503661
\(599\) 25.5990 1.04595 0.522974 0.852349i \(-0.324823\pi\)
0.522974 + 0.852349i \(0.324823\pi\)
\(600\) 3.21079 0.131080
\(601\) 25.3901 1.03569 0.517843 0.855476i \(-0.326735\pi\)
0.517843 + 0.855476i \(0.326735\pi\)
\(602\) −5.09934 −0.207833
\(603\) 0.510569 0.0207920
\(604\) 36.0665 1.46752
\(605\) −8.37209 −0.340374
\(606\) −26.9141 −1.09331
\(607\) 29.1121 1.18163 0.590813 0.806809i \(-0.298807\pi\)
0.590813 + 0.806809i \(0.298807\pi\)
\(608\) −27.5950 −1.11912
\(609\) 7.83095 0.317326
\(610\) −14.5988 −0.591090
\(611\) −38.7585 −1.56800
\(612\) 8.48161 0.342849
\(613\) 40.4891 1.63534 0.817670 0.575688i \(-0.195266\pi\)
0.817670 + 0.575688i \(0.195266\pi\)
\(614\) −13.6507 −0.550897
\(615\) −6.66014 −0.268563
\(616\) 0.215048 0.00866454
\(617\) 4.43962 0.178732 0.0893661 0.995999i \(-0.471516\pi\)
0.0893661 + 0.995999i \(0.471516\pi\)
\(618\) −2.78785 −0.112144
\(619\) 12.2384 0.491903 0.245951 0.969282i \(-0.420900\pi\)
0.245951 + 0.969282i \(0.420900\pi\)
\(620\) 0.745235 0.0299294
\(621\) 1.71339 0.0687561
\(622\) 17.7636 0.712254
\(623\) 5.88295 0.235695
\(624\) 17.4574 0.698854
\(625\) 16.5178 0.660711
\(626\) −16.3097 −0.651865
\(627\) 1.11244 0.0444268
\(628\) 9.61682 0.383753
\(629\) −19.8275 −0.790573
\(630\) −1.45913 −0.0581333
\(631\) 37.9108 1.50921 0.754603 0.656182i \(-0.227830\pi\)
0.754603 + 0.656182i \(0.227830\pi\)
\(632\) −1.40390 −0.0558441
\(633\) 0.221019 0.00878472
\(634\) 40.1639 1.59511
\(635\) −10.2974 −0.408641
\(636\) 11.6043 0.460142
\(637\) 3.77953 0.149751
\(638\) 4.40059 0.174221
\(639\) 7.64336 0.302367
\(640\) −4.38531 −0.173345
\(641\) −4.08103 −0.161191 −0.0805955 0.996747i \(-0.525682\pi\)
−0.0805955 + 0.996747i \(0.525682\pi\)
\(642\) −13.6123 −0.537236
\(643\) 23.8611 0.940991 0.470496 0.882402i \(-0.344075\pi\)
0.470496 + 0.882402i \(0.344075\pi\)
\(644\) −2.77110 −0.109197
\(645\) −2.05694 −0.0809920
\(646\) 37.5536 1.47753
\(647\) −34.4655 −1.35498 −0.677489 0.735533i \(-0.736932\pi\)
−0.677489 + 0.735533i \(0.736932\pi\)
\(648\) 0.727834 0.0285920
\(649\) 2.77187 0.108805
\(650\) 31.7110 1.24381
\(651\) −0.600616 −0.0235400
\(652\) 12.9901 0.508732
\(653\) 31.9447 1.25009 0.625046 0.780588i \(-0.285080\pi\)
0.625046 + 0.780588i \(0.285080\pi\)
\(654\) 18.1710 0.710541
\(655\) 6.34427 0.247891
\(656\) −40.0980 −1.56556
\(657\) 6.16649 0.240578
\(658\) 19.5039 0.760341
\(659\) −11.1976 −0.436196 −0.218098 0.975927i \(-0.569985\pi\)
−0.218098 + 0.975927i \(0.569985\pi\)
\(660\) −0.366606 −0.0142701
