Properties

Label 6013.2.a.e.1.12
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 1.12
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.23377 q^{2}\) \(-0.900406 q^{3}\) \(+2.98971 q^{4}\) \(+4.46215 q^{5}\) \(+2.01130 q^{6}\) \(+1.00000 q^{7}\) \(-2.21077 q^{8}\) \(-2.18927 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.23377 q^{2}\) \(-0.900406 q^{3}\) \(+2.98971 q^{4}\) \(+4.46215 q^{5}\) \(+2.01130 q^{6}\) \(+1.00000 q^{7}\) \(-2.21077 q^{8}\) \(-2.18927 q^{9}\) \(-9.96739 q^{10}\) \(-0.526347 q^{11}\) \(-2.69195 q^{12}\) \(-6.37545 q^{13}\) \(-2.23377 q^{14}\) \(-4.01775 q^{15}\) \(-1.04107 q^{16}\) \(+6.97364 q^{17}\) \(+4.89031 q^{18}\) \(+5.09549 q^{19}\) \(+13.3405 q^{20}\) \(-0.900406 q^{21}\) \(+1.17573 q^{22}\) \(-0.455611 q^{23}\) \(+1.99059 q^{24}\) \(+14.9108 q^{25}\) \(+14.2413 q^{26}\) \(+4.67245 q^{27}\) \(+2.98971 q^{28}\) \(-9.94990 q^{29}\) \(+8.97470 q^{30}\) \(+1.30521 q^{31}\) \(+6.74704 q^{32}\) \(+0.473926 q^{33}\) \(-15.5775 q^{34}\) \(+4.46215 q^{35}\) \(-6.54527 q^{36}\) \(+1.57662 q^{37}\) \(-11.3821 q^{38}\) \(+5.74050 q^{39}\) \(-9.86479 q^{40}\) \(+3.19420 q^{41}\) \(+2.01130 q^{42}\) \(-8.41675 q^{43}\) \(-1.57362 q^{44}\) \(-9.76884 q^{45}\) \(+1.01773 q^{46}\) \(-9.20136 q^{47}\) \(+0.937383 q^{48}\) \(+1.00000 q^{49}\) \(-33.3071 q^{50}\) \(-6.27911 q^{51}\) \(-19.0607 q^{52}\) \(+0.888546 q^{53}\) \(-10.4372 q^{54}\) \(-2.34864 q^{55}\) \(-2.21077 q^{56}\) \(-4.58801 q^{57}\) \(+22.2258 q^{58}\) \(+7.52327 q^{59}\) \(-12.0119 q^{60}\) \(+4.92384 q^{61}\) \(-2.91554 q^{62}\) \(-2.18927 q^{63}\) \(-12.9892 q^{64}\) \(-28.4482 q^{65}\) \(-1.05864 q^{66}\) \(+13.5970 q^{67}\) \(+20.8491 q^{68}\) \(+0.410235 q^{69}\) \(-9.96739 q^{70}\) \(-0.849215 q^{71}\) \(+4.83997 q^{72}\) \(-4.88653 q^{73}\) \(-3.52181 q^{74}\) \(-13.4257 q^{75}\) \(+15.2340 q^{76}\) \(-0.526347 q^{77}\) \(-12.8229 q^{78}\) \(+6.03715 q^{79}\) \(-4.64539 q^{80}\) \(+2.36070 q^{81}\) \(-7.13509 q^{82}\) \(-12.1878 q^{83}\) \(-2.69195 q^{84}\) \(+31.1174 q^{85}\) \(+18.8010 q^{86}\) \(+8.95896 q^{87}\) \(+1.16363 q^{88}\) \(+9.45755 q^{89}\) \(+21.8213 q^{90}\) \(-6.37545 q^{91}\) \(-1.36214 q^{92}\) \(-1.17522 q^{93}\) \(+20.5537 q^{94}\) \(+22.7368 q^{95}\) \(-6.07508 q^{96}\) \(+8.91376 q^{97}\) \(-2.23377 q^{98}\) \(+1.15231 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23377 −1.57951 −0.789755 0.613422i \(-0.789792\pi\)
−0.789755 + 0.613422i \(0.789792\pi\)
\(3\) −0.900406 −0.519850 −0.259925 0.965629i \(-0.583698\pi\)
−0.259925 + 0.965629i \(0.583698\pi\)
\(4\) 2.98971 1.49485
\(5\) 4.46215 1.99553 0.997766 0.0667999i \(-0.0212789\pi\)
0.997766 + 0.0667999i \(0.0212789\pi\)
\(6\) 2.01130 0.821108
\(7\) 1.00000 0.377964
\(8\) −2.21077 −0.781626
\(9\) −2.18927 −0.729756
\(10\) −9.96739 −3.15196
\(11\) −0.526347 −0.158699 −0.0793497 0.996847i \(-0.525284\pi\)
−0.0793497 + 0.996847i \(0.525284\pi\)
\(12\) −2.69195 −0.777099
\(13\) −6.37545 −1.76823 −0.884116 0.467267i \(-0.845239\pi\)
−0.884116 + 0.467267i \(0.845239\pi\)
\(14\) −2.23377 −0.596999
\(15\) −4.01775 −1.03738
\(16\) −1.04107 −0.260267
\(17\) 6.97364 1.69136 0.845678 0.533693i \(-0.179196\pi\)
0.845678 + 0.533693i \(0.179196\pi\)
\(18\) 4.89031 1.15266
\(19\) 5.09549 1.16899 0.584493 0.811399i \(-0.301293\pi\)
0.584493 + 0.811399i \(0.301293\pi\)
\(20\) 13.3405 2.98303
\(21\) −0.900406 −0.196485
\(22\) 1.17573 0.250668
\(23\) −0.455611 −0.0950016 −0.0475008 0.998871i \(-0.515126\pi\)
−0.0475008 + 0.998871i \(0.515126\pi\)
\(24\) 1.99059 0.406328
\(25\) 14.9108 2.98215
\(26\) 14.2413 2.79294
\(27\) 4.67245 0.899213
\(28\) 2.98971 0.565001
\(29\) −9.94990 −1.84765 −0.923825 0.382814i \(-0.874955\pi\)
−0.923825 + 0.382814i \(0.874955\pi\)
\(30\) 8.97470 1.63855
\(31\) 1.30521 0.234423 0.117212 0.993107i \(-0.462604\pi\)
0.117212 + 0.993107i \(0.462604\pi\)
\(32\) 6.74704 1.19272
\(33\) 0.473926 0.0824999
\(34\) −15.5775 −2.67151
\(35\) 4.46215 0.754240
\(36\) −6.54527 −1.09088
\(37\) 1.57662 0.259195 0.129598 0.991567i \(-0.458631\pi\)
0.129598 + 0.991567i \(0.458631\pi\)
\(38\) −11.3821 −1.84643
\(39\) 5.74050 0.919216
\(40\) −9.86479 −1.55976
\(41\) 3.19420 0.498850 0.249425 0.968394i \(-0.419758\pi\)
0.249425 + 0.968394i \(0.419758\pi\)
\(42\) 2.01130 0.310350
\(43\) −8.41675 −1.28354 −0.641771 0.766896i \(-0.721800\pi\)
−0.641771 + 0.766896i \(0.721800\pi\)
\(44\) −1.57362 −0.237232
\(45\) −9.76884 −1.45625
\(46\) 1.01773 0.150056
\(47\) −9.20136 −1.34216 −0.671078 0.741387i \(-0.734168\pi\)
−0.671078 + 0.741387i \(0.734168\pi\)
\(48\) 0.937383 0.135300
\(49\) 1.00000 0.142857
\(50\) −33.3071 −4.71034
\(51\) −6.27911 −0.879251
\(52\) −19.0607 −2.64325
\(53\) 0.888546 0.122051 0.0610256 0.998136i \(-0.480563\pi\)
0.0610256 + 0.998136i \(0.480563\pi\)
\(54\) −10.4372 −1.42032
\(55\) −2.34864 −0.316690
\(56\) −2.21077 −0.295427
\(57\) −4.58801 −0.607697
\(58\) 22.2258 2.91838
\(59\) 7.52327 0.979446 0.489723 0.871878i \(-0.337098\pi\)
0.489723 + 0.871878i \(0.337098\pi\)
\(60\) −12.0119 −1.55073
\(61\) 4.92384 0.630433 0.315216 0.949020i \(-0.397923\pi\)
