Properties

Label 4019.2.a.b.1.8
Level 4019
Weight 2
Character 4019.1
Self dual Yes
Analytic conductor 32.092
Analytic rank 0
Dimension 186
CM No

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Newspace parameters

Level: \( N \) = \( 4019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0918765724\)
Analytic rank: \(0\)
Dimension: \(186\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.67918 q^{2}\) \(+1.79491 q^{3}\) \(+5.17799 q^{4}\) \(+3.40719 q^{5}\) \(-4.80888 q^{6}\) \(+4.24264 q^{7}\) \(-8.51439 q^{8}\) \(+0.221695 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.67918 q^{2}\) \(+1.79491 q^{3}\) \(+5.17799 q^{4}\) \(+3.40719 q^{5}\) \(-4.80888 q^{6}\) \(+4.24264 q^{7}\) \(-8.51439 q^{8}\) \(+0.221695 q^{9}\) \(-9.12846 q^{10}\) \(+2.35460 q^{11}\) \(+9.29401 q^{12}\) \(-0.771756 q^{13}\) \(-11.3668 q^{14}\) \(+6.11559 q^{15}\) \(+12.4556 q^{16}\) \(-0.943428 q^{17}\) \(-0.593959 q^{18}\) \(+0.177774 q^{19}\) \(+17.6424 q^{20}\) \(+7.61515 q^{21}\) \(-6.30838 q^{22}\) \(+4.24430 q^{23}\) \(-15.2825 q^{24}\) \(+6.60893 q^{25}\) \(+2.06767 q^{26}\) \(-4.98680 q^{27}\) \(+21.9683 q^{28}\) \(-3.76412 q^{29}\) \(-16.3847 q^{30}\) \(+1.56412 q^{31}\) \(-16.3419 q^{32}\) \(+4.22628 q^{33}\) \(+2.52761 q^{34}\) \(+14.4555 q^{35}\) \(+1.14793 q^{36}\) \(-4.89927 q^{37}\) \(-0.476289 q^{38}\) \(-1.38523 q^{39}\) \(-29.0101 q^{40}\) \(+5.04113 q^{41}\) \(-20.4023 q^{42}\) \(+2.14408 q^{43}\) \(+12.1921 q^{44}\) \(+0.755355 q^{45}\) \(-11.3712 q^{46}\) \(-2.93352 q^{47}\) \(+22.3566 q^{48}\) \(+11.0000 q^{49}\) \(-17.7065 q^{50}\) \(-1.69337 q^{51}\) \(-3.99614 q^{52}\) \(-5.59078 q^{53}\) \(+13.3605 q^{54}\) \(+8.02255 q^{55}\) \(-36.1235 q^{56}\) \(+0.319089 q^{57}\) \(+10.0847 q^{58}\) \(-10.0882 q^{59}\) \(+31.6664 q^{60}\) \(+4.00902 q^{61}\) \(-4.19056 q^{62}\) \(+0.940570 q^{63}\) \(+18.8717 q^{64}\) \(-2.62952 q^{65}\) \(-11.3230 q^{66}\) \(-5.93967 q^{67}\) \(-4.88506 q^{68}\) \(+7.61813 q^{69}\) \(-38.7288 q^{70}\) \(+0.981034 q^{71}\) \(-1.88759 q^{72}\) \(+12.6623 q^{73}\) \(+13.1260 q^{74}\) \(+11.8624 q^{75}\) \(+0.920513 q^{76}\) \(+9.98970 q^{77}\) \(+3.71128 q^{78}\) \(+8.26770 q^{79}\) \(+42.4385 q^{80}\) \(-9.61594 q^{81}\) \(-13.5061 q^{82}\) \(+2.07952 q^{83}\) \(+39.4311 q^{84}\) \(-3.21444 q^{85}\) \(-5.74437 q^{86}\) \(-6.75625 q^{87}\) \(-20.0479 q^{88}\) \(+10.1165 q^{89}\) \(-2.02373 q^{90}\) \(-3.27428 q^{91}\) \(+21.9769 q^{92}\) \(+2.80746 q^{93}\) \(+7.85941 q^{94}\) \(+0.605711 q^{95}\) \(-29.3322 q^{96}\) \(+6.37714 q^{97}\) \(-29.4709 q^{98}\) \(+0.522001 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.67918 −1.89446 −0.947232 0.320549i \(-0.896133\pi\)
−0.947232 + 0.320549i \(0.896133\pi\)
\(3\) 1.79491 1.03629 0.518145 0.855293i \(-0.326623\pi\)
0.518145 + 0.855293i \(0.326623\pi\)
\(4\) 5.17799 2.58899
\(5\) 3.40719 1.52374 0.761870 0.647729i \(-0.224281\pi\)
0.761870 + 0.647729i \(0.224281\pi\)
\(6\) −4.80888 −1.96322
\(7\) 4.24264 1.60357 0.801784 0.597615i \(-0.203885\pi\)
0.801784 + 0.597615i \(0.203885\pi\)
\(8\) −8.51439 −3.01029
\(9\) 0.221695 0.0738982
\(10\) −9.12846 −2.88667
\(11\) 2.35460 0.709937 0.354969 0.934878i \(-0.384492\pi\)
0.354969 + 0.934878i \(0.384492\pi\)
\(12\) 9.29401 2.68295
\(13\) −0.771756 −0.214047 −0.107023 0.994257i \(-0.534132\pi\)
−0.107023 + 0.994257i \(0.534132\pi\)
\(14\) −11.3668 −3.03790
\(15\) 6.11559 1.57904
\(16\) 12.4556 3.11389
\(17\) −0.943428 −0.228815 −0.114407 0.993434i \(-0.536497\pi\)
−0.114407 + 0.993434i \(0.536497\pi\)
\(18\) −0.593959 −0.139997
\(19\) 0.177774 0.0407842 0.0203921 0.999792i \(-0.493509\pi\)
0.0203921 + 0.999792i \(0.493509\pi\)
\(20\) 17.6424 3.94496
\(21\) 7.61515 1.66176
\(22\) −6.30838 −1.34495
\(23\) 4.24430 0.884998 0.442499 0.896769i \(-0.354092\pi\)
0.442499 + 0.896769i \(0.354092\pi\)
\(24\) −15.2825 −3.11954
\(25\) 6.60893 1.32179
\(26\) 2.06767 0.405504
\(27\) −4.98680 −0.959711
\(28\) 21.9683 4.15163
\(29\) −3.76412 −0.698979 −0.349490 0.936940i \(-0.613645\pi\)
−0.349490 + 0.936940i \(0.613645\pi\)
\(30\) −16.3847 −2.99143
\(31\) 1.56412 0.280925 0.140462 0.990086i \(-0.455141\pi\)
0.140462 + 0.990086i \(0.455141\pi\)
\(32\) −16.3419 −2.88887
\(33\) 4.22628 0.735701
\(34\) 2.52761 0.433481
\(35\) 14.4555 2.44342
\(36\) 1.14793 0.191322
\(37\) −4.89927 −0.805435 −0.402718 0.915324i \(-0.631934\pi\)
−0.402718 + 0.915324i \(0.631934\pi\)
\(38\) −0.476289 −0.0772642
\(39\) −1.38523 −0.221815
\(40\) −29.0101 −4.58690
\(41\) 5.04113 0.787293 0.393646 0.919262i \(-0.371213\pi\)
0.393646 + 0.919262i \(0.371213\pi\)
\(42\) −20.4023 −3.14815
\(43\) 2.14408 0.326969 0.163485 0.986546i \(-0.447727\pi\)
0.163485 + 0.986546i \(0.447727\pi\)
\(44\) 12.1921 1.83802
\(45\) 0.755355 0.112602
\(46\) −11.3712 −1.67660
\(47\) −2.93352 −0.427897 −0.213949 0.976845i \(-0.568632\pi\)
−0.213949 + 0.976845i \(0.568632\pi\)
\(48\) 22.3566 3.22690
\(49\) 11.0000 1.57143
\(50\) −17.7065 −2.50408
\(51\) −1.69337 −0.237119
\(52\) −3.99614 −0.554165
\(53\) −5.59078 −0.767953 −0.383977 0.923343i \(-0.625446\pi\)
−0.383977 + 0.923343i \(0.625446\pi\)
\(54\) 13.3605 1.81814
