Properties

Label 8003.2.a.c.1.3
Level 8003
Weight 2
Character 8003.1
Self dual Yes
Analytic conductor 63.904
Analytic rank 0
Dimension 172
CM No

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Newspace parameters

Level: \( N \) = \( 8003 = 53 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(0\)
Dimension: \(172\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.76129 q^{2}\) \(+2.33703 q^{3}\) \(+5.62470 q^{4}\) \(-2.36515 q^{5}\) \(-6.45322 q^{6}\) \(+1.79490 q^{7}\) \(-10.0088 q^{8}\) \(+2.46173 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.76129 q^{2}\) \(+2.33703 q^{3}\) \(+5.62470 q^{4}\) \(-2.36515 q^{5}\) \(-6.45322 q^{6}\) \(+1.79490 q^{7}\) \(-10.0088 q^{8}\) \(+2.46173 q^{9}\) \(+6.53087 q^{10}\) \(-3.92879 q^{11}\) \(+13.1451 q^{12}\) \(+7.17497 q^{13}\) \(-4.95624 q^{14}\) \(-5.52745 q^{15}\) \(+16.3879 q^{16}\) \(-5.22520 q^{17}\) \(-6.79754 q^{18}\) \(+5.03522 q^{19}\) \(-13.3033 q^{20}\) \(+4.19475 q^{21}\) \(+10.8485 q^{22}\) \(+2.81115 q^{23}\) \(-23.3910 q^{24}\) \(+0.593953 q^{25}\) \(-19.8121 q^{26}\) \(-1.25795 q^{27}\) \(+10.0958 q^{28}\) \(+5.34023 q^{29}\) \(+15.2629 q^{30}\) \(-4.38643 q^{31}\) \(-25.2339 q^{32}\) \(-9.18172 q^{33}\) \(+14.4283 q^{34}\) \(-4.24522 q^{35}\) \(+13.8465 q^{36}\) \(-8.62816 q^{37}\) \(-13.9037 q^{38}\) \(+16.7682 q^{39}\) \(+23.6724 q^{40}\) \(+5.19348 q^{41}\) \(-11.5829 q^{42}\) \(-7.09294 q^{43}\) \(-22.0983 q^{44}\) \(-5.82237 q^{45}\) \(-7.76240 q^{46}\) \(+9.20357 q^{47}\) \(+38.2990 q^{48}\) \(-3.77832 q^{49}\) \(-1.64007 q^{50}\) \(-12.2115 q^{51}\) \(+40.3571 q^{52}\) \(-1.00000 q^{53}\) \(+3.47357 q^{54}\) \(+9.29219 q^{55}\) \(-17.9649 q^{56}\) \(+11.7675 q^{57}\) \(-14.7459 q^{58}\) \(+11.8676 q^{59}\) \(-31.0902 q^{60}\) \(-11.3443 q^{61}\) \(+12.1122 q^{62}\) \(+4.41857 q^{63}\) \(+36.9023 q^{64}\) \(-16.9699 q^{65}\) \(+25.3534 q^{66}\) \(+3.73957 q^{67}\) \(-29.3902 q^{68}\) \(+6.56976 q^{69}\) \(+11.7223 q^{70}\) \(+5.58484 q^{71}\) \(-24.6391 q^{72}\) \(+16.4782 q^{73}\) \(+23.8248 q^{74}\) \(+1.38809 q^{75}\) \(+28.3216 q^{76}\) \(-7.05180 q^{77}\) \(-46.3017 q^{78}\) \(-3.34689 q^{79}\) \(-38.7598 q^{80}\) \(-10.3251 q^{81}\) \(-14.3407 q^{82}\) \(+11.2123 q^{83}\) \(+23.5942 q^{84}\) \(+12.3584 q^{85}\) \(+19.5856 q^{86}\) \(+12.4803 q^{87}\) \(+39.3226 q^{88}\) \(-8.89396 q^{89}\) \(+16.0772 q^{90}\) \(+12.8784 q^{91}\) \(+15.8119 q^{92}\) \(-10.2512 q^{93}\) \(-25.4137 q^{94}\) \(-11.9091 q^{95}\) \(-58.9725 q^{96}\) \(+11.4072 q^{97}\) \(+10.4330 q^{98}\) \(-9.67163 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.76129 −1.95252 −0.976262 0.216593i \(-0.930506\pi\)
−0.976262 + 0.216593i \(0.930506\pi\)
\(3\) 2.33703 1.34929 0.674644 0.738143i \(-0.264297\pi\)
0.674644 + 0.738143i \(0.264297\pi\)
\(4\) 5.62470 2.81235
\(5\) −2.36515 −1.05773 −0.528864 0.848706i \(-0.677382\pi\)
−0.528864 + 0.848706i \(0.677382\pi\)
\(6\) −6.45322 −2.63452
\(7\) 1.79490 0.678410 0.339205 0.940713i \(-0.389842\pi\)
0.339205 + 0.940713i \(0.389842\pi\)
\(8\) −10.0088 −3.53866
\(9\) 2.46173 0.820577
\(10\) 6.53087 2.06524
\(11\) −3.92879 −1.18458 −0.592288 0.805727i \(-0.701775\pi\)
−0.592288 + 0.805727i \(0.701775\pi\)
\(12\) 13.1451 3.79467
\(13\) 7.17497 1.98998 0.994989 0.0999822i \(-0.0318786\pi\)
0.994989 + 0.0999822i \(0.0318786\pi\)
\(14\) −4.95624 −1.32461
\(15\) −5.52745 −1.42718
\(16\) 16.3879 4.09697
\(17\) −5.22520 −1.26730 −0.633649 0.773621i \(-0.718443\pi\)
−0.633649 + 0.773621i \(0.718443\pi\)
\(18\) −6.79754 −1.60220
\(19\) 5.03522 1.15516 0.577579 0.816335i \(-0.303998\pi\)
0.577579 + 0.816335i \(0.303998\pi\)
\(20\) −13.3033 −2.97470
\(21\) 4.19475 0.915370
\(22\) 10.8485 2.31291
\(23\) 2.81115 0.586166 0.293083 0.956087i \(-0.405319\pi\)
0.293083 + 0.956087i \(0.405319\pi\)
\(24\) −23.3910 −4.77467
\(25\) 0.593953 0.118791
\(26\) −19.8121 −3.88548
\(27\) −1.25795 −0.242093
\(28\) 10.0958 1.90793
\(29\) 5.34023 0.991656 0.495828 0.868421i \(-0.334865\pi\)
0.495828 + 0.868421i \(0.334865\pi\)
\(30\) 15.2629 2.78660
\(31\) −4.38643 −0.787826 −0.393913 0.919148i \(-0.628879\pi\)
−0.393913 + 0.919148i \(0.628879\pi\)
\(32\) −25.2339 −4.46077
\(33\) −9.18172 −1.59833
\(34\) 14.4283 2.47443
\(35\) −4.24522 −0.717574
\(36\) 13.8465 2.30775
\(37\) −8.62816 −1.41846 −0.709230 0.704977i \(-0.750957\pi\)
−0.709230 + 0.704977i \(0.750957\pi\)
\(38\) −13.9037 −2.25547
\(39\) 16.7682 2.68505
\(40\) 23.6724 3.74294
\(41\) 5.19348 0.811085 0.405542 0.914076i \(-0.367083\pi\)
0.405542 + 0.914076i \(0.367083\pi\)
\(42\) −11.5829 −1.78728
\(43\) −7.09294 −1.08166 −0.540831 0.841131i \(-0.681890\pi\)
−0.540831 + 0.841131i \(0.681890\pi\)
\(44\) −22.0983 −3.33144
\(45\) −5.82237 −0.867948
\(46\) −7.76240 −1.14450
\(47\) 9.20357 1.34248 0.671239 0.741241i \(-0.265762\pi\)
0.671239 + 0.741241i \(0.265762\pi\)
\(48\) 38.2990 5.52798
\(49\) −3.77832 −0.539760
\(50\) −1.64007 −0.231941
\(51\) −12.2115 −1.70995
\(52\) 40.3571 5.59652
\(53\) −1.00000 −0.137361
\(54\) 3.47357 0.472693
\(55\) 9.29219 1.25296
\(56\) −17.9649 −2.40066
\(57\) 11.7675 1.55864
