Properties

Label 8043.2.a.t.1.16
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(52\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.33568 q^{2}\) \(-1.00000 q^{3}\) \(-0.215968 q^{4}\) \(+1.69750 q^{5}\) \(+1.33568 q^{6}\) \(+1.00000 q^{7}\) \(+2.95982 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.33568 q^{2}\) \(-1.00000 q^{3}\) \(-0.215968 q^{4}\) \(+1.69750 q^{5}\) \(+1.33568 q^{6}\) \(+1.00000 q^{7}\) \(+2.95982 q^{8}\) \(+1.00000 q^{9}\) \(-2.26731 q^{10}\) \(+3.75523 q^{11}\) \(+0.215968 q^{12}\) \(+5.32280 q^{13}\) \(-1.33568 q^{14}\) \(-1.69750 q^{15}\) \(-3.52142 q^{16}\) \(-2.49651 q^{17}\) \(-1.33568 q^{18}\) \(+7.37835 q^{19}\) \(-0.366605 q^{20}\) \(-1.00000 q^{21}\) \(-5.01577 q^{22}\) \(-5.92366 q^{23}\) \(-2.95982 q^{24}\) \(-2.11851 q^{25}\) \(-7.10954 q^{26}\) \(-1.00000 q^{27}\) \(-0.215968 q^{28}\) \(-5.24120 q^{29}\) \(+2.26731 q^{30}\) \(+3.55339 q^{31}\) \(-1.21615 q^{32}\) \(-3.75523 q^{33}\) \(+3.33453 q^{34}\) \(+1.69750 q^{35}\) \(-0.215968 q^{36}\) \(-3.75035 q^{37}\) \(-9.85509 q^{38}\) \(-5.32280 q^{39}\) \(+5.02428 q^{40}\) \(+1.06302 q^{41}\) \(+1.33568 q^{42}\) \(+4.38892 q^{43}\) \(-0.811010 q^{44}\) \(+1.69750 q^{45}\) \(+7.91210 q^{46}\) \(+10.7838 q^{47}\) \(+3.52142 q^{48}\) \(+1.00000 q^{49}\) \(+2.82964 q^{50}\) \(+2.49651 q^{51}\) \(-1.14956 q^{52}\) \(+12.9604 q^{53}\) \(+1.33568 q^{54}\) \(+6.37448 q^{55}\) \(+2.95982 q^{56}\) \(-7.37835 q^{57}\) \(+7.00054 q^{58}\) \(+12.1700 q^{59}\) \(+0.366605 q^{60}\) \(+4.93871 q^{61}\) \(-4.74618 q^{62}\) \(+1.00000 q^{63}\) \(+8.66723 q^{64}\) \(+9.03543 q^{65}\) \(+5.01577 q^{66}\) \(+12.8390 q^{67}\) \(+0.539167 q^{68}\) \(+5.92366 q^{69}\) \(-2.26731 q^{70}\) \(-8.68290 q^{71}\) \(+2.95982 q^{72}\) \(+3.19139 q^{73}\) \(+5.00926 q^{74}\) \(+2.11851 q^{75}\) \(-1.59349 q^{76}\) \(+3.75523 q^{77}\) \(+7.10954 q^{78}\) \(-12.9595 q^{79}\) \(-5.97760 q^{80}\) \(+1.00000 q^{81}\) \(-1.41985 q^{82}\) \(-6.28392 q^{83}\) \(+0.215968 q^{84}\) \(-4.23782 q^{85}\) \(-5.86218 q^{86}\) \(+5.24120 q^{87}\) \(+11.1148 q^{88}\) \(+8.53964 q^{89}\) \(-2.26731 q^{90}\) \(+5.32280 q^{91}\) \(+1.27932 q^{92}\) \(-3.55339 q^{93}\) \(-14.4037 q^{94}\) \(+12.5247 q^{95}\) \(+1.21615 q^{96}\) \(-1.20766 q^{97}\) \(-1.33568 q^{98}\) \(+3.75523 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 61q^{12} \) \(\mathstrut +\mathstrut 44q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 95q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 21q^{20} \) \(\mathstrut -\mathstrut 52q^{21} \) \(\mathstrut +\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 83q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 61q^{28} \) \(\mathstrut +\mathstrut 31q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 71q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 17q^{34} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 61q^{36} \) \(\mathstrut +\mathstrut 71q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 44q^{39} \) \(\mathstrut +\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 25q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut +\mathstrut 75q^{43} \) \(\mathstrut +\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 36q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 95q^{48} \) \(\mathstrut +\mathstrut 52q^{49} \) \(\mathstrut +\mathstrut 26q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 88q^{52} \) \(\mathstrut +\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 7q^{57} \) \(\mathstrut +\mathstrut 48q^{58} \) \(\mathstrut -\mathstrut 27q^{59} \) \(\mathstrut +\mathstrut 21q^{60} \) \(\mathstrut +\mathstrut 59q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 138q^{64} \) \(\mathstrut +\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 65q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut -\mathstrut 83q^{75} \) \(\mathstrut +\mathstrut 31q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 52q^{81} \) \(\mathstrut +\mathstrut 51q^{82} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 61q^{84} \) \(\mathstrut +\mathstrut 70q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 31q^{87} \) \(\mathstrut +\mathstrut 90q^{88} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 34q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 27q^{94} \) \(\mathstrut +\mathstrut 9q^{95} \) \(\mathstrut -\mathstrut 71q^{96} \) \(\mathstrut +\mathstrut 73q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33568 −0.944466 −0.472233 0.881474i \(-0.656552\pi\)
−0.472233 + 0.881474i \(0.656552\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.215968 −0.107984
\(5\) 1.69750 0.759143 0.379572 0.925162i \(-0.376071\pi\)
0.379572 + 0.925162i \(0.376071\pi\)
\(6\) 1.33568 0.545288
\(7\) 1.00000 0.377964
\(8\) 2.95982 1.04645
\(9\) 1.00000 0.333333
\(10\) −2.26731 −0.716985
\(11\) 3.75523 1.13224 0.566122 0.824322i \(-0.308443\pi\)
0.566122 + 0.824322i \(0.308443\pi\)
\(12\) 0.215968 0.0623447
\(13\) 5.32280 1.47628 0.738139 0.674648i \(-0.235705\pi\)
0.738139 + 0.674648i \(0.235705\pi\)
\(14\) −1.33568 −0.356975
\(15\) −1.69750 −0.438292
\(16\) −3.52142 −0.880355
\(17\) −2.49651 −0.605493 −0.302746 0.953071i \(-0.597904\pi\)
−0.302746 + 0.953071i \(0.597904\pi\)
\(18\) −1.33568 −0.314822
\(19\) 7.37835 1.69271 0.846354 0.532620i \(-0.178792\pi\)
0.846354 + 0.532620i \(0.178792\pi\)
