Properties

Label 6041.2.a.f.1.13
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 0
Dimension 132
CM No

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Newspace parameters

Level: \( N \) = \( 6041 = 7 \cdot 863 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2376278611\)
Analytic rank: \(0\)
Dimension: \(132\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.49223 q^{2}\) \(+0.173328 q^{3}\) \(+4.21120 q^{4}\) \(+2.29751 q^{5}\) \(-0.431973 q^{6}\) \(+1.00000 q^{7}\) \(-5.51083 q^{8}\) \(-2.96996 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.49223 q^{2}\) \(+0.173328 q^{3}\) \(+4.21120 q^{4}\) \(+2.29751 q^{5}\) \(-0.431973 q^{6}\) \(+1.00000 q^{7}\) \(-5.51083 q^{8}\) \(-2.96996 q^{9}\) \(-5.72592 q^{10}\) \(+4.74692 q^{11}\) \(+0.729919 q^{12}\) \(+4.44530 q^{13}\) \(-2.49223 q^{14}\) \(+0.398222 q^{15}\) \(+5.31183 q^{16}\) \(+7.62429 q^{17}\) \(+7.40181 q^{18}\) \(-5.56550 q^{19}\) \(+9.67528 q^{20}\) \(+0.173328 q^{21}\) \(-11.8304 q^{22}\) \(+5.50036 q^{23}\) \(-0.955179 q^{24}\) \(+0.278548 q^{25}\) \(-11.0787 q^{26}\) \(-1.03476 q^{27}\) \(+4.21120 q^{28}\) \(-0.702971 q^{29}\) \(-0.992461 q^{30}\) \(+8.98471 q^{31}\) \(-2.21665 q^{32}\) \(+0.822773 q^{33}\) \(-19.0015 q^{34}\) \(+2.29751 q^{35}\) \(-12.5071 q^{36}\) \(+9.07414 q^{37}\) \(+13.8705 q^{38}\) \(+0.770494 q^{39}\) \(-12.6612 q^{40}\) \(-3.05811 q^{41}\) \(-0.431973 q^{42}\) \(+4.67944 q^{43}\) \(+19.9902 q^{44}\) \(-6.82350 q^{45}\) \(-13.7082 q^{46}\) \(+5.17442 q^{47}\) \(+0.920688 q^{48}\) \(+1.00000 q^{49}\) \(-0.694205 q^{50}\) \(+1.32150 q^{51}\) \(+18.7201 q^{52}\) \(+7.04975 q^{53}\) \(+2.57886 q^{54}\) \(+10.9061 q^{55}\) \(-5.51083 q^{56}\) \(-0.964655 q^{57}\) \(+1.75197 q^{58}\) \(-11.8939 q^{59}\) \(+1.67700 q^{60}\) \(+1.14576 q^{61}\) \(-22.3920 q^{62}\) \(-2.96996 q^{63}\) \(-5.09927 q^{64}\) \(+10.2131 q^{65}\) \(-2.05054 q^{66}\) \(-8.35343 q^{67}\) \(+32.1074 q^{68}\) \(+0.953366 q^{69}\) \(-5.72592 q^{70}\) \(-5.29454 q^{71}\) \(+16.3669 q^{72}\) \(-12.0571 q^{73}\) \(-22.6148 q^{74}\) \(+0.0482801 q^{75}\) \(-23.4374 q^{76}\) \(+4.74692 q^{77}\) \(-1.92025 q^{78}\) \(+16.6769 q^{79}\) \(+12.2040 q^{80}\) \(+8.73052 q^{81}\) \(+7.62150 q^{82}\) \(-5.73960 q^{83}\) \(+0.729919 q^{84}\) \(+17.5169 q^{85}\) \(-11.6622 q^{86}\) \(-0.121844 q^{87}\) \(-26.1594 q^{88}\) \(-4.50184 q^{89}\) \(+17.0057 q^{90}\) \(+4.44530 q^{91}\) \(+23.1632 q^{92}\) \(+1.55730 q^{93}\) \(-12.8958 q^{94}\) \(-12.7868 q^{95}\) \(-0.384207 q^{96}\) \(-5.85081 q^{97}\) \(-2.49223 q^{98}\) \(-14.0981 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.49223 −1.76227 −0.881136 0.472863i \(-0.843221\pi\)
−0.881136 + 0.472863i \(0.843221\pi\)
\(3\) 0.173328 0.100071 0.0500354 0.998747i \(-0.484067\pi\)
0.0500354 + 0.998747i \(0.484067\pi\)
\(4\) 4.21120 2.10560
\(5\) 2.29751 1.02748 0.513739 0.857947i \(-0.328260\pi\)
0.513739 + 0.857947i \(0.328260\pi\)
\(6\) −0.431973 −0.176352
\(7\) 1.00000 0.377964
\(8\) −5.51083 −1.94837
\(9\) −2.96996 −0.989986
\(10\) −5.72592 −1.81069
\(11\) 4.74692 1.43125 0.715625 0.698485i \(-0.246142\pi\)
0.715625 + 0.698485i \(0.246142\pi\)
\(12\) 0.729919 0.210709
\(13\) 4.44530 1.23290 0.616452 0.787392i \(-0.288569\pi\)
0.616452 + 0.787392i \(0.288569\pi\)
\(14\) −2.49223 −0.666076
\(15\) 0.398222 0.102821
\(16\) 5.31183 1.32796
\(17\) 7.62429 1.84916 0.924581 0.380985i \(-0.124415\pi\)
0.924581 + 0.380985i \(0.124415\pi\)
\(18\) 7.40181 1.74462
\(19\) −5.56550 −1.27681 −0.638406 0.769700i \(-0.720406\pi\)
−0.638406 + 0.769700i \(0.720406\pi\)
\(20\) 9.67528 2.16346
\(21\) 0.173328 0.0378232
\(22\) −11.8304 −2.52225
\(23\) 5.50036 1.14691 0.573453 0.819239i \(-0.305604\pi\)
0.573453 + 0.819239i \(0.305604\pi\)
\(24\) −0.955179 −0.194975
\(25\) 0.278548 0.0557096
\(26\) −11.0787 −2.17271
\(27\) −1.03476 −0.199140
\(28\) 4.21120 0.795843
\(29\) −0.702971 −0.130539 −0.0652693 0.997868i \(-0.520791\pi\)
−0.0652693 + 0.997868i \(0.520791\pi\)
\(30\) −0.992461 −0.181198
\(31\) 8.98471 1.61370 0.806851 0.590755i \(-0.201170\pi\)
0.806851 + 0.590755i \(0.201170\pi\)
\(32\) −2.21665 −0.391852
\(33\) 0.822773 0.143226
\(34\) −19.0015 −3.25873
\(35\) 2.29751 0.388350
\(36\) −12.5071 −2.08452
\(37\) 9.07414 1.49178 0.745890 0.666070i \(-0.232025\pi\)
0.745890 + 0.666070i \(0.232025\pi\)
\(38\) 13.8705 2.25009
\(39\) 0.770494 0.123378
\(40\) −12.6612 −2.00191
\(41\) −3.05811 −0.477596 −0.238798 0.971069i \(-0.576753\pi\)
−0.238798 + 0.971069i \(0.576753\pi\)
\(42\) −0.431973 −0.0666548
\(43\) 4.67944 0.713608 0.356804 0.934179i \(-0.383866\pi\)
0.356804 + 0.934179i \(0.383866\pi\)
\(44\) 19.9902 3.01364
\(45\) −6.82350 −1.01719
\(46\) −13.7082 −2.02116
\(47\) 5.17442 0.754767 0.377383 0.926057i \(-0.376824\pi\)
0.377383 + 0.926057i \(0.376824\pi\)
\(48\) 0.920688 0.132890
\(49\) 1.00000 0.142857
\(50\) −0.694205 −0.0981755
\(51\) 1.32150 0.185047
\(52\) 18.7201 2.59601
\(53\) 7.04975 0.968357 0.484179 0.874969i \(-0.339119\pi\)
0.484179 + 0.874969i \(0.339119\pi\)
\(54\) 2.57886 0.350938
\(55\) 10.9061 1.47058
\(56\) −5.51083 −0.736415
\(57\) −0.964655 −0.127772
\(58\) 1.75197 0.230044
