Properties

Label 6019.2.a.c.1.15
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 1.15
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.25939 q^{2}\) \(+2.42736 q^{3}\) \(+3.10485 q^{4}\) \(-0.500622 q^{5}\) \(-5.48435 q^{6}\) \(+4.41326 q^{7}\) \(-2.49629 q^{8}\) \(+2.89206 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.25939 q^{2}\) \(+2.42736 q^{3}\) \(+3.10485 q^{4}\) \(-0.500622 q^{5}\) \(-5.48435 q^{6}\) \(+4.41326 q^{7}\) \(-2.49629 q^{8}\) \(+2.89206 q^{9}\) \(+1.13110 q^{10}\) \(-1.42556 q^{11}\) \(+7.53659 q^{12}\) \(-1.00000 q^{13}\) \(-9.97128 q^{14}\) \(-1.21519 q^{15}\) \(-0.569596 q^{16}\) \(+3.13782 q^{17}\) \(-6.53430 q^{18}\) \(-7.27226 q^{19}\) \(-1.55436 q^{20}\) \(+10.7126 q^{21}\) \(+3.22091 q^{22}\) \(-8.26540 q^{23}\) \(-6.05940 q^{24}\) \(-4.74938 q^{25}\) \(+2.25939 q^{26}\) \(-0.262003 q^{27}\) \(+13.7025 q^{28}\) \(-1.90070 q^{29}\) \(+2.74559 q^{30}\) \(+5.25956 q^{31}\) \(+6.27953 q^{32}\) \(-3.46035 q^{33}\) \(-7.08957 q^{34}\) \(-2.20937 q^{35}\) \(+8.97943 q^{36}\) \(+6.75569 q^{37}\) \(+16.4309 q^{38}\) \(-2.42736 q^{39}\) \(+1.24970 q^{40}\) \(-10.9114 q^{41}\) \(-24.2039 q^{42}\) \(-6.84316 q^{43}\) \(-4.42616 q^{44}\) \(-1.44783 q^{45}\) \(+18.6748 q^{46}\) \(-4.39465 q^{47}\) \(-1.38261 q^{48}\) \(+12.4769 q^{49}\) \(+10.7307 q^{50}\) \(+7.61661 q^{51}\) \(-3.10485 q^{52}\) \(+3.05136 q^{53}\) \(+0.591968 q^{54}\) \(+0.713668 q^{55}\) \(-11.0168 q^{56}\) \(-17.6524 q^{57}\) \(+4.29444 q^{58}\) \(-11.4178 q^{59}\) \(-3.77298 q^{60}\) \(+12.7964 q^{61}\) \(-11.8834 q^{62}\) \(+12.7634 q^{63}\) \(-13.0487 q^{64}\) \(+0.500622 q^{65}\) \(+7.81829 q^{66}\) \(+1.26329 q^{67}\) \(+9.74247 q^{68}\) \(-20.0631 q^{69}\) \(+4.99184 q^{70}\) \(-9.87557 q^{71}\) \(-7.21944 q^{72}\) \(-7.90176 q^{73}\) \(-15.2638 q^{74}\) \(-11.5284 q^{75}\) \(-22.5793 q^{76}\) \(-6.29138 q^{77}\) \(+5.48435 q^{78}\) \(-6.88388 q^{79}\) \(+0.285152 q^{80}\) \(-9.31216 q^{81}\) \(+24.6532 q^{82}\) \(-2.36869 q^{83}\) \(+33.2609 q^{84}\) \(-1.57086 q^{85}\) \(+15.4614 q^{86}\) \(-4.61369 q^{87}\) \(+3.55863 q^{88}\) \(-3.70599 q^{89}\) \(+3.27121 q^{90}\) \(-4.41326 q^{91}\) \(-25.6628 q^{92}\) \(+12.7668 q^{93}\) \(+9.92924 q^{94}\) \(+3.64065 q^{95}\) \(+15.2427 q^{96}\) \(-15.1692 q^{97}\) \(-28.1901 q^{98}\) \(-4.12282 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.25939 −1.59763 −0.798816 0.601576i \(-0.794540\pi\)
−0.798816 + 0.601576i \(0.794540\pi\)
\(3\) 2.42736 1.40144 0.700718 0.713439i \(-0.252863\pi\)
0.700718 + 0.713439i \(0.252863\pi\)
\(4\) 3.10485 1.55243
\(5\) −0.500622 −0.223885 −0.111942 0.993715i \(-0.535707\pi\)
−0.111942 + 0.993715i \(0.535707\pi\)
\(6\) −5.48435 −2.23898
\(7\) 4.41326 1.66806 0.834028 0.551723i \(-0.186029\pi\)
0.834028 + 0.551723i \(0.186029\pi\)
\(8\) −2.49629 −0.882574
\(9\) 2.89206 0.964021
\(10\) 1.13110 0.357686
\(11\) −1.42556 −0.429823 −0.214912 0.976633i \(-0.568946\pi\)
−0.214912 + 0.976633i \(0.568946\pi\)
\(12\) 7.53659 2.17562
\(13\) −1.00000 −0.277350
\(14\) −9.97128 −2.66494
\(15\) −1.21519 −0.313760
\(16\) −0.569596 −0.142399
\(17\) 3.13782 0.761033 0.380517 0.924774i \(-0.375746\pi\)
0.380517 + 0.924774i \(0.375746\pi\)
\(18\) −6.53430 −1.54015
\(19\) −7.27226 −1.66837 −0.834186 0.551484i \(-0.814062\pi\)
−0.834186 + 0.551484i \(0.814062\pi\)
\(20\) −1.55436 −0.347565
\(21\) 10.7126 2.33767
\(22\) 3.22091 0.686700
\(23\) −8.26540 −1.72345 −0.861727 0.507372i \(-0.830617\pi\)
−0.861727 + 0.507372i \(0.830617\pi\)
\(24\) −6.05940 −1.23687
\(25\) −4.74938 −0.949876
\(26\) 2.25939 0.443103
\(27\) −0.262003 −0.0504225
\(28\) 13.7025 2.58953
\(29\) −1.90070 −0.352952 −0.176476 0.984305i \(-0.556470\pi\)
−0.176476 + 0.984305i \(0.556470\pi\)
\(30\) 2.74559 0.501273
\(31\) 5.25956 0.944645 0.472322 0.881426i \(-0.343416\pi\)
0.472322 + 0.881426i \(0.343416\pi\)
\(32\) 6.27953 1.11007
\(33\) −3.46035 −0.602370
\(34\) −7.08957 −1.21585
\(35\) −2.20937 −0.373452
\(36\) 8.97943 1.49657
\(37\) 6.75569 1.11063 0.555315 0.831640i \(-0.312598\pi\)
0.555315 + 0.831640i \(0.312598\pi\)
\(38\) 16.4309 2.66544
\(39\) −2.42736 −0.388688
\(40\) 1.24970 0.197595
\(41\) −10.9114 −1.70408 −0.852041 0.523475i \(-0.824635\pi\)
−0.852041 + 0.523475i \(0.824635\pi\)
\(42\) −24.2039 −3.73474
\(43\) −6.84316 −1.04357 −0.521786 0.853076i \(-0.674734\pi\)
−0.521786 + 0.853076i \(0.674734\pi\)
\(44\) −4.42616 −0.667269
\(45\) −1.44783 −0.215830
\(46\) 18.6748 2.75345
\(47\) −4.39465 −0.641026 −0.320513 0.947244i \(-0.603855\pi\)
−0.320513 + 0.947244i \(0.603855\pi\)
\(48\) −1.38261 −0.199563
\(49\) 12.4769 1.78241
\(50\) 10.7307 1.51755
\(51\) 7.61661 1.06654
\(52\) −3.10485 −0.430566
\(53\) 3.05136 0.419136 0.209568 0.977794i \(-0.432794\pi\)
0.209568 + 0.977794i \(0.432794\pi\)
\(54\) 0.591968 0.0805566
\(55\) 0.713668 0.0962310
\(56\) −11.0168 −1.47218
\(57\) −17.6524 −2.33811
\(58\) 4.29444 0.563887
\(59\) −11.4178 −1.48647 −0.743237 0.669028i \(-0.766710\pi\)
−0.743237 + 0.669028i \(0.766710\pi\)
\(60\) −3.77298 −0.487090
\(61\) 12.7964 1.63841 0.819205 0.573501i \(-0.194415\pi\)
