Properties

Label 8041.2.a.j.1.18
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 1.18
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.70166 q^{2}\) \(+2.90991 q^{3}\) \(+0.895633 q^{4}\) \(-0.762355 q^{5}\) \(-4.95167 q^{6}\) \(+4.85107 q^{7}\) \(+1.87925 q^{8}\) \(+5.46758 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.70166 q^{2}\) \(+2.90991 q^{3}\) \(+0.895633 q^{4}\) \(-0.762355 q^{5}\) \(-4.95167 q^{6}\) \(+4.85107 q^{7}\) \(+1.87925 q^{8}\) \(+5.46758 q^{9}\) \(+1.29727 q^{10}\) \(+1.00000 q^{11}\) \(+2.60621 q^{12}\) \(-1.16100 q^{13}\) \(-8.25485 q^{14}\) \(-2.21838 q^{15}\) \(-4.98911 q^{16}\) \(+1.00000 q^{17}\) \(-9.30394 q^{18}\) \(+3.00298 q^{19}\) \(-0.682790 q^{20}\) \(+14.1162 q^{21}\) \(-1.70166 q^{22}\) \(-6.18094 q^{23}\) \(+5.46846 q^{24}\) \(-4.41882 q^{25}\) \(+1.97562 q^{26}\) \(+7.18044 q^{27}\) \(+4.34478 q^{28}\) \(-0.453833 q^{29}\) \(+3.77493 q^{30}\) \(-6.53377 q^{31}\) \(+4.73124 q^{32}\) \(+2.90991 q^{33}\) \(-1.70166 q^{34}\) \(-3.69823 q^{35}\) \(+4.89695 q^{36}\) \(+1.16400 q^{37}\) \(-5.11004 q^{38}\) \(-3.37841 q^{39}\) \(-1.43266 q^{40}\) \(+4.26888 q^{41}\) \(-24.0209 q^{42}\) \(+1.00000 q^{43}\) \(+0.895633 q^{44}\) \(-4.16824 q^{45}\) \(+10.5178 q^{46}\) \(-1.17938 q^{47}\) \(-14.5179 q^{48}\) \(+16.5328 q^{49}\) \(+7.51930 q^{50}\) \(+2.90991 q^{51}\) \(-1.03983 q^{52}\) \(+11.6707 q^{53}\) \(-12.2186 q^{54}\) \(-0.762355 q^{55}\) \(+9.11638 q^{56}\) \(+8.73840 q^{57}\) \(+0.772268 q^{58}\) \(-4.03069 q^{59}\) \(-1.98686 q^{60}\) \(-5.54122 q^{61}\) \(+11.1182 q^{62}\) \(+26.5236 q^{63}\) \(+1.92727 q^{64}\) \(+0.885095 q^{65}\) \(-4.95167 q^{66}\) \(+2.59019 q^{67}\) \(+0.895633 q^{68}\) \(-17.9860 q^{69}\) \(+6.29312 q^{70}\) \(+14.4353 q^{71}\) \(+10.2750 q^{72}\) \(+0.103162 q^{73}\) \(-1.98073 q^{74}\) \(-12.8584 q^{75}\) \(+2.68957 q^{76}\) \(+4.85107 q^{77}\) \(+5.74889 q^{78}\) \(-0.329877 q^{79}\) \(+3.80347 q^{80}\) \(+4.49170 q^{81}\) \(-7.26416 q^{82}\) \(+11.1939 q^{83}\) \(+12.6429 q^{84}\) \(-0.762355 q^{85}\) \(-1.70166 q^{86}\) \(-1.32061 q^{87}\) \(+1.87925 q^{88}\) \(-7.70401 q^{89}\) \(+7.09290 q^{90}\) \(-5.63209 q^{91}\) \(-5.53586 q^{92}\) \(-19.0127 q^{93}\) \(+2.00690 q^{94}\) \(-2.28933 q^{95}\) \(+13.7675 q^{96}\) \(+5.71368 q^{97}\) \(-28.1332 q^{98}\) \(+5.46758 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.70166 −1.20325 −0.601626 0.798778i \(-0.705480\pi\)
−0.601626 + 0.798778i \(0.705480\pi\)
\(3\) 2.90991 1.68004 0.840019 0.542557i \(-0.182544\pi\)
0.840019 + 0.542557i \(0.182544\pi\)
\(4\) 0.895633 0.447817
\(5\) −0.762355 −0.340935 −0.170468 0.985363i \(-0.554528\pi\)
−0.170468 + 0.985363i \(0.554528\pi\)
\(6\) −4.95167 −2.02151
\(7\) 4.85107 1.83353 0.916765 0.399426i \(-0.130791\pi\)
0.916765 + 0.399426i \(0.130791\pi\)
\(8\) 1.87925 0.664416
\(9\) 5.46758 1.82253
\(10\) 1.29727 0.410231
\(11\) 1.00000 0.301511
\(12\) 2.60621 0.752349
\(13\) −1.16100 −0.322004 −0.161002 0.986954i \(-0.551473\pi\)
−0.161002 + 0.986954i \(0.551473\pi\)
\(14\) −8.25485 −2.20620
\(15\) −2.21838 −0.572784
\(16\) −4.98911 −1.24728
\(17\) 1.00000 0.242536
\(18\) −9.30394 −2.19296
\(19\) 3.00298 0.688931 0.344465 0.938799i \(-0.388060\pi\)
0.344465 + 0.938799i \(0.388060\pi\)
\(20\) −0.682790 −0.152677
\(21\) 14.1162 3.08040
\(22\) −1.70166 −0.362794
\(23\) −6.18094 −1.28882 −0.644408 0.764682i \(-0.722896\pi\)
−0.644408 + 0.764682i \(0.722896\pi\)
\(24\) 5.46846 1.11624
\(25\) −4.41882 −0.883763
\(26\) 1.97562 0.387452
\(27\) 7.18044 1.38188
\(28\) 4.34478 0.821086
\(29\) −0.453833 −0.0842747 −0.0421373 0.999112i \(-0.513417\pi\)
−0.0421373 + 0.999112i \(0.513417\pi\)
\(30\) 3.77493 0.689204
\(31\) −6.53377 −1.17350 −0.586749 0.809769i \(-0.699593\pi\)
−0.586749 + 0.809769i \(0.699593\pi\)
\(32\) 4.73124 0.836373
\(33\) 2.90991 0.506550
\(34\) −1.70166 −0.291832
\(35\) −3.69823 −0.625115
\(36\) 4.89695 0.816158
\(37\) 1.16400 0.191361 0.0956804 0.995412i \(-0.469497\pi\)
0.0956804 + 0.995412i \(0.469497\pi\)
\(38\) −5.11004 −0.828958
\(39\) −3.37841 −0.540979
\(40\) −1.43266 −0.226523
\(41\) 4.26888 0.666686 0.333343 0.942806i \(-0.391823\pi\)
0.333343 + 0.942806i \(0.391823\pi\)
\(42\) −24.0209 −3.70650
\(43\) 1.00000 0.152499
\(44\) 0.895633 0.135022
\(45\) −4.16824 −0.621364
\(46\) 10.5178 1.55077
\(47\) −1.17938 −0.172031 −0.0860153 0.996294i \(-0.527413\pi\)
−0.0860153 + 0.996294i \(0.527413\pi\)
\(48\) −14.5179 −2.09547
\(49\) 16.5328 2.36184
\(50\) 7.51930 1.06339
\(51\) 2.90991 0.407469
\(52\) −1.03983 −0.144199
\(53\) 11.6707 1.60309 0.801547 0.597932i \(-0.204011\pi\)
0.801547 + 0.597932i \(0.204011\pi\)
\(54\) −12.2186 −1.66275
\(55\) −0.762355 −0.102796
\(56\) 9.11638 1.21823
\(57\) 8.73840 1.15743
\(58\) 0.772268 0.101404
\(59\) −4.03069 −0.524752 −0.262376 0.964966i \(-0.584506\pi\)
−0.262376 + 0.964966i \(0.584506\pi\)
\(60\) −1.98686 −0.256502
\(61\) −5.54122 −0.709481 −0.354740 0.934965i \(-0.615431\pi\)
−0.354740 + 0.934965i \(0.615431\pi\)
\(62\) 11.1182 1.41202
\(63\) 26.5236 3.34166
\(64\) 1.92727 0.240909
\(65\) 0.885095 0.109782
\(66\) −4.95167 −0.609508
