Properties

Label 6019.2.a.c.1.11
Level 6019
Weight 2
Character 6019.1
Self dual Yes
Analytic conductor 48.062
Analytic rank 1
Dimension 108
CM No

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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 1.11
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.39631 q^{2}\) \(-0.467815 q^{3}\) \(+3.74231 q^{4}\) \(+2.01057 q^{5}\) \(+1.12103 q^{6}\) \(-2.84779 q^{7}\) \(-4.17511 q^{8}\) \(-2.78115 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.39631 q^{2}\) \(-0.467815 q^{3}\) \(+3.74231 q^{4}\) \(+2.01057 q^{5}\) \(+1.12103 q^{6}\) \(-2.84779 q^{7}\) \(-4.17511 q^{8}\) \(-2.78115 q^{9}\) \(-4.81795 q^{10}\) \(+3.93458 q^{11}\) \(-1.75071 q^{12}\) \(-1.00000 q^{13}\) \(+6.82420 q^{14}\) \(-0.940573 q^{15}\) \(+2.52025 q^{16}\) \(+6.24553 q^{17}\) \(+6.66450 q^{18}\) \(+4.17763 q^{19}\) \(+7.52416 q^{20}\) \(+1.33224 q^{21}\) \(-9.42848 q^{22}\) \(+2.17631 q^{23}\) \(+1.95318 q^{24}\) \(-0.957616 q^{25}\) \(+2.39631 q^{26}\) \(+2.70451 q^{27}\) \(-10.6573 q^{28}\) \(-10.0386 q^{29}\) \(+2.25391 q^{30}\) \(-5.13693 q^{31}\) \(+2.31092 q^{32}\) \(-1.84065 q^{33}\) \(-14.9662 q^{34}\) \(-5.72568 q^{35}\) \(-10.4079 q^{36}\) \(-5.97286 q^{37}\) \(-10.0109 q^{38}\) \(+0.467815 q^{39}\) \(-8.39434 q^{40}\) \(+9.83118 q^{41}\) \(-3.19246 q^{42}\) \(-9.39726 q^{43}\) \(+14.7244 q^{44}\) \(-5.59169 q^{45}\) \(-5.21512 q^{46}\) \(+4.75131 q^{47}\) \(-1.17901 q^{48}\) \(+1.10992 q^{49}\) \(+2.29475 q^{50}\) \(-2.92175 q^{51}\) \(-3.74231 q^{52}\) \(+4.79505 q^{53}\) \(-6.48084 q^{54}\) \(+7.91074 q^{55}\) \(+11.8898 q^{56}\) \(-1.95436 q^{57}\) \(+24.0555 q^{58}\) \(-10.1207 q^{59}\) \(-3.51991 q^{60}\) \(-2.61639 q^{61}\) \(+12.3097 q^{62}\) \(+7.92014 q^{63}\) \(-10.5782 q^{64}\) \(-2.01057 q^{65}\) \(+4.41078 q^{66}\) \(+7.15184 q^{67}\) \(+23.3727 q^{68}\) \(-1.01811 q^{69}\) \(+13.7205 q^{70}\) \(-11.5021 q^{71}\) \(+11.6116 q^{72}\) \(-13.4207 q^{73}\) \(+14.3128 q^{74}\) \(+0.447987 q^{75}\) \(+15.6340 q^{76}\) \(-11.2049 q^{77}\) \(-1.12103 q^{78}\) \(+2.13610 q^{79}\) \(+5.06713 q^{80}\) \(+7.07824 q^{81}\) \(-23.5586 q^{82}\) \(+4.34501 q^{83}\) \(+4.98565 q^{84}\) \(+12.5571 q^{85}\) \(+22.5188 q^{86}\) \(+4.69619 q^{87}\) \(-16.4273 q^{88}\) \(+16.8366 q^{89}\) \(+13.3994 q^{90}\) \(+2.84779 q^{91}\) \(+8.14443 q^{92}\) \(+2.40313 q^{93}\) \(-11.3856 q^{94}\) \(+8.39942 q^{95}\) \(-1.08108 q^{96}\) \(-0.381896 q^{97}\) \(-2.65971 q^{98}\) \(-10.9427 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.39631 −1.69445 −0.847224 0.531236i \(-0.821728\pi\)
−0.847224 + 0.531236i \(0.821728\pi\)
\(3\) −0.467815 −0.270093 −0.135046 0.990839i \(-0.543118\pi\)
−0.135046 + 0.990839i \(0.543118\pi\)
\(4\) 3.74231 1.87115
\(5\) 2.01057 0.899153 0.449577 0.893242i \(-0.351575\pi\)
0.449577 + 0.893242i \(0.351575\pi\)
\(6\) 1.12103 0.457658
\(7\) −2.84779 −1.07636 −0.538182 0.842829i \(-0.680889\pi\)
−0.538182 + 0.842829i \(0.680889\pi\)
\(8\) −4.17511 −1.47612
\(9\) −2.78115 −0.927050
\(10\) −4.81795 −1.52357
\(11\) 3.93458 1.18632 0.593160 0.805085i \(-0.297880\pi\)
0.593160 + 0.805085i \(0.297880\pi\)
\(12\) −1.75071 −0.505385
\(13\) −1.00000 −0.277350
\(14\) 6.82420 1.82384
\(15\) −0.940573 −0.242855
\(16\) 2.52025 0.630062
\(17\) 6.24553 1.51476 0.757381 0.652973i \(-0.226478\pi\)
0.757381 + 0.652973i \(0.226478\pi\)
\(18\) 6.66450 1.57084
\(19\) 4.17763 0.958415 0.479208 0.877702i \(-0.340924\pi\)
0.479208 + 0.877702i \(0.340924\pi\)
\(20\) 7.52416 1.68245
\(21\) 1.33224 0.290718
\(22\) −9.42848 −2.01016
\(23\) 2.17631 0.453793 0.226896 0.973919i \(-0.427142\pi\)
0.226896 + 0.973919i \(0.427142\pi\)
\(24\) 1.95318 0.398691
\(25\) −0.957616 −0.191523
\(26\) 2.39631 0.469955
\(27\) 2.70451 0.520483
\(28\) −10.6573 −2.01404
\(29\) −10.0386 −1.86411 −0.932057 0.362312i \(-0.881987\pi\)
−0.932057 + 0.362312i \(0.881987\pi\)
\(30\) 2.25391 0.411505
\(31\) −5.13693 −0.922620 −0.461310 0.887239i \(-0.652620\pi\)
−0.461310 + 0.887239i \(0.652620\pi\)
\(32\) 2.31092 0.408517
\(33\) −1.84065 −0.320417
\(34\) −14.9662 −2.56669
\(35\) −5.72568 −0.967816
\(36\) −10.4079 −1.73465
\(37\) −5.97286 −0.981932 −0.490966 0.871179i \(-0.663356\pi\)
−0.490966 + 0.871179i \(0.663356\pi\)
\(38\) −10.0109 −1.62398
\(39\) 0.467815 0.0749103
\(40\) −8.39434 −1.32726
\(41\) 9.83118 1.53537 0.767686 0.640826i \(-0.221408\pi\)
0.767686 + 0.640826i \(0.221408\pi\)
\(42\) −3.19246 −0.492607
\(43\) −9.39726 −1.43307 −0.716535 0.697552i \(-0.754273\pi\)
−0.716535 + 0.697552i \(0.754273\pi\)
\(44\) 14.7244 2.21979
\(45\) −5.59169 −0.833560
\(46\) −5.21512 −0.768928
\(47\) 4.75131 0.693049 0.346525 0.938041i \(-0.387362\pi\)
0.346525 + 0.938041i \(0.387362\pi\)
\(48\) −1.17901 −0.170175
\(49\) 1.10992 0.158560
\(50\) 2.29475 0.324526
\(51\) −2.92175 −0.409127
\(52\) −3.74231 −0.518965
\(53\) 4.79505 0.658651 0.329325 0.944217i \(-0.393179\pi\)
0.329325 + 0.944217i \(0.393179\pi\)
\(54\) −6.48084 −0.881930
\(55\) 7.91074 1.06668
\(56\) 11.8898 1.58885
\(57\) −1.95436 −0.258861
\(58\) 24.0555 3.15864
\(59\) −10.1207 −1.31761 −0.658804 0.752315i \(-0.728937\pi\)
