Properties

Label 6019.2.a.c.1.13
Level 6019
Weight 2
Character 6019.1
Self dual Yes
Analytic conductor 48.062
Analytic rank 1
Dimension 108
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6019 = 13 \cdot 463 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0619569766\)
Analytic rank: \(1\)
Dimension: \(108\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.34425 q^{2}\) \(-1.25776 q^{3}\) \(+3.49550 q^{4}\) \(-1.49624 q^{5}\) \(+2.94851 q^{6}\) \(+5.17811 q^{7}\) \(-3.50582 q^{8}\) \(-1.41803 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.34425 q^{2}\) \(-1.25776 q^{3}\) \(+3.49550 q^{4}\) \(-1.49624 q^{5}\) \(+2.94851 q^{6}\) \(+5.17811 q^{7}\) \(-3.50582 q^{8}\) \(-1.41803 q^{9}\) \(+3.50756 q^{10}\) \(-4.47445 q^{11}\) \(-4.39651 q^{12}\) \(-1.00000 q^{13}\) \(-12.1388 q^{14}\) \(+1.88192 q^{15}\) \(+1.22752 q^{16}\) \(-5.45792 q^{17}\) \(+3.32421 q^{18}\) \(-3.00133 q^{19}\) \(-5.23012 q^{20}\) \(-6.51284 q^{21}\) \(+10.4892 q^{22}\) \(+3.61702 q^{23}\) \(+4.40950 q^{24}\) \(-2.76126 q^{25}\) \(+2.34425 q^{26}\) \(+5.55684 q^{27}\) \(+18.1001 q^{28}\) \(+2.72607 q^{29}\) \(-4.41169 q^{30}\) \(+7.05094 q^{31}\) \(+4.13403 q^{32}\) \(+5.62780 q^{33}\) \(+12.7947 q^{34}\) \(-7.74771 q^{35}\) \(-4.95672 q^{36}\) \(-1.41371 q^{37}\) \(+7.03587 q^{38}\) \(+1.25776 q^{39}\) \(+5.24556 q^{40}\) \(+1.70197 q^{41}\) \(+15.2677 q^{42}\) \(+4.47900 q^{43}\) \(-15.6404 q^{44}\) \(+2.12172 q^{45}\) \(-8.47919 q^{46}\) \(-6.03160 q^{47}\) \(-1.54393 q^{48}\) \(+19.8128 q^{49}\) \(+6.47307 q^{50}\) \(+6.86477 q^{51}\) \(-3.49550 q^{52}\) \(-6.03994 q^{53}\) \(-13.0266 q^{54}\) \(+6.69486 q^{55}\) \(-18.1535 q^{56}\) \(+3.77497 q^{57}\) \(-6.39059 q^{58}\) \(+11.6259 q^{59}\) \(+6.57825 q^{60}\) \(+12.3219 q^{61}\) \(-16.5292 q^{62}\) \(-7.34271 q^{63}\) \(-12.1462 q^{64}\) \(+1.49624 q^{65}\) \(-13.1930 q^{66}\) \(-5.57653 q^{67}\) \(-19.0782 q^{68}\) \(-4.54936 q^{69}\) \(+18.1626 q^{70}\) \(+10.6909 q^{71}\) \(+4.97136 q^{72}\) \(+6.02805 q^{73}\) \(+3.31408 q^{74}\) \(+3.47301 q^{75}\) \(-10.4912 q^{76}\) \(-23.1692 q^{77}\) \(-2.94851 q^{78}\) \(-12.5624 q^{79}\) \(-1.83667 q^{80}\) \(-2.73510 q^{81}\) \(-3.98985 q^{82}\) \(-8.52121 q^{83}\) \(-22.7656 q^{84}\) \(+8.16637 q^{85}\) \(-10.4999 q^{86}\) \(-3.42876 q^{87}\) \(+15.6866 q^{88}\) \(-12.6743 q^{89}\) \(-4.97383 q^{90}\) \(-5.17811 q^{91}\) \(+12.6433 q^{92}\) \(-8.86842 q^{93}\) \(+14.1396 q^{94}\) \(+4.49073 q^{95}\) \(-5.19964 q^{96}\) \(+9.17600 q^{97}\) \(-46.4462 q^{98}\) \(+6.34490 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34425 −1.65763 −0.828817 0.559520i \(-0.810986\pi\)
−0.828817 + 0.559520i \(0.810986\pi\)
\(3\) −1.25776 −0.726170 −0.363085 0.931756i \(-0.618277\pi\)
−0.363085 + 0.931756i \(0.618277\pi\)
\(4\) 3.49550 1.74775
\(5\) −1.49624 −0.669140 −0.334570 0.942371i \(-0.608591\pi\)
−0.334570 + 0.942371i \(0.608591\pi\)
\(6\) 2.94851 1.20372
\(7\) 5.17811 1.95714 0.978571 0.205911i \(-0.0660158\pi\)
0.978571 + 0.205911i \(0.0660158\pi\)
\(8\) −3.50582 −1.23950
\(9\) −1.41803 −0.472677
\(10\) 3.50756 1.10919
\(11\) −4.47445 −1.34910 −0.674549 0.738231i \(-0.735662\pi\)
−0.674549 + 0.738231i \(0.735662\pi\)
\(12\) −4.39651 −1.26916
\(13\) −1.00000 −0.277350
\(14\) −12.1388 −3.24422
\(15\) 1.88192 0.485910
\(16\) 1.22752 0.306880
\(17\) −5.45792 −1.32374 −0.661870 0.749619i \(-0.730237\pi\)
−0.661870 + 0.749619i \(0.730237\pi\)
\(18\) 3.32421 0.783525
\(19\) −3.00133 −0.688553 −0.344277 0.938868i \(-0.611876\pi\)
−0.344277 + 0.938868i \(0.611876\pi\)
\(20\) −5.23012 −1.16949
\(21\) −6.51284 −1.42122
\(22\) 10.4892 2.23631
\(23\) 3.61702 0.754201 0.377100 0.926172i \(-0.376921\pi\)
0.377100 + 0.926172i \(0.376921\pi\)
\(24\) 4.40950 0.900085
\(25\) −2.76126 −0.552252
\(26\) 2.34425 0.459745
\(27\) 5.55684 1.06941
\(28\) 18.1001 3.42059
\(29\) 2.72607 0.506219 0.253110 0.967438i \(-0.418547\pi\)
0.253110 + 0.967438i \(0.418547\pi\)
\(30\) −4.41169 −0.805460
\(31\) 7.05094 1.26639 0.633193 0.773994i \(-0.281744\pi\)
0.633193 + 0.773994i \(0.281744\pi\)
\(32\) 4.13403 0.730801
\(33\) 5.62780 0.979674
\(34\) 12.7947 2.19428
\(35\) −7.74771 −1.30960
\(36\) −4.95672 −0.826121
\(37\) −1.41371 −0.232412 −0.116206 0.993225i \(-0.537073\pi\)
−0.116206 + 0.993225i \(0.537073\pi\)
\(38\) 7.03587 1.14137
\(39\) 1.25776 0.201403
\(40\) 5.24556 0.829396
\(41\) 1.70197 0.265803 0.132902 0.991129i \(-0.457571\pi\)
0.132902 + 0.991129i \(0.457571\pi\)
\(42\) 15.2677 2.35586
\(43\) 4.47900 0.683041 0.341520 0.939874i \(-0.389058\pi\)
0.341520 + 0.939874i \(0.389058\pi\)
\(44\) −15.6404 −2.35788
\(45\) 2.12172 0.316287
\(46\) −8.47919 −1.25019
\(47\) −6.03160 −0.879799 −0.439899 0.898047i \(-0.644986\pi\)
−0.439899 + 0.898047i \(0.644986\pi\)
\(48\) −1.54393 −0.222847
\(49\) 19.8128 2.83040
\(50\) 6.47307 0.915431
\(51\) 6.86477 0.961261
\(52\) −3.49550 −0.484739
\(53\) −6.03994 −0.829650 −0.414825 0.909901i \(-0.636157\pi\)
−0.414825 + 0.909901i \(0.636157\pi\)
\(54\) −13.0266 −1.77270
\(55\) 6.69486 0.902735
\(56\) −18.1535 −2.42587
\(57\) 3.77497 0.500007
\(58\) −6.39059 −0.839126
