Properties

Label 6026.2.a.h.1.17
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 24
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: \(24\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.48980 q^{3}\) \(+1.00000 q^{4}\) \(+3.56615 q^{5}\) \(-1.48980 q^{6}\) \(-2.69745 q^{7}\) \(-1.00000 q^{8}\) \(-0.780502 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.48980 q^{3}\) \(+1.00000 q^{4}\) \(+3.56615 q^{5}\) \(-1.48980 q^{6}\) \(-2.69745 q^{7}\) \(-1.00000 q^{8}\) \(-0.780502 q^{9}\) \(-3.56615 q^{10}\) \(-4.79381 q^{11}\) \(+1.48980 q^{12}\) \(+0.746865 q^{13}\) \(+2.69745 q^{14}\) \(+5.31284 q^{15}\) \(+1.00000 q^{16}\) \(+4.10189 q^{17}\) \(+0.780502 q^{18}\) \(+4.65428 q^{19}\) \(+3.56615 q^{20}\) \(-4.01866 q^{21}\) \(+4.79381 q^{22}\) \(-1.00000 q^{23}\) \(-1.48980 q^{24}\) \(+7.71742 q^{25}\) \(-0.746865 q^{26}\) \(-5.63218 q^{27}\) \(-2.69745 q^{28}\) \(-6.16822 q^{29}\) \(-5.31284 q^{30}\) \(-8.26320 q^{31}\) \(-1.00000 q^{32}\) \(-7.14180 q^{33}\) \(-4.10189 q^{34}\) \(-9.61952 q^{35}\) \(-0.780502 q^{36}\) \(-2.87867 q^{37}\) \(-4.65428 q^{38}\) \(+1.11268 q^{39}\) \(-3.56615 q^{40}\) \(-5.19872 q^{41}\) \(+4.01866 q^{42}\) \(+1.25728 q^{43}\) \(-4.79381 q^{44}\) \(-2.78339 q^{45}\) \(+1.00000 q^{46}\) \(-6.72119 q^{47}\) \(+1.48980 q^{48}\) \(+0.276254 q^{49}\) \(-7.71742 q^{50}\) \(+6.11098 q^{51}\) \(+0.746865 q^{52}\) \(+2.81932 q^{53}\) \(+5.63218 q^{54}\) \(-17.0954 q^{55}\) \(+2.69745 q^{56}\) \(+6.93393 q^{57}\) \(+6.16822 q^{58}\) \(+5.55324 q^{59}\) \(+5.31284 q^{60}\) \(-3.81590 q^{61}\) \(+8.26320 q^{62}\) \(+2.10537 q^{63}\) \(+1.00000 q^{64}\) \(+2.66343 q^{65}\) \(+7.14180 q^{66}\) \(-10.3918 q^{67}\) \(+4.10189 q^{68}\) \(-1.48980 q^{69}\) \(+9.61952 q^{70}\) \(+9.37733 q^{71}\) \(+0.780502 q^{72}\) \(-2.73400 q^{73}\) \(+2.87867 q^{74}\) \(+11.4974 q^{75}\) \(+4.65428 q^{76}\) \(+12.9311 q^{77}\) \(-1.11268 q^{78}\) \(-5.86082 q^{79}\) \(+3.56615 q^{80}\) \(-6.04931 q^{81}\) \(+5.19872 q^{82}\) \(-2.35445 q^{83}\) \(-4.01866 q^{84}\) \(+14.6279 q^{85}\) \(-1.25728 q^{86}\) \(-9.18940 q^{87}\) \(+4.79381 q^{88}\) \(-2.14139 q^{89}\) \(+2.78339 q^{90}\) \(-2.01463 q^{91}\) \(-1.00000 q^{92}\) \(-12.3105 q^{93}\) \(+6.72119 q^{94}\) \(+16.5979 q^{95}\) \(-1.48980 q^{96}\) \(-5.78968 q^{97}\) \(-0.276254 q^{98}\) \(+3.74158 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 27q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 39q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 13q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 21q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut +\mathstrut 7q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut +\mathstrut 23q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 29q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 17q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 36q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 39q^{78} \) \(\mathstrut -\mathstrut 53q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 37q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 7q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut +\mathstrut 13q^{90} \) \(\mathstrut -\mathstrut 44q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 23q^{93} \) \(\mathstrut -\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 13q^{98} \) \(\mathstrut -\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.48980 0.860135 0.430068 0.902797i \(-0.358490\pi\)
0.430068 + 0.902797i \(0.358490\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.56615 1.59483 0.797415 0.603431i \(-0.206200\pi\)
0.797415 + 0.603431i \(0.206200\pi\)
\(6\) −1.48980 −0.608207
\(7\) −2.69745 −1.01954 −0.509771 0.860310i \(-0.670270\pi\)
−0.509771 + 0.860310i \(0.670270\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.780502 −0.260167
\(10\) −3.56615 −1.12772
\(11\) −4.79381 −1.44539 −0.722694 0.691169i \(-0.757096\pi\)
−0.722694 + 0.691169i \(0.757096\pi\)
\(12\) 1.48980 0.430068
\(13\) 0.746865 0.207143 0.103572 0.994622i \(-0.466973\pi\)
0.103572 + 0.994622i \(0.466973\pi\)
\(14\) 2.69745 0.720925
\(15\) 5.31284 1.37177
\(16\) 1.00000 0.250000
\(17\) 4.10189 0.994854 0.497427 0.867506i \(-0.334278\pi\)
0.497427 + 0.867506i \(0.334278\pi\)
\(18\) 0.780502 0.183966
\(19\) 4.65428 1.06776 0.533882 0.845559i \(-0.320733\pi\)
0.533882 + 0.845559i \(0.320733\pi\)
\(20\) 3.56615 0.797415
\(21\) −4.01866 −0.876944
\(22\) 4.79381 1.02204
\(23\) −1.00000 −0.208514
\(24\) −1.48980 −0.304104
\(25\) 7.71742 1.54348
\(26\) −0.746865 −0.146472
\(27\) −5.63218 −1.08391
\(28\) −2.69745 −0.509771
\(29\) −6.16822 −1.14541 −0.572705 0.819762i \(-0.694106\pi\)
−0.572705 + 0.819762i \(0.694106\pi\)
\(30\) −5.31284 −0.969988
\(31\) −8.26320 −1.48411 −0.742057 0.670337i \(-0.766150\pi\)
−0.742057 + 0.670337i \(0.766150\pi\)
\(32\) −1.00000 −0.176777
\(33\) −7.14180 −1.24323
\(34\) −4.10189 −0.703468
\(35\) −9.61952 −1.62600
\(36\) −0.780502 −0.130084
\(37\) −2.87867 −0.473251 −0.236625 0.971601i \(-0.576041\pi\)
−0.236625 + 0.971601i \(0.576041\pi\)
\(38\) −4.65428 −0.755024
\(39\) 1.11268 0.178171
\(40\) −3.56615 −0.563858
\(41\) −5.19872 −0.811903 −0.405951 0.913895i \(-0.633060\pi\)
−0.405951 + 0.913895i \(0.633060\pi\)