\(67\) 2.59019 0.316442 0.158221 0.987404i \(-0.449424\pi\)
0.158221 + 0.987404i \(0.449424\pi\)
\(68\) 0.895633 0.108611
\(69\) −17.9860 −2.16526
\(70\) 6.29312 0.752172
\(71\) 14.4353 1.71316 0.856579 0.516016i \(-0.172586\pi\)
0.856579 + 0.516016i \(0.172586\pi\)
\(72\) 10.2750 1.21092
\(73\) 0.103162 0.0120742 0.00603710 0.999982i \(-0.498078\pi\)
0.00603710 + 0.999982i \(0.498078\pi\)
\(74\) −1.98073 −0.230255
\(75\) −12.8584 −1.48476
\(76\) 2.68957 0.308515
\(77\) 4.85107 0.552830
\(78\) 5.74889 0.650934
\(79\) −0.329877 −0.0371141 −0.0185571 0.999828i \(-0.505907\pi\)
−0.0185571 + 0.999828i \(0.505907\pi\)
\(80\) 3.80347 0.425241
\(81\) 4.49170 0.499077
\(82\) −7.26416 −0.802192
\(83\) 11.1939 1.22869 0.614344 0.789039i \(-0.289421\pi\)
0.614344 + 0.789039i \(0.289421\pi\)
\(84\) 12.6429 1.37945
\(85\) −0.762355 −0.0826890
\(86\) −1.70166 −0.183494
\(87\) −1.32061 −0.141585
\(88\) 1.87925 0.200329
\(89\) −7.70401 −0.816624 −0.408312 0.912843i \(-0.633882\pi\)
−0.408312 + 0.912843i \(0.633882\pi\)
\(90\) 7.09290 0.747658
\(91\) −5.63209 −0.590404
\(92\) −5.53586 −0.577153
\(93\) −19.0127 −1.97152
\(94\) 2.00690 0.206996
\(95\) −2.28933 −0.234881
\(96\) 13.7675 1.40514
\(97\) 5.71368 0.580136 0.290068 0.957006i \(-0.406322\pi\)
0.290068 + 0.957006i \(0.406322\pi\)
\(98\) −28.1332 −2.84188
\(99\) 5.46758 0.549513
\(100\) −3.95764 −0.395764
\(101\) 13.6973 1.36294 0.681468 0.731848i \(-0.261342\pi\)
0.681468 + 0.731848i \(0.261342\pi\)
\(102\) −4.95167 −0.490288
\(103\) 10.7993 1.06408 0.532042 0.846718i \(-0.321425\pi\)
0.532042 + 0.846718i \(0.321425\pi\)
\(104\) −2.18181 −0.213945
\(105\) −10.7615 −1.05022
\(106\) −19.8595 −1.92893
\(107\) 12.2453 1.18379 0.591897 0.806014i \(-0.298379\pi\)
0.591897 + 0.806014i \(0.298379\pi\)
\(108\) 6.43104 0.618827
\(109\) 13.4994 1.29301 0.646504 0.762911i \(-0.276230\pi\)
0.646504 + 0.762911i \(0.276230\pi\)
\(110\) 1.29727 0.123689
\(111\) 3.38714 0.321494
\(112\) −24.2025 −2.28692
\(113\) 11.6167 1.09281 0.546403 0.837522i \(-0.315997\pi\)
0.546403 + 0.837522i \(0.315997\pi\)
\(114\) −14.8698 −1.39268
\(115\) 4.71207 0.439403
\(116\) −0.406468 −0.0377396
\(117\) −6.34787 −0.586861
\(118\) 6.85885 0.631409
\(119\) 4.85107 0.444697
\(120\) −4.16890 −0.380567
\(121\) 1.00000 0.0909091
\(122\) 9.42925 0.853684
\(123\) 12.4220 1.12006
\(124\) −5.85186 −0.525512
\(125\) 7.18048 0.642241
\(126\) −45.1340 −4.02086
\(127\) −13.9686 −1.23952 −0.619758 0.784793i \(-0.712769\pi\)
−0.619758 + 0.784793i \(0.712769\pi\)
\(128\) −12.7420 −1.12625
\(129\) 2.90991 0.256203
\(130\) −1.50613 −0.132096
\(131\) −0.502347 −0.0438903 −0.0219451 0.999759i \(-0.506986\pi\)
−0.0219451 + 0.999759i \(0.506986\pi\)
\(132\) 2.60621 0.226842
\(133\) 14.5677 1.26318
\(134\) −4.40762 −0.380760
\(135\) −5.47404 −0.471130
\(136\) 1.87925 0.161145
\(137\) −6.56384 −0.560787 −0.280394 0.959885i \(-0.590465\pi\)
−0.280394 + 0.959885i \(0.590465\pi\)
\(138\) 30.6060 2.60535
\(139\) 17.4228 1.47778 0.738892 0.673823i \(-0.235349\pi\)
0.738892 + 0.673823i \(0.235349\pi\)
\(140\) −3.31226 −0.279937
\(141\) −3.43190 −0.289018
\(142\) −24.5640 −2.06136
\(143\) −1.16100 −0.0970878
\(144\) −27.2783 −2.27320
\(145\) 0.345982 0.0287322
\(146\) −0.175546 −0.0145283
\(147\) 48.1091 3.96797
\(148\) 1.04252 0.0856946
\(149\) 24.1066 1.97489 0.987446 0.157954i \(-0.0504899\pi\)
0.987446 + 0.157954i \(0.0504899\pi\)
\(150\) 21.8805 1.78654
\(151\) 16.6535 1.35524 0.677622 0.735411i \(-0.263011\pi\)
0.677622 + 0.735411i \(0.263011\pi\)
\(152\) 5.64336 0.457737
\(153\) 5.46758 0.442028
\(154\) −8.25485 −0.665195
\(155\) 4.98105 0.400087
\(156\) −3.02582 −0.242259
\(157\) 9.30870 0.742915 0.371458 0.928450i \(-0.378858\pi\)
0.371458 + 0.928450i \(0.378858\pi\)
\(158\) 0.561338 0.0446576
\(159\) 33.9607 2.69326
\(160\) −3.60688 −0.285149
\(161\) −29.9842 −2.36308
\(162\) −7.64332 −0.600516
\(163\) −7.60346 −0.595549 −0.297775 0.954636i \(-0.596244\pi\)
−0.297775 + 0.954636i \(0.596244\pi\)
\(164\) 3.82335 0.298553
\(165\) −2.21838 −0.172701
\(166\) −19.0481 −1.47842
\(167\) 13.1221 1.01542 0.507710 0.861528i \(-0.330492\pi\)
0.507710 + 0.861528i \(0.330492\pi\)
\(168\) 26.5278 2.04667
\(169\) −11.6521 −0.896314
\(170\) 1.29727 0.0994957
\(171\) 16.4190 1.25559
\(172\) 0.895633 0.0682914
\(173\) 12.7566 0.969865 0.484933 0.874551i \(-0.338844\pi\)
0.484933 + 0.874551i \(0.338844\pi\)
\(174\) 2.24723 0.170362
\(175\) −21.4360 −1.62041
\(176\) −4.98911 −0.376068
\(177\) −11.7290 −0.881602
\(178\) 13.1096 0.982605
\(179\) 17.6730 1.32094 0.660470 0.750853i \(-0.270357\pi\)
0.660470 + 0.750853i \(0.270357\pi\)
\(180\) −3.73321 −0.278257
\(181\) −2.86258 −0.212774 −0.106387 0.994325i \(-0.533928\pi\)
−0.106387 + 0.994325i \(0.533928\pi\)
\(182\) 9.58389 0.710405
\(183\) −16.1245 −1.19195
\(184\) −11.6155 −0.856310
\(185\) −0.887383 −0.0652417
\(186\) 32.3530 2.37224
\(187\) 1.00000 0.0731272
\(188\) −1.05629 −0.0770382
\(189\) 34.8328 2.53371
\(190\) 3.89566 0.282621
\(191\) −26.5347 −1.91998 −0.959992 0.280026i \(-0.909657\pi\)
−0.959992 + 0.280026i \(0.909657\pi\)
