Properties

Label 6013.2.a.e.1.4
Level 6013
Weight 2
Character 6013.1
Self dual Yes
Analytic conductor 48.014
Analytic rank 0
Dimension 109
CM No

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Newspace parameters

Level: \( N \) = \( 6013 = 7 \cdot 859 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0140467354\)
Analytic rank: \(0\)
Dimension: \(109\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.64232 q^{2}\) \(+0.320634 q^{3}\) \(+4.98185 q^{4}\) \(+3.17576 q^{5}\) \(-0.847217 q^{6}\) \(+1.00000 q^{7}\) \(-7.87900 q^{8}\) \(-2.89719 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.64232 q^{2}\) \(+0.320634 q^{3}\) \(+4.98185 q^{4}\) \(+3.17576 q^{5}\) \(-0.847217 q^{6}\) \(+1.00000 q^{7}\) \(-7.87900 q^{8}\) \(-2.89719 q^{9}\) \(-8.39136 q^{10}\) \(-2.25492 q^{11}\) \(+1.59735 q^{12}\) \(-4.14521 q^{13}\) \(-2.64232 q^{14}\) \(+1.01826 q^{15}\) \(+10.8551 q^{16}\) \(-4.34057 q^{17}\) \(+7.65531 q^{18}\) \(-3.45874 q^{19}\) \(+15.8211 q^{20}\) \(+0.320634 q^{21}\) \(+5.95822 q^{22}\) \(-0.0874563 q^{23}\) \(-2.52627 q^{24}\) \(+5.08544 q^{25}\) \(+10.9530 q^{26}\) \(-1.89084 q^{27}\) \(+4.98185 q^{28}\) \(+8.08271 q^{29}\) \(-2.69056 q^{30}\) \(-1.22874 q^{31}\) \(-12.9247 q^{32}\) \(-0.723004 q^{33}\) \(+11.4692 q^{34}\) \(+3.17576 q^{35}\) \(-14.4334 q^{36}\) \(+2.47866 q^{37}\) \(+9.13908 q^{38}\) \(-1.32909 q^{39}\) \(-25.0218 q^{40}\) \(+0.513039 q^{41}\) \(-0.847217 q^{42}\) \(+1.83803 q^{43}\) \(-11.2337 q^{44}\) \(-9.20079 q^{45}\) \(+0.231087 q^{46}\) \(+3.62406 q^{47}\) \(+3.48052 q^{48}\) \(+1.00000 q^{49}\) \(-13.4373 q^{50}\) \(-1.39173 q^{51}\) \(-20.6508 q^{52}\) \(+0.723055 q^{53}\) \(+4.99620 q^{54}\) \(-7.16108 q^{55}\) \(-7.87900 q^{56}\) \(-1.10899 q^{57}\) \(-21.3571 q^{58}\) \(-6.53732 q^{59}\) \(+5.07280 q^{60}\) \(-0.324330 q^{61}\) \(+3.24673 q^{62}\) \(-2.89719 q^{63}\) \(+12.4410 q^{64}\) \(-13.1642 q^{65}\) \(+1.91041 q^{66}\) \(+7.47223 q^{67}\) \(-21.6241 q^{68}\) \(-0.0280415 q^{69}\) \(-8.39136 q^{70}\) \(-6.11028 q^{71}\) \(+22.8270 q^{72}\) \(-1.38985 q^{73}\) \(-6.54942 q^{74}\) \(+1.63056 q^{75}\) \(-17.2309 q^{76}\) \(-2.25492 q^{77}\) \(+3.51189 q^{78}\) \(+4.31579 q^{79}\) \(+34.4733 q^{80}\) \(+8.08531 q^{81}\) \(-1.35561 q^{82}\) \(+16.0073 q^{83}\) \(+1.59735 q^{84}\) \(-13.7846 q^{85}\) \(-4.85667 q^{86}\) \(+2.59159 q^{87}\) \(+17.7665 q^{88}\) \(+0.168935 q^{89}\) \(+24.3114 q^{90}\) \(-4.14521 q^{91}\) \(-0.435694 q^{92}\) \(-0.393977 q^{93}\) \(-9.57591 q^{94}\) \(-10.9841 q^{95}\) \(-4.14410 q^{96}\) \(+4.41054 q^{97}\) \(-2.64232 q^{98}\) \(+6.53294 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.64232 −1.86840 −0.934201 0.356747i \(-0.883886\pi\)
−0.934201 + 0.356747i \(0.883886\pi\)
\(3\) 0.320634 0.185118 0.0925590 0.995707i \(-0.470495\pi\)
0.0925590 + 0.995707i \(0.470495\pi\)
\(4\) 4.98185 2.49093
\(5\) 3.17576 1.42024 0.710121 0.704080i \(-0.248640\pi\)
0.710121 + 0.704080i \(0.248640\pi\)
\(6\) −0.847217 −0.345875
\(7\) 1.00000 0.377964
\(8\) −7.87900 −2.78565
\(9\) −2.89719 −0.965731
\(10\) −8.39136 −2.65358
\(11\) −2.25492 −0.679884 −0.339942 0.940446i \(-0.610407\pi\)
−0.339942 + 0.940446i \(0.610407\pi\)
\(12\) 1.59735 0.461115
\(13\) −4.14521 −1.14967 −0.574837 0.818268i \(-0.694935\pi\)
−0.574837 + 0.818268i \(0.694935\pi\)
\(14\) −2.64232 −0.706189
\(15\) 1.01826 0.262912
\(16\) 10.8551 2.71378
\(17\) −4.34057 −1.05274 −0.526371 0.850255i \(-0.676448\pi\)
−0.526371 + 0.850255i \(0.676448\pi\)
\(18\) 7.65531 1.80437
\(19\) −3.45874 −0.793489 −0.396744 0.917929i \(-0.629860\pi\)
−0.396744 + 0.917929i \(0.629860\pi\)
\(20\) 15.8211 3.53772
\(21\) 0.320634 0.0699680
\(22\) 5.95822 1.27030
\(23\) −0.0874563 −0.0182359 −0.00911795 0.999958i \(-0.502902\pi\)
−0.00911795 + 0.999958i \(0.502902\pi\)
\(24\) −2.52627 −0.515674
\(25\) 5.08544 1.01709
\(26\) 10.9530 2.14805
\(27\) −1.89084 −0.363892
\(28\) 4.98185 0.941481
\(29\) 8.08271 1.50092 0.750461 0.660915i \(-0.229832\pi\)
0.750461 + 0.660915i \(0.229832\pi\)
\(30\) −2.69056 −0.491226
\(31\) −1.22874 −0.220689 −0.110345 0.993893i \(-0.535195\pi\)
−0.110345 + 0.993893i \(0.535195\pi\)
\(32\) −12.9247 −2.28479
\(33\) −0.723004 −0.125859
\(34\) 11.4692 1.96695
\(35\) 3.17576 0.536801
\(36\) −14.4334 −2.40556
\(37\) 2.47866 0.407490 0.203745 0.979024i \(-0.434689\pi\)
0.203745 + 0.979024i \(0.434689\pi\)
\(38\) 9.13908 1.48256
\(39\) −1.32909 −0.212825
\(40\) −25.0218 −3.95629
\(41\) 0.513039 0.0801232 0.0400616 0.999197i \(-0.487245\pi\)
0.0400616 + 0.999197i \(0.487245\pi\)
\(42\) −0.847217 −0.130728
\(43\) 1.83803 0.280297 0.140149 0.990130i \(-0.455242\pi\)
0.140149 + 0.990130i \(0.455242\pi\)
\(44\) −11.2337 −1.69354
\(45\) −9.20079 −1.37157
\(46\) 0.231087 0.0340720
\(47\) 3.62406 0.528623 0.264312 0.964437i \(-0.414855\pi\)
0.264312 + 0.964437i \(0.414855\pi\)
\(48\) 3.48052 0.502370
\(49\) 1.00000 0.142857
\(50\) −13.4373 −1.90033
\(51\) −1.39173 −0.194882
\(52\) −20.6508 −2.86375
\(53\) 0.723055 0.0993193 0.0496596 0.998766i \(-0.484186\pi\)
0.0496596 + 0.998766i \(0.484186\pi\)
\(54\) 4.99620 0.679897
\(55\) −7.16108 −0.965600
\(56\) −7.87900 −1.05288