\(42\) 4.01866 0.620093
\(43\) 1.25728 0.191734 0.0958668 0.995394i \(-0.469438\pi\)
0.0958668 + 0.995394i \(0.469438\pi\)
\(44\) −4.79381 −0.722694
\(45\) −2.78339 −0.414923
\(46\) 1.00000 0.147442
\(47\) −6.72119 −0.980387 −0.490193 0.871614i \(-0.663074\pi\)
−0.490193 + 0.871614i \(0.663074\pi\)
\(48\) 1.48980 0.215034
\(49\) 0.276254 0.0394649
\(50\) −7.71742 −1.09141
\(51\) 6.11098 0.855709
\(52\) 0.746865 0.103572
\(53\) 2.81932 0.387264 0.193632 0.981074i \(-0.437973\pi\)
0.193632 + 0.981074i \(0.437973\pi\)
\(54\) 5.63218 0.766443
\(55\) −17.0954 −2.30515
\(56\) 2.69745 0.360462
\(57\) 6.93393 0.918422
\(58\) 6.16822 0.809927
\(59\) 5.55324 0.722971 0.361485 0.932378i \(-0.382270\pi\)
0.361485 + 0.932378i \(0.382270\pi\)
\(60\) 5.31284 0.685885
\(61\) −3.81590 −0.488576 −0.244288 0.969703i \(-0.578554\pi\)
−0.244288 + 0.969703i \(0.578554\pi\)
\(62\) 8.26320 1.04943
\(63\) 2.10537 0.265252
\(64\) 1.00000 0.125000
\(65\) 2.66343 0.330358
\(66\) 7.14180 0.879095
\(67\) −10.3918 −1.26956 −0.634778 0.772694i \(-0.718909\pi\)
−0.634778 + 0.772694i \(0.718909\pi\)
\(68\) 4.10189 0.497427
\(69\) −1.48980 −0.179351
\(70\) 9.61952 1.14975
\(71\) 9.37733 1.11288 0.556442 0.830886i \(-0.312166\pi\)
0.556442 + 0.830886i \(0.312166\pi\)
\(72\) 0.780502 0.0919831
\(73\) −2.73400 −0.319991 −0.159995 0.987118i \(-0.551148\pi\)
−0.159995 + 0.987118i \(0.551148\pi\)
\(74\) 2.87867 0.334639
\(75\) 11.4974 1.32761
\(76\) 4.65428 0.533882
\(77\) 12.9311 1.47363
\(78\) −1.11268 −0.125986
\(79\) −5.86082 −0.659394 −0.329697 0.944087i \(-0.606947\pi\)
−0.329697 + 0.944087i \(0.606947\pi\)
\(80\) 3.56615 0.398708
\(81\) −6.04931 −0.672145
\(82\) 5.19872 0.574102
\(83\) −2.35445 −0.258434 −0.129217 0.991616i \(-0.541246\pi\)
−0.129217 + 0.991616i \(0.541246\pi\)
\(84\) −4.01866 −0.438472
\(85\) 14.6279 1.58662
\(86\) −1.25728 −0.135576
\(87\) −9.18940 −0.985208
\(88\) 4.79381 0.511022
\(89\) −2.14139 −0.226987 −0.113494 0.993539i \(-0.536204\pi\)
−0.113494 + 0.993539i \(0.536204\pi\)
\(90\) 2.78339 0.293395
\(91\) −2.01463 −0.211191
\(92\) −1.00000 −0.104257
\(93\) −12.3105 −1.27654
\(94\) 6.72119 0.693238
\(95\) 16.5979 1.70290
\(96\) −1.48980 −0.152052
\(97\) −5.78968 −0.587853 −0.293927 0.955828i \(-0.594962\pi\)
−0.293927 + 0.955828i \(0.594962\pi\)
\(98\) −0.276254 −0.0279059
\(99\) 3.74158 0.376043
\(100\) 7.71742 0.771742
\(101\) 4.56806 0.454539 0.227269 0.973832i \(-0.427020\pi\)
0.227269 + 0.973832i \(0.427020\pi\)
\(102\) −6.11098 −0.605077
\(103\) 7.62144 0.750963 0.375481 0.926830i \(-0.377477\pi\)
0.375481 + 0.926830i \(0.377477\pi\)
\(104\) −0.746865 −0.0732362
\(105\) −14.3311 −1.39858
\(106\) −2.81932 −0.273837
\(107\) −10.1233 −0.978661 −0.489330 0.872099i \(-0.662759\pi\)
−0.489330 + 0.872099i \(0.662759\pi\)
\(108\) −5.63218 −0.541957
\(109\) −0.727196 −0.0696527 −0.0348264 0.999393i \(-0.511088\pi\)
−0.0348264 + 0.999393i \(0.511088\pi\)
\(110\) 17.0954 1.62999
\(111\) −4.28864 −0.407060
\(112\) −2.69745 −0.254885
\(113\) 13.1529 1.23732 0.618659 0.785660i \(-0.287676\pi\)
0.618659 + 0.785660i \(0.287676\pi\)
\(114\) −6.93393 −0.649422
\(115\) −3.56615 −0.332545
\(116\) −6.16822 −0.572705
\(117\) −0.582930 −0.0538919
\(118\) −5.55324 −0.511217
\(119\) −11.0646 −1.01429
\(120\) −5.31284 −0.484994
\(121\) 11.9806 1.08914
\(122\) 3.81590 0.345476
\(123\) −7.74503 −0.698346
\(124\) −8.26320 −0.742057
\(125\) 9.69074 0.866766
\(126\) −2.10537 −0.187561
\(127\) −9.25234 −0.821012 −0.410506 0.911858i \(-0.634648\pi\)
−0.410506 + 0.911858i \(0.634648\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.87310 0.164917
\(130\) −2.66343 −0.233599
\(131\) −1.00000 −0.0873704
\(132\) −7.14180 −0.621614
\(133\) −12.5547 −1.08863
\(134\) 10.3918 0.897712
\(135\) −20.0852 −1.72866
\(136\) −4.10189 −0.351734
\(137\) −16.9974 −1.45219 −0.726093 0.687597i \(-0.758666\pi\)
−0.726093 + 0.687597i \(0.758666\pi\)
\(138\) 1.48980 0.126820
\(139\) −1.64747 −0.139737 −0.0698683 0.997556i \(-0.522258\pi\)
−0.0698683 + 0.997556i \(0.522258\pi\)
\(140\) −9.61952 −0.812998
\(141\) −10.0132 −0.843265
\(142\) −9.37733 −0.786928
\(143\) −3.58033 −0.299402
\(144\) −0.780502 −0.0650419
\(145\) −21.9968 −1.82674
\(146\) 2.73400 0.226268
\(147\) 0.411563 0.0339451
\(148\) −2.87867 −0.236625
\(149\) 5.21941 0.427591 0.213795 0.976878i \(-0.431417\pi\)
0.213795 + 0.976878i \(0.431417\pi\)
\(150\) −11.4974 −0.938759
\(151\) −0.660230 −0.0537288 −0.0268644 0.999639i \(-0.508552\pi\)
−0.0268644 + 0.999639i \(0.508552\pi\)
\(152\) −4.65428 −0.377512
\(153\) −3.20153 −0.258828
\(154\) −12.9311 −1.04202
\(155\) −29.4678 −2.36691
\(156\) 1.11268 0.0890856
\(157\) 9.01181 0.719221 0.359610 0.933103i \(-0.382910\pi\)
0.359610 + 0.933103i \(0.382910\pi\)
\(158\) 5.86082 0.466262
\(159\) 4.20022 0.333099
\(160\) −3.56615 −0.281929
\(161\) 2.69745 0.212589
\(162\) 6.04931 0.475279
\(163\) 6.96678 0.545681 0.272840 0.962059i \(-0.412037\pi\)
0.272840 + 0.962059i \(0.412037\pi\)
\(164\) −5.19872 −0.405951
\(165\) −25.4687 −1.98274
\(166\) 2.35445 0.182740
\(167\) −12.9286 −1.00045 −0.500224 0.865896i \(-0.666749\pi\)
−0.500224 + 0.865896i \(0.666749\pi\)
\(168\) 4.01866 0.310046
\(169\) −12.4422 −0.957092
\(170\) −14.6279 −1.12191
\(171\) −3.63268 −0.277798
