Properties

Label 6047.2.a.a.1.2
Level 6047
Weight 2
Character 6047.1
Self dual Yes
Analytic conductor 48.286
Analytic rank 1
Dimension 217
CM No

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Newspace parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(1\)
Dimension: \(217\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.78935 q^{2}\) \(+0.603668 q^{3}\) \(+5.78045 q^{4}\) \(+3.11422 q^{5}\) \(-1.68384 q^{6}\) \(+0.146622 q^{7}\) \(-10.5450 q^{8}\) \(-2.63558 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.78935 q^{2}\) \(+0.603668 q^{3}\) \(+5.78045 q^{4}\) \(+3.11422 q^{5}\) \(-1.68384 q^{6}\) \(+0.146622 q^{7}\) \(-10.5450 q^{8}\) \(-2.63558 q^{9}\) \(-8.68663 q^{10}\) \(+5.95238 q^{11}\) \(+3.48947 q^{12}\) \(-2.13466 q^{13}\) \(-0.408979 q^{14}\) \(+1.87995 q^{15}\) \(+17.8527 q^{16}\) \(-3.51865 q^{17}\) \(+7.35156 q^{18}\) \(+2.37433 q^{19}\) \(+18.0016 q^{20}\) \(+0.0885108 q^{21}\) \(-16.6032 q^{22}\) \(-3.35265 q^{23}\) \(-6.36567 q^{24}\) \(+4.69836 q^{25}\) \(+5.95430 q^{26}\) \(-3.40202 q^{27}\) \(+0.847539 q^{28}\) \(+1.70921 q^{29}\) \(-5.24384 q^{30}\) \(-2.22831 q^{31}\) \(-28.7074 q^{32}\) \(+3.59326 q^{33}\) \(+9.81474 q^{34}\) \(+0.456612 q^{35}\) \(-15.2349 q^{36}\) \(-6.81464 q^{37}\) \(-6.62283 q^{38}\) \(-1.28863 q^{39}\) \(-32.8394 q^{40}\) \(-2.99107 q^{41}\) \(-0.246887 q^{42}\) \(-7.86014 q^{43}\) \(+34.4074 q^{44}\) \(-8.20779 q^{45}\) \(+9.35171 q^{46}\) \(-6.38720 q^{47}\) \(+10.7771 q^{48}\) \(-6.97850 q^{49}\) \(-13.1053 q^{50}\) \(-2.12410 q^{51}\) \(-12.3393 q^{52}\) \(-8.02904 q^{53}\) \(+9.48942 q^{54}\) \(+18.5370 q^{55}\) \(-1.54612 q^{56}\) \(+1.43331 q^{57}\) \(-4.76758 q^{58}\) \(-0.780236 q^{59}\) \(+10.8670 q^{60}\) \(+10.2256 q^{61}\) \(+6.21552 q^{62}\) \(-0.386434 q^{63}\) \(+44.3694 q^{64}\) \(-6.64780 q^{65}\) \(-10.0229 q^{66}\) \(+0.544504 q^{67}\) \(-20.3394 q^{68}\) \(-2.02389 q^{69}\) \(-1.27365 q^{70}\) \(+0.166754 q^{71}\) \(+27.7922 q^{72}\) \(+3.03385 q^{73}\) \(+19.0084 q^{74}\) \(+2.83625 q^{75}\) \(+13.7247 q^{76}\) \(+0.872748 q^{77}\) \(+3.59442 q^{78}\) \(-17.2844 q^{79}\) \(+55.5972 q^{80}\) \(+5.85306 q^{81}\) \(+8.34312 q^{82}\) \(+13.5790 q^{83}\) \(+0.511632 q^{84}\) \(-10.9579 q^{85}\) \(+21.9246 q^{86}\) \(+1.03179 q^{87}\) \(-62.7677 q^{88}\) \(-9.95654 q^{89}\) \(+22.8944 q^{90}\) \(-0.312987 q^{91}\) \(-19.3798 q^{92}\) \(-1.34516 q^{93}\) \(+17.8161 q^{94}\) \(+7.39419 q^{95}\) \(-17.3297 q^{96}\) \(-13.2742 q^{97}\) \(+19.4655 q^{98}\) \(-15.6880 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut -\mathstrut 46q^{10} \) \(\mathstrut -\mathstrut 32q^{11} \) \(\mathstrut -\mathstrut 72q^{12} \) \(\mathstrut -\mathstrut 80q^{13} \) \(\mathstrut -\mathstrut 22q^{14} \) \(\mathstrut -\mathstrut 43q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut -\mathstrut 61q^{17} \) \(\mathstrut -\mathstrut 88q^{18} \) \(\mathstrut -\mathstrut 43q^{19} \) \(\mathstrut -\mathstrut 41q^{20} \) \(\mathstrut -\mathstrut 61q^{21} \) \(\mathstrut -\mathstrut 93q^{22} \) \(\mathstrut -\mathstrut 60q^{23} \) \(\mathstrut -\mathstrut 41q^{24} \) \(\mathstrut +\mathstrut 26q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 93q^{27} \) \(\mathstrut -\mathstrut 126q^{28} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut -\mathstrut 36q^{30} \) \(\mathstrut -\mathstrut 100q^{31} \) \(\mathstrut -\mathstrut 114q^{32} \) \(\mathstrut -\mathstrut 133q^{33} \) \(\mathstrut -\mathstrut 75q^{34} \) \(\mathstrut -\mathstrut 37q^{35} \) \(\mathstrut +\mathstrut 75q^{36} \) \(\mathstrut -\mathstrut 264q^{37} \) \(\mathstrut -\mathstrut 35q^{38} \) \(\mathstrut -\mathstrut 47q^{39} \) \(\mathstrut -\mathstrut 118q^{40} \) \(\mathstrut -\mathstrut 72q^{41} \) \(\mathstrut -\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 107q^{43} \) \(\mathstrut -\mathstrut 59q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 111q^{46} \) \(\mathstrut -\mathstrut 54q^{47} \) \(\mathstrut -\mathstrut 135q^{48} \) \(\mathstrut +\mathstrut 33q^{49} \) \(\mathstrut -\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 26q^{51} \) \(\mathstrut -\mathstrut 173q^{52} \) \(\mathstrut -\mathstrut 103q^{53} \) \(\mathstrut -\mathstrut 28q^{54} \) \(\mathstrut -\mathstrut 78q^{55} \) \(\mathstrut -\mathstrut 44q^{56} \) \(\mathstrut -\mathstrut 205q^{57} \) \(\mathstrut -\mathstrut 189q^{58} \) \(\mathstrut -\mathstrut 38q^{59} \) \(\mathstrut -\mathstrut 105q^{60} \) \(\mathstrut -\mathstrut 108q^{61} \) \(\mathstrut -\mathstrut 14q^{62} \) \(\mathstrut -\mathstrut 116q^{63} \) \(\mathstrut +\mathstrut 39q^{64} \) \(\mathstrut -\mathstrut 146q^{65} \) \(\mathstrut +\mathstrut 5q^{66} \) \(\mathstrut -\mathstrut 206q^{67} \) \(\mathstrut -\mathstrut 62q^{68} \) \(\mathstrut -\mathstrut 55q^{69} \) \(\mathstrut -\mathstrut 125q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 225q^{72} \) \(\mathstrut -\mathstrut 326q^{73} \) \(\mathstrut +\mathstrut 3q^{74} \) \(\mathstrut -\mathstrut 95q^{75} \) \(\mathstrut -\mathstrut 84q^{76} \) \(\mathstrut -\mathstrut 79q^{77} \) \(\mathstrut -\mathstrut 86q^{78} \) \(\mathstrut -\mathstrut 117q^{79} \) \(\mathstrut -\mathstrut 39q^{80} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut -\mathstrut 96q^{82} \) \(\mathstrut -\mathstrut 23q^{83} \) \(\mathstrut -\mathstrut 57q^{84} \) \(\mathstrut -\mathstrut 224q^{85} \) \(\mathstrut -\mathstrut 7q^{86} \) \(\mathstrut -\mathstrut 45q^{87} \) \(\mathstrut -\mathstrut 250q^{88} \) \(\mathstrut -\mathstrut 104q^{89} \) \(\mathstrut -\mathstrut 36q^{90} \) \(\mathstrut -\mathstrut 96q^{91} \) \(\mathstrut -\mathstrut 137q^{92} \) \(\mathstrut -\mathstrut 155q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 447q^{97} \) \(\mathstrut -\mathstrut 46q^{98} \) \(\mathstrut -\mathstrut 94q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.78935 −1.97237 −0.986183 0.165662i \(-0.947024\pi\)
