Properties

Label 6026.2.a.i.1.17
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+0.888297 q^{3}\) \(+1.00000 q^{4}\) \(+2.86945 q^{5}\) \(-0.888297 q^{6}\) \(-2.14877 q^{7}\) \(-1.00000 q^{8}\) \(-2.21093 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+0.888297 q^{3}\) \(+1.00000 q^{4}\) \(+2.86945 q^{5}\) \(-0.888297 q^{6}\) \(-2.14877 q^{7}\) \(-1.00000 q^{8}\) \(-2.21093 q^{9}\) \(-2.86945 q^{10}\) \(+1.49534 q^{11}\) \(+0.888297 q^{12}\) \(+6.87552 q^{13}\) \(+2.14877 q^{14}\) \(+2.54892 q^{15}\) \(+1.00000 q^{16}\) \(-7.83113 q^{17}\) \(+2.21093 q^{18}\) \(-1.29905 q^{19}\) \(+2.86945 q^{20}\) \(-1.90874 q^{21}\) \(-1.49534 q^{22}\) \(+1.00000 q^{23}\) \(-0.888297 q^{24}\) \(+3.23375 q^{25}\) \(-6.87552 q^{26}\) \(-4.62885 q^{27}\) \(-2.14877 q^{28}\) \(+1.47143 q^{29}\) \(-2.54892 q^{30}\) \(-3.46846 q^{31}\) \(-1.00000 q^{32}\) \(+1.32830 q^{33}\) \(+7.83113 q^{34}\) \(-6.16579 q^{35}\) \(-2.21093 q^{36}\) \(-2.73694 q^{37}\) \(+1.29905 q^{38}\) \(+6.10750 q^{39}\) \(-2.86945 q^{40}\) \(-4.87402 q^{41}\) \(+1.90874 q^{42}\) \(-11.0010 q^{43}\) \(+1.49534 q^{44}\) \(-6.34415 q^{45}\) \(-1.00000 q^{46}\) \(-8.21227 q^{47}\) \(+0.888297 q^{48}\) \(-2.38279 q^{49}\) \(-3.23375 q^{50}\) \(-6.95636 q^{51}\) \(+6.87552 q^{52}\) \(+4.48371 q^{53}\) \(+4.62885 q^{54}\) \(+4.29080 q^{55}\) \(+2.14877 q^{56}\) \(-1.15394 q^{57}\) \(-1.47143 q^{58}\) \(-13.2162 q^{59}\) \(+2.54892 q^{60}\) \(-15.1592 q^{61}\) \(+3.46846 q^{62}\) \(+4.75078 q^{63}\) \(+1.00000 q^{64}\) \(+19.7290 q^{65}\) \(-1.32830 q^{66}\) \(+4.82253 q^{67}\) \(-7.83113 q^{68}\) \(+0.888297 q^{69}\) \(+6.16579 q^{70}\) \(+6.94757 q^{71}\) \(+2.21093 q^{72}\) \(+6.40200 q^{73}\) \(+2.73694 q^{74}\) \(+2.87253 q^{75}\) \(-1.29905 q^{76}\) \(-3.21314 q^{77}\) \(-6.10750 q^{78}\) \(+10.0257 q^{79}\) \(+2.86945 q^{80}\) \(+2.52100 q^{81}\) \(+4.87402 q^{82}\) \(+3.93987 q^{83}\) \(-1.90874 q^{84}\) \(-22.4710 q^{85}\) \(+11.0010 q^{86}\) \(+1.30707 q^{87}\) \(-1.49534 q^{88}\) \(+5.77611 q^{89}\) \(+6.34415 q^{90}\) \(-14.7739 q^{91}\) \(+1.00000 q^{92}\) \(-3.08102 q^{93}\) \(+8.21227 q^{94}\) \(-3.72755 q^{95}\) \(-0.888297 q^{96}\) \(+1.86419 q^{97}\) \(+2.38279 q^{98}\) \(-3.30609 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(25q \) \(\mathstrut -\mathstrut 25q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut -\mathstrut 25q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 25q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut -\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 11q^{28} \) \(\mathstrut -\mathstrut 7q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 23q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 26q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 28q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 47q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 11q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut +\mathstrut 7q^{58} \) \(\mathstrut -\mathstrut 19q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 7q^{62} \) \(\mathstrut -\mathstrut 15q^{63} \) \(\mathstrut +\mathstrut 25q^{64} \) \(\mathstrut +\mathstrut 13q^{65} \) \(\mathstrut -\mathstrut 3q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 23q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut -\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 27q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 42q^{85} \) \(\mathstrut +\mathstrut 26q^{86} \) \(\mathstrut -\mathstrut 17q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 27q^{89} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 26q^{91} \) \(\mathstrut +\mathstrut 25q^{92} \) \(\mathstrut -\mathstrut 27q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 4q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.888297 0.512858 0.256429 0.966563i \(-0.417454\pi\)
0.256429 + 0.966563i \(0.417454\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.86945 1.28326 0.641629 0.767015i \(-0.278259\pi\)
0.641629 + 0.767015i \(0.278259\pi\)
\(6\) −0.888297 −0.362646
\(7\) −2.14877 −0.812158 −0.406079 0.913838i \(-0.633104\pi\)
−0.406079 + 0.913838i \(0.633104\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.21093 −0.736976
\(10\) −2.86945 −0.907400
\(11\) 1.49534 0.450862 0.225431 0.974259i \(-0.427621\pi\)
0.225431 + 0.974259i \(0.427621\pi\)
\(12\) 0.888297 0.256429
\(13\) 6.87552 1.90693 0.953463 0.301509i \(-0.0974902\pi\)
0.953463 + 0.301509i \(0.0974902\pi\)
\(14\) 2.14877 0.574283
\(15\) 2.54892 0.658129
\(16\) 1.00000 0.250000
\(17\) −7.83113 −1.89933 −0.949664 0.313271i \(-0.898575\pi\)
−0.949664 + 0.313271i \(0.898575\pi\)
\(18\) 2.21093 0.521121
\(19\) −1.29905 −0.298021 −0.149011 0.988836i \(-0.547609\pi\)
−0.149011 + 0.988836i \(0.547609\pi\)
\(20\) 2.86945 0.641629
\(21\) −1.90874 −0.416522
\(22\) −1.49534 −0.318807
\(23\) 1.00000 0.208514
\(24\) −0.888297 −0.181323
\(25\) 3.23375 0.646749
\(26\) −6.87552 −1.34840
\(27\) −4.62885 −0.890823
\(28\) −2.14877 −0.406079
\(29\) 1.47143 0.273239 0.136619 0.990624i \(-0.456376\pi\)
0.136619 + 0.990624i \(0.456376\pi\)
\(30\) −2.54892 −0.465368
\(31\) −3.46846 −0.622953 −0.311477 0.950254i \(-0.600824\pi\)
−0.311477 + 0.950254i \(0.600824\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.32830 0.231228