\(59\) 11.6259 1.51356 0.756779 0.653671i \(-0.226772\pi\)
0.756779 + 0.653671i \(0.226772\pi\)
\(60\) 6.57825 0.849249
\(61\) 12.3219 1.57765 0.788827 0.614616i \(-0.210689\pi\)
0.788827 + 0.614616i \(0.210689\pi\)
\(62\) −16.5292 −2.09920
\(63\) −7.34271 −0.925095
\(64\) −12.1462 −1.51828
\(65\) 1.49624 0.185586
\(66\) −13.1930 −1.62394
\(67\) −5.57653 −0.681281 −0.340641 0.940194i \(-0.610644\pi\)
−0.340641 + 0.940194i \(0.610644\pi\)
\(68\) −19.0782 −2.31357
\(69\) −4.54936 −0.547678
\(70\) 18.1626 2.17084
\(71\) 10.6909 1.26878 0.634390 0.773013i \(-0.281251\pi\)
0.634390 + 0.773013i \(0.281251\pi\)
\(72\) 4.97136 0.585881
\(73\) 6.02805 0.705530 0.352765 0.935712i \(-0.385241\pi\)
0.352765 + 0.935712i \(0.385241\pi\)
\(74\) 3.31408 0.385254
\(75\) 3.47301 0.401029
\(76\) −10.4912 −1.20342
\(77\) −23.1692 −2.64037
\(78\) −2.94851 −0.333853
\(79\) −12.5624 −1.41338 −0.706689 0.707525i \(-0.749812\pi\)
−0.706689 + 0.707525i \(0.749812\pi\)
\(80\) −1.83667 −0.205346
\(81\) −2.73510 −0.303900
\(82\) −3.98985 −0.440605
\(83\) −8.52121 −0.935325 −0.467662 0.883907i \(-0.654904\pi\)
−0.467662 + 0.883907i \(0.654904\pi\)
\(84\) −22.7656 −2.48393
\(85\) 8.16637 0.885767
\(86\) −10.4999 −1.13223
\(87\) −3.42876 −0.367601
\(88\) 15.6866 1.67220
\(89\) −12.6743 −1.34347 −0.671735 0.740792i \(-0.734451\pi\)
−0.671735 + 0.740792i \(0.734451\pi\)
\(90\) −4.97383 −0.524288
\(91\) −5.17811 −0.542813
\(92\) 12.6433 1.31815
\(93\) −8.86842 −0.919612
\(94\) 14.1396 1.45838
\(95\) 4.49073 0.460739
\(96\) −5.19964 −0.530686
\(97\) 9.17600 0.931682 0.465841 0.884868i \(-0.345752\pi\)
0.465841 + 0.884868i \(0.345752\pi\)
\(98\) −46.4462 −4.69177
\(99\) 6.34490 0.637687
\(100\) −9.65198 −0.965198
\(101\) −1.98041 −0.197058 −0.0985291 0.995134i \(-0.531414\pi\)
−0.0985291 + 0.995134i \(0.531414\pi\)
\(102\) −16.0927 −1.59342
\(103\) −0.854809 −0.0842269 −0.0421134 0.999113i \(-0.513409\pi\)
−0.0421134 + 0.999113i \(0.513409\pi\)
\(104\) 3.50582 0.343774
\(105\) 9.74479 0.950994
\(106\) 14.1591 1.37526
\(107\) −2.14887 −0.207739 −0.103870 0.994591i \(-0.533122\pi\)
−0.103870 + 0.994591i \(0.533122\pi\)
\(108\) 19.4239 1.86907
\(109\) −2.03410 −0.194831 −0.0974156 0.995244i \(-0.531058\pi\)
−0.0974156 + 0.995244i \(0.531058\pi\)
\(110\) −15.6944 −1.49640
\(111\) 1.77811 0.168771
\(112\) 6.35624 0.600608
\(113\) 6.47458 0.609077 0.304538 0.952500i \(-0.401498\pi\)
0.304538 + 0.952500i \(0.401498\pi\)
\(114\) −8.84947 −0.828829
\(115\) −5.41194 −0.504666
\(116\) 9.52899 0.884744
\(117\) 1.41803 0.131097
\(118\) −27.2539 −2.50892
\(119\) −28.2617 −2.59075
\(120\) −6.59768 −0.602283
\(121\) 9.02069 0.820063
\(122\) −28.8855 −2.61517
\(123\) −2.14068 −0.193019
\(124\) 24.6466 2.21333
\(125\) 11.6127 1.03867
\(126\) 17.2131 1.53347
\(127\) −4.75904 −0.422296 −0.211148 0.977454i \(-0.567720\pi\)
−0.211148 + 0.977454i \(0.567720\pi\)
\(128\) 20.2057 1.78595
\(129\) −5.63352 −0.496004
\(130\) −3.50756 −0.307634
\(131\) −6.29523 −0.550017 −0.275008 0.961442i \(-0.588681\pi\)
−0.275008 + 0.961442i \(0.588681\pi\)
\(132\) 19.6720 1.71223
\(133\) −15.5412 −1.34760
\(134\) 13.0728 1.12932
\(135\) −8.31438 −0.715588
\(136\) 19.1345 1.64077
\(137\) 11.9633 1.02209 0.511045 0.859554i \(-0.329259\pi\)
0.511045 + 0.859554i \(0.329259\pi\)
\(138\) 10.6648 0.907850
\(139\) 10.7427 0.911187 0.455593 0.890188i \(-0.349427\pi\)
0.455593 + 0.890188i \(0.349427\pi\)
\(140\) −27.0821 −2.28886
\(141\) 7.58633 0.638884
\(142\) −25.0622 −2.10317
\(143\) 4.47445 0.374172
\(144\) −1.74066 −0.145055
\(145\) −4.07887 −0.338731
\(146\) −14.1313 −1.16951
\(147\) −24.9198 −2.05535
\(148\) −4.94162 −0.406199
\(149\) 13.1390 1.07639 0.538194 0.842821i \(-0.319107\pi\)
0.538194 + 0.842821i \(0.319107\pi\)
\(150\) −8.14160 −0.664759
\(151\) −7.92367 −0.644819 −0.322409 0.946600i \(-0.604493\pi\)
−0.322409 + 0.946600i \(0.604493\pi\)
\(152\) 10.5221 0.853459
\(153\) 7.73949 0.625701
\(154\) 54.3143 4.37677
\(155\) −10.5499 −0.847390
\(156\) 4.39651 0.352003
\(157\) 8.43014 0.672799 0.336399 0.941719i \(-0.390791\pi\)
0.336399 + 0.941719i \(0.390791\pi\)
\(158\) 29.4493 2.34286
\(159\) 7.59682 0.602467
\(160\) −6.18552 −0.489008
\(161\) 18.7293 1.47608
\(162\) 6.41176 0.503755
\(163\) −10.6079 −0.830877 −0.415438 0.909621i \(-0.636372\pi\)
−0.415438 + 0.909621i \(0.636372\pi\)
\(164\) 5.94924 0.464558
\(165\) −8.42055 −0.655539
\(166\) 19.9758 1.55043
\(167\) 6.80047 0.526236 0.263118 0.964764i \(-0.415249\pi\)
0.263118 + 0.964764i \(0.415249\pi\)
\(168\) 22.8329 1.76159
\(169\) 1.00000 0.0769231
\(170\) −19.1440 −1.46828
\(171\) 4.25598 0.325463
\(172\) 15.6563 1.19378
\(173\) −18.7285 −1.42390 −0.711952 0.702228i \(-0.752189\pi\)
−0.711952 + 0.702228i \(0.752189\pi\)
\(174\) 8.03786 0.609348
\(175\) −14.2981 −1.08083
\(176\) −5.49248 −0.414011
\(177\) −14.6226 −1.09910
\(178\) 29.7116 2.22698
\(179\) −3.77954 −0.282496 −0.141248 0.989974i \(-0.545112\pi\)
−0.141248 + 0.989974i \(0.545112\pi\)
\(180\) 7.41646 0.552790
\(181\) −13.3727 −0.993985 −0.496993 0.867755i \(-0.665562\pi\)
−0.496993 + 0.867755i \(0.665562\pi\)
\(182\) 12.1388 0.899786
