Properties

Label 4031.2.a.c.1.18
Level 4031
Weight 2
Character 4031.1
Self dual Yes
Analytic conductor 32.188
Analytic rank 1
Dimension 61
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(61\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.44025 q^{2}\) \(+1.49462 q^{3}\) \(+0.0743258 q^{4}\) \(+2.03878 q^{5}\) \(-2.15264 q^{6}\) \(-3.27699 q^{7}\) \(+2.77346 q^{8}\) \(-0.766098 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.44025 q^{2}\) \(+1.49462 q^{3}\) \(+0.0743258 q^{4}\) \(+2.03878 q^{5}\) \(-2.15264 q^{6}\) \(-3.27699 q^{7}\) \(+2.77346 q^{8}\) \(-0.766098 q^{9}\) \(-2.93636 q^{10}\) \(+2.62027 q^{11}\) \(+0.111089 q^{12}\) \(-5.46435 q^{13}\) \(+4.71969 q^{14}\) \(+3.04721 q^{15}\) \(-4.14313 q^{16}\) \(+4.75105 q^{17}\) \(+1.10337 q^{18}\) \(+3.60952 q^{19}\) \(+0.151534 q^{20}\) \(-4.89787 q^{21}\) \(-3.77386 q^{22}\) \(-2.87506 q^{23}\) \(+4.14527 q^{24}\) \(-0.843373 q^{25}\) \(+7.87004 q^{26}\) \(-5.62890 q^{27}\) \(-0.243565 q^{28}\) \(-1.00000 q^{29}\) \(-4.38875 q^{30}\) \(+1.86600 q^{31}\) \(+0.420235 q^{32}\) \(+3.91633 q^{33}\) \(-6.84271 q^{34}\) \(-6.68106 q^{35}\) \(-0.0569409 q^{36}\) \(+9.24926 q^{37}\) \(-5.19862 q^{38}\) \(-8.16715 q^{39}\) \(+5.65447 q^{40}\) \(-7.59599 q^{41}\) \(+7.05416 q^{42}\) \(-2.51760 q^{43}\) \(+0.194754 q^{44}\) \(-1.56191 q^{45}\) \(+4.14082 q^{46}\) \(-0.622600 q^{47}\) \(-6.19242 q^{48}\) \(+3.73865 q^{49}\) \(+1.21467 q^{50}\) \(+7.10104 q^{51}\) \(-0.406142 q^{52}\) \(+3.25108 q^{53}\) \(+8.10704 q^{54}\) \(+5.34217 q^{55}\) \(-9.08858 q^{56}\) \(+5.39487 q^{57}\) \(+1.44025 q^{58}\) \(-1.92642 q^{59}\) \(+0.226486 q^{60}\) \(+0.556575 q^{61}\) \(-2.68751 q^{62}\) \(+2.51050 q^{63}\) \(+7.68101 q^{64}\) \(-11.1406 q^{65}\) \(-5.64050 q^{66}\) \(-8.15843 q^{67}\) \(+0.353126 q^{68}\) \(-4.29714 q^{69}\) \(+9.62241 q^{70}\) \(-0.307231 q^{71}\) \(-2.12474 q^{72}\) \(+4.83259 q^{73}\) \(-13.3213 q^{74}\) \(-1.26053 q^{75}\) \(+0.268280 q^{76}\) \(-8.58661 q^{77}\) \(+11.7628 q^{78}\) \(+0.0396770 q^{79}\) \(-8.44693 q^{80}\) \(-6.11480 q^{81}\) \(+10.9401 q^{82}\) \(-11.7301 q^{83}\) \(-0.364038 q^{84}\) \(+9.68636 q^{85}\) \(+3.62598 q^{86}\) \(-1.49462 q^{87}\) \(+7.26722 q^{88}\) \(-4.78814 q^{89}\) \(+2.24954 q^{90}\) \(+17.9066 q^{91}\) \(-0.213692 q^{92}\) \(+2.78897 q^{93}\) \(+0.896701 q^{94}\) \(+7.35902 q^{95}\) \(+0.628094 q^{96}\) \(-13.7411 q^{97}\) \(-5.38460 q^{98}\) \(-2.00739 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.44025 −1.01841 −0.509206 0.860645i \(-0.670061\pi\)
−0.509206 + 0.860645i \(0.670061\pi\)
\(3\) 1.49462 0.862922 0.431461 0.902132i \(-0.357998\pi\)
0.431461 + 0.902132i \(0.357998\pi\)
\(4\) 0.0743258 0.0371629
\(5\) 2.03878 0.911770 0.455885 0.890039i \(-0.349323\pi\)
0.455885 + 0.890039i \(0.349323\pi\)
\(6\) −2.15264 −0.878810
\(7\) −3.27699 −1.23859 −0.619293 0.785160i \(-0.712581\pi\)
−0.619293 + 0.785160i \(0.712581\pi\)
\(8\) 2.77346 0.980565
\(9\) −0.766098 −0.255366
\(10\) −2.93636 −0.928558
\(11\) 2.62027 0.790043 0.395021 0.918672i \(-0.370737\pi\)
0.395021 + 0.918672i \(0.370737\pi\)
\(12\) 0.111089 0.0320687
\(13\) −5.46435 −1.51554 −0.757769 0.652523i \(-0.773711\pi\)
−0.757769 + 0.652523i \(0.773711\pi\)
\(14\) 4.71969 1.26139
\(15\) 3.04721 0.786787
\(16\) −4.14313 −1.03578
\(17\) 4.75105 1.15230 0.576150 0.817344i \(-0.304554\pi\)
0.576150 + 0.817344i \(0.304554\pi\)
\(18\) 1.10337 0.260068
\(19\) 3.60952 0.828080 0.414040 0.910259i \(-0.364117\pi\)
0.414040 + 0.910259i \(0.364117\pi\)
\(20\) 0.151534 0.0338840
\(21\) −4.89787 −1.06880
\(22\) −3.77386 −0.804589
\(23\) −2.87506 −0.599492 −0.299746 0.954019i \(-0.596902\pi\)
−0.299746 + 0.954019i \(0.596902\pi\)
\(24\) 4.14527 0.846151
\(25\) −0.843373 −0.168675
\(26\) 7.87004 1.54344
\(27\) −5.62890 −1.08328
\(28\) −0.243565 −0.0460294
\(29\) −1.00000 −0.185695
\(30\) −4.38875 −0.801273
\(31\) 1.86600 0.335143 0.167572 0.985860i \(-0.446407\pi\)
0.167572 + 0.985860i \(0.446407\pi\)
\(32\) 0.420235 0.0742878
\(33\) 3.91633 0.681745
\(34\) −6.84271 −1.17352
\(35\) −6.68106 −1.12931
\(36\) −0.0569409 −0.00949015
\(37\) 9.24926 1.52057 0.760284 0.649591i \(-0.225060\pi\)
0.760284 + 0.649591i \(0.225060\pi\)
\(38\) −5.19862 −0.843327
\(39\) −8.16715 −1.30779
\(40\) 5.65447 0.894050
\(41\) −7.59599 −1.18629 −0.593147 0.805094i \(-0.702115\pi\)
−0.593147 + 0.805094i \(0.702115\pi\)
\(42\) 7.05416 1.08848
\(43\) −2.51760 −0.383931 −0.191965 0.981402i \(-0.561486\pi\)
−0.191965 + 0.981402i \(0.561486\pi\)
\(44\) 0.194754 0.0293603
\(45\) −1.56191 −0.232835
\(46\) 4.14082 0.610530
\(47\) −0.622600 −0.0908156 −0.0454078 0.998969i \(-0.514459\pi\)
−0.0454078 + 0.998969i \(0.514459\pi\)
\(48\) −6.19242 −0.893799
\(49\) 3.73865 0.534093
\(50\) 1.21467 0.171780
\(51\) 7.10104 0.994345
\(52\) −0.406142 −0.0563218
\(53\) 3.25108 0.446570 0.223285 0.974753i \(-0.428322\pi\)
0.223285 + 0.974753i \(0.428322\pi\)
\(54\) 8.10704 1.10323
\(55\) 5.34217 0.720337
\(56\) −9.08858 −1.21451
\(57\) 5.39487 0.714569
\(58\) 1.44025 0.189114
\(59\) −1.92642 −0.250798 −0.125399 0.992106i \(-0.540021\pi\)
−0.125399 + 0.992106i \(0.540021\pi\)
\(60\) 0.226486 0.0292393
