Properties

Label 8041.2.a.j.1.7
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 82
CM No

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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 1.7
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.40536 q^{2}\) \(-1.47389 q^{3}\) \(+3.78577 q^{4}\) \(-0.987275 q^{5}\) \(+3.54525 q^{6}\) \(+2.06145 q^{7}\) \(-4.29541 q^{8}\) \(-0.827635 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.40536 q^{2}\) \(-1.47389 q^{3}\) \(+3.78577 q^{4}\) \(-0.987275 q^{5}\) \(+3.54525 q^{6}\) \(+2.06145 q^{7}\) \(-4.29541 q^{8}\) \(-0.827635 q^{9}\) \(+2.37475 q^{10}\) \(+1.00000 q^{11}\) \(-5.57982 q^{12}\) \(-2.64454 q^{13}\) \(-4.95853 q^{14}\) \(+1.45514 q^{15}\) \(+2.76049 q^{16}\) \(+1.00000 q^{17}\) \(+1.99076 q^{18}\) \(+3.84969 q^{19}\) \(-3.73759 q^{20}\) \(-3.03836 q^{21}\) \(-2.40536 q^{22}\) \(-3.24980 q^{23}\) \(+6.33098 q^{24}\) \(-4.02529 q^{25}\) \(+6.36107 q^{26}\) \(+5.64153 q^{27}\) \(+7.80416 q^{28}\) \(+8.79752 q^{29}\) \(-3.50014 q^{30}\) \(-6.44883 q^{31}\) \(+1.95085 q^{32}\) \(-1.47389 q^{33}\) \(-2.40536 q^{34}\) \(-2.03522 q^{35}\) \(-3.13323 q^{36}\) \(+5.60389 q^{37}\) \(-9.25991 q^{38}\) \(+3.89777 q^{39}\) \(+4.24075 q^{40}\) \(-6.40638 q^{41}\) \(+7.30835 q^{42}\) \(+1.00000 q^{43}\) \(+3.78577 q^{44}\) \(+0.817103 q^{45}\) \(+7.81695 q^{46}\) \(+4.14107 q^{47}\) \(-4.06867 q^{48}\) \(-2.75043 q^{49}\) \(+9.68227 q^{50}\) \(-1.47389 q^{51}\) \(-10.0116 q^{52}\) \(-5.18596 q^{53}\) \(-13.5699 q^{54}\) \(-0.987275 q^{55}\) \(-8.85477 q^{56}\) \(-5.67404 q^{57}\) \(-21.1612 q^{58}\) \(+11.0935 q^{59}\) \(+5.50882 q^{60}\) \(-12.4336 q^{61}\) \(+15.5118 q^{62}\) \(-1.70613 q^{63}\) \(-10.2135 q^{64}\) \(+2.61089 q^{65}\) \(+3.54525 q^{66}\) \(-7.38800 q^{67}\) \(+3.78577 q^{68}\) \(+4.78986 q^{69}\) \(+4.89543 q^{70}\) \(-14.7253 q^{71}\) \(+3.55503 q^{72}\) \(+9.93884 q^{73}\) \(-13.4794 q^{74}\) \(+5.93285 q^{75}\) \(+14.5740 q^{76}\) \(+2.06145 q^{77}\) \(-9.37555 q^{78}\) \(+4.82250 q^{79}\) \(-2.72536 q^{80}\) \(-5.83212 q^{81}\) \(+15.4097 q^{82}\) \(+8.60895 q^{83}\) \(-11.5025 q^{84}\) \(-0.987275 q^{85}\) \(-2.40536 q^{86}\) \(-12.9666 q^{87}\) \(-4.29541 q^{88}\) \(+11.7923 q^{89}\) \(-1.96543 q^{90}\) \(-5.45158 q^{91}\) \(-12.3030 q^{92}\) \(+9.50490 q^{93}\) \(-9.96077 q^{94}\) \(-3.80071 q^{95}\) \(-2.87535 q^{96}\) \(+6.59082 q^{97}\) \(+6.61578 q^{98}\) \(-0.827635 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.40536 −1.70085 −0.850424 0.526098i \(-0.823654\pi\)
−0.850424 + 0.526098i \(0.823654\pi\)
\(3\) −1.47389 −0.850953 −0.425477 0.904969i \(-0.639894\pi\)
−0.425477 + 0.904969i \(0.639894\pi\)
\(4\) 3.78577 1.89288
\(5\) −0.987275 −0.441523 −0.220761 0.975328i \(-0.570854\pi\)
−0.220761 + 0.975328i \(0.570854\pi\)
\(6\) 3.54525 1.44734
\(7\) 2.06145 0.779154 0.389577 0.920994i \(-0.372621\pi\)
0.389577 + 0.920994i \(0.372621\pi\)
\(8\) −4.29541 −1.51866
\(9\) −0.827635 −0.275878
\(10\) 2.37475 0.750963
\(11\) 1.00000 0.301511
\(12\) −5.57982 −1.61075
\(13\) −2.64454 −0.733463 −0.366731 0.930327i \(-0.619523\pi\)
−0.366731 + 0.930327i \(0.619523\pi\)
\(14\) −4.95853 −1.32522
\(15\) 1.45514 0.375715
\(16\) 2.76049 0.690122
\(17\) 1.00000 0.242536
\(18\) 1.99076 0.469227
\(19\) 3.84969 0.883180 0.441590 0.897217i \(-0.354415\pi\)
0.441590 + 0.897217i \(0.354415\pi\)
\(20\) −3.73759 −0.835751
\(21\) −3.03836 −0.663024
\(22\) −2.40536 −0.512825
\(23\) −3.24980 −0.677630 −0.338815 0.940853i \(-0.610026\pi\)
−0.338815 + 0.940853i \(0.610026\pi\)
\(24\) 6.33098 1.29231
\(25\) −4.02529 −0.805058
\(26\) 6.36107 1.24751
\(27\) 5.64153 1.08571
\(28\) 7.80416 1.47485
\(29\) 8.79752 1.63366 0.816829 0.576879i \(-0.195730\pi\)
0.816829 + 0.576879i \(0.195730\pi\)
\(30\) −3.50014 −0.639035
\(31\) −6.44883 −1.15824 −0.579122 0.815241i \(-0.696605\pi\)
−0.579122 + 0.815241i \(0.696605\pi\)
\(32\) 1.95085 0.344865
\(33\) −1.47389 −0.256572
\(34\) −2.40536 −0.412516
\(35\) −2.03522 −0.344015
\(36\) −3.13323 −0.522205
\(37\) 5.60389 0.921274 0.460637 0.887589i \(-0.347621\pi\)
0.460637 + 0.887589i \(0.347621\pi\)
\(38\) −9.25991 −1.50216
\(39\) 3.89777 0.624143
\(40\) 4.24075 0.670522
\(41\) −6.40638 −1.00051 −0.500254 0.865879i \(-0.666760\pi\)
−0.500254 + 0.865879i \(0.666760\pi\)
\(42\) 7.30835 1.12770
\(43\) 1.00000 0.152499
\(44\) 3.78577 0.570726
\(45\) 0.817103 0.121807
\(46\) 7.81695 1.15255
\(47\) 4.14107 0.604037 0.302019 0.953302i \(-0.402340\pi\)
0.302019 + 0.953302i \(0.402340\pi\)
\(48\) −4.06867 −0.587261
\(49\) −2.75043 −0.392918
\(50\) 9.68227 1.36928
\(51\) −1.47389 −0.206387
\(52\) −10.0116 −1.38836
\(53\) −5.18596 −0.712346 −0.356173 0.934420i \(-0.615919\pi\)
−0.356173 + 0.934420i \(0.615919\pi\)
\(54\) −13.5699 −1.84663
\(55\) −0.987275 −0.133124
\(56\) −8.85477 −1.18327
\(57\) −5.67404 −0.751545
\(58\) −21.1612 −2.77860
\(59\) 11.0935 1.44425 0.722127 0.691760i \(-0.243164\pi\)
0.722127 + 0.691760i \(0.243164\pi\)
\(60\) 5.50882 0.711185
\(61\) −12.4336 −1.59196 −0.795980 0.605322i \(-0.793044\pi\)
−0.795980 + 0.605322i \(0.793044\pi\)
