Properties

Label 6001.2.a.b.1.10
Level 6001
Weight 2
Character 6001.1
Self dual Yes
Analytic conductor 47.918
Analytic rank 1
Dimension 114
CM No

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.918226253\)
Analytic rank: \(1\)
Dimension: \(114\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.39289 q^{2}\) \(-2.96659 q^{3}\) \(+3.72594 q^{4}\) \(+3.31044 q^{5}\) \(+7.09873 q^{6}\) \(+0.664206 q^{7}\) \(-4.12999 q^{8}\) \(+5.80065 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.39289 q^{2}\) \(-2.96659 q^{3}\) \(+3.72594 q^{4}\) \(+3.31044 q^{5}\) \(+7.09873 q^{6}\) \(+0.664206 q^{7}\) \(-4.12999 q^{8}\) \(+5.80065 q^{9}\) \(-7.92153 q^{10}\) \(+1.52127 q^{11}\) \(-11.0533 q^{12}\) \(-4.57960 q^{13}\) \(-1.58938 q^{14}\) \(-9.82071 q^{15}\) \(+2.43075 q^{16}\) \(+1.00000 q^{17}\) \(-13.8803 q^{18}\) \(-7.18664 q^{19}\) \(+12.3345 q^{20}\) \(-1.97043 q^{21}\) \(-3.64025 q^{22}\) \(+7.41494 q^{23}\) \(+12.2520 q^{24}\) \(+5.95900 q^{25}\) \(+10.9585 q^{26}\) \(-8.30836 q^{27}\) \(+2.47479 q^{28}\) \(+0.513282 q^{29}\) \(+23.4999 q^{30}\) \(-6.03318 q^{31}\) \(+2.44345 q^{32}\) \(-4.51299 q^{33}\) \(-2.39289 q^{34}\) \(+2.19881 q^{35}\) \(+21.6129 q^{36}\) \(+0.496483 q^{37}\) \(+17.1969 q^{38}\) \(+13.5858 q^{39}\) \(-13.6721 q^{40}\) \(-1.38303 q^{41}\) \(+4.71502 q^{42}\) \(+10.6191 q^{43}\) \(+5.66818 q^{44}\) \(+19.2027 q^{45}\) \(-17.7432 q^{46}\) \(+3.44692 q^{47}\) \(-7.21104 q^{48}\) \(-6.55883 q^{49}\) \(-14.2593 q^{50}\) \(-2.96659 q^{51}\) \(-17.0633 q^{52}\) \(+7.55815 q^{53}\) \(+19.8810 q^{54}\) \(+5.03608 q^{55}\) \(-2.74317 q^{56}\) \(+21.3198 q^{57}\) \(-1.22823 q^{58}\) \(-10.6847 q^{59}\) \(-36.5914 q^{60}\) \(+5.41605 q^{61}\) \(+14.4367 q^{62}\) \(+3.85283 q^{63}\) \(-10.7084 q^{64}\) \(-15.1605 q^{65}\) \(+10.7991 q^{66}\) \(-12.4063 q^{67}\) \(+3.72594 q^{68}\) \(-21.9971 q^{69}\) \(-5.26153 q^{70}\) \(+3.25374 q^{71}\) \(-23.9566 q^{72}\) \(-2.96888 q^{73}\) \(-1.18803 q^{74}\) \(-17.6779 q^{75}\) \(-26.7770 q^{76}\) \(+1.01044 q^{77}\) \(-32.5094 q^{78}\) \(-9.14033 q^{79}\) \(+8.04686 q^{80}\) \(+7.24556 q^{81}\) \(+3.30944 q^{82}\) \(-6.20141 q^{83}\) \(-7.34170 q^{84}\) \(+3.31044 q^{85}\) \(-25.4103 q^{86}\) \(-1.52270 q^{87}\) \(-6.28285 q^{88}\) \(+8.10180 q^{89}\) \(-45.9500 q^{90}\) \(-3.04180 q^{91}\) \(+27.6276 q^{92}\) \(+17.8979 q^{93}\) \(-8.24812 q^{94}\) \(-23.7909 q^{95}\) \(-7.24872 q^{96}\) \(+7.46187 q^{97}\) \(+15.6946 q^{98}\) \(+8.82437 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.39289 −1.69203 −0.846016 0.533158i \(-0.821005\pi\)
−0.846016 + 0.533158i \(0.821005\pi\)
\(3\) −2.96659 −1.71276 −0.856380 0.516346i \(-0.827292\pi\)
−0.856380 + 0.516346i \(0.827292\pi\)
\(4\) 3.72594 1.86297
\(5\) 3.31044 1.48047 0.740236 0.672347i \(-0.234714\pi\)
0.740236 + 0.672347i \(0.234714\pi\)
\(6\) 7.09873 2.89804
\(7\) 0.664206 0.251046 0.125523 0.992091i \(-0.459939\pi\)
0.125523 + 0.992091i \(0.459939\pi\)
\(8\) −4.12999 −1.46017
\(9\) 5.80065 1.93355
\(10\) −7.92153 −2.50501
\(11\) 1.52127 0.458681 0.229341 0.973346i \(-0.426343\pi\)
0.229341 + 0.973346i \(0.426343\pi\)
\(12\) −11.0533 −3.19082
\(13\) −4.57960 −1.27015 −0.635077 0.772449i \(-0.719031\pi\)
−0.635077 + 0.772449i \(0.719031\pi\)
\(14\) −1.58938 −0.424778
\(15\) −9.82071 −2.53570
\(16\) 2.43075 0.607688
\(17\) 1.00000 0.242536
\(18\) −13.8803 −3.27163
\(19\) −7.18664 −1.64873 −0.824364 0.566060i \(-0.808467\pi\)
−0.824364 + 0.566060i \(0.808467\pi\)
\(20\) 12.3345 2.75808
\(21\) −1.97043 −0.429982
\(22\) −3.64025 −0.776103
\(23\) 7.41494 1.54612 0.773061 0.634332i \(-0.218725\pi\)
0.773061 + 0.634332i \(0.218725\pi\)
\(24\) 12.2520 2.50093
\(25\) 5.95900 1.19180
\(26\) 10.9585 2.14914
\(27\) −8.30836 −1.59895
\(28\) 2.47479 0.467692
\(29\) 0.513282 0.0953141 0.0476571 0.998864i \(-0.484825\pi\)
0.0476571 + 0.998864i \(0.484825\pi\)
\(30\) 23.4999 4.29048
\(31\) −6.03318 −1.08359 −0.541795 0.840511i \(-0.682255\pi\)
−0.541795 + 0.840511i \(0.682255\pi\)
\(32\) 2.44345 0.431945
\(33\) −4.51299 −0.785611
\(34\) −2.39289 −0.410378
\(35\) 2.19881 0.371667
\(36\) 21.6129 3.60214
\(37\) 0.496483 0.0816214 0.0408107 0.999167i \(-0.487006\pi\)
0.0408107 + 0.999167i \(0.487006\pi\)
\(38\) 17.1969 2.78970
\(39\) 13.5858 2.17547
\(40\) −13.6721 −2.16175
\(41\) −1.38303 −0.215993 −0.107996 0.994151i \(-0.534443\pi\)
−0.107996 + 0.994151i \(0.534443\pi\)
\(42\) 4.71502 0.727544
\(43\) 10.6191 1.61939 0.809695 0.586851i \(-0.199633\pi\)
0.809695 + 0.586851i \(0.199633\pi\)
\(44\) 5.66818 0.854510
\(45\) 19.2027 2.86257
\(46\) −17.7432 −2.61609
\(47\) 3.44692 0.502786 0.251393 0.967885i \(-0.419111\pi\)
0.251393 + 0.967885i \(0.419111\pi\)
\(48\) −7.21104 −1.04082
\(49\) −6.55883 −0.936976
\(50\) −14.2593 −2.01656
\(51\) −2.96659 −0.415405
\(52\) −17.0633 −2.36626
\(53\) 7.55815 1.03819 0.519096 0.854716i \(-0.326269\pi\)
0.519096 + 0.854716i \(0.326269\pi\)
\(54\) 19.8810 2.70547
\(55\) 5.03608 0.679065
\(56\) −2.74317 −0.366571
\(57\) 21.3198 2.82388
\(58\) −1.22823 −0.161274
\(59\) −10.6847 −1.39102 −0.695512 0.718514i \(-0.744822\pi\)
