Properties

Label 6023.2.a.b.1.9
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 1.9
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.32426 q^{2}\) \(-2.85691 q^{3}\) \(+3.40220 q^{4}\) \(-3.59754 q^{5}\) \(+6.64022 q^{6}\) \(-1.30166 q^{7}\) \(-3.25907 q^{8}\) \(+5.16196 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.32426 q^{2}\) \(-2.85691 q^{3}\) \(+3.40220 q^{4}\) \(-3.59754 q^{5}\) \(+6.64022 q^{6}\) \(-1.30166 q^{7}\) \(-3.25907 q^{8}\) \(+5.16196 q^{9}\) \(+8.36162 q^{10}\) \(+1.01972 q^{11}\) \(-9.71978 q^{12}\) \(+1.77703 q^{13}\) \(+3.02539 q^{14}\) \(+10.2779 q^{15}\) \(+0.770542 q^{16}\) \(+4.28401 q^{17}\) \(-11.9977 q^{18}\) \(-1.00000 q^{19}\) \(-12.2395 q^{20}\) \(+3.71872 q^{21}\) \(-2.37009 q^{22}\) \(-2.91512 q^{23}\) \(+9.31088 q^{24}\) \(+7.94228 q^{25}\) \(-4.13029 q^{26}\) \(-6.17653 q^{27}\) \(-4.42849 q^{28}\) \(+0.460404 q^{29}\) \(-23.8884 q^{30}\) \(-7.46390 q^{31}\) \(+4.72720 q^{32}\) \(-2.91325 q^{33}\) \(-9.95717 q^{34}\) \(+4.68276 q^{35}\) \(+17.5620 q^{36}\) \(-1.62888 q^{37}\) \(+2.32426 q^{38}\) \(-5.07683 q^{39}\) \(+11.7246 q^{40}\) \(-2.27769 q^{41}\) \(-8.64329 q^{42}\) \(-1.77376 q^{43}\) \(+3.46928 q^{44}\) \(-18.5703 q^{45}\) \(+6.77550 q^{46}\) \(-1.27970 q^{47}\) \(-2.20137 q^{48}\) \(-5.30569 q^{49}\) \(-18.4599 q^{50}\) \(-12.2391 q^{51}\) \(+6.04581 q^{52}\) \(-7.64027 q^{53}\) \(+14.3559 q^{54}\) \(-3.66848 q^{55}\) \(+4.24219 q^{56}\) \(+2.85691 q^{57}\) \(-1.07010 q^{58}\) \(+14.0323 q^{59}\) \(+34.9673 q^{60}\) \(-1.48810 q^{61}\) \(+17.3481 q^{62}\) \(-6.71910 q^{63}\) \(-12.5283 q^{64}\) \(-6.39294 q^{65}\) \(+6.77116 q^{66}\) \(-6.96504 q^{67}\) \(+14.5750 q^{68}\) \(+8.32824 q^{69}\) \(-10.8840 q^{70}\) \(+8.86578 q^{71}\) \(-16.8232 q^{72}\) \(-14.3144 q^{73}\) \(+3.78593 q^{74}\) \(-22.6904 q^{75}\) \(-3.40220 q^{76}\) \(-1.32733 q^{77}\) \(+11.7999 q^{78}\) \(+9.52311 q^{79}\) \(-2.77205 q^{80}\) \(+2.15995 q^{81}\) \(+5.29395 q^{82}\) \(+2.69785 q^{83}\) \(+12.6518 q^{84}\) \(-15.4119 q^{85}\) \(+4.12268 q^{86}\) \(-1.31534 q^{87}\) \(-3.32334 q^{88}\) \(+6.84473 q^{89}\) \(+43.1624 q^{90}\) \(-2.31309 q^{91}\) \(-9.91779 q^{92}\) \(+21.3237 q^{93}\) \(+2.97435 q^{94}\) \(+3.59754 q^{95}\) \(-13.5052 q^{96}\) \(-13.5984 q^{97}\) \(+12.3318 q^{98}\) \(+5.26375 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 27q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 13q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 99q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 53q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 63q^{28} \) \(\mathstrut -\mathstrut 34q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 43q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 25q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 80q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 21q^{44} \) \(\mathstrut -\mathstrut 53q^{45} \) \(\mathstrut -\mathstrut 23q^{46} \) \(\mathstrut -\mathstrut 31q^{47} \) \(\mathstrut -\mathstrut 74q^{48} \) \(\mathstrut -\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 71q^{52} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 80q^{54} \) \(\mathstrut -\mathstrut 45q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 91q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 61q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut -\mathstrut 43q^{63} \) \(\mathstrut -\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 75q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut -\mathstrut 55q^{68} \) \(\mathstrut -\mathstrut 45q^{69} \) \(\mathstrut -\mathstrut 76q^{70} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 77q^{72} \) \(\mathstrut -\mathstrut 143q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 58q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 109q^{82} \) \(\mathstrut -\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 80q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 57q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut -\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 107q^{92} \) \(\mathstrut -\mathstrut 121q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 128q^{97} \) \(\mathstrut +\mathstrut 54q^{98} \) \(\mathstrut -\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.32426 −1.64350 −0.821751 0.569847i \(-0.807002\pi\)
−0.821751 + 0.569847i \(0.807002\pi\)
\(3\) −2.85691 −1.64944 −0.824720 0.565541i \(-0.808667\pi\)
−0.824720 + 0.565541i \(0.808667\pi\)
\(4\) 3.40220 1.70110
\(5\) −3.59754 −1.60887 −0.804434 0.594042i \(-0.797531\pi\)
−0.804434 + 0.594042i \(0.797531\pi\)
\(6\) 6.64022 2.71086
\(7\) −1.30166 −0.491980 −0.245990 0.969272i \(-0.579113\pi\)
−0.245990 + 0.969272i \(0.579113\pi\)
\(8\) −3.25907 −1.15226
\(9\) 5.16196 1.72065
\(10\) 8.36162 2.64418
\(11\) 1.01972 0.307457 0.153728 0.988113i \(-0.450872\pi\)
0.153728 + 0.988113i \(0.450872\pi\)
\(12\) −9.71978 −2.80586
\(13\) 1.77703 0.492860 0.246430 0.969161i \(-0.420742\pi\)
0.246430 + 0.969161i \(0.420742\pi\)
\(14\) 3.02539 0.808571
\(15\) 10.2779 2.65373
\(16\) 0.770542 0.192635
\(17\) 4.28401 1.03903 0.519513 0.854463i \(-0.326113\pi\)
0.519513 + 0.854463i \(0.326113\pi\)
\(18\) −11.9977 −2.82790
\(19\) −1.00000 −0.229416
\(20\) −12.2395 −2.73684
\(21\) 3.71872 0.811492
\(22\) −2.37009 −0.505306
