Properties

Label 8003.2.a.c.1.4
Level 8003
Weight 2
Character 8003.1
Self dual Yes
Analytic conductor 63.904
Analytic rank 0
Dimension 172
CM No

Related objects

Downloads

Learn more about

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 1.4
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.74848 q^{2}\) \(+0.238468 q^{3}\) \(+5.55414 q^{4}\) \(-0.412520 q^{5}\) \(-0.655426 q^{6}\) \(-2.19155 q^{7}\) \(-9.76848 q^{8}\) \(-2.94313 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.74848 q^{2}\) \(+0.238468 q^{3}\) \(+5.55414 q^{4}\) \(-0.412520 q^{5}\) \(-0.655426 q^{6}\) \(-2.19155 q^{7}\) \(-9.76848 q^{8}\) \(-2.94313 q^{9}\) \(+1.13380 q^{10}\) \(-2.64065 q^{11}\) \(+1.32449 q^{12}\) \(+3.93402 q^{13}\) \(+6.02344 q^{14}\) \(-0.0983731 q^{15}\) \(+15.7402 q^{16}\) \(-5.33110 q^{17}\) \(+8.08914 q^{18}\) \(-1.03684 q^{19}\) \(-2.29119 q^{20}\) \(-0.522616 q^{21}\) \(+7.25777 q^{22}\) \(+1.82853 q^{23}\) \(-2.32947 q^{24}\) \(-4.82983 q^{25}\) \(-10.8126 q^{26}\) \(-1.41725 q^{27}\) \(-12.1722 q^{28}\) \(+0.842287 q^{29}\) \(+0.270376 q^{30}\) \(+1.06010 q^{31}\) \(-23.7246 q^{32}\) \(-0.629712 q^{33}\) \(+14.6524 q^{34}\) \(+0.904060 q^{35}\) \(-16.3466 q^{36}\) \(+8.32535 q^{37}\) \(+2.84974 q^{38}\) \(+0.938141 q^{39}\) \(+4.02969 q^{40}\) \(-3.45194 q^{41}\) \(+1.43640 q^{42}\) \(+7.74054 q^{43}\) \(-14.6665 q^{44}\) \(+1.21410 q^{45}\) \(-5.02567 q^{46}\) \(-12.4113 q^{47}\) \(+3.75354 q^{48}\) \(-2.19710 q^{49}\) \(+13.2747 q^{50}\) \(-1.27130 q^{51}\) \(+21.8501 q^{52}\) \(-1.00000 q^{53}\) \(+3.89528 q^{54}\) \(+1.08932 q^{55}\) \(+21.4081 q^{56}\) \(-0.247255 q^{57}\) \(-2.31501 q^{58}\) \(-1.21403 q^{59}\) \(-0.546378 q^{60}\) \(-5.39749 q^{61}\) \(-2.91367 q^{62}\) \(+6.45003 q^{63}\) \(+33.7263 q^{64}\) \(-1.62286 q^{65}\) \(+1.73075 q^{66}\) \(+14.2947 q^{67}\) \(-29.6097 q^{68}\) \(+0.436046 q^{69}\) \(-2.48479 q^{70}\) \(+1.48424 q^{71}\) \(+28.7499 q^{72}\) \(-16.8540 q^{73}\) \(-22.8821 q^{74}\) \(-1.15176 q^{75}\) \(-5.75878 q^{76}\) \(+5.78712 q^{77}\) \(-2.57846 q^{78}\) \(-1.41339 q^{79}\) \(-6.49314 q^{80}\) \(+8.49143 q^{81}\) \(+9.48758 q^{82}\) \(-12.6163 q^{83}\) \(-2.90268 q^{84}\) \(+2.19919 q^{85}\) \(-21.2747 q^{86}\) \(+0.200859 q^{87}\) \(+25.7951 q^{88}\) \(-4.55754 q^{89}\) \(-3.33693 q^{90}\) \(-8.62162 q^{91}\) \(+10.1559 q^{92}\) \(+0.252801 q^{93}\) \(+34.1122 q^{94}\) \(+0.427719 q^{95}\) \(-5.65757 q^{96}\) \(-3.08528 q^{97}\) \(+6.03867 q^{98}\) \(+7.77178 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.74848 −1.94347 −0.971734 0.236077i \(-0.924138\pi\)
−0.971734 + 0.236077i \(0.924138\pi\)
\(3\) 0.238468 0.137680 0.0688399 0.997628i \(-0.478070\pi\)
0.0688399 + 0.997628i \(0.478070\pi\)
\(4\) 5.55414 2.77707
\(5\) −0.412520 −0.184485 −0.0922423 0.995737i \(-0.529403\pi\)
−0.0922423 + 0.995737i \(0.529403\pi\)
\(6\) −0.655426 −0.267576
\(7\) −2.19155 −0.828329 −0.414165 0.910202i \(-0.635926\pi\)
−0.414165 + 0.910202i \(0.635926\pi\)
\(8\) −9.76848 −3.45368
\(9\) −2.94313 −0.981044
\(10\) 1.13380 0.358540
\(11\) −2.64065 −0.796186 −0.398093 0.917345i \(-0.630328\pi\)
−0.398093 + 0.917345i \(0.630328\pi\)
\(12\) 1.32449 0.382346
\(13\) 3.93402 1.09110 0.545551 0.838078i \(-0.316320\pi\)
0.545551 + 0.838078i \(0.316320\pi\)
\(14\) 6.02344 1.60983
\(15\) −0.0983731 −0.0253998
\(16\) 15.7402 3.93505
\(17\) −5.33110 −1.29298 −0.646491 0.762921i \(-0.723764\pi\)
−0.646491 + 0.762921i \(0.723764\pi\)
\(18\) 8.08914 1.90663
\(19\) −1.03684 −0.237868 −0.118934 0.992902i \(-0.537948\pi\)
−0.118934 + 0.992902i \(0.537948\pi\)
\(20\) −2.29119 −0.512327
\(21\) −0.522616 −0.114044
\(22\) 7.25777 1.54736
\(23\) 1.82853 0.381274 0.190637 0.981661i \(-0.438945\pi\)
0.190637 + 0.981661i \(0.438945\pi\)
\(24\) −2.32947 −0.475502
\(25\) −4.82983 −0.965965
\(26\) −10.8126 −2.12052
\(27\) −1.41725 −0.272750
\(28\) −12.1722 −2.30033
\(29\) 0.842287 0.156409 0.0782044 0.996937i \(-0.475081\pi\)
0.0782044 + 0.996937i \(0.475081\pi\)
\(30\) 0.270376 0.0493637
\(31\) 1.06010 0.190400 0.0952000 0.995458i \(-0.469651\pi\)
0.0952000 + 0.995458i \(0.469651\pi\)
\(32\) −23.7246 −4.19396
\(33\) −0.629712 −0.109619
\(34\) 14.6524 2.51287
\(35\) 0.904060 0.152814
\(36\) −16.3466 −2.72443
\(37\) 8.32535 1.36868 0.684340 0.729164i \(-0.260091\pi\)
0.684340 + 0.729164i \(0.260091\pi\)
\(38\) 2.84974 0.462290
\(39\) 0.938141 0.150223
\(40\) 4.02969 0.637151
\(41\) −3.45194 −0.539102 −0.269551 0.962986i \(-0.586875\pi\)
−0.269551 + 0.962986i \(0.586875\pi\)
\(42\) 1.43640 0.221641
\(43\) 7.74054 1.18042 0.590211 0.807249i \(-0.299045\pi\)
0.590211 + 0.807249i \(0.299045\pi\)
\(44\) −14.6665 −2.21106
\(45\) 1.21410 0.180988
\(46\) −5.02567 −0.740995
\(47\) −12.4113 −1.81037 −0.905186 0.425015i \(-0.860269\pi\)
−0.905186 + 0.425015i \(0.860269\pi\)
\(48\) 3.75354 0.541777
\(49\) −2.19710 −0.313871
\(50\) 13.2747 1.87732
\(51\) −1.27130 −0.178018
\(52\) 21.8501 3.03007
\(53\) −1.00000 −0.137361
\(54\) 3.89528 0.530081
\(55\) 1.08932 0.146884
\(56\) 21.4081 2.86078
\(57\) −0.247255 −0.0327497
\(58\) −2.31501 −0.303975
\(59\) −1.21403 −0.158053 −0.0790263 0.996873i \(-0.525181\pi\)
