Properties

Label 6013.2.a.e.1.16
Level 6013
Weight 2
Character 6013.1
Self dual Yes
Analytic conductor 48.014
Analytic rank 0
Dimension 109
CM No

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Newspace parameters

Level: \( N \) = \( 6013 = 7 \cdot 859 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0140467354\)
Analytic rank: \(0\)
Dimension: \(109\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.06498 q^{2}\) \(-2.80647 q^{3}\) \(+2.26415 q^{4}\) \(-1.02377 q^{5}\) \(+5.79530 q^{6}\) \(+1.00000 q^{7}\) \(-0.545455 q^{8}\) \(+4.87626 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.06498 q^{2}\) \(-2.80647 q^{3}\) \(+2.26415 q^{4}\) \(-1.02377 q^{5}\) \(+5.79530 q^{6}\) \(+1.00000 q^{7}\) \(-0.545455 q^{8}\) \(+4.87626 q^{9}\) \(+2.11406 q^{10}\) \(-1.69199 q^{11}\) \(-6.35425 q^{12}\) \(+0.918283 q^{13}\) \(-2.06498 q^{14}\) \(+2.87317 q^{15}\) \(-3.40194 q^{16}\) \(-3.54697 q^{17}\) \(-10.0694 q^{18}\) \(+0.506076 q^{19}\) \(-2.31796 q^{20}\) \(-2.80647 q^{21}\) \(+3.49393 q^{22}\) \(+2.15124 q^{23}\) \(+1.53080 q^{24}\) \(-3.95190 q^{25}\) \(-1.89624 q^{26}\) \(-5.26567 q^{27}\) \(+2.26415 q^{28}\) \(-0.298985 q^{29}\) \(-5.93303 q^{30}\) \(-3.50472 q^{31}\) \(+8.11584 q^{32}\) \(+4.74852 q^{33}\) \(+7.32443 q^{34}\) \(-1.02377 q^{35}\) \(+11.0406 q^{36}\) \(-6.21713 q^{37}\) \(-1.04504 q^{38}\) \(-2.57713 q^{39}\) \(+0.558418 q^{40}\) \(+0.683643 q^{41}\) \(+5.79530 q^{42}\) \(+2.55384 q^{43}\) \(-3.83092 q^{44}\) \(-4.99215 q^{45}\) \(-4.44226 q^{46}\) \(-8.23934 q^{47}\) \(+9.54743 q^{48}\) \(+1.00000 q^{49}\) \(+8.16060 q^{50}\) \(+9.95447 q^{51}\) \(+2.07913 q^{52}\) \(+11.4304 q^{53}\) \(+10.8735 q^{54}\) \(+1.73220 q^{55}\) \(-0.545455 q^{56}\) \(-1.42029 q^{57}\) \(+0.617399 q^{58}\) \(+8.98046 q^{59}\) \(+6.50527 q^{60}\) \(-0.678469 q^{61}\) \(+7.23718 q^{62}\) \(+4.87626 q^{63}\) \(-9.95519 q^{64}\) \(-0.940107 q^{65}\) \(-9.80561 q^{66}\) \(-12.4267 q^{67}\) \(-8.03086 q^{68}\) \(-6.03738 q^{69}\) \(+2.11406 q^{70}\) \(+9.74559 q^{71}\) \(-2.65978 q^{72}\) \(+7.51330 q^{73}\) \(+12.8382 q^{74}\) \(+11.0909 q^{75}\) \(+1.14583 q^{76}\) \(-1.69199 q^{77}\) \(+5.32173 q^{78}\) \(-9.35537 q^{79}\) \(+3.48279 q^{80}\) \(+0.149151 q^{81}\) \(-1.41171 q^{82}\) \(+2.78477 q^{83}\) \(-6.35425 q^{84}\) \(+3.63127 q^{85}\) \(-5.27364 q^{86}\) \(+0.839092 q^{87}\) \(+0.922906 q^{88}\) \(-6.72030 q^{89}\) \(+10.3087 q^{90}\) \(+0.918283 q^{91}\) \(+4.87071 q^{92}\) \(+9.83588 q^{93}\) \(+17.0141 q^{94}\) \(-0.518104 q^{95}\) \(-22.7769 q^{96}\) \(+13.2887 q^{97}\) \(-2.06498 q^{98}\) \(-8.25060 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.06498 −1.46016 −0.730081 0.683361i \(-0.760518\pi\)
−0.730081 + 0.683361i \(0.760518\pi\)
\(3\) −2.80647 −1.62032 −0.810158 0.586212i \(-0.800618\pi\)
−0.810158 + 0.586212i \(0.800618\pi\)
\(4\) 2.26415 1.13207
\(5\) −1.02377 −0.457842 −0.228921 0.973445i \(-0.573520\pi\)
−0.228921 + 0.973445i \(0.573520\pi\)
\(6\) 5.79530 2.36592
\(7\) 1.00000 0.377964
\(8\) −0.545455 −0.192847
\(9\) 4.87626 1.62542
\(10\) 2.11406 0.668524
\(11\) −1.69199 −0.510155 −0.255077 0.966921i \(-0.582101\pi\)
−0.255077 + 0.966921i \(0.582101\pi\)
\(12\) −6.35425 −1.83431
\(13\) 0.918283 0.254686 0.127343 0.991859i \(-0.459355\pi\)
0.127343 + 0.991859i \(0.459355\pi\)
\(14\) −2.06498 −0.551889
\(15\) 2.87317 0.741849
\(16\) −3.40194 −0.850484
\(17\) −3.54697 −0.860267 −0.430134 0.902765i \(-0.641534\pi\)
−0.430134 + 0.902765i \(0.641534\pi\)
\(18\) −10.0694 −2.37338
\(19\) 0.506076 0.116102 0.0580509 0.998314i \(-0.481511\pi\)
0.0580509 + 0.998314i \(0.481511\pi\)
\(20\) −2.31796 −0.518311
\(21\) −2.80647 −0.612422
\(22\) 3.49393 0.744909
\(23\) 2.15124 0.448564 0.224282 0.974524i \(-0.427996\pi\)
0.224282 + 0.974524i \(0.427996\pi\)
\(24\) 1.53080 0.312474
\(25\) −3.95190 −0.790381
\(26\) −1.89624 −0.371883
\(27\) −5.26567 −1.01338
\(28\) 2.26415 0.427883
\(29\) −0.298985 −0.0555201 −0.0277601 0.999615i \(-0.508837\pi\)
−0.0277601 + 0.999615i \(0.508837\pi\)
\(30\) −5.93303 −1.08322
\(31\) −3.50472 −0.629466 −0.314733 0.949180i \(-0.601915\pi\)
−0.314733 + 0.949180i \(0.601915\pi\)
\(32\) 8.11584 1.43469
\(33\) 4.74852 0.826612
\(34\) 7.32443 1.25613
\(35\) −1.02377 −0.173048
\(36\) 11.0406 1.84009
\(37\) −6.21713 −1.02209 −0.511045 0.859554i \(-0.670741\pi\)
−0.511045 + 0.859554i \(0.670741\pi\)
\(38\) −1.04504 −0.169527
\(39\) −2.57713 −0.412671
\(40\) 0.558418 0.0882937
\(41\) 0.683643 0.106767 0.0533836 0.998574i \(-0.482999\pi\)
0.0533836 + 0.998574i \(0.482999\pi\)
\(42\) 5.79530 0.894235
\(43\) 2.55384 0.389458 0.194729 0.980857i \(-0.437617\pi\)
0.194729 + 0.980857i \(0.437617\pi\)
\(44\) −3.83092 −0.577532
\(45\) −4.99215 −0.744186
\(46\) −4.44226 −0.654976
\(47\) −8.23934 −1.20183 −0.600916 0.799313i \(-0.705197\pi\)
−0.600916 + 0.799313i \(0.705197\pi\)
\(48\) 9.54743 1.37805
\(49\) 1.00000 0.142857
\(50\) 8.16060 1.15408
\(51\) 9.95447 1.39390
\(52\) 2.07913 0.288323
\(53\) 11.4304 1.57009 0.785043 0.619442i \(-0.212641\pi\)
0.785043 + 0.619442i \(0.212641\pi\)
\(54\) 10.8735 1.47970
\(55\) 1.73220 0.233570
\(56\) −0.545455 −0.0728895
