Properties

Label 8041.2.a.j.1.11
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 82
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(82\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.26888 q^{2}\) \(+0.654424 q^{3}\) \(+3.14780 q^{4}\) \(-0.968068 q^{5}\) \(-1.48481 q^{6}\) \(+1.81018 q^{7}\) \(-2.60421 q^{8}\) \(-2.57173 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.26888 q^{2}\) \(+0.654424 q^{3}\) \(+3.14780 q^{4}\) \(-0.968068 q^{5}\) \(-1.48481 q^{6}\) \(+1.81018 q^{7}\) \(-2.60421 q^{8}\) \(-2.57173 q^{9}\) \(+2.19643 q^{10}\) \(+1.00000 q^{11}\) \(+2.05999 q^{12}\) \(+3.55823 q^{13}\) \(-4.10708 q^{14}\) \(-0.633527 q^{15}\) \(-0.386967 q^{16}\) \(+1.00000 q^{17}\) \(+5.83493 q^{18}\) \(-4.84794 q^{19}\) \(-3.04728 q^{20}\) \(+1.18463 q^{21}\) \(-2.26888 q^{22}\) \(-7.36907 q^{23}\) \(-1.70426 q^{24}\) \(-4.06284 q^{25}\) \(-8.07319 q^{26}\) \(-3.64627 q^{27}\) \(+5.69809 q^{28}\) \(+7.99930 q^{29}\) \(+1.43739 q^{30}\) \(-2.59561 q^{31}\) \(+6.08640 q^{32}\) \(+0.654424 q^{33}\) \(-2.26888 q^{34}\) \(-1.75238 q^{35}\) \(-8.09528 q^{36}\) \(-7.56763 q^{37}\) \(+10.9994 q^{38}\) \(+2.32859 q^{39}\) \(+2.52105 q^{40}\) \(+1.85905 q^{41}\) \(-2.68777 q^{42}\) \(+1.00000 q^{43}\) \(+3.14780 q^{44}\) \(+2.48961 q^{45}\) \(+16.7195 q^{46}\) \(-3.71881 q^{47}\) \(-0.253240 q^{48}\) \(-3.72324 q^{49}\) \(+9.21809 q^{50}\) \(+0.654424 q^{51}\) \(+11.2006 q^{52}\) \(-8.29080 q^{53}\) \(+8.27294 q^{54}\) \(-0.968068 q^{55}\) \(-4.71409 q^{56}\) \(-3.17261 q^{57}\) \(-18.1494 q^{58}\) \(-4.79436 q^{59}\) \(-1.99421 q^{60}\) \(+14.1516 q^{61}\) \(+5.88912 q^{62}\) \(-4.65530 q^{63}\) \(-13.0353 q^{64}\) \(-3.44461 q^{65}\) \(-1.48481 q^{66}\) \(-4.30268 q^{67}\) \(+3.14780 q^{68}\) \(-4.82250 q^{69}\) \(+3.97593 q^{70}\) \(+14.1314 q^{71}\) \(+6.69732 q^{72}\) \(+2.83925 q^{73}\) \(+17.1700 q^{74}\) \(-2.65882 q^{75}\) \(-15.2603 q^{76}\) \(+1.81018 q^{77}\) \(-5.28329 q^{78}\) \(+0.315578 q^{79}\) \(+0.374610 q^{80}\) \(+5.32898 q^{81}\) \(-4.21795 q^{82}\) \(+9.58463 q^{83}\) \(+3.72896 q^{84}\) \(-0.968068 q^{85}\) \(-2.26888 q^{86}\) \(+5.23493 q^{87}\) \(-2.60421 q^{88}\) \(+13.9904 q^{89}\) \(-5.64862 q^{90}\) \(+6.44105 q^{91}\) \(-23.1963 q^{92}\) \(-1.69863 q^{93}\) \(+8.43751 q^{94}\) \(+4.69314 q^{95}\) \(+3.98308 q^{96}\) \(+17.3930 q^{97}\) \(+8.44757 q^{98}\) \(-2.57173 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.26888 −1.60434 −0.802169 0.597097i \(-0.796321\pi\)
−0.802169 + 0.597097i \(0.796321\pi\)
\(3\) 0.654424 0.377832 0.188916 0.981993i \(-0.439503\pi\)
0.188916 + 0.981993i \(0.439503\pi\)
\(4\) 3.14780 1.57390
\(5\) −0.968068 −0.432933 −0.216467 0.976290i \(-0.569453\pi\)
−0.216467 + 0.976290i \(0.569453\pi\)
\(6\) −1.48481 −0.606170
\(7\) 1.81018 0.684185 0.342092 0.939666i \(-0.388864\pi\)
0.342092 + 0.939666i \(0.388864\pi\)
\(8\) −2.60421 −0.920727
\(9\) −2.57173 −0.857243
\(10\) 2.19643 0.694571
\(11\) 1.00000 0.301511
\(12\) 2.05999 0.594669
\(13\) 3.55823 0.986876 0.493438 0.869781i \(-0.335740\pi\)
0.493438 + 0.869781i \(0.335740\pi\)
\(14\) −4.10708 −1.09766
\(15\) −0.633527 −0.163576
\(16\) −0.386967 −0.0967417
\(17\) 1.00000 0.242536
\(18\) 5.83493 1.37531
\(19\) −4.84794 −1.11219 −0.556097 0.831117i \(-0.687702\pi\)
−0.556097 + 0.831117i \(0.687702\pi\)
\(20\) −3.04728 −0.681393
\(21\) 1.18463 0.258507
\(22\) −2.26888 −0.483726
\(23\) −7.36907 −1.53656 −0.768279 0.640115i \(-0.778887\pi\)
−0.768279 + 0.640115i \(0.778887\pi\)
\(24\) −1.70426 −0.347880
\(25\) −4.06284 −0.812569
\(26\) −8.07319 −1.58328
\(27\) −3.64627 −0.701726
\(28\) 5.69809 1.07684
\(29\) 7.99930 1.48543 0.742716 0.669606i \(-0.233537\pi\)
0.742716 + 0.669606i \(0.233537\pi\)
\(30\) 1.43739 0.262431
\(31\) −2.59561 −0.466186 −0.233093 0.972454i \(-0.574885\pi\)
−0.233093 + 0.972454i \(0.574885\pi\)
\(32\) 6.08640 1.07593
\(33\) 0.654424 0.113921
\(34\) −2.26888 −0.389109
\(35\) −1.75238 −0.296206
\(36\) −8.09528 −1.34921
\(37\) −7.56763 −1.24411 −0.622055 0.782973i \(-0.713702\pi\)
−0.622055 + 0.782973i \(0.713702\pi\)
\(38\) 10.9994 1.78434
\(39\) 2.32859 0.372873
\(40\) 2.52105 0.398613
\(41\) 1.85905 0.290335 0.145167 0.989407i \(-0.453628\pi\)
0.145167 + 0.989407i \(0.453628\pi\)
\(42\) −2.68777 −0.414732
\(43\) 1.00000 0.152499
\(44\) 3.14780 0.474548
\(45\) 2.48961 0.371129
\(46\) 16.7195 2.46516
\(47\) −3.71881 −0.542444 −0.271222 0.962517i \(-0.587428\pi\)
−0.271222 + 0.962517i \(0.587428\pi\)
\(48\) −0.253240 −0.0365521
\(49\) −3.72324 −0.531891
\(50\) 9.21809 1.30363
\(51\) 0.654424 0.0916377
\(52\) 11.2006 1.55324
\(53\) −8.29080 −1.13883 −0.569415 0.822050i \(-0.692830\pi\)
−0.569415 + 0.822050i \(0.692830\pi\)
\(54\) 8.27294 1.12580
\(55\) −0.968068 −0.130534
\(56\) −4.71409 −0.629947
\(57\) −3.17261 −0.420223
\(58\) −18.1494 −2.38314
\(59\) −4.79436 −0.624173 −0.312086 0.950054i \(-0.601028\pi\)
−0.312086 + 0.950054i \(0.601028\pi\)
\(60\) −1.99421 −0.257452
\(61\) 14.1516 1.81193 0.905966 0.423352i \(-0.139146\pi\)
0.905966 + 0.423352i \(0.139146\pi\)
\(62\) 5.88912 0.747919
\(63\) −4.65530 −0.586513