\(23\) −2.91512 −0.607844 −0.303922 0.952697i \(-0.598296\pi\)
−0.303922 + 0.952697i \(0.598296\pi\)
\(24\) 9.31088 1.90058
\(25\) 7.94228 1.58846
\(26\) −4.13029 −0.810016
\(27\) −6.17653 −1.18867
\(28\) −4.42849 −0.836907
\(29\) 0.460404 0.0854949 0.0427475 0.999086i \(-0.486389\pi\)
0.0427475 + 0.999086i \(0.486389\pi\)
\(30\) −23.8884 −4.36141
\(31\) −7.46390 −1.34056 −0.670278 0.742110i \(-0.733825\pi\)
−0.670278 + 0.742110i \(0.733825\pi\)
\(32\) 4.72720 0.835658
\(33\) −2.91325 −0.507132
\(34\) −9.95717 −1.70764
\(35\) 4.68276 0.791532
\(36\) 17.5620 2.92700
\(37\) −1.62888 −0.267785 −0.133893 0.990996i \(-0.542748\pi\)
−0.133893 + 0.990996i \(0.542748\pi\)
\(38\) 2.32426 0.377045
\(39\) −5.07683 −0.812943
\(40\) 11.7246 1.85383
\(41\) −2.27769 −0.355715 −0.177858 0.984056i \(-0.556917\pi\)
−0.177858 + 0.984056i \(0.556917\pi\)
\(42\) −8.64329 −1.33369
\(43\) −1.77376 −0.270496 −0.135248 0.990812i \(-0.543183\pi\)
−0.135248 + 0.990812i \(0.543183\pi\)
\(44\) 3.46928 0.523014
\(45\) −18.5703 −2.76830
\(46\) 6.77550 0.998992
\(47\) −1.27970 −0.186663 −0.0933314 0.995635i \(-0.529752\pi\)
−0.0933314 + 0.995635i \(0.529752\pi\)
\(48\) −2.20137 −0.317741
\(49\) −5.30569 −0.757955
\(50\) −18.4599 −2.61063
\(51\) −12.2391 −1.71381
\(52\) 6.04581 0.838403
\(53\) −7.64027 −1.04947 −0.524736 0.851265i \(-0.675836\pi\)
−0.524736 + 0.851265i \(0.675836\pi\)
\(54\) 14.3559 1.95359
\(55\) −3.66848 −0.494658
\(56\) 4.24219 0.566887
\(57\) 2.85691 0.378408
\(58\) −1.07010 −0.140511
\(59\) 14.0323 1.82685 0.913427 0.407003i \(-0.133426\pi\)
0.913427 + 0.407003i \(0.133426\pi\)
\(60\) 34.9673 4.51426
\(61\) −1.48810 −0.190531 −0.0952657 0.995452i \(-0.530370\pi\)
−0.0952657 + 0.995452i \(0.530370\pi\)
\(62\) 17.3481 2.20321
\(63\) −6.71910 −0.846528
\(64\) −12.5283 −1.56604
\(65\) −6.39294 −0.792946
\(66\) 6.77116 0.833472
\(67\) −6.96504 −0.850915 −0.425458 0.904978i \(-0.639887\pi\)
−0.425458 + 0.904978i \(0.639887\pi\)
\(68\) 14.5750 1.76748
\(69\) 8.32824 1.00260
\(70\) −10.8840 −1.30088
\(71\) 8.86578 1.05217 0.526087 0.850431i \(-0.323659\pi\)
0.526087 + 0.850431i \(0.323659\pi\)
\(72\) −16.8232 −1.98263
\(73\) −14.3144 −1.67538 −0.837689 0.546148i \(-0.816094\pi\)
−0.837689 + 0.546148i \(0.816094\pi\)
\(74\) 3.78593 0.440106
\(75\) −22.6904 −2.62006
\(76\) −3.40220 −0.390259
\(77\) −1.32733 −0.151263
\(78\) 11.7999 1.33607
\(79\) 9.52311 1.07143 0.535717 0.844398i \(-0.320041\pi\)
0.535717 + 0.844398i \(0.320041\pi\)
\(80\) −2.77205 −0.309925
\(81\) 2.15995 0.239995
\(82\) 5.29395 0.584619
\(83\) 2.69785 0.296127 0.148064 0.988978i \(-0.452696\pi\)
0.148064 + 0.988978i \(0.452696\pi\)
\(84\) 12.6518 1.38043
\(85\) −15.4119 −1.67166
\(86\) 4.12268 0.444560
\(87\) −1.31534 −0.141019
\(88\) −3.32334 −0.354269
\(89\) 6.84473 0.725540 0.362770 0.931879i \(-0.381831\pi\)
0.362770 + 0.931879i \(0.381831\pi\)
\(90\) 43.1624 4.54971
\(91\) −2.31309 −0.242477
\(92\) −9.91779 −1.03400
\(93\) 21.3237 2.21117
\(94\) 2.97435 0.306781
\(95\) 3.59754 0.369100
\(96\) −13.5052 −1.37837
\(97\) −13.5984 −1.38071 −0.690355 0.723470i \(-0.742546\pi\)
−0.690355 + 0.723470i \(0.742546\pi\)
\(98\) 12.3318 1.24570
\(99\) 5.26375 0.529027
\(100\) 27.0212 2.70212
\(101\) 16.3789 1.62976 0.814878 0.579632i \(-0.196804\pi\)
0.814878 + 0.579632i \(0.196804\pi\)
\(102\) 28.4468 2.81665
\(103\) 11.2349 1.10701 0.553503 0.832847i \(-0.313291\pi\)
0.553503 + 0.832847i \(0.313291\pi\)
\(104\) −5.79147 −0.567900
\(105\) −13.3783 −1.30558
\(106\) 17.7580 1.72481
\(107\) −10.5476 −1.01967 −0.509836 0.860272i \(-0.670294\pi\)
−0.509836 + 0.860272i \(0.670294\pi\)
\(108\) −21.0138 −2.02205
\(109\) 2.97084 0.284555 0.142277 0.989827i \(-0.454557\pi\)
0.142277 + 0.989827i \(0.454557\pi\)
\(110\) 8.52651 0.812971
\(111\) 4.65356 0.441696
\(112\) −1.00298 −0.0947729
\(113\) −4.21375 −0.396396 −0.198198 0.980162i \(-0.563509\pi\)
−0.198198 + 0.980162i \(0.563509\pi\)
\(114\) −6.64022 −0.621913
\(115\) 10.4872 0.977940
\(116\) 1.56638 0.145435
\(117\) 9.17296 0.848041
\(118\) −32.6148 −3.00244
\(119\) −5.57632 −0.511180
\(120\) −33.4963 −3.05778
\(121\) −9.96017 −0.905470
\(122\) 3.45873 0.313139
\(123\) 6.50717 0.586731
\(124\) −25.3936 −2.28042
\(125\) −10.5850 −0.946749
\(126\) 15.6170 1.39127
\(127\) −0.587363 −0.0521200 −0.0260600 0.999660i \(-0.508296\pi\)
−0.0260600 + 0.999660i \(0.508296\pi\)
\(128\) 19.6647 1.73813
\(129\) 5.06748 0.446167
\(130\) 14.8589 1.30321
\(131\) 21.0007 1.83484 0.917419 0.397923i \(-0.130269\pi\)
0.917419 + 0.397923i \(0.130269\pi\)
\(132\) −9.91145 −0.862681
\(133\) 1.30166 0.112868
\(134\) 16.1886 1.39848
\(135\) 22.2203 1.91242
\(136\) −13.9619 −1.19722
\(137\) −9.65340 −0.824746 −0.412373 0.911015i \(-0.635300\pi\)
−0.412373 + 0.911015i \(0.635300\pi\)
\(138\) −19.3570 −1.64778
\(139\) −6.84147 −0.580286 −0.290143 0.956983i \(-0.593703\pi\)
−0.290143 + 0.956983i \(0.593703\pi\)
\(140\) 15.9317 1.34647
\(141\) 3.65598 0.307889
\(142\) −20.6064 −1.72925
\(143\) 1.81207 0.151533
\(144\) 3.97751 0.331459
\(145\) −1.65632 −0.137550
\(146\) 33.2705 2.75349
\(147\) 15.1579 1.25020
\(148\) −5.54175 −0.455529
\(149\) 17.1466 1.40471 0.702353 0.711828i \(-0.252133\pi\)
0.702353 + 0.711828i \(0.252133\pi\)
\(150\) 52.7385 4.30608
\(151\) 11.2167 0.912806 0.456403 0.889773i \(-0.349138\pi\)
0.456403 + 0.889773i \(0.349138\pi\)