\(57\) −1.10899 −0.146889
\(58\) −21.3571 −2.80433
\(59\) −6.53732 −0.851086 −0.425543 0.904938i \(-0.639917\pi\)
−0.425543 + 0.904938i \(0.639917\pi\)
\(60\) 5.07280 0.654895
\(61\) −0.324330 −0.0415261 −0.0207631 0.999784i \(-0.506610\pi\)
−0.0207631 + 0.999784i \(0.506610\pi\)
\(62\) 3.24673 0.412336
\(63\) −2.89719 −0.365012
\(64\) 12.4410 1.55512
\(65\) −13.1642 −1.63282
\(66\) 1.91041 0.235155
\(67\) 7.47223 0.912879 0.456439 0.889755i \(-0.349125\pi\)
0.456439 + 0.889755i \(0.349125\pi\)
\(68\) −21.6241 −2.62230
\(69\) −0.0280415 −0.00337579
\(70\) −8.39136 −1.00296
\(71\) −6.11028 −0.725156 −0.362578 0.931953i \(-0.618103\pi\)
−0.362578 + 0.931953i \(0.618103\pi\)
\(72\) 22.8270 2.69019
\(73\) −1.38985 −0.162670 −0.0813349 0.996687i \(-0.525918\pi\)
−0.0813349 + 0.996687i \(0.525918\pi\)
\(74\) −6.54942 −0.761355
\(75\) 1.63056 0.188281
\(76\) −17.2309 −1.97652
\(77\) −2.25492 −0.256972
\(78\) 3.51189 0.397643
\(79\) 4.31579 0.485565 0.242782 0.970081i \(-0.421940\pi\)
0.242782 + 0.970081i \(0.421940\pi\)
\(80\) 34.4733 3.85423
\(81\) 8.08531 0.898368
\(82\) −1.35561 −0.149702
\(83\) 16.0073 1.75703 0.878515 0.477715i \(-0.158535\pi\)
0.878515 + 0.477715i \(0.158535\pi\)
\(84\) 1.59735 0.174285
\(85\) −13.7846 −1.49515
\(86\) −4.85667 −0.523708
\(87\) 2.59159 0.277848
\(88\) 17.7665 1.89392
\(89\) 0.168935 0.0179071 0.00895355 0.999960i \(-0.497150\pi\)
0.00895355 + 0.999960i \(0.497150\pi\)
\(90\) 24.3114 2.56265
\(91\) −4.14521 −0.434536
\(92\) −0.435694 −0.0454243
\(93\) −0.393977 −0.0408535
\(94\) −9.57591 −0.987680
\(95\) −10.9841 −1.12695
\(96\) −4.14410 −0.422956
\(97\) 4.41054 0.447822 0.223911 0.974610i \(-0.428117\pi\)
0.223911 + 0.974610i \(0.428117\pi\)
\(98\) −2.64232 −0.266915
\(99\) 6.53294 0.656585
\(100\) 25.3349 2.53349
\(101\) 14.1880 1.41176 0.705881 0.708331i \(-0.250552\pi\)
0.705881 + 0.708331i \(0.250552\pi\)
\(102\) 3.67740 0.364117
\(103\) 8.06600 0.794766 0.397383 0.917653i \(-0.369918\pi\)
0.397383 + 0.917653i \(0.369918\pi\)
\(104\) 32.6601 3.20259
\(105\) 1.01826 0.0993716
\(106\) −1.91054 −0.185568
\(107\) −3.05395 −0.295236 −0.147618 0.989044i \(-0.547161\pi\)
−0.147618 + 0.989044i \(0.547161\pi\)
\(108\) −9.41988 −0.906429
\(109\) −10.6433 −1.01945 −0.509724 0.860338i \(-0.670252\pi\)
−0.509724 + 0.860338i \(0.670252\pi\)
\(110\) 18.9219 1.80413
\(111\) 0.794744 0.0754337
\(112\) 10.8551 1.02571
\(113\) −4.99844 −0.470214 −0.235107 0.971969i \(-0.575544\pi\)
−0.235107 + 0.971969i \(0.575544\pi\)
\(114\) 2.93030 0.274448
\(115\) −0.277740 −0.0258994
\(116\) 40.2669 3.73868
\(117\) 12.0095 1.11028
\(118\) 17.2737 1.59017
\(119\) −4.34057 −0.397899
\(120\) −8.02283 −0.732381
\(121\) −5.91533 −0.537758
\(122\) 0.856982 0.0775875
\(123\) 0.164498 0.0148323
\(124\) −6.12142 −0.549720
\(125\) 0.271324 0.0242680
\(126\) 7.65531 0.681989
\(127\) 6.43874 0.571346 0.285673 0.958327i \(-0.407783\pi\)
0.285673 + 0.958327i \(0.407783\pi\)
\(128\) −7.02359 −0.620803
\(129\) 0.589335 0.0518881
\(130\) 34.7840 3.05076
\(131\) 7.45692 0.651514 0.325757 0.945454i \(-0.394381\pi\)
0.325757 + 0.945454i \(0.394381\pi\)
\(132\) −3.60190 −0.313505
\(133\) −3.45874 −0.299910
\(134\) −19.7440 −1.70562
\(135\) −6.00485 −0.516815
\(136\) 34.1993 2.93257
\(137\) 18.5423 1.58418 0.792088 0.610407i \(-0.208994\pi\)
0.792088 + 0.610407i \(0.208994\pi\)
\(138\) 0.0740945 0.00630734
\(139\) −12.4252 −1.05390 −0.526948 0.849898i \(-0.676664\pi\)
−0.526948 + 0.849898i \(0.676664\pi\)
\(140\) 15.8211 1.33713
\(141\) 1.16200 0.0978577
\(142\) 16.1453 1.35488
\(143\) 9.34712 0.781645
\(144\) −31.4494 −2.62079
\(145\) 25.6687 2.13167
\(146\) 3.67243 0.303933
\(147\) 0.320634 0.0264454
\(148\) 12.3483 1.01503
\(149\) 16.0116 1.31172 0.655860 0.754882i \(-0.272306\pi\)
0.655860 + 0.754882i \(0.272306\pi\)
\(150\) −4.30847 −0.351785
\(151\) 3.72561 0.303185 0.151593 0.988443i \(-0.451560\pi\)
0.151593 + 0.988443i \(0.451560\pi\)
\(152\) 27.2514 2.21038
\(153\) 12.5755 1.01667
\(154\) 5.95822 0.480127
\(155\) −3.90219 −0.313432
\(156\) −6.62135 −0.530132
\(157\) −13.5703 −1.08303 −0.541515 0.840691i \(-0.682149\pi\)
−0.541515 + 0.840691i \(0.682149\pi\)
\(158\) −11.4037 −0.907230
\(159\) 0.231836 0.0183858
\(160\) −41.0458 −3.24495
\(161\) −0.0874563 −0.00689252
\(162\) −21.3640 −1.67851
\(163\) 7.25112 0.567952 0.283976 0.958831i \(-0.408346\pi\)
0.283976 + 0.958831i \(0.408346\pi\)
\(164\) 2.55588 0.199581
\(165\) −2.29609 −0.178750
\(166\) −42.2964 −3.28284
\(167\) 13.2017 1.02158 0.510788 0.859706i \(-0.329354\pi\)
0.510788 + 0.859706i \(0.329354\pi\)
\(168\) −2.52627 −0.194906
\(169\) 4.18276 0.321751
\(170\) 36.4233 2.79354
\(171\) 10.0206 0.766297
\(172\) 9.15680 0.698200
\(173\) 12.3773 0.941030 0.470515 0.882392i \(-0.344068\pi\)
0.470515 + 0.882392i \(0.344068\pi\)
\(174\) −6.84781 −0.519131
\(175\) 5.08544 0.384423
\(176\) −24.4775 −1.84506
\(177\) −2.09609 −0.157551
\(178\) −0.446381 −0.0334577
\(179\) 19.9556 1.49155 0.745776 0.666197i \(-0.232079\pi\)
0.745776 + 0.666197i \(0.232079\pi\)
\(180\) −45.8369 −3.41648
\(181\) −0.979065 −0.0727734 −0.0363867 0.999338i \(-0.511585\pi\)
−0.0363867 + 0.999338i \(0.511585\pi\)