\(192\) 5.60819 0.404736
\(193\) −24.5924 −1.77020 −0.885101 0.465400i \(-0.845911\pi\)
−0.885101 + 0.465400i \(0.845911\pi\)
\(194\) −9.72272 −0.698050
\(195\) 2.57555 0.184439
\(196\) 14.8074 1.05767
\(197\) −13.9348 −0.992813 −0.496407 0.868090i \(-0.665348\pi\)
−0.496407 + 0.868090i \(0.665348\pi\)
\(198\) −9.30394 −0.661202
\(199\) −15.5954 −1.10553 −0.552765 0.833337i \(-0.686427\pi\)
−0.552765 + 0.833337i \(0.686427\pi\)
\(200\) −8.30407 −0.587186
\(201\) 7.53723 0.531635
\(202\) −23.3082 −1.63996
\(203\) −2.20157 −0.154520
\(204\) 2.60621 0.182471
\(205\) −3.25440 −0.227297
\(206\) −18.3766 −1.28036
\(207\) −33.7948 −2.34890
\(208\) 5.79236 0.401628
\(209\) 3.00298 0.207720
\(210\) 18.3124 1.26368
\(211\) 18.7580 1.29135 0.645676 0.763611i \(-0.276575\pi\)
0.645676 + 0.763611i \(0.276575\pi\)
\(212\) 10.4527 0.717892
\(213\) 42.0055 2.87817
\(214\) −20.8372 −1.42440
\(215\) −0.762355 −0.0519922
\(216\) 13.4939 0.918141
\(217\) −31.6957 −2.15165
\(218\) −22.9713 −1.55582
\(219\) 0.300192 0.0202851
\(220\) −0.682790 −0.0460337
\(221\) −1.16100 −0.0780974
\(222\) −5.76375 −0.386838
\(223\) 0.892655 0.0597766 0.0298883 0.999553i \(-0.490485\pi\)
0.0298883 + 0.999553i \(0.490485\pi\)
\(224\) 22.9516 1.53352
\(225\) −24.1602 −1.61068
\(226\) −19.7676 −1.31492
\(227\) −5.77038 −0.382994 −0.191497 0.981493i \(-0.561334\pi\)
−0.191497 + 0.981493i \(0.561334\pi\)
\(228\) 7.82640 0.518316
\(229\) 5.49590 0.363179 0.181590 0.983374i \(-0.441876\pi\)
0.181590 + 0.983374i \(0.441876\pi\)
\(230\) −8.01832 −0.528712
\(231\) 14.1162 0.928776
\(232\) −0.852867 −0.0559934
\(233\) 7.60808 0.498422 0.249211 0.968449i \(-0.419829\pi\)
0.249211 + 0.968449i \(0.419829\pi\)
\(234\) 10.8019 0.706142
\(235\) 0.899107 0.0586513
\(236\) −3.61002 −0.234992
\(237\) −0.959914 −0.0623531
\(238\) −8.25485 −0.535082
\(239\) 13.7662 0.890461 0.445230 0.895416i \(-0.353122\pi\)
0.445230 + 0.895416i \(0.353122\pi\)
\(240\) 11.0678 0.714421
\(241\) −29.4154 −1.89481 −0.947406 0.320036i \(-0.896305\pi\)
−0.947406 + 0.320036i \(0.896305\pi\)
\(242\) −1.70166 −0.109387
\(243\) −8.47088 −0.543407
\(244\) −4.96290 −0.317717
\(245\) −12.6039 −0.805233
\(246\) −21.1381 −1.34771
\(247\) −3.48646 −0.221838
\(248\) −12.2786 −0.779691
\(249\) 32.5732 2.06424
\(250\) −12.2187 −0.772779
\(251\) −1.42081 −0.0896810 −0.0448405 0.998994i \(-0.514278\pi\)
−0.0448405 + 0.998994i \(0.514278\pi\)
\(252\) 23.7554 1.49645
\(253\) −6.18094 −0.388593
\(254\) 23.7698 1.49145
\(255\) −2.21838 −0.138921
\(256\) 17.8280 1.11425
\(257\) 5.39743 0.336682 0.168341 0.985729i \(-0.446159\pi\)
0.168341 + 0.985729i \(0.446159\pi\)
\(258\) −4.95167 −0.308277
\(259\) 5.64666 0.350866
\(260\) 0.792720 0.0491624
\(261\) −2.48137 −0.153593
\(262\) 0.854823 0.0528111
\(263\) −16.1186 −0.993913 −0.496956 0.867776i \(-0.665549\pi\)
−0.496956 + 0.867776i \(0.665549\pi\)
\(264\) 5.46846 0.336560
\(265\) −8.89721 −0.546551
\(266\) −24.7891 −1.51992
\(267\) −22.4180 −1.37196
\(268\) 2.31986 0.141708
\(269\) 27.5344 1.67880 0.839400 0.543514i \(-0.182907\pi\)
0.839400 + 0.543514i \(0.182907\pi\)
\(270\) 9.31494 0.566889
\(271\) 13.0403 0.792144 0.396072 0.918219i \(-0.370373\pi\)
0.396072 + 0.918219i \(0.370373\pi\)
\(272\) −4.98911 −0.302509
\(273\) −16.3889 −0.991901
\(274\) 11.1694 0.674768
\(275\) −4.41882 −0.266465
\(276\) −16.1089 −0.969639
\(277\) −6.60009 −0.396561 −0.198281 0.980145i \(-0.563536\pi\)
−0.198281 + 0.980145i \(0.563536\pi\)
\(278\) −29.6477 −1.77815
\(279\) −35.7239 −2.13873
\(280\) −6.94991 −0.415337
\(281\) −27.0009 −1.61074 −0.805369 0.592774i \(-0.798033\pi\)
−0.805369 + 0.592774i \(0.798033\pi\)
\(282\) 5.83991 0.347761
\(283\) −14.9926 −0.891218 −0.445609 0.895228i \(-0.647013\pi\)
−0.445609 + 0.895228i \(0.647013\pi\)
\(284\) 12.9288 0.767180
\(285\) −6.66176 −0.394609
\(286\) 1.97562 0.116821
\(287\) 20.7086 1.22239
\(288\) 25.8684 1.52431
\(289\) 1.00000 0.0588235
\(290\) −0.588742 −0.0345721
\(291\) 16.6263 0.974651
\(292\) 0.0923954 0.00540703
\(293\) −32.5125 −1.89940 −0.949700 0.313162i \(-0.898612\pi\)
−0.949700 + 0.313162i \(0.898612\pi\)
\(294\) −81.8652 −4.77447
\(295\) 3.07282 0.178906
\(296\) 2.18745 0.127143
\(297\) 7.18044 0.416651
\(298\) −41.0212 −2.37629
\(299\) 7.17608 0.415004
\(300\) −11.5164 −0.664898
\(301\) 4.85107 0.279611
\(302\) −28.3385 −1.63070
\(303\) 39.8580 2.28978
\(304\) −14.9822 −0.859287
\(305\) 4.22438 0.241887
\(306\) −9.30394 −0.531871
\(307\) −1.88110 −0.107360 −0.0536800 0.998558i \(-0.517095\pi\)
−0.0536800 + 0.998558i \(0.517095\pi\)
\(308\) 4.34478 0.247567
\(309\) 31.4249 1.78770
\(310\) −8.47603 −0.481406
\(311\) 22.3152 1.26538 0.632689 0.774406i \(-0.281951\pi\)
0.632689 + 0.774406i \(0.281951\pi\)
\(312\) −6.34889 −0.359435
\(313\) −0.459320 −0.0259623 −0.0129811 0.999916i \(-0.504132\pi\)
−0.0129811 + 0.999916i \(0.504132\pi\)
\(314\) −15.8402 −0.893914
\(315\) −20.2204 −1.13929
\(316\) −0.295449 −0.0166203
\(317\) −9.73978 −0.547041 −0.273520 0.961866i \(-0.588188\pi\)
−0.273520 + 0.961866i \(0.588188\pi\)
\(318\) −57.7894 −3.24067
\(319\) −0.453833 −0.0254098