\(152\) 3.25907 0.264345
\(153\) 22.1139 1.78780
\(154\) 3.08505 0.248601
\(155\) 26.8517 2.15678
\(156\) −17.2724 −1.38289
\(157\) 8.02290 0.640297 0.320149 0.947367i \(-0.396267\pi\)
0.320149 + 0.947367i \(0.396267\pi\)
\(158\) −22.1342 −1.76090
\(159\) 21.8276 1.73104
\(160\) −17.0063 −1.34446
\(161\) 3.79448 0.299047
\(162\) −5.02029 −0.394431
\(163\) 5.04648 0.395271 0.197635 0.980276i \(-0.436674\pi\)
0.197635 + 0.980276i \(0.436674\pi\)
\(164\) −7.74915 −0.605107
\(165\) 10.4805 0.815908
\(166\) −6.27050 −0.486686
\(167\) −7.53517 −0.583089 −0.291545 0.956557i \(-0.594169\pi\)
−0.291545 + 0.956557i \(0.594169\pi\)
\(168\) −12.1196 −0.935046
\(169\) −9.84216 −0.757089
\(170\) 35.8213 2.74737
\(171\) −5.16196 −0.394745
\(172\) −6.03468 −0.460140
\(173\) −6.83023 −0.519293 −0.259647 0.965704i \(-0.583606\pi\)
−0.259647 + 0.965704i \(0.583606\pi\)
\(174\) 3.05718 0.231765
\(175\) −10.3381 −0.781489
\(176\) 0.785736 0.0592271
\(177\) −40.0892 −3.01329
\(178\) −15.9090 −1.19243
\(179\) 22.8432 1.70738 0.853692 0.520779i \(-0.174358\pi\)
0.853692 + 0.520779i \(0.174358\pi\)
\(180\) −63.1800 −4.70916
\(181\) −13.8191 −1.02717 −0.513583 0.858040i \(-0.671682\pi\)
−0.513583 + 0.858040i \(0.671682\pi\)
\(182\) 5.37622 0.398512
\(183\) 4.25137 0.314270
\(184\) 9.50057 0.700391
\(185\) 5.85994 0.430831
\(186\) −49.5619 −3.63406
\(187\) 4.36849 0.319456
\(188\) −4.35377 −0.317532
\(189\) 8.03973 0.584805
\(190\) −8.36162 −0.606616
\(191\) −0.138595 −0.0100284 −0.00501421 0.999987i \(-0.501596\pi\)
−0.00501421 + 0.999987i \(0.501596\pi\)
\(192\) 35.7924 2.58309
\(193\) 20.2671 1.45886 0.729430 0.684056i \(-0.239786\pi\)
0.729430 + 0.684056i \(0.239786\pi\)
\(194\) 31.6063 2.26920
\(195\) 18.2641 1.30792
\(196\) −18.0510 −1.28936
\(197\) −11.8133 −0.841660 −0.420830 0.907139i \(-0.638261\pi\)
−0.420830 + 0.907139i \(0.638261\pi\)
\(198\) −12.2343 −0.869456
\(199\) 22.1496 1.57014 0.785072 0.619404i \(-0.212626\pi\)
0.785072 + 0.619404i \(0.212626\pi\)
\(200\) −25.8845 −1.83031
\(201\) 19.8985 1.40353
\(202\) −38.0688 −2.67851
\(203\) −0.599289 −0.0420618
\(204\) −41.6397 −2.91536
\(205\) 8.19408 0.572299
\(206\) −26.1128 −1.81937
\(207\) −15.0477 −1.04589
\(208\) 1.36928 0.0949423
\(209\) −1.01972 −0.0705355
\(210\) 31.0946 2.14573
\(211\) −16.8265 −1.15838 −0.579191 0.815192i \(-0.696631\pi\)
−0.579191 + 0.815192i \(0.696631\pi\)
\(212\) −25.9937 −1.78525
\(213\) −25.3288 −1.73550
\(214\) 24.5153 1.67583
\(215\) 6.38117 0.435192
\(216\) 20.1298 1.36966
\(217\) 9.71544 0.659527
\(218\) −6.90501 −0.467667
\(219\) 40.8951 2.76343
\(220\) −12.4809 −0.841461
\(221\) 7.61283 0.512094
\(222\) −10.8161 −0.725928
\(223\) 18.0275 1.20721 0.603607 0.797282i \(-0.293730\pi\)
0.603607 + 0.797282i \(0.293730\pi\)
\(224\) −6.15319 −0.411127
\(225\) 40.9977 2.73318
\(226\) 9.79386 0.651478
\(227\) 0.370244 0.0245739 0.0122870 0.999925i \(-0.496089\pi\)
0.0122870 + 0.999925i \(0.496089\pi\)
\(228\) 9.71978 0.643708
\(229\) −1.09637 −0.0724500 −0.0362250 0.999344i \(-0.511533\pi\)
−0.0362250 + 0.999344i \(0.511533\pi\)
\(230\) −24.3751 −1.60725
\(231\) 3.79205 0.249499
\(232\) −1.50049 −0.0985119
\(233\) −10.9756 −0.719037 −0.359519 0.933138i \(-0.617059\pi\)
−0.359519 + 0.933138i \(0.617059\pi\)
\(234\) −21.3204 −1.39376
\(235\) 4.60375 0.300316
\(236\) 47.7407 3.10766
\(237\) −27.2067 −1.76727
\(238\) 12.9608 0.840126
\(239\) −26.3429 −1.70398 −0.851990 0.523558i \(-0.824604\pi\)
−0.851990 + 0.523558i \(0.824604\pi\)
\(240\) 7.91952 0.511203
\(241\) 18.0219 1.16089 0.580447 0.814298i \(-0.302878\pi\)
0.580447 + 0.814298i \(0.302878\pi\)
\(242\) 23.1501 1.48814
\(243\) 12.3588 0.792818
\(244\) −5.06280 −0.324113
\(245\) 19.0874 1.21945
\(246\) −15.1244 −0.964294
\(247\) −1.77703 −0.113070
\(248\) 24.3254 1.54466
\(249\) −7.70752 −0.488444
\(250\) 24.6023 1.55598
\(251\) −4.63808 −0.292753 −0.146376 0.989229i \(-0.546761\pi\)
−0.146376 + 0.989229i \(0.546761\pi\)
\(252\) −22.8597 −1.44003
\(253\) −2.97260 −0.186886
\(254\) 1.36519 0.0856593
\(255\) 44.0305 2.75730
\(256\) −20.6493 −1.29058
\(257\) 5.10498 0.318440 0.159220 0.987243i \(-0.449102\pi\)
0.159220 + 0.987243i \(0.449102\pi\)
\(258\) −11.7782 −0.733276
\(259\) 2.12024 0.131745
\(260\) −21.7500 −1.34888
\(261\) 2.37659 0.147107
\(262\) −48.8111 −3.01556
\(263\) −1.58968 −0.0980241 −0.0490120 0.998798i \(-0.515607\pi\)
−0.0490120 + 0.998798i \(0.515607\pi\)
\(264\) 9.49449 0.584345
\(265\) 27.4862 1.68846
\(266\) −3.02539 −0.185499
\(267\) −19.5548 −1.19673
\(268\) −23.6964 −1.44749
\(269\) −12.8635 −0.784304 −0.392152 0.919900i \(-0.628269\pi\)
−0.392152 + 0.919900i \(0.628269\pi\)
\(270\) −51.6459 −3.14307
\(271\) 13.5749 0.824615 0.412308 0.911045i \(-0.364723\pi\)
0.412308 + 0.911045i \(0.364723\pi\)
\(272\) 3.30101 0.200153
\(273\) 6.60829 0.399952
\(274\) 22.4370 1.35547
\(275\) 8.09890 0.488382
\(276\) 28.3343 1.70552
\(277\) 0.832058 0.0499935 0.0249968 0.999688i \(-0.492042\pi\)
0.0249968 + 0.999688i \(0.492042\pi\)
\(278\) 15.9014 0.953701
\(279\) −38.5283 −2.30663
\(280\) −15.2615 −0.912046
\(281\) 18.1606 1.08337 0.541685 0.840581i \(-0.317786\pi\)
0.541685 + 0.840581i \(0.317786\pi\)
\(282\) −8.49746 −0.506016
\(283\) 19.6797 1.16983 0.584917 0.811093i \(-0.301127\pi\)
0.584917 + 0.811093i \(0.301127\pi\)