\(55\) 8.02255 1.08176
\(56\) −36.1235 −4.82720
\(57\) 0.319089 0.0422643
\(58\) 10.0847 1.32419
\(59\) −10.0882 −1.31337 −0.656683 0.754167i \(-0.728041\pi\)
−0.656683 + 0.754167i \(0.728041\pi\)
\(60\) 31.6664 4.08812
\(61\) 4.00902 0.513303 0.256651 0.966504i \(-0.417381\pi\)
0.256651 + 0.966504i \(0.417381\pi\)
\(62\) −4.19056 −0.532202
\(63\) 0.940570 0.118501
\(64\) 18.8717 2.35897
\(65\) −2.62952 −0.326152
\(66\) −11.3230 −1.39376
\(67\) −5.93967 −0.725646 −0.362823 0.931858i \(-0.618187\pi\)
−0.362823 + 0.931858i \(0.618187\pi\)
\(68\) −4.88506 −0.592400
\(69\) 7.61813 0.917115
\(70\) −38.7288 −4.62897
\(71\) 0.981034 0.116427 0.0582137 0.998304i \(-0.481460\pi\)
0.0582137 + 0.998304i \(0.481460\pi\)
\(72\) −1.88759 −0.222455
\(73\) 12.6623 1.48200 0.741002 0.671502i \(-0.234351\pi\)
0.741002 + 0.671502i \(0.234351\pi\)
\(74\) 13.1260 1.52587
\(75\) 11.8624 1.36975
\(76\) 0.920513 0.105590
\(77\) 9.98970 1.13843
\(78\) 3.71128 0.420220
\(79\) 8.26770 0.930189 0.465094 0.885261i \(-0.346020\pi\)
0.465094 + 0.885261i \(0.346020\pi\)
\(80\) 42.4385 4.74477
\(81\) −9.61594 −1.06844
\(82\) −13.5061 −1.49150
\(83\) 2.07952 0.228257 0.114129 0.993466i \(-0.463592\pi\)
0.114129 + 0.993466i \(0.463592\pi\)
\(84\) 39.4311 4.30229
\(85\) −3.21444 −0.348654
\(86\) −5.74437 −0.619432
\(87\) −6.75625 −0.724346
\(88\) −20.0479 −2.13712
\(89\) 10.1165 1.07235 0.536176 0.844106i \(-0.319868\pi\)
0.536176 + 0.844106i \(0.319868\pi\)
\(90\) −2.02373 −0.213320
\(91\) −3.27428 −0.343238
\(92\) 21.9769 2.29125
\(93\) 2.80746 0.291120
\(94\) 7.85941 0.810636
\(95\) 0.605711 0.0621446
\(96\) −29.3322 −2.99371
\(97\) 6.37714 0.647500 0.323750 0.946143i \(-0.395056\pi\)
0.323750 + 0.946143i \(0.395056\pi\)
\(98\) −29.4709 −2.97701
\(99\) 0.522001 0.0524631
\(100\) 34.2210 3.42210
\(101\) 3.74303 0.372446 0.186223 0.982508i \(-0.440375\pi\)
0.186223 + 0.982508i \(0.440375\pi\)
\(102\) 4.53683 0.449213
\(103\) 15.4160 1.51898 0.759491 0.650518i \(-0.225448\pi\)
0.759491 + 0.650518i \(0.225448\pi\)
\(104\) 6.57103 0.644343
\(105\) 25.9462 2.53209
\(106\) 14.9787 1.45486
\(107\) 9.38689 0.907465 0.453733 0.891138i \(-0.350092\pi\)
0.453733 + 0.891138i \(0.350092\pi\)
\(108\) −25.8216 −2.48468
\(109\) 6.78692 0.650069 0.325035 0.945702i \(-0.394624\pi\)
0.325035 + 0.945702i \(0.394624\pi\)
\(110\) −21.4938 −2.04936
\(111\) −8.79374 −0.834665
\(112\) 52.8445 4.99334
\(113\) −12.7958 −1.20373 −0.601865 0.798598i \(-0.705576\pi\)
−0.601865 + 0.798598i \(0.705576\pi\)
\(114\) −0.854895 −0.0800682
\(115\) 14.4611 1.34851
\(116\) −19.4906 −1.80965
\(117\) −0.171094 −0.0158177
\(118\) 27.0279 2.48812
\(119\) −4.00262 −0.366920
\(120\) −52.0705 −4.75337
\(121\) −5.45588 −0.495989
\(122\) −10.7409 −0.972433
\(123\) 9.04837 0.815864
\(124\) 8.09901 0.727313
\(125\) 5.48193 0.490319
\(126\) −2.51995 −0.224495
\(127\) 16.2045 1.43791 0.718957 0.695055i \(-0.244620\pi\)
0.718957 + 0.695055i \(0.244620\pi\)
\(128\) −17.8768 −1.58010
\(129\) 3.84843 0.338835
\(130\) 7.04494 0.617882
\(131\) −11.4044 −0.996411 −0.498205 0.867059i \(-0.666007\pi\)
−0.498205 + 0.867059i \(0.666007\pi\)
\(132\) 21.8836 1.90473
\(133\) 0.754232 0.0654002
\(134\) 15.9134 1.37471
\(135\) −16.9910 −1.46235
\(136\) 8.03271 0.688799
\(137\) −10.4134 −0.889674 −0.444837 0.895612i \(-0.646738\pi\)
−0.444837 + 0.895612i \(0.646738\pi\)
\(138\) −20.4103 −1.73744
\(139\) 22.2147 1.88422 0.942111 0.335301i \(-0.108838\pi\)
0.942111 + 0.335301i \(0.108838\pi\)
\(140\) 74.8503 6.32600
\(141\) −5.26539 −0.443426
\(142\) −2.62836 −0.220567
\(143\) −1.81717 −0.151960
\(144\) 2.76133 0.230111
\(145\) −12.8251 −1.06506
\(146\) −33.9244 −2.80760
\(147\) 19.7440 1.62846
\(148\) −25.3684 −2.08527
\(149\) 18.7095 1.53274 0.766370 0.642399i \(-0.222061\pi\)
0.766370 + 0.642399i \(0.222061\pi\)
\(150\) −31.7815 −2.59495
\(151\) −9.87583 −0.803683 −0.401842 0.915709i \(-0.631630\pi\)
−0.401842 + 0.915709i \(0.631630\pi\)
\(152\) −1.51364 −0.122772
\(153\) −0.209153 −0.0169090
\(154\) −26.7642 −2.15672
\(155\) 5.32926 0.428057
\(156\) −7.17271 −0.574276
\(157\) −4.99671 −0.398781 −0.199390 0.979920i \(-0.563896\pi\)
−0.199390 + 0.979920i \(0.563896\pi\)
\(158\) −22.1506 −1.76221
\(159\) −10.0349 −0.795823
\(160\) −55.6800 −4.40189
\(161\) 18.0070 1.41915
\(162\) 25.7628 2.02412
\(163\) 17.3381 1.35802 0.679012 0.734127i \(-0.262408\pi\)
0.679012 + 0.734127i \(0.262408\pi\)
\(164\) 26.1029 2.03830
\(165\) 14.3997 1.12102
\(166\) −5.57141 −0.432425
\(167\) 11.9365 0.923673 0.461836 0.886965i \(-0.347191\pi\)
0.461836 + 0.886965i \(0.347191\pi\)
\(168\) −64.8383 −5.00239
\(169\) −12.4044 −0.954184
\(170\) 8.61204 0.660513
\(171\) 0.0394116 0.00301388
\(172\) 11.1020 0.846522
\(173\) −11.1659 −0.848925 −0.424462 0.905446i \(-0.639537\pi\)
−0.424462 + 0.905446i \(0.639537\pi\)
\(174\) 18.1012 1.37225
\(175\) 28.0393 2.11957
\(176\) 29.3279 2.21067
\(177\) −18.1073 −1.36103
\(178\) −27.1040 −2.03153
\(179\) −21.7682 −1.62703 −0.813517 0.581541i \(-0.802450\pi\)
−0.813517 + 0.581541i \(0.802450\pi\)
\(180\) 3.91122 0.291525
\(181\) −18.6499 −1.38624 −0.693118 0.720824i \(-0.743764\pi\)