\(62\) 15.5118 1.97000
\(63\) −1.70613 −0.214952
\(64\) −10.2135 −1.27668
\(65\) 2.61089 0.323841
\(66\) 3.54525 0.436390
\(67\) −7.38800 −0.902587 −0.451294 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(68\) 3.78577 0.459091
\(69\) 4.78986 0.576632
\(70\) 4.89543 0.585116
\(71\) −14.7253 −1.74758 −0.873788 0.486307i \(-0.838344\pi\)
−0.873788 + 0.486307i \(0.838344\pi\)
\(72\) 3.55503 0.418965
\(73\) 9.93884 1.16325 0.581627 0.813456i \(-0.302417\pi\)
0.581627 + 0.813456i \(0.302417\pi\)
\(74\) −13.4794 −1.56695
\(75\) 5.93285 0.685066
\(76\) 14.5740 1.67176
\(77\) 2.06145 0.234924
\(78\) −9.37555 −1.06157
\(79\) 4.82250 0.542574 0.271287 0.962499i \(-0.412551\pi\)
0.271287 + 0.962499i \(0.412551\pi\)
\(80\) −2.72536 −0.304705
\(81\) −5.83212 −0.648013
\(82\) 15.4097 1.70171
\(83\) 8.60895 0.944955 0.472477 0.881343i \(-0.343360\pi\)
0.472477 + 0.881343i \(0.343360\pi\)
\(84\) −11.5025 −1.25503
\(85\) −0.987275 −0.107085
\(86\) −2.40536 −0.259377
\(87\) −12.9666 −1.39017
\(88\) −4.29541 −0.457892
\(89\) 11.7923 1.24999 0.624993 0.780631i \(-0.285102\pi\)
0.624993 + 0.780631i \(0.285102\pi\)
\(90\) −1.96543 −0.207174
\(91\) −5.45158 −0.571481
\(92\) −12.3030 −1.28267
\(93\) 9.50490 0.985612
\(94\) −9.96077 −1.02738
\(95\) −3.80071 −0.389944
\(96\) −2.87535 −0.293464
\(97\) 6.59082 0.669197 0.334598 0.942361i \(-0.391399\pi\)
0.334598 + 0.942361i \(0.391399\pi\)
\(98\) 6.61578 0.668294
\(99\) −0.827635 −0.0831804
\(100\) −15.2388 −1.52388
\(101\) 7.51432 0.747703 0.373851 0.927489i \(-0.378037\pi\)
0.373851 + 0.927489i \(0.378037\pi\)
\(102\) 3.54525 0.351032
\(103\) −11.6014 −1.14312 −0.571559 0.820561i \(-0.693661\pi\)
−0.571559 + 0.820561i \(0.693661\pi\)
\(104\) 11.3594 1.11388
\(105\) 2.99970 0.292740
\(106\) 12.4741 1.21159
\(107\) 3.76762 0.364229 0.182115 0.983277i \(-0.441706\pi\)
0.182115 + 0.983277i \(0.441706\pi\)
\(108\) 21.3575 2.05513
\(109\) 15.0296 1.43957 0.719787 0.694195i \(-0.244239\pi\)
0.719787 + 0.694195i \(0.244239\pi\)
\(110\) 2.37475 0.226424
\(111\) −8.25955 −0.783962
\(112\) 5.69060 0.537711
\(113\) −12.7104 −1.19570 −0.597848 0.801609i \(-0.703977\pi\)
−0.597848 + 0.801609i \(0.703977\pi\)
\(114\) 13.6481 1.27826
\(115\) 3.20845 0.299189
\(116\) 33.3054 3.09232
\(117\) 2.18871 0.202347
\(118\) −26.6840 −2.45646
\(119\) 2.06145 0.188973
\(120\) −6.25042 −0.570583
\(121\) 1.00000 0.0909091
\(122\) 29.9073 2.70768
\(123\) 9.44232 0.851386
\(124\) −24.4138 −2.19242
\(125\) 8.91044 0.796974
\(126\) 4.10385 0.365600
\(127\) −7.43855 −0.660065 −0.330032 0.943970i \(-0.607060\pi\)
−0.330032 + 0.943970i \(0.607060\pi\)
\(128\) 20.6654 1.82658
\(129\) −1.47389 −0.129769
\(130\) −6.28013 −0.550804
\(131\) 8.64044 0.754919 0.377459 0.926026i \(-0.376798\pi\)
0.377459 + 0.926026i \(0.376798\pi\)
\(132\) −5.57982 −0.485661
\(133\) 7.93595 0.688134
\(134\) 17.7708 1.53516
\(135\) −5.56974 −0.479367
\(136\) −4.29541 −0.368328
\(137\) −15.3858 −1.31450 −0.657248 0.753674i \(-0.728280\pi\)
−0.657248 + 0.753674i \(0.728280\pi\)
\(138\) −11.5214 −0.980763
\(139\) 14.4728 1.22757 0.613785 0.789473i \(-0.289646\pi\)
0.613785 + 0.789473i \(0.289646\pi\)
\(140\) −7.70485 −0.651179
\(141\) −6.10350 −0.514008
\(142\) 35.4198 2.97236
\(143\) −2.64454 −0.221147
\(144\) −2.28468 −0.190390
\(145\) −8.68558 −0.721298
\(146\) −23.9065 −1.97852
\(147\) 4.05384 0.334355
\(148\) 21.2150 1.74386
\(149\) 9.15871 0.750311 0.375155 0.926962i \(-0.377589\pi\)
0.375155 + 0.926962i \(0.377589\pi\)
\(150\) −14.2706 −1.16519
\(151\) −17.5699 −1.42982 −0.714910 0.699217i \(-0.753532\pi\)
−0.714910 + 0.699217i \(0.753532\pi\)
\(152\) −16.5360 −1.34125
\(153\) −0.827635 −0.0669103
\(154\) −4.95853 −0.399570
\(155\) 6.36677 0.511392
\(156\) 14.7560 1.18143
\(157\) 4.74343 0.378567 0.189283 0.981922i \(-0.439384\pi\)
0.189283 + 0.981922i \(0.439384\pi\)
\(158\) −11.5999 −0.922835
\(159\) 7.64355 0.606173
\(160\) −1.92603 −0.152266
\(161\) −6.69930 −0.527979
\(162\) 14.0283 1.10217
\(163\) −17.2930 −1.35449 −0.677244 0.735758i \(-0.736826\pi\)
−0.677244 + 0.735758i \(0.736826\pi\)
\(164\) −24.2530 −1.89384
\(165\) 1.45514 0.113282
\(166\) −20.7076 −1.60722
\(167\) −8.95644 −0.693070 −0.346535 0.938037i \(-0.612642\pi\)
−0.346535 + 0.938037i \(0.612642\pi\)
\(168\) 13.0510 1.00691
\(169\) −6.00642 −0.462032
\(170\) 2.37475 0.182135
\(171\) −3.18614 −0.243650
\(172\) 3.78577 0.288662
\(173\) −0.349949 −0.0266061 −0.0133031 0.999912i \(-0.504235\pi\)
−0.0133031 + 0.999912i \(0.504235\pi\)
\(174\) 31.1894 2.36446
\(175\) −8.29792 −0.627264
\(176\) 2.76049 0.208080
\(177\) −16.3507 −1.22899
\(178\) −28.3648 −2.12603
\(179\) 21.3273 1.59408 0.797038 0.603929i \(-0.206399\pi\)
0.797038 + 0.603929i \(0.206399\pi\)
\(180\) 3.09336 0.230566
\(181\) 13.5630 1.00813 0.504066 0.863665i \(-0.331837\pi\)
0.504066 + 0.863665i \(0.331837\pi\)
\(182\) 13.1130 0.972002
\(183\) 18.3258 1.35468
\(184\) 13.9592 1.02909
\(185\) −5.53259 −0.406764
\(186\) −22.8627 −1.67638
\(187\) 1.00000 0.0731272
\(188\) 15.6771 1.14337
\(189\) 11.6297 0.845938
\(190\) 9.14208 0.663236