\(20\) −0.366605 −0.0819755
\(21\) −1.00000 −0.218218
\(22\) −5.01577 −1.06937
\(23\) −5.92366 −1.23517 −0.617584 0.786505i \(-0.711889\pi\)
−0.617584 + 0.786505i \(0.711889\pi\)
\(24\) −2.95982 −0.604170
\(25\) −2.11851 −0.423702
\(26\) −7.10954 −1.39429
\(27\) −1.00000 −0.192450
\(28\) −0.215968 −0.0408142
\(29\) −5.24120 −0.973266 −0.486633 0.873607i \(-0.661775\pi\)
−0.486633 + 0.873607i \(0.661775\pi\)
\(30\) 2.26731 0.413951
\(31\) 3.55339 0.638207 0.319104 0.947720i \(-0.396618\pi\)
0.319104 + 0.947720i \(0.396618\pi\)
\(32\) −1.21615 −0.214988
\(33\) −3.75523 −0.653701
\(34\) 3.33453 0.571867
\(35\) 1.69750 0.286929
\(36\) −0.215968 −0.0359947
\(37\) −3.75035 −0.616555 −0.308277 0.951297i \(-0.599752\pi\)
−0.308277 + 0.951297i \(0.599752\pi\)
\(38\) −9.85509 −1.59871
\(39\) −5.32280 −0.852330
\(40\) 5.02428 0.794408
\(41\) 1.06302 0.166015 0.0830077 0.996549i \(-0.473547\pi\)
0.0830077 + 0.996549i \(0.473547\pi\)
\(42\) 1.33568 0.206099
\(43\) 4.38892 0.669304 0.334652 0.942342i \(-0.391381\pi\)
0.334652 + 0.942342i \(0.391381\pi\)
\(44\) −0.811010 −0.122264
\(45\) 1.69750 0.253048
\(46\) 7.91210 1.16657
\(47\) 10.7838 1.57298 0.786489 0.617604i \(-0.211896\pi\)
0.786489 + 0.617604i \(0.211896\pi\)
\(48\) 3.52142 0.508273
\(49\) 1.00000 0.142857
\(50\) 2.82964 0.400172
\(51\) 2.49651 0.349581
\(52\) −1.14956 −0.159415
\(53\) 12.9604 1.78025 0.890124 0.455718i \(-0.150617\pi\)
0.890124 + 0.455718i \(0.150617\pi\)
\(54\) 1.33568 0.181763
\(55\) 6.37448 0.859535
\(56\) 2.95982 0.395522
\(57\) −7.37835 −0.977286
\(58\) 7.00054 0.919216
\(59\) 12.1700 1.58440 0.792201 0.610260i \(-0.208935\pi\)
0.792201 + 0.610260i \(0.208935\pi\)
\(60\) 0.366605 0.0473286
\(61\) 4.93871 0.632337 0.316169 0.948703i \(-0.397603\pi\)
0.316169 + 0.948703i \(0.397603\pi\)
\(62\) −4.74618 −0.602765
\(63\) 1.00000 0.125988
\(64\) 8.66723 1.08340
\(65\) 9.03543 1.12071
\(66\) 5.01577 0.617398
\(67\) 12.8390 1.56853 0.784266 0.620425i \(-0.213040\pi\)
0.784266 + 0.620425i \(0.213040\pi\)
\(68\) 0.539167 0.0653836
\(69\) 5.92366 0.713125
\(70\) −2.26731 −0.270995
\(71\) −8.68290 −1.03047 −0.515235 0.857049i \(-0.672295\pi\)
−0.515235 + 0.857049i \(0.672295\pi\)
\(72\) 2.95982 0.348818
\(73\) 3.19139 0.373524 0.186762 0.982405i \(-0.440201\pi\)
0.186762 + 0.982405i \(0.440201\pi\)
\(74\) 5.00926 0.582315
\(75\) 2.11851 0.244624
\(76\) −1.59349 −0.182786
\(77\) 3.75523 0.427948
\(78\) 7.10954 0.804996
\(79\) −12.9595 −1.45806 −0.729031 0.684481i \(-0.760029\pi\)
−0.729031 + 0.684481i \(0.760029\pi\)
\(80\) −5.97760 −0.668316
\(81\) 1.00000 0.111111
\(82\) −1.41985 −0.156796
\(83\) −6.28392 −0.689750 −0.344875 0.938649i \(-0.612079\pi\)
−0.344875 + 0.938649i \(0.612079\pi\)
\(84\) 0.215968 0.0235641
\(85\) −4.23782 −0.459656
\(86\) −5.86218 −0.632135
\(87\) 5.24120 0.561915
\(88\) 11.1148 1.18484
\(89\) 8.53964 0.905200 0.452600 0.891714i \(-0.350496\pi\)
0.452600 + 0.891714i \(0.350496\pi\)
\(90\) −2.26731 −0.238995
\(91\) 5.32280 0.557981
\(92\) 1.27932 0.133379
\(93\) −3.55339 −0.368469
\(94\) −14.4037 −1.48562
\(95\) 12.5247 1.28501
\(96\) 1.21615 0.124123
\(97\) −1.20766 −0.122619 −0.0613097 0.998119i \(-0.519528\pi\)
−0.0613097 + 0.998119i \(0.519528\pi\)
\(98\) −1.33568 −0.134924
\(99\) 3.75523 0.377414
\(100\) 0.457531 0.0457531
\(101\) 16.3275 1.62465 0.812324 0.583206i \(-0.198202\pi\)
0.812324 + 0.583206i \(0.198202\pi\)
\(102\) −3.33453 −0.330168
\(103\) 7.41862 0.730978 0.365489 0.930816i \(-0.380902\pi\)
0.365489 + 0.930816i \(0.380902\pi\)
\(104\) 15.7545 1.54486
\(105\) −1.69750 −0.165659
\(106\) −17.3109 −1.68138
\(107\) −18.8442 −1.82174 −0.910871 0.412691i \(-0.864589\pi\)
−0.910871 + 0.412691i \(0.864589\pi\)
\(108\) 0.215968 0.0207816
\(109\) −5.17771 −0.495935 −0.247967 0.968768i \(-0.579763\pi\)
−0.247967 + 0.968768i \(0.579763\pi\)
\(110\) −8.51424 −0.811801
\(111\) 3.75035 0.355968
\(112\) −3.52142 −0.332743
\(113\) −4.09944 −0.385643 −0.192821 0.981234i \(-0.561764\pi\)
−0.192821 + 0.981234i \(0.561764\pi\)
\(114\) 9.85509 0.923013
\(115\) −10.0554 −0.937670
\(116\) 1.13193 0.105097
\(117\) 5.32280 0.492093
\(118\) −16.2552 −1.49641
\(119\) −2.49651 −0.228855
\(120\) −5.02428 −0.458652
\(121\) 3.10172 0.281975
\(122\) −6.59652 −0.597221
\(123\) −1.06302 −0.0958491
\(124\) −0.767419 −0.0689163
\(125\) −12.0836 −1.08079
\(126\) −1.33568 −0.118992
\(127\) 6.02495 0.534628 0.267314 0.963610i \(-0.413864\pi\)
0.267314 + 0.963610i \(0.413864\pi\)
\(128\) −9.14431 −0.808250
\(129\) −4.38892 −0.386423
\(130\) −12.0684 −1.05847
\(131\) −7.33967 −0.641270 −0.320635 0.947203i \(-0.603896\pi\)
−0.320635 + 0.947203i \(0.603896\pi\)
\(132\) 0.811010 0.0705894
\(133\) 7.37835 0.639784
\(134\) −17.1487 −1.48143
\(135\) −1.69750 −0.146097
\(136\) −7.38921 −0.633620
\(137\) −8.68237 −0.741785 −0.370892 0.928676i \(-0.620948\pi\)
−0.370892 + 0.928676i \(0.620948\pi\)
\(138\) −7.91210 −0.673522
\(139\) −4.14693 −0.351738 −0.175869 0.984414i \(-0.556273\pi\)
−0.175869 + 0.984414i \(0.556273\pi\)
\(140\) −0.366605 −0.0309838
\(141\) −10.7838 −0.908160
\(142\) 11.5975 0.973244
\(143\) 19.9883 1.67151
\(144\) −3.52142 −0.293452
\(145\) −8.89691 −0.738848
\(146\) −4.26267 −0.352781
\(147\) −1.00000 −0.0824786
\(148\) 0.809958 0.0665781
\(149\) −20.5114 −1.68036 −0.840180 0.542307i \(-0.817551\pi\)
−0.840180 + 0.542307i \(0.817551\pi\)
\(150\) −2.82964 −0.231039