\(661\) −31.5028 −1.22532 −0.612658 0.790348i \(-0.709900\pi\)
−0.612658 + 0.790348i \(0.709900\pi\)
\(662\) 22.6791 0.881449
\(663\) −19.8208 −0.769777
\(664\) −3.38944 −0.131536
\(665\) −2.88853 −0.112012
\(666\) 7.19080 0.278638
\(667\) 13.4175 0.519528
\(668\) −4.85903 −0.188001
\(669\) −2.40462 −0.0929679
\(670\) −0.744988 −0.0287814
\(671\) 2.95615 0.114121
\(672\) −7.32917 −0.282729
\(673\) 6.63070 0.255595 0.127797 0.991800i \(-0.459209\pi\)
0.127797 + 0.991800i \(0.459209\pi\)
\(674\) 39.4666 1.52020
\(675\) 4.41142 0.169796
\(676\) 2.07804 0.0799248
\(677\) −6.09030 −0.234069 −0.117035 0.993128i \(-0.537339\pi\)
−0.117035 + 0.993128i \(0.537339\pi\)
\(678\) 6.38210 0.245103
\(679\) 18.0326 0.692029
\(680\) 2.92831 0.112296
\(681\) −19.0248 −0.729033
\(682\) −0.337515 −0.0129241
\(683\) 26.4849 1.01342 0.506709 0.862117i \(-0.330862\pi\)
0.506709 + 0.862117i \(0.330862\pi\)
\(684\) −6.08934 −0.232832
\(685\) 2.88444 0.110209
\(686\) −1.90192 −0.0726158
\(687\) −23.2092 −0.885488
\(688\) −12.3840 −0.472135
\(689\) −27.1184 −1.03313
\(690\) −2.50007 −0.0951760
\(691\) −26.3606 −1.00281 −0.501403 0.865214i \(-0.667183\pi\)
−0.501403 + 0.865214i \(0.667183\pi\)
\(692\) 22.9223 0.871376
\(693\) 0.295463 0.0112237
\(694\) −45.2563 −1.71790
\(695\) 15.1139 0.573302
\(696\) 5.69964 0.216044
\(697\) 45.5266 1.72444
\(698\) −52.4631 −1.98576
\(699\) −5.31731 −0.201119
\(700\) −7.13467 −0.269665
\(701\) 0.142946 0.00539901 0.00269951 0.999996i \(-0.499141\pi\)
0.00269951 + 0.999996i \(0.499141\pi\)
\(702\) 7.18839 0.271308
\(703\) 14.2351 0.536886
\(704\) −1.38917 −0.0523565
\(705\) 7.86738 0.296303
\(706\) −40.1575 −1.51135
\(707\) −14.1510 −0.532202
\(708\) −15.1727 −0.570227
\(709\) 12.7183 0.477644 0.238822 0.971063i \(-0.423239\pi\)
0.238822 + 0.971063i \(0.423239\pi\)
\(710\) −11.1527 −0.418552
\(711\) −1.92887 −0.0723383
\(712\) 4.28181 0.160468
\(713\) −1.02909 −0.0385398
\(714\) 9.97417 0.373274
\(715\) 0.856728 0.0320398
\(716\) −26.9077 −1.00559
\(717\) −9.26093 −0.345856
\(718\) 9.85377 0.367739
\(719\) 1.48639 0.0554329 0.0277164 0.999616i \(-0.491176\pi\)
0.0277164 + 0.999616i \(0.491176\pi\)
\(720\) −3.54358 −0.132061
\(721\) −1.46581 −0.0545895
\(722\) 9.17508 0.341461
\(723\) 22.2302 0.826751
\(724\) 5.48886 0.203992
\(725\) 34.5457 1.28299
\(726\) −20.7551 −0.770295
\(727\) 35.5619 1.31892 0.659458 0.751741i \(-0.270786\pi\)
0.659458 + 0.751741i \(0.270786\pi\)
\(728\) 2.75087 0.101954
\(729\) 1.00000 0.0370370
\(730\) −8.99774 −0.333021