\(57\) −1.42029 −0.188122
\(58\) 0.617399 0.0810684
\(59\) 8.98046 1.16916 0.584578 0.811338i \(-0.301260\pi\)
0.584578 + 0.811338i \(0.301260\pi\)
\(60\) 6.50527 0.839826
\(61\) −0.678469 −0.0868691 −0.0434346 0.999056i \(-0.513830\pi\)
−0.0434346 + 0.999056i \(0.513830\pi\)
\(62\) 7.23718 0.919123
\(63\) 4.87626 0.614351
\(64\) −9.95519 −1.24440
\(65\) −0.940107 −0.116606
\(66\) −9.80561 −1.20699
\(67\) −12.4267 −1.51816 −0.759082 0.650995i \(-0.774352\pi\)
−0.759082 + 0.650995i \(0.774352\pi\)
\(68\) −8.03086 −0.973885
\(69\) −6.03738 −0.726815
\(70\) 2.11406 0.252678
\(71\) 9.74559 1.15659 0.578295 0.815828i \(-0.303718\pi\)
0.578295 + 0.815828i \(0.303718\pi\)
\(72\) −2.65978 −0.313458
\(73\) 7.51330 0.879365 0.439682 0.898153i \(-0.355091\pi\)
0.439682 + 0.898153i \(0.355091\pi\)
\(74\) 12.8382 1.49242
\(75\) 11.0909 1.28067
\(76\) 1.14583 0.131436
\(77\) −1.69199 −0.192820
\(78\) 5.32173 0.602567
\(79\) −9.35537 −1.05256 −0.526281 0.850311i \(-0.676414\pi\)
−0.526281 + 0.850311i \(0.676414\pi\)
\(80\) 3.48279 0.389388
\(81\) 0.149151 0.0165723
\(82\) −1.41171 −0.155897
\(83\) 2.78477 0.305668 0.152834 0.988252i \(-0.451160\pi\)
0.152834 + 0.988252i \(0.451160\pi\)
\(84\) −6.35425 −0.693306
\(85\) 3.63127 0.393867
\(86\) −5.27364 −0.568671
\(87\) 0.839092 0.0899601
\(88\) 0.922906 0.0983821
\(89\) −6.72030 −0.712351 −0.356175 0.934419i \(-0.615919\pi\)
−0.356175 + 0.934419i \(0.615919\pi\)
\(90\) 10.3087 1.08663
\(91\) 0.918283 0.0962622
\(92\) 4.87071 0.507807
\(93\) 9.83588 1.01993
\(94\) 17.0141 1.75487
\(95\) −0.518104 −0.0531563
\(96\) −22.7769 −2.32465
\(97\) 13.2887 1.34927 0.674633 0.738153i \(-0.264302\pi\)
0.674633 + 0.738153i \(0.264302\pi\)
\(98\) −2.06498 −0.208595
\(99\) −8.25060 −0.829216
\(100\) −8.94768 −0.894768
\(101\) −1.03104 −0.102593 −0.0512963 0.998683i \(-0.516335\pi\)
−0.0512963 + 0.998683i \(0.516335\pi\)
\(102\) −20.5558 −2.03533
\(103\) 17.9419 1.76787 0.883934 0.467611i \(-0.154885\pi\)
0.883934 + 0.467611i \(0.154885\pi\)
\(104\) −0.500882 −0.0491155
\(105\) 2.87317 0.280392
\(106\) −23.6035 −2.29258
\(107\) −10.4986 −1.01493 −0.507467 0.861671i \(-0.669418\pi\)
−0.507467 + 0.861671i \(0.669418\pi\)
\(108\) −11.9222 −1.14722
\(109\) −17.6190 −1.68759 −0.843797 0.536663i \(-0.819685\pi\)
−0.843797 + 0.536663i \(0.819685\pi\)
\(110\) −3.57697 −0.341051
\(111\) 17.4482 1.65611
\(112\) −3.40194 −0.321453
\(113\) 5.43187 0.510987 0.255494 0.966811i \(-0.417762\pi\)
0.255494 + 0.966811i \(0.417762\pi\)
\(114\) 2.93286 0.274688
\(115\) −2.20236 −0.205371
\(116\) −0.676946 −0.0628528
\(117\) 4.47779 0.413972
\(118\) −18.5445 −1.70716
\(119\) −3.54697 −0.325150
\(120\) −1.56718 −0.143064
\(121\) −8.13716 −0.739742
\(122\) 1.40103 0.126843
\(123\) −1.91862 −0.172996
\(124\) −7.93519 −0.712601
\(125\) 9.16466 0.819712
\(126\) −10.0694 −0.897052
\(127\) −12.7951 −1.13538 −0.567690 0.823243i \(-0.692163\pi\)
−0.567690 + 0.823243i \(0.692163\pi\)
\(128\) 4.32558 0.382331
\(129\) −7.16728 −0.631044
\(130\) 1.94130 0.170264
\(131\) 9.84354 0.860034 0.430017 0.902821i \(-0.358507\pi\)
0.430017 + 0.902821i \(0.358507\pi\)
\(132\) 10.7513 0.935784
\(133\) 0.506076 0.0438824
\(134\) 25.6609 2.21677
\(135\) 5.39082 0.463968
\(136\) 1.93471 0.165900
\(137\) 3.81115 0.325609 0.162804 0.986658i \(-0.447946\pi\)
0.162804 + 0.986658i \(0.447946\pi\)
\(138\) 12.4671 1.06127
\(139\) 3.61791 0.306867 0.153433 0.988159i \(-0.450967\pi\)
0.153433 + 0.988159i \(0.450967\pi\)
\(140\) −2.31796 −0.195903
\(141\) 23.1234 1.94735
\(142\) −20.1245 −1.68881
\(143\) −1.55373 −0.129929
\(144\) −16.5887 −1.38239
\(145\) 0.306091 0.0254195
\(146\) −15.5148 −1.28401
\(147\) −2.80647 −0.231474
\(148\) −14.0765 −1.15708
\(149\) −6.58401 −0.539383 −0.269692 0.962947i \(-0.586922\pi\)
−0.269692 + 0.962947i \(0.586922\pi\)
\(150\) −22.9025 −1.86998
\(151\) −4.83357 −0.393350 −0.196675 0.980469i \(-0.563014\pi\)
−0.196675 + 0.980469i \(0.563014\pi\)
\(152\) −0.276042 −0.0223899
\(153\) −17.2960 −1.39830
\(154\) 3.49393 0.281549
\(155\) 3.58801 0.288196
\(156\) −5.83500 −0.467174
\(157\) −4.94014 −0.394266 −0.197133 0.980377i \(-0.563163\pi\)
−0.197133 + 0.980377i \(0.563163\pi\)
\(158\) 19.3187 1.53691
\(159\) −32.0790 −2.54403
\(160\) −8.30873 −0.656862
\(161\) 2.15124 0.169541
\(162\) −0.307994 −0.0241983
\(163\) −9.96978 −0.780893 −0.390447 0.920626i \(-0.627679\pi\)
−0.390447 + 0.920626i \(0.627679\pi\)
\(164\) 1.54787 0.120868
\(165\) −4.86138 −0.378458
\(166\) −5.75050 −0.446325
\(167\) −6.25304 −0.483875 −0.241937 0.970292i \(-0.577783\pi\)
−0.241937 + 0.970292i \(0.577783\pi\)
\(168\) 1.53080 0.118104
\(169\) −12.1568 −0.935135
\(170\) −7.49850 −0.575109
\(171\) 2.46776 0.188714
\(172\) 5.78228 0.440894
\(173\) 5.93575 0.451287 0.225643 0.974210i \(-0.427552\pi\)
0.225643 + 0.974210i \(0.427552\pi\)
\(174\) −1.73271 −0.131356
\(175\) −3.95190 −0.298736
\(176\) 5.75605 0.433879
\(177\) −25.2034 −1.89440
\(178\) 13.8773 1.04015
\(179\) −2.24032 −0.167449 −0.0837247 0.996489i \(-0.526682\pi\)
−0.0837247 + 0.996489i \(0.526682\pi\)
\(180\) −11.3030 −0.842473
\(181\) −7.49372 −0.557004 −0.278502 0.960436i \(-0.589838\pi\)