−0.986183 + 0.165662i \(0.947024\pi\)
\(3\) 0.603668 0.348528 0.174264 0.984699i \(-0.444245\pi\)
0.174264 + 0.984699i \(0.444245\pi\)
\(4\) 5.78045 2.89022
\(5\) 3.11422 1.39272 0.696360 0.717692i \(-0.254802\pi\)
0.696360 + 0.717692i \(0.254802\pi\)
\(6\) −1.68384 −0.687424
\(7\) 0.146622 0.0554178 0.0277089 0.999616i \(-0.491179\pi\)
0.0277089 + 0.999616i \(0.491179\pi\)
\(8\) −10.5450 −3.72821
\(9\) −2.63558 −0.878528
\(10\) −8.68663 −2.74695
\(11\) 5.95238 1.79471 0.897355 0.441309i \(-0.145486\pi\)
0.897355 + 0.441309i \(0.145486\pi\)
\(12\) 3.48947 1.00732
\(13\) −2.13466 −0.592048 −0.296024 0.955180i \(-0.595661\pi\)
−0.296024 + 0.955180i \(0.595661\pi\)
\(14\) −0.408979 −0.109304
\(15\) 1.87995 0.485402
\(16\) 17.8527 4.46317
\(17\) −3.51865 −0.853399 −0.426699 0.904393i \(-0.640324\pi\)
−0.426699 + 0.904393i \(0.640324\pi\)
\(18\) 7.35156 1.73278
\(19\) 2.37433 0.544709 0.272355 0.962197i \(-0.412198\pi\)
0.272355 + 0.962197i \(0.412198\pi\)
\(20\) 18.0016 4.02528
\(21\) 0.0885108 0.0193146
\(22\) −16.6032 −3.53982
\(23\) −3.35265 −0.699076 −0.349538 0.936922i \(-0.613661\pi\)
−0.349538 + 0.936922i \(0.613661\pi\)
\(24\) −6.36567 −1.29939
\(25\) 4.69836 0.939672
\(26\) 5.95430 1.16774
\(27\) −3.40202 −0.654720
\(28\) 0.847539 0.160170
\(29\) 1.70921 0.317392 0.158696 0.987327i \(-0.449271\pi\)
0.158696 + 0.987327i \(0.449271\pi\)
\(30\) −5.24384 −0.957390
\(31\) −2.22831 −0.400216 −0.200108 0.979774i \(-0.564129\pi\)
−0.200108 + 0.979774i \(0.564129\pi\)
\(32\) −28.7074 −5.07480
\(33\) 3.59326 0.625507
\(34\) 9.81474 1.68321
\(35\) 0.456612 0.0771815
\(36\) −15.2349 −2.53914
\(37\) −6.81464 −1.12032 −0.560160 0.828385i \(-0.689260\pi\)
−0.560160 + 0.828385i \(0.689260\pi\)
\(38\) −6.62283 −1.07437
\(39\) −1.28863 −0.206345
\(40\) −32.8394 −5.19236
\(41\) −2.99107 −0.467126 −0.233563 0.972342i \(-0.575038\pi\)
−0.233563 + 0.972342i \(0.575038\pi\)
\(42\) −0.246887 −0.0380955
\(43\) −7.86014 −1.19866 −0.599330 0.800502i \(-0.704566\pi\)
−0.599330 + 0.800502i \(0.704566\pi\)
\(44\) 34.4074 5.18712
\(45\) −8.20779 −1.22354
\(46\) 9.35171 1.37883
\(47\) −6.38720 −0.931668 −0.465834 0.884872i \(-0.654246\pi\)
−0.465834 + 0.884872i \(0.654246\pi\)
\(48\) 10.7771 1.55554
\(49\) −6.97850 −0.996929
\(50\) −13.1053 −1.85338
\(51\) −2.12410 −0.297433
\(52\) −12.3393 −1.71115
\(53\) −8.02904 −1.10287 −0.551437 0.834217i \(-0.685920\pi\)
−0.551437 + 0.834217i \(0.685920\pi\)
\(54\) 9.48942 1.29135
\(55\) 18.5370 2.49953
\(56\) −1.54612 −0.206609
\(57\) 1.43331 0.189846
\(58\) −4.76758 −0.626013
\(59\) −0.780236 −0.101578 −0.0507890 0.998709i \(-0.516174\pi\)
−0.0507890 + 0.998709i \(0.516174\pi\)
\(60\) 10.8670 1.40292
\(61\) 10.2256 1.30925 0.654626 0.755953i \(-0.272826\pi\)
0.654626 + 0.755953i \(0.272826\pi\)
\(62\) 6.21552 0.789372
\(63\) −0.386434 −0.0486861
\(64\) 44.3694 5.54618
\(65\) −6.64780 −0.824558
\(66\) −10.0229 −1.23373
\(67\) 0.544504 0.0665218 0.0332609 0.999447i \(-0.489411\pi\)
0.0332609 + 0.999447i \(0.489411\pi\)
\(68\) −20.3394 −2.46651
\(69\) −2.02389 −0.243648
\(70\) −1.27365 −0.152230
\(71\) 0.166754 0.0197900 0.00989501 0.999951i \(-0.496850\pi\)
0.00989501 + 0.999951i \(0.496850\pi\)
\(72\) 27.7922 3.27534
\(73\) 3.03385 0.355085 0.177543 0.984113i \(-0.443185\pi\)
0.177543 + 0.984113i \(0.443185\pi\)
\(74\) 19.0084 2.20968
\(75\) 2.83625 0.327502
\(76\) 13.7247 1.57433
\(77\) 0.872748 0.0994589
\(78\) 3.59442 0.406988
\(79\) −17.2844 −1.94465 −0.972325 0.233634i \(-0.924938\pi\)
−0.972325 + 0.233634i \(0.924938\pi\)
\(80\) 55.5972 6.21596
\(81\) 5.85306 0.650340
\(82\) 8.34312 0.921343
\(83\) 13.5790 1.49049 0.745244 0.666792i \(-0.232333\pi\)
0.745244 + 0.666792i \(0.232333\pi\)
\(84\) 0.511632 0.0558237
\(85\) −10.9579 −1.18855
\(86\) 21.9246 2.36419
\(87\) 1.03179 0.110620
\(88\) −62.7677 −6.69106
\(89\) −9.95654 −1.05539 −0.527695 0.849434i \(-0.676944\pi\)
−0.527695 + 0.849434i \(0.676944\pi\)
\(90\) 22.8944 2.41328
\(91\) −0.312987 −0.0328100
\(92\) −19.3798 −2.02049
\(93\) −1.34516 −0.139486
\(94\) 17.8161 1.83759
\(95\) 7.39419 0.758628
\(96\) −17.3297 −1.76871
\(97\) −13.2742 −1.34779 −0.673893 0.738829i \(-0.735379\pi\)
−0.673893 + 0.738829i \(0.735379\pi\)
\(98\) 19.4655 1.96631
\(99\) −15.6880 −1.57670
\(100\) 27.1586 2.71586
\(101\) 4.34471 0.432315 0.216158 0.976358i \(-0.430647\pi\)
0.216158 + 0.976358i \(0.430647\pi\)
\(102\) 5.92485 0.586647
\(103\) −7.59892 −0.748743 −0.374372 0.927279i \(-0.622142\pi\)
−0.374372 + 0.927279i \(0.622142\pi\)
\(104\) 22.5099 2.20728
\(105\) 0.275642 0.0268999
\(106\) 22.3958 2.17527
\(107\) −12.1109 −1.17081 −0.585403 0.810742i \(-0.699064\pi\)
−0.585403 + 0.810742i \(0.699064\pi\)
\(108\) −19.6652 −1.89229
\(109\) 14.0215 1.34302 0.671508 0.740998i \(-0.265647\pi\)
0.671508 + 0.740998i \(0.265647\pi\)
\(110\) −51.7061 −4.92999
\(111\) −4.11378 −0.390463
\(112\) 2.61759 0.247339
\(113\) −8.15613 −0.767264 −0.383632 0.923486i \(-0.625327\pi\)
−0.383632 + 0.923486i \(0.625327\pi\)
\(114\) −3.99799 −0.374446
\(115\) −10.4409 −0.973618
\(116\) 9.88000 0.917335
\(117\) 5.62608 0.520131
\(118\) 2.17635 0.200349
\(119\) −0.515911 −0.0472935
\(120\) −19.8241 −1.80968
\(121\) 24.4308 2.22099
