Properties

Label 8041.2.a.j.1.5
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 1.5
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.57949 q^{2}\) \(+2.85867 q^{3}\) \(+4.65376 q^{4}\) \(+3.17304 q^{5}\) \(-7.37390 q^{6}\) \(-3.48304 q^{7}\) \(-6.84534 q^{8}\) \(+5.17198 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.57949 q^{2}\) \(+2.85867 q^{3}\) \(+4.65376 q^{4}\) \(+3.17304 q^{5}\) \(-7.37390 q^{6}\) \(-3.48304 q^{7}\) \(-6.84534 q^{8}\) \(+5.17198 q^{9}\) \(-8.18483 q^{10}\) \(+1.00000 q^{11}\) \(+13.3035 q^{12}\) \(+1.45531 q^{13}\) \(+8.98446 q^{14}\) \(+9.07068 q^{15}\) \(+8.34995 q^{16}\) \(+1.00000 q^{17}\) \(-13.3411 q^{18}\) \(+7.42589 q^{19}\) \(+14.7666 q^{20}\) \(-9.95685 q^{21}\) \(-2.57949 q^{22}\) \(+6.93883 q^{23}\) \(-19.5685 q^{24}\) \(+5.06821 q^{25}\) \(-3.75394 q^{26}\) \(+6.20897 q^{27}\) \(-16.2092 q^{28}\) \(-6.94836 q^{29}\) \(-23.3977 q^{30}\) \(+3.05829 q^{31}\) \(-7.84792 q^{32}\) \(+2.85867 q^{33}\) \(-2.57949 q^{34}\) \(-11.0518 q^{35}\) \(+24.0692 q^{36}\) \(+0.00693868 q^{37}\) \(-19.1550 q^{38}\) \(+4.16023 q^{39}\) \(-21.7206 q^{40}\) \(+9.65861 q^{41}\) \(+25.6836 q^{42}\) \(+1.00000 q^{43}\) \(+4.65376 q^{44}\) \(+16.4109 q^{45}\) \(-17.8986 q^{46}\) \(-7.07691 q^{47}\) \(+23.8697 q^{48}\) \(+5.13155 q^{49}\) \(-13.0734 q^{50}\) \(+2.85867 q^{51}\) \(+6.77264 q^{52}\) \(+7.85931 q^{53}\) \(-16.0160 q^{54}\) \(+3.17304 q^{55}\) \(+23.8426 q^{56}\) \(+21.2282 q^{57}\) \(+17.9232 q^{58}\) \(-6.07479 q^{59}\) \(+42.2127 q^{60}\) \(-5.18905 q^{61}\) \(-7.88882 q^{62}\) \(-18.0142 q^{63}\) \(+3.54372 q^{64}\) \(+4.61775 q^{65}\) \(-7.37390 q^{66}\) \(+0.816633 q^{67}\) \(+4.65376 q^{68}\) \(+19.8358 q^{69}\) \(+28.5081 q^{70}\) \(+9.08175 q^{71}\) \(-35.4040 q^{72}\) \(+1.53699 q^{73}\) \(-0.0178982 q^{74}\) \(+14.4883 q^{75}\) \(+34.5583 q^{76}\) \(-3.48304 q^{77}\) \(-10.7313 q^{78}\) \(+10.7383 q^{79}\) \(+26.4948 q^{80}\) \(+2.23345 q^{81}\) \(-24.9143 q^{82}\) \(-5.34804 q^{83}\) \(-46.3368 q^{84}\) \(+3.17304 q^{85}\) \(-2.57949 q^{86}\) \(-19.8630 q^{87}\) \(-6.84534 q^{88}\) \(+7.34523 q^{89}\) \(-42.3318 q^{90}\) \(-5.06888 q^{91}\) \(+32.2916 q^{92}\) \(+8.74263 q^{93}\) \(+18.2548 q^{94}\) \(+23.5627 q^{95}\) \(-22.4346 q^{96}\) \(-11.4670 q^{97}\) \(-13.2368 q^{98}\) \(+5.17198 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57949 −1.82397 −0.911987 0.410220i \(-0.865452\pi\)
−0.911987 + 0.410220i \(0.865452\pi\)
\(3\) 2.85867 1.65045 0.825226 0.564802i \(-0.191048\pi\)
0.825226 + 0.564802i \(0.191048\pi\)
\(4\) 4.65376 2.32688
\(5\) 3.17304 1.41903 0.709514 0.704691i \(-0.248914\pi\)
0.709514 + 0.704691i \(0.248914\pi\)
\(6\) −7.37390 −3.01038
\(7\) −3.48304 −1.31646 −0.658232 0.752815i \(-0.728696\pi\)
−0.658232 + 0.752815i \(0.728696\pi\)
\(8\) −6.84534 −2.42019
\(9\) 5.17198 1.72399
\(10\) −8.18483 −2.58827
\(11\) 1.00000 0.301511
\(12\) 13.3035 3.84040
\(13\) 1.45531 0.403629 0.201815 0.979424i \(-0.435316\pi\)
0.201815 + 0.979424i \(0.435316\pi\)
\(14\) 8.98446 2.40120
\(15\) 9.07068 2.34204
\(16\) 8.34995 2.08749
\(17\) 1.00000 0.242536
\(18\) −13.3411 −3.14452
\(19\) 7.42589 1.70362 0.851808 0.523854i \(-0.175506\pi\)
0.851808 + 0.523854i \(0.175506\pi\)
\(20\) 14.7666 3.30191
\(21\) −9.95685 −2.17276
\(22\) −2.57949 −0.549949
\(23\) 6.93883 1.44685 0.723423 0.690405i \(-0.242568\pi\)
0.723423 + 0.690405i \(0.242568\pi\)
\(24\) −19.5685 −3.99441
\(25\) 5.06821 1.01364
\(26\) −3.75394 −0.736209
\(27\) 6.20897 1.19492
\(28\) −16.2092 −3.06325
\(29\) −6.94836 −1.29028 −0.645139 0.764065i \(-0.723200\pi\)
−0.645139 + 0.764065i \(0.723200\pi\)
\(30\) −23.3977 −4.27182
\(31\) 3.05829 0.549285 0.274642 0.961546i \(-0.411441\pi\)
0.274642 + 0.961546i \(0.411441\pi\)
\(32\) −7.84792 −1.38733
\(33\) 2.85867 0.497630
\(34\) −2.57949 −0.442379
\(35\) −11.0518 −1.86810
\(36\) 24.0692 4.01153
\(37\) 0.00693868 0.00114071 0.000570356 1.00000i \(-0.499818\pi\)
0.000570356 1.00000i \(0.499818\pi\)
\(38\) −19.1550 −3.10735
\(39\) 4.16023 0.666171
\(40\) −21.7206 −3.43432
\(41\) 9.65861 1.50842 0.754211 0.656633i \(-0.228020\pi\)
0.754211 + 0.656633i \(0.228020\pi\)
\(42\) 25.6836 3.96306
\(43\) 1.00000 0.152499
\(44\) 4.65376 0.701580
\(45\) 16.4109 2.44640
\(46\) −17.8986 −2.63901
\(47\) −7.07691 −1.03227 −0.516137 0.856506i \(-0.672630\pi\)
−0.516137 + 0.856506i \(0.672630\pi\)
\(48\) 23.8697 3.44530
\(49\) 5.13155 0.733079
\(50\) −13.0734 −1.84885
\(51\) 2.85867 0.400294
\(52\) 6.77264 0.939196
\(53\) 7.85931 1.07956 0.539780 0.841806i \(-0.318507\pi\)
0.539780 + 0.841806i \(0.318507\pi\)
\(54\) −16.0160 −2.17950
\(55\) 3.17304 0.427853
\(56\) 23.8426 3.18610
\(57\) 21.2282 2.81174
\(58\) 17.9232 2.35343
\(59\) −6.07479 −0.790870 −0.395435 0.918494i \(-0.629406\pi\)
−0.395435 + 0.918494i \(0.629406\pi\)
\(60\) 42.2127 5.44964
\(61\) −5.18905 −0.664390 −0.332195 0.943211i \(-0.607789\pi\)
−0.332195 + 0.943211i \(0.607789\pi\)
\(62\) −7.88882 −1.00188
\(63\) −18.0142 −2.26958
\(64\) 3.54372 0.442964
\(65\) 4.61775 0.572761
\(66\) −7.37390 −0.907664