\(59\) −11.8939 −1.54845 −0.774224 0.632912i \(-0.781860\pi\)
−0.774224 + 0.632912i \(0.781860\pi\)
\(60\) 1.67700 0.216499
\(61\) 1.14576 0.146699 0.0733495 0.997306i \(-0.476631\pi\)
0.0733495 + 0.997306i \(0.476631\pi\)
\(62\) −22.3920 −2.84378
\(63\) −2.96996 −0.374179
\(64\) −5.09927 −0.637409
\(65\) 10.2131 1.26678
\(66\) −2.05054 −0.252404
\(67\) −8.35343 −1.02053 −0.510267 0.860016i \(-0.670453\pi\)
−0.510267 + 0.860016i \(0.670453\pi\)
\(68\) 32.1074 3.89360
\(69\) 0.953366 0.114772
\(70\) −5.72592 −0.684378
\(71\) −5.29454 −0.628346 −0.314173 0.949366i \(-0.601727\pi\)
−0.314173 + 0.949366i \(0.601727\pi\)
\(72\) 16.3669 1.92886
\(73\) −12.0571 −1.41117 −0.705586 0.708625i \(-0.749316\pi\)
−0.705586 + 0.708625i \(0.749316\pi\)
\(74\) −22.6148 −2.62892
\(75\) 0.0482801 0.00557491
\(76\) −23.4374 −2.68846
\(77\) 4.74692 0.540961
\(78\) −1.92025 −0.217425
\(79\) 16.6769 1.87630 0.938149 0.346232i \(-0.112539\pi\)
0.938149 + 0.346232i \(0.112539\pi\)
\(80\) 12.2040 1.36445
\(81\) 8.73052 0.970058
\(82\) 7.62150 0.841654
\(83\) −5.73960 −0.630003 −0.315002 0.949091i \(-0.602005\pi\)
−0.315002 + 0.949091i \(0.602005\pi\)
\(84\) 0.729919 0.0796407
\(85\) 17.5169 1.89997
\(86\) −11.6622 −1.25757
\(87\) −0.121844 −0.0130631
\(88\) −26.1594 −2.78861
\(89\) −4.50184 −0.477194 −0.238597 0.971119i \(-0.576688\pi\)
−0.238597 + 0.971119i \(0.576688\pi\)
\(90\) 17.0057 1.79256
\(91\) 4.44530 0.465994
\(92\) 23.1632 2.41493
\(93\) 1.55730 0.161485
\(94\) −12.8958 −1.33010
\(95\) −12.7868 −1.31190
\(96\) −0.384207 −0.0392129
\(97\) −5.85081 −0.594060 −0.297030 0.954868i \(-0.595996\pi\)
−0.297030 + 0.954868i \(0.595996\pi\)
\(98\) −2.49223 −0.251753
\(99\) −14.0981 −1.41692
\(100\) 1.17302 0.117302
\(101\) 5.64318 0.561517 0.280759 0.959778i \(-0.409414\pi\)
0.280759 + 0.959778i \(0.409414\pi\)
\(102\) −3.29348 −0.326104
\(103\) −4.24701 −0.418470 −0.209235 0.977865i \(-0.567097\pi\)
−0.209235 + 0.977865i \(0.567097\pi\)
\(104\) −24.4973 −2.40216
\(105\) 0.398222 0.0388625
\(106\) −17.5696 −1.70651
\(107\) −1.53811 −0.148694 −0.0743471 0.997232i \(-0.523687\pi\)
−0.0743471 + 0.997232i \(0.523687\pi\)
\(108\) −4.35758 −0.419309
\(109\) −18.0590 −1.72974 −0.864870 0.501996i \(-0.832599\pi\)
−0.864870 + 0.501996i \(0.832599\pi\)
\(110\) −27.1805 −2.59156
\(111\) 1.57280 0.149284
\(112\) 5.31183 0.501921
\(113\) 1.58533 0.149135 0.0745677 0.997216i \(-0.476242\pi\)
0.0745677 + 0.997216i \(0.476242\pi\)
\(114\) 2.40414 0.225168
\(115\) 12.6371 1.17842
\(116\) −2.96036 −0.274862
\(117\) −13.2024 −1.22056
\(118\) 29.6422 2.72879
\(119\) 7.62429 0.698918
\(120\) −2.19453 −0.200333
\(121\) 11.5332 1.04847
\(122\) −2.85549 −0.258524
\(123\) −0.530055 −0.0477935
\(124\) 37.8365 3.39781
\(125\) −10.8476 −0.970237
\(126\) 7.40181 0.659406
\(127\) 13.4958 1.19756 0.598780 0.800914i \(-0.295652\pi\)
0.598780 + 0.800914i \(0.295652\pi\)
\(128\) 17.1418 1.51514
\(129\) 0.811077 0.0714114
\(130\) −25.4534 −2.23241
\(131\) 22.2050 1.94006 0.970031 0.242979i \(-0.0781247\pi\)
0.970031 + 0.242979i \(0.0781247\pi\)
\(132\) 3.46486 0.301578
\(133\) −5.56550 −0.482590
\(134\) 20.8187 1.79846
\(135\) −2.37737 −0.204611
\(136\) −42.0161 −3.60285
\(137\) 15.8926 1.35779 0.678897 0.734233i \(-0.262458\pi\)
0.678897 + 0.734233i \(0.262458\pi\)
\(138\) −2.37601 −0.202259
\(139\) 4.50633 0.382222 0.191111 0.981568i \(-0.438791\pi\)
0.191111 + 0.981568i \(0.438791\pi\)
\(140\) 9.67528 0.817710
\(141\) 0.896871 0.0755302
\(142\) 13.1952 1.10732
\(143\) 21.1015 1.76459
\(144\) −15.7759 −1.31466
\(145\) −1.61508 −0.134125
\(146\) 30.0489 2.48687
\(147\) 0.173328 0.0142958
\(148\) 38.2130 3.14109
\(149\) 0.463022 0.0379322 0.0189661 0.999820i \(-0.493963\pi\)
0.0189661 + 0.999820i \(0.493963\pi\)
\(150\) −0.120325 −0.00982450
\(151\) −2.44742 −0.199168 −0.0995841 0.995029i \(-0.531751\pi\)
−0.0995841 + 0.995029i \(0.531751\pi\)
\(152\) 30.6705 2.48770
\(153\) −22.6438 −1.83064
\(154\) −11.8304 −0.953321
\(155\) 20.6425 1.65804
\(156\) 3.24471 0.259785
\(157\) 13.7617 1.09830 0.549151 0.835723i \(-0.314951\pi\)
0.549151 + 0.835723i \(0.314951\pi\)
\(158\) −41.5626 −3.30655
\(159\) 1.22192 0.0969043
\(160\) −5.09277 −0.402619
\(161\) 5.50036 0.433489
\(162\) −21.7585 −1.70951
\(163\) −9.48515 −0.742934 −0.371467 0.928446i \(-0.621145\pi\)
−0.371467 + 0.928446i \(0.621145\pi\)
\(164\) −12.8783 −1.00563
\(165\) 1.89033 0.147162
\(166\) 14.3044 1.11024
\(167\) −14.5005 −1.12208 −0.561041 0.827788i \(-0.689599\pi\)
−0.561041 + 0.827788i \(0.689599\pi\)
\(168\) −0.955179 −0.0736937
\(169\) 6.76069 0.520053
\(170\) −43.6561 −3.34827
\(171\) 16.5293 1.26403
\(172\) 19.7061 1.50257
\(173\) −18.9478 −1.44057 −0.720286 0.693678i \(-0.755989\pi\)
−0.720286 + 0.693678i \(0.755989\pi\)
\(174\) 0.303664 0.0230207
\(175\) 0.278548 0.0210563
\(176\) 25.2148 1.90064
\(177\) −2.06154 −0.154955
\(178\) 11.2196 0.840946
\(179\) −8.94525 −0.668600 −0.334300 0.942467i \(-0.608500\pi\)
−0.334300 + 0.942467i \(0.608500\pi\)
\(180\) −28.7352 −2.14179
\(181\) −11.0723 −0.822994 −0.411497 0.911411i \(-0.634994\pi\)
−0.411497 + 0.911411i \(0.634994\pi\)