\(183\) −15.4980 −1.14565
\(184\) −12.6806 −0.934828
\(185\) 2.11525 0.155516
\(186\) 20.7898 1.52438
\(187\) 24.4212 1.78585
\(188\) −21.0834 −1.53767
\(189\) 28.7739 2.09299
\(190\) −10.5274 −0.763736
\(191\) −7.91727 −0.572873 −0.286437 0.958099i \(-0.592471\pi\)
−0.286437 + 0.958099i \(0.592471\pi\)
\(192\) 15.2771 1.10253
\(193\) 22.2458 1.60128 0.800642 0.599143i \(-0.204492\pi\)
0.800642 + 0.599143i \(0.204492\pi\)
\(194\) −21.5108 −1.54439
\(195\) −1.88192 −0.134767
\(196\) 69.2557 4.94684
\(197\) −0.758436 −0.0540364 −0.0270182 0.999635i \(-0.508601\pi\)
−0.0270182 + 0.999635i \(0.508601\pi\)
\(198\) −14.8740 −1.05705
\(199\) −9.48874 −0.672639 −0.336319 0.941748i \(-0.609182\pi\)
−0.336319 + 0.941748i \(0.609182\pi\)
\(200\) 9.68048 0.684514
\(201\) 7.01396 0.494726
\(202\) 4.64257 0.326650
\(203\) 14.1159 0.990742
\(204\) 23.9958 1.68004
\(205\) −2.54656 −0.177860
\(206\) 2.00389 0.139617
\(207\) −5.12904 −0.356493
\(208\) −1.22752 −0.0851132
\(209\) 13.4293 0.928925
\(210\) −22.8442 −1.57640
\(211\) 20.6423 1.42107 0.710536 0.703661i \(-0.248452\pi\)
0.710536 + 0.703661i \(0.248452\pi\)
\(212\) −21.1126 −1.45002
\(213\) −13.4467 −0.921351
\(214\) 5.03749 0.344355
\(215\) −6.70167 −0.457050
\(216\) −19.4813 −1.32553
\(217\) 36.5105 2.47850
\(218\) 4.76843 0.322959
\(219\) −7.58187 −0.512335
\(220\) 23.4019 1.57775
\(221\) 5.45792 0.367139
\(222\) −4.16833 −0.279760
\(223\) −6.11156 −0.409260 −0.204630 0.978839i \(-0.565599\pi\)
−0.204630 + 0.978839i \(0.565599\pi\)
\(224\) 21.4065 1.43028
\(225\) 3.91555 0.261036
\(226\) −15.1780 −1.00963
\(227\) −20.2571 −1.34451 −0.672257 0.740318i \(-0.734675\pi\)
−0.672257 + 0.740318i \(0.734675\pi\)
\(228\) 13.1954 0.873887
\(229\) −15.5043 −1.02455 −0.512275 0.858821i \(-0.671197\pi\)
−0.512275 + 0.858821i \(0.671197\pi\)
\(230\) 12.6869 0.836551
\(231\) 29.1414 1.91736
\(232\) −9.55713 −0.627456
\(233\) 8.37344 0.548562 0.274281 0.961650i \(-0.411560\pi\)
0.274281 + 0.961650i \(0.411560\pi\)
\(234\) −3.32421 −0.217311
\(235\) 9.02473 0.588709
\(236\) 40.6382 2.64532
\(237\) 15.8005 1.02635
\(238\) 66.2525 4.29451
\(239\) 4.87935 0.315619 0.157810 0.987470i \(-0.449557\pi\)
0.157810 + 0.987470i \(0.449557\pi\)
\(240\) 2.31010 0.149116
\(241\) −1.21542 −0.0782918 −0.0391459 0.999234i \(-0.512464\pi\)
−0.0391459 + 0.999234i \(0.512464\pi\)
\(242\) −21.1467 −1.35936
\(243\) −13.2304 −0.848731
\(244\) 43.0711 2.75734
\(245\) −29.6448 −1.89394
\(246\) 5.01828 0.319954
\(247\) 3.00133 0.190970
\(248\) −24.7193 −1.56968
\(249\) 10.7177 0.679205
\(250\) −27.2231 −1.72174
\(251\) −18.0708 −1.14062 −0.570308 0.821431i \(-0.693176\pi\)
−0.570308 + 0.821431i \(0.693176\pi\)
\(252\) −25.6665 −1.61683
\(253\) −16.1842 −1.01749
\(254\) 11.1564 0.700013
\(255\) −10.2714 −0.643218
\(256\) −23.0748 −1.44217
\(257\) −1.37292 −0.0856405 −0.0428203 0.999083i \(-0.513634\pi\)
−0.0428203 + 0.999083i \(0.513634\pi\)
\(258\) 13.2064 0.822193
\(259\) −7.32034 −0.454864
\(260\) 5.23012 0.324358
\(261\) −3.86565 −0.239278
\(262\) 14.7576 0.911727
\(263\) 7.53096 0.464379 0.232189 0.972671i \(-0.425411\pi\)
0.232189 + 0.972671i \(0.425411\pi\)
\(264\) −19.7301 −1.21430
\(265\) 9.03722 0.555152
\(266\) 36.4325 2.23382
\(267\) 15.9412 0.975588
\(268\) −19.4928 −1.19071
\(269\) −15.3063 −0.933244 −0.466622 0.884457i \(-0.654529\pi\)
−0.466622 + 0.884457i \(0.654529\pi\)
\(270\) 19.4910 1.18618
\(271\) 10.0882 0.612817 0.306409 0.951900i \(-0.400873\pi\)
0.306409 + 0.951900i \(0.400873\pi\)
\(272\) −6.69971 −0.406230
\(273\) 6.51284 0.394175
\(274\) −28.0448 −1.69425
\(275\) 12.3551 0.745041
\(276\) −15.9023 −0.957204
\(277\) 2.78531 0.167353 0.0836766 0.996493i \(-0.473334\pi\)
0.0836766 + 0.996493i \(0.473334\pi\)
\(278\) −25.1836 −1.51041
\(279\) −9.99844 −0.598591
\(280\) 27.1621 1.62325
\(281\) −23.3741 −1.39438 −0.697191 0.716886i \(-0.745567\pi\)
−0.697191 + 0.716886i \(0.745567\pi\)
\(282\) −17.7842 −1.05904
\(283\) −7.64565 −0.454486 −0.227243 0.973838i \(-0.572971\pi\)
−0.227243 + 0.973838i \(0.572971\pi\)
\(284\) 37.3702 2.21751
\(285\) −5.64827 −0.334575
\(286\) −10.4892 −0.620240
\(287\) 8.81300 0.520215
\(288\) −5.86218 −0.345432
\(289\) 12.7889 0.752287
\(290\) 9.56188 0.561493
\(291\) −11.5412 −0.676560
\(292\) 21.0711 1.23309
\(293\) −16.3217 −0.953526 −0.476763 0.879032i \(-0.658190\pi\)
−0.476763 + 0.879032i \(0.658190\pi\)
\(294\) 58.4183 3.40703
\(295\) −17.3951 −1.01278
\(296\) 4.95621 0.288074
\(297\) −24.8638 −1.44274
\(298\) −30.8010 −1.78426
\(299\) −3.61702 −0.209178
\(300\) 12.1399 0.700898
\(301\) 23.1927 1.33681
\(302\) 18.5750 1.06887
\(303\) 2.49089 0.143098
\(304\) −3.68420 −0.211303
\(305\) −18.4365 −1.05567
\(306\) −18.1433 −1.03718
\(307\) −13.0107 −0.742558 −0.371279 0.928521i \(-0.621081\pi\)
−0.371279 + 0.928521i \(0.621081\pi\)
\(308\) −80.9879 −4.61471
\(309\) 1.07515 0.0611631
\(310\) 24.7316 1.40466
\(311\) 30.6153 1.73603 0.868017 0.496534i \(-0.165394\pi\)
0.868017 + 0.496534i \(0.165394\pi\)
\(312\) −4.40950 −0.249639
\(313\) 11.6735 0.659825 0.329912 0.944012i \(-0.392981\pi\)