−0.658804 + 0.752315i \(0.728937\pi\)
\(60\) −3.51991 −0.454419
\(61\) −2.61639 −0.334994 −0.167497 0.985873i \(-0.553569\pi\)
−0.167497 + 0.985873i \(0.553569\pi\)
\(62\) 12.3097 1.56333
\(63\) 7.92014 0.997843
\(64\) −10.5782 −1.32227
\(65\) −2.01057 −0.249380
\(66\) 4.41078 0.542929
\(67\) 7.15184 0.873736 0.436868 0.899526i \(-0.356088\pi\)
0.436868 + 0.899526i \(0.356088\pi\)
\(68\) 23.3727 2.83435
\(69\) −1.01811 −0.122566
\(70\) 13.7205 1.63991
\(71\) −11.5021 −1.36504 −0.682522 0.730865i \(-0.739117\pi\)
−0.682522 + 0.730865i \(0.739117\pi\)
\(72\) 11.6116 1.36844
\(73\) −13.4207 −1.57078 −0.785389 0.619002i \(-0.787537\pi\)
−0.785389 + 0.619002i \(0.787537\pi\)
\(74\) 14.3128 1.66383
\(75\) 0.447987 0.0517291
\(76\) 15.6340 1.79334
\(77\) −11.2049 −1.27691
\(78\) −1.12103 −0.126932
\(79\) 2.13610 0.240329 0.120165 0.992754i \(-0.461658\pi\)
0.120165 + 0.992754i \(0.461658\pi\)
\(80\) 5.06713 0.566522
\(81\) 7.07824 0.786471
\(82\) −23.5586 −2.60161
\(83\) 4.34501 0.476927 0.238463 0.971152i \(-0.423356\pi\)
0.238463 + 0.971152i \(0.423356\pi\)
\(84\) 4.98565 0.543979
\(85\) 12.5571 1.36200
\(86\) 22.5188 2.42826
\(87\) 4.69619 0.503484
\(88\) −16.4273 −1.75116
\(89\) 16.8366 1.78468 0.892340 0.451364i \(-0.149062\pi\)
0.892340 + 0.451364i \(0.149062\pi\)
\(90\) 13.3994 1.41242
\(91\) 2.84779 0.298530
\(92\) 8.14443 0.849116
\(93\) 2.40313 0.249193
\(94\) −11.3856 −1.17434
\(95\) 8.39942 0.861762
\(96\) −1.08108 −0.110338
\(97\) −0.381896 −0.0387756 −0.0193878 0.999812i \(-0.506172\pi\)
−0.0193878 + 0.999812i \(0.506172\pi\)
\(98\) −2.65971 −0.268671
\(99\) −10.9427 −1.09978
\(100\) −3.58369 −0.358369
\(101\) 6.25916 0.622809 0.311405 0.950277i \(-0.399201\pi\)
0.311405 + 0.950277i \(0.399201\pi\)
\(102\) 7.00142 0.693244
\(103\) 5.22663 0.514996 0.257498 0.966279i \(-0.417102\pi\)
0.257498 + 0.966279i \(0.417102\pi\)
\(104\) 4.17511 0.409403
\(105\) 2.67856 0.261400
\(106\) −11.4904 −1.11605
\(107\) −6.75189 −0.652730 −0.326365 0.945244i \(-0.605824\pi\)
−0.326365 + 0.945244i \(0.605824\pi\)
\(108\) 10.1211 0.973903
\(109\) −1.76444 −0.169002 −0.0845012 0.996423i \(-0.526930\pi\)
−0.0845012 + 0.996423i \(0.526930\pi\)
\(110\) −18.9566 −1.80744
\(111\) 2.79419 0.265213
\(112\) −7.17714 −0.678176
\(113\) 15.1277 1.42309 0.711545 0.702640i \(-0.247996\pi\)
0.711545 + 0.702640i \(0.247996\pi\)
\(114\) 4.68325 0.438627
\(115\) 4.37563 0.408029
\(116\) −37.5674 −3.48804
\(117\) 2.78115 0.257117
\(118\) 24.2524 2.23262
\(119\) −17.7860 −1.63044
\(120\) 3.92700 0.358484
\(121\) 4.48091 0.407356
\(122\) 6.26969 0.567631
\(123\) −4.59917 −0.414693
\(124\) −19.2240 −1.72636
\(125\) −11.9782 −1.07136
\(126\) −18.9791 −1.69079
\(127\) −6.17853 −0.548256 −0.274128 0.961693i \(-0.588389\pi\)
−0.274128 + 0.961693i \(0.588389\pi\)
\(128\) 20.7268 1.83201
\(129\) 4.39618 0.387062
\(130\) 4.81795 0.422562
\(131\) −17.3072 −1.51214 −0.756070 0.654491i \(-0.772883\pi\)
−0.756070 + 0.654491i \(0.772883\pi\)
\(132\) −6.88829 −0.599549
\(133\) −11.8970 −1.03160
\(134\) −17.1380 −1.48050
\(135\) 5.43759 0.467994
\(136\) −26.0758 −2.23598
\(137\) −14.0679 −1.20190 −0.600950 0.799287i \(-0.705211\pi\)
−0.600950 + 0.799287i \(0.705211\pi\)
\(138\) 2.43971 0.207682
\(139\) −5.44710 −0.462017 −0.231009 0.972952i \(-0.574203\pi\)
−0.231009 + 0.972952i \(0.574203\pi\)
\(140\) −21.4272 −1.81093
\(141\) −2.22273 −0.187188
\(142\) 27.5625 2.31300
\(143\) −3.93458 −0.329026
\(144\) −7.00918 −0.584099
\(145\) −20.1832 −1.67612
\(146\) 32.1603 2.66160
\(147\) −0.519236 −0.0428259
\(148\) −22.3523 −1.83735
\(149\) −0.757208 −0.0620329 −0.0310165 0.999519i \(-0.509874\pi\)
−0.0310165 + 0.999519i \(0.509874\pi\)
\(150\) −1.07352 −0.0876522
\(151\) 12.1697 0.990355 0.495177 0.868792i \(-0.335103\pi\)
0.495177 + 0.868792i \(0.335103\pi\)
\(152\) −17.4421 −1.41474
\(153\) −17.3697 −1.40426
\(154\) 26.8503 2.16366
\(155\) −10.3281 −0.829577
\(156\) 1.75071 0.140169
\(157\) 21.0201 1.67759 0.838794 0.544449i \(-0.183261\pi\)
0.838794 + 0.544449i \(0.183261\pi\)
\(158\) −5.11875 −0.407226
\(159\) −2.24319 −0.177897
\(160\) 4.64627 0.367320
\(161\) −6.19769 −0.488446
\(162\) −16.9617 −1.33263
\(163\) −8.82872 −0.691518 −0.345759 0.938323i \(-0.612379\pi\)
−0.345759 + 0.938323i \(0.612379\pi\)
\(164\) 36.7913 2.87292
\(165\) −3.70076 −0.288104
\(166\) −10.4120 −0.808127
\(167\) 12.5955 0.974667 0.487333 0.873216i \(-0.337970\pi\)
0.487333 + 0.873216i \(0.337970\pi\)
\(168\) −5.56224 −0.429136
\(169\) 1.00000 0.0769231
\(170\) −30.0906 −2.30784
\(171\) −11.6186 −0.888499
\(172\) −35.1674 −2.68149
\(173\) −1.84505 −0.140276 −0.0701382 0.997537i \(-0.522344\pi\)
−0.0701382 + 0.997537i \(0.522344\pi\)
\(174\) −11.2535 −0.853127
\(175\) 2.72709 0.206149
\(176\) 9.91611 0.747455
\(177\) 4.73463 0.355877
\(178\) −40.3458 −3.02405
\(179\) −18.2217 −1.36195 −0.680976 0.732305i \(-0.738444\pi\)
−0.680976 + 0.732305i \(0.738444\pi\)
\(180\) −20.9258 −1.55972
\(181\) −26.3820 −1.96096 −0.980479 0.196625i \(-0.937002\pi\)
−0.980479 + 0.196625i \(0.937002\pi\)
\(182\) −6.82420 −0.505843
\(183\) 1.22399 0.0904796
