Properties

Label 6013.2.a.e.1.18
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 1.18
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.88015 q^{2}\) \(-2.98311 q^{3}\) \(+1.53497 q^{4}\) \(+2.43013 q^{5}\) \(+5.60869 q^{6}\) \(+1.00000 q^{7}\) \(+0.874328 q^{8}\) \(+5.89893 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.88015 q^{2}\) \(-2.98311 q^{3}\) \(+1.53497 q^{4}\) \(+2.43013 q^{5}\) \(+5.60869 q^{6}\) \(+1.00000 q^{7}\) \(+0.874328 q^{8}\) \(+5.89893 q^{9}\) \(-4.56900 q^{10}\) \(+4.23272 q^{11}\) \(-4.57898 q^{12}\) \(+2.14838 q^{13}\) \(-1.88015 q^{14}\) \(-7.24933 q^{15}\) \(-4.71381 q^{16}\) \(+3.69258 q^{17}\) \(-11.0909 q^{18}\) \(+1.95008 q^{19}\) \(+3.73017 q^{20}\) \(-2.98311 q^{21}\) \(-7.95815 q^{22}\) \(-1.47812 q^{23}\) \(-2.60822 q^{24}\) \(+0.905511 q^{25}\) \(-4.03929 q^{26}\) \(-8.64783 q^{27}\) \(+1.53497 q^{28}\) \(+2.82206 q^{29}\) \(+13.6298 q^{30}\) \(+7.67949 q^{31}\) \(+7.11402 q^{32}\) \(-12.6267 q^{33}\) \(-6.94260 q^{34}\) \(+2.43013 q^{35}\) \(+9.05468 q^{36}\) \(-0.784587 q^{37}\) \(-3.66645 q^{38}\) \(-6.40886 q^{39}\) \(+2.12473 q^{40}\) \(-7.66749 q^{41}\) \(+5.60869 q^{42}\) \(+7.36081 q^{43}\) \(+6.49709 q^{44}\) \(+14.3351 q^{45}\) \(+2.77909 q^{46}\) \(+6.79326 q^{47}\) \(+14.0618 q^{48}\) \(+1.00000 q^{49}\) \(-1.70250 q^{50}\) \(-11.0154 q^{51}\) \(+3.29770 q^{52}\) \(+7.85333 q^{53}\) \(+16.2592 q^{54}\) \(+10.2860 q^{55}\) \(+0.874328 q^{56}\) \(-5.81731 q^{57}\) \(-5.30589 q^{58}\) \(+0.0575512 q^{59}\) \(-11.1275 q^{60}\) \(+12.7978 q^{61}\) \(-14.4386 q^{62}\) \(+5.89893 q^{63}\) \(-3.94781 q^{64}\) \(+5.22084 q^{65}\) \(+23.7400 q^{66}\) \(+11.3642 q^{67}\) \(+5.66799 q^{68}\) \(+4.40940 q^{69}\) \(-4.56900 q^{70}\) \(+0.760785 q^{71}\) \(+5.15760 q^{72}\) \(-4.23400 q^{73}\) \(+1.47514 q^{74}\) \(-2.70124 q^{75}\) \(+2.99332 q^{76}\) \(+4.23272 q^{77}\) \(+12.0496 q^{78}\) \(-4.10291 q^{79}\) \(-11.4551 q^{80}\) \(+8.10061 q^{81}\) \(+14.4160 q^{82}\) \(+5.25120 q^{83}\) \(-4.57898 q^{84}\) \(+8.97342 q^{85}\) \(-13.8394 q^{86}\) \(-8.41850 q^{87}\) \(+3.70079 q^{88}\) \(+2.50755 q^{89}\) \(-26.9523 q^{90}\) \(+2.14838 q^{91}\) \(-2.26887 q^{92}\) \(-22.9087 q^{93}\) \(-12.7724 q^{94}\) \(+4.73895 q^{95}\) \(-21.2219 q^{96}\) \(+2.23817 q^{97}\) \(-1.88015 q^{98}\) \(+24.9685 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.88015 −1.32947 −0.664734 0.747080i \(-0.731455\pi\)
−0.664734 + 0.747080i \(0.731455\pi\)
\(3\) −2.98311 −1.72230 −0.861149 0.508352i \(-0.830255\pi\)
−0.861149 + 0.508352i \(0.830255\pi\)
\(4\) 1.53497 0.767485
\(5\) 2.43013 1.08679 0.543393 0.839479i \(-0.317140\pi\)
0.543393 + 0.839479i \(0.317140\pi\)
\(6\) 5.60869 2.28974
\(7\) 1.00000 0.377964
\(8\) 0.874328 0.309122
\(9\) 5.89893 1.96631
\(10\) −4.56900 −1.44485
\(11\) 4.23272 1.27621 0.638106 0.769948i \(-0.279718\pi\)
0.638106 + 0.769948i \(0.279718\pi\)
\(12\) −4.57898 −1.32184
\(13\) 2.14838 0.595854 0.297927 0.954589i \(-0.403705\pi\)
0.297927 + 0.954589i \(0.403705\pi\)
\(14\) −1.88015 −0.502492
\(15\) −7.24933 −1.87177
\(16\) −4.71381 −1.17845
\(17\) 3.69258 0.895581 0.447790 0.894139i \(-0.352211\pi\)
0.447790 + 0.894139i \(0.352211\pi\)
\(18\) −11.0909 −2.61415
\(19\) 1.95008 0.447380 0.223690 0.974660i \(-0.428190\pi\)
0.223690 + 0.974660i \(0.428190\pi\)
\(20\) 3.73017 0.834091
\(21\) −2.98311 −0.650968
\(22\) −7.95815 −1.69668
\(23\) −1.47812 −0.308210 −0.154105 0.988055i \(-0.549249\pi\)
−0.154105 + 0.988055i \(0.549249\pi\)
\(24\) −2.60822 −0.532400
\(25\) 0.905511 0.181102
\(26\) −4.03929 −0.792169
\(27\) −8.64783 −1.66428
\(28\) 1.53497 0.290082
\(29\) 2.82206 0.524043 0.262021 0.965062i \(-0.415611\pi\)
0.262021 + 0.965062i \(0.415611\pi\)
\(30\) 13.6298 2.48846
\(31\) 7.67949 1.37928 0.689638 0.724154i \(-0.257769\pi\)
0.689638 + 0.724154i \(0.257769\pi\)
\(32\) 7.11402 1.25759
\(33\) −12.6267 −2.19802
\(34\) −6.94260 −1.19065
\(35\) 2.43013 0.410766
\(36\) 9.05468 1.50911
\(37\) −0.784587 −0.128985 −0.0644927 0.997918i \(-0.520543\pi\)
−0.0644927 + 0.997918i \(0.520543\pi\)
\(38\) −3.66645 −0.594777
\(39\) −6.40886 −1.02624
\(40\) 2.12473 0.335949
\(41\) −7.66749 −1.19746 −0.598731 0.800951i \(-0.704328\pi\)
−0.598731 + 0.800951i \(0.704328\pi\)
\(42\) 5.60869 0.865440
\(43\) 7.36081 1.12251 0.561256 0.827642i \(-0.310318\pi\)
0.561256 + 0.827642i \(0.310318\pi\)
\(44\) 6.49709 0.979474
\(45\) 14.3351 2.13696
\(46\) 2.77909 0.409755
\(47\) 6.79326 0.990899 0.495449 0.868637i \(-0.335003\pi\)
0.495449 + 0.868637i \(0.335003\pi\)
\(48\) 14.0618 2.02965
\(49\) 1.00000 0.142857
\(50\) −1.70250 −0.240770
\(51\) −11.0154 −1.54246
\(52\) 3.29770 0.457309
\(53\) 7.85333 1.07874 0.539369 0.842070i \(-0.318663\pi\)
0.539369 + 0.842070i \(0.318663\pi\)
\(54\) 16.2592 2.21260
\(55\) 10.2860 1.38697
\(56\) 0.874328 0.116837
\(57\) −5.81731 −0.770522
\(58\) −5.30589 −0.696698
\(59\) 0.0575512 0.00749253 0.00374626 0.999993i \(-0.498808\pi\)
0.00374626 + 0.999993i \(0.498808\pi\)
\(60\) −11.1275 −1.43655
\(61\) 12.7978 1.63860 0.819298 0.573368i \(-0.194363\pi\)
0.819298 + 0.573368i \(0.194363\pi\)