\(172\) 1.25728 0.0958668
\(173\) −2.74653 −0.208815 −0.104407 0.994535i \(-0.533295\pi\)
−0.104407 + 0.994535i \(0.533295\pi\)
\(174\) 9.18940 0.696647
\(175\) −20.8174 −1.57365
\(176\) −4.79381 −0.361347
\(177\) 8.27321 0.621853
\(178\) 2.14139 0.160504
\(179\) −15.4429 −1.15425 −0.577127 0.816654i \(-0.695826\pi\)
−0.577127 + 0.816654i \(0.695826\pi\)
\(180\) −2.78339 −0.207462
\(181\) 18.1904 1.35208 0.676040 0.736865i \(-0.263694\pi\)
0.676040 + 0.736865i \(0.263694\pi\)
\(182\) 2.01463 0.149335
\(183\) −5.68492 −0.420242
\(184\) 1.00000 0.0737210
\(185\) −10.2658 −0.754755
\(186\) 12.3105 0.902649
\(187\) −19.6636 −1.43795
\(188\) −6.72119 −0.490193
\(189\) 15.1926 1.10510
\(190\) −16.5979 −1.20413
\(191\) 2.00049 0.144750 0.0723751 0.997377i \(-0.476942\pi\)
0.0723751 + 0.997377i \(0.476942\pi\)
\(192\) 1.48980 0.107517
\(193\) −1.38564 −0.0997404 −0.0498702 0.998756i \(-0.515881\pi\)
−0.0498702 + 0.998756i \(0.515881\pi\)
\(194\) 5.78968 0.415675
\(195\) 3.96798 0.284153
\(196\) 0.276254 0.0197324
\(197\) 0.933591 0.0665156 0.0332578 0.999447i \(-0.489412\pi\)
0.0332578 + 0.999447i \(0.489412\pi\)
\(198\) −3.74158 −0.265902
\(199\) 0.0385265 0.00273107 0.00136554 0.999999i \(-0.499565\pi\)
0.00136554 + 0.999999i \(0.499565\pi\)
\(200\) −7.71742 −0.545704
\(201\) −15.4816 −1.09199
\(202\) −4.56806 −0.321407
\(203\) 16.6385 1.16779
\(204\) 6.11098 0.427854
\(205\) −18.5394 −1.29485
\(206\) −7.62144 −0.531011
\(207\) 0.780502 0.0542487
\(208\) 0.746865 0.0517858
\(209\) −22.3117 −1.54333
\(210\) 14.3311 0.988943
\(211\) −1.69707 −0.116831 −0.0584155 0.998292i \(-0.518605\pi\)
−0.0584155 + 0.998292i \(0.518605\pi\)
\(212\) 2.81932 0.193632
\(213\) 13.9703 0.957231
\(214\) 10.1233 0.692018
\(215\) 4.48365 0.305783
\(216\) 5.63218 0.383222
\(217\) 22.2896 1.51312
\(218\) 0.727196 0.0492519
\(219\) −4.07311 −0.275235
\(220\) −17.0954 −1.15257
\(221\) 3.06356 0.206077
\(222\) 4.28864 0.287835
\(223\) 13.8360 0.926529 0.463265 0.886220i \(-0.346678\pi\)
0.463265 + 0.886220i \(0.346678\pi\)
\(224\) 2.69745 0.180231
\(225\) −6.02347 −0.401565
\(226\) −13.1529 −0.874915
\(227\) −10.5000 −0.696910 −0.348455 0.937326i \(-0.613294\pi\)
−0.348455 + 0.937326i \(0.613294\pi\)
\(228\) 6.93393 0.459211
\(229\) 12.3635 0.817005 0.408503 0.912757i \(-0.366051\pi\)
0.408503 + 0.912757i \(0.366051\pi\)
\(230\) 3.56615 0.235145
\(231\) 19.2647 1.26752
\(232\) 6.16822 0.404964
\(233\) 7.47482 0.489692 0.244846 0.969562i \(-0.421263\pi\)
0.244846 + 0.969562i \(0.421263\pi\)
\(234\) 0.582930 0.0381073
\(235\) −23.9688 −1.56355
\(236\) 5.55324 0.361485
\(237\) −8.73144 −0.567168
\(238\) 11.0646 0.717214
\(239\) 2.73435 0.176870 0.0884350 0.996082i \(-0.471813\pi\)
0.0884350 + 0.996082i \(0.471813\pi\)
\(240\) 5.31284 0.342942
\(241\) 25.7983 1.66181 0.830907 0.556412i \(-0.187822\pi\)
0.830907 + 0.556412i \(0.187822\pi\)
\(242\) −11.9806 −0.770141
\(243\) 7.88431 0.505778
\(244\) −3.81590 −0.244288
\(245\) 0.985164 0.0629398
\(246\) 7.74503 0.493805
\(247\) 3.47612 0.221180
\(248\) 8.26320 0.524714
\(249\) −3.50765 −0.222288
\(250\) −9.69074 −0.612896
\(251\) −16.1788 −1.02120 −0.510599 0.859819i \(-0.670577\pi\)
−0.510599 + 0.859819i \(0.670577\pi\)
\(252\) 2.10537 0.132626
\(253\) 4.79381 0.301384
\(254\) 9.25234 0.580543
\(255\) 21.7927 1.36471
\(256\) 1.00000 0.0625000
\(257\) −20.7693 −1.29555 −0.647777 0.761830i \(-0.724301\pi\)
−0.647777 + 0.761830i \(0.724301\pi\)
\(258\) −1.87310 −0.116614
\(259\) 7.76509 0.482499
\(260\) 2.66343 0.165179
\(261\) 4.81431 0.297998
\(262\) 1.00000 0.0617802
\(263\) −11.5028 −0.709296 −0.354648 0.935000i \(-0.615399\pi\)
−0.354648 + 0.935000i \(0.615399\pi\)
\(264\) 7.14180 0.439548
\(265\) 10.0541 0.617620
\(266\) 12.5547 0.769778
\(267\) −3.19024 −0.195240
\(268\) −10.3918 −0.634778
\(269\) 16.5846 1.01118 0.505590 0.862774i \(-0.331275\pi\)
0.505590 + 0.862774i \(0.331275\pi\)
\(270\) 20.0852 1.22235
\(271\) −7.01482 −0.426120 −0.213060 0.977039i \(-0.568343\pi\)
−0.213060 + 0.977039i \(0.568343\pi\)
\(272\) 4.10189 0.248713
\(273\) −3.00140 −0.181653
\(274\) 16.9974 1.02685
\(275\) −36.9958 −2.23093
\(276\) −1.48980 −0.0896753
\(277\) −28.5911 −1.71787 −0.858936 0.512083i \(-0.828874\pi\)
−0.858936 + 0.512083i \(0.828874\pi\)
\(278\) 1.64747 0.0988086
\(279\) 6.44945 0.386118
\(280\) 9.61952 0.574876
\(281\) −3.76526 −0.224617 −0.112308 0.993673i \(-0.535824\pi\)
−0.112308 + 0.993673i \(0.535824\pi\)
\(282\) 10.0132 0.596278
\(283\) 21.7158 1.29087 0.645436 0.763814i \(-0.276676\pi\)
0.645436 + 0.763814i \(0.276676\pi\)
\(284\) 9.37733 0.556442
\(285\) 24.7274 1.46473
\(286\) 3.58033 0.211709
\(287\) 14.0233 0.827769
\(288\) 0.780502 0.0459915
\(289\) −0.174531 −0.0102665
\(290\) 21.9968 1.29170
\(291\) −8.62545 −0.505633
\(292\) −2.73400 −0.159995
\(293\) −9.75958 −0.570161 −0.285080 0.958504i \(-0.592020\pi\)
−0.285080 + 0.958504i \(0.592020\pi\)
\(294\) −0.411563 −0.0240028
\(295\) 19.8037 1.15302
\(296\) 2.87867 0.167319
\(297\) 26.9996 1.56668
\(298\) −5.21941 −0.302352
\(299\) −0.746865 −0.0431923
\(300\) 11.4974 0.663803
\(301\) −3.39146 −0.195480
\(302\) 0.660230 0.0379920
\(303\) 6.80548 0.390965
\(304\) 4.65428 0.266941
\(305\) −13.6081 −0.779196
\(306\) 3.20153 0.183019
