Properties

Label 8007.2.a.e.1.12
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.58086 q^{2}\) \(+1.00000 q^{3}\) \(+0.499118 q^{4}\) \(-3.53760 q^{5}\) \(-1.58086 q^{6}\) \(-3.85230 q^{7}\) \(+2.37268 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.58086 q^{2}\) \(+1.00000 q^{3}\) \(+0.499118 q^{4}\) \(-3.53760 q^{5}\) \(-1.58086 q^{6}\) \(-3.85230 q^{7}\) \(+2.37268 q^{8}\) \(+1.00000 q^{9}\) \(+5.59245 q^{10}\) \(-4.80037 q^{11}\) \(+0.499118 q^{12}\) \(+2.42528 q^{13}\) \(+6.08995 q^{14}\) \(-3.53760 q^{15}\) \(-4.74912 q^{16}\) \(-1.00000 q^{17}\) \(-1.58086 q^{18}\) \(+1.75486 q^{19}\) \(-1.76568 q^{20}\) \(-3.85230 q^{21}\) \(+7.58871 q^{22}\) \(-7.27500 q^{23}\) \(+2.37268 q^{24}\) \(+7.51462 q^{25}\) \(-3.83402 q^{26}\) \(+1.00000 q^{27}\) \(-1.92275 q^{28}\) \(-1.01319 q^{29}\) \(+5.59245 q^{30}\) \(-0.736752 q^{31}\) \(+2.76232 q^{32}\) \(-4.80037 q^{33}\) \(+1.58086 q^{34}\) \(+13.6279 q^{35}\) \(+0.499118 q^{36}\) \(+0.762412 q^{37}\) \(-2.77418 q^{38}\) \(+2.42528 q^{39}\) \(-8.39361 q^{40}\) \(+4.24448 q^{41}\) \(+6.08995 q^{42}\) \(+7.99270 q^{43}\) \(-2.39595 q^{44}\) \(-3.53760 q^{45}\) \(+11.5007 q^{46}\) \(+11.0591 q^{47}\) \(-4.74912 q^{48}\) \(+7.84022 q^{49}\) \(-11.8796 q^{50}\) \(-1.00000 q^{51}\) \(+1.21050 q^{52}\) \(-7.96423 q^{53}\) \(-1.58086 q^{54}\) \(+16.9818 q^{55}\) \(-9.14029 q^{56}\) \(+1.75486 q^{57}\) \(+1.60171 q^{58}\) \(+0.229221 q^{59}\) \(-1.76568 q^{60}\) \(+7.63803 q^{61}\) \(+1.16470 q^{62}\) \(-3.85230 q^{63}\) \(+5.13139 q^{64}\) \(-8.57966 q^{65}\) \(+7.58871 q^{66}\) \(+2.68683 q^{67}\) \(-0.499118 q^{68}\) \(-7.27500 q^{69}\) \(-21.5438 q^{70}\) \(+5.96838 q^{71}\) \(+2.37268 q^{72}\) \(-5.15619 q^{73}\) \(-1.20527 q^{74}\) \(+7.51462 q^{75}\) \(+0.875880 q^{76}\) \(+18.4925 q^{77}\) \(-3.83402 q^{78}\) \(+3.52278 q^{79}\) \(+16.8005 q^{80}\) \(+1.00000 q^{81}\) \(-6.70993 q^{82}\) \(-3.41706 q^{83}\) \(-1.92275 q^{84}\) \(+3.53760 q^{85}\) \(-12.6353 q^{86}\) \(-1.01319 q^{87}\) \(-11.3898 q^{88}\) \(+5.27093 q^{89}\) \(+5.59245 q^{90}\) \(-9.34290 q^{91}\) \(-3.63108 q^{92}\) \(-0.736752 q^{93}\) \(-17.4830 q^{94}\) \(-6.20798 q^{95}\) \(+2.76232 q^{96}\) \(-9.65063 q^{97}\) \(-12.3943 q^{98}\) \(-4.80037 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 43q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 19q^{15} \) \(\mathstrut +\mathstrut 33q^{16} \) \(\mathstrut -\mathstrut 46q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 56q^{20} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 64q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 11q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut +\mathstrut 46q^{27} \) \(\mathstrut -\mathstrut 38q^{28} \) \(\mathstrut -\mathstrut 51q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 19q^{31} \) \(\mathstrut -\mathstrut 61q^{32} \) \(\mathstrut -\mathstrut 25q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 39q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut -\mathstrut 48q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 53q^{41} \) \(\mathstrut -\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 33q^{43} \) \(\mathstrut -\mathstrut 62q^{44} \) \(\mathstrut -\mathstrut 19q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 45q^{47} \) \(\mathstrut +\mathstrut 33q^{48} \) \(\mathstrut +\mathstrut 21q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 63q^{52} \) \(\mathstrut -\mathstrut 47q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 82q^{56} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 21q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 74q^{64} \) \(\mathstrut -\mathstrut 85q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut -\mathstrut 52q^{67} \) \(\mathstrut -\mathstrut 43q^{68} \) \(\mathstrut -\mathstrut 64q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 48q^{71} \) \(\mathstrut -\mathstrut 18q^{72} \) \(\mathstrut -\mathstrut 39q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 42q^{76} \) \(\mathstrut -\mathstrut 78q^{77} \) \(\mathstrut -\mathstrut 13q^{78} \) \(\mathstrut -\mathstrut 26q^{79} \) \(\mathstrut -\mathstrut 78q^{80} \) \(\mathstrut +\mathstrut 46q^{81} \) \(\mathstrut +\mathstrut 3q^{82} \) \(\mathstrut -\mathstrut 47q^{83} \) \(\mathstrut -\mathstrut 38q^{84} \) \(\mathstrut +\mathstrut 19q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 51q^{87} \) \(\mathstrut -\mathstrut 58q^{88} \) \(\mathstrut -\mathstrut 58q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 43q^{91} \) \(\mathstrut -\mathstrut 68q^{92} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 78q^{95} \) \(\mathstrut -\mathstrut 61q^{96} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 25q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.58086 −1.11784 −0.558918 0.829223i \(-0.688784\pi\)
−0.558918 + 0.829223i \(0.688784\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.499118 0.249559
\(5\) −3.53760 −1.58206 −0.791032 0.611775i \(-0.790456\pi\)
−0.791032 + 0.611775i \(0.790456\pi\)
\(6\) −1.58086 −0.645383
\(7\) −3.85230 −1.45603 −0.728016 0.685560i \(-0.759558\pi\)
−0.728016 + 0.685560i \(0.759558\pi\)
\(8\) 2.37268 0.838870
\(9\) 1.00000 0.333333
\(10\) 5.59245 1.76849
\(11\) −4.80037 −1.44737 −0.723683 0.690133i \(-0.757552\pi\)
−0.723683 + 0.690133i \(0.757552\pi\)
\(12\) 0.499118 0.144083
\(13\) 2.42528 0.672651 0.336326 0.941746i \(-0.390816\pi\)