\(34\) 7.83113 1.34303
\(35\) −6.16579 −1.04221
\(36\) −2.21093 −0.368488
\(37\) −2.73694 −0.449950 −0.224975 0.974365i \(-0.572230\pi\)
−0.224975 + 0.974365i \(0.572230\pi\)
\(38\) 1.29905 0.210733
\(39\) 6.10750 0.977983
\(40\) −2.86945 −0.453700
\(41\) −4.87402 −0.761193 −0.380597 0.924741i \(-0.624281\pi\)
−0.380597 + 0.924741i \(0.624281\pi\)
\(42\) 1.90874 0.294526
\(43\) −11.0010 −1.67764 −0.838822 0.544406i \(-0.816755\pi\)
−0.838822 + 0.544406i \(0.816755\pi\)
\(44\) 1.49534 0.225431
\(45\) −6.34415 −0.945730
\(46\) −1.00000 −0.147442
\(47\) −8.21227 −1.19788 −0.598941 0.800793i \(-0.704412\pi\)
−0.598941 + 0.800793i \(0.704412\pi\)
\(48\) 0.888297 0.128215
\(49\) −2.38279 −0.340399
\(50\) −3.23375 −0.457321
\(51\) −6.95636 −0.974086
\(52\) 6.87552 0.953463
\(53\) 4.48371 0.615885 0.307943 0.951405i \(-0.400359\pi\)
0.307943 + 0.951405i \(0.400359\pi\)
\(54\) 4.62885 0.629907
\(55\) 4.29080 0.578571
\(56\) 2.14877 0.287141
\(57\) −1.15394 −0.152843
\(58\) −1.47143 −0.193209
\(59\) −13.2162 −1.72060 −0.860301 0.509786i \(-0.829725\pi\)
−0.860301 + 0.509786i \(0.829725\pi\)
\(60\) 2.54892 0.329065
\(61\) −15.1592 −1.94094 −0.970469 0.241227i \(-0.922450\pi\)
−0.970469 + 0.241227i \(0.922450\pi\)
\(62\) 3.46846 0.440494
\(63\) 4.75078 0.598541
\(64\) 1.00000 0.125000
\(65\) 19.7290 2.44708
\(66\) −1.32830 −0.163503
\(67\) 4.82253 0.589165 0.294583 0.955626i \(-0.404819\pi\)
0.294583 + 0.955626i \(0.404819\pi\)
\(68\) −7.83113 −0.949664
\(69\) 0.888297 0.106938
\(70\) 6.16579 0.736952
\(71\) 6.94757 0.824525 0.412262 0.911065i \(-0.364739\pi\)
0.412262 + 0.911065i \(0.364739\pi\)
\(72\) 2.21093 0.260561
\(73\) 6.40200 0.749297 0.374649 0.927167i \(-0.377763\pi\)
0.374649 + 0.927167i \(0.377763\pi\)
\(74\) 2.73694 0.318163
\(75\) 2.87253 0.331691
\(76\) −1.29905 −0.149011
\(77\) −3.21314 −0.366171
\(78\) −6.10750 −0.691539
\(79\) 10.0257 1.12798 0.563989 0.825783i \(-0.309266\pi\)
0.563989 + 0.825783i \(0.309266\pi\)
\(80\) 2.86945 0.320814
\(81\) 2.52100 0.280111
\(82\) 4.87402 0.538245
\(83\) 3.93987 0.432457 0.216229 0.976343i \(-0.430624\pi\)
0.216229 + 0.976343i \(0.430624\pi\)
\(84\) −1.90874 −0.208261
\(85\) −22.4710 −2.43733
\(86\) 11.0010 1.18627
\(87\) 1.30707 0.140133
\(88\) −1.49534 −0.159404
\(89\) 5.77611 0.612266 0.306133 0.951989i \(-0.400965\pi\)
0.306133 + 0.951989i \(0.400965\pi\)
\(90\) 6.34415 0.668732
\(91\) −14.7739 −1.54873
\(92\) 1.00000 0.104257
\(93\) −3.08102 −0.319487
\(94\) 8.21227 0.847031
\(95\) −3.72755 −0.382438
\(96\) −0.888297 −0.0906614
\(97\) 1.86419 0.189280 0.0946401 0.995512i \(-0.469830\pi\)
0.0946401 + 0.995512i \(0.469830\pi\)
\(98\) 2.38279 0.240698
\(99\) −3.30609 −0.332274
\(100\) 3.23375 0.323375
\(101\) 12.4986 1.24366 0.621831 0.783152i \(-0.286389\pi\)
0.621831 + 0.783152i \(0.286389\pi\)
\(102\) 6.95636 0.688783
\(103\) −13.5984 −1.33989 −0.669944 0.742412i \(-0.733682\pi\)
−0.669944 + 0.742412i \(0.733682\pi\)
\(104\) −6.87552 −0.674200
\(105\) −5.47705 −0.534505
\(106\) −4.48371 −0.435497
\(107\) −17.1357 −1.65657 −0.828283 0.560310i \(-0.810682\pi\)
−0.828283 + 0.560310i \(0.810682\pi\)
\(108\) −4.62885 −0.445411
\(109\) −8.95367 −0.857606 −0.428803 0.903398i \(-0.641065\pi\)
−0.428803 + 0.903398i \(0.641065\pi\)
\(110\) −4.29080 −0.409112
\(111\) −2.43121 −0.230761
\(112\) −2.14877 −0.203040
\(113\) 14.9142 1.40301 0.701504 0.712666i \(-0.252512\pi\)
0.701504 + 0.712666i \(0.252512\pi\)
\(114\) 1.15394 0.108076
\(115\) 2.86945 0.267578
\(116\) 1.47143 0.136619
\(117\) −15.2013 −1.40536
\(118\) 13.2162 1.21665
\(119\) 16.8273 1.54255
\(120\) −2.54892 −0.232684
\(121\) −8.76396 −0.796724
\(122\) 15.1592 1.37245
\(123\) −4.32957 −0.390384
\(124\) −3.46846 −0.311477
\(125\) −5.06818 −0.453311
\(126\) −4.75078 −0.423233
\(127\) 7.67595 0.681130 0.340565 0.940221i \(-0.389382\pi\)
0.340565 + 0.940221i \(0.389382\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −9.77219 −0.860394
\(130\) −19.7290 −1.73035
\(131\) 1.00000 0.0873704
\(132\) 1.32830 0.115614
\(133\) 2.79135 0.242041
\(134\) −4.82253 −0.416603
\(135\) −13.2823 −1.14315
\(136\) 7.83113 0.671514
\(137\) 18.5406 1.58403 0.792015 0.610501i \(-0.209032\pi\)
0.792015 + 0.610501i \(0.209032\pi\)
\(138\) −0.888297 −0.0756168
\(139\) −4.23067 −0.358841 −0.179421 0.983772i \(-0.557422\pi\)
−0.179421 + 0.983772i \(0.557422\pi\)
\(140\) −6.16579 −0.521104
\(141\) −7.29493 −0.614344
\(142\) −6.94757 −0.583027
\(143\) 10.2812 0.859760
\(144\) −2.21093 −0.184244
\(145\) 4.22221 0.350635
\(146\) −6.40200 −0.529833
\(147\) −2.11663 −0.174576
\(148\) −2.73694 −0.224975
\(149\) −8.62805 −0.706838 −0.353419 0.935465i \(-0.614981\pi\)
−0.353419 + 0.935465i \(0.614981\pi\)
\(150\) −2.87253 −0.234541
\(151\) −10.7728 −0.876677 −0.438338 0.898810i \(-0.644433\pi\)
−0.438338 + 0.898810i \(0.644433\pi\)
\(152\) 1.29905 0.105366
\(153\) 17.3141 1.39976
\(154\) 3.21314 0.258922
\(155\) −9.95256 −0.799409
\(156\) 6.10750 0.488992
\(157\) −21.0032 −1.67624 −0.838119 0.545488i \(-0.816344\pi\)
−0.838119 + 0.545488i \(0.816344\pi\)
\(158\) −10.0257 −0.797600
\(159\) 3.98287 0.315862
\(160\) −2.86945 −0.226850
\(161\) −2.14877 −0.169347
\(162\) −2.52100 −0.198068
\(163\) 8.47783 0.664035 0.332017 0.943273i \(-0.392271\pi\)
0.332017 + 0.943273i \(0.392271\pi\)