−0.0790263 + 0.996873i \(0.525181\pi\)
\(60\) −0.546378 −0.0705371
\(61\) −5.39749 −0.691078 −0.345539 0.938404i \(-0.612304\pi\)
−0.345539 + 0.938404i \(0.612304\pi\)
\(62\) −2.91367 −0.370037
\(63\) 6.45003 0.812627
\(64\) 33.7263 4.21578
\(65\) −1.62286 −0.201292
\(66\) 1.73075 0.213041
\(67\) 14.2947 1.74638 0.873188 0.487383i \(-0.162049\pi\)
0.873188 + 0.487383i \(0.162049\pi\)
\(68\) −29.6097 −3.59070
\(69\) 0.436046 0.0524938
\(70\) −2.48479 −0.296989
\(71\) 1.48424 0.176147 0.0880734 0.996114i \(-0.471929\pi\)
0.0880734 + 0.996114i \(0.471929\pi\)
\(72\) 28.7499 3.38821
\(73\) −16.8540 −1.97261 −0.986304 0.164938i \(-0.947257\pi\)
−0.986304 + 0.164938i \(0.947257\pi\)
\(74\) −22.8821 −2.65998
\(75\) −1.15176 −0.132994
\(76\) −5.75878 −0.660577
\(77\) 5.78712 0.659504
\(78\) −2.57846 −0.291953
\(79\) −1.41339 −0.159019 −0.0795093 0.996834i \(-0.525335\pi\)
−0.0795093 + 0.996834i \(0.525335\pi\)
\(80\) −6.49314 −0.725956
\(81\) 8.49143 0.943492
\(82\) 9.48758 1.04773
\(83\) −12.6163 −1.38482 −0.692410 0.721504i \(-0.743451\pi\)
−0.692410 + 0.721504i \(0.743451\pi\)
\(84\) −2.90268 −0.316709
\(85\) 2.19919 0.238535
\(86\) −21.2747 −2.29411
\(87\) 0.200859 0.0215343
\(88\) 25.7951 2.74977
\(89\) −4.55754 −0.483099 −0.241549 0.970389i \(-0.577656\pi\)
−0.241549 + 0.970389i \(0.577656\pi\)
\(90\) −3.33693 −0.351744
\(91\) −8.62162 −0.903791
\(92\) 10.1559 1.05883
\(93\) 0.252801 0.0262143
\(94\) 34.1122 3.51840
\(95\) 0.427719 0.0438831
\(96\) −5.65757 −0.577424
\(97\) −3.08528 −0.313263 −0.156631 0.987657i \(-0.550063\pi\)
−0.156631 + 0.987657i \(0.550063\pi\)
\(98\) 6.03867 0.609998
\(99\) 7.77178 0.781094
\(100\) −26.8255 −2.68255
\(101\) 5.33388 0.530741 0.265371 0.964146i \(-0.414506\pi\)
0.265371 + 0.964146i \(0.414506\pi\)
\(102\) 3.49414 0.345972
\(103\) −17.0550 −1.68048 −0.840240 0.542214i \(-0.817586\pi\)
−0.840240 + 0.542214i \(0.817586\pi\)
\(104\) −38.4294 −3.76832
\(105\) 0.215590 0.0210394
\(106\) 2.74848 0.266956
\(107\) −3.80411 −0.367757 −0.183879 0.982949i \(-0.558865\pi\)
−0.183879 + 0.982949i \(0.558865\pi\)
\(108\) −7.87160 −0.757445
\(109\) −10.4944 −1.00518 −0.502592 0.864523i \(-0.667620\pi\)
−0.502592 + 0.864523i \(0.667620\pi\)
\(110\) −2.99398 −0.285465
\(111\) 1.98533 0.188440
\(112\) −34.4954 −3.25951
\(113\) −8.16366 −0.767973 −0.383986 0.923339i \(-0.625449\pi\)
−0.383986 + 0.923339i \(0.625449\pi\)
\(114\) 0.679574 0.0636480
\(115\) −0.754305 −0.0703393
\(116\) 4.67818 0.434358
\(117\) −11.5784 −1.07042
\(118\) 3.33672 0.307170
\(119\) 11.6834 1.07101
\(120\) 0.960955 0.0877228
\(121\) −4.02697 −0.366088
\(122\) 14.8349 1.34309
\(123\) −0.823178 −0.0742235
\(124\) 5.88796 0.528754
\(125\) 4.05500 0.362690
\(126\) −17.7278 −1.57932
\(127\) −20.4811 −1.81741 −0.908703 0.417443i \(-0.862926\pi\)
−0.908703 + 0.417443i \(0.862926\pi\)
\(128\) −45.2467 −3.99928
\(129\) 1.84587 0.162520
\(130\) 4.46041 0.391204
\(131\) −9.85467 −0.861007 −0.430503 0.902589i \(-0.641664\pi\)
−0.430503 + 0.902589i \(0.641664\pi\)
\(132\) −3.49751 −0.304419
\(133\) 2.27230 0.197033
\(134\) −39.2887 −3.39403
\(135\) 0.584644 0.0503182
\(136\) 52.0768 4.46555
\(137\) 14.5623 1.24414 0.622069 0.782962i \(-0.286292\pi\)
0.622069 + 0.782962i \(0.286292\pi\)
\(138\) −1.19846 −0.102020
\(139\) −12.1199 −1.02800 −0.513999 0.857791i \(-0.671837\pi\)
−0.513999 + 0.857791i \(0.671837\pi\)
\(140\) 5.02127 0.424375
\(141\) −2.95970 −0.249252
\(142\) −4.07940 −0.342336
\(143\) −10.3884 −0.868720
\(144\) −46.3255 −3.86045
\(145\) −0.347460 −0.0288550
\(146\) 46.3228 3.83370
\(147\) −0.523938 −0.0432137
\(148\) 46.2402 3.80092
\(149\) −20.8172 −1.70541 −0.852707 0.522389i \(-0.825041\pi\)
−0.852707 + 0.522389i \(0.825041\pi\)
\(150\) 3.16559 0.258470
\(151\) 1.00000 0.0813788
\(152\) 10.1284 0.821521
\(153\) 15.6901 1.26847
\(154\) −15.9058 −1.28173
\(155\) −0.437314 −0.0351259
\(156\) 5.21056 0.417179
\(157\) −0.0650482 −0.00519141 −0.00259571 0.999997i \(-0.500826\pi\)
−0.00259571 + 0.999997i \(0.500826\pi\)
\(158\) 3.88467 0.309047
\(159\) −0.238468 −0.0189118
\(160\) 9.78688 0.773721
\(161\) −4.00732 −0.315821
\(162\) −23.3385 −1.83365
\(163\) 21.2262 1.66257 0.831283 0.555850i \(-0.187607\pi\)
0.831283 + 0.555850i \(0.187607\pi\)
\(164\) −19.1725 −1.49712
\(165\) 0.259769 0.0202230
\(166\) 34.6757 2.69135
\(167\) 21.9854 1.70128 0.850639 0.525750i \(-0.176215\pi\)
0.850639 + 0.525750i \(0.176215\pi\)
\(168\) 5.10517 0.393872
\(169\) 2.47654 0.190503
\(170\) −6.04442 −0.463586
\(171\) 3.05157 0.233359
\(172\) 42.9920 3.27811
\(173\) −2.58642 −0.196642 −0.0983208 0.995155i \(-0.531347\pi\)
−0.0983208 + 0.995155i \(0.531347\pi\)
\(174\) −0.552056 −0.0418513
\(175\) 10.5848 0.800137
\(176\) −41.5643 −3.13303
\(177\) −0.289507 −0.0217607
\(178\) 12.5263 0.938887
\(179\) 5.69131 0.425388 0.212694 0.977119i \(-0.431776\pi\)
0.212694 + 0.977119i \(0.431776\pi\)
\(180\) 6.74329 0.502615
\(181\) −1.47326 −0.109507 −0.0547534 0.998500i \(-0.517437\pi\)
−0.0547534 + 0.998500i \(0.517437\pi\)
\(182\) 23.6963 1.75649
\(183\) −1.28713 −0.0951475
\(184\) −17.8619 −1.31680
\(185\) −3.43437 −0.252500