0.329912 + 0.944012i \(0.392981\pi\)
\(314\) −19.7623 −1.11525
\(315\) 10.9865 0.619018
\(316\) −43.9118 −2.47023
\(317\) 1.17065 0.0657500 0.0328750 0.999459i \(-0.489534\pi\)
0.0328750 + 0.999459i \(0.489534\pi\)
\(318\) −17.8088 −0.998670
\(319\) −12.1977 −0.682939
\(320\) 18.1737 1.01594
\(321\) 2.70277 0.150854
\(322\) −43.9062 −2.44680
\(323\) 16.3810 0.911466
\(324\) −9.56055 −0.531141
\(325\) 2.76126 0.153167
\(326\) 24.8676 1.37729
\(327\) 2.55842 0.141481
\(328\) −5.96682 −0.329462
\(329\) −31.2323 −1.72189
\(330\) 19.7399 1.08664
\(331\) −10.1935 −0.560286 −0.280143 0.959958i \(-0.590382\pi\)
−0.280143 + 0.959958i \(0.590382\pi\)
\(332\) −29.7859 −1.63471
\(333\) 2.00468 0.109856
\(334\) −15.9420 −0.872307
\(335\) 8.34384 0.455873
\(336\) −7.99464 −0.436144
\(337\) 13.4903 0.734861 0.367431 0.930051i \(-0.380238\pi\)
0.367431 + 0.930051i \(0.380238\pi\)
\(338\) −2.34425 −0.127510
\(339\) −8.14349 −0.442294
\(340\) 28.5456 1.54810
\(341\) −31.5491 −1.70848
\(342\) −9.97708 −0.539499
\(343\) 66.3462 3.58236
\(344\) −15.7026 −0.846626
\(345\) 6.80694 0.366473
\(346\) 43.9043 2.36031
\(347\) −11.4593 −0.615166 −0.307583 0.951521i \(-0.599520\pi\)
−0.307583 + 0.951521i \(0.599520\pi\)
\(348\) −11.9852 −0.642475
\(349\) 14.1602 0.757977 0.378989 0.925401i \(-0.376272\pi\)
0.378989 + 0.925401i \(0.376272\pi\)
\(350\) 33.5183 1.79163
\(351\) −5.55684 −0.296602
\(352\) −18.4975 −0.985921
\(353\) −31.4633 −1.67462 −0.837310 0.546728i \(-0.815873\pi\)
−0.837310 + 0.546728i \(0.815873\pi\)
\(354\) 34.2790 1.82191
\(355\) −15.9962 −0.848992
\(356\) −44.3029 −2.34805
\(357\) 35.5466 1.88132
\(358\) 8.86018 0.468275
\(359\) −1.11037 −0.0586030 −0.0293015 0.999571i \(-0.509328\pi\)
−0.0293015 + 0.999571i \(0.509328\pi\)
\(360\) −7.43836 −0.392036
\(361\) −9.99199 −0.525894
\(362\) 31.3489 1.64766
\(363\) −11.3459 −0.595505
\(364\) −18.1001 −0.948702
\(365\) −9.01943 −0.472099
\(366\) 36.3312 1.89906
\(367\) −5.93757 −0.309939 −0.154969 0.987919i \(-0.549528\pi\)
−0.154969 + 0.987919i \(0.549528\pi\)
\(368\) 4.43997 0.231449
\(369\) −2.41345 −0.125639
\(370\) −4.95867 −0.257789
\(371\) −31.2755 −1.62374
\(372\) −30.9996 −1.60725
\(373\) 11.6189 0.601602 0.300801 0.953687i \(-0.402746\pi\)
0.300801 + 0.953687i \(0.402746\pi\)
\(374\) −57.2493 −2.96029
\(375\) −14.6061 −0.754254
\(376\) 21.1457 1.09051
\(377\) −2.72607 −0.140400
\(378\) −67.4532 −3.46942
\(379\) −33.9626 −1.74454 −0.872270 0.489024i \(-0.837353\pi\)
−0.872270 + 0.489024i \(0.837353\pi\)
\(380\) 15.6973 0.805256
\(381\) 5.98575 0.306659
\(382\) 18.5600 0.949614
\(383\) −10.1446 −0.518367 −0.259184 0.965828i \(-0.583453\pi\)
−0.259184 + 0.965828i \(0.583453\pi\)
\(384\) −25.4141 −1.29691
\(385\) 34.6667 1.76678
\(386\) −52.1496 −2.65434
\(387\) −6.35135 −0.322857
\(388\) 32.0747 1.62835
\(389\) −24.8521 −1.26005 −0.630027 0.776573i \(-0.716956\pi\)
−0.630027 + 0.776573i \(0.716956\pi\)
\(390\) 4.41169 0.223394
\(391\) −19.7414 −0.998365
\(392\) −69.4602 −3.50827
\(393\) 7.91791 0.399406
\(394\) 1.77796 0.0895725
\(395\) 18.7964 0.945747
\(396\) 22.1786 1.11452
\(397\) 20.3186 1.01976 0.509882 0.860245i \(-0.329689\pi\)
0.509882 + 0.860245i \(0.329689\pi\)
\(398\) 22.2440 1.11499
\(399\) 19.5472 0.978585
\(400\) −3.38950 −0.169475
\(401\) −29.8307 −1.48968 −0.744838 0.667245i \(-0.767473\pi\)
−0.744838 + 0.667245i \(0.767473\pi\)
\(402\) −16.4425 −0.820075
\(403\) −7.05094 −0.351232
\(404\) −6.92252 −0.344408
\(405\) 4.09238 0.203352
\(406\) −33.0912 −1.64229
\(407\) 6.32557 0.313547
\(408\) −24.0667 −1.19148
\(409\) −34.3153 −1.69678 −0.848391 0.529370i \(-0.822428\pi\)
−0.848391 + 0.529370i \(0.822428\pi\)
\(410\) 5.96978 0.294826
\(411\) −15.0469 −0.742211
\(412\) −2.98799 −0.147208
\(413\) 60.2000 2.96225
\(414\) 12.0237 0.590935
\(415\) 12.7498 0.625863
\(416\) −4.13403 −0.202688
\(417\) −13.5118 −0.661677
\(418\) −31.4817 −1.53982
\(419\) −8.68179 −0.424133 −0.212067 0.977255i \(-0.568019\pi\)
−0.212067 + 0.977255i \(0.568019\pi\)
\(420\) 34.0629 1.66210
\(421\) 23.1844 1.12994 0.564970 0.825111i \(-0.308888\pi\)
0.564970 + 0.825111i \(0.308888\pi\)
\(422\) −48.3906 −2.35562
\(423\) 8.55299 0.415860
\(424\) 21.1750 1.02835
\(425\) 15.0707 0.731037
\(426\) 31.5223 1.52726
\(427\) 63.8040 3.08769
\(428\) −7.51138 −0.363076
\(429\) −5.62780 −0.271713
\(430\) 15.7104 0.757621
\(431\) −26.2127 −1.26262 −0.631311 0.775530i \(-0.717483\pi\)
−0.631311 + 0.775530i \(0.717483\pi\)
\(432\) 6.82113 0.328182
\(433\) 25.0046 1.20164 0.600822 0.799383i \(-0.294840\pi\)
0.600822 + 0.799383i \(0.294840\pi\)
\(434\) −85.5898 −4.10844
\(435\) 5.13025 0.245977
\(436\) −7.11019 −0.340516
\(437\) −10.8559 −0.519307
\(438\) 17.7738 0.849264
\(439\) 26.3766 1.25888 0.629442 0.777047i \(-0.283283\pi\)
0.629442 + 0.777047i \(0.283283\pi\)
\(440\) −23.4710 −1.11894
\(441\) −28.0952 −1.33787
\(442\) −12.7947 −0.608583
\(443\) 41.8703 1.98932 0.994660 0.103208i \(-0.0329107\pi\)
0.994660 + 0.103208i \(0.0329107\pi\)
\(444\) 6.21539 0.294969
\(445\) 18.9638 0.898970
\(446\) 14.3270 0.678404
\(447\) −16.5257 −0.781640
\(448\) −62.8946 −2.97149
