Properties

Label 6023.2.a.b.1.11
Level 6023
Weight 2
Character 6023.1
Self dual Yes
Analytic conductor 48.094
Analytic rank 1
Dimension 99
CM No

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Newspace parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(99\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.31836 q^{2}\) \(-0.700819 q^{3}\) \(+3.37481 q^{4}\) \(-1.53243 q^{5}\) \(+1.62475 q^{6}\) \(+2.29352 q^{7}\) \(-3.18731 q^{8}\) \(-2.50885 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.31836 q^{2}\) \(-0.700819 q^{3}\) \(+3.37481 q^{4}\) \(-1.53243 q^{5}\) \(+1.62475 q^{6}\) \(+2.29352 q^{7}\) \(-3.18731 q^{8}\) \(-2.50885 q^{9}\) \(+3.55272 q^{10}\) \(+3.05985 q^{11}\) \(-2.36513 q^{12}\) \(+4.49419 q^{13}\) \(-5.31722 q^{14}\) \(+1.07395 q^{15}\) \(+0.639730 q^{16}\) \(+5.90362 q^{17}\) \(+5.81643 q^{18}\) \(-1.00000 q^{19}\) \(-5.17165 q^{20}\) \(-1.60734 q^{21}\) \(-7.09385 q^{22}\) \(-3.12867 q^{23}\) \(+2.23373 q^{24}\) \(-2.65167 q^{25}\) \(-10.4192 q^{26}\) \(+3.86071 q^{27}\) \(+7.74020 q^{28}\) \(+6.50640 q^{29}\) \(-2.48982 q^{30}\) \(-3.82561 q^{31}\) \(+4.89150 q^{32}\) \(-2.14440 q^{33}\) \(-13.6867 q^{34}\) \(-3.51465 q^{35}\) \(-8.46690 q^{36}\) \(-11.3256 q^{37}\) \(+2.31836 q^{38}\) \(-3.14962 q^{39}\) \(+4.88433 q^{40}\) \(-2.44703 q^{41}\) \(+3.72641 q^{42}\) \(+5.67787 q^{43}\) \(+10.3264 q^{44}\) \(+3.84463 q^{45}\) \(+7.25339 q^{46}\) \(-5.21909 q^{47}\) \(-0.448335 q^{48}\) \(-1.73976 q^{49}\) \(+6.14753 q^{50}\) \(-4.13737 q^{51}\) \(+15.1671 q^{52}\) \(-3.78806 q^{53}\) \(-8.95053 q^{54}\) \(-4.68900 q^{55}\) \(-7.31017 q^{56}\) \(+0.700819 q^{57}\) \(-15.0842 q^{58}\) \(+0.392878 q^{59}\) \(+3.62439 q^{60}\) \(-10.2150 q^{61}\) \(+8.86916 q^{62}\) \(-5.75411 q^{63}\) \(-12.6197 q^{64}\) \(-6.88702 q^{65}\) \(+4.97150 q^{66}\) \(-8.40959 q^{67}\) \(+19.9236 q^{68}\) \(+2.19263 q^{69}\) \(+8.14825 q^{70}\) \(-3.94529 q^{71}\) \(+7.99650 q^{72}\) \(+10.2216 q^{73}\) \(+26.2568 q^{74}\) \(+1.85834 q^{75}\) \(-3.37481 q^{76}\) \(+7.01783 q^{77}\) \(+7.30196 q^{78}\) \(-6.51904 q^{79}\) \(-0.980340 q^{80}\) \(+4.82090 q^{81}\) \(+5.67311 q^{82}\) \(-3.59695 q^{83}\) \(-5.42448 q^{84}\) \(-9.04687 q^{85}\) \(-13.1634 q^{86}\) \(-4.55981 q^{87}\) \(-9.75271 q^{88}\) \(-5.40100 q^{89}\) \(-8.91326 q^{90}\) \(+10.3075 q^{91}\) \(-10.5587 q^{92}\) \(+2.68106 q^{93}\) \(+12.0998 q^{94}\) \(+1.53243 q^{95}\) \(-3.42806 q^{96}\) \(+6.82937 q^{97}\) \(+4.03340 q^{98}\) \(-7.67672 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 27q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 13q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 99q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 53q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 63q^{28} \) \(\mathstrut -\mathstrut 34q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 43q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 25q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 80q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 21q^{44} \) \(\mathstrut -\mathstrut 53q^{45} \) \(\mathstrut -\mathstrut 23q^{46} \) \(\mathstrut -\mathstrut 31q^{47} \) \(\mathstrut -\mathstrut 74q^{48} \) \(\mathstrut -\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 71q^{52} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 80q^{54} \) \(\mathstrut -\mathstrut 45q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 91q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 61q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut -\mathstrut 43q^{63} \) \(\mathstrut -\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 75q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut -\mathstrut 55q^{68} \) \(\mathstrut -\mathstrut 45q^{69} \) \(\mathstrut -\mathstrut 76q^{70} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 77q^{72} \) \(\mathstrut -\mathstrut 143q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 58q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 109q^{82} \) \(\mathstrut -\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 80q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 57q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut -\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 107q^{92} \) \(\mathstrut -\mathstrut 121q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 128q^{97} \) \(\mathstrut +\mathstrut 54q^{98} \) \(\mathstrut -\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.31836 −1.63933 −0.819665 0.572843i \(-0.805841\pi\)
−0.819665 + 0.572843i \(0.805841\pi\)
\(3\) −0.700819 −0.404618 −0.202309 0.979322i \(-0.564845\pi\)
−0.202309 + 0.979322i \(0.564845\pi\)
\(4\) 3.37481 1.68741
\(5\) −1.53243 −0.685322 −0.342661 0.939459i \(-0.611328\pi\)
−0.342661 + 0.939459i \(0.611328\pi\)
\(6\) 1.62475 0.663303
\(7\) 2.29352 0.866870 0.433435 0.901185i \(-0.357301\pi\)
0.433435 + 0.901185i \(0.357301\pi\)
\(8\) −3.18731 −1.12689
\(9\) −2.50885 −0.836284
\(10\) 3.55272 1.12347
\(11\) 3.05985 0.922580 0.461290 0.887249i \(-0.347387\pi\)
0.461290 + 0.887249i \(0.347387\pi\)
\(12\) −2.36513 −0.682755
\(13\) 4.49419 1.24646 0.623232 0.782037i \(-0.285819\pi\)
0.623232 + 0.782037i \(0.285819\pi\)
\(14\) −5.31722 −1.42109
\(15\) 1.07395 0.277294
\(16\) 0.639730 0.159933
\(17\) 5.90362 1.43184 0.715919 0.698183i \(-0.246008\pi\)