\(284\) 30.1631 1.78985
\(285\) −10.2779 −0.608808
\(286\) −4.21173 −0.249045
\(287\) 2.96477 0.175005
\(288\) 24.4016 1.43788
\(289\) 1.35277 0.0795747
\(290\) 3.84973 0.226064
\(291\) 38.8495 2.27740
\(292\) −48.7005 −2.84998
\(293\) 20.2349 1.18213 0.591067 0.806623i \(-0.298707\pi\)
0.591067 + 0.806623i \(0.298707\pi\)
\(294\) −35.2309 −2.05471
\(295\) −50.4818 −2.93917
\(296\) 5.30862 0.308557
\(297\) −6.29833 −0.365466
\(298\) −39.8533 −2.30864
\(299\) −5.18025 −0.299582
\(300\) −77.1973 −4.45699
\(301\) 2.30883 0.133079
\(302\) −26.0707 −1.50020
\(303\) −46.7930 −2.68819
\(304\) −0.770542 −0.0441936
\(305\) 5.35349 0.306540
\(306\) −51.3985 −2.93826
\(307\) 13.2117 0.754029 0.377015 0.926207i \(-0.376951\pi\)
0.377015 + 0.926207i \(0.376951\pi\)
\(308\) −4.51582 −0.257313
\(309\) −32.0971 −1.82594
\(310\) −62.4103 −3.54467
\(311\) −31.5206 −1.78737 −0.893683 0.448698i \(-0.851888\pi\)
−0.893683 + 0.448698i \(0.851888\pi\)
\(312\) 16.5457 0.936717
\(313\) −12.3338 −0.697149 −0.348575 0.937281i \(-0.613334\pi\)
−0.348575 + 0.937281i \(0.613334\pi\)
\(314\) −18.6473 −1.05233
\(315\) 24.1722 1.36195
\(316\) 32.3995 1.82261
\(317\) −1.00000 −0.0561656
\(318\) −50.7331 −2.84497
\(319\) 0.469483 0.0262860
\(320\) 45.0712 2.51955
\(321\) 30.1335 1.68189
\(322\) −8.81937 −0.491485
\(323\) −4.28401 −0.238369
\(324\) 7.34857 0.408254
\(325\) 14.1137 0.782886
\(326\) −11.7293 −0.649628
\(327\) −8.48744 −0.469356
\(328\) 7.42315 0.409875
\(329\) 1.66573 0.0918344
\(330\) −24.3595 −1.34095
\(331\) 22.1793 1.21908 0.609542 0.792754i \(-0.291353\pi\)
0.609542 + 0.792754i \(0.291353\pi\)
\(332\) 9.17860 0.503741
\(333\) −8.40819 −0.460766
\(334\) 17.5137 0.958308
\(335\) 25.0570 1.36901
\(336\) 2.86543 0.156322
\(337\) −24.8991 −1.35634 −0.678170 0.734905i \(-0.737227\pi\)
−0.678170 + 0.734905i \(0.737227\pi\)
\(338\) 22.8758 1.24428
\(339\) 12.0383 0.653832
\(340\) −52.4343 −2.84365
\(341\) −7.61108 −0.412163
\(342\) 11.9977 0.648764
\(343\) 16.0178 0.864879
\(344\) 5.78081 0.311680
\(345\) −29.9612 −1.61305
\(346\) 15.8753 0.853459
\(347\) 18.0693 0.970012 0.485006 0.874511i \(-0.338817\pi\)
0.485006 + 0.874511i \(0.338817\pi\)
\(348\) −4.47503 −0.239887
\(349\) 13.2237 0.707851 0.353925 0.935274i \(-0.384847\pi\)
0.353925 + 0.935274i \(0.384847\pi\)
\(350\) 24.0285 1.28438
\(351\) −10.9759 −0.585850
\(352\) 4.82041 0.256929
\(353\) 4.07529 0.216906 0.108453 0.994102i \(-0.465410\pi\)
0.108453 + 0.994102i \(0.465410\pi\)
\(354\) 93.1777 4.95234
\(355\) −31.8950 −1.69281
\(356\) 23.2871 1.23421
\(357\) 15.9311 0.843161
\(358\) −53.0937 −2.80609
\(359\) 15.8207 0.834985 0.417493 0.908680i \(-0.362909\pi\)
0.417493 + 0.908680i \(0.362909\pi\)
\(360\) 60.5221 3.18979
\(361\) 1.00000 0.0526316
\(362\) 32.1192 1.68815
\(363\) 28.4554 1.49352
\(364\) −7.86957 −0.412478
\(365\) 51.4967 2.69546
\(366\) −9.88130 −0.516504
\(367\) 4.51303 0.235578 0.117789 0.993039i \(-0.462419\pi\)
0.117789 + 0.993039i \(0.462419\pi\)
\(368\) −2.24622 −0.117092
\(369\) −11.7573 −0.612063
\(370\) −13.6200 −0.708072
\(371\) 9.94502 0.516320
\(372\) 72.5474 3.76141
\(373\) −32.6511 −1.69061 −0.845306 0.534282i \(-0.820582\pi\)
−0.845306 + 0.534282i \(0.820582\pi\)
\(374\) −10.1535 −0.525026
\(375\) 30.2404 1.56161
\(376\) 4.17062 0.215083
\(377\) 0.818153 0.0421370
\(378\) −18.6864 −0.961127
\(379\) 3.95146 0.202973 0.101486 0.994837i \(-0.467640\pi\)
0.101486 + 0.994837i \(0.467640\pi\)
\(380\) 12.2395 0.627875
\(381\) 1.67805 0.0859689
\(382\) 0.322132 0.0164817
\(383\) 32.0965 1.64005 0.820026 0.572326i \(-0.193959\pi\)
0.820026 + 0.572326i \(0.193959\pi\)
\(384\) −56.1805 −2.86695
\(385\) 4.77510 0.243362
\(386\) −47.1061 −2.39764
\(387\) −9.15608 −0.465430
\(388\) −46.2645 −2.34872
\(389\) 5.62983 0.285444 0.142722 0.989763i \(-0.454415\pi\)
0.142722 + 0.989763i \(0.454415\pi\)
\(390\) −42.4505 −2.14956
\(391\) −12.4884 −0.631565
\(392\) 17.2916 0.873358
\(393\) −59.9971 −3.02645
\(394\) 27.4571 1.38327
\(395\) −34.2598 −1.72380
\(396\) 17.9083 0.899926
\(397\) 8.26567 0.414842 0.207421 0.978252i \(-0.433493\pi\)
0.207421 + 0.978252i \(0.433493\pi\)
\(398\) −51.4815 −2.58053
\(399\) −3.71872 −0.186169
\(400\) 6.11986 0.305993
\(401\) 10.8257 0.540608 0.270304 0.962775i \(-0.412876\pi\)
0.270304 + 0.962775i \(0.412876\pi\)
\(402\) −46.2494 −2.30671
\(403\) −13.2636 −0.660706
\(404\) 55.7241 2.77238
\(405\) −7.77051 −0.386120
\(406\) 1.39290 0.0691287
\(407\) −1.66100 −0.0823325
\(408\) 39.8879 1.97475
\(409\) 21.4185 1.05908 0.529538 0.848286i \(-0.322365\pi\)
0.529538 + 0.848286i \(0.322365\pi\)
\(410\) −19.0452 −0.940575
\(411\) 27.5789 1.36037
\(412\) 38.2233 1.88313
\(413\) −18.2653 −0.898776
\(414\) 34.9748 1.71892
\(415\) −9.70561 −0.476430
\(416\) 8.40038 0.411862
\(417\) 19.5455 0.957147
\(418\) 2.37009 0.115925
\(419\) −23.7846 −1.16196 −0.580978 0.813919i \(-0.697330\pi\)
−0.580978 + 0.813919i \(0.697330\pi\)
\(420\) −45.5154 −2.22093
\(421\) 19.6735 0.958827 0.479413 0.877589i \(-0.340850\pi\)
0.479413 + 0.877589i \(0.340850\pi\)
\(422\) 39.1091 1.90380
\(423\) −6.60574 −0.321182
\(424\) 24.9002 1.20926
\(425\) 34.0248 1.65045
\(426\) 58.8707 2.85229
\(427\) 1.93699 0.0937377
\(428\) −35.8849 −1.73456
\(429\) −5.17694 −0.249945
\(430\) −14.8315 −0.715239
\(431\) 23.0458 1.11008 0.555039 0.831825i \(-0.312703\pi\)