\(449\) 25.6694 1.21141 0.605707 0.795688i \(-0.292890\pi\)
0.605707 + 0.795688i \(0.292890\pi\)
\(450\) −9.17901 −0.432703
\(451\) −7.61539 −0.358595
\(452\) 22.6319 1.06451
\(453\) 9.96610 0.468248
\(454\) 47.4878 2.22871
\(455\) 7.74771 0.363218
\(456\) −13.2344 −0.619757
\(457\) −35.1854 −1.64590 −0.822952 0.568111i \(-0.807674\pi\)
−0.822952 + 0.568111i \(0.807674\pi\)
\(458\) 36.3458 1.69833
\(459\) −30.3288 −1.41563
\(460\) −18.9174 −0.882030
\(461\) −4.98291 −0.232077 −0.116039 0.993245i \(-0.537020\pi\)
−0.116039 + 0.993245i \(0.537020\pi\)
\(462\) −68.3146 −3.17828
\(463\) −1.00000 −0.0464739
\(464\) 3.34631 0.155349
\(465\) 13.2693 0.615349
\(466\) −19.6294 −0.909316
\(467\) −7.17397 −0.331972 −0.165986 0.986128i \(-0.553081\pi\)
−0.165986 + 0.986128i \(0.553081\pi\)
\(468\) 4.95672 0.229125
\(469\) −28.8759 −1.33336
\(470\) −21.1562 −0.975863
\(471\) −10.6031 −0.488566
\(472\) −40.7582 −1.87605
\(473\) −20.0410 −0.921488
\(474\) −37.0403 −1.70132
\(475\) 8.28746 0.380255
\(476\) −98.7888 −4.52798
\(477\) 8.56482 0.392156
\(478\) −11.4384 −0.523181
\(479\) 24.7935 1.13284 0.566421 0.824116i \(-0.308327\pi\)
0.566421 + 0.824116i \(0.308327\pi\)
\(480\) 7.77992 0.355103
\(481\) 1.41371 0.0644596
\(482\) 2.84924 0.129779
\(483\) −23.5571 −1.07188
\(484\) 31.5318 1.43326
\(485\) −13.7295 −0.623426
\(486\) 31.0154 1.40688
\(487\) −24.6076 −1.11508 −0.557538 0.830151i \(-0.688254\pi\)
−0.557538 + 0.830151i \(0.688254\pi\)
\(488\) −43.1983 −1.95549
\(489\) 13.3423 0.603358
\(490\) 69.4947 3.13945
\(491\) 29.5530 1.33371 0.666855 0.745188i \(-0.267640\pi\)
0.666855 + 0.745188i \(0.267640\pi\)
\(492\) −7.48275 −0.337348
\(493\) −14.8787 −0.670102
\(494\) −7.03587 −0.316559
\(495\) −9.49351 −0.426702
\(496\) 8.65517 0.388629
\(497\) 55.3588 2.48318
\(498\) −25.1249 −1.12587
\(499\) 8.31014 0.372013 0.186006 0.982549i \(-0.440445\pi\)
0.186006 + 0.982549i \(0.440445\pi\)
\(500\) 40.5923 1.81534
\(501\) −8.55338 −0.382137
\(502\) 42.3624 1.89073
\(503\) 0.291253 0.0129863 0.00649316 0.999979i \(-0.497933\pi\)
0.00649316 + 0.999979i \(0.497933\pi\)
\(504\) 25.7423 1.14665
\(505\) 2.96317 0.131859
\(506\) 37.9397 1.68663
\(507\) −1.25776 −0.0558593
\(508\) −16.6352 −0.738068
\(509\) 38.3538 1.70000 0.850001 0.526782i \(-0.176601\pi\)
0.850001 + 0.526782i \(0.176601\pi\)
\(510\) 24.0786 1.06622
\(511\) 31.2139 1.38082
\(512\) 13.6816 0.604645
\(513\) −16.6779 −0.736349
\(514\) 3.21847 0.141961
\(515\) 1.27900 0.0563596
\(516\) −19.6920 −0.866891
\(517\) 26.9881 1.18693
\(518\) 17.1607 0.753997
\(519\) 23.5561 1.03400
\(520\) −5.24556 −0.230033
\(521\) 19.0432 0.834299 0.417150 0.908838i \(-0.363029\pi\)
0.417150 + 0.908838i \(0.363029\pi\)
\(522\) 9.06205 0.396635
\(523\) −34.1692 −1.49411 −0.747057 0.664760i \(-0.768534\pi\)
−0.747057 + 0.664760i \(0.768534\pi\)
\(524\) −22.0050 −0.961292
\(525\) 17.9836 0.784870
\(526\) −17.6544 −0.769770
\(527\) −38.4835 −1.67637
\(528\) 6.90824 0.300643
\(529\) −9.91717 −0.431182
\(530\) −21.1855 −0.920238
\(531\) −16.4858 −0.715423
\(532\) −54.3244 −2.35526
\(533\) −1.70197 −0.0737206
\(534\) −37.3702 −1.61717
\(535\) 3.21523 0.139007
\(536\) 19.5503 0.844445
\(537\) 4.75377 0.205140
\(538\) 35.8819 1.54698
\(539\) −88.6514 −3.81849
\(540\) −29.0629 −1.25067
\(541\) −21.0283 −0.904076 −0.452038 0.891999i \(-0.649303\pi\)
−0.452038 + 0.891999i \(0.649303\pi\)
\(542\) −23.6494 −1.01583
\(543\) 16.8197 0.721803
\(544\) −22.5632 −0.967390
\(545\) 3.04350 0.130369
\(546\) −15.2677 −0.653398
\(547\) −38.8685 −1.66190 −0.830948 0.556350i \(-0.812201\pi\)
−0.830948 + 0.556350i \(0.812201\pi\)
\(548\) 41.8176 1.78636
\(549\) −17.4728 −0.745720
\(550\) −28.9634 −1.23501
\(551\) −8.18186 −0.348559
\(552\) 15.9492 0.678845
\(553\) −65.0493 −2.76618
\(554\) −6.52947 −0.277410
\(555\) −2.66049 −0.112931
\(556\) 37.5512 1.59253
\(557\) 13.6806 0.579665 0.289832 0.957077i \(-0.406400\pi\)
0.289832 + 0.957077i \(0.406400\pi\)
\(558\) 23.4388 0.992245
\(559\) −4.47900 −0.189441
\(560\) −9.51047 −0.401891
\(561\) −30.7161 −1.29683
\(562\) 54.7947 2.31137
\(563\) 45.1411 1.90247 0.951236 0.308463i \(-0.0998147\pi\)
0.951236 + 0.308463i \(0.0998147\pi\)
\(564\) 26.5180 1.11661
\(565\) −9.68754 −0.407558
\(566\) 17.9233 0.753372
\(567\) −14.1627 −0.594776
\(568\) −37.4805 −1.57265
\(569\) 33.7443 1.41463 0.707317 0.706897i \(-0.249906\pi\)
0.707317 + 0.706897i \(0.249906\pi\)
\(570\) 13.2410 0.554602
\(571\) −13.9496 −0.583773 −0.291886 0.956453i \(-0.594283\pi\)
−0.291886 + 0.956453i \(0.594283\pi\)
\(572\) 15.6404 0.653959
\(573\) 9.95805 0.416004
\(574\) −20.6599 −0.862326
\(575\) −9.98752 −0.416508
\(576\) 17.2237 0.717656
\(577\) 26.1031 1.08668 0.543342 0.839511i \(-0.317159\pi\)
0.543342 + 0.839511i \(0.317159\pi\)
\(578\) −29.9803 −1.24702
\(579\) −27.9799 −1.16281
\(580\) −14.2577 −0.592018
\(581\) −44.1238 −1.83056
\(582\) 27.0555 1.12149
\(583\) 27.0254 1.11928
\(584\) −21.1333 −0.874502
\(585\) −2.12172 −0.0877222
\(586\) 38.2622 1.58060
\(587\) −44.9076 −1.85354 −0.926768 0.375635i \(-0.877425\pi\)
−0.926768 + 0.375635i \(0.877425\pi\)