\(164\) −4.87402 −0.380597
\(165\) 3.81150 0.296725
\(166\) −3.93987 −0.305793
\(167\) −10.0875 −0.780591 −0.390295 0.920690i \(-0.627627\pi\)
−0.390295 + 0.920690i \(0.627627\pi\)
\(168\) 1.90874 0.147263
\(169\) 34.2728 2.63637
\(170\) 22.4710 1.72345
\(171\) 2.87210 0.219635
\(172\) −11.0010 −0.838822
\(173\) −9.40755 −0.715243 −0.357621 0.933867i \(-0.616412\pi\)
−0.357621 + 0.933867i \(0.616412\pi\)
\(174\) −1.30707 −0.0990888
\(175\) −6.94857 −0.525263
\(176\) 1.49534 0.112715
\(177\) −11.7399 −0.882425
\(178\) −5.77611 −0.432938
\(179\) −5.52206 −0.412738 −0.206369 0.978474i \(-0.566165\pi\)
−0.206369 + 0.978474i \(0.566165\pi\)
\(180\) −6.34415 −0.472865
\(181\) 22.0647 1.64006 0.820029 0.572322i \(-0.193957\pi\)
0.820029 + 0.572322i \(0.193957\pi\)
\(182\) 14.7739 1.09511
\(183\) −13.4659 −0.995426
\(184\) −1.00000 −0.0737210
\(185\) −7.85351 −0.577402
\(186\) 3.08102 0.225911
\(187\) −11.7102 −0.856334
\(188\) −8.21227 −0.598941
\(189\) 9.94633 0.723489
\(190\) 3.72755 0.270425
\(191\) 8.60972 0.622977 0.311489 0.950250i \(-0.399172\pi\)
0.311489 + 0.950250i \(0.399172\pi\)
\(192\) 0.888297 0.0641073
\(193\) 3.34585 0.240839 0.120420 0.992723i \(-0.461576\pi\)
0.120420 + 0.992723i \(0.461576\pi\)
\(194\) −1.86419 −0.133841
\(195\) 17.5252 1.25500
\(196\) −2.38279 −0.170199
\(197\) −12.2456 −0.872461 −0.436231 0.899835i \(-0.643687\pi\)
−0.436231 + 0.899835i \(0.643687\pi\)
\(198\) 3.30609 0.234953
\(199\) 10.2126 0.723954 0.361977 0.932187i \(-0.382102\pi\)
0.361977 + 0.932187i \(0.382102\pi\)
\(200\) −3.23375 −0.228660
\(201\) 4.28383 0.302158
\(202\) −12.4986 −0.879402
\(203\) −3.16177 −0.221913
\(204\) −6.95636 −0.487043
\(205\) −13.9857 −0.976807
\(206\) 13.5984 0.947443
\(207\) −2.21093 −0.153670
\(208\) 6.87552 0.476732
\(209\) −1.94251 −0.134366
\(210\) 5.47705 0.377952
\(211\) −0.973024 −0.0669857 −0.0334929 0.999439i \(-0.510663\pi\)
−0.0334929 + 0.999439i \(0.510663\pi\)
\(212\) 4.48371 0.307943
\(213\) 6.17150 0.422864
\(214\) 17.1357 1.17137
\(215\) −31.5670 −2.15285
\(216\) 4.62885 0.314953
\(217\) 7.45291 0.505937
\(218\) 8.95367 0.606419
\(219\) 5.68687 0.384283
\(220\) 4.29080 0.289286
\(221\) −53.8431 −3.62188
\(222\) 2.43121 0.163172
\(223\) −18.6577 −1.24941 −0.624707 0.780859i \(-0.714782\pi\)
−0.624707 + 0.780859i \(0.714782\pi\)
\(224\) 2.14877 0.143571
\(225\) −7.14959 −0.476639
\(226\) −14.9142 −0.992076
\(227\) 22.0065 1.46062 0.730311 0.683115i \(-0.239375\pi\)
0.730311 + 0.683115i \(0.239375\pi\)
\(228\) −1.15394 −0.0764214
\(229\) 2.44656 0.161673 0.0808365 0.996727i \(-0.474241\pi\)
0.0808365 + 0.996727i \(0.474241\pi\)
\(230\) −2.86945 −0.189206
\(231\) −2.85422 −0.187794
\(232\) −1.47143 −0.0966044
\(233\) −19.5105 −1.27818 −0.639089 0.769133i \(-0.720689\pi\)
−0.639089 + 0.769133i \(0.720689\pi\)
\(234\) 15.2013 0.993740
\(235\) −23.5647 −1.53719
\(236\) −13.2162 −0.860301
\(237\) 8.90578 0.578492
\(238\) −16.8273 −1.09075
\(239\) −1.62909 −0.105377 −0.0526886 0.998611i \(-0.516779\pi\)
−0.0526886 + 0.998611i \(0.516779\pi\)
\(240\) 2.54892 0.164532
\(241\) −3.21233 −0.206924 −0.103462 0.994633i \(-0.532992\pi\)
−0.103462 + 0.994633i \(0.532992\pi\)
\(242\) 8.76396 0.563369
\(243\) 16.1259 1.03448
\(244\) −15.1592 −0.970469
\(245\) −6.83731 −0.436819
\(246\) 4.32957 0.276043
\(247\) −8.93162 −0.568305
\(248\) 3.46846 0.220247
\(249\) 3.49977 0.221789
\(250\) 5.06818 0.320540
\(251\) −3.13627 −0.197960 −0.0989798 0.995089i \(-0.531558\pi\)
−0.0989798 + 0.995089i \(0.531558\pi\)
\(252\) 4.75078 0.299271
\(253\) 1.49534 0.0940111
\(254\) −7.67595 −0.481632
\(255\) −19.9609 −1.25000
\(256\) 1.00000 0.0625000
\(257\) −23.5931 −1.47170 −0.735850 0.677145i \(-0.763217\pi\)
−0.735850 + 0.677145i \(0.763217\pi\)
\(258\) 9.77219 0.608390
\(259\) 5.88105 0.365431
\(260\) 19.7290 1.22354
\(261\) −3.25324 −0.201370
\(262\) −1.00000 −0.0617802
\(263\) −2.85590 −0.176103 −0.0880513 0.996116i \(-0.528064\pi\)
−0.0880513 + 0.996116i \(0.528064\pi\)
\(264\) −1.32830 −0.0817515
\(265\) 12.8658 0.790340
\(266\) −2.79135 −0.171149
\(267\) 5.13090 0.314006
\(268\) 4.82253 0.294583
\(269\) 9.48661 0.578409 0.289205 0.957267i \(-0.406609\pi\)
0.289205 + 0.957267i \(0.406609\pi\)
\(270\) 13.2823 0.808332
\(271\) −15.4057 −0.935831 −0.467916 0.883773i \(-0.654995\pi\)
−0.467916 + 0.883773i \(0.654995\pi\)
\(272\) −7.83113 −0.474832
\(273\) −13.1236 −0.794277
\(274\) −18.5406 −1.12008
\(275\) 4.83555 0.291594
\(276\) 0.888297 0.0534692
\(277\) −14.5217 −0.872526 −0.436263 0.899819i \(-0.643698\pi\)
−0.436263 + 0.899819i \(0.643698\pi\)
\(278\) 4.23067 0.253739
\(279\) 7.66851 0.459102
\(280\) 6.16579 0.368476
\(281\) −24.5581 −1.46501 −0.732506 0.680760i \(-0.761649\pi\)
−0.732506 + 0.680760i \(0.761649\pi\)
\(282\) 7.29493 0.434407
\(283\) 3.98728 0.237019 0.118510 0.992953i \(-0.462188\pi\)
0.118510 + 0.992953i \(0.462188\pi\)
\(284\) 6.94757 0.412262
\(285\) −3.31117 −0.196137
\(286\) −10.2812 −0.607942
\(287\) 10.4731 0.618209
\(288\) 2.21093 0.130280
\(289\) 44.3266 2.60745
\(290\) −4.22221 −0.247937
\(291\) 1.65596 0.0970739
\(292\) 6.40200 0.374649
\(293\) 31.0884 1.81620 0.908102 0.418750i \(-0.137532\pi\)
0.908102 + 0.418750i \(0.137532\pi\)
\(294\) 2.11663 0.123444
\(295\) −37.9232 −2.20798
\(296\) 2.73694 0.159081