−0.278502 + 0.960436i \(0.589838\pi\)
\(182\) −1.89624 −0.140558
\(183\) 1.90410 0.140755
\(184\) −1.17340 −0.0865044
\(185\) 6.36488 0.467956
\(186\) −20.3109 −1.48927
\(187\) 6.00145 0.438870
\(188\) −18.6551 −1.36056
\(189\) −5.26567 −0.383021
\(190\) 1.06987 0.0776168
\(191\) 2.28757 0.165523 0.0827614 0.996569i \(-0.473626\pi\)
0.0827614 + 0.996569i \(0.473626\pi\)
\(192\) 27.9389 2.01632
\(193\) 4.01124 0.288736 0.144368 0.989524i \(-0.453885\pi\)
0.144368 + 0.989524i \(0.453885\pi\)
\(194\) −27.4410 −1.97015
\(195\) 2.63838 0.188938
\(196\) 2.26415 0.161725
\(197\) −4.94340 −0.352203 −0.176101 0.984372i \(-0.556349\pi\)
−0.176101 + 0.984372i \(0.556349\pi\)
\(198\) 17.0373 1.21079
\(199\) −16.3570 −1.15952 −0.579759 0.814788i \(-0.696853\pi\)
−0.579759 + 0.814788i \(0.696853\pi\)
\(200\) 2.15559 0.152423
\(201\) 34.8752 2.45990
\(202\) 2.12908 0.149802
\(203\) −0.298985 −0.0209846
\(204\) 22.5384 1.57800
\(205\) −0.699891 −0.0488825
\(206\) −37.0497 −2.58137
\(207\) 10.4900 0.729105
\(208\) −3.12394 −0.216606
\(209\) −0.856277 −0.0592299
\(210\) −5.93303 −0.409418
\(211\) −24.5271 −1.68851 −0.844257 0.535938i \(-0.819958\pi\)
−0.844257 + 0.535938i \(0.819958\pi\)
\(212\) 25.8801 1.77745
\(213\) −27.3507 −1.87404
\(214\) 21.6793 1.48197
\(215\) −2.61454 −0.178310
\(216\) 2.87219 0.195428
\(217\) −3.50472 −0.237916
\(218\) 36.3829 2.46416
\(219\) −21.0858 −1.42485
\(220\) 3.92196 0.264419
\(221\) −3.25712 −0.219098
\(222\) −36.0301 −2.41818
\(223\) −12.6888 −0.849702 −0.424851 0.905263i \(-0.639674\pi\)
−0.424851 + 0.905263i \(0.639674\pi\)
\(224\) 8.11584 0.542263
\(225\) −19.2705 −1.28470
\(226\) −11.2167 −0.746124
\(227\) −9.39925 −0.623850 −0.311925 0.950107i \(-0.600974\pi\)
−0.311925 + 0.950107i \(0.600974\pi\)
\(228\) −3.21573 −0.212967
\(229\) 19.8059 1.30881 0.654404 0.756145i \(-0.272920\pi\)
0.654404 + 0.756145i \(0.272920\pi\)
\(230\) 4.54784 0.299876
\(231\) 4.74852 0.312430
\(232\) 0.163083 0.0107069
\(233\) −17.2889 −1.13263 −0.566317 0.824188i \(-0.691632\pi\)
−0.566317 + 0.824188i \(0.691632\pi\)
\(234\) −9.24655 −0.604466
\(235\) 8.43516 0.550249
\(236\) 20.3331 1.32357
\(237\) 26.2556 1.70548
\(238\) 7.32443 0.474772
\(239\) 9.35601 0.605190 0.302595 0.953119i \(-0.402147\pi\)
0.302595 + 0.953119i \(0.402147\pi\)
\(240\) −9.77433 −0.630930
\(241\) −24.2805 −1.56404 −0.782021 0.623252i \(-0.785811\pi\)
−0.782021 + 0.623252i \(0.785811\pi\)
\(242\) 16.8031 1.08014
\(243\) 15.3784 0.986527
\(244\) −1.53615 −0.0983421
\(245\) −1.02377 −0.0654060
\(246\) 3.96192 0.252603
\(247\) 0.464721 0.0295695
\(248\) 1.91167 0.121391
\(249\) −7.81537 −0.495279
\(250\) −18.9248 −1.19691
\(251\) 28.2892 1.78560 0.892799 0.450456i \(-0.148738\pi\)
0.892799 + 0.450456i \(0.148738\pi\)
\(252\) 11.0406 0.695490
\(253\) −3.63988 −0.228837
\(254\) 26.4216 1.65784
\(255\) −10.1910 −0.638188
\(256\) 10.9781 0.686133
\(257\) −17.1025 −1.06683 −0.533414 0.845855i \(-0.679091\pi\)
−0.533414 + 0.845855i \(0.679091\pi\)
\(258\) 14.8003 0.921427
\(259\) −6.21713 −0.386313
\(260\) −2.12854 −0.132006
\(261\) −1.45793 −0.0902436
\(262\) −20.3267 −1.25579
\(263\) −5.45041 −0.336087 −0.168043 0.985780i \(-0.553745\pi\)
−0.168043 + 0.985780i \(0.553745\pi\)
\(264\) −2.59011 −0.159410
\(265\) −11.7021 −0.718851
\(266\) −1.04504 −0.0640753
\(267\) 18.8603 1.15423
\(268\) −28.1359 −1.71867
\(269\) −21.8795 −1.33402 −0.667008 0.745050i \(-0.732425\pi\)
−0.667008 + 0.745050i \(0.732425\pi\)
\(270\) −11.1319 −0.677468
\(271\) 10.5405 0.640290 0.320145 0.947369i \(-0.396268\pi\)
0.320145 + 0.947369i \(0.396268\pi\)
\(272\) 12.0666 0.731644
\(273\) −2.57713 −0.155975
\(274\) −7.86996 −0.475442
\(275\) 6.68659 0.403216
\(276\) −13.6695 −0.822807
\(277\) 5.76946 0.346654 0.173327 0.984864i \(-0.444548\pi\)
0.173327 + 0.984864i \(0.444548\pi\)
\(278\) −7.47091 −0.448075
\(279\) −17.0899 −1.02315
\(280\) 0.558418 0.0333719
\(281\) −15.8397 −0.944915 −0.472457 0.881354i \(-0.656633\pi\)
−0.472457 + 0.881354i \(0.656633\pi\)
\(282\) −47.7495 −2.84344
\(283\) 4.44826 0.264422 0.132211 0.991222i \(-0.457792\pi\)
0.132211 + 0.991222i \(0.457792\pi\)
\(284\) 22.0654 1.30934
\(285\) 1.45404 0.0861300
\(286\) 3.20842 0.189718
\(287\) 0.683643 0.0403542
\(288\) 39.5750 2.33198
\(289\) −4.41898 −0.259940
\(290\) −0.632072 −0.0371165
\(291\) −37.2944 −2.18624
\(292\) 17.0112 0.995505
\(293\) 9.03014 0.527547 0.263773 0.964585i \(-0.415033\pi\)
0.263773 + 0.964585i \(0.415033\pi\)
\(294\) 5.79530 0.337989
\(295\) −9.19389 −0.535289
\(296\) 3.39116 0.197107
\(297\) 8.90948 0.516980
\(298\) 13.5959 0.787587
\(299\) 1.97544 0.114243
\(300\) 25.1114 1.44981
\(301\) 2.55384 0.147201
\(302\) 9.98123 0.574355
\(303\) 2.89359 0.166232
\(304\) −1.72164 −0.0987427
\(305\) 0.694594 0.0397723
\(306\) 35.7158 2.04174
\(307\) 8.87610 0.506586 0.253293 0.967390i \(-0.418486\pi\)
0.253293 + 0.967390i \(0.418486\pi\)
\(308\) −3.83092 −0.218287
\(309\) −50.3534 −2.86450
\(310\) −7.40918 −0.420813
\(311\) −2.34651 −0.133059 −0.0665293 0.997784i \(-0.521193\pi\)
−0.0665293 + 0.997784i \(0.521193\pi\)
\(312\) 1.40571 0.0795826
