Properties

Label 8042.2.a.a.1.9
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 1
Dimension 67
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(1\)
Dimension: \(67\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.46688 q^{3}\) \(+1.00000 q^{4}\) \(+0.597421 q^{5}\) \(-2.46688 q^{6}\) \(-5.04196 q^{7}\) \(+1.00000 q^{8}\) \(+3.08551 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.46688 q^{3}\) \(+1.00000 q^{4}\) \(+0.597421 q^{5}\) \(-2.46688 q^{6}\) \(-5.04196 q^{7}\) \(+1.00000 q^{8}\) \(+3.08551 q^{9}\) \(+0.597421 q^{10}\) \(-0.206237 q^{11}\) \(-2.46688 q^{12}\) \(-5.16007 q^{13}\) \(-5.04196 q^{14}\) \(-1.47377 q^{15}\) \(+1.00000 q^{16}\) \(+2.07476 q^{17}\) \(+3.08551 q^{18}\) \(+6.06110 q^{19}\) \(+0.597421 q^{20}\) \(+12.4379 q^{21}\) \(-0.206237 q^{22}\) \(+5.27834 q^{23}\) \(-2.46688 q^{24}\) \(-4.64309 q^{25}\) \(-5.16007 q^{26}\) \(-0.210949 q^{27}\) \(-5.04196 q^{28}\) \(+1.72108 q^{29}\) \(-1.47377 q^{30}\) \(+0.341745 q^{31}\) \(+1.00000 q^{32}\) \(+0.508761 q^{33}\) \(+2.07476 q^{34}\) \(-3.01217 q^{35}\) \(+3.08551 q^{36}\) \(-5.96190 q^{37}\) \(+6.06110 q^{38}\) \(+12.7293 q^{39}\) \(+0.597421 q^{40}\) \(+11.3004 q^{41}\) \(+12.4379 q^{42}\) \(-4.28605 q^{43}\) \(-0.206237 q^{44}\) \(+1.84335 q^{45}\) \(+5.27834 q^{46}\) \(-6.15907 q^{47}\) \(-2.46688 q^{48}\) \(+18.4214 q^{49}\) \(-4.64309 q^{50}\) \(-5.11820 q^{51}\) \(-5.16007 q^{52}\) \(+4.17344 q^{53}\) \(-0.210949 q^{54}\) \(-0.123210 q^{55}\) \(-5.04196 q^{56}\) \(-14.9520 q^{57}\) \(+1.72108 q^{58}\) \(+2.75819 q^{59}\) \(-1.47377 q^{60}\) \(+1.42361 q^{61}\) \(+0.341745 q^{62}\) \(-15.5570 q^{63}\) \(+1.00000 q^{64}\) \(-3.08273 q^{65}\) \(+0.508761 q^{66}\) \(+15.0329 q^{67}\) \(+2.07476 q^{68}\) \(-13.0211 q^{69}\) \(-3.01217 q^{70}\) \(-2.37465 q^{71}\) \(+3.08551 q^{72}\) \(-12.6825 q^{73}\) \(-5.96190 q^{74}\) \(+11.4540 q^{75}\) \(+6.06110 q^{76}\) \(+1.03984 q^{77}\) \(+12.7293 q^{78}\) \(+13.0518 q^{79}\) \(+0.597421 q^{80}\) \(-8.73615 q^{81}\) \(+11.3004 q^{82}\) \(+4.49973 q^{83}\) \(+12.4379 q^{84}\) \(+1.23951 q^{85}\) \(-4.28605 q^{86}\) \(-4.24570 q^{87}\) \(-0.206237 q^{88}\) \(-8.99137 q^{89}\) \(+1.84335 q^{90}\) \(+26.0169 q^{91}\) \(+5.27834 q^{92}\) \(-0.843046 q^{93}\) \(-6.15907 q^{94}\) \(+3.62103 q^{95}\) \(-2.46688 q^{96}\) \(-0.752092 q^{97}\) \(+18.4214 q^{98}\) \(-0.636345 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.46688 −1.42426 −0.712128 0.702050i \(-0.752268\pi\)
−0.712128 + 0.702050i \(0.752268\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.597421 0.267175 0.133587 0.991037i \(-0.457350\pi\)
0.133587 + 0.991037i \(0.457350\pi\)
\(6\) −2.46688 −1.00710
\(7\) −5.04196 −1.90568 −0.952841 0.303470i \(-0.901855\pi\)
−0.952841 + 0.303470i \(0.901855\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.08551 1.02850