\(67\) 0.816633 0.0997676 0.0498838 0.998755i \(-0.484115\pi\)
0.0498838 + 0.998755i \(0.484115\pi\)
\(68\) 4.65376 0.564351
\(69\) 19.8358 2.38795
\(70\) 28.5081 3.40737
\(71\) 9.08175 1.07781 0.538903 0.842368i \(-0.318839\pi\)
0.538903 + 0.842368i \(0.318839\pi\)
\(72\) −35.4040 −4.17240
\(73\) 1.53699 0.179891 0.0899456 0.995947i \(-0.471331\pi\)
0.0899456 + 0.995947i \(0.471331\pi\)
\(74\) −0.0178982 −0.00208063
\(75\) 14.4883 1.67297
\(76\) 34.5583 3.96411
\(77\) −3.48304 −0.396929
\(78\) −10.7313 −1.21508
\(79\) 10.7383 1.20816 0.604079 0.796924i \(-0.293541\pi\)
0.604079 + 0.796924i \(0.293541\pi\)
\(80\) 26.4948 2.96220
\(81\) 2.23345 0.248161
\(82\) −24.9143 −2.75132
\(83\) −5.34804 −0.587023 −0.293512 0.955955i \(-0.594824\pi\)
−0.293512 + 0.955955i \(0.594824\pi\)
\(84\) −46.3368 −5.05576
\(85\) 3.17304 0.344165
\(86\) −2.57949 −0.278153
\(87\) −19.8630 −2.12954
\(88\) −6.84534 −0.729715
\(89\) 7.34523 0.778593 0.389296 0.921113i \(-0.372718\pi\)
0.389296 + 0.921113i \(0.372718\pi\)
\(90\) −42.3318 −4.46216
\(91\) −5.06888 −0.531363
\(92\) 32.2916 3.36663
\(93\) 8.74263 0.906569
\(94\) 18.2548 1.88284
\(95\) 23.5627 2.41748
\(96\) −22.4346 −2.28972
\(97\) −11.4670 −1.16430 −0.582148 0.813083i \(-0.697788\pi\)
−0.582148 + 0.813083i \(0.697788\pi\)
\(98\) −13.2368 −1.33712
\(99\) 5.17198 0.519804
\(100\) 23.5862 2.35862
\(101\) 7.09074 0.705555 0.352777 0.935707i \(-0.385237\pi\)
0.352777 + 0.935707i \(0.385237\pi\)
\(102\) −7.37390 −0.730125
\(103\) −9.86660 −0.972185 −0.486093 0.873907i \(-0.661578\pi\)
−0.486093 + 0.873907i \(0.661578\pi\)
\(104\) −9.96205 −0.976860
\(105\) −31.5935 −3.08321
\(106\) −20.2730 −1.96909
\(107\) −18.3376 −1.77276 −0.886381 0.462956i \(-0.846789\pi\)
−0.886381 + 0.462956i \(0.846789\pi\)
\(108\) 28.8951 2.78043
\(109\) 6.28953 0.602428 0.301214 0.953557i \(-0.402608\pi\)
0.301214 + 0.953557i \(0.402608\pi\)
\(110\) −8.18483 −0.780393
\(111\) 0.0198354 0.00188269
\(112\) −29.0832 −2.74810
\(113\) −3.49567 −0.328845 −0.164423 0.986390i \(-0.552576\pi\)
−0.164423 + 0.986390i \(0.552576\pi\)
\(114\) −54.7578 −5.12854
\(115\) 22.0172 2.05311
\(116\) −32.3360 −3.00232
\(117\) 7.52681 0.695854
\(118\) 15.6698 1.44253
\(119\) −3.48304 −0.319290
\(120\) −62.0919 −5.66818
\(121\) 1.00000 0.0909091
\(122\) 13.3851 1.21183
\(123\) 27.6108 2.48958
\(124\) 14.2325 1.27812
\(125\) 0.216419 0.0193571
\(126\) 46.4674 4.13965
\(127\) −4.44126 −0.394098 −0.197049 0.980394i \(-0.563136\pi\)
−0.197049 + 0.980394i \(0.563136\pi\)
\(128\) 6.55487 0.579374
\(129\) 2.85867 0.251692
\(130\) −11.9114 −1.04470
\(131\) −6.39916 −0.559097 −0.279548 0.960132i \(-0.590185\pi\)
−0.279548 + 0.960132i \(0.590185\pi\)
\(132\) 13.3035 1.15793
\(133\) −25.8647 −2.24275
\(134\) −2.10650 −0.181973
\(135\) 19.7013 1.69562
\(136\) −6.84534 −0.586983
\(137\) −18.3699 −1.56945 −0.784724 0.619845i \(-0.787195\pi\)
−0.784724 + 0.619845i \(0.787195\pi\)
\(138\) −51.1662 −4.35556
\(139\) 16.9330 1.43624 0.718119 0.695920i \(-0.245003\pi\)
0.718119 + 0.695920i \(0.245003\pi\)
\(140\) −51.4326 −4.34684
\(141\) −20.2305 −1.70372
\(142\) −23.4263 −1.96589
\(143\) 1.45531 0.121699
\(144\) 43.1858 3.59882
\(145\) −22.0474 −1.83094
\(146\) −3.96465 −0.328117
\(147\) 14.6694 1.20991
\(148\) 0.0322909 0.00265430
\(149\) −21.1371 −1.73162 −0.865808 0.500376i \(-0.833195\pi\)
−0.865808 + 0.500376i \(0.833195\pi\)
\(150\) −37.3724 −3.05145
\(151\) −10.9796 −0.893511 −0.446755 0.894656i \(-0.647421\pi\)
−0.446755 + 0.894656i \(0.647421\pi\)
\(152\) −50.8327 −4.12308
\(153\) 5.17198 0.418130
\(154\) 8.98446 0.723988
\(155\) 9.70408 0.779451
\(156\) 19.3607 1.55010
\(157\) 11.8786 0.948017 0.474008 0.880520i \(-0.342807\pi\)
0.474008 + 0.880520i \(0.342807\pi\)
\(158\) −27.6994 −2.20365
\(159\) 22.4672 1.78176
\(160\) −24.9018 −1.96866
\(161\) −24.1682 −1.90472
\(162\) −5.76116 −0.452639
\(163\) 11.0766 0.867584 0.433792 0.901013i \(-0.357175\pi\)
0.433792 + 0.901013i \(0.357175\pi\)
\(164\) 44.9488 3.50991
\(165\) 9.07068 0.706151
\(166\) 13.7952 1.07072
\(167\) 3.05742 0.236590 0.118295 0.992979i \(-0.462257\pi\)
0.118295 + 0.992979i \(0.462257\pi\)
\(168\) 68.1580 5.25850
\(169\) −10.8821 −0.837084
\(170\) −8.18483 −0.627748
\(171\) 38.4066 2.93702
\(172\) 4.65376 0.354846
\(173\) 21.1352 1.60688 0.803439 0.595387i \(-0.203001\pi\)
0.803439 + 0.595387i \(0.203001\pi\)
\(174\) 51.2365 3.88423
\(175\) −17.6528 −1.33442
\(176\) 8.34995 0.629401
\(177\) −17.3658 −1.30529
\(178\) −18.9469 −1.42013
\(179\) −8.58174 −0.641429 −0.320715 0.947176i \(-0.603923\pi\)
−0.320715 + 0.947176i \(0.603923\pi\)
\(180\) 76.3725 5.69247
\(181\) −19.8941 −1.47872 −0.739359 0.673311i \(-0.764871\pi\)
−0.739359 + 0.673311i \(0.764871\pi\)
\(182\) 13.0751 0.969193
\(183\) −14.8338 −1.09654
\(184\) −47.4986 −3.50164
\(185\) 0.0220167 0.00161870
\(186\) −22.5515 −1.65356
\(187\) 1.00000 0.0731272
\(188\) −32.9342 −2.40197
\(189\) −21.6261 −1.57307
\(190\) −60.7797 −4.40942
\(191\) 15.0403 1.08828 0.544140 0.838994i \(-0.316856\pi\)
0.544140 + 0.838994i \(0.316856\pi\)