\(297\) −6.92170 −0.401638
\(298\) 8.62805 0.499810
\(299\) 6.87552 0.397622
\(300\) 2.87253 0.165845
\(301\) 23.6387 1.36251
\(302\) 10.7728 0.619904
\(303\) 11.1025 0.637822
\(304\) −1.29905 −0.0745054
\(305\) −43.4986 −2.49072
\(306\) −17.3141 −0.989780
\(307\) 22.5804 1.28873 0.644367 0.764716i \(-0.277121\pi\)
0.644367 + 0.764716i \(0.277121\pi\)
\(308\) −3.21314 −0.183085
\(309\) −12.0794 −0.687172
\(310\) 9.95256 0.565268
\(311\) −31.1172 −1.76449 −0.882247 0.470788i \(-0.843970\pi\)
−0.882247 + 0.470788i \(0.843970\pi\)
\(312\) −6.10750 −0.345769
\(313\) −1.89128 −0.106902 −0.0534508 0.998570i \(-0.517022\pi\)
−0.0534508 + 0.998570i \(0.517022\pi\)
\(314\) 21.0032 1.18528
\(315\) 13.6321 0.768083
\(316\) 10.0257 0.563989
\(317\) −14.8805 −0.835772 −0.417886 0.908500i \(-0.637229\pi\)
−0.417886 + 0.908500i \(0.637229\pi\)
\(318\) −3.98287 −0.223348
\(319\) 2.20029 0.123193
\(320\) 2.86945 0.160407
\(321\) −15.2215 −0.849584
\(322\) 2.14877 0.119746
\(323\) 10.1730 0.566040
\(324\) 2.52100 0.140055
\(325\) 22.2337 1.23330
\(326\) −8.47783 −0.469543
\(327\) −7.95351 −0.439830
\(328\) 4.87402 0.269122
\(329\) 17.6463 0.972871
\(330\) −3.81150 −0.209816
\(331\) 20.6824 1.13681 0.568403 0.822750i \(-0.307561\pi\)
0.568403 + 0.822750i \(0.307561\pi\)
\(332\) 3.93987 0.216229
\(333\) 6.05118 0.331603
\(334\) 10.0875 0.551961
\(335\) 13.8380 0.756051
\(336\) −1.90874 −0.104131
\(337\) 20.1008 1.09496 0.547479 0.836819i \(-0.315588\pi\)
0.547479 + 0.836819i \(0.315588\pi\)
\(338\) −34.2728 −1.86420
\(339\) 13.2482 0.719544
\(340\) −22.4710 −1.21866
\(341\) −5.18652 −0.280866
\(342\) −2.87210 −0.155305
\(343\) 20.1615 1.08862
\(344\) 11.0010 0.593137
\(345\) 2.54892 0.137229
\(346\) 9.40755 0.505753
\(347\) 2.12514 0.114084 0.0570418 0.998372i \(-0.481833\pi\)
0.0570418 + 0.998372i \(0.481833\pi\)
\(348\) 1.30707 0.0700663
\(349\) −7.05857 −0.377837 −0.188918 0.981993i \(-0.560498\pi\)
−0.188918 + 0.981993i \(0.560498\pi\)
\(350\) 6.94857 0.371417
\(351\) −31.8258 −1.69873
\(352\) −1.49534 −0.0797018
\(353\) 33.8595 1.80216 0.901079 0.433655i \(-0.142776\pi\)
0.901079 + 0.433655i \(0.142776\pi\)
\(354\) 11.7399 0.623969
\(355\) 19.9357 1.05808
\(356\) 5.77611 0.306133
\(357\) 14.9476 0.791112
\(358\) 5.52206 0.291850
\(359\) −18.6806 −0.985923 −0.492961 0.870051i \(-0.664086\pi\)
−0.492961 + 0.870051i \(0.664086\pi\)
\(360\) 6.34415 0.334366
\(361\) −17.3125 −0.911183
\(362\) −22.0647 −1.15970
\(363\) −7.78500 −0.408606
\(364\) −14.7739 −0.774363
\(365\) 18.3702 0.961541
\(366\) 13.4659 0.703872
\(367\) 23.7765 1.24112 0.620562 0.784158i \(-0.286905\pi\)
0.620562 + 0.784158i \(0.286905\pi\)
\(368\) 1.00000 0.0521286
\(369\) 10.7761 0.560981
\(370\) 7.85351 0.408285
\(371\) −9.63446 −0.500196
\(372\) −3.08102 −0.159743
\(373\) 14.5702 0.754417 0.377209 0.926128i \(-0.376884\pi\)
0.377209 + 0.926128i \(0.376884\pi\)
\(374\) 11.7102 0.605519
\(375\) −4.50204 −0.232485
\(376\) 8.21227 0.423516
\(377\) 10.1169 0.521046
\(378\) −9.94633 −0.511584
\(379\) −29.3309 −1.50663 −0.753313 0.657662i \(-0.771546\pi\)
−0.753313 + 0.657662i \(0.771546\pi\)
\(380\) −3.72755 −0.191219
\(381\) 6.81852 0.349323
\(382\) −8.60972 −0.440511
\(383\) 4.49489 0.229678 0.114839 0.993384i \(-0.463365\pi\)
0.114839 + 0.993384i \(0.463365\pi\)
\(384\) −0.888297 −0.0453307
\(385\) −9.21994 −0.469891
\(386\) −3.34585 −0.170299
\(387\) 24.3225 1.23638
\(388\) 1.86419 0.0946401
\(389\) 9.33414 0.473260 0.236630 0.971600i \(-0.423957\pi\)
0.236630 + 0.971600i \(0.423957\pi\)
\(390\) −17.5252 −0.887422
\(391\) −7.83113 −0.396037
\(392\) 2.38279 0.120349
\(393\) 0.888297 0.0448086
\(394\) 12.2456 0.616923
\(395\) 28.7682 1.44748
\(396\) −3.30609 −0.166137
\(397\) 11.3514 0.569709 0.284855 0.958571i \(-0.408055\pi\)
0.284855 + 0.958571i \(0.408055\pi\)
\(398\) −10.2126 −0.511913
\(399\) 2.47954 0.124133
\(400\) 3.23375 0.161687
\(401\) 5.72551 0.285918 0.142959 0.989729i \(-0.454338\pi\)
0.142959 + 0.989729i \(0.454338\pi\)
\(402\) −4.28383 −0.213658
\(403\) −23.8475 −1.18793
\(404\) 12.4986 0.621831
\(405\) 7.23387 0.359454
\(406\) 3.16177 0.156916
\(407\) −4.09265 −0.202865
\(408\) 6.95636 0.344391
\(409\) −17.5673 −0.868649 −0.434325 0.900756i \(-0.643013\pi\)
−0.434325 + 0.900756i \(0.643013\pi\)
\(410\) 13.9857 0.690707
\(411\) 16.4696 0.812383
\(412\) −13.5984 −0.669944
\(413\) 28.3986 1.39740
\(414\) 2.21093 0.108661
\(415\) 11.3053 0.554954
\(416\) −6.87552 −0.337100
\(417\) −3.75809 −0.184035
\(418\) 1.94251 0.0950114
\(419\) 11.5650 0.564986 0.282493 0.959269i \(-0.408839\pi\)
0.282493 + 0.959269i \(0.408839\pi\)
\(420\) −5.47705 −0.267252
\(421\) −13.8651 −0.675742 −0.337871 0.941192i \(-0.609707\pi\)
−0.337871 + 0.941192i \(0.609707\pi\)
\(422\) 0.973024 0.0473661
\(423\) 18.1568 0.882811
\(424\) −4.48371 −0.217748
\(425\) −25.3239 −1.22839
\(426\) −6.17150 −0.299010
\(427\) 32.5736 1.57635
\(428\) −17.1357 −0.828283
\(429\) 9.13278 0.440935
\(430\) 31.5670 1.52229
\(431\) −5.17016 −0.249038 −0.124519 0.992217i \(-0.539739\pi\)
−0.124519 + 0.992217i \(0.539739\pi\)
\(432\) −4.62885 −0.222706
\(433\) −17.3921 −0.835812 −0.417906 0.908490i \(-0.637236\pi\)
−0.417906 + 0.908490i \(0.637236\pi\)
\(434\) −7.45291 −0.357751
\(435\) 3.75057 0.179826