\(64\) −13.0353 −1.62942
\(65\) −3.44461 −0.427252
\(66\) −1.48481 −0.182767
\(67\) −4.30268 −0.525656 −0.262828 0.964843i \(-0.584655\pi\)
−0.262828 + 0.964843i \(0.584655\pi\)
\(68\) 3.14780 0.381726
\(69\) −4.82250 −0.580560
\(70\) 3.97593 0.475215
\(71\) 14.1314 1.67708 0.838542 0.544837i \(-0.183409\pi\)
0.838542 + 0.544837i \(0.183409\pi\)
\(72\) 6.69732 0.789287
\(73\) 2.83925 0.332309 0.166155 0.986100i \(-0.446865\pi\)
0.166155 + 0.986100i \(0.446865\pi\)
\(74\) 17.1700 1.99597
\(75\) −2.65882 −0.307014
\(76\) −15.2603 −1.75048
\(77\) 1.81018 0.206289
\(78\) −5.28329 −0.598214
\(79\) 0.315578 0.0355053 0.0177526 0.999842i \(-0.494349\pi\)
0.0177526 + 0.999842i \(0.494349\pi\)
\(80\) 0.374610 0.0418827
\(81\) 5.32898 0.592109
\(82\) −4.21795 −0.465795
\(83\) 9.58463 1.05205 0.526025 0.850469i \(-0.323682\pi\)
0.526025 + 0.850469i \(0.323682\pi\)
\(84\) 3.72896 0.406863
\(85\) −0.968068 −0.105002
\(86\) −2.26888 −0.244659
\(87\) 5.23493 0.561244
\(88\) −2.60421 −0.277610
\(89\) 13.9904 1.48298 0.741488 0.670966i \(-0.234120\pi\)
0.741488 + 0.670966i \(0.234120\pi\)
\(90\) −5.64862 −0.595416
\(91\) 6.44105 0.675206
\(92\) −23.1963 −2.41839
\(93\) −1.69863 −0.176140
\(94\) 8.43751 0.870263
\(95\) 4.69314 0.481506
\(96\) 3.98308 0.406522
\(97\) 17.3930 1.76600 0.882998 0.469377i \(-0.155522\pi\)
0.882998 + 0.469377i \(0.155522\pi\)
\(98\) 8.44757 0.853333
\(99\) −2.57173 −0.258469
\(100\) −12.7890 −1.27890
\(101\) −17.5068 −1.74199 −0.870994 0.491294i \(-0.836524\pi\)
−0.870994 + 0.491294i \(0.836524\pi\)
\(102\) −1.48481 −0.147018
\(103\) 8.82769 0.869818 0.434909 0.900474i \(-0.356781\pi\)
0.434909 + 0.900474i \(0.356781\pi\)
\(104\) −9.26638 −0.908644
\(105\) −1.14680 −0.111916
\(106\) 18.8108 1.82707
\(107\) 10.9388 1.05749 0.528745 0.848781i \(-0.322663\pi\)
0.528745 + 0.848781i \(0.322663\pi\)
\(108\) −11.4777 −1.10444
\(109\) −14.5544 −1.39406 −0.697031 0.717041i \(-0.745496\pi\)
−0.697031 + 0.717041i \(0.745496\pi\)
\(110\) 2.19643 0.209421
\(111\) −4.95244 −0.470064
\(112\) −0.700480 −0.0661892
\(113\) 9.18926 0.864453 0.432227 0.901765i \(-0.357728\pi\)
0.432227 + 0.901765i \(0.357728\pi\)
\(114\) 7.19826 0.674179
\(115\) 7.13377 0.665227
\(116\) 25.1802 2.33792
\(117\) −9.15081 −0.845993
\(118\) 10.8778 1.00138
\(119\) 1.81018 0.165939
\(120\) 1.64984 0.150609
\(121\) 1.00000 0.0909091
\(122\) −32.1083 −2.90695
\(123\) 1.21661 0.109698
\(124\) −8.17046 −0.733729
\(125\) 8.77345 0.784721
\(126\) 10.5623 0.940964
\(127\) 6.42299 0.569948 0.284974 0.958535i \(-0.408015\pi\)
0.284974 + 0.958535i \(0.408015\pi\)
\(128\) 17.4028 1.53820
\(129\) 0.654424 0.0576188
\(130\) 7.81540 0.685456
\(131\) 10.0152 0.875036 0.437518 0.899210i \(-0.355858\pi\)
0.437518 + 0.899210i \(0.355858\pi\)
\(132\) 2.05999 0.179299
\(133\) −8.77566 −0.760946
\(134\) 9.76224 0.843329
\(135\) 3.52984 0.303800
\(136\) −2.60421 −0.223309
\(137\) −20.1159 −1.71861 −0.859307 0.511461i \(-0.829104\pi\)
−0.859307 + 0.511461i \(0.829104\pi\)
\(138\) 10.9416 0.931415
\(139\) −22.4797 −1.90670 −0.953350 0.301867i \(-0.902390\pi\)
−0.953350 + 0.301867i \(0.902390\pi\)
\(140\) −5.51614 −0.466199
\(141\) −2.43368 −0.204953
\(142\) −32.0623 −2.69061
\(143\) 3.55823 0.297554
\(144\) 0.995174 0.0829311
\(145\) −7.74387 −0.643093
\(146\) −6.44190 −0.533136
\(147\) −2.43658 −0.200965
\(148\) −23.8214 −1.95810
\(149\) 6.68632 0.547764 0.273882 0.961763i \(-0.411692\pi\)
0.273882 + 0.961763i \(0.411692\pi\)
\(150\) 6.03254 0.492555
\(151\) −21.1487 −1.72106 −0.860528 0.509404i \(-0.829866\pi\)
−0.860528 + 0.509404i \(0.829866\pi\)
\(152\) 12.6251 1.02403
\(153\) −2.57173 −0.207912
\(154\) −4.10708 −0.330958
\(155\) 2.51273 0.201827
\(156\) 7.32994 0.586865
\(157\) 16.1279 1.28715 0.643575 0.765383i \(-0.277450\pi\)
0.643575 + 0.765383i \(0.277450\pi\)
\(158\) −0.716007 −0.0569624
\(159\) −5.42570 −0.430286
\(160\) −5.89205 −0.465807
\(161\) −13.3394 −1.05129
\(162\) −12.0908 −0.949942
\(163\) 12.9992 1.01818 0.509089 0.860714i \(-0.329983\pi\)
0.509089 + 0.860714i \(0.329983\pi\)
\(164\) 5.85191 0.456957
\(165\) −0.633527 −0.0493200
\(166\) −21.7463 −1.68784
\(167\) 24.9283 1.92901 0.964505 0.264065i \(-0.0850633\pi\)
0.964505 + 0.264065i \(0.0850633\pi\)
\(168\) −3.08502 −0.238014
\(169\) −0.338981 −0.0260754
\(170\) 2.19643 0.168458
\(171\) 12.4676 0.953421
\(172\) 3.14780 0.240017
\(173\) 9.67419 0.735515 0.367758 0.929922i \(-0.380126\pi\)
0.367758 + 0.929922i \(0.380126\pi\)
\(174\) −11.8774 −0.900424
\(175\) −7.35449 −0.555947
\(176\) −0.386967 −0.0291687
\(177\) −3.13755 −0.235832
\(178\) −31.7424 −2.37919
\(179\) −14.1103 −1.05465 −0.527326 0.849663i \(-0.676805\pi\)
−0.527326 + 0.849663i \(0.676805\pi\)
\(180\) 7.83679 0.584120
\(181\) −4.06005 −0.301781 −0.150890 0.988550i \(-0.548214\pi\)
−0.150890 + 0.988550i \(0.548214\pi\)
\(182\) −14.6139 −1.08326
\(183\) 9.26117 0.684605
\(184\) 19.1906 1.41475
\(185\) 7.32598 0.538617
\(186\) 3.85398 0.282588
\(187\) 1.00000 0.0731272
\(188\) −11.7061 −0.853752
\(189\) −6.60042 −0.480110
\(190\) −10.6482 −0.772498