\(61\) 0.556575 0.0712621 0.0356310 0.999365i \(-0.488656\pi\)
0.0356310 + 0.999365i \(0.488656\pi\)
\(62\) −2.68751 −0.341314
\(63\) 2.51050 0.316293
\(64\) 7.68101 0.960126
\(65\) −11.1406 −1.38182
\(66\) −5.64050 −0.694297
\(67\) −8.15843 −0.996711 −0.498355 0.866973i \(-0.666062\pi\)
−0.498355 + 0.866973i \(0.666062\pi\)
\(68\) 0.353126 0.0428228
\(69\) −4.29714 −0.517315
\(70\) 9.62241 1.15010
\(71\) −0.307231 −0.0364616 −0.0182308 0.999834i \(-0.505803\pi\)
−0.0182308 + 0.999834i \(0.505803\pi\)
\(72\) −2.12474 −0.250403
\(73\) 4.83259 0.565612 0.282806 0.959177i \(-0.408735\pi\)
0.282806 + 0.959177i \(0.408735\pi\)
\(74\) −13.3213 −1.54856
\(75\) −1.26053 −0.145553
\(76\) 0.268280 0.0307739
\(77\) −8.58661 −0.978535
\(78\) 11.7628 1.33187
\(79\) 0.0396770 0.00446401 0.00223201 0.999998i \(-0.499290\pi\)
0.00223201 + 0.999998i \(0.499290\pi\)
\(80\) −8.44693 −0.944395
\(81\) −6.11480 −0.679422
\(82\) 10.9401 1.20814
\(83\) −11.7301 −1.28755 −0.643774 0.765215i \(-0.722632\pi\)
−0.643774 + 0.765215i \(0.722632\pi\)
\(84\) −0.364038 −0.0397198
\(85\) 9.68636 1.05063
\(86\) 3.62598 0.390999
\(87\) −1.49462 −0.160241
\(88\) 7.26722 0.774688
\(89\) −4.78814 −0.507542 −0.253771 0.967264i \(-0.581671\pi\)
−0.253771 + 0.967264i \(0.581671\pi\)
\(90\) 2.24954 0.237122
\(91\) 17.9066 1.87712
\(92\) −0.213692 −0.0222789
\(93\) 2.78897 0.289202
\(94\) 0.896701 0.0924877
\(95\) 7.35902 0.755019
\(96\) 0.628094 0.0641046
\(97\) −13.7411 −1.39520 −0.697598 0.716489i \(-0.745748\pi\)
−0.697598 + 0.716489i \(0.745748\pi\)
\(98\) −5.38460 −0.543927
\(99\) −2.00739 −0.201750
\(100\) −0.0626844 −0.00626844
\(101\) −8.43626 −0.839439 −0.419720 0.907654i \(-0.637872\pi\)
−0.419720 + 0.907654i \(0.637872\pi\)
\(102\) −10.2273 −1.01265
\(103\) 6.94078 0.683895 0.341948 0.939719i \(-0.388913\pi\)
0.341948 + 0.939719i \(0.388913\pi\)
\(104\) −15.1551 −1.48608
\(105\) −9.98568 −0.974502
\(106\) −4.68237 −0.454792
\(107\) 1.58175 0.152914 0.0764569 0.997073i \(-0.475639\pi\)
0.0764569 + 0.997073i \(0.475639\pi\)
\(108\) −0.418373 −0.0402579
\(109\) −3.50678 −0.335889 −0.167944 0.985796i \(-0.553713\pi\)
−0.167944 + 0.985796i \(0.553713\pi\)
\(110\) −7.69406 −0.733600
\(111\) 13.8242 1.31213
\(112\) 13.5770 1.28290
\(113\) −1.31139 −0.123365 −0.0616827 0.998096i \(-0.519647\pi\)
−0.0616827 + 0.998096i \(0.519647\pi\)
\(114\) −7.76998 −0.727725
\(115\) −5.86163 −0.546599
\(116\) −0.0743258 −0.00690098
\(117\) 4.18623 0.387017
\(118\) 2.77453 0.255416
\(119\) −15.5691 −1.42722
\(120\) 8.45131 0.771495
\(121\) −4.13416 −0.375833
\(122\) −0.801608 −0.0725742
\(123\) −11.3531 −1.02368
\(124\) 0.138692 0.0124549
\(125\) −11.9134 −1.06556
\(126\) −3.61575 −0.322116
\(127\) −8.66197 −0.768626 −0.384313 0.923203i \(-0.625562\pi\)
−0.384313 + 0.923203i \(0.625562\pi\)
\(128\) −11.9031 −1.05209
\(129\) −3.76287 −0.331302
\(130\) 16.0453 1.40727
\(131\) −1.48069 −0.129368 −0.0646841 0.997906i \(-0.520604\pi\)
−0.0646841 + 0.997906i \(0.520604\pi\)
\(132\) 0.291084 0.0253356
\(133\) −11.8284 −1.02565
\(134\) 11.7502 1.01506
\(135\) −11.4761 −0.987705
\(136\) 13.1768 1.12990
\(137\) −7.71079 −0.658777 −0.329388 0.944194i \(-0.606843\pi\)
−0.329388 + 0.944194i \(0.606843\pi\)
\(138\) 6.18897 0.526840
\(139\) −1.00000 −0.0848189
\(140\) −0.496575 −0.0419683
\(141\) −0.930553 −0.0783667
\(142\) 0.442490 0.0371329
\(143\) −14.3181 −1.19734
\(144\) 3.17404 0.264504
\(145\) −2.03878 −0.169312
\(146\) −6.96015 −0.576026
\(147\) 5.58788 0.460881
\(148\) 0.687459 0.0565087
\(149\) −3.90340 −0.319779 −0.159889 0.987135i \(-0.551114\pi\)
−0.159889 + 0.987135i \(0.551114\pi\)
\(150\) 1.81547 0.148233
\(151\) −16.9343 −1.37810 −0.689048 0.724715i \(-0.741971\pi\)
−0.689048 + 0.724715i \(0.741971\pi\)
\(152\) 10.0108 0.811987
\(153\) −3.63977 −0.294258
\(154\) 12.3669 0.996552
\(155\) 3.80436 0.305574
\(156\) −0.607030 −0.0486013
\(157\) −5.48315 −0.437603 −0.218802 0.975769i \(-0.570215\pi\)
−0.218802 + 0.975769i \(0.570215\pi\)
\(158\) −0.0571449 −0.00454620
\(159\) 4.85914 0.385355
\(160\) 0.856768 0.0677334
\(161\) 9.42155 0.742522
\(162\) 8.80685 0.691932
\(163\) 17.8313 1.39665 0.698326 0.715780i \(-0.253929\pi\)
0.698326 + 0.715780i \(0.253929\pi\)
\(164\) −0.564578 −0.0440861
\(165\) 7.98453 0.621595
\(166\) 16.8943 1.31125
\(167\) 17.5572 1.35862 0.679309 0.733852i \(-0.262280\pi\)
0.679309 + 0.733852i \(0.262280\pi\)
\(168\) −13.5840 −1.04803
\(169\) 16.8591 1.29686
\(170\) −13.9508 −1.06998
\(171\) −2.76525 −0.211464
\(172\) −0.187123 −0.0142680
\(173\) −1.08352 −0.0823784 −0.0411892 0.999151i \(-0.513115\pi\)
−0.0411892 + 0.999151i \(0.513115\pi\)
\(174\) 2.15264 0.163191
\(175\) 2.76372 0.208918
\(176\) −10.8561 −0.818312
\(177\) −2.87927 −0.216419
\(178\) 6.89613 0.516887
\(179\) −9.97201 −0.745343 −0.372672 0.927963i \(-0.621558\pi\)
−0.372672 + 0.927963i \(0.621558\pi\)
\(180\) −0.116090 −0.00865284
\(181\) −0.387667 −0.0288151 −0.0144075 0.999896i \(-0.504586\pi\)
−0.0144075 + 0.999896i \(0.504586\pi\)
\(182\) −25.7900 −1.91169
\(183\) 0.831870 0.0614936
\(184\) −7.97386 −0.587841
\(185\) 18.8572 1.38641
\(186\) −4.01682 −0.294527
\(187\) 12.4491 0.910366