\(10\) 0.597421 0.188921
\(11\) −0.206237 −0.0621827 −0.0310913 0.999517i \(-0.509898\pi\)
−0.0310913 + 0.999517i \(0.509898\pi\)
\(12\) −2.46688 −0.712128
\(13\) −5.16007 −1.43115 −0.715573 0.698538i \(-0.753834\pi\)
−0.715573 + 0.698538i \(0.753834\pi\)
\(14\) −5.04196 −1.34752
\(15\) −1.47377 −0.380525
\(16\) 1.00000 0.250000
\(17\) 2.07476 0.503204 0.251602 0.967831i \(-0.419043\pi\)
0.251602 + 0.967831i \(0.419043\pi\)
\(18\) 3.08551 0.727262
\(19\) 6.06110 1.39051 0.695256 0.718762i \(-0.255291\pi\)
0.695256 + 0.718762i \(0.255291\pi\)
\(20\) 0.597421 0.133587
\(21\) 12.4379 2.71418
\(22\) −0.206237 −0.0439698
\(23\) 5.27834 1.10061 0.550305 0.834964i \(-0.314511\pi\)
0.550305 + 0.834964i \(0.314511\pi\)
\(24\) −2.46688 −0.503550
\(25\) −4.64309 −0.928618
\(26\) −5.16007 −1.01197
\(27\) −0.210949 −0.0405971
\(28\) −5.04196 −0.952841
\(29\) 1.72108 0.319596 0.159798 0.987150i \(-0.448916\pi\)
0.159798 + 0.987150i \(0.448916\pi\)
\(30\) −1.47377 −0.269072
\(31\) 0.341745 0.0613793 0.0306896 0.999529i \(-0.490230\pi\)
0.0306896 + 0.999529i \(0.490230\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.508761 0.0885640
\(34\) 2.07476 0.355819
\(35\) −3.01217 −0.509150
\(36\) 3.08551 0.514252
\(37\) −5.96190 −0.980130 −0.490065 0.871686i \(-0.663027\pi\)
−0.490065 + 0.871686i \(0.663027\pi\)
\(38\) 6.06110 0.983241
\(39\) 12.7293 2.03832
\(40\) 0.597421 0.0944605
\(41\) 11.3004 1.76482 0.882410 0.470481i \(-0.155920\pi\)
0.882410 + 0.470481i \(0.155920\pi\)
\(42\) 12.4379 1.91921
\(43\) −4.28605 −0.653617 −0.326809 0.945091i \(-0.605973\pi\)
−0.326809 + 0.945091i \(0.605973\pi\)
\(44\) −0.206237 −0.0310913
\(45\) 1.84335 0.274790
\(46\) 5.27834 0.778249
\(47\) −6.15907 −0.898392 −0.449196 0.893433i \(-0.648290\pi\)
−0.449196 + 0.893433i \(0.648290\pi\)
\(48\) −2.46688 −0.356064
\(49\) 18.4214 2.63162
\(50\) −4.64309 −0.656632
\(51\) −5.11820 −0.716691
\(52\) −5.16007 −0.715573
\(53\) 4.17344 0.573266 0.286633 0.958040i \(-0.407464\pi\)
0.286633 + 0.958040i \(0.407464\pi\)
\(54\) −0.210949 −0.0287065
\(55\) −0.123210 −0.0166136
\(56\) −5.04196 −0.673760
\(57\) −14.9520 −1.98045
\(58\) 1.72108 0.225988
\(59\) 2.75819 0.359086 0.179543 0.983750i \(-0.442538\pi\)
0.179543 + 0.983750i \(0.442538\pi\)
\(60\) −1.47377 −0.190263
\(61\) 1.42361 0.182275 0.0911375 0.995838i \(-0.470950\pi\)
0.0911375 + 0.995838i \(0.470950\pi\)
\(62\) 0.341745 0.0434017
\(63\) −15.5570 −1.96000
\(64\) 1.00000 0.125000
\(65\) −3.08273 −0.382366
\(66\) 0.508761 0.0626242
\(67\) 15.0329 1.83656 0.918280 0.395932i \(-0.129578\pi\)
0.918280 + 0.395932i \(0.129578\pi\)
\(68\) 2.07476 0.251602
\(69\) −13.0211 −1.56755
\(70\) −3.01217 −0.360023
\(71\) −2.37465 −0.281820 −0.140910 0.990022i \(-0.545003\pi\)
−0.140910 + 0.990022i \(0.545003\pi\)
\(72\) 3.08551 0.363631