0.555039 + 0.831825i \(0.312703\pi\)
\(432\) −4.75928 −0.228981
\(433\) 10.8217 0.520057 0.260029 0.965601i \(-0.416268\pi\)
0.260029 + 0.965601i \(0.416268\pi\)
\(434\) −22.5812 −1.08393
\(435\) 4.73197 0.226881
\(436\) 10.1074 0.484056
\(437\) 2.91512 0.139449
\(438\) −95.0509 −4.54171
\(439\) −18.0970 −0.863721 −0.431860 0.901940i \(-0.642143\pi\)
−0.431860 + 0.901940i \(0.642143\pi\)
\(440\) 11.9558 0.569972
\(441\) −27.3877 −1.30418
\(442\) −17.6942 −0.841627
\(443\) −8.32828 −0.395689 −0.197844 0.980233i \(-0.563394\pi\)
−0.197844 + 0.980233i \(0.563394\pi\)
\(444\) 15.8323 0.751368
\(445\) −24.6242 −1.16730
\(446\) −41.9007 −1.98406
\(447\) −48.9865 −2.31698
\(448\) 16.3076 0.770462
\(449\) 24.5350 1.15788 0.578939 0.815371i \(-0.303467\pi\)
0.578939 + 0.815371i \(0.303467\pi\)
\(450\) −95.2895 −4.49199
\(451\) −2.32260 −0.109367
\(452\) −14.3360 −0.674309
\(453\) −32.0453 −1.50562
\(454\) −0.860543 −0.0403873
\(455\) 8.32142 0.390114
\(456\) −9.31088 −0.436022
\(457\) −25.8799 −1.21061 −0.605304 0.795994i \(-0.706949\pi\)
−0.605304 + 0.795994i \(0.706949\pi\)
\(458\) 2.54824 0.119072
\(459\) −26.4604 −1.23506
\(460\) 35.6796 1.66357
\(461\) −30.0237 −1.39834 −0.699172 0.714954i \(-0.746448\pi\)
−0.699172 + 0.714954i \(0.746448\pi\)
\(462\) −8.81373 −0.410052
\(463\) −30.7224 −1.42779 −0.713896 0.700252i \(-0.753071\pi\)
−0.713896 + 0.700252i \(0.753071\pi\)
\(464\) 0.354761 0.0164694
\(465\) −76.7129 −3.55747
\(466\) 25.5102 1.18174
\(467\) −3.75436 −0.173731 −0.0868654 0.996220i \(-0.527685\pi\)
−0.0868654 + 0.996220i \(0.527685\pi\)
\(468\) 31.2082 1.44260
\(469\) 9.06610 0.418634
\(470\) −10.7003 −0.493570
\(471\) −22.9207 −1.05613
\(472\) −45.7323 −2.10500
\(473\) −1.80874 −0.0831658
\(474\) 63.2355 2.90450
\(475\) −7.94228 −0.364417
\(476\) −18.9717 −0.869568
\(477\) −39.4388 −1.80578
\(478\) 61.2278 2.80049
\(479\) −15.6377 −0.714506 −0.357253 0.934008i \(-0.616287\pi\)
−0.357253 + 0.934008i \(0.616287\pi\)
\(480\) 48.5855 2.21761
\(481\) −2.89456 −0.131981
\(482\) −41.8877 −1.90793
\(483\) −10.8405 −0.493260
\(484\) −33.8865 −1.54029
\(485\) 48.9209 2.22138
\(486\) −28.7251 −1.30300
\(487\) 18.1156 0.820898 0.410449 0.911883i \(-0.365372\pi\)
0.410449 + 0.911883i \(0.365372\pi\)
\(488\) 4.84981 0.219541
\(489\) −14.4174 −0.651976
\(490\) −44.3642 −2.00417
\(491\) −4.67052 −0.210778 −0.105389 0.994431i \(-0.533609\pi\)
−0.105389 + 0.994431i \(0.533609\pi\)
\(492\) 22.1386 0.998087
\(493\) 1.97238 0.0888314
\(494\) 4.13029 0.185830
\(495\) −18.9365 −0.851134
\(496\) −5.75125 −0.258239
\(497\) −11.5402 −0.517649
\(498\) 17.9143 0.802759
\(499\) −6.59196 −0.295097 −0.147548 0.989055i \(-0.547138\pi\)
−0.147548 + 0.989055i \(0.547138\pi\)
\(500\) −36.0122 −1.61051
\(501\) 21.5273 0.961771
\(502\) 10.7801 0.481140
\(503\) −10.0085 −0.446257 −0.223129 0.974789i \(-0.571627\pi\)
−0.223129 + 0.974789i \(0.571627\pi\)
\(504\) 21.8980 0.975416
\(505\) −58.9236 −2.62206
\(506\) 6.90910 0.307147
\(507\) 28.1182 1.24877
\(508\) −1.99832 −0.0886612
\(509\) 1.69031 0.0749217 0.0374608 0.999298i \(-0.488073\pi\)
0.0374608 + 0.999298i \(0.488073\pi\)
\(510\) −102.338 −4.53162
\(511\) 18.6325 0.824253
\(512\) 8.66500 0.382943
\(513\) 6.17653 0.272701
\(514\) −11.8653 −0.523356
\(515\) −40.4179 −1.78103
\(516\) 17.2406 0.758973
\(517\) −1.30493 −0.0573908
\(518\) −4.92799 −0.216523
\(519\) 19.5134 0.856543
\(520\) 20.8350 0.913676
\(521\) −13.7194 −0.601057 −0.300529 0.953773i \(-0.597163\pi\)
−0.300529 + 0.953773i \(0.597163\pi\)
\(522\) −5.52381 −0.241771
\(523\) −0.353857 −0.0154731 −0.00773653 0.999970i \(-0.502463\pi\)
−0.00773653 + 0.999970i \(0.502463\pi\)
\(524\) 71.4484 3.12124
\(525\) 29.5352 1.28902
\(526\) 3.69484 0.161103
\(527\) −31.9754 −1.39287
\(528\) −2.24478 −0.0976916
\(529\) −14.5021 −0.630526
\(530\) −63.8851 −2.77499
\(531\) 72.4343 3.14338
\(532\) 4.42849 0.192000
\(533\) −4.04753 −0.175318
\(534\) 45.4505 1.96684
\(535\) 37.9453 1.64052
\(536\) 22.6996 0.980471
\(537\) −65.2611 −2.81623
\(538\) 29.8982 1.28901
\(539\) −5.41031 −0.233039
\(540\) 75.5979 3.25321
\(541\) −0.712418 −0.0306292 −0.0153146 0.999883i \(-0.504875\pi\)
−0.0153146 + 0.999883i \(0.504875\pi\)
\(542\) −31.5516 −1.35526
\(543\) 39.4800 1.69425
\(544\) 20.2514 0.868271
\(545\) −10.6877 −0.457811
\(546\) −15.3594 −0.657322
\(547\) −0.750772 −0.0321007 −0.0160503 0.999871i \(-0.505109\pi\)
−0.0160503 + 0.999871i \(0.505109\pi\)
\(548\) −32.8428 −1.40297
\(549\) −7.68150 −0.327839
\(550\) −18.8240 −0.802657
\(551\) −0.460404 −0.0196139
\(552\) −27.1423 −1.15525
\(553\) −12.3958 −0.527124
\(554\) −1.93392 −0.0821645
\(555\) −16.7414 −0.710631
\(556\) −23.2760 −0.987123
\(557\) 28.0712 1.18942 0.594708 0.803942i \(-0.297268\pi\)
0.594708 + 0.803942i \(0.297268\pi\)
\(558\) 89.5500 3.79095
\(559\) −3.15203 −0.133317
\(560\) 3.60827 0.152477
\(561\) −12.4804 −0.526923
\(562\) −42.2100 −1.78052
\(563\) −0.383586 −0.0161662 −0.00808311 0.999967i \(-0.502573\pi\)
−0.00808311 + 0.999967i \(0.502573\pi\)
\(564\) 12.4384 0.523749
\(565\) 15.1591 0.637749
\(566\) −45.7407 −1.92262
\(567\) −2.81152 −0.118073
\(568\) −28.8942 −1.21237
\(569\) 21.2610 0.891309 0.445654 0.895205i \(-0.352971\pi\)
0.445654 + 0.895205i \(0.352971\pi\)
\(570\) 23.8884 1.00058
\(571\) 1.30414 0.0545765 0.0272882 0.999628i \(-0.491313\pi\)