\(313\) 23.5534 1.33131 0.665657 0.746257i \(-0.268151\pi\)
0.665657 + 0.746257i \(0.268151\pi\)
\(314\) 10.2013 0.575692
\(315\) −4.99215 −0.281276
\(316\) −21.1819 −1.19158
\(317\) 14.0310 0.788062 0.394031 0.919097i \(-0.371080\pi\)
0.394031 + 0.919097i \(0.371080\pi\)
\(318\) 66.2426 3.71470
\(319\) 0.505881 0.0283239
\(320\) 10.1918 0.569738
\(321\) 29.4639 1.64451
\(322\) −4.44226 −0.247558
\(323\) −1.79504 −0.0998786
\(324\) 0.337699 0.0187611
\(325\) −3.62897 −0.201299
\(326\) 20.5874 1.14023
\(327\) 49.4471 2.73443
\(328\) −0.372897 −0.0205898
\(329\) −8.23934 −0.454249
\(330\) 10.0386 0.552609
\(331\) 27.8594 1.53129 0.765644 0.643264i \(-0.222420\pi\)
0.765644 + 0.643264i \(0.222420\pi\)
\(332\) 6.30513 0.346039
\(333\) −30.3163 −1.66133
\(334\) 12.9124 0.706535
\(335\) 12.7220 0.695080
\(336\) 9.54743 0.520855
\(337\) 30.1419 1.64193 0.820966 0.570977i \(-0.193436\pi\)
0.820966 + 0.570977i \(0.193436\pi\)
\(338\) 25.1035 1.36545
\(339\) −15.2444 −0.827960
\(340\) 8.22173 0.445886
\(341\) 5.92996 0.321125
\(342\) −5.09588 −0.275553
\(343\) 1.00000 0.0539949
\(344\) −1.39301 −0.0751059
\(345\) 6.18086 0.332767
\(346\) −12.2572 −0.658952
\(347\) 29.5531 1.58649 0.793246 0.608901i \(-0.208389\pi\)
0.793246 + 0.608901i \(0.208389\pi\)
\(348\) 1.89983 0.101841
\(349\) −9.25469 −0.495392 −0.247696 0.968838i \(-0.579673\pi\)
−0.247696 + 0.968838i \(0.579673\pi\)
\(350\) 8.16060 0.436203
\(351\) −4.83538 −0.258093
\(352\) −13.7319 −0.731915
\(353\) 18.9944 1.01097 0.505486 0.862835i \(-0.331313\pi\)
0.505486 + 0.862835i \(0.331313\pi\)
\(354\) 52.0445 2.76613
\(355\) −9.97721 −0.529535
\(356\) −15.2157 −0.806433
\(357\) 9.95447 0.526846
\(358\) 4.62622 0.244503
\(359\) 33.8191 1.78490 0.892451 0.451144i \(-0.148984\pi\)
0.892451 + 0.451144i \(0.148984\pi\)
\(360\) 2.72299 0.143514
\(361\) −18.7439 −0.986520
\(362\) 15.4744 0.813315
\(363\) 22.8367 1.19862
\(364\) 2.07913 0.108976
\(365\) −7.69186 −0.402610
\(366\) −3.93194 −0.205526
\(367\) −7.79440 −0.406864 −0.203432 0.979089i \(-0.565210\pi\)
−0.203432 + 0.979089i \(0.565210\pi\)
\(368\) −7.31837 −0.381497
\(369\) 3.33362 0.173542
\(370\) −13.1434 −0.683291
\(371\) 11.4304 0.593437
\(372\) 22.2699 1.15464
\(373\) 7.52359 0.389557 0.194778 0.980847i \(-0.437601\pi\)
0.194778 + 0.980847i \(0.437601\pi\)
\(374\) −12.3929 −0.640821
\(375\) −25.7203 −1.32819
\(376\) 4.49419 0.231770
\(377\) −0.274553 −0.0141402
\(378\) 10.8735 0.559273
\(379\) 2.68578 0.137959 0.0689796 0.997618i \(-0.478026\pi\)
0.0689796 + 0.997618i \(0.478026\pi\)
\(380\) −1.17306 −0.0601768
\(381\) 35.9090 1.83967
\(382\) −4.72379 −0.241690
\(383\) −26.2743 −1.34255 −0.671277 0.741207i \(-0.734254\pi\)
−0.671277 + 0.741207i \(0.734254\pi\)
\(384\) −12.1396 −0.619497
\(385\) 1.73220 0.0882813
\(386\) −8.28314 −0.421601
\(387\) 12.4532 0.633033
\(388\) 30.0876 1.52747
\(389\) −9.07599 −0.460171 −0.230085 0.973170i \(-0.573901\pi\)
−0.230085 + 0.973170i \(0.573901\pi\)
\(390\) −5.44820 −0.275881
\(391\) −7.63038 −0.385885
\(392\) −0.545455 −0.0275496
\(393\) −27.6256 −1.39353
\(394\) 10.2080 0.514273
\(395\) 9.57772 0.481907
\(396\) −18.6806 −0.938733
\(397\) −22.1154 −1.10994 −0.554971 0.831870i \(-0.687271\pi\)
−0.554971 + 0.831870i \(0.687271\pi\)
\(398\) 33.7769 1.69308
\(399\) −1.42029 −0.0711032
\(400\) 13.4441 0.672206
\(401\) −12.8451 −0.641454 −0.320727 0.947172i \(-0.603927\pi\)
−0.320727 + 0.947172i \(0.603927\pi\)
\(402\) −72.0166 −3.59186
\(403\) −3.21832 −0.160316
\(404\) −2.33443 −0.116142
\(405\) −0.152696 −0.00758751
\(406\) 0.617399 0.0306410
\(407\) 10.5193 0.521424
\(408\) −5.42971 −0.268811
\(409\) −33.7890 −1.67076 −0.835379 0.549674i \(-0.814752\pi\)
−0.835379 + 0.549674i \(0.814752\pi\)
\(410\) 1.44526 0.0713764
\(411\) −10.6959 −0.527589
\(412\) 40.6231 2.00136
\(413\) 8.98046 0.441899
\(414\) −21.6616 −1.06461
\(415\) −2.85096 −0.139948
\(416\) 7.45264 0.365396
\(417\) −10.1535 −0.497221
\(418\) 1.76819 0.0864852
\(419\) 4.45896 0.217835 0.108917 0.994051i \(-0.465262\pi\)
0.108917 + 0.994051i \(0.465262\pi\)
\(420\) 6.50527 0.317425
\(421\) −10.9889 −0.535568 −0.267784 0.963479i \(-0.586291\pi\)
−0.267784 + 0.963479i \(0.586291\pi\)
\(422\) 50.6480 2.46550
\(423\) −40.1772 −1.95348
\(424\) −6.23477 −0.302787
\(425\) 14.0173 0.679939
\(426\) 56.4787 2.73640
\(427\) −0.678469 −0.0328334
\(428\) −23.7703 −1.14898
\(429\) 4.36049 0.210526
\(430\) 5.39897 0.260362
\(431\) −10.9556 −0.527713 −0.263856 0.964562i \(-0.584994\pi\)
−0.263856 + 0.964562i \(0.584994\pi\)
\(432\) 17.9135 0.861863
\(433\) 6.19954 0.297931 0.148965 0.988842i \(-0.452406\pi\)
0.148965 + 0.988842i \(0.452406\pi\)
\(434\) 7.23718 0.347396
\(435\) −0.859034 −0.0411875
\(436\) −39.8920 −1.91048
\(437\) 1.08869 0.0520791
\(438\) 43.5418 2.08051
\(439\) −32.1238 −1.53318 −0.766592 0.642135i \(-0.778049\pi\)
−0.766592 + 0.642135i \(0.778049\pi\)
\(440\) −0.944840 −0.0450435
\(441\) 4.87626 0.232203
\(442\) 6.72590 0.319918
\(443\) 10.4476 0.496380 0.248190 0.968711i \(-0.420164\pi\)
0.248190 + 0.968711i \(0.420164\pi\)
\(444\) 39.5052 1.87483
\(445\) 6.88002 0.326144
\(446\) 26.2020 1.24070
\(447\) 18.4778 0.873971