\(73\) −12.6825 −1.48437 −0.742185 0.670196i \(-0.766210\pi\)
−0.742185 + 0.670196i \(0.766210\pi\)
\(74\) −5.96190 −0.693056
\(75\) 11.4540 1.32259
\(76\) 6.06110 0.695256
\(77\) 1.03984 0.118500
\(78\) 12.7293 1.44131
\(79\) 13.0518 1.46844 0.734219 0.678913i \(-0.237549\pi\)
0.734219 + 0.678913i \(0.237549\pi\)
\(80\) 0.597421 0.0667937
\(81\) −8.73615 −0.970683
\(82\) 11.3004 1.24792
\(83\) 4.49973 0.493909 0.246955 0.969027i \(-0.420570\pi\)
0.246955 + 0.969027i \(0.420570\pi\)
\(84\) 12.4379 1.35709
\(85\) 1.23951 0.134443
\(86\) −4.28605 −0.462177
\(87\) −4.24570 −0.455186
\(88\) −0.206237 −0.0219849
\(89\) −8.99137 −0.953083 −0.476542 0.879152i \(-0.658110\pi\)
−0.476542 + 0.879152i \(0.658110\pi\)
\(90\) 1.84335 0.194306
\(91\) 26.0169 2.72731
\(92\) 5.27834 0.550305
\(93\) −0.843046 −0.0874198
\(94\) −6.15907 −0.635259
\(95\) 3.62103 0.371510
\(96\) −2.46688 −0.251775
\(97\) −0.752092 −0.0763633 −0.0381817 0.999271i \(-0.512157\pi\)
−0.0381817 + 0.999271i \(0.512157\pi\)
\(98\) 18.4214 1.86084
\(99\) −0.636345 −0.0639551
\(100\) −4.64309 −0.464309
\(101\) −4.41017 −0.438828 −0.219414 0.975632i \(-0.570415\pi\)
−0.219414 + 0.975632i \(0.570415\pi\)
\(102\) −5.11820 −0.506777
\(103\) 7.47654 0.736685 0.368343 0.929690i \(-0.379925\pi\)
0.368343 + 0.929690i \(0.379925\pi\)
\(104\) −5.16007 −0.505987
\(105\) 7.43068 0.725160
\(106\) 4.17344 0.405360
\(107\) −3.03143 −0.293059 −0.146529 0.989206i \(-0.546810\pi\)
−0.146529 + 0.989206i \(0.546810\pi\)
\(108\) −0.210949 −0.0202985
\(109\) −19.9203 −1.90802 −0.954009 0.299777i \(-0.903088\pi\)
−0.954009 + 0.299777i \(0.903088\pi\)
\(110\) −0.123210 −0.0117476
\(111\) 14.7073 1.39596
\(112\) −5.04196 −0.476420
\(113\) 6.24512 0.587492 0.293746 0.955884i \(-0.405098\pi\)
0.293746 + 0.955884i \(0.405098\pi\)
\(114\) −14.9520 −1.40039
\(115\) 3.15339 0.294055
\(116\) 1.72108 0.159798
\(117\) −15.9215 −1.47194
\(118\) 2.75819 0.253912
\(119\) −10.4609 −0.958947
\(120\) −1.47377 −0.134536
\(121\) −10.9575 −0.996133
\(122\) 1.42361 0.128888
\(123\) −27.8767 −2.51355
\(124\) 0.341745 0.0306896
\(125\) −5.76098 −0.515278
\(126\) −15.5570 −1.38593
\(127\) −15.8217 −1.40395 −0.701975 0.712201i \(-0.747698\pi\)
−0.701975 + 0.712201i \(0.747698\pi\)
\(128\) 1.00000 0.0883883
\(129\) 10.5732 0.930918
\(130\) −3.08273 −0.270374
\(131\) −15.9499 −1.39355 −0.696775 0.717289i \(-0.745383\pi\)
−0.696775 + 0.717289i \(0.745383\pi\)
\(132\) 0.508761 0.0442820
\(133\) −30.5598 −2.64987
\(134\) 15.0329 1.29864
\(135\) −0.126025 −0.0108465
\(136\) 2.07476 0.177909
\(137\) 8.79086 0.751054 0.375527 0.926811i \(-0.377462\pi\)
0.375527 + 0.926811i \(0.377462\pi\)
\(138\) −13.0211 −1.10843
\(139\) 5.01522 0.425386 0.212693 0.977119i \(-0.431777\pi\)
0.212693 + 0.977119i \(0.431777\pi\)
\(140\) −3.01217 −0.254575
\(141\) 15.1937 1.27954