−0.693118 + 0.720824i \(0.743764\pi\)
\(182\) 8.77238 0.650252
\(183\) 7.19582 0.531931
\(184\) −36.1376 −2.66410
\(185\) −16.6927 −1.22727
\(186\) −7.52167 −0.551516
\(187\) −2.22139 −0.162444
\(188\) −15.1897 −1.10782
\(189\) −21.1572 −1.53896
\(190\) −1.62281 −0.117731
\(191\) 23.1125 1.67236 0.836179 0.548456i \(-0.184784\pi\)
0.836179 + 0.548456i \(0.184784\pi\)
\(192\) 33.8730 2.44457
\(193\) −4.25147 −0.306027 −0.153014 0.988224i \(-0.548898\pi\)
−0.153014 + 0.988224i \(0.548898\pi\)
\(194\) −17.0855 −1.22667
\(195\) −4.71974 −0.337988
\(196\) 56.9578 4.06842
\(197\) −12.7225 −0.906444 −0.453222 0.891398i \(-0.649726\pi\)
−0.453222 + 0.891398i \(0.649726\pi\)
\(198\) −1.39853 −0.0993894
\(199\) 5.39041 0.382116 0.191058 0.981579i \(-0.438808\pi\)
0.191058 + 0.981579i \(0.438808\pi\)
\(200\) −56.2710 −3.97896
\(201\) −10.6612 −0.751980
\(202\) −10.0282 −0.705585
\(203\) −15.9698 −1.12086
\(204\) −8.76823 −0.613899
\(205\) 17.1761 1.19963
\(206\) −41.3021 −2.87766
\(207\) 0.940938 0.0653997
\(208\) −9.61267 −0.666519
\(209\) 0.418587 0.0289542
\(210\) −69.5146 −4.79696
\(211\) 13.0974 0.901665 0.450833 0.892609i \(-0.351127\pi\)
0.450833 + 0.892609i \(0.351127\pi\)
\(212\) −28.9490 −1.98823
\(213\) 1.76087 0.120653
\(214\) −25.1491 −1.71916
\(215\) 7.30529 0.498217
\(216\) 42.4596 2.88901
\(217\) 6.63601 0.450482
\(218\) −18.1834 −1.23153
\(219\) 22.7276 1.53579
\(220\) 41.5407 2.80067
\(221\) 0.728096 0.0489770
\(222\) 23.5600 1.58124
\(223\) −8.97763 −0.601187 −0.300593 0.953752i \(-0.597185\pi\)
−0.300593 + 0.953752i \(0.597185\pi\)
\(224\) −69.3329 −4.63250
\(225\) 1.46516 0.0976776
\(226\) 34.2823 2.28042
\(227\) −9.42563 −0.625601 −0.312801 0.949819i \(-0.601267\pi\)
−0.312801 + 0.949819i \(0.601267\pi\)
\(228\) 1.65224 0.109422
\(229\) 11.2643 0.744366 0.372183 0.928159i \(-0.378609\pi\)
0.372183 + 0.928159i \(0.378609\pi\)
\(230\) −38.7439 −2.55470
\(231\) 17.9306 1.17975
\(232\) 32.0492 2.10413
\(233\) −7.74021 −0.507078 −0.253539 0.967325i \(-0.581595\pi\)
−0.253539 + 0.967325i \(0.581595\pi\)
\(234\) 0.458391 0.0299660
\(235\) −9.99504 −0.652004
\(236\) −52.2363 −3.40030
\(237\) 14.8398 0.963946
\(238\) 10.7237 0.695117
\(239\) −19.7048 −1.27460 −0.637299 0.770617i \(-0.719948\pi\)
−0.637299 + 0.770617i \(0.719948\pi\)
\(240\) 76.1732 4.91696
\(241\) −22.2796 −1.43515 −0.717577 0.696480i \(-0.754749\pi\)
−0.717577 + 0.696480i \(0.754749\pi\)
\(242\) 14.6173 0.939633
\(243\) −2.29931 −0.147501
\(244\) 20.7587 1.32894
\(245\) 37.4790 2.39445
\(246\) −24.2422 −1.54562
\(247\) −0.137198 −0.00872973
\(248\) −13.3176 −0.845666
\(249\) 3.73255 0.236541
\(250\) −14.6871 −0.928892
\(251\) 7.14696 0.451112 0.225556 0.974230i \(-0.427580\pi\)
0.225556 + 0.974230i \(0.427580\pi\)
\(252\) 4.87026 0.306798
\(253\) 9.99361 0.628293
\(254\) −43.4146 −2.72408
\(255\) −5.76962 −0.361307
\(256\) 10.1518 0.634486
\(257\) −27.7660 −1.73200 −0.865999 0.500046i \(-0.833317\pi\)
−0.865999 + 0.500046i \(0.833317\pi\)
\(258\) −10.3106 −0.641911
\(259\) −20.7858 −1.29157
\(260\) −13.6156 −0.844404
\(261\) −0.834485 −0.0516533
\(262\) 30.5545 1.88766
\(263\) −10.3906 −0.640714 −0.320357 0.947297i \(-0.603803\pi\)
−0.320357 + 0.947297i \(0.603803\pi\)
\(264\) −35.9842 −2.21468
\(265\) −19.0488 −1.17016
\(266\) −2.02072 −0.123898
\(267\) 18.1583 1.11127
\(268\) −30.7555 −1.87869
\(269\) 6.80874 0.415136 0.207568 0.978221i \(-0.433445\pi\)
0.207568 + 0.978221i \(0.433445\pi\)
\(270\) 45.5218 2.77037
\(271\) −18.4643 −1.12163 −0.560813 0.827942i \(-0.689512\pi\)
−0.560813 + 0.827942i \(0.689512\pi\)
\(272\) −11.7509 −0.712505
\(273\) −5.87704 −0.355694
\(274\) 27.8992 1.68545
\(275\) 15.5614 0.938385
\(276\) 39.4466 2.37440
\(277\) 21.1513 1.27086 0.635428 0.772160i \(-0.280824\pi\)
0.635428 + 0.772160i \(0.280824\pi\)
\(278\) −59.5170 −3.56959
\(279\) 0.346758 0.0207598
\(280\) −123.080 −7.35541
\(281\) −1.12876 −0.0673359 −0.0336680 0.999433i \(-0.510719\pi\)
−0.0336680 + 0.999433i \(0.510719\pi\)
\(282\) 14.1069 0.840054
\(283\) 8.47831 0.503983 0.251992 0.967729i \(-0.418914\pi\)
0.251992 + 0.967729i \(0.418914\pi\)
\(284\) 5.07978 0.301430
\(285\) 1.08719 0.0643999
\(286\) 4.86853 0.287882
\(287\) 21.3877 1.26248
\(288\) −3.62291 −0.213482
\(289\) −16.1099 −0.947644
\(290\) 34.3606 2.01772
\(291\) 11.4464 0.670998
\(292\) 65.5650 3.83690
\(293\) −31.1792 −1.82151 −0.910755 0.412948i \(-0.864499\pi\)
−0.910755 + 0.412948i \(0.864499\pi\)
\(294\) −52.8976 −3.08505
\(295\) −34.3722 −2.00123
\(296\) 41.7143 2.42459
\(297\) −11.7419 −0.681334
\(298\) −50.1260 −2.90372
\(299\) −3.27556 −0.189431
\(300\) 61.4235 3.54629
\(301\) 9.09656 0.524317
\(302\) 26.4591 1.52255
\(303\) 6.71840 0.385962
\(304\) 2.21428 0.126998
\(305\) 13.6595 0.782140
\(306\) 0.560357 0.0320335
\(307\) −1.98032 −0.113023 −0.0565113 0.998402i \(-0.517998\pi\)
−0.0565113 + 0.998402i \(0.517998\pi\)
\(308\) 51.7265 2.94739
\(309\) 27.6703 1.57411
\(310\) −14.2780 −0.810938
\(311\) 6.38578 0.362104 0.181052 0.983474i \(-0.442050\pi\)
0.181052 + 0.983474i \(0.442050\pi\)
\(312\) 11.7944 0.667726
\(313\) −1.87494 −0.105978 −0.0529889 0.998595i \(-0.516875\pi\)