\(58\) −14.7459 −1.93623
\(59\) 11.8676 1.54503 0.772516 0.634996i \(-0.218998\pi\)
0.772516 + 0.634996i \(0.218998\pi\)
\(60\) −31.0902 −4.01373
\(61\) −11.3443 −1.45249 −0.726247 0.687434i \(-0.758737\pi\)
−0.726247 + 0.687434i \(0.758737\pi\)
\(62\) 12.1122 1.53825
\(63\) 4.41857 0.556687
\(64\) 36.9023 4.61279
\(65\) −16.9699 −2.10486
\(66\) 25.3534 3.12078
\(67\) 3.73957 0.456861 0.228430 0.973560i \(-0.426641\pi\)
0.228430 + 0.973560i \(0.426641\pi\)
\(68\) −29.3902 −3.56408
\(69\) 6.56976 0.790906
\(70\) 11.7223 1.40108
\(71\) 5.58484 0.662799 0.331400 0.943491i \(-0.392479\pi\)
0.331400 + 0.943491i \(0.392479\pi\)
\(72\) −24.6391 −2.90374
\(73\) 16.4782 1.92863 0.964316 0.264752i \(-0.0852902\pi\)
0.964316 + 0.264752i \(0.0852902\pi\)
\(74\) 23.8248 2.76958
\(75\) 1.38809 0.160283
\(76\) 28.3216 3.24871
\(77\) −7.05180 −0.803627
\(78\) −46.3017 −5.24263
\(79\) −3.34689 −0.376555 −0.188278 0.982116i \(-0.560290\pi\)
−0.188278 + 0.982116i \(0.560290\pi\)
\(80\) −38.7598 −4.33348
\(81\) −10.3251 −1.14723
\(82\) −14.3407 −1.58366
\(83\) 11.2123 1.23071 0.615357 0.788249i \(-0.289012\pi\)
0.615357 + 0.788249i \(0.289012\pi\)
\(84\) 23.5942 2.57434
\(85\) 12.3584 1.34046
\(86\) 19.5856 2.11197
\(87\) 12.4803 1.33803
\(88\) 39.3226 4.19181
\(89\) −8.89396 −0.942758 −0.471379 0.881931i \(-0.656244\pi\)
−0.471379 + 0.881931i \(0.656244\pi\)
\(90\) 16.0772 1.69469
\(91\) 12.8784 1.35002
\(92\) 15.8119 1.64850
\(93\) −10.2512 −1.06300
\(94\) −25.4137 −2.62122
\(95\) −11.9091 −1.22184
\(96\) −58.9725 −6.01886
\(97\) 11.4072 1.15823 0.579113 0.815247i \(-0.303399\pi\)
0.579113 + 0.815247i \(0.303399\pi\)
\(98\) 10.4330 1.05390
\(99\) −9.67163 −0.972035
\(100\) 3.34081 0.334081
\(101\) −1.50754 −0.150006 −0.0750031 0.997183i \(-0.523897\pi\)
−0.0750031 + 0.997183i \(0.523897\pi\)
\(102\) 33.7194 3.33872
\(103\) 14.3509 1.41404 0.707020 0.707193i \(-0.250039\pi\)
0.707020 + 0.707193i \(0.250039\pi\)
\(104\) −71.8131 −7.04185
\(105\) −9.92123 −0.968213
\(106\) 2.76129 0.268200
\(107\) 8.91867 0.862200 0.431100 0.902304i \(-0.358126\pi\)
0.431100 + 0.902304i \(0.358126\pi\)
\(108\) −7.07561 −0.680851
\(109\) 7.78466 0.745635 0.372817 0.927905i \(-0.378392\pi\)
0.372817 + 0.927905i \(0.378392\pi\)
\(110\) −25.6584 −2.44643
\(111\) −20.1643 −1.91391
\(112\) 29.4146 2.77942
\(113\) −9.48131 −0.891926 −0.445963 0.895051i \(-0.647139\pi\)
−0.445963 + 0.895051i \(0.647139\pi\)
\(114\) −32.4934 −3.04328
\(115\) −6.64881 −0.620004
\(116\) 30.0372 2.78888
\(117\) 17.6628 1.63293
\(118\) −32.7699 −3.01671
\(119\) −9.37873 −0.859747
\(120\) 55.3233 5.05030
\(121\) 4.43540 0.403218
\(122\) 31.3250 2.83603
\(123\) 12.1373 1.09439
\(124\) −24.6723 −2.21564
\(125\) 10.4210 0.932081
\(126\) −12.2009 −1.08695
\(127\) 4.86594 0.431782 0.215891 0.976417i \(-0.430734\pi\)
0.215891 + 0.976417i \(0.430734\pi\)
\(128\) −51.4300 −4.54581
\(129\) −16.5764 −1.45947
\(130\) 46.8588 4.10979
\(131\) 6.64485 0.580564 0.290282 0.956941i \(-0.406251\pi\)
0.290282 + 0.956941i \(0.406251\pi\)
\(132\) −51.6444 −4.49507
\(133\) 9.03773 0.783670
\(134\) −10.3260 −0.892032
\(135\) 2.97525 0.256069
\(136\) 52.2982 4.48453
\(137\) −6.76189 −0.577708 −0.288854 0.957373i \(-0.593274\pi\)
−0.288854 + 0.957373i \(0.593274\pi\)
\(138\) −18.1410 −1.54426
\(139\) 6.35654 0.539155 0.269578 0.962979i \(-0.413116\pi\)
0.269578 + 0.962979i \(0.413116\pi\)
\(140\) −23.8781 −2.01807
\(141\) 21.5091 1.81139
\(142\) −15.4214 −1.29413
\(143\) −28.1890 −2.35728
\(144\) 40.3425 3.36188
\(145\) −12.6305 −1.04890
\(146\) −45.5012 −3.76570
\(147\) −8.83007 −0.728292
\(148\) −48.5308 −3.98921
\(149\) −0.962559 −0.0788559 −0.0394279 0.999222i \(-0.512554\pi\)
−0.0394279 + 0.999222i \(0.512554\pi\)
\(150\) −3.83291 −0.312956
\(151\) 1.00000 0.0813788
\(152\) −50.3967 −4.08771
\(153\) −12.8630 −1.03991
\(154\) 19.4720 1.56910
\(155\) 10.3746 0.833306
\(156\) 94.3158 7.55131
\(157\) −23.1858 −1.85043 −0.925215 0.379444i \(-0.876115\pi\)
−0.925215 + 0.379444i \(0.876115\pi\)
\(158\) 9.24173 0.735233
\(159\) −2.33703 −0.185339
\(160\) 59.6821 4.71828
\(161\) 5.04575 0.397660
\(162\) 28.5105 2.24000
\(163\) −10.5937 −0.829762 −0.414881 0.909876i \(-0.636177\pi\)
−0.414881 + 0.909876i \(0.636177\pi\)
\(164\) 29.2118 2.28105
\(165\) 21.7162 1.69060
\(166\) −30.9605 −2.40300
\(167\) −7.58214 −0.586724 −0.293362 0.956001i \(-0.594774\pi\)
−0.293362 + 0.956001i \(0.594774\pi\)
\(168\) −41.9846 −3.23918
\(169\) 38.4802 2.96001
\(170\) −34.1251 −2.61727
\(171\) 12.3953 0.947896
\(172\) −39.8957 −3.04201
\(173\) −3.45146 −0.262410 −0.131205 0.991355i \(-0.541885\pi\)
−0.131205 + 0.991355i \(0.541885\pi\)
\(174\) −34.4617 −2.61253
\(175\) 1.06609 0.0805887
\(176\) −64.3845 −4.85316
\(177\) 27.7350 2.08469
\(178\) 24.5588 1.84076
\(179\) 12.8909 0.963512 0.481756 0.876305i \(-0.339999\pi\)
0.481756 + 0.876305i \(0.339999\pi\)
\(180\) −32.7491 −2.44097
\(181\) −18.1025 −1.34555 −0.672775 0.739847i \(-0.734898\pi\)
−0.672775 + 0.739847i \(0.734898\pi\)
\(182\) −35.5609 −2.63595
\(183\) −26.5121 −1.95983