\(62\) −14.4386 −1.83370
\(63\) 5.89893 0.743196
\(64\) −3.94781 −0.493476
\(65\) 5.22084 0.647566
\(66\) 23.7400 2.92220
\(67\) 11.3642 1.38836 0.694180 0.719802i \(-0.255767\pi\)
0.694180 + 0.719802i \(0.255767\pi\)
\(68\) 5.66799 0.687345
\(69\) 4.40940 0.530829
\(70\) −4.56900 −0.546100
\(71\) 0.760785 0.0902885 0.0451443 0.998980i \(-0.485625\pi\)
0.0451443 + 0.998980i \(0.485625\pi\)
\(72\) 5.15760 0.607829
\(73\) −4.23400 −0.495553 −0.247776 0.968817i \(-0.579700\pi\)
−0.247776 + 0.968817i \(0.579700\pi\)
\(74\) 1.47514 0.171482
\(75\) −2.70124 −0.311912
\(76\) 2.99332 0.343357
\(77\) 4.23272 0.482363
\(78\) 12.0496 1.36435
\(79\) −4.10291 −0.461614 −0.230807 0.973000i \(-0.574137\pi\)
−0.230807 + 0.973000i \(0.574137\pi\)
\(80\) −11.4551 −1.28072
\(81\) 8.10061 0.900068
\(82\) 14.4160 1.59199
\(83\) 5.25120 0.576394 0.288197 0.957571i \(-0.406944\pi\)
0.288197 + 0.957571i \(0.406944\pi\)
\(84\) −4.57898 −0.499608
\(85\) 8.97342 0.973304
\(86\) −13.8394 −1.49234
\(87\) −8.41850 −0.902558
\(88\) 3.70079 0.394505
\(89\) 2.50755 0.265800 0.132900 0.991129i \(-0.457571\pi\)
0.132900 + 0.991129i \(0.457571\pi\)
\(90\) −26.9523 −2.84102
\(91\) 2.14838 0.225212
\(92\) −2.26887 −0.236546
\(93\) −22.9087 −2.37553
\(94\) −12.7724 −1.31737
\(95\) 4.73895 0.486206
\(96\) −21.2219 −2.16595
\(97\) 2.23817 0.227251 0.113626 0.993524i \(-0.463754\pi\)
0.113626 + 0.993524i \(0.463754\pi\)
\(98\) −1.88015 −0.189924
\(99\) 24.9685 2.50943
\(100\) 1.38993 0.138993
\(101\) −10.7269 −1.06737 −0.533685 0.845683i \(-0.679193\pi\)
−0.533685 + 0.845683i \(0.679193\pi\)
\(102\) 20.7105 2.05065
\(103\) 15.8544 1.56218 0.781090 0.624418i \(-0.214664\pi\)
0.781090 + 0.624418i \(0.214664\pi\)
\(104\) 1.87839 0.184192
\(105\) −7.24933 −0.707462
\(106\) −14.7655 −1.43415
\(107\) 1.60570 0.155229 0.0776146 0.996983i \(-0.475270\pi\)
0.0776146 + 0.996983i \(0.475270\pi\)
\(108\) −13.2742 −1.27731
\(109\) −11.9969 −1.14909 −0.574547 0.818472i \(-0.694822\pi\)
−0.574547 + 0.818472i \(0.694822\pi\)
\(110\) −19.3393 −1.84393
\(111\) 2.34051 0.222151
\(112\) −4.71381 −0.445413
\(113\) 21.0140 1.97683 0.988417 0.151765i \(-0.0484956\pi\)
0.988417 + 0.151765i \(0.0484956\pi\)
\(114\) 10.9374 1.02438
\(115\) −3.59202 −0.334958
\(116\) 4.33177 0.402195
\(117\) 12.6732 1.17164
\(118\) −0.108205 −0.00996108
\(119\) 3.69258 0.338498
\(120\) −6.33829 −0.578604
\(121\) 6.91591 0.628719
\(122\) −24.0619 −2.17846
\(123\) 22.8730 2.06239
\(124\) 11.7878 1.05857
\(125\) −9.95012 −0.889966
\(126\) −11.0909 −0.988055
\(127\) 12.1581 1.07886 0.539430 0.842031i \(-0.318640\pi\)
0.539430 + 0.842031i \(0.318640\pi\)
\(128\) −6.80555 −0.601531
\(129\) −21.9581 −1.93330
\(130\) −9.81597 −0.860918
\(131\) −18.7159 −1.63522 −0.817610 0.575773i \(-0.804701\pi\)
−0.817610 + 0.575773i \(0.804701\pi\)
\(132\) −19.3815 −1.68695
\(133\) 1.95008 0.169094
\(134\) −21.3664 −1.84578
\(135\) −21.0153 −1.80871
\(136\) 3.22852 0.276844
\(137\) 0.152629 0.0130400 0.00652000 0.999979i \(-0.497925\pi\)
0.00652000 + 0.999979i \(0.497925\pi\)
\(138\) −8.29033 −0.705720
\(139\) 8.07727 0.685105 0.342552 0.939499i \(-0.388709\pi\)
0.342552 + 0.939499i \(0.388709\pi\)
\(140\) 3.73017 0.315257
\(141\) −20.2650 −1.70662
\(142\) −1.43039 −0.120036
\(143\) 9.09350 0.760437
\(144\) −27.8064 −2.31720
\(145\) 6.85795 0.569522
\(146\) 7.96057 0.658821
\(147\) −2.98311 −0.246043
\(148\) −1.20432 −0.0989943
\(149\) −5.66945 −0.464460 −0.232230 0.972661i \(-0.574602\pi\)
−0.232230 + 0.972661i \(0.574602\pi\)
\(150\) 5.07873 0.414677
\(151\) 20.4524 1.66439 0.832196 0.554482i \(-0.187083\pi\)
0.832196 + 0.554482i \(0.187083\pi\)
\(152\) 1.70501 0.138295
\(153\) 21.7823 1.76099
\(154\) −7.95815 −0.641286
\(155\) 18.6621 1.49898
\(156\) −9.83740 −0.787623
\(157\) −16.0509 −1.28100 −0.640501 0.767957i \(-0.721273\pi\)
−0.640501 + 0.767957i \(0.721273\pi\)
\(158\) 7.71410 0.613700
\(159\) −23.4273 −1.85791
\(160\) 17.2880 1.36673
\(161\) −1.47812 −0.116492
\(162\) −15.2304 −1.19661
\(163\) −6.98218 −0.546887 −0.273443 0.961888i \(-0.588163\pi\)
−0.273443 + 0.961888i \(0.588163\pi\)
\(164\) −11.7694 −0.919033
\(165\) −30.6844 −2.38877
\(166\) −9.87305 −0.766297
\(167\) 17.5545 1.35841 0.679205 0.733949i \(-0.262325\pi\)
0.679205 + 0.733949i \(0.262325\pi\)
\(168\) −2.60822 −0.201228
\(169\) −8.38445 −0.644958
\(170\) −16.8714 −1.29398
\(171\) 11.5034 0.879688
\(172\) 11.2986 0.861511
\(173\) −9.85217 −0.749047 −0.374523 0.927217i \(-0.622194\pi\)
−0.374523 + 0.927217i \(0.622194\pi\)
\(174\) 15.8281 1.19992
\(175\) 0.905511 0.0684502
\(176\) −19.9522 −1.50396
\(177\) −0.171681 −0.0129044
\(178\) −4.71457 −0.353372
\(179\) −4.06461 −0.303803 −0.151902 0.988396i \(-0.548540\pi\)
−0.151902 + 0.988396i \(0.548540\pi\)
\(180\) 22.0040 1.64008
\(181\) 2.19599 0.163226 0.0816132 0.996664i \(-0.473993\pi\)
0.0816132 + 0.996664i \(0.473993\pi\)
\(182\) −4.03929 −0.299412
\(183\) −38.1774 −2.82215
\(184\) −1.29236 −0.0952743
\(185\) −1.90665 −0.140179
\(186\) 43.0719 3.15819
\(187\) 15.6296 1.14295
\(188\) 10.4274 0.760499
\(189\) −8.64783 −0.629037
