Properties

Label 8018.2.a.d.1.15
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-0.785531 q^{3}\) \(+1.00000 q^{4}\) \(-1.33472 q^{5}\) \(-0.785531 q^{6}\) \(+4.52537 q^{7}\) \(+1.00000 q^{8}\) \(-2.38294 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-0.785531 q^{3}\) \(+1.00000 q^{4}\) \(-1.33472 q^{5}\) \(-0.785531 q^{6}\) \(+4.52537 q^{7}\) \(+1.00000 q^{8}\) \(-2.38294 q^{9}\) \(-1.33472 q^{10}\) \(+1.48724 q^{11}\) \(-0.785531 q^{12}\) \(-4.61463 q^{13}\) \(+4.52537 q^{14}\) \(+1.04847 q^{15}\) \(+1.00000 q^{16}\) \(-0.964875 q^{17}\) \(-2.38294 q^{18}\) \(+1.00000 q^{19}\) \(-1.33472 q^{20}\) \(-3.55482 q^{21}\) \(+1.48724 q^{22}\) \(-0.651869 q^{23}\) \(-0.785531 q^{24}\) \(-3.21851 q^{25}\) \(-4.61463 q^{26}\) \(+4.22847 q^{27}\) \(+4.52537 q^{28}\) \(-2.58471 q^{29}\) \(+1.04847 q^{30}\) \(-0.662929 q^{31}\) \(+1.00000 q^{32}\) \(-1.16827 q^{33}\) \(-0.964875 q^{34}\) \(-6.04012 q^{35}\) \(-2.38294 q^{36}\) \(+0.132488 q^{37}\) \(+1.00000 q^{38}\) \(+3.62493 q^{39}\) \(-1.33472 q^{40}\) \(+6.87438 q^{41}\) \(-3.55482 q^{42}\) \(-4.27253 q^{43}\) \(+1.48724 q^{44}\) \(+3.18057 q^{45}\) \(-0.651869 q^{46}\) \(+0.671226 q^{47}\) \(-0.785531 q^{48}\) \(+13.4790 q^{49}\) \(-3.21851 q^{50}\) \(+0.757939 q^{51}\) \(-4.61463 q^{52}\) \(-10.9718 q^{53}\) \(+4.22847 q^{54}\) \(-1.98506 q^{55}\) \(+4.52537 q^{56}\) \(-0.785531 q^{57}\) \(-2.58471 q^{58}\) \(+4.28390 q^{59}\) \(+1.04847 q^{60}\) \(-13.9582 q^{61}\) \(-0.662929 q^{62}\) \(-10.7837 q^{63}\) \(+1.00000 q^{64}\) \(+6.15925 q^{65}\) \(-1.16827 q^{66}\) \(+8.43327 q^{67}\) \(-0.964875 q^{68}\) \(+0.512063 q^{69}\) \(-6.04012 q^{70}\) \(-9.36871 q^{71}\) \(-2.38294 q^{72}\) \(-2.16707 q^{73}\) \(+0.132488 q^{74}\) \(+2.52824 q^{75}\) \(+1.00000 q^{76}\) \(+6.73032 q^{77}\) \(+3.62493 q^{78}\) \(-10.6617 q^{79}\) \(-1.33472 q^{80}\) \(+3.82724 q^{81}\) \(+6.87438 q^{82}\) \(-18.0058 q^{83}\) \(-3.55482 q^{84}\) \(+1.28784 q^{85}\) \(-4.27253 q^{86}\) \(+2.03037 q^{87}\) \(+1.48724 q^{88}\) \(+6.72822 q^{89}\) \(+3.18057 q^{90}\) \(-20.8829 q^{91}\) \(-0.651869 q^{92}\) \(+0.520751 q^{93}\) \(+0.671226 q^{94}\) \(-1.33472 q^{95}\) \(-0.785531 q^{96}\) \(-14.1929 q^{97}\) \(+13.4790 q^{98}\) \(-3.54401 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 17q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 19q^{13} \) \(\mathstrut -\mathstrut 15q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 10q^{18} \) \(\mathstrut +\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut -\mathstrut 17q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 10q^{24} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 19q^{26} \) \(\mathstrut -\mathstrut 37q^{27} \) \(\mathstrut -\mathstrut 15q^{28} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 30q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 10q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut +\mathstrut 30q^{38} \) \(\mathstrut -\mathstrut 12q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 14q^{42} \) \(\mathstrut -\mathstrut 61q^{43} \) \(\mathstrut -\mathstrut 17q^{44} \) \(\mathstrut -\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 19q^{52} \) \(\mathstrut -\mathstrut 19q^{53} \) \(\mathstrut -\mathstrut 37q^{54} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 37q^{58} \) \(\mathstrut -\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut -\mathstrut 11q^{62} \) \(\mathstrut -\mathstrut 24q^{63} \) \(\mathstrut +\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 18q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 10q^{72} \) \(\mathstrut -\mathstrut 58q^{73} \) \(\mathstrut -\mathstrut 46q^{74} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut -\mathstrut 32q^{77} \) \(\mathstrut -\mathstrut 42q^{79} \) \(\mathstrut -\mathstrut 12q^{80} \) \(\mathstrut -\mathstrut 38q^{81} \) \(\mathstrut -\mathstrut 28q^{82} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 48q^{85} \) \(\mathstrut -\mathstrut 61q^{86} \) \(\mathstrut -\mathstrut 15q^{87} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 39q^{89} \) \(\mathstrut -\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 45q^{93} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut -\mathstrut 38q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.785531 −0.453526 −0.226763 0.973950i \(-0.572814\pi\)
−0.226763 + 0.973950i \(0.572814\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.33472 −0.596907 −0.298453 0.954424i \(-0.596471\pi\)
−0.298453 + 0.954424i \(0.596471\pi\)
\(6\) −0.785531 −0.320692
\(7\) 4.52537 1.71043 0.855215 0.518274i \(-0.173425\pi\)
0.855215 + 0.518274i \(0.173425\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.38294 −0.794314
\(10\) −1.33472 −0.422077
\(11\) 1.48724 0.448420 0.224210 0.974541i \(-0.428020\pi\)
0.224210 + 0.974541i \(0.428020\pi\)
\(12\) −0.785531 −0.226763
\(13\) −4.61463 −1.27987 −0.639934 0.768430i \(-0.721038\pi\)
−0.639934 + 0.768430i \(0.721038\pi\)
\(14\) 4.52537 1.20946
\(15\) 1.04847 0.270713
\(16\) 1.00000 0.250000
\(17\) −0.964875 −0.234017 −0.117008 0.993131i \(-0.537330\pi\)
−0.117008 + 0.993131i \(0.537330\pi\)
\(18\) −2.38294 −0.561665
\(19\) 1.00000 0.229416
\(20\) −1.33472 −0.298453
\(21\) −3.55482 −0.775725
\(22\) 1.48724 0.317081
\(23\) −0.651869 −0.135924 −0.0679620 0.997688i \(-0.521650\pi\)
−0.0679620 + 0.997688i \(0.521650\pi\)
