Properties

Label 8003.2.a.c.1.8
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 1.8
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.60343 q^{2}\) \(-2.10556 q^{3}\) \(+4.77783 q^{4}\) \(-3.11826 q^{5}\) \(+5.48166 q^{6}\) \(-2.87442 q^{7}\) \(-7.23187 q^{8}\) \(+1.43337 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.60343 q^{2}\) \(-2.10556 q^{3}\) \(+4.77783 q^{4}\) \(-3.11826 q^{5}\) \(+5.48166 q^{6}\) \(-2.87442 q^{7}\) \(-7.23187 q^{8}\) \(+1.43337 q^{9}\) \(+8.11816 q^{10}\) \(+2.41839 q^{11}\) \(-10.0600 q^{12}\) \(+1.83452 q^{13}\) \(+7.48334 q^{14}\) \(+6.56568 q^{15}\) \(+9.27198 q^{16}\) \(-1.14681 q^{17}\) \(-3.73167 q^{18}\) \(-2.71976 q^{19}\) \(-14.8985 q^{20}\) \(+6.05226 q^{21}\) \(-6.29610 q^{22}\) \(+7.41319 q^{23}\) \(+15.2271 q^{24}\) \(+4.72355 q^{25}\) \(-4.77604 q^{26}\) \(+3.29863 q^{27}\) \(-13.7335 q^{28}\) \(-8.43840 q^{29}\) \(-17.0933 q^{30}\) \(-3.35203 q^{31}\) \(-9.67518 q^{32}\) \(-5.09206 q^{33}\) \(+2.98564 q^{34}\) \(+8.96320 q^{35}\) \(+6.84839 q^{36}\) \(+0.173988 q^{37}\) \(+7.08070 q^{38}\) \(-3.86269 q^{39}\) \(+22.5509 q^{40}\) \(+5.90198 q^{41}\) \(-15.7566 q^{42}\) \(+11.2608 q^{43}\) \(+11.5547 q^{44}\) \(-4.46962 q^{45}\) \(-19.2997 q^{46}\) \(+8.83444 q^{47}\) \(-19.5227 q^{48}\) \(+1.26230 q^{49}\) \(-12.2974 q^{50}\) \(+2.41468 q^{51}\) \(+8.76503 q^{52}\) \(-1.00000 q^{53}\) \(-8.58774 q^{54}\) \(-7.54117 q^{55}\) \(+20.7874 q^{56}\) \(+5.72662 q^{57}\) \(+21.9688 q^{58}\) \(-11.1936 q^{59}\) \(+31.3697 q^{60}\) \(+4.60522 q^{61}\) \(+8.72676 q^{62}\) \(-4.12011 q^{63}\) \(+6.64466 q^{64}\) \(-5.72052 q^{65}\) \(+13.2568 q^{66}\) \(+11.9446 q^{67}\) \(-5.47927 q^{68}\) \(-15.6089 q^{69}\) \(-23.3350 q^{70}\) \(+5.66784 q^{71}\) \(-10.3659 q^{72}\) \(+7.28201 q^{73}\) \(-0.452964 q^{74}\) \(-9.94570 q^{75}\) \(-12.9946 q^{76}\) \(-6.95148 q^{77}\) \(+10.0562 q^{78}\) \(+17.2164 q^{79}\) \(-28.9125 q^{80}\) \(-11.2456 q^{81}\) \(-15.3654 q^{82}\) \(+6.58375 q^{83}\) \(+28.9166 q^{84}\) \(+3.57606 q^{85}\) \(-29.3167 q^{86}\) \(+17.7675 q^{87}\) \(-17.4895 q^{88}\) \(-9.21899 q^{89}\) \(+11.6363 q^{90}\) \(-5.27319 q^{91}\) \(+35.4190 q^{92}\) \(+7.05788 q^{93}\) \(-22.9998 q^{94}\) \(+8.48093 q^{95}\) \(+20.3716 q^{96}\) \(+11.4975 q^{97}\) \(-3.28630 q^{98}\) \(+3.46645 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60343 −1.84090 −0.920450 0.390860i \(-0.872178\pi\)
−0.920450 + 0.390860i \(0.872178\pi\)
\(3\) −2.10556 −1.21564 −0.607822 0.794073i \(-0.707957\pi\)
−0.607822 + 0.794073i \(0.707957\pi\)
\(4\) 4.77783 2.38891
\(5\) −3.11826 −1.39453 −0.697264 0.716814i \(-0.745600\pi\)
−0.697264 + 0.716814i \(0.745600\pi\)
\(6\) 5.48166 2.23788
\(7\) −2.87442 −1.08643 −0.543215 0.839594i \(-0.682793\pi\)
−0.543215 + 0.839594i \(0.682793\pi\)
\(8\) −7.23187 −2.55685
\(9\) 1.43337 0.477790
\(10\) 8.11816 2.56719
\(11\) 2.41839 0.729172 0.364586 0.931170i \(-0.381210\pi\)
0.364586 + 0.931170i \(0.381210\pi\)
\(12\) −10.0600 −2.90407
\(13\) 1.83452 0.508805 0.254402 0.967098i \(-0.418121\pi\)
0.254402 + 0.967098i \(0.418121\pi\)
\(14\) 7.48334 2.00001
\(15\) 6.56568 1.69525
\(16\) 9.27198 2.31800
\(17\) −1.14681 −0.278143 −0.139071 0.990282i \(-0.544412\pi\)
−0.139071 + 0.990282i \(0.544412\pi\)
\(18\) −3.73167 −0.879563
\(19\) −2.71976 −0.623956 −0.311978 0.950089i \(-0.600992\pi\)
−0.311978 + 0.950089i \(0.600992\pi\)
\(20\) −14.8985 −3.33141
\(21\) 6.05226 1.32071
\(22\) −6.29610 −1.34233
\(23\) 7.41319 1.54576 0.772879 0.634554i \(-0.218816\pi\)
0.772879 + 0.634554i \(0.218816\pi\)
\(24\) 15.2271 3.10822
\(25\) 4.72355 0.944710
\(26\) −4.77604 −0.936659
\(27\) 3.29863 0.634822
\(28\) −13.7335 −2.59539
\(29\) −8.43840 −1.56697 −0.783486 0.621409i \(-0.786560\pi\)
−0.783486 + 0.621409i \(0.786560\pi\)
\(30\) −17.0933 −3.12079
\(31\) −3.35203 −0.602042 −0.301021 0.953618i \(-0.597327\pi\)
−0.301021 + 0.953618i \(0.597327\pi\)
\(32\) −9.67518 −1.71035
\(33\) −5.09206 −0.886414
\(34\) 2.98564 0.512033
\(35\) 8.96320 1.51506
\(36\) 6.84839 1.14140
\(37\) 0.173988 0.0286034 0.0143017 0.999898i \(-0.495447\pi\)
0.0143017 + 0.999898i \(0.495447\pi\)
\(38\) 7.08070 1.14864
\(39\) −3.86269 −0.618526
\(40\) 22.5509 3.56560
\(41\) 5.90198 0.921735 0.460868 0.887469i \(-0.347538\pi\)
0.460868 + 0.887469i \(0.347538\pi\)
\(42\) −15.7566 −2.43130
\(43\) 11.2608 1.71726 0.858629 0.512598i \(-0.171317\pi\)
0.858629 + 0.512598i \(0.171317\pi\)
\(44\) 11.5547 1.74193
\(45\) −4.46962 −0.666292
\(46\) −19.2997 −2.84559
\(47\) 8.83444 1.28863 0.644317 0.764758i \(-0.277142\pi\)
0.644317 + 0.764758i \(0.277142\pi\)
\(48\) −19.5227 −2.81786
\(49\) 1.26230 0.180328
\(50\) −12.2974 −1.73912
\(51\) 2.41468 0.338122
\(52\) 8.76503 1.21549
\(53\) −1.00000 −0.137361
\(54\) −8.58774 −1.16864
\(55\) −7.54117 −1.01685
\(56\) 20.7874 2.77784
\(57\) 5.72662 0.758509
\(58\) 21.9688 2.88464
\(59\) −11.1936 −1.45729 −0.728643 0.684894i \(-0.759849\pi\)
−0.728643 + 0.684894i \(0.759849\pi\)
\(60\) 31.3697 4.04981
\(61\) 4.60522 0.589638 0.294819 0.955553i \(-0.404741\pi\)