\(151\) −15.1657 −1.23417 −0.617085 0.786897i \(-0.711686\pi\)
−0.617085 + 0.786897i \(0.711686\pi\)
\(152\) 21.8386 1.77134
\(153\) −2.49651 −0.201831
\(154\) −5.01577 −0.404182
\(155\) 6.03186 0.484491
\(156\) 1.14956 0.0920381
\(157\) 8.17014 0.652048 0.326024 0.945361i \(-0.394291\pi\)
0.326024 + 0.945361i \(0.394291\pi\)
\(158\) 17.3098 1.37709
\(159\) −12.9604 −1.02783
\(160\) −2.06442 −0.163207
\(161\) −5.92366 −0.466850
\(162\) −1.33568 −0.104941
\(163\) −11.6560 −0.912968 −0.456484 0.889732i \(-0.650891\pi\)
−0.456484 + 0.889732i \(0.650891\pi\)
\(164\) −0.229578 −0.0179270
\(165\) −6.37448 −0.496253
\(166\) 8.39329 0.651446
\(167\) −5.42683 −0.419941 −0.209970 0.977708i \(-0.567337\pi\)
−0.209970 + 0.977708i \(0.567337\pi\)
\(168\) −2.95982 −0.228355
\(169\) 15.3322 1.17940
\(170\) 5.66035 0.434129
\(171\) 7.37835 0.564236
\(172\) −0.947868 −0.0722743
\(173\) 18.3772 1.39719 0.698597 0.715515i \(-0.253808\pi\)
0.698597 + 0.715515i \(0.253808\pi\)
\(174\) −7.00054 −0.530710
\(175\) −2.11851 −0.160144
\(176\) −13.2237 −0.996776
\(177\) −12.1700 −0.914755
\(178\) −11.4062 −0.854931
\(179\) 15.1027 1.12883 0.564416 0.825491i \(-0.309101\pi\)
0.564416 + 0.825491i \(0.309101\pi\)
\(180\) −0.366605 −0.0273252
\(181\) −6.32077 −0.469819 −0.234910 0.972017i \(-0.575479\pi\)
−0.234910 + 0.972017i \(0.575479\pi\)
\(182\) −7.10954 −0.526994
\(183\) −4.93871 −0.365080
\(184\) −17.5330 −1.29255
\(185\) −6.36621 −0.468053
\(186\) 4.74618 0.348006
\(187\) −9.37496 −0.685565
\(188\) −2.32896 −0.169857
\(189\) −1.00000 −0.0727393
\(190\) −16.7290 −1.21365
\(191\) 26.6769 1.93028 0.965138 0.261742i \(-0.0842970\pi\)
0.965138 + 0.261742i \(0.0842970\pi\)
\(192\) −8.66723 −0.625504
\(193\) 13.0202 0.937215 0.468608 0.883406i \(-0.344756\pi\)
0.468608 + 0.883406i \(0.344756\pi\)
\(194\) 1.61305 0.115810
\(195\) −9.03543 −0.647040
\(196\) −0.215968 −0.0154263
\(197\) −14.4235 −1.02763 −0.513815 0.857901i \(-0.671768\pi\)
−0.513815 + 0.857901i \(0.671768\pi\)
\(198\) −5.01577 −0.356455
\(199\) 2.51404 0.178216 0.0891078 0.996022i \(-0.471598\pi\)
0.0891078 + 0.996022i \(0.471598\pi\)
\(200\) −6.27039 −0.443384
\(201\) −12.8390 −0.905592
\(202\) −21.8083 −1.53442
\(203\) −5.24120 −0.367860
\(204\) −0.539167 −0.0377493
\(205\) 1.80447 0.126030
\(206\) −9.90887 −0.690384
\(207\) −5.92366 −0.411723
\(208\) −18.7438 −1.29965
\(209\) 27.7074 1.91656
\(210\) 2.26731 0.156459
\(211\) −5.58475 −0.384470 −0.192235 0.981349i \(-0.561574\pi\)
−0.192235 + 0.981349i \(0.561574\pi\)
\(212\) −2.79904 −0.192239
\(213\) 8.68290 0.594942
\(214\) 25.1698 1.72057
\(215\) 7.45018 0.508098
\(216\) −2.95982 −0.201390
\(217\) 3.55339 0.241220
\(218\) 6.91575 0.468393
\(219\) −3.19139 −0.215654
\(220\) −1.37669 −0.0928162
\(221\) −13.2884 −0.893876
\(222\) −5.00926 −0.336200
\(223\) 15.8619 1.06219 0.531095 0.847312i \(-0.321781\pi\)
0.531095 + 0.847312i \(0.321781\pi\)
\(224\) −1.21615 −0.0812577
\(225\) −2.11851 −0.141234
\(226\) 5.47552 0.364226
\(227\) 26.8776 1.78393 0.891964 0.452106i \(-0.149327\pi\)
0.891964 + 0.452106i \(0.149327\pi\)
\(228\) 1.59349 0.105531
\(229\) 15.2681 1.00895 0.504473 0.863427i \(-0.331687\pi\)
0.504473 + 0.863427i \(0.331687\pi\)
\(230\) 13.4308 0.885597
\(231\) −3.75523 −0.247076
\(232\) −15.5130 −1.01848
\(233\) 13.3056 0.871680 0.435840 0.900024i \(-0.356451\pi\)
0.435840 + 0.900024i \(0.356451\pi\)
\(234\) −7.10954 −0.464765
\(235\) 18.3055 1.19412
\(236\) −2.62834 −0.171090
\(237\) 12.9595 0.841812
\(238\) 3.33453 0.216146
\(239\) −18.3294 −1.18563 −0.592814 0.805340i \(-0.701983\pi\)
−0.592814 + 0.805340i \(0.701983\pi\)
\(240\) 5.97760 0.385852
\(241\) −7.63094 −0.491552 −0.245776 0.969327i \(-0.579043\pi\)
−0.245776 + 0.969327i \(0.579043\pi\)
\(242\) −4.14290 −0.266316
\(243\) −1.00000 −0.0641500
\(244\) −1.06661 −0.0682824
\(245\) 1.69750 0.108449
\(246\) 1.41985 0.0905262
\(247\) 39.2734 2.49891
\(248\) 10.5174 0.667854
\(249\) 6.28392 0.398227
\(250\) 16.1398 1.02077
\(251\) 13.5907 0.857839 0.428919 0.903343i \(-0.358894\pi\)
0.428919 + 0.903343i \(0.358894\pi\)
\(252\) −0.215968 −0.0136047
\(253\) −22.2447 −1.39851
\(254\) −8.04738 −0.504938
\(255\) 4.23782 0.265382
\(256\) −5.12063 −0.320039
\(257\) 0.642134 0.0400552 0.0200276 0.999799i \(-0.493625\pi\)
0.0200276 + 0.999799i \(0.493625\pi\)
\(258\) 5.86218 0.364963
\(259\) −3.75035 −0.233036
\(260\) −1.95137 −0.121019
\(261\) −5.24120 −0.324422
\(262\) 9.80342 0.605657
\(263\) −0.825121 −0.0508791 −0.0254396 0.999676i \(-0.508099\pi\)
−0.0254396 + 0.999676i \(0.508099\pi\)
\(264\) −11.1148 −0.684068
\(265\) 22.0002 1.35146
\(266\) −9.85509 −0.604254
\(267\) −8.53964 −0.522618
\(268\) −2.77282 −0.169377
\(269\) −18.9954 −1.15817 −0.579084 0.815268i \(-0.696590\pi\)
−0.579084 + 0.815268i \(0.696590\pi\)
\(270\) 2.26731 0.137984
\(271\) −11.4377 −0.694791 −0.347396 0.937719i \(-0.612934\pi\)
−0.347396 + 0.937719i \(0.612934\pi\)
\(272\) 8.79126 0.533049
\(273\) −5.32280 −0.322150
\(274\) 11.5968 0.700590
\(275\) −7.95548 −0.479733
\(276\) −1.27932 −0.0770062
\(277\) 16.8365 1.01161 0.505804 0.862649i \(-0.331196\pi\)
0.505804 + 0.862649i \(0.331196\pi\)
\(278\) 5.53895 0.332204
\(279\) 3.55339 0.212736
\(280\) 5.02428 0.300258
\(281\) −9.22285 −0.550189 −0.275094 0.961417i \(-0.588709\pi\)
−0.275094 + 0.961417i \(0.588709\pi\)
\(282\) 14.4037 0.857726