\(182\) 10.9530 0.811888
\(183\) −0.103991 −0.00768724
\(184\) 0.689068 0.0507988
\(185\) 7.87164 0.578734
\(186\) 1.04101 0.0763308
\(187\) 9.78763 0.715743
\(188\) 18.0545 1.31676
\(189\) −1.89084 −0.137538
\(190\) 29.0235 2.10559
\(191\) 7.02299 0.508166 0.254083 0.967182i \(-0.418226\pi\)
0.254083 + 0.967182i \(0.418226\pi\)
\(192\) 3.98900 0.287881
\(193\) 16.0737 1.15701 0.578506 0.815678i \(-0.303636\pi\)
0.578506 + 0.815678i \(0.303636\pi\)
\(194\) −11.6540 −0.836712
\(195\) −4.22088 −0.302264
\(196\) 4.98185 0.355846
\(197\) −8.03130 −0.572207 −0.286103 0.958199i \(-0.592360\pi\)
−0.286103 + 0.958199i \(0.592360\pi\)
\(198\) −17.2621 −1.22677
\(199\) 21.6683 1.53603 0.768013 0.640434i \(-0.221246\pi\)
0.768013 + 0.640434i \(0.221246\pi\)
\(200\) −40.0682 −2.83325
\(201\) 2.39585 0.168990
\(202\) −37.4893 −2.63774
\(203\) 8.08271 0.567295
\(204\) −6.93341 −0.485435
\(205\) 1.62929 0.113794
\(206\) −21.3129 −1.48494
\(207\) 0.253378 0.0176110
\(208\) −44.9968 −3.11997
\(209\) 7.79918 0.539480
\(210\) −2.69056 −0.185666
\(211\) −20.5592 −1.41535 −0.707677 0.706536i \(-0.750257\pi\)
−0.707677 + 0.706536i \(0.750257\pi\)
\(212\) 3.60215 0.247397
\(213\) −1.95916 −0.134240
\(214\) 8.06951 0.551620
\(215\) 5.83715 0.398090
\(216\) 14.8979 1.01368
\(217\) −1.22874 −0.0834126
\(218\) 28.1231 1.90474
\(219\) −0.445633 −0.0301131
\(220\) −35.6754 −2.40524
\(221\) 17.9926 1.21031
\(222\) −2.09997 −0.140941
\(223\) 22.4438 1.50295 0.751475 0.659762i \(-0.229343\pi\)
0.751475 + 0.659762i \(0.229343\pi\)
\(224\) −12.9247 −0.863569
\(225\) −14.7335 −0.982233
\(226\) 13.2075 0.878549
\(227\) 10.4453 0.693277 0.346638 0.937999i \(-0.387323\pi\)
0.346638 + 0.937999i \(0.387323\pi\)
\(228\) −5.52481 −0.365890
\(229\) 15.2443 1.00737 0.503686 0.863887i \(-0.331977\pi\)
0.503686 + 0.863887i \(0.331977\pi\)
\(230\) 0.733878 0.0483905
\(231\) −0.723004 −0.0475702
\(232\) −63.6837 −4.18104
\(233\) −25.4580 −1.66781 −0.833905 0.551907i \(-0.813900\pi\)
−0.833905 + 0.551907i \(0.813900\pi\)
\(234\) −31.7329 −2.07444
\(235\) 11.5091 0.750773
\(236\) −32.5679 −2.11999
\(237\) 1.38379 0.0898868
\(238\) 11.4692 0.743436
\(239\) −24.1092 −1.55950 −0.779749 0.626093i \(-0.784653\pi\)
−0.779749 + 0.626093i \(0.784653\pi\)
\(240\) 11.0533 0.713487
\(241\) −20.0411 −1.29096 −0.645482 0.763776i \(-0.723343\pi\)
−0.645482 + 0.763776i \(0.723343\pi\)
\(242\) 15.6302 1.00475
\(243\) 8.26495 0.530197
\(244\) −1.61576 −0.103439
\(245\) 3.17576 0.202892
\(246\) −0.434655 −0.0277126
\(247\) 14.3372 0.912253
\(248\) 9.68128 0.614762
\(249\) 5.13248 0.325258
\(250\) −0.716925 −0.0453423
\(251\) 21.6054 1.36372 0.681861 0.731481i \(-0.261171\pi\)
0.681861 + 0.731481i \(0.261171\pi\)
\(252\) −14.4334 −0.909218
\(253\) 0.197207 0.0123983
\(254\) −17.0132 −1.06750
\(255\) −4.41981 −0.276779
\(256\) −6.32340 −0.395212
\(257\) 23.0018 1.43482 0.717408 0.696654i \(-0.245329\pi\)
0.717408 + 0.696654i \(0.245329\pi\)
\(258\) −1.55721 −0.0969478
\(259\) 2.47866 0.154017
\(260\) −65.5820 −4.06722
\(261\) −23.4172 −1.44949
\(262\) −19.7036 −1.21729
\(263\) −2.20155 −0.135754 −0.0678768 0.997694i \(-0.521622\pi\)
−0.0678768 + 0.997694i \(0.521622\pi\)
\(264\) 5.69655 0.350598
\(265\) 2.29625 0.141057
\(266\) 9.13908 0.560353
\(267\) 0.0541664 0.00331493
\(268\) 37.2256 2.27391
\(269\) 18.5627 1.13178 0.565892 0.824479i \(-0.308532\pi\)
0.565892 + 0.824479i \(0.308532\pi\)
\(270\) 15.8667 0.965618
\(271\) −14.7983 −0.898930 −0.449465 0.893298i \(-0.648385\pi\)
−0.449465 + 0.893298i \(0.648385\pi\)
\(272\) −47.1174 −2.85691
\(273\) −1.32909 −0.0804405
\(274\) −48.9947 −2.95988
\(275\) −11.4673 −0.691501
\(276\) −0.139698 −0.00840885
\(277\) −12.6694 −0.761232 −0.380616 0.924733i \(-0.624288\pi\)
−0.380616 + 0.924733i \(0.624288\pi\)
\(278\) 32.8314 1.96910
\(279\) 3.55991 0.213126
\(280\) −25.0218 −1.49534
\(281\) −4.86512 −0.290229 −0.145114 0.989415i \(-0.546355\pi\)
−0.145114 + 0.989415i \(0.546355\pi\)
\(282\) −3.07036 −0.182837
\(283\) −5.17506 −0.307625 −0.153813 0.988100i \(-0.549155\pi\)
−0.153813 + 0.988100i \(0.549155\pi\)
\(284\) −30.4405 −1.80631
\(285\) −3.52188 −0.208618
\(286\) −24.6981 −1.46043
\(287\) 0.513039 0.0302837
\(288\) 37.4454 2.20649
\(289\) 1.84053 0.108266
\(290\) −67.8250 −3.98282
\(291\) 1.41417 0.0829000
\(292\) −6.92403 −0.405198
\(293\) −7.98020 −0.466208 −0.233104 0.972452i \(-0.574888\pi\)
−0.233104 + 0.972452i \(0.574888\pi\)
\(294\) −0.847217 −0.0494107
\(295\) −20.7609 −1.20875
\(296\) −19.5294 −1.13512
\(297\) 4.26369 0.247405
\(298\) −42.3077 −2.45082
\(299\) 0.362525 0.0209653
\(300\) 8.12322 0.468994
\(301\) 1.83803 0.105942
\(302\) −9.84424 −0.566472
\(303\) 4.54916 0.261342
\(304\) −37.5450 −2.15336
\(305\) −1.02999 −0.0589772
\(306\) −33.2284 −1.89954
\(307\) −13.5611 −0.773973 −0.386986 0.922085i \(-0.626484\pi\)
−0.386986 + 0.922085i \(0.626484\pi\)
\(308\) −11.2337 −0.640098
\(309\) 2.58623 0.147126
\(310\) 10.3108 0.585617
\(311\) −9.64570 −0.546957 −0.273479 0.961878i \(-0.588174\pi\)
−0.273479 + 0.961878i \(0.588174\pi\)
\(312\) 10.4719 0.592857
\(313\) 10.3211 0.583384 0.291692 0.956512i \(-0.405782\pi\)