0.336326 + 0.941746i \(0.390816\pi\)
\(14\) 6.08995 1.62761
\(15\) −3.53760 −0.913405
\(16\) −4.74912 −1.18728
\(17\) −1.00000 −0.242536
\(18\) −1.58086 −0.372612
\(19\) 1.75486 0.402591 0.201296 0.979531i \(-0.435485\pi\)
0.201296 + 0.979531i \(0.435485\pi\)
\(20\) −1.76568 −0.394818
\(21\) −3.85230 −0.840641
\(22\) 7.58871 1.61792
\(23\) −7.27500 −1.51694 −0.758471 0.651707i \(-0.774053\pi\)
−0.758471 + 0.651707i \(0.774053\pi\)
\(24\) 2.37268 0.484322
\(25\) 7.51462 1.50292
\(26\) −3.83402 −0.751914
\(27\) 1.00000 0.192450
\(28\) −1.92275 −0.363366
\(29\) −1.01319 −0.188145 −0.0940725 0.995565i \(-0.529989\pi\)
−0.0940725 + 0.995565i \(0.529989\pi\)
\(30\) 5.59245 1.02104
\(31\) −0.736752 −0.132325 −0.0661623 0.997809i \(-0.521076\pi\)
−0.0661623 + 0.997809i \(0.521076\pi\)
\(32\) 2.76232 0.488314
\(33\) −4.80037 −0.835637
\(34\) 1.58086 0.271115
\(35\) 13.6279 2.30354
\(36\) 0.499118 0.0831864
\(37\) 0.762412 0.125340 0.0626699 0.998034i \(-0.480038\pi\)
0.0626699 + 0.998034i \(0.480038\pi\)
\(38\) −2.77418 −0.450031
\(39\) 2.42528 0.388355
\(40\) −8.39361 −1.32715
\(41\) 4.24448 0.662876 0.331438 0.943477i \(-0.392466\pi\)
0.331438 + 0.943477i \(0.392466\pi\)
\(42\) 6.08995 0.939699
\(43\) 7.99270 1.21888 0.609438 0.792834i \(-0.291395\pi\)
0.609438 + 0.792834i \(0.291395\pi\)
\(44\) −2.39595 −0.361203
\(45\) −3.53760 −0.527354
\(46\) 11.5007 1.69569
\(47\) 11.0591 1.61314 0.806571 0.591137i \(-0.201321\pi\)
0.806571 + 0.591137i \(0.201321\pi\)
\(48\) −4.74912 −0.685476
\(49\) 7.84022 1.12003
\(50\) −11.8796 −1.68002
\(51\) −1.00000 −0.140028
\(52\) 1.21050 0.167866
\(53\) −7.96423 −1.09397 −0.546985 0.837142i \(-0.684225\pi\)
−0.546985 + 0.837142i \(0.684225\pi\)
\(54\) −1.58086 −0.215128
\(55\) 16.9818 2.28982
\(56\) −9.14029 −1.22142
\(57\) 1.75486 0.232436
\(58\) 1.60171 0.210315
\(59\) 0.229221 0.0298421 0.0149210 0.999889i \(-0.495250\pi\)
0.0149210 + 0.999889i \(0.495250\pi\)
\(60\) −1.76568 −0.227948
\(61\) 7.63803 0.977950 0.488975 0.872298i \(-0.337371\pi\)
0.488975 + 0.872298i \(0.337371\pi\)
\(62\) 1.16470 0.147917
\(63\) −3.85230 −0.485344
\(64\) 5.13139 0.641424
\(65\) −8.57966 −1.06418
\(66\) 7.58871 0.934106
\(67\) 2.68683 0.328249 0.164124 0.986440i \(-0.447520\pi\)
0.164124 + 0.986440i \(0.447520\pi\)
\(68\) −0.499118 −0.0605270
\(69\) −7.27500 −0.875807
\(70\) −21.5438 −2.57498
\(71\) 5.96838 0.708317 0.354158 0.935185i \(-0.384767\pi\)
0.354158 + 0.935185i \(0.384767\pi\)
\(72\) 2.37268 0.279623
\(73\) −5.15619 −0.603487 −0.301743 0.953389i \(-0.597569\pi\)
−0.301743 + 0.953389i \(0.597569\pi\)
\(74\) −1.20527 −0.140109
\(75\) 7.51462 0.867713
\(76\) 0.875880 0.100470
\(77\) 18.4925 2.10741
\(78\) −3.83402 −0.434118
\(79\) 3.52278 0.396343 0.198172 0.980167i \(-0.436500\pi\)
0.198172 + 0.980167i \(0.436500\pi\)
\(80\) 16.8005 1.87835
\(81\) 1.00000 0.111111
\(82\) −6.70993 −0.740988
\(83\) −3.41706 −0.375071 −0.187535 0.982258i \(-0.560050\pi\)
−0.187535 + 0.982258i \(0.560050\pi\)
\(84\) −1.92275 −0.209790
\(85\) 3.53760 0.383707
\(86\) −12.6353 −1.36250
\(87\) −1.01319 −0.108626
\(88\) −11.3898 −1.21415
\(89\) 5.27093 0.558717 0.279359 0.960187i \(-0.409878\pi\)
0.279359 + 0.960187i \(0.409878\pi\)
\(90\) 5.59245 0.589496
\(91\) −9.34290 −0.979402
\(92\) −3.63108 −0.378567
\(93\) −0.736752 −0.0763976
\(94\) −17.4830 −1.80323
\(95\) −6.20798 −0.636925
\(96\) 2.76232 0.281928
\(97\) −9.65063 −0.979873 −0.489937 0.871758i \(-0.662980\pi\)
−0.489937 + 0.871758i \(0.662980\pi\)
\(98\) −12.3943 −1.25201
\(99\) −4.80037 −0.482455
\(100\) 3.75068 0.375068
\(101\) 15.7385 1.56604 0.783021 0.621995i \(-0.213678\pi\)
0.783021 + 0.621995i \(0.213678\pi\)
\(102\) 1.58086 0.156528
\(103\) −9.19924 −0.906428 −0.453214 0.891402i \(-0.649723\pi\)
−0.453214 + 0.891402i \(0.649723\pi\)
\(104\) 5.75442 0.564267
\(105\) 13.6279 1.32995
\(106\) 12.5903 1.22288
\(107\) −5.65567 −0.546754 −0.273377 0.961907i \(-0.588141\pi\)
−0.273377 + 0.961907i \(0.588141\pi\)
\(108\) 0.499118 0.0480277
\(109\) 0.761443 0.0729330 0.0364665 0.999335i \(-0.488390\pi\)
0.0364665 + 0.999335i \(0.488390\pi\)
\(110\) −26.8458 −2.55965
\(111\) 0.762412 0.0723650
\(112\) 18.2950 1.72872
\(113\) −5.95512 −0.560210 −0.280105 0.959969i \(-0.590369\pi\)
−0.280105 + 0.959969i \(0.590369\pi\)
\(114\) −2.77418 −0.259826
\(115\) 25.7360 2.39990
\(116\) −0.505703 −0.0469533
\(117\) 2.42528 0.224217
\(118\) −0.362367 −0.0333586
\(119\) 3.85230 0.353140
\(120\) −8.39361 −0.766228
\(121\) 12.0435 1.09487
\(122\) −12.0747 −1.09319
\(123\) 4.24448 0.382712
\(124\) −0.367726 −0.0330228
\(125\) −8.89571 −0.795657
\(126\) 6.08995 0.542536
\(127\) 10.5579 0.936862 0.468431 0.883500i \(-0.344819\pi\)
0.468431 + 0.883500i \(0.344819\pi\)
\(128\) −13.6367 −1.20532
\(129\) 7.99270 0.703718
\(130\) 13.5632 1.18958
\(131\) −13.8248 −1.20788 −0.603941 0.797029i \(-0.706404\pi\)
−0.603941 + 0.797029i \(0.706404\pi\)
\(132\) −2.39595 −0.208541
\(133\) −6.76023 −0.586186
\(134\) −4.24750 −0.366928
\(135\) −3.53760 −0.304468
\(136\) −2.37268 −0.203456
\(137\) 15.3289 1.30964 0.654819 0.755786i \(-0.272745\pi\)
0.654819 + 0.755786i \(0.272745\pi\)
\(138\) 11.5007 0.979009
\(139\) −8.01914 −0.680175 −0.340087 0.940394i \(-0.610457\pi\)
−0.340087 + 0.940394i \(0.610457\pi\)
\(140\) 6.80194 0.574869
\(141\) 11.0591 0.931348
\(142\) −9.43518 −0.791782
\(143\) −11.6422 −0.973572