\(448\) −9.95519 −0.470338
\(449\) 4.45235 0.210119 0.105060 0.994466i \(-0.466497\pi\)
0.105060 + 0.994466i \(0.466497\pi\)
\(450\) 39.7932 1.87587
\(451\) −1.15672 −0.0544678
\(452\) 12.2985 0.578474
\(453\) 13.5653 0.637352
\(454\) 19.4093 0.910922
\(455\) −0.940107 −0.0440729
\(456\) 0.774702 0.0362788
\(457\) −5.83831 −0.273105 −0.136552 0.990633i \(-0.543602\pi\)
−0.136552 + 0.990633i \(0.543602\pi\)
\(458\) −40.8987 −1.91107
\(459\) 18.6772 0.871777
\(460\) −4.98647 −0.232495
\(461\) −20.6749 −0.962927 −0.481463 0.876466i \(-0.659895\pi\)
−0.481463 + 0.876466i \(0.659895\pi\)
\(462\) −9.80561 −0.456198
\(463\) 8.06727 0.374918 0.187459 0.982272i \(-0.439975\pi\)
0.187459 + 0.982272i \(0.439975\pi\)
\(464\) 1.01713 0.0472190
\(465\) −10.0696 −0.466969
\(466\) 35.7013 1.65383
\(467\) 16.8549 0.779951 0.389976 0.920825i \(-0.372483\pi\)
0.389976 + 0.920825i \(0.372483\pi\)
\(468\) 10.1384 0.468646
\(469\) −12.4267 −0.573812
\(470\) −17.4184 −0.803453
\(471\) 13.8643 0.638835
\(472\) −4.89843 −0.225469
\(473\) −4.32109 −0.198684
\(474\) −54.2172 −2.49028
\(475\) −1.99996 −0.0917646
\(476\) −8.03086 −0.368094
\(477\) 55.7376 2.55205
\(478\) −19.3200 −0.883676
\(479\) 11.7760 0.538060 0.269030 0.963132i \(-0.413297\pi\)
0.269030 + 0.963132i \(0.413297\pi\)
\(480\) 23.3182 1.06432
\(481\) −5.70908 −0.260312
\(482\) 50.1387 2.28376
\(483\) −6.03738 −0.274710
\(484\) −18.4237 −0.837442
\(485\) −13.6045 −0.617751
\(486\) −31.7562 −1.44049
\(487\) 32.8261 1.48749 0.743747 0.668462i \(-0.233047\pi\)
0.743747 + 0.668462i \(0.233047\pi\)
\(488\) 0.370075 0.0167525
\(489\) 27.9799 1.26529
\(490\) 2.11406 0.0955034
\(491\) −17.1690 −0.774828 −0.387414 0.921906i \(-0.626632\pi\)
−0.387414 + 0.921906i \(0.626632\pi\)
\(492\) −4.34404 −0.195845
\(493\) 1.06049 0.0477622
\(494\) −0.959640 −0.0431762
\(495\) 8.44668 0.379650
\(496\) 11.9228 0.535351
\(497\) 9.74559 0.437150
\(498\) 16.1386 0.723188
\(499\) −11.0580 −0.495026 −0.247513 0.968885i \(-0.579613\pi\)
−0.247513 + 0.968885i \(0.579613\pi\)
\(500\) 20.7501 0.927973
\(501\) 17.5490 0.784030
\(502\) −58.4166 −2.60726
\(503\) 37.8967 1.68973 0.844866 0.534978i \(-0.179680\pi\)
0.844866 + 0.534978i \(0.179680\pi\)
\(504\) −2.65978 −0.118476
\(505\) 1.05555 0.0469712
\(506\) 7.51627 0.334139
\(507\) 34.1175 1.51521
\(508\) −28.9699 −1.28533
\(509\) 26.1254 1.15799 0.578993 0.815333i \(-0.303446\pi\)
0.578993 + 0.815333i \(0.303446\pi\)
\(510\) 21.0443 0.931858
\(511\) 7.51330 0.332369
\(512\) −31.3208 −1.38420
\(513\) −2.66483 −0.117655
\(514\) 35.3164 1.55774
\(515\) −18.3683 −0.809405
\(516\) −16.2278 −0.714388
\(517\) 13.9409 0.613120
\(518\) 12.8382 0.564080
\(519\) −16.6585 −0.731227
\(520\) 0.512786 0.0224872
\(521\) −5.02881 −0.220316 −0.110158 0.993914i \(-0.535136\pi\)
−0.110158 + 0.993914i \(0.535136\pi\)
\(522\) 3.01060 0.131770
\(523\) 28.8535 1.26168 0.630838 0.775914i \(-0.282711\pi\)
0.630838 + 0.775914i \(0.282711\pi\)
\(524\) 22.2872 0.973621
\(525\) 11.0909 0.484046
\(526\) 11.2550 0.490741
\(527\) 12.4311 0.541509
\(528\) −16.1542 −0.703020
\(529\) −18.3722 −0.798790
\(530\) 24.1645 1.04964
\(531\) 43.7911 1.90037
\(532\) 1.14583 0.0496780
\(533\) 0.627778 0.0271921
\(534\) −38.9462 −1.68537
\(535\) 10.7481 0.464680
\(536\) 6.77821 0.292774
\(537\) 6.28738 0.271321
\(538\) 45.1807 1.94788
\(539\) −1.69199 −0.0728793
\(540\) 12.2056 0.525245
\(541\) 26.2011 1.12648 0.563238 0.826295i \(-0.309556\pi\)
0.563238 + 0.826295i \(0.309556\pi\)
\(542\) −21.7659 −0.934927
\(543\) 21.0309 0.902521
\(544\) −28.7867 −1.23422
\(545\) 18.0377 0.772651
\(546\) 5.32173 0.227749
\(547\) 31.5945 1.35088 0.675442 0.737413i \(-0.263953\pi\)
0.675442 + 0.737413i \(0.263953\pi\)
\(548\) 8.62901 0.368613
\(549\) −3.30840 −0.141199
\(550\) −13.8077 −0.588761
\(551\) −0.151309 −0.00644599
\(552\) 3.29312 0.140164
\(553\) −9.35537 −0.397831
\(554\) −11.9138 −0.506170
\(555\) −17.8628 −0.758236
\(556\) 8.19147 0.347396
\(557\) −24.8892 −1.05459 −0.527295 0.849682i \(-0.676794\pi\)
−0.527295 + 0.849682i \(0.676794\pi\)
\(558\) 35.2904 1.49396
\(559\) 2.34515 0.0991894
\(560\) 3.48279 0.147175
\(561\) −16.8429 −0.711107
\(562\) 32.7086 1.37973
\(563\) −24.9465 −1.05137 −0.525686 0.850679i \(-0.676191\pi\)
−0.525686 + 0.850679i \(0.676191\pi\)
\(564\) 52.3548 2.20454
\(565\) −5.56096 −0.233951
\(566\) −9.18558 −0.386099
\(567\) 0.149151 0.00626375
\(568\) −5.31578 −0.223045
\(569\) −16.3047 −0.683530 −0.341765 0.939786i \(-0.611025\pi\)
−0.341765 + 0.939786i \(0.611025\pi\)
\(570\) −3.00257 −0.125764
\(571\) 18.9627 0.793565 0.396782 0.917913i \(-0.370127\pi\)
0.396782 + 0.917913i \(0.370127\pi\)
\(572\) −3.51787 −0.147089
\(573\) −6.41999 −0.268199
\(574\) −1.41171 −0.0589237
\(575\) −8.50148 −0.354536
\(576\) −48.5441 −2.02267
\(577\) 17.9199 0.746016 0.373008 0.927828i \(-0.378326\pi\)
0.373008 + 0.927828i \(0.378326\pi\)
\(578\) 9.12511 0.379555
\(579\) −11.2574 −0.467843
\(580\) 0.693034 0.0287767
\(581\) 2.78477 0.115532
\(582\) 77.0122 3.19226
\(583\) −19.3401 −0.800987
\(584\) −4.09816 −0.169583
\(585\) −4.58421 −0.189534
\(586\) −18.6471 −0.770303