0.291692 + 0.956512i \(0.405782\pi\)
\(314\) 35.8572 2.02354
\(315\) −9.20079 −0.518406
\(316\) 21.5006 1.20951
\(317\) 4.47127 0.251132 0.125566 0.992085i \(-0.459925\pi\)
0.125566 + 0.992085i \(0.459925\pi\)
\(318\) −0.612585 −0.0343520
\(319\) −18.2259 −1.02045
\(320\) 39.5095 2.20865
\(321\) −0.979199 −0.0546536
\(322\) 0.231087 0.0128780
\(323\) 15.0129 0.835339
\(324\) 40.2798 2.23777
\(325\) −21.0802 −1.16932
\(326\) −19.1598 −1.06116
\(327\) −3.41262 −0.188718
\(328\) −4.04223 −0.223195
\(329\) 3.62406 0.199801
\(330\) 6.06699 0.333977
\(331\) 13.1757 0.724201 0.362100 0.932139i \(-0.382060\pi\)
0.362100 + 0.932139i \(0.382060\pi\)
\(332\) 79.7460 4.37663
\(333\) −7.18117 −0.393526
\(334\) −34.8831 −1.90872
\(335\) 23.7300 1.29651
\(336\) 3.48052 0.189878
\(337\) 7.32420 0.398975 0.199487 0.979900i \(-0.436072\pi\)
0.199487 + 0.979900i \(0.436072\pi\)
\(338\) −11.0522 −0.601159
\(339\) −1.60267 −0.0870451
\(340\) −68.6728 −3.72430
\(341\) 2.77072 0.150043
\(342\) −26.4777 −1.43175
\(343\) 1.00000 0.0539949
\(344\) −14.4819 −0.780809
\(345\) −0.0890529 −0.00479445
\(346\) −32.7048 −1.75822
\(347\) −27.5390 −1.47837 −0.739186 0.673501i \(-0.764790\pi\)
−0.739186 + 0.673501i \(0.764790\pi\)
\(348\) 12.9109 0.692098
\(349\) 26.4658 1.41668 0.708341 0.705870i \(-0.249444\pi\)
0.708341 + 0.705870i \(0.249444\pi\)
\(350\) −13.4373 −0.718256
\(351\) 7.83793 0.418358
\(352\) 29.1442 1.55339
\(353\) 5.00160 0.266208 0.133104 0.991102i \(-0.457506\pi\)
0.133104 + 0.991102i \(0.457506\pi\)
\(354\) 5.53853 0.294369
\(355\) −19.4048 −1.02990
\(356\) 0.841610 0.0446053
\(357\) −1.39173 −0.0736583
\(358\) −52.7291 −2.78682
\(359\) 25.4529 1.34335 0.671677 0.740844i \(-0.265574\pi\)
0.671677 + 0.740844i \(0.265574\pi\)
\(360\) 72.4930 3.82072
\(361\) −7.03714 −0.370376
\(362\) 2.58700 0.135970
\(363\) −1.89666 −0.0995486
\(364\) −20.6508 −1.08240
\(365\) −4.41383 −0.231030
\(366\) 0.274778 0.0143629
\(367\) −3.59788 −0.187808 −0.0939040 0.995581i \(-0.529935\pi\)
−0.0939040 + 0.995581i \(0.529935\pi\)
\(368\) −0.949350 −0.0494883
\(369\) −1.48637 −0.0773775
\(370\) −20.7994 −1.08131
\(371\) 0.723055 0.0375392
\(372\) −1.96273 −0.101763
\(373\) 3.59247 0.186011 0.0930054 0.995666i \(-0.470353\pi\)
0.0930054 + 0.995666i \(0.470353\pi\)
\(374\) −25.8621 −1.33730
\(375\) 0.0869958 0.00449244
\(376\) −28.5539 −1.47256
\(377\) −33.5045 −1.72557
\(378\) 4.99620 0.256977
\(379\) 1.68973 0.0867954 0.0433977 0.999058i \(-0.486182\pi\)
0.0433977 + 0.999058i \(0.486182\pi\)
\(380\) −54.7212 −2.80714
\(381\) 2.06448 0.105766
\(382\) −18.5570 −0.949458
\(383\) 10.7477 0.549181 0.274590 0.961561i \(-0.411458\pi\)
0.274590 + 0.961561i \(0.411458\pi\)
\(384\) −2.25200 −0.114922
\(385\) −7.16108 −0.364962
\(386\) −42.4719 −2.16176
\(387\) −5.32514 −0.270692
\(388\) 21.9726 1.11549
\(389\) 16.3811 0.830555 0.415278 0.909695i \(-0.363684\pi\)
0.415278 + 0.909695i \(0.363684\pi\)
\(390\) 11.1529 0.564750
\(391\) 0.379610 0.0191977
\(392\) −7.87900 −0.397950
\(393\) 2.39094 0.120607
\(394\) 21.2213 1.06911
\(395\) 13.7059 0.689619
\(396\) 32.5461 1.63551
\(397\) −16.5515 −0.830695 −0.415347 0.909663i \(-0.636340\pi\)
−0.415347 + 0.909663i \(0.636340\pi\)
\(398\) −57.2546 −2.86991
\(399\) −1.10899 −0.0555188
\(400\) 55.2031 2.76015
\(401\) 21.4851 1.07292 0.536458 0.843927i \(-0.319762\pi\)
0.536458 + 0.843927i \(0.319762\pi\)
\(402\) −6.33060 −0.315742
\(403\) 5.09340 0.253720
\(404\) 70.6826 3.51659
\(405\) 25.6770 1.27590
\(406\) −21.3571 −1.05994
\(407\) −5.58919 −0.277046
\(408\) 10.9655 0.542871
\(409\) −15.9226 −0.787321 −0.393661 0.919256i \(-0.628791\pi\)
−0.393661 + 0.919256i \(0.628791\pi\)
\(410\) −4.30510 −0.212614
\(411\) 5.94529 0.293259
\(412\) 40.1836 1.97970
\(413\) −6.53732 −0.321680
\(414\) −0.669505 −0.0329044
\(415\) 50.8353 2.49541
\(416\) 53.5757 2.62676
\(417\) −3.98395 −0.195095
\(418\) −20.6079 −1.00797
\(419\) −2.24045 −0.109453 −0.0547266 0.998501i \(-0.517429\pi\)
−0.0547266 + 0.998501i \(0.517429\pi\)
\(420\) 5.07280 0.247527
\(421\) 5.19408 0.253144 0.126572 0.991957i \(-0.459603\pi\)
0.126572 + 0.991957i \(0.459603\pi\)
\(422\) 54.3239 2.64445
\(423\) −10.4996 −0.510508
\(424\) −5.69695 −0.276668
\(425\) −22.0737 −1.07073
\(426\) 5.17673 0.250813
\(427\) −0.324330 −0.0156954
\(428\) −15.2143 −0.735412
\(429\) 2.99700 0.144697
\(430\) −15.4236 −0.743792
\(431\) 10.7555 0.518076 0.259038 0.965867i \(-0.416594\pi\)
0.259038 + 0.965867i \(0.416594\pi\)
\(432\) −20.5253 −0.987525
\(433\) 2.38804 0.114762 0.0573810 0.998352i \(-0.481725\pi\)
0.0573810 + 0.998352i \(0.481725\pi\)
\(434\) 3.24673 0.155848
\(435\) 8.23027 0.394611
\(436\) −53.0236 −2.53937
\(437\) 0.302488 0.0144700
\(438\) 1.17751 0.0562634
\(439\) 13.5279 0.645650 0.322825 0.946459i \(-0.395368\pi\)
0.322825 + 0.946459i \(0.395368\pi\)
\(440\) 56.4222 2.68982
\(441\) −2.89719 −0.137962
\(442\) −47.5421 −2.26135
\(443\) 15.3217 0.727956 0.363978 0.931408i \(-0.381418\pi\)
0.363978 + 0.931408i \(0.381418\pi\)
\(444\) 3.95929 0.187900
\(445\) 0.536498 0.0254324
\(446\) −59.3037 −2.80811
\(447\) 5.13386 0.242823