0.315216 + 0.949020i \(0.397923\pi\)
\(62\) −2.91554 −0.370274
\(63\) −2.18927 −0.275822
\(64\) −12.9892 −1.62365
\(65\) −28.4482 −3.52857
\(66\) −1.05864 −0.130309
\(67\) 13.5970 1.66114 0.830569 0.556916i \(-0.188015\pi\)
0.830569 + 0.556916i \(0.188015\pi\)
\(68\) 20.8491 2.52833
\(69\) 0.410235 0.0493865
\(70\) −9.96739 −1.19133
\(71\) −0.849215 −0.100783 −0.0503917 0.998730i \(-0.516047\pi\)
−0.0503917 + 0.998730i \(0.516047\pi\)
\(72\) 4.83997 0.570396
\(73\) −4.88653 −0.571925 −0.285963 0.958241i \(-0.592313\pi\)
−0.285963 + 0.958241i \(0.592313\pi\)
\(74\) −3.52181 −0.409402
\(75\) −13.4257 −1.55027
\(76\) 15.2340 1.74746
\(77\) −0.526347 −0.0599828
\(78\) −12.8229 −1.45191
\(79\) 6.03715 0.679232 0.339616 0.940564i \(-0.389703\pi\)
0.339616 + 0.940564i \(0.389703\pi\)
\(80\) −4.64539 −0.519371
\(81\) 2.36070 0.262300
\(82\) −7.13509 −0.787939
\(83\) −12.1878 −1.33778 −0.668890 0.743362i \(-0.733230\pi\)
−0.668890 + 0.743362i \(0.733230\pi\)
\(84\) −2.69195 −0.293716
\(85\) 31.1174 3.37516
\(86\) 18.8010 2.02737
\(87\) 8.95896 0.960501
\(88\) 1.16363 0.124044
\(89\) 9.45755 1.00250 0.501249 0.865303i \(-0.332874\pi\)
0.501249 + 0.865303i \(0.332874\pi\)
\(90\) 21.8213 2.30017
\(91\) −6.37545 −0.668329
\(92\) −1.36214 −0.142013
\(93\) −1.17522 −0.121865
\(94\) 20.5537 2.11995
\(95\) 22.7368 2.33275
\(96\) −6.07508 −0.620035
\(97\) 8.91376 0.905055 0.452527 0.891750i \(-0.350522\pi\)
0.452527 + 0.891750i \(0.350522\pi\)
\(98\) −2.23377 −0.225644
\(99\) 1.15231 0.115812
\(100\) 44.5788 4.45788
\(101\) −9.63298 −0.958517 −0.479259 0.877674i \(-0.659094\pi\)
−0.479259 + 0.877674i \(0.659094\pi\)
\(102\) 14.0261 1.38879
\(103\) 16.1299 1.58932 0.794661 0.607053i \(-0.207649\pi\)
0.794661 + 0.607053i \(0.207649\pi\)
\(104\) 14.0947 1.38210
\(105\) −4.01775 −0.392092
\(106\) −1.98480 −0.192781
\(107\) −1.76141 −0.170282 −0.0851410 0.996369i \(-0.527134\pi\)
−0.0851410 + 0.996369i \(0.527134\pi\)
\(108\) 13.9693 1.34419
\(109\) 2.29729 0.220040 0.110020 0.993929i \(-0.464908\pi\)
0.110020 + 0.993929i \(0.464908\pi\)
\(110\) 5.24630 0.500215
\(111\) −1.41960 −0.134743
\(112\) −1.04107 −0.0983716
\(113\) 13.1293 1.23510 0.617551 0.786531i \(-0.288125\pi\)
0.617551 + 0.786531i \(0.288125\pi\)
\(114\) 10.2485 0.959864
\(115\) −2.03301 −0.189579
\(116\) −29.7473 −2.76197
\(117\) 13.9576 1.29038
\(118\) −16.8052 −1.54705
\(119\) 6.97364 0.639272
\(120\) 8.88232 0.810841
\(121\) −10.7230 −0.974814
\(122\) −10.9987 −0.995775
\(123\) −2.87608 −0.259327
\(124\) 3.90221 0.350428
\(125\) 44.2232 3.95545
\(126\) 4.89031 0.435664
\(127\) 10.4781 0.929777 0.464888 0.885369i \(-0.346094\pi\)
0.464888 + 0.885369i \(0.346094\pi\)
\(128\) 15.5207 1.37185
\(129\) 7.57849 0.667249
\(130\) 63.5466 5.57341
\(131\) −10.0724 −0.880029 −0.440015 0.897991i \(-0.645027\pi\)
−0.440015 + 0.897991i \(0.645027\pi\)
\(132\) 1.41690 0.123325
\(133\) 5.09549 0.441835
\(134\) −30.3725 −2.62378
\(135\) 20.8492 1.79441
\(136\) −15.4171 −1.32201
\(137\) −18.5714 −1.58667 −0.793333 0.608788i \(-0.791656\pi\)
−0.793333 + 0.608788i \(0.791656\pi\)
\(138\) −0.916370 −0.0780066
\(139\) 3.15554 0.267649 0.133825 0.991005i \(-0.457274\pi\)
0.133825 + 0.991005i \(0.457274\pi\)
\(140\) 13.3405 1.12748
\(141\) 8.28496 0.697719
\(142\) 1.89695 0.159188
\(143\) 3.35570 0.280618
\(144\) 2.27918 0.189931
\(145\) −44.3979 −3.68705
\(146\) 10.9154 0.903362
\(147\) −0.900406 −0.0742643
\(148\) 4.71364 0.387459
\(149\) 15.7270 1.28840 0.644202 0.764855i \(-0.277190\pi\)
0.644202 + 0.764855i \(0.277190\pi\)
\(150\) 29.9899 2.44867
\(151\) −13.6738 −1.11276 −0.556379 0.830929i \(-0.687810\pi\)
−0.556379 + 0.830929i \(0.687810\pi\)
\(152\) −11.2650 −0.913710
\(153\) −15.2672 −1.23428
\(154\) 1.17573 0.0947434
\(155\) 5.82405 0.467799
\(156\) 17.1624 1.37409
\(157\) −7.00587 −0.559129 −0.279565 0.960127i \(-0.590190\pi\)
−0.279565 + 0.960127i \(0.590190\pi\)
\(158\) −13.4856 −1.07285
\(159\) −0.800052 −0.0634483
\(160\) 30.1063 2.38011
\(161\) −0.455611 −0.0359072
\(162\) −5.27325 −0.414306
\(163\) −8.16891 −0.639838 −0.319919 0.947445i \(-0.603656\pi\)
−0.319919 + 0.947445i \(0.603656\pi\)
\(164\) 9.54972 0.745708
\(165\) 2.11473 0.164631
\(166\) 27.2246 2.11304
\(167\) 21.0185 1.62646 0.813230 0.581942i \(-0.197707\pi\)
0.813230 + 0.581942i \(0.197707\pi\)
\(168\) 1.99059 0.153578
\(169\) 27.6464 2.12665
\(170\) −69.5090 −5.33109
\(171\) −11.1554 −0.853075
\(172\) −25.1636 −1.91871
\(173\) 3.92999 0.298792 0.149396 0.988777i \(-0.452267\pi\)
0.149396 + 0.988777i \(0.452267\pi\)
\(174\) −20.0122 −1.51712
\(175\) 14.9108 1.12715
\(176\) 0.547962 0.0413042
\(177\) −6.77400 −0.509165
\(178\) −21.1260 −1.58346
\(179\) 16.3309 1.22063 0.610313 0.792160i \(-0.291044\pi\)
0.610313 + 0.792160i \(0.291044\pi\)
\(180\) −29.2060 −2.17688
\(181\) −18.4709 −1.37293 −0.686464 0.727164i \(-0.740838\pi\)
−0.686464 + 0.727164i \(0.740838\pi\)
\(182\) 14.2413 1.05563
\(183\) −4.43345 −0.327730
\(184\) 1.00725 0.0742557
\(185\) 7.03512 0.517233
\(186\) 2.62517 0.192487
\(187\) −3.67055 −0.268417
\(188\) −27.5094 −2.00633