\(191\) −1.98654 −0.143741 −0.0718704 0.997414i \(-0.522897\pi\)
−0.0718704 + 0.997414i \(0.522897\pi\)
\(192\) 15.0536 1.08640
\(193\) −23.0371 −1.65825 −0.829125 0.559064i \(-0.811161\pi\)
−0.829125 + 0.559064i \(0.811161\pi\)
\(194\) −15.8533 −1.13820
\(195\) −3.84817 −0.275573
\(196\) −10.4125 −0.743748
\(197\) 16.3494 1.16485 0.582423 0.812886i \(-0.302105\pi\)
0.582423 + 0.812886i \(0.302105\pi\)
\(198\) 1.99076 0.141477
\(199\) 5.41930 0.384164 0.192082 0.981379i \(-0.438476\pi\)
0.192082 + 0.981379i \(0.438476\pi\)
\(200\) 17.2903 1.22261
\(201\) 10.8891 0.768060
\(202\) −18.0747 −1.27173
\(203\) 18.1356 1.27287
\(204\) −5.57982 −0.390665
\(205\) 6.32486 0.441747
\(206\) 27.9055 1.94427
\(207\) 2.68965 0.186943
\(208\) −7.30021 −0.506179
\(209\) 3.84969 0.266289
\(210\) −7.21535 −0.497907
\(211\) 6.29905 0.433645 0.216822 0.976211i \(-0.430431\pi\)
0.216822 + 0.976211i \(0.430431\pi\)
\(212\) −19.6328 −1.34839
\(213\) 21.7036 1.48711
\(214\) −9.06249 −0.619499
\(215\) −0.987275 −0.0673316
\(216\) −24.2327 −1.64883
\(217\) −13.2939 −0.902451
\(218\) −36.1516 −2.44850
\(219\) −14.6488 −0.989874
\(220\) −3.73759 −0.251988
\(221\) −2.64454 −0.177891
\(222\) 19.8672 1.33340
\(223\) −1.31950 −0.0883602 −0.0441801 0.999024i \(-0.514068\pi\)
−0.0441801 + 0.999024i \(0.514068\pi\)
\(224\) 4.02158 0.268703
\(225\) 3.33147 0.222098
\(226\) 30.5732 2.03370
\(227\) −29.2913 −1.94413 −0.972066 0.234709i \(-0.924586\pi\)
−0.972066 + 0.234709i \(0.924586\pi\)
\(228\) −21.4806 −1.42259
\(229\) −7.64512 −0.505203 −0.252602 0.967570i \(-0.581286\pi\)
−0.252602 + 0.967570i \(0.581286\pi\)
\(230\) −7.71748 −0.508875
\(231\) −3.03836 −0.199909
\(232\) −37.7890 −2.48097
\(233\) 12.7491 0.835220 0.417610 0.908626i \(-0.362868\pi\)
0.417610 + 0.908626i \(0.362868\pi\)
\(234\) −5.26464 −0.344161
\(235\) −4.08838 −0.266696
\(236\) 41.9975 2.73380
\(237\) −7.10786 −0.461705
\(238\) −4.95853 −0.321414
\(239\) 15.1406 0.979364 0.489682 0.871901i \(-0.337113\pi\)
0.489682 + 0.871901i \(0.337113\pi\)
\(240\) 4.01689 0.259289
\(241\) 22.0554 1.42072 0.710358 0.703841i \(-0.248533\pi\)
0.710358 + 0.703841i \(0.248533\pi\)
\(242\) −2.40536 −0.154623
\(243\) −8.32867 −0.534284
\(244\) −47.0707 −3.01339
\(245\) 2.71543 0.173483
\(246\) −22.7122 −1.44808
\(247\) −10.1807 −0.647780
\(248\) 27.7004 1.75898
\(249\) −12.6887 −0.804113
\(250\) −21.4328 −1.35553
\(251\) 13.7086 0.865282 0.432641 0.901566i \(-0.357582\pi\)
0.432641 + 0.901566i \(0.357582\pi\)
\(252\) −6.45900 −0.406878
\(253\) −3.24980 −0.204313
\(254\) 17.8924 1.12267
\(255\) 1.45514 0.0911244
\(256\) −29.2808 −1.83005
\(257\) 6.09794 0.380379 0.190189 0.981747i \(-0.439090\pi\)
0.190189 + 0.981747i \(0.439090\pi\)
\(258\) 3.54525 0.220718
\(259\) 11.5521 0.717815
\(260\) 9.88421 0.612992
\(261\) −7.28114 −0.450691
\(262\) −20.7834 −1.28400
\(263\) 15.0991 0.931049 0.465524 0.885035i \(-0.345866\pi\)
0.465524 + 0.885035i \(0.345866\pi\)
\(264\) 6.33098 0.389645
\(265\) 5.11997 0.314517
\(266\) −19.0888 −1.17041
\(267\) −17.3807 −1.06368
\(268\) −27.9692 −1.70849
\(269\) −13.6639 −0.833102 −0.416551 0.909112i \(-0.636761\pi\)
−0.416551 + 0.909112i \(0.636761\pi\)
\(270\) 13.3972 0.815330
\(271\) −17.4052 −1.05729 −0.528645 0.848843i \(-0.677300\pi\)
−0.528645 + 0.848843i \(0.677300\pi\)
\(272\) 2.76049 0.167379
\(273\) 8.03505 0.486304
\(274\) 37.0084 2.23576
\(275\) −4.02529 −0.242734
\(276\) 18.1333 1.09150
\(277\) 3.05875 0.183783 0.0918913 0.995769i \(-0.470709\pi\)
0.0918913 + 0.995769i \(0.470709\pi\)
\(278\) −34.8124 −2.08791
\(279\) 5.33728 0.319535
\(280\) 8.74209 0.522440
\(281\) −31.1221 −1.85659 −0.928293 0.371849i \(-0.878724\pi\)
−0.928293 + 0.371849i \(0.878724\pi\)
\(282\) 14.6811 0.874249
\(283\) −23.3710 −1.38926 −0.694629 0.719368i \(-0.744432\pi\)
−0.694629 + 0.719368i \(0.744432\pi\)
\(284\) −55.7467 −3.30796
\(285\) 5.60184 0.331824
\(286\) 6.36107 0.376138
\(287\) −13.2064 −0.779550
\(288\) −1.61459 −0.0951408
\(289\) 1.00000 0.0588235
\(290\) 20.8920 1.22682
\(291\) −9.71418 −0.569455
\(292\) 37.6261 2.20190
\(293\) −10.1359 −0.592144 −0.296072 0.955166i \(-0.595677\pi\)
−0.296072 + 0.955166i \(0.595677\pi\)
\(294\) −9.75096 −0.568687
\(295\) −10.9524 −0.637672
\(296\) −24.0710 −1.39910
\(297\) 5.64153 0.327355
\(298\) −22.0300 −1.27616
\(299\) 8.59422 0.497017
\(300\) 22.4604 1.29675
\(301\) 2.06145 0.118820
\(302\) 42.2620 2.43190
\(303\) −11.0753 −0.636260
\(304\) 10.6270 0.609502
\(305\) 12.2754 0.702887
\(306\) 1.99076 0.113804
\(307\) −22.4745 −1.28269 −0.641345 0.767253i \(-0.721623\pi\)
−0.641345 + 0.767253i \(0.721623\pi\)
\(308\) 7.80416 0.444683
\(309\) 17.0992 0.972739
\(310\) −15.3144 −0.869799
\(311\) 10.3116 0.584717 0.292358 0.956309i \(-0.405560\pi\)
0.292358 + 0.956309i \(0.405560\pi\)
\(312\) −16.7425 −0.947859
\(313\) −25.5763 −1.44566 −0.722828 0.691028i \(-0.757158\pi\)
−0.722828 + 0.691028i \(0.757158\pi\)
\(314\) −11.4097 −0.643884
\(315\) 1.68442 0.0949061
\(316\) 18.2569 1.02703
\(317\) 19.6776 1.10520 0.552602 0.833445i \(-0.313635\pi\)
0.552602 + 0.833445i \(0.313635\pi\)