\(320\) −1.46926 −0.0821344
\(321\) 35.6326 1.98882
\(322\) 51.0227 2.84339
\(323\) 3.00298 0.167090
\(324\) 4.02291 0.223495
\(325\) 5.13025 0.284575
\(326\) 12.9385 0.716596
\(327\) 39.2820 2.17230
\(328\) 8.02230 0.442957
\(329\) −5.72126 −0.315423
\(330\) 3.77493 0.207803
\(331\) 4.13443 0.227249 0.113624 0.993524i \(-0.463754\pi\)
0.113624 + 0.993524i \(0.463754\pi\)
\(332\) 10.0256 0.550227
\(333\) 6.36428 0.348760
\(334\) −22.3293 −1.22181
\(335\) −1.97465 −0.107886
\(336\) −70.4271 −3.84211
\(337\) −34.2926 −1.86804 −0.934019 0.357223i \(-0.883724\pi\)
−0.934019 + 0.357223i \(0.883724\pi\)
\(338\) 19.8278 1.07849
\(339\) 33.8035 1.83596
\(340\) −0.682790 −0.0370295
\(341\) −6.53377 −0.353823
\(342\) −27.9395 −1.51080
\(343\) 46.2445 2.49697
\(344\) 1.87925 0.101322
\(345\) 13.7117 0.738213
\(346\) −21.7073 −1.16699
\(347\) −25.6726 −1.37818 −0.689088 0.724678i \(-0.741989\pi\)
−0.689088 + 0.724678i \(0.741989\pi\)
\(348\) −1.18279 −0.0634040
\(349\) −17.0157 −0.910829 −0.455414 0.890280i \(-0.650509\pi\)
−0.455414 + 0.890280i \(0.650509\pi\)
\(350\) 36.4766 1.94976
\(351\) −8.33650 −0.444969
\(352\) 4.73124 0.252176
\(353\) 19.4200 1.03362 0.516811 0.856100i \(-0.327119\pi\)
0.516811 + 0.856100i \(0.327119\pi\)
\(354\) 19.9587 1.06079
\(355\) −11.0048 −0.584076
\(356\) −6.89997 −0.365698
\(357\) 14.1162 0.747107
\(358\) −30.0733 −1.58942
\(359\) 16.2396 0.857094 0.428547 0.903520i \(-0.359026\pi\)
0.428547 + 0.903520i \(0.359026\pi\)
\(360\) −7.83317 −0.412844
\(361\) −9.98212 −0.525375
\(362\) 4.87112 0.256021
\(363\) 2.90991 0.152731
\(364\) −5.04429 −0.264393
\(365\) −0.0786461 −0.00411652
\(366\) 27.4383 1.43422
\(367\) −4.61048 −0.240665 −0.120333 0.992734i \(-0.538396\pi\)
−0.120333 + 0.992734i \(0.538396\pi\)
\(368\) 30.8374 1.60751
\(369\) 23.3404 1.21505
\(370\) 1.51002 0.0785022
\(371\) 56.6153 2.93932
\(372\) −17.0284 −0.882881
\(373\) 6.26221 0.324245 0.162122 0.986771i \(-0.448166\pi\)
0.162122 + 0.986771i \(0.448166\pi\)
\(374\) −1.70166 −0.0879905
\(375\) 20.8945 1.07899
\(376\) −2.21636 −0.114300
\(377\) 0.526901 0.0271368
\(378\) −59.2734 −3.04870
\(379\) −0.362889 −0.0186404 −0.00932018 0.999957i \(-0.502967\pi\)
−0.00932018 + 0.999957i \(0.502967\pi\)
\(380\) −2.05040 −0.105184
\(381\) −40.6475 −2.08243
\(382\) 45.1530 2.31023
\(383\) 27.6383 1.41225 0.706126 0.708086i \(-0.250441\pi\)
0.706126 + 0.708086i \(0.250441\pi\)
\(384\) −37.0782 −1.89214
\(385\) −3.69823 −0.188479
\(386\) 41.8478 2.13000
\(387\) 5.46758 0.277933
\(388\) 5.11736 0.259795
\(389\) 15.2017 0.770759 0.385380 0.922758i \(-0.374071\pi\)
0.385380 + 0.922758i \(0.374071\pi\)
\(390\) −4.38269 −0.221926
\(391\) −6.18094 −0.312584
\(392\) 31.0694 1.56924
\(393\) −1.46179 −0.0737374
\(394\) 23.7122 1.19461
\(395\) 0.251484 0.0126535
\(396\) 4.89695 0.246081
\(397\) 24.1442 1.21176 0.605881 0.795555i \(-0.292821\pi\)
0.605881 + 0.795555i \(0.292821\pi\)
\(398\) 26.5380 1.33023
\(399\) 42.3906 2.12218
\(400\) 22.0459 1.10230
\(401\) −22.3239 −1.11480 −0.557401 0.830244i \(-0.688201\pi\)
−0.557401 + 0.830244i \(0.688201\pi\)
\(402\) −12.8258 −0.639691
\(403\) 7.58571 0.377871
\(404\) 12.2678 0.610345
\(405\) −3.42427 −0.170153
\(406\) 3.74632 0.185927
\(407\) 1.16400 0.0576975
\(408\) 5.46846 0.270729
\(409\) −31.0517 −1.53541 −0.767703 0.640806i \(-0.778600\pi\)
−0.767703 + 0.640806i \(0.778600\pi\)
\(410\) 5.53786 0.273496
\(411\) −19.1002 −0.942143
\(412\) 9.67218 0.476514
\(413\) −19.5532 −0.962148
\(414\) 57.5071 2.82632
\(415\) −8.53370 −0.418903
\(416\) −5.49298 −0.269315
\(417\) 50.6989 2.48273
\(418\) −5.11004 −0.249940
\(419\) 11.1652 0.545455 0.272727 0.962091i \(-0.412074\pi\)
0.272727 + 0.962091i \(0.412074\pi\)
\(420\) −9.63838 −0.470305
\(421\) 12.1029 0.589860 0.294930 0.955519i \(-0.404704\pi\)
0.294930 + 0.955519i \(0.404704\pi\)
\(422\) −31.9196 −1.55382
\(423\) −6.44837 −0.313530
\(424\) 21.9322 1.06512
\(425\) −4.41882 −0.214344
\(426\) −71.4789 −3.46316
\(427\) −26.8808 −1.30085
\(428\) 10.9673 0.530123
\(429\) −3.37841 −0.163111
\(430\) 1.29727 0.0625597
\(431\) −17.9494 −0.864592 −0.432296 0.901732i \(-0.642296\pi\)
−0.432296 + 0.901732i \(0.642296\pi\)
\(432\) −35.8240 −1.72358
\(433\) 15.5663 0.748069 0.374035 0.927415i \(-0.377974\pi\)
0.374035 + 0.927415i \(0.377974\pi\)
\(434\) 53.9352 2.58897
\(435\) 1.00678 0.0482712
\(436\) 12.0905 0.579030
\(437\) −18.5612 −0.887905
\(438\) −0.510824 −0.0244081
\(439\) −27.8099 −1.32729 −0.663646 0.748047i \(-0.730992\pi\)
−0.663646 + 0.748047i \(0.730992\pi\)
\(440\) −1.43266 −0.0682992
\(441\) 90.3947 4.30451
\(442\) 1.97562 0.0939709
\(443\) −0.274111 −0.0130234 −0.00651170 0.999979i \(-0.502073\pi\)
−0.00651170 + 0.999979i \(0.502073\pi\)
\(444\) 3.03364 0.143970
\(445\) 5.87319 0.278416
\(446\) −1.51899 −0.0719264
\(447\) 70.1482 3.31789
\(448\) 9.34932 0.441714
\(449\) 25.3890 1.19818 0.599092 0.800680i \(-0.295529\pi\)
0.599092 + 0.800680i \(0.295529\pi\)
\(450\) 41.1124 1.93806
\(451\) 4.26888 0.201014
\(452\) 10.4043 0.489377
\(453\) 48.4602 2.27686
\(454\) 9.81921 0.460838