0.715919 + 0.698183i \(0.246008\pi\)
\(18\) 5.81643 1.37095
\(19\) −1.00000 −0.229416
\(20\) −5.17165 −1.15642
\(21\) −1.60734 −0.350751
\(22\) −7.09385 −1.51241
\(23\) −3.12867 −0.652373 −0.326186 0.945306i \(-0.605764\pi\)
−0.326186 + 0.945306i \(0.605764\pi\)
\(24\) 2.23373 0.455958
\(25\) −2.65167 −0.530333
\(26\) −10.4192 −2.04337
\(27\) 3.86071 0.742994
\(28\) 7.74020 1.46276
\(29\) 6.50640 1.20821 0.604104 0.796906i \(-0.293531\pi\)
0.604104 + 0.796906i \(0.293531\pi\)
\(30\) −2.48982 −0.454576
\(31\) −3.82561 −0.687100 −0.343550 0.939134i \(-0.611629\pi\)
−0.343550 + 0.939134i \(0.611629\pi\)
\(32\) 4.89150 0.864703
\(33\) −2.14440 −0.373292
\(34\) −13.6867 −2.34726
\(35\) −3.51465 −0.594085
\(36\) −8.46690 −1.41115
\(37\) −11.3256 −1.86192 −0.930958 0.365127i \(-0.881025\pi\)
−0.930958 + 0.365127i \(0.881025\pi\)
\(38\) 2.31836 0.376088
\(39\) −3.14962 −0.504342
\(40\) 4.88433 0.772280
\(41\) −2.44703 −0.382162 −0.191081 0.981574i \(-0.561199\pi\)
−0.191081 + 0.981574i \(0.561199\pi\)
\(42\) 3.72641 0.574997
\(43\) 5.67787 0.865866 0.432933 0.901426i \(-0.357479\pi\)
0.432933 + 0.901426i \(0.357479\pi\)
\(44\) 10.3264 1.55677
\(45\) 3.84463 0.573124
\(46\) 7.25339 1.06945
\(47\) −5.21909 −0.761283 −0.380642 0.924723i \(-0.624297\pi\)
−0.380642 + 0.924723i \(0.624297\pi\)
\(48\) −0.448335 −0.0647116
\(49\) −1.73976 −0.248537
\(50\) 6.14753 0.869392
\(51\) −4.13737 −0.579348
\(52\) 15.1671 2.10329
\(53\) −3.78806 −0.520330 −0.260165 0.965564i \(-0.583777\pi\)
−0.260165 + 0.965564i \(0.583777\pi\)
\(54\) −8.95053 −1.21801
\(55\) −4.68900 −0.632264
\(56\) −7.31017 −0.976863
\(57\) 0.700819 0.0928258
\(58\) −15.0842 −1.98065
\(59\) 0.392878 0.0511484 0.0255742 0.999673i \(-0.491859\pi\)
0.0255742 + 0.999673i \(0.491859\pi\)
\(60\) 3.62439 0.467907
\(61\) −10.2150 −1.30789 −0.653946 0.756541i \(-0.726888\pi\)
−0.653946 + 0.756541i \(0.726888\pi\)
\(62\) 8.86916 1.12638
\(63\) −5.75411 −0.724949
\(64\) −12.6197 −1.57747
\(65\) −6.88702 −0.854230
\(66\) 4.97150 0.611950
\(67\) −8.40959 −1.02740 −0.513698 0.857971i \(-0.671725\pi\)
−0.513698 + 0.857971i \(0.671725\pi\)
\(68\) 19.9236 2.41609
\(69\) 2.19263 0.263962
\(70\) 8.14825 0.973902
\(71\) −3.94529 −0.468220 −0.234110 0.972210i \(-0.575218\pi\)
−0.234110 + 0.972210i \(0.575218\pi\)
\(72\) 7.99650 0.942397
\(73\) 10.2216 1.19635 0.598174 0.801366i \(-0.295893\pi\)
0.598174 + 0.801366i \(0.295893\pi\)
\(74\) 26.2568 3.05229
\(75\) 1.85834 0.214583
\(76\) −3.37481 −0.387117
\(77\) 7.01783 0.799756
\(78\) 7.30196 0.826784
\(79\) −6.51904 −0.733449 −0.366724 0.930330i \(-0.619521\pi\)
−0.366724 + 0.930330i \(0.619521\pi\)
\(80\) −0.980340 −0.109605
\(81\) 4.82090 0.535655
\(82\) 5.67311 0.626490
\(83\) −3.59695 −0.394816 −0.197408 0.980321i \(-0.563252\pi\)
−0.197408 + 0.980321i \(0.563252\pi\)
\(84\) −5.42448 −0.591859
\(85\) −9.04687 −0.981271
\(86\) −13.1634 −1.41944
\(87\) −4.55981 −0.488863
\(88\) −9.75271 −1.03964
\(89\) −5.40100 −0.572505 −0.286253 0.958154i \(-0.592410\pi\)
−0.286253 + 0.958154i \(0.592410\pi\)
\(90\) −8.91326 −0.939540
\(91\) 10.3075 1.08052
\(92\) −10.5587 −1.10082
\(93\) 2.68106 0.278013
\(94\) 12.0998 1.24799
\(95\) 1.53243 0.157224
\(96\) −3.42806 −0.349875
\(97\) 6.82937 0.693418 0.346709 0.937973i \(-0.387299\pi\)
0.346709 + 0.937973i \(0.387299\pi\)
\(98\) 4.03340 0.407435
\(99\) −7.67672 −0.771539
\(100\) −8.94888 −0.894888
\(101\) −12.1014 −1.20413 −0.602067 0.798445i \(-0.705656\pi\)
−0.602067 + 0.798445i \(0.705656\pi\)
\(102\) 9.59193 0.949743
\(103\) −2.21838 −0.218584 −0.109292 0.994010i \(-0.534858\pi\)
−0.109292 + 0.994010i \(0.534858\pi\)
\(104\) −14.3244 −1.40462
\(105\) 2.46314 0.240378
\(106\) 8.78211 0.852993
\(107\) 9.70867 0.938573 0.469286 0.883046i \(-0.344511\pi\)
0.469286 + 0.883046i \(0.344511\pi\)
\(108\) 13.0292 1.25373
\(109\) 9.71772 0.930789 0.465394 0.885103i \(-0.345912\pi\)
0.465394 + 0.885103i \(0.345912\pi\)
\(110\) 10.8708 1.03649
\(111\) 7.93719 0.753365
\(112\) 1.46724 0.138641
\(113\) −2.63095 −0.247499 −0.123750 0.992313i \(-0.539492\pi\)
−0.123750 + 0.992313i \(0.539492\pi\)
\(114\) −1.62475 −0.152172
\(115\) 4.79446 0.447085
\(116\) 21.9579 2.03874
\(117\) −11.2753 −1.04240
\(118\) −0.910835 −0.0838492
\(119\) 13.5401 1.24122
\(120\) −3.42303 −0.312478
\(121\) −1.63731 −0.148847
\(122\) 23.6820 2.14407
\(123\) 1.71493 0.154630
\(124\) −12.9107 −1.15942
\(125\) 11.7256 1.04877
\(126\) 13.3401 1.18843
\(127\) 8.42944 0.747992 0.373996 0.927430i \(-0.377987\pi\)
0.373996 + 0.927430i \(0.377987\pi\)
\(128\) 19.4741 1.72129
\(129\) −3.97916 −0.350345
\(130\) 15.9666 1.40037
\(131\) 2.51858 0.220049 0.110025 0.993929i \(-0.464907\pi\)
0.110025 + 0.993929i \(0.464907\pi\)
\(132\) −7.23695 −0.629896
\(133\) −2.29352 −0.198874
\(134\) 19.4965 1.68424
\(135\) −5.91626 −0.509190
\(136\) −18.8167 −1.61352
\(137\) −7.29735 −0.623455 −0.311727 0.950172i \(-0.600908\pi\)
−0.311727 + 0.950172i \(0.600908\pi\)
\(138\) −5.08332 −0.432721
\(139\) −13.3781 −1.13471 −0.567356 0.823473i \(-0.692034\pi\)
−0.567356 + 0.823473i \(0.692034\pi\)
\(140\) −11.8613 −1.00246
\(141\) 3.65764 0.308029
\(142\) 9.14663 0.767568
\(143\) 13.7516 1.14996
\(144\) −1.60499 −0.133749
\(145\) −9.97058 −0.828012
\(146\) −23.6974 −1.96121
\(147\) 1.21926 0.100563
\(148\) −38.2217 −3.14181
\(149\) −8.43854 −0.691312 −0.345656 0.938361i \(-0.612344\pi\)
