Properties

Label 8042.2.a.a.1.2
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 1
Dimension 67
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(1\)
Dimension: \(67\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-3.08937 q^{3}\) \(+1.00000 q^{4}\) \(-1.29634 q^{5}\) \(-3.08937 q^{6}\) \(+4.06006 q^{7}\) \(+1.00000 q^{8}\) \(+6.54422 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-3.08937 q^{3}\) \(+1.00000 q^{4}\) \(-1.29634 q^{5}\) \(-3.08937 q^{6}\) \(+4.06006 q^{7}\) \(+1.00000 q^{8}\) \(+6.54422 q^{9}\) \(-1.29634 q^{10}\) \(+2.11310 q^{11}\) \(-3.08937 q^{12}\) \(+1.62348 q^{13}\) \(+4.06006 q^{14}\) \(+4.00488 q^{15}\) \(+1.00000 q^{16}\) \(-2.05899 q^{17}\) \(+6.54422 q^{18}\) \(+1.37650 q^{19}\) \(-1.29634 q^{20}\) \(-12.5430 q^{21}\) \(+2.11310 q^{22}\) \(-2.66845 q^{23}\) \(-3.08937 q^{24}\) \(-3.31950 q^{25}\) \(+1.62348 q^{26}\) \(-10.9494 q^{27}\) \(+4.06006 q^{28}\) \(-1.01589 q^{29}\) \(+4.00488 q^{30}\) \(-3.05425 q^{31}\) \(+1.00000 q^{32}\) \(-6.52814 q^{33}\) \(-2.05899 q^{34}\) \(-5.26323 q^{35}\) \(+6.54422 q^{36}\) \(-7.60060 q^{37}\) \(+1.37650 q^{38}\) \(-5.01553 q^{39}\) \(-1.29634 q^{40}\) \(+5.22545 q^{41}\) \(-12.5430 q^{42}\) \(-9.75420 q^{43}\) \(+2.11310 q^{44}\) \(-8.48354 q^{45}\) \(-2.66845 q^{46}\) \(-11.0245 q^{47}\) \(-3.08937 q^{48}\) \(+9.48407 q^{49}\) \(-3.31950 q^{50}\) \(+6.36097 q^{51}\) \(+1.62348 q^{52}\) \(-6.35741 q^{53}\) \(-10.9494 q^{54}\) \(-2.73930 q^{55}\) \(+4.06006 q^{56}\) \(-4.25252 q^{57}\) \(-1.01589 q^{58}\) \(+10.0360 q^{59}\) \(+4.00488 q^{60}\) \(+3.96562 q^{61}\) \(-3.05425 q^{62}\) \(+26.5699 q^{63}\) \(+1.00000 q^{64}\) \(-2.10458 q^{65}\) \(-6.52814 q^{66}\) \(-8.49862 q^{67}\) \(-2.05899 q^{68}\) \(+8.24383 q^{69}\) \(-5.26323 q^{70}\) \(-12.7609 q^{71}\) \(+6.54422 q^{72}\) \(-14.3477 q^{73}\) \(-7.60060 q^{74}\) \(+10.2552 q^{75}\) \(+1.37650 q^{76}\) \(+8.57930 q^{77}\) \(-5.01553 q^{78}\) \(+4.45222 q^{79}\) \(-1.29634 q^{80}\) \(+14.1941 q^{81}\) \(+5.22545 q^{82}\) \(+13.3840 q^{83}\) \(-12.5430 q^{84}\) \(+2.66915 q^{85}\) \(-9.75420 q^{86}\) \(+3.13847 q^{87}\) \(+2.11310 q^{88}\) \(+1.76396 q^{89}\) \(-8.48354 q^{90}\) \(+6.59141 q^{91}\) \(-2.66845 q^{92}\) \(+9.43570 q^{93}\) \(-11.0245 q^{94}\) \(-1.78442 q^{95}\) \(-3.08937 q^{96}\) \(-6.28206 q^{97}\) \(+9.48407 q^{98}\) \(+13.8286 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −3.08937 −1.78365 −0.891825 0.452381i \(-0.850575\pi\)
−0.891825 + 0.452381i \(0.850575\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.29634 −0.579742 −0.289871 0.957066i \(-0.593612\pi\)
−0.289871 + 0.957066i \(0.593612\pi\)
\(6\) −3.08937 −1.26123
\(7\) 4.06006 1.53456 0.767279 0.641314i \(-0.221610\pi\)
0.767279 + 0.641314i \(0.221610\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.54422 2.18141
\(10\) −1.29634 −0.409939
\(11\) 2.11310 0.637123 0.318561 0.947902i \(-0.396800\pi\)
0.318561 + 0.947902i \(0.396800\pi\)
\(12\) −3.08937 −0.891825
\(13\) 1.62348 0.450272 0.225136 0.974327i \(-0.427717\pi\)
0.225136 + 0.974327i \(0.427717\pi\)
\(14\) 4.06006 1.08510
\(15\) 4.00488 1.03406
\(16\) 1.00000 0.250000
\(17\) −2.05899 −0.499377 −0.249689 0.968326i \(-0.580328\pi\)
−0.249689 + 0.968326i \(0.580328\pi\)
\(18\) 6.54422 1.54249
\(19\) 1.37650 0.315791 0.157896 0.987456i \(-0.449529\pi\)
0.157896 + 0.987456i \(0.449529\pi\)
\(20\) −1.29634 −0.289871
\(21\) −12.5430 −2.73711
\(22\) 2.11310 0.450514
\(23\) −2.66845 −0.556410 −0.278205 0.960522i \(-0.589740\pi\)
−0.278205 + 0.960522i \(0.589740\pi\)
\(24\) −3.08937 −0.630615
\(25\) −3.31950 −0.663899
\(26\) 1.62348 0.318390
\(27\) −10.9494 −2.10721
\(28\) 4.06006 0.767279
\(29\) −1.01589 −0.188647 −0.0943234 0.995542i \(-0.530069\pi\)
−0.0943234 + 0.995542i \(0.530069\pi\)
\(30\) 4.00488 0.731188
\(31\) −3.05425 −0.548559 −0.274280 0.961650i \(-0.588439\pi\)
−0.274280 + 0.961650i \(0.588439\pi\)
\(32\) 1.00000 0.176777
\(33\) −6.52814 −1.13640
\(34\) −2.05899 −0.353113
\(35\) −5.26323 −0.889647
\(36\) 6.54422 1.09070
\(37\) −7.60060 −1.24953 −0.624765 0.780813i \(-0.714805\pi\)
−0.624765 + 0.780813i \(0.714805\pi\)
\(38\) 1.37650 0.223298
\(39\) −5.01553 −0.803127
\(40\) −1.29634 −0.204970
\(41\) 5.22545 0.816079 0.408039 0.912964i \(-0.366213\pi\)
0.408039 + 0.912964i \(0.366213\pi\)
\(42\) −12.5430 −1.93543
\(43\) −9.75420 −1.48750 −0.743751 0.668457i \(-0.766955\pi\)
−0.743751 + 0.668457i \(0.766955\pi\)
\(44\) 2.11310 0.318561
\(45\) −8.48354 −1.26465
\(46\) −2.66845 −0.393441
\(47\) −11.0245 −1.60809 −0.804047 0.594565i \(-0.797324\pi\)
−0.804047 + 0.594565i \(0.797324\pi\)
\(48\) −3.08937 −0.445912
\(49\) 9.48407 1.35487
\(50\) −3.31950 −0.469448
\(51\) 6.36097 0.890714
\(52\) 1.62348 0.225136
\(53\) −6.35741 −0.873257 −0.436629 0.899642i \(-0.643828\pi\)
−0.436629 + 0.899642i \(0.643828\pi\)
\(54\) −10.9494 −1.49002
\(55\) −2.73930 −0.369367
\(56\) 4.06006 0.542548
\(57\) −4.25252 −0.563261
\(58\) −1.01589 −0.133393
\(59\) 10.0360 1.30658 0.653289 0.757108i \(-0.273388\pi\)
0.653289 + 0.757108i \(0.273388\pi\)
\(60\) 4.00488 0.517028
\(61\) 3.96562 0.507745 0.253873 0.967238i \(-0.418296\pi\)