\(142\) −2.37465 −0.199277
\(143\) 1.06420 0.0889925
\(144\) 3.08551 0.257126
\(145\) 1.02821 0.0853879
\(146\) −12.6825 −1.04961
\(147\) −45.4434 −3.74811
\(148\) −5.96190 −0.490065
\(149\) −8.33167 −0.682557 −0.341279 0.939962i \(-0.610860\pi\)
−0.341279 + 0.939962i \(0.610860\pi\)
\(150\) 11.4540 0.935212
\(151\) −1.08744 −0.0884946 −0.0442473 0.999021i \(-0.514089\pi\)
−0.0442473 + 0.999021i \(0.514089\pi\)
\(152\) 6.06110 0.491620
\(153\) 6.40171 0.517547
\(154\) 1.03984 0.0837924
\(155\) 0.204166 0.0163990
\(156\) 12.7293 1.01916
\(157\) −13.7631 −1.09842 −0.549209 0.835685i \(-0.685071\pi\)
−0.549209 + 0.835685i \(0.685071\pi\)
\(158\) 13.0518 1.03834
\(159\) −10.2954 −0.816477
\(160\) 0.597421 0.0472303
\(161\) −26.6132 −2.09741
\(162\) −8.73615 −0.686377
\(163\) 10.4848 0.821235 0.410618 0.911808i \(-0.365313\pi\)
0.410618 + 0.911808i \(0.365313\pi\)
\(164\) 11.3004 0.882410
\(165\) 0.303945 0.0236621
\(166\) 4.49973 0.349246
\(167\) −3.90386 −0.302090 −0.151045 0.988527i \(-0.548264\pi\)
−0.151045 + 0.988527i \(0.548264\pi\)
\(168\) 12.4379 0.959607
\(169\) 13.6263 1.04818
\(170\) 1.23951 0.0950658
\(171\) 18.7016 1.43015
\(172\) −4.28605 −0.326809
\(173\) −9.56419 −0.727152 −0.363576 0.931565i \(-0.618444\pi\)
−0.363576 + 0.931565i \(0.618444\pi\)
\(174\) −4.24570 −0.321865
\(175\) 23.4103 1.76965
\(176\) −0.206237 −0.0155457
\(177\) −6.80413 −0.511430
\(178\) −8.99137 −0.673932
\(179\) 11.2547 0.841212 0.420606 0.907243i \(-0.361817\pi\)
0.420606 + 0.907243i \(0.361817\pi\)
\(180\) 1.84335 0.137395
\(181\) 25.3725 1.88592 0.942962 0.332900i \(-0.108027\pi\)
0.942962 + 0.332900i \(0.108027\pi\)
\(182\) 26.0169 1.92850
\(183\) −3.51189 −0.259606
\(184\) 5.27834 0.389125
\(185\) −3.56176 −0.261866
\(186\) −0.843046 −0.0618151
\(187\) −0.427892 −0.0312906
\(188\) −6.15907 −0.449196
\(189\) 1.06359 0.0773651
\(190\) 3.62103 0.262697
\(191\) −10.3545 −0.749226 −0.374613 0.927181i \(-0.622224\pi\)
−0.374613 + 0.927181i \(0.622224\pi\)
\(192\) −2.46688 −0.178032
\(193\) −0.158094 −0.0113798 −0.00568992 0.999984i \(-0.501811\pi\)
−0.00568992 + 0.999984i \(0.501811\pi\)
\(194\) −0.752092 −0.0539970
\(195\) 7.60475 0.544587
\(196\) 18.4214 1.31581
\(197\) −18.1348 −1.29205 −0.646024 0.763317i \(-0.723569\pi\)
−0.646024 + 0.763317i \(0.723569\pi\)
\(198\) −0.636345 −0.0452231
\(199\) 7.36515 0.522101 0.261051 0.965325i \(-0.415931\pi\)
0.261051 + 0.965325i \(0.415931\pi\)
\(200\) −4.64309 −0.328316
\(201\) −37.0844 −2.61573
\(202\) −4.41017 −0.310298
\(203\) −8.67760 −0.609048
\(204\) −5.11820 −0.358346
\(205\) 6.75107 0.471515
\(206\) 7.47654 0.520915
\(207\) 16.2864 1.13198
\(208\) −5.16007 −0.357787
\(209\) −1.25002 −0.0864658
\(210\) 7.43068 0.512765
\(211\) 2.54089 0.174922 0.0874610 0.996168i \(-0.472125\pi\)
0.0874610 + 0.996168i \(0.472125\pi\)