\(731\) 14.0606 0.520050
\(732\) −16.1815 −0.598085
\(733\) 24.3035 0.897671 0.448835 0.893615i \(-0.351839\pi\)
0.448835 + 0.893615i \(0.351839\pi\)
\(734\) 61.1839 2.25834
\(735\) −0.767188 −0.0282981
\(736\) −12.5578 −0.462885
\(737\) 0.150854 0.00555679
\(738\) −16.5111 −0.607781
\(739\) −5.99935 −0.220690 −0.110345 0.993893i \(-0.535196\pi\)
−0.110345 + 0.993893i \(0.535196\pi\)
\(740\) −4.69117 −0.172451
\(741\) 14.2303 0.522762
\(742\) 13.6464 0.500976
\(743\) −5.87179 −0.215415 −0.107708 0.994183i \(-0.534351\pi\)
−0.107708 + 0.994183i \(0.534351\pi\)
\(744\) −0.437149 −0.0160266
\(745\) 13.0548 0.478290
\(746\) 26.0452 0.953582
\(747\) −4.65688 −0.170386
\(748\) 2.50600 0.0916286
\(749\) −7.15713 −0.261516
\(750\) −13.7325 −0.501441
\(751\) −29.3366 −1.07051 −0.535254 0.844691i \(-0.679784\pi\)
−0.535254 + 0.844691i \(0.679784\pi\)
\(752\) 47.3662 1.72727
\(753\) 27.8959 1.01658
\(754\) 56.2919 2.05003
\(755\) 17.1084 0.622640
\(756\) −1.61732 −0.0588212
\(757\) 24.4811 0.889780 0.444890 0.895585i \(-0.353243\pi\)
0.444890 + 0.895585i \(0.353243\pi\)
\(758\) −26.0289 −0.945414
\(759\) 0.506245 0.0183755
\(760\) −2.10237 −0.0762610
\(761\) 50.0059 1.81271 0.906356 0.422515i \(-0.138853\pi\)
0.906356 + 0.422515i \(0.138853\pi\)
\(762\) −25.5282 −0.924789
\(763\) 9.55398 0.345877
\(764\) −40.1483 −1.45251
\(765\) 4.02332 0.145464
\(766\) 1.90192 0.0687193
\(767\) 35.4574 1.28029
\(768\) −20.2749 −0.731609
\(769\) −35.6544 −1.28573 −0.642866 0.765979i \(-0.722255\pi\)
−0.642866 + 0.765979i \(0.722255\pi\)
\(770\) −0.431120 −0.0155365
\(771\) 7.42797 0.267512
\(772\) 3.06906 0.110458
\(773\) −14.7306 −0.529821 −0.264911 0.964273i \(-0.585342\pi\)
−0.264911 + 0.964273i \(0.585342\pi\)
\(774\) −5.09934 −0.183292
\(775\) −2.64957 −0.0951753
\(776\) 13.1248 0.471152
\(777\) 3.78080 0.135636
\(778\) −14.9066 −0.534426
\(779\) −32.6856 −1.17108
\(780\) −4.68959 −0.167914
\(781\) 2.25833 0.0808094
\(782\) 17.0897 0.611126
\(783\) 7.83095 0.279855
\(784\) −4.61892 −0.164961
\(785\) 4.56182 0.162818
\(786\) 15.7280 0.560998
\(787\) −3.71374 −0.132381 −0.0661903 0.997807i \(-0.521084\pi\)
−0.0661903 + 0.997807i \(0.521084\pi\)
\(788\) −25.2586 −0.899800
\(789\) −17.8180 −0.634339
\(790\) 2.81448 0.100135
\(791\) 3.35560 0.119311
\(792\) 0.215048 0.00764141
\(793\) 37.8148 1.34284
\(794\) −48.6233 −1.72558
\(795\) 5.50462 0.195229
\(796\) 9.82209 0.348135
\(797\) 21.3671 0.756860 0.378430 0.925630i \(-0.376464\pi\)
0.378430 + 0.925630i \(0.376464\pi\)