\(186\) −0.694819 −0.0509466
\(187\) 14.0776 1.02945
\(188\) −68.9340 −5.02753
\(189\) 3.10598 0.225927
\(190\) −1.17558 −0.0852853
\(191\) −12.8033 −0.926414 −0.463207 0.886250i \(-0.653301\pi\)
−0.463207 + 0.886250i \(0.653301\pi\)
\(192\) 8.04265 0.580428
\(193\) −21.2051 −1.52637 −0.763187 0.646177i \(-0.776367\pi\)
−0.763187 + 0.646177i \(0.776367\pi\)
\(194\) 8.47982 0.608816
\(195\) −0.387002 −0.0277138
\(196\) −12.2030 −0.871641
\(197\) 25.0498 1.78473 0.892363 0.451317i \(-0.149046\pi\)
0.892363 + 0.451317i \(0.149046\pi\)
\(198\) −21.3606 −1.51803
\(199\) −5.99756 −0.425156 −0.212578 0.977144i \(-0.568186\pi\)
−0.212578 + 0.977144i \(0.568186\pi\)
\(200\) 47.1801 3.33613
\(201\) 3.40884 0.240441
\(202\) −14.6601 −1.03148
\(203\) −1.84592 −0.129558
\(204\) −7.06098 −0.494367
\(205\) 1.42399 0.0994560
\(206\) 46.8754 3.26596
\(207\) −5.38160 −0.374047
\(208\) 61.9223 4.29354
\(209\) 2.73794 0.189387
\(210\) −0.592544 −0.0408894
\(211\) −0.935467 −0.0644002 −0.0322001 0.999481i \(-0.510251\pi\)
−0.0322001 + 0.999481i \(0.510251\pi\)
\(212\) −5.55414 −0.381460
\(213\) 0.353944 0.0242519
\(214\) 10.4555 0.714724
\(215\) −3.19313 −0.217770
\(216\) 13.8444 0.941990
\(217\) −2.32327 −0.157714
\(218\) 28.8437 1.95355
\(219\) −4.01914 −0.271588
\(220\) 6.05024 0.407907
\(221\) −20.9727 −1.41078
\(222\) −5.45665 −0.366226
\(223\) 28.1042 1.88200 0.940999 0.338409i \(-0.109889\pi\)
0.940999 + 0.338409i \(0.109889\pi\)
\(224\) 51.9938 3.47398
\(225\) 14.2148 0.947655
\(226\) 22.4377 1.49253
\(227\) −11.0889 −0.735994 −0.367997 0.929827i \(-0.619956\pi\)
−0.367997 + 0.929827i \(0.619956\pi\)
\(228\) −1.37329 −0.0909481
\(229\) −5.30945 −0.350858 −0.175429 0.984492i \(-0.556131\pi\)
−0.175429 + 0.984492i \(0.556131\pi\)
\(230\) 2.07319 0.136702
\(231\) 1.38005 0.0908004
\(232\) −8.22786 −0.540186
\(233\) 15.8837 1.04057 0.520287 0.853992i \(-0.325825\pi\)
0.520287 + 0.853992i \(0.325825\pi\)
\(234\) 31.8229 2.08033
\(235\) 5.11991 0.333986
\(236\) −6.74287 −0.438923
\(237\) −0.337048 −0.0218936
\(238\) −32.1116 −2.08148
\(239\) 20.7308 1.34096 0.670481 0.741926i \(-0.266088\pi\)
0.670481 + 0.741926i \(0.266088\pi\)
\(240\) −1.54841 −0.0999494
\(241\) 24.9321 1.60602 0.803009 0.595967i \(-0.203231\pi\)
0.803009 + 0.595967i \(0.203231\pi\)
\(242\) 11.0680 0.711480
\(243\) 6.27669 0.402650
\(244\) −29.9784 −1.91917
\(245\) 0.906347 0.0579044
\(246\) 2.26249 0.144251
\(247\) −4.07897 −0.259539
\(248\) −10.3556 −0.657581
\(249\) −3.00859 −0.190662
\(250\) −11.1451 −0.704877
\(251\) −7.61604 −0.480720 −0.240360 0.970684i \(-0.577266\pi\)
−0.240360 + 0.970684i \(0.577266\pi\)
\(252\) 35.8244 2.25672
\(253\) −4.82850 −0.303565
\(254\) 56.2920 3.53207
\(255\) 0.524437 0.0328415
\(256\) 56.9071 3.55669
\(257\) 23.2174 1.44826 0.724132 0.689661i \(-0.242241\pi\)
0.724132 + 0.689661i \(0.242241\pi\)
\(258\) −5.07335 −0.315853
\(259\) −18.2454 −1.13372
\(260\) −9.01361 −0.559001
\(261\) −2.47896 −0.153444
\(262\) 27.0854 1.67334
\(263\) −8.81371 −0.543477 −0.271738 0.962371i \(-0.587599\pi\)
−0.271738 + 0.962371i \(0.587599\pi\)
\(264\) 6.15133 0.378588
\(265\) 0.412520 0.0253409
\(266\) −6.24537 −0.382928
\(267\) −1.08683 −0.0665130
\(268\) 79.3948 4.84981
\(269\) −2.88827 −0.176101 −0.0880505 0.996116i \(-0.528064\pi\)
−0.0880505 + 0.996116i \(0.528064\pi\)
\(270\) −1.60688 −0.0977918
\(271\) 29.3948 1.78561 0.892804 0.450445i \(-0.148735\pi\)
0.892804 + 0.450445i \(0.148735\pi\)
\(272\) −83.9126 −5.08795
\(273\) −2.05598 −0.124434
\(274\) −40.0241 −2.41794
\(275\) 12.7539 0.769088
\(276\) 2.42186 0.145779
\(277\) 27.5132 1.65311 0.826555 0.562855i \(-0.190297\pi\)
0.826555 + 0.562855i \(0.190297\pi\)
\(278\) 33.3114 1.99788
\(279\) −3.12002 −0.186791
\(280\) −8.83129 −0.527770
\(281\) 15.4491 0.921619 0.460809 0.887499i \(-0.347559\pi\)
0.460809 + 0.887499i \(0.347559\pi\)
\(282\) 8.13468 0.484413
\(283\) 27.9123 1.65921 0.829606 0.558349i \(-0.188565\pi\)
0.829606 + 0.558349i \(0.188565\pi\)
\(284\) 8.24367 0.489172
\(285\) 0.101998 0.00604181
\(286\) 28.5523 1.68833
\(287\) 7.56510 0.446554
\(288\) 69.8247 4.11446
\(289\) 11.4207 0.671804
\(290\) 0.954988 0.0560788
\(291\) −0.735742 −0.0431299
\(292\) −93.6093 −5.47807
\(293\) −30.2037 −1.76452 −0.882261 0.470761i \(-0.843979\pi\)
−0.882261 + 0.470761i \(0.843979\pi\)
\(294\) 1.44003 0.0839845
\(295\) 0.500810 0.0291583
\(296\) −81.3260 −4.72698
\(297\) 3.74246 0.217160
\(298\) 57.2158 3.31442
\(299\) 7.19347 0.416009
\(300\) −6.39704 −0.369333
\(301\) −16.9638 −0.977777
\(302\) −2.74848 −0.158157
\(303\) 1.27196 0.0730724
\(304\) −16.3201 −0.936023
\(305\) 2.22657 0.127493
\(306\) −43.1240 −2.46524
\(307\) −20.6567 −1.17894 −0.589471 0.807790i \(-0.700664\pi\)
−0.589471 + 0.807790i \(0.700664\pi\)
\(308\) 32.1425 1.83149
\(309\) −4.06708 −0.231368
\(310\) 1.20195 0.0682661
\(311\) 22.7889 1.29224 0.646121 0.763235i \(-0.276390\pi\)
0.646121 + 0.763235i \(0.276390\pi\)
\(312\) −9.16421 −0.518821
\(313\) 16.7220 0.945185 0.472593 0.881281i \(-0.343318\pi\)
0.472593 + 0.881281i \(0.343318\pi\)
\(314\) 0.178784 0.0100894
\(315\) −2.66077 −0.149917