0.819205 + 0.573501i \(0.194415\pi\)
\(62\) −11.8834 −1.50919
\(63\) 12.7634 1.60804
\(64\) −13.0487 −1.63109
\(65\) 0.500622 0.0620945
\(66\) 7.81829 0.962365
\(67\) 1.26329 0.154336 0.0771679 0.997018i \(-0.475412\pi\)
0.0771679 + 0.997018i \(0.475412\pi\)
\(68\) 9.74247 1.18145
\(69\) −20.0631 −2.41531
\(70\) 4.99184 0.596639
\(71\) −9.87557 −1.17201 −0.586007 0.810306i \(-0.699301\pi\)
−0.586007 + 0.810306i \(0.699301\pi\)
\(72\) −7.21944 −0.850819
\(73\) −7.90176 −0.924831 −0.462416 0.886663i \(-0.653017\pi\)
−0.462416 + 0.886663i \(0.653017\pi\)
\(74\) −15.2638 −1.77438
\(75\) −11.5284 −1.33119
\(76\) −22.5793 −2.59002
\(77\) −6.29138 −0.716969
\(78\) 5.48435 0.620981
\(79\) −6.88388 −0.774497 −0.387249 0.921975i \(-0.626574\pi\)
−0.387249 + 0.921975i \(0.626574\pi\)
\(80\) 0.285152 0.0318810
\(81\) −9.31216 −1.03468
\(82\) 24.6532 2.72250
\(83\) −2.36869 −0.259997 −0.129999 0.991514i \(-0.541497\pi\)
−0.129999 + 0.991514i \(0.541497\pi\)
\(84\) 33.2609 3.62906
\(85\) −1.57086 −0.170384
\(86\) 15.4614 1.66724
\(87\) −4.61369 −0.494639
\(88\) 3.55863 0.379351
\(89\) −3.70599 −0.392834 −0.196417 0.980520i \(-0.562931\pi\)
−0.196417 + 0.980520i \(0.562931\pi\)
\(90\) 3.27121 0.344816
\(91\) −4.41326 −0.462635
\(92\) −25.6628 −2.67554
\(93\) 12.7668 1.32386
\(94\) 9.92924 1.02412
\(95\) 3.64065 0.373523
\(96\) 15.2427 1.55570
\(97\) −15.1692 −1.54020 −0.770100 0.637923i \(-0.779794\pi\)
−0.770100 + 0.637923i \(0.779794\pi\)
\(98\) −28.1901 −2.84763
\(99\) −4.12282 −0.414359
\(100\) −14.7461 −1.47461
\(101\) 8.31300 0.827175 0.413587 0.910464i \(-0.364276\pi\)
0.413587 + 0.910464i \(0.364276\pi\)
\(102\) −17.2089 −1.70394
\(103\) 17.1535 1.69019 0.845095 0.534617i \(-0.179544\pi\)
0.845095 + 0.534617i \(0.179544\pi\)
\(104\) 2.49629 0.244782
\(105\) −5.36294 −0.523369
\(106\) −6.89422 −0.669625
\(107\) −17.1940 −1.66221 −0.831105 0.556116i \(-0.812291\pi\)
−0.831105 + 0.556116i \(0.812291\pi\)
\(108\) −0.813481 −0.0782773
\(109\) −17.0135 −1.62959 −0.814797 0.579746i \(-0.803152\pi\)
−0.814797 + 0.579746i \(0.803152\pi\)
\(110\) −1.61246 −0.153742
\(111\) 16.3985 1.55647
\(112\) −2.51378 −0.237529
\(113\) 4.53839 0.426936 0.213468 0.976950i \(-0.431524\pi\)
0.213468 + 0.976950i \(0.431524\pi\)
\(114\) 39.8836 3.73545
\(115\) 4.13784 0.385855
\(116\) −5.90141 −0.547932
\(117\) −2.89206 −0.267371
\(118\) 25.7973 2.37484
\(119\) 13.8480 1.26945
\(120\) 3.03347 0.276916
\(121\) −8.96777 −0.815252
\(122\) −28.9121 −2.61757
\(123\) −26.4860 −2.38816
\(124\) 16.3302 1.46649
\(125\) 4.88075 0.436548
\(126\) −28.8376 −2.56905
\(127\) 11.3985 1.01145 0.505726 0.862694i \(-0.331225\pi\)
0.505726 + 0.862694i \(0.331225\pi\)
\(128\) 16.9231 1.49581
\(129\) −16.6108 −1.46250
\(130\) −1.13110 −0.0992041
\(131\) 8.05120 0.703437 0.351719 0.936106i \(-0.385597\pi\)
0.351719 + 0.936106i \(0.385597\pi\)
\(132\) −10.7439 −0.935135
\(133\) −32.0944 −2.78294
\(134\) −2.85428 −0.246572
\(135\) 0.131165 0.0112888
\(136\) −7.83293 −0.671668
\(137\) −10.4214 −0.890361 −0.445181 0.895441i \(-0.646861\pi\)
−0.445181 + 0.895441i \(0.646861\pi\)
\(138\) 45.3303 3.85877
\(139\) −8.35576 −0.708727 −0.354363 0.935108i \(-0.615302\pi\)
−0.354363 + 0.935108i \(0.615302\pi\)
\(140\) −6.85978 −0.579757
\(141\) −10.6674 −0.898356
\(142\) 22.3128 1.87245
\(143\) 1.42556 0.119212
\(144\) −1.64731 −0.137276
\(145\) 0.951534 0.0790206
\(146\) 17.8532 1.47754
\(147\) 30.2858 2.49793
\(148\) 20.9754 1.72417
\(149\) 3.81003 0.312130 0.156065 0.987747i \(-0.450119\pi\)
0.156065 + 0.987747i \(0.450119\pi\)
\(150\) 26.0473 2.12675
\(151\) 14.3357 1.16663 0.583313 0.812247i \(-0.301756\pi\)
0.583313 + 0.812247i \(0.301756\pi\)
\(152\) 18.1537 1.47246
\(153\) 9.07477 0.733652
\(154\) 14.2147 1.14545
\(155\) −2.63305 −0.211492
\(156\) −7.53659 −0.603410
\(157\) 2.13284 0.170219 0.0851094 0.996372i \(-0.472876\pi\)
0.0851094 + 0.996372i \(0.472876\pi\)
\(158\) 15.5534 1.23736
\(159\) 7.40674 0.587393
\(160\) −3.14367 −0.248529
\(161\) −36.4773 −2.87482
\(162\) 21.0398 1.65304
\(163\) −0.398816 −0.0312377 −0.0156188 0.999878i \(-0.504972\pi\)
−0.0156188 + 0.999878i \(0.504972\pi\)
\(164\) −33.8784 −2.64546
\(165\) 1.73233 0.134861
\(166\) 5.35180 0.415380
\(167\) −2.36092 −0.182693 −0.0913467 0.995819i \(-0.529117\pi\)
−0.0913467 + 0.995819i \(0.529117\pi\)
\(168\) −26.7417 −2.06317
\(169\) 1.00000 0.0769231
\(170\) 3.54919 0.272211
\(171\) −21.0318 −1.60834
\(172\) −21.2470 −1.62007
\(173\) −0.260989 −0.0198426 −0.00992132 0.999951i \(-0.503158\pi\)
−0.00992132 + 0.999951i \(0.503158\pi\)
\(174\) 10.4241 0.790251
\(175\) −20.9602 −1.58444
\(176\) 0.811995 0.0612064
\(177\) −27.7151 −2.08320
\(178\) 8.37329 0.627604
\(179\) 22.3568 1.67102 0.835512 0.549473i \(-0.185171\pi\)
0.835512 + 0.549473i \(0.185171\pi\)
\(180\) −4.49530 −0.335060
\(181\) 13.5208 1.00499 0.502496 0.864580i \(-0.332415\pi\)
0.502496 + 0.864580i \(0.332415\pi\)
\(182\) 9.97128 0.739121
\(183\) 31.0614 2.29613
\(184\) 20.6329 1.52108
\(185\) −3.38205 −0.248653
\(186\) −28.8453 −2.11504
\(187\) −4.47316 −0.327110
\(188\) −13.6447 −0.995146