\(283\) 25.6717 1.52602 0.763012 0.646384i \(-0.223720\pi\)
0.763012 + 0.646384i \(0.223720\pi\)
\(284\) 1.87523 0.111274
\(285\) −12.5247 −0.741900
\(286\) −26.6979 −1.57868
\(287\) 1.06302 0.0627480
\(288\) −1.21615 −0.0716626
\(289\) −10.7674 −0.633379
\(290\) 11.8834 0.697817
\(291\) 1.20766 0.0707944
\(292\) −0.689240 −0.0403347
\(293\) −30.9067 −1.80559 −0.902795 0.430070i \(-0.858489\pi\)
−0.902795 + 0.430070i \(0.858489\pi\)
\(294\) 1.33568 0.0778982
\(295\) 20.6586 1.20279
\(296\) −11.1004 −0.645195
\(297\) −3.75523 −0.217900
\(298\) 27.3966 1.58704
\(299\) −31.5305 −1.82345
\(300\) −0.457531 −0.0264155
\(301\) 4.38892 0.252973
\(302\) 20.2565 1.16563
\(303\) −16.3275 −0.937991
\(304\) −25.9823 −1.49019
\(305\) 8.38344 0.480034
\(306\) 3.33453 0.190622
\(307\) −20.8554 −1.19028 −0.595140 0.803622i \(-0.702903\pi\)
−0.595140 + 0.803622i \(0.702903\pi\)
\(308\) −0.811010 −0.0462116
\(309\) −7.41862 −0.422030
\(310\) −8.05661 −0.457585
\(311\) −17.0656 −0.967700 −0.483850 0.875151i \(-0.660762\pi\)
−0.483850 + 0.875151i \(0.660762\pi\)
\(312\) −15.7545 −0.891923
\(313\) −7.13261 −0.403159 −0.201580 0.979472i \(-0.564607\pi\)
−0.201580 + 0.979472i \(0.564607\pi\)
\(314\) −10.9127 −0.615837
\(315\) 1.69750 0.0956431
\(316\) 2.79885 0.157448
\(317\) −20.0951 −1.12865 −0.564326 0.825552i \(-0.690864\pi\)
−0.564326 + 0.825552i \(0.690864\pi\)
\(318\) 17.3109 0.970748
\(319\) −19.6819 −1.10197
\(320\) 14.7126 0.822459
\(321\) 18.8442 1.05178
\(322\) 7.91210 0.440924
\(323\) −18.4201 −1.02492
\(324\) −0.215968 −0.0119982
\(325\) −11.2764 −0.625501
\(326\) 15.5686 0.862267
\(327\) 5.17771 0.286328
\(328\) 3.14634 0.173727
\(329\) 10.7838 0.594530
\(330\) 8.51424 0.468694
\(331\) −8.46792 −0.465439 −0.232719 0.972544i \(-0.574762\pi\)
−0.232719 + 0.972544i \(0.574762\pi\)
\(332\) 1.35713 0.0744821
\(333\) −3.75035 −0.205518
\(334\) 7.24849 0.396620
\(335\) 21.7941 1.19074
\(336\) 3.52142 0.192109
\(337\) 22.2680 1.21302 0.606508 0.795077i \(-0.292570\pi\)
0.606508 + 0.795077i \(0.292570\pi\)
\(338\) −20.4788 −1.11390
\(339\) 4.09944 0.222651
\(340\) 0.915234 0.0496355
\(341\) 13.3438 0.722606
\(342\) −9.85509 −0.532902
\(343\) 1.00000 0.0539949
\(344\) 12.9904 0.700396
\(345\) 10.0554 0.541364
\(346\) −24.5460 −1.31960
\(347\) −9.10153 −0.488595 −0.244298 0.969700i \(-0.578557\pi\)
−0.244298 + 0.969700i \(0.578557\pi\)
\(348\) −1.13193 −0.0606780
\(349\) 3.77629 0.202140 0.101070 0.994879i \(-0.467773\pi\)
0.101070 + 0.994879i \(0.467773\pi\)
\(350\) 2.82964 0.151251
\(351\) −5.32280 −0.284110
\(352\) −4.56693 −0.243418
\(353\) 0.491194 0.0261436 0.0130718 0.999915i \(-0.495839\pi\)
0.0130718 + 0.999915i \(0.495839\pi\)
\(354\) 16.2552 0.863955
\(355\) −14.7392 −0.782275
\(356\) −1.84429 −0.0977473
\(357\) 2.49651 0.132129
\(358\) −20.1724 −1.06614
\(359\) 16.7852 0.885889 0.442944 0.896549i \(-0.353934\pi\)
0.442944 + 0.896549i \(0.353934\pi\)
\(360\) 5.02428 0.264803
\(361\) 35.4400 1.86526
\(362\) 8.44250 0.443728
\(363\) −3.10172 −0.162798
\(364\) −1.14956 −0.0602531
\(365\) 5.41738 0.283558
\(366\) 6.59652 0.344806
\(367\) 12.9189 0.674360 0.337180 0.941440i \(-0.390527\pi\)
0.337180 + 0.941440i \(0.390527\pi\)
\(368\) 20.8597 1.08739
\(369\) 1.06302 0.0553385
\(370\) 8.50320 0.442060
\(371\) 12.9604 0.672871
\(372\) 0.767419 0.0397888
\(373\) 4.10925 0.212769 0.106385 0.994325i \(-0.466073\pi\)
0.106385 + 0.994325i \(0.466073\pi\)
\(374\) 12.5219 0.647493
\(375\) 12.0836 0.623996
\(376\) 31.9181 1.64605
\(377\) −27.8978 −1.43681
\(378\) 1.33568 0.0686998
\(379\) 8.73671 0.448775 0.224387 0.974500i \(-0.427962\pi\)
0.224387 + 0.974500i \(0.427962\pi\)
\(380\) −2.70494 −0.138761
\(381\) −6.02495 −0.308667
\(382\) −35.6318 −1.82308
\(383\) −1.00000 −0.0510976
\(384\) 9.14431 0.466643
\(385\) 6.37448 0.324874
\(386\) −17.3908 −0.885168
\(387\) 4.38892 0.223101
\(388\) 0.260817 0.0132410
\(389\) −13.4081 −0.679819 −0.339909 0.940458i \(-0.610396\pi\)
−0.339909 + 0.940458i \(0.610396\pi\)
\(390\) 12.0684 0.611108
\(391\) 14.7885 0.747886
\(392\) 2.95982 0.149493
\(393\) 7.33967 0.370237
\(394\) 19.2651 0.970561
\(395\) −21.9988 −1.10688
\(396\) −0.811010 −0.0407548
\(397\) −16.3886 −0.822519 −0.411259 0.911518i \(-0.634911\pi\)
−0.411259 + 0.911518i \(0.634911\pi\)
\(398\) −3.35794 −0.168319
\(399\) −7.37835 −0.369379
\(400\) 7.46016 0.373008
\(401\) 27.3698 1.36678 0.683392 0.730052i \(-0.260504\pi\)
0.683392 + 0.730052i \(0.260504\pi\)
\(402\) 17.1487 0.855301
\(403\) 18.9140 0.942171
\(404\) −3.52623 −0.175436
\(405\) 1.69750 0.0843492
\(406\) 7.00054 0.347431
\(407\) −14.0834 −0.698090
\(408\) 7.38921 0.365821
\(409\) −10.9155 −0.539738 −0.269869 0.962897i \(-0.586980\pi\)
−0.269869 + 0.962897i \(0.586980\pi\)
\(410\) −2.41019 −0.119031
\(411\) 8.68237 0.428270
\(412\) −1.60219 −0.0789341
\(413\) 12.1700 0.598848
\(414\) 7.91210 0.388858
\(415\) −10.6669 −0.523619
\(416\) −6.47334 −0.317382
\(417\) 4.14693 0.203076
\(418\) −37.0081 −1.81012
\(419\) 30.2530 1.47795 0.738977 0.673730i \(-0.235309\pi\)
0.738977 + 0.673730i \(0.235309\pi\)
\(420\) 0.366605 0.0178885
\(421\) 5.90060 0.287577 0.143789 0.989608i \(-0.454071\pi\)
0.143789 + 0.989608i \(0.454071\pi\)
\(422\) 7.45942 0.363119
\(423\) 10.7838 0.524326
\(424\) 38.3604 1.86295
\(425\) 5.28888 0.256548
\(426\) −11.5975 −0.561903
\(427\) 4.93871 0.239001
\(428\) 4.06976 0.196719