\(192\) 10.1303 0.731092
\(193\) −3.21273 −0.231257 −0.115629 0.993293i \(-0.536888\pi\)
−0.115629 + 0.993293i \(0.536888\pi\)
\(194\) 29.5790 2.12365
\(195\) 13.2006 0.945315
\(196\) 23.8810 1.70579
\(197\) 8.96272 0.638568 0.319284 0.947659i \(-0.396558\pi\)
0.319284 + 0.947659i \(0.396558\pi\)
\(198\) −13.3411 −0.948108
\(199\) −6.56383 −0.465298 −0.232649 0.972561i \(-0.574739\pi\)
−0.232649 + 0.972561i \(0.574739\pi\)
\(200\) −34.6936 −2.45321
\(201\) 2.33448 0.164662
\(202\) −18.2905 −1.28691
\(203\) 24.2014 1.69860
\(204\) 13.3035 0.931435
\(205\) 30.6472 2.14049
\(206\) 25.4508 1.77324
\(207\) 35.8875 2.49435
\(208\) 12.1517 0.842570
\(209\) 7.42589 0.513660
\(210\) 81.4951 5.62370
\(211\) −1.86867 −0.128644 −0.0643222 0.997929i \(-0.520489\pi\)
−0.0643222 + 0.997929i \(0.520489\pi\)
\(212\) 36.5754 2.51201
\(213\) 25.9617 1.77887
\(214\) 47.3016 3.23347
\(215\) 3.17304 0.216400
\(216\) −42.5025 −2.89193
\(217\) −10.6521 −0.723114
\(218\) −16.2238 −1.09881
\(219\) 4.39375 0.296902
\(220\) 14.7666 0.995562
\(221\) 1.45531 0.0978944
\(222\) −0.0511651 −0.00343398
\(223\) 7.41821 0.496760 0.248380 0.968663i \(-0.420102\pi\)
0.248380 + 0.968663i \(0.420102\pi\)
\(224\) 27.3346 1.82637
\(225\) 26.2127 1.74751
\(226\) 9.01705 0.599805
\(227\) 12.5393 0.832263 0.416132 0.909304i \(-0.363386\pi\)
0.416132 + 0.909304i \(0.363386\pi\)
\(228\) 98.7907 6.54258
\(229\) 27.1169 1.79193 0.895966 0.444123i \(-0.146485\pi\)
0.895966 + 0.444123i \(0.146485\pi\)
\(230\) −56.7931 −3.74483
\(231\) −9.95685 −0.655113
\(232\) 47.5638 3.12272
\(233\) 1.97622 0.129466 0.0647331 0.997903i \(-0.479380\pi\)
0.0647331 + 0.997903i \(0.479380\pi\)
\(234\) −19.4153 −1.26922
\(235\) −22.4553 −1.46482
\(236\) −28.2706 −1.84026
\(237\) 30.6974 1.99401
\(238\) 8.98446 0.582376
\(239\) 3.06804 0.198455 0.0992273 0.995065i \(-0.468363\pi\)
0.0992273 + 0.995065i \(0.468363\pi\)
\(240\) 75.7397 4.88898
\(241\) 26.1365 1.68360 0.841799 0.539791i \(-0.181497\pi\)
0.841799 + 0.539791i \(0.181497\pi\)
\(242\) −2.57949 −0.165816
\(243\) −12.2422 −0.785339
\(244\) −24.1486 −1.54596
\(245\) 16.2826 1.04026
\(246\) −71.2216 −4.54092
\(247\) 10.8069 0.687629
\(248\) −20.9350 −1.32937
\(249\) −15.2883 −0.968854
\(250\) −0.558251 −0.0353069
\(251\) −24.3383 −1.53622 −0.768111 0.640317i \(-0.778803\pi\)
−0.768111 + 0.640317i \(0.778803\pi\)
\(252\) −83.8338 −5.28103
\(253\) 6.93883 0.436240
\(254\) 11.4562 0.718824
\(255\) 9.07068 0.568028
\(256\) −23.9956 −1.49973
\(257\) −4.65408 −0.290313 −0.145157 0.989409i \(-0.546369\pi\)
−0.145157 + 0.989409i \(0.546369\pi\)
\(258\) −7.37390 −0.459079
\(259\) −0.0241677 −0.00150171
\(260\) 21.4899 1.33275
\(261\) −35.9368 −2.22443
\(262\) 16.5066 1.01978
\(263\) −10.9858 −0.677416 −0.338708 0.940892i \(-0.609990\pi\)
−0.338708 + 0.940892i \(0.609990\pi\)
\(264\) −19.5685 −1.20436
\(265\) 24.9379 1.53193
\(266\) 66.7176 4.09072
\(267\) 20.9976 1.28503
\(268\) 3.80041 0.232147
\(269\) 29.4175 1.79362 0.896809 0.442418i \(-0.145879\pi\)
0.896809 + 0.442418i \(0.145879\pi\)
\(270\) −50.8194 −3.09277
\(271\) 3.62963 0.220484 0.110242 0.993905i \(-0.464837\pi\)
0.110242 + 0.993905i \(0.464837\pi\)
\(272\) 8.34995 0.506290
\(273\) −14.4903 −0.876990
\(274\) 47.3850 2.86263
\(275\) 5.06821 0.305624
\(276\) 92.3110 5.55647
\(277\) −14.9625 −0.899012 −0.449506 0.893277i \(-0.648400\pi\)
−0.449506 + 0.893277i \(0.648400\pi\)
\(278\) −43.6785 −2.61966
\(279\) 15.8174 0.946964
\(280\) 75.6535 4.52116
\(281\) −15.9304 −0.950328 −0.475164 0.879897i \(-0.657611\pi\)
−0.475164 + 0.879897i \(0.657611\pi\)
\(282\) 52.1844 3.10754
\(283\) 8.00925 0.476100 0.238050 0.971253i \(-0.423492\pi\)
0.238050 + 0.971253i \(0.423492\pi\)
\(284\) 42.2643 2.50792
\(285\) 67.3579 3.98994
\(286\) −3.75394 −0.221975
\(287\) −33.6413 −1.98578
\(288\) −40.5893 −2.39175
\(289\) 1.00000 0.0588235
\(290\) 56.8711 3.33959
\(291\) −32.7803 −1.92162
\(292\) 7.15279 0.418585
\(293\) 7.43616 0.434425 0.217212 0.976124i \(-0.430304\pi\)
0.217212 + 0.976124i \(0.430304\pi\)
\(294\) −37.8396 −2.20685
\(295\) −19.2756 −1.12227
\(296\) −0.0474976 −0.00276074
\(297\) 6.20897 0.360281
\(298\) 54.5228 3.15842
\(299\) 10.0981 0.583989
\(300\) 67.4251 3.89279
\(301\) −3.48304 −0.200759
\(302\) 28.3219 1.62974
\(303\) 20.2701 1.16448
\(304\) 62.0058 3.55628
\(305\) −16.4651 −0.942788
\(306\) −13.3411 −0.762658
\(307\) 8.80069 0.502282 0.251141 0.967951i \(-0.419194\pi\)
0.251141 + 0.967951i \(0.419194\pi\)
\(308\) −16.2092 −0.923606
\(309\) −28.2053 −1.60455
\(310\) −25.0316 −1.42170
\(311\) 19.6857 1.11628 0.558138 0.829748i \(-0.311516\pi\)
0.558138 + 0.829748i \(0.311516\pi\)
\(312\) −28.4782 −1.61226
\(313\) 21.9272 1.23940 0.619700 0.784839i \(-0.287254\pi\)
0.619700 + 0.784839i \(0.287254\pi\)
\(314\) −30.6407 −1.72916
\(315\) −57.1599 −3.22059
\(316\) 49.9737 2.81124
\(317\) −6.91146 −0.388186 −0.194093 0.980983i \(-0.562176\pi\)
−0.194093 + 0.980983i \(0.562176\pi\)
\(318\) −57.9538 −3.24989
\(319\) −6.94836 −0.389033
\(320\) 11.2444 0.628579