\(144\) −4.74912 −0.395760
\(145\) 3.58427 0.297657
\(146\) 8.15122 0.674600
\(147\) 7.84022 0.646651
\(148\) 0.380534 0.0312797
\(149\) −4.63856 −0.380006 −0.190003 0.981784i \(-0.560850\pi\)
−0.190003 + 0.981784i \(0.560850\pi\)
\(150\) −11.8796 −0.969962
\(151\) 11.1849 0.910216 0.455108 0.890436i \(-0.349601\pi\)
0.455108 + 0.890436i \(0.349601\pi\)
\(152\) 4.16372 0.337722
\(153\) −1.00000 −0.0808452
\(154\) −29.2340 −2.35574
\(155\) 2.60633 0.209346
\(156\) 1.21050 0.0969176
\(157\) 1.00000 0.0798087
\(158\) −5.56902 −0.443047
\(159\) −7.96423 −0.631604
\(160\) −9.77199 −0.772544
\(161\) 28.0255 2.20872
\(162\) −1.58086 −0.124204
\(163\) 12.6969 0.994499 0.497249 0.867608i \(-0.334343\pi\)
0.497249 + 0.867608i \(0.334343\pi\)
\(164\) 2.11850 0.165427
\(165\) 16.9818 1.32203
\(166\) 5.40189 0.419268
\(167\) 12.7587 0.987299 0.493649 0.869661i \(-0.335663\pi\)
0.493649 + 0.869661i \(0.335663\pi\)
\(168\) −9.14029 −0.705189
\(169\) −7.11803 −0.547541
\(170\) −5.59245 −0.428921
\(171\) 1.75486 0.134197
\(172\) 3.98930 0.304182
\(173\) −18.0809 −1.37467 −0.687333 0.726342i \(-0.741219\pi\)
−0.687333 + 0.726342i \(0.741219\pi\)
\(174\) 1.60171 0.121426
\(175\) −28.9486 −2.18831
\(176\) 22.7975 1.71843
\(177\) 0.229221 0.0172293
\(178\) −8.33260 −0.624555
\(179\) −8.85007 −0.661485 −0.330743 0.943721i \(-0.607299\pi\)
−0.330743 + 0.943721i \(0.607299\pi\)
\(180\) −1.76568 −0.131606
\(181\) 20.5968 1.53095 0.765473 0.643468i \(-0.222505\pi\)
0.765473 + 0.643468i \(0.222505\pi\)
\(182\) 14.7698 1.09481
\(183\) 7.63803 0.564620
\(184\) −17.2613 −1.27252
\(185\) −2.69711 −0.198295
\(186\) 1.16470 0.0854001
\(187\) 4.80037 0.351038
\(188\) 5.51982 0.402574
\(189\) −3.85230 −0.280214
\(190\) 9.81394 0.711978
\(191\) −14.1872 −1.02655 −0.513275 0.858224i \(-0.671568\pi\)
−0.513275 + 0.858224i \(0.671568\pi\)
\(192\) 5.13139 0.370326
\(193\) 1.19405 0.0859493 0.0429747 0.999076i \(-0.486317\pi\)
0.0429747 + 0.999076i \(0.486317\pi\)
\(194\) 15.2563 1.09534
\(195\) −8.57966 −0.614402
\(196\) 3.91320 0.279514
\(197\) 11.6432 0.829542 0.414771 0.909926i \(-0.363862\pi\)
0.414771 + 0.909926i \(0.363862\pi\)
\(198\) 7.58871 0.539306
\(199\) 12.0052 0.851028 0.425514 0.904952i \(-0.360093\pi\)
0.425514 + 0.904952i \(0.360093\pi\)
\(200\) 17.8298 1.26076
\(201\) 2.68683 0.189514
\(202\) −24.8804 −1.75058
\(203\) 3.90312 0.273945
\(204\) −0.499118 −0.0349453
\(205\) −15.0153 −1.04871
\(206\) 14.5427 1.01324
\(207\) −7.27500 −0.505647
\(208\) −11.5179 −0.798625
\(209\) −8.42395 −0.582697
\(210\) −21.5438 −1.48666
\(211\) −13.8510 −0.953544 −0.476772 0.879027i \(-0.658193\pi\)
−0.476772 + 0.879027i \(0.658193\pi\)
\(212\) −3.97509 −0.273010
\(213\) 5.96838 0.408947
\(214\) 8.94082 0.611182
\(215\) −28.2750 −1.92834
\(216\) 2.37268 0.161441
\(217\) 2.83819 0.192669
\(218\) −1.20373 −0.0815272
\(219\) −5.15619 −0.348423
\(220\) 8.47592 0.571446
\(221\) −2.42528 −0.163142
\(222\) −1.20527 −0.0808922
\(223\) 21.5425 1.44259 0.721297 0.692626i \(-0.243546\pi\)
0.721297 + 0.692626i \(0.243546\pi\)
\(224\) −10.6413 −0.711002
\(225\) 7.51462 0.500975
\(226\) 9.41421 0.626224
\(227\) −3.89994 −0.258848 −0.129424 0.991589i \(-0.541313\pi\)
−0.129424 + 0.991589i \(0.541313\pi\)
\(228\) 0.875880 0.0580066
\(229\) 28.8788 1.90837 0.954183 0.299224i \(-0.0967278\pi\)
0.954183 + 0.299224i \(0.0967278\pi\)
\(230\) −40.6851 −2.68269
\(231\) 18.4925 1.21671
\(232\) −2.40398 −0.157829
\(233\) 3.82664 0.250691 0.125346 0.992113i \(-0.459996\pi\)
0.125346 + 0.992113i \(0.459996\pi\)
\(234\) −3.83402 −0.250638
\(235\) −39.1228 −2.55209
\(236\) 0.114409 0.00744736
\(237\) 3.52278 0.228829
\(238\) −6.08995 −0.394753
\(239\) 16.4165 1.06190 0.530949 0.847404i \(-0.321836\pi\)
0.530949 + 0.847404i \(0.321836\pi\)
\(240\) 16.8005 1.08447
\(241\) −27.8172 −1.79186 −0.895932 0.444190i \(-0.853491\pi\)
−0.895932 + 0.444190i \(0.853491\pi\)
\(242\) −19.0391 −1.22388
\(243\) 1.00000 0.0641500
\(244\) 3.81228 0.244056
\(245\) −27.7356 −1.77196
\(246\) −6.70993 −0.427809
\(247\) 4.25601 0.270804
\(248\) −1.74808 −0.111003
\(249\) −3.41706 −0.216547
\(250\) 14.0629 0.889414
\(251\) 24.7440 1.56183 0.780913 0.624640i \(-0.214754\pi\)
0.780913 + 0.624640i \(0.214754\pi\)
\(252\) −1.92275 −0.121122
\(253\) 34.9227 2.19557
\(254\) −16.6906 −1.04726
\(255\) 3.53760 0.221533
\(256\) 11.2949 0.705929
\(257\) −18.2528 −1.13858 −0.569289 0.822137i \(-0.692781\pi\)
−0.569289 + 0.822137i \(0.692781\pi\)
\(258\) −12.6353 −0.786642
\(259\) −2.93704 −0.182499
\(260\) −4.28227 −0.265575
\(261\) −1.01319 −0.0627150
\(262\) 21.8551 1.35021
\(263\) 29.8867 1.84289 0.921445 0.388508i \(-0.127010\pi\)
0.921445 + 0.388508i \(0.127010\pi\)
\(264\) −11.3898 −0.700991
\(265\) 28.1743 1.73073
\(266\) 10.6870 0.655261
\(267\) 5.27093 0.322576
\(268\) 1.34105 0.0819175
\(269\) −6.43186 −0.392157 −0.196079 0.980588i \(-0.562821\pi\)
−0.196079 + 0.980588i \(0.562821\pi\)
\(270\) 5.59245 0.340346
\(271\) 10.0760 0.612076 0.306038 0.952019i \(-0.400997\pi\)
0.306038 + 0.952019i \(0.400997\pi\)
\(272\) 4.74912 0.287958
\(273\) −9.34290 −0.565458
\(274\) −24.2329 −1.46396
\(275\) −36.0729 −2.17528
\(276\) −3.63108 −0.218566
\(277\) 14.1352 0.849301 0.424650 0.905357i \(-0.360397\pi\)
0.424650 + 0.905357i \(0.360397\pi\)
\(278\) 12.6771 0.760324
\(279\) −0.736752 −0.0441082
\(280\) 32.3347 1.93237
\(281\) −30.2938 −1.80718 −0.903589 0.428401i \(-0.859077\pi\)