\(190\) −8.90994 −0.646395
\(191\) −23.0059 −1.66464 −0.832322 0.554292i \(-0.812989\pi\)
−0.832322 + 0.554292i \(0.812989\pi\)
\(192\) 11.7767 0.849914
\(193\) −24.1237 −1.73646 −0.868231 0.496160i \(-0.834743\pi\)
−0.868231 + 0.496160i \(0.834743\pi\)
\(194\) −4.20809 −0.302124
\(195\) −15.5743 −1.11530
\(196\) 1.53497 0.109641
\(197\) 7.86021 0.560017 0.280008 0.959998i \(-0.409663\pi\)
0.280008 + 0.959998i \(0.409663\pi\)
\(198\) −46.9446 −3.33621
\(199\) 19.6170 1.39061 0.695307 0.718713i \(-0.255268\pi\)
0.695307 + 0.718713i \(0.255268\pi\)
\(200\) 0.791714 0.0559826
\(201\) −33.9007 −2.39117
\(202\) 20.1683 1.41903
\(203\) 2.82206 0.198070
\(204\) −16.9082 −1.18381
\(205\) −18.6330 −1.30138
\(206\) −29.8087 −2.07687
\(207\) −8.71934 −0.606036
\(208\) −10.1271 −0.702186
\(209\) 8.25416 0.570952
\(210\) 13.6298 0.940548
\(211\) −18.8520 −1.29782 −0.648912 0.760863i \(-0.724776\pi\)
−0.648912 + 0.760863i \(0.724776\pi\)
\(212\) 12.0546 0.827915
\(213\) −2.26950 −0.155504
\(214\) −3.01897 −0.206372
\(215\) 17.8877 1.21993
\(216\) −7.56104 −0.514464
\(217\) 7.67949 0.521318
\(218\) 22.5560 1.52768
\(219\) 12.6305 0.853489
\(220\) 15.7888 1.06448
\(221\) 7.93307 0.533636
\(222\) −4.40051 −0.295343
\(223\) −4.50235 −0.301499 −0.150750 0.988572i \(-0.548169\pi\)
−0.150750 + 0.988572i \(0.548169\pi\)
\(224\) 7.11402 0.475325
\(225\) 5.34155 0.356103
\(226\) −39.5096 −2.62814
\(227\) −18.8493 −1.25107 −0.625535 0.780196i \(-0.715119\pi\)
−0.625535 + 0.780196i \(0.715119\pi\)
\(228\) −8.92940 −0.591364
\(229\) −29.9967 −1.98223 −0.991117 0.132990i \(-0.957542\pi\)
−0.991117 + 0.132990i \(0.957542\pi\)
\(230\) 6.75354 0.445315
\(231\) −12.6267 −0.830773
\(232\) 2.46740 0.161993
\(233\) 0.676619 0.0443268 0.0221634 0.999754i \(-0.492945\pi\)
0.0221634 + 0.999754i \(0.492945\pi\)
\(234\) −23.8275 −1.55765
\(235\) 16.5085 1.07689
\(236\) 0.0883393 0.00575040
\(237\) 12.2394 0.795036
\(238\) −6.94260 −0.450022
\(239\) 25.9148 1.67629 0.838143 0.545450i \(-0.183641\pi\)
0.838143 + 0.545450i \(0.183641\pi\)
\(240\) 34.1719 2.20579
\(241\) −1.06026 −0.0682974 −0.0341487 0.999417i \(-0.510872\pi\)
−0.0341487 + 0.999417i \(0.510872\pi\)
\(242\) −13.0029 −0.835861
\(243\) 1.77849 0.114090
\(244\) 19.6443 1.25760
\(245\) 2.43013 0.155255
\(246\) −43.0046 −2.74187
\(247\) 4.18953 0.266573
\(248\) 6.71439 0.426364
\(249\) −15.6649 −0.992723
\(250\) 18.7077 1.18318
\(251\) −1.84779 −0.116631 −0.0583156 0.998298i \(-0.518573\pi\)
−0.0583156 + 0.998298i \(0.518573\pi\)
\(252\) 9.05468 0.570391
\(253\) −6.25647 −0.393341
\(254\) −22.8591 −1.43431
\(255\) −26.7687 −1.67632
\(256\) 20.6911 1.29319
\(257\) 0.561345 0.0350157 0.0175079 0.999847i \(-0.494427\pi\)
0.0175079 + 0.999847i \(0.494427\pi\)
\(258\) 41.2845 2.57026
\(259\) −0.784587 −0.0487519
\(260\) 8.01383 0.496997
\(261\) 16.6471 1.03043
\(262\) 35.1888 2.17397
\(263\) 0.519382 0.0320265 0.0160132 0.999872i \(-0.494903\pi\)
0.0160132 + 0.999872i \(0.494903\pi\)
\(264\) −11.0398 −0.679455
\(265\) 19.0846 1.17236
\(266\) −3.66645 −0.224805
\(267\) −7.48029 −0.457786
\(268\) 17.4437 1.06554
\(269\) 8.89410 0.542283 0.271142 0.962539i \(-0.412599\pi\)
0.271142 + 0.962539i \(0.412599\pi\)
\(270\) 39.5120 2.40462
\(271\) −22.9266 −1.39269 −0.696345 0.717707i \(-0.745192\pi\)
−0.696345 + 0.717707i \(0.745192\pi\)
\(272\) −17.4061 −1.05540
\(273\) −6.40886 −0.387882
\(274\) −0.286966 −0.0173363
\(275\) 3.83277 0.231125
\(276\) 6.76829 0.407403
\(277\) −22.8258 −1.37147 −0.685734 0.727852i \(-0.740519\pi\)
−0.685734 + 0.727852i \(0.740519\pi\)
\(278\) −15.1865 −0.910825
\(279\) 45.3008 2.71209
\(280\) 2.12473 0.126977
\(281\) −0.582712 −0.0347617 −0.0173808 0.999849i \(-0.505533\pi\)
−0.0173808 + 0.999849i \(0.505533\pi\)
\(282\) 38.1013 2.26890
\(283\) −9.54163 −0.567191 −0.283596 0.958944i \(-0.591527\pi\)
−0.283596 + 0.958944i \(0.591527\pi\)
\(284\) 1.16778 0.0692951
\(285\) −14.1368 −0.837392
\(286\) −17.0972 −1.01098
\(287\) −7.66749 −0.452598
\(288\) 41.9651 2.47282
\(289\) −3.36489 −0.197935
\(290\) −12.8940 −0.757161
\(291\) −6.67670 −0.391395
\(292\) −6.49906 −0.380329
\(293\) 17.4206 1.01772 0.508860 0.860849i \(-0.330067\pi\)
0.508860 + 0.860849i \(0.330067\pi\)
\(294\) 5.60869 0.327106
\(295\) 0.139857 0.00814277
\(296\) −0.685987 −0.0398722
\(297\) −36.6038 −2.12397
\(298\) 10.6594 0.617484
\(299\) −3.17557 −0.183648
\(300\) −4.14632 −0.239388
\(301\) 7.36081 0.424270
\(302\) −38.4536 −2.21276
\(303\) 31.9996 1.83833
\(304\) −9.19232 −0.527216
\(305\) 31.1004 1.78080
\(306\) −40.9539 −2.34118
\(307\) 0.601170 0.0343106 0.0171553 0.999853i \(-0.494539\pi\)
0.0171553 + 0.999853i \(0.494539\pi\)
\(308\) 6.49709 0.370206
\(309\) −47.2954 −2.69054
\(310\) −35.0876 −1.99284
\(311\) −3.03774 −0.172254 −0.0861271 0.996284i \(-0.527449\pi\)
−0.0861271 + 0.996284i \(0.527449\pi\)
\(312\) −5.60345 −0.317233
\(313\) −18.4034 −1.04022 −0.520110 0.854099i \(-0.674109\pi\)
−0.520110 + 0.854099i \(0.674109\pi\)
\(314\) 30.1782 1.70305
\(315\) 14.3351 0.807694
\(316\) −6.29784 −0.354281
\(317\) −4.91107 −0.275833 −0.137917 0.990444i \(-0.544041\pi\)