\(24\) −0.785531 −0.160346
\(25\) −3.21851 −0.643702
\(26\) −4.61463 −0.905003
\(27\) 4.22847 0.813769
\(28\) 4.52537 0.855215
\(29\) −2.58471 −0.479969 −0.239984 0.970777i \(-0.577142\pi\)
−0.239984 + 0.970777i \(0.577142\pi\)
\(30\) 1.04847 0.191423
\(31\) −0.662929 −0.119066 −0.0595328 0.998226i \(-0.518961\pi\)
−0.0595328 + 0.998226i \(0.518961\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.16827 −0.203370
\(34\) −0.964875 −0.165475
\(35\) −6.04012 −1.02097
\(36\) −2.38294 −0.397157
\(37\) 0.132488 0.0217809 0.0108904 0.999941i \(-0.496533\pi\)
0.0108904 + 0.999941i \(0.496533\pi\)
\(38\) 1.00000 0.162221
\(39\) 3.62493 0.580453
\(40\) −1.33472 −0.211038
\(41\) 6.87438 1.07360 0.536799 0.843710i \(-0.319633\pi\)
0.536799 + 0.843710i \(0.319633\pi\)
\(42\) −3.55482 −0.548520
\(43\) −4.27253 −0.651554 −0.325777 0.945447i \(-0.605626\pi\)
−0.325777 + 0.945447i \(0.605626\pi\)
\(44\) 1.48724 0.224210
\(45\) 3.18057 0.474131
\(46\) −0.651869 −0.0961128
\(47\) 0.671226 0.0979084 0.0489542 0.998801i \(-0.484411\pi\)
0.0489542 + 0.998801i \(0.484411\pi\)
\(48\) −0.785531 −0.113382
\(49\) 13.4790 1.92557
\(50\) −3.21851 −0.455166
\(51\) 0.757939 0.106133
\(52\) −4.61463 −0.639934
\(53\) −10.9718 −1.50710 −0.753548 0.657393i \(-0.771659\pi\)
−0.753548 + 0.657393i \(0.771659\pi\)
\(54\) 4.22847 0.575421
\(55\) −1.98506 −0.267665
\(56\) 4.52537 0.604728
\(57\) −0.785531 −0.104046
\(58\) −2.58471 −0.339389
\(59\) 4.28390 0.557717 0.278858 0.960332i \(-0.410044\pi\)
0.278858 + 0.960332i \(0.410044\pi\)
\(60\) 1.04847 0.135356
\(61\) −13.9582 −1.78716 −0.893582 0.448899i \(-0.851816\pi\)
−0.893582 + 0.448899i \(0.851816\pi\)
\(62\) −0.662929 −0.0841921
\(63\) −10.7837 −1.35862
\(64\) 1.00000 0.125000
\(65\) 6.15925 0.763961
\(66\) −1.16827 −0.143804
\(67\) 8.43327 1.03029 0.515144 0.857104i \(-0.327738\pi\)
0.515144 + 0.857104i \(0.327738\pi\)
\(68\) −0.964875 −0.117008
\(69\) 0.512063 0.0616451
\(70\) −6.04012 −0.721933
\(71\) −9.36871 −1.11186 −0.555931 0.831229i \(-0.687638\pi\)
−0.555931 + 0.831229i \(0.687638\pi\)
\(72\) −2.38294 −0.280832
\(73\) −2.16707 −0.253636 −0.126818 0.991926i \(-0.540476\pi\)
−0.126818 + 0.991926i \(0.540476\pi\)
\(74\) 0.132488 0.0154014
\(75\) 2.52824 0.291936
\(76\) 1.00000 0.114708
\(77\) 6.73032 0.766991
\(78\) 3.62493 0.410443
\(79\) −10.6617 −1.19953 −0.599767 0.800174i \(-0.704740\pi\)
−0.599767 + 0.800174i \(0.704740\pi\)
\(80\) −1.33472 −0.149227
\(81\) 3.82724 0.425248
\(82\) 6.87438 0.759148
\(83\) −18.0058 −1.97639 −0.988197 0.153189i \(-0.951046\pi\)
−0.988197 + 0.153189i \(0.951046\pi\)
\(84\) −3.55482 −0.387862
\(85\) 1.28784 0.139686
\(86\) −4.27253 −0.460718
\(87\) 2.03037 0.217678
\(88\) 1.48724 0.158540
\(89\) 6.72822 0.713190 0.356595 0.934259i \(-0.383938\pi\)
0.356595 + 0.934259i \(0.383938\pi\)
\(90\) 3.18057 0.335262
\(91\) −20.8829 −2.18912
\(92\) −0.651869 −0.0679620
\(93\) 0.520751 0.0539994
\(94\) 0.671226 0.0692317
\(95\) −1.33472 −0.136940
\(96\) −0.785531 −0.0801729
\(97\) −14.1929 −1.44107 −0.720536 0.693418i \(-0.756104\pi\)
−0.720536 + 0.693418i \(0.756104\pi\)
\(98\) 13.4790 1.36158
\(99\) −3.54401 −0.356186
\(100\) −3.21851 −0.321851
\(101\) −1.21151 −0.120550 −0.0602750 0.998182i \(-0.519198\pi\)
−0.0602750 + 0.998182i \(0.519198\pi\)
\(102\) 0.757939 0.0750471
\(103\) 10.4983 1.03443 0.517213 0.855857i \(-0.326970\pi\)
0.517213 + 0.855857i \(0.326970\pi\)
\(104\) −4.61463 −0.452501
\(105\) 4.74470 0.463035
\(106\) −10.9718 −1.06568
\(107\) −12.8117 −1.23856 −0.619279 0.785171i \(-0.712575\pi\)
−0.619279 + 0.785171i \(0.712575\pi\)
\(108\) 4.22847 0.406884
\(109\) 17.3509 1.66192 0.830959 0.556334i \(-0.187793\pi\)
0.830959 + 0.556334i \(0.187793\pi\)
\(110\) −1.98506 −0.189268
\(111\) −0.104073 −0.00987821
\(112\) 4.52537 0.427607
\(113\) −7.90331 −0.743481 −0.371740 0.928337i \(-0.621239\pi\)
−0.371740 + 0.928337i \(0.621239\pi\)
\(114\) −0.785531 −0.0735717
\(115\) 0.870065 0.0811340
\(116\) −2.58471 −0.239984
\(117\) 10.9964 1.01662
\(118\) 4.28390 0.394365
\(119\) −4.36642 −0.400269
\(120\) 1.04847 0.0957115
\(121\) −8.78812 −0.798920
\(122\) −13.9582 −1.26372
\(123\) −5.40004 −0.486905
\(124\) −0.662929 −0.0595328
\(125\) 10.9694 0.981137
\(126\) −10.7837 −0.960688
\(127\) −17.4311 −1.54676 −0.773380 0.633943i \(-0.781435\pi\)
−0.773380 + 0.633943i \(0.781435\pi\)
\(128\) 1.00000 0.0883883
\(129\) 3.35620 0.295497
\(130\) 6.15925 0.540202
\(131\) 2.66865 0.233161 0.116581 0.993181i \(-0.462807\pi\)
0.116581 + 0.993181i \(0.462807\pi\)
\(132\) −1.16827 −0.101685
\(133\) 4.52537 0.392399
\(134\) 8.43327 0.728524
\(135\) −5.64384 −0.485744
\(136\) −0.964875 −0.0827374
\(137\) 16.2835 1.39119 0.695595 0.718434i \(-0.255141\pi\)
0.695595 + 0.718434i \(0.255141\pi\)
\(138\) 0.512063 0.0435897
\(139\) −13.8370 −1.17364 −0.586819 0.809718i \(-0.699620\pi\)
−0.586819 + 0.809718i \(0.699620\pi\)
\(140\) −6.04012 −0.510484
\(141\) −0.527269 −0.0444040
\(142\) −9.36871 −0.786205
\(143\) −6.86306 −0.573918
\(144\) −2.38294 −0.198578
\(145\) 3.44988 0.286497
\(146\) −2.16707 −0.179348
\(147\) −10.5882 −0.873296
\(148\) 0.132488 0.0108904
\(149\) 12.5642 1.02930 0.514650 0.857400i \(-0.327922\pi\)
0.514650 + 0.857400i \(0.327922\pi\)
\(150\) 2.52824 0.206430
\(151\) 15.8354 1.28867 0.644335 0.764743i \(-0.277134\pi\)
0.644335 + 0.764743i \(0.277134\pi\)
\(152\) 1.00000 0.0811107