\(588\) −87.1073 −3.59225
\(589\) −21.1622 −0.871974
\(590\) 40.7784 1.67882
\(591\) 0.953934 0.0392396
\(592\) −1.73536 −0.0713227
\(593\) −16.7387 −0.687376 −0.343688 0.939084i \(-0.611676\pi\)
−0.343688 + 0.939084i \(0.611676\pi\)
\(594\) 58.2869 2.39154
\(595\) 42.2864 1.73357
\(596\) 45.9273 1.88126
\(597\) 11.9346 0.488450
\(598\) 8.47919 0.346740
\(599\) 32.3789 1.32297 0.661483 0.749960i \(-0.269927\pi\)
0.661483 + 0.749960i \(0.269927\pi\)
\(600\) −12.1758 −0.497073
\(601\) −43.5766 −1.77753 −0.888764 0.458366i \(-0.848435\pi\)
−0.888764 + 0.458366i \(0.848435\pi\)
\(602\) −54.3695 −2.21594
\(603\) 7.90768 0.322026
\(604\) −27.6972 −1.12698
\(605\) −13.4971 −0.548737
\(606\) −5.83926 −0.237204
\(607\) −12.8822 −0.522871 −0.261435 0.965221i \(-0.584196\pi\)
−0.261435 + 0.965221i \(0.584196\pi\)
\(608\) −12.4076 −0.503195
\(609\) −17.7545 −0.719448
\(610\) 43.2197 1.74992
\(611\) 6.03160 0.244012
\(612\) 27.0534 1.09357
\(613\) −2.94338 −0.118882 −0.0594410 0.998232i \(-0.518932\pi\)
−0.0594410 + 0.998232i \(0.518932\pi\)
\(614\) 30.5003 1.23089
\(615\) 3.20298 0.129156
\(616\) 81.2271 3.27273
\(617\) −8.60947 −0.346604 −0.173302 0.984869i \(-0.555444\pi\)
−0.173302 + 0.984869i \(0.555444\pi\)
\(618\) −2.52042 −0.101386
\(619\) −38.6566 −1.55374 −0.776870 0.629660i \(-0.783194\pi\)
−0.776870 + 0.629660i \(0.783194\pi\)
\(620\) −36.8772 −1.48103
\(621\) 20.0992 0.806553
\(622\) −71.7699 −2.87771
\(623\) −65.6288 −2.62936
\(624\) 1.54393 0.0618067
\(625\) −3.56917 −0.142767
\(626\) −27.3656 −1.09375
\(627\) −16.8909 −0.674558
\(628\) 29.4676 1.17588
\(629\) 7.71591 0.307653
\(630\) −25.7550 −1.02611
\(631\) −32.3714 −1.28869 −0.644343 0.764736i \(-0.722869\pi\)
−0.644343 + 0.764736i \(0.722869\pi\)
\(632\) 44.0415 1.75188
\(633\) −25.9631 −1.03194
\(634\) −2.74429 −0.108989
\(635\) 7.12068 0.282575
\(636\) 26.5547 1.05296
\(637\) −19.8128 −0.785012
\(638\) 28.5944 1.13206
\(639\) −15.1601 −0.599723
\(640\) −30.2327 −1.19505
\(641\) 29.8244 1.17799 0.588997 0.808135i \(-0.299523\pi\)
0.588997 + 0.808135i \(0.299523\pi\)
\(642\) −6.33597 −0.250061
\(643\) −17.5453 −0.691919 −0.345959 0.938249i \(-0.612447\pi\)
−0.345959 + 0.938249i \(0.612447\pi\)
\(644\) 65.4683 2.57981
\(645\) 8.42911 0.331896
\(646\) −38.4012 −1.51088
\(647\) −8.17118 −0.321242 −0.160621 0.987016i \(-0.551350\pi\)
−0.160621 + 0.987016i \(0.551350\pi\)
\(648\) 9.58878 0.376683
\(649\) −52.0193 −2.04194
\(650\) −6.47307 −0.253895
\(651\) −45.9216 −1.79981
\(652\) −37.0800 −1.45216
\(653\) 20.1054 0.786786 0.393393 0.919370i \(-0.371301\pi\)
0.393393 + 0.919370i \(0.371301\pi\)
\(654\) −5.99756 −0.234523
\(655\) 9.41919 0.368038
\(656\) 2.08921 0.0815698
\(657\) −8.54796 −0.333488
\(658\) 73.2162 2.85426
\(659\) −10.3930 −0.404854 −0.202427 0.979297i \(-0.564883\pi\)
−0.202427 + 0.979297i \(0.564883\pi\)
\(660\) −29.4340 −1.14572
\(661\) −8.38998 −0.326332 −0.163166 0.986599i \(-0.552171\pi\)
−0.163166 + 0.986599i \(0.552171\pi\)
\(662\) 23.8961 0.928750
\(663\) −6.86477 −0.266606
\(664\) 29.8739 1.15933
\(665\) 23.2535 0.901731
\(666\) −4.69947 −0.182101
\(667\) 9.86026 0.381791
\(668\) 23.7710 0.919729
\(669\) 7.68690 0.297193
\(670\) −19.5600 −0.755670
\(671\) −55.1336 −2.12841
\(672\) −26.9243 −1.03863
\(673\) 25.5613 0.985317 0.492659 0.870223i \(-0.336025\pi\)
0.492659 + 0.870223i \(0.336025\pi\)
\(674\) −31.6245 −1.21813
\(675\) −15.3439 −0.590586
\(676\) 3.49550 0.134442
\(677\) −34.7542 −1.33571 −0.667856 0.744290i \(-0.732788\pi\)
−0.667856 + 0.744290i \(0.732788\pi\)
\(678\) 19.0904 0.733161
\(679\) 47.5143 1.82343
\(680\) −28.6299 −1.09790
\(681\) 25.4787 0.976346
\(682\) 73.9588 2.83203
\(683\) 26.2584 1.00475 0.502376 0.864650i \(-0.332459\pi\)
0.502376 + 0.864650i \(0.332459\pi\)
\(684\) 14.8768 0.568828
\(685\) −17.8999 −0.683921
\(686\) −155.532 −5.93824
\(687\) 19.5007 0.743998
\(688\) 5.49806 0.209612
\(689\) 6.03994 0.230103
\(690\) −15.9572 −0.607479
\(691\) −40.4953 −1.54051 −0.770257 0.637734i \(-0.779872\pi\)
−0.770257 + 0.637734i \(0.779872\pi\)
\(692\) −65.4656 −2.48863
\(693\) 32.8546 1.24804
\(694\) 26.8634 1.01972
\(695\) −16.0737 −0.609711
\(696\) 12.0206 0.455640
\(697\) −9.28923 −0.351855
\(698\) −33.1950 −1.25645
\(699\) −10.5318 −0.398350
\(700\) −49.9790 −1.88903
\(701\) −25.0260 −0.945218 −0.472609 0.881272i \(-0.656688\pi\)
−0.472609 + 0.881272i \(0.656688\pi\)
\(702\) 13.0266 0.491658
\(703\) 4.24301 0.160028
\(704\) 54.3477 2.04831
\(705\) −11.3510 −0.427503
\(706\) 73.7577 2.77591
\(707\) −10.2548 −0.385671
\(708\) −51.1132 −1.92095
\(709\) −34.3255 −1.28912 −0.644561 0.764553i \(-0.722960\pi\)
−0.644561 + 0.764553i \(0.722960\pi\)
\(710\) 37.4991 1.40732
\(711\) 17.8138 0.668070
\(712\) 44.4338 1.66523
\(713\) 25.5034 0.955109
\(714\) −83.3299 −3.11854
\(715\) −6.69486 −0.250374
\(716\) −13.2114 −0.493733
\(717\) −6.13708 −0.229193
\(718\) 2.60298 0.0971424
\(719\) 24.2101 0.902884 0.451442 0.892300i \(-0.350910\pi\)
0.451442 + 0.892300i \(0.350910\pi\)
\(720\) 2.60445 0.0970622
\(721\) −4.42630 −0.164844
\(722\) 23.4237 0.871740
\(723\) 1.52871 0.0568532