\(189\) −1.15629 −0.0841076
\(190\) −8.22566 −0.596752
\(191\) 9.04166 0.654231 0.327116 0.944984i \(-0.393923\pi\)
0.327116 + 0.944984i \(0.393923\pi\)
\(192\) −31.6739 −2.28587
\(193\) −5.67409 −0.408430 −0.204215 0.978926i \(-0.565464\pi\)
−0.204215 + 0.978926i \(0.565464\pi\)
\(194\) 34.2732 2.46067
\(195\) 1.21519 0.0870214
\(196\) 38.7388 2.76706
\(197\) −3.63596 −0.259051 −0.129526 0.991576i \(-0.541345\pi\)
−0.129526 + 0.991576i \(0.541345\pi\)
\(198\) 9.31506 0.661993
\(199\) −8.68652 −0.615771 −0.307886 0.951423i \(-0.599621\pi\)
−0.307886 + 0.951423i \(0.599621\pi\)
\(200\) 11.8558 0.838335
\(201\) 3.06646 0.216292
\(202\) −18.7823 −1.32152
\(203\) −8.38830 −0.588743
\(204\) 23.6485 1.65572
\(205\) 5.46251 0.381518
\(206\) −38.7566 −2.70030
\(207\) −23.9040 −1.66145
\(208\) 0.569596 0.0394944
\(209\) 10.3671 0.717105
\(210\) 12.1170 0.836151
\(211\) 13.1202 0.903230 0.451615 0.892213i \(-0.350848\pi\)
0.451615 + 0.892213i \(0.350848\pi\)
\(212\) 9.47402 0.650678
\(213\) −23.9715 −1.64250
\(214\) 38.8481 2.65560
\(215\) 3.42583 0.233640
\(216\) 0.654037 0.0445016
\(217\) 23.2118 1.57572
\(218\) 38.4401 2.60349
\(219\) −19.1804 −1.29609
\(220\) 2.21583 0.149392
\(221\) −3.13782 −0.211073
\(222\) −37.0506 −2.48667
\(223\) 7.26442 0.486461 0.243231 0.969968i \(-0.421793\pi\)
0.243231 + 0.969968i \(0.421793\pi\)
\(224\) 27.7132 1.85167
\(225\) −13.7355 −0.915700
\(226\) −10.2540 −0.682086
\(227\) −17.1791 −1.14022 −0.570108 0.821570i \(-0.693098\pi\)
−0.570108 + 0.821570i \(0.693098\pi\)
\(228\) −54.8080 −3.62975
\(229\) 13.1285 0.867553 0.433776 0.901021i \(-0.357181\pi\)
0.433776 + 0.901021i \(0.357181\pi\)
\(230\) −9.34900 −0.616455
\(231\) −15.2714 −1.00479
\(232\) 4.74472 0.311506
\(233\) 8.50600 0.557247 0.278623 0.960400i \(-0.410122\pi\)
0.278623 + 0.960400i \(0.410122\pi\)
\(234\) 6.53430 0.427161
\(235\) 2.20006 0.143516
\(236\) −35.4506 −2.30764
\(237\) −16.7096 −1.08541
\(238\) −31.2881 −2.02811
\(239\) −16.1972 −1.04771 −0.523854 0.851808i \(-0.675506\pi\)
−0.523854 + 0.851808i \(0.675506\pi\)
\(240\) 0.692166 0.0446791
\(241\) −12.8332 −0.826657 −0.413328 0.910582i \(-0.635634\pi\)
−0.413328 + 0.910582i \(0.635634\pi\)
\(242\) 20.2617 1.30247
\(243\) −21.8179 −1.39962
\(244\) 39.7309 2.54351
\(245\) −6.24619 −0.399054
\(246\) 59.8422 3.81540
\(247\) 7.27226 0.462723
\(248\) −13.1294 −0.833719
\(249\) −5.74965 −0.364370
\(250\) −11.0275 −0.697442
\(251\) −0.126202 −0.00796582 −0.00398291 0.999992i \(-0.501268\pi\)
−0.00398291 + 0.999992i \(0.501268\pi\)
\(252\) 39.6285 2.49636
\(253\) 11.7828 0.740781
\(254\) −25.7536 −1.61593
\(255\) −3.81304 −0.238782
\(256\) −12.1385 −0.758659
\(257\) 8.29401 0.517366 0.258683 0.965962i \(-0.416711\pi\)
0.258683 + 0.965962i \(0.416711\pi\)
\(258\) 37.5303 2.33653
\(259\) 29.8146 1.85259
\(260\) 1.55436 0.0963971
\(261\) −5.49696 −0.340253
\(262\) −18.1908 −1.12383
\(263\) 16.7730 1.03427 0.517133 0.855905i \(-0.326999\pi\)
0.517133 + 0.855905i \(0.326999\pi\)
\(264\) 8.63806 0.531636
\(265\) −1.52758 −0.0938383
\(266\) 72.5138 4.44611
\(267\) −8.99576 −0.550532
\(268\) 3.92234 0.239595
\(269\) −20.5132 −1.25071 −0.625355 0.780341i \(-0.715046\pi\)
−0.625355 + 0.780341i \(0.715046\pi\)
\(270\) −0.296352 −0.0180354
\(271\) 24.7716 1.50477 0.752385 0.658723i \(-0.228903\pi\)
0.752385 + 0.658723i \(0.228903\pi\)
\(272\) −1.78729 −0.108370
\(273\) −10.7126 −0.648353
\(274\) 23.5461 1.42247
\(275\) 6.77054 0.408279
\(276\) −62.2929 −3.74959
\(277\) 18.8033 1.12978 0.564890 0.825166i \(-0.308918\pi\)
0.564890 + 0.825166i \(0.308918\pi\)
\(278\) 18.8789 1.13228
\(279\) 15.2110 0.910657
\(280\) 5.51525 0.329599
\(281\) 29.7889 1.77705 0.888527 0.458824i \(-0.151729\pi\)
0.888527 + 0.458824i \(0.151729\pi\)
\(282\) 24.1018 1.43524
\(283\) 19.0897 1.13476 0.567381 0.823455i \(-0.307957\pi\)
0.567381 + 0.823455i \(0.307957\pi\)
\(284\) −30.6622 −1.81947
\(285\) 8.83717 0.523469
\(286\) −3.22091 −0.190456
\(287\) −48.1551 −2.84250
\(288\) 18.1608 1.07014
\(289\) −7.15408 −0.420828
\(290\) −2.14989 −0.126246
\(291\) −36.8211 −2.15849
\(292\) −24.5338 −1.43573
\(293\) −20.1293 −1.17597 −0.587983 0.808873i \(-0.700078\pi\)
−0.587983 + 0.808873i \(0.700078\pi\)
\(294\) −68.4275 −3.99077
\(295\) 5.71601 0.332799
\(296\) −16.8642 −0.980212
\(297\) 0.373502 0.0216728
\(298\) −8.60836 −0.498669
\(299\) 8.26540 0.478000
\(300\) −35.7941 −2.06657
\(301\) −30.2006 −1.74074
\(302\) −32.3901 −1.86384
\(303\) 20.1786 1.15923
\(304\) 4.14225 0.237574
\(305\) −6.40615 −0.366815
\(306\) −20.5035 −1.17211
\(307\) −21.2467 −1.21261 −0.606307 0.795231i \(-0.707350\pi\)
−0.606307 + 0.795231i \(0.707350\pi\)
\(308\) −19.5338 −1.11304
\(309\) 41.6378 2.36869
\(310\) 5.94909 0.337886
\(311\) −10.1016 −0.572808 −0.286404 0.958109i \(-0.592460\pi\)
−0.286404 + 0.958109i \(0.592460\pi\)
\(312\) 6.05940 0.343046
\(313\) −21.9204 −1.23901 −0.619507 0.784991i \(-0.712667\pi\)
−0.619507 + 0.784991i \(0.712667\pi\)
\(314\) −4.81891 −0.271947
\(315\) −6.38965 −0.360016
\(316\) −21.3734 −1.20235
\(317\) −24.1933 −1.35883 −0.679416 0.733753i \(-0.737767\pi\)