\(307\) −19.3190 −1.10259 −0.551297 0.834309i \(-0.685867\pi\)
−0.551297 + 0.834309i \(0.685867\pi\)
\(308\) 12.9311 0.736816
\(309\) 11.3544 0.645929
\(310\) 29.4678 1.67366
\(311\) 10.5007 0.595440 0.297720 0.954653i \(-0.403774\pi\)
0.297720 + 0.954653i \(0.403774\pi\)
\(312\) −1.11268 −0.0629930
\(313\) 6.56310 0.370968 0.185484 0.982647i \(-0.440615\pi\)
0.185484 + 0.982647i \(0.440615\pi\)
\(314\) −9.01181 −0.508566
\(315\) 7.50806 0.423031
\(316\) −5.86082 −0.329697
\(317\) −1.15264 −0.0647385 −0.0323693 0.999476i \(-0.510305\pi\)
−0.0323693 + 0.999476i \(0.510305\pi\)
\(318\) −4.20022 −0.235537
\(319\) 29.5693 1.65556
\(320\) 3.56615 0.199354
\(321\) −15.0817 −0.841781
\(322\) −2.69745 −0.150323
\(323\) 19.0913 1.06227
\(324\) −6.04931 −0.336073
\(325\) 5.76388 0.319722
\(326\) −6.96678 −0.385855
\(327\) −1.08337 −0.0599107
\(328\) 5.19872 0.287051
\(329\) 18.1301 0.999545
\(330\) 25.4687 1.40201
\(331\) −21.0778 −1.15854 −0.579271 0.815135i \(-0.696663\pi\)
−0.579271 + 0.815135i \(0.696663\pi\)
\(332\) −2.35445 −0.129217
\(333\) 2.24681 0.123124
\(334\) 12.9286 0.707424
\(335\) −37.0586 −2.02473
\(336\) −4.01866 −0.219236
\(337\) 17.8366 0.971622 0.485811 0.874064i \(-0.338524\pi\)
0.485811 + 0.874064i \(0.338524\pi\)
\(338\) 12.4422 0.676766
\(339\) 19.5951 1.06426
\(340\) 14.6279 0.793311
\(341\) 39.6122 2.14512
\(342\) 3.63268 0.196433
\(343\) 18.1370 0.979305
\(344\) −1.25728 −0.0677881
\(345\) −5.31284 −0.286034
\(346\) 2.74653 0.147654
\(347\) −30.1746 −1.61986 −0.809929 0.586529i \(-0.800494\pi\)
−0.809929 + 0.586529i \(0.800494\pi\)
\(348\) −9.18940 −0.492604
\(349\) −19.9201 −1.06630 −0.533148 0.846022i \(-0.678991\pi\)
−0.533148 + 0.846022i \(0.678991\pi\)
\(350\) 20.8174 1.11274
\(351\) −4.20648 −0.224525
\(352\) 4.79381 0.255511
\(353\) −3.43107 −0.182617 −0.0913087 0.995823i \(-0.529105\pi\)
−0.0913087 + 0.995823i \(0.529105\pi\)
\(354\) −8.27321 −0.439716
\(355\) 33.4410 1.77486
\(356\) −2.14139 −0.113494
\(357\) −16.4841 −0.872430
\(358\) 15.4429 0.816181
\(359\) −0.142270 −0.00750874 −0.00375437 0.999993i \(-0.501195\pi\)
−0.00375437 + 0.999993i \(0.501195\pi\)
\(360\) 2.78339 0.146697
\(361\) 2.66231 0.140121
\(362\) −18.1904 −0.956065
\(363\) 17.8486 0.936811
\(364\) −2.01463 −0.105596
\(365\) −9.74986 −0.510331
\(366\) 5.68492 0.297156
\(367\) −12.4235 −0.648500 −0.324250 0.945971i \(-0.605112\pi\)
−0.324250 + 0.945971i \(0.605112\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 4.05761 0.211231
\(370\) 10.2658 0.533692
\(371\) −7.60499 −0.394831
\(372\) −12.3105 −0.638270
\(373\) −34.9365 −1.80894 −0.904470 0.426536i \(-0.859734\pi\)
−0.904470 + 0.426536i \(0.859734\pi\)
\(374\) 19.6636 1.01678
\(375\) 14.4372 0.745536
\(376\) 6.72119 0.346619
\(377\) −4.60683 −0.237264
\(378\) −15.1926 −0.781421
\(379\) −21.9430 −1.12714 −0.563569 0.826069i \(-0.690572\pi\)
−0.563569 + 0.826069i \(0.690572\pi\)
\(380\) 16.5979 0.851452
\(381\) −13.7841 −0.706181
\(382\) −2.00049 −0.102354
\(383\) −25.5463 −1.30535 −0.652676 0.757637i \(-0.726354\pi\)
−0.652676 + 0.757637i \(0.726354\pi\)
\(384\) −1.48980 −0.0760259
\(385\) 46.1141 2.35019
\(386\) 1.38564 0.0705271
\(387\) −0.981311 −0.0498829
\(388\) −5.78968 −0.293927
\(389\) 1.15731 0.0586779 0.0293389 0.999570i \(-0.490660\pi\)
0.0293389 + 0.999570i \(0.490660\pi\)
\(390\) −3.96798 −0.200926
\(391\) −4.10189 −0.207441
\(392\) −0.276254 −0.0139529
\(393\) −1.48980 −0.0751504
\(394\) −0.933591 −0.0470336
\(395\) −20.9006 −1.05162
\(396\) 3.74158 0.188021
\(397\) 21.3912 1.07360 0.536798 0.843711i \(-0.319634\pi\)
0.536798 + 0.843711i \(0.319634\pi\)
\(398\) −0.0385265 −0.00193116
\(399\) −18.7040 −0.936369
\(400\) 7.71742 0.385871
\(401\) 32.6522 1.63057 0.815286 0.579059i \(-0.196580\pi\)
0.815286 + 0.579059i \(0.196580\pi\)
\(402\) 15.4816 0.772154
\(403\) −6.17150 −0.307424
\(404\) 4.56806 0.227269
\(405\) −21.5727 −1.07196
\(406\) −16.6385 −0.825754
\(407\) 13.7998 0.684031
\(408\) −6.11098 −0.302539
\(409\) −9.95033 −0.492012 −0.246006 0.969268i \(-0.579118\pi\)
−0.246006 + 0.969268i \(0.579118\pi\)
\(410\) 18.5394 0.915596
\(411\) −25.3227 −1.24908
\(412\) 7.62144 0.375481
\(413\) −14.9796 −0.737099
\(414\) −0.780502 −0.0383596
\(415\) −8.39630 −0.412158
\(416\) −0.746865 −0.0366181
\(417\) −2.45440 −0.120192
\(418\) 22.3117 1.09130
\(419\) −13.7916 −0.673763 −0.336881 0.941547i \(-0.609372\pi\)
−0.336881 + 0.941547i \(0.609372\pi\)
\(420\) −14.3311 −0.699288
\(421\) 8.50368 0.414444 0.207222 0.978294i \(-0.433558\pi\)
0.207222 + 0.978294i \(0.433558\pi\)
\(422\) 1.69707 0.0826121
\(423\) 5.24591 0.255065
\(424\) −2.81932 −0.136918
\(425\) 31.6560 1.53554
\(426\) −13.9703 −0.676864
\(427\) 10.2932 0.498124
\(428\) −10.1233 −0.489330
\(429\) −5.33396 −0.257526
\(430\) −4.48365 −0.216221
\(431\) −22.1517 −1.06701 −0.533505 0.845797i \(-0.679126\pi\)
−0.533505 + 0.845797i \(0.679126\pi\)
\(432\) −5.63218 −0.270979
\(433\) 33.6565 1.61743 0.808714 0.588202i \(-0.200164\pi\)
0.808714 + 0.588202i \(0.200164\pi\)
\(434\) −22.2896 −1.06993
\(435\) −32.7708 −1.57124
\(436\) −0.727196 −0.0348264
\(437\) −4.65428 −0.222644
\(438\) 4.07311 0.194621
\(439\) −15.3656 −0.733360 −0.366680 0.930347i \(-0.619506\pi\)
−0.366680 + 0.930347i \(0.619506\pi\)