0.253873 + 0.967238i \(0.418296\pi\)
\(62\) −3.05425 −0.387890
\(63\) 26.5699 3.34749
\(64\) 1.00000 0.125000
\(65\) −2.10458 −0.261041
\(66\) −6.52814 −0.803559
\(67\) −8.49862 −1.03827 −0.519136 0.854692i \(-0.673746\pi\)
−0.519136 + 0.854692i \(0.673746\pi\)
\(68\) −2.05899 −0.249689
\(69\) 8.24383 0.992441
\(70\) −5.26323 −0.629076
\(71\) −12.7609 −1.51444 −0.757218 0.653162i \(-0.773442\pi\)
−0.757218 + 0.653162i \(0.773442\pi\)
\(72\) 6.54422 0.771243
\(73\) −14.3477 −1.67928 −0.839638 0.543146i \(-0.817233\pi\)
−0.839638 + 0.543146i \(0.817233\pi\)
\(74\) −7.60060 −0.883552
\(75\) 10.2552 1.18416
\(76\) 1.37650 0.157896
\(77\) 8.57930 0.977702
\(78\) −5.01553 −0.567896
\(79\) 4.45222 0.500914 0.250457 0.968128i \(-0.419419\pi\)
0.250457 + 0.968128i \(0.419419\pi\)
\(80\) −1.29634 −0.144935
\(81\) 14.1941 1.57712
\(82\) 5.22545 0.577055
\(83\) 13.3840 1.46909 0.734545 0.678560i \(-0.237396\pi\)
0.734545 + 0.678560i \(0.237396\pi\)
\(84\) −12.5430 −1.36856
\(85\) 2.66915 0.289510
\(86\) −9.75420 −1.05182
\(87\) 3.13847 0.336480
\(88\) 2.11310 0.225257
\(89\) 1.76396 0.186980 0.0934899 0.995620i \(-0.470198\pi\)
0.0934899 + 0.995620i \(0.470198\pi\)
\(90\) −8.48354 −0.894244
\(91\) 6.59141 0.690968
\(92\) −2.66845 −0.278205
\(93\) 9.43570 0.978437
\(94\) −11.0245 −1.13709
\(95\) −1.78442 −0.183077
\(96\) −3.08937 −0.315308
\(97\) −6.28206 −0.637846 −0.318923 0.947781i \(-0.603321\pi\)
−0.318923 + 0.947781i \(0.603321\pi\)
\(98\) 9.48407 0.958036
\(99\) 13.8286 1.38982
\(100\) −3.31950 −0.331950
\(101\) −3.10164 −0.308625 −0.154312 0.988022i \(-0.549316\pi\)
−0.154312 + 0.988022i \(0.549316\pi\)
\(102\) 6.36097 0.629830
\(103\) −15.1890 −1.49661 −0.748307 0.663352i \(-0.769133\pi\)
−0.748307 + 0.663352i \(0.769133\pi\)
\(104\) 1.62348 0.159195
\(105\) 16.2601 1.58682
\(106\) −6.35741 −0.617486
\(107\) −10.0387 −0.970476 −0.485238 0.874382i \(-0.661267\pi\)
−0.485238 + 0.874382i \(0.661267\pi\)
\(108\) −10.9494 −1.05361
\(109\) 20.2167 1.93641 0.968207 0.250152i \(-0.0804805\pi\)
0.968207 + 0.250152i \(0.0804805\pi\)
\(110\) −2.73930 −0.261182
\(111\) 23.4811 2.22872
\(112\) 4.06006 0.383639
\(113\) −5.84705 −0.550044 −0.275022 0.961438i \(-0.588685\pi\)
−0.275022 + 0.961438i \(0.588685\pi\)
\(114\) −4.25252 −0.398285
\(115\) 3.45922 0.322574
\(116\) −1.01589 −0.0943234
\(117\) 10.6244 0.982225
\(118\) 10.0360 0.923891
\(119\) −8.35960 −0.766323
\(120\) 4.00488 0.365594
\(121\) −6.53482 −0.594074
\(122\) 3.96562 0.359030
\(123\) −16.1434 −1.45560
\(124\) −3.05425 −0.274280
\(125\) 10.7849 0.964632
\(126\) 26.5699 2.36703
\(127\) −3.85113 −0.341732 −0.170866 0.985294i \(-0.554657\pi\)
−0.170866 + 0.985294i \(0.554657\pi\)
\(128\) 1.00000 0.0883883
\(129\) 30.1344 2.65318
\(130\) −2.10458 −0.184584
\(131\) 10.6395 0.929581 0.464791 0.885421i \(-0.346130\pi\)
0.464791 + 0.885421i \(0.346130\pi\)
\(132\) −6.52814 −0.568202
\(133\) 5.58868 0.484600
\(134\) −8.49862 −0.734169
\(135\) 14.1942 1.22164
\(136\) −2.05899 −0.176557
\(137\) 21.6958 1.85360 0.926800 0.375555i \(-0.122548\pi\)
0.926800 + 0.375555i \(0.122548\pi\)
\(138\) 8.24383 0.701762
\(139\) 4.00382 0.339599 0.169800 0.985479i \(-0.445688\pi\)
0.169800 + 0.985479i \(0.445688\pi\)
\(140\) −5.26323 −0.444824
\(141\) 34.0589 2.86828
\(142\) −12.7609 −1.07087
\(143\) 3.43057 0.286878
\(144\) 6.54422 0.545351
\(145\) 1.31695 0.109366
\(146\) −14.3477 −1.18743
\(147\) −29.2998 −2.41661
\(148\) −7.60060 −0.624765
\(149\) −3.27870 −0.268602 −0.134301 0.990941i \(-0.542879\pi\)
−0.134301 + 0.990941i \(0.542879\pi\)
\(150\) 10.2552 0.837330
\(151\) −7.08842 −0.576848 −0.288424 0.957503i \(-0.593131\pi\)
−0.288424 + 0.957503i \(0.593131\pi\)
\(152\) 1.37650 0.111649
\(153\) −13.4744 −1.08934
\(154\) 8.57930 0.691340
\(155\) 3.95935 0.318023
\(156\) −5.01553 −0.401563
\(157\) 2.27988 0.181954 0.0909770 0.995853i \(-0.471001\pi\)
0.0909770 + 0.995853i \(0.471001\pi\)
\(158\) 4.45222 0.354200
\(159\) 19.6404 1.55758
\(160\) −1.29634 −0.102485
\(161\) −10.8341 −0.853844
\(162\) 14.1941 1.11519
\(163\) 6.05792 0.474493 0.237247 0.971449i \(-0.423755\pi\)
0.237247 + 0.971449i \(0.423755\pi\)
\(164\) 5.22545 0.408039
\(165\) 8.46271 0.658821
\(166\) 13.3840 1.03880
\(167\) −5.10081 −0.394713 −0.197356 0.980332i \(-0.563236\pi\)
−0.197356 + 0.980332i \(0.563236\pi\)
\(168\) −12.5430 −0.967716
\(169\) −10.3643 −0.797255
\(170\) 2.66915 0.204714
\(171\) 9.00812 0.688868
\(172\) −9.75420 −0.743751
\(173\) −1.16851 −0.0888403 −0.0444202 0.999013i \(-0.514144\pi\)
−0.0444202 + 0.999013i \(0.514144\pi\)
\(174\) 3.13847 0.237927
\(175\) −13.4774 −1.01879
\(176\) 2.11310 0.159281
\(177\) −31.0050 −2.33048
\(178\) 1.76396 0.132215
\(179\) −7.18255 −0.536849 −0.268424 0.963301i \(-0.586503\pi\)
−0.268424 + 0.963301i \(0.586503\pi\)
\(180\) −8.48354 −0.632326
\(181\) −8.04614 −0.598065 −0.299033 0.954243i \(-0.596664\pi\)
−0.299033 + 0.954243i \(0.596664\pi\)
\(182\) 6.59141 0.488588
\(183\) −12.2513 −0.905639
\(184\) −2.66845 −0.196721
\(185\) 9.85298 0.724405
\(186\) 9.43570 0.691859
\(187\) −4.35084 −0.318165
\(188\) −11.0245 −0.804047