\(188\) −0.0462753 −0.00337497
\(189\) 18.4458 1.34174
\(190\) −10.5988 −0.768921
\(191\) −15.9092 −1.15115 −0.575576 0.817749i \(-0.695222\pi\)
−0.575576 + 0.817749i \(0.695222\pi\)
\(192\) 11.4802 0.828514
\(193\) 1.38185 0.0994679 0.0497340 0.998763i \(-0.484163\pi\)
0.0497340 + 0.998763i \(0.484163\pi\)
\(194\) 19.7906 1.42088
\(195\) −16.6510 −1.19241
\(196\) 0.277878 0.0198485
\(197\) −3.42754 −0.244202 −0.122101 0.992518i \(-0.538963\pi\)
−0.122101 + 0.992518i \(0.538963\pi\)
\(198\) 2.89114 0.205465
\(199\) 2.78137 0.197166 0.0985829 0.995129i \(-0.468569\pi\)
0.0985829 + 0.995129i \(0.468569\pi\)
\(200\) −2.33906 −0.165396
\(201\) −12.1938 −0.860083
\(202\) 12.1503 0.854895
\(203\) 3.27699 0.230000
\(204\) 0.527791 0.0369527
\(205\) −15.4865 −1.08163
\(206\) −9.99647 −0.696487
\(207\) 2.20258 0.153090
\(208\) 22.6395 1.56977
\(209\) 9.45793 0.654219
\(210\) 14.3819 0.992445
\(211\) −3.24400 −0.223326 −0.111663 0.993746i \(-0.535618\pi\)
−0.111663 + 0.993746i \(0.535618\pi\)
\(212\) 0.241639 0.0165958
\(213\) −0.459195 −0.0314635
\(214\) −2.27812 −0.155729
\(215\) −5.13284 −0.350056
\(216\) −15.6115 −1.06223
\(217\) −6.11486 −0.415104
\(218\) 5.05065 0.342073
\(219\) 7.22291 0.488079
\(220\) 0.397061 0.0267698
\(221\) −25.9614 −1.74635
\(222\) −19.9103 −1.33629
\(223\) 6.97597 0.467146 0.233573 0.972339i \(-0.424958\pi\)
0.233573 + 0.972339i \(0.424958\pi\)
\(224\) −1.37711 −0.0920118
\(225\) 0.646107 0.0430738
\(226\) 1.88873 0.125637
\(227\) 2.69277 0.178725 0.0893627 0.995999i \(-0.471517\pi\)
0.0893627 + 0.995999i \(0.471517\pi\)
\(228\) 0.400979 0.0265555
\(229\) 1.37376 0.0907808 0.0453904 0.998969i \(-0.485547\pi\)
0.0453904 + 0.998969i \(0.485547\pi\)
\(230\) 8.44222 0.556663
\(231\) −12.8338 −0.844399
\(232\) −2.77346 −0.182086
\(233\) 7.13599 0.467494 0.233747 0.972297i \(-0.424901\pi\)
0.233747 + 0.972297i \(0.424901\pi\)
\(234\) −6.02923 −0.394143
\(235\) −1.26935 −0.0828030
\(236\) −0.143183 −0.00932039
\(237\) 0.0593022 0.00385209
\(238\) 22.4235 1.45350
\(239\) 12.3371 0.798023 0.399011 0.916946i \(-0.369353\pi\)
0.399011 + 0.916946i \(0.369353\pi\)
\(240\) −12.6250 −0.814939
\(241\) −27.0219 −1.74064 −0.870318 0.492490i \(-0.836087\pi\)
−0.870318 + 0.492490i \(0.836087\pi\)
\(242\) 5.95423 0.382753
\(243\) 7.74738 0.496995
\(244\) 0.0413679 0.00264831
\(245\) 7.62229 0.486971
\(246\) 16.3514 1.04253
\(247\) −19.7237 −1.25499
\(248\) 5.17527 0.328630
\(249\) −17.5321 −1.11105
\(250\) 17.1582 1.08518
\(251\) −14.6599 −0.925327 −0.462664 0.886534i \(-0.653106\pi\)
−0.462664 + 0.886534i \(0.653106\pi\)
\(252\) 0.186595 0.0117544
\(253\) −7.53346 −0.473624
\(254\) 12.4754 0.782778
\(255\) 14.4775 0.906614
\(256\) 1.78139 0.111337
\(257\) −12.4837 −0.778711 −0.389355 0.921088i \(-0.627302\pi\)
−0.389355 + 0.921088i \(0.627302\pi\)
\(258\) 5.41948 0.337402
\(259\) −30.3097 −1.88335
\(260\) −0.828035 −0.0513526
\(261\) 0.766098 0.0474203
\(262\) 2.13256 0.131750
\(263\) −6.88235 −0.424384 −0.212192 0.977228i \(-0.568060\pi\)
−0.212192 + 0.977228i \(0.568060\pi\)
\(264\) 10.8618 0.668495
\(265\) 6.62824 0.407169
\(266\) 17.0358 1.04453
\(267\) −7.15648 −0.437969
\(268\) −0.606382 −0.0370407
\(269\) 2.09390 0.127667 0.0638337 0.997961i \(-0.479667\pi\)
0.0638337 + 0.997961i \(0.479667\pi\)
\(270\) 16.5285 1.00589
\(271\) −6.48705 −0.394060 −0.197030 0.980397i \(-0.563130\pi\)
−0.197030 + 0.980397i \(0.563130\pi\)
\(272\) −19.6842 −1.19353
\(273\) 26.7637 1.61981
\(274\) 11.1055 0.670906
\(275\) −2.20987 −0.133260
\(276\) −0.319389 −0.0192249
\(277\) 0.612763 0.0368174 0.0184087 0.999831i \(-0.494140\pi\)
0.0184087 + 0.999831i \(0.494140\pi\)
\(278\) 1.44025 0.0863806
\(279\) −1.42954 −0.0855843
\(280\) −18.5296 −1.10736
\(281\) −8.04142 −0.479711 −0.239855 0.970809i \(-0.577100\pi\)
−0.239855 + 0.970809i \(0.577100\pi\)
\(282\) 1.34023 0.0798096
\(283\) −4.81380 −0.286151 −0.143075 0.989712i \(-0.545699\pi\)
−0.143075 + 0.989712i \(0.545699\pi\)
\(284\) −0.0228352 −0.00135502
\(285\) 10.9990 0.651523
\(286\) 20.6217 1.21939
\(287\) 24.8920 1.46933
\(288\) −0.321942 −0.0189706
\(289\) 5.57251 0.327795
\(290\) 2.93636 0.172429
\(291\) −20.5378 −1.20395
\(292\) 0.359187 0.0210198
\(293\) 31.3210 1.82979 0.914896 0.403689i \(-0.132272\pi\)
0.914896 + 0.403689i \(0.132272\pi\)
\(294\) −8.04796 −0.469366
\(295\) −3.92754 −0.228670
\(296\) 25.6524 1.49102
\(297\) −14.7493 −0.855839
\(298\) 5.62188 0.325667
\(299\) 15.7104 0.908554
\(300\) −0.0936896 −0.00540917
\(301\) 8.25015 0.475531
\(302\) 24.3897 1.40347
\(303\) −12.6090 −0.724370
\(304\) −14.9547 −0.857711
\(305\) 1.13473 0.0649747
\(306\) 5.24219 0.299676
\(307\) −27.1027 −1.54683 −0.773415 0.633900i \(-0.781453\pi\)
−0.773415 + 0.633900i \(0.781453\pi\)
\(308\) −0.638207 −0.0363652
\(309\) 10.3739 0.590148
\(310\) −5.47924 −0.311200
\(311\) 2.04215 0.115800 0.0578998 0.998322i \(-0.481560\pi\)
0.0578998 + 0.998322i \(0.481560\pi\)
\(312\) −22.6512 −1.28237
\(313\) 26.9743 1.52468 0.762340 0.647177i \(-0.224051\pi\)
0.762340 + 0.647177i \(0.224051\pi\)
\(314\) 7.89712 0.445660
\(315\) 5.11835 0.288386
\(316\) 0.00294903 0.000165896 0
\(317\) −8.45186 −0.474704 −0.237352 0.971424i \(-0.576279\pi\)