\(184\) −28.1364 −2.07424
\(185\) 20.4069 1.50035
\(186\) 28.3066 2.07554
\(187\) 20.5287 1.50121
\(188\) 51.7673 3.77552
\(189\) −2.25790 −0.164238
\(190\) 32.8843 2.38568
\(191\) 22.9101 1.65771 0.828857 0.559461i \(-0.188992\pi\)
0.828857 + 0.559461i \(0.188992\pi\)
\(192\) 86.2420 6.22398
\(193\) −12.6503 −0.910591 −0.455296 0.890340i \(-0.650466\pi\)
−0.455296 + 0.890340i \(0.650466\pi\)
\(194\) −31.4985 −2.26146
\(195\) −39.6593 −2.84006
\(196\) −21.2519 −1.51800
\(197\) −11.2199 −0.799383 −0.399692 0.916650i \(-0.630883\pi\)
−0.399692 + 0.916650i \(0.630883\pi\)
\(198\) 26.7061 1.89792
\(199\) −11.7382 −0.832102 −0.416051 0.909341i \(-0.636586\pi\)
−0.416051 + 0.909341i \(0.636586\pi\)
\(200\) −5.94478 −0.420359
\(201\) 8.73950 0.616437
\(202\) 4.16276 0.292891
\(203\) 9.58520 0.672749
\(204\) −68.6859 −4.80897
\(205\) −12.2834 −0.857908
\(206\) −39.6271 −2.76095
\(207\) 6.92030 0.480994
\(208\) 117.582 8.15287
\(209\) −19.7823 −1.36837
\(210\) 27.3954 1.89046
\(211\) 10.5115 0.723644 0.361822 0.932247i \(-0.382155\pi\)
0.361822 + 0.932247i \(0.382155\pi\)
\(212\) −5.62470 −0.386306
\(213\) 13.0520 0.894306
\(214\) −24.6270 −1.68347
\(215\) 16.7759 1.14411
\(216\) 12.5907 0.856685
\(217\) −7.87321 −0.534469
\(218\) −21.4957 −1.45587
\(219\) 38.5102 2.60228
\(220\) 52.2658 3.52376
\(221\) −37.4906 −2.52189
\(222\) 55.6794 3.73696
\(223\) 8.76755 0.587118 0.293559 0.955941i \(-0.405160\pi\)
0.293559 + 0.955941i \(0.405160\pi\)
\(224\) −45.2924 −3.02623
\(225\) 1.46215 0.0974768
\(226\) 26.1806 1.74151
\(227\) 11.7274 0.778376 0.389188 0.921158i \(-0.372756\pi\)
0.389188 + 0.921158i \(0.372756\pi\)
\(228\) 66.1885 4.38344
\(229\) 7.14519 0.472167 0.236084 0.971733i \(-0.424136\pi\)
0.236084 + 0.971733i \(0.424136\pi\)
\(230\) 18.3593 1.21057
\(231\) −16.4803 −1.08432
\(232\) −53.4495 −3.50913
\(233\) −4.78774 −0.313655 −0.156828 0.987626i \(-0.550127\pi\)
−0.156828 + 0.987626i \(0.550127\pi\)
\(234\) −48.7722 −3.18834
\(235\) −21.7679 −1.41998
\(236\) 66.7518 4.34517
\(237\) −7.82181 −0.508081
\(238\) 25.8974 1.67868
\(239\) −4.87259 −0.315182 −0.157591 0.987504i \(-0.550373\pi\)
−0.157591 + 0.987504i \(0.550373\pi\)
\(240\) −90.5830 −5.84711
\(241\) −15.8055 −1.01812 −0.509062 0.860730i \(-0.670008\pi\)
−0.509062 + 0.860730i \(0.670008\pi\)
\(242\) −12.2474 −0.787293
\(243\) −20.3562 −1.30585
\(244\) −63.8085 −4.08492
\(245\) 8.93631 0.570920
\(246\) −33.5146 −2.13682
\(247\) 36.1275 2.29874
\(248\) 43.9030 2.78785
\(249\) 26.2036 1.66059
\(250\) −28.7753 −1.81991
\(251\) −7.34957 −0.463901 −0.231950 0.972728i \(-0.574511\pi\)
−0.231950 + 0.972728i \(0.574511\pi\)
\(252\) 24.8531 1.56560
\(253\) −11.0444 −0.694357
\(254\) −13.4362 −0.843065
\(255\) 28.8820 1.80866
\(256\) 68.2084 4.26302
\(257\) 18.8184 1.17386 0.586929 0.809638i \(-0.300337\pi\)
0.586929 + 0.809638i \(0.300337\pi\)
\(258\) 45.7723 2.84966
\(259\) −15.4867 −0.962298
\(260\) −95.4507 −5.91960
\(261\) 13.1462 0.813730
\(262\) −18.3483 −1.13356
\(263\) 16.3997 1.01125 0.505623 0.862755i \(-0.331263\pi\)
0.505623 + 0.862755i \(0.331263\pi\)
\(264\) 91.8983 5.65595
\(265\) 2.36515 0.145290
\(266\) −24.9557 −1.53014
\(267\) −20.7855 −1.27205
\(268\) 21.0340 1.28485
\(269\) 26.1132 1.59215 0.796073 0.605200i \(-0.206907\pi\)
0.796073 + 0.605200i \(0.206907\pi\)
\(270\) −8.21553 −0.499981
\(271\) 29.6185 1.79919 0.899596 0.436722i \(-0.143861\pi\)
0.899596 + 0.436722i \(0.143861\pi\)
\(272\) −85.6299 −5.19207
\(273\) 30.0972 1.82157
\(274\) 18.6715 1.12799
\(275\) −2.33352 −0.140716
\(276\) 36.9529 2.22431
\(277\) 8.80288 0.528914 0.264457 0.964398i \(-0.414807\pi\)
0.264457 + 0.964398i \(0.414807\pi\)
\(278\) −17.5522 −1.05271
\(279\) −10.7982 −0.646472
\(280\) 42.4897 2.53925
\(281\) −6.38749 −0.381046 −0.190523 0.981683i \(-0.561018\pi\)
−0.190523 + 0.981683i \(0.561018\pi\)
\(282\) −59.3927 −3.53678
\(283\) 7.47971 0.444623 0.222311 0.974976i \(-0.428640\pi\)
0.222311 + 0.974976i \(0.428640\pi\)
\(284\) 31.4131 1.86402
\(285\) −27.8319 −1.64862
\(286\) 77.8378 4.60264
\(287\) 9.32179 0.550248
\(288\) −62.1191 −3.66040
\(289\) 10.3027 0.606042
\(290\) 34.8763 2.04801
\(291\) 26.6590 1.56278
\(292\) 92.6852 5.42399
\(293\) 11.4604 0.669523 0.334762 0.942303i \(-0.391344\pi\)
0.334762 + 0.942303i \(0.391344\pi\)
\(294\) 24.3824 1.42201
\(295\) −28.0687 −1.63422
\(296\) 86.3579 5.01945
\(297\) 4.94224 0.286778
\(298\) 2.65790 0.153968
\(299\) 20.1699 1.16646
\(300\) 7.80758 0.450771
\(301\) −12.7311 −0.733810
\(302\) −2.76129 −0.158894
\(303\) −3.52318 −0.202401
\(304\) 82.5164 4.73264
\(305\) 26.8311 1.53635
\(306\) 35.5185 2.03046
\(307\) 11.7556 0.670929 0.335464 0.942053i \(-0.391107\pi\)
0.335464 + 0.942053i \(0.391107\pi\)
\(308\) −39.6643 −2.26008
\(309\) 33.5387 1.90795
\(310\) −28.6472 −1.62705
\(311\) −5.05379 −0.286574 −0.143287 0.989681i \(-0.545767\pi\)
−0.143287 + 0.989681i \(0.545767\pi\)
\(312\) −167.830 −9.50149
\(313\) 29.5189 1.66851 0.834253 0.551382i \(-0.185899\pi\)
0.834253 + 0.551382i \(0.185899\pi\)
\(314\) 64.0227 3.61301