\(321\) −52.4211 −2.92586
\(322\) 62.3416 3.47416
\(323\) 7.42589 0.413188
\(324\) 10.3939 0.577441
\(325\) 7.37579 0.409135
\(326\) −28.5719 −1.58245
\(327\) 17.9797 0.994279
\(328\) −66.1164 −3.65067
\(329\) 24.6491 1.35895
\(330\) −23.3977 −1.28800
\(331\) −16.1677 −0.888657 −0.444328 0.895864i \(-0.646558\pi\)
−0.444328 + 0.895864i \(0.646558\pi\)
\(332\) −24.8885 −1.36593
\(333\) 0.0358867 0.00196658
\(334\) −7.88657 −0.431534
\(335\) 2.59121 0.141573
\(336\) −83.1392 −4.53561
\(337\) 6.93240 0.377632 0.188816 0.982013i \(-0.439535\pi\)
0.188816 + 0.982013i \(0.439535\pi\)
\(338\) 28.0702 1.52682
\(339\) −9.99297 −0.542744
\(340\) 14.7666 0.800830
\(341\) 3.05829 0.165616
\(342\) −99.0693 −5.35706
\(343\) 6.50787 0.351392
\(344\) −6.84534 −0.369076
\(345\) 62.9399 3.38857
\(346\) −54.5180 −2.93090
\(347\) 11.7894 0.632890 0.316445 0.948611i \(-0.397511\pi\)
0.316445 + 0.948611i \(0.397511\pi\)
\(348\) −92.4378 −4.95519
\(349\) −18.0749 −0.967529 −0.483764 0.875198i \(-0.660731\pi\)
−0.483764 + 0.875198i \(0.660731\pi\)
\(350\) 45.5351 2.43395
\(351\) 9.03595 0.482303
\(352\) −7.84792 −0.418296
\(353\) −19.7171 −1.04944 −0.524718 0.851276i \(-0.675829\pi\)
−0.524718 + 0.851276i \(0.675829\pi\)
\(354\) 44.7949 2.38082
\(355\) 28.8168 1.52944
\(356\) 34.1829 1.81169
\(357\) −9.95685 −0.526972
\(358\) 22.1365 1.16995
\(359\) 31.3533 1.65477 0.827383 0.561639i \(-0.189829\pi\)
0.827383 + 0.561639i \(0.189829\pi\)
\(360\) −112.338 −5.92075
\(361\) 36.1439 1.90231
\(362\) 51.3166 2.69714
\(363\) 2.85867 0.150041
\(364\) −23.5894 −1.23642
\(365\) 4.87694 0.255271
\(366\) 38.2635 2.00007
\(367\) −4.68191 −0.244394 −0.122197 0.992506i \(-0.538994\pi\)
−0.122197 + 0.992506i \(0.538994\pi\)
\(368\) 57.9389 3.02027
\(369\) 49.9541 2.60051
\(370\) −0.0567919 −0.00295247
\(371\) −27.3743 −1.42120
\(372\) 40.6861 2.10948
\(373\) −24.5168 −1.26943 −0.634715 0.772746i \(-0.718883\pi\)
−0.634715 + 0.772746i \(0.718883\pi\)
\(374\) −2.57949 −0.133382
\(375\) 0.618671 0.0319480
\(376\) 48.4438 2.49830
\(377\) −10.1120 −0.520793
\(378\) 55.7843 2.86923
\(379\) −26.7238 −1.37271 −0.686356 0.727266i \(-0.740791\pi\)
−0.686356 + 0.727266i \(0.740791\pi\)
\(380\) 109.655 5.62518
\(381\) −12.6961 −0.650440
\(382\) −38.7964 −1.98499
\(383\) 19.4974 0.996268 0.498134 0.867100i \(-0.334019\pi\)
0.498134 + 0.867100i \(0.334019\pi\)
\(384\) 18.7382 0.956229
\(385\) −11.0518 −0.563254
\(386\) 8.28719 0.421807
\(387\) 5.17198 0.262907
\(388\) −53.3646 −2.70918
\(389\) 26.8144 1.35954 0.679771 0.733424i \(-0.262079\pi\)
0.679771 + 0.733424i \(0.262079\pi\)
\(390\) −34.0508 −1.72423
\(391\) 6.93883 0.350912
\(392\) −35.1272 −1.77419
\(393\) −18.2931 −0.922763
\(394\) −23.1192 −1.16473
\(395\) 34.0732 1.71441
\(396\) 24.0692 1.20952
\(397\) −5.23791 −0.262883 −0.131442 0.991324i \(-0.541961\pi\)
−0.131442 + 0.991324i \(0.541961\pi\)
\(398\) 16.9313 0.848691
\(399\) −73.9385 −3.70155
\(400\) 42.3193 2.11596
\(401\) 34.8427 1.73996 0.869981 0.493085i \(-0.164131\pi\)
0.869981 + 0.493085i \(0.164131\pi\)
\(402\) −6.02177 −0.300339
\(403\) 4.45074 0.221707
\(404\) 32.9986 1.64174
\(405\) 7.08684 0.352148
\(406\) −62.4272 −3.09821
\(407\) 0.00693868 0.000343938 0
\(408\) −19.5685 −0.968787
\(409\) 3.69784 0.182846 0.0914232 0.995812i \(-0.470858\pi\)
0.0914232 + 0.995812i \(0.470858\pi\)
\(410\) −79.0540 −3.90420
\(411\) −52.5135 −2.59030
\(412\) −45.9168 −2.26216
\(413\) 21.1587 1.04115
\(414\) −92.5713 −4.54963
\(415\) −16.9696 −0.833003
\(416\) −11.4211 −0.559966
\(417\) 48.4058 2.37044
\(418\) −19.1550 −0.936902
\(419\) 15.9091 0.777213 0.388606 0.921404i \(-0.372957\pi\)
0.388606 + 0.921404i \(0.372957\pi\)
\(420\) −147.029 −7.17426
\(421\) −35.7580 −1.74274 −0.871368 0.490630i \(-0.836767\pi\)
−0.871368 + 0.490630i \(0.836767\pi\)
\(422\) 4.82021 0.234644
\(423\) −36.6016 −1.77963
\(424\) −53.7997 −2.61274
\(425\) 5.06821 0.245844
\(426\) −66.9679 −3.24461
\(427\) 18.0737 0.874646
\(428\) −85.3388 −4.12501
\(429\) 4.16023 0.200858
\(430\) −8.18483 −0.394707
\(431\) −0.873990 −0.0420986 −0.0210493 0.999778i \(-0.506701\pi\)
−0.0210493 + 0.999778i \(0.506701\pi\)
\(432\) 51.8446 2.49438
\(433\) −29.4113 −1.41342 −0.706708 0.707506i \(-0.749820\pi\)
−0.706708 + 0.707506i \(0.749820\pi\)
\(434\) 27.4771 1.31894
\(435\) −63.0263 −3.02188
\(436\) 29.2700 1.40178
\(437\) 51.5270 2.46487
\(438\) −11.3336 −0.541541
\(439\) 10.1115 0.482595 0.241298 0.970451i \(-0.422427\pi\)
0.241298 + 0.970451i \(0.422427\pi\)
\(440\) −21.7206 −1.03549
\(441\) 26.5403 1.26382
\(442\) −3.75394 −0.178557
\(443\) −15.5779 −0.740129 −0.370065 0.929006i \(-0.620664\pi\)
−0.370065 + 0.929006i \(0.620664\pi\)
\(444\) 0.0923091 0.00438079
\(445\) 23.3067 1.10485
\(446\) −19.1352 −0.906078
\(447\) −60.4239 −2.85795
\(448\) −12.3429 −0.583147
\(449\) 34.1424 1.61128 0.805639 0.592406i \(-0.201822\pi\)
0.805639 + 0.592406i \(0.201822\pi\)
\(450\) −67.6153 −3.18741
\(451\) 9.65861 0.454806
\(452\) −16.2680 −0.765183
\(453\) −31.3871 −1.47470
\(454\) −32.3450 −1.51803
\(455\) −16.0838 −0.754020