\(182\) −11.0787 −0.821208
\(183\) 0.198591 0.0146803
\(184\) −30.3116 −2.23460
\(185\) 20.8479 1.53277
\(186\) −3.88115 −0.284580
\(187\) 36.1919 2.64661
\(188\) 21.7905 1.58924
\(189\) −1.03476 −0.0752677
\(190\) 31.8676 2.31192
\(191\) −9.74477 −0.705107 −0.352553 0.935792i \(-0.614686\pi\)
−0.352553 + 0.935792i \(0.614686\pi\)
\(192\) −0.883846 −0.0637861
\(193\) 17.6514 1.27058 0.635288 0.772275i \(-0.280881\pi\)
0.635288 + 0.772275i \(0.280881\pi\)
\(194\) 14.5816 1.04690
\(195\) 1.77022 0.126768
\(196\) 4.21120 0.300800
\(197\) −18.0755 −1.28782 −0.643912 0.765099i \(-0.722690\pi\)
−0.643912 + 0.765099i \(0.722690\pi\)
\(198\) 35.1358 2.49699
\(199\) −3.02589 −0.214500 −0.107250 0.994232i \(-0.534205\pi\)
−0.107250 + 0.994232i \(0.534205\pi\)
\(200\) −1.53503 −0.108543
\(201\) −1.44788 −0.102126
\(202\) −14.0641 −0.989546
\(203\) −0.702971 −0.0493389
\(204\) 5.56511 0.389636
\(205\) −7.02603 −0.490719
\(206\) 10.5845 0.737458
\(207\) −16.3358 −1.13542
\(208\) 23.6127 1.63725
\(209\) −26.4189 −1.82744
\(210\) −0.992461 −0.0684863
\(211\) 4.69620 0.323300 0.161650 0.986848i \(-0.448318\pi\)
0.161650 + 0.986848i \(0.448318\pi\)
\(212\) 29.6879 2.03897
\(213\) −0.917691 −0.0628791
\(214\) 3.83331 0.262040
\(215\) 10.7511 0.733216
\(216\) 5.70238 0.387998
\(217\) 8.98471 0.609922
\(218\) 45.0072 3.04827
\(219\) −2.08982 −0.141217
\(220\) 45.9278 3.09645
\(221\) 33.8923 2.27984
\(222\) −3.91978 −0.263078
\(223\) 22.1866 1.48572 0.742861 0.669445i \(-0.233468\pi\)
0.742861 + 0.669445i \(0.233468\pi\)
\(224\) −2.21665 −0.148106
\(225\) −0.827276 −0.0551517
\(226\) −3.95101 −0.262817
\(227\) 5.94761 0.394756 0.197378 0.980327i \(-0.436757\pi\)
0.197378 + 0.980327i \(0.436757\pi\)
\(228\) −4.06236 −0.269036
\(229\) −15.7376 −1.03997 −0.519986 0.854175i \(-0.674063\pi\)
−0.519986 + 0.854175i \(0.674063\pi\)
\(230\) −31.4946 −2.07669
\(231\) 0.822773 0.0541345
\(232\) 3.87395 0.254338
\(233\) −2.23207 −0.146228 −0.0731140 0.997324i \(-0.523294\pi\)
−0.0731140 + 0.997324i \(0.523294\pi\)
\(234\) 32.9033 2.15095
\(235\) 11.8883 0.775506
\(236\) −50.0874 −3.26041
\(237\) 2.89057 0.187763
\(238\) −19.0015 −1.23168
\(239\) −20.4047 −1.31987 −0.659936 0.751322i \(-0.729416\pi\)
−0.659936 + 0.751322i \(0.729416\pi\)
\(240\) 2.11529 0.136541
\(241\) −3.11638 −0.200743 −0.100372 0.994950i \(-0.532003\pi\)
−0.100372 + 0.994950i \(0.532003\pi\)
\(242\) −28.7434 −1.84770
\(243\) 4.61752 0.296214
\(244\) 4.82501 0.308890
\(245\) 2.29751 0.146782
\(246\) 1.32102 0.0842251
\(247\) −24.7403 −1.57419
\(248\) −49.5132 −3.14409
\(249\) −0.994833 −0.0630450
\(250\) 27.0346 1.70982
\(251\) −19.5061 −1.23121 −0.615606 0.788054i \(-0.711089\pi\)
−0.615606 + 0.788054i \(0.711089\pi\)
\(252\) −12.5071 −0.787873
\(253\) 26.1098 1.64151
\(254\) −33.6347 −2.11043
\(255\) 3.03616 0.190132
\(256\) −32.5229 −2.03268
\(257\) 4.57248 0.285223 0.142612 0.989779i \(-0.454450\pi\)
0.142612 + 0.989779i \(0.454450\pi\)
\(258\) −2.02139 −0.125846
\(259\) 9.07414 0.563839
\(260\) 43.0095 2.66734
\(261\) 2.08780 0.129231
\(262\) −55.3400 −3.41892
\(263\) −13.0532 −0.804896 −0.402448 0.915443i \(-0.631841\pi\)
−0.402448 + 0.915443i \(0.631841\pi\)
\(264\) −4.53416 −0.279058
\(265\) 16.1969 0.994965
\(266\) 13.8705 0.850454
\(267\) −0.780294 −0.0477532
\(268\) −35.1780 −2.14884
\(269\) −3.32800 −0.202912 −0.101456 0.994840i \(-0.532350\pi\)
−0.101456 + 0.994840i \(0.532350\pi\)
\(270\) 5.92495 0.360581
\(271\) 0.195976 0.0119047 0.00595233 0.999982i \(-0.498105\pi\)
0.00595233 + 0.999982i \(0.498105\pi\)
\(272\) 40.4990 2.45561
\(273\) 0.770494 0.0466324
\(274\) −39.6079 −2.39280
\(275\) 1.32224 0.0797343
\(276\) 4.01482 0.241664
\(277\) −1.11536 −0.0670153 −0.0335076 0.999438i \(-0.510668\pi\)
−0.0335076 + 0.999438i \(0.510668\pi\)
\(278\) −11.2308 −0.673580
\(279\) −26.6842 −1.59754
\(280\) −12.6612 −0.756650
\(281\) −10.2548 −0.611751 −0.305876 0.952071i \(-0.598949\pi\)
−0.305876 + 0.952071i \(0.598949\pi\)
\(282\) −2.23521 −0.133105
\(283\) −14.3410 −0.852485 −0.426243 0.904609i \(-0.640163\pi\)
−0.426243 + 0.904609i \(0.640163\pi\)
\(284\) −22.2964 −1.32305
\(285\) −2.21630 −0.131283
\(286\) −52.5897 −3.10969
\(287\) −3.05811 −0.180514
\(288\) 6.58335 0.387928
\(289\) 41.1298 2.41940
\(290\) 4.02516 0.236365
\(291\) −1.01411 −0.0594481
\(292\) −50.7747 −2.97137
\(293\) −26.8965 −1.57131 −0.785655 0.618665i \(-0.787674\pi\)
−0.785655 + 0.618665i \(0.787674\pi\)
\(294\) −0.431973 −0.0251932
\(295\) −27.3262 −1.59099
\(296\) −50.0060 −2.90654
\(297\) −4.91192 −0.285018
\(298\) −1.15396 −0.0668469
\(299\) 24.4508 1.41402
\(300\) 0.203317 0.0117385
\(301\) 4.67944 0.269719
\(302\) 6.09953 0.350988
\(303\) 0.978119 0.0561915
\(304\) −29.5630 −1.69555
\(305\) 2.63238 0.150730
\(306\) 56.4336 3.22609
\(307\) −6.02151 −0.343666 −0.171833 0.985126i \(-0.554969\pi\)
−0.171833 + 0.985126i \(0.554969\pi\)
\(308\) 19.9902 1.13905
\(309\) −0.736124 −0.0418766
\(310\) −51.4457 −2.92192
\(311\) 29.9192 1.69656 0.848281 0.529546i \(-0.177638\pi\)
0.848281 + 0.529546i \(0.177638\pi\)
\(312\) −4.24606 −0.240386
\(313\) 26.0398 1.47185 0.735927 0.677061i \(-0.236747\pi\)