\(122\) −28.5227 −2.58232
\(123\) −1.80561 −0.162806
\(124\) −12.8806 −1.15671
\(125\) −0.939380 −0.0840207
\(126\) 1.07790 0.0960268
\(127\) −19.0134 −1.68716 −0.843581 0.537001i \(-0.819557\pi\)
−0.843581 + 0.537001i \(0.819557\pi\)
\(128\) −66.3469 −5.86429
\(129\) −4.74491 −0.417766
\(130\) 18.5430 1.62633
\(131\) −0.369172 −0.0322547 −0.0161274 0.999870i \(-0.505134\pi\)
−0.0161274 + 0.999870i \(0.505134\pi\)
\(132\) 20.7707 1.80785
\(133\) 0.348129 0.0301866
\(134\) −1.51881 −0.131205
\(135\) −10.5946 −0.911842
\(136\) 37.1041 3.18165
\(137\) 11.4170 0.975420 0.487710 0.873006i \(-0.337832\pi\)
0.487710 + 0.873006i \(0.337832\pi\)
\(138\) 5.64533 0.480562
\(139\) −11.6731 −0.990102 −0.495051 0.868864i \(-0.664851\pi\)
−0.495051 + 0.868864i \(0.664851\pi\)
\(140\) 2.63942 0.223072
\(141\) −3.85575 −0.324712
\(142\) −0.465134 −0.0390331
\(143\) −12.7063 −1.06255
\(144\) −47.0523 −3.92103
\(145\) 5.32285 0.442039
\(146\) −8.46245 −0.700358
\(147\) −4.21270 −0.347458
\(148\) −39.3917 −3.23798
\(149\) 5.31409 0.435348 0.217674 0.976022i \(-0.430153\pi\)
0.217674 + 0.976022i \(0.430153\pi\)
\(150\) −7.91128 −0.645953
\(151\) −3.89096 −0.316641 −0.158321 0.987388i \(-0.550608\pi\)
−0.158321 + 0.987388i \(0.550608\pi\)
\(152\) −25.0373 −2.03079
\(153\) 9.27371 0.749735
\(154\) −2.43440 −0.196169
\(155\) −6.93944 −0.557389
\(156\) −7.44884 −0.596384
\(157\) −7.19304 −0.574067 −0.287033 0.957921i \(-0.592669\pi\)
−0.287033 + 0.957921i \(0.592669\pi\)
\(158\) 48.2122 3.83556
\(159\) −4.84688 −0.384382
\(160\) −89.4011 −7.06778
\(161\) −0.491572 −0.0387413
\(162\) −16.3262 −1.28271
\(163\) 1.98301 0.155322 0.0776608 0.996980i \(-0.475255\pi\)
0.0776608 + 0.996980i \(0.475255\pi\)
\(164\) −17.2897 −1.35010
\(165\) 11.1902 0.871156
\(166\) −37.8765 −2.93979
\(167\) 21.3922 1.65538 0.827690 0.561185i \(-0.189654\pi\)
0.827690 + 0.561185i \(0.189654\pi\)
\(168\) −0.933345 −0.0720091
\(169\) −8.44323 −0.649479
\(170\) 30.5653 2.34425
\(171\) −6.25775 −0.478542
\(172\) −45.4351 −3.46440
\(173\) 22.0184 1.67403 0.837014 0.547182i \(-0.184300\pi\)
0.837014 + 0.547182i \(0.184300\pi\)
\(174\) −2.87803 −0.218183
\(175\) 0.688881 0.0520745
\(176\) 106.266 8.01011
\(177\) −0.471003 −0.0354028
\(178\) 27.7722 2.08162
\(179\) −13.7766 −1.02971 −0.514857 0.857276i \(-0.672155\pi\)
−0.514857 + 0.857276i \(0.672155\pi\)
\(180\) −47.4447 −3.53632
\(181\) 0.892525 0.0663409 0.0331704 0.999450i \(-0.489440\pi\)
0.0331704 + 0.999450i \(0.489440\pi\)
\(182\) 0.873030 0.0647133
\(183\) 6.17286 0.456311
\(184\) 35.3537 2.60631
\(185\) −21.2223 −1.56029
\(186\) 3.75211 0.275118
\(187\) −20.9444 −1.53160
\(188\) −36.9209 −2.69273
\(189\) −0.498810 −0.0362831
\(190\) −20.6249 −1.49629
\(191\) −24.4872 −1.77184 −0.885918 0.463843i \(-0.846470\pi\)
−0.885918 + 0.463843i \(0.846470\pi\)
\(192\) 26.7844 1.93300
\(193\) 9.34731 0.672834 0.336417 0.941713i \(-0.390785\pi\)
0.336417 + 0.941713i \(0.390785\pi\)
\(194\) 37.0262 2.65833
\(195\) −4.01306 −0.287381
\(196\) −40.3389 −2.88135
\(197\) −15.2725 −1.08812 −0.544060 0.839047i \(-0.683113\pi\)
−0.544060 + 0.839047i \(0.683113\pi\)
\(198\) 43.7593 3.10984
\(199\) −4.06137 −0.287903 −0.143951 0.989585i \(-0.545981\pi\)
−0.143951 + 0.989585i \(0.545981\pi\)
\(200\) −49.5441 −3.50330
\(201\) 0.328700 0.0231847
\(202\) −12.1189 −0.852684
\(203\) 0.250607 0.0175892
\(204\) −12.2782 −0.859649
\(205\) −9.31483 −0.650576
\(206\) 21.1960 1.47680
\(207\) 8.83620 0.614158
\(208\) −38.1094 −2.64241
\(209\) 14.1329 0.977595
\(210\) −0.768861 −0.0530565
\(211\) −2.51231 −0.172955 −0.0864773 0.996254i \(-0.527561\pi\)
−0.0864773 + 0.996254i \(0.527561\pi\)
\(212\) −46.4115 −3.18755
\(213\) 0.100664 0.00689737
\(214\) 33.7815 2.30926
\(215\) −24.4782 −1.66940
\(216\) 35.8743 2.44093
\(217\) −0.326718 −0.0221791
\(218\) −39.1108 −2.64892
\(219\) 1.83144 0.123757
\(220\) 107.152 7.22421
\(221\) 7.51113 0.505253
\(222\) 11.4748 0.770135
\(223\) −8.79909 −0.589230 −0.294615 0.955616i \(-0.595191\pi\)
−0.294615 + 0.955616i \(0.595191\pi\)
\(224\) −4.20913 −0.281234
\(225\) −12.3829 −0.825528
\(226\) 22.7503 1.51333
\(227\) 5.32608 0.353504 0.176752 0.984255i \(-0.443441\pi\)
0.176752 + 0.984255i \(0.443441\pi\)
\(228\) 8.28516 0.548698
\(229\) −5.46179 −0.360925 −0.180463 0.983582i \(-0.557760\pi\)
−0.180463 + 0.983582i \(0.557760\pi\)
\(230\) 29.1233 1.92033
\(231\) 0.526850 0.0346642
\(232\) −18.0236 −1.18331
\(233\) 12.6603 0.829401 0.414701 0.909958i \(-0.363886\pi\)
0.414701 + 0.909958i \(0.363886\pi\)
\(234\) −15.6931 −1.02589
\(235\) −19.8911 −1.29755
\(236\) −4.51011 −0.293583
\(237\) −10.4341 −0.677764
\(238\) 1.43905 0.0932800
\(239\) 23.0755 1.49263 0.746314 0.665595i \(-0.231822\pi\)
0.746314 + 0.665595i \(0.231822\pi\)
\(240\) 33.5623 2.16643
\(241\) −24.0218 −1.54738 −0.773690 0.633565i \(-0.781591\pi\)
−0.773690 + 0.633565i \(0.781591\pi\)
\(242\) −68.1461 −4.38059
\(243\) 13.7394 0.881381
\(244\) 59.1085 3.78403
\(245\) −21.7326 −1.38844
\(246\) 5.03647 0.321114
\(247\) −5.06839 −0.322494
\(248\) 23.4975 1.49209
\(249\) 8.19720 0.519477
\(250\) 2.62026 0.165720
\(251\) −10.5674 −0.667005 −0.333503 0.942749i \(-0.608231\pi\)
−0.333503 + 0.942749i \(0.608231\pi\)
\(252\) −2.23376 −0.140714
\(253\) −19.9563 −1.25464
\(254\) 53.0348 3.32770
\(255\) −6.61491 −0.414242
\(256\) 96.3256 6.02035
\(257\) 24.6727 1.53904 0.769522 0.638620i \(-0.220495\pi\)
0.769522 + 0.638620i \(0.220495\pi\)
\(258\) 13.2352 0.823988
\(259\) −0.999174 −0.0620856
\(260\) −38.4273 −2.38316
\(261\) −4.50477 −0.278838