\(456\) −145.314 −6.80495
\(457\) −23.1660 −1.08366 −0.541831 0.840488i \(-0.682269\pi\)
−0.541831 + 0.840488i \(0.682269\pi\)
\(458\) −69.9476 −3.26844
\(459\) 6.20897 0.289810
\(460\) 102.463 4.77735
\(461\) −0.00762920 −0.000355327 0 −0.000177664 1.00000i \(-0.500057\pi\)
−0.000177664 1.00000i \(0.500057\pi\)
\(462\) 25.6836 1.19491
\(463\) 22.0841 1.02634 0.513168 0.858288i \(-0.328472\pi\)
0.513168 + 0.858288i \(0.328472\pi\)
\(464\) −58.0184 −2.69344
\(465\) 27.7407 1.28645
\(466\) −5.09763 −0.236143
\(467\) −1.31579 −0.0608874 −0.0304437 0.999536i \(-0.509692\pi\)
−0.0304437 + 0.999536i \(0.509692\pi\)
\(468\) 35.0280 1.61917
\(469\) −2.84436 −0.131341
\(470\) 57.9233 2.67180
\(471\) 33.9570 1.56466
\(472\) 41.5840 1.91406
\(473\) 1.00000 0.0459800
\(474\) −79.1835 −3.63702
\(475\) 37.6360 1.72686
\(476\) −16.2092 −0.742948
\(477\) 40.6482 1.86115
\(478\) −7.91396 −0.361976
\(479\) 16.6264 0.759680 0.379840 0.925052i \(-0.375979\pi\)
0.379840 + 0.925052i \(0.375979\pi\)
\(480\) −71.1860 −3.24918
\(481\) 0.0100979 0.000460424 0
\(482\) −67.4187 −3.07084
\(483\) −69.0889 −3.14365
\(484\) 4.65376 0.211534
\(485\) −36.3853 −1.65217
\(486\) 31.5787 1.43244
\(487\) 24.5535 1.11262 0.556312 0.830973i \(-0.312216\pi\)
0.556312 + 0.830973i \(0.312216\pi\)
\(488\) 35.5208 1.60795
\(489\) 31.6643 1.43191
\(490\) −42.0009 −1.89741
\(491\) −14.2777 −0.644346 −0.322173 0.946681i \(-0.604413\pi\)
−0.322173 + 0.946681i \(0.604413\pi\)
\(492\) 128.494 5.79295
\(493\) −6.94836 −0.312938
\(494\) −27.8764 −1.25422
\(495\) 16.4109 0.737616
\(496\) 25.5366 1.14663
\(497\) −31.6321 −1.41889
\(498\) 39.4359 1.76716
\(499\) −32.9454 −1.47484 −0.737420 0.675434i \(-0.763956\pi\)
−0.737420 + 0.675434i \(0.763956\pi\)
\(500\) 1.00716 0.0450417
\(501\) 8.74014 0.390480
\(502\) 62.7804 2.80203
\(503\) −21.7659 −0.970493 −0.485246 0.874377i \(-0.661270\pi\)
−0.485246 + 0.874377i \(0.661270\pi\)
\(504\) 123.313 5.49281
\(505\) 22.4992 1.00120
\(506\) −17.8986 −0.795691
\(507\) −31.1083 −1.38157
\(508\) −20.6685 −0.917018
\(509\) 16.2226 0.719054 0.359527 0.933135i \(-0.382938\pi\)
0.359527 + 0.933135i \(0.382938\pi\)
\(510\) −23.3977 −1.03607
\(511\) −5.35340 −0.236820
\(512\) 48.7867 2.15609
\(513\) 46.1072 2.03568
\(514\) 12.0051 0.529524
\(515\) −31.3072 −1.37956
\(516\) 13.3035 0.585656
\(517\) −7.07691 −0.311242
\(518\) 0.0623403 0.00273907
\(519\) 60.4185 2.65208
\(520\) −31.6100 −1.38619
\(521\) 24.9552 1.09331 0.546654 0.837359i \(-0.315901\pi\)
0.546654 + 0.837359i \(0.315901\pi\)
\(522\) 92.6985 4.05730
\(523\) −28.4717 −1.24498 −0.622490 0.782628i \(-0.713879\pi\)
−0.622490 + 0.782628i \(0.713879\pi\)
\(524\) −29.7801 −1.30095
\(525\) −50.4634 −2.20240
\(526\) 28.3378 1.23559
\(527\) 3.05829 0.133221
\(528\) 23.8697 1.03880
\(529\) 25.1473 1.09336
\(530\) −64.3271 −2.79419
\(531\) −31.4187 −1.36346
\(532\) −120.368 −5.21861
\(533\) 14.0562 0.608843
\(534\) −54.1630 −2.34386
\(535\) −58.1860 −2.51560
\(536\) −5.59013 −0.241457
\(537\) −24.5323 −1.05865
\(538\) −75.8822 −3.27151
\(539\) 5.13155 0.221032
\(540\) 91.6853 3.94551
\(541\) 27.7773 1.19424 0.597120 0.802152i \(-0.296311\pi\)
0.597120 + 0.802152i \(0.296311\pi\)
\(542\) −9.36258 −0.402157
\(543\) −56.8707 −2.44055
\(544\) −7.84792 −0.336477
\(545\) 19.9570 0.854862
\(546\) 37.3774 1.59961
\(547\) −38.0504 −1.62692 −0.813458 0.581624i \(-0.802418\pi\)
−0.813458 + 0.581624i \(0.802418\pi\)
\(548\) −85.4892 −3.65192
\(549\) −26.8377 −1.14540
\(550\) −13.0734 −0.557451
\(551\) −51.5978 −2.19814
\(552\) −135.783 −5.77930
\(553\) −37.4021 −1.59050
\(554\) 38.5957 1.63977
\(555\) 0.0629385 0.00267159
\(556\) 78.8021 3.34195
\(557\) 36.3403 1.53979 0.769893 0.638173i \(-0.220309\pi\)
0.769893 + 0.638173i \(0.220309\pi\)
\(558\) −40.8008 −1.72724
\(559\) 1.45531 0.0615528
\(560\) −92.2822 −3.89964
\(561\) 2.85867 0.120693
\(562\) 41.0923 1.73337
\(563\) 14.2735 0.601556 0.300778 0.953694i \(-0.402754\pi\)
0.300778 + 0.953694i \(0.402754\pi\)
\(564\) −94.1480 −3.96435
\(565\) −11.0919 −0.466641
\(566\) −20.6598 −0.868394
\(567\) −7.77919 −0.326695
\(568\) −62.1676 −2.60850
\(569\) 13.8749 0.581666 0.290833 0.956774i \(-0.406068\pi\)
0.290833 + 0.956774i \(0.406068\pi\)
\(570\) −173.749 −7.27754
\(571\) −9.32921 −0.390415 −0.195208 0.980762i \(-0.562538\pi\)
−0.195208 + 0.980762i \(0.562538\pi\)
\(572\) 6.77264 0.283178
\(573\) 42.9953 1.79615
\(574\) 86.7773 3.62202
\(575\) 35.1674 1.46658
\(576\) 18.3280 0.763668
\(577\) −44.0516 −1.83389 −0.916946 0.399012i \(-0.869353\pi\)
−0.916946 + 0.399012i \(0.869353\pi\)
\(578\) −2.57949 −0.107293
\(579\) −9.18412 −0.381679
\(580\) −102.603 −4.26038
\(581\) 18.6274 0.772796
\(582\) 84.5564 3.50498
\(583\) 7.85931 0.325500
\(584\) −10.5212 −0.435371
\(585\) 23.8829 0.987436
\(586\) −19.1815 −0.792379
\(587\) 25.4858 1.05191 0.525955 0.850512i \(-0.323708\pi\)
0.525955 + 0.850512i \(0.323708\pi\)
\(588\) 68.2679 2.81532
\(589\) 22.7105 0.935771
\(590\) 49.7211 2.04699
\(591\) 25.6215 1.05393
\(592\) 0.0579376 0.00238122