\(724\) −46.7443 −1.73724
\(725\) −7.52739 −0.279560
\(726\) 26.5976 0.987130
\(727\) 17.6219 0.653560 0.326780 0.945100i \(-0.394036\pi\)
0.326780 + 0.945100i \(0.394036\pi\)
\(728\) 18.1535 0.672815
\(729\) 24.8460 0.920223
\(730\) 21.1438 0.782567
\(731\) −24.4460 −0.904168
\(732\) −54.1733 −2.00230
\(733\) −8.67013 −0.320238 −0.160119 0.987098i \(-0.551188\pi\)
−0.160119 + 0.987098i \(0.551188\pi\)
\(734\) 13.9191 0.513765
\(735\) 37.2861 1.37532
\(736\) 14.9529 0.551170
\(737\) 24.9519 0.919115
\(738\) 5.65772 0.208264
\(739\) 14.5765 0.536204 0.268102 0.963391i \(-0.413604\pi\)
0.268102 + 0.963391i \(0.413604\pi\)
\(740\) 7.39386 0.271804
\(741\) −3.77497 −0.138677
\(742\) 73.3175 2.69157
\(743\) 39.8004 1.46014 0.730068 0.683375i \(-0.239488\pi\)
0.730068 + 0.683375i \(0.239488\pi\)
\(744\) 31.0911 1.13986
\(745\) −19.6591 −0.720254
\(746\) −27.2375 −0.997236
\(747\) 12.0833 0.442106
\(748\) 85.3642 3.12123
\(749\) −11.1271 −0.406575
\(750\) 34.2402 1.25028
\(751\) 15.8084 0.576856 0.288428 0.957502i \(-0.406867\pi\)
0.288428 + 0.957502i \(0.406867\pi\)
\(752\) −7.40391 −0.269993
\(753\) 22.7288 0.828282
\(754\) 6.39059 0.232732
\(755\) 11.8557 0.431474
\(756\) 100.579 3.65803
\(757\) −13.0670 −0.474930 −0.237465 0.971396i \(-0.576316\pi\)
−0.237465 + 0.971396i \(0.576316\pi\)
\(758\) 79.6167 2.89181
\(759\) 20.3559 0.738871
\(760\) −15.7437 −0.571084
\(761\) −38.6858 −1.40236 −0.701179 0.712986i \(-0.747342\pi\)
−0.701179 + 0.712986i \(0.747342\pi\)
\(762\) −14.0321 −0.508328
\(763\) −10.5328 −0.381312
\(764\) −27.6748 −1.00124
\(765\) −11.5802 −0.418682
\(766\) 23.7816 0.859263
\(767\) −11.6259 −0.419785
\(768\) 29.0226 1.04726
\(769\) 19.2220 0.693162 0.346581 0.938020i \(-0.387343\pi\)
0.346581 + 0.938020i \(0.387343\pi\)
\(770\) −81.2674 −2.92867
\(771\) 1.72681 0.0621896
\(772\) 77.7601 2.79865
\(773\) −16.2179 −0.583319 −0.291659 0.956522i \(-0.594207\pi\)
−0.291659 + 0.956522i \(0.594207\pi\)
\(774\) 14.8891 0.535179
\(775\) −19.4695 −0.699364
\(776\) −32.1694 −1.15482
\(777\) 9.20726 0.330308
\(778\) 58.2596 2.08871
\(779\) −5.10819 −0.183020
\(780\) −6.57825 −0.235539
\(781\) −47.8360 −1.71171
\(782\) 46.2787 1.65492
\(783\) 15.1483 0.541358
\(784\) 24.3206 0.868594
\(785\) −12.6135 −0.450197
\(786\) −18.5616 −0.662069
\(787\) −37.8250 −1.34832 −0.674159 0.738587i \(-0.735494\pi\)
−0.674159 + 0.738587i \(0.735494\pi\)
\(788\) −2.65111 −0.0944420
\(789\) −9.47216 −0.337218
\(790\) −44.0633 −1.56770
\(791\) 33.5261 1.19205
\(792\) −22.2441 −0.790410
\(793\) −12.3219 −0.437562
\(794\) −47.6319 −1.69039
\(795\) −11.3667 −0.403135
\(796\) −33.1679 −1.17560
\(797\) −27.0933 −0.959692 −0.479846 0.877353i \(-0.659308\pi\)
−0.479846 + 0.877353i \(0.659308\pi\)
\(798\) −45.8235 −1.62213
\(799\) 32.9200 1.16462
\(800\) −11.4151 −0.403586
\(801\) 17.9725 0.635027
\(802\) 69.9307 2.46934
\(803\) −26.9722 −0.951829
\(804\) 24.5173 0.864658
\(805\) −28.0236 −0.987702
\(806\) 16.5292 0.582215
\(807\) 19.2518 0.677694
\(808\) 6.94297 0.244253
\(809\) −0.0911982 −0.00320636 −0.00160318 0.999999i \(-0.500510\pi\)
−0.00160318 + 0.999999i \(0.500510\pi\)
\(810\) −9.59354 −0.337083
\(811\) −46.4495 −1.63106 −0.815530 0.578714i \(-0.803555\pi\)
−0.815530 + 0.578714i \(0.803555\pi\)
\(812\) 49.3422 1.73157
\(813\) −12.6886 −0.445010
\(814\) −14.8287 −0.519746
\(815\) 15.8720 0.555973
\(816\) 8.42665 0.294992
\(817\) −13.4430 −0.470310
\(818\) 80.4436 2.81264
\(819\) 7.34271 0.256575
\(820\) −8.90151 −0.310854
\(821\) 1.00932 0.0352254 0.0176127 0.999845i \(-0.494393\pi\)
0.0176127 + 0.999845i \(0.494393\pi\)
\(822\) 35.2738 1.23031
\(823\) −45.9688 −1.60237 −0.801187 0.598415i \(-0.795798\pi\)
−0.801187 + 0.598415i \(0.795798\pi\)
\(824\) 2.99681 0.104399
\(825\) −15.5398 −0.541027
\(826\) −141.124 −4.91032
\(827\) −22.5703 −0.784845 −0.392423 0.919785i \(-0.628363\pi\)
−0.392423 + 0.919785i \(0.628363\pi\)
\(828\) −17.9286 −0.623061
\(829\) −0.880382 −0.0305769 −0.0152885 0.999883i \(-0.504867\pi\)
−0.0152885 + 0.999883i \(0.504867\pi\)
\(830\) −29.8887 −1.03745
\(831\) −3.50327 −0.121527
\(832\) 12.1462 0.421095
\(833\) −108.137 −3.74672
\(834\) 31.6751 1.09682
\(835\) −10.1752 −0.352126
\(836\) 46.9422 1.62353
\(837\) 39.1809 1.35429
\(838\) 20.3523 0.703058
\(839\) 0.0872672 0.00301280 0.00150640 0.999999i \(-0.499520\pi\)
0.00150640 + 0.999999i \(0.499520\pi\)
\(840\) −34.1635 −1.17875
\(841\) −21.5685 −0.743742
\(842\) −54.3501 −1.87303
\(843\) 29.3991 1.01256
\(844\) 72.1551 2.48368
\(845\) −1.49624 −0.0514723
\(846\) −20.0503 −0.689344
\(847\) 46.7101 1.60498
\(848\) −7.41415 −0.254603
\(849\) 9.61642 0.330035
\(850\) −35.3295 −1.21179
\(851\) −5.11341 −0.175285
\(852\) −47.0028 −1.61029
\(853\) 52.7980 1.80777 0.903885 0.427776i \(-0.140703\pi\)
0.903885 + 0.427776i \(0.140703\pi\)
\(854\) −149.572 −5.11826
\(855\) −6.36798 −0.217780
\(856\) 7.53356 0.257492
\(857\) 32.7020 1.11708 0.558539 0.829478i \(-0.311362\pi\)
0.558539 + 0.829478i \(0.311362\pi\)
\(858\) 13.1930 0.450400
\(859\) −23.0327 −0.785866 −0.392933 0.919567i \(-0.628540\pi\)