−0.137917 + 0.990444i \(0.544041\pi\)
\(318\) 44.0469 2.47003
\(319\) 11.9450 0.668790
\(320\) −9.59368 −0.536303
\(321\) −4.78999 −0.267351
\(322\) 2.77909 0.154873
\(323\) 7.20083 0.400665
\(324\) 12.4342 0.690789
\(325\) 1.94538 0.107911
\(326\) 13.1276 0.727068
\(327\) 35.7880 1.97908
\(328\) −6.70390 −0.370161
\(329\) 6.79326 0.374524
\(330\) 57.6912 3.17580
\(331\) 1.64051 0.0901703 0.0450852 0.998983i \(-0.485644\pi\)
0.0450852 + 0.998983i \(0.485644\pi\)
\(332\) 8.06043 0.442374
\(333\) −4.62823 −0.253625
\(334\) −33.0052 −1.80596
\(335\) 27.6165 1.50885
\(336\) 14.0618 0.767134
\(337\) 18.4121 1.00297 0.501484 0.865167i \(-0.332787\pi\)
0.501484 + 0.865167i \(0.332787\pi\)
\(338\) 15.7640 0.857450
\(339\) −62.6871 −3.40470
\(340\) 13.7739 0.746996
\(341\) 32.5051 1.76025
\(342\) −21.6282 −1.16952
\(343\) 1.00000 0.0539949
\(344\) 6.43576 0.346993
\(345\) 10.7154 0.576897
\(346\) 18.5236 0.995834
\(347\) −23.4993 −1.26151 −0.630755 0.775982i \(-0.717255\pi\)
−0.630755 + 0.775982i \(0.717255\pi\)
\(348\) −12.9221 −0.692699
\(349\) 15.5154 0.830522 0.415261 0.909702i \(-0.363690\pi\)
0.415261 + 0.909702i \(0.363690\pi\)
\(350\) −1.70250 −0.0910023
\(351\) −18.5789 −0.991666
\(352\) 30.1116 1.60496
\(353\) −25.1106 −1.33650 −0.668252 0.743935i \(-0.732957\pi\)
−0.668252 + 0.743935i \(0.732957\pi\)
\(354\) 0.322787 0.0171559
\(355\) 1.84880 0.0981242
\(356\) 3.84901 0.203997
\(357\) −11.0154 −0.582994
\(358\) 7.64209 0.403897
\(359\) −31.3686 −1.65557 −0.827786 0.561043i \(-0.810400\pi\)
−0.827786 + 0.561043i \(0.810400\pi\)
\(360\) 12.5336 0.660580
\(361\) −15.1972 −0.799851
\(362\) −4.12879 −0.217004
\(363\) −20.6309 −1.08284
\(364\) 3.29770 0.172847
\(365\) −10.2892 −0.538559
\(366\) 71.7792 3.75196
\(367\) 17.9629 0.937655 0.468828 0.883290i \(-0.344677\pi\)
0.468828 + 0.883290i \(0.344677\pi\)
\(368\) 6.96758 0.363210
\(369\) −45.2300 −2.35458
\(370\) 3.58478 0.186364
\(371\) 7.85333 0.407725
\(372\) −35.1642 −1.82318
\(373\) 4.96081 0.256861 0.128431 0.991718i \(-0.459006\pi\)
0.128431 + 0.991718i \(0.459006\pi\)
\(374\) −29.3861 −1.51952
\(375\) 29.6823 1.53279
\(376\) 5.93954 0.306308
\(377\) 6.06286 0.312253
\(378\) 16.2592 0.836285
\(379\) 1.00499 0.0516226 0.0258113 0.999667i \(-0.491783\pi\)
0.0258113 + 0.999667i \(0.491783\pi\)
\(380\) 7.27414 0.373156
\(381\) −36.2690 −1.85812
\(382\) 43.2545 2.21309
\(383\) 35.2561 1.80150 0.900752 0.434335i \(-0.143016\pi\)
0.900752 + 0.434335i \(0.143016\pi\)
\(384\) 20.3017 1.03602
\(385\) 10.2860 0.524225
\(386\) 45.3562 2.30857
\(387\) 43.4209 2.20721
\(388\) 3.43552 0.174412
\(389\) 11.5459 0.585399 0.292700 0.956204i \(-0.405446\pi\)
0.292700 + 0.956204i \(0.405446\pi\)
\(390\) 29.2821 1.48276
\(391\) −5.45807 −0.276027
\(392\) 0.874328 0.0441602
\(393\) 55.8317 2.81634
\(394\) −14.7784 −0.744525
\(395\) −9.97059 −0.501675
\(396\) 38.3259 1.92595
\(397\) 15.4627 0.776049 0.388025 0.921649i \(-0.373158\pi\)
0.388025 + 0.921649i \(0.373158\pi\)
\(398\) −36.8830 −1.84878
\(399\) −5.81731 −0.291230
\(400\) −4.26840 −0.213420
\(401\) 0.531699 0.0265518 0.0132759 0.999912i \(-0.495774\pi\)
0.0132759 + 0.999912i \(0.495774\pi\)
\(402\) 63.7384 3.17898
\(403\) 16.4985 0.821848
\(404\) −16.4655 −0.819190
\(405\) 19.6855 0.978181
\(406\) −5.30589 −0.263327
\(407\) −3.32094 −0.164613
\(408\) −9.63103 −0.476807
\(409\) −6.36430 −0.314695 −0.157347 0.987543i \(-0.550294\pi\)
−0.157347 + 0.987543i \(0.550294\pi\)
\(410\) 35.0328 1.73015
\(411\) −0.455310 −0.0224588
\(412\) 24.3360 1.19895
\(413\) 0.0575512 0.00283191
\(414\) 16.3937 0.805705
\(415\) 12.7611 0.626417
\(416\) 15.2836 0.749342
\(417\) −24.0954 −1.17996
\(418\) −15.5191 −0.759062
\(419\) 10.7068 0.523060 0.261530 0.965195i \(-0.415773\pi\)
0.261530 + 0.965195i \(0.415773\pi\)
\(420\) −11.1275 −0.542966
\(421\) 40.6602 1.98166 0.990828 0.135126i \(-0.0431440\pi\)
0.990828 + 0.135126i \(0.0431440\pi\)
\(422\) 35.4446 1.72542
\(423\) 40.0730 1.94841
\(424\) 6.86639 0.333461
\(425\) 3.34367 0.162192
\(426\) 4.26701 0.206737
\(427\) 12.7978 0.619331
\(428\) 2.46471 0.119136
\(429\) −27.1269 −1.30970
\(430\) −33.6315 −1.62186
\(431\) −14.1760 −0.682835 −0.341418 0.939912i \(-0.610907\pi\)
−0.341418 + 0.939912i \(0.610907\pi\)
\(432\) 40.7642 1.96127
\(433\) −7.21247 −0.346609 −0.173305 0.984868i \(-0.555445\pi\)
−0.173305 + 0.984868i \(0.555445\pi\)
\(434\) −14.4386 −0.693075
\(435\) −20.4580 −0.980887
\(436\) −18.4149 −0.881912
\(437\) −2.88246 −0.137887
\(438\) −23.7472 −1.13469
\(439\) −12.6409 −0.603318 −0.301659 0.953416i \(-0.597540\pi\)
−0.301659 + 0.953416i \(0.597540\pi\)
\(440\) 8.99337 0.428742
\(441\) 5.89893 0.280902
\(442\) −14.9154 −0.709452
\(443\) −37.1124 −1.76326 −0.881632 0.471938i \(-0.843555\pi\)
−0.881632 + 0.471938i \(0.843555\pi\)
\(444\) 3.59261 0.170498
\(445\) 6.09366 0.288867
\(446\) 8.46509 0.400834
\(447\) 16.9126 0.799938
\(448\) −3.94781 −0.186517
\(449\) 20.7910 0.981187 0.490593 0.871389i \(-0.336780\pi\)
0.490593 + 0.871389i \(0.336780\pi\)
\(450\) −10.0429 −0.473428
\(451\) −32.4543 −1.52822