\(436\) −8.95367 −0.428803
\(437\) −1.29905 −0.0621418
\(438\) −5.68687 −0.271729
\(439\) −30.9740 −1.47831 −0.739154 0.673536i \(-0.764775\pi\)
−0.739154 + 0.673536i \(0.764775\pi\)
\(440\) −4.29080 −0.204556
\(441\) 5.26819 0.250866
\(442\) 53.8431 2.56106
\(443\) −11.3353 −0.538557 −0.269278 0.963062i \(-0.586785\pi\)
−0.269278 + 0.963062i \(0.586785\pi\)
\(444\) −2.43121 −0.115380
\(445\) 16.5743 0.785695
\(446\) 18.6577 0.883470
\(447\) −7.66427 −0.362507
\(448\) −2.14877 −0.101520
\(449\) 21.6997 1.02407 0.512035 0.858964i \(-0.328892\pi\)
0.512035 + 0.858964i \(0.328892\pi\)
\(450\) 7.14959 0.337035
\(451\) −7.28830 −0.343193
\(452\) 14.9142 0.701504
\(453\) −9.56943 −0.449611
\(454\) −22.0065 −1.03282
\(455\) −42.3930 −1.98741
\(456\) 1.15394 0.0540381
\(457\) 25.3923 1.18780 0.593902 0.804537i \(-0.297587\pi\)
0.593902 + 0.804537i \(0.297587\pi\)
\(458\) −2.44656 −0.114320
\(459\) 36.2491 1.69196
\(460\) 2.86945 0.133789
\(461\) 35.7182 1.66356 0.831782 0.555102i \(-0.187321\pi\)
0.831782 + 0.555102i \(0.187321\pi\)
\(462\) 2.85422 0.132790
\(463\) −36.2088 −1.68276 −0.841382 0.540441i \(-0.818257\pi\)
−0.841382 + 0.540441i \(0.818257\pi\)
\(464\) 1.47143 0.0683096
\(465\) −8.84083 −0.409984
\(466\) 19.5105 0.903809
\(467\) −6.50101 −0.300831 −0.150415 0.988623i \(-0.548061\pi\)
−0.150415 + 0.988623i \(0.548061\pi\)
\(468\) −15.2013 −0.702680
\(469\) −10.3625 −0.478496
\(470\) 23.5647 1.08696
\(471\) −18.6571 −0.859672
\(472\) 13.2162 0.608325
\(473\) −16.4503 −0.756385
\(474\) −8.90578 −0.409056
\(475\) −4.20078 −0.192745
\(476\) 16.8273 0.771277
\(477\) −9.91317 −0.453893
\(478\) 1.62909 0.0745130
\(479\) 4.84459 0.221355 0.110678 0.993856i \(-0.464698\pi\)
0.110678 + 0.993856i \(0.464698\pi\)
\(480\) −2.54892 −0.116342
\(481\) −18.8179 −0.858022
\(482\) 3.21233 0.146318
\(483\) −1.90874 −0.0868509
\(484\) −8.76396 −0.398362
\(485\) 5.34921 0.242895
\(486\) −16.1259 −0.731488
\(487\) −15.0083 −0.680089 −0.340045 0.940409i \(-0.610442\pi\)
−0.340045 + 0.940409i \(0.610442\pi\)
\(488\) 15.1592 0.686225
\(489\) 7.53082 0.340556
\(490\) 6.83731 0.308878
\(491\) −33.5653 −1.51478 −0.757390 0.652963i \(-0.773526\pi\)
−0.757390 + 0.652963i \(0.773526\pi\)
\(492\) −4.32957 −0.195192
\(493\) −11.5230 −0.518970
\(494\) 8.93162 0.401852
\(495\) −9.48665 −0.426393
\(496\) −3.46846 −0.155738
\(497\) −14.9287 −0.669645
\(498\) −3.49977 −0.156829
\(499\) −28.2709 −1.26558 −0.632790 0.774323i \(-0.718090\pi\)
−0.632790 + 0.774323i \(0.718090\pi\)
\(500\) −5.06818 −0.226656
\(501\) −8.96065 −0.400332
\(502\) 3.13627 0.139979
\(503\) 22.9481 1.02321 0.511603 0.859222i \(-0.329052\pi\)
0.511603 + 0.859222i \(0.329052\pi\)
\(504\) −4.75078 −0.211616
\(505\) 35.8642 1.59594
\(506\) −1.49534 −0.0664759
\(507\) 30.4444 1.35208
\(508\) 7.67595 0.340565
\(509\) 8.27061 0.366589 0.183294 0.983058i \(-0.441324\pi\)
0.183294 + 0.983058i \(0.441324\pi\)
\(510\) 19.9609 0.883885
\(511\) −13.7564 −0.608548
\(512\) −1.00000 −0.0441942
\(513\) 6.01309 0.265484
\(514\) 23.5931 1.04065
\(515\) −39.0199 −1.71942
\(516\) −9.77219 −0.430197
\(517\) −12.2801 −0.540079
\(518\) −5.88105 −0.258398
\(519\) −8.35670 −0.366818
\(520\) −19.7290 −0.865173
\(521\) −13.4327 −0.588499 −0.294249 0.955729i \(-0.595070\pi\)
−0.294249 + 0.955729i \(0.595070\pi\)
\(522\) 3.25324 0.142390
\(523\) −23.0682 −1.00870 −0.504351 0.863499i \(-0.668268\pi\)
−0.504351 + 0.863499i \(0.668268\pi\)
\(524\) 1.00000 0.0436852
\(525\) −6.17239 −0.269385
\(526\) 2.85590 0.124523
\(527\) 27.1619 1.18319
\(528\) 1.32830 0.0578070
\(529\) 1.00000 0.0434783
\(530\) −12.8658 −0.558854
\(531\) 29.2201 1.26804
\(532\) 2.79135 0.121020
\(533\) −33.5114 −1.45154
\(534\) −5.13090 −0.222036
\(535\) −49.1699 −2.12580
\(536\) −4.82253 −0.208301
\(537\) −4.90523 −0.211676
\(538\) −9.48661 −0.408997
\(539\) −3.56308 −0.153473
\(540\) −13.2823 −0.571577
\(541\) −8.41824 −0.361928 −0.180964 0.983490i \(-0.557922\pi\)
−0.180964 + 0.983490i \(0.557922\pi\)
\(542\) 15.4057 0.661733
\(543\) 19.6000 0.841117
\(544\) 7.83113 0.335757
\(545\) −25.6921 −1.10053
\(546\) 13.1236 0.561639
\(547\) 7.70236 0.329329 0.164665 0.986350i \(-0.447346\pi\)
0.164665 + 0.986350i \(0.447346\pi\)
\(548\) 18.5406 0.792015
\(549\) 33.5159 1.43043
\(550\) −4.83555 −0.206188
\(551\) −1.91146 −0.0814310
\(552\) −0.888297 −0.0378084
\(553\) −21.5429 −0.916096
\(554\) 14.5217 0.616969
\(555\) −6.97625 −0.296125
\(556\) −4.23067 −0.179421
\(557\) −11.2718 −0.477602 −0.238801 0.971068i \(-0.576754\pi\)
−0.238801 + 0.971068i \(0.576754\pi\)
\(558\) −7.66851 −0.324634
\(559\) −75.6380 −3.19914
\(560\) −6.16579 −0.260552
\(561\) −10.4021 −0.439178
\(562\) 24.5581 1.03592
\(563\) −15.9068 −0.670393 −0.335196 0.942148i \(-0.608803\pi\)
−0.335196 + 0.942148i \(0.608803\pi\)
\(564\) −7.29493 −0.307172
\(565\) 42.7955 1.80042
\(566\) −3.98728 −0.167598
\(567\) −5.41704 −0.227494
\(568\) −6.94757 −0.291514
\(569\) 36.2453 1.51948 0.759742 0.650225i \(-0.225325\pi\)
0.759742 + 0.650225i \(0.225325\pi\)
\(570\) 3.31117 0.138690
\(571\) 23.7119 0.992311 0.496155 0.868234i \(-0.334745\pi\)
0.496155 + 0.868234i \(0.334745\pi\)
\(572\) 10.2812 0.429880
\(573\) 7.64798 0.319499
\(574\) −10.4731 −0.437140
\(575\) 3.23375 0.134857
\(576\) −2.21093 −0.0921221