−0.345656 + 0.938361i \(0.612344\pi\)
\(150\) −4.30831 −0.351772
\(151\) −5.81661 −0.473349 −0.236674 0.971589i \(-0.576057\pi\)
−0.236674 + 0.971589i \(0.576057\pi\)
\(152\) 3.18731 0.258525
\(153\) −14.8113 −1.19742
\(154\) −16.2699 −1.31107
\(155\) 5.86247 0.470885
\(156\) −10.6294 −0.851030
\(157\) −20.9298 −1.67038 −0.835189 0.549963i \(-0.814642\pi\)
−0.835189 + 0.549963i \(0.814642\pi\)
\(158\) 15.1135 1.20237
\(159\) 2.65475 0.210535
\(160\) −7.49587 −0.592600
\(161\) −7.17567 −0.565522
\(162\) −11.1766 −0.878116
\(163\) −4.08256 −0.319770 −0.159885 0.987136i \(-0.551112\pi\)
−0.159885 + 0.987136i \(0.551112\pi\)
\(164\) −8.25827 −0.644862
\(165\) 3.28614 0.255826
\(166\) 8.33903 0.647234
\(167\) 6.90837 0.534586 0.267293 0.963615i \(-0.413871\pi\)
0.267293 + 0.963615i \(0.413871\pi\)
\(168\) 5.12311 0.395256
\(169\) 7.19777 0.553674
\(170\) 20.9739 1.60863
\(171\) 2.50885 0.191857
\(172\) 19.1617 1.46107
\(173\) 5.82970 0.443224 0.221612 0.975135i \(-0.428868\pi\)
0.221612 + 0.975135i \(0.428868\pi\)
\(174\) 10.5713 0.801408
\(175\) −6.08165 −0.459730
\(176\) 1.95748 0.147551
\(177\) −0.275337 −0.0206956
\(178\) 12.5215 0.938525
\(179\) 2.86225 0.213935 0.106967 0.994263i \(-0.465886\pi\)
0.106967 + 0.994263i \(0.465886\pi\)
\(180\) 12.9749 0.967093
\(181\) −5.66425 −0.421021 −0.210510 0.977592i \(-0.567513\pi\)
−0.210510 + 0.977592i \(0.567513\pi\)
\(182\) −23.8966 −1.77133
\(183\) 7.15885 0.529197
\(184\) 9.97205 0.735149
\(185\) 17.3556 1.27601
\(186\) −6.21567 −0.455755
\(187\) 18.0642 1.32099
\(188\) −17.6135 −1.28459
\(189\) 8.85462 0.644079
\(190\) −3.55272 −0.257742
\(191\) 24.9685 1.80666 0.903328 0.428951i \(-0.141117\pi\)
0.903328 + 0.428951i \(0.141117\pi\)
\(192\) 8.84415 0.638272
\(193\) −19.4338 −1.39887 −0.699437 0.714694i \(-0.746566\pi\)
−0.699437 + 0.714694i \(0.746566\pi\)
\(194\) −15.8330 −1.13674
\(195\) 4.82656 0.345637
\(196\) −5.87136 −0.419383
\(197\) −2.03931 −0.145295 −0.0726476 0.997358i \(-0.523145\pi\)
−0.0726476 + 0.997358i \(0.523145\pi\)
\(198\) 17.7974 1.26481
\(199\) −6.42980 −0.455796 −0.227898 0.973685i \(-0.573185\pi\)
−0.227898 + 0.973685i \(0.573185\pi\)
\(200\) 8.45170 0.597625
\(201\) 5.89360 0.415703
\(202\) 28.0555 1.97398
\(203\) 14.9226 1.04736
\(204\) −13.9628 −0.977595
\(205\) 3.74990 0.261904
\(206\) 5.14302 0.358331
\(207\) 7.84937 0.545569
\(208\) 2.87507 0.199350
\(209\) −3.05985 −0.211654
\(210\) −5.71045 −0.394058
\(211\) −24.2772 −1.67131 −0.835655 0.549254i \(-0.814912\pi\)
−0.835655 + 0.549254i \(0.814912\pi\)
\(212\) −12.7840 −0.878008
\(213\) 2.76494 0.189450
\(214\) −22.5082 −1.53863
\(215\) −8.70092 −0.593398
\(216\) −12.3053 −0.837269
\(217\) −8.77412 −0.595626
\(218\) −22.5292 −1.52587
\(219\) −7.16350 −0.484064
\(220\) −15.8245 −1.06689
\(221\) 26.5320 1.78474
\(222\) −18.4013 −1.23501
\(223\) 0.762863 0.0510851 0.0255426 0.999674i \(-0.491869\pi\)
0.0255426 + 0.999674i \(0.491869\pi\)
\(224\) 11.2188 0.749585
\(225\) 6.65264 0.443509
\(226\) 6.09951 0.405733
\(227\) 3.56301 0.236485 0.118243 0.992985i \(-0.462274\pi\)
0.118243 + 0.992985i \(0.462274\pi\)
\(228\) 2.36513 0.156635
\(229\) 12.7267 0.841003 0.420502 0.907292i \(-0.361854\pi\)
0.420502 + 0.907292i \(0.361854\pi\)
\(230\) −11.1153 −0.732921
\(231\) −4.91823 −0.323596
\(232\) −20.7379 −1.36151
\(233\) −6.19207 −0.405656 −0.202828 0.979214i \(-0.565013\pi\)
−0.202828 + 0.979214i \(0.565013\pi\)
\(234\) 26.1402 1.70884
\(235\) 7.99788 0.521724
\(236\) 1.32589 0.0863081
\(237\) 4.56866 0.296767
\(238\) −31.3908 −2.03477
\(239\) 9.18512 0.594136 0.297068 0.954856i \(-0.403991\pi\)
0.297068 + 0.954856i \(0.403991\pi\)
\(240\) 0.687041 0.0443483
\(241\) 14.2719 0.919337 0.459668 0.888091i \(-0.347968\pi\)
0.459668 + 0.888091i \(0.347968\pi\)
\(242\) 3.79588 0.244009
\(243\) −14.9607 −0.959730
\(244\) −34.4736 −2.20695
\(245\) 2.66606 0.170328
\(246\) −3.97582 −0.253489
\(247\) −4.49419 −0.285959
\(248\) 12.1934 0.774283
\(249\) 2.52081 0.159750
\(250\) −27.1843 −1.71928
\(251\) −30.3128 −1.91332 −0.956662 0.291199i \(-0.905946\pi\)
−0.956662 + 0.291199i \(0.905946\pi\)
\(252\) −19.4190 −1.22328
\(253\) −9.57326 −0.601866
\(254\) −19.5425 −1.22621
\(255\) 6.34022 0.397040
\(256\) −19.9087 −1.24429
\(257\) 19.8252 1.23666 0.618331 0.785917i \(-0.287809\pi\)
0.618331 + 0.785917i \(0.287809\pi\)
\(258\) 9.22513 0.574332
\(259\) −25.9755 −1.61404
\(260\) −23.2424 −1.44143
\(261\) −16.3236 −1.01040
\(262\) −5.83899 −0.360734
\(263\) 20.4271 1.25959 0.629795 0.776762i \(-0.283139\pi\)
0.629795 + 0.776762i \(0.283139\pi\)
\(264\) 6.83488 0.420658
\(265\) 5.80493 0.356594
\(266\) 5.31722 0.326019
\(267\) 3.78513 0.231646
\(268\) −28.3808 −1.73363
\(269\) 25.8858 1.57828 0.789142 0.614210i \(-0.210525\pi\)
0.789142 + 0.614210i \(0.210525\pi\)
\(270\) 13.7160 0.834731
\(271\) 12.4516 0.756378 0.378189 0.925728i \(-0.376547\pi\)
0.378189 + 0.925728i \(0.376547\pi\)
\(272\) 3.77673 0.228998
\(273\) −7.22371 −0.437199
\(274\) 16.9179 1.02205
\(275\) −8.11371 −0.489275
\(276\) 7.39972 0.445411
\(277\) 17.6739 1.06192 0.530960 0.847397i \(-0.321831\pi\)
0.530960 + 0.847397i \(0.321831\pi\)
\(278\) 31.0152 1.86017
\(279\) 9.59789 0.574611
\(280\) 11.2023 0.669466
\(281\) −9.81644 −0.585599 −0.292800 0.956174i \(-0.594587\pi\)
−0.292800 + 0.956174i \(0.594587\pi\)
\(282\) −8.47974 −0.504961