−0.237352 + 0.971424i \(0.576279\pi\)
\(318\) −6.99839 −0.392450
\(319\) −2.62027 −0.146707
\(320\) 15.6599 0.875415
\(321\) 2.36413 0.131953
\(322\) −13.5694 −0.756194
\(323\) 17.1490 0.954197
\(324\) −0.454487 −0.0252493
\(325\) 4.60849 0.255633
\(326\) −25.6815 −1.42237
\(327\) −5.24132 −0.289846
\(328\) −21.0671 −1.16324
\(329\) 2.04025 0.112483
\(330\) −11.4997 −0.633040
\(331\) 24.3684 1.33941 0.669704 0.742628i \(-0.266421\pi\)
0.669704 + 0.742628i \(0.266421\pi\)
\(332\) −0.871851 −0.0478491
\(333\) −7.08584 −0.388302
\(334\) −25.2868 −1.38363
\(335\) −16.6332 −0.908771
\(336\) 20.2925 1.10705
\(337\) −3.94436 −0.214863 −0.107431 0.994213i \(-0.534263\pi\)
−0.107431 + 0.994213i \(0.534263\pi\)
\(338\) −24.2814 −1.32074
\(339\) −1.96004 −0.106455
\(340\) 0.719946 0.0390446
\(341\) 4.88943 0.264777
\(342\) 3.98265 0.215357
\(343\) 10.6874 0.577065
\(344\) −6.98245 −0.376469
\(345\) −8.76093 −0.471672
\(346\) 1.56054 0.0838951
\(347\) −13.7424 −0.737731 −0.368866 0.929483i \(-0.620254\pi\)
−0.368866 + 0.929483i \(0.620254\pi\)
\(348\) −0.111089 −0.00595501
\(349\) −17.4474 −0.933937 −0.466968 0.884274i \(-0.654654\pi\)
−0.466968 + 0.884274i \(0.654654\pi\)
\(350\) −3.98046 −0.212764
\(351\) 30.7583 1.64176
\(352\) 1.10113 0.0586905
\(353\) −18.6114 −0.990585 −0.495293 0.868726i \(-0.664939\pi\)
−0.495293 + 0.868726i \(0.664939\pi\)
\(354\) 4.14688 0.220404
\(355\) −0.626376 −0.0332446
\(356\) −0.355883 −0.0188618
\(357\) −23.2700 −1.23158
\(358\) 14.3622 0.759066
\(359\) −6.21832 −0.328190 −0.164095 0.986445i \(-0.552470\pi\)
−0.164095 + 0.986445i \(0.552470\pi\)
\(360\) −4.33188 −0.228310
\(361\) −5.97137 −0.314283
\(362\) 0.558339 0.0293456
\(363\) −6.17902 −0.324314
\(364\) 1.33092 0.0697594
\(365\) 9.85260 0.515709
\(366\) −1.19810 −0.0626258
\(367\) −24.5931 −1.28375 −0.641875 0.766809i \(-0.721843\pi\)
−0.641875 + 0.766809i \(0.721843\pi\)
\(368\) 11.9118 0.620943
\(369\) 5.81927 0.302939
\(370\) −27.1591 −1.41194
\(371\) −10.6537 −0.553115
\(372\) 0.207292 0.0107476
\(373\) 32.5691 1.68636 0.843181 0.537630i \(-0.180680\pi\)
0.843181 + 0.537630i \(0.180680\pi\)
\(374\) −17.9298 −0.927127
\(375\) −17.8060 −0.919497
\(376\) −1.72675 −0.0890506
\(377\) 5.46435 0.281428
\(378\) −26.5667 −1.36644
\(379\) −13.3120 −0.683793 −0.341897 0.939738i \(-0.611069\pi\)
−0.341897 + 0.939738i \(0.611069\pi\)
\(380\) 0.546965 0.0280587
\(381\) −12.9464 −0.663264
\(382\) 22.9133 1.17235
\(383\) −4.81382 −0.245975 −0.122987 0.992408i \(-0.539247\pi\)
−0.122987 + 0.992408i \(0.539247\pi\)
\(384\) −17.7906 −0.907873
\(385\) −17.5062 −0.892199
\(386\) −1.99022 −0.101299
\(387\) 1.92873 0.0980428
\(388\) −1.02132 −0.0518496
\(389\) 21.5087 1.09053 0.545266 0.838263i \(-0.316429\pi\)
0.545266 + 0.838263i \(0.316429\pi\)
\(390\) 23.9817 1.21436
\(391\) −13.6596 −0.690795
\(392\) 10.3690 0.523713
\(393\) −2.21307 −0.111635
\(394\) 4.93652 0.248698
\(395\) 0.0808927 0.00407015
\(396\) −0.149201 −0.00749762
\(397\) 30.3454 1.52299 0.761495 0.648170i \(-0.224466\pi\)
0.761495 + 0.648170i \(0.224466\pi\)
\(398\) −4.00587 −0.200796
\(399\) −17.6789 −0.885054
\(400\) 3.49420 0.174710
\(401\) 16.9002 0.843958 0.421979 0.906606i \(-0.361336\pi\)
0.421979 + 0.906606i \(0.361336\pi\)
\(402\) 17.5621 0.875919
\(403\) −10.1965 −0.507923
\(404\) −0.627032 −0.0311960
\(405\) −12.4667 −0.619477
\(406\) −4.71969 −0.234234
\(407\) 24.2356 1.20131
\(408\) 19.6944 0.975019
\(409\) 5.52258 0.273074 0.136537 0.990635i \(-0.456403\pi\)
0.136537 + 0.990635i \(0.456403\pi\)
\(410\) 22.3045 1.10154
\(411\) −11.5247 −0.568473
\(412\) 0.515879 0.0254155
\(413\) 6.31285 0.310635
\(414\) −3.17227 −0.155909
\(415\) −23.9152 −1.17395
\(416\) −2.29631 −0.112586
\(417\) −1.49462 −0.0731921
\(418\) −13.6218 −0.666264
\(419\) 15.9483 0.779128 0.389564 0.920999i \(-0.372626\pi\)
0.389564 + 0.920999i \(0.372626\pi\)
\(420\) −0.742194 −0.0362153
\(421\) −18.3099 −0.892371 −0.446186 0.894940i \(-0.647218\pi\)
−0.446186 + 0.894940i \(0.647218\pi\)
\(422\) 4.67218 0.227438
\(423\) 0.476973 0.0231912
\(424\) 9.01673 0.437891
\(425\) −4.00691 −0.194364
\(426\) 0.661356 0.0320428
\(427\) −1.82389 −0.0882642
\(428\) 0.117565 0.00568272
\(429\) −21.4002 −1.03321
\(430\) 7.39258 0.356502
\(431\) −29.8400 −1.43734 −0.718670 0.695351i \(-0.755249\pi\)
−0.718670 + 0.695351i \(0.755249\pi\)
\(432\) 23.3213 1.12204
\(433\) −4.86363 −0.233731 −0.116866 0.993148i \(-0.537285\pi\)
−0.116866 + 0.993148i \(0.537285\pi\)
\(434\) 8.80694 0.422746
\(435\) −3.04721 −0.146103
\(436\) −0.260644 −0.0124826
\(437\) −10.3776 −0.496428
\(438\) −10.4028 −0.497066
\(439\) −23.0085 −1.09814 −0.549068 0.835778i \(-0.685017\pi\)
−0.549068 + 0.835778i \(0.685017\pi\)
\(440\) 14.8163 0.706338
\(441\) −2.86418 −0.136389
\(442\) 37.3910 1.77851
\(443\) −6.77027 −0.321665 −0.160833 0.986982i \(-0.551418\pi\)
−0.160833 + 0.986982i \(0.551418\pi\)
\(444\) 1.02749 0.0487626
\(445\) −9.76198 −0.462762
\(446\) −10.0472 −0.475747
\(447\) −5.83411 −0.275944
\(448\) −25.1706 −1.18920
\(449\) −24.8000 −1.17038 −0.585192 0.810895i \(-0.698981\pi\)
−0.585192 + 0.810895i \(0.698981\pi\)