\(189\) 4.67245 0.339871
\(190\) −50.7888 −3.68460
\(191\) 9.46168 0.684623 0.342312 0.939587i \(-0.388790\pi\)
0.342312 + 0.939587i \(0.388790\pi\)
\(192\) 11.6955 0.844053
\(193\) 12.7772 0.919727 0.459863 0.887990i \(-0.347898\pi\)
0.459863 + 0.887990i \(0.347898\pi\)
\(194\) −19.9112 −1.42954
\(195\) 25.6150 1.83432
\(196\) 2.98971 0.213550
\(197\) 8.71604 0.620992 0.310496 0.950575i \(-0.399505\pi\)
0.310496 + 0.950575i \(0.399505\pi\)
\(198\) −2.57400 −0.182926
\(199\) 6.26668 0.444233 0.222117 0.975020i \(-0.428703\pi\)
0.222117 + 0.975020i \(0.428703\pi\)
\(200\) −32.9643 −2.33093
\(201\) −12.2428 −0.863542
\(202\) 21.5178 1.51399
\(203\) −9.94990 −0.698346
\(204\) −18.7727 −1.31435
\(205\) 14.2530 0.995472
\(206\) −36.0303 −2.51035
\(207\) 0.997456 0.0693280
\(208\) 6.63728 0.460212
\(209\) −2.68200 −0.185518
\(210\) 8.97470 0.619313
\(211\) 14.3154 0.985510 0.492755 0.870168i \(-0.335990\pi\)
0.492755 + 0.870168i \(0.335990\pi\)
\(212\) 2.65649 0.182449
\(213\) 0.764639 0.0523922
\(214\) 3.93458 0.268962
\(215\) −37.5568 −2.56135
\(216\) −10.3297 −0.702849
\(217\) 1.30521 0.0886037
\(218\) −5.13160 −0.347556
\(219\) 4.39987 0.297315
\(220\) −7.02173 −0.473405
\(221\) −44.4601 −2.99071
\(222\) 3.17106 0.212827
\(223\) −12.0828 −0.809126 −0.404563 0.914510i \(-0.632576\pi\)
−0.404563 + 0.914510i \(0.632576\pi\)
\(224\) 6.74704 0.450806
\(225\) −32.6436 −2.17624
\(226\) −29.3278 −1.95086
\(227\) 29.3129 1.94557 0.972784 0.231714i \(-0.0744335\pi\)
0.972784 + 0.231714i \(0.0744335\pi\)
\(228\) −13.7168 −0.908418
\(229\) 20.2013 1.33494 0.667468 0.744638i \(-0.267378\pi\)
0.667468 + 0.744638i \(0.267378\pi\)
\(230\) 4.54126 0.299442
\(231\) 0.473926 0.0311820
\(232\) 21.9970 1.44417
\(233\) −20.2075 −1.32384 −0.661918 0.749576i \(-0.730257\pi\)
−0.661918 + 0.749576i \(0.730257\pi\)
\(234\) −31.1780 −2.03817
\(235\) −41.0578 −2.67832
\(236\) 22.4924 1.46413
\(237\) −5.43589 −0.353099
\(238\) −15.5775 −1.00974
\(239\) 8.10770 0.524444 0.262222 0.965008i \(-0.415545\pi\)
0.262222 + 0.965008i \(0.415545\pi\)
\(240\) 4.18274 0.269995
\(241\) −21.9686 −1.41513 −0.707563 0.706651i \(-0.750205\pi\)
−0.707563 + 0.706651i \(0.750205\pi\)
\(242\) 23.9526 1.53973
\(243\) −16.1429 −1.03557
\(244\) 14.7208 0.942404
\(245\) 4.46215 0.285076
\(246\) 6.42448 0.409610
\(247\) −32.4861 −2.06704
\(248\) −2.88553 −0.183231
\(249\) 10.9739 0.695444
\(250\) −98.7843 −6.24767
\(251\) −7.79820 −0.492218 −0.246109 0.969242i \(-0.579152\pi\)
−0.246109 + 0.969242i \(0.579152\pi\)
\(252\) −6.54527 −0.412313
\(253\) 0.239810 0.0150767
\(254\) −23.4055 −1.46859
\(255\) −28.0183 −1.75457
\(256\) −8.69121 −0.543201
\(257\) −12.6254 −0.787548 −0.393774 0.919207i \(-0.628831\pi\)
−0.393774 + 0.919207i \(0.628831\pi\)
\(258\) −16.9286 −1.05393
\(259\) 1.57662 0.0979666
\(260\) −85.0518 −5.27469
\(261\) 21.7830 1.34833
\(262\) 22.4994 1.39002
\(263\) 6.50505 0.401118 0.200559 0.979682i \(-0.435724\pi\)
0.200559 + 0.979682i \(0.435724\pi\)
\(264\) −1.04774 −0.0644841
\(265\) 3.96482 0.243557
\(266\) −11.3821 −0.697883
\(267\) −8.51564 −0.521149
\(268\) 40.6510 2.48316
\(269\) −11.7000 −0.713359 −0.356679 0.934227i \(-0.616091\pi\)
−0.356679 + 0.934227i \(0.616091\pi\)
\(270\) −46.5721 −2.83429
\(271\) 5.26637 0.319909 0.159955 0.987124i \(-0.448865\pi\)
0.159955 + 0.987124i \(0.448865\pi\)
\(272\) −7.26003 −0.440204
\(273\) 5.74050 0.347431
\(274\) 41.4842 2.50615
\(275\) −7.84823 −0.473266
\(276\) 1.22648 0.0738256
\(277\) 24.3261 1.46161 0.730806 0.682585i \(-0.239144\pi\)
0.730806 + 0.682585i \(0.239144\pi\)
\(278\) −7.04872 −0.422754
\(279\) −2.85746 −0.171072
\(280\) −9.86479 −0.589534
\(281\) −4.64862 −0.277313 −0.138657 0.990341i \(-0.544278\pi\)
−0.138657 + 0.990341i \(0.544278\pi\)
\(282\) −18.5067 −1.10206
\(283\) −0.0973309 −0.00578572 −0.00289286 0.999996i \(-0.500921\pi\)
−0.00289286 + 0.999996i \(0.500921\pi\)
\(284\) −2.53890 −0.150656
\(285\) −20.4724 −1.21268
\(286\) −7.49584 −0.443239
\(287\) 3.19420 0.188548
\(288\) −14.7711 −0.870395
\(289\) 31.6316 1.86069
\(290\) 99.1746 5.82373
\(291\) −8.02600 −0.470493
\(292\) −14.6093 −0.854945
\(293\) 23.2352 1.35742 0.678708 0.734408i \(-0.262540\pi\)
0.678708 + 0.734408i \(0.262540\pi\)
\(294\) 2.01130 0.117301
\(295\) 33.5699 1.95452
\(296\) −3.48555 −0.202594
\(297\) −2.45933 −0.142705
\(298\) −35.1304 −2.03505
\(299\) 2.90473 0.167985
\(300\) −40.1390 −2.31743
\(301\) −8.41675 −0.485133
\(302\) 30.5441 1.75761
\(303\) 8.67359 0.498285
\(304\) −5.30475 −0.304248
\(305\) 21.9709 1.25805
\(306\) 34.1033 1.94955
\(307\) −8.13559 −0.464322 −0.232161 0.972677i \(-0.574580\pi\)
−0.232161 + 0.972677i \(0.574580\pi\)
\(308\) −1.57362 −0.0896654
\(309\) −14.5234 −0.826209
\(310\) −13.0096 −0.738894
\(311\) −10.3055 −0.584372 −0.292186 0.956361i \(-0.594383\pi\)
−0.292186 + 0.956361i \(0.594383\pi\)
\(312\) −12.6909 −0.718483
\(313\) 2.90599 0.164256 0.0821280 0.996622i \(-0.473828\pi\)
0.0821280 + 0.996622i \(0.473828\pi\)
\(314\) 15.6495 0.883150
\(315\) −9.76884 −0.550412
\(316\) 18.0493 1.01535