\(316\) −7.85015 −0.441605
\(317\) −1.93173 −0.108497 −0.0542484 0.998527i \(-0.517276\pi\)
−0.0542484 + 0.998527i \(0.517276\pi\)
\(318\) 0.655426 0.0367544
\(319\) −2.22419 −0.124530
\(320\) −13.9128 −0.777747
\(321\) −0.907160 −0.0506327
\(322\) 11.0140 0.613788
\(323\) 5.52752 0.307560
\(324\) 47.1626 2.62014
\(325\) −19.0007 −1.05397
\(326\) −58.3398 −3.23114
\(327\) −2.50259 −0.138394
\(328\) 33.7202 1.86188
\(329\) 27.2000 1.49958
\(330\) −0.713969 −0.0393027
\(331\) −15.4924 −0.851541 −0.425770 0.904831i \(-0.639997\pi\)
−0.425770 + 0.904831i \(0.639997\pi\)
\(332\) −70.0727 −3.84574
\(333\) −24.5026 −1.34273
\(334\) −60.4263 −3.30638
\(335\) −5.89685 −0.322180
\(336\) −8.22608 −0.448769
\(337\) 26.2758 1.43133 0.715666 0.698442i \(-0.246123\pi\)
0.715666 + 0.698442i \(0.246123\pi\)
\(338\) −6.80673 −0.370237
\(339\) −1.94678 −0.105734
\(340\) 12.2146 0.662429
\(341\) −2.79936 −0.151594
\(342\) −8.38718 −0.453527
\(343\) 20.1559 1.08832
\(344\) −75.6133 −4.07680
\(345\) −0.179878 −0.00968430
\(346\) 7.10872 0.382167
\(347\) −34.6702 −1.86120 −0.930598 0.366042i \(-0.880713\pi\)
−0.930598 + 0.366042i \(0.880713\pi\)
\(348\) 1.11560 0.0598023
\(349\) 10.6823 0.571808 0.285904 0.958258i \(-0.407706\pi\)
0.285904 + 0.958258i \(0.407706\pi\)
\(350\) −29.0922 −1.55504
\(351\) −5.57549 −0.297598
\(352\) 62.6484 3.33917
\(353\) 19.5956 1.04297 0.521485 0.853260i \(-0.325378\pi\)
0.521485 + 0.853260i \(0.325378\pi\)
\(354\) 0.795704 0.0422912
\(355\) −0.612279 −0.0324964
\(356\) −25.3132 −1.34160
\(357\) 2.78612 0.147457
\(358\) −15.6424 −0.826729
\(359\) 3.78090 0.199548 0.0997740 0.995010i \(-0.468188\pi\)
0.0997740 + 0.995010i \(0.468188\pi\)
\(360\) −11.8599 −0.625073
\(361\) −17.9250 −0.943419
\(362\) 4.04923 0.212823
\(363\) −0.960304 −0.0504029
\(364\) −47.8857 −2.50989
\(365\) 6.95260 0.363916
\(366\) 3.53766 0.184916
\(367\) −19.5281 −1.01936 −0.509678 0.860365i \(-0.670235\pi\)
−0.509678 + 0.860365i \(0.670235\pi\)
\(368\) 28.7814 1.50033
\(369\) 10.1595 0.528883
\(370\) 9.43931 0.490726
\(371\) 2.19155 0.113780
\(372\) 1.40409 0.0727988
\(373\) −26.7208 −1.38355 −0.691774 0.722114i \(-0.743171\pi\)
−0.691774 + 0.722114i \(0.743171\pi\)
\(374\) −38.6919 −2.00071
\(375\) 0.966990 0.0499352
\(376\) 121.239 6.25245
\(377\) 3.31358 0.170658
\(378\) −8.53672 −0.439081
\(379\) 14.0660 0.722519 0.361260 0.932465i \(-0.382347\pi\)
0.361260 + 0.932465i \(0.382347\pi\)
\(380\) 2.37561 0.121866
\(381\) −4.88410 −0.250220
\(382\) 35.1896 1.80046
\(383\) 24.7595 1.26515 0.632575 0.774499i \(-0.281998\pi\)
0.632575 + 0.774499i \(0.281998\pi\)
\(384\) −10.7899 −0.550620
\(385\) −2.38731 −0.121668
\(386\) 58.2817 2.96646
\(387\) −22.7814 −1.15805
\(388\) −17.1361 −0.869952
\(389\) −22.3343 −1.13240 −0.566198 0.824269i \(-0.691586\pi\)
−0.566198 + 0.824269i \(0.691586\pi\)
\(390\) 1.06367 0.0538609
\(391\) −9.74807 −0.492981
\(392\) 21.4623 1.08401
\(393\) −2.35003 −0.118543
\(394\) −68.8490 −3.46856
\(395\) 0.583051 0.0293365
\(396\) 43.1656 2.16915
\(397\) −5.95504 −0.298875 −0.149437 0.988771i \(-0.547746\pi\)
−0.149437 + 0.988771i \(0.547746\pi\)
\(398\) 16.4842 0.826277
\(399\) 0.541872 0.0271275
\(400\) −76.0224 −3.80112
\(401\) −12.1710 −0.607790 −0.303895 0.952706i \(-0.598287\pi\)
−0.303895 + 0.952706i \(0.598287\pi\)
\(402\) −9.36912 −0.467289
\(403\) 4.17047 0.207746
\(404\) 29.6251 1.47391
\(405\) −3.50289 −0.174060
\(406\) 5.07346 0.251792
\(407\) −21.9843 −1.08972
\(408\) 12.4187 0.614816
\(409\) 28.6059 1.41447 0.707236 0.706977i \(-0.249942\pi\)
0.707236 + 0.706977i \(0.249942\pi\)
\(410\) −3.91382 −0.193290
\(411\) 3.47264 0.171293
\(412\) −94.7260 −4.66681
\(413\) 2.66060 0.130920
\(414\) 14.7912 0.726949
\(415\) 5.20448 0.255478
\(416\) −93.3332 −4.57604
\(417\) −2.89022 −0.141535
\(418\) −7.52518 −0.368069
\(419\) −2.31252 −0.112974 −0.0564870 0.998403i \(-0.517990\pi\)
−0.0564870 + 0.998403i \(0.517990\pi\)
\(420\) 1.19742 0.0584279
\(421\) −25.7766 −1.25628 −0.628138 0.778102i \(-0.716183\pi\)
−0.628138 + 0.778102i \(0.716183\pi\)
\(422\) 2.57111 0.125160
\(423\) 36.5281 1.77606
\(424\) 9.76848 0.474399
\(425\) 25.7483 1.24898
\(426\) −0.972809 −0.0471327
\(427\) 11.8289 0.572440
\(428\) −21.1286 −1.02129
\(429\) −2.47730 −0.119605
\(430\) 8.77625 0.423228
\(431\) −22.2185 −1.07023 −0.535114 0.844780i \(-0.679731\pi\)
−0.535114 + 0.844780i \(0.679731\pi\)
\(432\) −22.3078 −1.07328
\(433\) −2.97650 −0.143042 −0.0715208 0.997439i \(-0.522785\pi\)
−0.0715208 + 0.997439i \(0.522785\pi\)
\(434\) 6.38546 0.306512
\(435\) −0.0828583 −0.00397275
\(436\) −58.2876 −2.79147
\(437\) −1.89590 −0.0906931
\(438\) 11.0465 0.527823
\(439\) −11.1916 −0.534147 −0.267073 0.963676i \(-0.586057\pi\)
−0.267073 + 0.963676i \(0.586057\pi\)
\(440\) −10.6410 −0.507291
\(441\) 6.46635 0.307921
\(442\) 57.6430 2.74180
\(443\) 3.31945 0.157712 0.0788560 0.996886i \(-0.474873\pi\)
0.0788560 + 0.996886i \(0.474873\pi\)
\(444\) 11.0268 0.523310
\(445\) 1.88008 0.0891243
\(446\) −77.2439 −3.65760
\(447\) −4.96426 −0.234801
\(448\) −73.9129 −3.49205
\(449\) 7.92122 0.373825 0.186913 0.982377i \(-0.440152\pi\)