−0.0529889 + 0.998595i \(0.516875\pi\)
\(314\) 13.3871 0.755475
\(315\) 3.20470 0.180564
\(316\) 42.8100 2.40825
\(317\) −27.5822 −1.54917 −0.774586 0.632469i \(-0.782042\pi\)
−0.774586 + 0.632469i \(0.782042\pi\)
\(318\) 26.8854 1.50766
\(319\) −8.86298 −0.496232
\(320\) 64.2995 3.59445
\(321\) 16.8486 0.940398
\(322\) −48.2440 −2.68854
\(323\) −0.167717 −0.00933203
\(324\) −49.7912 −2.76618
\(325\) −5.10048 −0.282924
\(326\) −46.4518 −2.57273
\(327\) 12.1819 0.673661
\(328\) −42.9222 −2.36998
\(329\) −12.4458 −0.686162
\(330\) −38.5794 −2.12373
\(331\) −4.17007 −0.229208 −0.114604 0.993411i \(-0.536560\pi\)
−0.114604 + 0.993411i \(0.536560\pi\)
\(332\) 10.7677 0.590957
\(333\) −1.08614 −0.0595202
\(334\) −31.9799 −1.74986
\(335\) −20.2376 −1.10570
\(336\) 94.8511 5.17455
\(337\) −21.6223 −1.17784 −0.588922 0.808190i \(-0.700447\pi\)
−0.588922 + 0.808190i \(0.700447\pi\)
\(338\) 33.2336 1.80767
\(339\) −22.9673 −1.24741
\(340\) −16.6443 −0.902664
\(341\) 3.68288 0.199439
\(342\) −0.105591 −0.00570969
\(343\) 16.9705 0.916322
\(344\) −18.2555 −0.984273
\(345\) 25.9564 1.39745
\(346\) 29.9153 1.60826
\(347\) 29.2605 1.57079 0.785393 0.618997i \(-0.212461\pi\)
0.785393 + 0.618997i \(0.212461\pi\)
\(348\) −34.9838 −1.87533
\(349\) 9.16072 0.490362 0.245181 0.969477i \(-0.421153\pi\)
0.245181 + 0.969477i \(0.421153\pi\)
\(350\) −75.1223 −4.01545
\(351\) 3.84860 0.205423
\(352\) −38.4786 −2.05092
\(353\) 6.04329 0.321652 0.160826 0.986983i \(-0.448584\pi\)
0.160826 + 0.986983i \(0.448584\pi\)
\(354\) 48.5127 2.57842
\(355\) 3.34257 0.177405
\(356\) 52.3834 2.77631
\(357\) −7.18434 −0.380236
\(358\) 58.3209 3.08236
\(359\) 6.32835 0.333997 0.166999 0.985957i \(-0.446592\pi\)
0.166999 + 0.985957i \(0.446592\pi\)
\(360\) −6.43139 −0.338964
\(361\) −18.9684 −0.998337
\(362\) 49.9664 2.62618
\(363\) −9.79280 −0.513989
\(364\) −16.9542 −0.888641
\(365\) 43.1427 2.25819
\(366\) −19.2789 −1.00772
\(367\) −22.5970 −1.17955 −0.589777 0.807566i \(-0.700784\pi\)
−0.589777 + 0.807566i \(0.700784\pi\)
\(368\) 52.8652 2.75579
\(369\) 1.11759 0.0581795
\(370\) 44.7228 2.32503
\(371\) −23.7197 −1.23146
\(372\) 14.5370 0.753707
\(373\) 34.0143 1.76119 0.880597 0.473867i \(-0.157142\pi\)
0.880597 + 0.473867i \(0.157142\pi\)
\(374\) 5.95150 0.307745
\(375\) 9.83956 0.508113
\(376\) 24.9771 1.28810
\(377\) 2.90498 0.149614
\(378\) 56.6839 2.91550
\(379\) 5.66019 0.290745 0.145372 0.989377i \(-0.453562\pi\)
0.145372 + 0.989377i \(0.453562\pi\)
\(380\) 3.13636 0.160892
\(381\) 29.0855 1.49010
\(382\) −61.9223 −3.16822
\(383\) −6.25319 −0.319523 −0.159762 0.987156i \(-0.551073\pi\)
−0.159762 + 0.987156i \(0.551073\pi\)
\(384\) −32.0873 −1.63745
\(385\) 34.0368 1.73468
\(386\) 11.3904 0.579758
\(387\) 0.475331 0.0241624
\(388\) 33.0207 1.67637
\(389\) −8.86145 −0.449294 −0.224647 0.974440i \(-0.572123\pi\)
−0.224647 + 0.974440i \(0.572123\pi\)
\(390\) 12.6450 0.640306
\(391\) −4.00419 −0.202501
\(392\) −93.6582 −4.73045
\(393\) −20.4699 −1.03257
\(394\) 34.0860 1.71723
\(395\) 28.1696 1.41737
\(396\) 2.70291 0.135827
\(397\) −20.3659 −1.02213 −0.511067 0.859541i \(-0.670750\pi\)
−0.511067 + 0.859541i \(0.670750\pi\)
\(398\) −14.4419 −0.723906
\(399\) 1.35378 0.0677737
\(400\) 82.3181 4.11590
\(401\) 19.5051 0.974037 0.487018 0.873392i \(-0.338084\pi\)
0.487018 + 0.873392i \(0.338084\pi\)
\(402\) 28.5631 1.42460
\(403\) −1.20712 −0.0601310
\(404\) 19.3814 0.964259
\(405\) −32.7633 −1.62802
\(406\) 42.7859 2.12343
\(407\) −11.5358 −0.571808
\(408\) 14.4180 0.713796
\(409\) 2.21382 0.109466 0.0547331 0.998501i \(-0.482569\pi\)
0.0547331 + 0.998501i \(0.482569\pi\)
\(410\) −46.0178 −2.27266
\(411\) −18.6910 −0.921960
\(412\) 79.8238 3.93263
\(413\) −42.8004 −2.10607
\(414\) −2.52094 −0.123897
\(415\) 7.08532 0.347805
\(416\) 12.6120 0.618353
\(417\) 39.8733 1.95260
\(418\) −1.12147 −0.0548528
\(419\) 12.9430 0.632308 0.316154 0.948708i \(-0.397608\pi\)
0.316154 + 0.948708i \(0.397608\pi\)
\(420\) 134.349 6.55558
\(421\) −23.5801 −1.14923 −0.574613 0.818425i \(-0.694847\pi\)
−0.574613 + 0.818425i \(0.694847\pi\)
\(422\) −35.0904 −1.70817
\(423\) −0.650344 −0.0316208
\(424\) 47.6021 2.31176
\(425\) −6.23505 −0.302444
\(426\) −4.71767 −0.228572
\(427\) 17.0088 0.823115
\(428\) 48.6052 2.34942
\(429\) −3.26166 −0.157474
\(430\) −19.5722 −0.943853
\(431\) −18.4420 −0.888321 −0.444160 0.895947i \(-0.646498\pi\)
−0.444160 + 0.895947i \(0.646498\pi\)
\(432\) −62.1135 −2.98844
\(433\) 25.9151 1.24540 0.622700 0.782461i \(-0.286036\pi\)
0.622700 + 0.782461i \(0.286036\pi\)
\(434\) −17.7790 −0.853422
\(435\) −23.0198 −1.10372
\(436\) 35.1426 1.68303
\(437\) 0.754528 0.0360940
\(438\) −60.8912 −2.90949
\(439\) −28.6625 −1.36799 −0.683994 0.729488i \(-0.739759\pi\)
−0.683994 + 0.729488i \(0.739759\pi\)
\(440\) −68.3071 −3.25641
\(441\) 2.43864 0.116126
\(442\) −1.95070 −0.0927852
\(443\) −7.73283 −0.367398 −0.183699 0.982983i \(-0.558807\pi\)
−0.183699 + 0.982983i \(0.558807\pi\)
\(444\) −45.5339 −2.16094
\(445\) 34.4690 1.63399
\(446\) 24.0527 1.13893
\(447\) 33.5818 1.58836
\(448\) 80.0659 3.78276