\(448\) 12.4410 0.587781
\(449\) −12.1618 −0.573951 −0.286976 0.957938i \(-0.592650\pi\)
−0.286976 + 0.957938i \(0.592650\pi\)
\(450\) 38.9306 1.83521
\(451\) −1.15686 −0.0544745
\(452\) −24.9015 −1.17127
\(453\) 1.19456 0.0561251
\(454\) −27.5997 −1.29532
\(455\) −13.1642 −0.617146
\(456\) 8.73772 0.409181
\(457\) −11.4311 −0.534724 −0.267362 0.963596i \(-0.586152\pi\)
−0.267362 + 0.963596i \(0.586152\pi\)
\(458\) −40.2803 −1.88218
\(459\) 8.20732 0.383085
\(460\) −1.38366 −0.0645135
\(461\) 0.207894 0.00968258 0.00484129 0.999988i \(-0.498459\pi\)
0.00484129 + 0.999988i \(0.498459\pi\)
\(462\) 1.91041 0.0888802
\(463\) 13.3184 0.618958 0.309479 0.950906i \(-0.399845\pi\)
0.309479 + 0.950906i \(0.399845\pi\)
\(464\) 87.7389 4.07318
\(465\) −1.25118 −0.0580219
\(466\) 67.2682 3.11614
\(467\) 39.7135 1.83772 0.918862 0.394580i \(-0.129110\pi\)
0.918862 + 0.394580i \(0.129110\pi\)
\(468\) 59.8294 2.76562
\(469\) 7.47223 0.345036
\(470\) −30.4108 −1.40274
\(471\) −4.35111 −0.200489
\(472\) 51.5075 2.37083
\(473\) −4.14462 −0.190570
\(474\) −3.65641 −0.167945
\(475\) −17.5892 −0.807047
\(476\) −21.6241 −0.991137
\(477\) −2.09483 −0.0959157
\(478\) 63.7043 2.91377
\(479\) −27.5611 −1.25930 −0.629649 0.776880i \(-0.716801\pi\)
−0.629649 + 0.776880i \(0.716801\pi\)
\(480\) −13.1607 −0.600700
\(481\) −10.2746 −0.468481
\(482\) 52.9551 2.41204
\(483\) −0.0280415 −0.00127593
\(484\) −29.4693 −1.33951
\(485\) 14.0068 0.636016
\(486\) −21.8386 −0.990620
\(487\) 24.9500 1.13059 0.565296 0.824888i \(-0.308762\pi\)
0.565296 + 0.824888i \(0.308762\pi\)
\(488\) 2.55539 0.115677
\(489\) 2.32495 0.105138
\(490\) −8.39136 −0.379083
\(491\) −3.63544 −0.164065 −0.0820326 0.996630i \(-0.526141\pi\)
−0.0820326 + 0.996630i \(0.526141\pi\)
\(492\) 0.819503 0.0369460
\(493\) −35.0836 −1.58008
\(494\) −37.8834 −1.70446
\(495\) 20.7470 0.932510
\(496\) −13.3382 −0.598902
\(497\) −6.11028 −0.274083
\(498\) −13.5617 −0.607713
\(499\) −39.5693 −1.77137 −0.885683 0.464290i \(-0.846310\pi\)
−0.885683 + 0.464290i \(0.846310\pi\)
\(500\) 1.35170 0.0604497
\(501\) 4.23291 0.189112
\(502\) −57.0884 −2.54798
\(503\) 2.80048 0.124867 0.0624336 0.998049i \(-0.480114\pi\)
0.0624336 + 0.998049i \(0.480114\pi\)
\(504\) 22.8270 1.01679
\(505\) 45.0577 2.00504
\(506\) −0.521084 −0.0231650
\(507\) 1.34113 0.0595618
\(508\) 32.0768 1.42318
\(509\) 14.0930 0.624662 0.312331 0.949973i \(-0.398890\pi\)
0.312331 + 0.949973i \(0.398890\pi\)
\(510\) 11.6785 0.517134
\(511\) −1.38985 −0.0614834
\(512\) 30.7556 1.35922
\(513\) 6.53992 0.288744
\(514\) −60.7782 −2.68081
\(515\) 25.6156 1.12876
\(516\) 2.93598 0.129249
\(517\) −8.17196 −0.359402
\(518\) −6.54942 −0.287765
\(519\) 3.96859 0.174202
\(520\) 103.721 4.54845
\(521\) 37.2880 1.63362 0.816809 0.576908i \(-0.195741\pi\)
0.816809 + 0.576908i \(0.195741\pi\)
\(522\) 61.8757 2.70822
\(523\) −25.1252 −1.09865 −0.549325 0.835609i \(-0.685115\pi\)
−0.549325 + 0.835609i \(0.685115\pi\)
\(524\) 37.1492 1.62287
\(525\) 1.63056 0.0711636
\(526\) 5.81720 0.253642
\(527\) 5.33345 0.232329
\(528\) −7.84830 −0.341554
\(529\) −22.9924 −0.999667
\(530\) −6.06742 −0.263552
\(531\) 18.9399 0.821921
\(532\) −17.2309 −0.747055
\(533\) −2.12665 −0.0921156
\(534\) −0.143125 −0.00619362
\(535\) −9.69860 −0.419307
\(536\) −58.8737 −2.54296
\(537\) 6.39844 0.276113
\(538\) −49.0485 −2.11463
\(539\) −2.25492 −0.0971263
\(540\) −29.9153 −1.28735
\(541\) −2.79764 −0.120280 −0.0601400 0.998190i \(-0.519155\pi\)
−0.0601400 + 0.998190i \(0.519155\pi\)
\(542\) 39.1017 1.67956
\(543\) −0.313922 −0.0134717
\(544\) 56.1006 2.40529
\(545\) −33.8007 −1.44786
\(546\) 3.51189 0.150295
\(547\) 1.01710 0.0434878 0.0217439 0.999764i \(-0.493078\pi\)
0.0217439 + 0.999764i \(0.493078\pi\)
\(548\) 92.3749 3.94606
\(549\) 0.939646 0.0401031
\(550\) 30.3001 1.29200
\(551\) −27.9560 −1.19096
\(552\) 0.220939 0.00940377
\(553\) 4.31579 0.183526
\(554\) 33.4767 1.42229
\(555\) 2.52391 0.107134
\(556\) −61.9007 −2.62517
\(557\) 11.3077 0.479121 0.239560 0.970881i \(-0.422997\pi\)
0.239560 + 0.970881i \(0.422997\pi\)
\(558\) −9.40642 −0.398206
\(559\) −7.61903 −0.322251
\(560\) 34.4733 1.45676
\(561\) 3.13825 0.132497
\(562\) 12.8552 0.542264
\(563\) −38.2528 −1.61217 −0.806083 0.591803i \(-0.798416\pi\)
−0.806083 + 0.591803i \(0.798416\pi\)
\(564\) 5.78889 0.243756
\(565\) −15.8738 −0.667818
\(566\) 13.6742 0.574768
\(567\) 8.08531 0.339551
\(568\) 48.1429 2.02003
\(569\) 23.1702 0.971346 0.485673 0.874141i \(-0.338575\pi\)
0.485673 + 0.874141i \(0.338575\pi\)
\(570\) 9.30592 0.389782
\(571\) 12.5117 0.523598 0.261799 0.965122i \(-0.415684\pi\)
0.261799 + 0.965122i \(0.415684\pi\)
\(572\) 46.5659 1.94702
\(573\) 2.25181 0.0940706
\(574\) −1.35561 −0.0565822
\(575\) −0.444754 −0.0185475
\(576\) −36.0439 −1.50183
\(577\) 18.0570 0.751721 0.375860 0.926676i \(-0.377347\pi\)
0.375860 + 0.926676i \(0.377347\pi\)
\(578\) −4.86326 −0.202285
\(579\) 5.15378 0.214184
\(580\) 127.878 5.30984
\(581\) 16.0073 0.664095
\(582\) −3.73668 −0.154890
\(583\) −1.63043 −0.0675256
\(584\) 10.9506 0.453141
\(585\) 38.1392 1.57686
\(586\) 21.0862 0.871064