\(262\) 1.02975 0.0636181
\(263\) 12.0946 0.745783 0.372892 0.927875i \(-0.378366\pi\)
0.372892 + 0.927875i \(0.378366\pi\)
\(264\) −37.8909 −2.33202
\(265\) −25.0042 −1.53600
\(266\) −0.971051 −0.0595389
\(267\) −6.01044 −0.367833
\(268\) 3.14748 0.192263
\(269\) −8.57163 −0.522622 −0.261311 0.965255i \(-0.584155\pi\)
−0.261311 + 0.965255i \(0.584155\pi\)
\(270\) 29.5521 1.79848
\(271\) −5.50129 −0.334179 −0.167090 0.985942i \(-0.553437\pi\)
−0.167090 + 0.985942i \(0.553437\pi\)
\(272\) −62.8175 −3.80887
\(273\) −0.188940 −0.0114352
\(274\) −31.8460 −1.92388
\(275\) 27.9664 1.68644
\(276\) −11.6990 −0.704196
\(277\) −11.3337 −0.680977 −0.340489 0.940249i \(-0.610592\pi\)
−0.340489 + 0.940249i \(0.610592\pi\)
\(278\) 32.5604 1.95284
\(279\) 5.87289 0.351601
\(280\) −4.81496 −0.287749
\(281\) −12.8954 −0.769275 −0.384637 0.923068i \(-0.625673\pi\)
−0.384637 + 0.923068i \(0.625673\pi\)
\(282\) 10.7550 0.640452
\(283\) 31.5986 1.87834 0.939170 0.343453i \(-0.111597\pi\)
0.939170 + 0.343453i \(0.111597\pi\)
\(284\) 0.963911 0.0571976
\(285\) 4.46363 0.264403
\(286\) 35.4423 2.09575
\(287\) −0.438555 −0.0258871
\(288\) 75.6608 4.45835
\(289\) −4.61907 −0.271710
\(290\) −14.8473 −0.871862
\(291\) −8.01318 −0.469741
\(292\) 17.5370 1.02628
\(293\) 19.0481 1.11280 0.556400 0.830914i \(-0.312182\pi\)
0.556400 + 0.830914i \(0.312182\pi\)
\(294\) 11.7507 0.685313
\(295\) −2.42982 −0.141470
\(296\) 71.8602 4.17679
\(297\) −20.2501 −1.17503
\(298\) −14.8228 −0.858664
\(299\) 7.15677 0.413887
\(300\) 16.3948 0.946554
\(301\) −1.15247 −0.0664271
\(302\) 10.8532 0.624533
\(303\) 2.62277 0.150674
\(304\) 42.3882 2.43113
\(305\) 31.8447 1.82342
\(306\) −25.8676 −1.47875
\(307\) 23.5582 1.34454 0.672268 0.740308i \(-0.265320\pi\)
0.672268 + 0.740308i \(0.265320\pi\)
\(308\) 5.04488 0.287459
\(309\) −4.58722 −0.260958
\(310\) 19.3565 1.09937
\(311\) 0.623393 0.0353494 0.0176747 0.999844i \(-0.494374\pi\)
0.0176747 + 0.999844i \(0.494374\pi\)
\(312\) 13.5885 0.769299
\(313\) 4.49134 0.253866 0.126933 0.991911i \(-0.459487\pi\)
0.126933 + 0.991911i \(0.459487\pi\)
\(314\) 20.0639 1.13227
\(315\) −1.20344 −0.0678061
\(316\) −99.9117 −5.62047
\(317\) 22.4566 1.26129 0.630644 0.776072i \(-0.282791\pi\)
0.630644 + 0.776072i \(0.282791\pi\)
\(318\) 13.5196 0.758142
\(319\) 10.1739 0.569627
\(320\) 138.176 7.72428
\(321\) −7.31097 −0.408059
\(322\) 1.37116 0.0764119
\(323\) −8.35445 −0.464854
\(324\) 33.8333 1.87963
\(325\) −10.0294 −0.556331
\(326\) −5.53131 −0.306351
\(327\) 8.46433 0.468078
\(328\) 31.5407 1.74155
\(329\) −0.936502 −0.0516310
\(330\) −31.2133 −1.71824
\(331\) 11.9739 0.658145 0.329072 0.944305i \(-0.393264\pi\)
0.329072 + 0.944305i \(0.393264\pi\)
\(332\) 78.4927 4.30784
\(333\) 17.9606 0.984232
\(334\) −59.6703 −3.26502
\(335\) 1.69570 0.0926462
\(336\) 1.58016 0.0862046
\(337\) −11.5360 −0.628408 −0.314204 0.949355i \(-0.601738\pi\)
−0.314204 + 0.949355i \(0.601738\pi\)
\(338\) 23.5511 1.28101
\(339\) −4.92360 −0.267413
\(340\) −63.3413 −3.43517
\(341\) −13.2637 −0.718272
\(342\) 17.4550 0.943860
\(343\) −2.04955 −0.110665
\(344\) 82.8850 4.46886
\(345\) −6.30283 −0.339333
\(346\) −61.4169 −3.30179
\(347\) 34.7824 1.86722 0.933609 0.358292i \(-0.116641\pi\)
0.933609 + 0.358292i \(0.116641\pi\)
\(348\) 5.96424 0.319717
\(349\) −14.7234 −0.788125 −0.394063 0.919084i \(-0.628931\pi\)
−0.394063 + 0.919084i \(0.628931\pi\)
\(350\) −1.92153 −0.102710
\(351\) 7.26216 0.387625
\(352\) −170.877 −9.10779
\(353\) −2.56771 −0.136665 −0.0683327 0.997663i \(-0.521768\pi\)
−0.0683327 + 0.997663i \(0.521768\pi\)
\(354\) 1.31379 0.0698272
\(355\) 0.519307 0.0275620
\(356\) −57.5533 −3.05032
\(357\) −0.311439 −0.0164831
\(358\) 38.4278 2.03097
\(359\) 5.99448 0.316376 0.158188 0.987409i \(-0.449435\pi\)
0.158188 + 0.987409i \(0.449435\pi\)
\(360\) 86.5510 4.56164
\(361\) −13.3625 −0.703292
\(362\) −2.48956 −0.130848
\(363\) 14.7481 0.774075
\(364\) −1.80921 −0.0948283
\(365\) 9.44807 0.494534
\(366\) −17.2182 −0.900012
\(367\) −14.8711 −0.776265 −0.388132 0.921604i \(-0.626880\pi\)
−0.388132 + 0.921604i \(0.626880\pi\)
\(368\) −59.8539 −3.12010
\(369\) 7.88321 0.410383
\(370\) 59.1963 3.07747
\(371\) −1.17723 −0.0611188
\(372\) −7.77562 −0.403147
\(373\) 33.6745 1.74360 0.871801 0.489860i \(-0.162952\pi\)
0.871801 + 0.489860i \(0.162952\pi\)
\(374\) 58.4211 3.02088
\(375\) −0.567074 −0.0292836
\(376\) 67.3529 3.47346
\(377\) −3.64858 −0.187911
\(378\) 1.39135 0.0715635
\(379\) −12.2864 −0.631110 −0.315555 0.948907i \(-0.602191\pi\)
−0.315555 + 0.948907i \(0.602191\pi\)
\(380\) 42.7417 2.19260
\(381\) −11.4778 −0.588023
\(382\) 68.3034 3.49471
\(383\) −3.59376 −0.183633 −0.0918164 0.995776i \(-0.529267\pi\)
−0.0918164 + 0.995776i \(0.529267\pi\)
\(384\) −40.0515 −2.04387
\(385\) 2.71793 0.138518
\(386\) −26.0729 −1.32708
\(387\) 20.7161 1.05306
\(388\) −76.7306 −3.89540
\(389\) −10.1484 −0.514545 −0.257273 0.966339i \(-0.582824\pi\)
−0.257273 + 0.966339i \(0.582824\pi\)
\(390\) 11.1938 0.566821
\(391\) 11.7968 0.596591
\(392\) 73.5882 3.71676
\(393\) −0.222858 −0.0112417
\(394\) 42.6002 2.14617
\(395\) −53.8275 −2.70835
\(396\) −90.6837 −4.55703
\(397\) −13.1624 −0.660600 −0.330300 0.943876i \(-0.607150\pi\)
−0.330300 + 0.943876i \(0.607150\pi\)
\(398\) 11.3286 0.567849
\(399\) 0.210154 0.0105209
\(400\) 83.8784 4.19392
\(401\) 32.6107 1.62850 0.814251 0.580513i \(-0.197148\pi\)
0.814251 + 0.580513i \(0.197148\pi\)
\(402\) −0.916857 −0.0457287
\(403\) 4.75668 0.236947
\(404\) 25.1144 1.24949
\(405\) 18.2277 0.905743