\(452\) 32.2559 1.51719
\(453\) −61.0117 −2.86658
\(454\) 35.4395 1.66326
\(455\) 5.22084 0.244757
\(456\) −5.08624 −0.238185
\(457\) −34.8733 −1.63130 −0.815652 0.578543i \(-0.803622\pi\)
−0.815652 + 0.578543i \(0.803622\pi\)
\(458\) 56.3983 2.63532
\(459\) −31.9328 −1.49049
\(460\) −5.51364 −0.257075
\(461\) 21.6083 1.00640 0.503200 0.864170i \(-0.332156\pi\)
0.503200 + 0.864170i \(0.332156\pi\)
\(462\) 23.7400 1.10449
\(463\) −40.4373 −1.87928 −0.939640 0.342164i \(-0.888840\pi\)
−0.939640 + 0.342164i \(0.888840\pi\)
\(464\) −13.3026 −0.617559
\(465\) −55.6711 −2.58169
\(466\) −1.27215 −0.0589310
\(467\) −8.53926 −0.395150 −0.197575 0.980288i \(-0.563307\pi\)
−0.197575 + 0.980288i \(0.563307\pi\)
\(468\) 19.4529 0.899212
\(469\) 11.3642 0.524751
\(470\) −31.0384 −1.43170
\(471\) 47.8816 2.20627
\(472\) 0.0503186 0.00231610
\(473\) 31.1562 1.43256
\(474\) −23.0120 −1.05698
\(475\) 1.76582 0.0810215
\(476\) 5.66799 0.259792
\(477\) 46.3263 2.12113
\(478\) −48.7237 −2.22857
\(479\) 4.78033 0.218419 0.109209 0.994019i \(-0.465168\pi\)
0.109209 + 0.994019i \(0.465168\pi\)
\(480\) −51.5718 −2.35392
\(481\) −1.68559 −0.0768565
\(482\) 1.99345 0.0907992
\(483\) 4.40940 0.200634
\(484\) 10.6157 0.482532
\(485\) 5.43903 0.246974
\(486\) −3.34382 −0.151679
\(487\) −10.1337 −0.459202 −0.229601 0.973285i \(-0.573742\pi\)
−0.229601 + 0.973285i \(0.573742\pi\)
\(488\) 11.1895 0.506526
\(489\) 20.8286 0.941902
\(490\) −4.56900 −0.206407
\(491\) −10.9689 −0.495019 −0.247510 0.968885i \(-0.579612\pi\)
−0.247510 + 0.968885i \(0.579612\pi\)
\(492\) 35.1093 1.58285
\(493\) 10.4207 0.469323
\(494\) −7.87695 −0.354401
\(495\) 60.6767 2.72721
\(496\) −36.1996 −1.62541
\(497\) 0.760785 0.0341259
\(498\) 29.4524 1.31979
\(499\) −14.5869 −0.652998 −0.326499 0.945198i \(-0.605869\pi\)
−0.326499 + 0.945198i \(0.605869\pi\)
\(500\) −15.2731 −0.683035
\(501\) −52.3670 −2.33959
\(502\) 3.47412 0.155058
\(503\) 17.3342 0.772896 0.386448 0.922311i \(-0.373702\pi\)
0.386448 + 0.922311i \(0.373702\pi\)
\(504\) 5.15760 0.229738
\(505\) −26.0678 −1.16000
\(506\) 11.7631 0.522934
\(507\) 25.0117 1.11081
\(508\) 18.6624 0.828008
\(509\) −0.936121 −0.0414928 −0.0207464 0.999785i \(-0.506604\pi\)
−0.0207464 + 0.999785i \(0.506604\pi\)
\(510\) 50.3292 2.22861
\(511\) −4.23400 −0.187301
\(512\) −25.2913 −1.11773
\(513\) −16.8640 −0.744564
\(514\) −1.05541 −0.0465523
\(515\) 38.5282 1.69775
\(516\) −33.7050 −1.48378
\(517\) 28.7539 1.26460
\(518\) 1.47514 0.0648140
\(519\) 29.3901 1.29008
\(520\) 4.56473 0.200177
\(521\) 11.4178 0.500221 0.250110 0.968217i \(-0.419533\pi\)
0.250110 + 0.968217i \(0.419533\pi\)
\(522\) −31.2991 −1.36992
\(523\) −10.1144 −0.442270 −0.221135 0.975243i \(-0.570976\pi\)
−0.221135 + 0.975243i \(0.570976\pi\)
\(524\) −28.7284 −1.25501
\(525\) −2.70124 −0.117892
\(526\) −0.976518 −0.0425782
\(527\) 28.3571 1.23525
\(528\) 59.5196 2.59026
\(529\) −20.8152 −0.905007
\(530\) −35.8819 −1.55861
\(531\) 0.339491 0.0147326
\(532\) 2.99332 0.129777
\(533\) −16.4727 −0.713512
\(534\) 14.0641 0.608612
\(535\) 3.90206 0.168701
\(536\) 9.93605 0.429172
\(537\) 12.1252 0.523240
\(538\) −16.7223 −0.720948
\(539\) 4.23272 0.182316
\(540\) −32.2579 −1.38816
\(541\) −25.4254 −1.09312 −0.546561 0.837419i \(-0.684064\pi\)
−0.546561 + 0.837419i \(0.684064\pi\)
\(542\) 43.1054 1.85154
\(543\) −6.55086 −0.281124
\(544\) 26.2690 1.12628
\(545\) −29.1539 −1.24882
\(546\) 12.0496 0.515676
\(547\) −13.4628 −0.575630 −0.287815 0.957686i \(-0.592929\pi\)
−0.287815 + 0.957686i \(0.592929\pi\)
\(548\) 0.234281 0.0100080
\(549\) 75.4937 3.22199
\(550\) −7.20619 −0.307273
\(551\) 5.50325 0.234446
\(552\) 3.85526 0.164091
\(553\) −4.10291 −0.174474
\(554\) 42.9159 1.82332
\(555\) 5.68773 0.241431
\(556\) 12.3984 0.525808
\(557\) −2.42993 −0.102959 −0.0514797 0.998674i \(-0.516394\pi\)
−0.0514797 + 0.998674i \(0.516394\pi\)
\(558\) −85.1724 −3.60563
\(559\) 15.8138 0.668854
\(560\) −11.4551 −0.484068
\(561\) −46.6249 −1.96850
\(562\) 1.09559 0.0462145
\(563\) −27.4660 −1.15755 −0.578776 0.815486i \(-0.696470\pi\)
−0.578776 + 0.815486i \(0.696470\pi\)
\(564\) −31.1062 −1.30981
\(565\) 51.0667 2.14839
\(566\) 17.9397 0.754062
\(567\) 8.10061 0.340194
\(568\) 0.665175 0.0279101
\(569\) 4.63762 0.194419 0.0972096 0.995264i \(-0.469008\pi\)
0.0972096 + 0.995264i \(0.469008\pi\)
\(570\) 26.5793 1.11329
\(571\) 28.7389 1.20269 0.601343 0.798991i \(-0.294633\pi\)
0.601343 + 0.798991i \(0.294633\pi\)
\(572\) 13.9582 0.583624
\(573\) 68.6289 2.86702
\(574\) 14.4160 0.601714
\(575\) −1.33846 −0.0558174
\(576\) −23.2879 −0.970328
\(577\) 43.0307 1.79139 0.895695 0.444669i \(-0.146679\pi\)
0.895695 + 0.444669i \(0.146679\pi\)
\(578\) 6.32650 0.263148
\(579\) 71.9636 2.99071
\(580\) 10.5267 0.437099
\(581\) 5.25120 0.217857
\(582\) 12.5532 0.520347
\(583\) 33.2409 1.37670
\(584\) −3.70191 −0.153186
\(585\) 30.7974 1.27332
\(586\) −32.7533 −1.35303
\(587\) 48.0993 1.98527 0.992634 0.121148i \(-0.0386576\pi\)
0.992634 + 0.121148i \(0.0386576\pi\)
\(588\) −4.57898 −0.188834
\(589\) 14.9757 0.617061