\(184\) −9.08635 −0.669854
\(185\) −12.0088 −0.882908
\(186\) −5.75865 −0.422245
\(187\) 24.5735 1.79699
\(188\) 17.7808 1.29680
\(189\) −7.70187 −0.560229
\(190\) −20.1276 −1.46021
\(191\) 4.49622 0.325335 0.162668 0.986681i \(-0.447990\pi\)
0.162668 + 0.986681i \(0.447990\pi\)
\(192\) 4.94863 0.357137
\(193\) −2.19085 −0.157701 −0.0788505 0.996886i \(-0.525125\pi\)
−0.0788505 + 0.996886i \(0.525125\pi\)
\(194\) 0.915140 0.0657033
\(195\) 0.940573 0.0673558
\(196\) 4.15366 0.296690
\(197\) −18.2275 −1.29865 −0.649327 0.760510i \(-0.724949\pi\)
−0.649327 + 0.760510i \(0.724949\pi\)
\(198\) 26.2220 1.86352
\(199\) 12.3473 0.875278 0.437639 0.899151i \(-0.355815\pi\)
0.437639 + 0.899151i \(0.355815\pi\)
\(200\) 3.99815 0.282712
\(201\) −3.34574 −0.235990
\(202\) −14.9989 −1.05532
\(203\) 28.5877 2.00647
\(204\) −10.9341 −0.765539
\(205\) 19.7663 1.38053
\(206\) −12.5246 −0.872633
\(207\) −6.05265 −0.420688
\(208\) −2.52025 −0.174748
\(209\) 16.4372 1.13699
\(210\) −6.41866 −0.442929
\(211\) 2.01021 0.138389 0.0691943 0.997603i \(-0.477957\pi\)
0.0691943 + 0.997603i \(0.477957\pi\)
\(212\) 17.9445 1.23244
\(213\) 5.38083 0.368689
\(214\) 16.1796 1.10602
\(215\) −18.8938 −1.28855
\(216\) −11.2916 −0.768297
\(217\) 14.6289 0.993075
\(218\) 4.22814 0.286366
\(219\) 6.27842 0.424256
\(220\) 29.6044 1.99593
\(221\) −6.24553 −0.420120
\(222\) −6.69575 −0.449389
\(223\) 19.9498 1.33593 0.667967 0.744191i \(-0.267165\pi\)
0.667967 + 0.744191i \(0.267165\pi\)
\(224\) −6.58103 −0.439713
\(225\) 2.66327 0.177552
\(226\) −36.2506 −2.41135
\(227\) −25.1071 −1.66641 −0.833207 0.552961i \(-0.813498\pi\)
−0.833207 + 0.552961i \(0.813498\pi\)
\(228\) −7.31381 −0.484369
\(229\) −11.8858 −0.785434 −0.392717 0.919659i \(-0.628465\pi\)
−0.392717 + 0.919659i \(0.628465\pi\)
\(230\) −10.4854 −0.691384
\(231\) 5.24180 0.344885
\(232\) 41.9121 2.75166
\(233\) 27.7935 1.82081 0.910407 0.413713i \(-0.135768\pi\)
0.910407 + 0.413713i \(0.135768\pi\)
\(234\) −6.66450 −0.435672
\(235\) 9.55282 0.623157
\(236\) −37.8749 −2.46545
\(237\) −0.999297 −0.0649113
\(238\) 42.6207 2.76269
\(239\) 15.6532 1.01252 0.506260 0.862381i \(-0.331028\pi\)
0.506260 + 0.862381i \(0.331028\pi\)
\(240\) −2.37048 −0.153014
\(241\) −12.6601 −0.815509 −0.407754 0.913092i \(-0.633688\pi\)
−0.407754 + 0.913092i \(0.633688\pi\)
\(242\) −10.7377 −0.690243
\(243\) −11.4248 −0.732903
\(244\) −9.79134 −0.626826
\(245\) 2.23157 0.142570
\(246\) 11.0210 0.702676
\(247\) −4.17763 −0.265817
\(248\) 21.4472 1.36190
\(249\) −2.03266 −0.128814
\(250\) 28.7035 1.81537
\(251\) −9.54280 −0.602336 −0.301168 0.953571i \(-0.597377\pi\)
−0.301168 + 0.953571i \(0.597377\pi\)
\(252\) 29.6396 1.86712
\(253\) 8.56288 0.538343
\(254\) 14.8057 0.928991
\(255\) −5.87437 −0.367868
\(256\) −28.5114 −1.78196
\(257\) 18.9925 1.18472 0.592361 0.805673i \(-0.298196\pi\)
0.592361 + 0.805673i \(0.298196\pi\)
\(258\) −10.5346 −0.655856
\(259\) 17.0095 1.05692
\(260\) −7.52416 −0.466629
\(261\) 27.9187 1.72813
\(262\) 41.4735 2.56224
\(263\) 23.2697 1.43487 0.717436 0.696624i \(-0.245315\pi\)
0.717436 + 0.696624i \(0.245315\pi\)
\(264\) 7.68493 0.472975
\(265\) 9.64077 0.592228
\(266\) 28.5090 1.74800
\(267\) −7.87643 −0.482029
\(268\) 26.7644 1.63489
\(269\) 22.7962 1.38991 0.694954 0.719054i \(-0.255425\pi\)
0.694954 + 0.719054i \(0.255425\pi\)
\(270\) −13.0302 −0.792991
\(271\) 11.7381 0.713042 0.356521 0.934287i \(-0.383963\pi\)
0.356521 + 0.934287i \(0.383963\pi\)
\(272\) 15.7403 0.954394
\(273\) −1.33224 −0.0806308
\(274\) 33.7110 2.03656
\(275\) −3.76782 −0.227208
\(276\) −3.81008 −0.229340
\(277\) −19.2798 −1.15841 −0.579206 0.815181i \(-0.696637\pi\)
−0.579206 + 0.815181i \(0.696637\pi\)
\(278\) 13.0529 0.782864
\(279\) 14.2866 0.855314
\(280\) 23.9053 1.42862
\(281\) −12.3166 −0.734746 −0.367373 0.930074i \(-0.619743\pi\)
−0.367373 + 0.930074i \(0.619743\pi\)
\(282\) 5.32635 0.317180
\(283\) −32.0267 −1.90379 −0.951896 0.306422i \(-0.900868\pi\)
−0.951896 + 0.306422i \(0.900868\pi\)
\(284\) −43.0442 −2.55421
\(285\) −3.92937 −0.232756
\(286\) 9.42848 0.557517
\(287\) −27.9971 −1.65262
\(288\) −6.42702 −0.378716
\(289\) 22.0066 1.29451
\(290\) 48.3652 2.84010
\(291\) 0.178656 0.0104730
\(292\) −50.2245 −2.93917
\(293\) −5.26310 −0.307474 −0.153737 0.988112i \(-0.549131\pi\)
−0.153737 + 0.988112i \(0.549131\pi\)
\(294\) 1.24425 0.0725662
\(295\) −20.3484 −1.18473
\(296\) 24.9373 1.44945
\(297\) 10.6411 0.617459
\(298\) 1.81451 0.105112
\(299\) −2.17631 −0.125859
\(300\) 1.67650 0.0967930
\(301\) 26.7615 1.54250
\(302\) −29.1623 −1.67810
\(303\) −2.92812 −0.168216
\(304\) 10.5287 0.603861
\(305\) −5.26043 −0.301211
\(306\) 41.6233 2.37945
\(307\) 3.53681 0.201856 0.100928 0.994894i \(-0.467819\pi\)
0.100928 + 0.994894i \(0.467819\pi\)
\(308\) −41.9320 −2.38930
\(309\) −2.44510 −0.139097
\(310\) 24.7494 1.40567
\(311\) −4.37339 −0.247992 −0.123996 0.992283i \(-0.539571\pi\)
−0.123996 + 0.992283i \(0.539571\pi\)
\(312\) −1.95318 −0.110577
\(313\) 15.5436 0.878574 0.439287 0.898347i \(-0.355231\pi\)
0.439287 + 0.898347i \(0.355231\pi\)
\(314\) −50.3708 −2.84259