\(406\) −0.699030 −0.0346923
\(407\) −40.5633 −2.01065
\(408\) 22.3986 1.10890
\(409\) 2.07085 0.102397 0.0511985 0.998688i \(-0.483696\pi\)
0.0511985 + 0.998688i \(0.483696\pi\)
\(410\) 25.9823 1.28317
\(411\) 6.89208 0.339961
\(412\) −43.9251 −2.16404
\(413\) −0.114399 −0.00562923
\(414\) −24.6472 −1.21134
\(415\) 42.2879 2.07583
\(416\) 61.2805 3.00452
\(417\) −7.04669 −0.345078
\(418\) −39.4216 −1.92817
\(419\) −34.9792 −1.70885 −0.854424 0.519577i \(-0.826090\pi\)
−0.854424 + 0.519577i \(0.826090\pi\)
\(420\) 1.59334 0.0777468
\(421\) 8.22263 0.400746 0.200373 0.979720i \(-0.435785\pi\)
0.200373 + 0.979720i \(0.435785\pi\)
\(422\) 7.00770 0.341129
\(423\) 16.8340 0.818497
\(424\) 84.6661 4.11175
\(425\) −16.5319 −0.801915
\(426\) −0.280786 −0.0136041
\(427\) 1.49929 0.0725559
\(428\) −70.0065 −3.38389
\(429\) −7.67039 −0.370330
\(430\) 68.2781 3.29266
\(431\) 16.3871 0.789337 0.394669 0.918824i \(-0.370859\pi\)
0.394669 + 0.918824i \(0.370859\pi\)
\(432\) −60.7353 −2.92213
\(433\) −21.8970 −1.05230 −0.526152 0.850390i \(-0.676366\pi\)
−0.526152 + 0.850390i \(0.676366\pi\)
\(434\) 0.911330 0.0437452
\(435\) 3.21324 0.154063
\(436\) 81.0505 3.88162
\(437\) −7.96031 −0.380793
\(438\) −5.10851 −0.244094
\(439\) 13.7995 0.658616 0.329308 0.944222i \(-0.393184\pi\)
0.329308 + 0.944222i \(0.393184\pi\)
\(440\) −195.472 −9.31878
\(441\) 18.3924 0.875830
\(442\) −20.9511 −0.996544
\(443\) −10.4209 −0.495110 −0.247555 0.968874i \(-0.579627\pi\)
−0.247555 + 0.968874i \(0.579627\pi\)
\(444\) −23.7795 −1.12852
\(445\) −31.0068 −1.46986
\(446\) 24.5437 1.16218
\(447\) 3.20795 0.151731
\(448\) 6.50552 0.307357
\(449\) 34.1754 1.61284 0.806418 0.591346i \(-0.201403\pi\)
0.806418 + 0.591346i \(0.201403\pi\)
\(450\) 34.5402 1.62824
\(451\) −17.8040 −0.838356
\(452\) −47.1461 −2.21757
\(453\) −2.34885 −0.110358
\(454\) −14.8563 −0.697240
\(455\) −0.974711 −0.0456952
\(456\) −15.1142 −0.707788
\(457\) −17.1955 −0.804369 −0.402185 0.915559i \(-0.631749\pi\)
−0.402185 + 0.915559i \(0.631749\pi\)
\(458\) 15.2348 0.711877
\(459\) 11.9705 0.558737
\(460\) −60.3530 −2.81398
\(461\) 5.44389 0.253547 0.126774 0.991932i \(-0.459538\pi\)
0.126774 + 0.991932i \(0.459538\pi\)
\(462\) −1.46957 −0.0683705
\(463\) 25.9390 1.20549 0.602744 0.797935i \(-0.294074\pi\)
0.602744 + 0.797935i \(0.294074\pi\)
\(464\) 30.5140 1.41658
\(465\) −4.18912 −0.194266
\(466\) −35.3139 −1.63588
\(467\) −4.87311 −0.225501 −0.112750 0.993623i \(-0.535966\pi\)
−0.112750 + 0.993623i \(0.535966\pi\)
\(468\) 32.5213 1.50330
\(469\) 0.0798361 0.00368649
\(470\) 55.4832 2.55925
\(471\) −4.34221 −0.200078
\(472\) 8.22757 0.378705
\(473\) −46.7865 −2.15125
\(474\) 29.1042 1.33680
\(475\) 11.1555 0.511848
\(476\) −2.98220 −0.136689
\(477\) 21.1612 0.968906
\(478\) −64.3654 −2.94401
\(479\) 21.5693 0.985528 0.492764 0.870163i \(-0.335987\pi\)
0.492764 + 0.870163i \(0.335987\pi\)
\(480\) −53.9686 −2.46332
\(481\) 14.5469 0.663283
\(482\) 67.0051 3.05200
\(483\) −0.296746 −0.0135024
\(484\) 141.221 6.41915
\(485\) −41.3386 −1.87709
\(486\) −38.3239 −1.73841
\(487\) −8.92980 −0.404648 −0.202324 0.979319i \(-0.564849\pi\)
−0.202324 + 0.979319i \(0.564849\pi\)
\(488\) −107.829 −4.88117
\(489\) 1.19708 0.0541339
\(490\) 60.6197 2.73852
\(491\) 30.2194 1.36378 0.681891 0.731454i \(-0.261158\pi\)
0.681891 + 0.731454i \(0.261158\pi\)
\(492\) −10.4372 −0.470547
\(493\) −6.01412 −0.270862
\(494\) 14.1375 0.636076
\(495\) −48.8559 −2.19591
\(496\) −39.7813 −1.78623
\(497\) 0.0244497 0.00109672
\(498\) −22.8648 −1.02460
\(499\) 12.7182 0.569347 0.284673 0.958625i \(-0.408115\pi\)
0.284673 + 0.958625i \(0.408115\pi\)
\(500\) −5.43004 −0.242839
\(501\) 12.9138 0.576946
\(502\) 29.4760 1.31558
\(503\) −35.4007 −1.57844 −0.789220 0.614110i \(-0.789515\pi\)
−0.789220 + 0.614110i \(0.789515\pi\)
\(504\) 4.07494 0.181512
\(505\) 13.5304 0.602094
\(506\) 55.6649 2.47461
\(507\) −5.09691 −0.226362
\(508\) −109.906 −4.87628
\(509\) 22.0016 0.975205 0.487602 0.873066i \(-0.337872\pi\)
0.487602 + 0.873066i \(0.337872\pi\)
\(510\) 18.4513 0.817036
\(511\) 0.444828 0.0196780
\(512\) −135.992 −6.01004
\(513\) −8.07753 −0.356632
\(514\) −68.8208 −3.03556
\(515\) −23.6647 −1.04279
\(516\) −27.4277 −1.20744
\(517\) −38.0190 −1.67208
\(518\) 2.78704 0.122456
\(519\) 13.2918 0.583445
\(520\) 70.1009 3.07413
\(521\) 23.3575 1.02331 0.511656 0.859190i \(-0.329032\pi\)
0.511656 + 0.859190i \(0.329032\pi\)
\(522\) 12.5654 0.549970
\(523\) 30.2439 1.32247 0.661237 0.750177i \(-0.270032\pi\)
0.661237 + 0.750177i \(0.270032\pi\)
\(524\) −2.13398 −0.0932234
\(525\) 0.415856 0.0181494
\(526\) −33.7359 −1.47096
\(527\) 7.84064 0.341544
\(528\) 64.1494 2.79175
\(529\) −11.7597 −0.511292
\(530\) 69.7453 3.02954
\(531\) 2.05638 0.0892392
\(532\) 2.01234 0.0872460
\(533\) 6.38491 0.276561
\(534\) 16.7652 0.725501
\(535\) −37.7160 −1.63061
\(536\) −5.74179 −0.248007
\(537\) −8.31651 −0.358884
\(538\) 23.9092 1.03080
\(539\) −41.5387 −1.78920
\(540\) −61.2418 −2.63543
\(541\) 25.6488 1.10273 0.551364 0.834265i \(-0.314108\pi\)
0.551364 + 0.834265i \(0.314108\pi\)
\(542\) 15.3450 0.659124
\(543\) 0.538789 0.0231216
\(544\) 101.011 4.33083
\(545\) 43.6660 1.87045
\(546\) 0.527020 0.0225544
\(547\) −27.4179 −1.17230 −0.586152 0.810201i \(-0.699358\pi\)
−0.586152 + 0.810201i \(0.699358\pi\)
\(548\) 65.9954 2.81918
\(549\) −26.9504 −1.15022
\(550\) −78.0080 −3.32627
\(551\) 4.05823 0.172886
\(552\) 21.3419 0.908370
\(553\) −2.53427 −0.107768
\(554\) 31.6137 1.34314
\(555\) −12.8112 −0.543805