−0.679416 + 0.733753i \(0.737767\pi\)
\(318\) −16.7347 −0.938437
\(319\) 2.70957 0.151707
\(320\) 6.53248 0.365177
\(321\) −41.7361 −2.32948
\(322\) 82.4166 4.59290
\(323\) −22.8191 −1.26969
\(324\) −28.9129 −1.60627
\(325\) 4.74938 0.263448
\(326\) 0.901081 0.0499063
\(327\) −41.2978 −2.28377
\(328\) 27.2382 1.50398
\(329\) −19.3947 −1.06927
\(330\) −3.91401 −0.215459
\(331\) 9.01493 0.495505 0.247753 0.968823i \(-0.420308\pi\)
0.247753 + 0.968823i \(0.420308\pi\)
\(332\) −7.35443 −0.403627
\(333\) 19.5379 1.07067
\(334\) 5.33424 0.291877
\(335\) −0.632432 −0.0345535
\(336\) −6.10183 −0.332882
\(337\) −21.9916 −1.19796 −0.598980 0.800764i \(-0.704427\pi\)
−0.598980 + 0.800764i \(0.704427\pi\)
\(338\) −2.25939 −0.122895
\(339\) 11.0163 0.598323
\(340\) −4.87729 −0.264508
\(341\) −7.49784 −0.406031
\(342\) 47.5192 2.56954
\(343\) 24.1708 1.30510
\(344\) 17.0825 0.921029
\(345\) 10.0440 0.540751
\(346\) 0.589677 0.0317012
\(347\) −13.8394 −0.742939 −0.371469 0.928445i \(-0.621146\pi\)
−0.371469 + 0.928445i \(0.621146\pi\)
\(348\) −14.3248 −0.767891
\(349\) 3.59936 0.192669 0.0963347 0.995349i \(-0.469288\pi\)
0.0963347 + 0.995349i \(0.469288\pi\)
\(350\) 47.3574 2.53136
\(351\) 0.262003 0.0139847
\(352\) −8.95187 −0.477136
\(353\) −3.85925 −0.205407 −0.102704 0.994712i \(-0.532749\pi\)
−0.102704 + 0.994712i \(0.532749\pi\)
\(354\) 62.6193 3.32818
\(355\) 4.94393 0.262396
\(356\) −11.5066 −0.609846
\(357\) 33.6141 1.77905
\(358\) −50.5127 −2.66968
\(359\) 8.30954 0.438561 0.219280 0.975662i \(-0.429629\pi\)
0.219280 + 0.975662i \(0.429629\pi\)
\(360\) 3.61421 0.190486
\(361\) 33.8858 1.78346
\(362\) −30.5488 −1.60561
\(363\) −21.7680 −1.14252
\(364\) −13.7025 −0.718207
\(365\) 3.95580 0.207056
\(366\) −70.1799 −3.66836
\(367\) 18.5090 0.966162 0.483081 0.875576i \(-0.339518\pi\)
0.483081 + 0.875576i \(0.339518\pi\)
\(368\) 4.70794 0.245418
\(369\) −31.5566 −1.64277
\(370\) 7.64137 0.397256
\(371\) 13.4664 0.699143
\(372\) 39.6391 2.05519
\(373\) −8.31567 −0.430569 −0.215284 0.976551i \(-0.569068\pi\)
−0.215284 + 0.976551i \(0.569068\pi\)
\(374\) 10.1066 0.522601
\(375\) 11.8473 0.611793
\(376\) 10.9703 0.565753
\(377\) 1.90070 0.0978913
\(378\) 2.61251 0.134373
\(379\) 25.1001 1.28930 0.644652 0.764476i \(-0.277002\pi\)
0.644652 + 0.764476i \(0.277002\pi\)
\(380\) 11.3037 0.579867
\(381\) 27.6682 1.41748
\(382\) −20.4286 −1.04522
\(383\) 19.9566 1.01973 0.509867 0.860253i \(-0.329694\pi\)
0.509867 + 0.860253i \(0.329694\pi\)
\(384\) 41.0785 2.09628
\(385\) 3.14960 0.160519
\(386\) 12.8200 0.652521
\(387\) −19.7908 −1.00603
\(388\) −47.0982 −2.39105
\(389\) −2.93457 −0.148788 −0.0743942 0.997229i \(-0.523702\pi\)
−0.0743942 + 0.997229i \(0.523702\pi\)
\(390\) −2.74559 −0.139028
\(391\) −25.9353 −1.31161
\(392\) −31.1459 −1.57311
\(393\) 19.5431 0.985821
\(394\) 8.21505 0.413868
\(395\) 3.44622 0.173398
\(396\) −12.8007 −0.643261
\(397\) 9.31463 0.467488 0.233744 0.972298i \(-0.424902\pi\)
0.233744 + 0.972298i \(0.424902\pi\)
\(398\) 19.6263 0.983776
\(399\) −77.9045 −3.90010
\(400\) 2.70523 0.135261
\(401\) 3.11165 0.155389 0.0776943 0.996977i \(-0.475244\pi\)
0.0776943 + 0.996977i \(0.475244\pi\)
\(402\) −6.92835 −0.345554
\(403\) −5.25956 −0.261997
\(404\) 25.8106 1.28413
\(405\) 4.66187 0.231650
\(406\) 18.9525 0.940595
\(407\) −9.63067 −0.477374
\(408\) −19.0133 −0.941299
\(409\) 3.93964 0.194802 0.0974012 0.995245i \(-0.468947\pi\)
0.0974012 + 0.995245i \(0.468947\pi\)
\(410\) −12.3420 −0.609526
\(411\) −25.2965 −1.24778
\(412\) 53.2592 2.62389
\(413\) −50.3898 −2.47952
\(414\) 54.0086 2.65438
\(415\) 1.18582 0.0582095
\(416\) −6.27953 −0.307879
\(417\) −20.2824 −0.993234
\(418\) −23.4233 −1.14567
\(419\) 13.7535 0.671905 0.335952 0.941879i \(-0.390942\pi\)
0.335952 + 0.941879i \(0.390942\pi\)
\(420\) −16.6511 −0.812492
\(421\) 28.7304 1.40024 0.700118 0.714028i \(-0.253131\pi\)
0.700118 + 0.714028i \(0.253131\pi\)
\(422\) −29.6436 −1.44303
\(423\) −12.7096 −0.617962
\(424\) −7.61709 −0.369919
\(425\) −14.9027 −0.722887
\(426\) 54.1611 2.62411
\(427\) 56.4738 2.73296
\(428\) −53.3849 −2.58046
\(429\) 3.46035 0.167067
\(430\) −7.74030 −0.373271
\(431\) −4.37709 −0.210837 −0.105419 0.994428i \(-0.533618\pi\)
−0.105419 + 0.994428i \(0.533618\pi\)
\(432\) 0.149236 0.00718012
\(433\) 29.8842 1.43614 0.718071 0.695970i \(-0.245025\pi\)
0.718071 + 0.695970i \(0.245025\pi\)
\(434\) −52.4446 −2.51742
\(435\) 2.30971 0.110742
\(436\) −52.8243 −2.52983
\(437\) 60.1081 2.87536
\(438\) 43.3360 2.07068
\(439\) 15.6911 0.748896 0.374448 0.927248i \(-0.377832\pi\)
0.374448 + 0.927248i \(0.377832\pi\)
\(440\) −1.78153 −0.0849309
\(441\) 36.0838 1.71828
\(442\) 7.08957 0.337216
\(443\) −22.0329 −1.04682 −0.523408 0.852082i \(-0.675340\pi\)
−0.523408 + 0.852082i \(0.675340\pi\)
\(444\) 50.9149 2.41631
\(445\) 1.85530 0.0879497
\(446\) −16.4132 −0.777186
\(447\) 9.24831 0.437430
\(448\) −57.5874 −2.72075
\(449\) 12.5016 0.589985 0.294992 0.955500i \(-0.404683\pi\)
0.294992 + 0.955500i \(0.404683\pi\)
\(450\) 31.0339 1.46295