\(590\) −0.262952 −0.0108255
\(591\) −23.4479 −0.964516
\(592\) 3.69839 0.152003
\(593\) 1.23744 0.0508154 0.0254077 0.999677i \(-0.491912\pi\)
0.0254077 + 0.999677i \(0.491912\pi\)
\(594\) 68.8208 2.82375
\(595\) 8.97342 0.367874
\(596\) −8.70243 −0.356466
\(597\) −58.5197 −2.39505
\(598\) 5.97056 0.244154
\(599\) −47.3178 −1.93335 −0.966676 0.256001i \(-0.917595\pi\)
−0.966676 + 0.256001i \(0.917595\pi\)
\(600\) −2.36177 −0.0964188
\(601\) 1.79915 0.0733887 0.0366943 0.999327i \(-0.488317\pi\)
0.0366943 + 0.999327i \(0.488317\pi\)
\(602\) −13.8394 −0.564053
\(603\) 67.0367 2.72995
\(604\) 31.3938 1.27740
\(605\) 16.8065 0.683282
\(606\) −60.1641 −2.44400
\(607\) 17.3578 0.704531 0.352265 0.935900i \(-0.385411\pi\)
0.352265 + 0.935900i \(0.385411\pi\)
\(608\) 13.8729 0.562622
\(609\) −8.41850 −0.341135
\(610\) −58.4734 −2.36752
\(611\) 14.5945 0.590431
\(612\) 33.4351 1.35153
\(613\) −42.6739 −1.72358 −0.861792 0.507262i \(-0.830658\pi\)
−0.861792 + 0.507262i \(0.830658\pi\)
\(614\) −1.13029 −0.0456148
\(615\) 55.5842 2.24137
\(616\) 3.70079 0.149109
\(617\) −31.8052 −1.28043 −0.640215 0.768196i \(-0.721155\pi\)
−0.640215 + 0.768196i \(0.721155\pi\)
\(618\) 88.9225 3.57699
\(619\) 13.8175 0.555372 0.277686 0.960672i \(-0.410433\pi\)
0.277686 + 0.960672i \(0.410433\pi\)
\(620\) 28.6458 1.15044
\(621\) 12.7825 0.512946
\(622\) 5.71140 0.229006
\(623\) 2.50755 0.100463
\(624\) 30.2101 1.20937
\(625\) −28.7076 −1.14830
\(626\) 34.6011 1.38294
\(627\) −24.6230 −0.983350
\(628\) −24.6377 −0.983150
\(629\) −2.89715 −0.115517
\(630\) −26.9523 −1.07380
\(631\) 14.6615 0.583666 0.291833 0.956469i \(-0.405735\pi\)
0.291833 + 0.956469i \(0.405735\pi\)
\(632\) −3.58729 −0.142695
\(633\) 56.2375 2.23524
\(634\) 9.23355 0.366711
\(635\) 29.5458 1.17249
\(636\) −35.9602 −1.42592
\(637\) 2.14838 0.0851221
\(638\) −22.4584 −0.889135
\(639\) 4.48782 0.177535
\(640\) −16.5383 −0.653735
\(641\) −22.2032 −0.876973 −0.438487 0.898738i \(-0.644485\pi\)
−0.438487 + 0.898738i \(0.644485\pi\)
\(642\) 9.00591 0.355435
\(643\) −13.0624 −0.515131 −0.257565 0.966261i \(-0.582920\pi\)
−0.257565 + 0.966261i \(0.582920\pi\)
\(644\) −2.26887 −0.0894060
\(645\) −53.3609 −2.10108
\(646\) −13.5387 −0.532671
\(647\) 30.8403 1.21246 0.606229 0.795290i \(-0.292681\pi\)
0.606229 + 0.795290i \(0.292681\pi\)
\(648\) 7.08260 0.278231
\(649\) 0.243598 0.00956206
\(650\) −3.65762 −0.143464
\(651\) −22.9087 −0.897865
\(652\) −10.7174 −0.419727
\(653\) 11.8203 0.462565 0.231282 0.972887i \(-0.425708\pi\)
0.231282 + 0.972887i \(0.425708\pi\)
\(654\) −67.2869 −2.63113
\(655\) −45.4821 −1.77713
\(656\) 36.1431 1.41115
\(657\) −24.9761 −0.974410
\(658\) −12.7724 −0.497918
\(659\) −4.67184 −0.181989 −0.0909945 0.995851i \(-0.529005\pi\)
−0.0909945 + 0.995851i \(0.529005\pi\)
\(660\) −47.0996 −1.83335
\(661\) −30.9954 −1.20558 −0.602790 0.797900i \(-0.705944\pi\)
−0.602790 + 0.797900i \(0.705944\pi\)
\(662\) −3.08440 −0.119879
\(663\) −23.6652 −0.919080
\(664\) 4.59127 0.178176
\(665\) 4.73895 0.183769
\(666\) 8.70177 0.337187
\(667\) −4.17134 −0.161515
\(668\) 26.9457 1.04256
\(669\) 13.4310 0.519272
\(670\) −51.9231 −2.00597
\(671\) 54.1697 2.09120
\(672\) −21.2219 −0.818652
\(673\) −24.7072 −0.952393 −0.476196 0.879339i \(-0.657985\pi\)
−0.476196 + 0.879339i \(0.657985\pi\)
\(674\) −34.6175 −1.33341
\(675\) −7.83071 −0.301404
\(676\) −12.8699 −0.494995
\(677\) 47.7495 1.83516 0.917580 0.397550i \(-0.130140\pi\)
0.917580 + 0.397550i \(0.130140\pi\)
\(678\) 117.861 4.52643
\(679\) 2.23817 0.0858930
\(680\) 7.84572 0.300869
\(681\) 56.2294 2.15472
\(682\) −61.1145 −2.34020
\(683\) 13.1543 0.503337 0.251668 0.967814i \(-0.419021\pi\)
0.251668 + 0.967814i \(0.419021\pi\)
\(684\) 17.6574 0.675147
\(685\) 0.370908 0.0141717
\(686\) −1.88015 −0.0717845
\(687\) 89.4833 3.41400
\(688\) −34.6974 −1.32283
\(689\) 16.8720 0.642771
\(690\) −20.1465 −0.766966
\(691\) −23.6172 −0.898442 −0.449221 0.893421i \(-0.648299\pi\)
−0.449221 + 0.893421i \(0.648299\pi\)
\(692\) −15.1228 −0.574882
\(693\) 24.9685 0.948476
\(694\) 44.1823 1.67714
\(695\) 19.6288 0.744562
\(696\) −7.36053 −0.279000
\(697\) −28.3128 −1.07242
\(698\) −29.1714 −1.10415
\(699\) −2.01843 −0.0763439
\(700\) 1.38993 0.0525345
\(701\) −12.5807 −0.475167 −0.237583 0.971367i \(-0.576355\pi\)
−0.237583 + 0.971367i \(0.576355\pi\)
\(702\) 34.9311 1.31839
\(703\) −1.53001 −0.0577055
\(704\) −16.7100 −0.629781
\(705\) −49.2466 −1.85473
\(706\) 47.2118 1.77684
\(707\) −10.7269 −0.403428
\(708\) −0.263526 −0.00990390
\(709\) 12.0330 0.451910 0.225955 0.974138i \(-0.427450\pi\)
0.225955 + 0.974138i \(0.427450\pi\)
\(710\) −3.47603 −0.130453
\(711\) −24.2028 −0.907676
\(712\) 2.19242 0.0821645
\(713\) −11.3512 −0.425106
\(714\) 20.7105 0.775072
\(715\) 22.0984 0.826432
\(716\) −6.23906 −0.233164
\(717\) −77.3065 −2.88707
\(718\) 58.9778 2.20103
\(719\) −2.47787 −0.0924090 −0.0462045 0.998932i \(-0.514713\pi\)
−0.0462045 + 0.998932i \(0.514713\pi\)
\(720\) −67.5731 −2.51830
\(721\) 15.8544 0.590449
\(722\) 28.5730 1.06338
\(723\) 3.16287 0.117628
\(724\) 3.37077 0.125274