\(318\) −18.3855 −1.03101
\(319\) 8.79752 0.492567
\(320\) 10.0835 0.563686
\(321\) −5.55307 −0.309942
\(322\) 16.1142 0.898011
\(323\) 3.84969 0.214203
\(324\) −22.0790 −1.22661
\(325\) 10.6450 0.590480
\(326\) 41.5958 2.30378
\(327\) −22.1520 −1.22501
\(328\) 27.5180 1.51943
\(329\) 8.53660 0.470638
\(330\) −3.50014 −0.192676
\(331\) −28.2756 −1.55417 −0.777083 0.629398i \(-0.783302\pi\)
−0.777083 + 0.629398i \(0.783302\pi\)
\(332\) 32.5915 1.78869
\(333\) −4.63798 −0.254160
\(334\) 21.5435 1.17881
\(335\) 7.29399 0.398513
\(336\) −8.38735 −0.457567
\(337\) 18.7095 1.01917 0.509585 0.860420i \(-0.329799\pi\)
0.509585 + 0.860420i \(0.329799\pi\)
\(338\) 14.4476 0.785846
\(339\) 18.7338 1.01748
\(340\) −3.73759 −0.202699
\(341\) −6.44883 −0.349224
\(342\) 7.66382 0.414412
\(343\) −20.1000 −1.08530
\(344\) −4.29541 −0.231593
\(345\) −4.72891 −0.254596
\(346\) 0.841753 0.0452529
\(347\) 2.92477 0.157010 0.0785049 0.996914i \(-0.474985\pi\)
0.0785049 + 0.996914i \(0.474985\pi\)
\(348\) −49.0886 −2.63142
\(349\) 10.0716 0.539119 0.269559 0.962984i \(-0.413122\pi\)
0.269559 + 0.962984i \(0.413122\pi\)
\(350\) 19.9595 1.06688
\(351\) −14.9192 −0.796330
\(352\) 1.95085 0.103981
\(353\) 7.49767 0.399061 0.199530 0.979892i \(-0.436058\pi\)
0.199530 + 0.979892i \(0.436058\pi\)
\(354\) 39.3293 2.09033
\(355\) 14.5380 0.771595
\(356\) 44.6430 2.36607
\(357\) −3.03836 −0.160807
\(358\) −51.2998 −2.71128
\(359\) 7.16623 0.378219 0.189110 0.981956i \(-0.439440\pi\)
0.189110 + 0.981956i \(0.439440\pi\)
\(360\) −3.50980 −0.184982
\(361\) −4.17986 −0.219992
\(362\) −32.6240 −1.71468
\(363\) −1.47389 −0.0773594
\(364\) −20.6384 −1.08175
\(365\) −9.81237 −0.513603
\(366\) −44.0803 −2.30411
\(367\) −24.1812 −1.26225 −0.631123 0.775682i \(-0.717406\pi\)
−0.631123 + 0.775682i \(0.717406\pi\)
\(368\) −8.97103 −0.467647
\(369\) 5.30214 0.276018
\(370\) 13.3079 0.691843
\(371\) −10.6906 −0.555027
\(372\) 35.9833 1.86565
\(373\) −4.72110 −0.244449 −0.122225 0.992502i \(-0.539003\pi\)
−0.122225 + 0.992502i \(0.539003\pi\)
\(374\) −2.40536 −0.124378
\(375\) −13.1331 −0.678188
\(376\) −17.7876 −0.917325
\(377\) −23.2654 −1.19823
\(378\) −27.9737 −1.43881
\(379\) 2.33631 0.120008 0.0600040 0.998198i \(-0.480889\pi\)
0.0600040 + 0.998198i \(0.480889\pi\)
\(380\) −14.3886 −0.738119
\(381\) 10.9636 0.561685
\(382\) 4.77834 0.244481
\(383\) −15.3444 −0.784064 −0.392032 0.919951i \(-0.628228\pi\)
−0.392032 + 0.919951i \(0.628228\pi\)
\(384\) −30.4586 −1.55434
\(385\) −2.03522 −0.103724
\(386\) 55.4126 2.82043
\(387\) −0.827635 −0.0420710
\(388\) 24.9513 1.26671
\(389\) 3.50565 0.177743 0.0888717 0.996043i \(-0.471674\pi\)
0.0888717 + 0.996043i \(0.471674\pi\)
\(390\) 9.25625 0.468708
\(391\) −3.24980 −0.164349
\(392\) 11.8142 0.596708
\(393\) −12.7351 −0.642401
\(394\) −39.3262 −1.98122
\(395\) −4.76114 −0.239559
\(396\) −3.13323 −0.157451
\(397\) −8.66248 −0.434758 −0.217379 0.976087i \(-0.569751\pi\)
−0.217379 + 0.976087i \(0.569751\pi\)
\(398\) −13.0354 −0.653405
\(399\) −11.6967 −0.585570
\(400\) −11.1118 −0.555588
\(401\) 11.0482 0.551720 0.275860 0.961198i \(-0.411037\pi\)
0.275860 + 0.961198i \(0.411037\pi\)
\(402\) −26.1923 −1.30635
\(403\) 17.0542 0.849529
\(404\) 28.4474 1.41531
\(405\) 5.75790 0.286113
\(406\) −43.6228 −2.16496
\(407\) 5.60389 0.277775
\(408\) 6.33098 0.313430
\(409\) 30.4248 1.50441 0.752204 0.658930i \(-0.228991\pi\)
0.752204 + 0.658930i \(0.228991\pi\)
\(410\) −15.2136 −0.751345
\(411\) 22.6770 1.11858
\(412\) −43.9201 −2.16379
\(413\) 22.8687 1.12530
\(414\) −6.46958 −0.317962
\(415\) −8.49940 −0.417219
\(416\) −5.15910 −0.252946
\(417\) −21.3315 −1.04461
\(418\) −9.25991 −0.452917
\(419\) −25.4592 −1.24377 −0.621883 0.783110i \(-0.713632\pi\)
−0.621883 + 0.783110i \(0.713632\pi\)
\(420\) 11.3561 0.554123
\(421\) 3.53805 0.172434 0.0862170 0.996276i \(-0.472522\pi\)
0.0862170 + 0.996276i \(0.472522\pi\)
\(422\) −15.1515 −0.737563
\(423\) −3.42729 −0.166641
\(424\) 22.2758 1.08181
\(425\) −4.02529 −0.195255
\(426\) −52.2050 −2.52934
\(427\) −25.6312 −1.24038
\(428\) 14.2633 0.689444
\(429\) 3.89777 0.188186
\(430\) 2.37475 0.114521
\(431\) 34.3999 1.65699 0.828493 0.560000i \(-0.189199\pi\)
0.828493 + 0.560000i \(0.189199\pi\)
\(432\) 15.5734 0.749274
\(433\) 27.1683 1.30563 0.652814 0.757519i \(-0.273589\pi\)
0.652814 + 0.757519i \(0.273589\pi\)
\(434\) 31.9767 1.53493
\(435\) 12.8016 0.613791
\(436\) 56.8985 2.72494
\(437\) −12.5107 −0.598470
\(438\) 35.2357 1.68363
\(439\) 12.5764 0.600237 0.300119 0.953902i \(-0.402974\pi\)
0.300119 + 0.953902i \(0.402974\pi\)
\(440\) 4.24075 0.202170
\(441\) 2.27635 0.108398
\(442\) 6.36107 0.302565
\(443\) −38.5505 −1.83159 −0.915795 0.401645i \(-0.868439\pi\)
−0.915795 + 0.401645i \(0.868439\pi\)
\(444\) −31.2687 −1.48395
\(445\) −11.6423 −0.551897
\(446\) 3.17387 0.150287
\(447\) −13.4990 −0.638479
\(448\) −21.0546 −0.994735
\(449\) −9.43354 −0.445196 −0.222598 0.974910i \(-0.571454\pi\)
−0.222598 + 0.974910i \(0.571454\pi\)
\(450\) −8.01339 −0.377755
\(451\) −6.40638 −0.301665
\(452\) −48.1187 −2.26331