\(455\) 4.29365 0.201290
\(456\) 16.4217 0.769015
\(457\) −36.6655 −1.71514 −0.857571 0.514366i \(-0.828027\pi\)
−0.857571 + 0.514366i \(0.828027\pi\)
\(458\) −9.35213 −0.436996
\(459\) 7.18044 0.335154
\(460\) 4.22029 0.196772
\(461\) −11.4090 −0.531371 −0.265685 0.964060i \(-0.585598\pi\)
−0.265685 + 0.964060i \(0.585598\pi\)
\(462\) −24.0209 −1.11755
\(463\) 19.2671 0.895418 0.447709 0.894179i \(-0.352240\pi\)
0.447709 + 0.894179i \(0.352240\pi\)
\(464\) 2.26422 0.105114
\(465\) 14.4944 0.672162
\(466\) −12.9463 −0.599728
\(467\) −18.7069 −0.865654 −0.432827 0.901477i \(-0.642484\pi\)
−0.432827 + 0.901477i \(0.642484\pi\)
\(468\) −5.68536 −0.262806
\(469\) 12.5652 0.580207
\(470\) −1.52997 −0.0705723
\(471\) 27.0875 1.24813
\(472\) −7.57469 −0.348653
\(473\) 1.00000 0.0459800
\(474\) 1.63344 0.0750265
\(475\) −13.2696 −0.608851
\(476\) 4.34478 0.199143
\(477\) 63.8105 2.92168
\(478\) −23.4253 −1.07145
\(479\) −40.4258 −1.84710 −0.923550 0.383478i \(-0.874726\pi\)
−0.923550 + 0.383478i \(0.874726\pi\)
\(480\) −10.4957 −0.479061
\(481\) −1.35141 −0.0616189
\(482\) 50.0549 2.27994
\(483\) −87.2512 −3.97007
\(484\) 0.895633 0.0407106
\(485\) −4.35585 −0.197789
\(486\) 14.4145 0.653856
\(487\) 18.8515 0.854242 0.427121 0.904194i \(-0.359528\pi\)
0.427121 + 0.904194i \(0.359528\pi\)
\(488\) −10.4134 −0.471390
\(489\) −22.1254 −1.00055
\(490\) 21.4475 0.968899
\(491\) −10.0230 −0.452331 −0.226166 0.974089i \(-0.572619\pi\)
−0.226166 + 0.974089i \(0.572619\pi\)
\(492\) 11.1256 0.501581
\(493\) −0.453833 −0.0204396
\(494\) 5.93276 0.266928
\(495\) −4.16824 −0.187348
\(496\) 32.5977 1.46368
\(497\) 70.0267 3.14113
\(498\) −55.4283 −2.48380
\(499\) −13.9057 −0.622504 −0.311252 0.950327i \(-0.600748\pi\)
−0.311252 + 0.950327i \(0.600748\pi\)
\(500\) 6.43107 0.287606
\(501\) 38.1842 1.70594
\(502\) 2.41774 0.107909
\(503\) 10.9632 0.488824 0.244412 0.969671i \(-0.421405\pi\)
0.244412 + 0.969671i \(0.421405\pi\)
\(504\) 49.8445 2.22025
\(505\) −10.4422 −0.464673
\(506\) 10.5178 0.467575
\(507\) −33.9065 −1.50584
\(508\) −12.5108 −0.555076
\(509\) −34.2212 −1.51683 −0.758414 0.651773i \(-0.774025\pi\)
−0.758414 + 0.651773i \(0.774025\pi\)
\(510\) 3.77493 0.167157
\(511\) 0.500446 0.0221384
\(512\) −4.85308 −0.214478
\(513\) 21.5627 0.952017
\(514\) −9.18457 −0.405114
\(515\) −8.23287 −0.362784
\(516\) 2.60621 0.114732
\(517\) −1.17938 −0.0518692
\(518\) −9.60866 −0.422180
\(519\) 37.1205 1.62941
\(520\) 1.66332 0.0729412
\(521\) −6.92194 −0.303256 −0.151628 0.988438i \(-0.548452\pi\)
−0.151628 + 0.988438i \(0.548452\pi\)
\(522\) 4.22244 0.184811
\(523\) −4.78597 −0.209276 −0.104638 0.994510i \(-0.533368\pi\)
−0.104638 + 0.994510i \(0.533368\pi\)
\(524\) −0.449919 −0.0196548
\(525\) −62.3768 −2.72234
\(526\) 27.4282 1.19593
\(527\) −6.53377 −0.284615
\(528\) −14.5179 −0.631809
\(529\) 15.2040 0.661045
\(530\) 15.1400 0.657639
\(531\) −22.0381 −0.956374
\(532\) 13.0473 0.565671
\(533\) −4.95617 −0.214676
\(534\) 38.1477 1.65081
\(535\) −9.33523 −0.403597
\(536\) 4.86763 0.210249
\(537\) 51.4267 2.21923
\(538\) −46.8540 −2.02002
\(539\) 16.5328 0.712120
\(540\) −4.90273 −0.210980
\(541\) −2.35057 −0.101059 −0.0505295 0.998723i \(-0.516091\pi\)
−0.0505295 + 0.998723i \(0.516091\pi\)
\(542\) −22.1902 −0.953149
\(543\) −8.32985 −0.357468
\(544\) 4.73124 0.202850
\(545\) −10.2913 −0.440832
\(546\) 27.8883 1.19351
\(547\) −28.9499 −1.23781 −0.618904 0.785466i \(-0.712423\pi\)
−0.618904 + 0.785466i \(0.712423\pi\)
\(548\) −5.87880 −0.251130
\(549\) −30.2971 −1.29305
\(550\) 7.51930 0.320624
\(551\) −1.36285 −0.0580594
\(552\) −33.8002 −1.43863
\(553\) −1.60026 −0.0680499
\(554\) 11.2311 0.477163
\(555\) −2.58220 −0.109608
\(556\) 15.6045 0.661777
\(557\) 24.8573 1.05324 0.526620 0.850101i \(-0.323459\pi\)
0.526620 + 0.850101i \(0.323459\pi\)
\(558\) 60.7898 2.57344
\(559\) −1.16100 −0.0491051
\(560\) 18.4509 0.779692
\(561\) 2.90991 0.122857
\(562\) 45.9462 1.93812
\(563\) 41.9189 1.76667 0.883336 0.468740i \(-0.155292\pi\)
0.883336 + 0.468740i \(0.155292\pi\)
\(564\) −3.07372 −0.129427
\(565\) −8.85604 −0.372576
\(566\) 25.5123 1.07236
\(567\) 21.7895 0.915074
\(568\) 27.1276 1.13825
\(569\) −6.29638 −0.263958 −0.131979 0.991253i \(-0.542133\pi\)
−0.131979 + 0.991253i \(0.542133\pi\)
\(570\) 11.3360 0.474814
\(571\) 16.1733 0.676831 0.338415 0.940997i \(-0.390109\pi\)
0.338415 + 0.940997i \(0.390109\pi\)
\(572\) −1.03983 −0.0434775
\(573\) −77.2137 −3.22565
\(574\) −35.2389 −1.47084
\(575\) 27.3124 1.13901
\(576\) 10.5375 0.439063
\(577\) 17.0022 0.707812 0.353906 0.935281i \(-0.384853\pi\)
0.353906 + 0.935281i \(0.384853\pi\)
\(578\) −1.70166 −0.0707796
\(579\) −71.5617 −2.97400
\(580\) 0.309873 0.0128668
\(581\) 54.3022 2.25284
\(582\) −28.2922 −1.17275
\(583\) 11.6707 0.483351
\(584\) 0.193868 0.00802229
\(585\) 4.83933 0.200082
\(586\) 55.3251 2.28546
\(587\) −29.1572 −1.20344 −0.601722 0.798705i \(-0.705519\pi\)
−0.601722 + 0.798705i \(0.705519\pi\)
\(588\) 43.0881 1.77692
\(589\) −19.6208 −0.808459
\(590\) −5.22888 −0.215270
\(591\) −40.5490 −1.66796
\(592\) −5.80734 −0.238680