\(451\) 15.5550 0.732455
\(452\) 14.0910 0.662787
\(453\) 34.7980 1.63495
\(454\) 38.8143 1.82164
\(455\) 2.20937 0.103577
\(456\) 44.0655 2.06356
\(457\) 31.6221 1.47922 0.739611 0.673035i \(-0.235010\pi\)
0.739611 + 0.673035i \(0.235010\pi\)
\(458\) −29.6623 −1.38603
\(459\) −0.822119 −0.0383732
\(460\) 12.8474 0.599012
\(461\) 15.7316 0.732695 0.366348 0.930478i \(-0.380608\pi\)
0.366348 + 0.930478i \(0.380608\pi\)
\(462\) 34.5041 1.60528
\(463\) −1.00000 −0.0464739
\(464\) 1.08263 0.0502600
\(465\) −6.39135 −0.296392
\(466\) −19.2184 −0.890275
\(467\) 35.0632 1.62253 0.811265 0.584679i \(-0.198779\pi\)
0.811265 + 0.584679i \(0.198779\pi\)
\(468\) −8.97943 −0.415074
\(469\) 5.57524 0.257441
\(470\) −4.97080 −0.229286
\(471\) 5.17716 0.238551
\(472\) 28.5022 1.31192
\(473\) 9.75536 0.448552
\(474\) 37.7536 1.73408
\(475\) 34.5387 1.58475
\(476\) 42.9960 1.97072
\(477\) 8.82472 0.404056
\(478\) 36.5957 1.67385
\(479\) 12.9719 0.592701 0.296350 0.955079i \(-0.404230\pi\)
0.296350 + 0.955079i \(0.404230\pi\)
\(480\) −7.63081 −0.348297
\(481\) −6.75569 −0.308033
\(482\) 28.9952 1.32069
\(483\) −88.5435 −4.02887
\(484\) −27.8436 −1.26562
\(485\) 7.59404 0.344828
\(486\) 49.2953 2.23608
\(487\) 15.8936 0.720207 0.360103 0.932912i \(-0.382741\pi\)
0.360103 + 0.932912i \(0.382741\pi\)
\(488\) −31.9436 −1.44602
\(489\) −0.968068 −0.0437776
\(490\) 14.1126 0.637542
\(491\) −2.49045 −0.112392 −0.0561962 0.998420i \(-0.517897\pi\)
−0.0561962 + 0.998420i \(0.517897\pi\)
\(492\) −82.2351 −3.70744
\(493\) −5.96407 −0.268608
\(494\) −16.4309 −0.739261
\(495\) 2.06397 0.0927687
\(496\) −2.99583 −0.134517
\(497\) −43.5834 −1.95498
\(498\) 12.9907 0.582128
\(499\) −14.9183 −0.667837 −0.333918 0.942602i \(-0.608371\pi\)
−0.333918 + 0.942602i \(0.608371\pi\)
\(500\) 15.1540 0.677708
\(501\) −5.73079 −0.256033
\(502\) 0.285141 0.0127265
\(503\) 4.68926 0.209084 0.104542 0.994520i \(-0.466662\pi\)
0.104542 + 0.994520i \(0.466662\pi\)
\(504\) −31.8613 −1.41921
\(505\) −4.16167 −0.185192
\(506\) −26.6221 −1.18350
\(507\) 2.42736 0.107803
\(508\) 35.3906 1.57020
\(509\) −1.28176 −0.0568131 −0.0284065 0.999596i \(-0.509043\pi\)
−0.0284065 + 0.999596i \(0.509043\pi\)
\(510\) 8.61516 0.381486
\(511\) −34.8725 −1.54267
\(512\) −6.42056 −0.283751
\(513\) 1.90536 0.0841235
\(514\) −18.7394 −0.826560
\(515\) −8.58744 −0.378408
\(516\) −51.5741 −2.27042
\(517\) 6.26486 0.275528
\(518\) −67.3629 −2.95976
\(519\) −0.633514 −0.0278082
\(520\) −1.24970 −0.0548030
\(521\) 9.27993 0.406561 0.203281 0.979121i \(-0.434840\pi\)
0.203281 + 0.979121i \(0.434840\pi\)
\(522\) 12.4198 0.543599
\(523\) 42.2067 1.84557 0.922786 0.385313i \(-0.125907\pi\)
0.922786 + 0.385313i \(0.125907\pi\)
\(524\) 24.9978 1.09203
\(525\) −50.8780 −2.22050
\(526\) −37.8967 −1.65237
\(527\) 16.5036 0.718906
\(528\) 1.97100 0.0857769
\(529\) 45.3168 1.97030
\(530\) 3.45140 0.149919
\(531\) −33.0210 −1.43299
\(532\) −99.6483 −4.32030
\(533\) 10.9114 0.472627
\(534\) 20.3250 0.879547
\(535\) 8.60771 0.372144
\(536\) −3.15355 −0.136213
\(537\) 54.2679 2.34183
\(538\) 46.3473 1.99817
\(539\) −17.7865 −0.766121
\(540\) 0.407247 0.0175251
\(541\) −42.4956 −1.82703 −0.913514 0.406807i \(-0.866642\pi\)
−0.913514 + 0.406807i \(0.866642\pi\)
\(542\) −55.9689 −2.40407
\(543\) 32.8198 1.40843
\(544\) 19.7040 0.844804
\(545\) 8.51731 0.364842
\(546\) 24.2039 1.03583
\(547\) 23.0202 0.984273 0.492136 0.870518i \(-0.336216\pi\)
0.492136 + 0.870518i \(0.336216\pi\)
\(548\) −32.3569 −1.38222
\(549\) 37.0080 1.57946
\(550\) −15.2973 −0.652279
\(551\) 13.8224 0.588855
\(552\) 50.0833 2.13169
\(553\) −30.3804 −1.29190
\(554\) −42.4840 −1.80497
\(555\) −8.20944 −0.348471
\(556\) −25.9434 −1.10025
\(557\) −33.1487 −1.40456 −0.702279 0.711902i \(-0.747834\pi\)
−0.702279 + 0.711902i \(0.747834\pi\)
\(558\) −34.3676 −1.45489
\(559\) 6.84316 0.289435
\(560\) 1.25845 0.0531793
\(561\) −10.8580 −0.458423
\(562\) −67.3047 −2.83908
\(563\) −32.9532 −1.38881 −0.694406 0.719583i \(-0.744333\pi\)
−0.694406 + 0.719583i \(0.744333\pi\)
\(564\) −33.1207 −1.39463
\(565\) −2.27202 −0.0955845
\(566\) −43.1310 −1.81293
\(567\) −41.0970 −1.72591
\(568\) 24.6523 1.03439
\(569\) −3.53665 −0.148264 −0.0741320 0.997248i \(-0.523619\pi\)
−0.0741320 + 0.997248i \(0.523619\pi\)
\(570\) −19.9666 −0.836310
\(571\) −9.42884 −0.394585 −0.197292 0.980345i \(-0.563215\pi\)
−0.197292 + 0.980345i \(0.563215\pi\)
\(572\) 4.42616 0.185067
\(573\) 21.9473 0.916863
\(574\) 108.801 4.54127
\(575\) 39.2555 1.63707
\(576\) −37.7377 −1.57241
\(577\) −44.3051 −1.84445 −0.922223 0.386659i \(-0.873629\pi\)
−0.922223 + 0.386659i \(0.873629\pi\)
\(578\) 16.1639 0.672329
\(579\) −13.7730 −0.572388
\(580\) 2.95437 0.122674
\(581\) −10.4536 −0.433690
\(582\) 83.1933 3.44847
\(583\) −4.34991 −0.180155
\(584\) 19.7251 0.816232
\(585\) 1.44783 0.0598604
\(586\) 45.4800 1.87876
\(587\) −4.45810 −0.184006 −0.0920028 0.995759i \(-0.529327\pi\)
−0.0920028 + 0.995759i \(0.529327\pi\)
\(588\) 94.0329 3.87785
\(589\) −38.2489 −1.57602
\(590\) −12.9147 −0.531690
\(591\) −8.82577 −0.363044