\(153\) 2.29924 0.185883
\(154\) 6.73032 0.542344
\(155\) 0.884828 0.0710711
\(156\) 3.62493 0.290227
\(157\) 7.09521 0.566259 0.283130 0.959082i \(-0.408627\pi\)
0.283130 + 0.959082i \(0.408627\pi\)
\(158\) −10.6617 −0.848199
\(159\) 8.61870 0.683508
\(160\) −1.33472 −0.105519
\(161\) −2.94995 −0.232488
\(162\) 3.82724 0.300696
\(163\) −5.15118 −0.403471 −0.201736 0.979440i \(-0.564658\pi\)
−0.201736 + 0.979440i \(0.564658\pi\)
\(164\) 6.87438 0.536799
\(165\) 1.55932 0.121393
\(166\) −18.0058 −1.39752
\(167\) −17.7890 −1.37655 −0.688276 0.725449i \(-0.741632\pi\)
−0.688276 + 0.725449i \(0.741632\pi\)
\(168\) −3.55482 −0.274260
\(169\) 8.29478 0.638060
\(170\) 1.28784 0.0987730
\(171\) −2.38294 −0.182228
\(172\) −4.27253 −0.325777
\(173\) 25.2983 1.92339 0.961696 0.274117i \(-0.0883855\pi\)
0.961696 + 0.274117i \(0.0883855\pi\)
\(174\) 2.03037 0.153922
\(175\) −14.5650 −1.10101
\(176\) 1.48724 0.112105
\(177\) −3.36514 −0.252939
\(178\) 6.72822 0.504302
\(179\) 12.8974 0.963995 0.481997 0.876173i \(-0.339911\pi\)
0.481997 + 0.876173i \(0.339911\pi\)
\(180\) 3.18057 0.237066
\(181\) −14.3121 −1.06381 −0.531905 0.846804i \(-0.678524\pi\)
−0.531905 + 0.846804i \(0.678524\pi\)
\(182\) −20.8829 −1.54794
\(183\) 10.9646 0.810526
\(184\) −0.651869 −0.0480564
\(185\) −0.176835 −0.0130012
\(186\) 0.520751 0.0381833
\(187\) −1.43500 −0.104938
\(188\) 0.671226 0.0489542
\(189\) 19.1354 1.39189
\(190\) −1.33472 −0.0968311
\(191\) −4.14979 −0.300269 −0.150134 0.988666i \(-0.547971\pi\)
−0.150134 + 0.988666i \(0.547971\pi\)
\(192\) −0.785531 −0.0566908
\(193\) 5.00873 0.360536 0.180268 0.983618i \(-0.442303\pi\)
0.180268 + 0.983618i \(0.442303\pi\)
\(194\) −14.1929 −1.01899
\(195\) −4.83828 −0.346477
\(196\) 13.4790 0.962785
\(197\) −7.38557 −0.526200 −0.263100 0.964769i \(-0.584745\pi\)
−0.263100 + 0.964769i \(0.584745\pi\)
\(198\) −3.54401 −0.251862
\(199\) 7.34587 0.520735 0.260368 0.965510i \(-0.416156\pi\)
0.260368 + 0.965510i \(0.416156\pi\)
\(200\) −3.21851 −0.227583
\(201\) −6.62459 −0.467263
\(202\) −1.21151 −0.0852418
\(203\) −11.6968 −0.820952
\(204\) 0.757939 0.0530663
\(205\) −9.17540 −0.640838
\(206\) 10.4983 0.731449
\(207\) 1.55337 0.107966
\(208\) −4.61463 −0.319967
\(209\) 1.48724 0.102875
\(210\) 4.74470 0.327416
\(211\) −1.00000 −0.0688428
\(212\) −10.9718 −0.753548
\(213\) 7.35941 0.504258
\(214\) −12.8117 −0.875792
\(215\) 5.70265 0.388917
\(216\) 4.22847 0.287711
\(217\) −3.00000 −0.203653
\(218\) 17.3509 1.17515
\(219\) 1.70230 0.115031
\(220\) −1.98506 −0.133832
\(221\) 4.45254 0.299510
\(222\) −0.104073 −0.00698495
\(223\) 29.6582 1.98606 0.993029 0.117867i \(-0.0376058\pi\)
0.993029 + 0.117867i \(0.0376058\pi\)
\(224\) 4.52537 0.302364
\(225\) 7.66952 0.511302
\(226\) −7.90331 −0.525720
\(227\) −26.9442 −1.78835 −0.894174 0.447719i \(-0.852236\pi\)
−0.894174 + 0.447719i \(0.852236\pi\)
\(228\) −0.785531 −0.0520230
\(229\) −25.0078 −1.65256 −0.826281 0.563259i \(-0.809547\pi\)
−0.826281 + 0.563259i \(0.809547\pi\)
\(230\) 0.870065 0.0573704
\(231\) −5.28687 −0.347850
\(232\) −2.58471 −0.169695
\(233\) 3.21801 0.210819 0.105410 0.994429i \(-0.466385\pi\)
0.105410 + 0.994429i \(0.466385\pi\)
\(234\) 10.9964 0.718856
\(235\) −0.895902 −0.0584422
\(236\) 4.28390 0.278858
\(237\) 8.37509 0.544021
\(238\) −4.36642 −0.283033
\(239\) 15.3880 0.995367 0.497684 0.867359i \(-0.334184\pi\)
0.497684 + 0.867359i \(0.334184\pi\)
\(240\) 1.04847 0.0676782
\(241\) −19.9991 −1.28826 −0.644128 0.764918i \(-0.722780\pi\)
−0.644128 + 0.764918i \(0.722780\pi\)
\(242\) −8.78812 −0.564921
\(243\) −15.6918 −1.00663
\(244\) −13.9582 −0.893582
\(245\) −17.9907 −1.14939
\(246\) −5.40004 −0.344294
\(247\) −4.61463 −0.293622
\(248\) −0.662929 −0.0420961
\(249\) 14.1441 0.896347
\(250\) 10.9694 0.693769
\(251\) 13.7911 0.870485 0.435243 0.900313i \(-0.356663\pi\)
0.435243 + 0.900313i \(0.356663\pi\)
\(252\) −10.7837 −0.679309
\(253\) −0.969486 −0.0609510
\(254\) −17.4311 −1.09372
\(255\) −1.01164 −0.0633513
\(256\) 1.00000 0.0625000
\(257\) −7.85922 −0.490245 −0.245122 0.969492i \(-0.578828\pi\)
−0.245122 + 0.969492i \(0.578828\pi\)
\(258\) 3.35620 0.208948
\(259\) 0.599557 0.0372547
\(260\) 6.15925 0.381981
\(261\) 6.15921 0.381246
\(262\) 2.66865 0.164870
\(263\) −18.4823 −1.13967 −0.569835 0.821759i \(-0.692993\pi\)
−0.569835 + 0.821759i \(0.692993\pi\)
\(264\) −1.16827 −0.0719022
\(265\) 14.6444 0.899596
\(266\) 4.52537 0.277468
\(267\) −5.28522 −0.323450
\(268\) 8.43327 0.515144
\(269\) −3.97144 −0.242143 −0.121072 0.992644i \(-0.538633\pi\)
−0.121072 + 0.992644i \(0.538633\pi\)
\(270\) −5.64384 −0.343473
\(271\) −10.9405 −0.664587 −0.332293 0.943176i \(-0.607822\pi\)
−0.332293 + 0.943176i \(0.607822\pi\)
\(272\) −0.964875 −0.0585042
\(273\) 16.4042 0.992825
\(274\) 16.2835 0.983720
\(275\) −4.78670 −0.288649
\(276\) 0.512063 0.0308226
\(277\) −4.64699 −0.279211 −0.139605 0.990207i \(-0.544583\pi\)
−0.139605 + 0.990207i \(0.544583\pi\)
\(278\) −13.8370 −0.829887
\(279\) 1.57972 0.0945755
\(280\) −6.04012 −0.360966
\(281\) −6.71636 −0.400664 −0.200332 0.979728i \(-0.564202\pi\)
−0.200332 + 0.979728i \(0.564202\pi\)
\(282\) −0.527269 −0.0313984
\(283\) −23.8289 −1.41648 −0.708242 0.705970i \(-0.750511\pi\)
−0.708242 + 0.705970i \(0.750511\pi\)
\(284\) −9.36871 −0.555931
\(285\) 1.04847 0.0621058
\(286\) −6.86306 −0.405821
\(287\) 31.1091 1.83631