\(189\) −44.4552 −3.23364
\(190\) −1.78442 −0.129455
\(191\) −0.946898 −0.0685151 −0.0342576 0.999413i \(-0.510907\pi\)
−0.0342576 + 0.999413i \(0.510907\pi\)
\(192\) −3.08937 −0.222956
\(193\) −8.90872 −0.641263 −0.320632 0.947204i \(-0.603895\pi\)
−0.320632 + 0.947204i \(0.603895\pi\)
\(194\) −6.28206 −0.451025
\(195\) 6.50184 0.465606
\(196\) 9.48407 0.677434
\(197\) −15.2659 −1.08765 −0.543826 0.839198i \(-0.683025\pi\)
−0.543826 + 0.839198i \(0.683025\pi\)
\(198\) 13.8286 0.982753
\(199\) 13.1743 0.933900 0.466950 0.884284i \(-0.345353\pi\)
0.466950 + 0.884284i \(0.345353\pi\)
\(200\) −3.31950 −0.234724
\(201\) 26.2554 1.85191
\(202\) −3.10164 −0.218231
\(203\) −4.12459 −0.289489
\(204\) 6.36097 0.445357
\(205\) −6.77398 −0.473115
\(206\) −15.1890 −1.05827
\(207\) −17.4629 −1.21376
\(208\) 1.62348 0.112568
\(209\) 2.90868 0.201198
\(210\) 16.2601 1.12205
\(211\) −0.619013 −0.0426146 −0.0213073 0.999773i \(-0.506783\pi\)
−0.0213073 + 0.999773i \(0.506783\pi\)
\(212\) −6.35741 −0.436629
\(213\) 39.4231 2.70122
\(214\) −10.0387 −0.686230
\(215\) 12.6448 0.862367
\(216\) −10.9494 −0.745012
\(217\) −12.4004 −0.841796
\(218\) 20.2167 1.36925
\(219\) 44.3255 2.99524
\(220\) −2.73930 −0.184683
\(221\) −3.34272 −0.224855
\(222\) 23.4811 1.57595
\(223\) −0.204315 −0.0136820 −0.00684098 0.999977i \(-0.502178\pi\)
−0.00684098 + 0.999977i \(0.502178\pi\)
\(224\) 4.06006 0.271274
\(225\) −21.7235 −1.44823
\(226\) −5.84705 −0.388940
\(227\) 0.393365 0.0261086 0.0130543 0.999915i \(-0.495845\pi\)
0.0130543 + 0.999915i \(0.495845\pi\)
\(228\) −4.25252 −0.281630
\(229\) 13.1248 0.867311 0.433655 0.901079i \(-0.357224\pi\)
0.433655 + 0.901079i \(0.357224\pi\)
\(230\) 3.45922 0.228094
\(231\) −26.5046 −1.74388
\(232\) −1.01589 −0.0666967
\(233\) 5.68219 0.372253 0.186126 0.982526i \(-0.440407\pi\)
0.186126 + 0.982526i \(0.440407\pi\)
\(234\) 10.6244 0.694538
\(235\) 14.2916 0.932280
\(236\) 10.0360 0.653289
\(237\) −13.7546 −0.893456
\(238\) −8.35960 −0.541872
\(239\) −6.22273 −0.402515 −0.201257 0.979538i \(-0.564503\pi\)
−0.201257 + 0.979538i \(0.564503\pi\)
\(240\) 4.00488 0.258514
\(241\) −0.356819 −0.0229847 −0.0114924 0.999934i \(-0.503658\pi\)
−0.0114924 + 0.999934i \(0.503658\pi\)
\(242\) −6.53482 −0.420074
\(243\) −11.0027 −0.705822
\(244\) 3.96562 0.253873
\(245\) −12.2946 −0.785474
\(246\) −16.1434 −1.02926
\(247\) 2.23472 0.142192
\(248\) −3.05425 −0.193945
\(249\) −41.3483 −2.62034
\(250\) 10.7849 0.682098
\(251\) 24.3385 1.53623 0.768115 0.640312i \(-0.221195\pi\)
0.768115 + 0.640312i \(0.221195\pi\)
\(252\) 26.5699 1.67375
\(253\) −5.63869 −0.354502
\(254\) −3.85113 −0.241641
\(255\) −8.24599 −0.516384
\(256\) 1.00000 0.0625000
\(257\) −8.64281 −0.539124 −0.269562 0.962983i \(-0.586879\pi\)
−0.269562 + 0.962983i \(0.586879\pi\)
\(258\) 30.1344 1.87608
\(259\) −30.8589 −1.91748
\(260\) −2.10458 −0.130521
\(261\) −6.64823 −0.411515
\(262\) 10.6395 0.657313
\(263\) −1.29572 −0.0798972 −0.0399486 0.999202i \(-0.512719\pi\)
−0.0399486 + 0.999202i \(0.512719\pi\)
\(264\) −6.52814 −0.401779
\(265\) 8.24138 0.506264
\(266\) 5.58868 0.342664
\(267\) −5.44954 −0.333506
\(268\) −8.49862 −0.519136
\(269\) −26.0035 −1.58546 −0.792731 0.609571i \(-0.791342\pi\)
−0.792731 + 0.609571i \(0.791342\pi\)
\(270\) 14.1942 0.863829
\(271\) −21.8067 −1.32466 −0.662332 0.749210i \(-0.730433\pi\)
−0.662332 + 0.749210i \(0.730433\pi\)
\(272\) −2.05899 −0.124844
\(273\) −20.3633 −1.23244
\(274\) 21.6958 1.31069
\(275\) −7.01442 −0.422985
\(276\) 8.24383 0.496220
\(277\) −16.3304 −0.981200 −0.490600 0.871385i \(-0.663222\pi\)
−0.490600 + 0.871385i \(0.663222\pi\)
\(278\) 4.00382 0.240133
\(279\) −19.9877 −1.19663
\(280\) −5.26323 −0.314538
\(281\) 0.876484 0.0522866 0.0261433 0.999658i \(-0.491677\pi\)
0.0261433 + 0.999658i \(0.491677\pi\)
\(282\) 34.0589 2.02818
\(283\) 7.00305 0.416288 0.208144 0.978098i \(-0.433258\pi\)
0.208144 + 0.978098i \(0.433258\pi\)
\(284\) −12.7609 −0.757218
\(285\) 5.51273 0.326546
\(286\) 3.43057 0.202854
\(287\) 21.2156 1.25232
\(288\) 6.54422 0.385622
\(289\) −12.7606 −0.750622
\(290\) 1.31695 0.0773338
\(291\) 19.4076 1.13769
\(292\) −14.3477 −0.839638
\(293\) 5.56377 0.325039 0.162520 0.986705i \(-0.448038\pi\)
0.162520 + 0.986705i \(0.448038\pi\)
\(294\) −29.2998 −1.70880
\(295\) −13.0101 −0.757478
\(296\) −7.60060 −0.441776
\(297\) −23.1371 −1.34255
\(298\) −3.27870 −0.189930
\(299\) −4.33217 −0.250536
\(300\) 10.2552 0.592082
\(301\) −39.6026 −2.28266
\(302\) −7.08842 −0.407893
\(303\) 9.58212 0.550478
\(304\) 1.37650 0.0789478
\(305\) −5.14080 −0.294361
\(306\) −13.4744 −0.770283
\(307\) −19.8160 −1.13096 −0.565479 0.824762i \(-0.691309\pi\)
−0.565479 + 0.824762i \(0.691309\pi\)
\(308\) 8.57930 0.488851
\(309\) 46.9244 2.66944
\(310\) 3.95935 0.224876
\(311\) −13.8156 −0.783412 −0.391706 0.920090i \(-0.628115\pi\)
−0.391706 + 0.920090i \(0.628115\pi\)
\(312\) −5.01553 −0.283948
\(313\) −3.51493 −0.198676 −0.0993379 0.995054i \(-0.531672\pi\)
−0.0993379 + 0.995054i \(0.531672\pi\)
\(314\) 2.27988 0.128661
\(315\) −34.4437 −1.94068
\(316\) 4.45222 0.250457