\(191\) 6.78214 0.490738 0.245369 0.969430i \(-0.421091\pi\)
0.245369 + 0.969430i \(0.421091\pi\)
\(192\) −8.53064 −0.615646
\(193\) −19.9960 −1.43934 −0.719671 0.694315i \(-0.755707\pi\)
−0.719671 + 0.694315i \(0.755707\pi\)
\(194\) −39.4626 −2.83325
\(195\) −2.25424 −0.161429
\(196\) −11.7200 −0.837143
\(197\) 7.21511 0.514055 0.257028 0.966404i \(-0.417257\pi\)
0.257028 + 0.966404i \(0.417257\pi\)
\(198\) 5.83493 0.414671
\(199\) 22.2752 1.57905 0.789523 0.613721i \(-0.210328\pi\)
0.789523 + 0.613721i \(0.210328\pi\)
\(200\) 10.5805 0.748154
\(201\) −2.81578 −0.198609
\(202\) 39.7206 2.79474
\(203\) 14.4802 1.01631
\(204\) 2.05999 0.144228
\(205\) −1.79969 −0.125696
\(206\) −20.0289 −1.39548
\(207\) 18.9513 1.31720
\(208\) −1.37692 −0.0954721
\(209\) −4.84794 −0.335339
\(210\) 2.60195 0.179551
\(211\) 18.0658 1.24370 0.621852 0.783135i \(-0.286381\pi\)
0.621852 + 0.783135i \(0.286381\pi\)
\(212\) −26.0978 −1.79240
\(213\) 9.24790 0.633655
\(214\) −24.8187 −1.69657
\(215\) −0.968068 −0.0660217
\(216\) 9.49566 0.646098
\(217\) −4.69853 −0.318957
\(218\) 33.0222 2.23655
\(219\) 1.85807 0.125557
\(220\) −3.04728 −0.205448
\(221\) 3.55823 0.239353
\(222\) 11.2365 0.754142
\(223\) −13.6552 −0.914420 −0.457210 0.889359i \(-0.651151\pi\)
−0.457210 + 0.889359i \(0.651151\pi\)
\(224\) 11.0175 0.736137
\(225\) 10.4485 0.696569
\(226\) −20.8493 −1.38687
\(227\) 24.1755 1.60459 0.802293 0.596931i \(-0.203613\pi\)
0.802293 + 0.596931i \(0.203613\pi\)
\(228\) −9.98673 −0.661388
\(229\) 3.55989 0.235244 0.117622 0.993058i \(-0.462473\pi\)
0.117622 + 0.993058i \(0.462473\pi\)
\(230\) −16.1856 −1.06725
\(231\) 1.18463 0.0779427
\(232\) −20.8319 −1.36768
\(233\) −4.44301 −0.291071 −0.145536 0.989353i \(-0.546491\pi\)
−0.145536 + 0.989353i \(0.546491\pi\)
\(234\) 20.7621 1.35726
\(235\) 3.60006 0.234842
\(236\) −15.0917 −0.982385
\(237\) 0.206522 0.0134150
\(238\) −4.10708 −0.266222
\(239\) 12.0797 0.781371 0.390686 0.920524i \(-0.372238\pi\)
0.390686 + 0.920524i \(0.372238\pi\)
\(240\) 0.245154 0.0158246
\(241\) −13.6638 −0.880165 −0.440082 0.897957i \(-0.645051\pi\)
−0.440082 + 0.897957i \(0.645051\pi\)
\(242\) −2.26888 −0.145849
\(243\) 14.4262 0.925443
\(244\) 44.5465 2.85180
\(245\) 3.60435 0.230274
\(246\) −2.76033 −0.175992
\(247\) −17.2501 −1.09760
\(248\) 6.75952 0.429230
\(249\) 6.27241 0.397498
\(250\) −19.9059 −1.25896
\(251\) 15.9799 1.00864 0.504322 0.863516i \(-0.331742\pi\)
0.504322 + 0.863516i \(0.331742\pi\)
\(252\) −14.6539 −0.923111
\(253\) −7.36907 −0.463290
\(254\) −14.5730 −0.914389
\(255\) −0.633527 −0.0396730
\(256\) −13.4141 −0.838379
\(257\) −13.6291 −0.850160 −0.425080 0.905156i \(-0.639754\pi\)
−0.425080 + 0.905156i \(0.639754\pi\)
\(258\) −1.48481 −0.0924400
\(259\) −13.6988 −0.851201
\(260\) −10.8429 −0.672451
\(261\) −20.5720 −1.27338
\(262\) −22.7233 −1.40385
\(263\) −28.3881 −1.75049 −0.875244 0.483682i \(-0.839299\pi\)
−0.875244 + 0.483682i \(0.839299\pi\)
\(264\) −1.70426 −0.104890
\(265\) 8.02606 0.493037
\(266\) 19.9109 1.22081
\(267\) 9.15563 0.560316
\(268\) −13.5440 −0.827329
\(269\) 21.8036 1.32939 0.664694 0.747116i \(-0.268562\pi\)
0.664694 + 0.747116i \(0.268562\pi\)
\(270\) −8.00877 −0.487398
\(271\) 15.1598 0.920894 0.460447 0.887687i \(-0.347689\pi\)
0.460447 + 0.887687i \(0.347689\pi\)
\(272\) −0.386967 −0.0234633
\(273\) 4.21518 0.255114
\(274\) 45.6404 2.75724
\(275\) −4.06284 −0.244999
\(276\) −15.1802 −0.913743
\(277\) 25.0059 1.50246 0.751230 0.660041i \(-0.229461\pi\)
0.751230 + 0.660041i \(0.229461\pi\)
\(278\) 51.0036 3.05899
\(279\) 6.67521 0.399634
\(280\) 4.56357 0.272725
\(281\) 19.1877 1.14464 0.572322 0.820029i \(-0.306043\pi\)
0.572322 + 0.820029i \(0.306043\pi\)
\(282\) 5.52171 0.328813
\(283\) 12.2974 0.731003 0.365501 0.930811i \(-0.380898\pi\)
0.365501 + 0.930811i \(0.380898\pi\)
\(284\) 44.4826 2.63956
\(285\) 3.07130 0.181928
\(286\) −8.07319 −0.477378
\(287\) 3.36522 0.198642
\(288\) −15.6526 −0.922337
\(289\) 1.00000 0.0588235
\(290\) 17.5699 1.03174
\(291\) 11.3824 0.667249
\(292\) 8.93738 0.523021
\(293\) 15.6074 0.911796 0.455898 0.890032i \(-0.349318\pi\)
0.455898 + 0.890032i \(0.349318\pi\)
\(294\) 5.52829 0.322416
\(295\) 4.64127 0.270225
\(296\) 19.7077 1.14549
\(297\) −3.64627 −0.211578
\(298\) −15.1704 −0.878799
\(299\) −26.2209 −1.51639
\(300\) −8.36943 −0.483209
\(301\) 1.81018 0.104337
\(302\) 47.9837 2.76115
\(303\) −11.4568 −0.658178
\(304\) 1.87599 0.107596
\(305\) −13.6997 −0.784445
\(306\) 5.83493 0.333561
\(307\) −9.02362 −0.515005 −0.257503 0.966278i \(-0.582900\pi\)
−0.257503 + 0.966278i \(0.582900\pi\)
\(308\) 5.69809 0.324679
\(309\) 5.77705 0.328645
\(310\) −5.70107 −0.323799
\(311\) 8.48774 0.481296 0.240648 0.970613i \(-0.422640\pi\)
0.240648 + 0.970613i \(0.422640\pi\)
\(312\) −6.06414 −0.343314
\(313\) 10.3944 0.587523 0.293762 0.955879i \(-0.405093\pi\)
0.293762 + 0.955879i \(0.405093\pi\)
\(314\) −36.5923 −2.06502
\(315\) 4.50665 0.253921
\(316\) 0.993375 0.0558817
\(317\) −31.8125 −1.78677 −0.893384 0.449293i \(-0.851676\pi\)
−0.893384 + 0.449293i \(0.851676\pi\)
\(318\) 12.3102 0.690324