\(593\) −17.6820 −0.726112 −0.363056 0.931767i \(-0.618267\pi\)
−0.363056 + 0.931767i \(0.618267\pi\)
\(594\) −12.2186 −0.501337
\(595\) −3.69823 −0.151613
\(596\) 21.5907 0.884390
\(597\) −45.3813 −1.85733
\(598\) −12.2112 −0.499354
\(599\) −34.0242 −1.39019 −0.695096 0.718917i \(-0.744638\pi\)
−0.695096 + 0.718917i \(0.744638\pi\)
\(600\) −24.1641 −0.986495
\(601\) 29.1288 1.18819 0.594094 0.804396i \(-0.297511\pi\)
0.594094 + 0.804396i \(0.297511\pi\)
\(602\) −8.25485 −0.336442
\(603\) 14.1621 0.576725
\(604\) 14.9154 0.606900
\(605\) −0.762355 −0.0309941
\(606\) −67.8247 −2.75519
\(607\) −29.2933 −1.18898 −0.594489 0.804104i \(-0.702646\pi\)
−0.594489 + 0.804104i \(0.702646\pi\)
\(608\) 14.2078 0.576203
\(609\) −6.40638 −0.259600
\(610\) −7.18843 −0.291051
\(611\) 1.36926 0.0553945
\(612\) 4.89695 0.197947
\(613\) 13.9395 0.563012 0.281506 0.959560i \(-0.409166\pi\)
0.281506 + 0.959560i \(0.409166\pi\)
\(614\) 3.20099 0.129181
\(615\) −9.47001 −0.381867
\(616\) 9.11638 0.367309
\(617\) 0.573538 0.0230898 0.0115449 0.999933i \(-0.496325\pi\)
0.0115449 + 0.999933i \(0.496325\pi\)
\(618\) −53.4744 −2.15105
\(619\) −47.6883 −1.91676 −0.958378 0.285503i \(-0.907839\pi\)
−0.958378 + 0.285503i \(0.907839\pi\)
\(620\) 4.46119 0.179166
\(621\) −44.3819 −1.78098
\(622\) −37.9728 −1.52257
\(623\) −37.3727 −1.49730
\(624\) 16.8553 0.674750
\(625\) 16.6200 0.664800
\(626\) 0.781604 0.0312392
\(627\) 8.73840 0.348978
\(628\) 8.33718 0.332690
\(629\) 1.16400 0.0464118
\(630\) 34.4081 1.37085
\(631\) −16.1955 −0.644731 −0.322366 0.946615i \(-0.604478\pi\)
−0.322366 + 0.946615i \(0.604478\pi\)
\(632\) −0.619923 −0.0246592
\(633\) 54.5841 2.16952
\(634\) 16.5738 0.658228
\(635\) 10.6491 0.422595
\(636\) 30.4163 1.20609
\(637\) −19.1947 −0.760520
\(638\) 0.772268 0.0305744
\(639\) 78.9263 3.12228
\(640\) 9.71395 0.383978
\(641\) −30.1235 −1.18981 −0.594904 0.803797i \(-0.702810\pi\)
−0.594904 + 0.803797i \(0.702810\pi\)
\(642\) −60.6345 −2.39305
\(643\) −26.6063 −1.04925 −0.524626 0.851333i \(-0.675795\pi\)
−0.524626 + 0.851333i \(0.675795\pi\)
\(644\) −26.8548 −1.05823
\(645\) −2.21838 −0.0873488
\(646\) −5.11004 −0.201052
\(647\) −7.53738 −0.296325 −0.148163 0.988963i \(-0.547336\pi\)
−0.148163 + 0.988963i \(0.547336\pi\)
\(648\) 8.44103 0.331595
\(649\) −4.03069 −0.158219
\(650\) −8.72992 −0.342416
\(651\) −92.2317 −3.61485
\(652\) −6.80992 −0.266697
\(653\) 47.4065 1.85516 0.927579 0.373627i \(-0.121886\pi\)
0.927579 + 0.373627i \(0.121886\pi\)
\(654\) −66.8445 −2.61383
\(655\) 0.382967 0.0149638
\(656\) −21.2979 −0.831543
\(657\) 0.564047 0.0220056
\(658\) 9.73562 0.379534
\(659\) −30.9022 −1.20378 −0.601889 0.798580i \(-0.705585\pi\)
−0.601889 + 0.798580i \(0.705585\pi\)
\(660\) −1.98686 −0.0773384
\(661\) −4.57688 −0.178020 −0.0890100 0.996031i \(-0.528370\pi\)
−0.0890100 + 0.996031i \(0.528370\pi\)
\(662\) −7.03538 −0.273438
\(663\) −3.37841 −0.131207
\(664\) 21.0361 0.816359
\(665\) −11.1057 −0.430661
\(666\) −10.8298 −0.419647
\(667\) 2.80512 0.108615
\(668\) 11.7526 0.454722
\(669\) 2.59755 0.100427
\(670\) 3.36017 0.129815
\(671\) −5.54122 −0.213916
\(672\) 66.7870 2.57636
\(673\) −16.9192 −0.652186 −0.326093 0.945338i \(-0.605732\pi\)
−0.326093 + 0.945338i \(0.605732\pi\)
\(674\) 58.3543 2.24772
\(675\) −31.7290 −1.22125
\(676\) −10.4360 −0.401384
\(677\) −0.491343 −0.0188838 −0.00944191 0.999955i \(-0.503005\pi\)
−0.00944191 + 0.999955i \(0.503005\pi\)
\(678\) −57.5220 −2.20912
\(679\) 27.7174 1.06370
\(680\) −1.43266 −0.0549399
\(681\) −16.7913 −0.643444
\(682\) 11.1182 0.425739
\(683\) −34.0326 −1.30222 −0.651111 0.758982i \(-0.725697\pi\)
−0.651111 + 0.758982i \(0.725697\pi\)
\(684\) 14.7054 0.562276
\(685\) 5.00398 0.191192
\(686\) −78.6922 −3.00448
\(687\) 15.9926 0.610155
\(688\) −4.98911 −0.190208
\(689\) −13.5497 −0.516202
\(690\) −23.3326 −0.888257
\(691\) 20.4091 0.776397 0.388199 0.921576i \(-0.373097\pi\)
0.388199 + 0.921576i \(0.373097\pi\)
\(692\) 11.4252 0.434322
\(693\) 26.5236 1.00755
\(694\) 43.6859 1.65829
\(695\) −13.2824 −0.503829
\(696\) −2.48177 −0.0940711
\(697\) 4.26888 0.161695
\(698\) 28.9549 1.09596
\(699\) 22.1388 0.837368
\(700\) −19.1988 −0.725645
\(701\) 39.9271 1.50803 0.754013 0.656859i \(-0.228115\pi\)
0.754013 + 0.656859i \(0.228115\pi\)
\(702\) 14.1859 0.535411
\(703\) 3.49548 0.131834
\(704\) 1.92727 0.0726368
\(705\) 2.61632 0.0985364
\(706\) −33.0461 −1.24371
\(707\) 66.4467 2.49899
\(708\) −10.5048 −0.394796
\(709\) −36.9640 −1.38821 −0.694106 0.719873i \(-0.744200\pi\)
−0.694106 + 0.719873i \(0.744200\pi\)
\(710\) 18.7264 0.702791
\(711\) −1.80363 −0.0676415
\(712\) −14.4778 −0.542578
\(713\) 40.3848 1.51242
\(714\) −24.0209 −0.898958
\(715\) 0.885095 0.0331007
\(716\) 15.8285 0.591539
\(717\) 40.0584 1.49601
\(718\) −27.6342 −1.03130
\(719\) −43.0630 −1.60598 −0.802989 0.595994i \(-0.796758\pi\)
−0.802989 + 0.595994i \(0.796758\pi\)
\(720\) 20.7958 0.775013
\(721\) 52.3880 1.95103
\(722\) 16.9861 0.632158
\(723\) −85.5961 −3.18335
\(724\) −2.56382 −0.0952836
\(725\) 2.00540 0.0744788
\(726\) −4.95167 −0.183774