\(450\) −0.930557 −0.0438669
\(451\) −19.9036 −0.937222
\(452\) −0.0974702 −0.00458461
\(453\) −25.3105 −1.18919
\(454\) −3.87827 −0.182016
\(455\) 36.5077 1.71151
\(456\) 14.9624 0.700681
\(457\) 10.0072 0.468117 0.234059 0.972222i \(-0.424799\pi\)
0.234059 + 0.972222i \(0.424799\pi\)
\(458\) −1.97856 −0.0924523
\(459\) −26.7432 −1.24827
\(460\) −0.435670 −0.0203132
\(461\) −13.3729 −0.622839 −0.311419 0.950273i \(-0.600804\pi\)
−0.311419 + 0.950273i \(0.600804\pi\)
\(462\) 18.4838 0.859946
\(463\) 10.4181 0.484170 0.242085 0.970255i \(-0.422169\pi\)
0.242085 + 0.970255i \(0.422169\pi\)
\(464\) 4.14313 0.192340
\(465\) 5.68609 0.263686
\(466\) −10.2776 −0.476102
\(467\) −9.04493 −0.418549 −0.209275 0.977857i \(-0.567110\pi\)
−0.209275 + 0.977857i \(0.567110\pi\)
\(468\) 0.311145 0.0143827
\(469\) 26.7351 1.23451
\(470\) 1.82818 0.0843275
\(471\) −8.19525 −0.377617
\(472\) −5.34283 −0.245924
\(473\) −6.59681 −0.303321
\(474\) −0.0854101 −0.00392302
\(475\) −3.04417 −0.139676
\(476\) −1.15719 −0.0530397
\(477\) −2.49065 −0.114039
\(478\) −17.7686 −0.812716
\(479\) −1.94424 −0.0888345 −0.0444173 0.999013i \(-0.514143\pi\)
−0.0444173 + 0.999013i \(0.514143\pi\)
\(480\) 1.28055 0.0584486
\(481\) −50.5412 −2.30448
\(482\) 38.9184 1.77268
\(483\) 14.0817 0.640739
\(484\) −0.307275 −0.0139670
\(485\) −28.0151 −1.27210
\(486\) −11.1582 −0.506145
\(487\) 34.1913 1.54936 0.774678 0.632356i \(-0.217912\pi\)
0.774678 + 0.632356i \(0.217912\pi\)
\(488\) 1.54364 0.0698771
\(489\) 26.6510 1.20520
\(490\) −10.9780 −0.495937
\(491\) −8.26060 −0.372796 −0.186398 0.982474i \(-0.559681\pi\)
−0.186398 + 0.982474i \(0.559681\pi\)
\(492\) −0.843832 −0.0380429
\(493\) −4.75105 −0.213977
\(494\) 28.4071 1.27809
\(495\) −4.09262 −0.183950
\(496\) −7.73107 −0.347135
\(497\) 1.00679 0.0451608
\(498\) 25.2507 1.13151
\(499\) −26.1719 −1.17161 −0.585807 0.810451i \(-0.699222\pi\)
−0.585807 + 0.810451i \(0.699222\pi\)
\(500\) −0.885470 −0.0395994
\(501\) 26.2414 1.17238
\(502\) 21.1140 0.942364
\(503\) −29.1687 −1.30057 −0.650283 0.759692i \(-0.725350\pi\)
−0.650283 + 0.759692i \(0.725350\pi\)
\(504\) 6.96275 0.310145
\(505\) −17.1997 −0.765376
\(506\) 10.8501 0.482345
\(507\) 25.1981 1.11909
\(508\) −0.643808 −0.0285644
\(509\) 7.98212 0.353801 0.176901 0.984229i \(-0.443393\pi\)
0.176901 + 0.984229i \(0.443393\pi\)
\(510\) −20.8512 −0.923306
\(511\) −15.8364 −0.700559
\(512\) 21.2405 0.938705
\(513\) −20.3176 −0.897045
\(514\) 17.9796 0.793048
\(515\) 14.1507 0.623556
\(516\) −0.279678 −0.0123121
\(517\) −1.63138 −0.0717482
\(518\) 43.6536 1.91803
\(519\) −1.61945 −0.0710861
\(520\) −30.8980 −1.35497
\(521\) 6.91447 0.302929 0.151464 0.988463i \(-0.451601\pi\)
0.151464 + 0.988463i \(0.451601\pi\)
\(522\) −1.10337 −0.0482934
\(523\) −42.3815 −1.85321 −0.926607 0.376032i \(-0.877288\pi\)
−0.926607 + 0.376032i \(0.877288\pi\)
\(524\) −0.110053 −0.00480770
\(525\) 4.13073 0.180280
\(526\) 9.91232 0.432198
\(527\) 8.86546 0.386186
\(528\) −16.2258 −0.706139
\(529\) −14.7340 −0.640609
\(530\) −9.54633 −0.414666
\(531\) 1.47583 0.0640454
\(532\) −0.879152 −0.0381161
\(533\) 41.5071 1.79787
\(534\) 10.3071 0.446033
\(535\) 3.22485 0.139422
\(536\) −22.6270 −0.977339
\(537\) −14.9044 −0.643173
\(538\) −3.01575 −0.130018
\(539\) 9.79630 0.421956
\(540\) −0.852970 −0.0367060
\(541\) −41.4801 −1.78337 −0.891684 0.452658i \(-0.850476\pi\)
−0.891684 + 0.452658i \(0.850476\pi\)
\(542\) 9.34298 0.401315
\(543\) −0.579417 −0.0248652
\(544\) 1.99656 0.0856018
\(545\) −7.14955 −0.306253
\(546\) −38.5464 −1.64963
\(547\) 5.11870 0.218860 0.109430 0.993995i \(-0.465097\pi\)
0.109430 + 0.993995i \(0.465097\pi\)
\(548\) −0.573111 −0.0244821
\(549\) −0.426391 −0.0181979
\(550\) 3.18277 0.135714
\(551\) −3.60952 −0.153771
\(552\) −11.9179 −0.507261
\(553\) −0.130021 −0.00552906
\(554\) −0.882534 −0.0374953
\(555\) 28.1844 1.19636
\(556\) −0.0743258 −0.00315212
\(557\) −21.6503 −0.917354 −0.458677 0.888603i \(-0.651677\pi\)
−0.458677 + 0.888603i \(0.651677\pi\)
\(558\) 2.05890 0.0871600
\(559\) 13.7571 0.581862
\(560\) 27.6805 1.16971
\(561\) 18.6067 0.785574
\(562\) 11.5817 0.488543
\(563\) 15.6360 0.658980 0.329490 0.944159i \(-0.393123\pi\)
0.329490 + 0.944159i \(0.393123\pi\)
\(564\) −0.0691641 −0.00291234
\(565\) −2.67364 −0.112481
\(566\) 6.93308 0.291419
\(567\) 20.0381 0.841522
\(568\) −0.852091 −0.0357529
\(569\) 11.0055 0.461374 0.230687 0.973028i \(-0.425903\pi\)
0.230687 + 0.973028i \(0.425903\pi\)
\(570\) −15.8413 −0.663518
\(571\) 27.5562 1.15319 0.576595 0.817030i \(-0.304381\pi\)
0.576595 + 0.817030i \(0.304381\pi\)
\(572\) −1.06420 −0.0444966
\(573\) −23.7783 −0.993353
\(574\) −35.8507 −1.49638
\(575\) 2.42475 0.101119
\(576\) −5.88441 −0.245184
\(577\) 7.89082 0.328499 0.164250 0.986419i \(-0.447480\pi\)
0.164250 + 0.986419i \(0.447480\pi\)
\(578\) −8.02582 −0.333830
\(579\) 2.06535 0.0858330
\(580\) −0.151534 −0.00629211
\(581\) 38.4395 1.59474
\(582\) 29.5796 1.22611
\(583\) 8.51872 0.352809
\(584\) 13.4030 0.554620
\(585\) 8.53481 0.352871
\(586\) −45.1101 −1.86348
\(587\) 0.971136 0.0400831 0.0200415 0.999799i \(-0.493620\pi\)
0.0200415 + 0.999799i \(0.493620\pi\)