0.186913 + 0.982377i \(0.440152\pi\)
\(450\) −39.0691 −1.84174
\(451\) 9.11536 0.429225
\(452\) −45.3421 −2.13271
\(453\) 0.238468 0.0112042
\(454\) 30.4775 1.43038
\(455\) 3.55659 0.166736
\(456\) 2.41530 0.113107
\(457\) 18.1734 0.850115 0.425058 0.905166i \(-0.360254\pi\)
0.425058 + 0.905166i \(0.360254\pi\)
\(458\) 14.5929 0.681882
\(459\) 7.55551 0.352661
\(460\) −4.18951 −0.195337
\(461\) 36.1755 1.68486 0.842431 0.538805i \(-0.181124\pi\)
0.842431 + 0.538805i \(0.181124\pi\)
\(462\) −3.79303 −0.176468
\(463\) 1.34779 0.0626372 0.0313186 0.999509i \(-0.490029\pi\)
0.0313186 + 0.999509i \(0.490029\pi\)
\(464\) 13.2578 0.615476
\(465\) −0.104286 −0.00483613
\(466\) −43.6559 −2.02232
\(467\) −19.3246 −0.894238 −0.447119 0.894474i \(-0.647550\pi\)
−0.447119 + 0.894474i \(0.647550\pi\)
\(468\) −64.3078 −2.97263
\(469\) −31.3276 −1.44657
\(470\) −14.0720 −0.649091
\(471\) −0.0155120 −0.000714753 0
\(472\) 11.8592 0.545863
\(473\) −20.4401 −0.939835
\(474\) 0.926370 0.0425496
\(475\) 5.00778 0.229773
\(476\) 64.8912 2.97428
\(477\) 2.94313 0.134757
\(478\) −56.9781 −2.60612
\(479\) −38.9174 −1.77818 −0.889090 0.457733i \(-0.848661\pi\)
−0.889090 + 0.457733i \(0.848661\pi\)
\(480\) 2.33386 0.106526
\(481\) 32.7521 1.49337
\(482\) −68.5254 −3.12125
\(483\) −0.955618 −0.0434821
\(484\) −22.3663 −1.01665
\(485\) 1.27274 0.0577921
\(486\) −17.2513 −0.782537
\(487\) −7.78220 −0.352645 −0.176323 0.984332i \(-0.556420\pi\)
−0.176323 + 0.984332i \(0.556420\pi\)
\(488\) 52.7253 2.38676
\(489\) 5.06178 0.228902
\(490\) −2.49108 −0.112535
\(491\) 3.54822 0.160129 0.0800644 0.996790i \(-0.474487\pi\)
0.0800644 + 0.996790i \(0.474487\pi\)
\(492\) −4.57204 −0.206124
\(493\) −4.49032 −0.202234
\(494\) 11.2110 0.504405
\(495\) −3.20602 −0.144100
\(496\) 16.6862 0.749233
\(497\) −3.25279 −0.145908
\(498\) 8.26905 0.370545
\(499\) −22.4647 −1.00566 −0.502828 0.864386i \(-0.667707\pi\)
−0.502828 + 0.864386i \(0.667707\pi\)
\(500\) 22.5220 1.00722
\(501\) 5.24281 0.234232
\(502\) 20.9325 0.934264
\(503\) 9.72259 0.433509 0.216754 0.976226i \(-0.430453\pi\)
0.216754 + 0.976226i \(0.430453\pi\)
\(504\) −63.0070 −2.80655
\(505\) −2.20033 −0.0979136
\(506\) 13.2710 0.589970
\(507\) 0.590577 0.0262285
\(508\) −113.755 −5.04706
\(509\) −18.8731 −0.836534 −0.418267 0.908324i \(-0.637362\pi\)
−0.418267 + 0.908324i \(0.637362\pi\)
\(510\) −1.44140 −0.0638265
\(511\) 36.9364 1.63397
\(512\) −65.9146 −2.91304
\(513\) 1.46947 0.0648786
\(514\) −63.8127 −2.81466
\(515\) 7.03554 0.310023
\(516\) 10.2522 0.451330
\(517\) 32.7739 1.44139
\(518\) 50.1472 2.20334
\(519\) −0.616779 −0.0270736
\(520\) 15.8529 0.695196
\(521\) 21.6984 0.950624 0.475312 0.879817i \(-0.342335\pi\)
0.475312 + 0.879817i \(0.342335\pi\)
\(522\) 6.81338 0.298213
\(523\) 28.0161 1.22506 0.612530 0.790447i \(-0.290152\pi\)
0.612530 + 0.790447i \(0.290152\pi\)
\(524\) −54.7342 −2.39108
\(525\) 2.52415 0.110163
\(526\) 24.2243 1.05623
\(527\) −5.65152 −0.246184
\(528\) −9.91178 −0.431355
\(529\) −19.6565 −0.854630
\(530\) −1.13380 −0.0492493
\(531\) 3.57304 0.155057
\(532\) 12.6207 0.547175
\(533\) −13.5800 −0.588215
\(534\) 2.98713 0.129266
\(535\) 1.56927 0.0678455
\(536\) −139.638 −6.03142
\(537\) 1.35720 0.0585674
\(538\) 7.93835 0.342247
\(539\) 5.80176 0.249900
\(540\) 3.24720 0.139737
\(541\) 11.9549 0.513980 0.256990 0.966414i \(-0.417269\pi\)
0.256990 + 0.966414i \(0.417269\pi\)
\(542\) −80.7911 −3.47027
\(543\) −0.351327 −0.0150769
\(544\) 126.478 5.42272
\(545\) 4.32917 0.185441
\(546\) 5.65083 0.241833
\(547\) 34.0535 1.45602 0.728010 0.685566i \(-0.240445\pi\)
0.728010 + 0.685566i \(0.240445\pi\)
\(548\) 80.8809 3.45506
\(549\) 15.8855 0.677978
\(550\) −35.0538 −1.49470
\(551\) −0.873320 −0.0372047
\(552\) −4.25951 −0.181297
\(553\) 3.09751 0.131720
\(554\) −75.6196 −3.21277
\(555\) −0.818990 −0.0347642
\(556\) −67.3157 −2.85482
\(557\) 15.8329 0.670863 0.335432 0.942065i \(-0.391118\pi\)
0.335432 + 0.942065i \(0.391118\pi\)
\(558\) 8.57532 0.363022
\(559\) 30.4515 1.28796
\(560\) 14.2301 0.601330
\(561\) 3.35706 0.141735
\(562\) −42.4617 −1.79114
\(563\) 15.2080 0.640940 0.320470 0.947259i \(-0.396159\pi\)
0.320470 + 0.947259i \(0.396159\pi\)
\(564\) −16.4386 −0.692190
\(565\) 3.36767 0.141679
\(566\) −76.7163 −3.22463
\(567\) −18.6094 −0.781522
\(568\) −14.4988 −0.608355
\(569\) −36.4444 −1.52783 −0.763914 0.645318i \(-0.776725\pi\)
−0.763914 + 0.645318i \(0.776725\pi\)
\(570\) −0.280338 −0.0117421
\(571\) −36.2681 −1.51777 −0.758887 0.651223i \(-0.774256\pi\)
−0.758887 + 0.651223i \(0.774256\pi\)
\(572\) −57.6985 −2.41250
\(573\) −3.05318 −0.127549
\(574\) −20.7925 −0.867863
\(575\) −8.83147 −0.368298
\(576\) −99.2609 −4.13587
\(577\) −17.9724 −0.748201 −0.374100 0.927388i \(-0.622048\pi\)
−0.374100 + 0.927388i \(0.622048\pi\)
\(578\) −31.3895 −1.30563
\(579\) −5.05674 −0.210151
\(580\) −1.92984 −0.0801324
\(581\) 27.6493 1.14709
\(582\) 2.02217 0.0838217
\(583\) 2.64065 0.109365
\(584\) 164.638 6.81275
\(585\) 4.77631 0.197476
\(586\) 83.0144 3.42929
\(587\) 35.3145 1.45758 0.728792 0.684735i \(-0.240082\pi\)
0.728792 + 0.684735i \(0.240082\pi\)