\(727\) 43.0776 1.59766 0.798829 0.601558i \(-0.205453\pi\)
0.798829 + 0.601558i \(0.205453\pi\)
\(728\) −10.5841 −0.392274
\(729\) −38.1246 −1.41202
\(730\) 0.133829 0.00495322
\(731\) 1.00000 0.0369863
\(732\) −14.4416 −0.533777
\(733\) −35.5631 −1.31355 −0.656777 0.754085i \(-0.728081\pi\)
−0.656777 + 0.754085i \(0.728081\pi\)
\(734\) 7.84545 0.289581
\(735\) −36.6762 −1.35282
\(736\) −29.2435 −1.07793
\(737\) 2.59019 0.0954110
\(738\) −39.7174 −1.46202
\(739\) 3.01489 0.110904 0.0554522 0.998461i \(-0.482340\pi\)
0.0554522 + 0.998461i \(0.482340\pi\)
\(740\) −0.794770 −0.0292163
\(741\) −10.1453 −0.372697
\(742\) −96.3398 −3.53675
\(743\) 38.3071 1.40535 0.702675 0.711511i \(-0.251989\pi\)
0.702675 + 0.711511i \(0.251989\pi\)
\(744\) −35.7296 −1.30991
\(745\) −18.3778 −0.673311
\(746\) −10.6561 −0.390148
\(747\) 61.2034 2.23932
\(748\) 0.895633 0.0327476
\(749\) 59.4026 2.17052
\(750\) −35.5553 −1.29830
\(751\) −22.5715 −0.823644 −0.411822 0.911264i \(-0.635107\pi\)
−0.411822 + 0.911264i \(0.635107\pi\)
\(752\) 5.88407 0.214570
\(753\) −4.13444 −0.150667
\(754\) −0.896604 −0.0326524
\(755\) −12.6959 −0.462050
\(756\) 31.1974 1.13464
\(757\) 36.0553 1.31045 0.655226 0.755433i \(-0.272573\pi\)
0.655226 + 0.755433i \(0.272573\pi\)
\(758\) 0.617512 0.0224291
\(759\) −17.9860 −0.652850
\(760\) −4.30224 −0.156059
\(761\) 4.40959 0.159848 0.0799238 0.996801i \(-0.474532\pi\)
0.0799238 + 0.996801i \(0.474532\pi\)
\(762\) 69.1680 2.50569
\(763\) 65.4865 2.37077
\(764\) −23.7654 −0.859801
\(765\) −4.16824 −0.150703
\(766\) −47.0309 −1.69930
\(767\) 4.67964 0.168972
\(768\) 51.8779 1.87198
\(769\) 14.6180 0.527140 0.263570 0.964640i \(-0.415100\pi\)
0.263570 + 0.964640i \(0.415100\pi\)
\(770\) 6.29312 0.226788
\(771\) 15.7060 0.565639
\(772\) −22.0258 −0.792726
\(773\) −53.4906 −1.92392 −0.961962 0.273183i \(-0.911924\pi\)
−0.961962 + 0.273183i \(0.911924\pi\)
\(774\) −9.30394 −0.334423
\(775\) 28.8715 1.03710
\(776\) 10.7374 0.385452
\(777\) 16.4313 0.589468
\(778\) −25.8681 −0.927418
\(779\) 12.8193 0.459301
\(780\) 2.30675 0.0825947
\(781\) 14.4353 0.516536
\(782\) 10.5178 0.376117
\(783\) −3.25872 −0.116457
\(784\) −82.4842 −2.94586
\(785\) −7.09653 −0.253286
\(786\) 2.48746 0.0887247
\(787\) 14.9521 0.532984 0.266492 0.963837i \(-0.414135\pi\)
0.266492 + 0.963837i \(0.414135\pi\)
\(788\) −12.4805 −0.444598
\(789\) −46.9036 −1.66981
\(790\) −0.427939 −0.0152254
\(791\) 56.3533 2.00369
\(792\) 10.2750 0.365105
\(793\) 6.43336 0.228455
\(794\) −41.0851 −1.45806
\(795\) −25.8901 −0.918227
\(796\) −13.9678 −0.495075
\(797\) 31.0101 1.09843 0.549217 0.835680i \(-0.314926\pi\)
0.549217 + 0.835680i \(0.314926\pi\)
\(798\) −72.1342 −2.55352
\(799\) −1.17938 −0.0417235
\(800\) −20.9065 −0.739156
\(801\) −42.1223 −1.48832
\(802\) 37.9876 1.34139
\(803\) 0.103162 0.00364051
\(804\) 6.75059 0.238075
\(805\) 22.8586 0.805659
\(806\) −12.9083 −0.454674
\(807\) 80.1225 2.82045
\(808\) 25.7408 0.905557
\(809\) 27.8537 0.979282 0.489641 0.871924i \(-0.337128\pi\)
0.489641 + 0.871924i \(0.337128\pi\)
\(810\) 5.82692 0.204737
\(811\) −35.2939 −1.23934 −0.619668 0.784864i \(-0.712733\pi\)
−0.619668 + 0.784864i \(0.712733\pi\)
\(812\) −1.97180 −0.0691967
\(813\) 37.9462 1.33083
\(814\) −1.98073 −0.0694246
\(815\) 5.79654 0.203044
\(816\) −14.5179 −0.508227
\(817\) 3.00298 0.105061
\(818\) 52.8393 1.84748
\(819\) −30.7939 −1.07603
\(820\) −2.91475 −0.101787
\(821\) 8.12327 0.283504 0.141752 0.989902i \(-0.454726\pi\)
0.141752 + 0.989902i \(0.454726\pi\)
\(822\) 32.5020 1.13364
\(823\) −18.3269 −0.638837 −0.319418 0.947614i \(-0.603488\pi\)
−0.319418 + 0.947614i \(0.603488\pi\)
\(824\) 20.2945 0.706994
\(825\) −12.8584 −0.447671
\(826\) 33.2728 1.15771
\(827\) −14.7052 −0.511350 −0.255675 0.966763i \(-0.582298\pi\)
−0.255675 + 0.966763i \(0.582298\pi\)
\(828\) −30.2677 −1.05188
\(829\) −40.6716 −1.41258 −0.706292 0.707921i \(-0.749633\pi\)
−0.706292 + 0.707921i \(0.749633\pi\)
\(830\) 14.5214 0.504046
\(831\) −19.2057 −0.666238
\(832\) −2.23756 −0.0775736
\(833\) 16.5328 0.572829
\(834\) −86.2720 −2.98736
\(835\) −10.0037 −0.346193
\(836\) 2.68957 0.0930207
\(837\) −46.9153 −1.62163
\(838\) −18.9993 −0.656320
\(839\) 19.3637 0.668509 0.334254 0.942483i \(-0.391516\pi\)
0.334254 + 0.942483i \(0.391516\pi\)
\(840\) −20.2236 −0.697781
\(841\) −28.7940 −0.992898
\(842\) −20.5950 −0.709751
\(843\) −78.5702 −2.70610
\(844\) 16.8003 0.578289
\(845\) 8.88301 0.305585
\(846\) 10.9729 0.377256
\(847\) 4.85107 0.166685
\(848\) −58.2264 −1.99950
\(849\) −43.6271 −1.49728
\(850\) 7.51930 0.257910
\(851\) −7.19463 −0.246629
\(852\) 37.6215 1.28889
\(853\) −31.4458 −1.07668 −0.538342 0.842726i \(-0.680949\pi\)
−0.538342 + 0.842726i \(0.680949\pi\)
\(854\) 45.7419 1.56526
\(855\) −12.5171 −0.428077
\(856\) 23.0119 0.786532
\(857\) −8.41670 −0.287509 −0.143754 0.989613i \(-0.545918\pi\)
−0.143754 + 0.989613i \(0.545918\pi\)
\(858\) 5.74889 0.196264
\(859\) 7.20630 0.245876 0.122938 0.992414i \(-0.460768\pi\)
0.122938 + 0.992414i \(0.460768\pi\)
\(860\) −0.682790 −0.0232830
\(861\) 60.2602 2.05366