\(588\) 0.415324 0.0171277
\(589\) 6.73536 0.277526
\(590\) 5.65665 0.232881
\(591\) −5.12288 −0.210727
\(592\) −38.3208 −1.57498
\(593\) −22.3549 −0.918007 −0.459004 0.888434i \(-0.651794\pi\)
−0.459004 + 0.888434i \(0.651794\pi\)
\(594\) 21.2427 0.871597
\(595\) −31.7421 −1.30130
\(596\) −0.290123 −0.0118839
\(597\) 4.15710 0.170139
\(598\) −22.6269 −0.925282
\(599\) 0.156273 0.00638513 0.00319256 0.999995i \(-0.498984\pi\)
0.00319256 + 0.999995i \(0.498984\pi\)
\(600\) −3.49601 −0.142724
\(601\) 15.2662 0.622720 0.311360 0.950292i \(-0.399215\pi\)
0.311360 + 0.950292i \(0.399215\pi\)
\(602\) −11.8823 −0.484286
\(603\) 6.25016 0.254526
\(604\) −1.25866 −0.0512141
\(605\) −8.42865 −0.342673
\(606\) 18.1602 0.737707
\(607\) 20.1916 0.819552 0.409776 0.912186i \(-0.365607\pi\)
0.409776 + 0.912186i \(0.365607\pi\)
\(608\) 1.51685 0.0615163
\(609\) 4.89787 0.198472
\(610\) −1.63430 −0.0661710
\(611\) 3.40211 0.137635
\(612\) −0.270529 −0.0109355
\(613\) −13.6585 −0.551661 −0.275831 0.961206i \(-0.588953\pi\)
−0.275831 + 0.961206i \(0.588953\pi\)
\(614\) 39.0347 1.57531
\(615\) −23.1466 −0.933360
\(616\) −23.8146 −0.959517
\(617\) −46.3670 −1.86667 −0.933333 0.359012i \(-0.883114\pi\)
−0.933333 + 0.359012i \(0.883114\pi\)
\(618\) −14.9410 −0.601014
\(619\) 21.2940 0.855880 0.427940 0.903807i \(-0.359240\pi\)
0.427940 + 0.903807i \(0.359240\pi\)
\(620\) 0.282762 0.0113560
\(621\) 16.1835 0.649420
\(622\) −2.94121 −0.117932
\(623\) 15.6907 0.628634
\(624\) 33.8376 1.35459
\(625\) −20.0719 −0.802874
\(626\) −38.8498 −1.55275
\(627\) 14.1361 0.564540
\(628\) −0.407540 −0.0162626
\(629\) 43.9437 1.75215
\(630\) −7.37171 −0.293696
\(631\) 31.1002 1.23808 0.619039 0.785360i \(-0.287522\pi\)
0.619039 + 0.785360i \(0.287522\pi\)
\(632\) 0.110042 0.00437725
\(633\) −4.84857 −0.192713
\(634\) 12.1728 0.483444
\(635\) −17.6599 −0.700810
\(636\) 0.361160 0.0143209
\(637\) −20.4293 −0.809439
\(638\) 3.77386 0.149408
\(639\) 0.235369 0.00931105
\(640\) −24.2677 −0.959266
\(641\) 14.4105 0.569181 0.284591 0.958649i \(-0.408142\pi\)
0.284591 + 0.958649i \(0.408142\pi\)
\(642\) −3.40494 −0.134382
\(643\) 2.04280 0.0805600 0.0402800 0.999188i \(-0.487175\pi\)
0.0402800 + 0.999188i \(0.487175\pi\)
\(644\) 0.700265 0.0275943
\(645\) −7.67166 −0.302071
\(646\) −24.6989 −0.971766
\(647\) 25.1709 0.989570 0.494785 0.869016i \(-0.335247\pi\)
0.494785 + 0.869016i \(0.335247\pi\)
\(648\) −16.9591 −0.666217
\(649\) −5.04774 −0.198141
\(650\) −6.63738 −0.260340
\(651\) −9.13941 −0.358202
\(652\) 1.32532 0.0519037
\(653\) 2.07204 0.0810851 0.0405425 0.999178i \(-0.487091\pi\)
0.0405425 + 0.999178i \(0.487091\pi\)
\(654\) 7.54882 0.295182
\(655\) −3.01880 −0.117954
\(656\) 31.4711 1.22874
\(657\) −3.70224 −0.144438
\(658\) −2.93848 −0.114554
\(659\) 29.1159 1.13419 0.567096 0.823651i \(-0.308067\pi\)
0.567096 + 0.823651i \(0.308067\pi\)
\(660\) 0.593457 0.0231003
\(661\) −32.1182 −1.24925 −0.624627 0.780923i \(-0.714749\pi\)
−0.624627 + 0.780923i \(0.714749\pi\)
\(662\) −35.0967 −1.36407
\(663\) −38.8026 −1.50697
\(664\) −32.5330 −1.26252
\(665\) −24.1154 −0.935156
\(666\) 10.2054 0.395451
\(667\) 2.87506 0.111323
\(668\) 1.30495 0.0504902
\(669\) 10.4265 0.403110
\(670\) 23.9561 0.925504
\(671\) 1.45838 0.0563001
\(672\) −2.05826 −0.0793990
\(673\) −29.5198 −1.13791 −0.568953 0.822370i \(-0.692651\pi\)
−0.568953 + 0.822370i \(0.692651\pi\)
\(674\) 5.68087 0.218819
\(675\) 4.74726 0.182722
\(676\) 1.25307 0.0481950
\(677\) −46.0987 −1.77172 −0.885859 0.463954i \(-0.846430\pi\)
−0.885859 + 0.463954i \(0.846430\pi\)
\(678\) 2.82295 0.108415
\(679\) 45.0294 1.72807
\(680\) 26.8647 1.03021
\(681\) 4.02468 0.154226
\(682\) −7.04201 −0.269653
\(683\) 6.04029 0.231125 0.115563 0.993300i \(-0.463133\pi\)
0.115563 + 0.993300i \(0.463133\pi\)
\(684\) −0.205529 −0.00785861
\(685\) −15.7206 −0.600653
\(686\) −15.3925 −0.587690
\(687\) 2.05326 0.0783367
\(688\) 10.4307 0.397668
\(689\) −17.7650 −0.676794
\(690\) 12.6179 0.480357
\(691\) −34.2188 −1.30175 −0.650873 0.759187i \(-0.725597\pi\)
−0.650873 + 0.759187i \(0.725597\pi\)
\(692\) −0.0805334 −0.00306142
\(693\) 6.57819 0.249885
\(694\) 19.7925 0.751314
\(695\) −2.03878 −0.0773354
\(696\) −4.14527 −0.157126
\(697\) −36.0889 −1.36697
\(698\) 25.1286 0.951132
\(699\) 10.6656 0.403411
\(700\) 0.205416 0.00776400
\(701\) 46.1790 1.74416 0.872079 0.489365i \(-0.162772\pi\)
0.872079 + 0.489365i \(0.162772\pi\)
\(702\) −44.2997 −1.67198
\(703\) 33.3854 1.25915
\(704\) 20.1264 0.758541
\(705\) −1.89719 −0.0714525
\(706\) 26.8051 1.00882
\(707\) 27.6455 1.03972
\(708\) −0.214004 −0.00804277
\(709\) 23.2692 0.873893 0.436946 0.899488i \(-0.356060\pi\)
0.436946 + 0.899488i \(0.356060\pi\)
\(710\) 0.902139 0.0338567
\(711\) −0.0303965 −0.00113996
\(712\) −13.2797 −0.497678
\(713\) −5.36487 −0.200916
\(714\) 33.5147 1.25426
\(715\) −29.1915 −1.09170
\(716\) −0.741178 −0.0276991
\(717\) 18.4394 0.688631
\(718\) 8.95595 0.334233
\(719\) 40.5027 1.51050 0.755248 0.655439i \(-0.227516\pi\)
0.755248 + 0.655439i \(0.227516\pi\)
\(720\) 6.47118 0.241167
\(721\) −22.7449 −0.847063
\(722\) 8.60028 0.320069
\(723\) −40.3876 −1.50203