\(315\) 15.9240 0.897214
\(316\) 7.99392 0.449693
\(317\) −9.49770 −0.533444 −0.266722 0.963773i \(-0.585941\pi\)
−0.266722 + 0.963773i \(0.585941\pi\)
\(318\) 5.37539 0.301437
\(319\) −39.4975 −2.21144
\(320\) −21.2682 −1.18893
\(321\) 3.15863 0.176298
\(322\) 14.8516 0.827647
\(323\) 26.0915 1.45177
\(324\) 26.4889 1.47161
\(325\) 0.957616 0.0531190
\(326\) 21.1564 1.17174
\(327\) 0.825430 0.0456464
\(328\) −41.0462 −2.26640
\(329\) −13.5307 −0.745973
\(330\) 8.86817 0.488177
\(331\) 14.3158 0.786865 0.393432 0.919354i \(-0.371288\pi\)
0.393432 + 0.919354i \(0.371288\pi\)
\(332\) 16.2604 0.892403
\(333\) 16.6114 0.910300
\(334\) −30.1827 −1.65152
\(335\) 14.3793 0.785623
\(336\) 3.35757 0.183171
\(337\) 32.7525 1.78415 0.892073 0.451892i \(-0.149251\pi\)
0.892073 + 0.451892i \(0.149251\pi\)
\(338\) −2.39631 −0.130342
\(339\) −7.07694 −0.384367
\(340\) 46.9924 2.54852
\(341\) −20.2117 −1.09452
\(342\) 27.8418 1.50551
\(343\) 16.7737 0.905696
\(344\) 39.2346 2.11539
\(345\) −2.04698 −0.110206
\(346\) 4.42131 0.237691
\(347\) 1.81334 0.0973454 0.0486727 0.998815i \(-0.484501\pi\)
0.0486727 + 0.998815i \(0.484501\pi\)
\(348\) 17.5746 0.942096
\(349\) −18.0235 −0.964774 −0.482387 0.875958i \(-0.660230\pi\)
−0.482387 + 0.875958i \(0.660230\pi\)
\(350\) −6.53496 −0.349308
\(351\) −2.70451 −0.144356
\(352\) 9.09251 0.484632
\(353\) −12.4036 −0.660177 −0.330089 0.943950i \(-0.607079\pi\)
−0.330089 + 0.943950i \(0.607079\pi\)
\(354\) −11.3456 −0.603014
\(355\) −23.1257 −1.22738
\(356\) 63.0079 3.33941
\(357\) 8.32053 0.440369
\(358\) 43.6648 2.30776
\(359\) −35.6576 −1.88194 −0.940968 0.338496i \(-0.890082\pi\)
−0.940968 + 0.338496i \(0.890082\pi\)
\(360\) 23.3459 1.23044
\(361\) −1.54737 −0.0814406
\(362\) 63.2195 3.32274
\(363\) −2.09624 −0.110024
\(364\) 10.6573 0.558595
\(365\) −26.9833 −1.41237
\(366\) −2.93305 −0.153313
\(367\) −0.292180 −0.0152517 −0.00762583 0.999971i \(-0.502427\pi\)
−0.00762583 + 0.999971i \(0.502427\pi\)
\(368\) 5.48485 0.285917
\(369\) −27.3420 −1.42337
\(370\) 28.7769 1.49604
\(371\) −13.6553 −0.708948
\(372\) 8.99325 0.466278
\(373\) −23.1064 −1.19640 −0.598202 0.801346i \(-0.704118\pi\)
−0.598202 + 0.801346i \(0.704118\pi\)
\(374\) −58.8858 −3.04491
\(375\) 5.60357 0.289367
\(376\) −19.8372 −1.02303
\(377\) 10.0386 0.517012
\(378\) 18.4561 0.949278
\(379\) −21.7120 −1.11527 −0.557635 0.830086i \(-0.688291\pi\)
−0.557635 + 0.830086i \(0.688291\pi\)
\(380\) 31.4332 1.61249
\(381\) 2.89041 0.148080
\(382\) −10.7744 −0.551264
\(383\) −3.86968 −0.197732 −0.0988658 0.995101i \(-0.531521\pi\)
−0.0988658 + 0.995101i \(0.531521\pi\)
\(384\) −9.69629 −0.494812
\(385\) −22.5281 −1.14814
\(386\) 5.24996 0.267216
\(387\) 26.1352 1.32853
\(388\) −1.42917 −0.0725551
\(389\) −37.7862 −1.91584 −0.957919 0.287037i \(-0.907330\pi\)
−0.957919 + 0.287037i \(0.907330\pi\)
\(390\) −2.25391 −0.114131
\(391\) 13.5922 0.687388
\(392\) −4.63403 −0.234054
\(393\) 8.09658 0.408418
\(394\) 43.6787 2.20050
\(395\) 4.29476 0.216093
\(396\) −40.9508 −2.05785
\(397\) −24.9587 −1.25264 −0.626320 0.779566i \(-0.715440\pi\)
−0.626320 + 0.779566i \(0.715440\pi\)
\(398\) −29.5880 −1.48311
\(399\) 5.56561 0.278629
\(400\) −2.41343 −0.120671
\(401\) −4.09085 −0.204287 −0.102144 0.994770i \(-0.532570\pi\)
−0.102144 + 0.994770i \(0.532570\pi\)
\(402\) 8.01742 0.399873
\(403\) 5.13693 0.255889
\(404\) 23.4237 1.16537
\(405\) 14.2313 0.707158
\(406\) −68.5051 −3.39985
\(407\) −23.5007 −1.16489
\(408\) 12.1986 0.603922
\(409\) −14.7898 −0.731309 −0.365654 0.930751i \(-0.619155\pi\)
−0.365654 + 0.930751i \(0.619155\pi\)
\(410\) −47.3661 −2.33924
\(411\) 6.58116 0.324625
\(412\) 19.5597 0.963636
\(413\) 28.8218 1.41823
\(414\) 14.5040 0.712835
\(415\) 8.73593 0.428830
\(416\) −2.31092 −0.113302
\(417\) 2.54823 0.124788
\(418\) −39.3887 −1.92657
\(419\) −32.0938 −1.56788 −0.783942 0.620834i \(-0.786794\pi\)
−0.783942 + 0.620834i \(0.786794\pi\)
\(420\) 10.0240 0.489120
\(421\) −34.6060 −1.68659 −0.843295 0.537450i \(-0.819388\pi\)
−0.843295 + 0.537450i \(0.819388\pi\)
\(422\) −4.81709 −0.234492
\(423\) −13.2141 −0.642491
\(424\) −20.0199 −0.972250
\(425\) −5.98082 −0.290112
\(426\) −12.8942 −0.624724
\(427\) 7.45094 0.360576
\(428\) −25.2676 −1.22136
\(429\) 1.84065 0.0888676
\(430\) 45.2755 2.18338
\(431\) 19.9857 0.962676 0.481338 0.876535i \(-0.340151\pi\)
0.481338 + 0.876535i \(0.340151\pi\)
\(432\) 6.81602 0.327936
\(433\) −17.5098 −0.841469 −0.420734 0.907184i \(-0.638228\pi\)
−0.420734 + 0.907184i \(0.638228\pi\)
\(434\) −35.0554 −1.68271
\(435\) 9.44200 0.452709
\(436\) −6.60307 −0.316229
\(437\) 9.09184 0.434922
\(438\) −15.0450 −0.718880
\(439\) −7.38986 −0.352699 −0.176349 0.984328i \(-0.556429\pi\)
−0.176349 + 0.984328i \(0.556429\pi\)
\(440\) −33.0282 −1.57456
\(441\) −3.08685 −0.146993
\(442\) 14.9662 0.711871
\(443\) 28.9317 1.37459 0.687293 0.726380i \(-0.258799\pi\)
0.687293 + 0.726380i \(0.258799\pi\)
\(444\) 10.4567 0.496254
\(445\) 33.8512 1.60470
\(446\) −47.8058 −2.26367
\(447\) 0.354233 0.0167547
\(448\) 30.1245 1.42325
\(449\) 10.7850 0.508976 0.254488 0.967076i \(-0.418093\pi\)