−0.695512 + 0.718514i \(0.744822\pi\)
\(60\) −36.5914 −4.72393
\(61\) 5.41605 0.693455 0.346727 0.937966i \(-0.387293\pi\)
0.346727 + 0.937966i \(0.387293\pi\)
\(62\) 14.4367 1.83347
\(63\) 3.85283 0.485411
\(64\) −10.7084 −1.33855
\(65\) −15.1605 −1.88043
\(66\) 10.7991 1.32928
\(67\) −12.4063 −1.51567 −0.757834 0.652447i \(-0.773742\pi\)
−0.757834 + 0.652447i \(0.773742\pi\)
\(68\) 3.72594 0.451837
\(69\) −21.9971 −2.64814
\(70\) −5.26153 −0.628873
\(71\) 3.25374 0.386148 0.193074 0.981184i \(-0.438154\pi\)
0.193074 + 0.981184i \(0.438154\pi\)
\(72\) −23.9566 −2.82332
\(73\) −2.96888 −0.347482 −0.173741 0.984791i \(-0.555585\pi\)
−0.173741 + 0.984791i \(0.555585\pi\)
\(74\) −1.18803 −0.138106
\(75\) −17.6779 −2.04127
\(76\) −26.7770 −3.07153
\(77\) 1.01044 0.115150
\(78\) −32.5094 −3.68096
\(79\) −9.14033 −1.02837 −0.514184 0.857680i \(-0.671905\pi\)
−0.514184 + 0.857680i \(0.671905\pi\)
\(80\) 8.04686 0.899666
\(81\) 7.24556 0.805062
\(82\) 3.30944 0.365466
\(83\) −6.20141 −0.680694 −0.340347 0.940300i \(-0.610544\pi\)
−0.340347 + 0.940300i \(0.610544\pi\)
\(84\) −7.34170 −0.801045
\(85\) 3.31044 0.359067
\(86\) −25.4103 −2.74006
\(87\) −1.52270 −0.163250
\(88\) −6.28285 −0.669754
\(89\) 8.10180 0.858789 0.429394 0.903117i \(-0.358727\pi\)
0.429394 + 0.903117i \(0.358727\pi\)
\(90\) −45.9500 −4.84355
\(91\) −3.04180 −0.318867
\(92\) 27.6276 2.88038
\(93\) 17.8979 1.85593
\(94\) −8.24812 −0.850729
\(95\) −23.7909 −2.44090
\(96\) −7.24872 −0.739819
\(97\) 7.46187 0.757638 0.378819 0.925471i \(-0.376330\pi\)
0.378819 + 0.925471i \(0.376330\pi\)
\(98\) 15.6946 1.58539
\(99\) 8.82437 0.886883
\(100\) 22.2029 2.22029
\(101\) −8.55186 −0.850942 −0.425471 0.904972i \(-0.639891\pi\)
−0.425471 + 0.904972i \(0.639891\pi\)
\(102\) 7.09873 0.702879
\(103\) −12.4538 −1.22711 −0.613553 0.789654i \(-0.710260\pi\)
−0.613553 + 0.789654i \(0.710260\pi\)
\(104\) 18.9137 1.85464
\(105\) −6.52298 −0.636577
\(106\) −18.0859 −1.75665
\(107\) 14.0075 1.35415 0.677077 0.735912i \(-0.263246\pi\)
0.677077 + 0.735912i \(0.263246\pi\)
\(108\) −30.9565 −2.97879
\(109\) 19.0845 1.82797 0.913983 0.405752i \(-0.132990\pi\)
0.913983 + 0.405752i \(0.132990\pi\)
\(110\) −12.0508 −1.14900
\(111\) −1.47286 −0.139798
\(112\) 1.61452 0.152558
\(113\) −6.46803 −0.608461 −0.304231 0.952598i \(-0.598399\pi\)
−0.304231 + 0.952598i \(0.598399\pi\)
\(114\) −51.0160 −4.77809
\(115\) 24.5467 2.28899
\(116\) 1.91246 0.177567
\(117\) −26.5647 −2.45590
\(118\) 25.5673 2.35366
\(119\) 0.664206 0.0608877
\(120\) 40.5594 3.70255
\(121\) −8.68573 −0.789612
\(122\) −12.9600 −1.17335
\(123\) 4.10287 0.369944
\(124\) −22.4793 −2.01870
\(125\) 3.17471 0.283955
\(126\) −9.21941 −0.821330
\(127\) −14.8891 −1.32119 −0.660597 0.750741i \(-0.729697\pi\)
−0.660597 + 0.750741i \(0.729697\pi\)
\(128\) 20.7372 1.83293
\(129\) −31.5024 −2.77363
\(130\) 36.2774 3.18174
\(131\) −7.57558 −0.661881 −0.330941 0.943652i \(-0.607366\pi\)
−0.330941 + 0.943652i \(0.607366\pi\)
\(132\) −16.8151 −1.46357
\(133\) −4.77341 −0.413907
\(134\) 29.6869 2.56456
\(135\) −27.5043 −2.36720
\(136\) −4.12999 −0.354144
\(137\) 3.84937 0.328874 0.164437 0.986388i \(-0.447419\pi\)
0.164437 + 0.986388i \(0.447419\pi\)
\(138\) 52.6366 4.48073
\(139\) 7.24027 0.614111 0.307056 0.951692i \(-0.400656\pi\)
0.307056 + 0.951692i \(0.400656\pi\)
\(140\) 8.19265 0.692405
\(141\) −10.2256 −0.861151
\(142\) −7.78585 −0.653374
\(143\) −6.96683 −0.582595
\(144\) 14.0999 1.17499
\(145\) 1.69919 0.141110
\(146\) 7.10422 0.587950
\(147\) 19.4573 1.60482
\(148\) 1.84987 0.152058
\(149\) 1.30583 0.106978 0.0534889 0.998568i \(-0.482966\pi\)
0.0534889 + 0.998568i \(0.482966\pi\)
\(150\) 42.3013 3.45389
\(151\) 12.9743 1.05584 0.527918 0.849295i \(-0.322973\pi\)
0.527918 + 0.849295i \(0.322973\pi\)
\(152\) 29.6808 2.40743
\(153\) 5.80065 0.468954
\(154\) −2.41788 −0.194838
\(155\) −19.9725 −1.60423
\(156\) 50.6199 4.05283
\(157\) −10.5795 −0.844336 −0.422168 0.906518i \(-0.638731\pi\)
−0.422168 + 0.906518i \(0.638731\pi\)
\(158\) 21.8718 1.74003
\(159\) −22.4219 −1.77817
\(160\) 8.08890 0.639483
\(161\) 4.92505 0.388148
\(162\) −17.3379 −1.36219
\(163\) −12.2255 −0.957574 −0.478787 0.877931i \(-0.658923\pi\)
−0.478787 + 0.877931i \(0.658923\pi\)
\(164\) −5.15308 −0.402388
\(165\) −14.9400 −1.16308
\(166\) 14.8393 1.15176
\(167\) −13.6663 −1.05753 −0.528765 0.848768i \(-0.677345\pi\)
−0.528765 + 0.848768i \(0.677345\pi\)
\(168\) 8.13785 0.627849
\(169\) 7.97275 0.613289
\(170\) −7.92153 −0.607553
\(171\) −41.6872 −3.18790
\(172\) 39.5660 3.01688
\(173\) −2.07228 −0.157553 −0.0787764 0.996892i \(-0.525101\pi\)
−0.0787764 + 0.996892i \(0.525101\pi\)
\(174\) 3.64365 0.276225
\(175\) 3.95801 0.299197
\(176\) 3.69784 0.278735
\(177\) 31.6970 2.38249
\(178\) −19.3867 −1.45310
\(179\) −11.3940 −0.851627 −0.425813 0.904811i \(-0.640012\pi\)
−0.425813 + 0.904811i \(0.640012\pi\)
\(180\) 71.5480 5.33288
\(181\) 14.6896 1.09187 0.545934 0.837828i \(-0.316175\pi\)
0.545934 + 0.837828i \(0.316175\pi\)
\(182\) 7.27871 0.539534
\(183\) −16.0672 −1.18772
\(184\) −30.6236 −2.25760