\(556\) −67.4759 −2.86162
\(557\) 16.6884 0.707111 0.353556 0.935414i \(-0.384973\pi\)
0.353556 + 0.935414i \(0.384973\pi\)
\(558\) −16.3815 −0.693486
\(559\) 16.7787 0.709664
\(560\) 8.15176 0.344475
\(561\) −12.6434 −0.533807
\(562\) 35.9697 1.51729
\(563\) −33.8088 −1.42487 −0.712435 0.701738i \(-0.752408\pi\)
−0.712435 + 0.701738i \(0.752408\pi\)
\(564\) −22.2879 −0.938492
\(565\) −25.4000 −1.06858
\(566\) −88.1393 −3.70477
\(567\) 0.858186 0.0360404
\(568\) −1.75841 −0.0737814
\(569\) 9.34218 0.391645 0.195822 0.980639i \(-0.437262\pi\)
0.195822 + 0.980639i \(0.437262\pi\)
\(570\) −12.4506 −0.521499
\(571\) −47.2998 −1.97944 −0.989718 0.143034i \(-0.954314\pi\)
−0.989718 + 0.143034i \(0.954314\pi\)
\(572\) −73.4482 −3.07102
\(573\) −14.7822 −0.617534
\(574\) 1.22328 0.0510588
\(575\) −15.7520 −0.656902
\(576\) −116.939 −4.87247
\(577\) 5.37219 0.223647 0.111824 0.993728i \(-0.464331\pi\)
0.111824 + 0.993728i \(0.464331\pi\)
\(578\) 12.8842 0.535912
\(579\) 5.64267 0.234502
\(580\) 30.7685 1.27759
\(581\) 1.99097 0.0825995
\(582\) 22.3515 0.926501
\(583\) −47.7919 −1.97934
\(584\) −31.9919 −1.32383
\(585\) 17.5208 0.724397
\(586\) −53.1317 −2.19485
\(587\) 12.4830 0.515229 0.257615 0.966248i \(-0.417064\pi\)
0.257615 + 0.966248i \(0.417064\pi\)
\(588\) −24.3513 −1.00423
\(589\) −5.29074 −0.218001
\(590\) 6.77762 0.279030
\(591\) −9.21951 −0.379240
\(592\) −121.660 −5.00018
\(593\) −34.2950 −1.40833 −0.704164 0.710038i \(-0.748678\pi\)
−0.704164 + 0.710038i \(0.748678\pi\)
\(594\) 56.4846 2.31759
\(595\) −1.60666 −0.0658666
\(596\) 30.7178 1.25825
\(597\) −2.45172 −0.100342
\(598\) −19.9627 −0.816336
\(599\) −46.8779 −1.91538 −0.957690 0.287800i \(-0.907076\pi\)
−0.957690 + 0.287800i \(0.907076\pi\)
\(600\) −29.9082 −1.22100
\(601\) −37.4903 −1.52926 −0.764630 0.644469i \(-0.777078\pi\)
−0.764630 + 0.644469i \(0.777078\pi\)
\(602\) 3.21463 0.131018
\(603\) −1.43509 −0.0584413
\(604\) −22.4915 −0.915165
\(605\) 76.0830 3.09321
\(606\) −7.31580 −0.297184
\(607\) −17.2696 −0.700952 −0.350476 0.936572i \(-0.613980\pi\)
−0.350476 + 0.936572i \(0.613980\pi\)
\(608\) −68.1609 −2.76429
\(609\) 0.151284 0.00613032
\(610\) −88.8259 −3.59646
\(611\) 13.6345 0.551592
\(612\) 53.6062 2.16690
\(613\) −21.1978 −0.856171 −0.428086 0.903738i \(-0.640812\pi\)
−0.428086 + 0.903738i \(0.640812\pi\)
\(614\) −65.7118 −2.65191
\(615\) −5.62307 −0.226744
\(616\) −9.20311 −0.370804
\(617\) 29.5842 1.19102 0.595508 0.803350i \(-0.296951\pi\)
0.595508 + 0.803350i \(0.296951\pi\)
\(618\) 12.7953 0.514704
\(619\) −34.3827 −1.38196 −0.690978 0.722875i \(-0.742820\pi\)
−0.690978 + 0.722875i \(0.742820\pi\)
\(620\) −40.1131 −1.61098
\(621\) 11.4058 0.457699
\(622\) −1.73886 −0.0697219
\(623\) −1.45984 −0.0584874
\(624\) −23.0054 −0.920955
\(625\) −26.4172 −1.05669
\(626\) −12.5279 −0.500716
\(627\) 8.53160 0.340719
\(628\) −41.5790 −1.65918
\(629\) 23.9784 0.956079
\(630\) 3.35681 0.133738
\(631\) 30.5125 1.21468 0.607341 0.794441i \(-0.292236\pi\)
0.607341 + 0.794441i \(0.292236\pi\)
\(632\) 182.264 7.25007
\(633\) −1.51660 −0.0602795
\(634\) −62.6392 −2.48772
\(635\) −59.2118 −2.34975
\(636\) −28.0171 −1.11095
\(637\) 14.8967 0.590230
\(638\) −28.3784 −1.12351
\(639\) −0.439493 −0.0173861
\(640\) −206.619 −8.16732
\(641\) −3.08571 −0.121878 −0.0609391 0.998141i \(-0.519410\pi\)
−0.0609391 + 0.998141i \(0.519410\pi\)
\(642\) 20.3928 0.804841
\(643\) −3.20195 −0.126273 −0.0631363 0.998005i \(-0.520110\pi\)
−0.0631363 + 0.998005i \(0.520110\pi\)
\(644\) −2.84150 −0.111971
\(645\) −14.7767 −0.581832
\(646\) 23.3035 0.916862
\(647\) 37.8012 1.48612 0.743060 0.669225i \(-0.233374\pi\)
0.743060 + 0.669225i \(0.233374\pi\)
\(648\) −61.7204 −2.42461
\(649\) −4.64426 −0.182303
\(650\) 27.9754 1.09729
\(651\) −0.197229 −0.00773003
\(652\) 11.4627 0.448914
\(653\) 18.3117 0.716593 0.358297 0.933608i \(-0.383358\pi\)
0.358297 + 0.933608i \(0.383358\pi\)
\(654\) −23.6099 −0.923221
\(655\) −1.14968 −0.0449218
\(656\) −53.3986 −2.08486
\(657\) −7.99597 −0.311952
\(658\) 2.61223 0.101835
\(659\) −44.5433 −1.73516 −0.867580 0.497297i \(-0.834326\pi\)
−0.867580 + 0.497297i \(0.834326\pi\)
\(660\) 64.6844 2.51784
\(661\) 2.66514 0.103662 0.0518310 0.998656i \(-0.483494\pi\)
0.0518310 + 0.998656i \(0.483494\pi\)
\(662\) −33.3993 −1.29810
\(663\) 4.53423 0.176095
\(664\) −143.190 −5.55686
\(665\) 1.08415 0.0420415
\(666\) −50.0982 −1.94127
\(667\) −5.73038 −0.221881
\(668\) 123.657 4.78442
\(669\) −5.31173 −0.205363
\(670\) −4.72991 −0.182732
\(671\) 60.8666 2.34973
\(672\) −2.54091 −0.0980179
\(673\) −21.1637 −0.815799 −0.407900 0.913027i \(-0.633739\pi\)
−0.407900 + 0.913027i \(0.633739\pi\)
\(674\) 32.1780 1.23945
\(675\) −15.9839 −0.615221
\(676\) −48.8057 −1.87714
\(677\) −32.4025 −1.24533 −0.622664 0.782489i \(-0.713950\pi\)
−0.622664 + 0.782489i \(0.713950\pi\)
\(678\) 13.7336 0.527436
\(679\) −1.94628 −0.0746913
\(680\) 115.550 4.43116
\(681\) 3.21519 0.123206
\(682\) 36.9971 1.41669
\(683\) 30.8331 1.17980 0.589899 0.807477i \(-0.299168\pi\)
0.589899 + 0.807477i \(0.299168\pi\)
\(684\) −36.1726 −1.38309
\(685\) 35.5550 1.35849
\(686\) 5.71691 0.218273
\(687\) −3.29711 −0.125793
\(688\) −140.325 −5.34983
\(689\) 17.1393 0.652954
\(690\) 17.5808 0.669289
\(691\) 27.7925 1.05728 0.528639 0.848847i \(-0.322703\pi\)
0.528639 + 0.848847i \(0.322703\pi\)
\(692\) 127.276 4.83831
\(693\) −2.30020 −0.0873774
\(694\) −97.0202 −3.68284
\(695\) −36.3527 −1.37894
\(696\) −10.8803 −0.412415
\(697\) 10.5245 0.398645
\(698\) 41.0686 1.55447
\(699\) 7.64260 0.289070