\(288\) −2.38294 −0.140416
\(289\) −16.0690 −0.945236
\(290\) 3.44988 0.202584
\(291\) 11.1490 0.653564
\(292\) −2.16707 −0.126818
\(293\) −14.9950 −0.876017 −0.438008 0.898971i \(-0.644316\pi\)
−0.438008 + 0.898971i \(0.644316\pi\)
\(294\) −10.5882 −0.617514
\(295\) −5.71783 −0.332905
\(296\) 0.132488 0.00770071
\(297\) 6.28875 0.364910
\(298\) 12.5642 0.727825
\(299\) 3.00813 0.173965
\(300\) 2.52824 0.145968
\(301\) −19.3348 −1.11444
\(302\) 15.8354 0.911228
\(303\) 0.951681 0.0546726
\(304\) 1.00000 0.0573539
\(305\) 18.6304 1.06677
\(306\) 2.29924 0.131439
\(307\) −4.36796 −0.249292 −0.124646 0.992201i \(-0.539780\pi\)
−0.124646 + 0.992201i \(0.539780\pi\)
\(308\) 6.73032 0.383495
\(309\) −8.24671 −0.469139
\(310\) 0.884828 0.0502549
\(311\) −29.5118 −1.67346 −0.836730 0.547616i \(-0.815536\pi\)
−0.836730 + 0.547616i \(0.815536\pi\)
\(312\) 3.62493 0.205221
\(313\) 13.5948 0.768422 0.384211 0.923245i \(-0.374474\pi\)
0.384211 + 0.923245i \(0.374474\pi\)
\(314\) 7.09521 0.400406
\(315\) 14.3933 0.810969
\(316\) −10.6617 −0.599767
\(317\) −11.3344 −0.636603 −0.318302 0.947989i \(-0.603112\pi\)
−0.318302 + 0.947989i \(0.603112\pi\)
\(318\) 8.61870 0.483313
\(319\) −3.84409 −0.215227
\(320\) −1.33472 −0.0746134
\(321\) 10.0640 0.561718
\(322\) −2.94995 −0.164394
\(323\) −0.964875 −0.0536871
\(324\) 3.82724 0.212624
\(325\) 14.8522 0.823853
\(326\) −5.15118 −0.285297
\(327\) −13.6297 −0.753723
\(328\) 6.87438 0.379574
\(329\) 3.03755 0.167465
\(330\) 1.55932 0.0858379
\(331\) −31.5592 −1.73465 −0.867325 0.497742i \(-0.834162\pi\)
−0.867325 + 0.497742i \(0.834162\pi\)
\(332\) −18.0058 −0.988197
\(333\) −0.315711 −0.0173009
\(334\) −17.7890 −0.973369
\(335\) −11.2561 −0.614986
\(336\) −3.55482 −0.193931
\(337\) −19.4932 −1.06186 −0.530932 0.847415i \(-0.678158\pi\)
−0.530932 + 0.847415i \(0.678158\pi\)
\(338\) 8.29478 0.451176
\(339\) 6.20829 0.337188
\(340\) 1.28784 0.0698431
\(341\) −0.985935 −0.0533914
\(342\) −2.38294 −0.128855
\(343\) 29.3198 1.58312
\(344\) −4.27253 −0.230359
\(345\) −0.683463 −0.0367964
\(346\) 25.2983 1.36004
\(347\) 13.3386 0.716054 0.358027 0.933711i \(-0.383449\pi\)
0.358027 + 0.933711i \(0.383449\pi\)
\(348\) 2.03037 0.108839
\(349\) 23.8538 1.27686 0.638431 0.769679i \(-0.279584\pi\)
0.638431 + 0.769679i \(0.279584\pi\)
\(350\) −14.5650 −0.778530
\(351\) −19.5128 −1.04152
\(352\) 1.48724 0.0792702
\(353\) −5.10964 −0.271959 −0.135979 0.990712i \(-0.543418\pi\)
−0.135979 + 0.990712i \(0.543418\pi\)
\(354\) −3.36514 −0.178855
\(355\) 12.5046 0.663678
\(356\) 6.72822 0.356595
\(357\) 3.42996 0.181532
\(358\) 12.8974 0.681647
\(359\) 5.44774 0.287521 0.143760 0.989613i \(-0.454081\pi\)
0.143760 + 0.989613i \(0.454081\pi\)
\(360\) 3.18057 0.167631
\(361\) 1.00000 0.0526316
\(362\) −14.3121 −0.752227
\(363\) 6.90333 0.362331
\(364\) −20.8829 −1.09456
\(365\) 2.89244 0.151397
\(366\) 10.9646 0.573129
\(367\) 10.1954 0.532194 0.266097 0.963946i \(-0.414266\pi\)
0.266097 + 0.963946i \(0.414266\pi\)
\(368\) −0.651869 −0.0339810
\(369\) −16.3813 −0.852774
\(370\) −0.176835 −0.00919321
\(371\) −49.6516 −2.57778
\(372\) 0.520751 0.0269997
\(373\) −16.0086 −0.828892 −0.414446 0.910074i \(-0.636025\pi\)
−0.414446 + 0.910074i \(0.636025\pi\)
\(374\) −1.43500 −0.0742022
\(375\) −8.61684 −0.444971
\(376\) 0.671226 0.0346158
\(377\) 11.9275 0.614296
\(378\) 19.1354 0.984218
\(379\) −12.1725 −0.625261 −0.312630 0.949875i \(-0.601210\pi\)
−0.312630 + 0.949875i \(0.601210\pi\)
\(380\) −1.33472 −0.0684699
\(381\) 13.6927 0.701496
\(382\) −4.14979 −0.212322
\(383\) −6.13654 −0.313563 −0.156781 0.987633i \(-0.550112\pi\)
−0.156781 + 0.987633i \(0.550112\pi\)
\(384\) −0.785531 −0.0400864
\(385\) −8.98312 −0.457822
\(386\) 5.00873 0.254937
\(387\) 10.1812 0.517539
\(388\) −14.1929 −0.720536
\(389\) −13.1518 −0.666821 −0.333410 0.942782i \(-0.608199\pi\)
−0.333410 + 0.942782i \(0.608199\pi\)
\(390\) −4.83828 −0.244996
\(391\) 0.628972 0.0318085
\(392\) 13.4790 0.680792
\(393\) −2.09631 −0.105745
\(394\) −7.38557 −0.372080
\(395\) 14.2304 0.716011
\(396\) −3.54401 −0.178093
\(397\) −31.4511 −1.57848 −0.789242 0.614083i \(-0.789526\pi\)
−0.789242 + 0.614083i \(0.789526\pi\)
\(398\) 7.34587 0.368215
\(399\) −3.55482 −0.177963
\(400\) −3.21851 −0.160926
\(401\) 36.0847 1.80199 0.900993 0.433834i \(-0.142839\pi\)
0.900993 + 0.433834i \(0.142839\pi\)
\(402\) −6.62459 −0.330405
\(403\) 3.05917 0.152388
\(404\) −1.21151 −0.0602750
\(405\) −5.10831 −0.253834
\(406\) −11.6968 −0.580501
\(407\) 0.197041 0.00976698
\(408\) 0.757939 0.0375236
\(409\) −17.9013 −0.885161 −0.442581 0.896729i \(-0.645937\pi\)
−0.442581 + 0.896729i \(0.645937\pi\)
\(410\) −9.17540 −0.453141
\(411\) −12.7912 −0.630941
\(412\) 10.4983 0.517213
\(413\) 19.3863 0.953935
\(414\) 1.55337 0.0763437
\(415\) 24.0328 1.17972
\(416\) −4.61463 −0.226251
\(417\) 10.8694 0.532276
\(418\) 1.48724 0.0727433
\(419\) 7.72808 0.377542 0.188771 0.982021i \(-0.439550\pi\)
0.188771 + 0.982021i \(0.439550\pi\)
\(420\) 4.74470 0.231518
\(421\) 34.4132 1.67719 0.838597 0.544752i \(-0.183376\pi\)
0.838597 + 0.544752i \(0.183376\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −1.59949 −0.0777700
\(424\) −10.9718 −0.532839
\(425\) 3.10546 0.150637
\(426\) 7.35941 0.356565
\(427\) −63.1661 −3.05682
\(428\) −12.8117 −0.619279
\(429\) 5.39114 0.260287
\(430\) 5.70265 0.275006