\(319\) 7.99930 0.447875
\(320\) 12.6191 0.705430
\(321\) 7.15858 0.399553
\(322\) 30.2654 1.68662
\(323\) −4.84794 −0.269747
\(324\) 16.7745 0.931919
\(325\) −14.4565 −0.801905
\(326\) −29.4936 −1.63350
\(327\) −9.52477 −0.526721
\(328\) −4.84135 −0.267319
\(329\) −6.73172 −0.371132
\(330\) 1.43739 0.0791260
\(331\) 4.20246 0.230988 0.115494 0.993308i \(-0.463155\pi\)
0.115494 + 0.993308i \(0.463155\pi\)
\(332\) 30.1705 1.65582
\(333\) 19.4619 1.06650
\(334\) −56.5592 −3.09478
\(335\) 4.16529 0.227574
\(336\) −0.458411 −0.0250084
\(337\) 18.7531 1.02154 0.510772 0.859716i \(-0.329360\pi\)
0.510772 + 0.859716i \(0.329360\pi\)
\(338\) 0.769105 0.0418338
\(339\) 6.01367 0.326618
\(340\) −3.04728 −0.165262
\(341\) −2.59561 −0.140560
\(342\) −28.2874 −1.52961
\(343\) −19.4110 −1.04810
\(344\) −2.60421 −0.140410
\(345\) 4.66851 0.251344
\(346\) −21.9495 −1.18001
\(347\) 19.5899 1.05164 0.525819 0.850596i \(-0.323759\pi\)
0.525819 + 0.850596i \(0.323759\pi\)
\(348\) 16.4785 0.883341
\(349\) −21.4986 −1.15079 −0.575396 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(350\) 16.6864 0.891927
\(351\) −12.9743 −0.692516
\(352\) 6.08640 0.324406
\(353\) −7.00756 −0.372975 −0.186487 0.982457i \(-0.559710\pi\)
−0.186487 + 0.982457i \(0.559710\pi\)
\(354\) 7.11870 0.378355
\(355\) −13.6801 −0.726065
\(356\) 44.0388 2.33405
\(357\) 1.18463 0.0626971
\(358\) 32.0145 1.69202
\(359\) −2.25680 −0.119109 −0.0595547 0.998225i \(-0.518968\pi\)
−0.0595547 + 0.998225i \(0.518968\pi\)
\(360\) −6.48347 −0.341709
\(361\) 4.50256 0.236977
\(362\) 9.21174 0.484158
\(363\) 0.654424 0.0343483
\(364\) 20.2751 1.06271
\(365\) −2.74859 −0.143868
\(366\) −21.0124 −1.09834
\(367\) −19.8758 −1.03751 −0.518753 0.854924i \(-0.673604\pi\)
−0.518753 + 0.854924i \(0.673604\pi\)
\(368\) 2.85159 0.148649
\(369\) −4.78097 −0.248887
\(370\) −16.6217 −0.864123
\(371\) −15.0079 −0.779170
\(372\) −5.34694 −0.277226
\(373\) −15.3983 −0.797294 −0.398647 0.917104i \(-0.630520\pi\)
−0.398647 + 0.917104i \(0.630520\pi\)
\(374\) −2.26888 −0.117321
\(375\) 5.74156 0.296493
\(376\) 9.68455 0.499443
\(377\) 28.4634 1.46594
\(378\) 14.9755 0.770258
\(379\) −34.2454 −1.75907 −0.879533 0.475838i \(-0.842145\pi\)
−0.879533 + 0.475838i \(0.842145\pi\)
\(380\) 14.7731 0.757842
\(381\) 4.20336 0.215345
\(382\) −15.3878 −0.787310
\(383\) 29.4784 1.50628 0.753138 0.657862i \(-0.228539\pi\)
0.753138 + 0.657862i \(0.228539\pi\)
\(384\) 11.3888 0.581182
\(385\) −1.75238 −0.0893096
\(386\) 45.3684 2.30919
\(387\) −2.57173 −0.130728
\(388\) 54.7498 2.77950
\(389\) −11.9208 −0.604407 −0.302203 0.953243i \(-0.597722\pi\)
−0.302203 + 0.953243i \(0.597722\pi\)
\(390\) 5.11458 0.258987
\(391\) −7.36907 −0.372670
\(392\) 9.69610 0.489727
\(393\) 6.55421 0.330616
\(394\) −16.3702 −0.824718
\(395\) −0.305501 −0.0153714
\(396\) −8.09528 −0.406803
\(397\) −6.38995 −0.320703 −0.160351 0.987060i \(-0.551263\pi\)
−0.160351 + 0.987060i \(0.551263\pi\)
\(398\) −50.5396 −2.53332
\(399\) −5.74300 −0.287510
\(400\) 1.57219 0.0786093
\(401\) 2.67473 0.133570 0.0667848 0.997767i \(-0.478726\pi\)
0.0667848 + 0.997767i \(0.478726\pi\)
\(402\) 6.38865 0.318637
\(403\) −9.23579 −0.460067
\(404\) −55.1077 −2.74171
\(405\) −5.15882 −0.256344
\(406\) −32.8538 −1.63050
\(407\) −7.56763 −0.375113
\(408\) −1.70426 −0.0843733
\(409\) 3.75111 0.185481 0.0927403 0.995690i \(-0.470437\pi\)
0.0927403 + 0.995690i \(0.470437\pi\)
\(410\) 4.08326 0.201658
\(411\) −13.1643 −0.649347
\(412\) 27.7878 1.36900
\(413\) −8.67867 −0.427049
\(414\) −42.9981 −2.11324
\(415\) −9.27858 −0.455468
\(416\) 21.6568 1.06181
\(417\) −14.7112 −0.720412
\(418\) 10.9994 0.537997
\(419\) −26.5650 −1.29778 −0.648892 0.760881i \(-0.724767\pi\)
−0.648892 + 0.760881i \(0.724767\pi\)
\(420\) −3.60989 −0.176145
\(421\) −19.5653 −0.953553 −0.476777 0.879024i \(-0.658195\pi\)
−0.476777 + 0.879024i \(0.658195\pi\)
\(422\) −40.9891 −1.99532
\(423\) 9.56377 0.465006
\(424\) 21.5910 1.04855
\(425\) −4.06284 −0.197077
\(426\) −20.9823 −1.01660
\(427\) 25.6170 1.23970
\(428\) 34.4330 1.66438
\(429\) 2.32859 0.112426
\(430\) 2.19643 0.105921
\(431\) 34.0784 1.64150 0.820750 0.571287i \(-0.193556\pi\)
0.820750 + 0.571287i \(0.193556\pi\)
\(432\) 1.41099 0.0678861
\(433\) −7.36781 −0.354074 −0.177037 0.984204i \(-0.556651\pi\)
−0.177037 + 0.984204i \(0.556651\pi\)
\(434\) 10.6604 0.511715
\(435\) −5.06777 −0.242981
\(436\) −45.8144 −2.19411
\(437\) 35.7248 1.70895
\(438\) −4.21574 −0.201436
\(439\) −6.48225 −0.309381 −0.154691 0.987963i \(-0.549438\pi\)
−0.154691 + 0.987963i \(0.549438\pi\)
\(440\) 2.52105 0.120186
\(441\) 9.57516 0.455960
\(442\) −8.07319 −0.384002
\(443\) −10.8793 −0.516893 −0.258447 0.966026i \(-0.583211\pi\)
−0.258447 + 0.966026i \(0.583211\pi\)
\(444\) −15.5893 −0.739834
\(445\) −13.5436 −0.642030
\(446\) 30.9820 1.46704
\(447\) 4.37569 0.206963
\(448\) −23.5964 −1.11482
\(449\) −20.0663 −0.946987 −0.473494 0.880797i \(-0.657007\pi\)
−0.473494 + 0.880797i \(0.657007\pi\)
\(450\) −23.7064 −1.11753
\(451\) 1.85905 0.0875392
\(452\) 28.9259 1.36056
\(453\) −13.8402 −0.650269