\(315\) −10.4506 −0.588824
\(316\) −18.8253 −1.05900
\(317\) −34.7865 −1.95380 −0.976901 0.213692i \(-0.931451\pi\)
−0.976901 + 0.213692i \(0.931451\pi\)
\(318\) 6.45322 0.361879
\(319\) −20.9807 −1.17469
\(320\) −87.2796 −4.87908
\(321\) 20.8432 1.16336
\(322\) −13.9327 −0.776442
\(323\) −26.3100 −1.46393
\(324\) −58.0755 −3.22641
\(325\) 4.26159 0.236391
\(326\) 29.2522 1.62013
\(327\) 18.1930 1.00608
\(328\) −51.9807 −2.87015
\(329\) 16.5195 0.910750
\(330\) −59.9646 −3.30094
\(331\) 20.1989 1.11023 0.555116 0.831773i \(-0.312674\pi\)
0.555116 + 0.831773i \(0.312674\pi\)
\(332\) 63.0660 3.46120
\(333\) −21.2402 −1.16396
\(334\) 20.9365 1.14559
\(335\) −8.84465 −0.483235
\(336\) 68.7430 3.75024
\(337\) 17.4053 0.948129 0.474065 0.880490i \(-0.342786\pi\)
0.474065 + 0.880490i \(0.342786\pi\)
\(338\) −106.255 −5.77950
\(339\) −22.1581 −1.20347
\(340\) 69.5123 3.76983
\(341\) 17.2334 0.933239
\(342\) −34.2271 −1.85079
\(343\) −19.3460 −1.04459
\(344\) 70.9921 3.82764
\(345\) −15.5385 −0.836564
\(346\) 9.53046 0.512361
\(347\) 23.1663 1.24363 0.621816 0.783164i \(-0.286395\pi\)
0.621816 + 0.783164i \(0.286395\pi\)
\(348\) 70.1980 3.76301
\(349\) −7.44983 −0.398781 −0.199390 0.979920i \(-0.563896\pi\)
−0.199390 + 0.979920i \(0.563896\pi\)
\(350\) −2.94377 −0.157351
\(351\) −9.02578 −0.481760
\(352\) 99.1387 5.28411
\(353\) −25.3894 −1.35134 −0.675670 0.737205i \(-0.736145\pi\)
−0.675670 + 0.737205i \(0.736145\pi\)
\(354\) −76.5843 −4.07041
\(355\) −13.2090 −0.701062
\(356\) −50.0259 −2.65137
\(357\) −21.9184 −1.16005
\(358\) −35.5955 −1.88128
\(359\) −5.21783 −0.275387 −0.137693 0.990475i \(-0.543969\pi\)
−0.137693 + 0.990475i \(0.543969\pi\)
\(360\) 58.2752 3.07137
\(361\) 6.35341 0.334390
\(362\) 49.9862 2.62722
\(363\) 10.3657 0.544057
\(364\) 72.4370 3.79673
\(365\) −38.9736 −2.03997
\(366\) 73.2076 3.82662
\(367\) −15.5521 −0.811811 −0.405906 0.913915i \(-0.633044\pi\)
−0.405906 + 0.913915i \(0.633044\pi\)
\(368\) 46.0688 2.40150
\(369\) 12.7849 0.665557
\(370\) −56.3494 −2.92946
\(371\) −1.79490 −0.0931867
\(372\) −57.6601 −2.98954
\(373\) 3.17049 0.164162 0.0820809 0.996626i \(-0.473843\pi\)
0.0820809 + 0.996626i \(0.473843\pi\)
\(374\) −56.6857 −2.93115
\(375\) 24.3542 1.25764
\(376\) −92.1170 −4.75057
\(377\) 38.3160 1.97337
\(378\) 6.23472 0.320679
\(379\) 28.1192 1.44439 0.722194 0.691691i \(-0.243134\pi\)
0.722194 + 0.691691i \(0.243134\pi\)
\(380\) −66.9849 −3.43625
\(381\) 11.3719 0.582598
\(382\) −63.2612 −3.23673
\(383\) 1.02985 0.0526231 0.0263115 0.999654i \(-0.491624\pi\)
0.0263115 + 0.999654i \(0.491624\pi\)
\(384\) −120.194 −6.13361
\(385\) 16.6786 0.850020
\(386\) 34.9312 1.77795
\(387\) −17.4609 −0.887588
\(388\) 64.1621 3.25734
\(389\) −6.63149 −0.336230 −0.168115 0.985767i \(-0.553768\pi\)
−0.168115 + 0.985767i \(0.553768\pi\)
\(390\) 109.511 5.54528
\(391\) −14.6888 −0.742846
\(392\) 37.8166 1.91003
\(393\) 15.5293 0.783347
\(394\) 30.9813 1.56082
\(395\) 7.91592 0.398293
\(396\) −54.4000 −2.73370
\(397\) 25.3921 1.27439 0.637195 0.770702i \(-0.280094\pi\)
0.637195 + 0.770702i \(0.280094\pi\)
\(398\) 32.4127 1.62470
\(399\) 21.1215 1.05740
\(400\) 9.73362 0.486681
\(401\) −8.75988 −0.437448 −0.218724 0.975787i \(-0.570189\pi\)
−0.218724 + 0.975787i \(0.570189\pi\)
\(402\) −24.1323 −1.20361
\(403\) −31.4725 −1.56776
\(404\) −8.47948 −0.421870
\(405\) 24.4204 1.21346
\(406\) −26.4675 −1.31356
\(407\) 33.8982 1.68027
\(408\) 122.223 6.05092
\(409\) −2.45200 −0.121244 −0.0606218 0.998161i \(-0.519308\pi\)
−0.0606218 + 0.998161i \(0.519308\pi\)
\(410\) 33.9179 1.67509
\(411\) −15.8028 −0.779494
\(412\) 80.7198 3.97678
\(413\) 21.3012 1.04816
\(414\) −19.1089 −0.939153
\(415\) −26.5189 −1.30176
\(416\) −181.052 −8.87683
\(417\) 14.8555 0.727475
\(418\) 54.6246 2.67178
\(419\) 15.4740 0.755955 0.377977 0.925815i \(-0.376620\pi\)
0.377977 + 0.925815i \(0.376620\pi\)
\(420\) −55.8040 −2.72295
\(421\) 10.9346 0.532920 0.266460 0.963846i \(-0.414146\pi\)
0.266460 + 0.963846i \(0.414146\pi\)
\(422\) −29.0254 −1.41293
\(423\) 22.6567 1.10161
\(424\) 10.0088 0.486072
\(425\) −3.10352 −0.150543
\(426\) −36.0402 −1.74616
\(427\) −20.3620 −0.985386
\(428\) 50.1649 2.42481
\(429\) −65.8786 −3.18065
\(430\) −46.3230 −2.23389
\(431\) −21.5242 −1.03678 −0.518392 0.855143i \(-0.673469\pi\)
−0.518392 + 0.855143i \(0.673469\pi\)
\(432\) −20.6152 −0.991848
\(433\) 5.38467 0.258771 0.129385 0.991594i \(-0.458700\pi\)
0.129385 + 0.991594i \(0.458700\pi\)
\(434\) 21.7402 1.04356
\(435\) −29.5178 −1.41527
\(436\) 43.7864 2.09699
\(437\) 14.1548 0.677114
\(438\) −106.338 −5.08102
\(439\) 8.33818 0.397960 0.198980 0.980004i \(-0.436237\pi\)
0.198980 + 0.980004i \(0.436237\pi\)
\(440\) −93.0041 −4.43380
\(441\) −9.30121 −0.442915
\(442\) 103.522 4.92406
\(443\) 16.9782 0.806658 0.403329 0.915055i \(-0.367853\pi\)
0.403329 + 0.915055i \(0.367853\pi\)
\(444\) −113.418 −5.38259
\(445\) 21.0356 0.997182
\(446\) −24.2097 −1.14636
\(447\) −2.24953 −0.106399
\(448\) 66.2361 3.12936
\(449\) 13.6749 0.645360 0.322680 0.946508i \(-0.395416\pi\)