−0.392933 + 0.919567i \(0.628540\pi\)
\(860\) −23.4257 −0.798809
\(861\) −11.0847 −0.377765
\(862\) 61.4491 2.09296
\(863\) 24.3247 0.828022 0.414011 0.910272i \(-0.364128\pi\)
0.414011 + 0.910272i \(0.364128\pi\)
\(864\) 22.9722 0.781529
\(865\) 28.0224 0.952791
\(866\) −58.6169 −1.99189
\(867\) −16.0854 −0.546289
\(868\) 127.623 4.33179
\(869\) 56.2097 1.90678
\(870\) −12.0266 −0.407739
\(871\) 5.57653 0.188953
\(872\) 7.13119 0.241493
\(873\) −13.0118 −0.440384
\(874\) 25.4489 0.860821
\(875\) 60.1320 2.03283
\(876\) −26.5024 −0.895434
\(877\) −51.6789 −1.74507 −0.872536 0.488550i \(-0.837526\pi\)
−0.872536 + 0.488550i \(0.837526\pi\)
\(878\) −61.8332 −2.08677
\(879\) 20.5289 0.692423
\(880\) 8.21808 0.277031
\(881\) −10.5804 −0.356462 −0.178231 0.983989i \(-0.557037\pi\)
−0.178231 + 0.983989i \(0.557037\pi\)
\(882\) 65.8621 2.21769
\(883\) 25.3609 0.853461 0.426731 0.904379i \(-0.359665\pi\)
0.426731 + 0.904379i \(0.359665\pi\)
\(884\) 19.0782 0.641668
\(885\) 21.8789 0.735452
\(886\) −98.1545 −3.29756
\(887\) 57.0846 1.91671 0.958357 0.285573i \(-0.0921838\pi\)
0.958357 + 0.285573i \(0.0921838\pi\)
\(888\) −6.23375 −0.209191
\(889\) −24.6428 −0.826494
\(890\) −44.4558 −1.49016
\(891\) 12.2381 0.409991
\(892\) −21.3630 −0.715285
\(893\) 18.1028 0.605788
\(894\) 38.7404 1.29567
\(895\) 5.65511 0.189029
\(896\) 104.628 3.49536
\(897\) 4.54936 0.151899
\(898\) −60.1755 −2.00808
\(899\) 19.2214 0.641069
\(900\) 13.6868 0.456226
\(901\) 32.9655 1.09824
\(902\) 17.8524 0.594419
\(903\) −29.1710 −0.970750
\(904\) −22.6987 −0.754948
\(905\) 20.0088 0.665115
\(906\) −23.3630 −0.776184
\(907\) −15.1131 −0.501823 −0.250912 0.968010i \(-0.580730\pi\)
−0.250912 + 0.968010i \(0.580730\pi\)
\(908\) −70.8088 −2.34987
\(909\) 2.80828 0.0931448
\(910\) −18.1626 −0.602083
\(911\) −51.4967 −1.70616 −0.853081 0.521778i \(-0.825269\pi\)
−0.853081 + 0.521778i \(0.825269\pi\)
\(912\) 4.63385 0.153442
\(913\) 38.1277 1.26184
\(914\) 82.4833 2.72830
\(915\) 23.1888 0.766597
\(916\) −54.1952 −1.79066
\(917\) −32.5974 −1.07646
\(918\) 71.0982 2.34659
\(919\) −32.7125 −1.07908 −0.539542 0.841958i \(-0.681403\pi\)
−0.539542 + 0.841958i \(0.681403\pi\)
\(920\) 18.9733 0.625531
\(921\) 16.3644 0.539224
\(922\) 11.6812 0.384699
\(923\) −10.6909 −0.351896
\(924\) 101.864 3.35107
\(925\) 3.90361 0.128350
\(926\) 2.34425 0.0770368
\(927\) 1.21215 0.0398121
\(928\) 11.2697 0.369945
\(929\) −36.3485 −1.19256 −0.596278 0.802778i \(-0.703355\pi\)
−0.596278 + 0.802778i \(0.703355\pi\)
\(930\) −31.1065 −1.02002
\(931\) −59.4649 −1.94888
\(932\) 29.2694 0.958750
\(933\) −38.5068 −1.26066
\(934\) 16.8176 0.550288
\(935\) −36.5400 −1.19499
\(936\) −4.97136 −0.162494
\(937\) 41.9524 1.37052 0.685262 0.728297i \(-0.259688\pi\)
0.685262 + 0.728297i \(0.259688\pi\)
\(938\) 67.6922 2.21023
\(939\) −14.6825 −0.479145
\(940\) 31.5460 1.02892
\(941\) 8.16376 0.266131 0.133065 0.991107i \(-0.457518\pi\)
0.133065 + 0.991107i \(0.457518\pi\)
\(942\) 24.8564 0.809864
\(943\) 6.15607 0.200469
\(944\) 14.2710 0.464481
\(945\) −43.0528 −1.40051
\(946\) 46.9812 1.52749
\(947\) 33.2129 1.07927 0.539637 0.841898i \(-0.318561\pi\)
0.539637 + 0.841898i \(0.318561\pi\)
\(948\) 55.2306 1.79381
\(949\) −6.02805 −0.195679
\(950\) −19.4279 −0.630323
\(951\) −1.47240 −0.0477457
\(952\) 99.0805 3.21122
\(953\) 50.3911 1.63233 0.816164 0.577821i \(-0.196097\pi\)
0.816164 + 0.577821i \(0.196097\pi\)
\(954\) −20.0781 −0.650051
\(955\) 11.8462 0.383333
\(956\) 17.0558 0.551623
\(957\) 15.3418 0.495930
\(958\) −58.1221 −1.87784
\(959\) 61.9470 2.00037
\(960\) −22.8583 −0.737747
\(961\) 18.7157 0.603734
\(962\) −3.31408 −0.106850
\(963\) 3.04716 0.0981934
\(964\) −4.24848 −0.136834
\(965\) −33.2851 −1.07148
\(966\) 55.2236 1.77679
\(967\) −30.5047 −0.980965 −0.490483 0.871451i \(-0.663179\pi\)
−0.490483 + 0.871451i \(0.663179\pi\)
\(968\) −31.6249 −1.01646
\(969\) −20.6035 −0.661879
\(970\) 32.1854 1.03341
\(971\) −37.9650 −1.21835 −0.609177 0.793034i \(-0.708500\pi\)
−0.609177 + 0.793034i \(0.708500\pi\)
\(972\) −46.2469 −1.48337
\(973\) 55.6270 1.78332
\(974\) 57.6863 1.84839
\(975\) −3.47301 −0.111225
\(976\) 15.1253 0.484151
\(977\) 5.70479 0.182512 0.0912561 0.995827i \(-0.470912\pi\)
0.0912561 + 0.995827i \(0.470912\pi\)
\(978\) −31.2776 −1.00015
\(979\) 56.7104 1.81247
\(980\) −103.623 −3.31013
\(981\) 2.88441 0.0920922
\(982\) −69.2796 −2.21080
\(983\) −14.9043 −0.475375 −0.237687 0.971342i \(-0.576389\pi\)
−0.237687 + 0.971342i \(0.576389\pi\)
\(984\) 7.50484 0.239246
\(985\) 1.13480 0.0361579
\(986\) 34.8793 1.11078
\(987\) 39.2828 1.25039
\(988\) 10.4912 0.333768
\(989\) 16.2006 0.515150
\(990\) 22.2552 0.707315
\(991\) 19.4828 0.618892 0.309446 0.950917i \(-0.399856\pi\)
0.309446 + 0.950917i \(0.399856\pi\)
\(992\) 29.1488 0.925476
\(993\) 12.8210 0.406863
\(994\) −129.775 −4.11621
\(995\) 14.1975 0.450090
\(996\) 37.4636 1.18708
\(997\) 16.8761 0.534473 0.267236 0.963631i \(-0.413890\pi\)
0.267236 + 0.963631i \(0.413890\pi\)
\(998\) −19.4810 −0.616661
\(999\) −7.85575 −0.248545
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 \(a_p\))