\(725\) 2.55540 0.0949053
\(726\) 38.7892 1.43960
\(727\) −29.3758 −1.08949 −0.544744 0.838602i \(-0.683373\pi\)
−0.544744 + 0.838602i \(0.683373\pi\)
\(728\) 1.87839 0.0696178
\(729\) −29.6073 −1.09657
\(730\) 19.3452 0.715997
\(731\) 27.1803 1.00530
\(732\) −58.6011 −2.16596
\(733\) −4.26488 −0.157527 −0.0787635 0.996893i \(-0.525097\pi\)
−0.0787635 + 0.996893i \(0.525097\pi\)
\(734\) −33.7729 −1.24658
\(735\) −7.24933 −0.267395
\(736\) −10.5154 −0.387602
\(737\) 48.1015 1.77184
\(738\) 85.0393 3.13034
\(739\) 20.3320 0.747924 0.373962 0.927444i \(-0.377999\pi\)
0.373962 + 0.927444i \(0.377999\pi\)
\(740\) −2.92664 −0.107585
\(741\) −12.4978 −0.459119
\(742\) −14.7655 −0.542057
\(743\) 31.1891 1.14422 0.572108 0.820178i \(-0.306126\pi\)
0.572108 + 0.820178i \(0.306126\pi\)
\(744\) −20.0298 −0.734327
\(745\) −13.7775 −0.504768
\(746\) −9.32708 −0.341489
\(747\) 30.9765 1.13337
\(748\) 23.9910 0.877198
\(749\) 1.60570 0.0586712
\(750\) −55.8072 −2.03779
\(751\) −13.3310 −0.486454 −0.243227 0.969969i \(-0.578206\pi\)
−0.243227 + 0.969969i \(0.578206\pi\)
\(752\) −32.0221 −1.16773
\(753\) 5.51215 0.200874
\(754\) −11.3991 −0.415131
\(755\) 49.7019 1.80884
\(756\) −13.2742 −0.482776
\(757\) −49.4978 −1.79903 −0.899515 0.436890i \(-0.856080\pi\)
−0.899515 + 0.436890i \(0.856080\pi\)
\(758\) −1.88952 −0.0686306
\(759\) 18.6637 0.677451
\(760\) 4.14340 0.150297
\(761\) −14.9291 −0.541178 −0.270589 0.962695i \(-0.587218\pi\)
−0.270589 + 0.962695i \(0.587218\pi\)
\(762\) 68.1912 2.47031
\(763\) −11.9969 −0.434317
\(764\) −35.3133 −1.27759
\(765\) 52.9336 1.91382
\(766\) −66.2868 −2.39504
\(767\) 0.123642 0.00446446
\(768\) −61.7237 −2.22726
\(769\) −21.6466 −0.780597 −0.390298 0.920688i \(-0.627628\pi\)
−0.390298 + 0.920688i \(0.627628\pi\)
\(770\) −19.3393 −0.696940
\(771\) −1.67455 −0.0603075
\(772\) −37.0292 −1.33271
\(773\) 37.3725 1.34419 0.672097 0.740463i \(-0.265394\pi\)
0.672097 + 0.740463i \(0.265394\pi\)
\(774\) −81.6379 −2.93441
\(775\) 6.95386 0.249790
\(776\) 1.95689 0.0702484
\(777\) 2.34051 0.0839653
\(778\) −21.7080 −0.778269
\(779\) −14.9523 −0.535720
\(780\) −23.9061 −0.855977
\(781\) 3.22019 0.115227
\(782\) 10.2620 0.366969
\(783\) −24.4047 −0.872152
\(784\) −4.71381 −0.168350
\(785\) −39.0057 −1.39217
\(786\) −104.972 −3.74423
\(787\) 10.9711 0.391078 0.195539 0.980696i \(-0.437354\pi\)
0.195539 + 0.980696i \(0.437354\pi\)
\(788\) 12.0652 0.429804
\(789\) −1.54937 −0.0551592
\(790\) 18.7462 0.666961
\(791\) 21.0140 0.747173
\(792\) 21.8307 0.775720
\(793\) 27.4947 0.976365
\(794\) −29.0722 −1.03173
\(795\) −56.9314 −2.01915
\(796\) 30.1115 1.06728
\(797\) −25.3396 −0.897575 −0.448788 0.893639i \(-0.648144\pi\)
−0.448788 + 0.893639i \(0.648144\pi\)
\(798\) 10.9374 0.387181
\(799\) 25.0846 0.887430
\(800\) 6.44182 0.227753
\(801\) 14.7919 0.522645
\(802\) −0.999675 −0.0352997
\(803\) −17.9213 −0.632430
\(804\) −52.0365 −1.83519
\(805\) −3.59202 −0.126602
\(806\) −31.0197 −1.09262
\(807\) −26.5321 −0.933973
\(808\) −9.37886 −0.329947
\(809\) −3.46266 −0.121741 −0.0608703 0.998146i \(-0.519388\pi\)
−0.0608703 + 0.998146i \(0.519388\pi\)
\(810\) −37.0117 −1.30046
\(811\) −23.3024 −0.818259 −0.409129 0.912476i \(-0.634168\pi\)
−0.409129 + 0.912476i \(0.634168\pi\)
\(812\) 4.33177 0.152015
\(813\) 68.3924 2.39863
\(814\) 6.24386 0.218847
\(815\) −16.9676 −0.594348
\(816\) 51.9242 1.81771
\(817\) 14.3542 0.502190
\(818\) 11.9659 0.418376
\(819\) 12.6732 0.442836
\(820\) −28.6010 −0.998792
\(821\) −6.34524 −0.221450 −0.110725 0.993851i \(-0.535317\pi\)
−0.110725 + 0.993851i \(0.535317\pi\)
\(822\) 0.856051 0.0298582
\(823\) −11.8112 −0.411712 −0.205856 0.978582i \(-0.565998\pi\)
−0.205856 + 0.978582i \(0.565998\pi\)
\(824\) 13.8619 0.482904
\(825\) −11.4336 −0.398066
\(826\) −0.108205 −0.00376493
\(827\) −11.6699 −0.405801 −0.202901 0.979199i \(-0.565037\pi\)
−0.202901 + 0.979199i \(0.565037\pi\)
\(828\) −13.3839 −0.465123
\(829\) −5.73727 −0.199263 −0.0996317 0.995024i \(-0.531766\pi\)
−0.0996317 + 0.995024i \(0.531766\pi\)
\(830\) −23.9928 −0.832801
\(831\) 68.0918 2.36208
\(832\) −8.48141 −0.294040
\(833\) 3.69258 0.127940
\(834\) 45.3029 1.56871
\(835\) 42.6597 1.47630
\(836\) 12.6699 0.438197
\(837\) −66.4109 −2.29550
\(838\) −20.1304 −0.695392
\(839\) −18.9897 −0.655598 −0.327799 0.944747i \(-0.606307\pi\)
−0.327799 + 0.944747i \(0.606307\pi\)
\(840\) −6.33829 −0.218692
\(841\) −21.0360 −0.725379
\(842\) −76.4473 −2.63455
\(843\) 1.73829 0.0598700
\(844\) −28.9372 −0.996060
\(845\) −20.3753 −0.700930
\(846\) −75.3433 −2.59035
\(847\) 6.91591 0.237633
\(848\) −37.0191 −1.27124
\(849\) 28.4637 0.976872
\(850\) −6.28660 −0.215629
\(851\) 1.15972 0.0397545
\(852\) −3.48362 −0.119347
\(853\) 37.3041 1.27727 0.638633 0.769511i \(-0.279500\pi\)
0.638633 + 0.769511i \(0.279500\pi\)
\(854\) −24.0619 −0.823381
\(855\) 27.9548 0.956032
\(856\) 1.40391 0.0479847
\(857\) 42.9116 1.46583 0.732916 0.680319i \(-0.238159\pi\)
0.732916 + 0.680319i \(0.238159\pi\)
\(858\) 51.0027 1.74120
\(859\) −1.00000 −0.0341196
\(860\) 27.4570 0.936277
\(861\) 22.8730 0.779508