\(317\) 8.03903 0.451517 0.225758 0.974183i \(-0.427514\pi\)
0.225758 + 0.974183i \(0.427514\pi\)
\(318\) 19.6404 1.10138
\(319\) −2.14668 −0.120191
\(320\) −1.29634 −0.0724677
\(321\) 31.0132 1.73099
\(322\) −10.8341 −0.603759
\(323\) −2.83420 −0.157699
\(324\) 14.1941 0.788561
\(325\) −5.38913 −0.298935
\(326\) 6.05792 0.335517
\(327\) −62.4570 −3.45388
\(328\) 5.22545 0.288527
\(329\) −44.7603 −2.46771
\(330\) 8.46271 0.465857
\(331\) 33.8157 1.85868 0.929340 0.369224i \(-0.120376\pi\)
0.929340 + 0.369224i \(0.120376\pi\)
\(332\) 13.3840 0.734545
\(333\) −49.7400 −2.72573
\(334\) −5.10081 −0.279104
\(335\) 11.0171 0.601929
\(336\) −12.5430 −0.684278
\(337\) −18.9839 −1.03412 −0.517060 0.855949i \(-0.672974\pi\)
−0.517060 + 0.855949i \(0.672974\pi\)
\(338\) −10.3643 −0.563745
\(339\) 18.0637 0.981085
\(340\) 2.66915 0.144755
\(341\) −6.45392 −0.349500
\(342\) 9.00812 0.487103
\(343\) 10.0855 0.544565
\(344\) −9.75420 −0.525911
\(345\) −10.6868 −0.575359
\(346\) −1.16851 −0.0628196
\(347\) 31.9817 1.71687 0.858434 0.512924i \(-0.171438\pi\)
0.858434 + 0.512924i \(0.171438\pi\)
\(348\) 3.13847 0.168240
\(349\) −23.9454 −1.28177 −0.640884 0.767638i \(-0.721432\pi\)
−0.640884 + 0.767638i \(0.721432\pi\)
\(350\) −13.4774 −0.720395
\(351\) −17.7761 −0.948818
\(352\) 2.11310 0.112628
\(353\) 5.51931 0.293763 0.146882 0.989154i \(-0.453076\pi\)
0.146882 + 0.989154i \(0.453076\pi\)
\(354\) −31.0050 −1.64790
\(355\) 16.5425 0.877982
\(356\) 1.76396 0.0934899
\(357\) 25.8259 1.36685
\(358\) −7.18255 −0.379610
\(359\) −5.60049 −0.295583 −0.147791 0.989019i \(-0.547216\pi\)
−0.147791 + 0.989019i \(0.547216\pi\)
\(360\) −8.48354 −0.447122
\(361\) −17.1052 −0.900276
\(362\) −8.04614 −0.422896
\(363\) 20.1885 1.05962
\(364\) 6.59141 0.345484
\(365\) 18.5996 0.973547
\(366\) −12.2513 −0.640384
\(367\) 5.33401 0.278433 0.139216 0.990262i \(-0.455542\pi\)
0.139216 + 0.990262i \(0.455542\pi\)
\(368\) −2.66845 −0.139103
\(369\) 34.1965 1.78020
\(370\) 9.85298 0.512232
\(371\) −25.8114 −1.34006
\(372\) 9.43570 0.489219
\(373\) 11.3224 0.586251 0.293125 0.956074i \(-0.405305\pi\)
0.293125 + 0.956074i \(0.405305\pi\)
\(374\) −4.35084 −0.224976
\(375\) −33.3186 −1.72057
\(376\) −11.0245 −0.568547
\(377\) −1.64928 −0.0849423
\(378\) −44.4552 −2.28653
\(379\) −1.48057 −0.0760519 −0.0380260 0.999277i \(-0.512107\pi\)
−0.0380260 + 0.999277i \(0.512107\pi\)
\(380\) −1.78442 −0.0915387
\(381\) 11.8976 0.609531
\(382\) −0.946898 −0.0484475
\(383\) 32.5825 1.66489 0.832443 0.554110i \(-0.186941\pi\)
0.832443 + 0.554110i \(0.186941\pi\)
\(384\) −3.08937 −0.157654
\(385\) −11.1217 −0.566815
\(386\) −8.90872 −0.453442
\(387\) −63.8336 −3.24484
\(388\) −6.28206 −0.318923
\(389\) −26.5123 −1.34423 −0.672114 0.740448i \(-0.734614\pi\)
−0.672114 + 0.740448i \(0.734614\pi\)
\(390\) 6.50184 0.329233
\(391\) 5.49430 0.277859
\(392\) 9.48407 0.479018
\(393\) −32.8695 −1.65805
\(394\) −15.2659 −0.769086
\(395\) −5.77161 −0.290401
\(396\) 13.8286 0.694911
\(397\) −17.5556 −0.881092 −0.440546 0.897730i \(-0.645215\pi\)
−0.440546 + 0.897730i \(0.645215\pi\)
\(398\) 13.1743 0.660367
\(399\) −17.2655 −0.864356
\(400\) −3.31950 −0.165975
\(401\) −2.24267 −0.111993 −0.0559967 0.998431i \(-0.517834\pi\)
−0.0559967 + 0.998431i \(0.517834\pi\)
\(402\) 26.2554 1.30950
\(403\) −4.95850 −0.247001
\(404\) −3.10164 −0.154312
\(405\) −18.4004 −0.914324
\(406\) −4.12459 −0.204700
\(407\) −16.0608 −0.796105
\(408\) 6.36097 0.314915
\(409\) 11.0297 0.545385 0.272693 0.962101i \(-0.412086\pi\)
0.272693 + 0.962101i \(0.412086\pi\)
\(410\) −6.77398 −0.334543
\(411\) −67.0265 −3.30617
\(412\) −15.1890 −0.748307
\(413\) 40.7468 2.00502
\(414\) −17.4629 −0.858255
\(415\) −17.3503 −0.851693
\(416\) 1.62348 0.0795975
\(417\) −12.3693 −0.605726
\(418\) 2.90868 0.142268
\(419\) 4.30389 0.210259 0.105129 0.994459i \(-0.466474\pi\)
0.105129 + 0.994459i \(0.466474\pi\)
\(420\) 16.2601 0.793410
\(421\) −22.5563 −1.09933 −0.549663 0.835387i \(-0.685244\pi\)
−0.549663 + 0.835387i \(0.685244\pi\)
\(422\) −0.619013 −0.0301331
\(423\) −72.1470 −3.50791
\(424\) −6.35741 −0.308743
\(425\) 6.83480 0.331536
\(426\) 39.4231 1.91005
\(427\) 16.1006 0.779164
\(428\) −10.0387 −0.485238
\(429\) −10.5983 −0.511690
\(430\) 12.6448 0.609786
\(431\) −39.0845 −1.88263 −0.941316 0.337527i \(-0.890410\pi\)
−0.941316 + 0.337527i \(0.890410\pi\)
\(432\) −10.9494 −0.526803
\(433\) 24.8409 1.19378 0.596889 0.802323i \(-0.296403\pi\)
0.596889 + 0.802323i \(0.296403\pi\)
\(434\) −12.4004 −0.595239
\(435\) −4.06854 −0.195071
\(436\) 20.2167 0.968207
\(437\) −3.67313 −0.175709
\(438\) 44.3255 2.11795
\(439\) 6.42377 0.306590 0.153295 0.988180i \(-0.451012\pi\)
0.153295 + 0.988180i \(0.451012\pi\)
\(440\) −2.73930 −0.130591
\(441\) 62.0658 2.95552
\(442\) −3.34272 −0.158997
\(443\) 31.7437 1.50819 0.754096 0.656765i \(-0.228076\pi\)
0.754096 + 0.656765i \(0.228076\pi\)
\(444\) 23.4811 1.11436
\(445\) −2.28670 −0.108400
\(446\) −0.204315 −0.00967461
\(447\) 10.1291 0.479091
\(448\) 4.06006 0.191820
\(449\) 20.8885 0.985790 0.492895 0.870089i \(-0.335939\pi\)
0.492895 + 0.870089i \(0.335939\pi\)