0.294819 + 0.955553i \(0.404741\pi\)
\(62\) 8.72676 1.10830
\(63\) −4.12011 −0.519085
\(64\) 6.64466 0.830582
\(65\) −5.72052 −0.709543
\(66\) 13.2568 1.63180
\(67\) 11.9446 1.45927 0.729634 0.683838i \(-0.239690\pi\)
0.729634 + 0.683838i \(0.239690\pi\)
\(68\) −5.47927 −0.664459
\(69\) −15.6089 −1.87909
\(70\) −23.3350 −2.78907
\(71\) 5.66784 0.672649 0.336325 0.941746i \(-0.390816\pi\)
0.336325 + 0.941746i \(0.390816\pi\)
\(72\) −10.3659 −1.22164
\(73\) 7.28201 0.852295 0.426148 0.904654i \(-0.359870\pi\)
0.426148 + 0.904654i \(0.359870\pi\)
\(74\) −0.452964 −0.0526560
\(75\) −9.94570 −1.14843
\(76\) −12.9946 −1.49058
\(77\) −6.95148 −0.792194
\(78\) 10.0562 1.13864
\(79\) 17.2164 1.93699 0.968497 0.249026i \(-0.0801104\pi\)
0.968497 + 0.249026i \(0.0801104\pi\)
\(80\) −28.9125 −3.23251
\(81\) −11.2456 −1.24951
\(82\) −15.3654 −1.69682
\(83\) 6.58375 0.722661 0.361330 0.932438i \(-0.382323\pi\)
0.361330 + 0.932438i \(0.382323\pi\)
\(84\) 28.9166 3.15506
\(85\) 3.57606 0.387878
\(86\) −29.3167 −3.16130
\(87\) 17.7675 1.90488
\(88\) −17.4895 −1.86439
\(89\) −9.21899 −0.977211 −0.488606 0.872505i \(-0.662494\pi\)
−0.488606 + 0.872505i \(0.662494\pi\)
\(90\) 11.6363 1.22658
\(91\) −5.27319 −0.552781
\(92\) 35.4190 3.69268
\(93\) 7.05788 0.731869
\(94\) −22.9998 −2.37225
\(95\) 8.48093 0.870125
\(96\) 20.3716 2.07917
\(97\) 11.4975 1.16740 0.583700 0.811970i \(-0.301605\pi\)
0.583700 + 0.811970i \(0.301605\pi\)
\(98\) −3.28630 −0.331967
\(99\) 3.46645 0.348391
\(100\) 22.5683 2.25683
\(101\) −1.09902 −0.109356 −0.0546781 0.998504i \(-0.517413\pi\)
−0.0546781 + 0.998504i \(0.517413\pi\)
\(102\) −6.28643 −0.622450
\(103\) −1.14210 −0.112534 −0.0562672 0.998416i \(-0.517920\pi\)
−0.0562672 + 0.998416i \(0.517920\pi\)
\(104\) −13.2670 −1.30094
\(105\) −18.8725 −1.84177
\(106\) 2.60343 0.252867
\(107\) −3.71761 −0.359395 −0.179698 0.983722i \(-0.557512\pi\)
−0.179698 + 0.983722i \(0.557512\pi\)
\(108\) 15.7603 1.51653
\(109\) 13.1796 1.26238 0.631188 0.775630i \(-0.282568\pi\)
0.631188 + 0.775630i \(0.282568\pi\)
\(110\) 19.6329 1.87192
\(111\) −0.366341 −0.0347716
\(112\) −26.6516 −2.51834
\(113\) −11.6824 −1.09899 −0.549495 0.835497i \(-0.685180\pi\)
−0.549495 + 0.835497i \(0.685180\pi\)
\(114\) −14.9088 −1.39634
\(115\) −23.1163 −2.15560
\(116\) −40.3172 −3.74336
\(117\) 2.62955 0.243102
\(118\) 29.1418 2.68272
\(119\) 3.29642 0.302182
\(120\) −47.4821 −4.33450
\(121\) −5.15138 −0.468308
\(122\) −11.9894 −1.08546
\(123\) −12.4270 −1.12050
\(124\) −16.0154 −1.43823
\(125\) 0.862042 0.0771034
\(126\) 10.7264 0.955583
\(127\) −16.1317 −1.43145 −0.715727 0.698380i \(-0.753905\pi\)
−0.715727 + 0.698380i \(0.753905\pi\)
\(128\) 2.05149 0.181328
\(129\) −23.7103 −2.08757
\(130\) 14.8929 1.30620
\(131\) −6.39654 −0.558868 −0.279434 0.960165i \(-0.590147\pi\)
−0.279434 + 0.960165i \(0.590147\pi\)
\(132\) −24.3290 −2.11757
\(133\) 7.81775 0.677885
\(134\) −31.0969 −2.68637
\(135\) −10.2860 −0.885277
\(136\) 8.29359 0.711170
\(137\) −17.7025 −1.51242 −0.756212 0.654327i \(-0.772952\pi\)
−0.756212 + 0.654327i \(0.772952\pi\)
\(138\) 40.6366 3.45922
\(139\) 8.82711 0.748706 0.374353 0.927286i \(-0.377865\pi\)
0.374353 + 0.927286i \(0.377865\pi\)
\(140\) 42.8246 3.61934
\(141\) −18.6014 −1.56652
\(142\) −14.7558 −1.23828
\(143\) 4.43659 0.371006
\(144\) 13.2902 1.10751
\(145\) 26.3131 2.18519
\(146\) −18.9582 −1.56899
\(147\) −2.65784 −0.219215
\(148\) 0.831284 0.0683311
\(149\) −7.70959 −0.631594 −0.315797 0.948827i \(-0.602272\pi\)
−0.315797 + 0.948827i \(0.602272\pi\)
\(150\) 25.8929 2.11415
\(151\) 1.00000 0.0813788
\(152\) 19.6690 1.59536
\(153\) −1.64381 −0.132894
\(154\) 18.0977 1.45835
\(155\) 10.4525 0.839565
\(156\) −18.4553 −1.47760
\(157\) 12.9140 1.03065 0.515323 0.856996i \(-0.327672\pi\)
0.515323 + 0.856996i \(0.327672\pi\)
\(158\) −44.8216 −3.56581
\(159\) 2.10556 0.166982
\(160\) 30.1697 2.38513
\(161\) −21.3086 −1.67936
\(162\) 29.2770 2.30022
\(163\) −10.5985 −0.830142 −0.415071 0.909789i \(-0.636243\pi\)
−0.415071 + 0.909789i \(0.636243\pi\)
\(164\) 28.1987 2.20195
\(165\) 15.8784 1.23613
\(166\) −17.1403 −1.33035
\(167\) −7.78287 −0.602256 −0.301128 0.953584i \(-0.597363\pi\)
−0.301128 + 0.953584i \(0.597363\pi\)
\(168\) −43.7691 −3.37686
\(169\) −9.63453 −0.741118
\(170\) −9.31000 −0.714045
\(171\) −3.89843 −0.298120
\(172\) 53.8022 4.10238
\(173\) 9.21198 0.700374 0.350187 0.936680i \(-0.386118\pi\)
0.350187 + 0.936680i \(0.386118\pi\)
\(174\) −46.2565 −3.50669
\(175\) −13.5775 −1.02636
\(176\) 22.4233 1.69022
\(177\) 23.5688 1.77154
\(178\) 24.0010 1.79895
\(179\) −16.7396 −1.25118 −0.625588 0.780154i \(-0.715141\pi\)
−0.625588 + 0.780154i \(0.715141\pi\)
\(180\) −21.3551 −1.59171
\(181\) −10.1252 −0.752599 −0.376300 0.926498i \(-0.622804\pi\)
−0.376300 + 0.926498i \(0.622804\pi\)
\(182\) 13.7284 1.01761
\(183\) −9.69655 −0.716790
\(184\) −53.6112 −3.95227
\(185\) −0.542539 −0.0398883
\(186\) −18.3747 −1.34730
\(187\) −2.77344 −0.202814
\(188\) 42.2094 3.07844
\(189\) −9.48165 −0.689689
\(190\) −22.0795 −1.60181