0.735927 + 0.677061i \(0.236747\pi\)
\(314\) −34.2973 −1.93551
\(315\) −6.82350 −0.384461
\(316\) 70.2298 3.95074
\(317\) −32.8485 −1.84495 −0.922477 0.386052i \(-0.873838\pi\)
−0.922477 + 0.386052i \(0.873838\pi\)
\(318\) −3.04530 −0.170772
\(319\) −3.33695 −0.186833
\(320\) −11.7156 −0.654923
\(321\) −0.266596 −0.0148800
\(322\) −13.7082 −0.763926
\(323\) −42.4330 −2.36103
\(324\) 36.7660 2.04256
\(325\) 1.23823 0.0686846
\(326\) 23.6392 1.30925
\(327\) −3.13013 −0.173097
\(328\) 16.8527 0.930535
\(329\) 5.17442 0.285275
\(330\) −4.71113 −0.259339
\(331\) −17.0855 −0.939106 −0.469553 0.882904i \(-0.655585\pi\)
−0.469553 + 0.882904i \(0.655585\pi\)
\(332\) −24.1706 −1.32654
\(333\) −26.9498 −1.47684
\(334\) 36.1385 1.97741
\(335\) −19.1921 −1.04858
\(336\) 0.920688 0.0502277
\(337\) 4.87510 0.265564 0.132782 0.991145i \(-0.457609\pi\)
0.132782 + 0.991145i \(0.457609\pi\)
\(338\) −16.8492 −0.916474
\(339\) 0.274782 0.0149241
\(340\) 73.7672 4.00059
\(341\) 42.6497 2.30961
\(342\) −41.1948 −2.22756
\(343\) 1.00000 0.0539949
\(344\) −25.7876 −1.39037
\(345\) 2.19037 0.117925
\(346\) 47.2221 2.53868
\(347\) −18.7327 −1.00563 −0.502813 0.864396i \(-0.667701\pi\)
−0.502813 + 0.864396i \(0.667701\pi\)
\(348\) −0.513112 −0.0275057
\(349\) −12.6052 −0.674743 −0.337371 0.941372i \(-0.609538\pi\)
−0.337371 + 0.941372i \(0.609538\pi\)
\(350\) −0.694205 −0.0371068
\(351\) −4.59982 −0.245520
\(352\) −10.5222 −0.560837
\(353\) 6.57308 0.349850 0.174925 0.984582i \(-0.444032\pi\)
0.174925 + 0.984582i \(0.444032\pi\)
\(354\) 5.13782 0.273072
\(355\) −12.1642 −0.645611
\(356\) −18.9582 −1.00478
\(357\) 1.32150 0.0699413
\(358\) 22.2936 1.17825
\(359\) −22.5557 −1.19045 −0.595223 0.803561i \(-0.702936\pi\)
−0.595223 + 0.803561i \(0.702936\pi\)
\(360\) 37.6031 1.98186
\(361\) 11.9747 0.630250
\(362\) 27.5946 1.45034
\(363\) 1.99903 0.104922
\(364\) 18.7201 0.981198
\(365\) −27.7012 −1.44995
\(366\) −0.494935 −0.0258707
\(367\) −31.6153 −1.65031 −0.825153 0.564909i \(-0.808911\pi\)
−0.825153 + 0.564909i \(0.808911\pi\)
\(368\) 29.2170 1.52304
\(369\) 9.08245 0.472813
\(370\) −51.9578 −2.70116
\(371\) 7.04975 0.366005
\(372\) 6.55811 0.340022
\(373\) −19.9713 −1.03408 −0.517038 0.855963i \(-0.672965\pi\)
−0.517038 + 0.855963i \(0.672965\pi\)
\(374\) −90.1984 −4.66405
\(375\) −1.88019 −0.0970924
\(376\) −28.5153 −1.47057
\(377\) −3.12492 −0.160941
\(378\) 2.57886 0.132642
\(379\) 33.6280 1.72736 0.863678 0.504045i \(-0.168155\pi\)
0.863678 + 0.504045i \(0.168155\pi\)
\(380\) −53.8477 −2.76233
\(381\) 2.33920 0.119841
\(382\) 24.2862 1.24259
\(383\) −1.36415 −0.0697049 −0.0348524 0.999392i \(-0.511096\pi\)
−0.0348524 + 0.999392i \(0.511096\pi\)
\(384\) 2.97116 0.151621
\(385\) 10.9061 0.555826
\(386\) −43.9913 −2.23910
\(387\) −13.8977 −0.706462
\(388\) −24.6390 −1.25085
\(389\) −36.3694 −1.84400 −0.922000 0.387189i \(-0.873446\pi\)
−0.922000 + 0.387189i \(0.873446\pi\)
\(390\) −4.41179 −0.223399
\(391\) 41.9364 2.12081
\(392\) −5.51083 −0.278339
\(393\) 3.84875 0.194144
\(394\) 45.0482 2.26950
\(395\) 38.3153 1.92785
\(396\) −59.3702 −2.98346
\(397\) 0.950346 0.0476965 0.0238483 0.999716i \(-0.492408\pi\)
0.0238483 + 0.999716i \(0.492408\pi\)
\(398\) 7.54122 0.378007
\(399\) −0.964655 −0.0482932
\(400\) 1.47960 0.0739800
\(401\) −11.4641 −0.572489 −0.286244 0.958157i \(-0.592407\pi\)
−0.286244 + 0.958157i \(0.592407\pi\)
\(402\) 3.60845 0.179973
\(403\) 39.9397 1.98954
\(404\) 23.7646 1.18233
\(405\) 20.0584 0.996712
\(406\) 1.75197 0.0869486
\(407\) 43.0742 2.13511
\(408\) −7.28257 −0.360541
\(409\) 27.2286 1.34637 0.673184 0.739475i \(-0.264926\pi\)
0.673184 + 0.739475i \(0.264926\pi\)
\(410\) 17.5105 0.864781
\(411\) 2.75463 0.135876
\(412\) −17.8850 −0.881131
\(413\) −11.8939 −0.585258
\(414\) 40.7127 2.00092
\(415\) −13.1868 −0.647314
\(416\) −9.85366 −0.483115
\(417\) 0.781073 0.0382493
\(418\) 65.8421 3.22044
\(419\) 21.5419 1.05239 0.526196 0.850363i \(-0.323618\pi\)
0.526196 + 0.850363i \(0.323618\pi\)
\(420\) 1.67700 0.0818290
\(421\) 39.6151 1.93072 0.965362 0.260916i \(-0.0840245\pi\)
0.965362 + 0.260916i \(0.0840245\pi\)
\(422\) −11.7040 −0.569742
\(423\) −15.3678 −0.747208
\(424\) −38.8499 −1.88672
\(425\) 2.12373 0.103016
\(426\) 2.28710 0.110810
\(427\) 1.14576 0.0554470
\(428\) −6.47728 −0.313091
\(429\) 3.65747 0.176584
\(430\) −26.7941 −1.29213
\(431\) −11.3523 −0.546820 −0.273410 0.961898i \(-0.588152\pi\)
−0.273410 + 0.961898i \(0.588152\pi\)
\(432\) −5.49647 −0.264449
\(433\) −13.8755 −0.666812 −0.333406 0.942783i \(-0.608198\pi\)
−0.333406 + 0.942783i \(0.608198\pi\)
\(434\) −22.3920 −1.07485
\(435\) −0.279939 −0.0134220
\(436\) −76.0502 −3.64214
\(437\) −30.6123 −1.46438
\(438\) 5.20832 0.248863
\(439\) −21.6239 −1.03205 −0.516027 0.856572i \(-0.672590\pi\)
−0.516027 + 0.856572i \(0.672590\pi\)
\(440\) −60.1015 −2.86523
\(441\) −2.96996 −0.141427
\(442\) −84.4673 −4.01770
\(443\) 8.92232 0.423912 0.211956 0.977279i \(-0.432017\pi\)
0.211956 + 0.977279i \(0.432017\pi\)
\(444\) 6.62338 0.314332
\(445\) −10.3430 −0.490306
\(446\) −55.2940 −2.61825