0.0272882 + 0.999628i \(0.491313\pi\)
\(572\) 6.16503 0.257773
\(573\) 0.395955 0.0165413
\(574\) −6.89091 −0.287621
\(575\) −23.1527 −0.965534
\(576\) −64.6707 −2.69461
\(577\) −5.62347 −0.234108 −0.117054 0.993126i \(-0.537345\pi\)
−0.117054 + 0.993126i \(0.537345\pi\)
\(578\) −3.14419 −0.130781
\(579\) −57.9014 −2.40630
\(580\) −5.63513 −0.233986
\(581\) −3.51167 −0.145689
\(582\) −90.2965 −3.74291
\(583\) −7.79093 −0.322667
\(584\) 46.6517 1.93046
\(585\) −33.0001 −1.36439
\(586\) −47.0311 −1.94284
\(587\) 0.267226 0.0110296 0.00551479 0.999985i \(-0.498245\pi\)
0.00551479 + 0.999985i \(0.498245\pi\)
\(588\) 51.5701 2.12672
\(589\) 7.46390 0.307545
\(590\) 117.333 4.83052
\(591\) 33.7495 1.38827
\(592\) −1.25512 −0.0515850
\(593\) −8.31496 −0.341454 −0.170727 0.985318i \(-0.554612\pi\)
−0.170727 + 0.985318i \(0.554612\pi\)
\(594\) 14.6390 0.600644
\(595\) 20.0610 0.822422
\(596\) 58.3362 2.38954
\(597\) −63.2795 −2.58986
\(598\) 12.0403 0.492363
\(599\) −0.998290 −0.0407890 −0.0203945 0.999792i \(-0.506492\pi\)
−0.0203945 + 0.999792i \(0.506492\pi\)
\(600\) 73.9497 3.01898
\(601\) −26.1436 −1.06642 −0.533210 0.845983i \(-0.679014\pi\)
−0.533210 + 0.845983i \(0.679014\pi\)
\(602\) −5.36632 −0.218715
\(603\) −35.9533 −1.46413
\(604\) 38.1616 1.55277
\(605\) 35.8321 1.45678
\(606\) 108.759 4.41804
\(607\) −31.3809 −1.27371 −0.636856 0.770983i \(-0.719765\pi\)
−0.636856 + 0.770983i \(0.719765\pi\)
\(608\) −4.72720 −0.191713
\(609\) 1.71212 0.0693784
\(610\) −12.4429 −0.503799
\(611\) −2.27406 −0.0919986
\(612\) 75.2358 3.04123
\(613\) −34.0844 −1.37665 −0.688327 0.725401i \(-0.741655\pi\)
−0.688327 + 0.725401i \(0.741655\pi\)
\(614\) −30.7074 −1.23925
\(615\) −23.4098 −0.943973
\(616\) 4.32585 0.174293
\(617\) −42.6856 −1.71846 −0.859228 0.511593i \(-0.829056\pi\)
−0.859228 + 0.511593i \(0.829056\pi\)
\(618\) 74.6021 3.00094
\(619\) 16.7458 0.673069 0.336534 0.941671i \(-0.390745\pi\)
0.336534 + 0.941671i \(0.390745\pi\)
\(620\) 91.3546 3.66889
\(621\) 18.0053 0.722528
\(622\) 73.2620 2.93754
\(623\) −8.90950 −0.356951
\(624\) −3.91191 −0.156602
\(625\) −1.63155 −0.0652621
\(626\) 28.6671 1.14577
\(627\) 2.91325 0.116344
\(628\) 27.2955 1.08921
\(629\) −6.97812 −0.278236
\(630\) −56.1826 −2.23837
\(631\) 1.50185 0.0597879 0.0298939 0.999553i \(-0.490483\pi\)
0.0298939 + 0.999553i \(0.490483\pi\)
\(632\) −31.0365 −1.23456
\(633\) 48.0718 1.91068
\(634\) 2.32426 0.0923082
\(635\) 2.11306 0.0838542
\(636\) 74.2618 2.94467
\(637\) −9.42837 −0.373566
\(638\) −1.09120 −0.0432011
\(639\) 45.7648 1.81043
\(640\) −70.7446 −2.79643
\(641\) −1.44007 −0.0568795 −0.0284397 0.999596i \(-0.509054\pi\)
−0.0284397 + 0.999596i \(0.509054\pi\)
\(642\) −70.0381 −2.76418
\(643\) −1.17620 −0.0463850 −0.0231925 0.999731i \(-0.507383\pi\)
−0.0231925 + 0.999731i \(0.507383\pi\)
\(644\) 12.9096 0.508708
\(645\) −18.2305 −0.717824
\(646\) 9.95717 0.391760
\(647\) 22.8445 0.898110 0.449055 0.893504i \(-0.351761\pi\)
0.449055 + 0.893504i \(0.351761\pi\)
\(648\) −7.03943 −0.276535
\(649\) 14.3090 0.561679
\(650\) −32.8039 −1.28668
\(651\) −27.7562 −1.08785
\(652\) 17.1691 0.672394
\(653\) 21.6630 0.847737 0.423868 0.905724i \(-0.360672\pi\)
0.423868 + 0.905724i \(0.360672\pi\)
\(654\) 19.7270 0.771388
\(655\) −75.5507 −2.95201
\(656\) −1.75506 −0.0685234
\(657\) −73.8905 −2.88274
\(658\) −3.87158 −0.150930
\(659\) 29.2566 1.13968 0.569839 0.821757i \(-0.307006\pi\)
0.569839 + 0.821757i \(0.307006\pi\)
\(660\) 35.6568 1.38794
\(661\) 17.1222 0.665975 0.332988 0.942931i \(-0.391943\pi\)
0.332988 + 0.942931i \(0.391943\pi\)
\(662\) −51.5505 −2.00357
\(663\) −21.7492 −0.844669
\(664\) −8.79247 −0.341214
\(665\) −4.68276 −0.181590
\(666\) 19.5428 0.757270
\(667\) −1.34213 −0.0519675
\(668\) −25.6361 −0.991891
\(669\) −51.5031 −1.99123
\(670\) −58.2391 −2.24997
\(671\) −1.51744 −0.0585802
\(672\) 17.5791 0.678130
\(673\) 20.6483 0.795934 0.397967 0.917400i \(-0.369716\pi\)
0.397967 + 0.917400i \(0.369716\pi\)
\(674\) 57.8720 2.22915
\(675\) −49.0558 −1.88816
\(676\) −33.4850 −1.28788
\(677\) −6.21631 −0.238912 −0.119456 0.992839i \(-0.538115\pi\)
−0.119456 + 0.992839i \(0.538115\pi\)
\(678\) −27.9802 −1.07457
\(679\) 17.7005 0.679283
\(680\) 50.2285 1.92617
\(681\) −1.05775 −0.0405332
\(682\) 17.6901 0.677391
\(683\) −16.5600 −0.633652 −0.316826 0.948484i \(-0.602617\pi\)
−0.316826 + 0.948484i \(0.602617\pi\)
\(684\) −17.5620 −0.671500
\(685\) 34.7285 1.32691
\(686\) −37.2296 −1.42143
\(687\) 3.13223 0.119502
\(688\) −1.36676 −0.0521071
\(689\) −13.5770 −0.517243
\(690\) 69.6376 2.65106
\(691\) −13.4996 −0.513551 −0.256775 0.966471i \(-0.582660\pi\)
−0.256775 + 0.966471i \(0.582660\pi\)
\(692\) −23.2378 −0.883368
\(693\) −6.85160 −0.260271
\(694\) −41.9978 −1.59422
\(695\) 24.6125 0.933604
\(696\) 4.28677 0.162490
\(697\) −9.75765 −0.369598
\(698\) −30.7354 −1.16335
\(699\) 31.3564 1.18601
\(700\) −35.1723 −1.32939
\(701\) −12.0595 −0.455481 −0.227740 0.973722i \(-0.573134\pi\)
−0.227740 + 0.973722i \(0.573134\pi\)
\(702\) 25.5109 0.962845
\(703\) 1.62888 0.0614342
\(704\) −12.7754 −0.481490
\(705\) −13.1525 −0.495353
\(706\) −9.47204 −0.356485
\(707\) −21.3197 −0.801808
\(708\) −136.391 −5.12589
\(709\) 22.5716 0.847695 0.423847 0.905734i \(-0.360679\pi\)
0.423847 + 0.905734i \(0.360679\pi\)