\(587\) 7.35993 0.303777 0.151888 0.988398i \(-0.451465\pi\)
0.151888 + 0.988398i \(0.451465\pi\)
\(588\) −6.35425 −0.262045
\(589\) −1.77365 −0.0730822
\(590\) 18.9852 0.781608
\(591\) 13.8735 0.570679
\(592\) 21.1503 0.869271
\(593\) −10.5947 −0.435071 −0.217535 0.976052i \(-0.569802\pi\)
−0.217535 + 0.976052i \(0.569802\pi\)
\(594\) −18.3979 −0.754875
\(595\) 3.63127 0.148868
\(596\) −14.9072 −0.610621
\(597\) 45.9054 1.87878
\(598\) −4.07925 −0.166813
\(599\) −18.6385 −0.761550 −0.380775 0.924668i \(-0.624343\pi\)
−0.380775 + 0.924668i \(0.624343\pi\)
\(600\) −6.04958 −0.246973
\(601\) −35.2608 −1.43832 −0.719158 0.694846i \(-0.755472\pi\)
−0.719158 + 0.694846i \(0.755472\pi\)
\(602\) −5.27364 −0.214938
\(603\) −60.5959 −2.46766
\(604\) −10.9439 −0.445301
\(605\) 8.33055 0.338685
\(606\) −5.97521 −0.242726
\(607\) 30.6163 1.24268 0.621339 0.783542i \(-0.286589\pi\)
0.621339 + 0.783542i \(0.286589\pi\)
\(608\) 4.10723 0.166570
\(609\) 0.839092 0.0340017
\(610\) −1.43432 −0.0580741
\(611\) −7.56604 −0.306089
\(612\) −39.1606 −1.58297
\(613\) 6.52551 0.263563 0.131781 0.991279i \(-0.457930\pi\)
0.131781 + 0.991279i \(0.457930\pi\)
\(614\) −18.3290 −0.739697
\(615\) 1.96422 0.0792051
\(616\) 0.922906 0.0371849
\(617\) 1.28114 0.0515767 0.0257883 0.999667i \(-0.491790\pi\)
0.0257883 + 0.999667i \(0.491790\pi\)
\(618\) 103.979 4.18264
\(619\) 40.2356 1.61721 0.808603 0.588354i \(-0.200224\pi\)
0.808603 + 0.588354i \(0.200224\pi\)
\(620\) 8.12378 0.326259
\(621\) −11.3277 −0.454565
\(622\) 4.84551 0.194287
\(623\) −6.72030 −0.269243
\(624\) 8.76724 0.350970
\(625\) 10.3770 0.415082
\(626\) −48.6372 −1.94394
\(627\) 2.40311 0.0959711
\(628\) −11.1852 −0.446338
\(629\) 22.0520 0.879270
\(630\) 10.3087 0.410708
\(631\) 0.641080 0.0255210 0.0127605 0.999919i \(-0.495938\pi\)
0.0127605 + 0.999919i \(0.495938\pi\)
\(632\) 5.10294 0.202984
\(633\) 68.8345 2.73593
\(634\) −28.9738 −1.15070
\(635\) 13.0992 0.519825
\(636\) −72.6316 −2.88003
\(637\) 0.918283 0.0363837
\(638\) −1.04463 −0.0413574
\(639\) 47.5221 1.87994
\(640\) −4.42838 −0.175047
\(641\) 34.7040 1.37072 0.685362 0.728202i \(-0.259644\pi\)
0.685362 + 0.728202i \(0.259644\pi\)
\(642\) −60.8423 −2.40126
\(643\) 7.88103 0.310797 0.155399 0.987852i \(-0.450334\pi\)
0.155399 + 0.987852i \(0.450334\pi\)
\(644\) 4.87071 0.191933
\(645\) 7.33762 0.288919
\(646\) 3.70672 0.145839
\(647\) −42.1567 −1.65735 −0.828675 0.559731i \(-0.810905\pi\)
−0.828675 + 0.559731i \(0.810905\pi\)
\(648\) −0.0813551 −0.00319593
\(649\) −15.1949 −0.596450
\(650\) 7.49374 0.293929
\(651\) 9.83588 0.385499
\(652\) −22.5730 −0.884028
\(653\) −2.49133 −0.0974931 −0.0487466 0.998811i \(-0.515523\pi\)
−0.0487466 + 0.998811i \(0.515523\pi\)
\(654\) −102.107 −3.99271
\(655\) −10.0775 −0.393760
\(656\) −2.32571 −0.0908038
\(657\) 36.6368 1.42934
\(658\) 17.0141 0.663278
\(659\) 43.8459 1.70799 0.853997 0.520277i \(-0.174171\pi\)
0.853997 + 0.520277i \(0.174171\pi\)
\(660\) −11.0069 −0.428442
\(661\) 1.49016 0.0579606 0.0289803 0.999580i \(-0.490774\pi\)
0.0289803 + 0.999580i \(0.490774\pi\)
\(662\) −57.5290 −2.23593
\(663\) 9.14102 0.355008
\(664\) −1.51897 −0.0589474
\(665\) −0.518104 −0.0200912
\(666\) 62.6027 2.42580
\(667\) −0.643188 −0.0249043
\(668\) −14.1578 −0.547781
\(669\) 35.6106 1.37679
\(670\) −26.2708 −1.01493
\(671\) 1.14796 0.0443167
\(672\) −22.7769 −0.878636
\(673\) 3.72213 0.143478 0.0717388 0.997423i \(-0.477145\pi\)
0.0717388 + 0.997423i \(0.477145\pi\)
\(674\) −62.2424 −2.39749
\(675\) 20.8094 0.800955
\(676\) −27.5247 −1.05864
\(677\) 15.4724 0.594651 0.297326 0.954776i \(-0.403905\pi\)
0.297326 + 0.954776i \(0.403905\pi\)
\(678\) 31.4793 1.20896
\(679\) 13.2887 0.509975
\(680\) −1.98069 −0.0759562
\(681\) 26.3787 1.01083
\(682\) −12.2452 −0.468895
\(683\) 27.0697 1.03579 0.517897 0.855443i \(-0.326715\pi\)
0.517897 + 0.855443i \(0.326715\pi\)
\(684\) 5.58737 0.213638
\(685\) −3.90173 −0.149077
\(686\) −2.06498 −0.0788413
\(687\) −55.5845 −2.12068
\(688\) −8.68802 −0.331228
\(689\) 10.4963 0.399879
\(690\) −12.7634 −0.485893
\(691\) 16.7655 0.637788 0.318894 0.947790i \(-0.396689\pi\)
0.318894 + 0.947790i \(0.396689\pi\)
\(692\) 13.4394 0.510889
\(693\) −8.25060 −0.313414
\(694\) −61.0265 −2.31654
\(695\) −3.70389 −0.140497
\(696\) −0.457687 −0.0173486
\(697\) −2.42486 −0.0918483
\(698\) 19.1108 0.723353
\(699\) 48.5208 1.83522
\(700\) −8.94768 −0.338191
\(701\) −37.9058 −1.43168 −0.715842 0.698263i \(-0.753957\pi\)
−0.715842 + 0.698263i \(0.753957\pi\)
\(702\) 9.98496 0.376858
\(703\) −3.14634 −0.118666
\(704\) 16.8441 0.634836
\(705\) −23.6730 −0.891577
\(706\) −39.2231 −1.47618
\(707\) −1.03104 −0.0387764
\(708\) −57.0641 −2.14460
\(709\) −30.1518 −1.13237 −0.566187 0.824277i \(-0.691582\pi\)
−0.566187 + 0.824277i \(0.691582\pi\)
\(710\) 20.6027 0.773207
\(711\) −45.6193 −1.71086
\(712\) 3.66562 0.137375
\(713\) −7.53948 −0.282356
\(714\) −20.5558 −0.769281
\(715\) 1.59065 0.0594871
\(716\) −5.07241 −0.189565
\(717\) −26.2574 −0.980599
\(718\) −69.8357 −2.60625
\(719\) −15.6781 −0.584693 −0.292346 0.956312i \(-0.594436\pi\)
−0.292346 + 0.956312i \(0.594436\pi\)
\(720\) 16.9830 0.632919