\(440\) 17.0954 0.814993
\(441\) −0.215617 −0.0102675
\(442\) −3.06356 −0.145719
\(443\) 22.7407 1.08044 0.540222 0.841523i \(-0.318340\pi\)
0.540222 + 0.841523i \(0.318340\pi\)
\(444\) −4.28864 −0.203530
\(445\) −7.63653 −0.362006
\(446\) −13.8360 −0.655155
\(447\) 7.77587 0.367786
\(448\) −2.69745 −0.127443
\(449\) 14.9135 0.703813 0.351907 0.936035i \(-0.385533\pi\)
0.351907 + 0.936035i \(0.385533\pi\)
\(450\) 6.02347 0.283949
\(451\) 24.9216 1.17351
\(452\) 13.1529 0.618659
\(453\) −0.983610 −0.0462140
\(454\) 10.5000 0.492790
\(455\) −7.18449 −0.336814
\(456\) −6.93393 −0.324711
\(457\) −22.3010 −1.04320 −0.521599 0.853191i \(-0.674664\pi\)
−0.521599 + 0.853191i \(0.674664\pi\)
\(458\) −12.3635 −0.577710
\(459\) −23.1026 −1.07834
\(460\) −3.56615 −0.166273
\(461\) 1.90159 0.0885657 0.0442829 0.999019i \(-0.485900\pi\)
0.0442829 + 0.999019i \(0.485900\pi\)
\(462\) −19.2647 −0.896274
\(463\) −29.3617 −1.36455 −0.682277 0.731094i \(-0.739010\pi\)
−0.682277 + 0.731094i \(0.739010\pi\)
\(464\) −6.16822 −0.286353
\(465\) −43.9011 −2.03586
\(466\) −7.47482 −0.346264
\(467\) 24.7902 1.14715 0.573577 0.819152i \(-0.305556\pi\)
0.573577 + 0.819152i \(0.305556\pi\)
\(468\) −0.582930 −0.0269460
\(469\) 28.0313 1.29437
\(470\) 23.9688 1.10560
\(471\) 13.4258 0.618627
\(472\) −5.55324 −0.255609
\(473\) −6.02716 −0.277129
\(474\) 8.73144 0.401048
\(475\) 35.9190 1.64808
\(476\) −11.0646 −0.507147
\(477\) −2.20049 −0.100753
\(478\) −2.73435 −0.125066
\(479\) −15.1463 −0.692052 −0.346026 0.938225i \(-0.612469\pi\)
−0.346026 + 0.938225i \(0.612469\pi\)
\(480\) −5.31284 −0.242497
\(481\) −2.14998 −0.0980307
\(482\) −25.7983 −1.17508
\(483\) 4.01866 0.182855
\(484\) 11.9806 0.544572
\(485\) −20.6469 −0.937526
\(486\) −7.88431 −0.357639
\(487\) −21.9472 −0.994522 −0.497261 0.867601i \(-0.665661\pi\)
−0.497261 + 0.867601i \(0.665661\pi\)
\(488\) 3.81590 0.172738
\(489\) 10.3791 0.469359
\(490\) −0.985164 −0.0445052
\(491\) −2.23531 −0.100878 −0.0504390 0.998727i \(-0.516062\pi\)
−0.0504390 + 0.998727i \(0.516062\pi\)
\(492\) −7.74503 −0.349173
\(493\) −25.3013 −1.13952
\(494\) −3.47612 −0.156398
\(495\) 13.3430 0.599724
\(496\) −8.26320 −0.371029
\(497\) −25.2949 −1.13463
\(498\) 3.50765 0.157181
\(499\) −10.8109 −0.483961 −0.241980 0.970281i \(-0.577797\pi\)
−0.241980 + 0.970281i \(0.577797\pi\)
\(500\) 9.69074 0.433383
\(501\) −19.2611 −0.860521
\(502\) 16.1788 0.722097
\(503\) 37.7272 1.68217 0.841086 0.540901i \(-0.181917\pi\)
0.841086 + 0.540901i \(0.181917\pi\)
\(504\) −2.10537 −0.0937806
\(505\) 16.2904 0.724912
\(506\) −4.79381 −0.213111
\(507\) −18.5364 −0.823228
\(508\) −9.25234 −0.410506
\(509\) −1.72412 −0.0764205 −0.0382102 0.999270i \(-0.512166\pi\)
−0.0382102 + 0.999270i \(0.512166\pi\)
\(510\) −21.7927 −0.964996
\(511\) 7.37484 0.326244
\(512\) −1.00000 −0.0441942
\(513\) −26.2138 −1.15737
\(514\) 20.7693 0.916096
\(515\) 27.1792 1.19766
\(516\) 1.87310 0.0824584
\(517\) 32.2201 1.41704
\(518\) −7.76509 −0.341178
\(519\) −4.09178 −0.179609
\(520\) −2.66343 −0.116799
\(521\) 44.3691 1.94384 0.971922 0.235302i \(-0.0756080\pi\)
0.971922 + 0.235302i \(0.0756080\pi\)
\(522\) −4.81431 −0.210717
\(523\) 2.24719 0.0982626 0.0491313 0.998792i \(-0.484355\pi\)
0.0491313 + 0.998792i \(0.484355\pi\)
\(524\) −1.00000 −0.0436852
\(525\) −31.0137 −1.35355
\(526\) 11.5028 0.501548
\(527\) −33.8947 −1.47648
\(528\) −7.14180 −0.310807
\(529\) 1.00000 0.0434783
\(530\) −10.0541 −0.436723
\(531\) −4.33432 −0.188093
\(532\) −12.5547 −0.544315
\(533\) −3.88274 −0.168180
\(534\) 3.19024 0.138055
\(535\) −36.1014 −1.56080
\(536\) 10.3918 0.448856
\(537\) −23.0068 −0.992815
\(538\) −16.5846 −0.715013
\(539\) −1.32431 −0.0570420
\(540\) −20.0852 −0.864330
\(541\) 29.7587 1.27943 0.639714 0.768613i \(-0.279053\pi\)
0.639714 + 0.768613i \(0.279053\pi\)
\(542\) 7.01482 0.301312
\(543\) 27.1000 1.16297
\(544\) −4.10189 −0.175867
\(545\) −2.59329 −0.111084
\(546\) 3.00140 0.128448
\(547\) 23.6462 1.01104 0.505520 0.862815i \(-0.331301\pi\)
0.505520 + 0.862815i \(0.331301\pi\)
\(548\) −16.9974 −0.726093
\(549\) 2.97832 0.127112
\(550\) 36.9958 1.57751
\(551\) −28.7086 −1.22303
\(552\) 1.48980 0.0634100
\(553\) 15.8093 0.672279
\(554\) 28.5911 1.21472
\(555\) −15.2939 −0.649191
\(556\) −1.64747 −0.0698683
\(557\) 35.2034 1.49162 0.745808 0.666161i \(-0.232064\pi\)
0.745808 + 0.666161i \(0.232064\pi\)
\(558\) −6.44945 −0.273027
\(559\) 0.939020 0.0397163
\(560\) −9.61952 −0.406499
\(561\) −29.2949 −1.23683
\(562\) 3.76526 0.158828
\(563\) −9.43221 −0.397520 −0.198760 0.980048i \(-0.563691\pi\)
−0.198760 + 0.980048i \(0.563691\pi\)
\(564\) −10.0132 −0.421633
\(565\) 46.9051 1.97331
\(566\) −21.7158 −0.912784
\(567\) 16.3177 0.685280
\(568\) −9.37733 −0.393464
\(569\) 1.53518 0.0643581 0.0321791 0.999482i \(-0.489755\pi\)
0.0321791 + 0.999482i \(0.489755\pi\)
\(570\) −24.7274 −1.03572
\(571\) −33.2809 −1.39276 −0.696382 0.717671i \(-0.745208\pi\)
−0.696382 + 0.717671i \(0.745208\pi\)
\(572\) −3.58033 −0.149701
\(573\) 2.98032 0.124505
\(574\) −14.0233 −0.585321
\(575\) −7.71742 −0.321839
\(576\) −0.780502 −0.0325209
\(577\) −20.4334 −0.850652 −0.425326 0.905040i \(-0.639840\pi\)
−0.425326 + 0.905040i \(0.639840\pi\)