\(450\) −21.7235 −1.02406
\(451\) 11.0419 0.519942
\(452\) −5.84705 −0.275022
\(453\) 21.8988 1.02889
\(454\) 0.393365 0.0184615
\(455\) −8.54473 −0.400583
\(456\) −4.25252 −0.199143
\(457\) −5.10176 −0.238650 −0.119325 0.992855i \(-0.538073\pi\)
−0.119325 + 0.992855i \(0.538073\pi\)
\(458\) 13.1248 0.613281
\(459\) 22.5446 1.05229
\(460\) 3.45922 0.161287
\(461\) −11.3630 −0.529227 −0.264614 0.964354i \(-0.585244\pi\)
−0.264614 + 0.964354i \(0.585244\pi\)
\(462\) −26.5046 −1.23311
\(463\) −24.4595 −1.13673 −0.568365 0.822777i \(-0.692424\pi\)
−0.568365 + 0.822777i \(0.692424\pi\)
\(464\) −1.01589 −0.0471617
\(465\) −12.2319 −0.567241
\(466\) 5.68219 0.263222
\(467\) 2.83365 0.131126 0.0655628 0.997848i \(-0.479116\pi\)
0.0655628 + 0.997848i \(0.479116\pi\)
\(468\) 10.6244 0.491112
\(469\) −34.5049 −1.59329
\(470\) 14.2916 0.659221
\(471\) −7.04339 −0.324542
\(472\) 10.0360 0.461945
\(473\) −20.6116 −0.947722
\(474\) −13.7546 −0.631769
\(475\) −4.56929 −0.209653
\(476\) −8.35960 −0.383162
\(477\) −41.6042 −1.90493
\(478\) −6.22273 −0.284621
\(479\) 23.1850 1.05935 0.529674 0.848201i \(-0.322314\pi\)
0.529674 + 0.848201i \(0.322314\pi\)
\(480\) 4.00488 0.182797
\(481\) −12.3394 −0.562628
\(482\) −0.356819 −0.0162527
\(483\) 33.4704 1.52296
\(484\) −6.53482 −0.297037
\(485\) 8.14370 0.369786
\(486\) −11.0027 −0.499091
\(487\) 17.6224 0.798549 0.399274 0.916831i \(-0.369262\pi\)
0.399274 + 0.916831i \(0.369262\pi\)
\(488\) 3.96562 0.179515
\(489\) −18.7152 −0.846330
\(490\) −12.2946 −0.555414
\(491\) 11.0642 0.499319 0.249660 0.968334i \(-0.419681\pi\)
0.249660 + 0.968334i \(0.419681\pi\)
\(492\) −16.1434 −0.727799
\(493\) 2.09171 0.0942060
\(494\) 2.23472 0.100545
\(495\) −17.9266 −0.805739
\(496\) −3.05425 −0.137140
\(497\) −51.8099 −2.32399
\(498\) −41.3483 −1.85286
\(499\) −0.501950 −0.0224704 −0.0112352 0.999937i \(-0.503576\pi\)
−0.0112352 + 0.999937i \(0.503576\pi\)
\(500\) 10.7849 0.482316
\(501\) 15.7583 0.704029
\(502\) 24.3385 1.08628
\(503\) −9.01821 −0.402102 −0.201051 0.979581i \(-0.564436\pi\)
−0.201051 + 0.979581i \(0.564436\pi\)
\(504\) 26.5699 1.18352
\(505\) 4.02079 0.178923
\(506\) −5.63869 −0.250671
\(507\) 32.0192 1.42202
\(508\) −3.85113 −0.170866
\(509\) 12.9461 0.573828 0.286914 0.957956i \(-0.407371\pi\)
0.286914 + 0.957956i \(0.407371\pi\)
\(510\) −8.24599 −0.365139
\(511\) −58.2527 −2.57695
\(512\) 1.00000 0.0441942
\(513\) −15.0719 −0.665439
\(514\) −8.64281 −0.381218
\(515\) 19.6901 0.867650
\(516\) 30.1344 1.32659
\(517\) −23.2959 −1.02455
\(518\) −30.8589 −1.35586
\(519\) 3.60997 0.158460
\(520\) −2.10458 −0.0922921
\(521\) 8.71704 0.381900 0.190950 0.981600i \(-0.438843\pi\)
0.190950 + 0.981600i \(0.438843\pi\)
\(522\) −6.64823 −0.290985
\(523\) −0.781995 −0.0341943 −0.0170971 0.999854i \(-0.505442\pi\)
−0.0170971 + 0.999854i \(0.505442\pi\)
\(524\) 10.6395 0.464791
\(525\) 41.6365 1.81717
\(526\) −1.29572 −0.0564959
\(527\) 6.28865 0.273938
\(528\) −6.52814 −0.284101
\(529\) −15.8794 −0.690408
\(530\) 8.24138 0.357983
\(531\) 65.6779 2.85018
\(532\) 5.58868 0.242300
\(533\) 8.48341 0.367457
\(534\) −5.44954 −0.235825
\(535\) 13.0136 0.562626
\(536\) −8.49862 −0.367084
\(537\) 22.1896 0.957550
\(538\) −26.0035 −1.12109
\(539\) 20.0408 0.863217
\(540\) 14.1942 0.610820
\(541\) 31.8528 1.36946 0.684730 0.728797i \(-0.259920\pi\)
0.684730 + 0.728797i \(0.259920\pi\)
\(542\) −21.8067 −0.936680
\(543\) 24.8575 1.06674
\(544\) −2.05899 −0.0882783
\(545\) −26.2078 −1.12262
\(546\) −20.3633 −0.871470
\(547\) −31.8632 −1.36237 −0.681185 0.732111i \(-0.738535\pi\)
−0.681185 + 0.732111i \(0.738535\pi\)
\(548\) 21.6958 0.926800
\(549\) 25.9518 1.10760
\(550\) −7.01442 −0.299096
\(551\) −1.39838 −0.0595730
\(552\) 8.24383 0.350881
\(553\) 18.0763 0.768682
\(554\) −16.3304 −0.693813
\(555\) −30.4395 −1.29208
\(556\) 4.00382 0.169800
\(557\) 7.89836 0.334664 0.167332 0.985901i \(-0.446485\pi\)
0.167332 + 0.985901i \(0.446485\pi\)
\(558\) −19.9877 −0.846145
\(559\) −15.8357 −0.669780
\(560\) −5.26323 −0.222412
\(561\) 13.4414 0.567494
\(562\) 0.876484 0.0369722
\(563\) −20.3205 −0.856406 −0.428203 0.903683i \(-0.640853\pi\)
−0.428203 + 0.903683i \(0.640853\pi\)
\(564\) 34.0589 1.43414
\(565\) 7.57977 0.318883
\(566\) 7.00305 0.294360
\(567\) 57.6289 2.42019
\(568\) −12.7609 −0.535434
\(569\) 12.4138 0.520412 0.260206 0.965553i \(-0.416209\pi\)
0.260206 + 0.965553i \(0.416209\pi\)
\(570\) 5.51273 0.230903
\(571\) −1.87974 −0.0786648 −0.0393324 0.999226i \(-0.512523\pi\)
−0.0393324 + 0.999226i \(0.512523\pi\)
\(572\) 3.43057 0.143439
\(573\) 2.92532 0.122207
\(574\) 21.2156 0.885524
\(575\) 8.85791 0.369400
\(576\) 6.54422 0.272676
\(577\) −9.01851 −0.375445 −0.187723 0.982222i \(-0.560111\pi\)
−0.187723 + 0.982222i \(0.560111\pi\)
\(578\) −12.7606 −0.530770
\(579\) 27.5223 1.14379
\(580\) 1.31695 0.0546832
\(581\) 54.3400 2.25440
\(582\) 19.4076 0.804471
\(583\) −13.4338 −0.556372
\(584\) −14.3477 −0.593714
\(585\) −13.7728 −0.569437
\(586\) 5.56377 0.229837
\(587\) 31.0377 1.28106 0.640532 0.767931i \(-0.278714\pi\)
0.640532 + 0.767931i \(0.278714\pi\)