\(185\) 1.64358 0.120838
\(186\) −42.8279 −3.14029
\(187\) 1.52127 0.111247
\(188\) 12.8430 0.936675
\(189\) −5.51847 −0.401410
\(190\) 56.9292 4.13008
\(191\) −23.3121 −1.68681 −0.843404 0.537280i \(-0.819452\pi\)
−0.843404 + 0.537280i \(0.819452\pi\)
\(192\) 31.7675 2.29262
\(193\) 0.0943234 0.00678955 0.00339477 0.999994i \(-0.498919\pi\)
0.00339477 + 0.999994i \(0.498919\pi\)
\(194\) −17.8555 −1.28195
\(195\) 44.9749 3.22072
\(196\) −24.4378 −1.74556
\(197\) 11.9398 0.850676 0.425338 0.905035i \(-0.360155\pi\)
0.425338 + 0.905035i \(0.360155\pi\)
\(198\) −21.1158 −1.50063
\(199\) −3.25428 −0.230689 −0.115345 0.993326i \(-0.536797\pi\)
−0.115345 + 0.993326i \(0.536797\pi\)
\(200\) −24.6106 −1.74023
\(201\) 36.8043 2.59598
\(202\) 20.4637 1.43982
\(203\) 0.340925 0.0239283
\(204\) −11.0533 −0.773888
\(205\) −4.57843 −0.319771
\(206\) 29.8005 2.07630
\(207\) 43.0114 2.98950
\(208\) −11.1319 −0.771857
\(209\) −10.9328 −0.756241
\(210\) 15.6088 1.07711
\(211\) −15.9941 −1.10108 −0.550539 0.834810i \(-0.685578\pi\)
−0.550539 + 0.834810i \(0.685578\pi\)
\(212\) 28.1612 1.93412
\(213\) −9.65250 −0.661378
\(214\) −33.5184 −2.29127
\(215\) 35.1537 2.39746
\(216\) 34.3135 2.33474
\(217\) −4.00727 −0.272032
\(218\) −45.6673 −3.09298
\(219\) 8.80746 0.595153
\(220\) 18.7641 1.26508
\(221\) −4.57960 −0.308057
\(222\) 3.52440 0.236542
\(223\) 23.2597 1.55759 0.778793 0.627281i \(-0.215832\pi\)
0.778793 + 0.627281i \(0.215832\pi\)
\(224\) 1.62296 0.108438
\(225\) 34.5661 2.30440
\(226\) 15.4773 1.02954
\(227\) 12.5582 0.833517 0.416759 0.909017i \(-0.363166\pi\)
0.416759 + 0.909017i \(0.363166\pi\)
\(228\) 79.4363 5.26080
\(229\) −5.46352 −0.361039 −0.180520 0.983571i \(-0.557778\pi\)
−0.180520 + 0.983571i \(0.557778\pi\)
\(230\) −58.7376 −3.87304
\(231\) −2.99756 −0.197225
\(232\) −2.11985 −0.139175
\(233\) 16.0949 1.05441 0.527207 0.849737i \(-0.323239\pi\)
0.527207 + 0.849737i \(0.323239\pi\)
\(234\) 63.5664 4.15546
\(235\) 11.4108 0.744360
\(236\) −39.8104 −2.59144
\(237\) 27.1156 1.76135
\(238\) −1.58938 −0.103024
\(239\) 11.4399 0.739982 0.369991 0.929035i \(-0.379361\pi\)
0.369991 + 0.929035i \(0.379361\pi\)
\(240\) −23.8717 −1.54091
\(241\) −1.91523 −0.123371 −0.0616853 0.998096i \(-0.519648\pi\)
−0.0616853 + 0.998096i \(0.519648\pi\)
\(242\) 20.7840 1.33605
\(243\) 3.43050 0.220067
\(244\) 20.1799 1.29189
\(245\) −21.7126 −1.38717
\(246\) −9.81774 −0.625956
\(247\) 32.9120 2.09414
\(248\) 24.9170 1.58223
\(249\) 18.3970 1.16587
\(250\) −7.59674 −0.480460
\(251\) −29.0417 −1.83310 −0.916548 0.399924i \(-0.869037\pi\)
−0.916548 + 0.399924i \(0.869037\pi\)
\(252\) 14.3554 0.904306
\(253\) 11.2801 0.709177
\(254\) 35.6280 2.23550
\(255\) −9.82071 −0.614997
\(256\) −28.2051 −1.76282
\(257\) −25.4618 −1.58826 −0.794132 0.607746i \(-0.792074\pi\)
−0.794132 + 0.607746i \(0.792074\pi\)
\(258\) 75.3818 4.69306
\(259\) 0.329768 0.0204908
\(260\) −56.4871 −3.50318
\(261\) 2.97737 0.184295
\(262\) 18.1275 1.11992
\(263\) 10.3690 0.639382 0.319691 0.947522i \(-0.396421\pi\)
0.319691 + 0.947522i \(0.396421\pi\)
\(264\) 18.6386 1.14713
\(265\) 25.0208 1.53702
\(266\) 11.4223 0.700344
\(267\) −24.0347 −1.47090
\(268\) −46.2251 −2.82364
\(269\) 26.9442 1.64282 0.821409 0.570339i \(-0.193188\pi\)
0.821409 + 0.570339i \(0.193188\pi\)
\(270\) 65.8149 4.00537
\(271\) −14.9819 −0.910085 −0.455043 0.890470i \(-0.650376\pi\)
−0.455043 + 0.890470i \(0.650376\pi\)
\(272\) 2.43075 0.147386
\(273\) 9.02377 0.546144
\(274\) −9.21114 −0.556466
\(275\) 9.06527 0.546656
\(276\) −81.9598 −4.93340
\(277\) 28.3994 1.70635 0.853176 0.521623i \(-0.174673\pi\)
0.853176 + 0.521623i \(0.174673\pi\)
\(278\) −17.3252 −1.03910
\(279\) −34.9963 −2.09517
\(280\) −9.08109 −0.542699
\(281\) −31.3888 −1.87250 −0.936250 0.351334i \(-0.885728\pi\)
−0.936250 + 0.351334i \(0.885728\pi\)
\(282\) 24.4688 1.45710
\(283\) 14.5001 0.861944 0.430972 0.902365i \(-0.358171\pi\)
0.430972 + 0.902365i \(0.358171\pi\)
\(284\) 12.1232 0.719381
\(285\) 70.5779 4.18067
\(286\) 16.6709 0.985770
\(287\) −0.918616 −0.0542242
\(288\) 14.1736 0.835188
\(289\) 1.00000 0.0588235
\(290\) −4.06598 −0.238763
\(291\) −22.1363 −1.29765
\(292\) −11.0619 −0.647348
\(293\) −4.82214 −0.281712 −0.140856 0.990030i \(-0.544986\pi\)
−0.140856 + 0.990030i \(0.544986\pi\)
\(294\) −46.5594 −2.71540
\(295\) −35.3709 −2.05937
\(296\) −2.05047 −0.119181
\(297\) −12.6393 −0.733406
\(298\) −3.12471 −0.181010
\(299\) −33.9575 −1.96381
\(300\) −65.8668 −3.80282
\(301\) 7.05324 0.406542
\(302\) −31.0462 −1.78651
\(303\) 25.3698 1.45746
\(304\) −17.4689 −1.00191
\(305\) 17.9295 1.02664
\(306\) −13.8803 −0.793486
\(307\) −19.6934 −1.12396 −0.561980 0.827151i \(-0.689960\pi\)
−0.561980 + 0.827151i \(0.689960\pi\)
\(308\) 3.76484 0.214522
\(309\) 36.9452 2.10174
\(310\) 47.7920 2.71440
\(311\) −2.09304 −0.118685 −0.0593427 0.998238i \(-0.518900\pi\)
−0.0593427 + 0.998238i \(0.518900\pi\)
\(312\) −56.1092 −3.17656
\(313\) −32.5181 −1.83803 −0.919017 0.394219i \(-0.871015\pi\)
−0.919017 + 0.394219i \(0.871015\pi\)
\(314\) 25.3156 1.42864