\(431\) 38.5759 1.85814 0.929069 0.369907i \(-0.120611\pi\)
0.929069 + 0.369907i \(0.120611\pi\)
\(432\) 4.22847 0.203442
\(433\) −19.6714 −0.945346 −0.472673 0.881238i \(-0.656711\pi\)
−0.472673 + 0.881238i \(0.656711\pi\)
\(434\) −3.00000 −0.144005
\(435\) −2.70998 −0.129934
\(436\) 17.3509 0.830959
\(437\) −0.651869 −0.0311831
\(438\) 1.70230 0.0813389
\(439\) 7.86573 0.375411 0.187705 0.982225i \(-0.439895\pi\)
0.187705 + 0.982225i \(0.439895\pi\)
\(440\) −1.98506 −0.0946338
\(441\) −32.1196 −1.52951
\(442\) 4.45254 0.211786
\(443\) −33.2036 −1.57755 −0.788775 0.614682i \(-0.789284\pi\)
−0.788775 + 0.614682i \(0.789284\pi\)
\(444\) −0.104073 −0.00493910
\(445\) −8.98032 −0.425708
\(446\) 29.6582 1.40436
\(447\) −9.86957 −0.466815
\(448\) 4.52537 0.213804
\(449\) −5.33328 −0.251693 −0.125847 0.992050i \(-0.540165\pi\)
−0.125847 + 0.992050i \(0.540165\pi\)
\(450\) 7.66952 0.361545
\(451\) 10.2239 0.481423
\(452\) −7.90331 −0.371740
\(453\) −12.4392 −0.584446
\(454\) −26.9442 −1.26455
\(455\) 27.8729 1.30670
\(456\) −0.785531 −0.0367858
\(457\) 15.5604 0.727884 0.363942 0.931422i \(-0.381431\pi\)
0.363942 + 0.931422i \(0.381431\pi\)
\(458\) −25.0078 −1.16854
\(459\) −4.07994 −0.190435
\(460\) 0.870065 0.0405670
\(461\) 0.313118 0.0145834 0.00729168 0.999973i \(-0.497679\pi\)
0.00729168 + 0.999973i \(0.497679\pi\)
\(462\) −5.28687 −0.245967
\(463\) 34.5413 1.60527 0.802635 0.596471i \(-0.203431\pi\)
0.802635 + 0.596471i \(0.203431\pi\)
\(464\) −2.58471 −0.119992
\(465\) −0.695059 −0.0322326
\(466\) 3.21801 0.149072
\(467\) −10.4156 −0.481977 −0.240988 0.970528i \(-0.577472\pi\)
−0.240988 + 0.970528i \(0.577472\pi\)
\(468\) 10.9964 0.508308
\(469\) 38.1637 1.76224
\(470\) −0.895902 −0.0413249
\(471\) −5.57350 −0.256813
\(472\) 4.28390 0.197183
\(473\) −6.35428 −0.292170
\(474\) 8.37509 0.384681
\(475\) −3.21851 −0.147675
\(476\) −4.36642 −0.200134
\(477\) 26.1452 1.19711
\(478\) 15.3880 0.703831
\(479\) 32.5625 1.48782 0.743909 0.668281i \(-0.232970\pi\)
0.743909 + 0.668281i \(0.232970\pi\)
\(480\) 1.04847 0.0478557
\(481\) −0.611382 −0.0278766
\(482\) −19.9991 −0.910935
\(483\) 2.31727 0.105440
\(484\) −8.78812 −0.399460
\(485\) 18.9436 0.860186
\(486\) −15.6918 −0.711795
\(487\) −36.0060 −1.63159 −0.815794 0.578343i \(-0.803699\pi\)
−0.815794 + 0.578343i \(0.803699\pi\)
\(488\) −13.9582 −0.631858
\(489\) 4.04641 0.182985
\(490\) −17.9907 −0.812739
\(491\) −38.4646 −1.73589 −0.867943 0.496665i \(-0.834558\pi\)
−0.867943 + 0.496665i \(0.834558\pi\)
\(492\) −5.40004 −0.243452
\(493\) 2.49392 0.112321
\(494\) −4.61463 −0.207622
\(495\) 4.73027 0.212610
\(496\) −0.662929 −0.0297664
\(497\) −42.3969 −1.90176
\(498\) 14.1441 0.633813
\(499\) −1.73263 −0.0775634 −0.0387817 0.999248i \(-0.512348\pi\)
−0.0387817 + 0.999248i \(0.512348\pi\)
\(500\) 10.9694 0.490569
\(501\) 13.9738 0.624302
\(502\) 13.7911 0.615526
\(503\) −21.4042 −0.954365 −0.477182 0.878804i \(-0.658342\pi\)
−0.477182 + 0.878804i \(0.658342\pi\)
\(504\) −10.7837 −0.480344
\(505\) 1.61704 0.0719572
\(506\) −0.969486 −0.0430989
\(507\) −6.51580 −0.289377
\(508\) −17.4311 −0.773380
\(509\) 14.0876 0.624421 0.312211 0.950013i \(-0.398931\pi\)
0.312211 + 0.950013i \(0.398931\pi\)
\(510\) −1.01164 −0.0447962
\(511\) −9.80678 −0.433826
\(512\) 1.00000 0.0441942
\(513\) 4.22847 0.186691
\(514\) −7.85922 −0.346655
\(515\) −14.0123 −0.617456
\(516\) 3.35620 0.147749
\(517\) 0.998274 0.0439041
\(518\) 0.599557 0.0263430
\(519\) −19.8726 −0.872309
\(520\) 6.15925 0.270101
\(521\) 15.2345 0.667436 0.333718 0.942673i \(-0.391697\pi\)
0.333718 + 0.942673i \(0.391697\pi\)
\(522\) 6.15921 0.269581
\(523\) −17.7220 −0.774930 −0.387465 0.921884i \(-0.626649\pi\)
−0.387465 + 0.921884i \(0.626649\pi\)
\(524\) 2.66865 0.116581
\(525\) 11.4412 0.499336
\(526\) −18.4823 −0.805868
\(527\) 0.639644 0.0278633
\(528\) −1.16827 −0.0508426
\(529\) −22.5751 −0.981525
\(530\) 14.6444 0.636110
\(531\) −10.2083 −0.443002
\(532\) 4.52537 0.196200
\(533\) −31.7227 −1.37406
\(534\) −5.28522 −0.228714
\(535\) 17.1001 0.739303
\(536\) 8.43327 0.364262
\(537\) −10.1313 −0.437197
\(538\) −3.97144 −0.171221
\(539\) 20.0465 0.863464
\(540\) −5.64384 −0.242872
\(541\) 5.34488 0.229794 0.114897 0.993377i \(-0.463346\pi\)
0.114897 + 0.993377i \(0.463346\pi\)
\(542\) −10.9405 −0.469934
\(543\) 11.2426 0.482466
\(544\) −0.964875 −0.0413687
\(545\) −23.1587 −0.992010
\(546\) 16.4042 0.702033
\(547\) 28.9231 1.23666 0.618332 0.785917i \(-0.287809\pi\)
0.618332 + 0.785917i \(0.287809\pi\)
\(548\) 16.2835 0.695595
\(549\) 33.2616 1.41957
\(550\) −4.78670 −0.204106
\(551\) −2.58471 −0.110112
\(552\) 0.512063 0.0217948
\(553\) −48.2482 −2.05172
\(554\) −4.64699 −0.197432
\(555\) 0.138909 0.00589637
\(556\) −13.8370 −0.586819
\(557\) −29.9995 −1.27112 −0.635561 0.772051i \(-0.719231\pi\)
−0.635561 + 0.772051i \(0.719231\pi\)
\(558\) 1.57972 0.0668750
\(559\) 19.7161 0.833903
\(560\) −6.04012 −0.255242
\(561\) 1.12724 0.0475920
\(562\) −6.71636 −0.283312
\(563\) 18.8024 0.792425 0.396212 0.918159i \(-0.370324\pi\)
0.396212 + 0.918159i \(0.370324\pi\)
\(564\) −0.527269 −0.0222020
\(565\) 10.5487 0.443789
\(566\) −23.8289 −1.00160
\(567\) 17.3197 0.727358
\(568\) −9.36871 −0.393102
\(569\) 19.5082 0.817826 0.408913 0.912573i \(-0.365908\pi\)
0.408913 + 0.912573i \(0.365908\pi\)
\(570\) 1.04847 0.0439154
\(571\) −25.3545 −1.06105 −0.530526 0.847669i \(-0.678005\pi\)