\(592\) −3.84802 −0.158152
\(593\) −34.5096 −1.41714 −0.708571 0.705640i \(-0.750660\pi\)
−0.708571 + 0.705640i \(0.750660\pi\)
\(594\) −0.843888 −0.0346251
\(595\) −6.93262 −0.284210
\(596\) 11.8296 0.484559
\(597\) −21.0853 −0.862964
\(598\) −18.6748 −0.763668
\(599\) −41.1084 −1.67965 −0.839823 0.542861i \(-0.817341\pi\)
−0.839823 + 0.542861i \(0.817341\pi\)
\(600\) 28.7784 1.17487
\(601\) −12.3698 −0.504573 −0.252286 0.967653i \(-0.581182\pi\)
−0.252286 + 0.967653i \(0.581182\pi\)
\(602\) 68.2351 2.78105
\(603\) 3.65352 0.148783
\(604\) 44.5104 1.81110
\(605\) 4.48946 0.182523
\(606\) −45.5914 −1.85203
\(607\) −17.4467 −0.708139 −0.354070 0.935219i \(-0.615202\pi\)
−0.354070 + 0.935219i \(0.615202\pi\)
\(608\) −45.6664 −1.85202
\(609\) −20.3614 −0.825086
\(610\) 14.4740 0.586035
\(611\) 4.39465 0.177789
\(612\) 28.1758 1.13894
\(613\) −21.9841 −0.887931 −0.443966 0.896044i \(-0.646429\pi\)
−0.443966 + 0.896044i \(0.646429\pi\)
\(614\) 48.0046 1.93731
\(615\) 13.2595 0.534673
\(616\) 15.7051 0.632778
\(617\) −17.1761 −0.691485 −0.345743 0.938329i \(-0.612373\pi\)
−0.345743 + 0.938329i \(0.612373\pi\)
\(618\) −94.0761 −3.78430
\(619\) 12.1978 0.490273 0.245136 0.969489i \(-0.421167\pi\)
0.245136 + 0.969489i \(0.421167\pi\)
\(620\) −8.17523 −0.328325
\(621\) 2.16556 0.0869010
\(622\) 22.8234 0.915136
\(623\) −16.3555 −0.655269
\(624\) 1.38261 0.0553488
\(625\) 21.3035 0.852139
\(626\) 49.5267 1.97949
\(627\) 25.1646 1.00498
\(628\) 6.62214 0.264252
\(629\) 21.1981 0.845226
\(630\) 14.4367 0.575173
\(631\) 24.4143 0.971918 0.485959 0.873982i \(-0.338470\pi\)
0.485959 + 0.873982i \(0.338470\pi\)
\(632\) 17.1842 0.683551
\(633\) 31.8473 1.26582
\(634\) 54.6622 2.17091
\(635\) −5.70633 −0.226449
\(636\) 22.9968 0.911884
\(637\) −12.4769 −0.494351
\(638\) −6.12199 −0.242372
\(639\) −28.5608 −1.12985
\(640\) −8.47209 −0.334889
\(641\) −37.7005 −1.48908 −0.744540 0.667578i \(-0.767331\pi\)
−0.744540 + 0.667578i \(0.767331\pi\)
\(642\) 94.2981 3.72165
\(643\) −47.1181 −1.85816 −0.929079 0.369882i \(-0.879398\pi\)
−0.929079 + 0.369882i \(0.879398\pi\)
\(644\) −113.257 −4.46294
\(645\) 8.31572 0.327431
\(646\) 51.5572 2.02849
\(647\) −19.8341 −0.779760 −0.389880 0.920866i \(-0.627483\pi\)
−0.389880 + 0.920866i \(0.627483\pi\)
\(648\) 23.2459 0.913185
\(649\) 16.2768 0.638921
\(650\) −10.7307 −0.420893
\(651\) 56.3433 2.20827
\(652\) −1.23826 −0.0484942
\(653\) 17.5247 0.685796 0.342898 0.939373i \(-0.388592\pi\)
0.342898 + 0.939373i \(0.388592\pi\)
\(654\) 93.3078 3.64863
\(655\) −4.03061 −0.157489
\(656\) 6.21512 0.242660
\(657\) −22.8524 −0.891557
\(658\) 43.8203 1.70829
\(659\) 19.2598 0.750254 0.375127 0.926973i \(-0.377599\pi\)
0.375127 + 0.926973i \(0.377599\pi\)
\(660\) 5.37862 0.209363
\(661\) 33.1412 1.28904 0.644521 0.764586i \(-0.277057\pi\)
0.644521 + 0.764586i \(0.277057\pi\)
\(662\) −20.3683 −0.791635
\(663\) −7.61661 −0.295805
\(664\) 5.91295 0.229467
\(665\) 16.0671 0.623057
\(666\) −44.1437 −1.71054
\(667\) 15.7101 0.608297
\(668\) −7.33030 −0.283618
\(669\) 17.6333 0.681744
\(670\) 1.42891 0.0552037
\(671\) −18.2421 −0.704227
\(672\) 67.2698 2.59499
\(673\) −41.3761 −1.59493 −0.797466 0.603363i \(-0.793827\pi\)
−0.797466 + 0.603363i \(0.793827\pi\)
\(674\) 49.6877 1.91390
\(675\) 1.24435 0.0478951
\(676\) 3.10485 0.119417
\(677\) −0.406026 −0.0156048 −0.00780242 0.999970i \(-0.502484\pi\)
−0.00780242 + 0.999970i \(0.502484\pi\)
\(678\) −24.8901 −0.955900
\(679\) −66.9457 −2.56914
\(680\) 3.92133 0.150376
\(681\) −41.6997 −1.59794
\(682\) 16.9406 0.648687
\(683\) −21.2673 −0.813771 −0.406885 0.913479i \(-0.633385\pi\)
−0.406885 + 0.913479i \(0.633385\pi\)
\(684\) −65.3008 −2.49684
\(685\) 5.21719 0.199338
\(686\) −54.6113 −2.08507
\(687\) 31.8675 1.21582
\(688\) 3.89784 0.148604
\(689\) −3.05136 −0.116248
\(690\) −22.6934 −0.863921
\(691\) −25.6566 −0.976023 −0.488011 0.872837i \(-0.662278\pi\)
−0.488011 + 0.872837i \(0.662278\pi\)
\(692\) −0.810333 −0.0308042
\(693\) −18.1951 −0.691173
\(694\) 31.2687 1.18694
\(695\) 4.18308 0.158673
\(696\) 11.5171 0.436556
\(697\) −34.2382 −1.29686
\(698\) −8.13237 −0.307815
\(699\) 20.6471 0.780945
\(700\) −65.0784 −2.45973
\(701\) −20.3870 −0.770007 −0.385003 0.922915i \(-0.625800\pi\)
−0.385003 + 0.922915i \(0.625800\pi\)
\(702\) −0.591968 −0.0223424
\(703\) −49.1292 −1.85294
\(704\) 18.6018 0.701081
\(705\) 5.34033 0.201128
\(706\) 8.71956 0.328165
\(707\) 36.6874 1.37977
\(708\) −86.0514 −3.23401
\(709\) −14.8967 −0.559456 −0.279728 0.960079i \(-0.590244\pi\)
−0.279728 + 0.960079i \(0.590244\pi\)
\(710\) −11.1703 −0.419213
\(711\) −19.9086 −0.746631
\(712\) 9.25125 0.346705
\(713\) −43.4724 −1.62805
\(714\) −75.9474 −2.84226
\(715\) −0.713668 −0.0266897
\(716\) 69.4145 2.59414
\(717\) −39.3163 −1.46829
\(718\) −18.7745 −0.700658
\(719\) −15.0128 −0.559881 −0.279941 0.960017i \(-0.590315\pi\)
−0.279941 + 0.960017i \(0.590315\pi\)
\(720\) 0.824678 0.0307339
\(721\) 75.7031 2.81933
\(722\) −76.5613 −2.84932
\(723\) −31.1507 −1.15851
\(724\) 41.9800 1.56018
\(725\) 9.02717 0.335261
\(726\) 49.1824 1.82533