\(593\) 16.1458 0.663027 0.331514 0.943450i \(-0.392441\pi\)
0.331514 + 0.943450i \(0.392441\pi\)
\(594\) −16.0160 −0.657143
\(595\) −11.0518 −0.453081
\(596\) −98.3668 −4.02926
\(597\) −18.7638 −0.767952
\(598\) −26.0480 −1.06518
\(599\) −16.2707 −0.664802 −0.332401 0.943138i \(-0.607859\pi\)
−0.332401 + 0.943138i \(0.607859\pi\)
\(600\) −99.1774 −4.04890
\(601\) −16.7779 −0.684385 −0.342193 0.939630i \(-0.611170\pi\)
−0.342193 + 0.939630i \(0.611170\pi\)
\(602\) 8.98446 0.366179
\(603\) 4.22361 0.171999
\(604\) −51.0966 −2.07909
\(605\) 3.17304 0.129003
\(606\) −52.2864 −2.12399
\(607\) −4.21312 −0.171005 −0.0855027 0.996338i \(-0.527250\pi\)
−0.0855027 + 0.996338i \(0.527250\pi\)
\(608\) −58.2778 −2.36348
\(609\) 69.1837 2.80347
\(610\) 42.4715 1.71962
\(611\) −10.2991 −0.416655
\(612\) 24.0692 0.972938
\(613\) 27.4560 1.10894 0.554469 0.832205i \(-0.312922\pi\)
0.554469 + 0.832205i \(0.312922\pi\)
\(614\) −22.7013 −0.916149
\(615\) 87.6101 3.53278
\(616\) 23.8426 0.960645
\(617\) −2.72131 −0.109556 −0.0547779 0.998499i \(-0.517445\pi\)
−0.0547779 + 0.998499i \(0.517445\pi\)
\(618\) 72.7553 2.92665
\(619\) −21.2527 −0.854220 −0.427110 0.904200i \(-0.640468\pi\)
−0.427110 + 0.904200i \(0.640468\pi\)
\(620\) 45.1605 1.81369
\(621\) 43.0830 1.72886
\(622\) −50.7791 −2.03606
\(623\) −25.5837 −1.02499
\(624\) 34.7377 1.39062
\(625\) −24.6543 −0.986173
\(626\) −56.5610 −2.26063
\(627\) 21.2282 0.847771
\(628\) 55.2802 2.20592
\(629\) 0.00693868 0.000276663 0
\(630\) 147.443 5.87428
\(631\) 3.66855 0.146043 0.0730214 0.997330i \(-0.476736\pi\)
0.0730214 + 0.997330i \(0.476736\pi\)
\(632\) −73.5076 −2.92398
\(633\) −5.34190 −0.212322
\(634\) 17.8280 0.708042
\(635\) −14.0923 −0.559236
\(636\) 104.557 4.14595
\(637\) 7.46798 0.295892
\(638\) 17.9232 0.709586
\(639\) 46.9706 1.85813
\(640\) 20.7989 0.822148
\(641\) −28.3812 −1.12099 −0.560494 0.828158i \(-0.689389\pi\)
−0.560494 + 0.828158i \(0.689389\pi\)
\(642\) 135.220 5.33669
\(643\) 1.72159 0.0678931 0.0339465 0.999424i \(-0.489192\pi\)
0.0339465 + 0.999424i \(0.489192\pi\)
\(644\) −112.473 −4.43206
\(645\) 9.07068 0.357158
\(646\) −19.1550 −0.753643
\(647\) 42.4169 1.66758 0.833790 0.552082i \(-0.186167\pi\)
0.833790 + 0.552082i \(0.186167\pi\)
\(648\) −15.2887 −0.600598
\(649\) −6.07479 −0.238456
\(650\) −19.0257 −0.746251
\(651\) −30.4509 −1.19347
\(652\) 51.5477 2.01876
\(653\) 3.21274 0.125724 0.0628621 0.998022i \(-0.479977\pi\)
0.0628621 + 0.998022i \(0.479977\pi\)
\(654\) −46.3784 −1.81354
\(655\) −20.3048 −0.793374
\(656\) 80.6489 3.14881
\(657\) 7.94929 0.310131
\(658\) −63.5822 −2.47869
\(659\) −24.7268 −0.963219 −0.481610 0.876386i \(-0.659948\pi\)
−0.481610 + 0.876386i \(0.659948\pi\)
\(660\) 42.2127 1.64313
\(661\) −41.4402 −1.61184 −0.805919 0.592026i \(-0.798328\pi\)
−0.805919 + 0.592026i \(0.798328\pi\)
\(662\) 41.7044 1.62089
\(663\) 4.16023 0.161570
\(664\) 36.6091 1.42071
\(665\) −82.0697 −3.18253
\(666\) −0.0925694 −0.00358699
\(667\) −48.2134 −1.86683
\(668\) 14.2285 0.550516
\(669\) 21.2062 0.819879
\(670\) −6.68400 −0.258225
\(671\) −5.18905 −0.200321
\(672\) 78.1406 3.01434
\(673\) 24.3170 0.937351 0.468675 0.883370i \(-0.344731\pi\)
0.468675 + 0.883370i \(0.344731\pi\)
\(674\) −17.8820 −0.688790
\(675\) 31.4684 1.21122
\(676\) −50.6426 −1.94779
\(677\) −5.12549 −0.196989 −0.0984944 0.995138i \(-0.531403\pi\)
−0.0984944 + 0.995138i \(0.531403\pi\)
\(678\) 25.7767 0.989950
\(679\) 39.9400 1.53275
\(680\) −21.7206 −0.832945
\(681\) 35.8457 1.37361
\(682\) −7.88882 −0.302078
\(683\) −24.9339 −0.954070 −0.477035 0.878884i \(-0.658289\pi\)
−0.477035 + 0.878884i \(0.658289\pi\)
\(684\) 178.735 6.83410
\(685\) −58.2886 −2.22709
\(686\) −16.7870 −0.640929
\(687\) 77.5181 2.95750
\(688\) 8.34995 0.318339
\(689\) 11.4377 0.435742
\(690\) −162.353 −6.18066
\(691\) 48.0767 1.82892 0.914462 0.404672i \(-0.132614\pi\)
0.914462 + 0.404672i \(0.132614\pi\)
\(692\) 98.3580 3.73901
\(693\) −18.0142 −0.684303
\(694\) −30.4107 −1.15437
\(695\) 53.7291 2.03806
\(696\) 135.969 5.15390
\(697\) 9.65861 0.365846
\(698\) 46.6241 1.76475
\(699\) 5.64935 0.213678
\(700\) −82.1516 −3.10504
\(701\) −21.5113 −0.812469 −0.406235 0.913769i \(-0.633158\pi\)
−0.406235 + 0.913769i \(0.633158\pi\)
\(702\) −23.3081 −0.879709
\(703\) 0.0515259 0.00194334
\(704\) 3.54372 0.133559
\(705\) −64.1923 −2.41762
\(706\) 50.8600 1.91414
\(707\) −24.6973 −0.928838
\(708\) −80.8162 −3.03726
\(709\) 26.3183 0.988405 0.494202 0.869347i \(-0.335460\pi\)
0.494202 + 0.869347i \(0.335460\pi\)
\(710\) −74.3326 −2.78965
\(711\) 55.5385 2.08286
\(712\) −50.2806 −1.88434
\(713\) 21.2209 0.794730
\(714\) 25.6836 0.961184
\(715\) 4.61775 0.172694
\(716\) −39.9374 −1.49253
\(717\) 8.77049 0.327540
\(718\) −80.8755 −3.01825
\(719\) 47.8250 1.78357 0.891787 0.452456i \(-0.149452\pi\)
0.891787 + 0.452456i \(0.149452\pi\)
\(720\) 137.030 5.10682
\(721\) 34.3658 1.27985
\(722\) −93.2327 −3.46976
\(723\) 74.7155 2.77870
\(724\) −92.5824 −3.44080
\(725\) −35.2157 −1.30788
\(726\) −7.37390 −0.273671