\(577\) 9.34963 0.389230 0.194615 0.980880i \(-0.437654\pi\)
0.194615 + 0.980880i \(0.437654\pi\)
\(578\) −44.3266 −1.84374
\(579\) 2.97210 0.123516
\(580\) 4.22221 0.175318
\(581\) −8.46587 −0.351224
\(582\) −1.65596 −0.0686416
\(583\) 6.70467 0.277679
\(584\) −6.40200 −0.264917
\(585\) −43.6194 −1.80344
\(586\) −31.0884 −1.28425
\(587\) −21.2709 −0.877944 −0.438972 0.898501i \(-0.644657\pi\)
−0.438972 + 0.898501i \(0.644657\pi\)
\(588\) −2.11663 −0.0872882
\(589\) 4.50568 0.185653
\(590\) 37.9232 1.56127
\(591\) −10.8777 −0.447449
\(592\) −2.73694 −0.112488
\(593\) 16.1332 0.662509 0.331255 0.943541i \(-0.392528\pi\)
0.331255 + 0.943541i \(0.392528\pi\)
\(594\) 6.92170 0.284001
\(595\) 48.2851 1.97949
\(596\) −8.62805 −0.353419
\(597\) 9.07185 0.371286
\(598\) −6.87552 −0.281161
\(599\) 36.7174 1.50023 0.750116 0.661306i \(-0.229998\pi\)
0.750116 + 0.661306i \(0.229998\pi\)
\(600\) −2.87253 −0.117270
\(601\) −35.4335 −1.44536 −0.722681 0.691182i \(-0.757090\pi\)
−0.722681 + 0.691182i \(0.757090\pi\)
\(602\) −23.6387 −0.963442
\(603\) −10.6623 −0.434201
\(604\) −10.7728 −0.438338
\(605\) −25.1478 −1.02240
\(606\) −11.1025 −0.451008
\(607\) −1.18066 −0.0479217 −0.0239608 0.999713i \(-0.507628\pi\)
−0.0239608 + 0.999713i \(0.507628\pi\)
\(608\) 1.29905 0.0526832
\(609\) −2.80859 −0.113810
\(610\) 43.4986 1.76121
\(611\) −56.4637 −2.28428
\(612\) 17.3141 0.699880
\(613\) −2.46986 −0.0997566 −0.0498783 0.998755i \(-0.515883\pi\)
−0.0498783 + 0.998755i \(0.515883\pi\)
\(614\) −22.5804 −0.911273
\(615\) −12.4235 −0.500963
\(616\) 3.21314 0.129461
\(617\) 19.7654 0.795726 0.397863 0.917445i \(-0.369752\pi\)
0.397863 + 0.917445i \(0.369752\pi\)
\(618\) 12.0794 0.485904
\(619\) 5.19737 0.208900 0.104450 0.994530i \(-0.466692\pi\)
0.104450 + 0.994530i \(0.466692\pi\)
\(620\) −9.95256 −0.399705
\(621\) −4.62885 −0.185749
\(622\) 31.1172 1.24768
\(623\) −12.4115 −0.497257
\(624\) 6.10750 0.244496
\(625\) −30.7116 −1.22846
\(626\) 1.89128 0.0755909
\(627\) −1.72553 −0.0689109
\(628\) −21.0032 −0.838119
\(629\) 21.4333 0.854603
\(630\) −13.6321 −0.543117
\(631\) −16.4053 −0.653086 −0.326543 0.945182i \(-0.605884\pi\)
−0.326543 + 0.945182i \(0.605884\pi\)
\(632\) −10.0257 −0.398800
\(633\) −0.864334 −0.0343542
\(634\) 14.8805 0.590980
\(635\) 22.0257 0.874065
\(636\) 3.98287 0.157931
\(637\) −16.3829 −0.649116
\(638\) −2.20029 −0.0871104
\(639\) −15.3606 −0.607655
\(640\) −2.86945 −0.113425
\(641\) 16.1098 0.636300 0.318150 0.948040i \(-0.396938\pi\)
0.318150 + 0.948040i \(0.396938\pi\)
\(642\) 15.2215 0.600746
\(643\) 5.83140 0.229968 0.114984 0.993367i \(-0.463318\pi\)
0.114984 + 0.993367i \(0.463318\pi\)
\(644\) −2.14877 −0.0846734
\(645\) −28.0408 −1.10411
\(646\) −10.1730 −0.400251
\(647\) 18.5538 0.729426 0.364713 0.931120i \(-0.381167\pi\)
0.364713 + 0.931120i \(0.381167\pi\)
\(648\) −2.52100 −0.0990341
\(649\) −19.7627 −0.775754
\(650\) −22.2337 −0.872077
\(651\) 6.62040 0.259474
\(652\) 8.47783 0.332017
\(653\) −12.6599 −0.495421 −0.247710 0.968834i \(-0.579678\pi\)
−0.247710 + 0.968834i \(0.579678\pi\)
\(654\) 7.95351 0.311007
\(655\) 2.86945 0.112119
\(656\) −4.87402 −0.190298
\(657\) −14.1544 −0.552214
\(658\) −17.6463 −0.687923
\(659\) −13.8286 −0.538687 −0.269344 0.963044i \(-0.586807\pi\)
−0.269344 + 0.963044i \(0.586807\pi\)
\(660\) 3.81150 0.148363
\(661\) 36.9623 1.43767 0.718833 0.695183i \(-0.244677\pi\)
0.718833 + 0.695183i \(0.244677\pi\)
\(662\) −20.6824 −0.803844
\(663\) −47.8286 −1.85751
\(664\) −3.93987 −0.152897
\(665\) 8.00964 0.310600
\(666\) −6.05118 −0.234478
\(667\) 1.47143 0.0569742
\(668\) −10.0875 −0.390295
\(669\) −16.5736 −0.640773
\(670\) −13.8380 −0.534609
\(671\) −22.6681 −0.875094
\(672\) 1.90874 0.0736314
\(673\) −39.0563 −1.50551 −0.752755 0.658300i \(-0.771276\pi\)
−0.752755 + 0.658300i \(0.771276\pi\)
\(674\) −20.1008 −0.774252
\(675\) −14.9685 −0.576139
\(676\) 34.2728 1.31819
\(677\) −3.90091 −0.149924 −0.0749621 0.997186i \(-0.523884\pi\)
−0.0749621 + 0.997186i \(0.523884\pi\)
\(678\) −13.2482 −0.508794
\(679\) −4.00572 −0.153725
\(680\) 22.4710 0.861725
\(681\) 19.5483 0.749092
\(682\) 5.18652 0.198602
\(683\) −22.1783 −0.848629 −0.424314 0.905515i \(-0.639485\pi\)
−0.424314 + 0.905515i \(0.639485\pi\)
\(684\) 2.87210 0.109817
\(685\) 53.2013 2.03272
\(686\) −20.1615 −0.769768
\(687\) 2.17327 0.0829153
\(688\) −11.0010 −0.419411
\(689\) 30.8279 1.17445
\(690\) −2.54892 −0.0970358
\(691\) −11.3886 −0.433241 −0.216621 0.976256i \(-0.569503\pi\)
−0.216621 + 0.976256i \(0.569503\pi\)
\(692\) −9.40755 −0.357621
\(693\) 7.10402 0.269859
\(694\) −2.12514 −0.0806693
\(695\) −12.1397 −0.460486
\(696\) −1.30707 −0.0495444
\(697\) 38.1690 1.44576
\(698\) 7.05857 0.267171
\(699\) −17.3312 −0.655524
\(700\) −6.94857 −0.262631
\(701\) −20.5642 −0.776697 −0.388349 0.921512i \(-0.626954\pi\)
−0.388349 + 0.921512i \(0.626954\pi\)
\(702\) 31.8258 1.20119
\(703\) 3.55541 0.134095
\(704\) 1.49534 0.0563577
\(705\) −20.9324 −0.788362
\(706\) −33.8595 −1.27432
\(707\) −26.8567 −1.01005
\(708\) −11.7399 −0.441213
\(709\) −35.5163 −1.33384 −0.666921 0.745128i \(-0.732388\pi\)
−0.666921 + 0.745128i \(0.732388\pi\)
\(710\) −19.9357 −0.748174
\(711\) −22.1661 −0.831293
\(712\) −5.77611 −0.216469
\(713\) −3.46846 −0.129895
\(714\) −14.9476 −0.559401