\(447\) 0.0802545 0.00379591
\(448\) −5.09927 −0.240918
\(449\) −13.4689 −0.635639 −0.317819 0.948151i \(-0.602951\pi\)
−0.317819 + 0.948151i \(0.602951\pi\)
\(450\) 2.06176 0.0971923
\(451\) −14.5166 −0.683559
\(452\) 6.67615 0.314020
\(453\) −0.424206 −0.0199309
\(454\) −14.8228 −0.695668
\(455\) 10.2131 0.478798
\(456\) 5.31605 0.248947
\(457\) 31.7931 1.48722 0.743608 0.668615i \(-0.233113\pi\)
0.743608 + 0.668615i \(0.233113\pi\)
\(458\) 39.2217 1.83271
\(459\) −7.88931 −0.368241
\(460\) 53.2176 2.48128
\(461\) 14.3153 0.666731 0.333366 0.942798i \(-0.391816\pi\)
0.333366 + 0.942798i \(0.391816\pi\)
\(462\) −2.05054 −0.0953997
\(463\) 35.4821 1.64899 0.824496 0.565867i \(-0.191459\pi\)
0.824496 + 0.565867i \(0.191459\pi\)
\(464\) −3.73407 −0.173350
\(465\) 3.57791 0.165922
\(466\) 5.56284 0.257693
\(467\) 3.44580 0.159452 0.0797262 0.996817i \(-0.474595\pi\)
0.0797262 + 0.996817i \(0.474595\pi\)
\(468\) −55.5978 −2.57001
\(469\) −8.35343 −0.385726
\(470\) −29.6283 −1.36665
\(471\) 2.38528 0.109908
\(472\) 65.5450 3.01695
\(473\) 22.2129 1.02135
\(474\) −7.20396 −0.330889
\(475\) −1.55026 −0.0711307
\(476\) 32.1074 1.47164
\(477\) −20.9374 −0.958660
\(478\) 50.8532 2.32597
\(479\) 27.2486 1.24502 0.622510 0.782612i \(-0.286113\pi\)
0.622510 + 0.782612i \(0.286113\pi\)
\(480\) −0.882718 −0.0402904
\(481\) 40.3373 1.83922
\(482\) 7.76672 0.353765
\(483\) 0.953366 0.0433797
\(484\) 48.5687 2.20767
\(485\) −13.4423 −0.610383
\(486\) −11.5079 −0.522010
\(487\) 23.9708 1.08622 0.543110 0.839662i \(-0.317247\pi\)
0.543110 + 0.839662i \(0.317247\pi\)
\(488\) −6.31406 −0.285824
\(489\) −1.64404 −0.0743461
\(490\) −5.72592 −0.258671
\(491\) 29.4978 1.33122 0.665609 0.746300i \(-0.268172\pi\)
0.665609 + 0.746300i \(0.268172\pi\)
\(492\) −2.23217 −0.100634
\(493\) −5.35966 −0.241387
\(494\) 61.6585 2.77415
\(495\) −32.3906 −1.45585
\(496\) 47.7253 2.14293
\(497\) −5.29454 −0.237492
\(498\) 2.47935 0.111102
\(499\) 11.3620 0.508634 0.254317 0.967121i \(-0.418149\pi\)
0.254317 + 0.967121i \(0.418149\pi\)
\(500\) −45.6814 −2.04293
\(501\) −2.51334 −0.112288
\(502\) 48.6136 2.16973
\(503\) 38.8200 1.73090 0.865449 0.500997i \(-0.167033\pi\)
0.865449 + 0.500997i \(0.167033\pi\)
\(504\) 16.3669 0.729041
\(505\) 12.9652 0.576946
\(506\) −65.0715 −2.89278
\(507\) 1.17182 0.0520421
\(508\) 56.8336 2.52158
\(509\) −40.3600 −1.78893 −0.894464 0.447141i \(-0.852442\pi\)
−0.894464 + 0.447141i \(0.852442\pi\)
\(510\) −7.56681 −0.335064
\(511\) −12.0571 −0.533373
\(512\) 46.7707 2.06699
\(513\) 5.75895 0.254264
\(514\) −11.3957 −0.502641
\(515\) −9.75753 −0.429968
\(516\) 3.41561 0.150364
\(517\) 24.5625 1.08026
\(518\) −22.6148 −0.993638
\(519\) −3.28417 −0.144159
\(520\) −56.2827 −2.46816
\(521\) −18.6212 −0.815811 −0.407906 0.913024i \(-0.633741\pi\)
−0.407906 + 0.913024i \(0.633741\pi\)
\(522\) −5.20326 −0.227741
\(523\) −14.9812 −0.655081 −0.327541 0.944837i \(-0.606220\pi\)
−0.327541 + 0.944837i \(0.606220\pi\)
\(524\) 93.5099 4.08500
\(525\) 0.0482801 0.00210712
\(526\) 32.5316 1.41845
\(527\) 68.5021 2.98400
\(528\) 4.37043 0.190199
\(529\) 7.25401 0.315392
\(530\) −40.3663 −1.75340
\(531\) 35.3242 1.53294
\(532\) −23.4374 −1.01614
\(533\) −13.5942 −0.588830
\(534\) 1.94467 0.0841542
\(535\) −3.53381 −0.152780
\(536\) 46.0343 1.98838
\(537\) −1.55046 −0.0669073
\(538\) 8.29414 0.357586
\(539\) 4.74692 0.204464
\(540\) −10.0116 −0.430830
\(541\) 26.6191 1.14444 0.572222 0.820099i \(-0.306082\pi\)
0.572222 + 0.820099i \(0.306082\pi\)
\(542\) −0.488416 −0.0209793
\(543\) −1.91913 −0.0823577
\(544\) −16.9004 −0.724597
\(545\) −41.4908 −1.77727
\(546\) −1.92025 −0.0821790
\(547\) −33.7569 −1.44334 −0.721671 0.692236i \(-0.756626\pi\)
−0.721671 + 0.692236i \(0.756626\pi\)
\(548\) 66.9269 2.85897
\(549\) −3.40285 −0.145230
\(550\) −3.29534 −0.140514
\(551\) 3.91238 0.166673
\(552\) −5.25384 −0.223618
\(553\) 16.6769 0.709174
\(554\) 2.77972 0.118099
\(555\) 3.61352 0.153386
\(556\) 18.9771 0.804808
\(557\) −42.8417 −1.81526 −0.907631 0.419769i \(-0.862111\pi\)
−0.907631 + 0.419769i \(0.862111\pi\)
\(558\) 66.5032 2.81530
\(559\) 20.8015 0.879811
\(560\) 12.2040 0.515712
\(561\) 6.27306 0.264849
\(562\) 25.5574 1.07807
\(563\) −28.9599 −1.22051 −0.610257 0.792204i \(-0.708934\pi\)
−0.610257 + 0.792204i \(0.708934\pi\)
\(564\) 3.77691 0.159036
\(565\) 3.64231 0.153233
\(566\) 35.7411 1.50231
\(567\) 8.73052 0.366647
\(568\) 29.1773 1.22425
\(569\) 29.9084 1.25382 0.626912 0.779090i \(-0.284318\pi\)
0.626912 + 0.779090i \(0.284318\pi\)
\(570\) 5.52354 0.231356
\(571\) −10.3344 −0.432479 −0.216240 0.976340i \(-0.569379\pi\)
−0.216240 + 0.976340i \(0.569379\pi\)
\(572\) 88.8626 3.71553
\(573\) −1.68904 −0.0705606
\(574\) 7.62150 0.318115
\(575\) 1.53212 0.0638936
\(576\) 15.1446 0.631026
\(577\) 18.6240 0.775325 0.387663 0.921801i \(-0.373283\pi\)
0.387663 + 0.921801i \(0.373283\pi\)
\(578\) −102.505 −4.26364
\(579\) 3.05948 0.127148
\(580\) −6.80144 −0.282415
\(581\) −5.73960 −0.238119
\(582\) 2.52739 0.104764
\(583\) 33.4646 1.38596
\(584\) 66.4443 2.74949
\(585\) −30.3325 −1.25410
\(586\) 67.0322 2.76907