\(315\) 12.7545 0.718637
\(316\) −34.0563 −1.91582
\(317\) 18.0121 1.01166 0.505831 0.862632i \(-0.331186\pi\)
0.505831 + 0.862632i \(0.331186\pi\)
\(318\) 53.6533 3.00873
\(319\) 0.780843 0.0437188
\(320\) −35.4496 −1.98169
\(321\) −41.5544 −2.31934
\(322\) −11.7851 −0.656759
\(323\) −7.18664 −0.399875
\(324\) 26.9965 1.49981
\(325\) −27.2898 −1.51377
\(326\) 29.2543 1.62025
\(327\) −56.6159 −3.13087
\(328\) 5.71189 0.315387
\(329\) 2.28947 0.126223
\(330\) 35.7498 1.96796
\(331\) 0.686909 0.0377560 0.0188780 0.999822i \(-0.493991\pi\)
0.0188780 + 0.999822i \(0.493991\pi\)
\(332\) −23.1061 −1.26811
\(333\) 2.87993 0.157819
\(334\) 32.7020 1.78937
\(335\) −41.0702 −2.24391
\(336\) −4.78962 −0.261295
\(337\) −22.2664 −1.21293 −0.606465 0.795110i \(-0.707413\pi\)
−0.606465 + 0.795110i \(0.707413\pi\)
\(338\) −19.0780 −1.03770
\(339\) 19.1880 1.04215
\(340\) 12.3345 0.668932
\(341\) −9.17811 −0.497023
\(342\) 99.7530 5.39402
\(343\) −9.00586 −0.486271
\(344\) −43.8566 −2.36459
\(345\) −72.8199 −3.92049
\(346\) 4.95875 0.266584
\(347\) 32.1424 1.72549 0.862747 0.505635i \(-0.168742\pi\)
0.862747 + 0.505635i \(0.168742\pi\)
\(348\) −5.67348 −0.304130
\(349\) 34.4468 1.84389 0.921947 0.387317i \(-0.126598\pi\)
0.921947 + 0.387317i \(0.126598\pi\)
\(350\) −9.47109 −0.506251
\(351\) 38.0490 2.03091
\(352\) 3.71716 0.198125
\(353\) 1.00000 0.0532246
\(354\) −75.8475 −4.03125
\(355\) 10.7713 0.571681
\(356\) 30.1868 1.59990
\(357\) −1.97043 −0.104286
\(358\) 27.2646 1.44098
\(359\) −24.2077 −1.27763 −0.638816 0.769359i \(-0.720576\pi\)
−0.638816 + 0.769359i \(0.720576\pi\)
\(360\) −79.3069 −4.17984
\(361\) 32.6478 1.71831
\(362\) −35.1506 −1.84747
\(363\) 25.7670 1.35242
\(364\) −11.3336 −0.594041
\(365\) −9.82831 −0.514437
\(366\) 38.4471 2.00966
\(367\) 7.67252 0.400502 0.200251 0.979745i \(-0.435824\pi\)
0.200251 + 0.979745i \(0.435824\pi\)
\(368\) 18.0239 0.939560
\(369\) −8.02245 −0.417632
\(370\) −3.93291 −0.204462
\(371\) 5.02017 0.260634
\(372\) 66.6867 3.45754
\(373\) −4.16614 −0.215715 −0.107857 0.994166i \(-0.534399\pi\)
−0.107857 + 0.994166i \(0.534399\pi\)
\(374\) −3.64025 −0.188233
\(375\) −9.41806 −0.486346
\(376\) −14.2358 −0.734154
\(377\) −2.35063 −0.121064
\(378\) 13.2051 0.679198
\(379\) −9.94519 −0.510850 −0.255425 0.966829i \(-0.582215\pi\)
−0.255425 + 0.966829i \(0.582215\pi\)
\(380\) −88.6436 −4.54732
\(381\) 44.1698 2.26289
\(382\) 55.7835 2.85413
\(383\) 29.7105 1.51814 0.759068 0.651012i \(-0.225655\pi\)
0.759068 + 0.651012i \(0.225655\pi\)
\(384\) −61.5188 −3.13937
\(385\) 3.34500 0.170477
\(386\) −0.225706 −0.0114881
\(387\) 61.5974 3.13117
\(388\) 27.8025 1.41146
\(389\) −28.5712 −1.44862 −0.724309 0.689476i \(-0.757841\pi\)
−0.724309 + 0.689476i \(0.757841\pi\)
\(390\) −107.620 −5.44956
\(391\) 7.41494 0.374990
\(392\) 27.0879 1.36815
\(393\) 22.4736 1.13364
\(394\) −28.5707 −1.43937
\(395\) −30.2585 −1.52247
\(396\) 32.8791 1.65224
\(397\) −35.7002 −1.79174 −0.895870 0.444317i \(-0.853446\pi\)
−0.895870 + 0.444317i \(0.853446\pi\)
\(398\) 7.78713 0.390334
\(399\) 14.1608 0.708924
\(400\) 14.4849 0.724243
\(401\) −28.2692 −1.41170 −0.705848 0.708363i \(-0.749434\pi\)
−0.705848 + 0.708363i \(0.749434\pi\)
\(402\) −88.0688 −4.39247
\(403\) 27.6295 1.37633
\(404\) −31.8637 −1.58528
\(405\) 23.9860 1.19187
\(406\) −0.815798 −0.0404874
\(407\) 0.755287 0.0374382
\(408\) 12.2520 0.606564
\(409\) −2.06218 −0.101968 −0.0509841 0.998699i \(-0.516236\pi\)
−0.0509841 + 0.998699i \(0.516236\pi\)
\(410\) 10.9557 0.541063
\(411\) −11.4195 −0.563283
\(412\) −46.4020 −2.28606
\(413\) −7.09682 −0.349212
\(414\) −102.922 −5.05833
\(415\) −20.5294 −1.00775
\(416\) −11.1900 −0.548637
\(417\) −21.4789 −1.05183
\(418\) 26.1611 1.27958
\(419\) −2.11486 −0.103318 −0.0516588 0.998665i \(-0.516451\pi\)
−0.0516588 + 0.998665i \(0.516451\pi\)
\(420\) −24.3042 −1.18592
\(421\) 23.6134 1.15085 0.575424 0.817855i \(-0.304837\pi\)
0.575424 + 0.817855i \(0.304837\pi\)
\(422\) 38.2721 1.86306
\(423\) 19.9944 0.972161
\(424\) −31.2151 −1.51594
\(425\) 5.95900 0.289054
\(426\) 23.0974 1.11907
\(427\) 3.59738 0.174089
\(428\) 52.1910 2.52275
\(429\) 20.6677 0.997846
\(430\) −84.1191 −4.05658
\(431\) −10.0667 −0.484894 −0.242447 0.970165i \(-0.577950\pi\)
−0.242447 + 0.970165i \(0.577950\pi\)
\(432\) −20.1956 −0.971660
\(433\) −20.2518 −0.973238 −0.486619 0.873614i \(-0.661770\pi\)
−0.486619 + 0.873614i \(0.661770\pi\)
\(434\) 9.58898 0.460286
\(435\) −5.04079 −0.241688
\(436\) 71.1078 3.40545
\(437\) −53.2885 −2.54913
\(438\) −21.0753 −1.00702
\(439\) 1.13571 0.0542044 0.0271022 0.999633i \(-0.491372\pi\)
0.0271022 + 0.999633i \(0.491372\pi\)
\(440\) −20.7990 −0.991553
\(441\) −38.0455 −1.81169
\(442\) 10.9585 0.521243
\(443\) 11.4368 0.543381 0.271690 0.962385i \(-0.412417\pi\)
0.271690 + 0.962385i \(0.412417\pi\)
\(444\) −5.48780 −0.260439
\(445\) 26.8205 1.27141
\(446\) −55.6580 −2.63548
\(447\) −3.87386 −0.183227
\(448\) −7.11261 −0.336039
\(449\) −0.799392 −0.0377257 −0.0188628 0.999822i \(-0.506005\pi\)
−0.0188628 + 0.999822i \(0.506005\pi\)