−0.903589 + 0.428401i \(0.859077\pi\)
\(282\) −17.4830 −1.04110
\(283\) 22.8584 1.35879 0.679395 0.733773i \(-0.262242\pi\)
0.679395 + 0.733773i \(0.262242\pi\)
\(284\) 2.97893 0.176767
\(285\) −6.20798 −0.367729
\(286\) 18.4047 1.08829
\(287\) −16.3510 −0.965170
\(288\) 2.76232 0.162771
\(289\) 1.00000 0.0588235
\(290\) −5.66623 −0.332732
\(291\) −9.65063 −0.565730
\(292\) −2.57355 −0.150606
\(293\) −18.5166 −1.08175 −0.540877 0.841102i \(-0.681908\pi\)
−0.540877 + 0.841102i \(0.681908\pi\)
\(294\) −12.3943 −0.722850
\(295\) −0.810893 −0.0472120
\(296\) 1.80896 0.105144
\(297\) −4.80037 −0.278546
\(298\) 7.33292 0.424785
\(299\) −17.6439 −1.02037
\(300\) 3.75068 0.216546
\(301\) −30.7903 −1.77472
\(302\) −17.6818 −1.01747
\(303\) 15.7385 0.904155
\(304\) −8.33401 −0.477988
\(305\) −27.0203 −1.54718
\(306\) 1.58086 0.0903718
\(307\) −7.26341 −0.414545 −0.207272 0.978283i \(-0.566459\pi\)
−0.207272 + 0.978283i \(0.566459\pi\)
\(308\) 9.22993 0.525924
\(309\) −9.19924 −0.523327
\(310\) −4.12025 −0.234014
\(311\) −25.0635 −1.42122 −0.710611 0.703585i \(-0.751581\pi\)
−0.710611 + 0.703585i \(0.751581\pi\)
\(312\) 5.75442 0.325780
\(313\) −11.8317 −0.668767 −0.334384 0.942437i \(-0.608528\pi\)
−0.334384 + 0.942437i \(0.608528\pi\)
\(314\) −1.58086 −0.0892131
\(315\) 13.6279 0.767845
\(316\) 1.75828 0.0989111
\(317\) 3.63674 0.204260 0.102130 0.994771i \(-0.467434\pi\)
0.102130 + 0.994771i \(0.467434\pi\)
\(318\) 12.5903 0.706031
\(319\) 4.86369 0.272315
\(320\) −18.1528 −1.01477
\(321\) −5.65567 −0.315669
\(322\) −44.3043 −2.46898
\(323\) −1.75486 −0.0976428
\(324\) 0.499118 0.0277288
\(325\) 18.2250 1.01094
\(326\) −20.0720 −1.11169
\(327\) 0.761443 0.0421079
\(328\) 10.0708 0.556067
\(329\) −42.6032 −2.34879
\(330\) −26.8458 −1.47781
\(331\) −17.6453 −0.969874 −0.484937 0.874549i \(-0.661157\pi\)
−0.484937 + 0.874549i \(0.661157\pi\)
\(332\) −1.70552 −0.0936023
\(333\) 0.762412 0.0417799
\(334\) −20.1697 −1.10364
\(335\) −9.50493 −0.519310
\(336\) 18.2950 0.998076
\(337\) −17.4892 −0.952695 −0.476348 0.879257i \(-0.658040\pi\)
−0.476348 + 0.879257i \(0.658040\pi\)
\(338\) 11.2526 0.612061
\(339\) −5.95512 −0.323438
\(340\) 1.76568 0.0957575
\(341\) 3.53668 0.191522
\(342\) −2.77418 −0.150010
\(343\) −3.23679 −0.174770
\(344\) 18.9642 1.02248
\(345\) 25.7360 1.38558
\(346\) 28.5834 1.53665
\(347\) −11.4729 −0.615898 −0.307949 0.951403i \(-0.599643\pi\)
−0.307949 + 0.951403i \(0.599643\pi\)
\(348\) −0.505703 −0.0271085
\(349\) −28.9256 −1.54835 −0.774176 0.632971i \(-0.781835\pi\)
−0.774176 + 0.632971i \(0.781835\pi\)
\(350\) 45.7636 2.44617
\(351\) 2.42528 0.129452
\(352\) −13.2602 −0.706769
\(353\) −24.9696 −1.32900 −0.664499 0.747289i \(-0.731355\pi\)
−0.664499 + 0.747289i \(0.731355\pi\)
\(354\) −0.362367 −0.0192596
\(355\) −21.1137 −1.12060
\(356\) 2.63082 0.139433
\(357\) 3.85230 0.203885
\(358\) 13.9907 0.739432
\(359\) 10.3710 0.547358 0.273679 0.961821i \(-0.411759\pi\)
0.273679 + 0.961821i \(0.411759\pi\)
\(360\) −8.39361 −0.442382
\(361\) −15.9205 −0.837920
\(362\) −32.5606 −1.71135
\(363\) 12.0435 0.632122
\(364\) −4.66321 −0.244419
\(365\) 18.2406 0.954754
\(366\) −12.0747 −0.631153
\(367\) −24.3395 −1.27051 −0.635255 0.772303i \(-0.719105\pi\)
−0.635255 + 0.772303i \(0.719105\pi\)
\(368\) 34.5498 1.80103
\(369\) 4.24448 0.220959
\(370\) 4.26375 0.221662
\(371\) 30.6806 1.59286
\(372\) −0.367726 −0.0190657
\(373\) 4.47354 0.231631 0.115816 0.993271i \(-0.463052\pi\)
0.115816 + 0.993271i \(0.463052\pi\)
\(374\) −7.58871 −0.392403
\(375\) −8.89571 −0.459373
\(376\) 26.2399 1.35322
\(377\) −2.45727 −0.126556
\(378\) 6.08995 0.313233
\(379\) 0.986729 0.0506849 0.0253424 0.999679i \(-0.491932\pi\)
0.0253424 + 0.999679i \(0.491932\pi\)
\(380\) −3.09852 −0.158950
\(381\) 10.5579 0.540898
\(382\) 22.4280 1.14751
\(383\) 16.1312 0.824266 0.412133 0.911124i \(-0.364784\pi\)
0.412133 + 0.911124i \(0.364784\pi\)
\(384\) −13.6367 −0.695893
\(385\) −65.4189 −3.33406
\(386\) −1.88762 −0.0960773
\(387\) 7.99270 0.406292
\(388\) −4.81681 −0.244536
\(389\) −26.5216 −1.34470 −0.672348 0.740235i \(-0.734714\pi\)
−0.672348 + 0.740235i \(0.734714\pi\)
\(390\) 13.5632 0.686802
\(391\) 7.27500 0.367912
\(392\) 18.6024 0.939561
\(393\) −13.8248 −0.697371
\(394\) −18.4062 −0.927292
\(395\) −12.4622 −0.627040
\(396\) −2.39595 −0.120401
\(397\) −1.06167 −0.0532835 −0.0266417 0.999645i \(-0.508481\pi\)
−0.0266417 + 0.999645i \(0.508481\pi\)
\(398\) −18.9786 −0.951310
\(399\) −6.76023 −0.338435
\(400\) −35.6878 −1.78439
\(401\) −12.6139 −0.629907 −0.314953 0.949107i \(-0.601989\pi\)
−0.314953 + 0.949107i \(0.601989\pi\)
\(402\) −4.24750 −0.211846
\(403\) −1.78683 −0.0890083
\(404\) 7.85539 0.390820
\(405\) −3.53760 −0.175785
\(406\) −6.17029 −0.306226
\(407\) −3.65986 −0.181412
\(408\) −2.37268 −0.117465
\(409\) −10.4223 −0.515351 −0.257675 0.966232i \(-0.582957\pi\)
−0.257675 + 0.966232i \(0.582957\pi\)
\(410\) 23.7370 1.17229
\(411\) 15.3289 0.756120
\(412\) −4.59151 −0.226208
\(413\) −0.883029 −0.0434510
\(414\) 11.5007 0.565231
\(415\) 12.0882 0.593385
\(416\) 6.69940 0.328465
\(417\) −8.01914 −0.392699
\(418\) 13.3171 0.651360
\(419\) 2.42233 0.118338 0.0591692 0.998248i \(-0.481155\pi\)
0.0591692 + 0.998248i \(0.481155\pi\)
\(420\) 6.80194 0.331900
\(421\) 4.98654 0.243029 0.121515 0.992590i \(-0.461225\pi\)
0.121515 + 0.992590i \(0.461225\pi\)