\(578\) 0.174531 0.00725951
\(579\) −2.06432 −0.0857902
\(580\) −21.9968 −0.913368
\(581\) 6.35101 0.263484
\(582\) 8.62545 0.357537
\(583\) −13.5153 −0.559746
\(584\) 2.73400 0.113134
\(585\) −2.07882 −0.0859485
\(586\) 9.75958 0.403165
\(587\) −6.44000 −0.265807 −0.132904 0.991129i \(-0.542430\pi\)
−0.132904 + 0.991129i \(0.542430\pi\)
\(588\) 0.411563 0.0169726
\(589\) −38.4592 −1.58468
\(590\) −19.8037 −0.815305
\(591\) 1.39086 0.0572124
\(592\) −2.87867 −0.118313
\(593\) 43.3150 1.77873 0.889367 0.457194i \(-0.151146\pi\)
0.889367 + 0.457194i \(0.151146\pi\)
\(594\) −26.9996 −1.10781
\(595\) −39.4582 −1.61763
\(596\) 5.21941 0.213795
\(597\) 0.0573967 0.00234909
\(598\) 0.746865 0.0305416
\(599\) 40.6066 1.65914 0.829571 0.558401i \(-0.188585\pi\)
0.829571 + 0.558401i \(0.188585\pi\)
\(600\) −11.4974 −0.469379
\(601\) 42.2059 1.72162 0.860808 0.508929i \(-0.169959\pi\)
0.860808 + 0.508929i \(0.169959\pi\)
\(602\) 3.39146 0.138226
\(603\) 8.11080 0.330297
\(604\) −0.660230 −0.0268644
\(605\) 42.7246 1.73700
\(606\) −6.80548 −0.276454
\(607\) −26.3401 −1.06911 −0.534556 0.845133i \(-0.679521\pi\)
−0.534556 + 0.845133i \(0.679521\pi\)
\(608\) −4.65428 −0.188756
\(609\) 24.7880 1.00446
\(610\) 13.6081 0.550975
\(611\) −5.01983 −0.203080
\(612\) −3.20153 −0.129414
\(613\) 18.7395 0.756883 0.378442 0.925625i \(-0.376460\pi\)
0.378442 + 0.925625i \(0.376460\pi\)
\(614\) 19.3190 0.779652
\(615\) −27.6200 −1.11374
\(616\) −12.9311 −0.521008
\(617\) −0.893218 −0.0359596 −0.0179798 0.999838i \(-0.505723\pi\)
−0.0179798 + 0.999838i \(0.505723\pi\)
\(618\) −11.3544 −0.456741
\(619\) 16.3533 0.657295 0.328647 0.944453i \(-0.393407\pi\)
0.328647 + 0.944453i \(0.393407\pi\)
\(620\) −29.4678 −1.18346
\(621\) 5.63218 0.226012
\(622\) −10.5007 −0.421040
\(623\) 5.77631 0.231423
\(624\) 1.11268 0.0445428
\(625\) −4.02848 −0.161139
\(626\) −6.56310 −0.262314
\(627\) −33.2399 −1.32748
\(628\) 9.01181 0.359610
\(629\) −11.8080 −0.470815
\(630\) −7.50806 −0.299128
\(631\) −8.13369 −0.323797 −0.161899 0.986807i \(-0.551762\pi\)
−0.161899 + 0.986807i \(0.551762\pi\)
\(632\) 5.86082 0.233131
\(633\) −2.52829 −0.100491
\(634\) 1.15264 0.0457770
\(635\) −32.9952 −1.30938
\(636\) 4.20022 0.166549
\(637\) 0.206325 0.00817488
\(638\) −29.5693 −1.17066
\(639\) −7.31903 −0.289536
\(640\) −3.56615 −0.140964
\(641\) −40.5643 −1.60219 −0.801096 0.598535i \(-0.795750\pi\)
−0.801096 + 0.598535i \(0.795750\pi\)
\(642\) 15.0817 0.595229
\(643\) 30.9504 1.22056 0.610282 0.792184i \(-0.291056\pi\)
0.610282 + 0.792184i \(0.291056\pi\)
\(644\) 2.69745 0.106295
\(645\) 6.67974 0.263014
\(646\) −19.0913 −0.751138
\(647\) 25.9875 1.02167 0.510837 0.859678i \(-0.329336\pi\)
0.510837 + 0.859678i \(0.329336\pi\)
\(648\) 6.04931 0.237639
\(649\) −26.6212 −1.04497
\(650\) −5.76388 −0.226078
\(651\) 33.2070 1.30148
\(652\) 6.96678 0.272840
\(653\) 5.55371 0.217334 0.108667 0.994078i \(-0.465342\pi\)
0.108667 + 0.994078i \(0.465342\pi\)
\(654\) 1.08337 0.0423633
\(655\) −3.56615 −0.139341
\(656\) −5.19872 −0.202976
\(657\) 2.13389 0.0832511
\(658\) −18.1301 −0.706785
\(659\) −1.49785 −0.0583480 −0.0291740 0.999574i \(-0.509288\pi\)
−0.0291740 + 0.999574i \(0.509288\pi\)
\(660\) −25.4687 −0.991369
\(661\) 10.6508 0.414269 0.207135 0.978312i \(-0.433586\pi\)
0.207135 + 0.978312i \(0.433586\pi\)
\(662\) 21.0778 0.819213
\(663\) 4.56408 0.177254
\(664\) 2.35445 0.0913702
\(665\) −44.7719 −1.73618
\(666\) −2.24681 −0.0870622
\(667\) 6.16822 0.238835
\(668\) −12.9286 −0.500224
\(669\) 20.6129 0.796940
\(670\) 37.0586 1.43170
\(671\) 18.2927 0.706182
\(672\) 4.01866 0.155023
\(673\) 19.9996 0.770928 0.385464 0.922723i \(-0.374041\pi\)
0.385464 + 0.922723i \(0.374041\pi\)
\(674\) −17.8366 −0.687040
\(675\) −43.4660 −1.67301
\(676\) −12.4422 −0.478546
\(677\) −10.3796 −0.398921 −0.199460 0.979906i \(-0.563919\pi\)
−0.199460 + 0.979906i \(0.563919\pi\)
\(678\) −19.5951 −0.752546
\(679\) 15.6174 0.599341
\(680\) −14.6279 −0.560956
\(681\) −15.6429 −0.599436
\(682\) −39.6122 −1.51683
\(683\) 25.7090 0.983729 0.491864 0.870672i \(-0.336316\pi\)
0.491864 + 0.870672i \(0.336316\pi\)
\(684\) −3.63268 −0.138899
\(685\) −60.6152 −2.31599
\(686\) −18.1370 −0.692474
\(687\) 18.4192 0.702735
\(688\) 1.25728 0.0479334
\(689\) 2.10565 0.0802190
\(690\) 5.31284 0.202256
\(691\) −40.2532 −1.53130 −0.765651 0.643256i \(-0.777583\pi\)
−0.765651 + 0.643256i \(0.777583\pi\)
\(692\) −2.74653 −0.104407
\(693\) −10.0927 −0.383391
\(694\) 30.1746 1.14541
\(695\) −5.87512 −0.222856
\(696\) 9.18940 0.348323
\(697\) −21.3245 −0.807724
\(698\) 19.9201 0.753986
\(699\) 11.1360 0.421201
\(700\) −20.8174 −0.786823
\(701\) 13.1463 0.496528 0.248264 0.968692i \(-0.420140\pi\)
0.248264 + 0.968692i \(0.420140\pi\)
\(702\) 4.20648 0.158763
\(703\) −13.3981 −0.505321
\(704\) −4.79381 −0.180673
\(705\) −35.7086 −1.34487
\(706\) 3.43107 0.129130
\(707\) −12.3221 −0.463421
\(708\) 8.27321 0.310926
\(709\) −14.6856 −0.551529 −0.275765 0.961225i \(-0.588931\pi\)
−0.275765 + 0.961225i \(0.588931\pi\)
\(710\) −33.4410 −1.25502
\(711\) 4.57438 0.171553
\(712\) 2.14139 0.0802521
\(713\) 8.26320 0.309459
\(714\) 16.4841 0.616901
\(715\) −12.7680 −0.477496
\(716\) −15.4429 −0.577127
\(717\) 4.07362 0.152132