\(450\) −82.7129 −3.89912
\(451\) −2.10396 −0.0990718
\(452\) −24.0995 −1.13355
\(453\) −38.4895 −1.80839
\(454\) −30.0505 −1.41034
\(455\) −10.0697 −0.472075
\(456\) −88.0506 −4.12335
\(457\) 13.0399 0.609983 0.304992 0.952355i \(-0.401346\pi\)
0.304992 + 0.952355i \(0.401346\pi\)
\(458\) 13.0736 0.610890
\(459\) −8.30836 −0.387801
\(460\) 91.4595 4.26432
\(461\) 36.6927 1.70895 0.854475 0.519492i \(-0.173879\pi\)
0.854475 + 0.519492i \(0.173879\pi\)
\(462\) 7.17284 0.333711
\(463\) −32.4335 −1.50731 −0.753656 0.657270i \(-0.771711\pi\)
−0.753656 + 0.657270i \(0.771711\pi\)
\(464\) 1.24766 0.0579213
\(465\) 59.2500 2.74766
\(466\) −38.5134 −1.78410
\(467\) −12.6535 −0.585532 −0.292766 0.956184i \(-0.594576\pi\)
−0.292766 + 0.956184i \(0.594576\pi\)
\(468\) −98.9783 −4.57527
\(469\) −8.24033 −0.380503
\(470\) −27.3049 −1.25948
\(471\) 31.3850 1.44615
\(472\) 44.1276 2.03114
\(473\) 16.1545 0.742784
\(474\) −64.8847 −2.98025
\(475\) −42.8252 −1.96495
\(476\) 2.47479 0.113432
\(477\) 43.8422 2.00740
\(478\) −27.3743 −1.25207
\(479\) −17.3201 −0.791375 −0.395687 0.918385i \(-0.629494\pi\)
−0.395687 + 0.918385i \(0.629494\pi\)
\(480\) −23.9964 −1.09528
\(481\) −2.27370 −0.103672
\(482\) 4.58293 0.208747
\(483\) −14.6106 −0.664805
\(484\) −32.3625 −1.47102
\(485\) 24.7021 1.12166
\(486\) −8.20883 −0.372360
\(487\) 11.0941 0.502723 0.251361 0.967893i \(-0.419122\pi\)
0.251361 + 0.967893i \(0.419122\pi\)
\(488\) −22.3683 −1.01256
\(489\) 36.2680 1.64010
\(490\) 51.9559 2.34713
\(491\) 23.2433 1.04895 0.524477 0.851425i \(-0.324261\pi\)
0.524477 + 0.851425i \(0.324261\pi\)
\(492\) 15.2871 0.689194
\(493\) 0.513282 0.0231171
\(494\) −78.7548 −3.54335
\(495\) 29.2125 1.31301
\(496\) −14.6652 −0.658485
\(497\) 2.16115 0.0969410
\(498\) −44.0222 −1.97268
\(499\) −40.4438 −1.81051 −0.905256 0.424867i \(-0.860321\pi\)
−0.905256 + 0.424867i \(0.860321\pi\)
\(500\) 11.8288 0.528999
\(501\) 40.5423 1.81130
\(502\) 69.4937 3.10166
\(503\) −6.49672 −0.289674 −0.144837 0.989456i \(-0.546266\pi\)
−0.144837 + 0.989456i \(0.546266\pi\)
\(504\) −15.9121 −0.708783
\(505\) −28.3104 −1.25980
\(506\) −26.9922 −1.19995
\(507\) −23.6519 −1.05042
\(508\) −55.4759 −2.46135
\(509\) −7.85252 −0.348057 −0.174028 0.984741i \(-0.555678\pi\)
−0.174028 + 0.984741i \(0.555678\pi\)
\(510\) 23.4999 1.04059
\(511\) −1.97195 −0.0872340
\(512\) 26.0174 1.14982
\(513\) 59.7092 2.63623
\(514\) 60.9274 2.68739
\(515\) −41.2274 −1.81670
\(516\) −117.376 −5.16719
\(517\) 5.24372 0.230618
\(518\) −0.789099 −0.0346710
\(519\) 6.14761 0.269850
\(520\) 62.6127 2.74575
\(521\) 24.5419 1.07520 0.537600 0.843200i \(-0.319331\pi\)
0.537600 + 0.843200i \(0.319331\pi\)
\(522\) −7.12453 −0.311832
\(523\) −5.67476 −0.248140 −0.124070 0.992273i \(-0.539595\pi\)
−0.124070 + 0.992273i \(0.539595\pi\)
\(524\) −28.2261 −1.23306
\(525\) −11.7418 −0.512453
\(526\) −24.8120 −1.08185
\(527\) −6.03318 −0.262809
\(528\) −10.9700 −0.477407
\(529\) 31.9813 1.39049
\(530\) −59.8721 −2.60068
\(531\) −61.9779 −2.68961
\(532\) −17.7855 −0.771097
\(533\) 6.33371 0.274344
\(534\) 57.5125 2.48881
\(535\) 46.3709 2.00479
\(536\) 51.2378 2.21314
\(537\) 33.8013 1.45863
\(538\) −64.4747 −2.77970
\(539\) −9.97777 −0.429773
\(540\) −102.479 −4.41002
\(541\) 9.12384 0.392265 0.196132 0.980577i \(-0.437162\pi\)
0.196132 + 0.980577i \(0.437162\pi\)
\(542\) 35.8501 1.53989
\(543\) −43.5779 −1.87011
\(544\) 2.44345 0.104762
\(545\) 63.1782 2.70625
\(546\) −21.5929 −0.924092
\(547\) 45.4620 1.94381 0.971907 0.235365i \(-0.0756285\pi\)
0.971907 + 0.235365i \(0.0756285\pi\)
\(548\) 14.3425 0.612683
\(549\) 31.4166 1.34083
\(550\) −21.6922 −0.924960
\(551\) −3.68878 −0.157147
\(552\) 90.8477 3.86674
\(553\) −6.07107 −0.258168
\(554\) −67.9566 −2.88720
\(555\) −4.87582 −0.206967
\(556\) 26.9768 1.14407
\(557\) −8.19119 −0.347072 −0.173536 0.984828i \(-0.555519\pi\)
−0.173536 + 0.984828i \(0.555519\pi\)
\(558\) 83.7425 3.54510
\(559\) −48.6310 −2.05687
\(560\) 5.34477 0.225858
\(561\) −4.51299 −0.190539
\(562\) 75.1101 3.16833
\(563\) −25.0413 −1.05536 −0.527682 0.849442i \(-0.676939\pi\)
−0.527682 + 0.849442i \(0.676939\pi\)
\(564\) −38.1000 −1.60430
\(565\) −21.4120 −0.900811
\(566\) −34.6973 −1.45844
\(567\) 4.81255 0.202108
\(568\) −13.4379 −0.563842
\(569\) 2.12544 0.0891032 0.0445516 0.999007i \(-0.485814\pi\)
0.0445516 + 0.999007i \(0.485814\pi\)
\(570\) −168.885 −7.07383
\(571\) −12.3339 −0.516157 −0.258078 0.966124i \(-0.583089\pi\)
−0.258078 + 0.966124i \(0.583089\pi\)
\(572\) −25.9580 −1.08536
\(573\) 69.1575 2.88910
\(574\) 2.19815 0.0917490
\(575\) 44.1856 1.84267
\(576\) −62.1158 −2.58816
\(577\) −40.0784 −1.66849 −0.834243 0.551397i \(-0.814095\pi\)
−0.834243 + 0.551397i \(0.814095\pi\)
\(578\) −2.39289 −0.0995313
\(579\) −0.279819 −0.0116289
\(580\) 6.33108 0.262884
\(581\) −4.11902 −0.170886
\(582\) 52.9698 2.19567
\(583\) 11.4980 0.476199
\(584\) 12.2615 0.507383
\(585\) −87.9406 −3.63590
\(586\) 11.5389 0.476666
\(587\) 4.83871 0.199715 0.0998575 0.995002i \(-0.468161\pi\)
0.0998575 + 0.995002i \(0.468161\pi\)
\(588\) 72.4969 2.98972