\(191\) −8.28663 −0.599599 −0.299800 0.954002i \(-0.596920\pi\)
−0.299800 + 0.954002i \(0.596920\pi\)
\(192\) −13.9907 −1.00969
\(193\) 8.42519 0.606458 0.303229 0.952918i \(-0.401935\pi\)
0.303229 + 0.952918i \(0.401935\pi\)
\(194\) −29.9330 −2.14907
\(195\) 12.0449 0.862552
\(196\) 6.03105 0.430789
\(197\) −10.8513 −0.773120 −0.386560 0.922264i \(-0.626337\pi\)
−0.386560 + 0.922264i \(0.626337\pi\)
\(198\) −9.02464 −0.641353
\(199\) 8.15319 0.577964 0.288982 0.957334i \(-0.406683\pi\)
0.288982 + 0.957334i \(0.406683\pi\)
\(200\) −34.1601 −2.41548
\(201\) −25.1501 −1.77395
\(202\) 2.86121 0.201314
\(203\) 24.2555 1.70240
\(204\) 11.5369 0.807745
\(205\) −18.4039 −1.28539
\(206\) 2.97337 0.207165
\(207\) 10.6258 0.738547
\(208\) 17.0097 1.17941
\(209\) −6.57745 −0.454972
\(210\) 49.1332 3.39051
\(211\) 15.9063 1.09503 0.547517 0.836795i \(-0.315573\pi\)
0.547517 + 0.836795i \(0.315573\pi\)
\(212\) −4.77783 −0.328143
\(213\) −11.9340 −0.817702
\(214\) 9.67853 0.661611
\(215\) −35.1142 −2.39477
\(216\) −23.8553 −1.62314
\(217\) 9.63514 0.654076
\(218\) −34.3121 −2.32391
\(219\) −15.3327 −1.03609
\(220\) −36.0304 −2.42917
\(221\) −2.10385 −0.141520
\(222\) 0.953742 0.0640110
\(223\) −6.17856 −0.413747 −0.206874 0.978368i \(-0.566329\pi\)
−0.206874 + 0.978368i \(0.566329\pi\)
\(224\) 27.8105 1.85817
\(225\) 6.77059 0.451373
\(226\) 30.4143 2.02313
\(227\) 13.1201 0.870808 0.435404 0.900235i \(-0.356605\pi\)
0.435404 + 0.900235i \(0.356605\pi\)
\(228\) 27.3608 1.81201
\(229\) 27.5176 1.81841 0.909206 0.416347i \(-0.136690\pi\)
0.909206 + 0.416347i \(0.136690\pi\)
\(230\) 60.1815 3.96825
\(231\) 14.6367 0.963026
\(232\) 61.0254 4.00652
\(233\) −11.7976 −0.772888 −0.386444 0.922313i \(-0.626297\pi\)
−0.386444 + 0.922313i \(0.626297\pi\)
\(234\) −6.84583 −0.447526
\(235\) −27.5481 −1.79704
\(236\) −53.4812 −3.48133
\(237\) −36.2501 −2.35469
\(238\) −8.58199 −0.556288
\(239\) 17.6842 1.14390 0.571949 0.820289i \(-0.306187\pi\)
0.571949 + 0.820289i \(0.306187\pi\)
\(240\) 60.8768 3.92958
\(241\) 26.1273 1.68301 0.841504 0.540252i \(-0.181671\pi\)
0.841504 + 0.540252i \(0.181671\pi\)
\(242\) 13.4112 0.862108
\(243\) 13.7823 0.884134
\(244\) 22.0030 1.40859
\(245\) −3.93618 −0.251473
\(246\) 32.3527 2.06273
\(247\) −4.98947 −0.317472
\(248\) 24.2414 1.53933
\(249\) −13.8625 −0.878498
\(250\) −2.24426 −0.141940
\(251\) 7.36307 0.464753 0.232376 0.972626i \(-0.425350\pi\)
0.232376 + 0.972626i \(0.425350\pi\)
\(252\) −19.6852 −1.24005
\(253\) 17.9280 1.12712
\(254\) 41.9976 2.63516
\(255\) −7.52959 −0.471521
\(256\) −18.6302 −1.16439
\(257\) 9.21560 0.574853 0.287427 0.957803i \(-0.407200\pi\)
0.287427 + 0.957803i \(0.407200\pi\)
\(258\) 61.7280 3.84302
\(259\) −0.500114 −0.0310756
\(260\) −27.3317 −1.69504
\(261\) −12.0954 −0.748683
\(262\) 16.6529 1.02882
\(263\) 5.45855 0.336589 0.168294 0.985737i \(-0.446174\pi\)
0.168294 + 0.985737i \(0.446174\pi\)
\(264\) 36.8251 2.26643
\(265\) 3.11826 0.191553
\(266\) −20.3529 −1.24792
\(267\) 19.4111 1.18794
\(268\) 57.0693 3.48607
\(269\) 0.229111 0.0139692 0.00698458 0.999976i \(-0.497777\pi\)
0.00698458 + 0.999976i \(0.497777\pi\)
\(270\) 26.7788 1.62971
\(271\) −27.0134 −1.64095 −0.820474 0.571683i \(-0.806291\pi\)
−0.820474 + 0.571683i \(0.806291\pi\)
\(272\) −10.6332 −0.644734
\(273\) 11.1030 0.671984
\(274\) 46.0871 2.78422
\(275\) 11.4234 0.688856
\(276\) −74.5766 −4.48899
\(277\) −7.48661 −0.449827 −0.224913 0.974379i \(-0.572210\pi\)
−0.224913 + 0.974379i \(0.572210\pi\)
\(278\) −22.9807 −1.37829
\(279\) −4.80469 −0.287650
\(280\) −64.8207 −3.87378
\(281\) −9.40201 −0.560877 −0.280438 0.959872i \(-0.590480\pi\)
−0.280438 + 0.959872i \(0.590480\pi\)
\(282\) 48.4274 2.88381
\(283\) 3.56935 0.212176 0.106088 0.994357i \(-0.466167\pi\)
0.106088 + 0.994357i \(0.466167\pi\)
\(284\) 27.0800 1.60690
\(285\) −17.8571 −1.05776
\(286\) −11.5503 −0.682986
\(287\) −16.9648 −1.00140
\(288\) −13.8681 −0.817186
\(289\) −15.6848 −0.922637
\(290\) −68.5043 −4.02271
\(291\) −24.2087 −1.41914
\(292\) 34.7922 2.03606
\(293\) −1.73143 −0.101151 −0.0505756 0.998720i \(-0.516106\pi\)
−0.0505756 + 0.998720i \(0.516106\pi\)
\(294\) 6.91949 0.403553
\(295\) 34.9046 2.03223
\(296\) −1.25826 −0.0731347
\(297\) 7.97738 0.462894
\(298\) 20.0713 1.16270
\(299\) 13.5997 0.786489
\(300\) −47.5189 −2.74350
\(301\) −32.3683 −1.86568
\(302\) −2.60343 −0.149810
\(303\) 2.31404 0.132938
\(304\) −25.2176 −1.44633
\(305\) −14.3603 −0.822267
\(306\) 4.27953 0.244644
\(307\) 20.9626 1.19640 0.598200 0.801347i \(-0.295883\pi\)
0.598200 + 0.801347i \(0.295883\pi\)
\(308\) −33.2130 −1.89248
\(309\) 2.40476 0.136802
\(310\) −27.2123 −1.54555
\(311\) −28.8653 −1.63680 −0.818401 0.574648i \(-0.805139\pi\)
−0.818401 + 0.574648i \(0.805139\pi\)
\(312\) 27.9345 1.58148
\(313\) 3.01806 0.170591 0.0852953 0.996356i \(-0.472817\pi\)
0.0852953 + 0.996356i \(0.472817\pi\)
\(314\) −33.6206 −1.89732
\(315\) 12.8476 0.723879
\(316\) 82.2569 4.62731
\(317\) −10.0915 −0.566796 −0.283398 0.959002i \(-0.591462\pi\)
−0.283398 + 0.959002i \(0.591462\pi\)