\(588\) −2.91003 −0.120007
\(589\) −1.09916 −0.0452902
\(590\) −1.37647 −0.0566682
\(591\) 5.97360 0.245721
\(592\) 131.043 5.38582
\(593\) 27.2470 1.11890 0.559450 0.828864i \(-0.311012\pi\)
0.559450 + 0.828864i \(0.311012\pi\)
\(594\) −10.2861 −0.422043
\(595\) −4.81964 −0.197586
\(596\) −115.622 −4.73606
\(597\) −1.43023 −0.0585354
\(598\) −19.7711 −0.808501
\(599\) −14.4232 −0.589314 −0.294657 0.955603i \(-0.595205\pi\)
−0.294657 + 0.955603i \(0.595205\pi\)
\(600\) 11.2510 0.459318
\(601\) 42.7442 1.74357 0.871786 0.489886i \(-0.162962\pi\)
0.871786 + 0.489886i \(0.162962\pi\)
\(602\) 46.6247 1.90028
\(603\) −42.0712 −1.71327
\(604\) 5.55414 0.225995
\(605\) 1.66120 0.0675376
\(606\) −3.49596 −0.142014
\(607\) 5.15322 0.209163 0.104581 0.994516i \(-0.466650\pi\)
0.104581 + 0.994516i \(0.466650\pi\)
\(608\) 24.5987 0.997610
\(609\) −0.440193 −0.0178375
\(610\) −6.11970 −0.247779
\(611\) −48.8263 −1.97530
\(612\) 87.1453 3.52264
\(613\) 23.8602 0.963703 0.481852 0.876253i \(-0.339964\pi\)
0.481852 + 0.876253i \(0.339964\pi\)
\(614\) 56.7746 2.29124
\(615\) 0.339578 0.0136931
\(616\) −56.5314 −2.27772
\(617\) 17.6555 0.710785 0.355393 0.934717i \(-0.384347\pi\)
0.355393 + 0.934717i \(0.384347\pi\)
\(618\) 11.1783 0.449657
\(619\) −29.4338 −1.18304 −0.591521 0.806289i \(-0.701472\pi\)
−0.591521 + 0.806289i \(0.701472\pi\)
\(620\) −2.42890 −0.0975471
\(621\) −2.59148 −0.103993
\(622\) −62.6349 −2.51143
\(623\) 9.98810 0.400165
\(624\) 14.7665 0.591133
\(625\) 22.4764 0.899055
\(626\) −45.9602 −1.83694
\(627\) 0.652913 0.0260748
\(628\) −0.361287 −0.0144169
\(629\) −44.3833 −1.76968
\(630\) 7.31307 0.291360
\(631\) 29.2421 1.16411 0.582055 0.813149i \(-0.302249\pi\)
0.582055 + 0.813149i \(0.302249\pi\)
\(632\) 13.8066 0.549199
\(633\) −0.223079 −0.00886661
\(634\) 5.30933 0.210860
\(635\) 8.44888 0.335284
\(636\) −1.32449 −0.0525193
\(637\) −8.64343 −0.342465
\(638\) 6.11313 0.242021
\(639\) −4.36831 −0.172808
\(640\) 18.6652 0.737806
\(641\) 34.1225 1.34776 0.673878 0.738843i \(-0.264627\pi\)
0.673878 + 0.738843i \(0.264627\pi\)
\(642\) 2.49331 0.0984031
\(643\) 20.0041 0.788884 0.394442 0.918921i \(-0.370938\pi\)
0.394442 + 0.918921i \(0.370938\pi\)
\(644\) −22.2572 −0.877056
\(645\) −0.761461 −0.0299825
\(646\) −15.1923 −0.597732
\(647\) 26.0194 1.02293 0.511464 0.859305i \(-0.329104\pi\)
0.511464 + 0.859305i \(0.329104\pi\)
\(648\) −82.9483 −3.25852
\(649\) 3.20582 0.125839
\(650\) 52.2229 2.04835
\(651\) −0.554027 −0.0217140
\(652\) 117.893 4.61706
\(653\) −12.3743 −0.484244 −0.242122 0.970246i \(-0.577843\pi\)
−0.242122 + 0.970246i \(0.577843\pi\)
\(654\) 6.87832 0.268964
\(655\) 4.06525 0.158843
\(656\) −54.3341 −2.12139
\(657\) 49.6035 1.93522
\(658\) −74.7586 −2.91439
\(659\) −8.72013 −0.339688 −0.169844 0.985471i \(-0.554326\pi\)
−0.169844 + 0.985471i \(0.554326\pi\)
\(660\) 1.44279 0.0561606
\(661\) 47.1666 1.83457 0.917284 0.398234i \(-0.130377\pi\)
0.917284 + 0.398234i \(0.130377\pi\)
\(662\) 42.5806 1.65494
\(663\) −5.00132 −0.194235
\(664\) 123.242 4.78272
\(665\) −0.937369 −0.0363496
\(666\) 67.3449 2.60956
\(667\) 1.54014 0.0596346
\(668\) 122.110 4.72457
\(669\) 6.70197 0.259113
\(670\) 16.2074 0.626146
\(671\) 14.2529 0.550227
\(672\) 12.3989 0.478297
\(673\) 21.6516 0.834607 0.417303 0.908767i \(-0.362975\pi\)
0.417303 + 0.908767i \(0.362975\pi\)
\(674\) −72.2184 −2.78175
\(675\) 6.84507 0.263467
\(676\) 13.7551 0.529041
\(677\) 37.5664 1.44379 0.721897 0.692001i \(-0.243270\pi\)
0.721897 + 0.692001i \(0.243270\pi\)
\(678\) 5.35067 0.205491
\(679\) 6.76155 0.259484
\(680\) −21.4827 −0.823825
\(681\) −2.64434 −0.101332
\(682\) 7.69399 0.294618
\(683\) 45.4196 1.73793 0.868967 0.494870i \(-0.164785\pi\)
0.868967 + 0.494870i \(0.164785\pi\)
\(684\) 16.9488 0.648055
\(685\) −6.00723 −0.229525
\(686\) −55.3981 −2.11511
\(687\) −1.26614 −0.0483061
\(688\) 121.838 4.64501
\(689\) −3.93402 −0.149874
\(690\) 0.494391 0.0188211
\(691\) 47.9918 1.82570 0.912848 0.408301i \(-0.133878\pi\)
0.912848 + 0.408301i \(0.133878\pi\)
\(692\) −14.3653 −0.546088
\(693\) −17.0323 −0.647003
\(694\) 95.2905 3.61718
\(695\) 4.99971 0.189650
\(696\) −1.96209 −0.0743727
\(697\) 18.4026 0.697049
\(698\) −29.3600 −1.11129
\(699\) 3.78775 0.143266
\(700\) 58.7896 2.22204
\(701\) −38.7490 −1.46353 −0.731765 0.681558i \(-0.761303\pi\)
−0.731765 + 0.681558i \(0.761303\pi\)
\(702\) 15.3241 0.578372
\(703\) −8.63209 −0.325565
\(704\) −89.0593 −3.35655
\(705\) 1.22094 0.0459831
\(706\) −53.8582 −2.02698
\(707\) −11.6895 −0.439628
\(708\) −1.60796 −0.0604309
\(709\) 34.2842 1.28757 0.643785 0.765207i \(-0.277363\pi\)
0.643785 + 0.765207i \(0.277363\pi\)
\(710\) 1.68284 0.0631557
\(711\) 4.15979 0.156004
\(712\) 44.5203 1.66847
\(713\) 1.93843 0.0725947
\(714\) −7.65760 −0.286578
\(715\) 4.28542 0.160266
\(716\) 31.6103 1.18133
\(717\) 4.94364 0.184623
\(718\) −10.3917 −0.387815
\(719\) −5.36942 −0.200246 −0.100123 0.994975i \(-0.531924\pi\)
−0.100123 + 0.994975i \(0.531924\pi\)
\(720\) 19.1102 0.712195
\(721\) 37.3770 1.39199
\(722\) 49.2664 1.83350
\(723\) 5.94552 0.221116
\(724\) −8.18271 −0.304108
\(725\) −4.06810 −0.151085