\(589\) 43.3583 1.78655
\(590\) 84.6388 3.48453
\(591\) −35.4205 −1.45700
\(592\) 1.20683 0.0496004
\(593\) −16.1196 −0.661953 −0.330976 0.943639i \(-0.607378\pi\)
−0.330976 + 0.943639i \(0.607378\pi\)
\(594\) 30.2445 1.24095
\(595\) 2.19881 0.0901426
\(596\) 4.86544 0.199296
\(597\) 9.65409 0.395116
\(598\) 81.2566 3.32283
\(599\) −39.1231 −1.59853 −0.799264 0.600980i \(-0.794777\pi\)
−0.799264 + 0.600980i \(0.794777\pi\)
\(600\) 73.0096 2.98060
\(601\) −4.43535 −0.180922 −0.0904608 0.995900i \(-0.528834\pi\)
−0.0904608 + 0.995900i \(0.528834\pi\)
\(602\) −16.8777 −0.687882
\(603\) −71.9644 −2.93062
\(604\) 48.3416 1.96699
\(605\) −28.7536 −1.16900
\(606\) −60.7073 −2.46607
\(607\) 12.5813 0.510660 0.255330 0.966854i \(-0.417816\pi\)
0.255330 + 0.966854i \(0.417816\pi\)
\(608\) −17.5602 −0.712161
\(609\) −1.01139 −0.0409834
\(610\) −42.9034 −1.73711
\(611\) −15.7855 −0.638615
\(612\) 21.6129 0.873648
\(613\) −16.6562 −0.672736 −0.336368 0.941731i \(-0.609199\pi\)
−0.336368 + 0.941731i \(0.609199\pi\)
\(614\) 47.1242 1.90178
\(615\) 13.5823 0.547691
\(616\) −4.17311 −0.168139
\(617\) 38.4925 1.54965 0.774824 0.632177i \(-0.217838\pi\)
0.774824 + 0.632177i \(0.217838\pi\)
\(618\) −88.4059 −3.55621
\(619\) −11.9418 −0.479980 −0.239990 0.970775i \(-0.577144\pi\)
−0.239990 + 0.970775i \(0.577144\pi\)
\(620\) −74.4162 −2.98863
\(621\) −61.6060 −2.47216
\(622\) 5.00842 0.200819
\(623\) 5.38127 0.215596
\(624\) 33.0237 1.32201
\(625\) −19.2853 −0.771413
\(626\) 77.8124 3.11001
\(627\) 32.4333 1.29526
\(628\) −39.4186 −1.57297
\(629\) 0.496483 0.0197961
\(630\) −30.5203 −1.21596
\(631\) 2.20919 0.0879466 0.0439733 0.999033i \(-0.485998\pi\)
0.0439733 + 0.999033i \(0.485998\pi\)
\(632\) 37.7495 1.50159
\(633\) 47.4478 1.88588
\(634\) −43.1011 −1.71177
\(635\) −49.2894 −1.95599
\(636\) −83.5428 −3.31269
\(637\) 30.0368 1.19010
\(638\) −1.86847 −0.0739736
\(639\) 18.8738 0.746635
\(640\) 68.6493 2.71360
\(641\) 26.7565 1.05682 0.528410 0.848989i \(-0.322788\pi\)
0.528410 + 0.848989i \(0.322788\pi\)
\(642\) 99.4353 3.92440
\(643\) 5.95750 0.234941 0.117470 0.993076i \(-0.462521\pi\)
0.117470 + 0.993076i \(0.462521\pi\)
\(644\) 18.3504 0.723109
\(645\) −104.287 −4.10628
\(646\) 17.1969 0.676602
\(647\) −18.0701 −0.710408 −0.355204 0.934789i \(-0.615589\pi\)
−0.355204 + 0.934789i \(0.615589\pi\)
\(648\) −29.9241 −1.17553
\(649\) −16.2543 −0.638037
\(650\) 65.3017 2.56134
\(651\) 11.8879 0.465925
\(652\) −45.5514 −1.78393
\(653\) 32.9171 1.28815 0.644073 0.764964i \(-0.277243\pi\)
0.644073 + 0.764964i \(0.277243\pi\)
\(654\) 135.476 5.29753
\(655\) −25.0785 −0.979897
\(656\) −3.36180 −0.131256
\(657\) −17.2214 −0.671873
\(658\) −5.47846 −0.213573
\(659\) −44.0159 −1.71462 −0.857309 0.514802i \(-0.827865\pi\)
−0.857309 + 0.514802i \(0.827865\pi\)
\(660\) −55.6655 −2.16678
\(661\) 38.3417 1.49132 0.745660 0.666326i \(-0.232134\pi\)
0.745660 + 0.666326i \(0.232134\pi\)
\(662\) −1.64370 −0.0638843
\(663\) 13.5858 0.527628
\(664\) 25.6118 0.993931
\(665\) −15.8021 −0.612779
\(666\) −6.89135 −0.267035
\(667\) 3.80596 0.147367
\(668\) −50.9198 −1.97015
\(669\) −69.0020 −2.66777
\(670\) 98.2767 3.79676
\(671\) 8.23930 0.318075
\(672\) −4.81464 −0.185729
\(673\) 0.394697 0.0152145 0.00760723 0.999971i \(-0.497579\pi\)
0.00760723 + 0.999971i \(0.497579\pi\)
\(674\) 53.2812 2.05232
\(675\) −49.5095 −1.90562
\(676\) 29.7060 1.14254
\(677\) 27.3401 1.05077 0.525383 0.850866i \(-0.323922\pi\)
0.525383 + 0.850866i \(0.323922\pi\)
\(678\) −45.9148 −1.76335
\(679\) 4.95622 0.190202
\(680\) −13.6721 −0.524301
\(681\) −37.2550 −1.42762
\(682\) 21.9622 0.840978
\(683\) −24.9374 −0.954203 −0.477101 0.878848i \(-0.658313\pi\)
−0.477101 + 0.878848i \(0.658313\pi\)
\(684\) −155.324 −5.93896
\(685\) 12.7431 0.486889
\(686\) 21.5501 0.822786
\(687\) 16.2080 0.618374
\(688\) 25.8123 0.984084
\(689\) −34.6133 −1.31866
\(690\) 174.250 6.63360
\(691\) 12.2531 0.466131 0.233066 0.972461i \(-0.425124\pi\)
0.233066 + 0.972461i \(0.425124\pi\)
\(692\) −7.72121 −0.293516
\(693\) 5.86120 0.222649
\(694\) −76.9134 −2.91959
\(695\) 23.9685 0.909175
\(696\) 6.28873 0.238374
\(697\) −1.38303 −0.0523859
\(698\) −82.4275 −3.11993
\(699\) −47.7470 −1.80596
\(700\) 14.7473 0.557395
\(701\) 25.8486 0.976289 0.488144 0.872763i \(-0.337674\pi\)
0.488144 + 0.872763i \(0.337674\pi\)
\(702\) −91.0472 −3.43636
\(703\) −3.56805 −0.134571
\(704\) −16.2904 −0.613969
\(705\) −33.8512 −1.27491
\(706\) −2.39289 −0.0900577
\(707\) −5.68020 −0.213626
\(708\) 118.101 4.43851
\(709\) −2.08673 −0.0783688 −0.0391844 0.999232i \(-0.512476\pi\)
−0.0391844 + 0.999232i \(0.512476\pi\)
\(710\) −25.7746 −0.967302
\(711\) −53.0198 −1.98840
\(712\) −33.4604 −1.25398
\(713\) −44.7356 −1.67536
\(714\) 4.71502 0.176455
\(715\) −23.0633 −0.862517
\(716\) −42.4533 −1.58656
\(717\) −33.9373 −1.26741
\(718\) 57.9264 2.16179
\(719\) −10.2721 −0.383086 −0.191543 0.981484i \(-0.561349\pi\)
−0.191543 + 0.981484i \(0.561349\pi\)
\(720\) 46.6770 1.73955
\(721\) −8.27187 −0.308060
\(722\) −78.1227 −2.90743
\(723\) 5.68169 0.211304