\(318\) −5.48166 −0.307396
\(319\) −20.4074 −1.14259
\(320\) −20.7198 −1.15827
\(321\) 7.82765 0.436897
\(322\) 55.4755 3.09153
\(323\) 3.11906 0.173549
\(324\) −53.7293 −2.98496
\(325\) 8.66546 0.480673
\(326\) 27.5925 1.52821
\(327\) −27.7504 −1.53460
\(328\) −42.6824 −2.35674
\(329\) −25.3939 −1.40001
\(330\) −41.3382 −2.27559
\(331\) −11.0858 −0.609332 −0.304666 0.952459i \(-0.598545\pi\)
−0.304666 + 0.952459i \(0.598545\pi\)
\(332\) 31.4560 1.72637
\(333\) 0.249389 0.0136664
\(334\) 20.2621 1.10869
\(335\) −37.2464 −2.03499
\(336\) 56.1164 3.06140
\(337\) −31.3708 −1.70888 −0.854438 0.519553i \(-0.826098\pi\)
−0.854438 + 0.519553i \(0.826098\pi\)
\(338\) 25.0828 1.36432
\(339\) 24.5980 1.33598
\(340\) 17.0858 0.926607
\(341\) −8.10651 −0.438992
\(342\) 10.1493 0.548809
\(343\) 16.4926 0.890515
\(344\) −81.4367 −4.39077
\(345\) 48.6726 2.62045
\(346\) −23.9827 −1.28932
\(347\) −34.2494 −1.83860 −0.919302 0.393552i \(-0.871246\pi\)
−0.919302 + 0.393552i \(0.871246\pi\)
\(348\) 84.8902 4.55059
\(349\) −24.6937 −1.32182 −0.660912 0.750464i \(-0.729830\pi\)
−0.660912 + 0.750464i \(0.729830\pi\)
\(350\) 35.3480 1.88943
\(351\) 6.05141 0.323000
\(352\) −23.3984 −1.24714
\(353\) −4.84620 −0.257937 −0.128969 0.991649i \(-0.541167\pi\)
−0.128969 + 0.991649i \(0.541167\pi\)
\(354\) −61.3597 −3.26123
\(355\) −17.6738 −0.938028
\(356\) −44.0468 −2.33447
\(357\) −6.94080 −0.367346
\(358\) 43.5803 2.30329
\(359\) 3.40300 0.179604 0.0898018 0.995960i \(-0.471377\pi\)
0.0898018 + 0.995960i \(0.471377\pi\)
\(360\) 32.3237 1.70361
\(361\) −11.6029 −0.610678
\(362\) 26.3602 1.38546
\(363\) 10.8465 0.569295
\(364\) −25.1944 −1.32055
\(365\) −22.7072 −1.18855
\(366\) 25.2443 1.31954
\(367\) −13.7289 −0.716643 −0.358322 0.933598i \(-0.616651\pi\)
−0.358322 + 0.933598i \(0.616651\pi\)
\(368\) 68.7350 3.58306
\(369\) 8.45973 0.440396
\(370\) 1.41246 0.0734304
\(371\) 2.87442 0.149233
\(372\) 33.7214 1.74837
\(373\) −12.5540 −0.650020 −0.325010 0.945711i \(-0.605368\pi\)
−0.325010 + 0.945711i \(0.605368\pi\)
\(374\) 7.22045 0.373360
\(375\) −1.81508 −0.0937302
\(376\) −63.8895 −3.29485
\(377\) −15.4804 −0.797283
\(378\) 24.6848 1.26965
\(379\) 10.7005 0.549646 0.274823 0.961495i \(-0.411381\pi\)
0.274823 + 0.961495i \(0.411381\pi\)
\(380\) 40.5204 2.07865
\(381\) 33.9661 1.74014
\(382\) 21.5736 1.10380
\(383\) −5.56562 −0.284390 −0.142195 0.989839i \(-0.545416\pi\)
−0.142195 + 0.989839i \(0.545416\pi\)
\(384\) −4.31953 −0.220430
\(385\) 21.6765 1.10474
\(386\) −21.9344 −1.11643
\(387\) 16.1409 0.820488
\(388\) 54.9333 2.78882
\(389\) 1.98394 0.100590 0.0502948 0.998734i \(-0.483984\pi\)
0.0502948 + 0.998734i \(0.483984\pi\)
\(390\) −31.3579 −1.58787
\(391\) −8.50154 −0.429941
\(392\) −9.12878 −0.461073
\(393\) 13.4683 0.679385
\(394\) 28.2505 1.42324
\(395\) −53.6852 −2.70119
\(396\) 16.5621 0.832276
\(397\) 4.54884 0.228300 0.114150 0.993464i \(-0.463586\pi\)
0.114150 + 0.993464i \(0.463586\pi\)
\(398\) −21.2262 −1.06397
\(399\) −16.4607 −0.824066
\(400\) 43.7967 2.18983
\(401\) 10.2916 0.513938 0.256969 0.966420i \(-0.417276\pi\)
0.256969 + 0.966420i \(0.417276\pi\)
\(402\) 65.4764 3.26566
\(403\) −6.14937 −0.306322
\(404\) −5.25091 −0.261243
\(405\) 35.0666 1.74247
\(406\) −63.1475 −3.13396
\(407\) 0.420771 0.0208568
\(408\) −17.4626 −0.864529
\(409\) 23.1406 1.14423 0.572113 0.820174i \(-0.306124\pi\)
0.572113 + 0.820174i \(0.306124\pi\)
\(410\) 47.9133 2.36627
\(411\) 37.2735 1.83857
\(412\) −5.45676 −0.268835
\(413\) 32.1752 1.58324
\(414\) −27.6636 −1.35959
\(415\) −20.5299 −1.00777
\(416\) −17.7493 −0.870233
\(417\) −18.5860 −0.910160
\(418\) 17.1239 0.837558
\(419\) −32.6233 −1.59375 −0.796877 0.604141i \(-0.793516\pi\)
−0.796877 + 0.604141i \(0.793516\pi\)
\(420\) −90.1696 −4.39983
\(421\) 1.56663 0.0763527 0.0381763 0.999271i \(-0.487845\pi\)
0.0381763 + 0.999271i \(0.487845\pi\)
\(422\) −41.4108 −2.01585
\(423\) 12.6630 0.615697
\(424\) 7.23187 0.351211
\(425\) −5.41702 −0.262764
\(426\) 31.0692 1.50531
\(427\) −13.2373 −0.640600
\(428\) −17.7621 −0.858564
\(429\) −9.34150 −0.451012
\(430\) 91.4171 4.40852
\(431\) −7.61945 −0.367016 −0.183508 0.983018i \(-0.558745\pi\)
−0.183508 + 0.983018i \(0.558745\pi\)
\(432\) 30.5848 1.47151
\(433\) 36.3567 1.74719 0.873595 0.486653i \(-0.161783\pi\)
0.873595 + 0.486653i \(0.161783\pi\)
\(434\) −25.0844 −1.20409
\(435\) −55.4038 −2.65641
\(436\) 62.9698 3.01571
\(437\) −20.1621 −0.964485
\(438\) 39.9175 1.90733
\(439\) 0.259507 0.0123856 0.00619279 0.999981i \(-0.498029\pi\)
0.00619279 + 0.999981i \(0.498029\pi\)
\(440\) 54.5368 2.59994
\(441\) 1.80934 0.0861591
\(442\) 5.47722 0.260525
\(443\) −1.00607 −0.0478000 −0.0239000 0.999714i \(-0.507608\pi\)
−0.0239000 + 0.999714i \(0.507608\pi\)
\(444\) −1.75032 −0.0830663
\(445\) 28.7472 1.36275
\(446\) 16.0854 0.761667
\(447\) 16.2330 0.767793
\(448\) −19.0995 −0.902369
\(449\) 37.5862 1.77380 0.886901 0.461960i \(-0.152853\pi\)
0.886901 + 0.461960i \(0.152853\pi\)
\(450\) −17.6267 −0.830933
\(451\) 14.2733 0.672104