\(727\) −6.05656 −0.224625 −0.112313 0.993673i \(-0.535826\pi\)
−0.112313 + 0.993673i \(0.535826\pi\)
\(728\) 11.0168 0.408310
\(729\) −25.0234 −0.926794
\(730\) −8.93769 −0.330799
\(731\) −21.4726 −0.794193
\(732\) 96.4411 3.56456
\(733\) 3.08414 0.113915 0.0569577 0.998377i \(-0.481860\pi\)
0.0569577 + 0.998377i \(0.481860\pi\)
\(734\) −41.8191 −1.54357
\(735\) −15.1617 −0.559249
\(736\) −51.9028 −1.91316
\(737\) −1.80090 −0.0663372
\(738\) 71.2987 2.62454
\(739\) 20.5392 0.755548 0.377774 0.925898i \(-0.376690\pi\)
0.377774 + 0.925898i \(0.376690\pi\)
\(740\) −10.5008 −0.386016
\(741\) 17.6524 0.648476
\(742\) −30.4260 −1.11697
\(743\) 8.00492 0.293672 0.146836 0.989161i \(-0.453091\pi\)
0.146836 + 0.989161i \(0.453091\pi\)
\(744\) −31.8698 −1.16840
\(745\) −1.90739 −0.0698812
\(746\) 18.7884 0.687890
\(747\) −6.85040 −0.250643
\(748\) −13.8885 −0.507814
\(749\) −75.8817 −2.77266
\(750\) −26.7678 −0.977420
\(751\) 8.36300 0.305170 0.152585 0.988290i \(-0.451240\pi\)
0.152585 + 0.988290i \(0.451240\pi\)
\(752\) 2.50318 0.0912815
\(753\) −0.306338 −0.0111636
\(754\) −4.29444 −0.156394
\(755\) −7.17679 −0.261190
\(756\) −3.59010 −0.130571
\(757\) −33.9896 −1.23537 −0.617686 0.786425i \(-0.711930\pi\)
−0.617686 + 0.786425i \(0.711930\pi\)
\(758\) −56.7109 −2.05983
\(759\) 28.6012 1.03816
\(760\) −9.08815 −0.329662
\(761\) 44.7848 1.62345 0.811724 0.584041i \(-0.198529\pi\)
0.811724 + 0.584041i \(0.198529\pi\)
\(762\) −62.5133 −2.26462
\(763\) −75.0849 −2.71825
\(764\) 28.0730 1.01565
\(765\) −4.54303 −0.164254
\(766\) −45.0898 −1.62916
\(767\) 11.4178 0.412274
\(768\) −29.4646 −1.06321
\(769\) −55.0355 −1.98463 −0.992315 0.123734i \(-0.960513\pi\)
−0.992315 + 0.123734i \(0.960513\pi\)
\(770\) −7.11619 −0.256450
\(771\) 20.1325 0.725055
\(772\) −17.6172 −0.634058
\(773\) −26.2196 −0.943052 −0.471526 0.881852i \(-0.656297\pi\)
−0.471526 + 0.881852i \(0.656297\pi\)
\(774\) 44.7153 1.60726
\(775\) −24.9796 −0.897295
\(776\) 37.8668 1.35934
\(777\) 72.3707 2.59629
\(778\) 6.63033 0.237709
\(779\) 79.3509 2.84304
\(780\) 3.77298 0.135094
\(781\) 14.0782 0.503759
\(782\) 58.5981 2.09546
\(783\) 0.497991 0.0177967
\(784\) −7.10677 −0.253813
\(785\) −1.06774 −0.0381094
\(786\) −44.1556 −1.57498
\(787\) −11.8062 −0.420845 −0.210423 0.977610i \(-0.567484\pi\)
−0.210423 + 0.977610i \(0.567484\pi\)
\(788\) −11.2891 −0.402158
\(789\) 40.7140 1.44946
\(790\) −7.78637 −0.277026
\(791\) 20.0291 0.712153
\(792\) 10.2918 0.365702
\(793\) −12.7964 −0.454413
\(794\) −21.0454 −0.746873
\(795\) −3.70797 −0.131508
\(796\) −26.9704 −0.955940
\(797\) −23.6726 −0.838528 −0.419264 0.907864i \(-0.637712\pi\)
−0.419264 + 0.907864i \(0.637712\pi\)
\(798\) 176.017 6.23093
\(799\) −13.7896 −0.487842
\(800\) −29.8239 −1.05443
\(801\) −10.7180 −0.378700
\(802\) −7.03045 −0.248254
\(803\) 11.2645 0.397514
\(804\) 9.52092 0.335777
\(805\) 18.2614 0.643628
\(806\) 11.8834 0.418575
\(807\) −49.7928 −1.75279
\(808\) −20.7517 −0.730042
\(809\) 12.4371 0.437265 0.218633 0.975807i \(-0.429840\pi\)
0.218633 + 0.975807i \(0.429840\pi\)
\(810\) −10.5330 −0.370092
\(811\) 28.5505 1.00254 0.501271 0.865290i \(-0.332866\pi\)
0.501271 + 0.865290i \(0.332866\pi\)
\(812\) −26.0444 −0.913981
\(813\) 60.1296 2.10884
\(814\) 21.7595 0.762668
\(815\) 0.199656 0.00699364
\(816\) −4.33839 −0.151874
\(817\) 49.7653 1.74107
\(818\) −8.90118 −0.311223
\(819\) −12.7634 −0.445990
\(820\) 16.9603 0.592279
\(821\) 28.5283 0.995643 0.497822 0.867279i \(-0.334133\pi\)
0.497822 + 0.867279i \(0.334133\pi\)
\(822\) 57.1547 1.99350
\(823\) 0.611865 0.0213283 0.0106641 0.999943i \(-0.496605\pi\)
0.0106641 + 0.999943i \(0.496605\pi\)
\(824\) −42.8203 −1.49172
\(825\) 16.4345 0.572176
\(826\) 113.850 3.96136
\(827\) −1.39672 −0.0485688 −0.0242844 0.999705i \(-0.507731\pi\)
−0.0242844 + 0.999705i \(0.507731\pi\)
\(828\) −74.2185 −2.57927
\(829\) 19.8978 0.691079 0.345540 0.938404i \(-0.387696\pi\)
0.345540 + 0.938404i \(0.387696\pi\)
\(830\) −2.67923 −0.0929973
\(831\) 45.6423 1.58331
\(832\) 13.0487 0.452383
\(833\) 39.1501 1.35647
\(834\) 45.8259 1.58682
\(835\) 1.18193 0.0409023
\(836\) 32.1882 1.11325
\(837\) −1.37802 −0.0476314
\(838\) −31.0747 −1.07346
\(839\) −46.8515 −1.61749 −0.808747 0.588156i \(-0.799854\pi\)
−0.808747 + 0.588156i \(0.799854\pi\)
\(840\) 13.3875 0.461912
\(841\) −25.3873 −0.875425
\(842\) −64.9133 −2.23706
\(843\) 72.3082 2.49043
\(844\) 40.7362 1.40220
\(845\) −0.500622 −0.0172219
\(846\) 28.7160 0.987276
\(847\) −39.5771 −1.35988
\(848\) −1.73804 −0.0596846
\(849\) 46.3374 1.59030
\(850\) 33.6710 1.15491
\(851\) −55.8385 −1.91412
\(852\) −74.4281 −2.54986
\(853\) −2.82819 −0.0968352 −0.0484176 0.998827i \(-0.515418\pi\)
−0.0484176 + 0.998827i \(0.515418\pi\)
\(854\) −127.596 −4.36626
\(855\) 10.5290 0.360084
\(856\) 42.9214 1.46702
\(857\) 47.7385 1.63072 0.815358 0.578958i \(-0.196540\pi\)
0.815358 + 0.578958i \(0.196540\pi\)
\(858\) −7.81829 −0.266912
\(859\) −22.4413 −0.765689 −0.382844 0.923813i \(-0.625055\pi\)
−0.382844 + 0.923813i \(0.625055\pi\)
\(860\) 10.6367 0.362709
\(861\) −116.890 −3.98358