\(317\) 19.9611 1.12113 0.560564 0.828111i \(-0.310584\pi\)
0.560564 + 0.828111i \(0.310584\pi\)
\(318\) 1.78713 0.100217
\(319\) 5.23710 0.293221
\(320\) −57.9596 −3.24004
\(321\) 1.58599 0.0885211
\(322\) 1.01773 0.0567158
\(323\) 35.5341 1.97717
\(324\) 7.05781 0.392100
\(325\) −95.0628 −5.27314
\(326\) 18.2474 1.01063
\(327\) −2.06849 −0.114388
\(328\) −7.06165 −0.389914
\(329\) −9.20136 −0.507287
\(330\) −4.72380 −0.260037
\(331\) 20.9048 1.14903 0.574515 0.818494i \(-0.305191\pi\)
0.574515 + 0.818494i \(0.305191\pi\)
\(332\) −36.4378 −1.99978
\(333\) −3.45165 −0.189149
\(334\) −46.9504 −2.56901
\(335\) 60.6718 3.31486
\(336\) 0.937383 0.0511385
\(337\) −10.9159 −0.594627 −0.297313 0.954780i \(-0.596091\pi\)
−0.297313 + 0.954780i \(0.596091\pi\)
\(338\) −61.7556 −3.35906
\(339\) −11.8217 −0.642068
\(340\) 93.0319 5.04536
\(341\) −0.686995 −0.0372029
\(342\) 24.9185 1.34744
\(343\) 1.00000 0.0539949
\(344\) 18.6075 1.00325
\(345\) 1.83053 0.0985525
\(346\) −8.77867 −0.471944
\(347\) 2.97742 0.159836 0.0799181 0.996801i \(-0.474534\pi\)
0.0799181 + 0.996801i \(0.474534\pi\)
\(348\) 26.7847 1.43581
\(349\) −23.7661 −1.27217 −0.636085 0.771619i \(-0.719447\pi\)
−0.636085 + 0.771619i \(0.719447\pi\)
\(350\) −33.3071 −1.78034
\(351\) −29.7890 −1.59002
\(352\) −3.55128 −0.189284
\(353\) 17.6298 0.938342 0.469171 0.883107i \(-0.344553\pi\)
0.469171 + 0.883107i \(0.344553\pi\)
\(354\) 15.1315 0.804231
\(355\) −3.78932 −0.201116
\(356\) 28.2753 1.49859
\(357\) −6.27911 −0.332326
\(358\) −36.4793 −1.92799
\(359\) 6.94661 0.366628 0.183314 0.983054i \(-0.441317\pi\)
0.183314 + 0.983054i \(0.441317\pi\)
\(360\) 21.5967 1.13824
\(361\) 6.96404 0.366529
\(362\) 41.2595 2.16855
\(363\) 9.65502 0.506757
\(364\) −19.0607 −0.999054
\(365\) −21.8044 −1.14130
\(366\) 9.90329 0.517653
\(367\) 1.10669 0.0577685 0.0288843 0.999583i \(-0.490805\pi\)
0.0288843 + 0.999583i \(0.490805\pi\)
\(368\) 0.474322 0.0247257
\(369\) −6.99296 −0.364039
\(370\) −15.7148 −0.816974
\(371\) 0.888546 0.0461310
\(372\) −3.51357 −0.182170
\(373\) 27.2695 1.41196 0.705981 0.708230i \(-0.250506\pi\)
0.705981 + 0.708230i \(0.250506\pi\)
\(374\) 8.19915 0.423968
\(375\) −39.8189 −2.05624
\(376\) 20.3421 1.04906
\(377\) 63.4352 3.26708
\(378\) −10.4372 −0.536829
\(379\) 30.2000 1.55127 0.775635 0.631181i \(-0.217430\pi\)
0.775635 + 0.631181i \(0.217430\pi\)
\(380\) 67.9765 3.48712
\(381\) −9.43450 −0.483344
\(382\) −21.1352 −1.08137
\(383\) 14.8636 0.759497 0.379749 0.925090i \(-0.376011\pi\)
0.379749 + 0.925090i \(0.376011\pi\)
\(384\) −13.9749 −0.713155
\(385\) −2.34864 −0.119698
\(386\) −28.5414 −1.45272
\(387\) 18.4265 0.936673
\(388\) 26.6495 1.35292
\(389\) −10.5505 −0.534930 −0.267465 0.963568i \(-0.586186\pi\)
−0.267465 + 0.963568i \(0.586186\pi\)
\(390\) −57.2178 −2.89734
\(391\) −3.17727 −0.160681
\(392\) −2.21077 −0.111661
\(393\) 9.06925 0.457483
\(394\) −19.4696 −0.980863
\(395\) 26.9386 1.35543
\(396\) 3.44508 0.173122
\(397\) 4.74814 0.238302 0.119151 0.992876i \(-0.461983\pi\)
0.119151 + 0.992876i \(0.461983\pi\)
\(398\) −13.9983 −0.701671
\(399\) −4.58801 −0.229688
\(400\) −15.5231 −0.776155
\(401\) −5.06567 −0.252968 −0.126484 0.991969i \(-0.540369\pi\)
−0.126484 + 0.991969i \(0.540369\pi\)
\(402\) 27.3476 1.36397
\(403\) −8.32133 −0.414515
\(404\) −28.7998 −1.43284
\(405\) 10.5338 0.523429
\(406\) 22.2258 1.10305
\(407\) −0.829850 −0.0411341
\(408\) 13.8817 0.687246
\(409\) −27.4733 −1.35847 −0.679234 0.733922i \(-0.737688\pi\)
−0.679234 + 0.733922i \(0.737688\pi\)
\(410\) −31.8378 −1.57236
\(411\) 16.7218 0.824828
\(412\) 48.2236 2.37580
\(413\) 7.52327 0.370196
\(414\) −2.22808 −0.109504
\(415\) −54.3835 −2.66958
\(416\) −43.0155 −2.10901
\(417\) −2.84126 −0.139137
\(418\) 5.99095 0.293027
\(419\) 15.3996 0.752318 0.376159 0.926555i \(-0.377245\pi\)
0.376159 + 0.926555i \(0.377245\pi\)
\(420\) −12.0119 −0.586120
\(421\) −17.1872 −0.837654 −0.418827 0.908066i \(-0.637559\pi\)
−0.418827 + 0.908066i \(0.637559\pi\)
\(422\) −31.9772 −1.55662
\(423\) 20.1442 0.979446
\(424\) −1.96437 −0.0953984
\(425\) 103.982 5.04388
\(426\) −1.70802 −0.0827540
\(427\) 4.92384 0.238281
\(428\) −5.26610 −0.254547
\(429\) −3.02149 −0.145879
\(430\) 83.8930 4.04568
\(431\) −7.39071 −0.355998 −0.177999 0.984031i \(-0.556962\pi\)
−0.177999 + 0.984031i \(0.556962\pi\)
\(432\) −4.86433 −0.234035
\(433\) 11.3784 0.546809 0.273404 0.961899i \(-0.411850\pi\)
0.273404 + 0.961899i \(0.411850\pi\)
\(434\) −2.91554 −0.139950
\(435\) 39.9762 1.91671
\(436\) 6.86822 0.328928
\(437\) −2.32156 −0.111055
\(438\) −9.82827 −0.469613
\(439\) −28.1959 −1.34572 −0.672860 0.739770i \(-0.734934\pi\)
−0.672860 + 0.739770i \(0.734934\pi\)
\(440\) 5.19230 0.247533
\(441\) −2.18927 −0.104251
\(442\) 99.3135 4.72386
\(443\) 7.45278 0.354092 0.177046 0.984203i \(-0.443346\pi\)
0.177046 + 0.984203i \(0.443346\pi\)
\(444\) −4.24419 −0.201420
\(445\) 42.2010 2.00052
\(446\) 26.9902 1.27802
\(447\) −14.1607 −0.669777
\(448\) −12.9892 −0.613681
\(449\) −26.3820 −1.24505 −0.622523 0.782602i \(-0.713892\pi\)
−0.622523 + 0.782602i \(0.713892\pi\)