\(862\) 26.6531 0.907808
\(863\) 12.0886 0.411499 0.205750 0.978605i \(-0.434037\pi\)
0.205750 + 0.978605i \(0.434037\pi\)
\(864\) −61.5208 −2.09298
\(865\) −23.9420 −0.814053
\(866\) 13.5605 0.460806
\(867\) 10.0378 0.340903
\(868\) 11.7878 0.400103
\(869\) −17.3665 −0.589117
\(870\) 38.4642 1.30406
\(871\) 24.4147 0.827260
\(872\) −10.4892 −0.355210
\(873\) 13.2028 0.446847
\(874\) 5.41946 0.183316
\(875\) −9.95012 −0.336376
\(876\) 19.3874 0.655040
\(877\) −5.98177 −0.201990 −0.100995 0.994887i \(-0.532203\pi\)
−0.100995 + 0.994887i \(0.532203\pi\)
\(878\) 23.7668 0.802092
\(879\) −51.9674 −1.75282
\(880\) −48.4864 −1.63448
\(881\) −23.4919 −0.791463 −0.395731 0.918366i \(-0.629509\pi\)
−0.395731 + 0.918366i \(0.629509\pi\)
\(882\) −11.0909 −0.373450
\(883\) −10.9339 −0.367955 −0.183977 0.982930i \(-0.558897\pi\)
−0.183977 + 0.982930i \(0.558897\pi\)
\(884\) 12.1770 0.409557
\(885\) −0.417208 −0.0140243
\(886\) 69.7769 2.34420
\(887\) −4.72661 −0.158704 −0.0793520 0.996847i \(-0.525285\pi\)
−0.0793520 + 0.996847i \(0.525285\pi\)
\(888\) 2.04637 0.0686718
\(889\) 12.1581 0.407771
\(890\) −11.4570 −0.384040
\(891\) 34.2876 1.14868
\(892\) −6.91096 −0.231396
\(893\) 13.2474 0.443308
\(894\) −31.7982 −1.06349
\(895\) −9.87752 −0.330169
\(896\) −6.80555 −0.227357
\(897\) 9.47307 0.316297
\(898\) −39.0902 −1.30446
\(899\) 21.6720 0.722800
\(900\) 8.19911 0.273304
\(901\) 28.9990 0.966097
\(902\) 61.0191 2.03171
\(903\) −21.9581 −0.730719
\(904\) 18.3732 0.611082
\(905\) 5.33652 0.177392
\(906\) 114.711 3.81102
\(907\) 50.5053 1.67700 0.838500 0.544901i \(-0.183433\pi\)
0.838500 + 0.544901i \(0.183433\pi\)
\(908\) −28.9331 −0.960178
\(909\) −63.2775 −2.09878
\(910\) −9.81597 −0.325396
\(911\) −34.4612 −1.14175 −0.570875 0.821037i \(-0.693396\pi\)
−0.570875 + 0.821037i \(0.693396\pi\)
\(912\) 27.4217 0.908023
\(913\) 22.2269 0.735601
\(914\) 65.5671 2.16877
\(915\) −92.7758 −3.06707
\(916\) −46.0439 −1.52133
\(917\) −18.7159 −0.618055
\(918\) 60.0384 1.98156
\(919\) −19.1409 −0.631400 −0.315700 0.948859i \(-0.602239\pi\)
−0.315700 + 0.948859i \(0.602239\pi\)
\(920\) −3.14061 −0.103543
\(921\) −1.79335 −0.0590930
\(922\) −40.6270 −1.33798
\(923\) 1.63446 0.0537988
\(924\) −19.3815 −0.637606
\(925\) −0.710452 −0.0233595
\(926\) 76.0282 2.49844
\(927\) 93.5240 3.07173
\(928\) 20.0762 0.659032
\(929\) 9.31605 0.305650 0.152825 0.988253i \(-0.451163\pi\)
0.152825 + 0.988253i \(0.451163\pi\)
\(930\) 104.670 3.43227
\(931\) 1.95008 0.0639114
\(932\) 1.03859 0.0340201
\(933\) 9.06190 0.296673
\(934\) 16.0551 0.525339
\(935\) 37.9820 1.24214
\(936\) 11.0805 0.362178
\(937\) −18.0358 −0.589202 −0.294601 0.955620i \(-0.595187\pi\)
−0.294601 + 0.955620i \(0.595187\pi\)
\(938\) −21.3664 −0.697639
\(939\) 54.8993 1.79157
\(940\) 25.3400 0.826500
\(941\) −34.1725 −1.11399 −0.556996 0.830515i \(-0.688046\pi\)
−0.556996 + 0.830515i \(0.688046\pi\)
\(942\) −90.0247 −2.93316
\(943\) 11.3335 0.369069
\(944\) −0.271285 −0.00882959
\(945\) −21.0153 −0.683628
\(946\) −58.5784 −1.90455
\(947\) 42.3790 1.37713 0.688566 0.725174i \(-0.258241\pi\)
0.688566 + 0.725174i \(0.258241\pi\)
\(948\) 18.7871 0.610178
\(949\) −9.09626 −0.295277
\(950\) −3.32001 −0.107715
\(951\) 14.6502 0.475067
\(952\) 3.22852 0.104637
\(953\) 10.7973 0.349757 0.174879 0.984590i \(-0.444047\pi\)
0.174879 + 0.984590i \(0.444047\pi\)
\(954\) −87.1004 −2.81998
\(955\) −55.9071 −1.80911
\(956\) 39.7784 1.28652
\(957\) −35.6331 −1.15186
\(958\) −8.98774 −0.290381
\(959\) 0.152629 0.00492866
\(960\) 28.6190 0.923674
\(961\) 27.9746 0.902405
\(962\) 3.16917 0.102178
\(963\) 9.47194 0.305229
\(964\) −1.62747 −0.0524172
\(965\) −58.6236 −1.88716
\(966\) −8.29033 −0.266737
\(967\) −10.9672 −0.352680 −0.176340 0.984329i \(-0.556426\pi\)
−0.176340 + 0.984329i \(0.556426\pi\)
\(968\) 6.04677 0.194351
\(969\) −21.4809 −0.690065
\(970\) −10.2262 −0.328343
\(971\) −29.4700 −0.945739 −0.472869 0.881133i \(-0.656782\pi\)
−0.472869 + 0.881133i \(0.656782\pi\)
\(972\) 2.72992 0.0875623
\(973\) 8.07727 0.258945
\(974\) 19.0529 0.610495
\(975\) −5.80329 −0.185854
\(976\) −60.3266 −1.93101
\(977\) −11.8726 −0.379837 −0.189918 0.981800i \(-0.560822\pi\)
−0.189918 + 0.981800i \(0.560822\pi\)
\(978\) −39.1609 −1.25223
\(979\) 10.6138 0.339217
\(980\) 3.73017 0.119156
\(981\) −70.7688 −2.25948
\(982\) 20.6232 0.658112
\(983\) −3.50769 −0.111878 −0.0559390 0.998434i \(-0.517815\pi\)
−0.0559390 + 0.998434i \(0.517815\pi\)
\(984\) 19.9985 0.637528
\(985\) 19.1013 0.608618
\(986\) −19.5924 −0.623949
\(987\) −20.2650 −0.645043
\(988\) 6.43080 0.204591
\(989\) −10.8802 −0.345969
\(990\) −114.081 −3.62574
\(991\) 36.4756 1.15868 0.579342 0.815085i \(-0.303310\pi\)
0.579342 + 0.815085i \(0.303310\pi\)
\(992\) 54.6320 1.73457
\(993\) −4.89380 −0.155300
\(994\) −1.43039 −0.0453692
\(995\) 47.6718 1.51130
\(996\) −24.0451 −0.761899
\(997\) −22.8953 −0.725102 −0.362551 0.931964i \(-0.618094\pi\)
−0.362551 + 0.931964i \(0.618094\pi\)
\(998\) 27.4255 0.868140
\(999\) 6.78498 0.214667
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 \(a_p\))