\(452\) −55.8166 −2.62539
\(453\) −2.10556 −0.0989277
\(454\) −34.1571 −1.60307
\(455\) 16.4432 0.770868
\(456\) −41.4141 −1.93939
\(457\) 3.90339 0.182593 0.0912965 0.995824i \(-0.470899\pi\)
0.0912965 + 0.995824i \(0.470899\pi\)
\(458\) −71.6399 −3.34751
\(459\) −3.78291 −0.176571
\(460\) −110.446 −5.14955
\(461\) −10.7162 −0.499102 −0.249551 0.968362i \(-0.580283\pi\)
−0.249551 + 0.968362i \(0.580283\pi\)
\(462\) −38.1056 −1.77283
\(463\) −20.1213 −0.935118 −0.467559 0.883962i \(-0.654866\pi\)
−0.467559 + 0.883962i \(0.654866\pi\)
\(464\) −78.2407 −3.63223
\(465\) −22.0083 −1.02061
\(466\) 30.7143 1.42281
\(467\) −20.2956 −0.939168 −0.469584 0.882888i \(-0.655596\pi\)
−0.469584 + 0.882888i \(0.655596\pi\)
\(468\) 12.5635 0.580749
\(469\) −34.3339 −1.58539
\(470\) 71.7194 3.30817
\(471\) −27.1911 −1.25290
\(472\) 80.9508 3.72606
\(473\) 27.2331 1.25218
\(474\) 94.3744 4.33476
\(475\) −12.8469 −0.589458
\(476\) 15.7497 0.721888
\(477\) −1.43337 −0.0656295
\(478\) −46.0396 −2.10580
\(479\) −13.6281 −0.622682 −0.311341 0.950298i \(-0.600778\pi\)
−0.311341 + 0.950298i \(0.600778\pi\)
\(480\) −63.5241 −2.89947
\(481\) 0.319184 0.0145536
\(482\) −68.0205 −3.09825
\(483\) 44.8666 2.04150
\(484\) −24.6124 −1.11875
\(485\) −35.8524 −1.62797
\(486\) −35.8811 −1.62760
\(487\) −32.7962 −1.48614 −0.743068 0.669216i \(-0.766630\pi\)
−0.743068 + 0.669216i \(0.766630\pi\)
\(488\) −33.3044 −1.50762
\(489\) 22.3158 1.00916
\(490\) 10.2475 0.462937
\(491\) 28.7546 1.29768 0.648839 0.760926i \(-0.275255\pi\)
0.648839 + 0.760926i \(0.275255\pi\)
\(492\) −59.3739 −2.67678
\(493\) 9.67726 0.435842
\(494\) 12.9897 0.584434
\(495\) −10.8093 −0.485841
\(496\) −31.0799 −1.39553
\(497\) −16.2918 −0.730786
\(498\) 36.0899 1.61723
\(499\) −40.7905 −1.82603 −0.913017 0.407922i \(-0.866254\pi\)
−0.913017 + 0.407922i \(0.866254\pi\)
\(500\) 4.11869 0.184193
\(501\) 16.3873 0.732129
\(502\) −19.1692 −0.855564
\(503\) 7.43127 0.331344 0.165672 0.986181i \(-0.447021\pi\)
0.165672 + 0.986181i \(0.447021\pi\)
\(504\) 29.7961 1.32722
\(505\) 3.42702 0.152500
\(506\) −46.6742 −2.07492
\(507\) 20.2860 0.900935
\(508\) −77.0743 −3.41962
\(509\) 24.5901 1.08994 0.544969 0.838456i \(-0.316541\pi\)
0.544969 + 0.838456i \(0.316541\pi\)
\(510\) 19.6027 0.868024
\(511\) −20.9316 −0.925958
\(512\) 44.3994 1.96220
\(513\) −8.97149 −0.396101
\(514\) −23.9921 −1.05825
\(515\) 3.56137 0.156933
\(516\) −113.284 −4.98703
\(517\) 21.3651 0.939637
\(518\) 1.30201 0.0572071
\(519\) −19.3964 −0.851405
\(520\) 41.3700 1.81420
\(521\) 18.9188 0.828849 0.414425 0.910084i \(-0.363983\pi\)
0.414425 + 0.910084i \(0.363983\pi\)
\(522\) 31.4894 1.37825
\(523\) −2.54933 −0.111475 −0.0557373 0.998445i \(-0.517751\pi\)
−0.0557373 + 0.998445i \(0.517751\pi\)
\(524\) −30.5616 −1.33509
\(525\) 28.5881 1.24769
\(526\) −14.2109 −0.619626
\(527\) 3.84415 0.167454
\(528\) −47.2135 −2.05470
\(529\) 31.9554 1.38937
\(530\) −8.11816 −0.352630
\(531\) −16.0446 −0.696276
\(532\) 37.3518 1.61941
\(533\) 10.8273 0.468983
\(534\) −50.5354 −2.18688
\(535\) 11.5925 0.501187
\(536\) −86.3819 −3.73113
\(537\) 35.2462 1.52098
\(538\) −0.596474 −0.0257158
\(539\) 3.05273 0.131490
\(540\) −49.1447 −2.11485
\(541\) −1.87421 −0.0805787 −0.0402894 0.999188i \(-0.512828\pi\)
−0.0402894 + 0.999188i \(0.512828\pi\)
\(542\) 70.3275 3.02082
\(543\) 21.3192 0.914893
\(544\) 11.0956 0.475720
\(545\) −41.0974 −1.76042
\(546\) −28.9058 −1.23706
\(547\) 26.1275 1.11713 0.558566 0.829460i \(-0.311352\pi\)
0.558566 + 0.829460i \(0.311352\pi\)
\(548\) −84.5793 −3.61305
\(549\) 6.60098 0.281723
\(550\) −29.7400 −1.26812
\(551\) 22.9505 0.977722
\(552\) 112.882 4.80456
\(553\) −49.4871 −2.10441
\(554\) 19.4908 0.828086
\(555\) 1.14235 0.0484899
\(556\) 42.1744 1.78859
\(557\) −10.6045 −0.449328 −0.224664 0.974436i \(-0.572128\pi\)
−0.224664 + 0.974436i \(0.572128\pi\)
\(558\) 12.5087 0.529534
\(559\) 20.6582 0.873749
\(560\) 83.1066 3.51189
\(561\) 5.83963 0.246550
\(562\) 24.4774 1.03252
\(563\) 36.1406 1.52315 0.761573 0.648079i \(-0.224428\pi\)
0.761573 + 0.648079i \(0.224428\pi\)
\(564\) −88.8743 −3.74228
\(565\) 36.4289 1.53257
\(566\) −9.29255 −0.390595
\(567\) 32.3245 1.35750
\(568\) −40.9891 −1.71986
\(569\) 19.6044 0.821859 0.410930 0.911667i \(-0.365204\pi\)
0.410930 + 0.911667i \(0.365204\pi\)
\(570\) 46.4896 1.94723
\(571\) −11.3403 −0.474575 −0.237287 0.971439i \(-0.576258\pi\)
−0.237287 + 0.971439i \(0.576258\pi\)
\(572\) 21.1973 0.886302
\(573\) 17.4480 0.728899
\(574\) 44.1666 1.84348
\(575\) 35.0166 1.46029
\(576\) 9.52425 0.396844
\(577\) 26.6265 1.10848 0.554239 0.832358i \(-0.313009\pi\)
0.554239 + 0.832358i \(0.313009\pi\)
\(578\) 40.8343 1.69848
\(579\) −17.7397 −0.737237
\(580\) 125.720 5.22023
\(581\) −18.9245 −0.785120
\(582\) 63.0257 2.61250
\(583\) −2.41839 −0.100160
\(584\) −52.6626 −2.17919
\(585\) −8.19962 −0.339012
\(586\) 4.50765 0.186209
\(587\) 13.8787 0.572837 0.286418 0.958105i \(-0.407535\pi\)
0.286418 + 0.958105i \(0.407535\pi\)
\(588\) −12.6987 −0.523686
\(589\) 9.11672 0.375648