\(724\) 54.7325 2.03412
\(725\) 3.05865 0.113595
\(726\) −61.6576 −2.28833
\(727\) −10.3579 −0.384152 −0.192076 0.981380i \(-0.561522\pi\)
−0.192076 + 0.981380i \(0.561522\pi\)
\(728\) 12.5626 0.465602
\(729\) −31.9136 −1.18198
\(730\) 23.5181 0.870444
\(731\) 10.6191 0.392760
\(732\) −59.8654 −2.21269
\(733\) −6.60155 −0.243834 −0.121917 0.992540i \(-0.538904\pi\)
−0.121917 + 0.992540i \(0.538904\pi\)
\(734\) −18.3595 −0.677662
\(735\) 64.4123 2.37589
\(736\) 18.1180 0.667840
\(737\) −18.8733 −0.695209
\(738\) 19.1969 0.706647
\(739\) −23.1340 −0.850996 −0.425498 0.904959i \(-0.639901\pi\)
−0.425498 + 0.904959i \(0.639901\pi\)
\(740\) 6.12387 0.225118
\(741\) −97.6362 −3.58676
\(742\) −12.0127 −0.441002
\(743\) −14.5616 −0.534212 −0.267106 0.963667i \(-0.586067\pi\)
−0.267106 + 0.963667i \(0.586067\pi\)
\(744\) −73.9184 −2.70998
\(745\) 4.32287 0.158378
\(746\) 9.96913 0.364996
\(747\) −35.9722 −1.31615
\(748\) 5.66818 0.207249
\(749\) 9.30385 0.339955
\(750\) 22.5364 0.822913
\(751\) −14.0225 −0.511689 −0.255844 0.966718i \(-0.582353\pi\)
−0.255844 + 0.966718i \(0.582353\pi\)
\(752\) 8.37862 0.305537
\(753\) 86.1548 3.13966
\(754\) 5.62480 0.204843
\(755\) 42.9507 1.56314
\(756\) −20.5615 −0.747814
\(757\) 19.2348 0.699102 0.349551 0.936917i \(-0.386334\pi\)
0.349551 + 0.936917i \(0.386334\pi\)
\(758\) 23.7978 0.864374
\(759\) −33.4636 −1.21465
\(760\) 98.2564 3.56413
\(761\) −50.9408 −1.84660 −0.923301 0.384078i \(-0.874519\pi\)
−0.923301 + 0.384078i \(0.874519\pi\)
\(762\) −105.694 −3.82888
\(763\) 12.6761 0.458904
\(764\) −86.8597 −3.14247
\(765\) 19.2027 0.694274
\(766\) −71.0941 −2.56873
\(767\) 48.9315 1.76681
\(768\) 83.6730 3.01929
\(769\) 8.70472 0.313900 0.156950 0.987607i \(-0.449834\pi\)
0.156950 + 0.987607i \(0.449834\pi\)
\(770\) −8.00423 −0.288452
\(771\) 75.5347 2.72031
\(772\) 0.351443 0.0126487
\(773\) −12.6343 −0.454424 −0.227212 0.973845i \(-0.572961\pi\)
−0.227212 + 0.973845i \(0.572961\pi\)
\(774\) −147.396 −5.29804
\(775\) −35.9517 −1.29142
\(776\) −30.8175 −1.10628
\(777\) −0.978285 −0.0350958
\(778\) 68.3678 2.45111
\(779\) 9.93932 0.356113
\(780\) 167.574 6.00011
\(781\) 4.94982 0.177119
\(782\) −17.7432 −0.634494
\(783\) −4.26454 −0.152402
\(784\) −15.9429 −0.569389
\(785\) −35.0228 −1.25002
\(786\) −53.7770 −1.91816
\(787\) 3.44042 0.122638 0.0613188 0.998118i \(-0.480469\pi\)
0.0613188 + 0.998118i \(0.480469\pi\)
\(788\) 44.4870 1.58478
\(789\) −30.7606 −1.09511
\(790\) 72.4053 2.57607
\(791\) −4.29611 −0.152752
\(792\) −36.4446 −1.29500
\(793\) −24.8034 −0.880793
\(794\) 85.4267 3.03168
\(795\) −74.2264 −2.63254
\(796\) −12.1252 −0.429768
\(797\) 41.1756 1.45851 0.729256 0.684240i \(-0.239866\pi\)
0.729256 + 0.684240i \(0.239866\pi\)
\(798\) −33.8852 −1.19952
\(799\) 3.44692 0.121943
\(800\) 14.5605 0.514793
\(801\) 46.9957 1.66051
\(802\) 67.6452 2.38863
\(803\) −4.51649 −0.159383
\(804\) 137.131 4.83623
\(805\) 16.3041 0.574643
\(806\) −66.1146 −2.32879
\(807\) −79.9324 −2.81375
\(808\) 35.3191 1.24252
\(809\) 6.91375 0.243075 0.121537 0.992587i \(-0.461218\pi\)
0.121537 + 0.992587i \(0.461218\pi\)
\(810\) −57.3959 −2.01669
\(811\) 2.15880 0.0758056 0.0379028 0.999281i \(-0.487932\pi\)
0.0379028 + 0.999281i \(0.487932\pi\)
\(812\) 1.27027 0.0445777
\(813\) 44.4451 1.55876
\(814\) −1.80732 −0.0633466
\(815\) −40.4717 −1.41766
\(816\) −7.21104 −0.252437
\(817\) −76.3153 −2.66993
\(818\) 4.93457 0.172533
\(819\) −17.6444 −0.616546
\(820\) −17.0589 −0.595724
\(821\) 6.86394 0.239553 0.119777 0.992801i \(-0.461782\pi\)
0.119777 + 0.992801i \(0.461782\pi\)
\(822\) 27.3257 0.953092
\(823\) 3.42194 0.119281 0.0596406 0.998220i \(-0.481005\pi\)
0.0596406 + 0.998220i \(0.481005\pi\)
\(824\) 51.4339 1.79179
\(825\) −26.8929 −0.936291
\(826\) 16.9819 0.590877
\(827\) 5.66646 0.197042 0.0985210 0.995135i \(-0.468589\pi\)
0.0985210 + 0.995135i \(0.468589\pi\)
\(828\) 160.258 5.56935
\(829\) 45.1402 1.56778 0.783892 0.620897i \(-0.213231\pi\)
0.783892 + 0.620897i \(0.213231\pi\)
\(830\) 49.1247 1.70514
\(831\) −84.2492 −2.92257
\(832\) 49.0403 1.70017
\(833\) −6.55883 −0.227250
\(834\) 51.3967 1.77972
\(835\) −45.2414 −1.56564
\(836\) −40.7351 −1.40885
\(837\) 50.1258 1.73260
\(838\) 5.06063 0.174817
\(839\) −25.5119 −0.880768 −0.440384 0.897809i \(-0.645158\pi\)
−0.440384 + 0.897809i \(0.645158\pi\)
\(840\) 26.9398 0.929513
\(841\) −28.7365 −0.990915
\(842\) −56.5045 −1.94727
\(843\) 93.1177 3.20715
\(844\) −59.5930 −2.05127
\(845\) 26.3933 0.907957
\(846\) −47.8445 −1.64493
\(847\) −5.76912 −0.198229
\(848\) 18.3720 0.630897
\(849\) −43.0160 −1.47630
\(850\) −14.2593 −0.489088
\(851\) 3.68139 0.126197
\(852\) −35.9646 −1.23213
\(853\) −42.9552 −1.47076 −0.735378 0.677657i \(-0.762995\pi\)
−0.735378 + 0.677657i \(0.762995\pi\)
\(854\) −8.60814 −0.294565
\(855\) −138.003 −4.71960
\(856\) −57.8508 −1.97730
\(857\) −38.7699 −1.32435 −0.662177 0.749347i \(-0.730367\pi\)
−0.662177 + 0.749347i \(0.730367\pi\)
\(858\) −49.4556 −1.68839
\(859\) 9.42261 0.321495 0.160748 0.986996i \(-0.448609\pi\)
0.160748 + 0.986996i \(0.448609\pi\)