\(700\) 3.98204 0.150507
\(701\) −9.87871 −0.373114 −0.186557 0.982444i \(-0.559733\pi\)
−0.186557 + 0.982444i \(0.559733\pi\)
\(702\) −20.2567 −0.764539
\(703\) −16.1802 −0.610248
\(704\) 264.104 9.95378
\(705\) −12.0076 −0.452234
\(706\) 7.16223 0.269554
\(707\) 0.637029 0.0239580
\(708\) −2.72261 −0.102322
\(709\) 11.5740 0.434672 0.217336 0.976097i \(-0.430263\pi\)
0.217336 + 0.976097i \(0.430263\pi\)
\(710\) −1.44853 −0.0543623
\(711\) 45.5546 1.70843
\(712\) 104.991 3.93472
\(713\) 7.47074 0.279781
\(714\) 0.868711 0.0325107
\(715\) −39.5702 −1.47984
\(716\) −79.6351 −2.97610
\(717\) 13.9299 0.520222
\(718\) −16.7207 −0.624010
\(719\) −2.99122 −0.111554 −0.0557769 0.998443i \(-0.517764\pi\)
−0.0557769 + 0.998443i \(0.517764\pi\)
\(720\) −146.531 −5.46089
\(721\) −1.11417 −0.0414937
\(722\) 37.2728 1.38715
\(723\) −14.5012 −0.539305
\(724\) 5.15920 0.191740
\(725\) 8.03048 0.298244
\(726\) −41.1376 −1.52676
\(727\) 14.4920 0.537477 0.268738 0.963213i \(-0.413393\pi\)
0.268738 + 0.963213i \(0.413393\pi\)
\(728\) 3.30045 0.122323
\(729\) −9.26517 −0.343154
\(730\) −26.3539 −0.975403
\(731\) 27.6571 1.02293
\(732\) 35.6819 1.31884
\(733\) −0.529893 −0.0195720 −0.00978602 0.999952i \(-0.503115\pi\)
−0.00978602 + 0.999952i \(0.503115\pi\)
\(734\) 41.4806 1.53108
\(735\) −13.1193 −0.483911
\(736\) 96.2459 3.54767
\(737\) 3.24110 0.119387
\(738\) −21.9890 −0.809426
\(739\) 7.16136 0.263435 0.131718 0.991287i \(-0.457951\pi\)
0.131718 + 0.991287i \(0.457951\pi\)
\(740\) −122.674 −4.50960
\(741\) −3.05962 −0.112398
\(742\) 3.28371 0.120549
\(743\) 7.98146 0.292811 0.146406 0.989225i \(-0.453230\pi\)
0.146406 + 0.989225i \(0.453230\pi\)
\(744\) 14.1847 0.520035
\(745\) 16.5492 0.606318
\(746\) −93.9300 −3.43902
\(747\) −35.7886 −1.30944
\(748\) −121.068 −4.42668
\(749\) −1.77572 −0.0648835
\(750\) 1.58176 0.0577579
\(751\) 9.51391 0.347168 0.173584 0.984819i \(-0.444465\pi\)
0.173584 + 0.984819i \(0.444465\pi\)
\(752\) −114.029 −4.15820
\(753\) −6.37917 −0.232470
\(754\) 10.1772 0.370630
\(755\) −12.1173 −0.440993
\(756\) −2.88335 −0.104866
\(757\) 2.81053 0.102150 0.0510752 0.998695i \(-0.483735\pi\)
0.0510752 + 0.998695i \(0.483735\pi\)
\(758\) 34.2710 1.24478
\(759\) −12.0470 −0.437277
\(760\) −77.9716 −2.82833
\(761\) −41.2442 −1.49510 −0.747550 0.664206i \(-0.768770\pi\)
−0.747550 + 0.664206i \(0.768770\pi\)
\(762\) 32.0154 1.15980
\(763\) 2.05585 0.0744269
\(764\) −141.547 −5.12100
\(765\) 28.8804 1.04417
\(766\) 10.0243 0.362191
\(767\) 1.66554 0.0601391
\(768\) 58.1487 2.09826
\(769\) 5.90954 0.213103 0.106552 0.994307i \(-0.466019\pi\)
0.106552 + 0.994307i \(0.466019\pi\)
\(770\) −7.58124 −0.273209
\(771\) 14.8942 0.536400
\(772\) 54.0317 1.94464
\(773\) −34.7797 −1.25094 −0.625469 0.780249i \(-0.715093\pi\)
−0.625469 + 0.780249i \(0.715093\pi\)
\(774\) −57.7842 −2.07701
\(775\) −10.4694 −0.376071
\(776\) 139.976 5.02483
\(777\) −0.603169 −0.0216386
\(778\) 28.3074 1.01487
\(779\) −7.10178 −0.254448
\(780\) −23.1973 −0.830597
\(781\) 0.992581 0.0355173
\(782\) −32.9054 −1.17670
\(783\) −5.81477 −0.207803
\(784\) −124.585 −4.44947
\(785\) −22.4007 −0.799515
\(786\) 0.621627 0.0221727
\(787\) −2.26503 −0.0807396 −0.0403698 0.999185i \(-0.512854\pi\)
−0.0403698 + 0.999185i \(0.512854\pi\)
\(788\) −88.2818 −3.14491
\(789\) 7.30111 0.259926
\(790\) 150.143 5.34186
\(791\) −1.19587 −0.0425201
\(792\) 165.430 5.87829
\(793\) −21.8281 −0.775140
\(794\) 36.7144 1.30294
\(795\) −15.0942 −0.535337
\(796\) −23.4765 −0.832104
\(797\) 32.9420 1.16687 0.583433 0.812161i \(-0.301709\pi\)
0.583433 + 0.812161i \(0.301709\pi\)
\(798\) −0.586192 −0.0207510
\(799\) 22.4743 0.795085
\(800\) −134.878 −4.76864
\(801\) 26.2413 0.927191
\(802\) −90.9626 −3.21200
\(803\) 18.0586 0.637275
\(804\) 1.90003 0.0670090
\(805\) −1.53086 −0.0539558
\(806\) −13.2680 −0.467346
\(807\) −5.17442 −0.182148
\(808\) −45.8149 −1.61176
\(809\) 44.0717 1.54948 0.774740 0.632280i \(-0.217881\pi\)
0.774740 + 0.632280i \(0.217881\pi\)
\(810\) −50.8434 −1.78646
\(811\) −47.7442 −1.67653 −0.838263 0.545265i \(-0.816429\pi\)
−0.838263 + 0.545265i \(0.816429\pi\)
\(812\) 1.44862 0.0508367
\(813\) −3.32095 −0.116471
\(814\) 113.145 3.96573
\(815\) 6.17554 0.216320
\(816\) −37.9209 −1.32750
\(817\) −18.6626 −0.652921
\(818\) −5.77632 −0.201964
\(819\) 0.824905 0.0288245
\(820\) −53.8439 −1.88031
\(821\) 1.76381 0.0615575 0.0307788 0.999526i \(-0.490201\pi\)
0.0307788 + 0.999526i \(0.490201\pi\)
\(822\) −19.2244 −0.670528
\(823\) 46.3728 1.61645 0.808226 0.588872i \(-0.200428\pi\)
0.808226 + 0.588872i \(0.200428\pi\)
\(824\) 80.1304 2.79148
\(825\) 16.8824 0.587771
\(826\) 0.319100 0.0111029
\(827\) 46.9845 1.63381 0.816905 0.576772i \(-0.195688\pi\)
0.816905 + 0.576772i \(0.195688\pi\)
\(828\) 51.0772 1.77506
\(829\) 46.9269 1.62984 0.814919 0.579575i \(-0.196781\pi\)
0.814919 + 0.579575i \(0.196781\pi\)
\(830\) −117.956 −4.09430
\(831\) −6.84180 −0.237340
\(832\) −94.7136 −3.28360
\(833\) 24.5549 0.850778
\(834\) 19.6557 0.680620
\(835\) 66.6201 2.30548
\(836\) 81.6947 2.82547
\(837\) 7.58075 0.262029
\(838\) 97.5692 3.37047
\(839\) −9.60690 −0.331667 −0.165834 0.986154i \(-0.553031\pi\)
−0.165834 + 0.986154i \(0.553031\pi\)
\(840\) −2.90664 −0.100289
\(841\) −26.0786 −0.899262
\(842\) −22.9358 −0.790418
\(843\) −7.78454 −0.268114
\(844\) −14.5223 −0.499877
\(845\) −26.2941 −0.904543
\(846\) −46.9558 −1.61438
\(847\) 3.58209 0.123082
\(848\) −143.340 −4.92232
\(849\) 19.0750 0.654654
\(850\) 46.1132 1.58167
\(851\) 22.8471 0.783189