\(727\) −7.77841 −0.288485 −0.144243 0.989542i \(-0.546075\pi\)
−0.144243 + 0.989542i \(0.546075\pi\)
\(728\) 34.6982 1.28600
\(729\) −41.6968 −1.54433
\(730\) −12.5800 −0.465607
\(731\) 1.00000 0.0369863
\(732\) −69.0328 −2.55153
\(733\) −33.3170 −1.23059 −0.615295 0.788297i \(-0.710963\pi\)
−0.615295 + 0.788297i \(0.710963\pi\)
\(734\) 12.0769 0.445767
\(735\) 46.5467 1.71690
\(736\) −54.4554 −2.00725
\(737\) 0.816633 0.0300811
\(738\) −128.856 −4.74326
\(739\) −10.0595 −0.370045 −0.185022 0.982734i \(-0.559236\pi\)
−0.185022 + 0.982734i \(0.559236\pi\)
\(740\) 0.102461 0.00376653
\(741\) 30.8935 1.13490
\(742\) 70.6117 2.59224
\(743\) −21.3763 −0.784220 −0.392110 0.919918i \(-0.628255\pi\)
−0.392110 + 0.919918i \(0.628255\pi\)
\(744\) −59.8463 −2.19407
\(745\) −67.0689 −2.45721
\(746\) 63.2407 2.31541
\(747\) −27.6600 −1.01202
\(748\) 4.65376 0.170158
\(749\) 63.8706 2.33378
\(750\) −1.59585 −0.0582724
\(751\) 15.6299 0.570344 0.285172 0.958476i \(-0.407949\pi\)
0.285172 + 0.958476i \(0.407949\pi\)
\(752\) −59.0918 −2.15486
\(753\) −69.5752 −2.53546
\(754\) 26.0837 0.949913
\(755\) −34.8389 −1.26792
\(756\) −100.643 −3.66034
\(757\) −21.5597 −0.783601 −0.391800 0.920050i \(-0.628148\pi\)
−0.391800 + 0.920050i \(0.628148\pi\)
\(758\) 68.9338 2.50379
\(759\) 19.8358 0.719994
\(760\) −161.295 −5.85077
\(761\) 40.7739 1.47805 0.739027 0.673676i \(-0.235286\pi\)
0.739027 + 0.673676i \(0.235286\pi\)
\(762\) 32.7494 1.18638
\(763\) −21.9067 −0.793075
\(764\) 69.9941 2.53230
\(765\) 16.4109 0.593338
\(766\) −50.2932 −1.81717
\(767\) −8.84067 −0.319218
\(768\) −68.5956 −2.47523
\(769\) −12.8762 −0.464327 −0.232164 0.972677i \(-0.574580\pi\)
−0.232164 + 0.972677i \(0.574580\pi\)
\(770\) 28.5081 1.02736
\(771\) −13.3045 −0.479149
\(772\) −14.9513 −0.538108
\(773\) −36.4363 −1.31052 −0.655262 0.755402i \(-0.727442\pi\)
−0.655262 + 0.755402i \(0.727442\pi\)
\(774\) −13.3411 −0.479535
\(775\) 15.5000 0.556778
\(776\) 78.4954 2.81782
\(777\) −0.0690874 −0.00247850
\(778\) −69.1673 −2.47977
\(779\) 71.7238 2.56977
\(780\) 61.4324 2.19963
\(781\) 9.08175 0.324971
\(782\) −17.8986 −0.640053
\(783\) −43.1422 −1.54178
\(784\) 42.8482 1.53029
\(785\) 37.6914 1.34526
\(786\) 47.1867 1.68310
\(787\) 22.6060 0.805817 0.402909 0.915240i \(-0.367999\pi\)
0.402909 + 0.915240i \(0.367999\pi\)
\(788\) 41.7104 1.48587
\(789\) −31.4049 −1.11804
\(790\) −87.8915 −3.12704
\(791\) 12.1756 0.432913
\(792\) −35.4040 −1.25803
\(793\) −7.55165 −0.268167
\(794\) 13.5111 0.479492
\(795\) 71.2893 2.52837
\(796\) −30.5465 −1.08269
\(797\) −42.2821 −1.49771 −0.748854 0.662735i \(-0.769396\pi\)
−0.748854 + 0.662735i \(0.769396\pi\)
\(798\) 190.723 6.75154
\(799\) −7.07691 −0.250363
\(800\) −39.7749 −1.40625
\(801\) 37.9894 1.34229
\(802\) −89.8764 −3.17364
\(803\) 1.53699 0.0542393
\(804\) 10.8641 0.383148
\(805\) −76.6867 −2.70285
\(806\) −11.4806 −0.404388
\(807\) 84.0949 2.96028
\(808\) −48.5385 −1.70758
\(809\) −42.0314 −1.47775 −0.738873 0.673845i \(-0.764642\pi\)
−0.738873 + 0.673845i \(0.764642\pi\)
\(810\) −18.2804 −0.642308
\(811\) −15.4375 −0.542085 −0.271043 0.962567i \(-0.587368\pi\)
−0.271043 + 0.962567i \(0.587368\pi\)
\(812\) 112.627 3.95245
\(813\) 10.3759 0.363899
\(814\) −0.0178982 −0.000627333 0
\(815\) 35.1465 1.23113
\(816\) 23.8697 0.835608
\(817\) 7.42589 0.259799
\(818\) −9.53853 −0.333507
\(819\) −26.2162 −0.916067
\(820\) 142.625 4.98067
\(821\) 13.8982 0.485051 0.242525 0.970145i \(-0.422024\pi\)
0.242525 + 0.970145i \(0.422024\pi\)
\(822\) 135.458 4.72464
\(823\) −4.78934 −0.166946 −0.0834729 0.996510i \(-0.526601\pi\)
−0.0834729 + 0.996510i \(0.526601\pi\)
\(824\) 67.5402 2.35288
\(825\) 14.4883 0.504418
\(826\) −54.5787 −1.89903
\(827\) 40.4287 1.40584 0.702922 0.711267i \(-0.251878\pi\)
0.702922 + 0.711267i \(0.251878\pi\)
\(828\) 167.012 5.80406
\(829\) −45.4337 −1.57798 −0.788989 0.614408i \(-0.789395\pi\)
−0.788989 + 0.614408i \(0.789395\pi\)
\(830\) 43.7728 1.51938
\(831\) −42.7730 −1.48378
\(832\) 5.15719 0.178793
\(833\) 5.13155 0.177798
\(834\) −124.862 −4.32363
\(835\) 9.70131 0.335728
\(836\) 34.5583 1.19522
\(837\) 18.9888 0.656350
\(838\) −41.0375 −1.41762
\(839\) −5.28211 −0.182359 −0.0911794 0.995834i \(-0.529064\pi\)
−0.0911794 + 0.995834i \(0.529064\pi\)
\(840\) 216.268 7.46196
\(841\) 19.2797 0.664816
\(842\) 92.2372 3.17870
\(843\) −45.5397 −1.56847
\(844\) −8.69633 −0.299340
\(845\) −34.5293 −1.18785
\(846\) 94.4135 3.24600
\(847\) −3.48304 −0.119679
\(848\) 65.6249 2.25357
\(849\) 22.8958 0.785781
\(850\) −13.0734 −0.448413
\(851\) 0.0481463 0.00165043
\(852\) 120.819 4.13921
\(853\) 25.8875 0.886370 0.443185 0.896430i \(-0.353848\pi\)
0.443185 + 0.896430i \(0.353848\pi\)
\(854\) −46.6208 −1.59533
\(855\) 121.866 4.16772
\(856\) 125.527 4.29043
\(857\) −19.4618 −0.664804 −0.332402 0.943138i \(-0.607859\pi\)
−0.332402 + 0.943138i \(0.607859\pi\)
\(858\) −10.7313 −0.366360
\(859\) 18.9855 0.647777 0.323889 0.946095i \(-0.395010\pi\)
0.323889 + 0.946095i \(0.395010\pi\)
\(860\) 14.7666 0.503536
\(861\) −96.1693 −3.27744