\(422\) 21.8965 1.06591
\(423\) 11.0591 0.537714
\(424\) −18.8966 −0.917700
\(425\) −7.51462 −0.364513
\(426\) −9.43518 −0.457136
\(427\) −29.4240 −1.42393
\(428\) −2.82285 −0.136448
\(429\) −11.6422 −0.562092
\(430\) 44.6988 2.15557
\(431\) −8.26742 −0.398228 −0.199114 0.979976i \(-0.563806\pi\)
−0.199114 + 0.979976i \(0.563806\pi\)
\(432\) −4.74912 −0.228492
\(433\) 2.46995 0.118698 0.0593490 0.998237i \(-0.481098\pi\)
0.0593490 + 0.998237i \(0.481098\pi\)
\(434\) −4.48678 −0.215372
\(435\) 3.58427 0.171853
\(436\) 0.380050 0.0182011
\(437\) −12.7666 −0.610708
\(438\) 8.15122 0.389480
\(439\) 15.7951 0.753861 0.376930 0.926242i \(-0.376980\pi\)
0.376930 + 0.926242i \(0.376980\pi\)
\(440\) 40.2924 1.92087
\(441\) 7.84022 0.373344
\(442\) 3.83402 0.182366
\(443\) 10.3206 0.490347 0.245174 0.969479i \(-0.421155\pi\)
0.245174 + 0.969479i \(0.421155\pi\)
\(444\) 0.380534 0.0180593
\(445\) −18.6464 −0.883926
\(446\) −34.0557 −1.61259
\(447\) −4.63856 −0.219396
\(448\) −19.7677 −0.933934
\(449\) 25.0616 1.18273 0.591364 0.806405i \(-0.298590\pi\)
0.591364 + 0.806405i \(0.298590\pi\)
\(450\) −11.8796 −0.560008
\(451\) −20.3751 −0.959424
\(452\) −2.97231 −0.139806
\(453\) 11.1849 0.525514
\(454\) 6.16527 0.289350
\(455\) 33.0514 1.54948
\(456\) 4.16372 0.194984
\(457\) −23.3835 −1.09383 −0.546916 0.837187i \(-0.684198\pi\)
−0.546916 + 0.837187i \(0.684198\pi\)
\(458\) −45.6534 −2.13324
\(459\) −1.00000 −0.0466760
\(460\) 12.8453 0.598916
\(461\) −17.9057 −0.833952 −0.416976 0.908917i \(-0.636910\pi\)
−0.416976 + 0.908917i \(0.636910\pi\)
\(462\) −29.2340 −1.36009
\(463\) 21.4086 0.994943 0.497471 0.867480i \(-0.334262\pi\)
0.497471 + 0.867480i \(0.334262\pi\)
\(464\) 4.81177 0.223381
\(465\) 2.60633 0.120866
\(466\) −6.04937 −0.280232
\(467\) −32.4640 −1.50225 −0.751127 0.660158i \(-0.770489\pi\)
−0.751127 + 0.660158i \(0.770489\pi\)
\(468\) 1.21050 0.0559554
\(469\) −10.3505 −0.477941
\(470\) 61.8477 2.85282
\(471\) 1.00000 0.0460776
\(472\) 0.543870 0.0250336
\(473\) −38.3679 −1.76416
\(474\) −5.56902 −0.255793
\(475\) 13.1871 0.605064
\(476\) 1.92275 0.0881293
\(477\) −7.96423 −0.364657
\(478\) −25.9522 −1.18703
\(479\) −23.7640 −1.08580 −0.542901 0.839796i \(-0.682674\pi\)
−0.542901 + 0.839796i \(0.682674\pi\)
\(480\) −9.77199 −0.446028
\(481\) 1.84906 0.0843099
\(482\) 43.9751 2.00301
\(483\) 28.0255 1.27520
\(484\) 6.01115 0.273234
\(485\) 34.1401 1.55022
\(486\) −1.58086 −0.0717093
\(487\) 14.2473 0.645608 0.322804 0.946466i \(-0.395375\pi\)
0.322804 + 0.946466i \(0.395375\pi\)
\(488\) 18.1226 0.820373
\(489\) 12.6969 0.574174
\(490\) 43.8461 1.98076
\(491\) −13.8647 −0.625704 −0.312852 0.949802i \(-0.601284\pi\)
−0.312852 + 0.949802i \(0.601284\pi\)
\(492\) 2.11850 0.0955092
\(493\) 1.01319 0.0456319
\(494\) −6.72816 −0.302714
\(495\) 16.9818 0.763275
\(496\) 3.49892 0.157106
\(497\) −22.9920 −1.03133
\(498\) 5.40189 0.242064
\(499\) −28.3173 −1.26766 −0.633829 0.773473i \(-0.718518\pi\)
−0.633829 + 0.773473i \(0.718518\pi\)
\(500\) −4.44001 −0.198563
\(501\) 12.7587 0.570017
\(502\) −39.1167 −1.74587
\(503\) −22.3818 −0.997953 −0.498977 0.866615i \(-0.666291\pi\)
−0.498977 + 0.866615i \(0.666291\pi\)
\(504\) −9.14029 −0.407141
\(505\) −55.6766 −2.47758
\(506\) −55.2078 −2.45429
\(507\) −7.11803 −0.316123
\(508\) 5.26964 0.233803
\(509\) −23.7814 −1.05409 −0.527047 0.849836i \(-0.676701\pi\)
−0.527047 + 0.849836i \(0.676701\pi\)
\(510\) −5.59245 −0.247638
\(511\) 19.8632 0.878697
\(512\) 9.41771 0.416208
\(513\) 1.75486 0.0774788
\(514\) 28.8551 1.27274
\(515\) 32.5433 1.43403
\(516\) 3.98930 0.175619
\(517\) −53.0880 −2.33481
\(518\) 4.64305 0.204004
\(519\) −18.0809 −0.793664
\(520\) −20.3568 −0.892706
\(521\) 30.9013 1.35381 0.676906 0.736070i \(-0.263321\pi\)
0.676906 + 0.736070i \(0.263321\pi\)
\(522\) 1.60171 0.0701051
\(523\) 21.0092 0.918668 0.459334 0.888264i \(-0.348088\pi\)
0.459334 + 0.888264i \(0.348088\pi\)
\(524\) −6.90023 −0.301438
\(525\) −28.9486 −1.26342
\(526\) −47.2466 −2.06005
\(527\) 0.736752 0.0320934
\(528\) 22.7975 0.992134
\(529\) 29.9256 1.30111
\(530\) −44.5396 −1.93467
\(531\) 0.229221 0.00994736
\(532\) −3.37416 −0.146288
\(533\) 10.2940 0.445884
\(534\) −8.33260 −0.360587
\(535\) 20.0075 0.865000
\(536\) 6.37500 0.275358
\(537\) −8.85007 −0.381909
\(538\) 10.1679 0.438368
\(539\) −37.6360 −1.62110
\(540\) −1.76568 −0.0759828
\(541\) 12.6476 0.543762 0.271881 0.962331i \(-0.412354\pi\)
0.271881 + 0.962331i \(0.412354\pi\)
\(542\) −15.9288 −0.684201
\(543\) 20.5968 0.883892
\(544\) −2.76232 −0.118434
\(545\) −2.69368 −0.115385
\(546\) 14.7698 0.632090
\(547\) 27.0303 1.15573 0.577867 0.816131i \(-0.303885\pi\)
0.577867 + 0.816131i \(0.303885\pi\)
\(548\) 7.65095 0.326832
\(549\) 7.63803 0.325983
\(550\) 57.0263 2.43161
\(551\) −1.77801 −0.0757456
\(552\) −17.2613 −0.734688
\(553\) −13.5708 −0.577089
\(554\) −22.3457 −0.949379
\(555\) −2.69711 −0.114486
\(556\) −4.00250 −0.169744
\(557\) 30.6429 1.29838 0.649191 0.760626i \(-0.275108\pi\)
0.649191 + 0.760626i \(0.275108\pi\)
\(558\) 1.16470 0.0493058
\(559\) 19.3845 0.819878
\(560\) −64.7205 −2.73494
\(561\) 4.80037 0.202672
\(562\) 47.8903 2.02013
\(563\) −34.0002 −1.43294 −0.716469 0.697619i \(-0.754243\pi\)
−0.716469 + 0.697619i \(0.754243\pi\)
\(564\) 5.51982 0.232426
\(565\) 21.0668 0.886288
\(566\) −36.1359 −1.51891
\(567\) −3.85230 −0.161781
\(568\) 14.1611 0.594186