\(283\) −23.5226 −1.39827 −0.699136 0.714988i \(-0.746432\pi\)
−0.699136 + 0.714988i \(0.746432\pi\)
\(284\) −13.3146 −0.790078
\(285\) −1.07395 −0.0636156
\(286\) −31.8811 −1.88517
\(287\) −5.61232 −0.331285
\(288\) −12.2721 −0.723138
\(289\) 17.8527 1.05016
\(290\) 23.1154 1.35739
\(291\) −4.78616 −0.280569
\(292\) 34.4960 2.01873
\(293\) 15.5363 0.907642 0.453821 0.891093i \(-0.350061\pi\)
0.453821 + 0.891093i \(0.350061\pi\)
\(294\) −2.82668 −0.164855
\(295\) −0.602057 −0.0350531
\(296\) 36.0982 2.09817
\(297\) 11.8132 0.685471
\(298\) 19.5636 1.13329
\(299\) −14.0608 −0.813159
\(300\) 6.27154 0.362088
\(301\) 13.0223 0.750593
\(302\) 13.4850 0.775975
\(303\) 8.48090 0.487215
\(304\) −0.639730 −0.0366911
\(305\) 15.6537 0.896328
\(306\) 34.3380 1.96297
\(307\) 13.1880 0.752680 0.376340 0.926482i \(-0.377182\pi\)
0.376340 + 0.926482i \(0.377182\pi\)
\(308\) 23.6839 1.34951
\(309\) 1.55469 0.0884430
\(310\) −13.5913 −0.771936
\(311\) 27.7005 1.57075 0.785376 0.619019i \(-0.212470\pi\)
0.785376 + 0.619019i \(0.212470\pi\)
\(312\) 10.0388 0.568336
\(313\) −9.85480 −0.557026 −0.278513 0.960432i \(-0.589842\pi\)
−0.278513 + 0.960432i \(0.589842\pi\)
\(314\) 48.5229 2.73830
\(315\) 8.81775 0.496824
\(316\) −22.0005 −1.23763
\(317\) −1.00000 −0.0561656
\(318\) −6.15467 −0.345137
\(319\) 19.9086 1.11467
\(320\) 19.3388 1.08107
\(321\) −6.80402 −0.379763
\(322\) 16.6358 0.927077
\(323\) −5.90362 −0.328486
\(324\) 16.2696 0.903868
\(325\) −11.9171 −0.661042
\(326\) 9.46485 0.524210
\(327\) −6.81036 −0.376614
\(328\) 7.79945 0.430653
\(329\) −11.9701 −0.659933
\(330\) −7.61847 −0.419383
\(331\) −5.46716 −0.300502 −0.150251 0.988648i \(-0.548008\pi\)
−0.150251 + 0.988648i \(0.548008\pi\)
\(332\) −12.1390 −0.666215
\(333\) 28.4142 1.55709
\(334\) −16.0161 −0.876363
\(335\) 12.8871 0.704097
\(336\) −1.02827 −0.0560965
\(337\) 2.32056 0.126409 0.0632045 0.998001i \(-0.479868\pi\)
0.0632045 + 0.998001i \(0.479868\pi\)
\(338\) −16.6870 −0.907655
\(339\) 1.84382 0.100143
\(340\) −30.5315 −1.65580
\(341\) −11.7058 −0.633904
\(342\) −5.81643 −0.314517
\(343\) −20.0448 −1.08232
\(344\) −18.0971 −0.975732
\(345\) −3.36005 −0.180899
\(346\) −13.5154 −0.726590
\(347\) −31.1622 −1.67288 −0.836438 0.548061i \(-0.815366\pi\)
−0.836438 + 0.548061i \(0.815366\pi\)
\(348\) −15.3885 −0.824910
\(349\) −34.6400 −1.85424 −0.927119 0.374768i \(-0.877722\pi\)
−0.927119 + 0.374768i \(0.877722\pi\)
\(350\) 14.0995 0.753649
\(351\) 17.3508 0.926116
\(352\) 14.9673 0.797758
\(353\) 4.42746 0.235650 0.117825 0.993034i \(-0.462408\pi\)
0.117825 + 0.993034i \(0.462408\pi\)
\(354\) 0.638331 0.0339269
\(355\) 6.04587 0.320882
\(356\) −18.2274 −0.966048
\(357\) −9.48915 −0.502219
\(358\) −6.63574 −0.350710
\(359\) −11.6747 −0.616166 −0.308083 0.951359i \(-0.599688\pi\)
−0.308083 + 0.951359i \(0.599688\pi\)
\(360\) −12.2541 −0.645845
\(361\) 1.00000 0.0526316
\(362\) 13.1318 0.690192
\(363\) 1.14746 0.0602260
\(364\) 34.7860 1.82328
\(365\) −15.6639 −0.819884
\(366\) −16.5968 −0.867529
\(367\) −1.78932 −0.0934018 −0.0467009 0.998909i \(-0.514871\pi\)
−0.0467009 + 0.998909i \(0.514871\pi\)
\(368\) −2.00150 −0.104336
\(369\) 6.13924 0.319596
\(370\) −40.2367 −2.09181
\(371\) −8.68800 −0.451058
\(372\) 9.04807 0.469121
\(373\) 2.87610 0.148919 0.0744594 0.997224i \(-0.476277\pi\)
0.0744594 + 0.997224i \(0.476277\pi\)
\(374\) −41.8794 −2.16553
\(375\) −8.21754 −0.424352
\(376\) 16.6349 0.857879
\(377\) 29.2410 1.50599
\(378\) −20.5282 −1.05586
\(379\) −4.96967 −0.255275 −0.127637 0.991821i \(-0.540739\pi\)
−0.127637 + 0.991821i \(0.540739\pi\)
\(380\) 5.17165 0.265300
\(381\) −5.90751 −0.302651
\(382\) −57.8860 −2.96171
\(383\) −18.7425 −0.957699 −0.478850 0.877897i \(-0.658946\pi\)
−0.478850 + 0.877897i \(0.658946\pi\)
\(384\) −13.6479 −0.696464
\(385\) −10.7543 −0.548091
\(386\) 45.0546 2.29322
\(387\) −14.2449 −0.724110
\(388\) 23.0479 1.17008
\(389\) 16.8796 0.855831 0.427915 0.903819i \(-0.359248\pi\)
0.427915 + 0.903819i \(0.359248\pi\)
\(390\) −11.1897 −0.566613
\(391\) −18.4705 −0.934092
\(392\) 5.54516 0.280073
\(393\) −1.76507 −0.0890360
\(394\) 4.72787 0.238187
\(395\) 9.98995 0.502649
\(396\) −25.9075 −1.30190
\(397\) −11.8596 −0.595218 −0.297609 0.954688i \(-0.596189\pi\)
−0.297609 + 0.954688i \(0.596189\pi\)
\(398\) 14.9066 0.747201
\(399\) 1.60734 0.0804678
\(400\) −1.69635 −0.0848176
\(401\) 32.8910 1.64250 0.821249 0.570570i \(-0.193278\pi\)
0.821249 + 0.570570i \(0.193278\pi\)
\(402\) −13.6635 −0.681474
\(403\) −17.1930 −0.856446
\(404\) −40.8400 −2.03186
\(405\) −7.38768 −0.367097
\(406\) −34.5959 −1.71697
\(407\) −34.6546 −1.71777
\(408\) 13.1871 0.652859
\(409\) −21.1017 −1.04341 −0.521707 0.853125i \(-0.674705\pi\)
−0.521707 + 0.853125i \(0.674705\pi\)
\(410\) −8.69362 −0.429347
\(411\) 5.11412 0.252261
\(412\) −7.48663 −0.368840
\(413\) 0.901075 0.0443390
\(414\) −18.1977 −0.894368
\(415\) 5.51206 0.270576
\(416\) 21.9833 1.07782
\(417\) 9.37560 0.459125
\(418\) 7.09385 0.346971
\(419\) 16.0635 0.784753 0.392376 0.919805i \(-0.371653\pi\)
0.392376 + 0.919805i \(0.371653\pi\)
\(420\) 8.31262 0.405614
\(421\) 28.6613 1.39687 0.698433 0.715675i \(-0.253881\pi\)
0.698433 + 0.715675i \(0.253881\pi\)
\(422\) 56.2834 2.73983
\(423\) 13.0939 0.636649
\(424\) 12.0737 0.586353
\(425\) −15.6544 −0.759352
\(426\) −6.41013 −0.310572