\(429\) −19.9883 −0.965045
\(430\) −9.95103 −0.479881
\(431\) −1.01165 −0.0487294 −0.0243647 0.999703i \(-0.507756\pi\)
−0.0243647 + 0.999703i \(0.507756\pi\)
\(432\) 3.52142 0.169424
\(433\) 31.7253 1.52462 0.762311 0.647211i \(-0.224065\pi\)
0.762311 + 0.647211i \(0.224065\pi\)
\(434\) −4.74618 −0.227824
\(435\) 8.89691 0.426574
\(436\) 1.11822 0.0535531
\(437\) −43.7068 −2.09078
\(438\) 4.26267 0.203678
\(439\) 21.5617 1.02909 0.514543 0.857465i \(-0.327962\pi\)
0.514543 + 0.857465i \(0.327962\pi\)
\(440\) 18.8673 0.899463
\(441\) 1.00000 0.0476190
\(442\) 17.7490 0.844235
\(443\) −35.5429 −1.68869 −0.844346 0.535798i \(-0.820011\pi\)
−0.844346 + 0.535798i \(0.820011\pi\)
\(444\) −0.809958 −0.0384389
\(445\) 14.4960 0.687177
\(446\) −21.1863 −1.00320
\(447\) 20.5114 0.970157
\(448\) 8.66723 0.409488
\(449\) −31.2291 −1.47379 −0.736896 0.676006i \(-0.763709\pi\)
−0.736896 + 0.676006i \(0.763709\pi\)
\(450\) 2.82964 0.133391
\(451\) 3.99187 0.187970
\(452\) 0.885349 0.0416433
\(453\) 15.1657 0.712548
\(454\) −35.8998 −1.68486
\(455\) 9.03543 0.423587
\(456\) −21.8386 −1.02268
\(457\) 14.8037 0.692487 0.346243 0.938145i \(-0.387457\pi\)
0.346243 + 0.938145i \(0.387457\pi\)
\(458\) −20.3933 −0.952915
\(459\) 2.49651 0.116527
\(460\) 2.17165 0.101254
\(461\) −26.9870 −1.25691 −0.628455 0.777846i \(-0.716312\pi\)
−0.628455 + 0.777846i \(0.716312\pi\)
\(462\) 5.01577 0.233355
\(463\) 20.7330 0.963545 0.481772 0.876296i \(-0.339993\pi\)
0.481772 + 0.876296i \(0.339993\pi\)
\(464\) 18.4565 0.856820
\(465\) −6.03186 −0.279721
\(466\) −17.7720 −0.823272
\(467\) −26.8341 −1.24174 −0.620868 0.783915i \(-0.713220\pi\)
−0.620868 + 0.783915i \(0.713220\pi\)
\(468\) −1.14956 −0.0531382
\(469\) 12.8390 0.592849
\(470\) −24.4502 −1.12780
\(471\) −8.17014 −0.376460
\(472\) 36.0210 1.65800
\(473\) 16.4814 0.757816
\(474\) −17.3098 −0.795063
\(475\) −15.6311 −0.717203
\(476\) 0.539167 0.0247127
\(477\) 12.9604 0.593416
\(478\) 24.4821 1.11978
\(479\) 24.6417 1.12591 0.562954 0.826488i \(-0.309665\pi\)
0.562954 + 0.826488i \(0.309665\pi\)
\(480\) 2.06442 0.0942273
\(481\) −19.9624 −0.910206
\(482\) 10.1925 0.464254
\(483\) 5.92366 0.269536
\(484\) −0.669874 −0.0304488
\(485\) −2.05000 −0.0930858
\(486\) 1.33568 0.0605875
\(487\) 18.0099 0.816108 0.408054 0.912958i \(-0.366208\pi\)
0.408054 + 0.912958i \(0.366208\pi\)
\(488\) 14.6177 0.661711
\(489\) 11.6560 0.527102
\(490\) −2.26731 −0.102426
\(491\) −19.2469 −0.868601 −0.434301 0.900768i \(-0.643004\pi\)
−0.434301 + 0.900768i \(0.643004\pi\)
\(492\) 0.229578 0.0103502
\(493\) 13.0847 0.589305
\(494\) −52.4566 −2.36013
\(495\) 6.37448 0.286512
\(496\) −12.5130 −0.561849
\(497\) −8.68290 −0.389481
\(498\) −8.39329 −0.376112
\(499\) 16.4691 0.737260 0.368630 0.929576i \(-0.379827\pi\)
0.368630 + 0.929576i \(0.379827\pi\)
\(500\) 2.60968 0.116709
\(501\) 5.42683 0.242453
\(502\) −18.1528 −0.810199
\(503\) 3.03448 0.135301 0.0676504 0.997709i \(-0.478450\pi\)
0.0676504 + 0.997709i \(0.478450\pi\)
\(504\) 2.95982 0.131841
\(505\) 27.7159 1.23334
\(506\) 29.7117 1.32085
\(507\) −15.3322 −0.680926
\(508\) −1.30120 −0.0577313
\(509\) 23.0428 1.02135 0.510677 0.859773i \(-0.329395\pi\)
0.510677 + 0.859773i \(0.329395\pi\)
\(510\) −5.66035 −0.250645
\(511\) 3.19139 0.141179
\(512\) 25.1281 1.11052
\(513\) −7.37835 −0.325762
\(514\) −0.857684 −0.0378308
\(515\) 12.5931 0.554917
\(516\) 0.947868 0.0417276
\(517\) 40.4956 1.78099
\(518\) 5.00926 0.220094
\(519\) −18.3772 −0.806670
\(520\) 26.7432 1.17277
\(521\) −22.8920 −1.00291 −0.501457 0.865182i \(-0.667203\pi\)
−0.501457 + 0.865182i \(0.667203\pi\)
\(522\) 7.00054 0.306405
\(523\) −20.1557 −0.881347 −0.440674 0.897667i \(-0.645260\pi\)
−0.440674 + 0.897667i \(0.645260\pi\)
\(524\) 1.58514 0.0692470
\(525\) 2.11851 0.0924593
\(526\) 1.10209 0.0480536
\(527\) −8.87107 −0.386430
\(528\) 13.2237 0.575489
\(529\) 12.0898 0.525642
\(530\) −29.3852 −1.27641
\(531\) 12.1700 0.528134
\(532\) −1.59349 −0.0690865
\(533\) 5.65823 0.245085
\(534\) 11.4062 0.493595
\(535\) −31.9880 −1.38296
\(536\) 38.0011 1.64140
\(537\) −15.1027 −0.651731
\(538\) 25.3717 1.09385
\(539\) 3.75523 0.161749
\(540\) 0.366605 0.0157762
\(541\) 22.4002 0.963062 0.481531 0.876429i \(-0.340081\pi\)
0.481531 + 0.876429i \(0.340081\pi\)
\(542\) 15.2771 0.656206
\(543\) 6.32077 0.271250
\(544\) 3.03614 0.130174
\(545\) −8.78914 −0.376485
\(546\) 7.10954 0.304260
\(547\) −31.9766 −1.36722 −0.683610 0.729847i \(-0.739591\pi\)
−0.683610 + 0.729847i \(0.739591\pi\)
\(548\) 1.87512 0.0801010
\(549\) 4.93871 0.210779
\(550\) 10.6259 0.453092
\(551\) −38.6714 −1.64746
\(552\) 17.5330 0.746252
\(553\) −12.9595 −0.551096
\(554\) −22.4881 −0.955429
\(555\) 6.36621 0.270231
\(556\) 0.895605 0.0379821
\(557\) −1.77205 −0.0750841 −0.0375421 0.999295i \(-0.511953\pi\)
−0.0375421 + 0.999295i \(0.511953\pi\)
\(558\) −4.74618 −0.200922
\(559\) 23.3613 0.988080
\(560\) −5.97760 −0.252600
\(561\) 9.37496 0.395811
\(562\) 12.3187 0.519635
\(563\) −33.1272 −1.39615 −0.698073 0.716027i \(-0.745959\pi\)
−0.698073 + 0.716027i \(0.745959\pi\)
\(564\) 2.32896 0.0980669
\(565\) −6.95878 −0.292758
\(566\) −34.2891 −1.44128
\(567\) 1.00000 0.0419961
\(568\) −25.6998 −1.07834
\(569\) −41.5393 −1.74142 −0.870710 0.491798i \(-0.836340\pi\)
−0.870710 + 0.491798i \(0.836340\pi\)
\(570\) 16.7290 0.700699