\(852\) 0.581882 0.0199350
\(853\) 13.4838 0.461675 0.230837 0.972992i \(-0.425853\pi\)
0.230837 + 0.972992i \(0.425853\pi\)
\(854\) −4.18205 −0.143107
\(855\) −19.4880 −0.666476
\(856\) 127.709 4.36502
\(857\) 6.64582 0.227017 0.113508 0.993537i \(-0.463791\pi\)
0.113508 + 0.993537i \(0.463791\pi\)
\(858\) 21.3954 0.730426
\(859\) 20.9278 0.714046 0.357023 0.934096i \(-0.383792\pi\)
0.357023 + 0.934096i \(0.383792\pi\)
\(860\) −141.495 −4.82494
\(861\) −0.264742 −0.00902237
\(862\) −45.7092 −1.55686
\(863\) 13.7324 0.467456 0.233728 0.972302i \(-0.424907\pi\)
0.233728 + 0.972302i \(0.424907\pi\)
\(864\) 97.6632 3.32257
\(865\) 68.5701 2.33145
\(866\) 61.0784 2.07553
\(867\) −2.78839 −0.0946986
\(868\) −1.88858 −0.0641025
\(869\) −102.883 −3.49008
\(870\) −8.96282 −0.303868
\(871\) −1.16233 −0.0393841
\(872\) −147.856 −5.00705
\(873\) 34.9852 1.18407
\(874\) 22.2040 0.751063
\(875\) −0.137734 −0.00465624
\(876\) 10.5865 0.357686
\(877\) 13.2694 0.448075 0.224038 0.974580i \(-0.428076\pi\)
0.224038 + 0.974580i \(0.428076\pi\)
\(878\) −38.4917 −1.29903
\(879\) 11.4987 0.387842
\(880\) 330.936 11.1558
\(881\) −36.0131 −1.21331 −0.606656 0.794965i \(-0.707489\pi\)
−0.606656 + 0.794965i \(0.707489\pi\)
\(882\) −51.3029 −1.72746
\(883\) 10.4730 0.352444 0.176222 0.984350i \(-0.443612\pi\)
0.176222 + 0.984350i \(0.443612\pi\)
\(884\) 43.4177 1.46030
\(885\) −1.46681 −0.0493062
\(886\) 29.0674 0.976537
\(887\) 19.5314 0.655801 0.327901 0.944712i \(-0.393659\pi\)
0.327901 + 0.944712i \(0.393659\pi\)
\(888\) 43.3797 1.45573
\(889\) −2.78777 −0.0934988
\(890\) 86.4888 2.89911
\(891\) 34.8397 1.16717
\(892\) −50.8627 −1.70301
\(893\) −15.1653 −0.507488
\(894\) −8.94808 −0.299268
\(895\) −42.9034 −1.43410
\(896\) −9.72790 −0.324986
\(897\) 4.32031 0.144251
\(898\) −95.3270 −3.18110
\(899\) −3.80864 −0.127025
\(900\) −71.5788 −2.38596
\(901\) 28.2514 0.941191
\(902\) 49.6614 1.65354
\(903\) −0.695707 −0.0231517
\(904\) 86.0062 2.86053
\(905\) 2.77952 0.0923943
\(906\) 6.55174 0.217667
\(907\) −12.6400 −0.419704 −0.209852 0.977733i \(-0.567298\pi\)
−0.209852 + 0.977733i \(0.567298\pi\)
\(908\) 30.7871 1.02171
\(909\) −11.4509 −0.379801
\(910\) 2.71881 0.0901276
\(911\) 52.4979 1.73933 0.869667 0.493638i \(-0.164333\pi\)
0.869667 + 0.493638i \(0.164333\pi\)
\(912\) 25.5884 0.847317
\(913\) 80.8273 2.67499
\(914\) 47.9641 1.58651
\(915\) 19.2236 0.635514
\(916\) −31.5716 −1.04316
\(917\) −0.0541287 −0.00178749
\(918\) −33.3900 −1.10203
\(919\) 10.0680 0.332112 0.166056 0.986116i \(-0.446897\pi\)
0.166056 + 0.986116i \(0.446897\pi\)
\(920\) 110.099 3.62986
\(921\) 14.2213 0.468608
\(922\) −15.1849 −0.500088
\(923\) −0.355962 −0.0117166
\(924\) 3.04543 0.100187
\(925\) −32.0176 −1.05273
\(926\) −72.3528 −2.37766
\(927\) 20.0276 0.657792
\(928\) −49.0669 −1.61070
\(929\) −34.3278 −1.12626 −0.563130 0.826368i \(-0.690403\pi\)
−0.563130 + 0.826368i \(0.690403\pi\)
\(930\) 11.6849 0.383163
\(931\) −16.5693 −0.543036
\(932\) 73.1820 2.39716
\(933\) 0.376323 0.0123202
\(934\) 13.5928 0.444770
\(935\) −65.2253 −2.13310
\(936\) −59.3269 −1.93916
\(937\) 4.49397 0.146811 0.0734057 0.997302i \(-0.476613\pi\)
0.0734057 + 0.997302i \(0.476613\pi\)
\(938\) −0.222691 −0.00727110
\(939\) 2.71128 0.0884792
\(940\) −114.980 −3.75022
\(941\) −27.2886 −0.889584 −0.444792 0.895634i \(-0.646722\pi\)
−0.444792 + 0.895634i \(0.646722\pi\)
\(942\) 12.1119 0.394627
\(943\) 10.0280 0.326557
\(944\) −13.9293 −0.453360
\(945\) −1.55340 −0.0505322
\(946\) 130.504 4.24304
\(947\) 41.9448 1.36302 0.681512 0.731807i \(-0.261323\pi\)
0.681512 + 0.731807i \(0.261323\pi\)
\(948\) −60.3135 −1.95889
\(949\) −6.47623 −0.210227
\(950\) −31.1164 −1.00955
\(951\) 13.5563 0.439594
\(952\) 5.44027 0.176320
\(953\) −36.9496 −1.19692 −0.598458 0.801154i \(-0.704220\pi\)
−0.598458 + 0.801154i \(0.704220\pi\)
\(954\) −59.0260 −1.91104
\(955\) −76.2586 −2.46767
\(956\) 133.387 4.31403
\(957\) 6.14164 0.198531
\(958\) −60.1643 −1.94382
\(959\) 1.67398 0.0540556
\(960\) 83.4125 2.69213
\(961\) −26.0346 −0.839827
\(962\) −40.5764 −1.30824
\(963\) 31.9193 1.02859
\(964\) −138.857 −4.47227
\(965\) 29.1096 0.937070
\(966\) 0.827727 0.0266317
\(967\) 25.0645 0.806021 0.403011 0.915195i \(-0.367964\pi\)
0.403011 + 0.915195i \(0.367964\pi\)
\(968\) −257.623 −8.28031
\(969\) −5.04331 −0.162015
\(970\) 115.308 3.70231
\(971\) −3.03491 −0.0973948 −0.0486974 0.998814i \(-0.515507\pi\)
−0.0486974 + 0.998814i \(0.515507\pi\)
\(972\) 79.4198 2.54739
\(973\) −1.71153 −0.0548692
\(974\) 24.9083 0.798113
\(975\) −6.05442 −0.193897
\(976\) 182.554 5.84342
\(977\) 7.18446 0.229851 0.114926 0.993374i \(-0.463337\pi\)
0.114926 + 0.993374i \(0.463337\pi\)
\(978\) −3.33908 −0.106772
\(979\) −59.2651 −1.89412
\(980\) −125.624 −4.01291
\(981\) −36.9548 −1.17988
\(982\) −84.2923 −2.68988
\(983\) 2.54157 0.0810635 0.0405318 0.999178i \(-0.487095\pi\)
0.0405318 + 0.999178i \(0.487095\pi\)
\(984\) 19.0401 0.606977
\(985\) −47.5618 −1.51545
\(986\) 16.7754 0.534239
\(987\) −0.565336 −0.0179948
\(988\) −29.2976 −0.932080
\(989\) 26.3523 0.837955
\(990\) 136.276 4.33113
\(991\) −31.7026 −1.00707 −0.503533 0.863976i \(-0.667967\pi\)
−0.503533 + 0.863976i \(0.667967\pi\)
\(992\) 63.9689 2.03101
\(993\) 7.22826 0.229382
\(994\) −0.0681987 −0.00216313
\(995\) −12.6480 −0.400968
\(996\) 47.3835 1.50140
\(997\) −24.9331 −0.789638 −0.394819 0.918759i \(-0.629193\pi\)
−0.394819 + 0.918759i \(0.629193\pi\)
\(998\) −35.4756 −1.12296
\(999\) 23.1836 0.733495
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 \(a_p\))