\(590\) −90.8717 −3.74113
\(591\) 22.8480 0.939839
\(592\) 1.61321 0.0663026
\(593\) 27.5515 1.13141 0.565703 0.824609i \(-0.308605\pi\)
0.565703 + 0.824609i \(0.308605\pi\)
\(594\) −20.7685 −0.852142
\(595\) −10.2791 −0.421402
\(596\) −36.8351 −1.50882
\(597\) −17.1670 −0.702599
\(598\) −35.4057 −1.44785
\(599\) −22.3145 −0.911747 −0.455873 0.890045i \(-0.650673\pi\)
−0.455873 + 0.890045i \(0.650673\pi\)
\(600\) 71.9260 2.93637
\(601\) 26.4895 1.08053 0.540265 0.841495i \(-0.318324\pi\)
0.540265 + 0.841495i \(0.318324\pi\)
\(602\) 84.2685 3.43453
\(603\) 17.1211 0.697223
\(604\) 4.77783 0.194407
\(605\) 16.0634 0.653068
\(606\) −6.02444 −0.244726
\(607\) −32.4369 −1.31658 −0.658288 0.752767i \(-0.728719\pi\)
−0.658288 + 0.752767i \(0.728719\pi\)
\(608\) 26.3142 1.06718
\(609\) −51.0714 −2.06952
\(610\) 37.3859 1.51371
\(611\) 16.2070 0.655664
\(612\) −7.85382 −0.317472
\(613\) 13.1127 0.529616 0.264808 0.964301i \(-0.414691\pi\)
0.264808 + 0.964301i \(0.414691\pi\)
\(614\) −54.5746 −2.20245
\(615\) 38.7505 1.56257
\(616\) 50.2722 2.02552
\(617\) −15.8369 −0.637571 −0.318786 0.947827i \(-0.603275\pi\)
−0.318786 + 0.947827i \(0.603275\pi\)
\(618\) −6.26061 −0.251838
\(619\) 25.4218 1.02179 0.510894 0.859643i \(-0.329314\pi\)
0.510894 + 0.859643i \(0.329314\pi\)
\(620\) 49.9402 2.00565
\(621\) 24.4534 0.981280
\(622\) 75.1487 3.01319
\(623\) 26.4993 1.06167
\(624\) −35.8148 −1.43374
\(625\) −26.3058 −1.05223
\(626\) −7.85729 −0.314040
\(627\) 13.8492 0.553084
\(628\) 61.7007 2.46213
\(629\) −0.199531 −0.00795583
\(630\) −33.4477 −1.33259
\(631\) 19.7801 0.787431 0.393716 0.919232i \(-0.371189\pi\)
0.393716 + 0.919232i \(0.371189\pi\)
\(632\) −124.507 −4.95261
\(633\) −33.4916 −1.33117
\(634\) 26.2725 1.04342
\(635\) 50.3028 1.99620
\(636\) 10.0600 0.398904
\(637\) 2.31571 0.0917520
\(638\) 53.1291 2.10340
\(639\) 8.12411 0.321385
\(640\) −6.39708 −0.252867
\(641\) −42.1216 −1.66371 −0.831853 0.554997i \(-0.812719\pi\)
−0.831853 + 0.554997i \(0.812719\pi\)
\(642\) −20.3787 −0.804283
\(643\) 31.7401 1.25171 0.625855 0.779940i \(-0.284750\pi\)
0.625855 + 0.779940i \(0.284750\pi\)
\(644\) −101.809 −4.01184
\(645\) 73.9348 2.91118
\(646\) −8.12023 −0.319486
\(647\) 35.3864 1.39118 0.695592 0.718437i \(-0.255142\pi\)
0.695592 + 0.718437i \(0.255142\pi\)
\(648\) 81.3264 3.19480
\(649\) −27.0706 −1.06261
\(650\) −22.5599 −0.884871
\(651\) −20.2873 −0.795123
\(652\) −50.6380 −1.98314
\(653\) 33.1889 1.29878 0.649390 0.760455i \(-0.275024\pi\)
0.649390 + 0.760455i \(0.275024\pi\)
\(654\) 72.2460 2.82504
\(655\) 19.9461 0.779358
\(656\) 54.7231 2.13658
\(657\) 10.4378 0.407218
\(658\) 66.1111 2.57728
\(659\) −17.9433 −0.698973 −0.349486 0.936941i \(-0.613644\pi\)
−0.349486 + 0.936941i \(0.613644\pi\)
\(660\) 75.8641 2.95301
\(661\) 42.7462 1.66263 0.831317 0.555799i \(-0.187587\pi\)
0.831317 + 0.555799i \(0.187587\pi\)
\(662\) 28.8611 1.12172
\(663\) 4.42978 0.172038
\(664\) −47.6128 −1.84774
\(665\) −24.3778 −0.945329
\(666\) −0.649265 −0.0251585
\(667\) −62.5555 −2.42216
\(668\) −37.1852 −1.43874
\(669\) 13.0093 0.502969
\(670\) 96.9684 3.74622
\(671\) 11.1372 0.429948
\(672\) −58.5567 −2.25887
\(673\) −38.0184 −1.46550 −0.732752 0.680496i \(-0.761764\pi\)
−0.732752 + 0.680496i \(0.761764\pi\)
\(674\) 81.6715 3.14587
\(675\) 15.5812 0.599722
\(676\) −46.0321 −1.77047
\(677\) −38.3302 −1.47315 −0.736574 0.676356i \(-0.763558\pi\)
−0.736574 + 0.676356i \(0.763558\pi\)
\(678\) −64.0391 −2.45941
\(679\) −33.0488 −1.26830
\(680\) −25.8616 −0.991747
\(681\) −27.6250 −1.05859
\(682\) 21.1047 0.808141
\(683\) 48.9025 1.87120 0.935601 0.353059i \(-0.114859\pi\)
0.935601 + 0.353059i \(0.114859\pi\)
\(684\) −18.6260 −0.712183
\(685\) 55.2009 2.10912
\(686\) −42.9372 −1.63935
\(687\) −57.9398 −2.21054
\(688\) 104.410 3.98060
\(689\) −1.83452 −0.0698897
\(690\) −126.716 −4.82398
\(691\) −23.2103 −0.882962 −0.441481 0.897270i \(-0.645547\pi\)
−0.441481 + 0.897270i \(0.645547\pi\)
\(692\) 44.0133 1.67313
\(693\) −9.96403 −0.378502
\(694\) 89.1658 3.38469
\(695\) −27.5252 −1.04409
\(696\) −128.493 −4.87050
\(697\) −6.76847 −0.256374
\(698\) 64.2882 2.43335
\(699\) 24.8406 0.939557
\(700\) −64.8708 −2.45189
\(701\) 10.5649 0.399031 0.199516 0.979895i \(-0.436063\pi\)
0.199516 + 0.979895i \(0.436063\pi\)
\(702\) −15.7544 −0.594611
\(703\) −0.473206 −0.0178473
\(704\) 16.0694 0.605638
\(705\) 58.0040 2.18456
\(706\) 12.6167 0.474837
\(707\) 3.15904 0.118808
\(708\) 112.608 4.23206
\(709\) 1.86325 0.0699759 0.0349879 0.999388i \(-0.488861\pi\)
0.0349879 + 0.999388i \(0.488861\pi\)
\(710\) 46.0125 1.72682
\(711\) 24.6774 0.925476
\(712\) 66.6705 2.49858
\(713\) −24.8492 −0.930611
\(714\) 18.0699 0.676248
\(715\) −13.8345 −0.517379
\(716\) −79.9789 −2.98895
\(717\) −37.2352 −1.39057
\(718\) −8.85947 −0.330632
\(719\) 30.4429 1.13533 0.567664 0.823261i \(-0.307847\pi\)
0.567664 + 0.823261i \(0.307847\pi\)
\(720\) −41.4422 −1.54446
\(721\) 3.28288 0.122261
\(722\) 30.2073 1.12420
\(723\) −55.0125 −2.04594
\(724\) −48.3764 −1.79790
\(725\) −39.8592 −1.48033