0.254488 + 0.967076i \(0.418093\pi\)
\(450\) −6.38203 −0.300852
\(451\) 38.6815 1.82144
\(452\) 56.6123 2.66282
\(453\) −5.69316 −0.267488
\(454\) 60.1643 2.82365
\(455\) 5.72568 0.268424
\(456\) 8.15966 0.382111
\(457\) 7.80116 0.364923 0.182461 0.983213i \(-0.441594\pi\)
0.182461 + 0.983213i \(0.441594\pi\)
\(458\) 28.4820 1.33088
\(459\) 16.8911 0.788408
\(460\) 16.3749 0.763485
\(461\) −3.48670 −0.162392 −0.0811960 0.996698i \(-0.525874\pi\)
−0.0811960 + 0.996698i \(0.525874\pi\)
\(462\) −12.5610 −0.584390
\(463\) −1.00000 −0.0464739
\(464\) −25.2996 −1.17451
\(465\) 4.83166 0.224063
\(466\) −66.6019 −3.08527
\(467\) 18.0970 0.837428 0.418714 0.908118i \(-0.362481\pi\)
0.418714 + 0.908118i \(0.362481\pi\)
\(468\) 10.4079 0.481106
\(469\) −20.3670 −0.940458
\(470\) −22.8915 −1.05591
\(471\) −9.83352 −0.453105
\(472\) 42.2552 1.94495
\(473\) −36.9743 −1.70008
\(474\) 2.39463 0.109989
\(475\) −4.00057 −0.183559
\(476\) −66.5605 −3.05080
\(477\) −13.3357 −0.610602
\(478\) −37.5099 −1.71566
\(479\) −10.2940 −0.470346 −0.235173 0.971953i \(-0.575566\pi\)
−0.235173 + 0.971953i \(0.575566\pi\)
\(480\) −2.17359 −0.0992104
\(481\) 5.97286 0.272339
\(482\) 30.3375 1.38184
\(483\) 2.89937 0.131926
\(484\) 16.7690 0.762225
\(485\) −0.767827 −0.0348652
\(486\) 27.3774 1.24187
\(487\) −9.82419 −0.445176 −0.222588 0.974913i \(-0.571451\pi\)
−0.222588 + 0.974913i \(0.571451\pi\)
\(488\) 10.9237 0.494493
\(489\) 4.13020 0.186774
\(490\) −5.34753 −0.241577
\(491\) 4.04593 0.182590 0.0912951 0.995824i \(-0.470899\pi\)
0.0912951 + 0.995824i \(0.470899\pi\)
\(492\) −17.2115 −0.775954
\(493\) −62.6961 −2.82369
\(494\) 10.0109 0.450412
\(495\) −22.0009 −0.988869
\(496\) −12.9463 −0.581307
\(497\) 32.7555 1.46928
\(498\) 4.87088 0.218269
\(499\) 8.22113 0.368028 0.184014 0.982924i \(-0.441091\pi\)
0.184014 + 0.982924i \(0.441091\pi\)
\(500\) −44.8261 −2.00468
\(501\) −5.89235 −0.263251
\(502\) 22.8675 1.02063
\(503\) 18.2359 0.813098 0.406549 0.913629i \(-0.366732\pi\)
0.406549 + 0.913629i \(0.366732\pi\)
\(504\) −33.0674 −1.47294
\(505\) 12.5845 0.560001
\(506\) −20.5193 −0.912195
\(507\) −0.467815 −0.0207764
\(508\) −23.1219 −1.02587
\(509\) 7.95577 0.352634 0.176317 0.984333i \(-0.443582\pi\)
0.176317 + 0.984333i \(0.443582\pi\)
\(510\) 14.0768 0.623333
\(511\) 38.2195 1.69073
\(512\) 26.8687 1.18744
\(513\) 11.2984 0.498838
\(514\) −45.5120 −2.00745
\(515\) 10.5085 0.463060
\(516\) 16.4518 0.724252
\(517\) 18.6944 0.822178
\(518\) −40.7600 −1.79089
\(519\) 0.863140 0.0378877
\(520\) 8.39434 0.368116
\(521\) −12.2503 −0.536696 −0.268348 0.963322i \(-0.586478\pi\)
−0.268348 + 0.963322i \(0.586478\pi\)
\(522\) −66.9020 −2.92822
\(523\) 29.8998 1.30743 0.653713 0.756742i \(-0.273210\pi\)
0.653713 + 0.756742i \(0.273210\pi\)
\(524\) −64.7690 −2.82945
\(525\) −1.27577 −0.0556793
\(526\) −55.7615 −2.43132
\(527\) −32.0828 −1.39755
\(528\) −4.63890 −0.201882
\(529\) −18.2637 −0.794072
\(530\) −23.1023 −1.00350
\(531\) 28.1473 1.22149
\(532\) −44.5224 −1.93029
\(533\) −9.83118 −0.425836
\(534\) 18.8744 0.816774
\(535\) −13.5751 −0.586904
\(536\) −29.8597 −1.28974
\(537\) 8.52437 0.367854
\(538\) −54.6268 −2.35513
\(539\) 4.36706 0.188103
\(540\) 20.3491 0.875688
\(541\) −37.3343 −1.60513 −0.802564 0.596566i \(-0.796532\pi\)
−0.802564 + 0.596566i \(0.796532\pi\)
\(542\) −28.1282 −1.20821
\(543\) 12.3419 0.529641
\(544\) 14.4329 0.618807
\(545\) −3.54752 −0.151959
\(546\) 3.19246 0.136625
\(547\) 22.5833 0.965592 0.482796 0.875733i \(-0.339621\pi\)
0.482796 + 0.875733i \(0.339621\pi\)
\(548\) −52.6463 −2.24894
\(549\) 7.27657 0.310557
\(550\) 9.02886 0.384992
\(551\) −41.9374 −1.78659
\(552\) 4.25073 0.180923
\(553\) −6.08315 −0.258682
\(554\) 46.2004 1.96287
\(555\) 5.61791 0.238467
\(556\) −20.3847 −0.864505
\(557\) −7.57210 −0.320840 −0.160420 0.987049i \(-0.551285\pi\)
−0.160420 + 0.987049i \(0.551285\pi\)
\(558\) −34.2351 −1.44929
\(559\) 9.39726 0.397462
\(560\) −14.4301 −0.609784
\(561\) −11.4959 −0.485355
\(562\) 29.5144 1.24499
\(563\) −31.4051 −1.32357 −0.661784 0.749695i \(-0.730200\pi\)
−0.661784 + 0.749695i \(0.730200\pi\)
\(564\) −8.31814 −0.350257
\(565\) 30.4152 1.27958
\(566\) 76.7460 3.22588
\(567\) −20.1574 −0.846529
\(568\) 48.0224 2.01497
\(569\) −33.4899 −1.40397 −0.701985 0.712192i \(-0.747703\pi\)
−0.701985 + 0.712192i \(0.747703\pi\)
\(570\) 9.41599 0.394393
\(571\) 26.8201 1.12239 0.561194 0.827684i \(-0.310342\pi\)
0.561194 + 0.827684i \(0.310342\pi\)
\(572\) −14.7244 −0.615658
\(573\) −2.10340 −0.0878708
\(574\) 67.0899 2.80028
\(575\) −2.08407 −0.0869119
\(576\) 29.4195 1.22581
\(577\) −7.95789 −0.331291 −0.165646 0.986185i \(-0.552971\pi\)
−0.165646 + 0.986185i \(0.552971\pi\)
\(578\) −52.7347 −2.19347
\(579\) 1.02491 0.0425939
\(580\) −75.5318 −3.13629
\(581\) −12.3737 −0.513347
\(582\) −0.428116 −0.0177460
\(583\) 18.8665 0.781371
\(584\) 56.0331 2.31866
\(585\) 5.59169 0.231188
\(586\) 12.6120 0.520998
\(587\) 13.5868 0.560786 0.280393 0.959885i \(-0.409535\pi\)
0.280393 + 0.959885i \(0.409535\pi\)
\(588\) −1.94314 −0.0801338
\(589\) −21.4602 −0.884253