\(721\) 17.9419 0.668192
\(722\) 38.7058 1.44048
\(723\) 68.1424 2.53424
\(724\) −16.9669 −0.630569
\(725\) 1.18156 0.0438820
\(726\) −47.1573 −1.75017
\(727\) 11.8202 0.438389 0.219194 0.975681i \(-0.429657\pi\)
0.219194 + 0.975681i \(0.429657\pi\)
\(728\) −0.500882 −0.0185639
\(729\) −43.6065 −1.61506
\(730\) 15.8835 0.587876
\(731\) −9.05842 −0.335038
\(732\) 4.31117 0.159345
\(733\) 6.42038 0.237142 0.118571 0.992946i \(-0.462169\pi\)
0.118571 + 0.992946i \(0.462169\pi\)
\(734\) 16.0953 0.594088
\(735\) 2.87317 0.105978
\(736\) 17.4591 0.643551
\(737\) 21.0259 0.774499
\(738\) −6.88387 −0.253399
\(739\) −12.9192 −0.475242 −0.237621 0.971358i \(-0.576368\pi\)
−0.237621 + 0.971358i \(0.576368\pi\)
\(740\) 14.4110 0.529760
\(741\) −1.30422 −0.0479119
\(742\) −23.6035 −0.866513
\(743\) 5.08323 0.186486 0.0932428 0.995643i \(-0.470277\pi\)
0.0932428 + 0.995643i \(0.470277\pi\)
\(744\) −5.36503 −0.196692
\(745\) 6.74049 0.246953
\(746\) −15.5361 −0.568816
\(747\) 13.5793 0.496840
\(748\) 13.5882 0.496832
\(749\) −10.4986 −0.383609
\(750\) 53.1120 1.93937
\(751\) 23.8574 0.870567 0.435284 0.900293i \(-0.356648\pi\)
0.435284 + 0.900293i \(0.356648\pi\)
\(752\) 28.0297 1.02214
\(753\) −79.3927 −2.89323
\(754\) 0.566947 0.0206470
\(755\) 4.94845 0.180092
\(756\) −11.9222 −0.433608
\(757\) −51.1511 −1.85912 −0.929560 0.368672i \(-0.879813\pi\)
−0.929560 + 0.368672i \(0.879813\pi\)
\(758\) −5.54608 −0.201443
\(759\) 10.2152 0.370788
\(760\) 0.282602 0.0102511
\(761\) −6.54358 −0.237205 −0.118602 0.992942i \(-0.537841\pi\)
−0.118602 + 0.992942i \(0.537841\pi\)
\(762\) −74.1513 −2.68622
\(763\) −17.6190 −0.637850
\(764\) 5.17939 0.187384
\(765\) 17.7070 0.640199
\(766\) 54.2559 1.96035
\(767\) 8.24660 0.297767
\(768\) −30.8098 −1.11175
\(769\) 27.3743 0.987143 0.493571 0.869705i \(-0.335691\pi\)
0.493571 + 0.869705i \(0.335691\pi\)
\(770\) −3.57697 −0.128905
\(771\) 47.9977 1.72860
\(772\) 9.08204 0.326870
\(773\) 2.22136 0.0798967 0.0399484 0.999202i \(-0.487281\pi\)
0.0399484 + 0.999202i \(0.487281\pi\)
\(774\) −25.7157 −0.924330
\(775\) 13.8503 0.497518
\(776\) −7.24840 −0.260202
\(777\) 17.4482 0.625950
\(778\) 18.7417 0.671924
\(779\) 0.345976 0.0123959
\(780\) 5.97368 0.213892
\(781\) −16.4895 −0.590040
\(782\) 15.7566 0.563454
\(783\) 1.57436 0.0562630
\(784\) −3.40194 −0.121498
\(785\) 5.05754 0.180512
\(786\) 57.0463 2.03477
\(787\) −11.0694 −0.394580 −0.197290 0.980345i \(-0.563214\pi\)
−0.197290 + 0.980345i \(0.563214\pi\)
\(788\) −11.1926 −0.398719
\(789\) 15.2964 0.544566
\(790\) −19.7778 −0.703663
\(791\) 5.43187 0.193135
\(792\) 4.50033 0.159912
\(793\) −0.623027 −0.0221243
\(794\) 45.6680 1.62070
\(795\) 32.8414 1.16477
\(796\) −37.0346 −1.31266
\(797\) 30.4505 1.07861 0.539306 0.842110i \(-0.318687\pi\)
0.539306 + 0.842110i \(0.318687\pi\)
\(798\) 2.93286 0.103822
\(799\) 29.2247 1.03390
\(800\) −32.0730 −1.13395
\(801\) −32.7700 −1.15787
\(802\) 26.5249 0.936626
\(803\) −12.7124 −0.448612
\(804\) 78.9625 2.78479
\(805\) −2.20236 −0.0776231
\(806\) 6.64578 0.234088
\(807\) 61.4041 2.16153
\(808\) 0.562388 0.0197847
\(809\) 33.0142 1.16072 0.580359 0.814360i \(-0.302912\pi\)
0.580359 + 0.814360i \(0.302912\pi\)
\(810\) 0.315314 0.0110790
\(811\) 6.39049 0.224400 0.112200 0.993686i \(-0.464210\pi\)
0.112200 + 0.993686i \(0.464210\pi\)
\(812\) −0.676946 −0.0237561
\(813\) −29.5816 −1.03747
\(814\) −21.7222 −0.761363
\(815\) 10.2067 0.357526
\(816\) −33.8645 −1.18549
\(817\) 1.29244 0.0452167
\(818\) 69.7736 2.43958
\(819\) 4.47779 0.156467
\(820\) −1.58465 −0.0553386
\(821\) 46.6974 1.62975 0.814876 0.579636i \(-0.196805\pi\)
0.814876 + 0.579636i \(0.196805\pi\)
\(822\) 22.0868 0.770365
\(823\) 52.3912 1.82624 0.913122 0.407687i \(-0.133664\pi\)
0.913122 + 0.407687i \(0.133664\pi\)
\(824\) −9.78650 −0.340929
\(825\) −18.7657 −0.653338
\(826\) −18.5445 −0.645245
\(827\) 34.1972 1.18915 0.594576 0.804039i \(-0.297320\pi\)
0.594576 + 0.804039i \(0.297320\pi\)
\(828\) 23.7509 0.825400
\(829\) −20.3583 −0.707072 −0.353536 0.935421i \(-0.615021\pi\)
−0.353536 + 0.935421i \(0.615021\pi\)
\(830\) 5.88717 0.204347
\(831\) −16.1918 −0.561688
\(832\) −9.14168 −0.316931
\(833\) −3.54697 −0.122895
\(834\) 20.9669 0.726023
\(835\) 6.40165 0.221538
\(836\) −1.93873 −0.0670526
\(837\) 18.4547 0.637888
\(838\) −9.20767 −0.318074
\(839\) −19.5348 −0.674417 −0.337208 0.941430i \(-0.609483\pi\)
−0.337208 + 0.941430i \(0.609483\pi\)
\(840\) −1.56718 −0.0540730
\(841\) −28.9106 −0.996918
\(842\) 22.6919 0.782016
\(843\) 44.4535 1.53106
\(844\) −55.5329 −1.91152
\(845\) 12.4457 0.428144
\(846\) 82.9651 2.85240
\(847\) −8.13716 −0.279596
\(848\) −38.8855 −1.33533
\(849\) −12.4839 −0.428447
\(850\) −28.9454 −0.992820
\(851\) −13.3745 −0.458472
\(852\) −61.9260 −2.12155
\(853\) 38.2627 1.31009 0.655044 0.755590i \(-0.272650\pi\)
0.655044 + 0.755590i \(0.272650\pi\)
\(854\) 1.40103 0.0479421
\(855\) −2.52641 −0.0864014
\(856\) 5.72649 0.195728
\(857\) −3.55161 −0.121321 −0.0606604 0.998158i \(-0.519321\pi\)
−0.0606604 + 0.998158i \(0.519321\pi\)
\(858\) −9.00432 −0.307402
\(859\) −1.00000 −0.0341196
\(860\) −5.91970 −0.201860