\(450\) 72.9182 3.43740
\(451\) −1.68126 −0.0791673
\(452\) 39.2528 1.84630
\(453\) 12.3120 0.578467
\(454\) −65.4782 −3.07304
\(455\) −28.4482 −1.33367
\(456\) 10.1431 0.474992
\(457\) −23.9595 −1.12078 −0.560388 0.828230i \(-0.689348\pi\)
−0.560388 + 0.828230i \(0.689348\pi\)
\(458\) −45.1249 −2.10855
\(459\) 32.5840 1.52089
\(460\) −6.07809 −0.283392
\(461\) 4.60432 0.214445 0.107222 0.994235i \(-0.465804\pi\)
0.107222 + 0.994235i \(0.465804\pi\)
\(462\) −1.05864 −0.0492524
\(463\) −1.08285 −0.0503244 −0.0251622 0.999683i \(-0.508010\pi\)
−0.0251622 + 0.999683i \(0.508010\pi\)
\(464\) 10.3585 0.480882
\(465\) −5.24402 −0.243185
\(466\) 45.1388 2.09101
\(467\) 27.2429 1.26065 0.630324 0.776332i \(-0.282922\pi\)
0.630324 + 0.776332i \(0.282922\pi\)
\(468\) 41.7291 1.92893
\(469\) 13.5970 0.627851
\(470\) 91.7135 4.23043
\(471\) 6.30813 0.290663
\(472\) −16.6322 −0.765561
\(473\) 4.43013 0.203697
\(474\) 12.1425 0.557723
\(475\) 75.9776 3.48609
\(476\) 20.8491 0.955619
\(477\) −1.94527 −0.0890676
\(478\) −18.1107 −0.828364
\(479\) 30.6303 1.39953 0.699766 0.714372i \(-0.253287\pi\)
0.699766 + 0.714372i \(0.253287\pi\)
\(480\) −27.1079 −1.23730
\(481\) −10.0517 −0.458317
\(482\) 49.0728 2.23520
\(483\) 0.410235 0.0186664
\(484\) −32.0585 −1.45720
\(485\) 39.7745 1.80607
\(486\) 36.0595 1.63569
\(487\) −41.0110 −1.85838 −0.929192 0.369598i \(-0.879496\pi\)
−0.929192 + 0.369598i \(0.879496\pi\)
\(488\) −10.8855 −0.492763
\(489\) 7.35534 0.332620
\(490\) −9.96739 −0.450281
\(491\) −1.40166 −0.0632559 −0.0316279 0.999500i \(-0.510069\pi\)
−0.0316279 + 0.999500i \(0.510069\pi\)
\(492\) −8.59863 −0.387656
\(493\) −69.3871 −3.12504
\(494\) 72.5663 3.26491
\(495\) 5.14180 0.231107
\(496\) −1.35881 −0.0610126
\(497\) −0.849215 −0.0380925
\(498\) −24.5132 −1.09846
\(499\) −13.3476 −0.597519 −0.298759 0.954328i \(-0.596573\pi\)
−0.298759 + 0.954328i \(0.596573\pi\)
\(500\) 132.215 5.91281
\(501\) −18.9252 −0.845515
\(502\) 17.4194 0.777464
\(503\) −29.2391 −1.30371 −0.651853 0.758346i \(-0.726008\pi\)
−0.651853 + 0.758346i \(0.726008\pi\)
\(504\) 4.83997 0.215590
\(505\) −42.9838 −1.91275
\(506\) −0.535678 −0.0238138
\(507\) −24.8930 −1.10554
\(508\) 31.3263 1.38988
\(509\) −43.9838 −1.94955 −0.974773 0.223199i \(-0.928350\pi\)
−0.974773 + 0.223199i \(0.928350\pi\)
\(510\) 62.5863 2.77137
\(511\) −4.88653 −0.216167
\(512\) −11.6273 −0.513857
\(513\) 23.8084 1.05117
\(514\) 28.2021 1.24394
\(515\) 71.9738 3.17155
\(516\) 22.6575 0.997439
\(517\) 4.84310 0.212999
\(518\) −3.52181 −0.154739
\(519\) −3.53859 −0.155327
\(520\) 62.8925 2.75802
\(521\) 0.145470 0.00637317 0.00318658 0.999995i \(-0.498986\pi\)
0.00318658 + 0.999995i \(0.498986\pi\)
\(522\) −48.6581 −2.12971
\(523\) 20.5747 0.899671 0.449835 0.893112i \(-0.351483\pi\)
0.449835 + 0.893112i \(0.351483\pi\)
\(524\) −30.1135 −1.31551
\(525\) −13.4257 −0.585947
\(526\) −14.5307 −0.633571
\(527\) 9.10209 0.396493
\(528\) −0.493389 −0.0214720
\(529\) −22.7924 −0.990975
\(530\) −8.85648 −0.384701
\(531\) −16.4705 −0.714757
\(532\) 15.2340 0.660479
\(533\) −20.3645 −0.882083
\(534\) 19.0219 0.823160
\(535\) −7.85967 −0.339803
\(536\) −30.0599 −1.29839
\(537\) −14.7044 −0.634543
\(538\) 26.1350 1.12676
\(539\) −0.526347 −0.0226714
\(540\) 62.3329 2.68238
\(541\) −14.0739 −0.605086 −0.302543 0.953136i \(-0.597836\pi\)
−0.302543 + 0.953136i \(0.597836\pi\)
\(542\) −11.7638 −0.505300
\(543\) 16.6313 0.713716
\(544\) 47.0515 2.01731
\(545\) 10.2508 0.439098
\(546\) −12.8229 −0.548771
\(547\) −3.28065 −0.140271 −0.0701353 0.997537i \(-0.522343\pi\)
−0.0701353 + 0.997537i \(0.522343\pi\)
\(548\) −55.5232 −2.37183
\(549\) −10.7796 −0.460062
\(550\) 17.5311 0.747528
\(551\) −50.6997 −2.15988
\(552\) −0.906937 −0.0386018
\(553\) 6.03715 0.256726
\(554\) −54.3387 −2.30863
\(555\) −6.33447 −0.268883
\(556\) 9.43413 0.400096
\(557\) 14.1173 0.598170 0.299085 0.954227i \(-0.403319\pi\)
0.299085 + 0.954227i \(0.403319\pi\)
\(558\) 6.38290 0.270210
\(559\) 53.6606 2.26960
\(560\) −4.64539 −0.196304
\(561\) 3.30499 0.139537
\(562\) 10.3839 0.438019
\(563\) 28.2079 1.18882 0.594410 0.804162i \(-0.297385\pi\)
0.594410 + 0.804162i \(0.297385\pi\)
\(564\) 24.7696 1.04299
\(565\) 58.5849 2.46469
\(566\) 0.217414 0.00913861
\(567\) 2.36070 0.0991401
\(568\) 1.87742 0.0787749
\(569\) −25.8420 −1.08335 −0.541677 0.840586i \(-0.682211\pi\)
−0.541677 + 0.840586i \(0.682211\pi\)
\(570\) 45.7305 1.91544
\(571\) 20.8890 0.874178 0.437089 0.899418i \(-0.356010\pi\)
0.437089 + 0.899418i \(0.356010\pi\)
\(572\) 10.0326 0.419482
\(573\) −8.51936 −0.355901
\(574\) −7.13509 −0.297813
\(575\) −6.79351 −0.283309
\(576\) 28.4368 1.18487
\(577\) −1.39398 −0.0580323 −0.0290162 0.999579i \(-0.509237\pi\)
−0.0290162 + 0.999579i \(0.509237\pi\)
\(578\) −70.6577 −2.93897
\(579\) −11.5047 −0.478120
\(580\) −132.737 −5.51160
\(581\) −12.1878 −0.505633
\(582\) 17.9282 0.743148
\(583\) −0.467683 −0.0193695
\(584\) 10.8030 0.447032
\(585\) 62.2808 2.57499
\(586\) −51.9021 −2.14405
\(587\) 27.0529 1.11659 0.558297 0.829641i \(-0.311455\pi\)
0.558297 + 0.829641i \(0.311455\pi\)