\(453\) 25.8962 1.21671
\(454\) 70.4561 3.30667
\(455\) 5.38221 0.252322
\(456\) 24.3723 1.14134
\(457\) −19.3286 −0.904155 −0.452077 0.891979i \(-0.649317\pi\)
−0.452077 + 0.891979i \(0.649317\pi\)
\(458\) 18.3893 0.859274
\(459\) 5.64153 0.263324
\(460\) 12.1464 0.566330
\(461\) −17.0327 −0.793292 −0.396646 0.917972i \(-0.629826\pi\)
−0.396646 + 0.917972i \(0.629826\pi\)
\(462\) 7.30835 0.340015
\(463\) 1.05646 0.0490977 0.0245488 0.999699i \(-0.492185\pi\)
0.0245488 + 0.999699i \(0.492185\pi\)
\(464\) 24.2854 1.12742
\(465\) −9.38395 −0.435170
\(466\) −30.6662 −1.42058
\(467\) 16.5290 0.764871 0.382435 0.923982i \(-0.375085\pi\)
0.382435 + 0.923982i \(0.375085\pi\)
\(468\) 8.28595 0.383018
\(469\) −15.2300 −0.703255
\(470\) 9.83402 0.453610
\(471\) −6.99131 −0.322143
\(472\) −47.6513 −2.19333
\(473\) 1.00000 0.0459800
\(474\) 17.0970 0.785290
\(475\) −15.4961 −0.711011
\(476\) 7.80416 0.357703
\(477\) 4.29208 0.196521
\(478\) −36.4186 −1.66575
\(479\) 13.0759 0.597452 0.298726 0.954339i \(-0.403438\pi\)
0.298726 + 0.954339i \(0.403438\pi\)
\(480\) 2.83876 0.129571
\(481\) −14.8197 −0.675721
\(482\) −53.0513 −2.41642
\(483\) 9.87406 0.449285
\(484\) 3.78577 0.172080
\(485\) −6.50696 −0.295466
\(486\) 20.0335 0.908736
\(487\) 25.7698 1.16774 0.583870 0.811847i \(-0.301538\pi\)
0.583870 + 0.811847i \(0.301538\pi\)
\(488\) 53.4075 2.41764
\(489\) 25.4880 1.15261
\(490\) −6.53159 −0.295067
\(491\) −37.0485 −1.67197 −0.835987 0.548749i \(-0.815104\pi\)
−0.835987 + 0.548749i \(0.815104\pi\)
\(492\) 35.7464 1.61157
\(493\) 8.79752 0.396220
\(494\) 24.4882 1.10178
\(495\) 0.817103 0.0367261
\(496\) −17.8019 −0.799330
\(497\) −30.3555 −1.36163
\(498\) 30.5209 1.36767
\(499\) −7.09788 −0.317745 −0.158872 0.987299i \(-0.550786\pi\)
−0.158872 + 0.987299i \(0.550786\pi\)
\(500\) 33.7328 1.50858
\(501\) 13.2008 0.589770
\(502\) −32.9743 −1.47171
\(503\) 23.2120 1.03497 0.517486 0.855691i \(-0.326868\pi\)
0.517486 + 0.855691i \(0.326868\pi\)
\(504\) 7.32852 0.326438
\(505\) −7.41870 −0.330128
\(506\) 7.81695 0.347506
\(507\) 8.85283 0.393168
\(508\) −28.1606 −1.24943
\(509\) 5.44423 0.241311 0.120656 0.992694i \(-0.461500\pi\)
0.120656 + 0.992694i \(0.461500\pi\)
\(510\) −3.50014 −0.154989
\(511\) 20.4884 0.906354
\(512\) 29.1002 1.28606
\(513\) 21.7182 0.958880
\(514\) −14.6677 −0.646966
\(515\) 11.4537 0.504712
\(516\) −5.57982 −0.245638
\(517\) 4.14107 0.182124
\(518\) −27.7871 −1.22089
\(519\) 0.515787 0.0226406
\(520\) −11.2148 −0.491803
\(521\) 23.2761 1.01975 0.509873 0.860250i \(-0.329692\pi\)
0.509873 + 0.860250i \(0.329692\pi\)
\(522\) 17.5138 0.766557
\(523\) 45.5096 1.99000 0.994999 0.0998876i \(-0.0318483\pi\)
0.994999 + 0.0998876i \(0.0318483\pi\)
\(524\) 32.7107 1.42897
\(525\) 12.2303 0.533773
\(526\) −36.3187 −1.58357
\(527\) −6.44883 −0.280916
\(528\) −4.06867 −0.177066
\(529\) −12.4388 −0.540817
\(530\) −12.3154 −0.534946
\(531\) −9.18139 −0.398439
\(532\) 30.0436 1.30256
\(533\) 16.9419 0.733836
\(534\) 41.8068 1.80916
\(535\) −3.71968 −0.160816
\(536\) 31.7345 1.37072
\(537\) −31.4342 −1.35648
\(538\) 32.8666 1.41698
\(539\) −2.75043 −0.118469
\(540\) −21.0857 −0.907386
\(541\) −0.628675 −0.0270288 −0.0135144 0.999909i \(-0.504302\pi\)
−0.0135144 + 0.999909i \(0.504302\pi\)
\(542\) 41.8657 1.79829
\(543\) −19.9905 −0.857873
\(544\) 1.95085 0.0836421
\(545\) −14.8383 −0.635605
\(546\) −19.3272 −0.827128
\(547\) 7.36356 0.314843 0.157422 0.987531i \(-0.449682\pi\)
0.157422 + 0.987531i \(0.449682\pi\)
\(548\) −58.2470 −2.48819
\(549\) 10.2905 0.439187
\(550\) 9.68227 0.412853
\(551\) 33.8678 1.44282
\(552\) −20.5744 −0.875706
\(553\) 9.94134 0.422749
\(554\) −7.35741 −0.312586
\(555\) 8.15445 0.346137
\(556\) 54.7908 2.32365
\(557\) 20.2286 0.857112 0.428556 0.903515i \(-0.359022\pi\)
0.428556 + 0.903515i \(0.359022\pi\)
\(558\) −12.8381 −0.543480
\(559\) −2.64454 −0.111852
\(560\) −5.61819 −0.237412
\(561\) −1.47389 −0.0622279
\(562\) 74.8598 3.15777
\(563\) 9.48037 0.399550 0.199775 0.979842i \(-0.435979\pi\)
0.199775 + 0.979842i \(0.435979\pi\)
\(564\) −23.1064 −0.972956
\(565\) 12.5487 0.527927
\(566\) 56.2156 2.36292
\(567\) −12.0226 −0.504902
\(568\) 63.2514 2.65397
\(569\) 21.9908 0.921902 0.460951 0.887426i \(-0.347508\pi\)
0.460951 + 0.887426i \(0.347508\pi\)
\(570\) −13.4745 −0.564383
\(571\) 15.3929 0.644171 0.322085 0.946711i \(-0.395616\pi\)
0.322085 + 0.946711i \(0.395616\pi\)
\(572\) −10.0116 −0.418606
\(573\) 2.92795 0.122317
\(574\) 31.7662 1.32590
\(575\) 13.0814 0.545531
\(576\) 8.45303 0.352210
\(577\) 13.0014 0.541256 0.270628 0.962684i \(-0.412769\pi\)
0.270628 + 0.962684i \(0.412769\pi\)
\(578\) −2.40536 −0.100050
\(579\) 33.9543 1.41109
\(580\) −32.8815 −1.36533
\(581\) 17.7469 0.736266
\(582\) 23.3661 0.968557
\(583\) −5.18596 −0.214780
\(584\) −42.6914 −1.76658
\(585\) −2.16086 −0.0893406
\(586\) 24.3805 1.00715
\(587\) 26.3874 1.08912 0.544562 0.838720i \(-0.316696\pi\)
0.544562 + 0.838720i \(0.316696\pi\)
\(588\) 15.3469 0.632895
\(589\) −24.8260 −1.02294
\(590\) 26.3444 1.08458
\(591\) −24.0973 −0.991229