\(726\) 2.63938 0.0979565
\(727\) 27.8642 1.03343 0.516713 0.856159i \(-0.327156\pi\)
0.516713 + 0.856159i \(0.327156\pi\)
\(728\) 84.2201 3.12141
\(729\) −23.9775 −0.888055
\(730\) −19.1091 −0.707259
\(731\) −41.2656 −1.52626
\(732\) −7.14891 −0.264231
\(733\) −11.7695 −0.434718 −0.217359 0.976092i \(-0.569744\pi\)
−0.217359 + 0.976092i \(0.569744\pi\)
\(734\) 53.6725 1.98109
\(735\) 0.216135 0.00797226
\(736\) −43.3811 −1.59905
\(737\) −37.7473 −1.39044
\(738\) −27.9232 −1.02787
\(739\) −23.0687 −0.848598 −0.424299 0.905522i \(-0.639479\pi\)
−0.424299 + 0.905522i \(0.639479\pi\)
\(740\) −19.0750 −0.701211
\(741\) −0.972706 −0.0357332
\(742\) −6.02344 −0.221127
\(743\) −46.5146 −1.70646 −0.853228 0.521539i \(-0.825358\pi\)
−0.853228 + 0.521539i \(0.825358\pi\)
\(744\) −2.46948 −0.0905356
\(745\) 8.58753 0.314623
\(746\) 73.4415 2.68888
\(747\) 37.1315 1.35857
\(748\) 78.1888 2.85887
\(749\) 8.33690 0.304624
\(750\) −2.65775 −0.0970474
\(751\) −33.1354 −1.20913 −0.604564 0.796556i \(-0.706653\pi\)
−0.604564 + 0.796556i \(0.706653\pi\)
\(752\) −195.356 −7.12390
\(753\) −1.81619 −0.0661855
\(754\) −9.10730 −0.331668
\(755\) −0.412520 −0.0150131
\(756\) 17.2510 0.627414
\(757\) 53.5118 1.94492 0.972459 0.233074i \(-0.0748784\pi\)
0.972459 + 0.233074i \(0.0748784\pi\)
\(758\) −38.6600 −1.40419
\(759\) −1.15145 −0.0417948
\(760\) −4.17817 −0.151558
\(761\) −36.0192 −1.30570 −0.652848 0.757489i \(-0.726426\pi\)
−0.652848 + 0.757489i \(0.726426\pi\)
\(762\) 13.4239 0.486295
\(763\) 22.9991 0.832624
\(764\) −71.1113 −2.57272
\(765\) −6.47250 −0.234014
\(766\) −68.0509 −2.45878
\(767\) −4.77601 −0.172452
\(768\) 13.5705 0.489685
\(769\) 33.3401 1.20227 0.601136 0.799146i \(-0.294715\pi\)
0.601136 + 0.799146i \(0.294715\pi\)
\(770\) 6.56146 0.236459
\(771\) 5.53663 0.199397
\(772\) −117.776 −4.23885
\(773\) −24.5740 −0.883864 −0.441932 0.897049i \(-0.645707\pi\)
−0.441932 + 0.897049i \(0.645707\pi\)
\(774\) 62.6143 2.25063
\(775\) −5.12011 −0.183920
\(776\) 30.1385 1.08191
\(777\) −4.35096 −0.156090
\(778\) 61.3855 2.20078
\(779\) 3.57912 0.128235
\(780\) −2.14946 −0.0769631
\(781\) −3.91936 −0.140246
\(782\) 26.7924 0.958093
\(783\) −1.19373 −0.0426605
\(784\) −34.5827 −1.23510
\(785\) 0.0268337 0.000957736 0
\(786\) 6.45901 0.230385
\(787\) −40.7178 −1.45143 −0.725716 0.687995i \(-0.758491\pi\)
−0.725716 + 0.687995i \(0.758491\pi\)
\(788\) 139.130 4.95631
\(789\) −2.10179 −0.0748258
\(790\) −1.60250 −0.0570145
\(791\) 17.8911 0.636134
\(792\) −75.9185 −2.69765
\(793\) −21.2339 −0.754037
\(794\) 16.3673 0.580854
\(795\) 0.0983731 0.00348893
\(796\) −33.3113 −1.18069
\(797\) 32.0546 1.13543 0.567716 0.823224i \(-0.307827\pi\)
0.567716 + 0.823224i \(0.307827\pi\)
\(798\) −1.48932 −0.0527215
\(799\) 66.1659 2.34078
\(800\) 114.586 4.05122
\(801\) 13.4135 0.473941
\(802\) 33.4517 1.18122
\(803\) 44.5054 1.57056
\(804\) 18.9332 0.667721
\(805\) 1.65310 0.0582641
\(806\) −11.4625 −0.403748
\(807\) −0.688761 −0.0242455
\(808\) −52.1039 −1.83301
\(809\) 6.27117 0.220482 0.110241 0.993905i \(-0.464838\pi\)
0.110241 + 0.993905i \(0.464838\pi\)
\(810\) 9.62761 0.338280
\(811\) −40.1550 −1.41003 −0.705016 0.709191i \(-0.749060\pi\)
−0.705016 + 0.709191i \(0.749060\pi\)
\(812\) −10.2525 −0.359791
\(813\) 7.00974 0.245842
\(814\) 60.4235 2.11784
\(815\) −8.75624 −0.306718
\(816\) −20.0105 −0.700508
\(817\) −8.02573 −0.280785
\(818\) −78.6228 −2.74898
\(819\) 25.3746 0.886659
\(820\) 7.90906 0.276196
\(821\) 6.98921 0.243925 0.121963 0.992535i \(-0.461081\pi\)
0.121963 + 0.992535i \(0.461081\pi\)
\(822\) −9.54449 −0.332902
\(823\) −24.3141 −0.847537 −0.423769 0.905771i \(-0.639293\pi\)
−0.423769 + 0.905771i \(0.639293\pi\)
\(824\) 166.602 5.80384
\(825\) 3.04140 0.105888
\(826\) −7.31261 −0.254438
\(827\) 25.7913 0.896850 0.448425 0.893821i \(-0.351985\pi\)
0.448425 + 0.893821i \(0.351985\pi\)
\(828\) −29.8902 −1.03875
\(829\) −16.2924 −0.565859 −0.282929 0.959141i \(-0.591306\pi\)
−0.282929 + 0.959141i \(0.591306\pi\)
\(830\) −14.3044 −0.496513
\(831\) 6.56104 0.227600
\(832\) 132.680 4.59985
\(833\) 11.7129 0.405830
\(834\) 7.94371 0.275068
\(835\) −9.06940 −0.313860
\(836\) 15.2069 0.525942
\(837\) −1.50243 −0.0519316
\(838\) 6.35592 0.219562
\(839\) −5.07065 −0.175058 −0.0875291 0.996162i \(-0.527897\pi\)
−0.0875291 + 0.996162i \(0.527897\pi\)
\(840\) −2.10598 −0.0726633
\(841\) −28.2906 −0.975536
\(842\) 70.8466 2.44153
\(843\) 3.68413 0.126888
\(844\) −5.19571 −0.178844
\(845\) −1.02162 −0.0351449
\(846\) −100.397 −3.45171
\(847\) 8.82531 0.303241
\(848\) −15.7402 −0.540520
\(849\) 6.65619 0.228440
\(850\) −70.7687 −2.42735
\(851\) 15.2231 0.521842
\(852\) 1.96586 0.0673491
\(853\) −19.6202 −0.671782 −0.335891 0.941901i \(-0.609037\pi\)
−0.335891 + 0.941901i \(0.609037\pi\)
\(854\) −32.5115 −1.11252
\(855\) −1.25883 −0.0430512
\(856\) 37.1604 1.27011
\(857\) −35.1597 −1.20103 −0.600516 0.799613i \(-0.705038\pi\)
−0.600516 + 0.799613i \(0.705038\pi\)
\(858\) 6.80881 0.232449
\(859\) −25.0893 −0.856037 −0.428019 0.903770i \(-0.640788\pi\)
−0.428019 + 0.903770i \(0.640788\pi\)
\(860\) −17.7351 −0.604761