\(427\) −23.4282 −1.13377
\(428\) 32.7649 1.58375
\(429\) −9.63736 −0.465296
\(430\) 20.1719 0.972775
\(431\) −18.3345 −0.883140 −0.441570 0.897227i \(-0.645578\pi\)
−0.441570 + 0.897227i \(0.645578\pi\)
\(432\) 2.46981 0.118829
\(433\) −31.7402 −1.52534 −0.762669 0.646789i \(-0.776112\pi\)
−0.762669 + 0.646789i \(0.776112\pi\)
\(434\) 20.3416 0.976428
\(435\) 6.98757 0.335028
\(436\) 32.7955 1.57062
\(437\) 3.12867 0.149665
\(438\) 16.6076 0.793542
\(439\) −16.1010 −0.768461 −0.384230 0.923237i \(-0.625533\pi\)
−0.384230 + 0.923237i \(0.625533\pi\)
\(440\) 14.9453 0.712490
\(441\) 4.36480 0.207848
\(442\) −61.5109 −2.92577
\(443\) −23.9462 −1.13772 −0.568858 0.822436i \(-0.692615\pi\)
−0.568858 + 0.822436i \(0.692615\pi\)
\(444\) 26.7865 1.27123
\(445\) 8.27664 0.392350
\(446\) −1.76859 −0.0837454
\(447\) 5.91389 0.279717
\(448\) −28.9436 −1.36746
\(449\) 16.3768 0.772869 0.386435 0.922317i \(-0.373707\pi\)
0.386435 + 0.922317i \(0.373707\pi\)
\(450\) −15.4232 −0.727059
\(451\) −7.48755 −0.352575
\(452\) −8.87897 −0.417632
\(453\) 4.07639 0.191525
\(454\) −8.26035 −0.387677
\(455\) −15.7955 −0.740506
\(456\) −2.23373 −0.104604
\(457\) 19.8276 0.927496 0.463748 0.885967i \(-0.346504\pi\)
0.463748 + 0.885967i \(0.346504\pi\)
\(458\) −29.5051 −1.37868
\(459\) 22.7922 1.06385
\(460\) 16.1804 0.754415
\(461\) 1.95158 0.0908943 0.0454471 0.998967i \(-0.485529\pi\)
0.0454471 + 0.998967i \(0.485529\pi\)
\(462\) 11.4023 0.530481
\(463\) −2.25967 −0.105016 −0.0525080 0.998621i \(-0.516721\pi\)
−0.0525080 + 0.998621i \(0.516721\pi\)
\(464\) 4.16234 0.193232
\(465\) −4.10853 −0.190529
\(466\) 14.3555 0.665004
\(467\) −30.5428 −1.41335 −0.706676 0.707537i \(-0.749806\pi\)
−0.706676 + 0.707537i \(0.749806\pi\)
\(468\) −38.0519 −1.75895
\(469\) −19.2876 −0.890617
\(470\) −18.5420 −0.855279
\(471\) 14.6680 0.675865
\(472\) −1.25223 −0.0576384
\(473\) 17.3734 0.798831
\(474\) −10.5918 −0.486499
\(475\) 2.65167 0.121667
\(476\) 45.6952 2.09444
\(477\) 9.50369 0.435144
\(478\) −21.2945 −0.973986
\(479\) 10.0176 0.457714 0.228857 0.973460i \(-0.426501\pi\)
0.228857 + 0.973460i \(0.426501\pi\)
\(480\) 5.25325 0.239777
\(481\) −50.8994 −2.32081
\(482\) −33.0876 −1.50710
\(483\) 5.02885 0.228820
\(484\) −5.52562 −0.251164
\(485\) −10.4655 −0.475215
\(486\) 34.6844 1.57331
\(487\) 16.0387 0.726784 0.363392 0.931636i \(-0.381619\pi\)
0.363392 + 0.931636i \(0.381619\pi\)
\(488\) 32.5583 1.47385
\(489\) 2.86113 0.129385
\(490\) −6.18089 −0.279224
\(491\) 24.2447 1.09415 0.547074 0.837084i \(-0.315742\pi\)
0.547074 + 0.837084i \(0.315742\pi\)
\(492\) 5.78755 0.260923
\(493\) 38.4113 1.72996
\(494\) 10.4192 0.468781
\(495\) 11.7640 0.528753
\(496\) −2.44736 −0.109890
\(497\) −9.04861 −0.405886
\(498\) −5.84415 −0.261883
\(499\) 10.2282 0.457877 0.228938 0.973441i \(-0.426475\pi\)
0.228938 + 0.973441i \(0.426475\pi\)
\(500\) 39.5718 1.76970
\(501\) −4.84152 −0.216303
\(502\) 70.2760 3.13657
\(503\) −28.2089 −1.25777 −0.628887 0.777497i \(-0.716489\pi\)
−0.628887 + 0.777497i \(0.716489\pi\)
\(504\) 18.3401 0.816935
\(505\) 18.5445 0.825220
\(506\) 22.1943 0.986657
\(507\) −5.04433 −0.224027
\(508\) 28.4478 1.26217
\(509\) −2.37235 −0.105153 −0.0525763 0.998617i \(-0.516743\pi\)
−0.0525763 + 0.998617i \(0.516743\pi\)
\(510\) −14.6989 −0.650880
\(511\) 23.4435 1.03708
\(512\) 7.20728 0.318520
\(513\) −3.86071 −0.170454
\(514\) −45.9621 −2.02730
\(515\) 3.39951 0.149800
\(516\) −13.4289 −0.591175
\(517\) −15.9697 −0.702344
\(518\) 60.2206 2.64594
\(519\) −4.08556 −0.179336
\(520\) 21.9511 0.962620
\(521\) −19.5247 −0.855391 −0.427696 0.903923i \(-0.640674\pi\)
−0.427696 + 0.903923i \(0.640674\pi\)
\(522\) 37.8440 1.65639
\(523\) 5.16467 0.225835 0.112918 0.993604i \(-0.463980\pi\)
0.112918 + 0.993604i \(0.463980\pi\)
\(524\) 8.49974 0.371313
\(525\) 4.26214 0.186015
\(526\) −47.3575 −2.06488
\(527\) −22.5849 −0.983816
\(528\) −1.37184 −0.0597016
\(529\) −13.2114 −0.574410
\(530\) −13.4579 −0.584575
\(531\) −0.985674 −0.0427746
\(532\) −7.74020 −0.335580
\(533\) −10.9974 −0.476351
\(534\) −8.77530 −0.379744
\(535\) −14.8778 −0.643225
\(536\) 26.8040 1.15776
\(537\) −2.00592 −0.0865619
\(538\) −60.0127 −2.58733
\(539\) −5.32341 −0.229295
\(540\) −19.9662 −0.859211
\(541\) 20.6395 0.887359 0.443680 0.896185i \(-0.353673\pi\)
0.443680 + 0.896185i \(0.353673\pi\)
\(542\) −28.8673 −1.23995
\(543\) 3.96962 0.170353
\(544\) 28.8776 1.23812
\(545\) −14.8917 −0.637890
\(546\) 16.7472 0.716714
\(547\) 17.6926 0.756480 0.378240 0.925708i \(-0.376529\pi\)
0.378240 + 0.925708i \(0.376529\pi\)
\(548\) −24.6272 −1.05202
\(549\) 25.6279 1.09377
\(550\) 18.8105 0.802083
\(551\) −6.50640 −0.277182
\(552\) −6.98860 −0.297455
\(553\) −14.9515 −0.635804
\(554\) −40.9745 −1.74084
\(555\) −12.1632 −0.516297
\(556\) −45.1484 −1.91472
\(557\) −27.7720 −1.17674 −0.588369 0.808593i \(-0.700230\pi\)
−0.588369 + 0.808593i \(0.700230\pi\)
\(558\) −22.2514 −0.941977
\(559\) 25.5174 1.07927
\(560\) −2.24843 −0.0950136
\(561\) −12.6597 −0.534494
\(562\) 22.7581 0.959991
\(563\) −5.14822 −0.216972 −0.108486 0.994098i \(-0.534600\pi\)
−0.108486 + 0.994098i \(0.534600\pi\)
\(564\) 12.3438 0.519770
\(565\) 4.03174 0.169617
\(566\) 54.5339 2.29223
\(567\) 11.0568 0.464343
\(568\) 12.5749 0.527631
\(569\) −30.7962 −1.29104 −0.645522 0.763742i \(-0.723360\pi\)
−0.645522 + 0.763742i \(0.723360\pi\)