\(449\) 3.24019 0.152914 0.0764571 0.997073i \(-0.475639\pi\)
0.0764571 + 0.997073i \(0.475639\pi\)
\(450\) −3.92543 −0.185047
\(451\) 11.8698 0.558928
\(452\) −66.2567 −3.11645
\(453\) −17.7262 −0.832849
\(454\) 25.2529 1.18518
\(455\) −11.1561 −0.523006
\(456\) −2.71684 −0.127228
\(457\) −34.2988 −1.60443 −0.802214 0.597036i \(-0.796345\pi\)
−0.802214 + 0.597036i \(0.796345\pi\)
\(458\) −30.1791 −1.41018
\(459\) 4.70469 0.219596
\(460\) 74.8796 3.49128
\(461\) −25.7584 −1.19969 −0.599843 0.800118i \(-0.704770\pi\)
−0.599843 + 0.800118i \(0.704770\pi\)
\(462\) −48.0392 −2.23499
\(463\) 0.610424 0.0283688 0.0141844 0.999899i \(-0.495485\pi\)
0.0141844 + 0.999899i \(0.495485\pi\)
\(464\) −46.8843 −2.17655
\(465\) 9.56554 0.443591
\(466\) 20.7374 0.960641
\(467\) −39.9655 −1.84938 −0.924691 0.380718i \(-0.875677\pi\)
−0.924691 + 0.380718i \(0.875677\pi\)
\(468\) −0.885923 −0.0409518
\(469\) −25.1999 −1.16362
\(470\) 26.7785 1.23520
\(471\) −8.96863 −0.413252
\(472\) 85.8945 3.95361
\(473\) 5.04844 0.232128
\(474\) −39.7583 −1.82616
\(475\) 1.17490 0.0539080
\(476\) −20.7255 −0.949953
\(477\) −1.23945 −0.0567503
\(478\) 52.7926 2.41468
\(479\) 11.6561 0.532580 0.266290 0.963893i \(-0.414202\pi\)
0.266290 + 0.963893i \(0.414202\pi\)
\(480\) −99.9404 −4.56164
\(481\) 3.78104 0.172401
\(482\) 59.6909 2.71885
\(483\) 32.3210 1.47066
\(484\) −28.2505 −1.28411
\(485\) 21.7281 0.986622
\(486\) 6.16026 0.279435
\(487\) 15.2904 0.692873 0.346437 0.938073i \(-0.387392\pi\)
0.346437 + 0.938073i \(0.387392\pi\)
\(488\) −34.1344 −1.54519
\(489\) 31.1203 1.40731
\(490\) −100.413 −4.53620
\(491\) 11.1860 0.504816 0.252408 0.967621i \(-0.418777\pi\)
0.252408 + 0.967621i \(0.418777\pi\)
\(492\) 46.8523 2.11227
\(493\) 3.55117 0.159937
\(494\) 0.367579 0.0165382
\(495\) 1.77856 0.0799401
\(496\) 19.4821 0.874770
\(497\) 4.16217 0.186699
\(498\) −10.0002 −0.448118
\(499\) 21.6594 0.969608 0.484804 0.874623i \(-0.338891\pi\)
0.484804 + 0.874623i \(0.338891\pi\)
\(500\) 28.3854 1.26943
\(501\) 21.4249 0.957193
\(502\) −19.1480 −0.854616
\(503\) −34.8968 −1.55597 −0.777986 0.628282i \(-0.783758\pi\)
−0.777986 + 0.628282i \(0.783758\pi\)
\(504\) −8.00838 −0.356722
\(505\) 12.7532 0.567511
\(506\) −26.7747 −1.19028
\(507\) −22.2647 −0.988812
\(508\) 83.9065 3.72275
\(509\) 1.90425 0.0844043 0.0422021 0.999109i \(-0.486563\pi\)
0.0422021 + 0.999109i \(0.486563\pi\)
\(510\) 15.4578 0.684484
\(511\) 53.7214 2.37649
\(512\) 8.55527 0.378093
\(513\) −0.886525 −0.0391411
\(514\) 74.3901 3.28121
\(515\) 52.5251 2.31453
\(516\) 19.9271 0.877242
\(517\) −6.90724 −0.303780
\(518\) 55.6889 2.44683
\(519\) −20.0417 −0.879733
\(520\) 22.3887 0.981811
\(521\) −9.02708 −0.395484 −0.197742 0.980254i \(-0.563361\pi\)
−0.197742 + 0.980254i \(0.563361\pi\)
\(522\) 2.23573 0.0978553
\(523\) 30.9607 1.35382 0.676908 0.736068i \(-0.263320\pi\)
0.676908 + 0.736068i \(0.263320\pi\)
\(524\) −59.0521 −2.57970
\(525\) 50.3280 2.19649
\(526\) 27.8384 1.21381
\(527\) −1.47564 −0.0642798
\(528\) 52.6408 2.29090
\(529\) −4.98591 −0.216779
\(530\) 51.0352 2.21683
\(531\) −2.23649 −0.0970553
\(532\) 3.90541 0.169321
\(533\) −3.89052 −0.168517
\(534\) −48.6492 −2.10526
\(535\) 31.9829 1.38274
\(536\) 50.5727 2.18441
\(537\) −39.0720 −1.68608
\(538\) −18.2418 −0.786461
\(539\) 25.9005 1.11562
\(540\) −87.9791 −3.78602
\(541\) −28.6160 −1.23030 −0.615148 0.788411i \(-0.710904\pi\)
−0.615148 + 0.788411i \(0.710904\pi\)
\(542\) 49.4691 2.12488
\(543\) −33.4749 −1.43654
\(544\) 15.4174 0.661016
\(545\) 23.1243 0.990537
\(546\) 15.7456 0.673850
\(547\) 6.72599 0.287582 0.143791 0.989608i \(-0.454071\pi\)
0.143791 + 0.989608i \(0.454071\pi\)
\(548\) −53.9203 −2.30336
\(549\) 0.888778 0.0379321
\(550\) −41.6916 −1.77774
\(551\) −0.669164 −0.0285073
\(552\) −64.8637 −2.76078
\(553\) 35.0769 1.49162
\(554\) −56.6680 −2.40759
\(555\) −29.9619 −1.27181
\(556\) 115.027 4.87824
\(557\) −15.6976 −0.665127 −0.332564 0.943081i \(-0.607914\pi\)
−0.332564 + 0.943081i \(0.607914\pi\)
\(558\) −0.929025 −0.0393288
\(559\) −1.65471 −0.0699867
\(560\) 180.051 7.60856
\(561\) −3.98719 −0.168339
\(562\) 3.02414 0.127565
\(563\) 8.44214 0.355794 0.177897 0.984049i \(-0.443071\pi\)
0.177897 + 0.984049i \(0.443071\pi\)
\(564\) −27.2641 −1.14803
\(565\) −43.5978 −1.83417
\(566\) −22.7149 −0.954778
\(567\) −40.7969 −1.71331
\(568\) −8.35291 −0.350480
\(569\) 32.6999 1.37085 0.685425 0.728144i \(-0.259617\pi\)
0.685425 + 0.728144i \(0.259617\pi\)
\(570\) −2.91279 −0.122003
\(571\) 10.7769 0.451000 0.225500 0.974243i \(-0.427598\pi\)
0.225500 + 0.974243i \(0.427598\pi\)
\(572\) −9.40930 −0.393423
\(573\) 41.4847 1.73305
\(574\) −57.3014 −2.39172
\(575\) 28.0503 1.16978
\(576\) 4.18376 0.174323
\(577\) 11.9981 0.499487 0.249744 0.968312i \(-0.419654\pi\)
0.249744 + 0.968312i \(0.419654\pi\)
\(578\) 43.1614 1.79528
\(579\) −7.63099 −0.317133
\(580\) −66.4080 −2.75744
\(581\) 8.82266 0.366026
\(582\) −30.6669 −1.27118
\(583\) −13.1640 −0.545199
\(584\) −107.811 −4.46127
\(585\) −0.582950 −0.0241020
\(586\) 83.5346 3.45078
\(587\) 28.4798 1.17549 0.587744 0.809047i \(-0.300016\pi\)