\(569\) −31.7725 −1.33197 −0.665986 0.745964i \(-0.731989\pi\)
−0.665986 + 0.745964i \(0.731989\pi\)
\(570\) 9.81394 0.411061
\(571\) 26.3491 1.10267 0.551337 0.834283i \(-0.314118\pi\)
0.551337 + 0.834283i \(0.314118\pi\)
\(572\) −5.81085 −0.242964
\(573\) −14.1872 −0.592678
\(574\) 25.8487 1.07890
\(575\) −54.6688 −2.27985
\(576\) 5.13139 0.213808
\(577\) 6.91871 0.288030 0.144015 0.989576i \(-0.453999\pi\)
0.144015 + 0.989576i \(0.453999\pi\)
\(578\) −1.58086 −0.0657551
\(579\) 1.19405 0.0496229
\(580\) 1.78897 0.0742831
\(581\) 13.1635 0.546115
\(582\) 15.2563 0.632394
\(583\) 38.2312 1.58338
\(584\) −12.2340 −0.506247
\(585\) −8.57966 −0.354725
\(586\) 29.2722 1.20922
\(587\) 7.67877 0.316937 0.158468 0.987364i \(-0.449344\pi\)
0.158468 + 0.987364i \(0.449344\pi\)
\(588\) 3.91320 0.161378
\(589\) −1.29289 −0.0532727
\(590\) 1.28191 0.0527753
\(591\) 11.6432 0.478936
\(592\) −3.62078 −0.148813
\(593\) −17.8218 −0.731855 −0.365927 0.930643i \(-0.619248\pi\)
−0.365927 + 0.930643i \(0.619248\pi\)
\(594\) 7.58871 0.311369
\(595\) −13.6279 −0.558690
\(596\) −2.31519 −0.0948340
\(597\) 12.0052 0.491341
\(598\) 27.8925 1.14061
\(599\) −9.41239 −0.384580 −0.192290 0.981338i \(-0.561591\pi\)
−0.192290 + 0.981338i \(0.561591\pi\)
\(600\) 17.8298 0.727899
\(601\) 26.7330 1.09046 0.545231 0.838286i \(-0.316442\pi\)
0.545231 + 0.838286i \(0.316442\pi\)
\(602\) 48.6751 1.98385
\(603\) 2.68683 0.109416
\(604\) 5.58260 0.227153
\(605\) −42.6052 −1.73215
\(606\) −24.8804 −1.01070
\(607\) −41.0397 −1.66575 −0.832875 0.553461i \(-0.813307\pi\)
−0.832875 + 0.553461i \(0.813307\pi\)
\(608\) 4.84748 0.196591
\(609\) 3.90312 0.158162
\(610\) 42.7153 1.72949
\(611\) 26.8215 1.08508
\(612\) −0.499118 −0.0201757
\(613\) −45.4730 −1.83664 −0.918319 0.395841i \(-0.870453\pi\)
−0.918319 + 0.395841i \(0.870453\pi\)
\(614\) 11.4824 0.463394
\(615\) −15.0153 −0.605474
\(616\) 43.8768 1.76785
\(617\) 2.09276 0.0842514 0.0421257 0.999112i \(-0.486587\pi\)
0.0421257 + 0.999112i \(0.486587\pi\)
\(618\) 14.5427 0.584994
\(619\) 17.4035 0.699505 0.349752 0.936842i \(-0.386266\pi\)
0.349752 + 0.936842i \(0.386266\pi\)
\(620\) 1.30087 0.0522442
\(621\) −7.27500 −0.291936
\(622\) 39.6219 1.58869
\(623\) −20.3052 −0.813511
\(624\) −11.5179 −0.461086
\(625\) −6.10361 −0.244144
\(626\) 18.7043 0.747573
\(627\) −8.42395 −0.336420
\(628\) 0.499118 0.0199170
\(629\) −0.762412 −0.0303994
\(630\) −21.5438 −0.858326
\(631\) 34.0744 1.35648 0.678240 0.734840i \(-0.262743\pi\)
0.678240 + 0.734840i \(0.262743\pi\)
\(632\) 8.35843 0.332481
\(633\) −13.8510 −0.550529
\(634\) −5.74918 −0.228329
\(635\) −37.3496 −1.48218
\(636\) −3.97509 −0.157623
\(637\) 19.0147 0.753390
\(638\) −7.68882 −0.304403
\(639\) 5.96838 0.236106
\(640\) 48.2410 1.90689
\(641\) 25.3528 1.00137 0.500687 0.865628i \(-0.333081\pi\)
0.500687 + 0.865628i \(0.333081\pi\)
\(642\) 8.94082 0.352866
\(643\) 28.8439 1.13749 0.568747 0.822513i \(-0.307428\pi\)
0.568747 + 0.822513i \(0.307428\pi\)
\(644\) 13.9880 0.551205
\(645\) −28.2750 −1.11333
\(646\) 2.77418 0.109149
\(647\) −30.0805 −1.18259 −0.591294 0.806456i \(-0.701383\pi\)
−0.591294 + 0.806456i \(0.701383\pi\)
\(648\) 2.37268 0.0932078
\(649\) −1.10035 −0.0431924
\(650\) −28.8112 −1.13007
\(651\) 2.83819 0.111237
\(652\) 6.33726 0.248186
\(653\) −5.84435 −0.228707 −0.114354 0.993440i \(-0.536480\pi\)
−0.114354 + 0.993440i \(0.536480\pi\)
\(654\) −1.20373 −0.0470697
\(655\) 48.9068 1.91095
\(656\) −20.1575 −0.787019
\(657\) −5.15619 −0.201162
\(658\) 67.3496 2.62556
\(659\) −5.79259 −0.225647 −0.112824 0.993615i \(-0.535990\pi\)
−0.112824 + 0.993615i \(0.535990\pi\)
\(660\) 8.47592 0.329925
\(661\) 10.1149 0.393424 0.196712 0.980461i \(-0.436974\pi\)
0.196712 + 0.980461i \(0.436974\pi\)
\(662\) 27.8948 1.08416
\(663\) −2.42528 −0.0941900
\(664\) −8.10759 −0.314636
\(665\) 23.9150 0.927384
\(666\) −1.20527 −0.0467031
\(667\) 7.37097 0.285405
\(668\) 6.36811 0.246389
\(669\) 21.5425 0.832882
\(670\) 15.0260 0.580504
\(671\) −36.6654 −1.41545
\(672\) −10.6413 −0.410497
\(673\) −41.0567 −1.58262 −0.791309 0.611416i \(-0.790600\pi\)
−0.791309 + 0.611416i \(0.790600\pi\)
\(674\) 27.6479 1.06496
\(675\) 7.51462 0.289238
\(676\) −3.55274 −0.136644
\(677\) −0.224724 −0.00863685 −0.00431843 0.999991i \(-0.501375\pi\)
−0.00431843 + 0.999991i \(0.501375\pi\)
\(678\) 9.41421 0.361550
\(679\) 37.1771 1.42673
\(680\) 8.39361 0.321880
\(681\) −3.89994 −0.149446
\(682\) −5.59100 −0.214090
\(683\) 26.8739 1.02830 0.514151 0.857699i \(-0.328107\pi\)
0.514151 + 0.857699i \(0.328107\pi\)
\(684\) 0.875880 0.0334901
\(685\) −54.2276 −2.07193
\(686\) 5.11691 0.195364
\(687\) 28.8788 1.10180
\(688\) −37.9583 −1.44715
\(689\) −19.3155 −0.735861
\(690\) −40.6851 −1.54885
\(691\) 37.4828 1.42591 0.712956 0.701209i \(-0.247356\pi\)
0.712956 + 0.701209i \(0.247356\pi\)
\(692\) −9.02451 −0.343061
\(693\) 18.4925 0.702471
\(694\) 18.1371 0.688473
\(695\) 28.3685 1.07608
\(696\) −2.40398 −0.0911228
\(697\) −4.24448 −0.160771
\(698\) 45.7273 1.73080
\(699\) 3.82664 0.144737
\(700\) −14.4488 −0.546112
\(701\) −25.0402 −0.945756 −0.472878 0.881128i \(-0.656785\pi\)
−0.472878 + 0.881128i \(0.656785\pi\)
\(702\) −3.83402 −0.144706
\(703\) 1.33792 0.0504607
\(704\) −24.6326 −0.928375
\(705\) −39.1228 −1.47345
\(706\) 39.4735 1.48560
\(707\) −60.6295 −2.28021
\(708\) 0.114409 0.00429974
\(709\) −8.84718 −0.332263 −0.166131 0.986104i \(-0.553128\pi\)