\(798\) −7.16091 −0.253494
\(799\) −53.7789 −1.90256
\(800\) −32.3321 −1.14311
\(801\) 5.88295 0.207864
\(802\) 10.1318 0.357766
\(803\) 1.82197 0.0642960
\(804\) −0.825752 −0.0291220
\(805\) −1.31449 −0.0463299
\(806\) −4.31746 −0.152076
\(807\) −12.2074 −0.429721
\(808\) −10.2996 −0.362337
\(809\) −2.55237 −0.0897365 −0.0448683 0.998993i \(-0.514287\pi\)
−0.0448683 + 0.998993i \(0.514287\pi\)
\(810\) −1.45913 −0.0512687
\(811\) 7.37838 0.259090 0.129545 0.991574i \(-0.458648\pi\)
0.129545 + 0.991574i \(0.458648\pi\)
\(812\) −12.6651 −0.444459
\(813\) −6.36680 −0.223293
\(814\) 2.12462 0.0744678
\(815\) 6.16197 0.215844
\(816\) 24.2228 0.847967
\(817\) −10.0948 −0.353171
\(818\) −2.78679 −0.0974377
\(819\) 3.77953 0.132068
\(820\) 10.7716 0.376159
\(821\) 8.86130 0.309262 0.154631 0.987972i \(-0.450581\pi\)
0.154631 + 0.987972i \(0.450581\pi\)
\(822\) 7.15077 0.249412
\(823\) 26.1096 0.910122 0.455061 0.890460i \(-0.349617\pi\)
0.455061 + 0.890460i \(0.349617\pi\)
\(824\) −1.06687 −0.0371660
\(825\) 1.30341 0.0453790
\(826\) −17.8428 −0.620829
\(827\) 39.7746 1.38310 0.691549 0.722329i \(-0.256928\pi\)
0.691549 + 0.722329i \(0.256928\pi\)
\(828\) −2.77110 −0.0963024
\(829\) 12.4044 0.430822 0.215411 0.976523i \(-0.430891\pi\)
0.215411 + 0.976523i \(0.430891\pi\)
\(830\) 6.79501 0.235858
\(831\) −23.3907 −0.811415
\(832\) −17.7702 −0.616070
\(833\) 5.24425 0.181702
\(834\) 37.4686 1.29743
\(835\) −2.30492 −0.0797650
\(836\) −1.79918 −0.0622258
\(837\) −0.600616 −0.0207603
\(838\) 44.0956 1.52326
\(839\) 24.7912 0.855888 0.427944 0.903805i \(-0.359238\pi\)
0.427944 + 0.903805i \(0.359238\pi\)
\(840\) −0.558386 −0.0192661
\(841\) 32.3238 1.11462
\(842\) −63.2927 −2.18121
\(843\) 13.8862 0.478266
\(844\) −0.357458 −0.0123042
\(845\) 0.985738 0.0339104
\(846\) 19.5039 0.670558
\(847\) −10.9127 −0.374965
\(848\) 33.1410 1.13807
\(849\) −15.0386 −0.516124
\(850\) 44.0003 1.50920
\(851\) 6.47801 0.222063
\(852\) −12.3617 −0.423506
\(853\) 19.6021 0.671161 0.335581 0.942011i \(-0.391067\pi\)
0.335581 + 0.942011i \(0.391067\pi\)
\(854\) −19.0290 −0.651160
\(855\) −2.88853 −0.0987856
\(856\) −5.20921 −0.178047
\(857\) −53.8625 −1.83991 −0.919954 0.392027i \(-0.871774\pi\)
−0.919954 + 0.392027i \(0.871774\pi\)
\(858\) 2.12390 0.0725088
\(859\) −30.7683 −1.04980 −0.524900 0.851164i \(-0.675897\pi\)
−0.524900 + 0.851164i \(0.675897\pi\)
\(860\) 3.32673 0.113440
\(861\) −8.68124 −0.295856
\(862\) 6.83561 0.232822
\(863\) −26.2585 −0.893851 −0.446926 0.894571i \(-0.647481\pi\)