\(590\) 48.7612 2.00747
\(591\) 8.52708 0.350757
\(592\) −15.0531 −0.618678
\(593\) −23.3075 −0.957124 −0.478562 0.878054i \(-0.658842\pi\)
−0.478562 + 0.878054i \(0.658842\pi\)
\(594\) −25.4994 −1.04625
\(595\) −35.7599 −1.46601
\(596\) −2.83371 −0.116073
\(597\) −5.77626 −0.236407
\(598\) 5.21512 0.213262
\(599\) −12.4832 −0.510048 −0.255024 0.966935i \(-0.582083\pi\)
−0.255024 + 0.966935i \(0.582083\pi\)
\(600\) −1.87039 −0.0763585
\(601\) 5.84598 0.238462 0.119231 0.992867i \(-0.461957\pi\)
0.119231 + 0.992867i \(0.461957\pi\)
\(602\) −64.1288 −2.61369
\(603\) −19.8903 −0.809997
\(604\) 45.5427 1.85311
\(605\) 9.00918 0.366275
\(606\) 7.01670 0.285034
\(607\) 3.92658 0.159375 0.0796874 0.996820i \(-0.474608\pi\)
0.0796874 + 0.996820i \(0.474608\pi\)
\(608\) 9.65419 0.391529
\(609\) −13.3738 −0.541932
\(610\) 12.6056 0.510387
\(611\) −4.75131 −0.192217
\(612\) −65.0029 −2.62759
\(613\) 27.6069 1.11503 0.557516 0.830167i \(-0.311755\pi\)
0.557516 + 0.830167i \(0.311755\pi\)
\(614\) −8.47530 −0.342035
\(615\) −9.24694 −0.372873
\(616\) 46.7815 1.88488
\(617\) −39.8336 −1.60364 −0.801821 0.597565i \(-0.796135\pi\)
−0.801821 + 0.597565i \(0.796135\pi\)
\(618\) 5.85921 0.235692
\(619\) −12.4259 −0.499438 −0.249719 0.968318i \(-0.580338\pi\)
−0.249719 + 0.968318i \(0.580338\pi\)
\(620\) −38.6511 −1.55227
\(621\) 5.88585 0.236191
\(622\) 10.4800 0.420210
\(623\) −47.9472 −1.92097
\(624\) 1.17901 0.0471981
\(625\) −19.2949 −0.771796
\(626\) −37.2472 −1.48870
\(627\) −7.68958 −0.307092
\(628\) 78.6637 3.13903
\(629\) −37.3037 −1.48739
\(630\) −38.1588 −1.52028
\(631\) 20.2478 0.806054 0.403027 0.915188i \(-0.367958\pi\)
0.403027 + 0.915188i \(0.367958\pi\)
\(632\) −8.91843 −0.354756
\(633\) −0.940406 −0.0373778
\(634\) 22.7595 0.903893
\(635\) −12.4224 −0.492966
\(636\) −8.39472 −0.332872
\(637\) −1.10992 −0.0439766
\(638\) 94.6483 3.74716
\(639\) 31.9890 1.26546
\(640\) 41.6726 1.64725
\(641\) −29.4215 −1.16208 −0.581040 0.813875i \(-0.697354\pi\)
−0.581040 + 0.813875i \(0.697354\pi\)
\(642\) −7.56907 −0.298727
\(643\) −13.2214 −0.521402 −0.260701 0.965420i \(-0.583954\pi\)
−0.260701 + 0.965420i \(0.583954\pi\)
\(644\) −23.1936 −0.913958
\(645\) 8.83881 0.348028
\(646\) −62.5234 −2.45995
\(647\) −6.70718 −0.263687 −0.131843 0.991271i \(-0.542090\pi\)
−0.131843 + 0.991271i \(0.542090\pi\)
\(648\) −29.5524 −1.16093
\(649\) −39.8209 −1.56311
\(650\) −2.29475 −0.0900074
\(651\) −6.84362 −0.268222
\(652\) −33.0398 −1.29394
\(653\) 12.6801 0.496210 0.248105 0.968733i \(-0.420192\pi\)
0.248105 + 0.968733i \(0.420192\pi\)
\(654\) −1.97799 −0.0773454
\(655\) −34.7974 −1.35965
\(656\) 24.7770 0.967379
\(657\) 37.3251 1.45619
\(658\) 32.4238 1.26401
\(659\) −8.87171 −0.345593 −0.172796 0.984958i \(-0.555280\pi\)
−0.172796 + 0.984958i \(0.555280\pi\)
\(660\) −13.8494 −0.539086
\(661\) −12.1598 −0.472960 −0.236480 0.971636i \(-0.575994\pi\)
−0.236480 + 0.971636i \(0.575994\pi\)
\(662\) −34.3050 −1.33330
\(663\) 2.92175 0.113471
\(664\) −18.1409 −0.704003
\(665\) −23.9198 −0.927570
\(666\) −39.8061 −1.54246
\(667\) −21.8471 −0.845921
\(668\) 47.1361 1.82375
\(669\) −9.33279 −0.360826
\(670\) −34.4572 −1.33120
\(671\) −10.2944 −0.397411
\(672\) 3.07870 0.118763
\(673\) 32.9877 1.27158 0.635792 0.771861i \(-0.280674\pi\)
0.635792 + 0.771861i \(0.280674\pi\)
\(674\) −78.4853 −3.02314
\(675\) −2.58988 −0.0996845
\(676\) 3.74231 0.143935
\(677\) −2.49942 −0.0960606 −0.0480303 0.998846i \(-0.515294\pi\)
−0.0480303 + 0.998846i \(0.515294\pi\)
\(678\) 16.9585 0.651289
\(679\) 1.08756 0.0417367
\(680\) −52.4271 −2.01049
\(681\) 11.7455 0.450087
\(682\) 48.4334 1.85461
\(683\) −20.1647 −0.771581 −0.385790 0.922586i \(-0.626071\pi\)
−0.385790 + 0.922586i \(0.626071\pi\)
\(684\) −43.4805 −1.66252
\(685\) −28.2844 −1.08069
\(686\) −40.1951 −1.53465
\(687\) 5.56034 0.212140
\(688\) −23.6834 −0.902922
\(689\) −4.79505 −0.182677
\(690\) 4.90521 0.186738
\(691\) 3.89707 0.148251 0.0741257 0.997249i \(-0.476383\pi\)
0.0741257 + 0.997249i \(0.476383\pi\)
\(692\) −6.90473 −0.262479
\(693\) 31.1624 1.18376
\(694\) −4.34533 −0.164947
\(695\) −10.9518 −0.415424
\(696\) −19.6071 −0.743205
\(697\) 61.4009 2.32572
\(698\) 43.1898 1.63476
\(699\) −13.0022 −0.491789
\(700\) 10.2056 0.385736
\(701\) −11.3525 −0.428778 −0.214389 0.976748i \(-0.568776\pi\)
−0.214389 + 0.976748i \(0.568776\pi\)
\(702\) 6.48084 0.244603
\(703\) −24.9524 −0.941098
\(704\) −41.6207 −1.56864
\(705\) −4.46895 −0.168310
\(706\) 29.7229 1.11864
\(707\) −17.8248 −0.670370
\(708\) 17.7184 0.665900
\(709\) −38.2924 −1.43810 −0.719051 0.694958i \(-0.755423\pi\)
−0.719051 + 0.694958i \(0.755423\pi\)
\(710\) 55.4163 2.07974
\(711\) −5.94080 −0.222797
\(712\) −70.2948 −2.63441
\(713\) −11.1796 −0.418678
\(714\) −19.9386 −0.746183
\(715\) −7.91074 −0.295845
\(716\) −68.1911 −2.54842
\(717\) −7.32278 −0.273474
\(718\) 85.4467 3.18884
\(719\) −4.37499 −0.163160 −0.0815798 0.996667i \(-0.525997\pi\)
−0.0815798 + 0.996667i \(0.525997\pi\)
\(720\) −14.0924 −0.525194
\(721\) −14.8844 −0.554323
\(722\) 3.70798 0.137997
\(723\) 5.92258 0.220263
\(724\) −98.7295 −3.66925