−0.166131 + 0.986104i \(0.553128\pi\)
\(710\) 33.3779 1.25265
\(711\) 3.52278 0.132114
\(712\) 12.5062 0.468691
\(713\) 5.35987 0.200729
\(714\) −6.08995 −0.227911
\(715\) 41.1855 1.54025
\(716\) −4.41723 −0.165080
\(717\) 16.4165 0.613087
\(718\) −16.3950 −0.611857
\(719\) 15.6770 0.584655 0.292327 0.956318i \(-0.405570\pi\)
0.292327 + 0.956318i \(0.405570\pi\)
\(720\) 16.8005 0.626117
\(721\) 35.4383 1.31979
\(722\) 25.1681 0.936658
\(723\) −27.8172 −1.03453
\(724\) 10.2802 0.382061
\(725\) −7.61375 −0.282768
\(726\) −19.0391 −0.706609
\(727\) 26.7565 0.992343 0.496172 0.868225i \(-0.334739\pi\)
0.496172 + 0.868225i \(0.334739\pi\)
\(728\) −22.1677 −0.821591
\(729\) 1.00000 0.0370370
\(730\) −28.8358 −1.06726
\(731\) −7.99270 −0.295621
\(732\) 3.81228 0.140906
\(733\) 4.26635 0.157581 0.0787906 0.996891i \(-0.474894\pi\)
0.0787906 + 0.996891i \(0.474894\pi\)
\(734\) 38.4773 1.42022
\(735\) −27.7356 −1.02304
\(736\) −20.0959 −0.740744
\(737\) −12.8978 −0.475096
\(738\) −6.70993 −0.246996
\(739\) −30.5678 −1.12445 −0.562227 0.826983i \(-0.690055\pi\)
−0.562227 + 0.826983i \(0.690055\pi\)
\(740\) −1.34618 −0.0494864
\(741\) 4.25601 0.156348
\(742\) −48.5017 −1.78055
\(743\) 7.08018 0.259747 0.129873 0.991531i \(-0.458543\pi\)
0.129873 + 0.991531i \(0.458543\pi\)
\(744\) −1.74808 −0.0640877
\(745\) 16.4094 0.601193
\(746\) −7.07204 −0.258926
\(747\) −3.41706 −0.125024
\(748\) 2.39595 0.0876047
\(749\) 21.7873 0.796092
\(750\) 14.0629 0.513504
\(751\) −16.6583 −0.607869 −0.303934 0.952693i \(-0.598300\pi\)
−0.303934 + 0.952693i \(0.598300\pi\)
\(752\) −52.5212 −1.91525
\(753\) 24.7440 0.901720
\(754\) 3.88460 0.141469
\(755\) −39.5678 −1.44002
\(756\) −1.92275 −0.0699299
\(757\) −18.1079 −0.658142 −0.329071 0.944305i \(-0.606736\pi\)
−0.329071 + 0.944305i \(0.606736\pi\)
\(758\) −1.55988 −0.0566574
\(759\) 34.9227 1.26761
\(760\) −14.7296 −0.534298
\(761\) −16.4803 −0.597411 −0.298706 0.954345i \(-0.596555\pi\)
−0.298706 + 0.954345i \(0.596555\pi\)
\(762\) −16.6906 −0.604635
\(763\) −2.93331 −0.106193
\(764\) −7.08109 −0.256185
\(765\) 3.53760 0.127902
\(766\) −25.5012 −0.921395
\(767\) 0.555925 0.0200733
\(768\) 11.2949 0.407568
\(769\) 33.7503 1.21707 0.608534 0.793528i \(-0.291758\pi\)
0.608534 + 0.793528i \(0.291758\pi\)
\(770\) 103.418 3.72693
\(771\) −18.2528 −0.657358
\(772\) 0.595970 0.0214494
\(773\) 22.7886 0.819649 0.409824 0.912164i \(-0.365590\pi\)
0.409824 + 0.912164i \(0.365590\pi\)
\(774\) −12.6353 −0.454168
\(775\) −5.53641 −0.198874
\(776\) −22.8979 −0.821987
\(777\) −2.93704 −0.105366
\(778\) 41.9269 1.50315
\(779\) 7.44845 0.266868
\(780\) −4.28227 −0.153330
\(781\) −28.6504 −1.02519
\(782\) −11.5007 −0.411266
\(783\) −1.01319 −0.0362085
\(784\) −37.2341 −1.32979
\(785\) −3.53760 −0.126262
\(786\) 21.8551 0.779547
\(787\) −39.8451 −1.42032 −0.710162 0.704039i \(-0.751378\pi\)
−0.710162 + 0.704039i \(0.751378\pi\)
\(788\) 5.81132 0.207020
\(789\) 29.8867 1.06399
\(790\) 19.7010 0.700929
\(791\) 22.9409 0.815685
\(792\) −11.3898 −0.404717
\(793\) 18.5243 0.657819
\(794\) 1.67834 0.0595622
\(795\) 28.1743 0.999238
\(796\) 5.99203 0.212382
\(797\) −54.9131 −1.94512 −0.972561 0.232648i \(-0.925261\pi\)
−0.972561 + 0.232648i \(0.925261\pi\)
\(798\) 10.6870 0.378315
\(799\) −11.0591 −0.391244
\(800\) 20.7578 0.733899
\(801\) 5.27093 0.186239
\(802\) 19.9408 0.704133
\(803\) 24.7516 0.873466
\(804\) 1.34105 0.0472951
\(805\) −99.1429 −3.49433
\(806\) 2.82473 0.0994967
\(807\) −6.43186 −0.226412
\(808\) 37.3425 1.31371
\(809\) 48.0642 1.68985 0.844923 0.534887i \(-0.179646\pi\)
0.844923 + 0.534887i \(0.179646\pi\)
\(810\) 5.59245 0.196499
\(811\) 52.4064 1.84024 0.920119 0.391638i \(-0.128092\pi\)
0.920119 + 0.391638i \(0.128092\pi\)
\(812\) 1.94812 0.0683656
\(813\) 10.0760 0.353382
\(814\) 5.78572 0.202790
\(815\) −44.9166 −1.57336
\(816\) 4.74912 0.166252
\(817\) 14.0260 0.490709
\(818\) 16.4762 0.576078
\(819\) −9.34290 −0.326467
\(820\) −7.49440 −0.261716
\(821\) 27.0103 0.942666 0.471333 0.881955i \(-0.343773\pi\)
0.471333 + 0.881955i \(0.343773\pi\)
\(822\) −24.2329 −0.845219
\(823\) 21.4070 0.746202 0.373101 0.927791i \(-0.378294\pi\)
0.373101 + 0.927791i \(0.378294\pi\)
\(824\) −21.8269 −0.760376
\(825\) −36.0729 −1.25590
\(826\) 1.39595 0.0485712
\(827\) 2.54490 0.0884948 0.0442474 0.999021i \(-0.485911\pi\)
0.0442474 + 0.999021i \(0.485911\pi\)
\(828\) −3.63108 −0.126189
\(829\) −4.45015 −0.154560 −0.0772800 0.997009i \(-0.524624\pi\)
−0.0772800 + 0.997009i \(0.524624\pi\)
\(830\) −19.1097 −0.663308
\(831\) 14.1352 0.490344
\(832\) 12.4450 0.431454
\(833\) −7.84022 −0.271648
\(834\) 12.6771 0.438973
\(835\) −45.1352 −1.56197
\(836\) −4.20455 −0.145417
\(837\) −0.736752 −0.0254659
\(838\) −3.82936 −0.132283
\(839\) −3.53469 −0.122031 −0.0610156 0.998137i \(-0.519434\pi\)
−0.0610156 + 0.998137i \(0.519434\pi\)
\(840\) 32.3347 1.11565
\(841\) −27.9734 −0.964601
\(842\) −7.88303 −0.271667
\(843\) −30.2938 −1.04337
\(844\) −6.91330 −0.237966
\(845\) 25.1807 0.866244
\(846\) −17.4830 −0.601077
\(847\) −46.3953 −1.59416
\(848\) 37.8231 1.29885
\(849\) 22.8584 0.784498
\(850\) 11.8796 0.407466
\(851\) −5.54654 −0.190133
\(852\) 2.97893 0.102056
\(853\) −10.1369 −0.347082 −0.173541 0.984827i \(-0.555521\pi\)
−0.173541 + 0.984827i \(0.555521\pi\)
\(854\) 46.5152 1.59172
\(855\) −6.20798 −0.212308
\(856\) −13.4191 −0.458656