\(726\) −28.2381 −1.04802
\(727\) 13.0250 0.483071 0.241536 0.970392i \(-0.422349\pi\)
0.241536 + 0.970392i \(0.422349\pi\)
\(728\) 38.1350 1.41338
\(729\) 4.71731 0.174715
\(730\) 59.1166 2.18800
\(731\) −12.9140 −0.477643
\(732\) −46.3285 −1.71235
\(733\) −4.39230 −0.162233 −0.0811166 0.996705i \(-0.525849\pi\)
−0.0811166 + 0.996705i \(0.525849\pi\)
\(734\) 35.7422 1.31927
\(735\) 8.28784 0.305702
\(736\) −71.7240 −2.64378
\(737\) 28.8868 1.06406
\(738\) −22.0243 −0.810725
\(739\) 13.0948 0.481701 0.240850 0.970562i \(-0.422574\pi\)
0.240850 + 0.970562i \(0.422574\pi\)
\(740\) −2.59216 −0.0952897
\(741\) 10.5056 0.385933
\(742\) −7.48334 −0.274722
\(743\) 31.9827 1.17333 0.586666 0.809829i \(-0.300440\pi\)
0.586666 + 0.809829i \(0.300440\pi\)
\(744\) −51.0417 −1.87128
\(745\) 24.0405 0.880776
\(746\) 32.6833 1.19662
\(747\) 9.43695 0.345280
\(748\) −13.2510 −0.484505
\(749\) 10.6860 0.390457
\(750\) 4.72542 0.172548
\(751\) 15.5328 0.566800 0.283400 0.959002i \(-0.408538\pi\)
0.283400 + 0.959002i \(0.408538\pi\)
\(752\) 81.9127 2.98705
\(753\) −15.5034 −0.564974
\(754\) 40.3022 1.46772
\(755\) −3.11826 −0.113485
\(756\) −45.3017 −1.64761
\(757\) 28.2029 1.02505 0.512527 0.858671i \(-0.328710\pi\)
0.512527 + 0.858671i \(0.328710\pi\)
\(758\) −27.8579 −1.01184
\(759\) −37.7484 −1.37018
\(760\) −61.3330 −2.22478
\(761\) −14.4565 −0.524049 −0.262024 0.965061i \(-0.584390\pi\)
−0.262024 + 0.965061i \(0.584390\pi\)
\(762\) −88.4284 −3.20342
\(763\) −37.8837 −1.37148
\(764\) −39.5921 −1.43239
\(765\) 5.12581 0.185324
\(766\) 14.4897 0.523534
\(767\) −20.5350 −0.741474
\(768\) 39.2270 1.41548
\(769\) −50.5303 −1.82217 −0.911085 0.412218i \(-0.864754\pi\)
−0.911085 + 0.412218i \(0.864754\pi\)
\(770\) −56.4332 −2.03371
\(771\) −19.4040 −0.698817
\(772\) 40.2541 1.44878
\(773\) 24.5709 0.883755 0.441878 0.897075i \(-0.354313\pi\)
0.441878 + 0.897075i \(0.354313\pi\)
\(774\) −42.0217 −1.51044
\(775\) −15.8335 −0.568755
\(776\) −83.1488 −2.98487
\(777\) 1.05302 0.0377768
\(778\) −5.16504 −0.185176
\(779\) −16.0520 −0.575123
\(780\) 57.5483 2.06056
\(781\) 13.7071 0.490477
\(782\) 22.1331 0.791479
\(783\) −27.8352 −0.994748
\(784\) 11.7040 0.418000
\(785\) −40.2691 −1.43727
\(786\) −35.0637 −1.25068
\(787\) 0.712695 0.0254048 0.0127024 0.999919i \(-0.495957\pi\)
0.0127024 + 0.999919i \(0.495957\pi\)
\(788\) −51.8455 −1.84692
\(789\) −11.4933 −0.409172
\(790\) 139.765 4.97263
\(791\) 33.5802 1.19398
\(792\) −25.0689 −0.890785
\(793\) 8.44838 0.300011
\(794\) −11.8426 −0.420277
\(795\) −6.56568 −0.232861
\(796\) 38.9545 1.38071
\(797\) −15.5735 −0.551643 −0.275821 0.961209i \(-0.588950\pi\)
−0.275821 + 0.961209i \(0.588950\pi\)
\(798\) 42.8542 1.51702
\(799\) −10.1314 −0.358424
\(800\) −45.7012 −1.61578
\(801\) −13.2142 −0.466902
\(802\) −26.7934 −0.946109
\(803\) 17.6108 0.621470
\(804\) −120.163 −4.23781
\(805\) 66.4459 2.34191
\(806\) 16.0094 0.563908
\(807\) −0.482407 −0.0169815
\(808\) 7.94794 0.279608
\(809\) 24.9084 0.875731 0.437866 0.899040i \(-0.355735\pi\)
0.437866 + 0.899040i \(0.355735\pi\)
\(810\) −91.2933 −3.20772
\(811\) 0.626148 0.0219870 0.0109935 0.999940i \(-0.496501\pi\)
0.0109935 + 0.999940i \(0.496501\pi\)
\(812\) 115.889 4.06690
\(813\) 56.8783 1.99481
\(814\) −1.09545 −0.0383953
\(815\) 33.0490 1.15766
\(816\) 22.3888 0.783766
\(817\) −30.6267 −1.07149
\(818\) −60.2447 −2.10641
\(819\) −7.55843 −0.264113
\(820\) −87.9308 −3.07068
\(821\) −27.7072 −0.966990 −0.483495 0.875347i \(-0.660633\pi\)
−0.483495 + 0.875347i \(0.660633\pi\)
\(822\) −97.0389 −3.38462
\(823\) −0.527453 −0.0183858 −0.00919292 0.999958i \(-0.502926\pi\)
−0.00919292 + 0.999958i \(0.502926\pi\)
\(824\) 8.25952 0.287734
\(825\) −24.0526 −0.837404
\(826\) −83.7657 −2.91458
\(827\) 23.5939 0.820439 0.410219 0.911987i \(-0.365452\pi\)
0.410219 + 0.911987i \(0.365452\pi\)
\(828\) 50.7685 1.76433
\(829\) 39.9718 1.38828 0.694139 0.719841i \(-0.255786\pi\)
0.694139 + 0.719841i \(0.255786\pi\)
\(830\) 53.4480 1.85521
\(831\) 15.7635 0.546829
\(832\) 12.1898 0.422604
\(833\) −1.44762 −0.0501570
\(834\) 48.3873 1.67551
\(835\) 24.2690 0.839864
\(836\) −31.4259 −1.08689
\(837\) −11.0571 −0.382189
\(838\) 84.9325 2.93394
\(839\) 44.8442 1.54819 0.774097 0.633066i \(-0.218204\pi\)
0.774097 + 0.633066i \(0.218204\pi\)
\(840\) 136.484 4.70913
\(841\) 42.2067 1.45540
\(842\) −4.07859 −0.140558
\(843\) 19.7965 0.681827
\(844\) 75.9974 2.61594
\(845\) 30.0430 1.03351
\(846\) −32.9672 −1.13344
\(847\) 14.8073 0.508783
\(848\) −9.27198 −0.318401
\(849\) −7.51547 −0.257930
\(850\) 14.1028 0.483723
\(851\) 1.28981 0.0442140
\(852\) −57.0184 −1.95342
\(853\) 13.9018 0.475987 0.237994 0.971267i \(-0.423510\pi\)
0.237994 + 0.971267i \(0.423510\pi\)
\(854\) 34.4625 1.17928
\(855\) 12.1563 0.415737
\(856\) 26.8853 0.918920
\(857\) −4.62121 −0.157858 −0.0789288 0.996880i \(-0.525150\pi\)
−0.0789288 + 0.996880i \(0.525150\pi\)
\(858\) 24.3199 0.830268
\(859\) −39.2826 −1.34030 −0.670152 0.742224i \(-0.733771\pi\)
−0.670152 + 0.742224i \(0.733771\pi\)
\(860\) −167.769 −5.72089