\(571\) −32.2555 −1.34985 −0.674926 0.737885i \(-0.735824\pi\)
−0.674926 + 0.737885i \(0.735824\pi\)
\(572\) −4.31684 −0.180496
\(573\) −26.6769 −1.11445
\(574\) −1.41985 −0.0592633
\(575\) 12.5493 0.523343
\(576\) 8.66723 0.361135
\(577\) 33.6431 1.40058 0.700289 0.713859i \(-0.253054\pi\)
0.700289 + 0.713859i \(0.253054\pi\)
\(578\) 14.3818 0.598204
\(579\) −13.0202 −0.541101
\(580\) 1.92145 0.0797839
\(581\) −6.28392 −0.260701
\(582\) −1.61305 −0.0668629
\(583\) 48.6693 2.01567
\(584\) 9.44594 0.390876
\(585\) 9.03543 0.373569
\(586\) 41.2814 1.70532
\(587\) −40.6368 −1.67726 −0.838631 0.544700i \(-0.816643\pi\)
−0.838631 + 0.544700i \(0.816643\pi\)
\(588\) 0.215968 0.00890638
\(589\) 26.2181 1.08030
\(590\) −27.5932 −1.13599
\(591\) 14.4235 0.593302
\(592\) 13.2066 0.542787
\(593\) 7.77946 0.319464 0.159732 0.987160i \(-0.448937\pi\)
0.159732 + 0.987160i \(0.448937\pi\)
\(594\) 5.01577 0.205799
\(595\) −4.23782 −0.173734
\(596\) 4.42982 0.181452
\(597\) −2.51404 −0.102893
\(598\) 42.1145 1.72219
\(599\) −19.5135 −0.797300 −0.398650 0.917103i \(-0.630521\pi\)
−0.398650 + 0.917103i \(0.630521\pi\)
\(600\) 6.27039 0.255988
\(601\) 10.6220 0.433281 0.216640 0.976251i \(-0.430490\pi\)
0.216640 + 0.976251i \(0.430490\pi\)
\(602\) −5.86218 −0.238925
\(603\) 12.8390 0.522844
\(604\) 3.27532 0.133271
\(605\) 5.26516 0.214059
\(606\) 21.8083 0.885900
\(607\) −28.0475 −1.13841 −0.569207 0.822194i \(-0.692750\pi\)
−0.569207 + 0.822194i \(0.692750\pi\)
\(608\) −8.97321 −0.363912
\(609\) 5.24120 0.212384
\(610\) −11.1976 −0.453376
\(611\) 57.4000 2.32215
\(612\) 0.539167 0.0217945
\(613\) −16.2849 −0.657743 −0.328871 0.944375i \(-0.606668\pi\)
−0.328871 + 0.944375i \(0.606668\pi\)
\(614\) 27.8560 1.12418
\(615\) −1.80447 −0.0727632
\(616\) 11.1148 0.447827
\(617\) −0.624218 −0.0251301 −0.0125650 0.999921i \(-0.504000\pi\)
−0.0125650 + 0.999921i \(0.504000\pi\)
\(618\) 9.90887 0.398593
\(619\) 2.50764 0.100791 0.0503953 0.998729i \(-0.483952\pi\)
0.0503953 + 0.998729i \(0.483952\pi\)
\(620\) −1.30269 −0.0523173
\(621\) 5.92366 0.237708
\(622\) 22.7941 0.913960
\(623\) 8.53964 0.342134
\(624\) 18.7438 0.750353
\(625\) −9.91939 −0.396775
\(626\) 9.52687 0.380770
\(627\) −27.7074 −1.10653
\(628\) −1.76449 −0.0704109
\(629\) 9.36280 0.373319
\(630\) −2.26731 −0.0903316
\(631\) −40.3774 −1.60740 −0.803699 0.595037i \(-0.797138\pi\)
−0.803699 + 0.595037i \(0.797138\pi\)
\(632\) −38.3579 −1.52579
\(633\) 5.58475 0.221974
\(634\) 26.8405 1.06597
\(635\) 10.2273 0.405859
\(636\) 2.79904 0.110989
\(637\) 5.32280 0.210897
\(638\) 26.2886 1.04078
\(639\) −8.68290 −0.343490
\(640\) −15.5224 −0.613578
\(641\) 13.2862 0.524773 0.262386 0.964963i \(-0.415491\pi\)
0.262386 + 0.964963i \(0.415491\pi\)
\(642\) −25.1698 −0.993374
\(643\) −17.4125 −0.686682 −0.343341 0.939211i \(-0.611559\pi\)
−0.343341 + 0.939211i \(0.611559\pi\)
\(644\) 1.27932 0.0504124
\(645\) −7.45018 −0.293351
\(646\) 24.6033 0.968005
\(647\) 18.5961 0.731088 0.365544 0.930794i \(-0.380883\pi\)
0.365544 + 0.930794i \(0.380883\pi\)
\(648\) 2.95982 0.116273
\(649\) 45.7012 1.79393
\(650\) 15.0616 0.590765
\(651\) −3.55339 −0.139268
\(652\) 2.51733 0.0985861
\(653\) 33.8070 1.32297 0.661485 0.749958i \(-0.269926\pi\)
0.661485 + 0.749958i \(0.269926\pi\)
\(654\) −6.91575 −0.270427
\(655\) −12.4591 −0.486816
\(656\) −3.74333 −0.146153
\(657\) 3.19139 0.124508
\(658\) −14.4037 −0.561513
\(659\) −33.3206 −1.29798 −0.648992 0.760795i \(-0.724809\pi\)
−0.648992 + 0.760795i \(0.724809\pi\)
\(660\) 1.37669 0.0535874
\(661\) 12.2738 0.477396 0.238698 0.971094i \(-0.423279\pi\)
0.238698 + 0.971094i \(0.423279\pi\)
\(662\) 11.3104 0.439591
\(663\) 13.2884 0.516079
\(664\) −18.5993 −0.721791
\(665\) 12.5247 0.485688
\(666\) 5.00926 0.194105
\(667\) 31.0471 1.20215
\(668\) 1.17202 0.0453469
\(669\) −15.8619 −0.613256
\(670\) −29.1099 −1.12461
\(671\) 18.5460 0.715959
\(672\) 1.21615 0.0469142
\(673\) 41.9057 1.61535 0.807673 0.589631i \(-0.200727\pi\)
0.807673 + 0.589631i \(0.200727\pi\)
\(674\) −29.7429 −1.14565
\(675\) 2.11851 0.0815414
\(676\) −3.31126 −0.127356
\(677\) 12.0934 0.464788 0.232394 0.972622i \(-0.425344\pi\)
0.232394 + 0.972622i \(0.425344\pi\)
\(678\) −5.47552 −0.210286
\(679\) −1.20766 −0.0463458
\(680\) −12.5432 −0.481008
\(681\) −26.8776 −1.02995
\(682\) −17.8230 −0.682476
\(683\) 4.74954 0.181736 0.0908680 0.995863i \(-0.471036\pi\)
0.0908680 + 0.995863i \(0.471036\pi\)
\(684\) −1.59349 −0.0609286
\(685\) −14.7383 −0.563121
\(686\) −1.33568 −0.0509964
\(687\) −15.2681 −0.582515
\(688\) −15.4552 −0.589226
\(689\) 68.9856 2.62814
\(690\) −13.4308 −0.511300
\(691\) 37.1894 1.41475 0.707376 0.706837i \(-0.249879\pi\)
0.707376 + 0.706837i \(0.249879\pi\)
\(692\) −3.96890 −0.150875
\(693\) 3.75523 0.142649
\(694\) 12.1567 0.461462
\(695\) −7.03939 −0.267019
\(696\) 15.5130 0.588018
\(697\) −2.65384 −0.100521
\(698\) −5.04390 −0.190914
\(699\) −13.3056 −0.503265
\(700\) 0.457531 0.0172930
\(701\) −16.9795 −0.641308 −0.320654 0.947196i \(-0.603903\pi\)
−0.320654 + 0.947196i \(0.603903\pi\)
\(702\) 7.10954 0.268332
\(703\) −27.6714 −1.04365
\(704\) 32.5474 1.22668
\(705\) −18.3055 −0.689423
\(706\) −0.656077 −0.0246918
\(707\) 16.3275 0.614059
\(708\) 2.62834 0.0987790
\(709\) −3.88506 −0.145906 −0.0729532 0.997335i \(-0.523242\pi\)
−0.0729532 + 0.997335i \(0.523242\pi\)
\(710\) 19.6868 0.738832