\(588\) −29.2998 −1.20830
\(589\) −4.20418 −0.173230
\(590\) −13.0101 −0.535618
\(591\) 47.1621 1.93999
\(592\) −7.60060 −0.312383
\(593\) −33.6345 −1.38120 −0.690602 0.723235i \(-0.742654\pi\)
−0.690602 + 0.723235i \(0.742654\pi\)
\(594\) −23.1371 −0.949328
\(595\) 10.8369 0.444270
\(596\) −3.27870 −0.134301
\(597\) −40.7003 −1.66575
\(598\) −4.33217 −0.177156
\(599\) 7.06471 0.288656 0.144328 0.989530i \(-0.453898\pi\)
0.144328 + 0.989530i \(0.453898\pi\)
\(600\) 10.2552 0.418665
\(601\) 10.6039 0.432540 0.216270 0.976334i \(-0.430611\pi\)
0.216270 + 0.976334i \(0.430611\pi\)
\(602\) −39.6026 −1.61408
\(603\) −55.6168 −2.26489
\(604\) −7.08842 −0.288424
\(605\) 8.47136 0.344410
\(606\) 9.58212 0.389247
\(607\) −2.86115 −0.116130 −0.0580652 0.998313i \(-0.518493\pi\)
−0.0580652 + 0.998313i \(0.518493\pi\)
\(608\) 1.37650 0.0558245
\(609\) 12.7424 0.516348
\(610\) −5.14080 −0.208145
\(611\) −17.8981 −0.724080
\(612\) −13.4744 −0.544672
\(613\) 31.7484 1.28231 0.641153 0.767413i \(-0.278456\pi\)
0.641153 + 0.767413i \(0.278456\pi\)
\(614\) −19.8160 −0.799709
\(615\) 20.9273 0.843871
\(616\) 8.57930 0.345670
\(617\) −21.9552 −0.883883 −0.441942 0.897044i \(-0.645710\pi\)
−0.441942 + 0.897044i \(0.645710\pi\)
\(618\) 46.9244 1.88758
\(619\) −11.2808 −0.453416 −0.226708 0.973963i \(-0.572796\pi\)
−0.226708 + 0.973963i \(0.572796\pi\)
\(620\) 3.95935 0.159011
\(621\) 29.2179 1.17247
\(622\) −13.8156 −0.553956
\(623\) 7.16180 0.286931
\(624\) −5.01553 −0.200782
\(625\) 2.61654 0.104662
\(626\) −3.51493 −0.140485
\(627\) −8.98600 −0.358866
\(628\) 2.27988 0.0909770
\(629\) 15.6495 0.623987
\(630\) −34.4437 −1.37227
\(631\) −33.2046 −1.32185 −0.660926 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(632\) 4.45222 0.177100
\(633\) 1.91236 0.0760095
\(634\) 8.03903 0.319271
\(635\) 4.99238 0.198117
\(636\) 19.6404 0.778792
\(637\) 15.3972 0.610059
\(638\) −2.14668 −0.0849880
\(639\) −83.5099 −3.30360
\(640\) −1.29634 −0.0512424
\(641\) 22.4413 0.886378 0.443189 0.896428i \(-0.353847\pi\)
0.443189 + 0.896428i \(0.353847\pi\)
\(642\) 31.0132 1.22399
\(643\) 34.6292 1.36564 0.682821 0.730586i \(-0.260753\pi\)
0.682821 + 0.730586i \(0.260753\pi\)
\(644\) −10.8341 −0.426922
\(645\) −39.0644 −1.53816
\(646\) −2.83420 −0.111510
\(647\) 24.1715 0.950282 0.475141 0.879910i \(-0.342397\pi\)
0.475141 + 0.879910i \(0.342397\pi\)
\(648\) 14.1941 0.557597
\(649\) 21.2071 0.832451
\(650\) −5.38913 −0.211379
\(651\) 38.3095 1.50147
\(652\) 6.05792 0.237247
\(653\) 18.3575 0.718386 0.359193 0.933263i \(-0.383052\pi\)
0.359193 + 0.933263i \(0.383052\pi\)
\(654\) −62.4570 −2.44226
\(655\) −13.7925 −0.538917
\(656\) 5.22545 0.204020
\(657\) −93.8947 −3.66318
\(658\) −44.7603 −1.74494
\(659\) −46.7204 −1.81997 −0.909985 0.414641i \(-0.863907\pi\)
−0.909985 + 0.414641i \(0.863907\pi\)
\(660\) 8.46271 0.329410
\(661\) −13.2024 −0.513514 −0.256757 0.966476i \(-0.582654\pi\)
−0.256757 + 0.966476i \(0.582654\pi\)
\(662\) 33.8157 1.31429
\(663\) 10.3269 0.401063
\(664\) 13.3840 0.519402
\(665\) −7.24484 −0.280943
\(666\) −49.7400 −1.92738
\(667\) 2.71086 0.104965
\(668\) −5.10081 −0.197356
\(669\) 0.631206 0.0244038
\(670\) 11.0171 0.425628
\(671\) 8.37973 0.323496
\(672\) −12.5430 −0.483858
\(673\) −17.1502 −0.661093 −0.330547 0.943790i \(-0.607233\pi\)
−0.330547 + 0.943790i \(0.607233\pi\)
\(674\) −18.9839 −0.731234
\(675\) 36.3465 1.39898
\(676\) −10.3643 −0.398628
\(677\) −19.0405 −0.731786 −0.365893 0.930657i \(-0.619236\pi\)
−0.365893 + 0.930657i \(0.619236\pi\)
\(678\) 18.0637 0.693732
\(679\) −25.5055 −0.978812
\(680\) 2.66915 0.102357
\(681\) −1.21525 −0.0465685
\(682\) −6.45392 −0.247133
\(683\) 1.16481 0.0445704 0.0222852 0.999752i \(-0.492906\pi\)
0.0222852 + 0.999752i \(0.492906\pi\)
\(684\) 9.00812 0.344434
\(685\) −28.1252 −1.07461
\(686\) 10.0855 0.385066
\(687\) −40.5474 −1.54698
\(688\) −9.75420 −0.371876
\(689\) −10.3211 −0.393203
\(690\) −10.6868 −0.406841
\(691\) 30.9579 1.17769 0.588847 0.808244i \(-0.299582\pi\)
0.588847 + 0.808244i \(0.299582\pi\)
\(692\) −1.16851 −0.0444202
\(693\) 56.1448 2.13276
\(694\) 31.9817 1.21401
\(695\) −5.19032 −0.196880
\(696\) 3.13847 0.118964
\(697\) −10.7591 −0.407531
\(698\) −23.9454 −0.906346
\(699\) −17.5544 −0.663968
\(700\) −13.4774 −0.509396
\(701\) −51.8275 −1.95750 −0.978748 0.205066i \(-0.934259\pi\)
−0.978748 + 0.205066i \(0.934259\pi\)
\(702\) −17.7761 −0.670916
\(703\) −10.4622 −0.394591
\(704\) 2.11310 0.0796404
\(705\) −44.1520 −1.66286
\(706\) 5.51931 0.207722
\(707\) −12.5928 −0.473602
\(708\) −31.0050 −1.16524
\(709\) −39.9155 −1.49906 −0.749529 0.661971i \(-0.769720\pi\)
−0.749529 + 0.661971i \(0.769720\pi\)
\(710\) 16.5425 0.620827
\(711\) 29.1363 1.09270
\(712\) 1.76396 0.0661073
\(713\) 8.15011 0.305224
\(714\) 25.8259 0.966510
\(715\) −4.44719 −0.166315
\(716\) −7.18255 −0.268424
\(717\) 19.2243 0.717946
\(718\) −5.60049 −0.209009
\(719\) 10.3363 0.385478 0.192739 0.981250i \(-0.438263\pi\)
0.192739 + 0.981250i \(0.438263\pi\)
\(720\) −8.48354 −0.316163
\(721\) −61.6681 −2.29664
\(722\) −17.1052 −0.636591
\(723\) 1.10235 0.0409967