\(715\) 29.5015 1.10329
\(716\) −5.52206 −0.206369
\(717\) −1.44712 −0.0540436
\(718\) 18.6806 0.697153
\(719\) 6.76104 0.252144 0.126072 0.992021i \(-0.459763\pi\)
0.126072 + 0.992021i \(0.459763\pi\)
\(720\) −6.34415 −0.236433
\(721\) 29.2198 1.08820
\(722\) 17.3125 0.644304
\(723\) −2.85350 −0.106123
\(724\) 22.0647 0.820029
\(725\) 4.75825 0.176717
\(726\) 7.78500 0.288928
\(727\) −37.4105 −1.38748 −0.693740 0.720226i \(-0.744038\pi\)
−0.693740 + 0.720226i \(0.744038\pi\)
\(728\) 14.7739 0.547557
\(729\) 6.76163 0.250431
\(730\) −18.3702 −0.679912
\(731\) 86.1506 3.18640
\(732\) −13.4659 −0.497713
\(733\) −2.66065 −0.0982733 −0.0491366 0.998792i \(-0.515647\pi\)
−0.0491366 + 0.998792i \(0.515647\pi\)
\(734\) −23.7765 −0.877607
\(735\) −6.07355 −0.224026
\(736\) −1.00000 −0.0368605
\(737\) 7.21131 0.265632
\(738\) −10.7761 −0.396674
\(739\) 10.1172 0.372167 0.186084 0.982534i \(-0.440420\pi\)
0.186084 + 0.982534i \(0.440420\pi\)
\(740\) −7.85351 −0.288701
\(741\) −7.93392 −0.291460
\(742\) 9.63446 0.353692
\(743\) 29.0855 1.06704 0.533521 0.845787i \(-0.320868\pi\)
0.533521 + 0.845787i \(0.320868\pi\)
\(744\) 3.08102 0.112956
\(745\) −24.7578 −0.907055
\(746\) −14.5702 −0.533453
\(747\) −8.71078 −0.318711
\(748\) −11.7102 −0.428167
\(749\) 36.8206 1.34539
\(750\) 4.50204 0.164391
\(751\) −38.4742 −1.40395 −0.701973 0.712204i \(-0.747697\pi\)
−0.701973 + 0.712204i \(0.747697\pi\)
\(752\) −8.21227 −0.299471
\(753\) −2.78594 −0.101525
\(754\) −10.1169 −0.368435
\(755\) −30.9120 −1.12500
\(756\) 9.94633 0.361745
\(757\) −21.1410 −0.768381 −0.384191 0.923254i \(-0.625519\pi\)
−0.384191 + 0.923254i \(0.625519\pi\)
\(758\) 29.3309 1.06535
\(759\) 1.32830 0.0482144
\(760\) 3.72755 0.135212
\(761\) 38.5314 1.39676 0.698381 0.715726i \(-0.253904\pi\)
0.698381 + 0.715726i \(0.253904\pi\)
\(762\) −6.81852 −0.247009
\(763\) 19.2394 0.696512
\(764\) 8.60972 0.311489
\(765\) 49.6819 1.79625
\(766\) −4.49489 −0.162407
\(767\) −90.8683 −3.28106
\(768\) 0.888297 0.0320536
\(769\) 37.6293 1.35695 0.678474 0.734625i \(-0.262642\pi\)
0.678474 + 0.734625i \(0.262642\pi\)
\(770\) 9.21994 0.332263
\(771\) −20.9577 −0.754773
\(772\) 3.34585 0.120420
\(773\) 38.6786 1.39117 0.695586 0.718442i \(-0.255145\pi\)
0.695586 + 0.718442i \(0.255145\pi\)
\(774\) −24.3225 −0.874256
\(775\) −11.2161 −0.402895
\(776\) −1.86419 −0.0669207
\(777\) 5.22412 0.187414
\(778\) −9.33414 −0.334645
\(779\) 6.33157 0.226852
\(780\) 17.5252 0.627502
\(781\) 10.3890 0.371747
\(782\) 7.83113 0.280041
\(783\) −6.81105 −0.243407
\(784\) −2.38279 −0.0850997
\(785\) −60.2676 −2.15104
\(786\) −0.888297 −0.0316845
\(787\) 0.621240 0.0221448 0.0110724 0.999939i \(-0.496475\pi\)
0.0110724 + 0.999939i \(0.496475\pi\)
\(788\) −12.2456 −0.436231
\(789\) −2.53689 −0.0903157
\(790\) −28.7682 −1.02353
\(791\) −32.0471 −1.13946
\(792\) 3.30609 0.117477
\(793\) −104.227 −3.70123
\(794\) −11.3514 −0.402845
\(795\) 11.4286 0.405332
\(796\) 10.2126 0.361977
\(797\) −49.1968 −1.74264 −0.871320 0.490716i \(-0.836735\pi\)
−0.871320 + 0.490716i \(0.836735\pi\)
\(798\) −2.47954 −0.0877749
\(799\) 64.3114 2.27517
\(800\) −3.23375 −0.114330
\(801\) −12.7706 −0.451226
\(802\) −5.72551 −0.202175
\(803\) 9.57316 0.337829
\(804\) 4.28383 0.151079
\(805\) −6.16579 −0.217315
\(806\) 23.8475 0.839991
\(807\) 8.42693 0.296642
\(808\) −12.4986 −0.439701
\(809\) −4.30605 −0.151393 −0.0756964 0.997131i \(-0.524118\pi\)
−0.0756964 + 0.997131i \(0.524118\pi\)
\(810\) −7.23387 −0.254172
\(811\) 10.5130 0.369161 0.184581 0.982817i \(-0.440907\pi\)
0.184581 + 0.982817i \(0.440907\pi\)
\(812\) −3.16177 −0.110956
\(813\) −13.6849 −0.479949
\(814\) 4.09265 0.143447
\(815\) 24.3267 0.852127
\(816\) −6.95636 −0.243521
\(817\) 14.2909 0.499974
\(818\) 17.5673 0.614228
\(819\) 32.6641 1.14137
\(820\) −13.9857 −0.488403
\(821\) −14.8357 −0.517769 −0.258885 0.965908i \(-0.583355\pi\)
−0.258885 + 0.965908i \(0.583355\pi\)
\(822\) −16.4696 −0.574442
\(823\) −10.0718 −0.351083 −0.175541 0.984472i \(-0.556168\pi\)
−0.175541 + 0.984472i \(0.556168\pi\)
\(824\) 13.5984 0.473722
\(825\) 4.29540 0.149547
\(826\) −28.3986 −0.988112
\(827\) −40.8248 −1.41962 −0.709809 0.704395i \(-0.751219\pi\)
−0.709809 + 0.704395i \(0.751219\pi\)
\(828\) −2.21093 −0.0768351
\(829\) 27.6272 0.959533 0.479766 0.877396i \(-0.340721\pi\)
0.479766 + 0.877396i \(0.340721\pi\)
\(830\) −11.3053 −0.392412
\(831\) −12.8996 −0.447482
\(832\) 6.87552 0.238366
\(833\) 18.6600 0.646529
\(834\) 3.75809 0.130132
\(835\) −28.9454 −1.00170
\(836\) −1.94251 −0.0671832
\(837\) 16.0550 0.554941
\(838\) −11.5650 −0.399505
\(839\) −23.3755 −0.807012 −0.403506 0.914977i \(-0.632209\pi\)
−0.403506 + 0.914977i \(0.632209\pi\)
\(840\) 5.47705 0.188976
\(841\) −26.8349 −0.925341
\(842\) 13.8651 0.477822
\(843\) −21.8149 −0.751344
\(844\) −0.973024 −0.0334929
\(845\) 98.3441 3.38314
\(846\) −18.1568 −0.624242
\(847\) 18.8317 0.647066
\(848\) 4.48371 0.153971
\(849\) 3.54189 0.121557
\(850\) 25.3239 0.868602
\(851\) −2.73694 −0.0938211
\(852\) 6.17150 0.211432
\(853\) −49.3008 −1.68803 −0.844014 0.536321i \(-0.819814\pi\)
−0.844014 + 0.536321i \(0.819814\pi\)
\(854\) −32.5736 −1.11465
\(855\) 8.24134 0.281848
\(856\) 17.1357 0.585685
\(857\) 8.78162 0.299975 0.149987 0.988688i \(-0.452077\pi\)