\(862\) 9.88956 0.336840
\(863\) −26.3657 −0.897498 −0.448749 0.893658i \(-0.648130\pi\)
−0.448749 + 0.893658i \(0.648130\pi\)
\(864\) −1.64526 −0.0559728
\(865\) 0.130657 0.00444247
\(866\) −67.5200 −2.29442
\(867\) −17.3655 −0.589764
\(868\) 72.0692 2.44619
\(869\) 9.81341 0.332897
\(870\) −5.21855 −0.176925
\(871\) −1.26329 −0.0428051
\(872\) 42.4706 1.43824
\(873\) −43.8703 −1.48479
\(874\) −135.808 −4.59377
\(875\) 21.5400 0.728186
\(876\) −59.5523 −2.01209
\(877\) 20.4596 0.690872 0.345436 0.938442i \(-0.387731\pi\)
0.345436 + 0.938442i \(0.387731\pi\)
\(878\) −35.4524 −1.19646
\(879\) −48.8610 −1.64804
\(880\) −0.406503 −0.0137032
\(881\) −44.1552 −1.48763 −0.743813 0.668388i \(-0.766985\pi\)
−0.743813 + 0.668388i \(0.766985\pi\)
\(882\) −81.5276 −2.74518
\(883\) −20.4976 −0.689800 −0.344900 0.938640i \(-0.612087\pi\)
−0.344900 + 0.938640i \(0.612087\pi\)
\(884\) −9.74247 −0.327675
\(885\) 13.8748 0.466396
\(886\) 49.7811 1.67243
\(887\) −51.8347 −1.74044 −0.870219 0.492665i \(-0.836023\pi\)
−0.870219 + 0.492665i \(0.836023\pi\)
\(888\) −40.9354 −1.37370
\(889\) 50.3044 1.68716
\(890\) −4.19185 −0.140511
\(891\) 13.2751 0.444732
\(892\) 22.5549 0.755195
\(893\) 31.9591 1.06947
\(894\) −20.8956 −0.698852
\(895\) −11.1923 −0.374117
\(896\) 74.6862 2.49509
\(897\) 20.0631 0.669886
\(898\) −28.2459 −0.942578
\(899\) −9.99687 −0.333414
\(900\) −42.6467 −1.42156
\(901\) 9.57462 0.318977
\(902\) −35.1448 −1.17019
\(903\) −73.3077 −2.43953
\(904\) −11.3292 −0.376802
\(905\) −6.76880 −0.225003
\(906\) −78.6223 −2.61205
\(907\) −6.46458 −0.214653 −0.107326 0.994224i \(-0.534229\pi\)
−0.107326 + 0.994224i \(0.534229\pi\)
\(908\) −53.3385 −1.77010
\(909\) 24.0417 0.797414
\(910\) −4.99184 −0.165478
\(911\) 9.59642 0.317943 0.158972 0.987283i \(-0.449182\pi\)
0.158972 + 0.987283i \(0.449182\pi\)
\(912\) 10.0547 0.332945
\(913\) 3.37672 0.111753
\(914\) −71.4468 −2.36325
\(915\) −15.5500 −0.514068
\(916\) 40.7619 1.34681
\(917\) 35.5321 1.17337
\(918\) 1.85749 0.0613063
\(919\) −6.55296 −0.216162 −0.108081 0.994142i \(-0.534471\pi\)
−0.108081 + 0.994142i \(0.534471\pi\)
\(920\) −10.3293 −0.340546
\(921\) −51.5734 −1.69940
\(922\) −35.5439 −1.17058
\(923\) 9.87557 0.325058
\(924\) −47.4155 −1.55986
\(925\) −32.0853 −1.05496
\(926\) 2.25939 0.0742482
\(927\) 49.6091 1.62938
\(928\) −11.9355 −0.391803
\(929\) −3.94686 −0.129492 −0.0647462 0.997902i \(-0.520624\pi\)
−0.0647462 + 0.997902i \(0.520624\pi\)
\(930\) 14.4406 0.473525
\(931\) −90.7350 −2.97372
\(932\) 26.4099 0.865084
\(933\) −24.5201 −0.802753
\(934\) −79.2214 −2.59220
\(935\) 2.23936 0.0732350
\(936\) 7.21944 0.235975
\(937\) −21.9296 −0.716408 −0.358204 0.933643i \(-0.616611\pi\)
−0.358204 + 0.933643i \(0.616611\pi\)
\(938\) −12.5967 −0.411295
\(939\) −53.2086 −1.73640
\(940\) 6.83086 0.222798
\(941\) 13.0132 0.424219 0.212109 0.977246i \(-0.431967\pi\)
0.212109 + 0.977246i \(0.431967\pi\)
\(942\) −11.6972 −0.381116
\(943\) 90.1875 2.93691
\(944\) 6.50355 0.211672
\(945\) 0.578863 0.0188304
\(946\) −22.0412 −0.716620
\(947\) −21.2379 −0.690139 −0.345070 0.938577i \(-0.612145\pi\)
−0.345070 + 0.938577i \(0.612145\pi\)
\(948\) −51.8810 −1.68502
\(949\) 7.90176 0.256502
\(950\) −78.0365 −2.53184
\(951\) −58.7258 −1.90431
\(952\) −34.5687 −1.12038
\(953\) 47.9556 1.55343 0.776717 0.629850i \(-0.216883\pi\)
0.776717 + 0.629850i \(0.216883\pi\)
\(954\) −19.9385 −0.645533
\(955\) −4.52645 −0.146473
\(956\) −50.2898 −1.62649
\(957\) 6.57711 0.212608
\(958\) −29.3086 −0.946917
\(959\) −45.9924 −1.48517
\(960\) 15.8567 0.511771
\(961\) −3.33702 −0.107646
\(962\) 15.2638 0.492123
\(963\) −49.7262 −1.60240
\(964\) −39.8451 −1.28332
\(965\) 2.84057 0.0914413
\(966\) 200.055 6.43665
\(967\) 29.2656 0.941119 0.470560 0.882368i \(-0.344052\pi\)
0.470560 + 0.882368i \(0.344052\pi\)
\(968\) 22.3862 0.719520
\(969\) −55.3900 −1.77938
\(970\) −17.1579 −0.550908
\(971\) 4.15655 0.133390 0.0666951 0.997773i \(-0.478755\pi\)
0.0666951 + 0.997773i \(0.478755\pi\)
\(972\) −67.7415 −2.17281
\(973\) −36.8761 −1.18220
\(974\) −35.9098 −1.15062
\(975\) 11.5284 0.369205
\(976\) −7.28877 −0.233308
\(977\) 27.3819 0.876025 0.438012 0.898969i \(-0.355683\pi\)
0.438012 + 0.898969i \(0.355683\pi\)
\(978\) 2.18725 0.0699404
\(979\) 5.28312 0.168849
\(980\) −19.3935 −0.619502
\(981\) −49.2040 −1.57096
\(982\) 5.62691 0.179562
\(983\) 37.8216 1.20632 0.603161 0.797620i \(-0.293908\pi\)
0.603161 + 0.797620i \(0.293908\pi\)
\(984\) 66.1168 2.10773
\(985\) 1.82024 0.0579977
\(986\) 13.4752 0.429137
\(987\) −47.0780 −1.49851
\(988\) 22.5793 0.718343
\(989\) 56.5614 1.79855
\(990\) −4.66332 −0.148210
\(991\) 21.0434 0.668466 0.334233 0.942491i \(-0.391523\pi\)
0.334233 + 0.942491i \(0.391523\pi\)
\(992\) 33.0276 1.04863
\(993\) 21.8824 0.694419
\(994\) 98.4721 3.12335
\(995\) 4.34866 0.137862
\(996\) −17.8518 −0.565657
\(997\) 12.1203 0.383853 0.191927 0.981409i \(-0.438526\pi\)
0.191927 + 0.981409i \(0.438526\pi\)
\(998\) 33.7064 1.06696
\(999\) −1.77001 −0.0560007
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 \(a_p\))