\(710\) 74.1323 2.78214
\(711\) 49.1579 1.84357
\(712\) −22.3075 −0.836007
\(713\) 21.7581 0.814848
\(714\) −37.0280 −1.38574
\(715\) −6.51900 −0.243797
\(716\) 77.7171 2.90443
\(717\) 75.2594 2.81061
\(718\) −36.7715 −1.37230
\(719\) −18.3565 −0.684583 −0.342292 0.939594i \(-0.611203\pi\)
−0.342292 + 0.939594i \(0.611203\pi\)
\(720\) −14.3092 −0.533274
\(721\) −14.6240 −0.544625
\(722\) −2.32426 −0.0865001
\(723\) −51.4871 −1.91482
\(724\) −47.0153 −1.74731
\(725\) 3.65666 0.135805
\(726\) −66.1377 −2.45460
\(727\) 42.9041 1.59122 0.795612 0.605807i \(-0.207150\pi\)
0.795612 + 0.605807i \(0.207150\pi\)
\(728\) 7.53851 0.279396
\(729\) −41.7879 −1.54770
\(730\) −119.692 −4.42999
\(731\) −7.59881 −0.281052
\(732\) 14.4640 0.534604
\(733\) −17.9159 −0.661741 −0.330870 0.943676i \(-0.607342\pi\)
−0.330870 + 0.943676i \(0.607342\pi\)
\(734\) −10.4895 −0.387173
\(735\) −54.5311 −2.01141
\(736\) −13.7803 −0.507950
\(737\) −7.10239 −0.261620
\(738\) 27.3272 1.00593
\(739\) 5.22000 0.192021 0.0960104 0.995380i \(-0.469392\pi\)
0.0960104 + 0.995380i \(0.469392\pi\)
\(740\) 19.9367 0.732886
\(741\) 5.07683 0.186502
\(742\) −23.1148 −0.848572
\(743\) −19.9907 −0.733389 −0.366694 0.930341i \(-0.619511\pi\)
−0.366694 + 0.930341i \(0.619511\pi\)
\(744\) −69.4955 −2.54783
\(745\) −61.6857 −2.25999
\(746\) 75.8898 2.77852
\(747\) 13.9262 0.509532
\(748\) 14.8625 0.543425
\(749\) 13.7293 0.501658
\(750\) −70.2866 −2.56650
\(751\) −47.4673 −1.73211 −0.866054 0.499950i \(-0.833352\pi\)
−0.866054 + 0.499950i \(0.833352\pi\)
\(752\) −0.986059 −0.0359579
\(753\) 13.2506 0.482878
\(754\) −1.90160 −0.0692522
\(755\) −40.3527 −1.46858
\(756\) 27.3527 0.994810
\(757\) 14.0132 0.509318 0.254659 0.967031i \(-0.418037\pi\)
0.254659 + 0.967031i \(0.418037\pi\)
\(758\) −9.18423 −0.333586
\(759\) 8.49246 0.308257
\(760\) −11.7246 −0.425297
\(761\) −26.5320 −0.961784 −0.480892 0.876780i \(-0.659687\pi\)
−0.480892 + 0.876780i \(0.659687\pi\)
\(762\) −3.90022 −0.141290
\(763\) −3.86702 −0.139995
\(764\) −0.471529 −0.0170593
\(765\) −79.5556 −2.87634
\(766\) −74.6006 −2.69543
\(767\) 24.9359 0.900383
\(768\) 58.9934 2.12874
\(769\) −41.4813 −1.49585 −0.747927 0.663781i \(-0.768951\pi\)
−0.747927 + 0.663781i \(0.768951\pi\)
\(770\) −11.0986 −0.399966
\(771\) −14.5845 −0.525248
\(772\) 68.9527 2.48166
\(773\) 32.2486 1.15990 0.579950 0.814652i \(-0.303072\pi\)
0.579950 + 0.814652i \(0.303072\pi\)
\(774\) 21.2811 0.764934
\(775\) −59.2804 −2.12941
\(776\) 44.3182 1.59093
\(777\) −6.05734 −0.217306
\(778\) −13.0852 −0.469127
\(779\) 2.27769 0.0816067
\(780\) 62.1380 2.22490
\(781\) 9.04060 0.323498
\(782\) 29.0263 1.03798
\(783\) −2.84370 −0.101626
\(784\) −4.08825 −0.146009
\(785\) −28.8627 −1.03015
\(786\) 139.449 4.97398
\(787\) 31.6441 1.12799 0.563995 0.825778i \(-0.309264\pi\)
0.563995 + 0.825778i \(0.309264\pi\)
\(788\) −40.1910 −1.43175
\(789\) 4.54159 0.161685
\(790\) 79.6287 2.83306
\(791\) 5.48486 0.195019
\(792\) −17.1549 −0.609574
\(793\) −2.64440 −0.0939053
\(794\) −19.2116 −0.681794
\(795\) −78.5257 −2.78502
\(796\) 75.3573 2.67097
\(797\) −33.1965 −1.17588 −0.587940 0.808905i \(-0.700061\pi\)
−0.587940 + 0.808905i \(0.700061\pi\)
\(798\) 8.64329 0.305969
\(799\) −5.48223 −0.193947
\(800\) 37.5447 1.32741
\(801\) 35.3322 1.24840
\(802\) −25.1617 −0.888490
\(803\) −14.5967 −0.515106
\(804\) 67.6987 2.38755
\(805\) −13.6508 −0.481128
\(806\) 30.8280 1.08587
\(807\) 36.7500 1.29366
\(808\) −53.3798 −1.87790
\(809\) −7.58574 −0.266700 −0.133350 0.991069i \(-0.542573\pi\)
−0.133350 + 0.991069i \(0.542573\pi\)
\(810\) 18.0607 0.634588
\(811\) −35.3672 −1.24191 −0.620955 0.783846i \(-0.713255\pi\)
−0.620955 + 0.783846i \(0.713255\pi\)
\(812\) −2.03890 −0.0715512
\(813\) −38.7823 −1.36015
\(814\) 3.86059 0.135314
\(815\) −18.1549 −0.635939
\(816\) −9.43071 −0.330141
\(817\) 1.77376 0.0620560
\(818\) −49.7822 −1.74059
\(819\) −11.9401 −0.417219
\(820\) 27.8779 0.973537
\(821\) 48.5866 1.69568 0.847842 0.530248i \(-0.177901\pi\)
0.847842 + 0.530248i \(0.177901\pi\)
\(822\) −64.1007 −2.23577
\(823\) −34.0486 −1.18686 −0.593431 0.804885i \(-0.702227\pi\)
−0.593431 + 0.804885i \(0.702227\pi\)
\(824\) −36.6153 −1.27555
\(825\) −23.1379 −0.805557
\(826\) 42.4533 1.47714
\(827\) −0.753964 −0.0262179 −0.0131090 0.999914i \(-0.504173\pi\)
−0.0131090 + 0.999914i \(0.504173\pi\)
\(828\) −51.1953 −1.77916
\(829\) 28.2018 0.979488 0.489744 0.871866i \(-0.337090\pi\)
0.489744 + 0.871866i \(0.337090\pi\)
\(830\) 22.5584 0.783013
\(831\) −2.37712 −0.0824613
\(832\) −22.2632 −0.771839
\(833\) −22.7296 −0.787535
\(834\) −45.4289 −1.57307
\(835\) 27.1081 0.938113
\(836\) −3.46928 −0.119988
\(837\) 46.1010 1.59348
\(838\) 55.2818 1.90968
\(839\) 56.4767 1.94979 0.974896 0.222660i \(-0.0714741\pi\)
0.974896 + 0.222660i \(0.0714741\pi\)
\(840\) 43.6007 1.50437
\(841\) −28.7880 −0.992691
\(842\) −45.7263 −1.57583
\(843\) −51.8833 −1.78696
\(844\) −57.2469 −1.97052
\(845\) 35.4076 1.21806
\(846\) 15.3535 0.527863
\(847\) 12.9647 0.445474
\(848\) −5.88715 −0.202166
\(849\) −56.2231 −1.92957
\(850\) −79.0827 −2.71251
\(851\) 4.74836 0.162772
\(852\) −86.1734 −2.95225
\(853\) 8.76156 0.299990 0.149995 0.988687i \(-0.452074\pi\)
0.149995 + 0.988687i \(0.452074\pi\)
\(854\) −4.50208 −0.154058
\(855\) 18.5703 0.635093
\(856\) 34.3752 1.17492