\(570\) 2.48982 0.104287
\(571\) 4.82490 0.201916 0.100958 0.994891i \(-0.467809\pi\)
0.100958 + 0.994891i \(0.467809\pi\)
\(572\) 46.4089 1.94045
\(573\) −17.4984 −0.731006
\(574\) 13.0114 0.543085
\(575\) 8.29619 0.345975
\(576\) 31.6611 1.31921
\(577\) −41.3191 −1.72014 −0.860069 0.510177i \(-0.829580\pi\)
−0.860069 + 0.510177i \(0.829580\pi\)
\(578\) −41.3891 −1.72156
\(579\) 13.6196 0.566010
\(580\) −33.6488 −1.39719
\(581\) −8.24967 −0.342254
\(582\) 11.0961 0.459946
\(583\) −11.5909 −0.480046
\(584\) −32.5795 −1.34815
\(585\) 17.2785 0.714379
\(586\) −36.0189 −1.48793
\(587\) −16.8767 −0.696576 −0.348288 0.937388i \(-0.613237\pi\)
−0.348288 + 0.937388i \(0.613237\pi\)
\(588\) 4.11476 0.169690
\(589\) 3.82561 0.157632
\(590\) 1.39579 0.0574637
\(591\) 1.42919 0.0587891
\(592\) −7.24532 −0.297781
\(593\) −6.70968 −0.275533 −0.137767 0.990465i \(-0.543992\pi\)
−0.137767 + 0.990465i \(0.543992\pi\)
\(594\) −27.3873 −1.12371
\(595\) −20.7492 −0.850634
\(596\) −28.4785 −1.16652
\(597\) 4.50612 0.184423
\(598\) 32.5981 1.33304
\(599\) −9.46843 −0.386870 −0.193435 0.981113i \(-0.561963\pi\)
−0.193435 + 0.981113i \(0.561963\pi\)
\(600\) −5.92311 −0.241810
\(601\) 38.2634 1.56080 0.780399 0.625281i \(-0.215016\pi\)
0.780399 + 0.625281i \(0.215016\pi\)
\(602\) −30.1904 −1.23047
\(603\) 21.0984 0.859194
\(604\) −19.6300 −0.798731
\(605\) 2.50906 0.102008
\(606\) −19.6618 −0.798706
\(607\) 6.67079 0.270759 0.135380 0.990794i \(-0.456775\pi\)
0.135380 + 0.990794i \(0.456775\pi\)
\(608\) −4.89150 −0.198377
\(609\) −10.4580 −0.423780
\(610\) −36.2910 −1.46938
\(611\) −23.4556 −0.948913
\(612\) −49.9854 −2.02054
\(613\) −39.7813 −1.60675 −0.803375 0.595473i \(-0.796965\pi\)
−0.803375 + 0.595473i \(0.796965\pi\)
\(614\) −30.5746 −1.23389
\(615\) −2.62800 −0.105971
\(616\) −22.3680 −0.901234
\(617\) −31.7927 −1.27992 −0.639962 0.768406i \(-0.721050\pi\)
−0.639962 + 0.768406i \(0.721050\pi\)
\(618\) −3.60433 −0.144987
\(619\) −34.1797 −1.37380 −0.686898 0.726754i \(-0.741028\pi\)
−0.686898 + 0.726754i \(0.741028\pi\)
\(620\) 19.7847 0.794574
\(621\) −12.0789 −0.484709
\(622\) −64.2199 −2.57498
\(623\) −12.3873 −0.496287
\(624\) −2.01491 −0.0806608
\(625\) −4.71033 −0.188413
\(626\) 22.8470 0.913151
\(627\) 2.14440 0.0856392
\(628\) −70.6341 −2.81861
\(629\) −66.8620 −2.66596
\(630\) −20.4428 −0.814459
\(631\) 23.8865 0.950906 0.475453 0.879741i \(-0.342284\pi\)
0.475453 + 0.879741i \(0.342284\pi\)
\(632\) 20.7782 0.826513
\(633\) 17.0139 0.676242
\(634\) 2.31836 0.0920740
\(635\) −12.9175 −0.512616
\(636\) 8.95927 0.355258
\(637\) −7.81882 −0.309793
\(638\) −46.1554 −1.82731
\(639\) 9.89816 0.391565
\(640\) −29.8427 −1.17964
\(641\) −26.7229 −1.05549 −0.527745 0.849403i \(-0.676962\pi\)
−0.527745 + 0.849403i \(0.676962\pi\)
\(642\) 15.7742 0.622558
\(643\) −19.6302 −0.774138 −0.387069 0.922051i \(-0.626513\pi\)
−0.387069 + 0.922051i \(0.626513\pi\)
\(644\) −24.2165 −0.954265
\(645\) 6.09777 0.240099
\(646\) 13.6867 0.538498
\(647\) 7.15265 0.281200 0.140600 0.990067i \(-0.455097\pi\)
0.140600 + 0.990067i \(0.455097\pi\)
\(648\) −15.3657 −0.603622
\(649\) 1.20215 0.0471885
\(650\) 27.6282 1.08367
\(651\) 6.14907 0.241001
\(652\) −13.7779 −0.539582
\(653\) −48.0497 −1.88033 −0.940164 0.340721i \(-0.889329\pi\)
−0.940164 + 0.340721i \(0.889329\pi\)
\(654\) 15.7889 0.617395
\(655\) −3.85954 −0.150805
\(656\) −1.56544 −0.0611201
\(657\) −25.6445 −1.00049
\(658\) 27.7511 1.08185
\(659\) −26.9418 −1.04950 −0.524752 0.851255i \(-0.675842\pi\)
−0.524752 + 0.851255i \(0.675842\pi\)
\(660\) 11.0901 0.431682
\(661\) 32.0555 1.24681 0.623407 0.781898i \(-0.285748\pi\)
0.623407 + 0.781898i \(0.285748\pi\)
\(662\) 12.6749 0.492623
\(663\) −18.5941 −0.722136
\(664\) 11.4646 0.444913
\(665\) 3.51465 0.136292
\(666\) −65.8745 −2.55259
\(667\) −20.3564 −0.788201
\(668\) 23.3144 0.902063
\(669\) −0.534629 −0.0206700
\(670\) −29.8770 −1.15425
\(671\) −31.2563 −1.20664
\(672\) −7.86232 −0.303296
\(673\) −18.6513 −0.718956 −0.359478 0.933154i \(-0.617045\pi\)
−0.359478 + 0.933154i \(0.617045\pi\)
\(674\) −5.37990 −0.207226
\(675\) −10.2373 −0.394034
\(676\) 24.2911 0.934273
\(677\) 10.4939 0.403314 0.201657 0.979456i \(-0.435367\pi\)
0.201657 + 0.979456i \(0.435367\pi\)
\(678\) −4.27465 −0.164167
\(679\) 15.6633 0.601103
\(680\) 28.8352 1.10578
\(681\) −2.49702 −0.0956861
\(682\) 27.1383 1.03918
\(683\) 42.1440 1.61260 0.806298 0.591510i \(-0.201468\pi\)
0.806298 + 0.591510i \(0.201468\pi\)
\(684\) 8.46690 0.323740
\(685\) 11.1827 0.427268
\(686\) 46.4712 1.77428
\(687\) −8.91910 −0.340285
\(688\) 3.63230 0.138480
\(689\) −17.0243 −0.648573
\(690\) 7.78981 0.296553
\(691\) −42.1473 −1.60336 −0.801679 0.597755i \(-0.796060\pi\)
−0.801679 + 0.597755i \(0.796060\pi\)
\(692\) 19.6741 0.747898
\(693\) −17.6067 −0.668824
\(694\) 72.2454 2.74240
\(695\) 20.5009 0.777643
\(696\) 14.5335 0.550892
\(697\) −14.4463 −0.547194
\(698\) 80.3082 3.03971
\(699\) 4.33952 0.164136
\(700\) −20.5244 −0.775751
\(701\) 41.2164 1.55672 0.778361 0.627818i \(-0.216052\pi\)
0.778361 + 0.627818i \(0.216052\pi\)
\(702\) −40.2254 −1.51821
\(703\) 11.3256 0.427153
\(704\) −38.6145 −1.45534
\(705\) −5.60507 −0.211099
\(706\) −10.2645 −0.386308
\(707\) −27.7548 −1.04383
\(708\) −0.929209 −0.0349218
\(709\) −50.6508 −1.90223 −0.951115 0.308838i \(-0.900060\pi\)