\(724\) −8.04614 −0.299033
\(725\) 3.37226 0.125243
\(726\) 20.1885 0.749265
\(727\) 8.75877 0.324845 0.162422 0.986721i \(-0.448069\pi\)
0.162422 + 0.986721i \(0.448069\pi\)
\(728\) 6.59141 0.244294
\(729\) −8.59097 −0.318184
\(730\) 18.5996 0.688402
\(731\) 20.0838 0.742825
\(732\) −12.2513 −0.452820
\(733\) −46.2230 −1.70729 −0.853643 0.520858i \(-0.825612\pi\)
−0.853643 + 0.520858i \(0.825612\pi\)
\(734\) 5.33401 0.196882
\(735\) 37.9826 1.40101
\(736\) −2.66845 −0.0983604
\(737\) −17.9584 −0.661506
\(738\) 34.1965 1.25879
\(739\) 35.6242 1.31046 0.655229 0.755430i \(-0.272572\pi\)
0.655229 + 0.755430i \(0.272572\pi\)
\(740\) 9.85298 0.362203
\(741\) −6.90388 −0.253620
\(742\) −25.8114 −0.947568
\(743\) 50.3343 1.84658 0.923292 0.384098i \(-0.125488\pi\)
0.923292 + 0.384098i \(0.125488\pi\)
\(744\) 9.43570 0.345930
\(745\) 4.25032 0.155720
\(746\) 11.3224 0.414542
\(747\) 87.5880 3.20468
\(748\) −4.35084 −0.159082
\(749\) −40.7576 −1.48925
\(750\) −33.3186 −1.21662
\(751\) 34.6928 1.26596 0.632979 0.774169i \(-0.281832\pi\)
0.632979 + 0.774169i \(0.281832\pi\)
\(752\) −11.0245 −0.402024
\(753\) −75.1905 −2.74010
\(754\) −1.64928 −0.0600633
\(755\) 9.18902 0.334423
\(756\) −44.4552 −1.61682
\(757\) −22.6917 −0.824743 −0.412372 0.911016i \(-0.635300\pi\)
−0.412372 + 0.911016i \(0.635300\pi\)
\(758\) −1.48057 −0.0537768
\(759\) 17.4200 0.632307
\(760\) −1.78442 −0.0647276
\(761\) 38.3794 1.39125 0.695627 0.718403i \(-0.255127\pi\)
0.695627 + 0.718403i \(0.255127\pi\)
\(762\) 11.8976 0.431003
\(763\) 82.0812 2.97154
\(764\) −0.946898 −0.0342576
\(765\) 17.4675 0.631538
\(766\) 32.5825 1.17725
\(767\) 16.2933 0.588315
\(768\) −3.08937 −0.111478
\(769\) 47.1485 1.70022 0.850109 0.526607i \(-0.176536\pi\)
0.850109 + 0.526607i \(0.176536\pi\)
\(770\) −11.1217 −0.400799
\(771\) 26.7009 0.961608
\(772\) −8.90872 −0.320632
\(773\) −13.7478 −0.494474 −0.247237 0.968955i \(-0.579523\pi\)
−0.247237 + 0.968955i \(0.579523\pi\)
\(774\) −63.8336 −2.29445
\(775\) 10.1386 0.364188
\(776\) −6.28206 −0.225513
\(777\) 95.3345 3.42011
\(778\) −26.5123 −0.950513
\(779\) 7.19284 0.257710
\(780\) 6.50184 0.232803
\(781\) −26.9650 −0.964882
\(782\) 5.49430 0.196476
\(783\) 11.1234 0.397519
\(784\) 9.48407 0.338717
\(785\) −2.95550 −0.105486
\(786\) −32.8695 −1.17242
\(787\) −32.2917 −1.15107 −0.575537 0.817776i \(-0.695207\pi\)
−0.575537 + 0.817776i \(0.695207\pi\)
\(788\) −15.2659 −0.543826
\(789\) 4.00295 0.142509
\(790\) −5.77161 −0.205345
\(791\) −23.7394 −0.844074
\(792\) 13.8286 0.491377
\(793\) 6.43809 0.228623
\(794\) −17.5556 −0.623026
\(795\) −25.4607 −0.902997
\(796\) 13.1743 0.466950
\(797\) 2.86355 0.101432 0.0507161 0.998713i \(-0.483850\pi\)
0.0507161 + 0.998713i \(0.483850\pi\)
\(798\) −17.2655 −0.611192
\(799\) 22.6994 0.803046
\(800\) −3.31950 −0.117362
\(801\) 11.5438 0.407879
\(802\) −2.24267 −0.0791913
\(803\) −30.3182 −1.06991
\(804\) 26.2554 0.925956
\(805\) 14.0447 0.495009
\(806\) −4.95850 −0.174656
\(807\) 80.3345 2.82791
\(808\) −3.10164 −0.109115
\(809\) −48.6359 −1.70995 −0.854974 0.518671i \(-0.826427\pi\)
−0.854974 + 0.518671i \(0.826427\pi\)
\(810\) −18.4004 −0.646525
\(811\) 28.8391 1.01268 0.506339 0.862335i \(-0.330999\pi\)
0.506339 + 0.862335i \(0.330999\pi\)
\(812\) −4.12459 −0.144745
\(813\) 67.3691 2.36274
\(814\) −16.0608 −0.562931
\(815\) −7.85314 −0.275084
\(816\) 6.36097 0.222679
\(817\) −13.4267 −0.469740
\(818\) 11.0297 0.385645
\(819\) 43.1356 1.50728
\(820\) −6.77398 −0.236557
\(821\) 23.0737 0.805277 0.402638 0.915359i \(-0.368093\pi\)
0.402638 + 0.915359i \(0.368093\pi\)
\(822\) −67.0265 −2.33782
\(823\) −15.4743 −0.539399 −0.269699 0.962945i \(-0.586924\pi\)
−0.269699 + 0.962945i \(0.586924\pi\)
\(824\) −15.1890 −0.529133
\(825\) 21.6701 0.754458
\(826\) 40.7468 1.41776
\(827\) 13.2760 0.461650 0.230825 0.972995i \(-0.425857\pi\)
0.230825 + 0.972995i \(0.425857\pi\)
\(828\) −17.4629 −0.606878
\(829\) −12.0588 −0.418821 −0.209410 0.977828i \(-0.567154\pi\)
−0.209410 + 0.977828i \(0.567154\pi\)
\(830\) −17.3503 −0.602238
\(831\) 50.4507 1.75012
\(832\) 1.62348 0.0562840
\(833\) −19.5276 −0.676590
\(834\) −12.3693 −0.428313
\(835\) 6.61240 0.228831
\(836\) 2.90868 0.100599
\(837\) 33.4422 1.15593
\(838\) 4.30389 0.148675
\(839\) −24.5569 −0.847798 −0.423899 0.905710i \(-0.639339\pi\)
−0.423899 + 0.905710i \(0.639339\pi\)
\(840\) 16.2601 0.561025
\(841\) −27.9680 −0.964412
\(842\) −22.5563 −0.777340
\(843\) −2.70778 −0.0932610
\(844\) −0.619013 −0.0213073
\(845\) 13.4357 0.462202
\(846\) −72.1470 −2.48046
\(847\) −26.5317 −0.911642
\(848\) −6.35741 −0.218314
\(849\) −21.6350 −0.742512
\(850\) 6.83480 0.234432
\(851\) 20.2818 0.695252
\(852\) 39.4231 1.35061
\(853\) −24.9643 −0.854760 −0.427380 0.904072i \(-0.640563\pi\)
−0.427380 + 0.904072i \(0.640563\pi\)
\(854\) 16.1006 0.550952
\(855\) −11.6776 −0.399366
\(856\) −10.0387 −0.343115
\(857\) −10.4137 −0.355726 −0.177863 0.984055i \(-0.556918\pi\)
−0.177863 + 0.984055i \(0.556918\pi\)
\(858\) −10.5983 −0.361820
\(859\) 25.0221 0.853743 0.426872 0.904312i \(-0.359616\pi\)
0.426872 + 0.904312i \(0.359616\pi\)