0.322680 + 0.946508i \(0.395416\pi\)
\(450\) −4.03742 −0.190326
\(451\) −20.4041 −0.960791
\(452\) −53.3295 −2.50841
\(453\) 2.33703 0.109803
\(454\) −32.3828 −1.51980
\(455\) −30.4593 −1.42796
\(456\) −117.779 −5.51550
\(457\) 31.2714 1.46282 0.731408 0.681940i \(-0.238864\pi\)
0.731408 + 0.681940i \(0.238864\pi\)
\(458\) −19.7299 −0.921918
\(459\) 6.57306 0.306804
\(460\) −37.3976 −1.74367
\(461\) −1.92748 −0.0897717 −0.0448858 0.998992i \(-0.514292\pi\)
−0.0448858 + 0.998992i \(0.514292\pi\)
\(462\) 45.5068 2.11717
\(463\) 10.4675 0.486464 0.243232 0.969968i \(-0.421792\pi\)
0.243232 + 0.969968i \(0.421792\pi\)
\(464\) 87.5150 4.06278
\(465\) 24.2457 1.12437
\(466\) 13.2203 0.612420
\(467\) −34.4614 −1.59469 −0.797343 0.603527i \(-0.793762\pi\)
−0.797343 + 0.603527i \(0.793762\pi\)
\(468\) 99.3482 4.59237
\(469\) 6.71216 0.309939
\(470\) 60.1073 2.77254
\(471\) −54.1861 −2.49676
\(472\) −118.781 −5.46734
\(473\) 27.8667 1.28131
\(474\) 21.5983 0.992041
\(475\) 2.99068 0.137222
\(476\) −52.7525 −2.41791
\(477\) −2.46173 −0.112715
\(478\) 13.4546 0.615400
\(479\) 9.19771 0.420254 0.210127 0.977674i \(-0.432612\pi\)
0.210127 + 0.977674i \(0.432612\pi\)
\(480\) 139.479 6.36632
\(481\) −61.9068 −2.82271
\(482\) 43.6436 1.98791
\(483\) 11.7921 0.536558
\(484\) 24.9478 1.13399
\(485\) −26.9798 −1.22509
\(486\) 56.2093 2.54970
\(487\) −23.0931 −1.04645 −0.523224 0.852195i \(-0.675271\pi\)
−0.523224 + 0.852195i \(0.675271\pi\)
\(488\) 113.544 5.13988
\(489\) −24.7578 −1.11959
\(490\) −24.6757 −1.11474
\(491\) 1.29987 0.0586623 0.0293311 0.999570i \(-0.490662\pi\)
0.0293311 + 0.999570i \(0.490662\pi\)
\(492\) 68.2689 3.07780
\(493\) −27.9038 −1.25672
\(494\) −99.7584 −4.48834
\(495\) 22.8749 1.02815
\(496\) −71.8842 −3.22770
\(497\) 10.0243 0.449649
\(498\) −72.3557 −3.24234
\(499\) −35.0347 −1.56837 −0.784184 0.620528i \(-0.786918\pi\)
−0.784184 + 0.620528i \(0.786918\pi\)
\(500\) 58.6149 2.62134
\(501\) −17.7197 −0.791659
\(502\) 20.2943 0.905777
\(503\) −0.114212 −0.00509244 −0.00254622 0.999997i \(-0.500810\pi\)
−0.00254622 + 0.999997i \(0.500810\pi\)
\(504\) −44.2247 −1.96993
\(505\) 3.56557 0.158666
\(506\) 30.4968 1.35575
\(507\) 89.9295 3.99391
\(508\) 27.3694 1.21432
\(509\) 11.0101 0.488014 0.244007 0.969773i \(-0.421538\pi\)
0.244007 + 0.969773i \(0.421538\pi\)
\(510\) −79.7515 −3.53146
\(511\) 29.5769 1.30840
\(512\) −85.4828 −3.77784
\(513\) −6.33407 −0.279656
\(514\) −51.9629 −2.29199
\(515\) −33.9422 −1.49567
\(516\) −93.2375 −4.10455
\(517\) −36.1589 −1.59027
\(518\) 42.7632 1.87891
\(519\) −8.06618 −0.354066
\(520\) 169.849 7.44837
\(521\) 6.63159 0.290535 0.145268 0.989392i \(-0.453596\pi\)
0.145268 + 0.989392i \(0.453596\pi\)
\(522\) −36.3005 −1.58883
\(523\) −27.2968 −1.19361 −0.596804 0.802387i \(-0.703563\pi\)
−0.596804 + 0.802387i \(0.703563\pi\)
\(524\) 37.3753 1.63275
\(525\) 2.49148 0.108737
\(526\) −45.2841 −1.97448
\(527\) 22.9200 0.998409
\(528\) −150.469 −6.54831
\(529\) −15.0974 −0.656410
\(530\) −6.53087 −0.283683
\(531\) 29.2149 1.26782
\(532\) 50.8345 2.20396
\(533\) 37.2630 1.61404
\(534\) 57.3947 2.48371
\(535\) −21.0940 −0.911974
\(536\) −37.4287 −1.61667
\(537\) 30.1265 1.30005
\(538\) −72.1059 −3.10871
\(539\) 14.8442 0.639387
\(540\) 16.7349 0.720156
\(541\) 30.0273 1.29097 0.645486 0.763772i \(-0.276655\pi\)
0.645486 + 0.763772i \(0.276655\pi\)
\(542\) −81.7850 −3.51297
\(543\) −42.3062 −1.81553
\(544\) 131.852 5.65312
\(545\) −18.4119 −0.788679
\(546\) −83.1070 −3.55665
\(547\) 4.82485 0.206296 0.103148 0.994666i \(-0.467108\pi\)
0.103148 + 0.994666i \(0.467108\pi\)
\(548\) −38.0336 −1.62472
\(549\) −27.9267 −1.19188
\(550\) 6.44351 0.274752
\(551\) 26.8892 1.14552
\(552\) −65.7557 −2.79875
\(553\) −6.00735 −0.255459
\(554\) −24.3073 −1.03272
\(555\) 47.6917 2.02440
\(556\) 35.7537 1.51629
\(557\) 34.4899 1.46138 0.730692 0.682707i \(-0.239198\pi\)
0.730692 + 0.682707i \(0.239198\pi\)
\(558\) 29.8169 1.26225
\(559\) −50.8916 −2.15249
\(560\) −69.5701 −2.93987
\(561\) 47.9763 2.02556
\(562\) 17.6377 0.744001
\(563\) −26.7370 −1.12683 −0.563415 0.826174i \(-0.690513\pi\)
−0.563415 + 0.826174i \(0.690513\pi\)
\(564\) 120.982 5.09426
\(565\) 22.4247 0.943416
\(566\) −20.6536 −0.868136
\(567\) −18.5325 −0.778292
\(568\) −55.8978 −2.34542
\(569\) 7.15467 0.299940 0.149970 0.988691i \(-0.452082\pi\)
0.149970 + 0.988691i \(0.452082\pi\)
\(570\) 76.8518 3.21897
\(571\) −42.0543 −1.75992 −0.879959 0.475049i \(-0.842430\pi\)
−0.879959 + 0.475049i \(0.842430\pi\)
\(572\) −158.554 −6.62949
\(573\) 53.5416 2.23673
\(574\) −25.7401 −1.07437
\(575\) 1.66969 0.0696310
\(576\) 90.8435 3.78515
\(577\) 22.4821 0.935943 0.467971 0.883744i \(-0.344985\pi\)
0.467971 + 0.883744i \(0.344985\pi\)
\(578\) −28.4487 −1.18331
\(579\) −29.5643 −1.22865
\(580\) −71.0426 −2.94988
\(581\) 20.1251 0.834928
\(582\) −73.6132 −3.05136
\(583\) 3.92879 0.162714
\(584\) −164.928 −6.82477
\(585\) −41.7753 −1.72720
\(586\) −31.6454 −1.30726
\(587\) 15.9550 0.658535 0.329267 0.944237i \(-0.393198\pi\)
0.329267 + 0.944237i \(0.393198\pi\)