−0.951115 + 0.308838i \(0.900060\pi\)
\(710\) −14.0165 −0.526031
\(711\) 16.3553 0.613372
\(712\) 17.2147 0.645148
\(713\) 11.9691 0.448245
\(714\) 21.9993 0.823303
\(715\) −21.0733 −0.788095
\(716\) 9.65956 0.360995
\(717\) −6.43711 −0.240398
\(718\) 27.0662 1.01010
\(719\) −16.4111 −0.612030 −0.306015 0.952027i \(-0.598996\pi\)
−0.306015 + 0.952027i \(0.598996\pi\)
\(720\) 2.45953 0.0916612
\(721\) −5.08791 −0.189484
\(722\) −2.31836 −0.0862806
\(723\) −10.0021 −0.371980
\(724\) −19.1158 −0.710433
\(725\) −17.2528 −0.640753
\(726\) −2.66023 −0.0987303
\(727\) −51.7902 −1.92079 −0.960396 0.278640i \(-0.910116\pi\)
−0.960396 + 0.278640i \(0.910116\pi\)
\(728\) −32.8533 −1.21763
\(729\) −3.97795 −0.147331
\(730\) 36.3146 1.34406
\(731\) 33.5200 1.23978
\(732\) 24.1598 0.892970
\(733\) 7.24464 0.267587 0.133793 0.991009i \(-0.457284\pi\)
0.133793 + 0.991009i \(0.457284\pi\)
\(734\) 4.14830 0.153117
\(735\) −1.86842 −0.0689178
\(736\) −15.3039 −0.564109
\(737\) −25.7321 −0.947854
\(738\) −14.2330 −0.523924
\(739\) 8.46646 0.311444 0.155722 0.987801i \(-0.450230\pi\)
0.155722 + 0.987801i \(0.450230\pi\)
\(740\) 58.5720 2.15315
\(741\) 3.14962 0.115704
\(742\) 20.1419 0.739434
\(743\) 14.2262 0.521907 0.260954 0.965351i \(-0.415963\pi\)
0.260954 + 0.965351i \(0.415963\pi\)
\(744\) −8.54538 −0.313289
\(745\) 12.9315 0.473772
\(746\) −6.66784 −0.244127
\(747\) 9.02421 0.330179
\(748\) 60.9633 2.22904
\(749\) 22.2670 0.813620
\(750\) 19.0512 0.695653
\(751\) 17.9306 0.654298 0.327149 0.944973i \(-0.393912\pi\)
0.327149 + 0.944973i \(0.393912\pi\)
\(752\) −3.33881 −0.121754
\(753\) 21.2438 0.774166
\(754\) −67.7913 −2.46881
\(755\) 8.91353 0.324396
\(756\) 29.8827 1.08682
\(757\) 4.12622 0.149970 0.0749850 0.997185i \(-0.476109\pi\)
0.0749850 + 0.997185i \(0.476109\pi\)
\(758\) 11.5215 0.418480
\(759\) 6.70912 0.243526
\(760\) −4.88433 −0.177173
\(761\) −15.0894 −0.546989 −0.273494 0.961874i \(-0.588180\pi\)
−0.273494 + 0.961874i \(0.588180\pi\)
\(762\) 13.6958 0.496145
\(763\) 22.2878 0.806873
\(764\) 84.2639 3.04856
\(765\) 22.6973 0.820621
\(766\) 43.4520 1.56999
\(767\) 1.76567 0.0637547
\(768\) 13.9524 0.503463
\(769\) 20.6291 0.743903 0.371951 0.928252i \(-0.378689\pi\)
0.371951 + 0.928252i \(0.378689\pi\)
\(770\) 24.9324 0.898502
\(771\) −13.8939 −0.500376
\(772\) −65.5854 −2.36047
\(773\) −50.6866 −1.82307 −0.911536 0.411221i \(-0.865102\pi\)
−0.911536 + 0.411221i \(0.865102\pi\)
\(774\) 33.0249 1.18706
\(775\) 10.1442 0.364392
\(776\) −21.7674 −0.781403
\(777\) 18.2041 0.653069
\(778\) −39.1331 −1.40299
\(779\) 2.44703 0.0876739
\(780\) 16.2887 0.583230
\(781\) −12.0720 −0.431970
\(782\) 42.8213 1.53129
\(783\) 25.1193 0.897691
\(784\) −1.11298 −0.0397492
\(785\) 32.0734 1.14475
\(786\) 4.09207 0.145959
\(787\) 16.2764 0.580193 0.290096 0.956997i \(-0.406313\pi\)
0.290096 + 0.956997i \(0.406313\pi\)
\(788\) −6.88230 −0.245172
\(789\) −14.3157 −0.509653
\(790\) −23.1603 −0.824008
\(791\) −6.03415 −0.214550
\(792\) 24.4681 0.869436
\(793\) −45.9080 −1.63024
\(794\) 27.4950 0.975760
\(795\) −4.06820 −0.144284
\(796\) −21.6993 −0.769113
\(797\) 14.6502 0.518937 0.259469 0.965752i \(-0.416453\pi\)
0.259469 + 0.965752i \(0.416453\pi\)
\(798\) −3.72641 −0.131913
\(799\) −30.8116 −1.09003
\(800\) −12.9706 −0.458581
\(801\) 13.5503 0.478777
\(802\) −76.2533 −2.69260
\(803\) 31.2766 1.10373
\(804\) 19.8898 0.701459
\(805\) 10.9962 0.387565
\(806\) 39.8597 1.40400
\(807\) −18.1413 −0.638602
\(808\) 38.5710 1.35692
\(809\) 34.4021 1.20951 0.604756 0.796411i \(-0.293271\pi\)
0.604756 + 0.796411i \(0.293271\pi\)
\(810\) 17.1273 0.601793
\(811\) −11.2004 −0.393300 −0.196650 0.980474i \(-0.563006\pi\)
−0.196650 + 0.980474i \(0.563006\pi\)
\(812\) 50.3608 1.76732
\(813\) −8.72629 −0.306044
\(814\) 80.3420 2.81599
\(815\) 6.25622 0.219146
\(816\) −2.64680 −0.0926566
\(817\) −5.67787 −0.198643
\(818\) 48.9215 1.71050
\(819\) −25.8601 −0.903624
\(820\) 12.6552 0.441938
\(821\) −26.1875 −0.913950 −0.456975 0.889479i \(-0.651067\pi\)
−0.456975 + 0.889479i \(0.651067\pi\)
\(822\) −11.8564 −0.413540
\(823\) −50.2026 −1.74995 −0.874976 0.484167i \(-0.839123\pi\)
−0.874976 + 0.484167i \(0.839123\pi\)
\(824\) 7.07069 0.246319
\(825\) 5.68624 0.197969
\(826\) −2.08902 −0.0726863
\(827\) 18.6532 0.648637 0.324318 0.945948i \(-0.394865\pi\)
0.324318 + 0.945948i \(0.394865\pi\)
\(828\) 26.4901 0.920596
\(829\) 20.6627 0.717646 0.358823 0.933406i \(-0.383178\pi\)
0.358823 + 0.933406i \(0.383178\pi\)
\(830\) −12.7790 −0.443564
\(831\) −12.3862 −0.429672
\(832\) −56.7155 −1.96626
\(833\) −10.2709 −0.355865
\(834\) −21.7360 −0.752658
\(835\) −10.5866 −0.366364
\(836\) −10.3264 −0.357147
\(837\) −14.7696 −0.510511
\(838\) −37.2410 −1.28647
\(839\) −29.7914 −1.02851 −0.514257 0.857636i \(-0.671932\pi\)
−0.514257 + 0.857636i \(0.671932\pi\)
\(840\) −7.85079 −0.270878
\(841\) 13.3332 0.459766
\(842\) −66.4473 −2.28993
\(843\) 6.87955 0.236944
\(844\) −81.9309 −2.82018
\(845\) −11.0301 −0.379445
\(846\) −30.3565 −1.04368
\(847\) −3.75521 −0.129031
\(848\) −2.42334 −0.0832178
\(849\) 16.4851 0.565766
\(850\) 36.2927 1.24483
\(851\) 35.4340 1.21466
\(852\) 9.33114 0.319680
\(853\) 4.32088 0.147944 0.0739720 0.997260i \(-0.476432\pi\)
0.0739720 + 0.997260i \(0.476432\pi\)
\(854\) 54.3152 1.85863
\(855\) −3.84463 −0.131484
\(856\) −30.9446 −1.05766