\(725\) 9.61309 0.357021
\(726\) 5.02324 0.186430
\(727\) −16.7606 −0.621616 −0.310808 0.950473i \(-0.600600\pi\)
−0.310808 + 0.950473i \(0.600600\pi\)
\(728\) −11.8898 −0.440667
\(729\) −15.8900 −0.588519
\(730\) 64.6604 2.39319
\(731\) −58.6909 −2.17076
\(732\) 4.58053 0.169301
\(733\) −45.3073 −1.67346 −0.836732 0.547613i \(-0.815537\pi\)
−0.836732 + 0.547613i \(0.815537\pi\)
\(734\) 0.700154 0.0258431
\(735\) −1.04396 −0.0385070
\(736\) 5.02929 0.185382
\(737\) 28.1395 1.03653
\(738\) 65.5199 2.41182
\(739\) 16.1646 0.594626 0.297313 0.954780i \(-0.403909\pi\)
0.297313 + 0.954780i \(0.403909\pi\)
\(740\) −44.9408 −1.65206
\(741\) 1.95436 0.0717952
\(742\) 32.7224 1.20128
\(743\) −13.9951 −0.513429 −0.256715 0.966487i \(-0.582640\pi\)
−0.256715 + 0.966487i \(0.582640\pi\)
\(744\) −10.0333 −0.367840
\(745\) −1.52242 −0.0557771
\(746\) 55.3701 2.02724
\(747\) −12.0841 −0.442135
\(748\) 91.9617 3.36245
\(749\) 19.2280 0.702575
\(750\) −13.4279 −0.490318
\(751\) 35.9601 1.31220 0.656101 0.754673i \(-0.272205\pi\)
0.656101 + 0.754673i \(0.272205\pi\)
\(752\) 11.9745 0.436664
\(753\) 4.46426 0.162687
\(754\) −24.0555 −0.876050
\(755\) 24.4680 0.890481
\(756\) −28.8228 −1.04827
\(757\) −33.8182 −1.22915 −0.614573 0.788860i \(-0.710671\pi\)
−0.614573 + 0.788860i \(0.710671\pi\)
\(758\) 52.0287 1.88977
\(759\) −4.00584 −0.145403
\(760\) −35.0685 −1.27207
\(761\) 52.7614 1.91260 0.956300 0.292386i \(-0.0944492\pi\)
0.956300 + 0.292386i \(0.0944492\pi\)
\(762\) −6.92631 −0.250914
\(763\) 5.02475 0.181908
\(764\) 16.8262 0.608752
\(765\) −34.9231 −1.26265
\(766\) 9.27296 0.335046
\(767\) 10.1207 0.365439
\(768\) 13.3381 0.481296
\(769\) 15.4646 0.557666 0.278833 0.960340i \(-0.410052\pi\)
0.278833 + 0.960340i \(0.410052\pi\)
\(770\) 53.9844 1.94546
\(771\) −8.88499 −0.319985
\(772\) −8.19884 −0.295083
\(773\) −27.7960 −0.999753 −0.499877 0.866097i \(-0.666621\pi\)
−0.499877 + 0.866097i \(0.666621\pi\)
\(774\) −62.6281 −2.25112
\(775\) 4.91921 0.176703
\(776\) 1.59446 0.0572376
\(777\) −7.95728 −0.285466
\(778\) 90.5476 3.24629
\(779\) 41.0711 1.47152
\(780\) 3.51991 0.126033
\(781\) −45.2558 −1.61938
\(782\) −32.5712 −1.16474
\(783\) −27.1493 −0.970239
\(784\) 2.79727 0.0999025
\(785\) 42.2624 1.50841
\(786\) −19.4019 −0.692044
\(787\) 13.5449 0.482825 0.241412 0.970423i \(-0.422389\pi\)
0.241412 + 0.970423i \(0.422389\pi\)
\(788\) −68.2128 −2.42998
\(789\) −10.8859 −0.387549
\(790\) −10.2916 −0.366158
\(791\) −43.0804 −1.53176
\(792\) 45.6868 1.62341
\(793\) 2.61639 0.0929107
\(794\) 59.8087 2.12253
\(795\) −4.51009 −0.159957
\(796\) 46.2075 1.63778
\(797\) 1.77673 0.0629352 0.0314676 0.999505i \(-0.489982\pi\)
0.0314676 + 0.999505i \(0.489982\pi\)
\(798\) −13.3369 −0.472122
\(799\) 29.6744 1.04980
\(800\) −2.21298 −0.0782406
\(801\) −46.8252 −1.65449
\(802\) 9.80295 0.346154
\(803\) −52.8050 −1.86345
\(804\) −12.5208 −0.441573
\(805\) −12.4609 −0.439188
\(806\) −12.3097 −0.433590
\(807\) −10.6644 −0.375404
\(808\) −26.1327 −0.919344
\(809\) 28.0992 0.987916 0.493958 0.869486i \(-0.335550\pi\)
0.493958 + 0.869486i \(0.335550\pi\)
\(810\) −34.1026 −1.19824
\(811\) −17.8135 −0.625518 −0.312759 0.949833i \(-0.601253\pi\)
−0.312759 + 0.949833i \(0.601253\pi\)
\(812\) 106.984 3.75440
\(813\) −5.49128 −0.192587
\(814\) 56.3150 1.97384
\(815\) −17.7507 −0.621781
\(816\) −7.36353 −0.257775
\(817\) −39.2583 −1.37348
\(818\) 35.4410 1.23916
\(819\) −7.92014 −0.276752
\(820\) 73.9714 2.58319
\(821\) −2.41218 −0.0841857 −0.0420929 0.999114i \(-0.513403\pi\)
−0.0420929 + 0.999114i \(0.513403\pi\)
\(822\) −15.7705 −0.550059
\(823\) −29.8032 −1.03887 −0.519437 0.854509i \(-0.673858\pi\)
−0.519437 + 0.854509i \(0.673858\pi\)
\(824\) −21.8218 −0.760197
\(825\) 1.76264 0.0613672
\(826\) −69.0659 −2.40311
\(827\) 22.4131 0.779381 0.389691 0.920946i \(-0.372582\pi\)
0.389691 + 0.920946i \(0.372582\pi\)
\(828\) −22.6509 −0.787173
\(829\) −41.7553 −1.45022 −0.725111 0.688632i \(-0.758211\pi\)
−0.725111 + 0.688632i \(0.758211\pi\)
\(830\) −20.9340 −0.726630
\(831\) 9.01938 0.312879
\(832\) 10.5782 0.366733
\(833\) 6.93203 0.240181
\(834\) −6.10636 −0.211446
\(835\) 25.3241 0.876375
\(836\) 61.5132 2.12748
\(837\) −13.8929 −0.480207
\(838\) 76.9067 2.65670
\(839\) −24.4753 −0.844980 −0.422490 0.906368i \(-0.638844\pi\)
−0.422490 + 0.906368i \(0.638844\pi\)
\(840\) −11.1833 −0.385859
\(841\) 71.7727 2.47492
\(842\) 82.9266 2.85784
\(843\) 5.76188 0.198450
\(844\) 7.52282 0.258946
\(845\) 2.01057 0.0691656
\(846\) 31.6651 1.08867
\(847\) −12.7607 −0.438463
\(848\) 12.0847 0.414991
\(849\) 14.9826 0.514201
\(850\) 14.3319 0.491580
\(851\) −12.9988 −0.445594
\(852\) 20.1367 0.689873
\(853\) 5.20965 0.178375 0.0891875 0.996015i \(-0.471573\pi\)
0.0891875 + 0.996015i \(0.471573\pi\)
\(854\) −17.8548 −0.610977
\(855\) −23.3600 −0.798896
\(856\) 28.1899 0.963510
\(857\) 33.4396 1.14228 0.571138 0.820854i \(-0.306502\pi\)
0.571138 + 0.820854i \(0.306502\pi\)
\(858\) −4.41078 −0.150582
\(859\) −49.7923 −1.69889 −0.849446 0.527676i \(-0.823064\pi\)
−0.849446 + 0.527676i \(0.823064\pi\)
\(860\) −70.7065 −2.41107