\(588\) −49.6665 −2.04821
\(589\) −22.0866 −0.910063
\(590\) 77.5058 3.19086
\(591\) −26.2212 −1.07860
\(592\) −141.397 −5.81139
\(593\) 6.71413 0.275716 0.137858 0.990452i \(-0.455978\pi\)
0.137858 + 0.990452i \(0.455978\pi\)
\(594\) −13.6469 −0.559940
\(595\) 22.1821 0.909379
\(596\) −5.41410 −0.221770
\(597\) −27.4327 −1.12275
\(598\) −55.6949 −2.27754
\(599\) −36.7167 −1.50020 −0.750101 0.661323i \(-0.769995\pi\)
−0.750101 + 0.661323i \(0.769995\pi\)
\(600\) −13.8931 −0.567185
\(601\) 8.78601 0.358389 0.179194 0.983814i \(-0.442651\pi\)
0.179194 + 0.983814i \(0.442651\pi\)
\(602\) 35.1543 1.43278
\(603\) 9.20581 0.374890
\(604\) 5.62470 0.228866
\(605\) −10.4904 −0.426495
\(606\) 9.72851 0.395194
\(607\) −34.6363 −1.40585 −0.702923 0.711266i \(-0.748122\pi\)
−0.702923 + 0.711266i \(0.748122\pi\)
\(608\) −127.058 −5.15289
\(609\) 22.4009 0.907732
\(610\) −74.0884 −2.99975
\(611\) 66.0353 2.67150
\(612\) −72.3507 −2.92461
\(613\) 22.6588 0.915180 0.457590 0.889163i \(-0.348713\pi\)
0.457590 + 0.889163i \(0.348713\pi\)
\(614\) −32.4606 −1.31000
\(615\) −28.7067 −1.15756
\(616\) 70.5803 2.84376
\(617\) 36.3186 1.46213 0.731065 0.682307i \(-0.239023\pi\)
0.731065 + 0.682307i \(0.239023\pi\)
\(618\) −92.6098 −3.72531
\(619\) 19.2407 0.773348 0.386674 0.922216i \(-0.373624\pi\)
0.386674 + 0.922216i \(0.373624\pi\)
\(620\) 58.3539 2.34355
\(621\) −3.53630 −0.141907
\(622\) 13.9550 0.559543
\(623\) −15.9638 −0.639576
\(624\) 274.794 11.0006
\(625\) −27.6170 −1.10468
\(626\) −81.5101 −3.25780
\(627\) −46.2320 −1.84633
\(628\) −130.413 −5.20406
\(629\) 45.0839 1.79761
\(630\) 28.8571 1.14969
\(631\) 27.9064 1.11094 0.555468 0.831538i \(-0.312539\pi\)
0.555468 + 0.831538i \(0.312539\pi\)
\(632\) 33.4985 1.33250
\(633\) 24.5658 0.976404
\(634\) 96.0554 3.81485
\(635\) −11.5087 −0.456708
\(636\) −13.1451 −0.521238
\(637\) −27.1093 −1.07411
\(638\) 57.9336 2.29361
\(639\) 13.7484 0.543878
\(640\) 121.640 4.80824
\(641\) 26.8581 1.06083 0.530416 0.847737i \(-0.322036\pi\)
0.530416 + 0.847737i \(0.322036\pi\)
\(642\) −57.5542 −2.27148
\(643\) 0.470811 0.0185670 0.00928348 0.999957i \(-0.497045\pi\)
0.00928348 + 0.999957i \(0.497045\pi\)
\(644\) 28.3808 1.11836
\(645\) 39.2058 1.54373
\(646\) 72.6495 2.85836
\(647\) 39.1129 1.53769 0.768843 0.639437i \(-0.220833\pi\)
0.768843 + 0.639437i \(0.220833\pi\)
\(648\) 103.342 4.05966
\(649\) −46.6254 −1.83021
\(650\) −11.7675 −0.461558
\(651\) −18.4000 −0.721152
\(652\) −59.5864 −2.33358
\(653\) −50.1561 −1.96276 −0.981380 0.192078i \(-0.938477\pi\)
−0.981380 + 0.192078i \(0.938477\pi\)
\(654\) −50.2361 −1.96439
\(655\) −15.7161 −0.614079
\(656\) 85.1100 3.32299
\(657\) 40.5650 1.58259
\(658\) −45.6151 −1.77826
\(659\) 38.8976 1.51524 0.757618 0.652698i \(-0.226363\pi\)
0.757618 + 0.652698i \(0.226363\pi\)
\(660\) 122.147 4.75457
\(661\) 30.8760 1.20094 0.600469 0.799648i \(-0.294980\pi\)
0.600469 + 0.799648i \(0.294980\pi\)
\(662\) −55.7750 −2.16776
\(663\) −87.6169 −3.40276
\(664\) −112.222 −4.35507
\(665\) −21.3756 −0.828911
\(666\) 58.6503 2.27265
\(667\) 15.0122 0.581275
\(668\) −42.6473 −1.65007
\(669\) 20.4901 0.792192
\(670\) 24.4226 0.943528
\(671\) 44.5695 1.72059
\(672\) −105.850 −4.08325
\(673\) −31.8844 −1.22905 −0.614526 0.788896i \(-0.710653\pi\)
−0.614526 + 0.788896i \(0.710653\pi\)
\(674\) −48.0611 −1.85125
\(675\) −0.747165 −0.0287584
\(676\) 216.440 8.32460
\(677\) 15.1325 0.581587 0.290794 0.956786i \(-0.406081\pi\)
0.290794 + 0.956786i \(0.406081\pi\)
\(678\) 61.1850 2.34979
\(679\) 20.4748 0.785751
\(680\) −123.693 −4.74342
\(681\) 27.4074 1.05025
\(682\) −47.5862 −1.82217
\(683\) 7.29998 0.279326 0.139663 0.990199i \(-0.455398\pi\)
0.139663 + 0.990199i \(0.455398\pi\)
\(684\) 69.7201 2.66582
\(685\) 15.9929 0.611058
\(686\) 53.4200 2.03958
\(687\) 16.6986 0.637090
\(688\) −116.238 −4.43154
\(689\) −7.17497 −0.273345
\(690\) 42.9062 1.63341
\(691\) 21.4149 0.814661 0.407330 0.913281i \(-0.366460\pi\)
0.407330 + 0.913281i \(0.366460\pi\)
\(692\) −19.4134 −0.737988
\(693\) −17.3596 −0.659438
\(694\) −63.9688 −2.42822
\(695\) −15.0342 −0.570280
\(696\) −124.913 −4.73483
\(697\) −27.1369 −1.02789
\(698\) 20.5711 0.778629
\(699\) −11.1891 −0.423211
\(700\) 5.99642 0.226644
\(701\) 13.1337 0.496054 0.248027 0.968753i \(-0.420218\pi\)
0.248027 + 0.968753i \(0.420218\pi\)
\(702\) 24.9228 0.940649
\(703\) −43.4447 −1.63855
\(704\) −144.981 −5.46419
\(705\) −50.8722 −1.91596
\(706\) 70.1073 2.63852
\(707\) −2.70589 −0.101766
\(708\) 156.001 5.86288
\(709\) 16.7147 0.627735 0.313868 0.949467i \(-0.398375\pi\)
0.313868 + 0.949467i \(0.398375\pi\)
\(710\) 36.4739 1.36884
\(711\) −8.23915 −0.308992
\(712\) 89.0182 3.33610
\(713\) −12.3309 −0.461796
\(714\) 60.5230 2.26502
\(715\) 66.6712 2.49336
\(716\) 72.5075 2.70973
\(717\) −11.3874 −0.425271
\(718\) 14.4079 0.537699
\(719\) −8.02992 −0.299466 −0.149733 0.988726i \(-0.547841\pi\)
−0.149733 + 0.988726i \(0.547841\pi\)
\(720\) −95.4162 −3.55595
\(721\) 25.7586 0.959299
\(722\) −17.5436 −0.652904
\(723\) −36.9381 −1.37374