\(862\) 2.25445 0.0767867
\(863\) 20.6580 0.703205 0.351603 0.936149i \(-0.385637\pi\)
0.351603 + 0.936149i \(0.385637\pi\)
\(864\) −48.7275 −1.65774
\(865\) 67.0629 2.28021
\(866\) 75.8660 2.57803
\(867\) 2.85867 0.0970854
\(868\) −49.5725 −1.68260
\(869\) 10.7383 0.364274
\(870\) 162.576 5.51183
\(871\) 1.18845 0.0402691
\(872\) −43.0540 −1.45799
\(873\) −59.3071 −2.00724
\(874\) −132.913 −4.49586
\(875\) −0.753797 −0.0254830
\(876\) 20.4474 0.690855
\(877\) −54.9034 −1.85396 −0.926978 0.375117i \(-0.877603\pi\)
−0.926978 + 0.375117i \(0.877603\pi\)
\(878\) −26.0825 −0.880241
\(879\) 21.2575 0.716998
\(880\) 26.4948 0.893138
\(881\) −18.1700 −0.612162 −0.306081 0.952005i \(-0.599018\pi\)
−0.306081 + 0.952005i \(0.599018\pi\)
\(882\) −68.4604 −2.30518
\(883\) −43.5776 −1.46650 −0.733251 0.679958i \(-0.761998\pi\)
−0.733251 + 0.679958i \(0.761998\pi\)
\(884\) 6.77264 0.227788
\(885\) −55.1024 −1.85225
\(886\) 40.1831 1.34998
\(887\) −28.5835 −0.959741 −0.479870 0.877339i \(-0.659316\pi\)
−0.479870 + 0.877339i \(0.659316\pi\)
\(888\) −0.135780 −0.00455647
\(889\) 15.4691 0.518816
\(890\) −60.1194 −2.01521
\(891\) 2.23345 0.0748234
\(892\) 34.5226 1.15590
\(893\) −52.5524 −1.75860
\(894\) 155.863 5.21283
\(895\) −27.2302 −0.910207
\(896\) −22.8309 −0.762725
\(897\) 28.8671 0.963846
\(898\) −88.0699 −2.93893
\(899\) −21.2501 −0.708730
\(900\) 121.987 4.06625
\(901\) 7.85931 0.261832
\(902\) −24.9143 −0.829554
\(903\) −9.95685 −0.331343
\(904\) 23.9291 0.795869
\(905\) −63.1249 −2.09834
\(906\) 80.9628 2.68981
\(907\) 16.8456 0.559350 0.279675 0.960095i \(-0.409773\pi\)
0.279675 + 0.960095i \(0.409773\pi\)
\(908\) 58.3549 1.93658
\(909\) 36.6732 1.21637
\(910\) 41.4879 1.37531
\(911\) 56.7182 1.87916 0.939579 0.342332i \(-0.111217\pi\)
0.939579 + 0.342332i \(0.111217\pi\)
\(912\) 177.254 5.86947
\(913\) −5.34804 −0.176994
\(914\) 59.7565 1.97657
\(915\) −47.0682 −1.55603
\(916\) 126.195 4.16961
\(917\) 22.2885 0.736031
\(918\) −16.0160 −0.528606
\(919\) −6.06103 −0.199935 −0.0999675 0.994991i \(-0.531874\pi\)
−0.0999675 + 0.994991i \(0.531874\pi\)
\(920\) −150.715 −4.96893
\(921\) 25.1582 0.828992
\(922\) 0.0196794 0.000648108 0
\(923\) 13.2167 0.435033
\(924\) −46.3368 −1.52437
\(925\) 0.0351667 0.00115627
\(926\) −56.9657 −1.87201
\(927\) −51.0299 −1.67604
\(928\) 54.5301 1.79004
\(929\) 45.9885 1.50884 0.754418 0.656395i \(-0.227919\pi\)
0.754418 + 0.656395i \(0.227919\pi\)
\(930\) −71.5569 −2.34644
\(931\) 38.1064 1.24889
\(932\) 9.19683 0.301252
\(933\) 56.2750 1.84236
\(934\) 3.39406 0.111057
\(935\) 3.17304 0.103770
\(936\) −51.5236 −1.68410
\(937\) −16.8144 −0.549304 −0.274652 0.961544i \(-0.588563\pi\)
−0.274652 + 0.961544i \(0.588563\pi\)
\(938\) 7.33700 0.239562
\(939\) 62.6827 2.04557
\(940\) −104.502 −3.40847
\(941\) 3.83010 0.124858 0.0624289 0.998049i \(-0.480115\pi\)
0.0624289 + 0.998049i \(0.480115\pi\)
\(942\) −87.5917 −2.85389
\(943\) 67.0194 2.18245
\(944\) −50.7242 −1.65093
\(945\) −68.6205 −2.23223
\(946\) −2.57949 −0.0838664
\(947\) −55.8572 −1.81511 −0.907557 0.419929i \(-0.862055\pi\)
−0.907557 + 0.419929i \(0.862055\pi\)
\(948\) 142.858 4.63982
\(949\) 2.23679 0.0726093
\(950\) −97.0815 −3.14974
\(951\) −19.7576 −0.640683
\(952\) 23.8426 0.772742
\(953\) −17.6334 −0.571202 −0.285601 0.958349i \(-0.592193\pi\)
−0.285601 + 0.958349i \(0.592193\pi\)
\(954\) −104.852 −3.39470
\(955\) 47.7236 1.54430
\(956\) 14.2779 0.461780
\(957\) −19.8630 −0.642081
\(958\) −42.8876 −1.38564
\(959\) 63.9831 2.06612
\(960\) 32.1439 1.03744
\(961\) −21.6469 −0.698286
\(962\) −0.0260474 −0.000839802 0
\(963\) −94.8417 −3.05623
\(964\) 121.633 3.91753
\(965\) −10.1941 −0.328160
\(966\) 178.214 5.73394
\(967\) 32.0118 1.02943 0.514716 0.857361i \(-0.327898\pi\)
0.514716 + 0.857361i \(0.327898\pi\)
\(968\) −6.84534 −0.220017
\(969\) 21.2282 0.681947
\(970\) 93.8553 3.01351
\(971\) 47.9414 1.53851 0.769256 0.638940i \(-0.220627\pi\)
0.769256 + 0.638940i \(0.220627\pi\)
\(972\) −56.9724 −1.82739
\(973\) −58.9783 −1.89076
\(974\) −63.3354 −2.02940
\(975\) 21.0849 0.675258
\(976\) −43.3283 −1.38691
\(977\) 54.1739 1.73318 0.866588 0.499025i \(-0.166308\pi\)
0.866588 + 0.499025i \(0.166308\pi\)
\(978\) −81.6776 −2.61176
\(979\) 7.34523 0.234755
\(980\) 75.7755 2.42056
\(981\) 32.5293 1.03858
\(982\) 36.8293 1.17527
\(983\) 33.1749 1.05811 0.529057 0.848586i \(-0.322546\pi\)
0.529057 + 0.848586i \(0.322546\pi\)
\(984\) −189.005 −6.02526
\(985\) 28.4391 0.906146
\(986\) 17.9232 0.570791
\(987\) 70.4637 2.24288
\(988\) 50.2929 1.60003
\(989\) 6.93883 0.220642
\(990\) −42.3318 −1.34539
\(991\) −17.6291 −0.560006 −0.280003 0.959999i \(-0.590335\pi\)
−0.280003 + 0.959999i \(0.590335\pi\)
\(992\) −24.0012 −0.762039
\(993\) −46.2181 −1.46669
\(994\) 81.5946 2.58802
\(995\) −20.8273 −0.660271
\(996\) −71.1479 −2.25441
\(997\) −11.3245 −0.358651 −0.179326 0.983790i \(-0.557392\pi\)
−0.179326 + 0.983790i \(0.557392\pi\)
\(998\) 84.9824 2.69007
\(999\) 0.0430821 0.00136306
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 \(a_p\))