\(592\) 15.4695 0.635791
\(593\) −15.4234 −0.633361 −0.316681 0.948532i \(-0.602568\pi\)
−0.316681 + 0.948532i \(0.602568\pi\)
\(594\) −13.5699 −0.556781
\(595\) −2.03522 −0.0834358
\(596\) 34.6727 1.42025
\(597\) −7.98748 −0.326906
\(598\) −20.6722 −0.845350
\(599\) −10.7494 −0.439207 −0.219604 0.975589i \(-0.570476\pi\)
−0.219604 + 0.975589i \(0.570476\pi\)
\(600\) −25.4840 −1.04038
\(601\) −40.4766 −1.65107 −0.825537 0.564347i \(-0.809128\pi\)
−0.825537 + 0.564347i \(0.809128\pi\)
\(602\) −4.95853 −0.202095
\(603\) 6.11456 0.249004
\(604\) −66.5156 −2.70648
\(605\) −0.987275 −0.0401384
\(606\) 26.6401 1.08218
\(607\) 28.2905 1.14827 0.574137 0.818759i \(-0.305338\pi\)
0.574137 + 0.818759i \(0.305338\pi\)
\(608\) 7.51019 0.304578
\(609\) −26.7300 −1.08316
\(610\) −29.5268 −1.19550
\(611\) −10.9512 −0.443039
\(612\) −3.13323 −0.126653
\(613\) −32.1870 −1.30002 −0.650010 0.759925i \(-0.725235\pi\)
−0.650010 + 0.759925i \(0.725235\pi\)
\(614\) 54.0594 2.18166
\(615\) −9.32217 −0.375906
\(616\) −8.85477 −0.356769
\(617\) 11.3483 0.456865 0.228433 0.973560i \(-0.426640\pi\)
0.228433 + 0.973560i \(0.426640\pi\)
\(618\) −41.1298 −1.65448
\(619\) 19.7454 0.793634 0.396817 0.917898i \(-0.370115\pi\)
0.396817 + 0.917898i \(0.370115\pi\)
\(620\) 24.1031 0.968004
\(621\) −18.3338 −0.735712
\(622\) −24.8031 −0.994514
\(623\) 24.3093 0.973931
\(624\) 10.7597 0.430734
\(625\) 11.3294 0.453175
\(626\) 61.5202 2.45884
\(627\) −5.67404 −0.226599
\(628\) 17.9575 0.716582
\(629\) 5.60389 0.223442
\(630\) −4.05163 −0.161421
\(631\) 16.9738 0.675716 0.337858 0.941197i \(-0.390298\pi\)
0.337858 + 0.941197i \(0.390298\pi\)
\(632\) −20.7146 −0.823984
\(633\) −9.28414 −0.369011
\(634\) −47.3317 −1.87978
\(635\) 7.34390 0.291434
\(636\) 28.9367 1.14741
\(637\) 7.27362 0.288191
\(638\) −21.1612 −0.837781
\(639\) 12.1872 0.482118
\(640\) −20.4024 −0.806477
\(641\) 35.5955 1.40594 0.702970 0.711220i \(-0.251857\pi\)
0.702970 + 0.711220i \(0.251857\pi\)
\(642\) 13.3571 0.527165
\(643\) 32.6214 1.28646 0.643232 0.765672i \(-0.277593\pi\)
0.643232 + 0.765672i \(0.277593\pi\)
\(644\) −25.3620 −0.999401
\(645\) 1.45514 0.0572961
\(646\) −9.25991 −0.364326
\(647\) 19.9820 0.785575 0.392787 0.919629i \(-0.371511\pi\)
0.392787 + 0.919629i \(0.371511\pi\)
\(648\) 25.0513 0.984109
\(649\) 11.0935 0.435459
\(650\) −25.6051 −1.00432
\(651\) 19.5939 0.767944
\(652\) −65.4671 −2.56389
\(653\) −46.1641 −1.80654 −0.903270 0.429073i \(-0.858840\pi\)
−0.903270 + 0.429073i \(0.858840\pi\)
\(654\) 53.2837 2.08356
\(655\) −8.53049 −0.333314
\(656\) −17.6847 −0.690472
\(657\) −8.22573 −0.320916
\(658\) −20.5336 −0.800484
\(659\) −29.4285 −1.14637 −0.573187 0.819425i \(-0.694293\pi\)
−0.573187 + 0.819425i \(0.694293\pi\)
\(660\) 5.50882 0.214430
\(661\) 37.7954 1.47007 0.735036 0.678029i \(-0.237165\pi\)
0.735036 + 0.678029i \(0.237165\pi\)
\(662\) 68.0130 2.64340
\(663\) 3.89777 0.151377
\(664\) −36.9790 −1.43506
\(665\) −7.83496 −0.303827
\(666\) 11.1560 0.432287
\(667\) −28.5902 −1.10702
\(668\) −33.9070 −1.31190
\(669\) 1.94480 0.0751904
\(670\) −17.5447 −0.677810
\(671\) −12.4336 −0.479994
\(672\) −5.92739 −0.228654
\(673\) −11.5302 −0.444458 −0.222229 0.974994i \(-0.571333\pi\)
−0.222229 + 0.974994i \(0.571333\pi\)
\(674\) −45.0031 −1.73345
\(675\) −22.7088 −0.874061
\(676\) −22.7389 −0.874573
\(677\) −22.4057 −0.861120 −0.430560 0.902562i \(-0.641684\pi\)
−0.430560 + 0.902562i \(0.641684\pi\)
\(678\) −45.0616 −1.73058
\(679\) 13.5866 0.521408
\(680\) 4.24075 0.162625
\(681\) 43.1723 1.65437
\(682\) 15.5118 0.593977
\(683\) 19.5024 0.746238 0.373119 0.927784i \(-0.378288\pi\)
0.373119 + 0.927784i \(0.378288\pi\)
\(684\) −12.0620 −0.461201
\(685\) 15.1900 0.580380
\(686\) 48.3478 1.84593
\(687\) 11.2681 0.429905
\(688\) 2.76049 0.105243
\(689\) 13.7145 0.522479
\(690\) 11.3747 0.433029
\(691\) −29.4952 −1.12205 −0.561025 0.827799i \(-0.689593\pi\)
−0.561025 + 0.827799i \(0.689593\pi\)
\(692\) −1.32482 −0.0503622
\(693\) −1.70613 −0.0648104
\(694\) −7.03513 −0.267050
\(695\) −14.2887 −0.542001
\(696\) 55.6970 2.11119
\(697\) −6.40638 −0.242659
\(698\) −24.2258 −0.916959
\(699\) −18.7908 −0.710734
\(700\) −31.4140 −1.18734
\(701\) 33.2824 1.25706 0.628530 0.777785i \(-0.283657\pi\)
0.628530 + 0.777785i \(0.283657\pi\)
\(702\) 35.8862 1.35444
\(703\) 21.5733 0.813652
\(704\) −10.2135 −0.384935
\(705\) 6.02584 0.226946
\(706\) −18.0346 −0.678741
\(707\) 15.4904 0.582576
\(708\) −61.8999 −2.32634
\(709\) −0.673003 −0.0252751 −0.0126376 0.999920i \(-0.504023\pi\)
−0.0126376 + 0.999920i \(0.504023\pi\)
\(710\) −34.9691 −1.31237
\(711\) −3.99127 −0.149684
\(712\) −50.6529 −1.89830
\(713\) 20.9574 0.784862
\(714\) 7.30835 0.273508
\(715\) 2.61089 0.0976416
\(716\) 80.7401 3.01740
\(717\) −22.3156 −0.833393
\(718\) −17.2374 −0.643294
\(719\) 17.9741 0.670320 0.335160 0.942161i \(-0.391210\pi\)
0.335160 + 0.942161i \(0.391210\pi\)
\(720\) 2.25560 0.0840614
\(721\) −23.9156 −0.890665
\(722\) 10.0541 0.374174
\(723\) −32.5074 −1.20896
\(724\) 51.3464 1.90827
\(725\) −35.4126 −1.31519