\(588\) −2.69195 −0.111014
\(589\) 6.65071 0.274038
\(590\) −74.9873 −3.08718
\(591\) −7.84798 −0.322823
\(592\) −1.64137 −0.0674599
\(593\) 3.23856 0.132992 0.0664958 0.997787i \(-0.478818\pi\)
0.0664958 + 0.997787i \(0.478818\pi\)
\(594\) 5.49356 0.225404
\(595\) 31.1174 1.27569
\(596\) 47.0191 1.92598
\(597\) −5.64256 −0.230935
\(598\) −6.48848 −0.265334
\(599\) 17.5819 0.718378 0.359189 0.933265i \(-0.383053\pi\)
0.359189 + 0.933265i \(0.383053\pi\)
\(600\) 29.6813 1.21173
\(601\) −16.9088 −0.689724 −0.344862 0.938653i \(-0.612074\pi\)
−0.344862 + 0.938653i \(0.612074\pi\)
\(602\) 18.8010 0.766273
\(603\) −29.7675 −1.21223
\(604\) −40.8807 −1.66341
\(605\) −47.8474 −1.94527
\(606\) −19.3748 −0.787046
\(607\) −12.4774 −0.506442 −0.253221 0.967408i \(-0.581490\pi\)
−0.253221 + 0.967408i \(0.581490\pi\)
\(608\) 34.3795 1.39427
\(609\) 8.95896 0.363035
\(610\) −49.0778 −1.98710
\(611\) 58.6628 2.37324
\(612\) −45.6444 −1.84506
\(613\) 4.18629 0.169083 0.0845414 0.996420i \(-0.473057\pi\)
0.0845414 + 0.996420i \(0.473057\pi\)
\(614\) 18.1730 0.733402
\(615\) −12.8335 −0.517496
\(616\) 1.16363 0.0468841
\(617\) −27.7996 −1.11917 −0.559584 0.828774i \(-0.689039\pi\)
−0.559584 + 0.828774i \(0.689039\pi\)
\(618\) 32.4419 1.30501
\(619\) −13.6357 −0.548066 −0.274033 0.961720i \(-0.588358\pi\)
−0.274033 + 0.961720i \(0.588358\pi\)
\(620\) 17.4122 0.699291
\(621\) −2.12882 −0.0854267
\(622\) 23.0201 0.923022
\(623\) 9.45755 0.378909
\(624\) −5.97625 −0.239241
\(625\) 122.777 4.91107
\(626\) −6.49129 −0.259444
\(627\) 2.41489 0.0964412
\(628\) −20.9455 −0.835816
\(629\) 10.9948 0.438391
\(630\) 21.8213 0.869381
\(631\) 40.0848 1.59575 0.797875 0.602823i \(-0.205958\pi\)
0.797875 + 0.602823i \(0.205958\pi\)
\(632\) −13.3468 −0.530906
\(633\) −12.8896 −0.512317
\(634\) −44.5885 −1.77083
\(635\) 46.7546 1.85540
\(636\) −2.39192 −0.0948459
\(637\) −6.37545 −0.252605
\(638\) −11.6985 −0.463146
\(639\) 1.85916 0.0735472
\(640\) 69.2556 2.73757
\(641\) 7.01529 0.277087 0.138544 0.990356i \(-0.455758\pi\)
0.138544 + 0.990356i \(0.455758\pi\)
\(642\) −3.54272 −0.139820
\(643\) 3.16092 0.124655 0.0623273 0.998056i \(-0.480148\pi\)
0.0623273 + 0.998056i \(0.480148\pi\)
\(644\) −1.36214 −0.0536760
\(645\) 33.8163 1.33152
\(646\) −79.3749 −3.12296
\(647\) −16.1403 −0.634541 −0.317270 0.948335i \(-0.602766\pi\)
−0.317270 + 0.948335i \(0.602766\pi\)
\(648\) −5.21897 −0.205021
\(649\) −3.95985 −0.155438
\(650\) 212.348 8.32898
\(651\) −1.17522 −0.0460606
\(652\) −24.4226 −0.956464
\(653\) 19.5090 0.763445 0.381723 0.924277i \(-0.375331\pi\)
0.381723 + 0.924277i \(0.375331\pi\)
\(654\) 4.62053 0.180677
\(655\) −44.9445 −1.75613
\(656\) −3.32538 −0.129834
\(657\) 10.6979 0.417366
\(658\) 20.5537 0.801265
\(659\) −37.8607 −1.47485 −0.737423 0.675432i \(-0.763957\pi\)
−0.737423 + 0.675432i \(0.763957\pi\)
\(660\) 6.32241 0.246100
\(661\) −7.06400 −0.274758 −0.137379 0.990519i \(-0.543868\pi\)
−0.137379 + 0.990519i \(0.543868\pi\)
\(662\) −46.6964 −1.81491
\(663\) 40.0322 1.55472
\(664\) 26.9443 1.04564
\(665\) 22.7368 0.881697
\(666\) 7.71018 0.298763
\(667\) 4.53329 0.175530
\(668\) 62.8392 2.43132
\(669\) 10.8795 0.420624
\(670\) −135.527 −5.23585
\(671\) −2.59165 −0.100049
\(672\) −6.07508 −0.234351
\(673\) 12.9456 0.499015 0.249507 0.968373i \(-0.419731\pi\)
0.249507 + 0.968373i \(0.419731\pi\)
\(674\) 24.3836 0.939220
\(675\) 69.6698 2.68159
\(676\) 82.6547 3.17903
\(677\) 25.9069 0.995681 0.497841 0.867269i \(-0.334126\pi\)
0.497841 + 0.867269i \(0.334126\pi\)
\(678\) 26.4069 1.01415
\(679\) 8.91376 0.342079
\(680\) −68.7935 −2.63811
\(681\) −26.3936 −1.01140
\(682\) 1.53458 0.0587623
\(683\) 32.0846 1.22768 0.613842 0.789429i \(-0.289623\pi\)
0.613842 + 0.789429i \(0.289623\pi\)
\(684\) −33.3514 −1.27522
\(685\) −82.8685 −3.16624
\(686\) −2.23377 −0.0852855
\(687\) −18.1893 −0.693967
\(688\) 8.76240 0.334063
\(689\) −5.66488 −0.215815
\(690\) −4.08898 −0.155665
\(691\) 25.3423 0.964068 0.482034 0.876153i \(-0.339898\pi\)
0.482034 + 0.876153i \(0.339898\pi\)
\(692\) 11.7495 0.446650
\(693\) 1.15231 0.0437728
\(694\) −6.65085 −0.252463
\(695\) 14.0805 0.534102
\(696\) −19.8062 −0.750753
\(697\) 22.2752 0.843733
\(698\) 53.0879 2.00941
\(699\) 18.1949 0.688196
\(700\) 44.5788 1.68492
\(701\) 50.6849 1.91434 0.957170 0.289525i \(-0.0934974\pi\)
0.957170 + 0.289525i \(0.0934974\pi\)
\(702\) 66.5416 2.51145
\(703\) 8.03367 0.302996
\(704\) 6.83681 0.257672
\(705\) 36.9687 1.39232
\(706\) −39.3809 −1.48212
\(707\) −9.63298 −0.362285
\(708\) −20.2523 −0.761127
\(709\) −3.08392 −0.115819 −0.0579096 0.998322i \(-0.518444\pi\)
−0.0579096 + 0.998322i \(0.518444\pi\)
\(710\) 8.46446 0.317665
\(711\) −13.2169 −0.495674
\(712\) −20.9085 −0.783579
\(713\) −0.594670 −0.0222706
\(714\) 14.0261 0.524912
\(715\) 14.9736 0.559982
\(716\) 48.8245 1.82466
\(717\) −7.30022 −0.272632
\(718\) −15.5171 −0.579093
\(719\) 31.9019 1.18974 0.594871 0.803821i \(-0.297203\pi\)
0.594871 + 0.803821i \(0.297203\pi\)
\(720\) 10.1700 0.379014
\(721\) 16.1299 0.600707
\(722\) −15.5560 −0.578936