\(724\) −101.821 −3.78416
\(725\) 3.17185 0.117799
\(726\) −28.6226 −1.06228
\(727\) −17.1457 −0.635898 −0.317949 0.948108i \(-0.602994\pi\)
−0.317949 + 0.948108i \(0.602994\pi\)
\(728\) −128.898 −4.77726
\(729\) −16.5979 −0.614737
\(730\) 107.617 3.98309
\(731\) 37.0620 1.37079
\(732\) −149.123 −5.51174
\(733\) −35.5926 −1.31464 −0.657321 0.753610i \(-0.728311\pi\)
−0.657321 + 0.753610i \(0.728311\pi\)
\(734\) 42.9437 1.58508
\(735\) 20.8845 0.770335
\(736\) −70.9363 −2.61475
\(737\) −14.6920 −0.541186
\(738\) −35.3029 −1.29952
\(739\) 29.2693 1.07669 0.538344 0.842725i \(-0.319050\pi\)
0.538344 + 0.842725i \(0.319050\pi\)
\(740\) 114.783 4.21950
\(741\) 84.4313 3.10166
\(742\) 4.95624 0.181949
\(743\) 40.4073 1.48240 0.741200 0.671284i \(-0.234257\pi\)
0.741200 + 0.671284i \(0.234257\pi\)
\(744\) 102.603 3.76161
\(745\) 2.27660 0.0834081
\(746\) −8.75464 −0.320530
\(747\) 27.6017 1.00990
\(748\) 115.468 4.22192
\(749\) 16.0081 0.584925
\(750\) −67.2489 −2.45558
\(751\) 5.98975 0.218569 0.109285 0.994011i \(-0.465144\pi\)
0.109285 + 0.994011i \(0.465144\pi\)
\(752\) 150.827 5.50009
\(753\) −17.1762 −0.625935
\(754\) −105.801 −3.85306
\(755\) −2.36515 −0.0860768
\(756\) −12.7000 −0.461896
\(757\) 5.32614 0.193582 0.0967909 0.995305i \(-0.469142\pi\)
0.0967909 + 0.995305i \(0.469142\pi\)
\(758\) −77.6453 −2.82020
\(759\) −25.8112 −0.936888
\(760\) 119.196 4.32369
\(761\) −28.4337 −1.03072 −0.515360 0.856974i \(-0.672342\pi\)
−0.515360 + 0.856974i \(0.672342\pi\)
\(762\) −31.4010 −1.13754
\(763\) 13.9727 0.505846
\(764\) 128.862 4.66207
\(765\) 30.4231 1.09995
\(766\) −2.84372 −0.102748
\(767\) 85.1498 3.07458
\(768\) 159.405 5.75204
\(769\) −18.4136 −0.664012 −0.332006 0.943277i \(-0.607725\pi\)
−0.332006 + 0.943277i \(0.607725\pi\)
\(770\) −46.0544 −1.65968
\(771\) 43.9792 1.58387
\(772\) −71.1544 −2.56090
\(773\) −4.33310 −0.155851 −0.0779255 0.996959i \(-0.524830\pi\)
−0.0779255 + 0.996959i \(0.524830\pi\)
\(774\) 48.2145 1.73304
\(775\) −2.60533 −0.0935863
\(776\) −114.173 −4.09857
\(777\) −36.1930 −1.29842
\(778\) 18.3114 0.656497
\(779\) 26.1503 0.936931
\(780\) −223.071 −7.98724
\(781\) −21.9417 −0.785135
\(782\) 40.5601 1.45043
\(783\) −6.71776 −0.240073
\(784\) −61.9186 −2.21138
\(785\) 54.8380 1.95725
\(786\) −42.8807 −1.52950
\(787\) 37.5204 1.33746 0.668728 0.743507i \(-0.266839\pi\)
0.668728 + 0.743507i \(0.266839\pi\)
\(788\) −63.1085 −2.24815
\(789\) 38.3266 1.36446
\(790\) −21.8581 −0.777677
\(791\) −17.0180 −0.605091
\(792\) 96.8017 3.43970
\(793\) −81.3953 −2.89043
\(794\) −70.1147 −2.48828
\(795\) 5.52745 0.196038
\(796\) −66.0241 −2.34016
\(797\) −19.0892 −0.676172 −0.338086 0.941115i \(-0.609780\pi\)
−0.338086 + 0.941115i \(0.609780\pi\)
\(798\) −58.3225 −2.06459
\(799\) −48.0905 −1.70132
\(800\) −14.9877 −0.529897
\(801\) −21.8945 −0.773605
\(802\) 24.1885 0.854127
\(803\) −64.7396 −2.28461
\(804\) 49.1571 1.73364
\(805\) −11.9340 −0.420617
\(806\) 86.9045 3.06108
\(807\) 61.0273 2.14826
\(808\) 15.0888 0.530821
\(809\) −32.7474 −1.15134 −0.575669 0.817683i \(-0.695258\pi\)
−0.575669 + 0.817683i \(0.695258\pi\)
\(810\) −67.4317 −2.36931
\(811\) −11.2508 −0.395070 −0.197535 0.980296i \(-0.563294\pi\)
−0.197535 + 0.980296i \(0.563294\pi\)
\(812\) 53.9139 1.89201
\(813\) 69.2194 2.42763
\(814\) −93.6027 −3.28077
\(815\) 25.0557 0.877664
\(816\) −200.120 −7.00560
\(817\) −35.7145 −1.24949
\(818\) 6.77067 0.236731
\(819\) 31.7031 1.10780
\(820\) −69.0903 −2.41274
\(821\) 15.8790 0.554180 0.277090 0.960844i \(-0.410630\pi\)
0.277090 + 0.960844i \(0.410630\pi\)
\(822\) 43.6360 1.52198
\(823\) −27.1915 −0.947837 −0.473918 0.880569i \(-0.657161\pi\)
−0.473918 + 0.880569i \(0.657161\pi\)
\(824\) −143.636 −5.00381
\(825\) −5.45351 −0.189867
\(826\) −58.8188 −2.04657
\(827\) −31.0013 −1.07802 −0.539011 0.842299i \(-0.681202\pi\)
−0.539011 + 0.842299i \(0.681202\pi\)
\(828\) 38.9246 1.35272
\(829\) 22.2474 0.772684 0.386342 0.922356i \(-0.373739\pi\)
0.386342 + 0.922356i \(0.373739\pi\)
\(830\) 73.2263 2.54172
\(831\) 20.5726 0.713656
\(832\) 264.773 9.17935
\(833\) 19.7425 0.684037
\(834\) −41.0202 −1.42041
\(835\) 17.9329 0.620595
\(836\) −111.270 −3.84834
\(837\) 5.51792 0.190727
\(838\) −42.7282 −1.47602
\(839\) 24.5429 0.847314 0.423657 0.905823i \(-0.360746\pi\)
0.423657 + 0.905823i \(0.360746\pi\)
\(840\) 99.3000 3.42618
\(841\) −0.481922 −0.0166180
\(842\) −30.1936 −1.04054
\(843\) −14.9278 −0.514140
\(844\) 59.1243 2.03514
\(845\) −91.0116 −3.13089
\(846\) −62.5616 −2.15091
\(847\) 7.96111 0.273547
\(848\) −16.3879 −0.562762
\(849\) 17.4803 0.599924
\(850\) 8.56971 0.293939
\(851\) −24.2551 −0.831453
\(852\) 73.4135 2.51510
\(853\) −47.2614 −1.61820 −0.809100 0.587672i \(-0.800045\pi\)
−0.809100 + 0.587672i \(0.800045\pi\)
\(854\) 56.2253 1.92399
\(855\) −29.3169 −1.00262
\(856\) −89.2655 −3.05103
\(857\) 30.9901 1.05860 0.529300 0.848435i \(-0.322455\pi\)
0.529300 + 0.848435i \(0.322455\pi\)
\(858\) 181.910 6.21029
\(859\) 13.6456 0.465582 0.232791 0.972527i \(-0.425214\pi\)
0.232791 + 0.972527i \(0.425214\pi\)