\(454\) −54.8513 −2.57430
\(455\) −6.23538 −0.292319
\(456\) 8.26214 0.386910
\(457\) 2.75446 0.128848 0.0644241 0.997923i \(-0.479479\pi\)
0.0644241 + 0.997923i \(0.479479\pi\)
\(458\) −8.07695 −0.377411
\(459\) −3.64627 −0.170193
\(460\) 22.4556 1.04700
\(461\) 17.8701 0.832296 0.416148 0.909297i \(-0.363380\pi\)
0.416148 + 0.909297i \(0.363380\pi\)
\(462\) −2.68777 −0.125046
\(463\) −15.5482 −0.722587 −0.361294 0.932452i \(-0.617665\pi\)
−0.361294 + 0.932452i \(0.617665\pi\)
\(464\) −3.09546 −0.143703
\(465\) 1.64439 0.0762568
\(466\) 10.0806 0.466977
\(467\) −8.86413 −0.410183 −0.205091 0.978743i \(-0.565749\pi\)
−0.205091 + 0.978743i \(0.565749\pi\)
\(468\) −28.8049 −1.33151
\(469\) −7.78863 −0.359646
\(470\) −8.16809 −0.376766
\(471\) 10.5545 0.486326
\(472\) 12.4855 0.574693
\(473\) 1.00000 0.0459800
\(474\) −0.468572 −0.0215222
\(475\) 19.6964 0.903735
\(476\) 5.69809 0.261171
\(477\) 21.3217 0.976254
\(478\) −27.4073 −1.25358
\(479\) 39.4044 1.80044 0.900218 0.435440i \(-0.143407\pi\)
0.900218 + 0.435440i \(0.143407\pi\)
\(480\) −3.85590 −0.175997
\(481\) −26.9274 −1.22778
\(482\) 31.0015 1.41208
\(483\) −8.72960 −0.397211
\(484\) 3.14780 0.143082
\(485\) −16.8377 −0.764558
\(486\) −32.7313 −1.48472
\(487\) 26.3199 1.19267 0.596335 0.802736i \(-0.296623\pi\)
0.596335 + 0.802736i \(0.296623\pi\)
\(488\) −36.8538 −1.66829
\(489\) 8.50700 0.384700
\(490\) −8.17782 −0.369436
\(491\) 10.5119 0.474394 0.237197 0.971462i \(-0.423771\pi\)
0.237197 + 0.971462i \(0.423771\pi\)
\(492\) 3.82963 0.172653
\(493\) 7.99930 0.360270
\(494\) 39.1384 1.76092
\(495\) 2.48961 0.111900
\(496\) 1.00442 0.0450996
\(497\) 25.5803 1.14743
\(498\) −14.2313 −0.637721
\(499\) 27.3220 1.22310 0.611550 0.791206i \(-0.290546\pi\)
0.611550 + 0.791206i \(0.290546\pi\)
\(500\) 27.6170 1.23507
\(501\) 16.3137 0.728841
\(502\) −36.2565 −1.61821
\(503\) 4.46103 0.198907 0.0994537 0.995042i \(-0.468290\pi\)
0.0994537 + 0.995042i \(0.468290\pi\)
\(504\) 12.1234 0.540018
\(505\) 16.9477 0.754164
\(506\) 16.7195 0.743273
\(507\) −0.221837 −0.00985213
\(508\) 20.2183 0.897041
\(509\) 10.2339 0.453612 0.226806 0.973940i \(-0.427172\pi\)
0.226806 + 0.973940i \(0.427172\pi\)
\(510\) 1.43739 0.0636489
\(511\) 5.13956 0.227361
\(512\) −4.37072 −0.193160
\(513\) 17.6769 0.780455
\(514\) 30.9227 1.36394
\(515\) −8.54580 −0.376573
\(516\) 2.05999 0.0906862
\(517\) −3.71881 −0.163553
\(518\) 31.0808 1.36561
\(519\) 6.33102 0.277901
\(520\) 8.97049 0.393382
\(521\) 23.7011 1.03837 0.519183 0.854663i \(-0.326236\pi\)
0.519183 + 0.854663i \(0.326236\pi\)
\(522\) 46.6754 2.04293
\(523\) −38.7691 −1.69526 −0.847628 0.530591i \(-0.821970\pi\)
−0.847628 + 0.530591i \(0.821970\pi\)
\(524\) 31.5260 1.37722
\(525\) −4.81295 −0.210054
\(526\) 64.4092 2.80837
\(527\) −2.59561 −0.113067
\(528\) −0.253240 −0.0110209
\(529\) 31.3032 1.36101
\(530\) −18.2101 −0.790998
\(531\) 12.3298 0.535068
\(532\) −27.6240 −1.19765
\(533\) 6.61493 0.286524
\(534\) −20.7730 −0.898935
\(535\) −10.5895 −0.457822
\(536\) 11.2051 0.483986
\(537\) −9.23411 −0.398481
\(538\) −49.4696 −2.13279
\(539\) −3.72324 −0.160371
\(540\) 11.1112 0.478151
\(541\) −11.3462 −0.487812 −0.243906 0.969799i \(-0.578429\pi\)
−0.243906 + 0.969799i \(0.578429\pi\)
\(542\) −34.3958 −1.47742
\(543\) −2.65699 −0.114022
\(544\) 6.08640 0.260952
\(545\) 14.0897 0.603536
\(546\) −9.56371 −0.409289
\(547\) 18.4261 0.787842 0.393921 0.919144i \(-0.371118\pi\)
0.393921 + 0.919144i \(0.371118\pi\)
\(548\) −63.3206 −2.70492
\(549\) −36.3942 −1.55327
\(550\) 9.21809 0.393061
\(551\) −38.7802 −1.65209
\(552\) 12.5588 0.534538
\(553\) 0.571253 0.0242922
\(554\) −56.7353 −2.41045
\(555\) 4.79430 0.203507
\(556\) −70.7614 −3.00095
\(557\) −0.497729 −0.0210895 −0.0105447 0.999944i \(-0.503357\pi\)
−0.0105447 + 0.999944i \(0.503357\pi\)
\(558\) −15.1452 −0.641148
\(559\) 3.55823 0.150497
\(560\) 0.678113 0.0286555
\(561\) 0.654424 0.0276298
\(562\) −43.5346 −1.83640
\(563\) 23.0984 0.973480 0.486740 0.873547i \(-0.338186\pi\)
0.486740 + 0.873547i \(0.338186\pi\)
\(564\) −7.66072 −0.322575
\(565\) −8.89584 −0.374251
\(566\) −27.9012 −1.17277
\(567\) 9.64643 0.405112
\(568\) −36.8010 −1.54414
\(569\) −5.81738 −0.243877 −0.121939 0.992538i \(-0.538911\pi\)
−0.121939 + 0.992538i \(0.538911\pi\)
\(570\) −6.96841 −0.291874
\(571\) −22.2688 −0.931920 −0.465960 0.884806i \(-0.654291\pi\)
−0.465960 + 0.884806i \(0.654291\pi\)
\(572\) 11.2006 0.468320
\(573\) 4.43839 0.185417
\(574\) −7.63526 −0.318690
\(575\) 29.9394 1.24856
\(576\) 33.5234 1.39681
\(577\) −14.5687 −0.606504 −0.303252 0.952910i \(-0.598072\pi\)
−0.303252 + 0.952910i \(0.598072\pi\)
\(578\) −2.26888 −0.0943728
\(579\) −13.0858 −0.543829
\(580\) −24.3761 −1.01216
\(581\) 17.3499 0.719797
\(582\) −25.8253 −1.07049
\(583\) −8.29080 −0.343370
\(584\) −7.39400 −0.305966
\(585\) 8.85861 0.366258
\(586\) −35.4113 −1.46283
\(587\) 28.5016 1.17639 0.588193 0.808720i \(-0.299839\pi\)
0.588193 + 0.808720i \(0.299839\pi\)
\(588\) −7.66985 −0.316299
\(589\) 12.5834 0.518489
\(590\) −10.5305 −0.433532
\(591\) 4.72174 0.194226