\(587\) −12.2949 −0.507464 −0.253732 0.967275i \(-0.581658\pi\)
−0.253732 + 0.967275i \(0.581658\pi\)
\(588\) 0.729919 0.0301013
\(589\) −50.0044 −2.06039
\(590\) 68.1032 2.80377
\(591\) −3.13298 −0.128874
\(592\) 48.2003 1.98102
\(593\) −15.9500 −0.654990 −0.327495 0.944853i \(-0.606204\pi\)
−0.327495 + 0.944853i \(0.606204\pi\)
\(594\) 12.2416 0.502280
\(595\) 17.5169 0.718122
\(596\) 1.94988 0.0798702
\(597\) −0.524472 −0.0214652
\(598\) −60.9369 −2.49190
\(599\) 12.3125 0.503075 0.251537 0.967848i \(-0.419064\pi\)
0.251537 + 0.967848i \(0.419064\pi\)
\(600\) −0.266063 −0.0108620
\(601\) 8.93720 0.364556 0.182278 0.983247i \(-0.441653\pi\)
0.182278 + 0.983247i \(0.441653\pi\)
\(602\) −11.6622 −0.475317
\(603\) 24.8093 1.01031
\(604\) −10.3066 −0.419369
\(605\) 26.4977 1.07728
\(606\) −2.43770 −0.0990247
\(607\) −2.79850 −0.113587 −0.0567937 0.998386i \(-0.518088\pi\)
−0.0567937 + 0.998386i \(0.518088\pi\)
\(608\) 12.3367 0.500321
\(609\) −0.121844 −0.00493739
\(610\) −6.56051 −0.265627
\(611\) 23.0018 0.930555
\(612\) −95.3578 −3.85461
\(613\) −19.1133 −0.771979 −0.385990 0.922503i \(-0.626140\pi\)
−0.385990 + 0.922503i \(0.626140\pi\)
\(614\) 15.0070 0.605632
\(615\) −1.21781 −0.0491067
\(616\) −26.1594 −1.05399
\(617\) 10.8463 0.436654 0.218327 0.975876i \(-0.429940\pi\)
0.218327 + 0.975876i \(0.429940\pi\)
\(618\) 1.83459 0.0737980
\(619\) 37.8949 1.52312 0.761562 0.648092i \(-0.224433\pi\)
0.761562 + 0.648092i \(0.224433\pi\)
\(620\) 86.9296 3.49118
\(621\) −5.69156 −0.228394
\(622\) −74.5655 −2.98981
\(623\) −4.50184 −0.180362
\(624\) 4.09273 0.163841
\(625\) −26.3152 −1.05261
\(626\) −64.8970 −2.59381
\(627\) −4.57914 −0.182873
\(628\) 57.9533 2.31259
\(629\) 69.1839 2.75854
\(630\) 17.0057 0.677525
\(631\) −37.5224 −1.49374 −0.746871 0.664969i \(-0.768445\pi\)
−0.746871 + 0.664969i \(0.768445\pi\)
\(632\) −91.9035 −3.65572
\(633\) 0.813982 0.0323529
\(634\) 81.8659 3.25131
\(635\) 31.0068 1.23047
\(636\) 5.14574 0.204042
\(637\) 4.44530 0.176129
\(638\) 8.31643 0.329251
\(639\) 15.7246 0.622054
\(640\) 39.3835 1.55677
\(641\) −45.0884 −1.78089 −0.890443 0.455096i \(-0.849605\pi\)
−0.890443 + 0.455096i \(0.849605\pi\)
\(642\) 0.664419 0.0262225
\(643\) −45.7955 −1.80600 −0.903000 0.429642i \(-0.858640\pi\)
−0.903000 + 0.429642i \(0.858640\pi\)
\(644\) 23.1632 0.912756
\(645\) 1.86346 0.0733736
\(646\) 105.753 4.16078
\(647\) −14.4987 −0.570004 −0.285002 0.958527i \(-0.591994\pi\)
−0.285002 + 0.958527i \(0.591994\pi\)
\(648\) −48.1124 −1.89003
\(649\) −56.4591 −2.21621
\(650\) −3.08595 −0.121041
\(651\) 1.55730 0.0610354
\(652\) −39.9439 −1.56432
\(653\) 31.3208 1.22568 0.612838 0.790209i \(-0.290028\pi\)
0.612838 + 0.790209i \(0.290028\pi\)
\(654\) 7.80100 0.305043
\(655\) 51.0163 1.99337
\(656\) −16.2442 −0.634228
\(657\) 35.8089 1.39704
\(658\) −12.8958 −0.502732
\(659\) 28.5345 1.11155 0.555774 0.831334i \(-0.312422\pi\)
0.555774 + 0.831334i \(0.312422\pi\)
\(660\) 7.96056 0.309864
\(661\) 26.4881 1.03027 0.515134 0.857109i \(-0.327742\pi\)
0.515134 + 0.857109i \(0.327742\pi\)
\(662\) 42.5811 1.65496
\(663\) 5.87447 0.228146
\(664\) 31.6300 1.22748
\(665\) −12.7868 −0.495850
\(666\) 67.1651 2.60259
\(667\) −3.86660 −0.149715
\(668\) −61.0645 −2.36266
\(669\) 3.84555 0.148678
\(670\) 47.8311 1.84787
\(671\) 5.43881 0.209963
\(672\) −0.384207 −0.0148211
\(673\) 19.5956 0.755354 0.377677 0.925938i \(-0.376723\pi\)
0.377677 + 0.925938i \(0.376723\pi\)
\(674\) −12.1499 −0.467995
\(675\) −0.288230 −0.0110940
\(676\) 28.4706 1.09502
\(677\) 13.2267 0.508343 0.254172 0.967159i \(-0.418197\pi\)
0.254172 + 0.967159i \(0.418197\pi\)
\(678\) −0.684819 −0.0263003
\(679\) −5.85081 −0.224534
\(680\) −96.5325 −3.70185
\(681\) 1.03089 0.0395036
\(682\) −106.293 −4.07016
\(683\) 16.4729 0.630317 0.315158 0.949039i \(-0.397942\pi\)
0.315158 + 0.949039i \(0.397942\pi\)
\(684\) 69.6082 2.66154
\(685\) 36.5133 1.39510
\(686\) −2.49223 −0.0951537
\(687\) −2.72777 −0.104071
\(688\) 24.8564 0.947642
\(689\) 31.3382 1.19389
\(690\) −5.45890 −0.207817
\(691\) 35.4706 1.34937 0.674684 0.738107i \(-0.264280\pi\)
0.674684 + 0.738107i \(0.264280\pi\)
\(692\) −79.7929 −3.03327
\(693\) −14.0981 −0.535544
\(694\) 46.6862 1.77218
\(695\) 10.3533 0.392725
\(696\) 0.671464 0.0254518
\(697\) −23.3159 −0.883153
\(698\) 31.4151 1.18908
\(699\) −0.386880 −0.0146332
\(700\) 1.17302 0.0443361
\(701\) 8.17549 0.308784 0.154392 0.988010i \(-0.450658\pi\)
0.154392 + 0.988010i \(0.450658\pi\)
\(702\) 11.4638 0.432673
\(703\) −50.5021 −1.90472
\(704\) −24.2058 −0.912291
\(705\) 2.06057 0.0776055
\(706\) −16.3816 −0.616530
\(707\) 5.64318 0.212233
\(708\) −8.68155 −0.326273
\(709\) 5.62194 0.211136 0.105568 0.994412i \(-0.466334\pi\)
0.105568 + 0.994412i \(0.466334\pi\)
\(710\) 30.3161 1.13774
\(711\) −49.5297 −1.85751
\(712\) 24.8089 0.929752
\(713\) 49.4192 1.85076
\(714\) −3.29348 −0.123256
\(715\) 48.4808 1.81308
\(716\) −37.6703 −1.40780
\(717\) −3.53670 −0.132081
\(718\) 56.2140 2.09789
\(719\) 19.8931 0.741888 0.370944 0.928655i \(-0.379034\pi\)
0.370944 + 0.928655i \(0.379034\pi\)
\(720\) −36.2453 −1.35078
\(721\) −4.24701 −0.158167