\(857\) 12.2463 0.418325 0.209162 0.977881i \(-0.432926\pi\)
0.209162 + 0.977881i \(0.432926\pi\)
\(858\) 18.4047 0.628327
\(859\) −24.7164 −0.843314 −0.421657 0.906755i \(-0.638551\pi\)
−0.421657 + 0.906755i \(0.638551\pi\)
\(860\) −14.1126 −0.481234
\(861\) −16.3510 −0.557241
\(862\) 13.0696 0.445153
\(863\) 45.0279 1.53277 0.766385 0.642382i \(-0.222054\pi\)
0.766385 + 0.642382i \(0.222054\pi\)
\(864\) 2.76232 0.0939761
\(865\) 63.9630 2.17481
\(866\) −3.90464 −0.132685
\(867\) 1.00000 0.0339618
\(868\) 1.41659 0.0480823
\(869\) −16.9106 −0.573654
\(870\) −5.66623 −0.192103
\(871\) 6.51631 0.220797
\(872\) 1.80666 0.0611813
\(873\) −9.65063 −0.326624
\(874\) 20.1822 0.682671
\(875\) 34.2690 1.15850
\(876\) −2.57355 −0.0869522
\(877\) −21.4479 −0.724244 −0.362122 0.932131i \(-0.617948\pi\)
−0.362122 + 0.932131i \(0.617948\pi\)
\(878\) −24.9699 −0.842693
\(879\) −18.5166 −0.624551
\(880\) −80.6485 −2.71866
\(881\) 3.83436 0.129183 0.0645915 0.997912i \(-0.479426\pi\)
0.0645915 + 0.997912i \(0.479426\pi\)
\(882\) −12.3943 −0.417338
\(883\) 33.3115 1.12102 0.560510 0.828147i \(-0.310605\pi\)
0.560510 + 0.828147i \(0.310605\pi\)
\(884\) −1.21050 −0.0407135
\(885\) −0.810893 −0.0272579
\(886\) −16.3154 −0.548128
\(887\) 53.4388 1.79430 0.897150 0.441727i \(-0.145634\pi\)
0.897150 + 0.441727i \(0.145634\pi\)
\(888\) 1.80896 0.0607048
\(889\) −40.6722 −1.36410
\(890\) 29.4774 0.988085
\(891\) −4.80037 −0.160818
\(892\) 10.7523 0.360013
\(893\) 19.4072 0.649437
\(894\) 7.33292 0.245249
\(895\) 31.3080 1.04651
\(896\) 52.5325 1.75499
\(897\) −17.6439 −0.589112
\(898\) −39.6188 −1.32210
\(899\) 0.746471 0.0248962
\(900\) 3.75068 0.125023
\(901\) 7.96423 0.265327
\(902\) 32.2101 1.07248
\(903\) −30.7903 −1.02464
\(904\) −14.1296 −0.469944
\(905\) −72.8631 −2.42205
\(906\) −17.6818 −0.587439
\(907\) 26.7813 0.889258 0.444629 0.895715i \(-0.353336\pi\)
0.444629 + 0.895715i \(0.353336\pi\)
\(908\) −1.94653 −0.0645980
\(909\) 15.7385 0.522014
\(910\) −52.2497 −1.73206
\(911\) 53.1814 1.76198 0.880989 0.473138i \(-0.156879\pi\)
0.880989 + 0.473138i \(0.156879\pi\)
\(912\) −8.33401 −0.275967
\(913\) 16.4031 0.542864
\(914\) 36.9660 1.22273
\(915\) −27.0203 −0.893264
\(916\) 14.4139 0.476250
\(917\) 53.2574 1.75872
\(918\) 1.58086 0.0521762
\(919\) −24.2882 −0.801194 −0.400597 0.916254i \(-0.631197\pi\)
−0.400597 + 0.916254i \(0.631197\pi\)
\(920\) 61.0635 2.01320
\(921\) −7.26341 −0.239338
\(922\) 28.3064 0.932222
\(923\) 14.4750 0.476450
\(924\) 9.22993 0.303642
\(925\) 5.72924 0.188376
\(926\) −33.8440 −1.11218
\(927\) −9.19924 −0.302143
\(928\) −2.79876 −0.0918739
\(929\) −21.3849 −0.701615 −0.350807 0.936448i \(-0.614093\pi\)
−0.350807 + 0.936448i \(0.614093\pi\)
\(930\) −4.12025 −0.135108
\(931\) 13.7585 0.450915
\(932\) 1.90994 0.0625623
\(933\) −25.0635 −0.820543
\(934\) 51.3210 1.67927
\(935\) −16.9818 −0.555364
\(936\) 5.75442 0.188089
\(937\) −40.6432 −1.32776 −0.663878 0.747841i \(-0.731090\pi\)
−0.663878 + 0.747841i \(0.731090\pi\)
\(938\) 16.3627 0.534260
\(939\) −11.8317 −0.386113
\(940\) −19.5269 −0.636898
\(941\) 44.7569 1.45903 0.729517 0.683963i \(-0.239745\pi\)
0.729517 + 0.683963i \(0.239745\pi\)
\(942\) −1.58086 −0.0515072
\(943\) −30.8786 −1.00554
\(944\) −1.08860 −0.0354309
\(945\) 13.6279 0.443316
\(946\) 60.6543 1.97204
\(947\) −19.5829 −0.636359 −0.318180 0.948030i \(-0.603072\pi\)
−0.318180 + 0.948030i \(0.603072\pi\)
\(948\) 1.75828 0.0571064
\(949\) −12.5052 −0.405936
\(950\) −20.8469 −0.676363
\(951\) 3.63674 0.117929
\(952\) 9.14029 0.296239
\(953\) −16.1190 −0.522146 −0.261073 0.965319i \(-0.584076\pi\)
−0.261073 + 0.965319i \(0.584076\pi\)
\(954\) 12.5903 0.407627
\(955\) 50.1886 1.62407
\(956\) 8.19379 0.265006
\(957\) 4.86369 0.157221
\(958\) 37.5675 1.21375
\(959\) −59.0516 −1.90688
\(960\) −18.1528 −0.585879
\(961\) −30.4572 −0.982490
\(962\) −2.92311 −0.0942447
\(963\) −5.65567 −0.182251
\(964\) −13.8841 −0.447176
\(965\) −4.22406 −0.135977
\(966\) −44.3043 −1.42547
\(967\) 12.3387 0.396786 0.198393 0.980123i \(-0.436428\pi\)
0.198393 + 0.980123i \(0.436428\pi\)
\(968\) 28.5755 0.918451
\(969\) −1.75486 −0.0563741
\(970\) −53.9707 −1.73289
\(971\) −24.6652 −0.791545 −0.395772 0.918349i \(-0.629523\pi\)
−0.395772 + 0.918349i \(0.629523\pi\)
\(972\) 0.499118 0.0160092
\(973\) 30.8921 0.990357
\(974\) −22.5230 −0.721684
\(975\) 18.2250 0.583668
\(976\) −36.2739 −1.16110
\(977\) −48.4016 −1.54850 −0.774252 0.632878i \(-0.781873\pi\)
−0.774252 + 0.632878i \(0.781873\pi\)
\(978\) −20.0720 −0.641833
\(979\) −25.3024 −0.808668
\(980\) −13.8433 −0.442209
\(981\) 0.761443 0.0243110
\(982\) 21.9181 0.699435
\(983\) −38.7403 −1.23562 −0.617812 0.786326i \(-0.711981\pi\)
−0.617812 + 0.786326i \(0.711981\pi\)
\(984\) 10.0708 0.321046
\(985\) −41.1889 −1.31239
\(986\) −1.60171 −0.0510090
\(987\) −42.6032 −1.35607
\(988\) 2.12425 0.0675815
\(989\) −58.1469 −1.84896
\(990\) −26.8458 −0.853216
\(991\) −30.7620 −0.977187 −0.488594 0.872512i \(-0.662490\pi\)
−0.488594 + 0.872512i \(0.662490\pi\)
\(992\) −2.03515 −0.0646160
\(993\) −17.6453 −0.559957
\(994\) 36.3471 1.15286
\(995\) −42.4697 −1.34638
\(996\) −1.70552 −0.0540413
\(997\) −26.0982 −0.826537 −0.413269 0.910609i \(-0.635613\pi\)
−0.413269 + 0.910609i \(0.635613\pi\)
\(998\) 44.7658 1.41704
\(999\) 0.762412 0.0241217
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 \(a_p\))