0.587744 + 0.809047i \(0.300016\pi\)
\(588\) 102.234 4.21606
\(589\) 0.278061 0.0114573
\(590\) 92.0893 3.79126
\(591\) −22.8358 −0.939339
\(592\) −61.0232 −2.50804
\(593\) −35.1838 −1.44483 −0.722413 0.691462i \(-0.756967\pi\)
−0.722413 + 0.691462i \(0.756967\pi\)
\(594\) 31.4586 1.29076
\(595\) −13.6377 −0.559091
\(596\) 96.8775 3.96826
\(597\) 9.67530 0.395984
\(598\) 8.77582 0.358870
\(599\) −8.77130 −0.358385 −0.179193 0.983814i \(-0.557349\pi\)
−0.179193 + 0.983814i \(0.557349\pi\)
\(600\) −101.001 −4.12336
\(601\) 13.2025 0.538539 0.269270 0.963065i \(-0.413218\pi\)
0.269270 + 0.963065i \(0.413218\pi\)
\(602\) −24.3713 −0.993300
\(603\) −1.31679 −0.0536239
\(604\) −51.1369 −2.08073
\(605\) −18.5892 −0.755759
\(606\) −17.9998 −0.731191
\(607\) −23.3907 −0.949399 −0.474699 0.880148i \(-0.657443\pi\)
−0.474699 + 0.880148i \(0.657443\pi\)
\(608\) −2.90517 −0.117820
\(609\) −28.6643 −1.16154
\(610\) −36.5962 −1.48174
\(611\) 2.26396 0.0915899
\(612\) −1.08299 −0.0437773
\(613\) −2.94124 −0.118796 −0.0593978 0.998234i \(-0.518918\pi\)
−0.0593978 + 0.998234i \(0.518918\pi\)
\(614\) 5.30562 0.214117
\(615\) 30.8295 1.24317
\(616\) −85.0562 −3.42701
\(617\) 4.69305 0.188935 0.0944675 0.995528i \(-0.469885\pi\)
0.0944675 + 0.995528i \(0.469885\pi\)
\(618\) −74.1335 −2.98209
\(619\) 18.4708 0.742404 0.371202 0.928552i \(-0.378946\pi\)
0.371202 + 0.928552i \(0.378946\pi\)
\(620\) 27.5949 1.10824
\(621\) −21.1655 −0.849342
\(622\) −17.1086 −0.685993
\(623\) 42.9209 1.71959
\(624\) −17.2539 −0.690707
\(625\) −14.3667 −0.574667
\(626\) 5.02330 0.200771
\(627\) 0.751324 0.0300050
\(628\) −25.8729 −1.03244
\(629\) 4.62211 0.184295
\(630\) −8.58596 −0.342073
\(631\) −31.2103 −1.24246 −0.621232 0.783627i \(-0.713367\pi\)
−0.621232 + 0.783627i \(0.713367\pi\)
\(632\) −70.3944 −2.80014
\(633\) 23.5087 0.934387
\(634\) 73.8976 2.93485
\(635\) 55.2117 2.19101
\(636\) −51.9608 −2.06038
\(637\) −8.48931 −0.336359
\(638\) 23.7455 0.940093
\(639\) 0.217490 0.00860377
\(640\) −60.9098 −2.40767
\(641\) 10.4899 0.414327 0.207164 0.978306i \(-0.433577\pi\)
0.207164 + 0.978306i \(0.433577\pi\)
\(642\) −45.1404 −1.78155
\(643\) 9.94229 0.392086 0.196043 0.980595i \(-0.437191\pi\)
0.196043 + 0.980595i \(0.437191\pi\)
\(644\) 93.2402 3.67418
\(645\) 13.1123 0.516297
\(646\) 0.449344 0.0176792
\(647\) −22.1163 −0.869481 −0.434740 0.900556i \(-0.643160\pi\)
−0.434740 + 0.900556i \(0.643160\pi\)
\(648\) 81.8738 3.21631
\(649\) −23.7535 −0.932407
\(650\) 13.6651 0.535989
\(651\) 11.9110 0.466830
\(652\) 89.7764 3.51591
\(653\) 26.4649 1.03565 0.517825 0.855486i \(-0.326742\pi\)
0.517825 + 0.855486i \(0.326742\pi\)
\(654\) −32.6375 −1.27623
\(655\) −38.8571 −1.51827
\(656\) 62.7902 2.45155
\(657\) 2.80715 0.109517
\(658\) 33.3446 1.29991
\(659\) 41.2127 1.60542 0.802710 0.596370i \(-0.203391\pi\)
0.802710 + 0.596370i \(0.203391\pi\)
\(660\) 74.5617 2.90231
\(661\) 35.0407 1.36293 0.681463 0.731853i \(-0.261344\pi\)
0.681463 + 0.731853i \(0.261344\pi\)
\(662\) 11.1724 0.434226
\(663\) 1.30687 0.0507544
\(664\) −17.7059 −0.687121
\(665\) 2.56981 0.0996530
\(666\) 2.90996 0.112759
\(667\) −15.9761 −0.618595
\(668\) 61.8070 2.39138
\(669\) −16.1140 −0.623004
\(670\) 54.2200 2.09470
\(671\) 9.43962 0.364413
\(672\) −124.446 −4.80061
\(673\) 12.9361 0.498649 0.249325 0.968420i \(-0.419791\pi\)
0.249325 + 0.968420i \(0.419791\pi\)
\(674\) 57.9300 2.23138
\(675\) −32.9574 −1.26853
\(676\) −64.2298 −2.47038
\(677\) −23.0474 −0.885785 −0.442892 0.896575i \(-0.646048\pi\)
−0.442892 + 0.896575i \(0.646048\pi\)
\(678\) 61.5336 2.36318
\(679\) 27.0559 1.03831
\(680\) 27.3690 1.04955
\(681\) −16.9181 −0.648305
\(682\) −9.86708 −0.377830
\(683\) −12.7869 −0.489279 −0.244639 0.969614i \(-0.578670\pi\)
−0.244639 + 0.969614i \(0.578670\pi\)
\(684\) 0.204073 0.00780292
\(685\) −35.4803 −1.35563
\(686\) −45.4670 −1.73594
\(687\) 20.2184 0.771380
\(688\) 26.7058 1.01815
\(689\) 4.31472 0.164378
\(690\) −69.5418 −2.64741
\(691\) −7.55565 −0.287430 −0.143715 0.989619i \(-0.545905\pi\)
−0.143715 + 0.989619i \(0.545905\pi\)
\(692\) −57.8167 −2.19786
\(693\) 2.21466 0.0841281
\(694\) −78.3941 −2.97580
\(695\) 75.6895 2.87107
\(696\) 57.5253 2.18049
\(697\) −4.75594 −0.180144
\(698\) −24.5432 −0.928973
\(699\) −13.8930 −0.525480
\(700\) 145.187 5.48756
\(701\) 47.9056 1.80937 0.904686 0.426080i \(-0.140106\pi\)
0.904686 + 0.426080i \(0.140106\pi\)
\(702\) −10.3111 −0.389166
\(703\) −0.870964 −0.0328490
\(704\) 44.4353 1.67472
\(705\) −17.9402 −0.675666
\(706\) −16.1910 −0.609358
\(707\) 15.8803 0.597241
\(708\) −93.7594 −3.52369
\(709\) −2.30619 −0.0866106 −0.0433053 0.999062i \(-0.513789\pi\)
−0.0433053 + 0.999062i \(0.513789\pi\)
\(710\) −8.95533 −0.336087
\(711\) 1.83290 0.0687392
\(712\) −86.1362 −3.22809
\(713\) 6.63861 0.248618
\(714\) 19.2481 0.720343
\(715\) −6.19145 −0.231547
\(716\) −112.716 −4.21238
\(717\) −35.3683 −1.32085
\(718\) −16.9548 −0.632746
\(719\) −38.3734 −1.43109 −0.715543 0.698569i \(-0.753821\pi\)
−0.715543 + 0.698569i \(0.753821\pi\)
\(720\) 9.40838 0.350630
\(721\) 65.4045 2.43579
\(722\) 50.8197 1.89131
\(723\) −39.9898 −1.48724