\(723\) 19.7807 0.735653
\(724\) −55.2224 −2.05233
\(725\) −148.361 −5.50997
\(726\) −21.5670 −0.800428
\(727\) −40.0122 −1.48397 −0.741985 0.670416i \(-0.766116\pi\)
−0.741985 + 0.670416i \(0.766116\pi\)
\(728\) 14.0947 0.522384
\(729\) 7.45310 0.276041
\(730\) 48.7060 1.80269
\(731\) −58.6954 −2.17093
\(732\) −13.2547 −0.489909
\(733\) −26.3432 −0.973009 −0.486505 0.873678i \(-0.661728\pi\)
−0.486505 + 0.873678i \(0.661728\pi\)
\(734\) −2.47208 −0.0912460
\(735\) −4.01775 −0.148197
\(736\) −3.07403 −0.113310
\(737\) −7.15674 −0.263622
\(738\) 15.6206 0.575003
\(739\) −19.4173 −0.714277 −0.357139 0.934051i \(-0.616248\pi\)
−0.357139 + 0.934051i \(0.616248\pi\)
\(740\) 21.0330 0.773187
\(741\) 29.2507 1.07455
\(742\) −1.98480 −0.0728644
\(743\) 28.7863 1.05607 0.528033 0.849224i \(-0.322930\pi\)
0.528033 + 0.849224i \(0.322930\pi\)
\(744\) 2.59815 0.0952528
\(745\) 70.1761 2.57105
\(746\) −60.9137 −2.23021
\(747\) 26.6823 0.976253
\(748\) −10.9739 −0.401245
\(749\) −1.76141 −0.0643605
\(750\) 88.9461 3.24785
\(751\) 18.3207 0.668531 0.334265 0.942479i \(-0.391512\pi\)
0.334265 + 0.942479i \(0.391512\pi\)
\(752\) 9.57923 0.349319
\(753\) 7.02155 0.255880
\(754\) −141.699 −5.16038
\(755\) −61.0145 −2.22055
\(756\) 13.9693 0.508057
\(757\) 11.1744 0.406141 0.203071 0.979164i \(-0.434908\pi\)
0.203071 + 0.979164i \(0.434908\pi\)
\(758\) −67.4597 −2.45025
\(759\) −0.215926 −0.00783762
\(760\) −50.2660 −1.82334
\(761\) −14.4258 −0.522934 −0.261467 0.965212i \(-0.584206\pi\)
−0.261467 + 0.965212i \(0.584206\pi\)
\(762\) 21.0745 0.763447
\(763\) 2.29729 0.0831674
\(764\) 28.2876 1.02341
\(765\) −68.1244 −2.46304
\(766\) −33.2019 −1.19963
\(767\) −47.9643 −1.73189
\(768\) 7.82562 0.282383
\(769\) −1.82075 −0.0656581 −0.0328290 0.999461i \(-0.510452\pi\)
−0.0328290 + 0.999461i \(0.510452\pi\)
\(770\) 5.24630 0.189064
\(771\) 11.3679 0.409407
\(772\) 38.2002 1.37486
\(773\) 13.9081 0.500240 0.250120 0.968215i \(-0.419530\pi\)
0.250120 + 0.968215i \(0.419530\pi\)
\(774\) −41.1605 −1.47948
\(775\) 19.4617 0.699086
\(776\) −19.7063 −0.707414
\(777\) −1.41960 −0.0509279
\(778\) 23.5673 0.844927
\(779\) 16.2760 0.583149
\(780\) 76.5812 2.74205
\(781\) 0.446982 0.0159943
\(782\) 7.09727 0.253798
\(783\) −46.4904 −1.66143
\(784\) −1.04107 −0.0371810
\(785\) −31.2612 −1.11576
\(786\) −20.2586 −0.722599
\(787\) 12.5241 0.446437 0.223219 0.974768i \(-0.428344\pi\)
0.223219 + 0.974768i \(0.428344\pi\)
\(788\) 26.0584 0.928292
\(789\) −5.85719 −0.208521
\(790\) −60.1746 −2.14092
\(791\) 13.1293 0.466825
\(792\) −2.54750 −0.0905216
\(793\) −31.3917 −1.11475
\(794\) −10.6062 −0.376401
\(795\) −3.56995 −0.126613
\(796\) 18.7355 0.664064
\(797\) 15.3340 0.543157 0.271579 0.962416i \(-0.412454\pi\)
0.271579 + 0.962416i \(0.412454\pi\)
\(798\) 10.2485 0.362795
\(799\) −64.1669 −2.27006
\(800\) 100.604 3.55687
\(801\) −20.7051 −0.731580
\(802\) 11.3155 0.399565
\(803\) 2.57201 0.0907643
\(804\) −36.6025 −1.29087
\(805\) −2.03301 −0.0716540
\(806\) 18.5879 0.654731
\(807\) 10.5347 0.370840
\(808\) 21.2963 0.749202
\(809\) −30.7417 −1.08082 −0.540410 0.841402i \(-0.681731\pi\)
−0.540410 + 0.841402i \(0.681731\pi\)
\(810\) −23.5300 −0.826761
\(811\) 10.3123 0.362114 0.181057 0.983473i \(-0.442048\pi\)
0.181057 + 0.983473i \(0.442048\pi\)
\(812\) −29.7473 −1.04393
\(813\) −4.74187 −0.166305
\(814\) 1.85369 0.0649718
\(815\) −36.4509 −1.27682
\(816\) 6.53697 0.228840
\(817\) −42.8875 −1.50044
\(818\) 61.3689 2.14571
\(819\) 13.9576 0.487717
\(820\) 42.6122 1.48808
\(821\) 33.6972 1.17604 0.588020 0.808846i \(-0.299908\pi\)
0.588020 + 0.808846i \(0.299908\pi\)
\(822\) −37.3527 −1.30282
\(823\) −7.52834 −0.262421 −0.131211 0.991354i \(-0.541886\pi\)
−0.131211 + 0.991354i \(0.541886\pi\)
\(824\) −35.6595 −1.24226
\(825\) 7.06659 0.246027
\(826\) −16.8052 −0.584728
\(827\) −9.02053 −0.313674 −0.156837 0.987624i \(-0.550130\pi\)
−0.156837 + 0.987624i \(0.550130\pi\)
\(828\) 2.98210 0.103635
\(829\) 20.3771 0.707727 0.353863 0.935297i \(-0.384868\pi\)
0.353863 + 0.935297i \(0.384868\pi\)
\(830\) 121.480 4.21663
\(831\) −21.9033 −0.759819
\(832\) 82.8119 2.87099
\(833\) 6.97364 0.241622
\(834\) 6.34672 0.219769
\(835\) 93.7877 3.24566
\(836\) −8.01838 −0.277321
\(837\) 6.09854 0.210797
\(838\) −34.3990 −1.18829
\(839\) −16.6884 −0.576149 −0.288074 0.957608i \(-0.593015\pi\)
−0.288074 + 0.957608i \(0.593015\pi\)
\(840\) 8.88232 0.306469
\(841\) 70.0006 2.41381
\(842\) 38.3922 1.32308
\(843\) 4.18564 0.144161
\(844\) 42.7987 1.47319
\(845\) 123.362 4.24379
\(846\) −44.9975 −1.54705
\(847\) −10.7230 −0.368445
\(848\) −0.925036 −0.0317659
\(849\) 0.0876373 0.00300771
\(850\) −232.272 −7.96686
\(851\) −0.718327 −0.0246239
\(852\) 2.28605 0.0783186
\(853\) −44.1223 −1.51072 −0.755360 0.655310i \(-0.772538\pi\)
−0.755360 + 0.655310i \(0.772538\pi\)
\(854\) −10.9987 −0.376368
\(855\) −49.7770 −1.70234
\(856\) 3.89408 0.133097
\(857\) 25.5337 0.872215 0.436107 0.899895i \(-0.356357\pi\)
0.436107 + 0.899895i \(0.356357\pi\)
\(858\) 6.74931 0.230417
\(859\) −1.00000 −0.0341196