\(857\) 1.00357 0.0342813 0.0171407 0.999853i \(-0.494544\pi\)
0.0171407 + 0.999853i \(0.494544\pi\)
\(858\) 12.0326 0.410785
\(859\) 6.84314 0.233485 0.116742 0.993162i \(-0.462755\pi\)
0.116742 + 0.993162i \(0.462755\pi\)
\(860\) 21.7100 0.740304
\(861\) −8.47010 −0.288660
\(862\) −53.5645 −1.82441
\(863\) −41.0014 −1.39570 −0.697851 0.716243i \(-0.745860\pi\)
−0.697851 + 0.716243i \(0.745860\pi\)
\(864\) −29.1977 −0.993326
\(865\) 24.5720 0.835474
\(866\) −25.1524 −0.854715
\(867\) −3.86475 −0.131254
\(868\) 33.0538 1.12192
\(869\) 9.71090 0.329420
\(870\) −10.9983 −0.372879
\(871\) −12.3771 −0.419382
\(872\) −9.68218 −0.327880
\(873\) −70.1945 −2.37572
\(874\) −6.77550 −0.229185
\(875\) 13.7780 0.465782
\(876\) 139.133 4.70087
\(877\) 2.31682 0.0782333 0.0391167 0.999235i \(-0.487546\pi\)
0.0391167 + 0.999235i \(0.487546\pi\)
\(878\) 42.0621 1.41953
\(879\) −57.8093 −1.94986
\(880\) −2.82672 −0.0952886
\(881\) −1.20304 −0.0405313 −0.0202657 0.999795i \(-0.506451\pi\)
−0.0202657 + 0.999795i \(0.506451\pi\)
\(882\) 63.6563 2.14342
\(883\) 25.8459 0.869785 0.434893 0.900482i \(-0.356786\pi\)
0.434893 + 0.900482i \(0.356786\pi\)
\(884\) 25.9003 0.871122
\(885\) 144.222 4.84798
\(886\) 19.3571 0.650315
\(887\) 39.3071 1.31980 0.659901 0.751352i \(-0.270598\pi\)
0.659901 + 0.751352i \(0.270598\pi\)
\(888\) −15.1663 −0.508947
\(889\) 0.764545 0.0256420
\(890\) 57.2331 1.91846
\(891\) 2.20254 0.0737880
\(892\) 61.3332 2.05359
\(893\) 1.27970 0.0428234
\(894\) 113.857 3.80796
\(895\) −82.1794 −2.74695
\(896\) −25.5967 −0.855127
\(897\) 14.7995 0.494142
\(898\) −57.0258 −1.90297
\(899\) −3.43641 −0.114611
\(900\) 139.482 4.64941
\(901\) −32.7310 −1.09043
\(902\) 5.39834 0.179745
\(903\) −6.59613 −0.219505
\(904\) 13.7329 0.456750
\(905\) 49.7148 1.65257
\(906\) 74.4816 2.47449
\(907\) 23.6072 0.783864 0.391932 0.919994i \(-0.371807\pi\)
0.391932 + 0.919994i \(0.371807\pi\)
\(908\) 1.25964 0.0418026
\(909\) 84.5470 2.80425
\(910\) −19.3412 −0.641153
\(911\) 44.9189 1.48823 0.744115 0.668052i \(-0.232872\pi\)
0.744115 + 0.668052i \(0.232872\pi\)
\(912\) 2.20137 0.0728947
\(913\) 2.75105 0.0910464
\(914\) 60.1516 1.98964
\(915\) −15.2945 −0.505619
\(916\) −3.73005 −0.123244
\(917\) −27.3357 −0.902704
\(918\) 61.5008 2.02983
\(919\) −46.5171 −1.53446 −0.767229 0.641374i \(-0.778365\pi\)
−0.767229 + 0.641374i \(0.778365\pi\)
\(920\) −34.1787 −1.12684
\(921\) −37.7446 −1.24373
\(922\) 69.7830 2.29818
\(923\) 15.7548 0.518574
\(924\) 12.9013 0.424422
\(925\) −12.9370 −0.425366
\(926\) 71.4069 2.34658
\(927\) 57.9940 1.90477
\(928\) 2.17642 0.0714445
\(929\) 5.98712 0.196431 0.0982154 0.995165i \(-0.468687\pi\)
0.0982154 + 0.995165i \(0.468687\pi\)
\(930\) 178.301 5.84672
\(931\) 5.30569 0.173887
\(932\) −37.3412 −1.22315
\(933\) 90.0515 2.94815
\(934\) 8.72611 0.285527
\(935\) −15.7158 −0.513962
\(936\) −29.8953 −0.977159
\(937\) 24.3789 0.796424 0.398212 0.917293i \(-0.369631\pi\)
0.398212 + 0.917293i \(0.369631\pi\)
\(938\) −21.0720 −0.688025
\(939\) 35.2367 1.14991
\(940\) 15.6629 0.510866
\(941\) 40.8512 1.33171 0.665856 0.746080i \(-0.268067\pi\)
0.665856 + 0.746080i \(0.268067\pi\)
\(942\) 53.2738 1.73575
\(943\) 6.63973 0.216219
\(944\) 10.8125 0.351917
\(945\) −28.9233 −0.940873
\(946\) 4.20398 0.136683
\(947\) 11.9160 0.387218 0.193609 0.981079i \(-0.437981\pi\)
0.193609 + 0.981079i \(0.437981\pi\)
\(948\) −92.5625 −3.00629
\(949\) −25.4372 −0.825726
\(950\) 18.4599 0.598920
\(951\) 2.85691 0.0926418
\(952\) 18.1736 0.589010
\(953\) −21.1437 −0.684911 −0.342456 0.939534i \(-0.611259\pi\)
−0.342456 + 0.939534i \(0.611259\pi\)
\(954\) 91.6661 2.96780
\(955\) 0.498602 0.0161344
\(956\) −89.6236 −2.89864
\(957\) −1.34127 −0.0433572
\(958\) 36.3462 1.17429
\(959\) 12.5654 0.405759
\(960\) −128.764 −4.15585
\(961\) 24.7098 0.797089
\(962\) 6.72772 0.216910
\(963\) −54.4461 −1.75450
\(964\) 61.3141 1.97479
\(965\) −72.9117 −2.34711
\(966\) 25.1962 0.810674
\(967\) 13.9928 0.449979 0.224989 0.974361i \(-0.427765\pi\)
0.224989 + 0.974361i \(0.427765\pi\)
\(968\) 32.4609 1.04333
\(969\) 12.2391 0.393175
\(970\) −113.705 −3.65084
\(971\) −10.9855 −0.352540 −0.176270 0.984342i \(-0.556403\pi\)
−0.176270 + 0.984342i \(0.556403\pi\)
\(972\) 42.0471 1.34866
\(973\) 8.90525 0.285489
\(974\) −42.1055 −1.34915
\(975\) −40.3216 −1.29132
\(976\) −1.14664 −0.0367031
\(977\) −14.0359 −0.449048 −0.224524 0.974469i \(-0.572083\pi\)
−0.224524 + 0.974469i \(0.572083\pi\)
\(978\) 33.5097 1.07152
\(979\) 6.97970 0.223072
\(980\) 64.9391 2.07440
\(981\) 15.3354 0.489620
\(982\) 10.8555 0.346413
\(983\) −10.5177 −0.335463 −0.167731 0.985833i \(-0.553644\pi\)
−0.167731 + 0.985833i \(0.553644\pi\)
\(984\) −21.2073 −0.676064
\(985\) 42.4987 1.35412
\(986\) −4.58432 −0.145995
\(987\) −4.75884 −0.151475
\(988\) −6.04581 −0.192343
\(989\) 5.17072 0.164419
\(990\) 44.0135 1.39884
\(991\) −15.4340 −0.490279 −0.245139 0.969488i \(-0.578834\pi\)
−0.245139 + 0.969488i \(0.578834\pi\)
\(992\) −35.2833 −1.12025
\(993\) −63.3643 −2.01081
\(994\) 26.8225 0.850757
\(995\) −79.6841 −2.52616
\(996\) −26.2225 −0.830891
\(997\) 51.7570 1.63916 0.819580 0.572965i \(-0.194207\pi\)
0.819580 + 0.572965i \(0.194207\pi\)
\(998\) 15.3215 0.484992
\(999\) 10.0608 0.318310
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 \(a_p\))