\(718\) 0.142270 0.00530948
\(719\) 21.4588 0.800279 0.400139 0.916454i \(-0.368962\pi\)
0.400139 + 0.916454i \(0.368962\pi\)
\(720\) −2.78339 −0.103731
\(721\) −20.5585 −0.765638
\(722\) −2.66231 −0.0990808
\(723\) 38.4342 1.42938
\(724\) 18.1904 0.676040
\(725\) −47.6028 −1.76792
\(726\) −17.8486 −0.662425
\(727\) −11.1963 −0.415248 −0.207624 0.978209i \(-0.566573\pi\)
−0.207624 + 0.978209i \(0.566573\pi\)
\(728\) 2.01463 0.0746673
\(729\) 29.8939 1.10718
\(730\) 9.74986 0.360858
\(731\) 5.15723 0.190747
\(732\) −5.68492 −0.210121
\(733\) −7.95722 −0.293906 −0.146953 0.989143i \(-0.546947\pi\)
−0.146953 + 0.989143i \(0.546947\pi\)
\(734\) 12.4235 0.458559
\(735\) 1.46769 0.0541367
\(736\) 1.00000 0.0368605
\(737\) 49.8161 1.83500
\(738\) −4.05761 −0.149363
\(739\) −11.5665 −0.425481 −0.212741 0.977109i \(-0.568239\pi\)
−0.212741 + 0.977109i \(0.568239\pi\)
\(740\) −10.2658 −0.377378
\(741\) 5.17871 0.190245
\(742\) 7.60499 0.279188
\(743\) −7.81447 −0.286685 −0.143343 0.989673i \(-0.545785\pi\)
−0.143343 + 0.989673i \(0.545785\pi\)
\(744\) 12.3105 0.451325
\(745\) 18.6132 0.681935
\(746\) 34.9365 1.27911
\(747\) 1.83765 0.0672361
\(748\) −19.6636 −0.718974
\(749\) 27.3072 0.997785
\(750\) −14.4372 −0.527174
\(751\) 11.0866 0.404555 0.202277 0.979328i \(-0.435166\pi\)
0.202277 + 0.979328i \(0.435166\pi\)
\(752\) −6.72119 −0.245097
\(753\) −24.1032 −0.878369
\(754\) 4.60683 0.167771
\(755\) −2.35448 −0.0856883
\(756\) 15.1926 0.552548
\(757\) −27.4416 −0.997381 −0.498690 0.866780i \(-0.666186\pi\)
−0.498690 + 0.866780i \(0.666186\pi\)
\(758\) 21.9430 0.797007
\(759\) 7.14180 0.259231
\(760\) −16.5979 −0.602067
\(761\) −27.3015 −0.989680 −0.494840 0.868984i \(-0.664773\pi\)
−0.494840 + 0.868984i \(0.664773\pi\)
\(762\) 13.7841 0.499346
\(763\) 1.96158 0.0710138
\(764\) 2.00049 0.0723751
\(765\) −11.4171 −0.412788
\(766\) 25.5463 0.923024
\(767\) 4.14752 0.149758
\(768\) 1.48980 0.0537584
\(769\) −36.1673 −1.30423 −0.652113 0.758122i \(-0.726117\pi\)
−0.652113 + 0.758122i \(0.726117\pi\)
\(770\) −46.1141 −1.66184
\(771\) −30.9421 −1.11435
\(772\) −1.38564 −0.0498702
\(773\) 28.7322 1.03343 0.516713 0.856159i \(-0.327155\pi\)
0.516713 + 0.856159i \(0.327155\pi\)
\(774\) 0.981311 0.0352725
\(775\) −63.7706 −2.29071
\(776\) 5.78968 0.207837
\(777\) 11.5684 0.415014
\(778\) −1.15731 −0.0414915
\(779\) −24.1963 −0.866921
\(780\) 3.96798 0.142076
\(781\) −44.9531 −1.60855
\(782\) 4.10189 0.146683
\(783\) 34.7406 1.24153
\(784\) 0.276254 0.00986622
\(785\) 32.1375 1.14704
\(786\) 1.48980 0.0531393
\(787\) 46.7334 1.66587 0.832934 0.553373i \(-0.186660\pi\)
0.832934 + 0.553373i \(0.186660\pi\)
\(788\) 0.933591 0.0332578
\(789\) −17.1369 −0.610090
\(790\) 20.9006 0.743609
\(791\) −35.4792 −1.26150
\(792\) −3.74158 −0.132951
\(793\) −2.84997 −0.101205
\(794\) −21.3912 −0.759147
\(795\) 14.9786 0.531236
\(796\) 0.0385265 0.00136554
\(797\) 12.0369 0.426369 0.213185 0.977012i \(-0.431616\pi\)
0.213185 + 0.977012i \(0.431616\pi\)
\(798\) 18.7040 0.662113
\(799\) −27.5696 −0.975341
\(800\) −7.71742 −0.272852
\(801\) 1.67136 0.0590547
\(802\) −32.6522 −1.15299
\(803\) 13.1063 0.462510
\(804\) −15.4816 −0.545995
\(805\) 9.61952 0.339044
\(806\) 6.17150 0.217382
\(807\) 24.7077 0.869752
\(808\) −4.56806 −0.160704
\(809\) 49.6868 1.74690 0.873448 0.486918i \(-0.161879\pi\)
0.873448 + 0.486918i \(0.161879\pi\)
\(810\) 21.5727 0.757989
\(811\) −26.9745 −0.947204 −0.473602 0.880739i \(-0.657046\pi\)
−0.473602 + 0.880739i \(0.657046\pi\)
\(812\) 16.6385 0.583897
\(813\) −10.4507 −0.366521
\(814\) −13.7998 −0.483683
\(815\) 24.8446 0.870268
\(816\) 6.11098 0.213927
\(817\) 5.85174 0.204726
\(818\) 9.95033 0.347905
\(819\) 1.57243 0.0549450
\(820\) −18.5394 −0.647424
\(821\) 17.6996 0.617720 0.308860 0.951107i \(-0.400053\pi\)
0.308860 + 0.951107i \(0.400053\pi\)
\(822\) 25.3227 0.883230
\(823\) 49.8018 1.73598 0.867991 0.496580i \(-0.165411\pi\)
0.867991 + 0.496580i \(0.165411\pi\)
\(824\) −7.62144 −0.265505
\(825\) −55.1163 −1.91890
\(826\) 14.9796 0.521207
\(827\) −4.66362 −0.162170 −0.0810850 0.996707i \(-0.525839\pi\)
−0.0810850 + 0.996707i \(0.525839\pi\)
\(828\) 0.780502 0.0271243
\(829\) −8.20300 −0.284902 −0.142451 0.989802i \(-0.545498\pi\)
−0.142451 + 0.989802i \(0.545498\pi\)
\(830\) 8.39630 0.291440
\(831\) −42.5949 −1.47760
\(832\) 0.746865 0.0258929
\(833\) 1.13316 0.0392618
\(834\) 2.45440 0.0849888
\(835\) −46.1055 −1.59555
\(836\) −22.3117 −0.771667
\(837\) 46.5399 1.60865
\(838\) 13.7916 0.476422
\(839\) 27.2736 0.941589 0.470795 0.882243i \(-0.343967\pi\)
0.470795 + 0.882243i \(0.343967\pi\)
\(840\) 14.3311 0.494471
\(841\) 9.04696 0.311964
\(842\) −8.50368 −0.293056
\(843\) −5.60948 −0.193201
\(844\) −1.69707 −0.0584155
\(845\) −44.3707 −1.52640
\(846\) −5.24591 −0.180358
\(847\) −32.3171 −1.11043
\(848\) 2.81932 0.0968159
\(849\) 32.3522 1.11032
\(850\) −31.6560 −1.08579
\(851\) 2.87867 0.0986796
\(852\) 13.9703 0.478615
\(853\) −53.4894 −1.83144 −0.915722 0.401813i \(-0.868380\pi\)
−0.915722 + 0.401813i \(0.868380\pi\)
\(854\) −10.2932 −0.352227
\(855\) −12.9547 −0.443040
\(856\) 10.1233 0.346009
\(857\) −45.9350 −1.56911 −0.784554 0.620060i \(-0.787108\pi\)
−0.784554 + 0.620060i \(0.787108\pi\)