\(587\) −28.2171 −1.16464 −0.582322 0.812958i \(-0.697856\pi\)
−0.582322 + 0.812958i \(0.697856\pi\)
\(588\) 1.59735 0.0658736
\(589\) 4.24990 0.175114
\(590\) 54.8570 2.25843
\(591\) −2.57511 −0.105926
\(592\) 26.9062 1.10584
\(593\) 15.5471 0.638442 0.319221 0.947680i \(-0.396579\pi\)
0.319221 + 0.947680i \(0.396579\pi\)
\(594\) −11.2660 −0.462251
\(595\) −13.7846 −0.565113
\(596\) 79.7674 3.26740
\(597\) 6.94760 0.284346
\(598\) −0.957906 −0.0391717
\(599\) −23.3398 −0.953638 −0.476819 0.879002i \(-0.658210\pi\)
−0.476819 + 0.879002i \(0.658210\pi\)
\(600\) −12.8472 −0.524485
\(601\) −7.53645 −0.307418 −0.153709 0.988116i \(-0.549122\pi\)
−0.153709 + 0.988116i \(0.549122\pi\)
\(602\) −4.85667 −0.197943
\(603\) −21.6485 −0.881596
\(604\) 18.5604 0.755212
\(605\) −18.7857 −0.763746
\(606\) −12.0203 −0.488293
\(607\) 31.0866 1.26177 0.630883 0.775878i \(-0.282693\pi\)
0.630883 + 0.775878i \(0.282693\pi\)
\(608\) 44.7032 1.81295
\(609\) 2.59159 0.105017
\(610\) 2.72157 0.110193
\(611\) −15.0225 −0.607744
\(612\) 62.6491 2.53244
\(613\) −2.93536 −0.118558 −0.0592790 0.998241i \(-0.518880\pi\)
−0.0592790 + 0.998241i \(0.518880\pi\)
\(614\) 35.8328 1.44609
\(615\) 0.522405 0.0210654
\(616\) 17.7665 0.715833
\(617\) 42.2244 1.69989 0.849944 0.526873i \(-0.176636\pi\)
0.849944 + 0.526873i \(0.176636\pi\)
\(618\) −6.83365 −0.274890
\(619\) −23.9597 −0.963020 −0.481510 0.876440i \(-0.659912\pi\)
−0.481510 + 0.876440i \(0.659912\pi\)
\(620\) −19.4401 −0.780735
\(621\) 0.165366 0.00663591
\(622\) 25.4870 1.02194
\(623\) 0.168935 0.00676825
\(624\) −14.4275 −0.577562
\(625\) −24.5655 −0.982621
\(626\) −27.2717 −1.09000
\(627\) 2.50068 0.0998675
\(628\) −67.6054 −2.69775
\(629\) −10.7588 −0.428982
\(630\) 24.3114 0.968590
\(631\) 21.9157 0.872449 0.436224 0.899838i \(-0.356315\pi\)
0.436224 + 0.899838i \(0.356315\pi\)
\(632\) −34.0041 −1.35261
\(633\) −6.59197 −0.262007
\(634\) −11.8145 −0.469215
\(635\) 20.4479 0.811449
\(636\) 1.15497 0.0457976
\(637\) −4.14521 −0.164239
\(638\) 48.1586 1.90662
\(639\) 17.7027 0.700306
\(640\) −22.3052 −0.881691
\(641\) 2.78360 0.109945 0.0549727 0.998488i \(-0.482493\pi\)
0.0549727 + 0.998488i \(0.482493\pi\)
\(642\) 2.58736 0.102115
\(643\) −1.77914 −0.0701625 −0.0350812 0.999384i \(-0.511169\pi\)
−0.0350812 + 0.999384i \(0.511169\pi\)
\(644\) −0.435694 −0.0171688
\(645\) 1.87159 0.0736937
\(646\) −39.6688 −1.56075
\(647\) 10.0738 0.396041 0.198021 0.980198i \(-0.436549\pi\)
0.198021 + 0.980198i \(0.436549\pi\)
\(648\) −63.7042 −2.50254
\(649\) 14.7411 0.578640
\(650\) 55.7006 2.18476
\(651\) −0.393977 −0.0154412
\(652\) 36.1240 1.41472
\(653\) 10.7235 0.419643 0.209821 0.977740i \(-0.432712\pi\)
0.209821 + 0.977740i \(0.432712\pi\)
\(654\) 9.01723 0.352601
\(655\) 23.6814 0.925307
\(656\) 5.56910 0.217437
\(657\) 4.02667 0.157095
\(658\) −9.57591 −0.373308
\(659\) 16.0478 0.625135 0.312568 0.949896i \(-0.398811\pi\)
0.312568 + 0.949896i \(0.398811\pi\)
\(660\) −11.4388 −0.445253
\(661\) −46.2532 −1.79904 −0.899520 0.436879i \(-0.856084\pi\)
−0.899520 + 0.436879i \(0.856084\pi\)
\(662\) −34.8143 −1.35310
\(663\) 5.76902 0.224050
\(664\) −126.122 −4.89447
\(665\) −10.9841 −0.425945
\(666\) 18.9749 0.735264
\(667\) −0.706884 −0.0273707
\(668\) 65.7688 2.54467
\(669\) 7.19625 0.278223
\(670\) −62.7022 −2.42240
\(671\) 0.731337 0.0282330
\(672\) −4.14410 −0.159862
\(673\) 12.6888 0.489118 0.244559 0.969634i \(-0.421357\pi\)
0.244559 + 0.969634i \(0.421357\pi\)
\(674\) −19.3529 −0.745445
\(675\) −9.61575 −0.370110
\(676\) 20.8379 0.801457
\(677\) 35.3157 1.35729 0.678646 0.734466i \(-0.262567\pi\)
0.678646 + 0.734466i \(0.262567\pi\)
\(678\) 4.23477 0.162635
\(679\) 4.41054 0.169261
\(680\) 108.609 4.16496
\(681\) 3.34911 0.128338
\(682\) −7.32113 −0.280341
\(683\) −35.6799 −1.36525 −0.682627 0.730767i \(-0.739163\pi\)
−0.682627 + 0.730767i \(0.739163\pi\)
\(684\) 49.9213 1.90879
\(685\) 58.8858 2.24991
\(686\) −2.64232 −0.100884
\(687\) 4.88784 0.186483
\(688\) 19.9521 0.760666
\(689\) −2.99722 −0.114185
\(690\) 0.235306 0.00895795
\(691\) −27.7905 −1.05720 −0.528599 0.848871i \(-0.677283\pi\)
−0.528599 + 0.848871i \(0.677283\pi\)
\(692\) 61.6619 2.34403
\(693\) 6.53294 0.248166
\(694\) 72.7669 2.76219
\(695\) −39.4595 −1.49679
\(696\) −20.4191 −0.773986
\(697\) −2.22688 −0.0843491
\(698\) −69.9311 −2.64693
\(699\) −8.16271 −0.308742
\(700\) 25.3349 0.957569
\(701\) −23.7986 −0.898860 −0.449430 0.893316i \(-0.648373\pi\)
−0.449430 + 0.893316i \(0.648373\pi\)
\(702\) −20.7103 −0.781660
\(703\) −8.57305 −0.323339
\(704\) −28.0534 −1.05730
\(705\) 3.69022 0.138982
\(706\) −13.2158 −0.497384
\(707\) 14.1880 0.533596
\(708\) −10.4424 −0.392449
\(709\) 2.40624 0.0903683 0.0451842 0.998979i \(-0.485613\pi\)
0.0451842 + 0.998979i \(0.485613\pi\)
\(710\) 51.2736 1.92426
\(711\) −12.5037 −0.468925
\(712\) −1.33104 −0.0498829
\(713\) 0.107461 0.00402446
\(714\) 3.67740 0.137623
\(715\) 29.6842 1.11013
\(716\) 99.4158 3.71534
\(717\) −7.73024 −0.288691
\(718\) −67.2548 −2.50993
\(719\) −2.49024 −0.0928703 −0.0464352 0.998921i \(-0.514786\pi\)
−0.0464352 + 0.998921i \(0.514786\pi\)
\(720\) −99.8757 −3.72215
\(721\) 8.06600 0.300393