\(860\) 130.981 4.46640
\(861\) 2.72515 0.0928730
\(862\) 24.0885 0.820457
\(863\) −10.0989 −0.343771 −0.171885 0.985117i \(-0.554986\pi\)
−0.171885 + 0.985117i \(0.554986\pi\)
\(864\) −20.3011 −0.690657
\(865\) −6.86017 −0.233253
\(866\) 48.4603 1.64675
\(867\) −2.96659 −0.100751
\(868\) −14.9309 −0.506787
\(869\) −13.9049 −0.471693
\(870\) 12.0621 0.408943
\(871\) 56.8158 1.92513
\(872\) −78.8190 −2.66915
\(873\) 43.2837 1.46493
\(874\) 127.514 4.31322
\(875\) 2.10866 0.0712858
\(876\) 32.8161 1.10875
\(877\) 10.0707 0.340064 0.170032 0.985438i \(-0.445613\pi\)
0.170032 + 0.985438i \(0.445613\pi\)
\(878\) −2.71763 −0.0917156
\(879\) 14.3053 0.482506
\(880\) 12.2415 0.412660
\(881\) 17.7225 0.597086 0.298543 0.954396i \(-0.403499\pi\)
0.298543 + 0.954396i \(0.403499\pi\)
\(882\) 91.0387 3.06543
\(883\) −12.4113 −0.417672 −0.208836 0.977951i \(-0.566967\pi\)
−0.208836 + 0.977951i \(0.566967\pi\)
\(884\) −17.0633 −0.573902
\(885\) 104.931 3.52721
\(886\) −27.3671 −0.919417
\(887\) −19.6307 −0.659134 −0.329567 0.944132i \(-0.606903\pi\)
−0.329567 + 0.944132i \(0.606903\pi\)
\(888\) 6.08291 0.204129
\(889\) −9.88944 −0.331681
\(890\) −64.1786 −2.15127
\(891\) 11.0225 0.369267
\(892\) 86.6643 2.90174
\(893\) −24.7718 −0.828957
\(894\) 9.26973 0.310026
\(895\) −37.7191 −1.26081
\(896\) 13.7738 0.460150
\(897\) 100.738 3.36354
\(898\) 1.91286 0.0638330
\(899\) −3.09672 −0.103281
\(900\) 128.791 4.29304
\(901\) 7.55815 0.251799
\(902\) 5.03456 0.167633
\(903\) −20.9241 −0.696309
\(904\) 26.7129 0.888459
\(905\) 48.6289 1.61648
\(906\) 92.1013 3.05986
\(907\) −52.0106 −1.72698 −0.863492 0.504363i \(-0.831727\pi\)
−0.863492 + 0.504363i \(0.831727\pi\)
\(908\) 46.7911 1.55282
\(909\) −49.6063 −1.64534
\(910\) 24.0957 0.798765
\(911\) 0.973267 0.0322458 0.0161229 0.999870i \(-0.494868\pi\)
0.0161229 + 0.999870i \(0.494868\pi\)
\(912\) 51.8232 1.71604
\(913\) −9.43405 −0.312221
\(914\) −31.2032 −1.03211
\(915\) −53.1895 −1.75839
\(916\) −20.3567 −0.672605
\(917\) −5.03175 −0.166163
\(918\) 19.8810 0.656172
\(919\) −3.05292 −0.100707 −0.0503533 0.998731i \(-0.516035\pi\)
−0.0503533 + 0.998731i \(0.516035\pi\)
\(920\) −101.378 −3.34232
\(921\) 58.4222 1.92508
\(922\) −87.8018 −2.89160
\(923\) −14.9008 −0.490466
\(924\) −11.1687 −0.367424
\(925\) 2.95854 0.0972764
\(926\) 77.6098 2.55042
\(927\) −72.2398 −2.37267
\(928\) 1.25418 0.0411705
\(929\) 5.72496 0.187830 0.0939150 0.995580i \(-0.470062\pi\)
0.0939150 + 0.995580i \(0.470062\pi\)
\(930\) −141.779 −4.64912
\(931\) 47.1360 1.54482
\(932\) 59.9687 1.96434
\(933\) 6.20918 0.203280
\(934\) 30.2784 0.990739
\(935\) 5.03608 0.164697
\(936\) 109.712 3.58604
\(937\) −5.60332 −0.183053 −0.0915263 0.995803i \(-0.529175\pi\)
−0.0915263 + 0.995803i \(0.529175\pi\)
\(938\) 19.7182 0.643823
\(939\) 96.4679 3.14811
\(940\) 42.5161 1.38672
\(941\) 29.0085 0.945649 0.472824 0.881157i \(-0.343234\pi\)
0.472824 + 0.881157i \(0.343234\pi\)
\(942\) −75.1010 −2.44692
\(943\) −10.2551 −0.333951
\(944\) −25.9718 −0.845309
\(945\) −18.2686 −0.594276
\(946\) −38.6560 −1.25681
\(947\) 53.1651 1.72763 0.863817 0.503806i \(-0.168067\pi\)
0.863817 + 0.503806i \(0.168067\pi\)
\(948\) 101.031 3.28134
\(949\) 13.5963 0.441355
\(950\) 102.476 3.32476
\(951\) −53.4346 −1.73274
\(952\) −2.74317 −0.0889066
\(953\) −56.1998 −1.82049 −0.910245 0.414070i \(-0.864107\pi\)
−0.910245 + 0.414070i \(0.864107\pi\)
\(954\) −104.910 −3.39658
\(955\) −77.1734 −2.49727
\(956\) 42.6242 1.37857
\(957\) −2.31644 −0.0748798
\(958\) 41.4451 1.33903
\(959\) 2.55678 0.0825627
\(960\) 105.164 3.39416
\(961\) 5.39921 0.174168
\(962\) 5.44071 0.175416
\(963\) 81.2524 2.61832
\(964\) −7.13602 −0.229836
\(965\) 0.312252 0.0100517
\(966\) 34.9616 1.12487
\(967\) 28.2464 0.908342 0.454171 0.890915i \(-0.349936\pi\)
0.454171 + 0.890915i \(0.349936\pi\)
\(968\) 35.8720 1.15297
\(969\) 21.3198 0.684891
\(970\) −59.1094 −1.89789
\(971\) 9.23425 0.296341 0.148171 0.988962i \(-0.452662\pi\)
0.148171 + 0.988962i \(0.452662\pi\)
\(972\) 12.7818 0.409978
\(973\) 4.80903 0.154170
\(974\) −26.5471 −0.850623
\(975\) 80.9577 2.59272
\(976\) 13.1651 0.421404
\(977\) 7.32781 0.234438 0.117219 0.993106i \(-0.462602\pi\)
0.117219 + 0.993106i \(0.462602\pi\)
\(978\) −86.7855 −2.77509
\(979\) 12.3251 0.393910
\(980\) −80.8999 −2.58425
\(981\) 110.703 3.53446
\(982\) −55.6186 −1.77486
\(983\) −13.1255 −0.418638 −0.209319 0.977847i \(-0.567125\pi\)
−0.209319 + 0.977847i \(0.567125\pi\)
\(984\) −16.9448 −0.540182
\(985\) 39.5260 1.25940
\(986\) −1.22823 −0.0391148
\(987\) −6.79191 −0.216189
\(988\) 122.628 3.90132
\(989\) 78.7396 2.50377
\(990\) −69.9025 −2.22165
\(991\) 46.8070 1.48687 0.743437 0.668806i \(-0.233194\pi\)
0.743437 + 0.668806i \(0.233194\pi\)
\(992\) −14.7418 −0.468052
\(993\) −2.03778 −0.0646669
\(994\) −5.17141 −0.164027
\(995\) −10.7731 −0.341529
\(996\) 68.5463 2.17197
\(997\) 15.9560 0.505333 0.252666 0.967553i \(-0.418693\pi\)
0.252666 + 0.967553i \(0.418693\pi\)
\(998\) 96.7777 3.06344
\(999\) −4.12497 −0.130508
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 \(a_p\))