\(724\) −96.5690 −3.58896
\(725\) −24.8768 −0.923901
\(726\) 26.2366 0.973733
\(727\) −30.0976 −1.11626 −0.558130 0.829754i \(-0.688481\pi\)
−0.558130 + 0.829754i \(0.688481\pi\)
\(728\) 27.8785 1.03325
\(729\) 24.7208 0.915583
\(730\) −115.587 −4.27806
\(731\) −2.02279 −0.0748154
\(732\) 37.2599 1.37716
\(733\) −7.95287 −0.293746 −0.146873 0.989155i \(-0.546921\pi\)
−0.146873 + 0.989155i \(0.546921\pi\)
\(734\) 60.5413 2.23462
\(735\) 67.2714 2.48134
\(736\) −69.3600 −2.55664
\(737\) −13.9855 −0.515163
\(738\) −2.99423 −0.110219
\(739\) −21.4214 −0.788000 −0.394000 0.919110i \(-0.628909\pi\)
−0.394000 + 0.919110i \(0.628909\pi\)
\(740\) −86.4348 −3.17741
\(741\) −0.246259 −0.00904653
\(742\) 63.5492 2.33296
\(743\) −36.8867 −1.35324 −0.676620 0.736332i \(-0.736556\pi\)
−0.676620 + 0.736332i \(0.736556\pi\)
\(744\) −23.9038 −0.876355
\(745\) 63.7467 2.33550
\(746\) −91.1303 −3.33652
\(747\) 0.461019 0.0168678
\(748\) −11.5023 −0.420567
\(749\) 39.8252 1.45518
\(750\) −26.3619 −0.962602
\(751\) −16.0621 −0.586116 −0.293058 0.956095i \(-0.594673\pi\)
−0.293058 + 0.956095i \(0.594673\pi\)
\(752\) −36.5386 −1.33243
\(753\) 12.8281 0.467483
\(754\) −7.78296 −0.283439
\(755\) −33.6488 −1.22461
\(756\) −109.552 −3.98436
\(757\) −16.3826 −0.595437 −0.297719 0.954654i \(-0.596226\pi\)
−0.297719 + 0.954654i \(0.596226\pi\)
\(758\) −15.1647 −0.550805
\(759\) 17.9376 0.651094
\(760\) −5.15726 −0.187073
\(761\) −1.60901 −0.0583266 −0.0291633 0.999575i \(-0.509284\pi\)
−0.0291633 + 0.999575i \(0.509284\pi\)
\(762\) −77.9253 −2.82293
\(763\) 28.7945 1.04243
\(764\) 119.676 4.32973
\(765\) −0.712623 −0.0257649
\(766\) 16.7534 0.605325
\(767\) 7.78559 0.281122
\(768\) 18.2215 0.657512
\(769\) −13.9207 −0.501992 −0.250996 0.967988i \(-0.580758\pi\)
−0.250996 + 0.967988i \(0.580758\pi\)
\(770\) −91.1906 −3.28628
\(771\) −49.8375 −1.79485
\(772\) −22.0140 −0.792303
\(773\) −24.9483 −0.897327 −0.448663 0.893701i \(-0.648100\pi\)
−0.448663 + 0.893701i \(0.648100\pi\)
\(774\) −1.27350 −0.0457749
\(775\) 10.3372 0.371323
\(776\) −54.2974 −1.94916
\(777\) −37.3087 −1.33844
\(778\) 23.7414 0.851170
\(779\) 0.896184 0.0321091
\(780\) −24.4388 −0.875048
\(781\) 2.30994 0.0826561
\(782\) 10.7279 0.383630
\(783\) 18.7709 0.670818
\(784\) 137.011 4.89326
\(785\) −17.0247 −0.607638
\(786\) 54.8426 1.95617
\(787\) −40.5409 −1.44513 −0.722564 0.691304i \(-0.757037\pi\)
−0.722564 + 0.691304i \(0.757037\pi\)
\(788\) −65.8772 −2.34678
\(789\) −18.6502 −0.663966
\(790\) −75.4713 −2.68515
\(791\) −54.2881 −1.93026
\(792\) −4.44452 −0.157929
\(793\) −3.09399 −0.109871
\(794\) 54.5638 1.93640
\(795\) −34.1909 −1.21263
\(796\) 27.9115 0.989297
\(797\) −5.18440 −0.183641 −0.0918205 0.995776i \(-0.529269\pi\)
−0.0918205 + 0.995776i \(0.529269\pi\)
\(798\) −3.62701 −0.128395
\(799\) 2.76756 0.0979092
\(800\) −108.003 −3.81847
\(801\) 2.24278 0.0792449
\(802\) −52.2575 −1.84528
\(803\) 29.8145 1.05213
\(804\) −55.2033 −1.94687
\(805\) 61.3534 2.16242
\(806\) 3.23409 0.113916
\(807\) 12.2211 0.430202
\(808\) −31.8696 −1.12117
\(809\) 40.8795 1.43725 0.718624 0.695399i \(-0.244772\pi\)
0.718624 + 0.695399i \(0.244772\pi\)
\(810\) 87.7787 3.08423
\(811\) −12.7566 −0.447944 −0.223972 0.974596i \(-0.571902\pi\)
−0.223972 + 0.974596i \(0.571902\pi\)
\(812\) −82.6914 −2.90190
\(813\) −33.1417 −1.16233
\(814\) 30.9064 1.08327
\(815\) 59.0741 2.06928
\(816\) −21.0919 −0.738362
\(817\) 0.381163 0.0133352
\(818\) −5.93120 −0.207380
\(819\) −0.725891 −0.0253647
\(820\) 88.9376 3.10583
\(821\) −24.2367 −0.845865 −0.422933 0.906161i \(-0.638999\pi\)
−0.422933 + 0.906161i \(0.638999\pi\)
\(822\) 50.0766 1.74662
\(823\) −50.0340 −1.74408 −0.872039 0.489437i \(-0.837202\pi\)
−0.872039 + 0.489437i \(0.837202\pi\)
\(824\) −131.258 −4.57258
\(825\) 27.9312 0.972440
\(826\) 114.670 3.98987
\(827\) 6.53424 0.227218 0.113609 0.993526i \(-0.463759\pi\)
0.113609 + 0.993526i \(0.463759\pi\)
\(828\) 4.87217 0.169319
\(829\) 12.4686 0.433052 0.216526 0.976277i \(-0.430527\pi\)
0.216526 + 0.976277i \(0.430527\pi\)
\(830\) −18.9828 −0.658904
\(831\) 37.9646 1.31698
\(832\) −14.5644 −0.504929
\(833\) −10.3777 −0.359566
\(834\) −106.827 −3.69913
\(835\) 40.6698 1.40744
\(836\) 2.16744 0.0749624
\(837\) −7.79997 −0.269607
\(838\) −34.6766 −1.19788
\(839\) 3.46998 0.119797 0.0598985 0.998204i \(-0.480922\pi\)
0.0598985 + 0.998204i \(0.480922\pi\)
\(840\) −220.916 −7.62234
\(841\) −14.8314 −0.511428
\(842\) 63.1754 2.17717
\(843\) −2.02601 −0.0697796
\(844\) 67.8184 2.33441
\(845\) −42.2641 −1.45393
\(846\) 1.74239 0.0599045
\(847\) −23.1473 −0.795352
\(848\) −69.6364 −2.39132
\(849\) 15.2178 0.522273
\(850\) 16.7048 0.572970
\(851\) −20.7940 −0.712808
\(852\) 9.11774 0.312369
\(853\) 18.7247 0.641120 0.320560 0.947228i \(-0.396129\pi\)
0.320560 + 0.947228i \(0.396129\pi\)
\(854\) −45.5697 −1.55936
\(855\) 0.134283 0.00459237
\(856\) −79.9237 −2.73173
\(857\) −11.2670 −0.384872 −0.192436 0.981310i \(-0.561639\pi\)
−0.192436 + 0.981310i \(0.561639\pi\)
\(858\) 8.73856 0.298330
\(859\) 16.5295 0.563978 0.281989 0.959418i \(-0.409006\pi\)