−0.530526 + 0.847669i \(0.678005\pi\)
\(572\) −6.86306 −0.286959
\(573\) 3.25979 0.136180
\(574\) 31.1091 1.29847
\(575\) 2.09805 0.0874946
\(576\) −2.38294 −0.0992892
\(577\) 36.0228 1.49965 0.749825 0.661636i \(-0.230138\pi\)
0.749825 + 0.661636i \(0.230138\pi\)
\(578\) −16.0690 −0.668383
\(579\) −3.93451 −0.163513
\(580\) 3.44988 0.143248
\(581\) −81.4830 −3.38048
\(582\) 11.1490 0.462139
\(583\) −16.3177 −0.675812
\(584\) −2.16707 −0.0896738
\(585\) −14.6771 −0.606825
\(586\) −14.9950 −0.619437
\(587\) −10.4339 −0.430655 −0.215327 0.976542i \(-0.569082\pi\)
−0.215327 + 0.976542i \(0.569082\pi\)
\(588\) −10.5882 −0.436648
\(589\) −0.662929 −0.0273155
\(590\) −5.71783 −0.235399
\(591\) 5.80159 0.238646
\(592\) 0.132488 0.00544522
\(593\) 40.1153 1.64734 0.823670 0.567070i \(-0.191923\pi\)
0.823670 + 0.567070i \(0.191923\pi\)
\(594\) 6.28875 0.258030
\(595\) 5.82797 0.238923
\(596\) 12.5642 0.514650
\(597\) −5.77041 −0.236167
\(598\) 3.00813 0.123012
\(599\) −17.1126 −0.699201 −0.349601 0.936899i \(-0.613683\pi\)
−0.349601 + 0.936899i \(0.613683\pi\)
\(600\) 2.52824 0.103215
\(601\) 28.6467 1.16852 0.584261 0.811566i \(-0.301384\pi\)
0.584261 + 0.811566i \(0.301384\pi\)
\(602\) −19.3348 −0.788027
\(603\) −20.0960 −0.818372
\(604\) 15.8354 0.644335
\(605\) 11.7297 0.476881
\(606\) 0.951681 0.0386594
\(607\) 31.1669 1.26503 0.632513 0.774550i \(-0.282023\pi\)
0.632513 + 0.774550i \(0.282023\pi\)
\(608\) 1.00000 0.0405554
\(609\) 9.18817 0.372324
\(610\) 18.6304 0.754321
\(611\) −3.09746 −0.125310
\(612\) 2.29924 0.0929413
\(613\) −33.5357 −1.35449 −0.677246 0.735757i \(-0.736827\pi\)
−0.677246 + 0.735757i \(0.736827\pi\)
\(614\) −4.36796 −0.176276
\(615\) 7.20756 0.290637
\(616\) 6.73032 0.271172
\(617\) 28.6099 1.15179 0.575896 0.817523i \(-0.304653\pi\)
0.575896 + 0.817523i \(0.304653\pi\)
\(618\) −8.24671 −0.331731
\(619\) −20.2862 −0.815370 −0.407685 0.913123i \(-0.633664\pi\)
−0.407685 + 0.913123i \(0.633664\pi\)
\(620\) 0.884828 0.0355355
\(621\) −2.75640 −0.110611
\(622\) −29.5118 −1.18331
\(623\) 30.4477 1.21986
\(624\) 3.62493 0.145113
\(625\) 1.45137 0.0580546
\(626\) 13.5948 0.543356
\(627\) −1.16827 −0.0466563
\(628\) 7.09521 0.283130
\(629\) −0.127834 −0.00509709
\(630\) 14.3933 0.573441
\(631\) 22.1256 0.880804 0.440402 0.897801i \(-0.354836\pi\)
0.440402 + 0.897801i \(0.354836\pi\)
\(632\) −10.6617 −0.424100
\(633\) 0.785531 0.0312220
\(634\) −11.3344 −0.450146
\(635\) 23.2657 0.923271
\(636\) 8.61870 0.341754
\(637\) −62.2005 −2.46447
\(638\) −3.84409 −0.152189
\(639\) 22.3251 0.883167
\(640\) −1.33472 −0.0527596
\(641\) −9.92429 −0.391986 −0.195993 0.980605i \(-0.562793\pi\)
−0.195993 + 0.980605i \(0.562793\pi\)
\(642\) 10.0640 0.397195
\(643\) 35.3372 1.39356 0.696781 0.717284i \(-0.254615\pi\)
0.696781 + 0.717284i \(0.254615\pi\)
\(644\) −2.94995 −0.116244
\(645\) −4.47960 −0.176384
\(646\) −0.964875 −0.0379625
\(647\) 50.2227 1.97446 0.987229 0.159306i \(-0.0509255\pi\)
0.987229 + 0.159306i \(0.0509255\pi\)
\(648\) 3.82724 0.150348
\(649\) 6.37119 0.250091
\(650\) 14.8522 0.582552
\(651\) 2.35659 0.0923622
\(652\) −5.15118 −0.201736
\(653\) −45.9899 −1.79972 −0.899862 0.436176i \(-0.856333\pi\)
−0.899862 + 0.436176i \(0.856333\pi\)
\(654\) −13.6297 −0.532963
\(655\) −3.56191 −0.139175
\(656\) 6.87438 0.268400
\(657\) 5.16399 0.201467
\(658\) 3.03755 0.118416
\(659\) 15.1580 0.590472 0.295236 0.955424i \(-0.404602\pi\)
0.295236 + 0.955424i \(0.404602\pi\)
\(660\) 1.55932 0.0606965
\(661\) 32.1229 1.24944 0.624718 0.780851i \(-0.285214\pi\)
0.624718 + 0.780851i \(0.285214\pi\)
\(662\) −31.5592 −1.22658
\(663\) −3.49761 −0.135836
\(664\) −18.0058 −0.698761
\(665\) −6.04012 −0.234226
\(666\) −0.315711 −0.0122336
\(667\) 1.68489 0.0652393
\(668\) −17.7890 −0.688276
\(669\) −23.2974 −0.900730
\(670\) −11.2561 −0.434861
\(671\) −20.7592 −0.801400
\(672\) −3.55482 −0.137130
\(673\) −31.9772 −1.23263 −0.616315 0.787499i \(-0.711375\pi\)
−0.616315 + 0.787499i \(0.711375\pi\)
\(674\) −19.4932 −0.750851
\(675\) −13.6094 −0.523825
\(676\) 8.29478 0.319030
\(677\) 26.0429 1.00091 0.500454 0.865763i \(-0.333166\pi\)
0.500454 + 0.865763i \(0.333166\pi\)
\(678\) 6.20829 0.238428
\(679\) −64.2282 −2.46485
\(680\) 1.28784 0.0493865
\(681\) 21.1655 0.811063
\(682\) −0.985935 −0.0377534
\(683\) 35.2973 1.35061 0.675306 0.737538i \(-0.264012\pi\)
0.675306 + 0.737538i \(0.264012\pi\)
\(684\) −2.38294 −0.0911141
\(685\) −21.7339 −0.830411
\(686\) 29.3198 1.11944
\(687\) 19.6444 0.749480
\(688\) −4.27253 −0.162889
\(689\) 50.6309 1.92888
\(690\) −0.683463 −0.0260190
\(691\) −10.4885 −0.399003 −0.199502 0.979897i \(-0.563932\pi\)
−0.199502 + 0.979897i \(0.563932\pi\)
\(692\) 25.2983 0.961696
\(693\) −16.0380 −0.609231
\(694\) 13.3386 0.506327
\(695\) 18.4686 0.700553
\(696\) 2.03037 0.0769609
\(697\) −6.63292 −0.251240
\(698\) 23.8538 0.902878
\(699\) −2.52785 −0.0956120
\(700\) −14.5650 −0.550504
\(701\) 1.94649 0.0735178 0.0367589 0.999324i \(-0.488297\pi\)
0.0367589 + 0.999324i \(0.488297\pi\)
\(702\) −19.5128 −0.736463
\(703\) 0.132488 0.00499688
\(704\) 1.48724 0.0560525
\(705\) 0.703758 0.0265051
\(706\) −5.10964 −0.192304
\(707\) −5.48255 −0.206192
\(708\) −3.36514 −0.126470
\(709\) −16.8116 −0.631371 −0.315686 0.948864i \(-0.602235\pi\)
−0.315686 + 0.948864i \(0.602235\pi\)
\(710\) 12.5046 0.469291