\(711\) −12.9595 −0.486021
\(712\) 25.2758 0.947250
\(713\) −21.0491 −0.788294
\(714\) −3.33453 −0.124792
\(715\) 33.9301 1.26891
\(716\) −3.26171 −0.121896
\(717\) 18.3294 0.684522
\(718\) −22.4196 −0.836692
\(719\) −11.0565 −0.412338 −0.206169 0.978516i \(-0.566100\pi\)
−0.206169 + 0.978516i \(0.566100\pi\)
\(720\) −5.97760 −0.222772
\(721\) 7.41862 0.276284
\(722\) −47.3364 −1.76168
\(723\) 7.63094 0.283798
\(724\) 1.36509 0.0507330
\(725\) 11.1035 0.412374
\(726\) 4.14290 0.153757
\(727\) 13.0931 0.485597 0.242799 0.970077i \(-0.421935\pi\)
0.242799 + 0.970077i \(0.421935\pi\)
\(728\) 15.7545 0.583901
\(729\) 1.00000 0.0370370
\(730\) −7.23586 −0.267811
\(731\) −10.9570 −0.405259
\(732\) 1.06661 0.0394229
\(733\) −0.249606 −0.00921942 −0.00460971 0.999989i \(-0.501467\pi\)
−0.00460971 + 0.999989i \(0.501467\pi\)
\(734\) −17.2554 −0.636910
\(735\) −1.69750 −0.0626131
\(736\) 7.20409 0.265546
\(737\) 48.2133 1.77596
\(738\) −1.41985 −0.0522653
\(739\) 30.4472 1.12002 0.560010 0.828486i \(-0.310797\pi\)
0.560010 + 0.828486i \(0.310797\pi\)
\(740\) 1.37490 0.0505423
\(741\) −39.2734 −1.44275
\(742\) −17.3109 −0.635504
\(743\) −13.0890 −0.480190 −0.240095 0.970749i \(-0.577179\pi\)
−0.240095 + 0.970749i \(0.577179\pi\)
\(744\) −10.5174 −0.385586
\(745\) −34.8180 −1.27563
\(746\) −5.48863 −0.200953
\(747\) −6.28392 −0.229917
\(748\) 2.02470 0.0740302
\(749\) −18.8442 −0.688554
\(750\) −16.1398 −0.589343
\(751\) −11.8460 −0.432267 −0.216134 0.976364i \(-0.569345\pi\)
−0.216134 + 0.976364i \(0.569345\pi\)
\(752\) −37.9743 −1.38478
\(753\) −13.5907 −0.495273
\(754\) 37.2625 1.35702
\(755\) −25.7438 −0.936912
\(756\) 0.215968 0.00785469
\(757\) 43.1212 1.56727 0.783634 0.621223i \(-0.213364\pi\)
0.783634 + 0.621223i \(0.213364\pi\)
\(758\) −11.6694 −0.423852
\(759\) 22.2447 0.807431
\(760\) 37.0709 1.34470
\(761\) 34.2917 1.24307 0.621537 0.783385i \(-0.286508\pi\)
0.621537 + 0.783385i \(0.286508\pi\)
\(762\) 8.04738 0.291526
\(763\) −5.17771 −0.187446
\(764\) −5.76137 −0.208439
\(765\) −4.23782 −0.153219
\(766\) 1.33568 0.0482600
\(767\) 64.7786 2.33902
\(768\) 5.12063 0.184775
\(769\) −3.46281 −0.124872 −0.0624361 0.998049i \(-0.519887\pi\)
−0.0624361 + 0.998049i \(0.519887\pi\)
\(770\) −8.51424 −0.306832
\(771\) −0.642134 −0.0231259
\(772\) −2.81195 −0.101204
\(773\) 36.8435 1.32517 0.662584 0.748987i \(-0.269460\pi\)
0.662584 + 0.748987i \(0.269460\pi\)
\(774\) −5.86218 −0.210712
\(775\) −7.52788 −0.270409
\(776\) −3.57446 −0.128316
\(777\) 3.75035 0.134543
\(778\) 17.9089 0.642066
\(779\) 7.84331 0.281016
\(780\) 1.95137 0.0698701
\(781\) −32.6062 −1.16674
\(782\) −19.7526 −0.706353
\(783\) 5.24120 0.187305
\(784\) −3.52142 −0.125765
\(785\) 13.8688 0.494998
\(786\) −9.80342 −0.349676
\(787\) −14.4079 −0.513588 −0.256794 0.966466i \(-0.582666\pi\)
−0.256794 + 0.966466i \(0.582666\pi\)
\(788\) 3.11501 0.110968
\(789\) 0.825121 0.0293751
\(790\) 29.3832 1.04541
\(791\) −4.09944 −0.145759
\(792\) 11.1148 0.394947
\(793\) 26.2878 0.933506
\(794\) 21.8898 0.776841
\(795\) −22.0002 −0.780268
\(796\) −0.542953 −0.0192445
\(797\) −6.27037 −0.222108 −0.111054 0.993814i \(-0.535423\pi\)
−0.111054 + 0.993814i \(0.535423\pi\)
\(798\) 9.85509 0.348866
\(799\) −26.9219 −0.952427
\(800\) 2.57643 0.0910906
\(801\) 8.53964 0.301733
\(802\) −36.5572 −1.29088
\(803\) 11.9844 0.422920
\(804\) 2.77282 0.0977896
\(805\) −10.0554 −0.354406
\(806\) −25.2629 −0.889849
\(807\) 18.9954 0.668668
\(808\) 48.3264 1.70012
\(809\) 20.4750 0.719864 0.359932 0.932979i \(-0.382800\pi\)
0.359932 + 0.932979i \(0.382800\pi\)
\(810\) −2.26731 −0.0796650
\(811\) −23.8349 −0.836956 −0.418478 0.908227i \(-0.637436\pi\)
−0.418478 + 0.908227i \(0.637436\pi\)
\(812\) 1.13193 0.0397231
\(813\) 11.4377 0.401138
\(814\) 18.8109 0.659322
\(815\) −19.7860 −0.693073
\(816\) −8.79126 −0.307756
\(817\) 32.3830 1.13294
\(818\) 14.5796 0.509764
\(819\) 5.32280 0.185994
\(820\) −0.389708 −0.0136092
\(821\) 35.7441 1.24748 0.623739 0.781633i \(-0.285613\pi\)
0.623739 + 0.781633i \(0.285613\pi\)
\(822\) −11.5968 −0.404486
\(823\) 10.3709 0.361507 0.180753 0.983528i \(-0.442146\pi\)
0.180753 + 0.983528i \(0.442146\pi\)
\(824\) 21.9577 0.764934
\(825\) 7.95548 0.276974
\(826\) −16.2552 −0.565591
\(827\) −2.86561 −0.0996469 −0.0498234 0.998758i \(-0.515866\pi\)
−0.0498234 + 0.998758i \(0.515866\pi\)
\(828\) 1.27932 0.0444596
\(829\) 30.2709 1.05135 0.525676 0.850685i \(-0.323812\pi\)
0.525676 + 0.850685i \(0.323812\pi\)
\(830\) 14.2476 0.494540
\(831\) −16.8365 −0.584052
\(832\) 46.1339 1.59941
\(833\) −2.49651 −0.0864990
\(834\) −5.53895 −0.191798
\(835\) −9.21202 −0.318795
\(836\) −5.98391 −0.206958
\(837\) −3.55339 −0.122823
\(838\) −40.4082 −1.39588
\(839\) 16.7672 0.578867 0.289433 0.957198i \(-0.406533\pi\)
0.289433 + 0.957198i \(0.406533\pi\)
\(840\) −5.02428 −0.173354
\(841\) −1.52985 −0.0527534
\(842\) −7.88129 −0.271607
\(843\) 9.22285 0.317652
\(844\) 1.20613 0.0415167
\(845\) 26.0263 0.895332
\(846\) −14.4037 −0.495208
\(847\) 3.10172 0.106576
\(848\) −45.6390 −1.56725
\(849\) −25.6717 −0.881051
\(850\) −7.06423 −0.242301
\(851\) 22.2158 0.761549
\(852\) −1.87523 −0.0642444
\(853\) 23.4945 0.804438 0.402219 0.915544i \(-0.368239\pi\)
0.402219 + 0.915544i \(0.368239\pi\)
\(854\) −6.59652 −0.225728
\(855\) 12.5247 0.428336
\(856\) −55.7755 −1.90637