\(722\) 18.5944 0.692011
\(723\) −6.42587 −0.238981
\(724\) −4.87756 −0.181273
\(725\) 41.1041 1.52657
\(726\) 5.01157 0.185997
\(727\) 20.1483 0.747261 0.373630 0.927578i \(-0.378113\pi\)
0.373630 + 0.927578i \(0.378113\pi\)
\(728\) 32.6601 1.21046
\(729\) −21.6059 −0.800219
\(730\) 11.6628 0.431658
\(731\) −7.97810 −0.295081
\(732\) −0.518068 −0.0191483
\(733\) 32.3164 1.19363 0.596817 0.802378i \(-0.296432\pi\)
0.596817 + 0.802378i \(0.296432\pi\)
\(734\) 9.50676 0.350901
\(735\) 1.01826 0.0375589
\(736\) 1.13035 0.0416652
\(737\) −16.8493 −0.620652
\(738\) 3.92747 0.144572
\(739\) −5.43566 −0.199954 −0.0999771 0.994990i \(-0.531877\pi\)
−0.0999771 + 0.994990i \(0.531877\pi\)
\(740\) 39.2153 1.44158
\(741\) 4.59699 0.168875
\(742\) −1.91054 −0.0701382
\(743\) −4.12811 −0.151446 −0.0757229 0.997129i \(-0.524126\pi\)
−0.0757229 + 0.997129i \(0.524126\pi\)
\(744\) 3.10415 0.113803
\(745\) 50.8489 1.86296
\(746\) −9.49244 −0.347543
\(747\) −46.3763 −1.69682
\(748\) 48.7605 1.78286
\(749\) −3.05395 −0.111589
\(750\) −0.229871 −0.00839369
\(751\) 29.8530 1.08935 0.544676 0.838647i \(-0.316653\pi\)
0.544676 + 0.838647i \(0.316653\pi\)
\(752\) 39.3396 1.43457
\(753\) 6.92743 0.252450
\(754\) 88.5297 3.22406
\(755\) 11.8316 0.430597
\(756\) −9.41988 −0.342598
\(757\) −4.74385 −0.172418 −0.0862090 0.996277i \(-0.527475\pi\)
−0.0862090 + 0.996277i \(0.527475\pi\)
\(758\) −4.46479 −0.162169
\(759\) 0.0632313 0.00229515
\(760\) 86.5438 3.13927
\(761\) −3.31318 −0.120103 −0.0600513 0.998195i \(-0.519126\pi\)
−0.0600513 + 0.998195i \(0.519126\pi\)
\(762\) −5.45501 −0.197614
\(763\) −10.6433 −0.385315
\(764\) 34.9875 1.26580
\(765\) 39.9366 1.44391
\(766\) −28.3988 −1.02609
\(767\) 27.0985 0.978472
\(768\) −2.02750 −0.0731609
\(769\) −5.16827 −0.186373 −0.0931863 0.995649i \(-0.529705\pi\)
−0.0931863 + 0.995649i \(0.529705\pi\)
\(770\) 18.9219 0.681897
\(771\) 7.37517 0.265610
\(772\) 80.0768 2.88203
\(773\) 43.4416 1.56249 0.781243 0.624228i \(-0.214586\pi\)
0.781243 + 0.624228i \(0.214586\pi\)
\(774\) 14.0707 0.505761
\(775\) −6.24870 −0.224460
\(776\) −34.7506 −1.24747
\(777\) 0.794744 0.0285113
\(778\) −43.2841 −1.55181
\(779\) −1.77447 −0.0635768
\(780\) −21.0278 −0.752916
\(781\) 13.7782 0.493022
\(782\) −1.00305 −0.0358690
\(783\) −15.2831 −0.546174
\(784\) 10.8551 0.387683
\(785\) −43.0961 −1.53817
\(786\) −6.31763 −0.225342
\(787\) 2.28367 0.0814040 0.0407020 0.999171i \(-0.487041\pi\)
0.0407020 + 0.999171i \(0.487041\pi\)
\(788\) −40.0107 −1.42532
\(789\) −0.705892 −0.0251304
\(790\) −36.2154 −1.28849
\(791\) −4.99844 −0.177724
\(792\) −51.4731 −1.82902
\(793\) 1.34441 0.0477415
\(794\) 43.7343 1.55207
\(795\) 0.736255 0.0261123
\(796\) 107.948 3.82613
\(797\) −36.6606 −1.29859 −0.649293 0.760539i \(-0.724935\pi\)
−0.649293 + 0.760539i \(0.724935\pi\)
\(798\) 2.93030 0.103732
\(799\) −15.7305 −0.556504
\(800\) −65.7278 −2.32383
\(801\) −0.489438 −0.0172935
\(802\) −56.7705 −2.00464
\(803\) 3.13400 0.110597
\(804\) 11.9358 0.420942
\(805\) −0.277740 −0.00978905
\(806\) −13.4584 −0.474052
\(807\) 5.95182 0.209514
\(808\) −111.787 −3.93267
\(809\) −46.7473 −1.64355 −0.821774 0.569814i \(-0.807015\pi\)
−0.821774 + 0.569814i \(0.807015\pi\)
\(810\) −67.8468 −2.38389
\(811\) −43.6072 −1.53126 −0.765628 0.643284i \(-0.777571\pi\)
−0.765628 + 0.643284i \(0.777571\pi\)
\(812\) 40.2669 1.41309
\(813\) −4.74482 −0.166408
\(814\) 14.7684 0.517633
\(815\) 23.0278 0.806629
\(816\) −15.1074 −0.528866
\(817\) −6.35727 −0.222413
\(818\) 42.0726 1.47103
\(819\) 12.0095 0.419645
\(820\) 8.11686 0.283453
\(821\) 22.3921 0.781489 0.390745 0.920499i \(-0.372218\pi\)
0.390745 + 0.920499i \(0.372218\pi\)
\(822\) −15.7093 −0.547926
\(823\) 11.4757 0.400019 0.200010 0.979794i \(-0.435903\pi\)
0.200010 + 0.979794i \(0.435903\pi\)
\(824\) −63.5520 −2.21394
\(825\) −3.67679 −0.128009
\(826\) 17.2737 0.601028
\(827\) 21.5012 0.747670 0.373835 0.927495i \(-0.378043\pi\)
0.373835 + 0.927495i \(0.378043\pi\)
\(828\) 1.26229 0.0438676
\(829\) −10.1045 −0.350945 −0.175472 0.984484i \(-0.556145\pi\)
−0.175472 + 0.984484i \(0.556145\pi\)
\(830\) −134.323 −4.66242
\(831\) −4.06225 −0.140918
\(832\) −51.5704 −1.78788
\(833\) −4.34057 −0.150392
\(834\) 10.5269 0.364516
\(835\) 41.9253 1.45089
\(836\) 38.8543 1.34380
\(837\) 2.32336 0.0803070
\(838\) 5.91999 0.204503
\(839\) −18.7556 −0.647514 −0.323757 0.946140i \(-0.604946\pi\)
−0.323757 + 0.946140i \(0.604946\pi\)
\(840\) −8.02283 −0.276814
\(841\) 36.3302 1.25277
\(842\) −13.7244 −0.472975
\(843\) −1.55992 −0.0537265
\(844\) −102.423 −3.52554
\(845\) 13.2834 0.456964
\(846\) 27.7433 0.953834
\(847\) −5.91533 −0.203253
\(848\) 7.84886 0.269531
\(849\) −1.65930 −0.0569470
\(850\) 58.3257 2.00056
\(851\) −0.216775 −0.00743095
\(852\) −9.76025 −0.334381
\(853\) 36.4910 1.24943 0.624713 0.780854i \(-0.285216\pi\)
0.624713 + 0.780854i \(0.285216\pi\)
\(854\) 0.856982 0.0293253
\(855\) 31.8231 1.08833
\(856\) 24.0621 0.822424
\(857\) −25.8429 −0.882777 −0.441388 0.897316i \(-0.645514\pi\)
−0.441388 + 0.897316i \(0.645514\pi\)
\(858\) −7.91904 −0.270351
\(859\) −1.00000 −0.0341196