\(724\) −0.0288137 −0.00107085
\(725\) 0.843373 0.0313221
\(726\) 8.89934 0.330286
\(727\) 39.5308 1.46612 0.733059 0.680165i \(-0.238092\pi\)
0.733059 + 0.680165i \(0.238092\pi\)
\(728\) 49.6632 1.84064
\(729\) 29.9238 1.10829
\(730\) −14.1902 −0.525204
\(731\) −11.9613 −0.442403
\(732\) 0.0618294 0.00228528
\(733\) −10.7227 −0.396051 −0.198026 0.980197i \(-0.563453\pi\)
−0.198026 + 0.980197i \(0.563453\pi\)
\(734\) 35.4203 1.30739
\(735\) 11.3925 0.420217
\(736\) −1.20820 −0.0445350
\(737\) −21.3773 −0.787444
\(738\) −8.38122 −0.308517
\(739\) −25.2786 −0.929888 −0.464944 0.885340i \(-0.653926\pi\)
−0.464944 + 0.885340i \(0.653926\pi\)
\(740\) 1.40158 0.0515230
\(741\) −29.4795 −1.08296
\(742\) 15.3441 0.563299
\(743\) −3.34340 −0.122657 −0.0613287 0.998118i \(-0.519534\pi\)
−0.0613287 + 0.998118i \(0.519534\pi\)
\(744\) 7.73508 0.283582
\(745\) −7.95817 −0.291565
\(746\) −46.9076 −1.71741
\(747\) 8.98643 0.328796
\(748\) 0.925287 0.0338318
\(749\) −5.18339 −0.189397
\(750\) 25.6451 0.936427
\(751\) −14.7805 −0.539349 −0.269675 0.962952i \(-0.586916\pi\)
−0.269675 + 0.962952i \(0.586916\pi\)
\(752\) 2.57951 0.0940651
\(753\) −21.9111 −0.798485
\(754\) −7.87004 −0.286610
\(755\) −34.5254 −1.25651
\(756\) 1.37100 0.0498629
\(757\) 8.90434 0.323634 0.161817 0.986821i \(-0.448265\pi\)
0.161817 + 0.986821i \(0.448265\pi\)
\(758\) 19.1727 0.696383
\(759\) −11.2597 −0.408701
\(760\) 20.4099 0.740345
\(761\) 4.07376 0.147674 0.0738369 0.997270i \(-0.476476\pi\)
0.0738369 + 0.997270i \(0.476476\pi\)
\(762\) 18.6461 0.675476
\(763\) 11.4917 0.416027
\(764\) −1.18247 −0.0427801
\(765\) −7.42070 −0.268296
\(766\) 6.93311 0.250504
\(767\) 10.5266 0.380094
\(768\) 2.66250 0.0960748
\(769\) −14.3603 −0.517846 −0.258923 0.965898i \(-0.583368\pi\)
−0.258923 + 0.965898i \(0.583368\pi\)
\(770\) 25.2134 0.908626
\(771\) −18.6584 −0.671966
\(772\) 0.102707 0.00369652
\(773\) 44.9513 1.61679 0.808393 0.588643i \(-0.200338\pi\)
0.808393 + 0.588643i \(0.200338\pi\)
\(774\) −2.77786 −0.0998480
\(775\) −1.57373 −0.0565302
\(776\) −38.1103 −1.36808
\(777\) −45.3016 −1.62519
\(778\) −30.9779 −1.11061
\(779\) −27.4179 −0.982347
\(780\) −1.23760 −0.0443133
\(781\) −0.805029 −0.0288062
\(782\) 19.6732 0.703514
\(783\) 5.62890 0.201161
\(784\) −15.4897 −0.553204
\(785\) −11.1789 −0.398994
\(786\) 3.18738 0.113690
\(787\) 11.9629 0.426431 0.213216 0.977005i \(-0.431606\pi\)
0.213216 + 0.977005i \(0.431606\pi\)
\(788\) −0.254755 −0.00907525
\(789\) −10.2865 −0.366210
\(790\) −0.116506 −0.00414509
\(791\) 4.29741 0.152798
\(792\) −5.56740 −0.197829
\(793\) −3.04132 −0.108000
\(794\) −43.7050 −1.55103
\(795\) 9.90673 0.351355
\(796\) 0.206727 0.00732726
\(797\) 7.01175 0.248369 0.124184 0.992259i \(-0.460369\pi\)
0.124184 + 0.992259i \(0.460369\pi\)
\(798\) 25.4621 0.901350
\(799\) −2.95801 −0.104647
\(800\) −0.354415 −0.0125305
\(801\) 3.66819 0.129609
\(802\) −24.3406 −0.859497
\(803\) 12.6627 0.446858
\(804\) −0.906313 −0.0319632
\(805\) 19.2085 0.677010
\(806\) 14.6855 0.517275
\(807\) 3.12960 0.110167
\(808\) −23.3976 −0.823125
\(809\) −25.0102 −0.879311 −0.439655 0.898167i \(-0.644899\pi\)
−0.439655 + 0.898167i \(0.644899\pi\)
\(810\) 17.9552 0.630883
\(811\) −46.2665 −1.62464 −0.812318 0.583215i \(-0.801795\pi\)
−0.812318 + 0.583215i \(0.801795\pi\)
\(812\) 0.243565 0.00854745
\(813\) −9.69570 −0.340043
\(814\) −34.9054 −1.22343
\(815\) 36.3540 1.27343
\(816\) −29.4205 −1.02992
\(817\) −9.08733 −0.317925
\(818\) −7.95391 −0.278102
\(819\) −13.7182 −0.479354
\(820\) −1.15105 −0.0401964
\(821\) 14.0006 0.488624 0.244312 0.969697i \(-0.421438\pi\)
0.244312 + 0.969697i \(0.421438\pi\)
\(822\) 16.5985 0.578940
\(823\) 42.5382 1.48279 0.741395 0.671069i \(-0.234165\pi\)
0.741395 + 0.671069i \(0.234165\pi\)
\(824\) 19.2499 0.670604
\(825\) −3.30292 −0.114993
\(826\) −9.09209 −0.316354
\(827\) 31.9840 1.11219 0.556097 0.831117i \(-0.312298\pi\)
0.556097 + 0.831117i \(0.312298\pi\)
\(828\) 0.163709 0.00568927
\(829\) 51.6858 1.79512 0.897560 0.440891i \(-0.145338\pi\)
0.897560 + 0.440891i \(0.145338\pi\)
\(830\) 34.4439 1.19556
\(831\) 0.915851 0.0317705
\(832\) −41.9717 −1.45511
\(833\) 17.7625 0.615436
\(834\) 2.15264 0.0745397
\(835\) 35.7953 1.23875
\(836\) 0.702969 0.0243127
\(837\) −10.5035 −0.363055
\(838\) −22.9696 −0.793473
\(839\) 4.86296 0.167888 0.0839441 0.996470i \(-0.473248\pi\)
0.0839441 + 0.996470i \(0.473248\pi\)
\(840\) −27.6948 −0.955563
\(841\) 1.00000 0.0344828
\(842\) 26.3709 0.908802
\(843\) −12.0189 −0.413953
\(844\) −0.241113 −0.00829946
\(845\) 34.3721 1.18244
\(846\) −0.686961 −0.0236182
\(847\) 13.5476 0.465501
\(848\) −13.4696 −0.462549
\(849\) −7.19482 −0.246926
\(850\) 5.77096 0.197942
\(851\) −26.5922 −0.911569
\(852\) −0.0341300 −0.00116927
\(853\) −18.0804 −0.619061 −0.309531 0.950889i \(-0.600172\pi\)
−0.309531 + 0.950889i \(0.600172\pi\)
\(854\) 2.62686 0.0898893
\(855\) −5.63773 −0.192806
\(856\) 4.38692 0.149942
\(857\) 33.3957 1.14078 0.570388 0.821376i \(-0.306793\pi\)
0.570388 + 0.821376i \(0.306793\pi\)
\(858\) 30.8217 1.05223
\(859\) 40.4650 1.38065 0.690325 0.723500i \(-0.257468\pi\)
0.690325 + 0.723500i \(0.257468\pi\)