−0.446926 + 0.894571i \(0.647481\pi\)
\(864\) −7.32917 −0.249343
\(865\) 10.8734 0.369707
\(866\) 22.0195 0.748254
\(867\) −10.5022 −0.356672
\(868\) 0.971386 0.0329710
\(869\) −0.569910 −0.0193329
\(870\) −11.4264 −0.387391
\(871\) 1.92971 0.0653858
\(872\) 6.95372 0.235483
\(873\) 18.0326 0.610312
\(874\) −12.2695 −0.415021
\(875\) −7.22033 −0.244092
\(876\) −9.97317 −0.336962
\(877\) −9.51226 −0.321206 −0.160603 0.987019i \(-0.551344\pi\)
−0.160603 + 0.987019i \(0.551344\pi\)
\(878\) 34.1454 1.15235
\(879\) −7.98940 −0.269476
\(880\) −1.04700 −0.0352942
\(881\) 25.2562 0.850901 0.425451 0.904982i \(-0.360116\pi\)
0.425451 + 0.904982i \(0.360116\pi\)
\(882\) −1.90192 −0.0640411
\(883\) 5.80893 0.195486 0.0977431 0.995212i \(-0.468838\pi\)
0.0977431 + 0.995212i \(0.468838\pi\)
\(884\) 32.0565 1.07818
\(885\) −7.19732 −0.241935
\(886\) 31.8827 1.07112
\(887\) 22.1020 0.742113 0.371057 0.928610i \(-0.378996\pi\)
0.371057 + 0.928610i \(0.378996\pi\)
\(888\) 2.75180 0.0923444
\(889\) −13.4223 −0.450169
\(890\) −8.58401 −0.287737
\(891\) 0.295463 0.00989839
\(892\) 3.88903 0.130214
\(893\) 38.6103 1.29205
\(894\) 32.3639 1.08241
\(895\) −12.7639 −0.426650
\(896\) −5.71609 −0.190961
\(897\) 6.47583 0.216222
\(898\) 51.5315 1.71963
\(899\) −4.70339 −0.156867
\(900\) −7.13467 −0.237822
\(901\) −37.6278 −1.25356
\(902\) −4.87841 −0.162433
\(903\) −2.68115 −0.0892229
\(904\) 2.44232 0.0812305
\(905\) 2.60369 0.0865495
\(906\) 42.4133 1.40909
\(907\) −11.3382 −0.376478 −0.188239 0.982123i \(-0.560278\pi\)
−0.188239 + 0.982123i \(0.560278\pi\)
\(908\) 30.7692 1.02111
\(909\) −14.1510 −0.469358
\(910\) −5.51484 −0.182815
\(911\) 0.809435 0.0268178 0.0134089 0.999910i \(-0.495732\pi\)
0.0134089 + 0.999910i \(0.495732\pi\)
\(912\) −17.3906 −0.575862
\(913\) −1.37594 −0.0455369
\(914\) −12.5935 −0.416557
\(915\) −7.67582 −0.253755
\(916\) 37.5367 1.24025
\(917\) 8.26951 0.273083
\(918\) 9.97417 0.329197
\(919\) −12.4541 −0.410821 −0.205411 0.978676i \(-0.565853\pi\)
−0.205411 + 0.978676i \(0.565853\pi\)
\(920\) −0.956735 −0.0315426
\(921\) −7.17730 −0.236500
\(922\) −61.8868 −2.03813
\(923\) 28.8883 0.950871
\(924\) −0.477857 −0.0157204
\(925\) 16.6787 0.548393
\(926\) 37.8551 1.24399
\(927\) −1.46581 −0.0481434
\(928\) −57.3944 −1.88406
\(929\) −42.2794 −1.38714 −0.693571 0.720389i \(-0.743963\pi\)
−0.693571 + 0.720389i \(0.743963\pi\)
\(930\) 0.876378 0.0287376
\(931\) −3.76509 −0.123396
\(932\) 8.59978 0.281695
\(933\) 9.33978 0.305771
\(934\) 36.1719 1.18358