\(857\) 9.66184 0.330042 0.165021 0.986290i \(-0.447231\pi\)
0.165021 + 0.986290i \(0.447231\pi\)
\(858\) 22.3429 0.762774
\(859\) 3.61233 0.123251 0.0616256 0.998099i \(-0.480372\pi\)
0.0616256 + 0.998099i \(0.480372\pi\)
\(860\) −29.3640 −1.00130
\(861\) 3.93322 0.134044
\(862\) 42.5059 1.44776
\(863\) −41.8604 −1.42494 −0.712472 0.701700i \(-0.752425\pi\)
−0.712472 + 0.701700i \(0.752425\pi\)
\(864\) 18.8847 0.642469
\(865\) −8.93358 −0.303751
\(866\) 73.5854 2.50053
\(867\) −12.5115 −0.424914
\(868\) −29.6110 −1.00506
\(869\) −19.9473 −0.676665
\(870\) −16.1997 −0.549223
\(871\) −37.7943 −1.28061
\(872\) −30.9734 −1.04889
\(873\) −17.1339 −0.579894
\(874\) −7.25339 −0.245350
\(875\) 26.8930 0.909148
\(876\) −24.1755 −0.816813
\(877\) 30.1589 1.01839 0.509197 0.860650i \(-0.329942\pi\)
0.509197 + 0.860650i \(0.329942\pi\)
\(878\) 37.3281 1.25976
\(879\) −10.8882 −0.367248
\(880\) −2.99969 −0.101120
\(881\) 48.2302 1.62492 0.812458 0.583020i \(-0.198129\pi\)
0.812458 + 0.583020i \(0.198129\pi\)
\(882\) −10.1192 −0.340731
\(883\) 14.2176 0.478460 0.239230 0.970963i \(-0.423105\pi\)
0.239230 + 0.970963i \(0.423105\pi\)
\(884\) 89.5405 3.01157
\(885\) 0.421933 0.0141831
\(886\) 55.5159 1.86509
\(887\) −51.0269 −1.71332 −0.856658 0.515885i \(-0.827463\pi\)
−0.856658 + 0.515885i \(0.827463\pi\)
\(888\) −25.2983 −0.848956
\(889\) 19.3331 0.648411
\(890\) −19.1883 −0.643192
\(891\) 14.7512 0.494185
\(892\) 2.57452 0.0862013
\(893\) 5.21909 0.174650
\(894\) −13.7106 −0.458550
\(895\) −4.38619 −0.146614
\(896\) 44.6644 1.49213
\(897\) 9.85411 0.329019
\(898\) −37.9674 −1.26699
\(899\) −24.8909 −0.830159
\(900\) 22.4514 0.748380
\(901\) −22.3633 −0.745029
\(902\) 17.3589 0.577987
\(903\) −9.12628 −0.303704
\(904\) 8.38567 0.278903
\(905\) 8.68005 0.288535
\(906\) −9.45055 −0.313974
\(907\) 29.6849 0.985672 0.492836 0.870122i \(-0.335960\pi\)
0.492836 + 0.870122i \(0.335960\pi\)
\(908\) 12.0245 0.399046
\(909\) 30.3606 1.00700
\(910\) 36.6198 1.21393
\(911\) −20.7632 −0.687914 −0.343957 0.938985i \(-0.611767\pi\)
−0.343957 + 0.938985i \(0.611767\pi\)
\(912\) 0.448335 0.0148459
\(913\) −11.0061 −0.364249
\(914\) −45.9676 −1.52047
\(915\) −10.9704 −0.362671
\(916\) 42.9502 1.41911
\(917\) 5.77642 0.190754
\(918\) −52.8405 −1.74400
\(919\) −33.0495 −1.09020 −0.545102 0.838370i \(-0.683509\pi\)
−0.545102 + 0.838370i \(0.683509\pi\)
\(920\) −15.2814 −0.503814
\(921\) −9.24242 −0.304548
\(922\) −4.52448 −0.149006
\(923\) −17.7309 −0.583620
\(924\) −16.5981 −0.546038
\(925\) 30.0317 0.987436
\(926\) 5.23874 0.172156
\(927\) 5.56560 0.182798
\(928\) 31.8260 1.04474
\(929\) −22.4774 −0.737460 −0.368730 0.929536i \(-0.620207\pi\)
−0.368730 + 0.929536i \(0.620207\pi\)
\(930\) 9.52507 0.312339
\(931\) 1.73976 0.0570183
\(932\) −20.8971 −0.684506
\(933\) −19.4131 −0.635555
\(934\) 70.8094 2.31695
\(935\) −27.6821 −0.905300
\(936\) 35.9378 1.17466
\(937\) 10.4904 0.342707 0.171354 0.985210i \(-0.445186\pi\)
0.171354 + 0.985210i \(0.445186\pi\)
\(938\) 44.7156 1.46002
\(939\) 6.90643 0.225383
\(940\) 26.9913 0.880361
\(941\) 9.60578 0.313139 0.156570 0.987667i \(-0.449956\pi\)
0.156570 + 0.987667i \(0.449956\pi\)
\(942\) −34.0057 −1.10797
\(943\) 7.65595 0.249312
\(944\) 0.251336 0.00818030
\(945\) −13.5691 −0.441401
\(946\) −40.2779 −1.30955
\(947\) 7.86729 0.255653 0.127826 0.991797i \(-0.459200\pi\)
0.127826 + 0.991797i \(0.459200\pi\)
\(948\) 15.4184 0.500766
\(949\) 45.9379 1.49121
\(950\) −6.14753 −0.199452
\(951\) 0.700819 0.0227256
\(952\) −43.1565 −1.39871
\(953\) 35.6790 1.15576 0.577878 0.816123i \(-0.303881\pi\)
0.577878 + 0.816123i \(0.303881\pi\)
\(954\) −22.0330 −0.713345
\(955\) −38.2624 −1.23814
\(956\) 30.9981 1.00255
\(957\) −13.9523 −0.451015
\(958\) −23.2244 −0.750345
\(959\) −16.7366 −0.540454
\(960\) −13.5530 −0.437422
\(961\) −16.3647 −0.527894
\(962\) 118.003 3.80458
\(963\) −24.3576 −0.784913
\(964\) 48.1651 1.55129
\(965\) 29.7809 0.958680
\(966\) −11.6587 −0.375112
\(967\) −38.1453 −1.22667 −0.613334 0.789823i \(-0.710172\pi\)
−0.613334 + 0.789823i \(0.710172\pi\)
\(968\) 5.21863 0.167733
\(969\) 4.13737 0.132911
\(970\) 24.2629 0.779034
\(971\) 48.9845 1.57199 0.785994 0.618235i \(-0.212152\pi\)
0.785994 + 0.618235i \(0.212152\pi\)
\(972\) −50.4896 −1.61945
\(973\) −30.6828 −0.983647
\(974\) −37.1836 −1.19144
\(975\) 8.35173 0.267470
\(976\) −6.53483 −0.209175
\(977\) −37.5320 −1.20076 −0.600378 0.799717i \(-0.704983\pi\)
−0.600378 + 0.799717i \(0.704983\pi\)
\(978\) −6.63315 −0.212105
\(979\) −16.5263 −0.528182
\(980\) 8.99744 0.287413
\(981\) −24.3803 −0.778404
\(982\) −56.2081 −1.79367
\(983\) 35.8462 1.14332 0.571658 0.820492i \(-0.306300\pi\)
0.571658 + 0.820492i \(0.306300\pi\)
\(984\) −5.46601 −0.174250
\(985\) 3.12510 0.0995740
\(986\) −89.0514 −2.83597
\(987\) 8.38888 0.267021
\(988\) −15.1671 −0.482528
\(989\) −17.7642 −0.564867
\(990\) −27.2732 −0.866801
\(991\) 33.3493 1.05937 0.529687 0.848193i \(-0.322309\pi\)
0.529687 + 0.848193i \(0.322309\pi\)
\(992\) −18.7130 −0.594137
\(993\) 3.83149 0.121589
\(994\) 20.9780 0.665381
\(995\) 9.85319 0.312367
\(996\) 8.50726 0.269563
\(997\) 10.9816 0.347789 0.173895 0.984764i \(-0.444365\pi\)
0.173895 + 0.984764i \(0.444365\pi\)
\(998\) −23.7127 −0.750611
\(999\) −43.7248 −1.38339
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 \(a_p\))