\(592\) 2.92842 0.120357
\(593\) 40.9865 1.68312 0.841558 0.540167i \(-0.181639\pi\)
0.841558 + 0.540167i \(0.181639\pi\)
\(594\) 8.27294 0.339443
\(595\) −1.75238 −0.0718406
\(596\) 21.0472 0.862126
\(597\) 14.5774 0.596614
\(598\) 59.4919 2.43280
\(599\) 8.64990 0.353425 0.176713 0.984262i \(-0.443454\pi\)
0.176713 + 0.984262i \(0.443454\pi\)
\(600\) 6.92413 0.282676
\(601\) 1.52981 0.0624024 0.0312012 0.999513i \(-0.490067\pi\)
0.0312012 + 0.999513i \(0.490067\pi\)
\(602\) −4.10708 −0.167392
\(603\) 11.0653 0.450615
\(604\) −66.5718 −2.70877
\(605\) −0.968068 −0.0393576
\(606\) 25.9941 1.05594
\(607\) −19.8845 −0.807088 −0.403544 0.914960i \(-0.632222\pi\)
−0.403544 + 0.914960i \(0.632222\pi\)
\(608\) −29.5065 −1.19665
\(609\) 9.47618 0.383994
\(610\) 31.0830 1.25852
\(611\) −13.2324 −0.535325
\(612\) −8.09528 −0.327232
\(613\) −22.9660 −0.927586 −0.463793 0.885943i \(-0.653512\pi\)
−0.463793 + 0.885943i \(0.653512\pi\)
\(614\) 20.4735 0.826242
\(615\) −1.17776 −0.0474918
\(616\) −4.71409 −0.189936
\(617\) −42.0033 −1.69099 −0.845494 0.533985i \(-0.820694\pi\)
−0.845494 + 0.533985i \(0.820694\pi\)
\(618\) −13.1074 −0.527257
\(619\) 17.8147 0.716033 0.358017 0.933715i \(-0.383453\pi\)
0.358017 + 0.933715i \(0.383453\pi\)
\(620\) 7.90956 0.317656
\(621\) 26.8696 1.07824
\(622\) −19.2576 −0.772160
\(623\) 25.3251 1.01463
\(624\) −0.901088 −0.0360724
\(625\) 11.8209 0.472837
\(626\) −23.5835 −0.942586
\(627\) −3.17261 −0.126702
\(628\) 50.7675 2.02584
\(629\) −7.56763 −0.301741
\(630\) −10.2250 −0.407375
\(631\) −40.0166 −1.59304 −0.796519 0.604614i \(-0.793327\pi\)
−0.796519 + 0.604614i \(0.793327\pi\)
\(632\) −0.821831 −0.0326907
\(633\) 11.8227 0.469911
\(634\) 72.1786 2.86658
\(635\) −6.21789 −0.246750
\(636\) −17.0790 −0.677227
\(637\) −13.2482 −0.524911
\(638\) −18.1494 −0.718542
\(639\) −36.3420 −1.43767
\(640\) −16.8471 −0.665940
\(641\) −24.7790 −0.978710 −0.489355 0.872085i \(-0.662768\pi\)
−0.489355 + 0.872085i \(0.662768\pi\)
\(642\) −16.2419 −0.641018
\(643\) 33.7086 1.32934 0.664668 0.747139i \(-0.268573\pi\)
0.664668 + 0.747139i \(0.268573\pi\)
\(644\) −41.9896 −1.65462
\(645\) −0.633527 −0.0249451
\(646\) 10.9994 0.432765
\(647\) 13.0771 0.514112 0.257056 0.966396i \(-0.417247\pi\)
0.257056 + 0.966396i \(0.417247\pi\)
\(648\) −13.8778 −0.545171
\(649\) −4.79436 −0.188195
\(650\) 32.8001 1.28653
\(651\) −3.07483 −0.120512
\(652\) 40.9189 1.60251
\(653\) −1.62862 −0.0637329 −0.0318665 0.999492i \(-0.510145\pi\)
−0.0318665 + 0.999492i \(0.510145\pi\)
\(654\) 21.6105 0.845038
\(655\) −9.69544 −0.378832
\(656\) −0.719390 −0.0280875
\(657\) −7.30178 −0.284870
\(658\) 15.2734 0.595421
\(659\) 18.9684 0.738902 0.369451 0.929250i \(-0.379546\pi\)
0.369451 + 0.929250i \(0.379546\pi\)
\(660\) −1.99421 −0.0776247
\(661\) −15.6090 −0.607121 −0.303561 0.952812i \(-0.598176\pi\)
−0.303561 + 0.952812i \(0.598176\pi\)
\(662\) −9.53485 −0.370583
\(663\) 2.32859 0.0904350
\(664\) −24.9604 −0.968651
\(665\) 8.49544 0.329439
\(666\) −44.1566 −1.71103
\(667\) −58.9474 −2.28245
\(668\) 78.4692 3.03607
\(669\) −8.93629 −0.345497
\(670\) −9.45052 −0.365105
\(671\) 14.1516 0.546318
\(672\) 7.21011 0.278136
\(673\) 36.4052 1.40332 0.701659 0.712513i \(-0.252443\pi\)
0.701659 + 0.712513i \(0.252443\pi\)
\(674\) −42.5483 −1.63890
\(675\) 14.8142 0.570200
\(676\) −1.06704 −0.0410401
\(677\) −0.0296180 −0.00113831 −0.000569156 1.00000i \(-0.500181\pi\)
−0.000569156 1.00000i \(0.500181\pi\)
\(678\) −13.6443 −0.524005
\(679\) 31.4846 1.20827
\(680\) 2.52105 0.0966780
\(681\) 15.8210 0.606264
\(682\) 5.88912 0.225506
\(683\) −36.6564 −1.40262 −0.701309 0.712858i \(-0.747401\pi\)
−0.701309 + 0.712858i \(0.747401\pi\)
\(684\) 39.2455 1.50059
\(685\) 19.4735 0.744045
\(686\) 44.0412 1.68150
\(687\) 2.32968 0.0888828
\(688\) −0.386967 −0.0147530
\(689\) −29.5006 −1.12388
\(690\) −10.5923 −0.403241
\(691\) 13.4801 0.512805 0.256403 0.966570i \(-0.417463\pi\)
0.256403 + 0.966570i \(0.417463\pi\)
\(692\) 30.4524 1.15763
\(693\) −4.65530 −0.176840
\(694\) −44.4470 −1.68718
\(695\) 21.7618 0.825474
\(696\) −13.6329 −0.516752
\(697\) 1.85905 0.0704165
\(698\) 48.7775 1.84626
\(699\) −2.90761 −0.109976
\(700\) −23.1504 −0.875004
\(701\) −15.7723 −0.595713 −0.297856 0.954611i \(-0.596272\pi\)
−0.297856 + 0.954611i \(0.596272\pi\)
\(702\) 29.4370 1.11103
\(703\) 36.6874 1.38369
\(704\) −13.0353 −0.491288
\(705\) 2.35597 0.0887308
\(706\) 15.8993 0.598378
\(707\) −31.6904 −1.19184
\(708\) −9.87636 −0.371176
\(709\) 27.8722 1.04676 0.523381 0.852099i \(-0.324670\pi\)
0.523381 + 0.852099i \(0.324670\pi\)
\(710\) 31.0385 1.16485
\(711\) −0.811581 −0.0304366
\(712\) −36.4338 −1.36542
\(713\) 19.1272 0.716321
\(714\) −2.68777 −0.100587
\(715\) −3.44461 −0.128821
\(716\) −44.4163 −1.65992
\(717\) 7.90525 0.295227
\(718\) 5.12040 0.191092
\(719\) 5.58871 0.208424 0.104212 0.994555i \(-0.466768\pi\)
0.104212 + 0.994555i \(0.466768\pi\)
\(720\) −0.963396 −0.0359037
\(721\) 15.9797 0.595116
\(722\) −10.2158 −0.380191
\(723\) −8.94194 −0.332554
\(724\) −12.7802 −0.474972