\(861\) −1.91862 −0.0653865
\(862\) 22.6231 0.770546
\(863\) 0.131365 0.00447170 0.00223585 0.999998i \(-0.499288\pi\)
0.00223585 + 0.999998i \(0.499288\pi\)
\(864\) −42.7354 −1.45389
\(865\) −6.07682 −0.206618
\(866\) −12.8019 −0.435027
\(867\) 12.4017 0.421185
\(868\) −7.93519 −0.269338
\(869\) 15.8292 0.536970
\(870\) 1.77389 0.0601405
\(871\) −11.4112 −0.386655
\(872\) 9.61037 0.325448
\(873\) 64.7993 2.19312
\(874\) −2.24812 −0.0760439
\(875\) 9.16466 0.309822
\(876\) −47.7414 −1.61303
\(877\) −23.8128 −0.804100 −0.402050 0.915618i \(-0.631702\pi\)
−0.402050 + 0.915618i \(0.631702\pi\)
\(878\) 66.3350 2.23870
\(879\) −25.3428 −0.854792
\(880\) −5.89285 −0.198648
\(881\) 20.5719 0.693086 0.346543 0.938034i \(-0.387355\pi\)
0.346543 + 0.938034i \(0.387355\pi\)
\(882\) −10.0694 −0.339054
\(883\) −47.0017 −1.58173 −0.790866 0.611989i \(-0.790370\pi\)
−0.790866 + 0.611989i \(0.790370\pi\)
\(884\) −7.37460 −0.248035
\(885\) 25.8024 0.867337
\(886\) −21.5741 −0.724795
\(887\) −31.9223 −1.07185 −0.535923 0.844267i \(-0.680036\pi\)
−0.535923 + 0.844267i \(0.680036\pi\)
\(888\) −9.51719 −0.319376
\(889\) −12.7951 −0.429133
\(890\) −14.2071 −0.476223
\(891\) −0.252362 −0.00845445
\(892\) −28.7292 −0.961924
\(893\) −4.16973 −0.139535
\(894\) −38.1564 −1.27614
\(895\) 2.29356 0.0766654
\(896\) 4.32558 0.144508
\(897\) −5.54402 −0.185109
\(898\) −9.19402 −0.306808
\(899\) 1.04786 0.0349481
\(900\) −43.6312 −1.45437
\(901\) −40.5433 −1.35069
\(902\) 2.38860 0.0795318
\(903\) −7.16728 −0.238512
\(904\) −2.96284 −0.0985426
\(905\) 7.67182 0.255020
\(906\) −28.0120 −0.930637
\(907\) −48.6997 −1.61705 −0.808524 0.588463i \(-0.799733\pi\)
−0.808524 + 0.588463i \(0.799733\pi\)
\(908\) −21.2813 −0.706243
\(909\) −5.02764 −0.166756
\(910\) 1.94130 0.0643536
\(911\) 14.7902 0.490020 0.245010 0.969521i \(-0.421209\pi\)
0.245010 + 0.969521i \(0.421209\pi\)
\(912\) 4.83172 0.159994
\(913\) −4.71181 −0.155938
\(914\) 12.0560 0.398777
\(915\) −1.94936 −0.0644437
\(916\) 44.8434 1.48167
\(917\) 9.84354 0.325062
\(918\) −38.5680 −1.27294
\(919\) −5.45164 −0.179833 −0.0899165 0.995949i \(-0.528660\pi\)
−0.0899165 + 0.995949i \(0.528660\pi\)
\(920\) 1.20129 0.0396054
\(921\) −24.9105 −0.820828
\(922\) 42.6933 1.40603
\(923\) 8.94921 0.294567
\(924\) 10.7513 0.353693
\(925\) 24.5695 0.807840
\(926\) −16.6587 −0.547440
\(927\) 87.4895 2.87353
\(928\) −2.42652 −0.0796543
\(929\) 12.8561 0.421795 0.210898 0.977508i \(-0.432361\pi\)
0.210898 + 0.977508i \(0.432361\pi\)
\(930\) 20.7936 0.681850
\(931\) 0.506076 0.0165860
\(932\) −39.1446 −1.28222
\(933\) 6.58542 0.215597
\(934\) −34.8050 −1.13885
\(935\) −6.14408 −0.200933
\(936\) −2.44243 −0.0798334
\(937\) −0.858776 −0.0280550 −0.0140275 0.999902i \(-0.504465\pi\)
−0.0140275 + 0.999902i \(0.504465\pi\)
\(938\) 25.6609 0.837859
\(939\) −66.1018 −2.15715
\(940\) 19.0984 0.622922
\(941\) 43.0100 1.40209 0.701043 0.713119i \(-0.252718\pi\)
0.701043 + 0.713119i \(0.252718\pi\)
\(942\) −28.6296 −0.932802
\(943\) 1.47068 0.0478919
\(944\) −30.5509 −0.994348
\(945\) 5.39082 0.175363
\(946\) 8.92296 0.290110
\(947\) 49.4424 1.60666 0.803331 0.595533i \(-0.203059\pi\)
0.803331 + 0.595533i \(0.203059\pi\)
\(948\) 59.4464 1.93073
\(949\) 6.89933 0.223962
\(950\) 4.12989 0.133991
\(951\) −39.3777 −1.27691
\(952\) 1.93471 0.0627044
\(953\) −7.99729 −0.259058 −0.129529 0.991576i \(-0.541346\pi\)
−0.129529 + 0.991576i \(0.541346\pi\)
\(954\) −115.097 −3.72641
\(955\) −2.34194 −0.0757833
\(956\) 21.1834 0.685119
\(957\) −1.41974 −0.0458936
\(958\) −24.3172 −0.785654
\(959\) 3.81115 0.123069
\(960\) −28.6029 −0.923155
\(961\) −18.7169 −0.603772
\(962\) 11.7891 0.380097
\(963\) −51.1938 −1.64970
\(964\) −54.9745 −1.77061
\(965\) −4.10658 −0.132195
\(966\) 12.4671 0.401121
\(967\) −45.0748 −1.44951 −0.724753 0.689009i \(-0.758046\pi\)
−0.724753 + 0.689009i \(0.758046\pi\)
\(968\) 4.43846 0.142657
\(969\) 5.03772 0.161835
\(970\) 28.0931 0.902016
\(971\) 42.1611 1.35301 0.676507 0.736437i \(-0.263493\pi\)
0.676507 + 0.736437i \(0.263493\pi\)
\(972\) 34.8190 1.11682
\(973\) 3.61791 0.115985
\(974\) −67.7853 −2.17198
\(975\) 10.1846 0.326167
\(976\) 2.30811 0.0738808
\(977\) 32.1161 1.02748 0.513742 0.857944i \(-0.328259\pi\)
0.513742 + 0.857944i \(0.328259\pi\)
\(978\) −57.7779 −1.84753
\(979\) 11.3707 0.363409
\(980\) −2.31796 −0.0740444
\(981\) −85.9148 −2.74305
\(982\) 35.4537 1.13137
\(983\) 10.5460 0.336364 0.168182 0.985756i \(-0.446210\pi\)
0.168182 + 0.985756i \(0.446210\pi\)
\(984\) 1.04652 0.0333619
\(985\) 5.06089 0.161253
\(986\) −2.18990 −0.0697405
\(987\) 23.1234 0.736027
\(988\) 1.05220 0.0334748
\(989\) 5.49393 0.174697
\(990\) −17.4422 −0.554351
\(991\) 23.2410 0.738275 0.369138 0.929375i \(-0.379653\pi\)
0.369138 + 0.929375i \(0.379653\pi\)
\(992\) −28.4438 −0.903090
\(993\) −78.1864 −2.48117
\(994\) −20.1245 −0.638309
\(995\) 16.7457 0.530876
\(996\) −17.6951 −0.560692
\(997\) 55.8652 1.76927 0.884635 0.466285i \(-0.154408\pi\)
0.884635 + 0.466285i \(0.154408\pi\)
\(998\) 22.8346 0.722818
\(999\) 32.7373 1.03576
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 \(a_p\))