\(857\) −25.6041 −0.874621 −0.437311 0.899311i \(-0.644069\pi\)
−0.437311 + 0.899311i \(0.644069\pi\)
\(858\) 26.6979 0.911452
\(859\) −31.5902 −1.07784 −0.538922 0.842356i \(-0.681168\pi\)
−0.538922 + 0.842356i \(0.681168\pi\)
\(860\) −1.60900 −0.0548665
\(861\) −1.06302 −0.0362275
\(862\) 1.35123 0.0460232
\(863\) 41.3966 1.40916 0.704578 0.709626i \(-0.251136\pi\)
0.704578 + 0.709626i \(0.251136\pi\)
\(864\) 1.21615 0.0413744
\(865\) 31.1953 1.06067
\(866\) −42.3748 −1.43995
\(867\) 10.7674 0.365681
\(868\) −0.767419 −0.0260479
\(869\) −48.6660 −1.65088
\(870\) −11.8834 −0.402885
\(871\) 68.3393 2.31559
\(872\) −15.3251 −0.518972
\(873\) −1.20766 −0.0408732
\(874\) 58.3782 1.97467
\(875\) −12.0836 −0.408502
\(876\) 0.689240 0.0232873
\(877\) 12.6263 0.426361 0.213181 0.977013i \(-0.431618\pi\)
0.213181 + 0.977013i \(0.431618\pi\)
\(878\) −28.7995 −0.971936
\(879\) 30.9067 1.04246
\(880\) −22.4472 −0.756696
\(881\) 30.2927 1.02059 0.510294 0.860000i \(-0.329536\pi\)
0.510294 + 0.860000i \(0.329536\pi\)
\(882\) −1.33568 −0.0449746
\(883\) 40.5711 1.36533 0.682663 0.730733i \(-0.260822\pi\)
0.682663 + 0.730733i \(0.260822\pi\)
\(884\) 2.86988 0.0965244
\(885\) −20.6586 −0.694430
\(886\) 47.4738 1.59491
\(887\) −23.1901 −0.778646 −0.389323 0.921101i \(-0.627291\pi\)
−0.389323 + 0.921101i \(0.627291\pi\)
\(888\) 11.1004 0.372504
\(889\) 6.02495 0.202070
\(890\) −19.3620 −0.649015
\(891\) 3.75523 0.125805
\(892\) −3.42566 −0.114700
\(893\) 79.5666 2.66260
\(894\) −27.3966 −0.916280
\(895\) 25.6368 0.856945
\(896\) −9.14431 −0.305490
\(897\) 31.5305 1.05277
\(898\) 41.7120 1.39195
\(899\) −18.6240 −0.621145
\(900\) 0.457531 0.0152510
\(901\) −32.3558 −1.07793
\(902\) −5.33185 −0.177531
\(903\) −4.38892 −0.146054
\(904\) −12.1336 −0.403557
\(905\) −10.7295 −0.356660
\(906\) −20.2565 −0.672977
\(907\) −49.3629 −1.63907 −0.819534 0.573031i \(-0.805768\pi\)
−0.819534 + 0.573031i \(0.805768\pi\)
\(908\) −5.80471 −0.192636
\(909\) 16.3275 0.541549
\(910\) −12.0684 −0.400064
\(911\) 18.8909 0.625884 0.312942 0.949772i \(-0.398686\pi\)
0.312942 + 0.949772i \(0.398686\pi\)
\(912\) 25.9823 0.860359
\(913\) −23.5976 −0.780965
\(914\) −19.7729 −0.654030
\(915\) −8.38344 −0.277148
\(916\) −3.29743 −0.108950
\(917\) −7.33967 −0.242377
\(918\) −3.33453 −0.110056
\(919\) 7.76030 0.255989 0.127994 0.991775i \(-0.459146\pi\)
0.127994 + 0.991775i \(0.459146\pi\)
\(920\) −29.7621 −0.981228
\(921\) 20.8554 0.687208
\(922\) 36.0459 1.18711
\(923\) −46.2173 −1.52126
\(924\) 0.811010 0.0266803
\(925\) 7.94516 0.261235
\(926\) −27.6926 −0.910035
\(927\) 7.41862 0.243659
\(928\) 6.37411 0.209240
\(929\) −38.2558 −1.25513 −0.627566 0.778564i \(-0.715949\pi\)
−0.627566 + 0.778564i \(0.715949\pi\)
\(930\) 8.05661 0.264187
\(931\) 7.37835 0.241816
\(932\) −2.87359 −0.0941276
\(933\) 17.0656 0.558702
\(934\) 35.8417 1.17278
\(935\) −15.9140 −0.520442
\(936\) 15.7545 0.514952
\(937\) −13.5973 −0.444205 −0.222103 0.975023i \(-0.571292\pi\)
−0.222103 + 0.975023i \(0.571292\pi\)
\(938\) −17.1487 −0.559926
\(939\) 7.13261 0.232764
\(940\) −3.95340 −0.128946
\(941\) 40.9053 1.33348 0.666738 0.745292i \(-0.267690\pi\)
0.666738 + 0.745292i \(0.267690\pi\)
\(942\) 10.9127 0.355554
\(943\) −6.29696 −0.205057
\(944\) −42.8558 −1.39484
\(945\) −1.69750 −0.0552195
\(946\) −22.0138 −0.715731
\(947\) 4.79280 0.155745 0.0778726 0.996963i \(-0.475187\pi\)
0.0778726 + 0.996963i \(0.475187\pi\)
\(948\) −2.79885 −0.0909024
\(949\) 16.9871 0.551426
\(950\) 20.8781 0.677374
\(951\) 20.0951 0.651627
\(952\) −7.38921 −0.239486
\(953\) −37.5412 −1.21608 −0.608040 0.793907i \(-0.708044\pi\)
−0.608040 + 0.793907i \(0.708044\pi\)
\(954\) −17.3109 −0.560461
\(955\) 45.2840 1.46536
\(956\) 3.95856 0.128029
\(957\) 19.6819 0.636225
\(958\) −32.9134 −1.06338
\(959\) −8.68237 −0.280368
\(960\) −14.7126 −0.474847
\(961\) −18.3734 −0.592692
\(962\) 26.6633 0.859659
\(963\) −18.8442 −0.607247
\(964\) 1.64804 0.0530798
\(965\) 22.1018 0.711481
\(966\) −7.91210 −0.254568
\(967\) 31.0487 0.998458 0.499229 0.866470i \(-0.333617\pi\)
0.499229 + 0.866470i \(0.333617\pi\)
\(968\) 9.18053 0.295074
\(969\) 18.4201 0.591740
\(970\) 2.73814 0.0879163
\(971\) −36.0446 −1.15673 −0.578363 0.815779i \(-0.696308\pi\)
−0.578363 + 0.815779i \(0.696308\pi\)
\(972\) 0.215968 0.00692719
\(973\) −4.14693 −0.132944
\(974\) −24.0554 −0.770786
\(975\) 11.2764 0.361133
\(976\) −17.3913 −0.556681
\(977\) −13.4368 −0.429883 −0.214941 0.976627i \(-0.568956\pi\)
−0.214941 + 0.976627i \(0.568956\pi\)
\(978\) −15.5686 −0.497830
\(979\) 32.0683 1.02491
\(980\) −0.366605 −0.0117108
\(981\) −5.17771 −0.165312
\(982\) 25.7077 0.820364
\(983\) −55.3856 −1.76653 −0.883263 0.468879i \(-0.844658\pi\)
−0.883263 + 0.468879i \(0.844658\pi\)
\(984\) −3.14634 −0.100302
\(985\) −24.4838 −0.780118
\(986\) −17.4769 −0.556579
\(987\) −10.7838 −0.343252
\(988\) −8.48182 −0.269843
\(989\) −25.9985 −0.826704
\(990\) −8.51424 −0.270600
\(991\) −34.1703 −1.08546 −0.542728 0.839909i \(-0.682608\pi\)
−0.542728 + 0.839909i \(0.682608\pi\)
\(992\) −4.32147 −0.137207
\(993\) 8.46792 0.268721
\(994\) 11.5975 0.367852
\(995\) 4.26757 0.135291
\(996\) −1.35713 −0.0430023
\(997\) 44.0089 1.39378 0.696888 0.717180i \(-0.254567\pi\)
0.696888 + 0.717180i \(0.254567\pi\)
\(998\) −21.9975 −0.696317
\(999\) 3.75035 0.118656
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 \(a_p\))