\(862\) 30.5437 1.04032
\(863\) −12.1313 −0.412956 −0.206478 0.978451i \(-0.566200\pi\)
−0.206478 + 0.978451i \(0.566200\pi\)
\(864\) 33.9724 1.15576
\(865\) −9.72504 −0.330661
\(866\) −26.4885 −0.900116
\(867\) 2.90991 0.0988258
\(868\) −28.3878 −0.963543
\(869\) −0.329877 −0.0111903
\(870\) −1.71319 −0.0580824
\(871\) −3.00722 −0.101896
\(872\) 25.3688 0.859095
\(873\) 31.2400 1.05731
\(874\) 31.5848 1.06837
\(875\) 34.8330 1.17757
\(876\) 0.268862 0.00908401
\(877\) −40.7127 −1.37477 −0.687385 0.726293i \(-0.741242\pi\)
−0.687385 + 0.726293i \(0.741242\pi\)
\(878\) 47.3228 1.59707
\(879\) −94.6084 −3.19106
\(880\) 3.80347 0.128215
\(881\) −13.3840 −0.450918 −0.225459 0.974253i \(-0.572388\pi\)
−0.225459 + 0.974253i \(0.572388\pi\)
\(882\) −153.821 −5.17941
\(883\) 4.13366 0.139109 0.0695544 0.997578i \(-0.477842\pi\)
0.0695544 + 0.997578i \(0.477842\pi\)
\(884\) −1.03983 −0.0349733
\(885\) 8.94162 0.300569
\(886\) 0.466442 0.0156704
\(887\) 33.9265 1.13914 0.569571 0.821942i \(-0.307109\pi\)
0.569571 + 0.821942i \(0.307109\pi\)
\(888\) 6.36530 0.213605
\(889\) −67.7628 −2.27269
\(890\) −9.99415 −0.335005
\(891\) 4.49170 0.150478
\(892\) 0.799492 0.0267690
\(893\) −3.54166 −0.118517
\(894\) −119.368 −3.99227
\(895\) −13.4731 −0.450355
\(896\) −61.8125 −2.06501
\(897\) 20.8818 0.697222
\(898\) −43.2034 −1.44172
\(899\) 2.96524 0.0988962
\(900\) −21.6387 −0.721290
\(901\) 11.6707 0.388807
\(902\) −7.26416 −0.241870
\(903\) 14.1162 0.469757
\(904\) 21.8307 0.726078
\(905\) 2.18230 0.0725421
\(906\) −82.4626 −2.73964
\(907\) 12.7248 0.422519 0.211260 0.977430i \(-0.432243\pi\)
0.211260 + 0.977430i \(0.432243\pi\)
\(908\) −5.16815 −0.171511
\(909\) 74.8913 2.48399
\(910\) −7.30632 −0.242202
\(911\) 2.28872 0.0758287 0.0379144 0.999281i \(-0.487929\pi\)
0.0379144 + 0.999281i \(0.487929\pi\)
\(912\) −43.5968 −1.44364
\(913\) 11.1939 0.370463
\(914\) 62.3921 2.06375
\(915\) 12.2926 0.406379
\(916\) 4.92231 0.162638
\(917\) −2.43692 −0.0804742
\(918\) −12.2186 −0.403275
\(919\) −52.0715 −1.71768 −0.858840 0.512244i \(-0.828814\pi\)
−0.858840 + 0.512244i \(0.828814\pi\)
\(920\) 8.85517 0.291946
\(921\) −5.47383 −0.180369
\(922\) 19.4142 0.639373
\(923\) −16.7594 −0.551643
\(924\) 12.6429 0.415921
\(925\) −5.14351 −0.169118
\(926\) −32.7860 −1.07741
\(927\) 59.0459 1.93932
\(928\) −2.14719 −0.0704851
\(929\) 8.63984 0.283464 0.141732 0.989905i \(-0.454733\pi\)
0.141732 + 0.989905i \(0.454733\pi\)
\(930\) −24.6645 −0.808780
\(931\) 49.6478 1.62714
\(932\) 6.81405 0.223202
\(933\) 64.9352 2.12588
\(934\) 31.8328 1.04160
\(935\) −0.762355 −0.0249317
\(936\) −11.9292 −0.389920
\(937\) 29.5769 0.966236 0.483118 0.875555i \(-0.339504\pi\)
0.483118 + 0.875555i \(0.339504\pi\)
\(938\) −21.3816 −0.698135
\(939\) −1.33658 −0.0436176
\(940\) 0.805271 0.0262650
\(941\) −44.8128 −1.46085 −0.730427 0.682991i \(-0.760679\pi\)
−0.730427 + 0.682991i \(0.760679\pi\)
\(942\) −46.0936 −1.50181
\(943\) −26.3857 −0.859236
\(944\) 20.1096 0.654510
\(945\) −26.5549 −0.863832
\(946\) −1.70166 −0.0553256
\(947\) −18.6867 −0.607237 −0.303618 0.952794i \(-0.598195\pi\)
−0.303618 + 0.952794i \(0.598195\pi\)
\(948\) −0.859731 −0.0279228
\(949\) −0.119771 −0.00388794
\(950\) 22.5803 0.732602
\(951\) −28.3419 −0.919049
\(952\) 9.11638 0.295464
\(953\) 25.1447 0.814518 0.407259 0.913313i \(-0.366485\pi\)
0.407259 + 0.913313i \(0.366485\pi\)
\(954\) −108.583 −3.51552
\(955\) 20.2289 0.654591
\(956\) 12.3295 0.398763
\(957\) −1.32061 −0.0426894
\(958\) 68.7907 2.22253
\(959\) −31.8416 −1.02822
\(960\) −4.27543 −0.137989
\(961\) 11.6901 0.377100
\(962\) 2.29963 0.0741431
\(963\) 66.9520 2.15750
\(964\) −26.3454 −0.848528
\(965\) 18.7481 0.603524
\(966\) 148.472 4.77700
\(967\) 7.68107 0.247007 0.123503 0.992344i \(-0.460587\pi\)
0.123503 + 0.992344i \(0.460587\pi\)
\(968\) 1.87925 0.0604015
\(969\) 8.73840 0.280718
\(970\) 7.41216 0.237990
\(971\) 34.2057 1.09771 0.548857 0.835916i \(-0.315063\pi\)
0.548857 + 0.835916i \(0.315063\pi\)
\(972\) −7.58680 −0.243347
\(973\) 84.5193 2.70956
\(974\) −32.0787 −1.02787
\(975\) 14.9286 0.478097
\(976\) 27.6457 0.884919
\(977\) 39.3289 1.25824 0.629122 0.777306i \(-0.283414\pi\)
0.629122 + 0.777306i \(0.283414\pi\)
\(978\) 37.6498 1.20391
\(979\) −7.70401 −0.246221
\(980\) −11.2885 −0.360597
\(981\) 73.8091 2.35654
\(982\) 17.0557 0.544269
\(983\) −48.2168 −1.53788 −0.768938 0.639323i \(-0.779215\pi\)
−0.768938 + 0.639323i \(0.779215\pi\)
\(984\) 23.3442 0.744185
\(985\) 10.6233 0.338485
\(986\) 0.772268 0.0245940
\(987\) −16.6484 −0.529923
\(988\) −3.12259 −0.0993429
\(989\) −6.18094 −0.196543
\(990\) 7.09290 0.225427
\(991\) −7.02450 −0.223140 −0.111570 0.993757i \(-0.535588\pi\)
−0.111570 + 0.993757i \(0.535588\pi\)
\(992\) −30.9128 −0.981483
\(993\) 12.0308 0.381787
\(994\) −119.161 −3.77957
\(995\) 11.8892 0.376914
\(996\) 29.1736 0.924401
\(997\) 5.96495 0.188912 0.0944559 0.995529i \(-0.469889\pi\)
0.0944559 + 0.995529i \(0.469889\pi\)
\(998\) 23.6627 0.749030
\(999\) 8.35805 0.264437
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 \(a_p\))