\(858\) 5.33396 0.182099
\(859\) 3.53685 0.120676 0.0603379 0.998178i \(-0.480782\pi\)
0.0603379 + 0.998178i \(0.480782\pi\)
\(860\) 4.48365 0.152891
\(861\) 20.8919 0.711993
\(862\) 22.1517 0.754491
\(863\) 50.0558 1.70392 0.851959 0.523608i \(-0.175414\pi\)
0.851959 + 0.523608i \(0.175414\pi\)
\(864\) 5.63218 0.191611
\(865\) −9.79454 −0.333025
\(866\) −33.6565 −1.14369
\(867\) −0.260015 −0.00883058
\(868\) 22.2896 0.756558
\(869\) 28.0956 0.953079
\(870\) 32.7708 1.11103
\(871\) −7.76125 −0.262980
\(872\) 0.727196 0.0246260
\(873\) 4.51886 0.152940
\(874\) 4.65428 0.157433
\(875\) −26.1403 −0.883704
\(876\) −4.07311 −0.137618
\(877\) 20.8561 0.704261 0.352131 0.935951i \(-0.385457\pi\)
0.352131 + 0.935951i \(0.385457\pi\)
\(878\) 15.3656 0.518564
\(879\) −14.5398 −0.490415
\(880\) −17.0954 −0.576287
\(881\) 9.62865 0.324398 0.162199 0.986758i \(-0.448141\pi\)
0.162199 + 0.986758i \(0.448141\pi\)
\(882\) 0.215617 0.00726020
\(883\) 16.4198 0.552570 0.276285 0.961076i \(-0.410897\pi\)
0.276285 + 0.961076i \(0.410897\pi\)
\(884\) 3.06356 0.103039
\(885\) 29.5035 0.991749
\(886\) −22.7407 −0.763989
\(887\) 48.5468 1.63004 0.815022 0.579431i \(-0.196725\pi\)
0.815022 + 0.579431i \(0.196725\pi\)
\(888\) 4.28864 0.143917
\(889\) 24.9577 0.837056
\(890\) 7.63653 0.255977
\(891\) 28.9992 0.971510
\(892\) 13.8360 0.463265
\(893\) −31.2823 −1.04682
\(894\) −7.77587 −0.260064
\(895\) −55.0716 −1.84084
\(896\) 2.69745 0.0901156
\(897\) −1.11268 −0.0371512
\(898\) −14.9135 −0.497671
\(899\) 50.9692 1.69992
\(900\) −6.02347 −0.200782
\(901\) 11.5645 0.385270
\(902\) −24.9216 −0.829800
\(903\) −5.05259 −0.168140
\(904\) −13.1529 −0.437458
\(905\) 64.8696 2.15634
\(906\) 0.983610 0.0326783
\(907\) −23.4932 −0.780079 −0.390040 0.920798i \(-0.627539\pi\)
−0.390040 + 0.920798i \(0.627539\pi\)
\(908\) −10.5000 −0.348455
\(909\) −3.56538 −0.118256
\(910\) 7.18449 0.238163
\(911\) −0.163661 −0.00542232 −0.00271116 0.999996i \(-0.500863\pi\)
−0.00271116 + 0.999996i \(0.500863\pi\)
\(912\) 6.93393 0.229605
\(913\) 11.2868 0.373537
\(914\) 22.3010 0.737653
\(915\) −20.2733 −0.670214
\(916\) 12.3635 0.408503
\(917\) 2.69745 0.0890778
\(918\) 23.1026 0.762499
\(919\) −13.7266 −0.452799 −0.226400 0.974034i \(-0.572696\pi\)
−0.226400 + 0.974034i \(0.572696\pi\)
\(920\) 3.56615 0.117572
\(921\) −28.7814 −0.948381
\(922\) −1.90159 −0.0626254
\(923\) 7.00360 0.230526
\(924\) 19.2647 0.633761
\(925\) −22.2159 −0.730456
\(926\) 29.3617 0.964885
\(927\) −5.94855 −0.195376
\(928\) 6.16822 0.202482
\(929\) −0.724085 −0.0237565 −0.0118782 0.999929i \(-0.503781\pi\)
−0.0118782 + 0.999929i \(0.503781\pi\)
\(930\) 43.9011 1.43957
\(931\) 1.28576 0.0421392
\(932\) 7.47482 0.244846
\(933\) 15.6439 0.512159
\(934\) −24.7902 −0.811160
\(935\) −70.1235 −2.29328
\(936\) 0.582930 0.0190537
\(937\) 14.3312 0.468181 0.234091 0.972215i \(-0.424789\pi\)
0.234091 + 0.972215i \(0.424789\pi\)
\(938\) −28.0313 −0.915255
\(939\) 9.77769 0.319083
\(940\) −23.9688 −0.781775
\(941\) 45.7456 1.49126 0.745632 0.666358i \(-0.232148\pi\)
0.745632 + 0.666358i \(0.232148\pi\)
\(942\) −13.4258 −0.437435
\(943\) 5.19872 0.169293
\(944\) 5.55324 0.180743
\(945\) 54.1789 1.76244
\(946\) 6.02716 0.195960
\(947\) 34.3980 1.11778 0.558892 0.829240i \(-0.311227\pi\)
0.558892 + 0.829240i \(0.311227\pi\)
\(948\) −8.73144 −0.283584
\(949\) −2.04193 −0.0662839
\(950\) −35.9190 −1.16537
\(951\) −1.71720 −0.0556839
\(952\) 11.0646 0.358607
\(953\) −47.9522 −1.55333 −0.776663 0.629917i \(-0.783089\pi\)
−0.776663 + 0.629917i \(0.783089\pi\)
\(954\) 2.20049 0.0712434
\(955\) 7.13404 0.230852
\(956\) 2.73435 0.0884350
\(957\) 44.0522 1.42401
\(958\) 15.1463 0.489354
\(959\) 45.8497 1.48056
\(960\) 5.31284 0.171471
\(961\) 37.2805 1.20260
\(962\) 2.14998 0.0693182
\(963\) 7.90129 0.254616
\(964\) 25.7983 0.830907
\(965\) −4.94139 −0.159069
\(966\) −4.01866 −0.129298
\(967\) −53.9920 −1.73627 −0.868133 0.496332i \(-0.834680\pi\)
−0.868133 + 0.496332i \(0.834680\pi\)
\(968\) −11.9806 −0.385071
\(969\) 28.4422 0.913695
\(970\) 20.6469 0.662931
\(971\) 31.6232 1.01484 0.507418 0.861700i \(-0.330600\pi\)
0.507418 + 0.861700i \(0.330600\pi\)
\(972\) 7.88431 0.252889
\(973\) 4.44397 0.142467
\(974\) 21.9472 0.703234
\(975\) 8.58701 0.275004
\(976\) −3.81590 −0.122144
\(977\) 33.5811 1.07435 0.537177 0.843469i \(-0.319491\pi\)
0.537177 + 0.843469i \(0.319491\pi\)
\(978\) −10.3791 −0.331887
\(979\) 10.2654 0.328084
\(980\) 0.985164 0.0314699
\(981\) 0.567578 0.0181214
\(982\) 2.23531 0.0713315
\(983\) −14.6335 −0.466735 −0.233368 0.972389i \(-0.574975\pi\)
−0.233368 + 0.972389i \(0.574975\pi\)
\(984\) 7.74503 0.246903
\(985\) 3.32933 0.106081
\(986\) 25.3013 0.805759
\(987\) 27.0102 0.859744
\(988\) 3.47612 0.110590
\(989\) −1.25728 −0.0399792
\(990\) −13.3430 −0.424069
\(991\) 54.6984 1.73755 0.868777 0.495204i \(-0.164907\pi\)
0.868777 + 0.495204i \(0.164907\pi\)
\(992\) 8.26320 0.262357
\(993\) −31.4017 −0.996503
\(994\) 25.2949 0.802306
\(995\) 0.137391 0.00435560
\(996\) −3.50765 −0.111144
\(997\) 3.56303 0.112842 0.0564212 0.998407i \(-0.482031\pi\)
0.0564212 + 0.998407i \(0.482031\pi\)
\(998\) 10.8109 0.342212
\(999\) 16.2132 0.512964
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 \(a_p\))