\(861\) 1.80404 0.0614814
\(862\) 61.0671 2.07995
\(863\) 9.16258 0.311898 0.155949 0.987765i \(-0.450156\pi\)
0.155949 + 0.987765i \(0.450156\pi\)
\(864\) 33.6237 1.14390
\(865\) 1.06695 0.0362774
\(866\) 8.18086 0.277997
\(867\) 2.72347 0.0924938
\(868\) −12.9038 −0.437983
\(869\) 3.73226 0.126608
\(870\) 0.227734 0.00772092
\(871\) 56.2357 1.90547
\(872\) 102.515 3.47159
\(873\) 9.08038 0.307324
\(874\) 5.21084 0.176259
\(875\) −8.88675 −0.300427
\(876\) −22.3229 −0.754220
\(877\) −21.1278 −0.713436 −0.356718 0.934212i \(-0.616104\pi\)
−0.356718 + 0.934212i \(0.616104\pi\)
\(878\) 30.7599 1.03810
\(879\) −7.20264 −0.242939
\(880\) 17.1461 0.577996
\(881\) 53.2948 1.79555 0.897775 0.440455i \(-0.145183\pi\)
0.897775 + 0.440455i \(0.145183\pi\)
\(882\) −17.7726 −0.598435
\(883\) −6.76432 −0.227638 −0.113819 0.993502i \(-0.536308\pi\)
−0.113819 + 0.993502i \(0.536308\pi\)
\(884\) −116.485 −3.91782
\(885\) 0.119427 0.00401451
\(886\) −9.12344 −0.306508
\(887\) −37.7121 −1.26625 −0.633124 0.774050i \(-0.718228\pi\)
−0.633124 + 0.774050i \(0.718228\pi\)
\(888\) −19.3937 −0.650810
\(889\) 44.8855 1.50541
\(890\) −5.16736 −0.173210
\(891\) −22.4229 −0.751195
\(892\) 156.095 5.22644
\(893\) 12.8686 0.430630
\(894\) 13.6442 0.456329
\(895\) −2.34778 −0.0784776
\(896\) 99.1605 3.31272
\(897\) 1.71542 0.0572761
\(898\) −21.7713 −0.726518
\(899\) 0.892911 0.0297802
\(900\) 78.9511 2.63170
\(901\) 5.33110 0.177605
\(902\) −25.0534 −0.834186
\(903\) −4.04533 −0.134620
\(904\) 79.7465 2.65233
\(905\) 0.607751 0.0202023
\(906\) −0.655426 −0.0217751
\(907\) −30.5305 −1.01375 −0.506875 0.862020i \(-0.669199\pi\)
−0.506875 + 0.862020i \(0.669199\pi\)
\(908\) −61.5891 −2.04391
\(909\) −15.6983 −0.520681
\(910\) −9.77522 −0.324045
\(911\) −40.7746 −1.35092 −0.675462 0.737395i \(-0.736056\pi\)
−0.675462 + 0.737395i \(0.736056\pi\)
\(912\) −3.89183 −0.128872
\(913\) 33.3153 1.10257
\(914\) −49.9492 −1.65217
\(915\) 0.530968 0.0175533
\(916\) −29.4894 −0.974358
\(917\) 21.5970 0.713197
\(918\) −20.7662 −0.685385
\(919\) −19.6351 −0.647701 −0.323850 0.946108i \(-0.604977\pi\)
−0.323850 + 0.946108i \(0.604977\pi\)
\(920\) 7.36841 0.242929
\(921\) −4.92598 −0.162316
\(922\) −99.4276 −3.27447
\(923\) 5.83903 0.192194
\(924\) 7.66497 0.252159
\(925\) −40.2100 −1.32210
\(926\) −3.70438 −0.121733
\(927\) 50.1952 1.64863
\(928\) −19.9829 −0.655972
\(929\) −12.8998 −0.423229 −0.211614 0.977353i \(-0.567872\pi\)
−0.211614 + 0.977353i \(0.567872\pi\)
\(930\) 0.286627 0.00939886
\(931\) 2.27805 0.0746600
\(932\) 88.2201 2.88975
\(933\) 5.43444 0.177916
\(934\) 53.1134 1.73792
\(935\) −5.80729 −0.189919
\(936\) 113.103 3.69688
\(937\) −1.81698 −0.0593583 −0.0296791 0.999559i \(-0.509449\pi\)
−0.0296791 + 0.999559i \(0.509449\pi\)
\(938\) 86.1033 2.81137
\(939\) 3.98768 0.130133
\(940\) 28.4367 0.927502
\(941\) 9.20764 0.300160 0.150080 0.988674i \(-0.452047\pi\)
0.150080 + 0.988674i \(0.452047\pi\)
\(942\) 0.0426343 0.00138910
\(943\) −6.31196 −0.205546
\(944\) −19.1090 −0.621945
\(945\) −1.28128 −0.0416800
\(946\) 56.1791 1.82654
\(947\) 53.8833 1.75097 0.875485 0.483245i \(-0.160542\pi\)
0.875485 + 0.483245i \(0.160542\pi\)
\(948\) −1.87201 −0.0608002
\(949\) −66.3039 −2.15232
\(950\) −13.7638 −0.446556
\(951\) −0.460657 −0.0149378
\(952\) −114.129 −3.69894
\(953\) −4.40191 −0.142592 −0.0712960 0.997455i \(-0.522713\pi\)
−0.0712960 + 0.997455i \(0.522713\pi\)
\(954\) −8.08914 −0.261896
\(955\) 5.28162 0.170909
\(956\) 115.142 3.72395
\(957\) −0.530398 −0.0171453
\(958\) 106.964 3.45584
\(959\) −31.9140 −1.03056
\(960\) −3.31776 −0.107080
\(961\) −29.8762 −0.963748
\(962\) −90.0185 −2.90231
\(963\) 11.1960 0.360786
\(964\) 138.476 4.46002
\(965\) 8.74752 0.281593
\(966\) 2.62650 0.0845062
\(967\) −19.8485 −0.638286 −0.319143 0.947707i \(-0.603395\pi\)
−0.319143 + 0.947707i \(0.603395\pi\)
\(968\) 39.3373 1.26435
\(969\) 1.31814 0.0423448
\(970\) −3.49810 −0.112317
\(971\) 44.4251 1.42567 0.712835 0.701331i \(-0.247411\pi\)
0.712835 + 0.701331i \(0.247411\pi\)
\(972\) 34.8616 1.11819
\(973\) 26.5614 0.851521
\(974\) 21.3892 0.685355
\(975\) −4.53106 −0.145110
\(976\) −84.9575 −2.71942
\(977\) −28.6370 −0.916179 −0.458089 0.888906i \(-0.651466\pi\)
−0.458089 + 0.888906i \(0.651466\pi\)
\(978\) −13.9122 −0.444863
\(979\) 12.0349 0.384636
\(980\) 5.03398 0.160804
\(981\) 30.8865 0.986131
\(982\) −9.75220 −0.311205
\(983\) 13.7442 0.438373 0.219187 0.975683i \(-0.429660\pi\)
0.219187 + 0.975683i \(0.429660\pi\)
\(984\) 8.04120 0.256344
\(985\) −10.3336 −0.329255
\(986\) 12.3415 0.393035
\(987\) 6.48634 0.206463
\(988\) −22.6552 −0.720757
\(989\) 14.1538 0.450065
\(990\) 8.81168 0.280053
\(991\) −14.6537 −0.465489 −0.232745 0.972538i \(-0.574771\pi\)
−0.232745 + 0.972538i \(0.574771\pi\)
\(992\) −25.1505 −0.798530
\(993\) −3.69446 −0.117240
\(994\) 8.94022 0.283567
\(995\) 2.47411 0.0784347
\(996\) −16.7101 −0.529481
\(997\) −27.0195 −0.855718 −0.427859 0.903846i \(-0.640732\pi\)
−0.427859 + 0.903846i \(0.640732\pi\)
\(998\) 61.7436 1.95446
\(999\) −11.7991 −0.373307
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 \(a_p\))