\(722\) −29.8438 −1.11067
\(723\) −0.540155 −0.0200886
\(724\) −46.6275 −1.73290
\(725\) −0.195811 −0.00727225
\(726\) −4.98203 −0.184901
\(727\) 28.2937 1.04936 0.524678 0.851301i \(-0.324186\pi\)
0.524678 + 0.851301i \(0.324186\pi\)
\(728\) −24.4973 −0.907929
\(729\) −25.3912 −0.940415
\(730\) 69.0377 2.55520
\(731\) 35.6774 1.31958
\(732\) 0.836309 0.0309109
\(733\) −50.8733 −1.87905 −0.939524 0.342483i \(-0.888732\pi\)
−0.939524 + 0.342483i \(0.888732\pi\)
\(734\) 78.7926 2.90829
\(735\) 0.398222 0.0146886
\(736\) −12.1924 −0.449417
\(737\) −39.6530 −1.46064
\(738\) −22.6355 −0.833226
\(739\) 0.586872 0.0215884 0.0107942 0.999942i \(-0.496564\pi\)
0.0107942 + 0.999942i \(0.496564\pi\)
\(740\) 87.7948 3.22740
\(741\) −4.28818 −0.157530
\(742\) −17.5696 −0.645000
\(743\) −46.8964 −1.72046 −0.860230 0.509906i \(-0.829680\pi\)
−0.860230 + 0.509906i \(0.829680\pi\)
\(744\) −8.58201 −0.314632
\(745\) 1.06380 0.0389745
\(746\) 49.7731 1.82232
\(747\) 17.0464 0.623694
\(748\) 152.411 5.57271
\(749\) −1.53811 −0.0562011
\(750\) 4.68586 0.171103
\(751\) −3.87881 −0.141540 −0.0707700 0.997493i \(-0.522546\pi\)
−0.0707700 + 0.997493i \(0.522546\pi\)
\(752\) 27.4857 1.00230
\(753\) −3.38094 −0.123208
\(754\) 7.78801 0.283623
\(755\) −5.62297 −0.204641
\(756\) −4.35758 −0.158484
\(757\) 7.16382 0.260373 0.130187 0.991489i \(-0.458442\pi\)
0.130187 + 0.991489i \(0.458442\pi\)
\(758\) −83.8087 −3.04407
\(759\) 4.52555 0.164267
\(760\) 70.4657 2.55606
\(761\) 51.2063 1.85623 0.928114 0.372296i \(-0.121430\pi\)
0.928114 + 0.372296i \(0.121430\pi\)
\(762\) −5.82982 −0.211192
\(763\) −18.0590 −0.653780
\(764\) −41.0372 −1.48467
\(765\) −52.0244 −1.88095
\(766\) 3.39978 0.122839
\(767\) −52.8717 −1.90909
\(768\) −5.63712 −0.203412
\(769\) 10.7227 0.386672 0.193336 0.981133i \(-0.438069\pi\)
0.193336 + 0.981133i \(0.438069\pi\)
\(770\) −27.1805 −0.979516
\(771\) 0.792538 0.0285425
\(772\) 74.3337 2.67533
\(773\) −38.1132 −1.37084 −0.685419 0.728149i \(-0.740381\pi\)
−0.685419 + 0.728149i \(0.740381\pi\)
\(774\) 34.6364 1.24498
\(775\) 2.50267 0.0898987
\(776\) 32.2428 1.15745
\(777\) 1.57280 0.0564239
\(778\) 90.6408 3.24963
\(779\) 17.0199 0.609801
\(780\) 7.45475 0.266923
\(781\) −25.1327 −0.899320
\(782\) −104.515 −3.73745
\(783\) 0.727406 0.0259954
\(784\) 5.31183 0.189708
\(785\) 31.6176 1.12848
\(786\) −9.59197 −0.342134
\(787\) 18.9969 0.677167 0.338583 0.940936i \(-0.390052\pi\)
0.338583 + 0.940936i \(0.390052\pi\)
\(788\) −76.1195 −2.71165
\(789\) −2.26249 −0.0805466
\(790\) −95.4906 −3.39740
\(791\) 1.58533 0.0563679
\(792\) 77.6924 2.76068
\(793\) 5.09323 0.180866
\(794\) −2.36848 −0.0840542
\(795\) 2.80737 0.0995670
\(796\) −12.7427 −0.451652
\(797\) −3.70336 −0.131180 −0.0655899 0.997847i \(-0.520893\pi\)
−0.0655899 + 0.997847i \(0.520893\pi\)
\(798\) 2.40414 0.0851057
\(799\) 39.4513 1.39569
\(800\) −0.617443 −0.0218299
\(801\) 13.3703 0.472416
\(802\) 28.5711 1.00888
\(803\) −57.2338 −2.01974
\(804\) −6.09732 −0.215036
\(805\) 12.6371 0.445401
\(806\) −99.5390 −3.50611
\(807\) −0.576835 −0.0203055
\(808\) −31.0986 −1.09404
\(809\) −28.9623 −1.01826 −0.509130 0.860690i \(-0.670033\pi\)
−0.509130 + 0.860690i \(0.670033\pi\)
\(810\) −49.9902 −1.75648
\(811\) 22.9619 0.806303 0.403151 0.915133i \(-0.367915\pi\)
0.403151 + 0.915133i \(0.367915\pi\)
\(812\) −2.96036 −0.103888
\(813\) 0.0339680 0.00119131
\(814\) −107.351 −3.76264
\(815\) −21.7922 −0.763348
\(816\) 7.01960 0.245735
\(817\) −26.0434 −0.911144
\(818\) −67.8599 −2.37267
\(819\) −13.2024 −0.461327
\(820\) −29.5880 −1.03326
\(821\) 17.4961 0.610616 0.305308 0.952254i \(-0.401241\pi\)
0.305308 + 0.952254i \(0.401241\pi\)
\(822\) −6.86516 −0.239450
\(823\) 1.39813 0.0487357 0.0243678 0.999703i \(-0.492243\pi\)
0.0243678 + 0.999703i \(0.492243\pi\)
\(824\) 23.4045 0.815335
\(825\) 0.229182 0.00797908
\(826\) 29.6422 1.03138
\(827\) −14.2691 −0.496186 −0.248093 0.968736i \(-0.579804\pi\)
−0.248093 + 0.968736i \(0.579804\pi\)
\(828\) −68.7936 −2.39074
\(829\) 44.3472 1.54024 0.770121 0.637898i \(-0.220196\pi\)
0.770121 + 0.637898i \(0.220196\pi\)
\(830\) 32.8645 1.14074
\(831\) −0.193322 −0.00670628
\(832\) −22.6678 −0.785864
\(833\) 7.62429 0.264166
\(834\) −1.94661 −0.0674057
\(835\) −33.3150 −1.15291
\(836\) −111.256 −3.84785
\(837\) −9.29702 −0.321352
\(838\) −53.6874 −1.85460
\(839\) −10.3940 −0.358839 −0.179420 0.983773i \(-0.557422\pi\)
−0.179420 + 0.983773i \(0.557422\pi\)
\(840\) −2.19453 −0.0757186
\(841\) −28.5058 −0.982960
\(842\) −98.7300 −3.40246
\(843\) −1.77745 −0.0612185
\(844\) 19.7767 0.680740
\(845\) 15.5327 0.534342
\(846\) 38.3001 1.31678
\(847\) 11.5332 0.396286
\(848\) 37.4471 1.28594
\(849\) −2.48570 −0.0853089
\(850\) −5.29282 −0.181542
\(851\) 49.9111 1.71093
\(852\) −3.86458 −0.132398
\(853\) 40.3933 1.38304 0.691520 0.722357i \(-0.256941\pi\)
0.691520 + 0.722357i \(0.256941\pi\)
\(854\) −2.85549 −0.0977127
\(855\) 37.9762 1.29876
\(856\) 8.47623 0.289712
\(857\) 33.6418 1.14918 0.574591 0.818441i \(-0.305161\pi\)
0.574591 + 0.818441i \(0.305161\pi\)
\(858\) −9.11525 −0.311190