\(725\) −32.4999 −1.20702
\(726\) −1.48481 −0.0551063
\(727\) 30.6023 1.13498 0.567488 0.823382i \(-0.307915\pi\)
0.567488 + 0.823382i \(0.307915\pi\)
\(728\) −16.7738 −0.621680
\(729\) −6.54607 −0.242447
\(730\) 6.23620 0.230812
\(731\) 1.00000 0.0369863
\(732\) 29.1523 1.07750
\(733\) 34.0003 1.25583 0.627914 0.778283i \(-0.283909\pi\)
0.627914 + 0.778283i \(0.283909\pi\)
\(734\) 45.0956 1.66451
\(735\) 2.35877 0.0870047
\(736\) −44.8511 −1.65323
\(737\) −4.30268 −0.158491
\(738\) 10.8474 0.399299
\(739\) 40.7938 1.50062 0.750312 0.661084i \(-0.229903\pi\)
0.750312 + 0.661084i \(0.229903\pi\)
\(740\) 23.0607 0.847728
\(741\) −11.2889 −0.414708
\(742\) 34.0510 1.25005
\(743\) −21.7604 −0.798313 −0.399157 0.916883i \(-0.630697\pi\)
−0.399157 + 0.916883i \(0.630697\pi\)
\(744\) 4.42359 0.162177
\(745\) −6.47281 −0.237145
\(746\) 34.9368 1.27913
\(747\) −24.6491 −0.901863
\(748\) 3.14780 0.115095
\(749\) 19.8011 0.723518
\(750\) −13.0269 −0.475674
\(751\) 16.4297 0.599528 0.299764 0.954013i \(-0.403092\pi\)
0.299764 + 0.954013i \(0.403092\pi\)
\(752\) 1.43905 0.0524769
\(753\) 10.4576 0.381098
\(754\) −64.5798 −2.35186
\(755\) 20.4734 0.745102
\(756\) −20.7768 −0.755644
\(757\) 36.0582 1.31056 0.655279 0.755387i \(-0.272551\pi\)
0.655279 + 0.755387i \(0.272551\pi\)
\(758\) 77.6984 2.82213
\(759\) −4.82250 −0.175046
\(760\) −12.2219 −0.443336
\(761\) 19.7761 0.716885 0.358442 0.933552i \(-0.383308\pi\)
0.358442 + 0.933552i \(0.383308\pi\)
\(762\) −9.53690 −0.345485
\(763\) −26.3462 −0.953796
\(764\) 21.3488 0.772372
\(765\) 2.48961 0.0900120
\(766\) −66.8829 −2.41658
\(767\) −17.0595 −0.615981
\(768\) −8.77849 −0.316766
\(769\) −16.3780 −0.590605 −0.295302 0.955404i \(-0.595420\pi\)
−0.295302 + 0.955404i \(0.595420\pi\)
\(770\) 3.97593 0.143283
\(771\) −8.91921 −0.321218
\(772\) −62.9433 −2.26538
\(773\) 2.86226 0.102948 0.0514742 0.998674i \(-0.483608\pi\)
0.0514742 + 0.998674i \(0.483608\pi\)
\(774\) 5.83493 0.209732
\(775\) 10.5456 0.378808
\(776\) −45.2951 −1.62600
\(777\) −8.96481 −0.321611
\(778\) 27.0467 0.969672
\(779\) −9.01256 −0.322909
\(780\) −7.09588 −0.254073
\(781\) 14.1314 0.505660
\(782\) 16.7195 0.597888
\(783\) −29.1676 −1.04237
\(784\) 1.44077 0.0514561
\(785\) −15.6130 −0.557250
\(786\) −14.8707 −0.530420
\(787\) 47.8343 1.70511 0.852554 0.522639i \(-0.175052\pi\)
0.852554 + 0.522639i \(0.175052\pi\)
\(788\) 22.7117 0.809071
\(789\) −18.5779 −0.661390
\(790\) 0.693143 0.0246609
\(791\) 16.6342 0.591446
\(792\) 6.69732 0.237979
\(793\) 50.3548 1.78815
\(794\) 14.4980 0.514515
\(795\) 5.25245 0.186285
\(796\) 70.1178 2.48526
\(797\) 31.3080 1.10899 0.554494 0.832188i \(-0.312912\pi\)
0.554494 + 0.832188i \(0.312912\pi\)
\(798\) 13.0302 0.461263
\(799\) −3.71881 −0.131562
\(800\) −24.7281 −0.874270
\(801\) −35.9794 −1.27127
\(802\) −6.06863 −0.214291
\(803\) 2.83925 0.100195
\(804\) −8.86349 −0.312591
\(805\) 12.9134 0.455138
\(806\) 20.9549 0.738103
\(807\) 14.2688 0.502285
\(808\) 45.5913 1.60389
\(809\) −7.12766 −0.250595 −0.125298 0.992119i \(-0.539989\pi\)
−0.125298 + 0.992119i \(0.539989\pi\)
\(810\) 11.7047 0.411262
\(811\) 43.1598 1.51555 0.757773 0.652518i \(-0.226287\pi\)
0.757773 + 0.652518i \(0.226287\pi\)
\(812\) 45.5807 1.59957
\(813\) 9.92095 0.347943
\(814\) 17.1700 0.601808
\(815\) −12.5841 −0.440803
\(816\) −0.253240 −0.00886518
\(817\) −4.84794 −0.169608
\(818\) −8.51081 −0.297574
\(819\) −16.5646 −0.578815
\(820\) −5.66505 −0.197832
\(821\) 17.8483 0.622911 0.311456 0.950261i \(-0.399184\pi\)
0.311456 + 0.950261i \(0.399184\pi\)
\(822\) 29.8681 1.04177
\(823\) −28.9802 −1.01019 −0.505094 0.863065i \(-0.668542\pi\)
−0.505094 + 0.863065i \(0.668542\pi\)
\(824\) −22.9891 −0.800865
\(825\) −2.65882 −0.0925683
\(826\) 19.6908 0.685131
\(827\) 30.6810 1.06688 0.533441 0.845838i \(-0.320899\pi\)
0.533441 + 0.845838i \(0.320899\pi\)
\(828\) 59.6547 2.07314
\(829\) 31.1394 1.08151 0.540757 0.841179i \(-0.318138\pi\)
0.540757 + 0.841179i \(0.318138\pi\)
\(830\) 21.0519 0.730724
\(831\) 16.3645 0.567677
\(832\) −46.3828 −1.60803
\(833\) −3.72324 −0.129003
\(834\) 33.3779 1.15578
\(835\) −24.1323 −0.835133
\(836\) −15.2603 −0.527790
\(837\) 9.46431 0.327134
\(838\) 60.2726 2.08208
\(839\) −51.9366 −1.79305 −0.896525 0.442993i \(-0.853917\pi\)
−0.896525 + 0.442993i \(0.853917\pi\)
\(840\) 2.98651 0.103044
\(841\) 34.9888 1.20651
\(842\) 44.3912 1.52982
\(843\) 12.5569 0.432483
\(844\) 56.8676 1.95746
\(845\) 0.328156 0.0112889
\(846\) −21.6990 −0.746027
\(847\) 1.81018 0.0621986
\(848\) 3.20827 0.110172
\(849\) 8.04769 0.276196
\(850\) 9.21809 0.316178
\(851\) 55.7664 1.91165
\(852\) 29.1105 0.997309
\(853\) −7.03745 −0.240958 −0.120479 0.992716i \(-0.538443\pi\)
−0.120479 + 0.992716i \(0.538443\pi\)
\(854\) −58.1219 −1.98889
\(855\) −12.0695 −0.412768
\(856\) −28.4868 −0.973659
\(857\) 32.9687 1.12619 0.563094 0.826393i \(-0.309611\pi\)
0.563094 + 0.826393i \(0.309611\pi\)
\(858\) −5.28329 −0.180368
\(859\) −22.6709 −0.773520 −0.386760 0.922180i \(-0.626406\pi\)
−0.386760 + 0.922180i \(0.626406\pi\)
\(860\) −3.04728 −0.103911