\(726\) 3.54525 0.131577
\(727\) −7.94965 −0.294836 −0.147418 0.989074i \(-0.547096\pi\)
−0.147418 + 0.989074i \(0.547096\pi\)
\(728\) 23.4168 0.867883
\(729\) 29.7719 1.10266
\(730\) 23.6023 0.873560
\(731\) 1.00000 0.0369863
\(732\) 69.3773 2.56426
\(733\) −2.62809 −0.0970706 −0.0485353 0.998821i \(-0.515455\pi\)
−0.0485353 + 0.998821i \(0.515455\pi\)
\(734\) 58.1645 2.14689
\(735\) −4.00226 −0.147626
\(736\) −6.33988 −0.233691
\(737\) −7.38800 −0.272140
\(738\) −12.7536 −0.469465
\(739\) −19.4104 −0.714024 −0.357012 0.934100i \(-0.616204\pi\)
−0.357012 + 0.934100i \(0.616204\pi\)
\(740\) −20.9451 −0.769956
\(741\) 15.0052 0.551231
\(742\) 25.7147 0.944017
\(743\) 2.48204 0.0910574 0.0455287 0.998963i \(-0.485503\pi\)
0.0455287 + 0.998963i \(0.485503\pi\)
\(744\) −40.8274 −1.49681
\(745\) −9.04217 −0.331279
\(746\) 11.3560 0.415771
\(747\) −7.12507 −0.260693
\(748\) 3.78577 0.138421
\(749\) 7.76675 0.283791
\(750\) 31.5897 1.15349
\(751\) 43.4560 1.58573 0.792867 0.609395i \(-0.208588\pi\)
0.792867 + 0.609395i \(0.208588\pi\)
\(752\) 11.4314 0.416859
\(753\) −20.2051 −0.736315
\(754\) 55.9617 2.03800
\(755\) 17.3463 0.631298
\(756\) 44.0274 1.60126
\(757\) 4.22737 0.153647 0.0768233 0.997045i \(-0.475522\pi\)
0.0768233 + 0.997045i \(0.475522\pi\)
\(758\) −5.61966 −0.204115
\(759\) 4.78986 0.173861
\(760\) 16.3256 0.592192
\(761\) 18.1964 0.659618 0.329809 0.944048i \(-0.393016\pi\)
0.329809 + 0.944048i \(0.393016\pi\)
\(762\) −26.3715 −0.955340
\(763\) 30.9827 1.12165
\(764\) −7.52057 −0.272085
\(765\) 0.817103 0.0295424
\(766\) 36.9089 1.33357
\(767\) −29.3373 −1.05931
\(768\) 43.1568 1.55729
\(769\) −10.8017 −0.389520 −0.194760 0.980851i \(-0.562393\pi\)
−0.194760 + 0.980851i \(0.562393\pi\)
\(770\) 4.89543 0.176419
\(771\) −8.98771 −0.323685
\(772\) −87.2132 −3.13887
\(773\) 9.23912 0.332308 0.166154 0.986100i \(-0.446865\pi\)
0.166154 + 0.986100i \(0.446865\pi\)
\(774\) 1.99076 0.0715564
\(775\) 25.9584 0.932454
\(776\) −28.3103 −1.01628
\(777\) −17.0266 −0.610827
\(778\) −8.43235 −0.302314
\(779\) −24.6626 −0.883629
\(780\) −14.5683 −0.521628
\(781\) −14.7253 −0.526914
\(782\) 7.81695 0.279533
\(783\) 49.6315 1.77368
\(784\) −7.59252 −0.271162
\(785\) −4.68307 −0.167146
\(786\) 30.6325 1.09263
\(787\) −17.2385 −0.614485 −0.307242 0.951631i \(-0.599406\pi\)
−0.307242 + 0.951631i \(0.599406\pi\)
\(788\) 61.8949 2.20492
\(789\) −22.2544 −0.792279
\(790\) 11.4523 0.407453
\(791\) −26.2019 −0.931632
\(792\) 3.55503 0.126323
\(793\) 32.8812 1.16764
\(794\) 20.8364 0.739456
\(795\) −7.54629 −0.267639
\(796\) 20.5162 0.727178
\(797\) 2.00217 0.0709206 0.0354603 0.999371i \(-0.488710\pi\)
0.0354603 + 0.999371i \(0.488710\pi\)
\(798\) 28.1349 0.995965
\(799\) 4.14107 0.146501
\(800\) −7.85274 −0.277636
\(801\) −9.75975 −0.344844
\(802\) −26.5749 −0.938391
\(803\) 9.93884 0.350734
\(804\) 41.2237 1.45385
\(805\) 6.61405 0.233115
\(806\) −41.0215 −1.44492
\(807\) 20.1391 0.708931
\(808\) −32.2771 −1.13550
\(809\) 31.3323 1.10159 0.550793 0.834642i \(-0.314325\pi\)
0.550793 + 0.834642i \(0.314325\pi\)
\(810\) −13.8498 −0.486634
\(811\) 8.42017 0.295672 0.147836 0.989012i \(-0.452769\pi\)
0.147836 + 0.989012i \(0.452769\pi\)
\(812\) 68.6573 2.40940
\(813\) 25.6534 0.899704
\(814\) −13.4794 −0.472452
\(815\) 17.0729 0.598038
\(816\) −4.06867 −0.142432
\(817\) 3.84969 0.134684
\(818\) −73.1826 −2.55877
\(819\) 4.51192 0.157659
\(820\) 23.9444 0.836176
\(821\) 5.50003 0.191952 0.0959761 0.995384i \(-0.469403\pi\)
0.0959761 + 0.995384i \(0.469403\pi\)
\(822\) −54.5464 −1.90253
\(823\) 31.6995 1.10498 0.552488 0.833521i \(-0.313678\pi\)
0.552488 + 0.833521i \(0.313678\pi\)
\(824\) 49.8327 1.73600
\(825\) 5.93285 0.206555
\(826\) −55.0076 −1.91396
\(827\) 29.8951 1.03955 0.519777 0.854302i \(-0.326015\pi\)
0.519777 + 0.854302i \(0.326015\pi\)
\(828\) 10.1824 0.353862
\(829\) 15.0707 0.523427 0.261714 0.965146i \(-0.415712\pi\)
0.261714 + 0.965146i \(0.415712\pi\)
\(830\) 20.4441 0.709626
\(831\) −4.50828 −0.156391
\(832\) 27.0099 0.936401
\(833\) −2.75043 −0.0952967
\(834\) 51.3099 1.77672
\(835\) 8.84247 0.306006
\(836\) 14.5740 0.504054
\(837\) −36.3813 −1.25752
\(838\) 61.2387 2.11546
\(839\) 21.8486 0.754296 0.377148 0.926153i \(-0.376905\pi\)
0.377148 + 0.926153i \(0.376905\pi\)
\(840\) −12.8849 −0.444572
\(841\) 48.3964 1.66884
\(842\) −8.51029 −0.293284
\(843\) 45.8706 1.57987
\(844\) 23.8467 0.820838
\(845\) 5.92999 0.203998
\(846\) 8.24388 0.283431
\(847\) 2.06145 0.0708322
\(848\) −14.3158 −0.491605
\(849\) 34.4463 1.18219
\(850\) 9.68227 0.332099
\(851\) −18.2115 −0.624283
\(852\) 82.1647 2.81492
\(853\) −17.4996 −0.599174 −0.299587 0.954069i \(-0.596849\pi\)
−0.299587 + 0.954069i \(0.596849\pi\)
\(854\) 61.6524 2.10970
\(855\) 3.14560 0.107577
\(856\) −16.1835 −0.553140
\(857\) −12.5450 −0.428528 −0.214264 0.976776i \(-0.568735\pi\)
−0.214264 + 0.976776i \(0.568735\pi\)
\(858\) −9.37555 −0.320076
\(859\) −27.7860 −0.948045 −0.474023 0.880513i \(-0.657199\pi\)
−0.474023 + 0.880513i \(0.657199\pi\)
\(860\) −3.73759 −0.127451
\(861\) 19.4649 0.663361