\(711\) 25.4062 0.952807
\(712\) 6.72822 0.252151
\(713\) 0.432143 0.0161839
\(714\) 3.42996 0.128363
\(715\) 9.16029 0.342576
\(716\) 12.8974 0.481997
\(717\) −12.0877 −0.451425
\(718\) 5.44774 0.203308
\(719\) 0.0700285 0.00261162 0.00130581 0.999999i \(-0.499584\pi\)
0.00130581 + 0.999999i \(0.499584\pi\)
\(720\) 3.18057 0.118533
\(721\) 47.5086 1.76931
\(722\) 1.00000 0.0372161
\(723\) 15.7099 0.584258
\(724\) −14.3121 −0.531905
\(725\) 8.31892 0.308957
\(726\) 6.90333 0.256207
\(727\) −10.1670 −0.377072 −0.188536 0.982066i \(-0.560374\pi\)
−0.188536 + 0.982066i \(0.560374\pi\)
\(728\) −20.8829 −0.773972
\(729\) 0.844685 0.0312846
\(730\) 2.89244 0.107054
\(731\) 4.12246 0.152475
\(732\) 10.9646 0.405263
\(733\) 28.6433 1.05797 0.528983 0.848632i \(-0.322573\pi\)
0.528983 + 0.848632i \(0.322573\pi\)
\(734\) 10.1954 0.376318
\(735\) 14.1323 0.521277
\(736\) −0.651869 −0.0240282
\(737\) 12.5423 0.462002
\(738\) −16.3813 −0.603002
\(739\) −38.9553 −1.43299 −0.716497 0.697590i \(-0.754256\pi\)
−0.716497 + 0.697590i \(0.754256\pi\)
\(740\) −0.176835 −0.00650058
\(741\) 3.62493 0.133165
\(742\) −49.6516 −1.82277
\(743\) −32.3995 −1.18862 −0.594312 0.804235i \(-0.702575\pi\)
−0.594312 + 0.804235i \(0.702575\pi\)
\(744\) 0.520751 0.0190917
\(745\) −16.7698 −0.614396
\(746\) −16.0086 −0.586115
\(747\) 42.9068 1.56988
\(748\) −1.43500 −0.0524689
\(749\) −57.9779 −2.11847
\(750\) −8.61684 −0.314642
\(751\) −43.1364 −1.57407 −0.787036 0.616907i \(-0.788385\pi\)
−0.787036 + 0.616907i \(0.788385\pi\)
\(752\) 0.671226 0.0244771
\(753\) −10.8333 −0.394788
\(754\) 11.9275 0.434373
\(755\) −21.1360 −0.769216
\(756\) 19.1354 0.695947
\(757\) −27.1804 −0.987887 −0.493943 0.869494i \(-0.664445\pi\)
−0.493943 + 0.869494i \(0.664445\pi\)
\(758\) −12.1725 −0.442126
\(759\) 0.761561 0.0276429
\(760\) −1.33472 −0.0484155
\(761\) −42.5952 −1.54408 −0.772038 0.635577i \(-0.780762\pi\)
−0.772038 + 0.635577i \(0.780762\pi\)
\(762\) 13.6927 0.496033
\(763\) 78.5194 2.84259
\(764\) −4.14979 −0.150134
\(765\) −3.06885 −0.110955
\(766\) −6.13654 −0.221722
\(767\) −19.7686 −0.713803
\(768\) −0.785531 −0.0283454
\(769\) −8.56664 −0.308921 −0.154461 0.987999i \(-0.549364\pi\)
−0.154461 + 0.987999i \(0.549364\pi\)
\(770\) −8.98312 −0.323729
\(771\) 6.17366 0.222339
\(772\) 5.00873 0.180268
\(773\) 33.8724 1.21831 0.609153 0.793053i \(-0.291510\pi\)
0.609153 + 0.793053i \(0.291510\pi\)
\(774\) 10.1812 0.365955
\(775\) 2.13365 0.0766428
\(776\) −14.1929 −0.509496
\(777\) −0.470971 −0.0168960
\(778\) −13.1518 −0.471514
\(779\) 6.87438 0.246300
\(780\) −4.83828 −0.173238
\(781\) −13.9335 −0.498581
\(782\) 0.628972 0.0224920
\(783\) −10.9294 −0.390583
\(784\) 13.4790 0.481392
\(785\) −9.47015 −0.338004
\(786\) −2.09631 −0.0747728
\(787\) −16.4589 −0.586698 −0.293349 0.956005i \(-0.594770\pi\)
−0.293349 + 0.956005i \(0.594770\pi\)
\(788\) −7.38557 −0.263100
\(789\) 14.5184 0.516870
\(790\) 14.2304 0.506296
\(791\) −35.7654 −1.27167
\(792\) −3.54401 −0.125931
\(793\) 64.4119 2.28733
\(794\) −31.4511 −1.11616
\(795\) −11.5036 −0.407990
\(796\) 7.34587 0.260368
\(797\) 0.442603 0.0156778 0.00783890 0.999969i \(-0.497505\pi\)
0.00783890 + 0.999969i \(0.497505\pi\)
\(798\) −3.55482 −0.125839
\(799\) −0.647649 −0.0229122
\(800\) −3.21851 −0.113792
\(801\) −16.0330 −0.566497
\(802\) 36.0847 1.27420
\(803\) −3.22295 −0.113735
\(804\) −6.62459 −0.233631
\(805\) 3.93737 0.138774
\(806\) 3.05917 0.107755
\(807\) 3.11969 0.109818
\(808\) −1.21151 −0.0426209
\(809\) −28.7421 −1.01052 −0.505259 0.862968i \(-0.668603\pi\)
−0.505259 + 0.862968i \(0.668603\pi\)
\(810\) −5.10831 −0.179488
\(811\) 41.5537 1.45915 0.729574 0.683902i \(-0.239719\pi\)
0.729574 + 0.683902i \(0.239719\pi\)
\(812\) −11.6968 −0.410476
\(813\) 8.59408 0.301407
\(814\) 0.197041 0.00690630
\(815\) 6.87540 0.240835
\(816\) 0.757939 0.0265332
\(817\) −4.27253 −0.149477
\(818\) −17.9013 −0.625904
\(819\) 49.7627 1.73885
\(820\) −9.17540 −0.320419
\(821\) 33.3244 1.16303 0.581514 0.813536i \(-0.302461\pi\)
0.581514 + 0.813536i \(0.302461\pi\)
\(822\) −12.7912 −0.446143
\(823\) −6.41918 −0.223759 −0.111879 0.993722i \(-0.535687\pi\)
−0.111879 + 0.993722i \(0.535687\pi\)
\(824\) 10.4983 0.365725
\(825\) 3.76010 0.130910
\(826\) 19.3863 0.674534
\(827\) −34.5689 −1.20208 −0.601039 0.799220i \(-0.705246\pi\)
−0.601039 + 0.799220i \(0.705246\pi\)
\(828\) 1.55337 0.0539832
\(829\) −20.6219 −0.716229 −0.358114 0.933678i \(-0.616580\pi\)
−0.358114 + 0.933678i \(0.616580\pi\)
\(830\) 24.0328 0.834190
\(831\) 3.65035 0.126629
\(832\) −4.61463 −0.159983
\(833\) −13.0055 −0.450615
\(834\) 10.8694 0.376376
\(835\) 23.7434 0.821673
\(836\) 1.48724 0.0514373
\(837\) −2.80317 −0.0968919
\(838\) 7.72808 0.266962
\(839\) −14.4075 −0.497403 −0.248702 0.968580i \(-0.580004\pi\)
−0.248702 + 0.968580i \(0.580004\pi\)
\(840\) 4.74470 0.163708
\(841\) −22.3193 −0.769630
\(842\) 34.4132 1.18596
\(843\) 5.27590 0.181712
\(844\) −1.00000 −0.0344214
\(845\) −11.0712 −0.380862
\(846\) −1.59949 −0.0549917
\(847\) −39.7695 −1.36650
\(848\) −10.9718 −0.376774
\(849\) 18.7184 0.642412
\(850\) 3.10546 0.106516
\(851\) −0.0863648 −0.00296055
\(852\) 7.35941 0.252129
\(853\) −34.7785 −1.19079 −0.595396 0.803432i \(-0.703005\pi\)
−0.595396 + 0.803432i \(0.703005\pi\)
\(854\) −63.1661 −2.16150
\(855\) 3.18057 0.108773
\(856\) −12.8117 −0.437896