0.149987 + 0.988688i \(0.452077\pi\)
\(858\) −9.13278 −0.311788
\(859\) −57.7972 −1.97202 −0.986008 0.166701i \(-0.946689\pi\)
−0.986008 + 0.166701i \(0.946689\pi\)
\(860\) −31.5670 −1.07642
\(861\) 9.30325 0.317054
\(862\) 5.17016 0.176096
\(863\) −28.6663 −0.975812 −0.487906 0.872896i \(-0.662239\pi\)
−0.487906 + 0.872896i \(0.662239\pi\)
\(864\) 4.62885 0.157477
\(865\) −26.9945 −0.917841
\(866\) 17.3921 0.591009
\(867\) 39.3751 1.33725
\(868\) 7.45291 0.252968
\(869\) 14.9918 0.508561
\(870\) −3.75057 −0.127156
\(871\) 33.1574 1.12350
\(872\) 8.95367 0.303210
\(873\) −4.12160 −0.139495
\(874\) 1.29905 0.0439409
\(875\) 10.8903 0.368161
\(876\) 5.68687 0.192142
\(877\) 22.9529 0.775063 0.387532 0.921856i \(-0.373328\pi\)
0.387532 + 0.921856i \(0.373328\pi\)
\(878\) 30.9740 1.04532
\(879\) 27.6157 0.931455
\(880\) 4.29080 0.144643
\(881\) 11.3285 0.381665 0.190833 0.981623i \(-0.438881\pi\)
0.190833 + 0.981623i \(0.438881\pi\)
\(882\) −5.26819 −0.177389
\(883\) −10.5768 −0.355939 −0.177970 0.984036i \(-0.556953\pi\)
−0.177970 + 0.984036i \(0.556953\pi\)
\(884\) −53.8431 −1.81094
\(885\) −33.6871 −1.13238
\(886\) 11.3353 0.380817
\(887\) 15.3868 0.516639 0.258319 0.966060i \(-0.416831\pi\)
0.258319 + 0.966060i \(0.416831\pi\)
\(888\) 2.43121 0.0815862
\(889\) −16.4938 −0.553185
\(890\) −16.5743 −0.555571
\(891\) 3.76974 0.126291
\(892\) −18.6577 −0.624707
\(893\) 10.6681 0.356995
\(894\) 7.66427 0.256332
\(895\) −15.8453 −0.529649
\(896\) 2.14877 0.0717853
\(897\) 6.10750 0.203924
\(898\) −21.6997 −0.724128
\(899\) −5.10361 −0.170215
\(900\) −7.14959 −0.238320
\(901\) −35.1125 −1.16977
\(902\) 7.28830 0.242674
\(903\) 20.9982 0.698776
\(904\) −14.9142 −0.496038
\(905\) 63.3136 2.10462
\(906\) 9.56943 0.317923
\(907\) 16.0984 0.534540 0.267270 0.963622i \(-0.413878\pi\)
0.267270 + 0.963622i \(0.413878\pi\)
\(908\) 22.0065 0.730311
\(909\) −27.6336 −0.916549
\(910\) 42.3930 1.40531
\(911\) −41.5425 −1.37636 −0.688182 0.725538i \(-0.741591\pi\)
−0.688182 + 0.725538i \(0.741591\pi\)
\(912\) −1.15394 −0.0382107
\(913\) 5.89144 0.194978
\(914\) −25.3923 −0.839904
\(915\) −38.6397 −1.27739
\(916\) 2.44656 0.0808365
\(917\) −2.14877 −0.0709586
\(918\) −36.2491 −1.19640
\(919\) −13.2529 −0.437173 −0.218586 0.975818i \(-0.570145\pi\)
−0.218586 + 0.975818i \(0.570145\pi\)
\(920\) −2.86945 −0.0946030
\(921\) 20.0581 0.660938
\(922\) −35.7182 −1.17632
\(923\) 47.7682 1.57231
\(924\) −2.85422 −0.0938969
\(925\) −8.85057 −0.291005
\(926\) 36.2088 1.18989
\(927\) 30.0650 0.987465
\(928\) −1.47143 −0.0483022
\(929\) −7.76446 −0.254744 −0.127372 0.991855i \(-0.540654\pi\)
−0.127372 + 0.991855i \(0.540654\pi\)
\(930\) 8.84083 0.289902
\(931\) 3.09536 0.101446
\(932\) −19.5105 −0.639089
\(933\) −27.6413 −0.904935
\(934\) 6.50101 0.212719
\(935\) −33.6018 −1.09890
\(936\) 15.2013 0.496870
\(937\) −7.15902 −0.233875 −0.116938 0.993139i \(-0.537308\pi\)
−0.116938 + 0.993139i \(0.537308\pi\)
\(938\) 10.3625 0.338347
\(939\) −1.68002 −0.0548254
\(940\) −23.5647 −0.768596
\(941\) 45.9779 1.49884 0.749418 0.662097i \(-0.230334\pi\)
0.749418 + 0.662097i \(0.230334\pi\)
\(942\) 18.6571 0.607880
\(943\) −4.87402 −0.158720
\(944\) −13.2162 −0.430151
\(945\) 28.5405 0.928423
\(946\) 16.4503 0.534845
\(947\) 4.68722 0.152314 0.0761571 0.997096i \(-0.475735\pi\)
0.0761571 + 0.997096i \(0.475735\pi\)
\(948\) 8.90578 0.289246
\(949\) 44.0171 1.42886
\(950\) 4.20078 0.136291
\(951\) −13.2183 −0.428632
\(952\) −16.8273 −0.545375
\(953\) 48.2781 1.56388 0.781940 0.623354i \(-0.214230\pi\)
0.781940 + 0.623354i \(0.214230\pi\)
\(954\) 9.91317 0.320951
\(955\) 24.7052 0.799440
\(956\) −1.62909 −0.0526886
\(957\) 1.95451 0.0631804
\(958\) −4.84459 −0.156522
\(959\) −39.8395 −1.28648
\(960\) 2.54892 0.0822661
\(961\) −18.9698 −0.611929
\(962\) 18.8179 0.606713
\(963\) 37.8857 1.22085
\(964\) −3.21233 −0.103462
\(965\) 9.60074 0.309059
\(966\) 1.90874 0.0614128
\(967\) 32.1640 1.03432 0.517162 0.855888i \(-0.326988\pi\)
0.517162 + 0.855888i \(0.326988\pi\)
\(968\) 8.76396 0.281684
\(969\) 9.03663 0.290298
\(970\) −5.34921 −0.171753
\(971\) 32.0340 1.02802 0.514009 0.857785i \(-0.328160\pi\)
0.514009 + 0.857785i \(0.328160\pi\)
\(972\) 16.1259 0.517240
\(973\) 9.09074 0.291436
\(974\) 15.0083 0.480896
\(975\) 19.7501 0.632510
\(976\) −15.1592 −0.485234
\(977\) 28.6881 0.917813 0.458906 0.888485i \(-0.348241\pi\)
0.458906 + 0.888485i \(0.348241\pi\)
\(978\) −7.53082 −0.240809
\(979\) 8.63724 0.276047
\(980\) −6.83731 −0.218410
\(981\) 19.7959 0.632035
\(982\) 33.5653 1.07111
\(983\) −31.5071 −1.00492 −0.502460 0.864601i \(-0.667571\pi\)
−0.502460 + 0.864601i \(0.667571\pi\)
\(984\) 4.32957 0.138022
\(985\) −35.1381 −1.11959
\(986\) 11.5230 0.366967
\(987\) 15.6751 0.498945
\(988\) −8.93162 −0.284153
\(989\) −11.0010 −0.349813
\(990\) 9.48665 0.301506
\(991\) 54.0970 1.71845 0.859224 0.511599i \(-0.170947\pi\)
0.859224 + 0.511599i \(0.170947\pi\)
\(992\) 3.46846 0.110124
\(993\) 18.3721 0.583021
\(994\) 14.9287 0.473510
\(995\) 29.3046 0.929020
\(996\) 3.49977 0.110895
\(997\) −14.0064 −0.443586 −0.221793 0.975094i \(-0.571191\pi\)
−0.221793 + 0.975094i \(0.571191\pi\)
\(998\) 28.2709 0.894900
\(999\) 12.6689 0.400826
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 \(a_p\))