\(861\) 35.7203 1.21735
\(862\) 19.8367 0.675639
\(863\) −55.4728 −1.88831 −0.944157 0.329495i \(-0.893122\pi\)
−0.944157 + 0.329495i \(0.893122\pi\)
\(864\) −31.9148 −1.08576
\(865\) −28.7254 −0.976692
\(866\) −94.6519 −3.21640
\(867\) 33.0253 1.12160
\(868\) 46.0350 1.56253
\(869\) 41.6359 1.41240
\(870\) 144.240 4.89019
\(871\) 21.9127 0.742483
\(872\) −95.3130 −3.22771
\(873\) 16.4802 0.557771
\(874\) 52.4906 1.77552
\(875\) −2.47787 −0.0837673
\(876\) −73.2570 −2.47512
\(877\) 46.2162 1.56061 0.780306 0.625398i \(-0.215063\pi\)
0.780306 + 0.625398i \(0.215063\pi\)
\(878\) −0.675606 −0.0228006
\(879\) 3.64562 0.122964
\(880\) −69.9216 −2.35706
\(881\) 26.1018 0.879391 0.439696 0.898147i \(-0.355086\pi\)
0.439696 + 0.898147i \(0.355086\pi\)
\(882\) −4.71048 −0.158610
\(883\) −55.1670 −1.85652 −0.928258 0.371936i \(-0.878694\pi\)
−0.928258 + 0.371936i \(0.878694\pi\)
\(884\) −10.0518 −0.338080
\(885\) −73.4937 −2.47046
\(886\) 2.61924 0.0879951
\(887\) −38.9198 −1.30680 −0.653400 0.757013i \(-0.726658\pi\)
−0.653400 + 0.757013i \(0.726658\pi\)
\(888\) 2.64933 0.0889058
\(889\) 46.3692 1.55517
\(890\) −74.8413 −2.50869
\(891\) −27.1962 −0.911106
\(892\) −29.5201 −0.988406
\(893\) −24.0276 −0.804052
\(894\) −42.2614 −1.41343
\(895\) 52.1984 1.74480
\(896\) −5.89685 −0.197000
\(897\) −28.6349 −0.956091
\(898\) −97.8529 −3.26539
\(899\) 28.2858 0.943383
\(900\) 32.3487 1.07829
\(901\) 1.14681 0.0382058
\(902\) −37.1595 −1.23728
\(903\) 68.1533 2.26800
\(904\) 84.4858 2.80996
\(905\) 31.5730 1.04952
\(906\) 5.48166 0.182116
\(907\) −18.2342 −0.605457 −0.302729 0.953077i \(-0.597898\pi\)
−0.302729 + 0.953077i \(0.597898\pi\)
\(908\) 62.6853 2.08029
\(909\) −1.57530 −0.0522493
\(910\) −42.8086 −1.41909
\(911\) 27.0337 0.895666 0.447833 0.894117i \(-0.352196\pi\)
0.447833 + 0.894117i \(0.352196\pi\)
\(912\) 53.0971 1.75822
\(913\) 15.9221 0.526944
\(914\) −10.1622 −0.336136
\(915\) 30.2364 0.999584
\(916\) 131.474 4.34403
\(917\) 18.3864 0.607171
\(918\) 9.84852 0.325050
\(919\) −54.9028 −1.81108 −0.905538 0.424265i \(-0.860532\pi\)
−0.905538 + 0.424265i \(0.860532\pi\)
\(920\) 167.174 5.51156
\(921\) −44.1380 −1.45440
\(922\) 27.8988 0.918797
\(923\) 10.3978 0.342247
\(924\) 69.9318 2.30059
\(925\) 0.821840 0.0270219
\(926\) 52.3844 1.72146
\(927\) −1.63705 −0.0537678
\(928\) 81.6431 2.68007
\(929\) 58.2546 1.91127 0.955636 0.294549i \(-0.0951695\pi\)
0.955636 + 0.294549i \(0.0951695\pi\)
\(930\) 57.2970 1.87884
\(931\) −3.43315 −0.112517
\(932\) −56.3670 −1.84636
\(933\) 60.7776 1.98977
\(934\) 52.8381 1.72891
\(935\) 8.64831 0.282830
\(936\) −19.0165 −0.621575
\(937\) 14.0538 0.459117 0.229559 0.973295i \(-0.426272\pi\)
0.229559 + 0.973295i \(0.426272\pi\)
\(938\) 89.3857 2.91855
\(939\) −6.35469 −0.207377
\(940\) −131.620 −4.29297
\(941\) −45.4867 −1.48282 −0.741412 0.671050i \(-0.765844\pi\)
−0.741412 + 0.671050i \(0.765844\pi\)
\(942\) 70.7900 2.30646
\(943\) 43.7526 1.42478
\(944\) −103.787 −3.37798
\(945\) 29.5663 0.961791
\(946\) −70.8992 −2.30513
\(947\) −47.0870 −1.53012 −0.765061 0.643958i \(-0.777291\pi\)
−0.765061 + 0.643958i \(0.777291\pi\)
\(948\) −173.197 −5.62516
\(949\) 13.3590 0.433652
\(950\) 33.4461 1.08513
\(951\) 21.2483 0.689022
\(952\) −23.8393 −0.772636
\(953\) 26.0336 0.843310 0.421655 0.906756i \(-0.361449\pi\)
0.421655 + 0.906756i \(0.361449\pi\)
\(954\) 3.73167 0.120817
\(955\) 25.8399 0.836159
\(956\) 84.4923 2.73268
\(957\) 42.9689 1.38899
\(958\) 35.4796 1.14630
\(959\) 50.8843 1.64314
\(960\) 43.6267 1.40804
\(961\) −19.7639 −0.637546
\(962\) −0.830973 −0.0267917
\(963\) −5.32871 −0.171715
\(964\) 124.832 4.02056
\(965\) −26.2719 −0.845724
\(966\) −116.807 −3.75820
\(967\) 29.5476 0.950185 0.475093 0.879936i \(-0.342415\pi\)
0.475093 + 0.879936i \(0.342415\pi\)
\(968\) 37.2541 1.19739
\(969\) −6.56735 −0.210974
\(970\) 93.3390 2.99693
\(971\) 10.7230 0.344116 0.172058 0.985087i \(-0.444958\pi\)
0.172058 + 0.985087i \(0.444958\pi\)
\(972\) 65.8494 2.11212
\(973\) −25.3728 −0.813416
\(974\) 85.3824 2.73583
\(975\) −18.2456 −0.584327
\(976\) 42.6995 1.36678
\(977\) 45.7562 1.46387 0.731935 0.681374i \(-0.238617\pi\)
0.731935 + 0.681374i \(0.238617\pi\)
\(978\) −58.0976 −1.85776
\(979\) −22.2951 −0.712555
\(980\) −18.8064 −0.600748
\(981\) 18.8912 0.603150
\(982\) −74.8605 −2.38890
\(983\) 37.1895 1.18616 0.593080 0.805143i \(-0.297912\pi\)
0.593080 + 0.805143i \(0.297912\pi\)
\(984\) 89.8702 2.86496
\(985\) 33.8371 1.07814
\(986\) −25.1940 −0.802342
\(987\) 53.4683 1.70191
\(988\) −23.8388 −0.758414
\(989\) 83.4786 2.65446
\(990\) 28.1412 0.894386
\(991\) −13.4779 −0.428138 −0.214069 0.976818i \(-0.568672\pi\)
−0.214069 + 0.976818i \(0.568672\pi\)
\(992\) 32.4315 1.02970
\(993\) 23.3418 0.740731
\(994\) 42.4144 1.34530
\(995\) −25.4238 −0.805988
\(996\) −66.2325 −2.09866
\(997\) 23.6733 0.749741 0.374870 0.927077i \(-0.377687\pi\)
0.374870 + 0.927077i \(0.377687\pi\)
\(998\) 106.195 3.36155
\(999\) 0.573921 0.0181581
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 \(a_p\))