\(857\) 23.9704 0.818813 0.409406 0.912352i \(-0.365736\pi\)
0.409406 + 0.912352i \(0.365736\pi\)
\(858\) 5.39114 0.184051
\(859\) −26.2240 −0.894752 −0.447376 0.894346i \(-0.647641\pi\)
−0.447376 + 0.894346i \(0.647641\pi\)
\(860\) 5.70265 0.194459
\(861\) −24.4372 −0.832817
\(862\) 38.5759 1.31390
\(863\) 28.9721 0.986222 0.493111 0.869966i \(-0.335860\pi\)
0.493111 + 0.869966i \(0.335860\pi\)
\(864\) 4.22847 0.143855
\(865\) −33.7662 −1.14809
\(866\) −19.6714 −0.668461
\(867\) 12.6227 0.428689
\(868\) −3.00000 −0.101827
\(869\) −15.8565 −0.537895
\(870\) −2.70998 −0.0918770
\(871\) −38.9164 −1.31863
\(872\) 17.3509 0.587577
\(873\) 33.8209 1.14466
\(874\) −0.651869 −0.0220498
\(875\) 49.6408 1.67817
\(876\) 1.70230 0.0575153
\(877\) 23.6996 0.800278 0.400139 0.916454i \(-0.368962\pi\)
0.400139 + 0.916454i \(0.368962\pi\)
\(878\) 7.86573 0.265456
\(879\) 11.7790 0.397297
\(880\) −1.98506 −0.0669162
\(881\) 30.9644 1.04322 0.521609 0.853184i \(-0.325332\pi\)
0.521609 + 0.853184i \(0.325332\pi\)
\(882\) −32.1196 −1.08152
\(883\) 42.5498 1.43191 0.715957 0.698144i \(-0.245991\pi\)
0.715957 + 0.698144i \(0.245991\pi\)
\(884\) 4.45254 0.149755
\(885\) 4.49153 0.150981
\(886\) −33.2036 −1.11550
\(887\) −2.39695 −0.0804816 −0.0402408 0.999190i \(-0.512813\pi\)
−0.0402408 + 0.999190i \(0.512813\pi\)
\(888\) −0.104073 −0.00349247
\(889\) −78.8822 −2.64562
\(890\) −8.98032 −0.301021
\(891\) 5.69202 0.190690
\(892\) 29.6582 0.993029
\(893\) 0.671226 0.0224617
\(894\) −9.86957 −0.330088
\(895\) −17.2144 −0.575415
\(896\) 4.52537 0.151182
\(897\) −2.36298 −0.0788976
\(898\) −5.33328 −0.177974
\(899\) 1.71348 0.0571478
\(900\) 7.66952 0.255651
\(901\) 10.5864 0.352685
\(902\) 10.2239 0.340417
\(903\) 15.1881 0.505427
\(904\) −7.90331 −0.262860
\(905\) 19.1027 0.634995
\(906\) −12.4392 −0.413266
\(907\) 15.5791 0.517296 0.258648 0.965972i \(-0.416723\pi\)
0.258648 + 0.965972i \(0.416723\pi\)
\(908\) −26.9442 −0.894174
\(909\) 2.88697 0.0957546
\(910\) 27.8729 0.923978
\(911\) −29.8880 −0.990234 −0.495117 0.868826i \(-0.664875\pi\)
−0.495117 + 0.868826i \(0.664875\pi\)
\(912\) −0.785531 −0.0260115
\(913\) −26.7790 −0.886254
\(914\) 15.5604 0.514692
\(915\) −14.6347 −0.483809
\(916\) −25.0078 −0.826281
\(917\) 12.0766 0.398806
\(918\) −4.07994 −0.134658
\(919\) 50.6550 1.67096 0.835478 0.549524i \(-0.185191\pi\)
0.835478 + 0.549524i \(0.185191\pi\)
\(920\) 0.870065 0.0286852
\(921\) 3.43116 0.113061
\(922\) 0.313118 0.0103120
\(923\) 43.2331 1.42303
\(924\) −5.28687 −0.173925
\(925\) −0.426414 −0.0140204
\(926\) 34.5413 1.13510
\(927\) −25.0168 −0.821659
\(928\) −2.58471 −0.0848473
\(929\) 34.0584 1.11742 0.558710 0.829363i \(-0.311296\pi\)
0.558710 + 0.829363i \(0.311296\pi\)
\(930\) −0.695059 −0.0227919
\(931\) 13.4790 0.441756
\(932\) 3.21801 0.105410
\(933\) 23.1824 0.758958
\(934\) −10.4156 −0.340809
\(935\) 1.91533 0.0626380
\(936\) 10.9964 0.359428
\(937\) 28.3162 0.925051 0.462525 0.886606i \(-0.346943\pi\)
0.462525 + 0.886606i \(0.346943\pi\)
\(938\) 38.1637 1.24609
\(939\) −10.6791 −0.348499
\(940\) −0.895902 −0.0292211
\(941\) 1.54472 0.0503563 0.0251782 0.999683i \(-0.491985\pi\)
0.0251782 + 0.999683i \(0.491985\pi\)
\(942\) −5.57350 −0.181595
\(943\) −4.48119 −0.145928
\(944\) 4.28390 0.139429
\(945\) −25.5405 −0.830831
\(946\) −6.35428 −0.206595
\(947\) 33.3676 1.08430 0.542151 0.840281i \(-0.317610\pi\)
0.542151 + 0.840281i \(0.317610\pi\)
\(948\) 8.37509 0.272010
\(949\) 10.0002 0.324620
\(950\) −3.21851 −0.104422
\(951\) 8.90352 0.288716
\(952\) −4.36642 −0.141516
\(953\) 48.3612 1.56657 0.783286 0.621661i \(-0.213542\pi\)
0.783286 + 0.621661i \(0.213542\pi\)
\(954\) 26.1452 0.846483
\(955\) 5.53883 0.179232
\(956\) 15.3880 0.497684
\(957\) 3.01965 0.0976113
\(958\) 32.5625 1.05205
\(959\) 73.6887 2.37953
\(960\) 1.04847 0.0338391
\(961\) −30.5605 −0.985823
\(962\) −0.611382 −0.0197118
\(963\) 30.5296 0.983803
\(964\) −19.9991 −0.644128
\(965\) −6.68527 −0.215206
\(966\) 2.31727 0.0745571
\(967\) −50.1503 −1.61273 −0.806363 0.591421i \(-0.798567\pi\)
−0.806363 + 0.591421i \(0.798567\pi\)
\(968\) −8.78812 −0.282461
\(969\) 0.757939 0.0243485
\(970\) 18.9436 0.608243
\(971\) 45.5027 1.46025 0.730125 0.683313i \(-0.239462\pi\)
0.730125 + 0.683313i \(0.239462\pi\)
\(972\) −15.6918 −0.503315
\(973\) −62.6175 −2.00743
\(974\) −36.0060 −1.15371
\(975\) −11.6669 −0.373639
\(976\) −13.9582 −0.446791
\(977\) −29.7040 −0.950314 −0.475157 0.879901i \(-0.657609\pi\)
−0.475157 + 0.879901i \(0.657609\pi\)
\(978\) 4.04641 0.129390
\(979\) 10.0065 0.319809
\(980\) −17.9907 −0.574693
\(981\) −41.3462 −1.32008
\(982\) −38.4646 −1.22746
\(983\) −15.0044 −0.478567 −0.239283 0.970950i \(-0.576913\pi\)
−0.239283 + 0.970950i \(0.576913\pi\)
\(984\) −5.40004 −0.172147
\(985\) 9.85770 0.314093
\(986\) 2.49392 0.0794227
\(987\) −2.38609 −0.0759500
\(988\) −4.61463 −0.146811
\(989\) 2.78513 0.0885619
\(990\) 4.73027 0.150338
\(991\) −8.18906 −0.260134 −0.130067 0.991505i \(-0.541519\pi\)
−0.130067 + 0.991505i \(0.541519\pi\)
\(992\) −0.662929 −0.0210480
\(993\) 24.7907 0.786709
\(994\) −42.3969 −1.34475
\(995\) −9.80472 −0.310830
\(996\) 14.1441 0.448173
\(997\) 34.5425 1.09397 0.546986 0.837142i \(-0.315775\pi\)
0.546986 + 0.837142i \(0.315775\pi\)
\(998\) −1.73263 −0.0548456
\(999\) 0.560221 0.0177246
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 \(a_p\))