\(860\) 94.3594 3.21763
\(861\) 21.7853 0.742442
\(862\) 59.4345 2.02435
\(863\) 29.3074 0.997635 0.498818 0.866707i \(-0.333768\pi\)
0.498818 + 0.866707i \(0.333768\pi\)
\(864\) 31.7431 1.07992
\(865\) 8.16323 0.277558
\(866\) −14.8686 −0.505256
\(867\) 24.0778 0.817725
\(868\) −44.2845 −1.50311
\(869\) 13.1492 0.446058
\(870\) 81.5072 2.76335
\(871\) 26.8313 0.909143
\(872\) −77.9154 −2.63855
\(873\) 28.0815 0.950413
\(874\) −39.0853 −1.32208
\(875\) 18.7046 0.632333
\(876\) 216.609 7.31853
\(877\) 49.0892 1.65763 0.828813 0.559526i \(-0.189017\pi\)
0.828813 + 0.559526i \(0.189017\pi\)
\(878\) −23.0241 −0.777026
\(879\) 26.7833 0.903379
\(880\) 152.279 5.13333
\(881\) 22.6078 0.761675 0.380838 0.924642i \(-0.375636\pi\)
0.380838 + 0.924642i \(0.375636\pi\)
\(882\) 25.6833 0.864802
\(883\) 49.0082 1.64926 0.824628 0.565675i \(-0.191384\pi\)
0.824628 + 0.565675i \(0.191384\pi\)
\(884\) −210.874 −7.09245
\(885\) −65.5976 −2.20504
\(886\) −46.8816 −1.57502
\(887\) −19.3206 −0.648724 −0.324362 0.945933i \(-0.605150\pi\)
−0.324362 + 0.945933i \(0.605150\pi\)
\(888\) 201.821 6.77268
\(889\) 8.73388 0.292925
\(890\) −58.0853 −1.94702
\(891\) 40.5651 1.35898
\(892\) 49.3148 1.65118
\(893\) 46.3420 1.55077
\(894\) 6.21160 0.207747
\(895\) −30.4890 −1.01913
\(896\) −92.3119 −3.08392
\(897\) 47.1378 1.57389
\(898\) −37.7604 −1.26008
\(899\) −23.4245 −0.781252
\(900\) 8.22417 0.274139
\(901\) 5.22520 0.174077
\(902\) 56.3415 1.87597
\(903\) −29.7531 −0.990121
\(904\) 94.8969 3.15622
\(905\) 42.8152 1.42323
\(906\) −6.45322 −0.214394
\(907\) 19.2189 0.638153 0.319076 0.947729i \(-0.396627\pi\)
0.319076 + 0.947729i \(0.396627\pi\)
\(908\) 65.9632 2.18907
\(909\) −3.71117 −0.123092
\(910\) 84.1070 2.78812
\(911\) 35.0012 1.15964 0.579821 0.814744i \(-0.303122\pi\)
0.579821 + 0.814744i \(0.303122\pi\)
\(912\) 192.844 6.38570
\(913\) −44.0509 −1.45787
\(914\) −86.3493 −2.85618
\(915\) 62.7052 2.07297
\(916\) 40.1895 1.32790
\(917\) 11.9269 0.393860
\(918\) −18.1501 −0.599042
\(919\) 48.5539 1.60165 0.800823 0.598901i \(-0.204396\pi\)
0.800823 + 0.598901i \(0.204396\pi\)
\(920\) 66.5468 2.19398
\(921\) 27.4733 0.905276
\(922\) 5.32232 0.175281
\(923\) 40.0711 1.31896
\(924\) −92.6968 −3.04950
\(925\) −5.12472 −0.168500
\(926\) −28.9037 −0.949833
\(927\) 35.3282 1.16033
\(928\) −134.755 −4.42355
\(929\) −9.62734 −0.315863 −0.157931 0.987450i \(-0.550482\pi\)
−0.157931 + 0.987450i \(0.550482\pi\)
\(930\) −66.9494 −2.19536
\(931\) −19.0247 −0.623508
\(932\) −26.9296 −0.882109
\(933\) −11.8109 −0.386671
\(934\) 95.1579 3.11366
\(935\) −48.5536 −1.58787
\(936\) −176.785 −5.77838
\(937\) 15.3328 0.500902 0.250451 0.968129i \(-0.419421\pi\)
0.250451 + 0.968129i \(0.419421\pi\)
\(938\) −18.5342 −0.605163
\(939\) 68.9866 2.25129
\(940\) −122.438 −3.99348
\(941\) −31.6146 −1.03061 −0.515303 0.857008i \(-0.672321\pi\)
−0.515303 + 0.857008i \(0.672321\pi\)
\(942\) 149.623 4.87499
\(943\) 14.5997 0.475430
\(944\) 194.485 6.32994
\(945\) 5.34029 0.173720
\(946\) −76.9478 −2.50179
\(947\) 54.4648 1.76987 0.884934 0.465717i \(-0.154203\pi\)
0.884934 + 0.465717i \(0.154203\pi\)
\(948\) −43.9953 −1.42890
\(949\) 118.231 3.83794
\(950\) −8.25813 −0.267929
\(951\) −81.2972 −2.63624
\(952\) 93.8702 3.04235
\(953\) −46.5677 −1.50848 −0.754238 0.656601i \(-0.771993\pi\)
−0.754238 + 0.656601i \(0.771993\pi\)
\(954\) 6.79754 0.220079
\(955\) −54.1858 −1.75341
\(956\) −27.4069 −0.886401
\(957\) −49.0325 −1.58500
\(958\) −25.3975 −0.820556
\(959\) −12.1369 −0.391922
\(960\) −203.976 −6.58328
\(961\) −11.7592 −0.379331
\(962\) 170.942 5.51140
\(963\) 21.9554 0.707502
\(964\) −88.9015 −2.86332
\(965\) 29.9200 0.963159
\(966\) −32.5613 −1.04764
\(967\) 35.9410 1.15578 0.577892 0.816113i \(-0.303876\pi\)
0.577892 + 0.816113i \(0.303876\pi\)
\(968\) −44.3932 −1.42685
\(969\) −61.4874 −1.97526
\(970\) 74.4989 2.39202
\(971\) 45.0837 1.44681 0.723403 0.690426i \(-0.242577\pi\)
0.723403 + 0.690426i \(0.242577\pi\)
\(972\) −114.498 −3.67251
\(973\) 11.4094 0.365768
\(974\) 63.7667 2.04322
\(975\) 9.95949 0.318959
\(976\) −185.910 −5.95082
\(977\) −9.74460 −0.311757 −0.155879 0.987776i \(-0.549821\pi\)
−0.155879 + 0.987776i \(0.549821\pi\)
\(978\) 68.3635 2.18602
\(979\) 34.9425 1.11677
\(980\) 50.2641 1.60563
\(981\) 19.1637 0.611851
\(982\) −3.58931 −0.114540
\(983\) 27.2791 0.870069 0.435034 0.900414i \(-0.356736\pi\)
0.435034 + 0.900414i \(0.356736\pi\)
\(984\) −121.481 −3.87266
\(985\) 26.5367 0.845531
\(986\) 77.0503 2.45378
\(987\) 38.6067 1.22886
\(988\) 203.207 6.46486
\(989\) −19.9393 −0.634034
\(990\) −63.1641 −2.00749
\(991\) −17.3512 −0.551180 −0.275590 0.961275i \(-0.588873\pi\)
−0.275590 + 0.961275i \(0.588873\pi\)
\(992\) 110.687 3.51431
\(993\) 47.2056 1.49802
\(994\) −27.6798 −0.877951
\(995\) 27.7628 0.880139
\(996\) 147.387 4.67015
\(997\) −60.2153 −1.90704 −0.953518 0.301335i \(-0.902568\pi\)
−0.953518 + 0.301335i \(0.902568\pi\)
\(998\) 96.7408 3.06228
\(999\) 10.8538 0.343400
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 \(a_p\))