\(860\) 29.0798 0.991612
\(861\) 0.164498 0.00560606
\(862\) −28.4196 −0.967974
\(863\) 6.51288 0.221701 0.110851 0.993837i \(-0.464643\pi\)
0.110851 + 0.993837i \(0.464643\pi\)
\(864\) 24.4386 0.831417
\(865\) 39.3073 1.33649
\(866\) −6.30997 −0.214421
\(867\) 0.590135 0.0200420
\(868\) −6.12142 −0.207775
\(869\) −9.73177 −0.330128
\(870\) −21.7470 −0.737292
\(871\) −30.9740 −1.04951
\(872\) 83.8589 2.83982
\(873\) −12.7782 −0.432476
\(874\) −0.799271 −0.0270357
\(875\) 0.271324 0.00917244
\(876\) −2.22008 −0.0750095
\(877\) −23.5377 −0.794813 −0.397407 0.917643i \(-0.630090\pi\)
−0.397407 + 0.917643i \(0.630090\pi\)
\(878\) −35.7449 −1.20633
\(879\) −2.55872 −0.0863036
\(880\) −77.7345 −2.62043
\(881\) −56.5228 −1.90430 −0.952152 0.305626i \(-0.901134\pi\)
−0.952152 + 0.305626i \(0.901134\pi\)
\(882\) 7.65531 0.257768
\(883\) 7.00314 0.235674 0.117837 0.993033i \(-0.462404\pi\)
0.117837 + 0.993033i \(0.462404\pi\)
\(884\) 89.6362 3.01479
\(885\) −6.65666 −0.223761
\(886\) −40.4848 −1.36011
\(887\) 14.8868 0.499849 0.249925 0.968265i \(-0.419594\pi\)
0.249925 + 0.968265i \(0.419594\pi\)
\(888\) −6.26179 −0.210132
\(889\) 6.43874 0.215948
\(890\) −1.41760 −0.0475180
\(891\) −18.2317 −0.610786
\(892\) 111.812 3.74373
\(893\) −12.5347 −0.419456
\(894\) −13.5653 −0.453691
\(895\) 63.3742 2.11836
\(896\) −7.02359 −0.234642
\(897\) 0.116238 0.00388106
\(898\) 32.1354 1.07237
\(899\) −9.93159 −0.331237
\(900\) −73.4001 −2.44667
\(901\) −3.13847 −0.104558
\(902\) 3.05680 0.101780
\(903\) 0.589335 0.0196119
\(904\) 39.3827 1.30985
\(905\) −3.10927 −0.103356
\(906\) −3.15640 −0.104864
\(907\) 34.0339 1.13008 0.565039 0.825065i \(-0.308861\pi\)
0.565039 + 0.825065i \(0.308861\pi\)
\(908\) 52.0368 1.72690
\(909\) −41.1055 −1.36338
\(910\) 34.7840 1.15308
\(911\) 40.8576 1.35367 0.676836 0.736134i \(-0.263350\pi\)
0.676836 + 0.736134i \(0.263350\pi\)
\(912\) −12.0382 −0.398625
\(913\) −36.0952 −1.19458
\(914\) 30.2046 0.999079
\(915\) −0.330250 −0.0109177
\(916\) 75.9449 2.50929
\(917\) 7.45692 0.246249
\(918\) −21.6864 −0.715756
\(919\) −31.7728 −1.04809 −0.524045 0.851691i \(-0.675578\pi\)
−0.524045 + 0.851691i \(0.675578\pi\)
\(920\) 2.18831 0.0721466
\(921\) −4.34815 −0.143276
\(922\) −0.549322 −0.0180909
\(923\) 25.3284 0.833694
\(924\) −3.60190 −0.118494
\(925\) 12.6051 0.414453
\(926\) −35.1914 −1.15646
\(927\) −23.3688 −0.767531
\(928\) −104.467 −3.42929
\(929\) 44.8537 1.47160 0.735802 0.677197i \(-0.236806\pi\)
0.735802 + 0.677197i \(0.236806\pi\)
\(930\) 3.30601 0.108408
\(931\) −3.45874 −0.113356
\(932\) −126.828 −4.15439
\(933\) −3.09274 −0.101252
\(934\) −104.936 −3.43360
\(935\) 31.0832 1.01653
\(936\) −94.6226 −3.09284
\(937\) −36.9287 −1.20641 −0.603204 0.797587i \(-0.706110\pi\)
−0.603204 + 0.797587i \(0.706110\pi\)
\(938\) −19.7440 −0.644665
\(939\) 3.30930 0.107995
\(940\) 57.3367 1.87012
\(941\) −38.0152 −1.23926 −0.619630 0.784894i \(-0.712717\pi\)
−0.619630 + 0.784894i \(0.712717\pi\)
\(942\) 11.4970 0.374593
\(943\) −0.0448685 −0.00146112
\(944\) −70.9634 −2.30966
\(945\) −6.00485 −0.195338
\(946\) 10.9514 0.356061
\(947\) 5.88590 0.191266 0.0956331 0.995417i \(-0.469512\pi\)
0.0956331 + 0.995417i \(0.469512\pi\)
\(948\) 6.89383 0.223901
\(949\) 5.76122 0.187017
\(950\) 46.4762 1.50789
\(951\) 1.43364 0.0464890
\(952\) 34.1993 1.10841
\(953\) −1.04219 −0.0337600 −0.0168800 0.999858i \(-0.505373\pi\)
−0.0168800 + 0.999858i \(0.505373\pi\)
\(954\) 5.53521 0.179209
\(955\) 22.3033 0.721718
\(956\) −120.109 −3.88459
\(957\) −5.84383 −0.188904
\(958\) 72.8251 2.35287
\(959\) 18.5423 0.598762
\(960\) 12.6681 0.408861
\(961\) −29.4902 −0.951296
\(962\) 27.1487 0.875310
\(963\) 8.84788 0.285119
\(964\) −99.8420 −3.21569
\(965\) 51.0462 1.64324
\(966\) 0.0740945 0.00238395
\(967\) 28.1286 0.904553 0.452277 0.891878i \(-0.350612\pi\)
0.452277 + 0.891878i \(0.350612\pi\)
\(968\) 46.6069 1.49800
\(969\) 4.81364 0.154636
\(970\) −37.0104 −1.18833
\(971\) 29.8038 0.956451 0.478225 0.878237i \(-0.341280\pi\)
0.478225 + 0.878237i \(0.341280\pi\)
\(972\) 41.1747 1.32068
\(973\) −12.4252 −0.398335
\(974\) −65.9259 −2.11240
\(975\) −6.75902 −0.216462
\(976\) −3.52064 −0.112693
\(977\) 5.27992 0.168920 0.0844599 0.996427i \(-0.473084\pi\)
0.0844599 + 0.996427i \(0.473084\pi\)
\(978\) −6.14327 −0.196440
\(979\) −0.380936 −0.0121748
\(980\) 15.8211 0.505388
\(981\) 30.8358 0.984513
\(982\) 9.60600 0.306540
\(983\) −3.92318 −0.125130 −0.0625651 0.998041i \(-0.519928\pi\)
−0.0625651 + 0.998041i \(0.519928\pi\)
\(984\) −1.29608 −0.0413174
\(985\) −25.5055 −0.812672
\(986\) 92.7019 2.95223
\(987\) 1.16200 0.0369867
\(988\) 71.4257 2.27235
\(989\) −0.160748 −0.00511147
\(990\) −54.8203 −1.74230
\(991\) −41.8517 −1.32946 −0.664732 0.747082i \(-0.731454\pi\)
−0.664732 + 0.747082i \(0.731454\pi\)
\(992\) 15.8812 0.504228
\(993\) 4.22457 0.134063
\(994\) 16.1453 0.512098
\(995\) 68.8133 2.18153
\(996\) 25.5693 0.810193
\(997\) −18.4242 −0.583502 −0.291751 0.956494i \(-0.594238\pi\)
−0.291751 + 0.956494i \(0.594238\pi\)
\(998\) 104.555 3.30962
\(999\) −4.68676 −0.148282
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 \(a_p\))