\(861\) 2.20228 0.0750535
\(862\) −77.3198 −2.63352
\(863\) −41.5480 −1.41431 −0.707155 0.707058i \(-0.750022\pi\)
−0.707155 + 0.707058i \(0.750022\pi\)
\(864\) −22.1927 −0.755010
\(865\) −9.36528 −0.318429
\(866\) 16.7166 0.568054
\(867\) 0.654424 0.0222254
\(868\) −14.7900 −0.502006
\(869\) 0.315578 0.0107052
\(870\) 11.4981 0.389824
\(871\) −15.3099 −0.518757
\(872\) 37.9028 1.28355
\(873\) −44.7302 −1.51389
\(874\) −81.0552 −2.74173
\(875\) 15.8815 0.536894
\(876\) 5.84884 0.197614
\(877\) 42.8331 1.44637 0.723185 0.690655i \(-0.242678\pi\)
0.723185 + 0.690655i \(0.242678\pi\)
\(878\) 14.7074 0.496352
\(879\) 10.2139 0.344506
\(880\) 0.374610 0.0126281
\(881\) 28.0970 0.946612 0.473306 0.880898i \(-0.343061\pi\)
0.473306 + 0.880898i \(0.343061\pi\)
\(882\) −21.7249 −0.731514
\(883\) 29.1559 0.981172 0.490586 0.871393i \(-0.336783\pi\)
0.490586 + 0.871393i \(0.336783\pi\)
\(884\) 11.2006 0.376717
\(885\) 3.03736 0.102100
\(886\) 24.6839 0.829271
\(887\) −43.5924 −1.46369 −0.731845 0.681471i \(-0.761341\pi\)
−0.731845 + 0.681471i \(0.761341\pi\)
\(888\) 12.8972 0.432801
\(889\) 11.6268 0.389950
\(890\) 30.7288 1.03003
\(891\) 5.32898 0.178528
\(892\) −42.9838 −1.43920
\(893\) 18.0286 0.603303
\(894\) −9.92789 −0.332038
\(895\) 13.6597 0.456594
\(896\) 31.5022 1.05242
\(897\) −17.1596 −0.572941
\(898\) 45.5280 1.51929
\(899\) −20.7631 −0.692487
\(900\) 32.8899 1.09633
\(901\) −8.29080 −0.276207
\(902\) −4.21795 −0.140442
\(903\) 1.18463 0.0394219
\(904\) −23.9308 −0.795926
\(905\) 3.93040 0.130651
\(906\) 31.4017 1.04325
\(907\) −16.2688 −0.540195 −0.270098 0.962833i \(-0.587056\pi\)
−0.270098 + 0.962833i \(0.587056\pi\)
\(908\) 76.0996 2.52546
\(909\) 45.0226 1.49331
\(910\) 14.1473 0.468978
\(911\) −11.0011 −0.364484 −0.182242 0.983254i \(-0.558335\pi\)
−0.182242 + 0.983254i \(0.558335\pi\)
\(912\) 1.22769 0.0406530
\(913\) 9.58463 0.317205
\(914\) −6.24952 −0.206716
\(915\) −8.96544 −0.296388
\(916\) 11.2058 0.370251
\(917\) 18.1294 0.598686
\(918\) 8.27294 0.273048
\(919\) 11.3109 0.373111 0.186556 0.982444i \(-0.440268\pi\)
0.186556 + 0.982444i \(0.440268\pi\)
\(920\) −18.5778 −0.612493
\(921\) −5.90527 −0.194585
\(922\) −40.5451 −1.33528
\(923\) 50.2826 1.65507
\(924\) 3.72896 0.122674
\(925\) 30.7461 1.01093
\(926\) 35.2770 1.15927
\(927\) −22.7024 −0.745645
\(928\) 48.6869 1.59823
\(929\) 51.7569 1.69809 0.849044 0.528322i \(-0.177179\pi\)
0.849044 + 0.528322i \(0.177179\pi\)
\(930\) −3.73092 −0.122342
\(931\) 18.0501 0.591567
\(932\) −13.9857 −0.458117
\(933\) 5.55458 0.181849
\(934\) 20.1116 0.658072
\(935\) −0.968068 −0.0316592
\(936\) 23.8306 0.778928
\(937\) 13.0178 0.425272 0.212636 0.977132i \(-0.431795\pi\)
0.212636 + 0.977132i \(0.431795\pi\)
\(938\) 17.6714 0.576993
\(939\) 6.80231 0.221985
\(940\) 11.3323 0.369618
\(941\) −27.7311 −0.904009 −0.452004 0.892016i \(-0.649291\pi\)
−0.452004 + 0.892016i \(0.649291\pi\)
\(942\) −23.9469 −0.780231
\(943\) −13.6995 −0.446116
\(944\) 1.85526 0.0603835
\(945\) 6.38966 0.207856
\(946\) −2.26888 −0.0737675
\(947\) 12.6634 0.411504 0.205752 0.978604i \(-0.434036\pi\)
0.205752 + 0.978604i \(0.434036\pi\)
\(948\) 0.650088 0.0211139
\(949\) 10.1027 0.327948
\(950\) −44.6888 −1.44990
\(951\) −20.8189 −0.675098
\(952\) −4.71409 −0.152785
\(953\) 53.2090 1.72361 0.861805 0.507240i \(-0.169334\pi\)
0.861805 + 0.507240i \(0.169334\pi\)
\(954\) −48.3763 −1.56624
\(955\) −6.56557 −0.212457
\(956\) 38.0245 1.22980
\(957\) 5.23493 0.169221
\(958\) −89.4038 −2.88851
\(959\) −36.4134 −1.17585
\(960\) 8.25825 0.266534
\(961\) −24.2628 −0.782671
\(962\) 61.0949 1.96978
\(963\) −28.1315 −0.906525
\(964\) −43.0110 −1.38529
\(965\) 19.3575 0.623139
\(966\) 19.8064 0.637260
\(967\) −28.9666 −0.931502 −0.465751 0.884916i \(-0.654216\pi\)
−0.465751 + 0.884916i \(0.654216\pi\)
\(968\) −2.60421 −0.0837025
\(969\) −3.17261 −0.101919
\(970\) 38.2025 1.22661
\(971\) 3.85560 0.123732 0.0618661 0.998084i \(-0.480295\pi\)
0.0618661 + 0.998084i \(0.480295\pi\)
\(972\) 45.4108 1.45655
\(973\) −40.6923 −1.30453
\(974\) −59.7166 −1.91344
\(975\) −9.46071 −0.302985
\(976\) −5.47621 −0.175289
\(977\) −54.2208 −1.73468 −0.867339 0.497719i \(-0.834171\pi\)
−0.867339 + 0.497719i \(0.834171\pi\)
\(978\) −19.3013 −0.617188
\(979\) 13.9904 0.447134
\(980\) 11.3458 0.362427
\(981\) 37.4301 1.19505
\(982\) −23.8501 −0.761087
\(983\) −22.7208 −0.724680 −0.362340 0.932046i \(-0.618022\pi\)
−0.362340 + 0.932046i \(0.618022\pi\)
\(984\) −3.16830 −0.101002
\(985\) −6.98472 −0.222552
\(986\) −18.1494 −0.577995
\(987\) −4.40540 −0.140225
\(988\) −54.2999 −1.72751
\(989\) −7.36907 −0.234323
\(990\) −5.64862 −0.179525
\(991\) −12.2064 −0.387750 −0.193875 0.981026i \(-0.562106\pi\)
−0.193875 + 0.981026i \(0.562106\pi\)
\(992\) −15.7979 −0.501585
\(993\) 2.75019 0.0872746
\(994\) −58.0386 −1.84087
\(995\) −21.5639 −0.683622
\(996\) 19.7443 0.625622
\(997\) 15.7306 0.498192 0.249096 0.968479i \(-0.419866\pi\)
0.249096 + 0.968479i \(0.419866\pi\)
\(998\) −61.9902 −1.96226
\(999\) 27.5936 0.873024
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 \(a_p\))