\(861\) 13.0975 0.446361
\(862\) −47.8919 −1.63120
\(863\) −7.94831 −0.270564 −0.135282 0.990807i \(-0.543194\pi\)
−0.135282 + 0.990807i \(0.543194\pi\)
\(864\) 6.24991 0.212626
\(865\) −3.70959 −0.126130
\(866\) 41.9590 1.42582
\(867\) −10.2950 −0.349637
\(868\) 54.7459 1.85820
\(869\) 8.40464 0.285108
\(870\) −22.6260 −0.767092
\(871\) −7.15184 −0.242331
\(872\) 7.36672 0.249469
\(873\) 1.06211 0.0359469
\(874\) −21.7869 −0.736952
\(875\) 34.1114 1.15318
\(876\) 23.4958 0.793849
\(877\) −24.7177 −0.834658 −0.417329 0.908756i \(-0.637034\pi\)
−0.417329 + 0.908756i \(0.637034\pi\)
\(878\) 17.7084 0.597630
\(879\) 2.46215 0.0830464
\(880\) 19.9370 0.672077
\(881\) −49.4786 −1.66698 −0.833488 0.552537i \(-0.813660\pi\)
−0.833488 + 0.552537i \(0.813660\pi\)
\(882\) 7.39705 0.249072
\(883\) 22.8327 0.768380 0.384190 0.923254i \(-0.374481\pi\)
0.384190 + 0.923254i \(0.374481\pi\)
\(884\) −23.3727 −0.786108
\(885\) 9.51930 0.319988
\(886\) −69.3294 −2.32917
\(887\) 32.7464 1.09952 0.549758 0.835324i \(-0.314720\pi\)
0.549758 + 0.835324i \(0.314720\pi\)
\(888\) −11.6661 −0.391487
\(889\) 17.5952 0.590123
\(890\) −81.1180 −2.71908
\(891\) 27.8499 0.933007
\(892\) 74.6581 2.49974
\(893\) 19.8492 0.664229
\(894\) −0.848853 −0.0283899
\(895\) −36.6359 −1.22460
\(896\) −59.0255 −1.97190
\(897\) 1.01811 0.0339937
\(898\) −25.8442 −0.862433
\(899\) 51.5674 1.71987
\(900\) 9.96679 0.332226
\(901\) 29.9476 0.997700
\(902\) −92.6930 −3.08634
\(903\) −12.5194 −0.416619
\(904\) −63.1596 −2.10066
\(905\) −53.0428 −1.76320
\(906\) 13.6426 0.453244
\(907\) 16.6782 0.553790 0.276895 0.960900i \(-0.410695\pi\)
0.276895 + 0.960900i \(0.410695\pi\)
\(908\) −93.9583 −3.11812
\(909\) −17.4076 −0.577375
\(910\) −13.7205 −0.454830
\(911\) 50.3435 1.66796 0.833978 0.551798i \(-0.186058\pi\)
0.833978 + 0.551798i \(0.186058\pi\)
\(912\) −4.92547 −0.163098
\(913\) 17.0958 0.565788
\(914\) −18.6940 −0.618343
\(915\) 2.46091 0.0813551
\(916\) −44.4802 −1.46967
\(917\) 49.2874 1.62761
\(918\) −40.4763 −1.33592
\(919\) −24.6359 −0.812665 −0.406332 0.913725i \(-0.633193\pi\)
−0.406332 + 0.913725i \(0.633193\pi\)
\(920\) −18.2687 −0.602302
\(921\) −1.65457 −0.0545200
\(922\) 8.35523 0.275165
\(923\) 11.5021 0.378595
\(924\) 19.6164 0.645333
\(925\) 5.71971 0.188063
\(926\) 2.39631 0.0787477
\(927\) −14.5361 −0.477427
\(928\) −23.1983 −0.761523
\(929\) −7.41679 −0.243337 −0.121668 0.992571i \(-0.538824\pi\)
−0.121668 + 0.992571i \(0.538824\pi\)
\(930\) −11.5782 −0.379663
\(931\) 4.63684 0.151966
\(932\) 104.012 3.40702
\(933\) 2.04594 0.0669809
\(934\) −43.3660 −1.41898
\(935\) 49.4067 1.61577
\(936\) −11.6116 −0.379537
\(937\) 41.4803 1.35510 0.677551 0.735476i \(-0.263041\pi\)
0.677551 + 0.735476i \(0.263041\pi\)
\(938\) 48.8056 1.59356
\(939\) −7.27151 −0.237297
\(940\) 35.7496 1.16602
\(941\) 27.0010 0.880206 0.440103 0.897947i \(-0.354942\pi\)
0.440103 + 0.897947i \(0.354942\pi\)
\(942\) 23.5642 0.767762
\(943\) 21.3957 0.696741
\(944\) −25.5068 −0.830175
\(945\) −15.4851 −0.503732
\(946\) 88.6019 2.88070
\(947\) −3.25673 −0.105829 −0.0529147 0.998599i \(-0.516851\pi\)
−0.0529147 + 0.998599i \(0.516851\pi\)
\(948\) −3.73967 −0.121459
\(949\) 13.4207 0.435656
\(950\) 9.58661 0.311031
\(951\) 4.44316 0.144079
\(952\) 74.2583 2.40673
\(953\) −33.9932 −1.10115 −0.550574 0.834786i \(-0.685591\pi\)
−0.550574 + 0.834786i \(0.685591\pi\)
\(954\) 31.9566 1.03463
\(955\) 9.03996 0.292526
\(956\) 58.5790 1.89458
\(957\) 18.4775 0.597293
\(958\) 24.6677 0.796978
\(959\) 40.0624 1.29368
\(960\) 9.94956 0.321121
\(961\) −4.61196 −0.148773
\(962\) −14.3128 −0.461464
\(963\) 18.7780 0.605113
\(964\) −47.3780 −1.52594
\(965\) −4.40486 −0.141797
\(966\) −6.94779 −0.223541
\(967\) −47.6609 −1.53267 −0.766335 0.642441i \(-0.777922\pi\)
−0.766335 + 0.642441i \(0.777922\pi\)
\(968\) −18.7083 −0.601308
\(969\) −12.2060 −0.392113
\(970\) 1.83995 0.0590773
\(971\) −53.3486 −1.71204 −0.856018 0.516946i \(-0.827069\pi\)
−0.856018 + 0.516946i \(0.827069\pi\)
\(972\) −42.7552 −1.37137
\(973\) 15.5122 0.497299
\(974\) 23.5418 0.754328
\(975\) −0.447987 −0.0143471
\(976\) −6.59395 −0.211067
\(977\) −21.0622 −0.673840 −0.336920 0.941533i \(-0.609385\pi\)
−0.336920 + 0.941533i \(0.609385\pi\)
\(978\) −9.89725 −0.316479
\(979\) 66.2451 2.11720
\(980\) 8.35121 0.266770
\(981\) 4.90716 0.156674
\(982\) −9.69531 −0.309390
\(983\) −33.6243 −1.07245 −0.536224 0.844076i \(-0.680150\pi\)
−0.536224 + 0.844076i \(0.680150\pi\)
\(984\) 19.2020 0.612138
\(985\) −36.6476 −1.16769
\(986\) 150.239 4.78460
\(987\) 6.32987 0.201482
\(988\) −15.6340 −0.497383
\(989\) −20.4514 −0.650316
\(990\) 52.7211 1.67559
\(991\) 43.5186 1.38241 0.691207 0.722657i \(-0.257079\pi\)
0.691207 + 0.722657i \(0.257079\pi\)
\(992\) −11.8710 −0.376906
\(993\) −6.69712 −0.212527
\(994\) −78.4923 −2.48963
\(995\) 24.8251 0.787010
\(996\) −7.60683 −0.241032
\(997\) −47.2702 −1.49706 −0.748531 0.663100i \(-0.769240\pi\)
−0.748531 + 0.663100i \(0.769240\pi\)
\(998\) −19.7004 −0.623605
\(999\) −16.1536 −0.511078
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 \(a_p\))