0.281989 + 0.959418i \(0.409006\pi\)
\(860\) 37.8267 1.28988
\(861\) 38.3890 1.30829
\(862\) 49.4094 1.68289
\(863\) −56.9291 −1.93789 −0.968944 0.247279i \(-0.920464\pi\)
−0.968944 + 0.247279i \(0.920464\pi\)
\(864\) 81.4939 2.77248
\(865\) −38.0442 −1.29354
\(866\) −69.4311 −2.35936
\(867\) −28.9159 −0.982034
\(868\) 34.3612 1.16629
\(869\) 19.4671 0.660376
\(870\) 61.6741 2.09095
\(871\) 4.58398 0.155322
\(872\) −57.7865 −1.95690
\(873\) 1.41378 0.0478491
\(874\) −2.02151 −0.0683787
\(875\) 23.2579 0.786259
\(876\) 117.683 3.97614
\(877\) 45.8775 1.54917 0.774587 0.632468i \(-0.217958\pi\)
0.774587 + 0.632468i \(0.217958\pi\)
\(878\) 76.7920 2.59160
\(879\) −55.9638 −1.88761
\(880\) 99.9255 3.36849
\(881\) 24.1818 0.814706 0.407353 0.913271i \(-0.366452\pi\)
0.407353 + 0.913271i \(0.366452\pi\)
\(882\) −6.53354 −0.219996
\(883\) −46.3884 −1.56109 −0.780547 0.625097i \(-0.785059\pi\)
−0.780547 + 0.625097i \(0.785059\pi\)
\(884\) 3.77007 0.126801
\(885\) −61.6950 −2.07385
\(886\) 20.7176 0.696022
\(887\) −50.3969 −1.69216 −0.846082 0.533053i \(-0.821045\pi\)
−0.846082 + 0.533053i \(0.821045\pi\)
\(888\) 74.8733 2.51258
\(889\) 68.7497 2.30579
\(890\) −92.3485 −3.09553
\(891\) −22.6416 −0.758523
\(892\) −46.4861 −1.55647
\(893\) −0.521504 −0.0174515
\(894\) −89.9716 −3.00910
\(895\) −74.1685 −2.47918
\(896\) −75.8450 −2.53380
\(897\) −5.87934 −0.196305
\(898\) −8.68105 −0.289690
\(899\) −5.88755 −0.196361
\(900\) 7.58660 0.252887
\(901\) 5.27450 0.175719
\(902\) −31.8014 −1.05887
\(903\) 16.3275 0.543345
\(904\) 108.949 3.62358
\(905\) −63.5438 −2.11227
\(906\) 47.4916 1.57780
\(907\) 19.3106 0.641199 0.320600 0.947215i \(-0.396116\pi\)
0.320600 + 0.947215i \(0.396116\pi\)
\(908\) −48.8058 −1.61968
\(909\) 0.829810 0.0275231
\(910\) 29.8892 0.990816
\(911\) 43.9721 1.45686 0.728430 0.685121i \(-0.240250\pi\)
0.728430 + 0.685121i \(0.240250\pi\)
\(912\) 3.97443 0.131607
\(913\) 4.89643 0.162048
\(914\) 91.8924 3.03953
\(915\) 24.5175 0.810524
\(916\) 58.3264 1.92716
\(917\) −48.3849 −1.59781
\(918\) −12.6047 −0.416017
\(919\) 19.0386 0.628024 0.314012 0.949419i \(-0.398327\pi\)
0.314012 + 0.949419i \(0.398327\pi\)
\(920\) −123.128 −4.05940
\(921\) −3.55449 −0.117124
\(922\) 69.0112 2.27276
\(923\) −0.757119 −0.0249209
\(924\) 92.8444 3.05436
\(925\) −32.3789 −1.06461
\(926\) −1.63543 −0.0537437
\(927\) 3.41764 0.112250
\(928\) 61.5129 2.01926
\(929\) 14.1864 0.465442 0.232721 0.972544i \(-0.425237\pi\)
0.232721 + 0.972544i \(0.425237\pi\)
\(930\) −25.6278 −0.840367
\(931\) 1.95552 0.0640895
\(932\) −40.0787 −1.31282
\(933\) 11.4619 0.375245
\(934\) 107.075 3.50359
\(935\) −7.56870 −0.247523
\(936\) 1.45676 0.0476158
\(937\) −4.35334 −0.142217 −0.0711086 0.997469i \(-0.522654\pi\)
−0.0711086 + 0.997469i \(0.522654\pi\)
\(938\) 67.5149 2.20444
\(939\) −3.36535 −0.109824
\(940\) −51.7542 −1.68804
\(941\) 47.0485 1.53374 0.766869 0.641803i \(-0.221813\pi\)
0.766869 + 0.641803i \(0.221813\pi\)
\(942\) 24.0285 0.782892
\(943\) 21.3961 0.696752
\(944\) −125.654 −4.08968
\(945\) −72.0866 −2.34498
\(946\) −13.5257 −0.439758
\(947\) −50.1049 −1.62819 −0.814096 0.580730i \(-0.802767\pi\)
−0.814096 + 0.580730i \(0.802767\pi\)
\(948\) 76.8401 2.49565
\(949\) −9.77217 −0.317218
\(950\) −3.14776 −0.102127
\(951\) −49.5076 −1.60539
\(952\) 34.0799 1.10454
\(953\) −51.4249 −1.66582 −0.832908 0.553411i \(-0.813326\pi\)
−0.832908 + 0.553411i \(0.813326\pi\)
\(954\) 3.32069 0.107511
\(955\) 78.7485 2.54824
\(956\) −102.031 −3.29993
\(957\) −15.9082 −0.514240
\(958\) −31.2287 −1.00895
\(959\) −44.1801 −1.42665
\(960\) 115.412 3.72490
\(961\) −28.5535 −0.921081
\(962\) −10.1301 −0.326607
\(963\) 2.08102 0.0670600
\(964\) −115.363 −3.71560
\(965\) −14.4856 −0.466306
\(966\) −86.5936 −2.78610
\(967\) −40.2974 −1.29588 −0.647938 0.761693i \(-0.724369\pi\)
−0.647938 + 0.761693i \(0.724369\pi\)
\(968\) 46.4535 1.49307
\(969\) −0.301037 −0.00967070
\(970\) −58.2134 −1.86912
\(971\) 15.5865 0.500195 0.250097 0.968221i \(-0.419537\pi\)
0.250097 + 0.968221i \(0.419537\pi\)
\(972\) −11.9058 −0.381879
\(973\) 94.2488 3.02148
\(974\) −40.9656 −1.31262
\(975\) −9.15490 −0.293191
\(976\) 49.9347 1.59837
\(977\) 26.5625 0.849810 0.424905 0.905238i \(-0.360307\pi\)
0.424905 + 0.905238i \(0.360307\pi\)
\(978\) −83.3767 −2.66609
\(979\) 23.8204 0.761303
\(980\) 194.066 6.19921
\(981\) 1.50462 0.0480389
\(982\) −29.9692 −0.956356
\(983\) 56.0787 1.78863 0.894316 0.447436i \(-0.147663\pi\)
0.894316 + 0.447436i \(0.147663\pi\)
\(984\) −77.0413 −2.45599
\(985\) −43.3481 −1.38119
\(986\) −9.51422 −0.302995
\(987\) −22.3392 −0.711063
\(988\) −0.710412 −0.0226012
\(989\) 9.10013 0.289367
\(990\) −4.76507 −0.151444
\(991\) 14.5768 0.463048 0.231524 0.972829i \(-0.425629\pi\)
0.231524 + 0.972829i \(0.425629\pi\)
\(992\) −25.5608 −0.811555
\(993\) −7.48489 −0.237526
\(994\) −11.1512 −0.353695
\(995\) 18.3662 0.582246
\(996\) 19.3271 0.612403
\(997\) −55.2501 −1.74979 −0.874894 0.484314i \(-0.839069\pi\)
−0.874894 + 0.484314i \(0.839069\pi\)
\(998\) −58.0294 −1.83689
\(999\) 24.4317 0.772985
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 \(a_p\))