\(860\) 12.6448 0.431184
\(861\) −65.5430 −2.23370
\(862\) −39.0845 −1.33122
\(863\) 30.7530 1.04685 0.523423 0.852073i \(-0.324655\pi\)
0.523423 + 0.852073i \(0.324655\pi\)
\(864\) −10.9494 −0.372506
\(865\) 1.51479 0.0515045
\(866\) 24.8409 0.844129
\(867\) 39.4222 1.33885
\(868\) −12.4004 −0.420898
\(869\) 9.40798 0.319144
\(870\) −4.06854 −0.137936
\(871\) −13.7973 −0.467504
\(872\) 20.2167 0.684626
\(873\) −41.1111 −1.39140
\(874\) −3.67313 −0.124245
\(875\) 43.7874 1.48028
\(876\) 44.3255 1.49762
\(877\) −9.00643 −0.304126 −0.152063 0.988371i \(-0.548592\pi\)
−0.152063 + 0.988371i \(0.548592\pi\)
\(878\) 6.42377 0.216792
\(879\) −17.1886 −0.579756
\(880\) −2.73930 −0.0923417
\(881\) −8.55682 −0.288287 −0.144143 0.989557i \(-0.546043\pi\)
−0.144143 + 0.989557i \(0.546043\pi\)
\(882\) 62.0658 2.08986
\(883\) −15.3471 −0.516470 −0.258235 0.966082i \(-0.583141\pi\)
−0.258235 + 0.966082i \(0.583141\pi\)
\(884\) −3.34272 −0.112428
\(885\) 40.1931 1.35108
\(886\) 31.7437 1.06645
\(887\) 44.9107 1.50795 0.753977 0.656901i \(-0.228133\pi\)
0.753977 + 0.656901i \(0.228133\pi\)
\(888\) 23.4811 0.787973
\(889\) −15.6358 −0.524408
\(890\) −2.28670 −0.0766504
\(891\) 29.9935 1.00482
\(892\) −0.204315 −0.00684098
\(893\) −15.1753 −0.507822
\(894\) 10.1291 0.338769
\(895\) 9.31104 0.311234
\(896\) 4.06006 0.135637
\(897\) 13.3837 0.446868
\(898\) 20.8885 0.697059
\(899\) 3.10279 0.103484
\(900\) −21.7235 −0.724117
\(901\) 13.0898 0.436085
\(902\) 11.0419 0.367655
\(903\) 122.347 4.07146
\(904\) −5.84705 −0.194470
\(905\) 10.4306 0.346723
\(906\) 21.8988 0.727538
\(907\) 12.3194 0.409059 0.204529 0.978860i \(-0.434434\pi\)
0.204529 + 0.978860i \(0.434434\pi\)
\(908\) 0.393365 0.0130543
\(909\) −20.2978 −0.673235
\(910\) −8.54473 −0.283255
\(911\) −39.3485 −1.30368 −0.651838 0.758358i \(-0.726002\pi\)
−0.651838 + 0.758358i \(0.726002\pi\)
\(912\) −4.25252 −0.140815
\(913\) 28.2818 0.935990
\(914\) −5.10176 −0.168751
\(915\) 15.8818 0.525037
\(916\) 13.1248 0.433655
\(917\) 43.1972 1.42650
\(918\) 22.5446 0.744084
\(919\) −39.7912 −1.31259 −0.656295 0.754505i \(-0.727877\pi\)
−0.656295 + 0.754505i \(0.727877\pi\)
\(920\) 3.45922 0.114047
\(921\) 61.2190 2.01723
\(922\) −11.3630 −0.374220
\(923\) −20.7170 −0.681908
\(924\) −26.5046 −0.871939
\(925\) 25.2302 0.829563
\(926\) −24.4595 −0.803789
\(927\) −99.3999 −3.26472
\(928\) −1.01589 −0.0333484
\(929\) −20.0133 −0.656616 −0.328308 0.944571i \(-0.606478\pi\)
−0.328308 + 0.944571i \(0.606478\pi\)
\(930\) −12.2319 −0.401100
\(931\) 13.0548 0.427855
\(932\) 5.68219 0.186126
\(933\) 42.6816 1.39733
\(934\) 2.83365 0.0927197
\(935\) 5.64017 0.184453
\(936\) 10.6244 0.347269
\(937\) −3.20578 −0.104728 −0.0523642 0.998628i \(-0.516676\pi\)
−0.0523642 + 0.998628i \(0.516676\pi\)
\(938\) −34.5049 −1.12662
\(939\) 10.8589 0.354368
\(940\) 14.2916 0.466140
\(941\) 29.5916 0.964659 0.482330 0.875990i \(-0.339791\pi\)
0.482330 + 0.875990i \(0.339791\pi\)
\(942\) −7.04339 −0.229486
\(943\) −13.9439 −0.454075
\(944\) 10.0360 0.326645
\(945\) 57.6291 1.87468
\(946\) −20.6116 −0.670140
\(947\) −4.28243 −0.139160 −0.0695802 0.997576i \(-0.522166\pi\)
−0.0695802 + 0.997576i \(0.522166\pi\)
\(948\) −13.7546 −0.446728
\(949\) −23.2932 −0.756131
\(950\) −4.56929 −0.148247
\(951\) −24.8356 −0.805348
\(952\) −8.35960 −0.270936
\(953\) 32.7192 1.05988 0.529940 0.848035i \(-0.322214\pi\)
0.529940 + 0.848035i \(0.322214\pi\)
\(954\) −41.6042 −1.34699
\(955\) 1.22750 0.0397211
\(956\) −6.22273 −0.201257
\(957\) 6.63190 0.214379
\(958\) 23.1850 0.749072
\(959\) 88.0864 2.84446
\(960\) 4.00488 0.129257
\(961\) −21.6716 −0.699083
\(962\) −12.3394 −0.397838
\(963\) −65.6953 −2.11700
\(964\) −0.356819 −0.0114924
\(965\) 11.5487 0.371767
\(966\) 33.4704 1.07689
\(967\) 36.4107 1.17089 0.585444 0.810713i \(-0.300920\pi\)
0.585444 + 0.810713i \(0.300920\pi\)
\(968\) −6.53482 −0.210037
\(969\) 8.75589 0.281280
\(970\) 8.14370 0.261478
\(971\) 15.4501 0.495817 0.247909 0.968783i \(-0.420257\pi\)
0.247909 + 0.968783i \(0.420257\pi\)
\(972\) −11.0027 −0.352911
\(973\) 16.2557 0.521135
\(974\) 17.6224 0.564659
\(975\) 16.6490 0.533195
\(976\) 3.96562 0.126936
\(977\) 35.9023 1.14862 0.574309 0.818639i \(-0.305271\pi\)
0.574309 + 0.818639i \(0.305271\pi\)
\(978\) −18.7152 −0.598445
\(979\) 3.72743 0.119129
\(980\) −12.2946 −0.392737
\(981\) 132.303 4.22410
\(982\) 11.0642 0.353072
\(983\) −57.4177 −1.83134 −0.915670 0.401930i \(-0.868340\pi\)
−0.915670 + 0.401930i \(0.868340\pi\)
\(984\) −16.1434 −0.514632
\(985\) 19.7899 0.630557
\(986\) 2.09171 0.0666137
\(987\) 138.281 4.40154
\(988\) 2.23472 0.0710959
\(989\) 26.0286 0.827662
\(990\) −17.9266 −0.569743
\(991\) −45.0499 −1.43106 −0.715529 0.698583i \(-0.753814\pi\)
−0.715529 + 0.698583i \(0.753814\pi\)
\(992\) −3.05425 −0.0969725
\(993\) −104.469 −3.31524
\(994\) −51.8099 −1.64331
\(995\) −17.0784 −0.541421
\(996\) −41.3483 −1.31017
\(997\) 42.1523 1.33498 0.667488 0.744621i \(-0.267370\pi\)
0.667488 + 0.744621i \(0.267370\pi\)
\(998\) −0.501950 −0.0158890
\(999\) 83.2220 2.63303
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 \(a_p\))