\(935\) 1.18874 0.0388761
\(936\) 2.75087 0.0899151
\(937\) −16.6054 −0.542474 −0.271237 0.962513i \(-0.587433\pi\)
−0.271237 + 0.962513i \(0.587433\pi\)
\(938\) −0.971064 −0.0317064
\(939\) −8.57535 −0.279846
\(940\) −12.7240 −0.415012
\(941\) 19.4063 0.632626 0.316313 0.948655i \(-0.397555\pi\)
0.316313 + 0.948655i \(0.397555\pi\)
\(942\) 11.3091 0.368472
\(943\) −14.8744 −0.484377
\(944\) −43.3321 −1.41034
\(945\) −0.767188 −0.0249566
\(946\) −1.50667 −0.0489859
\(947\) −46.2388 −1.50256 −0.751280 0.659984i \(-0.770563\pi\)
−0.751280 + 0.659984i \(0.770563\pi\)
\(948\) 3.11959 0.101320
\(949\) 23.3065 0.756560
\(950\) −31.5898 −1.02491
\(951\) 21.1175 0.684783
\(952\) 3.81695 0.123708
\(953\) 38.1796 1.23676 0.618379 0.785880i \(-0.287790\pi\)
0.618379 + 0.785880i \(0.287790\pi\)
\(954\) 13.6464 0.441819
\(955\) −19.0447 −0.616271
\(956\) 14.9779 0.484418
\(957\) 2.31376 0.0747932
\(958\) −60.1233 −1.94250
\(959\) 3.75976 0.121409
\(960\) 3.60707 0.116418
\(961\) −30.6393 −0.988363
\(962\) 27.1779 0.876250
\(963\) −7.15713 −0.230635
\(964\) −35.9533 −1.15798
\(965\) 1.45583 0.0468649
\(966\) −3.25875 −0.104848
\(967\) −49.8459 −1.60293 −0.801467 0.598038i \(-0.795947\pi\)
−0.801467 + 0.598038i \(0.795947\pi\)
\(968\) −7.94264 −0.255286
\(969\) 19.7451 0.634303
\(970\) −26.3120 −0.844828
\(971\) −35.2170 −1.13017 −0.565084 0.825033i \(-0.691156\pi\)
−0.565084 + 0.825033i \(0.691156\pi\)
\(972\) −1.61732 −0.0518755
\(973\) 19.7004 0.631565
\(974\) −22.9787 −0.736285
\(975\) 16.6731 0.533967
\(976\) −46.2130 −1.47924
\(977\) −14.0709 −0.450166 −0.225083 0.974340i \(-0.572265\pi\)
−0.225083 + 0.974340i \(0.572265\pi\)
\(978\) 15.2761 0.488474
\(979\) 1.73819 0.0555529
\(980\) 1.24079 0.0396354
\(981\) 9.55398 0.305035
\(982\) 10.5590 0.336951
\(983\) −23.1123 −0.737168 −0.368584 0.929595i \(-0.620157\pi\)
−0.368584 + 0.929595i \(0.620157\pi\)
\(984\) −6.31851 −0.201427
\(985\) −11.9816 −0.381766
\(986\) 78.1072 2.48744
\(987\) 10.2548 0.326415
\(988\) −23.0149 −0.732201
\(989\) −4.59386 −0.146076
\(990\) −0.431120 −0.0137019
\(991\) −40.0720 −1.27293 −0.636465 0.771306i \(-0.719604\pi\)
−0.636465 + 0.771306i \(0.719604\pi\)
\(992\) 4.40201 0.139764
\(993\) 11.9243 0.378406
\(994\) −14.5371 −0.461088
\(995\) 4.65919 0.147706
\(996\) 7.53166 0.238650
\(997\) 7.16819 0.227019 0.113509 0.993537i \(-0.463791\pi\)
0.113509 + 0.993537i \(0.463791\pi\)
\(998\) 35.8072 1.13346
\(999\) 3.78080 0.119619
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 \(a_p\))