\(860\) −0.381502 −0.0130091
\(861\) 37.2041 1.26791
\(862\) 42.9771 1.46380
\(863\) −18.3769 −0.625558 −0.312779 0.949826i \(-0.601260\pi\)
−0.312779 + 0.949826i \(0.601260\pi\)
\(864\) −2.36546 −0.0804747
\(865\) −2.20906 −0.0751102
\(866\) 7.00486 0.238035
\(867\) 8.32881 0.282861
\(868\) −0.454492 −0.0154265
\(869\) 0.103965 0.00352676
\(870\) 4.38875 0.148793
\(871\) 44.5805 1.51055
\(872\) −9.72590 −0.329360
\(873\) 10.5270 0.356286
\(874\) 14.9464 0.505568
\(875\) 39.0399 1.31979
\(876\) 0.536849 0.0181384
\(877\) −8.75942 −0.295784 −0.147892 0.989003i \(-0.547249\pi\)
−0.147892 + 0.989003i \(0.547249\pi\)
\(878\) 33.1380 1.11835
\(879\) 46.8131 1.57897
\(880\) −22.1333 −0.746112
\(881\) −11.6701 −0.393176 −0.196588 0.980486i \(-0.562986\pi\)
−0.196588 + 0.980486i \(0.562986\pi\)
\(882\) 4.12514 0.138901
\(883\) 7.97115 0.268251 0.134125 0.990964i \(-0.457178\pi\)
0.134125 + 0.990964i \(0.457178\pi\)
\(884\) −1.92960 −0.0648996
\(885\) −5.87020 −0.197325
\(886\) 9.75090 0.327588
\(887\) 10.6962 0.359144 0.179572 0.983745i \(-0.442529\pi\)
0.179572 + 0.983745i \(0.442529\pi\)
\(888\) 38.3407 1.28663
\(889\) 28.3852 0.952009
\(890\) 14.0597 0.471282
\(891\) −16.0225 −0.536772
\(892\) 0.518495 0.0173605
\(893\) −2.24729 −0.0752026
\(894\) 8.40259 0.281025
\(895\) −20.3307 −0.679582
\(896\) 39.0062 1.30311
\(897\) 23.4811 0.784011
\(898\) 35.7182 1.19193
\(899\) −1.86600 −0.0622346
\(900\) 0.0480224 0.00160075
\(901\) 15.4461 0.514583
\(902\) 28.6662 0.954479
\(903\) 12.3309 0.410346
\(904\) −3.63709 −0.120968
\(905\) −0.790369 −0.0262727
\(906\) 36.4535 1.21109
\(907\) 47.5710 1.57957 0.789784 0.613385i \(-0.210193\pi\)
0.789784 + 0.613385i \(0.210193\pi\)
\(908\) 0.200142 0.00664196
\(909\) 6.46301 0.214364
\(910\) −52.5802 −1.74302
\(911\) 6.78371 0.224754 0.112377 0.993666i \(-0.464154\pi\)
0.112377 + 0.993666i \(0.464154\pi\)
\(912\) −22.3517 −0.740137
\(913\) −30.7362 −1.01722
\(914\) −14.4129 −0.476736
\(915\) 1.69600 0.0560680
\(916\) 0.102106 0.00337368
\(917\) 4.85220 0.160234
\(918\) 38.5170 1.27125
\(919\) 46.1874 1.52358 0.761791 0.647823i \(-0.224320\pi\)
0.761791 + 0.647823i \(0.224320\pi\)
\(920\) −16.2570 −0.535976
\(921\) −40.5083 −1.33479
\(922\) 19.2604 0.634307
\(923\) 1.67882 0.0552589
\(924\) −0.953879 −0.0313803
\(925\) −7.80057 −0.256481
\(926\) −15.0047 −0.493085
\(927\) −5.31732 −0.174644
\(928\) −0.420235 −0.0137949
\(929\) 35.1911 1.15458 0.577292 0.816538i \(-0.304110\pi\)
0.577292 + 0.816538i \(0.304110\pi\)
\(930\) −8.18941 −0.268541
\(931\) 13.4947 0.442272
\(932\) 0.530388 0.0173734
\(933\) 3.05224 0.0999260
\(934\) 13.0270 0.426256
\(935\) 25.3809 0.830045
\(936\) 11.6103 0.379495
\(937\) 47.2913 1.54494 0.772469 0.635052i \(-0.219022\pi\)
0.772469 + 0.635052i \(0.219022\pi\)
\(938\) −38.5052 −1.25724
\(939\) 40.3165 1.31568
\(940\) −0.0943451 −0.00307720
\(941\) 5.46226 0.178065 0.0890323 0.996029i \(-0.471623\pi\)
0.0890323 + 0.996029i \(0.471623\pi\)
\(942\) 11.8032 0.384570
\(943\) 21.8389 0.711174
\(944\) 7.98139 0.259772
\(945\) 37.6070 1.22336
\(946\) 9.50106 0.308906
\(947\) −30.8434 −1.00228 −0.501138 0.865368i \(-0.667085\pi\)
−0.501138 + 0.865368i \(0.667085\pi\)
\(948\) 0.00440768 0.000143155 0
\(949\) −26.4070 −0.857208
\(950\) 4.38437 0.142248
\(951\) −12.6324 −0.409632
\(952\) −43.1803 −1.39948
\(953\) −52.1811 −1.69031 −0.845155 0.534521i \(-0.820492\pi\)
−0.845155 + 0.534521i \(0.820492\pi\)
\(954\) 3.58716 0.116139
\(955\) −32.4354 −1.04959
\(956\) 0.916968 0.0296569
\(957\) −3.91633 −0.126597
\(958\) 2.80019 0.0904701
\(959\) 25.2682 0.815951
\(960\) 23.4057 0.755414
\(961\) −27.5180 −0.887679
\(962\) 72.7921 2.34691
\(963\) −1.21178 −0.0390490
\(964\) −2.00843 −0.0646871
\(965\) 2.81729 0.0906919
\(966\) −20.2812 −0.652536
\(967\) −8.64602 −0.278037 −0.139019 0.990290i \(-0.544395\pi\)
−0.139019 + 0.990290i \(0.544395\pi\)
\(968\) −11.4659 −0.368528
\(969\) 25.6313 0.823397
\(970\) 40.3488 1.29552
\(971\) −3.69431 −0.118556 −0.0592781 0.998242i \(-0.518880\pi\)
−0.0592781 + 0.998242i \(0.518880\pi\)
\(972\) 0.575830 0.0184698
\(973\) 3.27699 0.105055
\(974\) −49.2441 −1.57788
\(975\) 6.88796 0.220591
\(976\) −2.30596 −0.0738120
\(977\) −35.5479 −1.13728 −0.568639 0.822587i \(-0.692530\pi\)
−0.568639 + 0.822587i \(0.692530\pi\)
\(978\) −38.3842 −1.22739
\(979\) −12.5463 −0.400980
\(980\) 0.566533 0.0180972
\(981\) 2.68654 0.0857746
\(982\) 11.8973 0.379660
\(983\) −41.1796 −1.31343 −0.656713 0.754141i \(-0.728054\pi\)
−0.656713 + 0.754141i \(0.728054\pi\)
\(984\) −31.4874 −1.00378
\(985\) −6.98800 −0.222656
\(986\) 6.84271 0.217916
\(987\) 3.04941 0.0970639
\(988\) −1.46598 −0.0466390
\(989\) 7.23826 0.230163
\(990\) 5.89441 0.187337
\(991\) 42.6212 1.35391 0.676953 0.736026i \(-0.263300\pi\)
0.676953 + 0.736026i \(0.263300\pi\)
\(992\) 0.784159 0.0248971
\(993\) 36.4216 1.15581
\(994\) −1.45003 −0.0459923
\(995\) 5.67059 0.179770
\(996\) −1.30309 −0.0412900
\(997\) 22.5489 0.714132 0.357066 0.934079i \(-0.383777\pi\)
0.357066 + 0.934079i \(0.383777\pi\)
\(998\) 37.6941 1.19319
\(999\) −52.0632 −1.64721
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 \(a_p\))