\(862\) −82.7442 −2.81828
\(863\) 57.2248 1.94796 0.973978 0.226643i \(-0.0727752\pi\)
0.973978 + 0.226643i \(0.0727752\pi\)
\(864\) 11.0058 0.374425
\(865\) 0.345496 0.0117472
\(866\) −65.3497 −2.22067
\(867\) −1.47389 −0.0500561
\(868\) −50.3277 −1.70823
\(869\) 4.82250 0.163592
\(870\) −30.7925 −1.04396
\(871\) 19.5378 0.662014
\(872\) −64.5583 −2.18622
\(873\) −5.45480 −0.184617
\(874\) 30.0929 1.01791
\(875\) 18.3684 0.620966
\(876\) −55.4569 −1.87372
\(877\) −33.2111 −1.12146 −0.560729 0.828000i \(-0.689479\pi\)
−0.560729 + 0.828000i \(0.689479\pi\)
\(878\) −30.2507 −1.02091
\(879\) 14.9392 0.503887
\(880\) −2.72536 −0.0918719
\(881\) 21.6329 0.728830 0.364415 0.931237i \(-0.381269\pi\)
0.364415 + 0.931237i \(0.381269\pi\)
\(882\) −5.47545 −0.184368
\(883\) 28.7331 0.966945 0.483472 0.875360i \(-0.339375\pi\)
0.483472 + 0.875360i \(0.339375\pi\)
\(884\) −10.0116 −0.336727
\(885\) 16.1426 0.542629
\(886\) 92.7280 3.11526
\(887\) −24.3445 −0.817408 −0.408704 0.912667i \(-0.634019\pi\)
−0.408704 + 0.912667i \(0.634019\pi\)
\(888\) 35.4782 1.19057
\(889\) −15.3342 −0.514292
\(890\) 28.0039 0.938693
\(891\) −5.83212 −0.195383
\(892\) −4.99531 −0.167256
\(893\) 15.9419 0.533474
\(894\) 32.4699 1.08596
\(895\) −21.0559 −0.703821
\(896\) 42.6007 1.42319
\(897\) −12.6670 −0.422938
\(898\) 22.6911 0.757211
\(899\) −56.7338 −1.89218
\(900\) 12.6122 0.420405
\(901\) −5.18596 −0.172769
\(902\) 15.4097 0.513085
\(903\) −3.03836 −0.101110
\(904\) 54.5965 1.81585
\(905\) −13.3904 −0.445113
\(906\) −62.2897 −2.06944
\(907\) 45.0911 1.49722 0.748612 0.663008i \(-0.230721\pi\)
0.748612 + 0.663008i \(0.230721\pi\)
\(908\) −110.890 −3.68001
\(909\) −6.21911 −0.206275
\(910\) −12.9462 −0.429161
\(911\) 29.6073 0.980933 0.490467 0.871460i \(-0.336826\pi\)
0.490467 + 0.871460i \(0.336826\pi\)
\(912\) −15.6631 −0.518658
\(913\) 8.60895 0.284915
\(914\) 46.4923 1.53783
\(915\) −18.0926 −0.598124
\(916\) −28.9426 −0.956291
\(917\) 17.8118 0.588198
\(918\) −13.5699 −0.447874
\(919\) 59.7985 1.97257 0.986285 0.165054i \(-0.0527799\pi\)
0.986285 + 0.165054i \(0.0527799\pi\)
\(920\) −13.7816 −0.454366
\(921\) 33.1251 1.09151
\(922\) 40.9698 1.34927
\(923\) 38.9417 1.28178
\(924\) −11.5025 −0.378405
\(925\) −22.5573 −0.741679
\(926\) −2.54116 −0.0835077
\(927\) 9.60170 0.315361
\(928\) 17.1627 0.563392
\(929\) 19.0077 0.623623 0.311812 0.950144i \(-0.399064\pi\)
0.311812 + 0.950144i \(0.399064\pi\)
\(930\) 22.5718 0.740158
\(931\) −10.5883 −0.347018
\(932\) 48.2650 1.58097
\(933\) −15.1982 −0.497567
\(934\) −39.7582 −1.30093
\(935\) −0.987275 −0.0322874
\(936\) −9.40142 −0.307295
\(937\) 41.3137 1.34966 0.674830 0.737973i \(-0.264217\pi\)
0.674830 + 0.737973i \(0.264217\pi\)
\(938\) 36.6336 1.19613
\(939\) 37.6967 1.23019
\(940\) −15.4776 −0.504825
\(941\) −20.5984 −0.671489 −0.335745 0.941953i \(-0.608988\pi\)
−0.335745 + 0.941953i \(0.608988\pi\)
\(942\) 16.8166 0.547916
\(943\) 20.8194 0.677975
\(944\) 30.6235 0.996712
\(945\) −11.4817 −0.373501
\(946\) −2.40536 −0.0782051
\(947\) −42.5498 −1.38268 −0.691341 0.722529i \(-0.742980\pi\)
−0.691341 + 0.722529i \(0.742980\pi\)
\(948\) −26.9087 −0.873953
\(949\) −26.2836 −0.853203
\(950\) 37.2738 1.20932
\(951\) −29.0027 −0.940477
\(952\) −8.85477 −0.286985
\(953\) 9.20992 0.298338 0.149169 0.988812i \(-0.452340\pi\)
0.149169 + 0.988812i \(0.452340\pi\)
\(954\) −10.3240 −0.334252
\(955\) 1.96126 0.0634649
\(956\) 57.3187 1.85382
\(957\) −12.9666 −0.419151
\(958\) −31.4522 −1.01617
\(959\) −31.7170 −1.02420
\(960\) −14.8620 −0.479670
\(961\) 10.5874 0.341531
\(962\) 35.6468 1.14930
\(963\) −3.11821 −0.100483
\(964\) 83.4967 2.68925
\(965\) 22.7440 0.732155
\(966\) −23.7507 −0.764166
\(967\) 3.71476 0.119459 0.0597293 0.998215i \(-0.480976\pi\)
0.0597293 + 0.998215i \(0.480976\pi\)
\(968\) −4.29541 −0.138060
\(969\) −5.67404 −0.182277
\(970\) 15.6516 0.502542
\(971\) 34.6745 1.11276 0.556379 0.830928i \(-0.312190\pi\)
0.556379 + 0.830928i \(0.312190\pi\)
\(972\) −31.5304 −1.01134
\(973\) 29.8350 0.956467
\(974\) −61.9857 −1.98615
\(975\) −15.6896 −0.502471
\(976\) −34.3228 −1.09865
\(977\) 11.2460 0.359792 0.179896 0.983686i \(-0.442424\pi\)
0.179896 + 0.983686i \(0.442424\pi\)
\(978\) −61.3078 −1.96041
\(979\) 11.7923 0.376885
\(980\) 10.2800 0.328382
\(981\) −12.4390 −0.397147
\(982\) 89.1150 2.84377
\(983\) −31.6420 −1.00922 −0.504611 0.863347i \(-0.668364\pi\)
−0.504611 + 0.863347i \(0.668364\pi\)
\(984\) −40.5587 −1.29296
\(985\) −16.1413 −0.514306
\(986\) −21.1612 −0.673911
\(987\) −12.5821 −0.400491
\(988\) −38.5416 −1.22617
\(989\) −3.24980 −0.103338
\(990\) −1.96543 −0.0624654
\(991\) −16.0853 −0.510967 −0.255483 0.966813i \(-0.582235\pi\)
−0.255483 + 0.966813i \(0.582235\pi\)
\(992\) −12.5807 −0.399438
\(993\) 41.6752 1.32252
\(994\) 73.0160 2.31593
\(995\) −5.35034 −0.169617
\(996\) −48.0364 −1.52209
\(997\) 48.8873 1.54827 0.774137 0.633018i \(-0.218184\pi\)
0.774137 + 0.633018i \(0.218184\pi\)
\(998\) 17.0730 0.540436
\(999\) 31.6145 1.00024
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 \(a_p\))