\(860\) −112.284 −3.82884
\(861\) −2.87608 −0.0980164
\(862\) 16.5091 0.562303
\(863\) 34.9600 1.19005 0.595026 0.803707i \(-0.297142\pi\)
0.595026 + 0.803707i \(0.297142\pi\)
\(864\) 31.5252 1.07251
\(865\) 17.5362 0.596248
\(866\) −25.4166 −0.863690
\(867\) −28.4813 −0.967277
\(868\) 3.90221 0.132449
\(869\) −3.17763 −0.107794
\(870\) −89.2974 −3.02747
\(871\) −86.6870 −2.93728
\(872\) −5.07878 −0.171989
\(873\) −19.5146 −0.660469
\(874\) 5.18583 0.175413
\(875\) 44.2232 1.49502
\(876\) 13.1543 0.444443
\(877\) 25.5168 0.861642 0.430821 0.902437i \(-0.358224\pi\)
0.430821 + 0.902437i \(0.358224\pi\)
\(878\) 62.9831 2.12558
\(879\) −20.9212 −0.705653
\(880\) 2.44509 0.0824239
\(881\) 39.9157 1.34479 0.672397 0.740191i \(-0.265265\pi\)
0.672397 + 0.740191i \(0.265265\pi\)
\(882\) 4.89031 0.164665
\(883\) 6.50507 0.218913 0.109456 0.993992i \(-0.465089\pi\)
0.109456 + 0.993992i \(0.465089\pi\)
\(884\) −132.923 −4.47067
\(885\) −30.2266 −1.01606
\(886\) −16.6478 −0.559293
\(887\) −46.4962 −1.56119 −0.780595 0.625037i \(-0.785084\pi\)
−0.780595 + 0.625037i \(0.785084\pi\)
\(888\) 3.13842 0.105318
\(889\) 10.4781 0.351423
\(890\) −94.2671 −3.15984
\(891\) −1.24255 −0.0416269
\(892\) −36.1241 −1.20952
\(893\) −46.8854 −1.56896
\(894\) 31.6316 1.05792
\(895\) 72.8707 2.43580
\(896\) 15.5207 0.518510
\(897\) −2.61544 −0.0873269
\(898\) 58.9313 1.96656
\(899\) −12.9867 −0.433132
\(900\) −97.5949 −3.25316
\(901\) 6.19640 0.206432
\(902\) 3.75553 0.125046
\(903\) 7.57849 0.252196
\(904\) −29.0259 −0.965388
\(905\) −82.4197 −2.73972
\(906\) −27.5021 −0.913695
\(907\) 16.1269 0.535485 0.267743 0.963490i \(-0.413722\pi\)
0.267743 + 0.963490i \(0.413722\pi\)
\(908\) 87.6371 2.90834
\(909\) 21.0892 0.699484
\(910\) 63.5466 2.10655
\(911\) 6.97312 0.231030 0.115515 0.993306i \(-0.463148\pi\)
0.115515 + 0.993306i \(0.463148\pi\)
\(912\) 4.77643 0.158163
\(913\) 6.41498 0.212305
\(914\) 53.5198 1.77028
\(915\) −19.7827 −0.653997
\(916\) 60.3958 1.99553
\(917\) −10.0724 −0.332620
\(918\) −72.7850 −2.40226
\(919\) −21.7103 −0.716157 −0.358079 0.933691i \(-0.616568\pi\)
−0.358079 + 0.933691i \(0.616568\pi\)
\(920\) 4.49451 0.148180
\(921\) 7.32533 0.241378
\(922\) −10.2850 −0.338718
\(923\) 5.41413 0.178208
\(924\) 1.41690 0.0466126
\(925\) 23.5086 0.772959
\(926\) 2.41884 0.0794879
\(927\) −35.3126 −1.15982
\(928\) −67.1324 −2.20373
\(929\) −23.1620 −0.759919 −0.379960 0.925003i \(-0.624062\pi\)
−0.379960 + 0.925003i \(0.624062\pi\)
\(930\) 11.7139 0.384114
\(931\) 5.09549 0.166998
\(932\) −60.4144 −1.97894
\(933\) 9.27916 0.303786
\(934\) −60.8541 −1.99121
\(935\) −16.3785 −0.535636
\(936\) −30.8570 −1.00859
\(937\) 24.3243 0.794639 0.397319 0.917680i \(-0.369941\pi\)
0.397319 + 0.917680i \(0.369941\pi\)
\(938\) −30.3725 −0.991697
\(939\) −2.61657 −0.0853885
\(940\) −122.751 −4.00369
\(941\) 15.3427 0.500158 0.250079 0.968225i \(-0.419543\pi\)
0.250079 + 0.968225i \(0.419543\pi\)
\(942\) −14.0909 −0.459106
\(943\) −1.45531 −0.0473915
\(944\) −7.83223 −0.254917
\(945\) 20.8492 0.678223
\(946\) −9.89586 −0.321742
\(947\) 53.0561 1.72409 0.862046 0.506830i \(-0.169183\pi\)
0.862046 + 0.506830i \(0.169183\pi\)
\(948\) −16.2517 −0.527831
\(949\) 31.1539 1.01130
\(950\) −169.716 −5.50632
\(951\) −17.9731 −0.582819
\(952\) −15.4171 −0.499672
\(953\) 57.3018 1.85619 0.928093 0.372348i \(-0.121447\pi\)
0.928093 + 0.372348i \(0.121447\pi\)
\(954\) 4.34527 0.140683
\(955\) 42.2194 1.36619
\(956\) 24.2396 0.783966
\(957\) −4.71552 −0.152431
\(958\) −68.4208 −2.21058
\(959\) −18.5714 −0.599703
\(960\) 52.1872 1.68433
\(961\) −29.2964 −0.945046
\(962\) 22.4531 0.723917
\(963\) 3.85620 0.124264
\(964\) −65.6798 −2.11540
\(965\) 57.0140 1.83534
\(966\) −0.916370 −0.0294837
\(967\) 6.52011 0.209673 0.104836 0.994489i \(-0.466568\pi\)
0.104836 + 0.994489i \(0.466568\pi\)
\(968\) 23.7060 0.761940
\(969\) −31.9952 −1.02783
\(970\) −88.8469 −2.85270
\(971\) 3.39692 0.109012 0.0545062 0.998513i \(-0.482642\pi\)
0.0545062 + 0.998513i \(0.482642\pi\)
\(972\) −48.2627 −1.54803
\(973\) 3.15554 0.101162
\(974\) 91.6088 2.93534
\(975\) 85.5952 2.74124
\(976\) −5.12604 −0.164081
\(977\) 42.8930 1.37227 0.686134 0.727475i \(-0.259306\pi\)
0.686134 + 0.727475i \(0.259306\pi\)
\(978\) −16.4301 −0.525376
\(979\) −4.97795 −0.159096
\(980\) 13.3405 0.426147
\(981\) −5.02938 −0.160576
\(982\) 3.13097 0.0999133
\(983\) 19.1984 0.612333 0.306166 0.951978i \(-0.400954\pi\)
0.306166 + 0.951978i \(0.400954\pi\)
\(984\) 6.35835 0.202697
\(985\) 38.8922 1.23921
\(986\) 154.994 4.93603
\(987\) 8.28496 0.263713
\(988\) −97.1238 −3.08992
\(989\) 3.83477 0.121938
\(990\) −11.4856 −0.365035
\(991\) 1.65063 0.0524341 0.0262171 0.999656i \(-0.491654\pi\)
0.0262171 + 0.999656i \(0.491654\pi\)
\(992\) 8.80633 0.279601
\(993\) −18.8228 −0.597324
\(994\) 1.89695 0.0601675
\(995\) 27.9629 0.886482
\(996\) 32.8088 1.03959
\(997\) 47.2251 1.49563 0.747817 0.663905i \(-0.231102\pi\)
0.747817 + 0.663905i \(0.231102\pi\)
\(998\) 29.8153 0.943787
\(999\) 7.36669 0.233072
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 \(a_p\))