\(859\) −29.5627 −1.00867 −0.504333 0.863509i \(-0.668262\pi\)
−0.504333 + 0.863509i \(0.668262\pi\)
\(860\) 45.2749 1.54386
\(861\) −0.530055 −0.0180642
\(862\) 28.2925 0.963646
\(863\) −1.00000 −0.0340404
\(864\) 2.29370 0.0780332
\(865\) −43.5326 −1.48015
\(866\) 34.5808 1.17510
\(867\) 7.12894 0.242112
\(868\) 37.8365 1.28425
\(869\) 79.1639 2.68545
\(870\) 0.697672 0.0236533
\(871\) −37.1335 −1.25822
\(872\) 99.5201 3.37018
\(873\) 17.3767 0.588111
\(874\) 76.2927 2.58064
\(875\) −10.8476 −0.366715
\(876\) −8.80067 −0.297347
\(877\) 6.11912 0.206628 0.103314 0.994649i \(-0.467055\pi\)
0.103314 + 0.994649i \(0.467055\pi\)
\(878\) 53.8918 1.81876
\(879\) −4.66191 −0.157242
\(880\) 57.9313 1.95286
\(881\) −42.3782 −1.42776 −0.713878 0.700270i \(-0.753063\pi\)
−0.713878 + 0.700270i \(0.753063\pi\)
\(882\) 7.40181 0.249232
\(883\) 14.4968 0.487855 0.243928 0.969793i \(-0.421564\pi\)
0.243928 + 0.969793i \(0.421564\pi\)
\(884\) 142.727 4.80044
\(885\) −4.73640 −0.159212
\(886\) −22.2365 −0.747048
\(887\) 20.6720 0.694097 0.347048 0.937847i \(-0.387184\pi\)
0.347048 + 0.937847i \(0.387184\pi\)
\(888\) −8.66743 −0.290860
\(889\) 13.4958 0.452635
\(890\) 25.7772 0.864053
\(891\) 41.4431 1.38839
\(892\) 93.4322 3.12834
\(893\) −28.7982 −0.963696
\(894\) −0.200013 −0.00668942
\(895\) −20.5518 −0.686971
\(896\) 17.1418 0.572669
\(897\) 4.23800 0.141503
\(898\) 33.5677 1.12017
\(899\) −6.31600 −0.210650
\(900\) −3.48383 −0.116128
\(901\) 53.7493 1.79065
\(902\) 36.1786 1.20462
\(903\) 0.811077 0.0269910
\(904\) −8.73648 −0.290571
\(905\) −25.4386 −0.845608
\(906\) 1.05722 0.0351237
\(907\) 12.8102 0.425356 0.212678 0.977122i \(-0.431781\pi\)
0.212678 + 0.977122i \(0.431781\pi\)
\(908\) 25.0466 0.831200
\(909\) −16.7600 −0.555894
\(910\) −25.4534 −0.843773
\(911\) −37.6111 −1.24611 −0.623055 0.782178i \(-0.714109\pi\)
−0.623055 + 0.782178i \(0.714109\pi\)
\(912\) −5.12409 −0.169675
\(913\) −27.2454 −0.901692
\(914\) −79.2356 −2.62088
\(915\) 0.456266 0.0150837
\(916\) −66.2743 −2.18977
\(917\) 22.2050 0.733275
\(918\) 19.6620 0.648941
\(919\) 51.8458 1.71024 0.855118 0.518433i \(-0.173484\pi\)
0.855118 + 0.518433i \(0.173484\pi\)
\(920\) −69.6411 −2.29600
\(921\) −1.04370 −0.0343909
\(922\) −35.6771 −1.17496
\(923\) −23.5358 −0.774690
\(924\) 3.46486 0.113986
\(925\) 2.52758 0.0831064
\(926\) −88.4295 −2.90597
\(927\) 12.6134 0.414279
\(928\) 1.55824 0.0511517
\(929\) 15.5155 0.509048 0.254524 0.967066i \(-0.418081\pi\)
0.254524 + 0.967066i \(0.418081\pi\)
\(930\) −8.91697 −0.292399
\(931\) −5.56550 −0.182402
\(932\) −9.39972 −0.307898
\(933\) 5.18583 0.169777
\(934\) −8.58771 −0.280998
\(935\) 83.1512 2.71933
\(936\) 72.7559 2.37810
\(937\) −45.3080 −1.48015 −0.740073 0.672526i \(-0.765209\pi\)
−0.740073 + 0.672526i \(0.765209\pi\)
\(938\) 20.8187 0.679753
\(939\) 4.51341 0.147290
\(940\) 50.0640 1.63291
\(941\) −20.3497 −0.663380 −0.331690 0.943388i \(-0.607619\pi\)
−0.331690 + 0.943388i \(0.607619\pi\)
\(942\) −5.94467 −0.193688
\(943\) −16.8207 −0.547758
\(944\) −63.1782 −2.05627
\(945\) −2.37737 −0.0773358
\(946\) −55.3597 −1.79990
\(947\) 33.8198 1.09900 0.549498 0.835495i \(-0.314819\pi\)
0.549498 + 0.835495i \(0.314819\pi\)
\(948\) 12.1728 0.395354
\(949\) −53.5972 −1.73984
\(950\) 3.86360 0.125352
\(951\) −5.69355 −0.184626
\(952\) −42.0161 −1.36175
\(953\) 54.0496 1.75084 0.875419 0.483365i \(-0.160586\pi\)
0.875419 + 0.483365i \(0.160586\pi\)
\(954\) 52.1809 1.68942
\(955\) −22.3887 −0.724481
\(956\) −85.9284 −2.77912
\(957\) −0.578386 −0.0186966
\(958\) −67.9097 −2.19406
\(959\) 15.8926 0.513198
\(960\) −2.03064 −0.0655387
\(961\) 49.7250 1.60403
\(962\) −100.530 −3.24121
\(963\) 4.56811 0.147205
\(964\) −13.1237 −0.422686
\(965\) 40.5543 1.30549
\(966\) −2.37601 −0.0764468
\(967\) −24.7111 −0.794655 −0.397327 0.917677i \(-0.630062\pi\)
−0.397327 + 0.917677i \(0.630062\pi\)
\(968\) −63.5576 −2.04282
\(969\) −7.35481 −0.236271
\(970\) 33.5013 1.07566
\(971\) 3.66325 0.117559 0.0587796 0.998271i \(-0.481279\pi\)
0.0587796 + 0.998271i \(0.481279\pi\)
\(972\) 19.4453 0.623709
\(973\) 4.50633 0.144466
\(974\) −59.7406 −1.91421
\(975\) 0.214620 0.00687333
\(976\) 6.08606 0.194810
\(977\) −8.76216 −0.280326 −0.140163 0.990128i \(-0.544763\pi\)
−0.140163 + 0.990128i \(0.544763\pi\)
\(978\) 4.09732 0.131018
\(979\) −21.3699 −0.682984
\(980\) 9.67528 0.309065
\(981\) 53.6345 1.71242
\(982\) −73.5153 −2.34597
\(983\) 55.7992 1.77972 0.889860 0.456234i \(-0.150802\pi\)
0.889860 + 0.456234i \(0.150802\pi\)
\(984\) 2.92104 0.0931194
\(985\) −41.5286 −1.32321
\(986\) 13.3575 0.425389
\(987\) 0.896871 0.0285477
\(988\) −104.186 −3.31461
\(989\) 25.7386 0.818441
\(990\) 80.7248 2.56560
\(991\) 24.6850 0.784146 0.392073 0.919934i \(-0.371758\pi\)
0.392073 + 0.919934i \(0.371758\pi\)
\(992\) −19.9159 −0.632332
\(993\) −2.96140 −0.0939771
\(994\) 13.1952 0.418526
\(995\) −6.95202 −0.220394
\(996\) −4.18945 −0.132748
\(997\) −27.8325 −0.881463 −0.440731 0.897639i \(-0.645281\pi\)
−0.440731 + 0.897639i \(0.645281\pi\)
\(998\) −28.3168 −0.896352
\(999\) −9.38955 −0.297072
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 \(a_p\))