\(212\) 4.17344 0.286633
\(213\) 5.85799 0.401383
\(214\) −3.03143 −0.207224
\(215\) −2.56058 −0.174630
\(216\) −0.210949 −0.0143532
\(217\) −1.72307 −0.116969
\(218\) −19.9203 −1.34917
\(219\) 31.2861 2.11412
\(220\) −0.123210 −0.00830682
\(221\) −10.7059 −0.720159
\(222\) 14.7073 0.987089
\(223\) −9.24713 −0.619233 −0.309617 0.950861i \(-0.600201\pi\)
−0.309617 + 0.950861i \(0.600201\pi\)
\(224\) −5.04196 −0.336880
\(225\) −14.3263 −0.955087
\(226\) 6.24512 0.415419
\(227\) 9.89379 0.656674 0.328337 0.944561i \(-0.393512\pi\)
0.328337 + 0.944561i \(0.393512\pi\)
\(228\) −14.9520 −0.990223
\(229\) −19.8534 −1.31195 −0.655974 0.754783i \(-0.727742\pi\)
−0.655974 + 0.754783i \(0.727742\pi\)
\(230\) 3.15339 0.207928
\(231\) −2.56516 −0.168775
\(232\) 1.72108 0.112994
\(233\) −15.2656 −1.00008 −0.500041 0.866002i \(-0.666682\pi\)
−0.500041 + 0.866002i \(0.666682\pi\)
\(234\) −15.9215 −1.04082
\(235\) −3.67955 −0.240028
\(236\) 2.75819 0.179543
\(237\) −32.1972 −2.09143
\(238\) −10.4609 −0.678078
\(239\) 1.48746 0.0962161 0.0481080 0.998842i \(-0.484681\pi\)
0.0481080 + 0.998842i \(0.484681\pi\)
\(240\) −1.47377 −0.0951313
\(241\) −15.6219 −1.00630 −0.503149 0.864200i \(-0.667825\pi\)
−0.503149 + 0.864200i \(0.667825\pi\)
\(242\) −10.9575 −0.704373
\(243\) 22.1839 1.42310
\(244\) 1.42361 0.0911375
\(245\) 11.0053 0.703103
\(246\) −27.8767 −1.77735
\(247\) −31.2757 −1.99003
\(248\) 0.341745 0.0217009
\(249\) −11.1003 −0.703453
\(250\) −5.76098 −0.364356
\(251\) −22.3682 −1.41187 −0.705933 0.708278i \(-0.749472\pi\)
−0.705933 + 0.708278i \(0.749472\pi\)
\(252\) −15.5570 −0.980001
\(253\) −1.08859 −0.0684389
\(254\) −15.8217 −0.992743
\(255\) −3.05772 −0.191482
\(256\) 1.00000 0.0625000
\(257\) 23.9305 1.49274 0.746371 0.665530i \(-0.231794\pi\)
0.746371 + 0.665530i \(0.231794\pi\)
\(258\) 10.5732 0.658258
\(259\) 30.0596 1.86782
\(260\) −3.08273 −0.191183
\(261\) 5.31040 0.328706
\(262\) −15.9499 −0.985389
\(263\) −22.0985 −1.36265 −0.681325 0.731981i \(-0.738596\pi\)
−0.681325 + 0.731981i \(0.738596\pi\)
\(264\) 0.508761 0.0313121
\(265\) 2.49330 0.153162
\(266\) −30.5598 −1.87374
\(267\) 22.1807 1.35743
\(268\) 15.0329 0.918280
\(269\) 2.90026 0.176832 0.0884161 0.996084i \(-0.471819\pi\)
0.0884161 + 0.996084i \(0.471819\pi\)
\(270\) −0.126025 −0.00766964
\(271\) 30.6715 1.86316 0.931581 0.363535i \(-0.118430\pi\)
0.931581 + 0.363535i \(0.118430\pi\)
\(272\) 2.07476 0.125801
\(273\) −64.1806 −3.88439
\(274\) 8.79086 0.531075
\(275\) 0.957575 0.0577439
\(276\) −13.0211 −0.783775
\(277\) 12.1559 0.730375 0.365188 0.930934i \(-0.381005\pi\)
0.365188 + 0.930934i \(0.381005\pi\)
\(278\) 5.01522 0.300793
\(279\) 1.05446 0.0631288
\(280\) −3.01217 −0.180012
\(281\) −5.51172 −0.328802 −0.164401 0.986394i \(-0.552569\pi\)
−0.164401 + 0.986394i \(0.552569\pi\)
\(282\) 15.1937 0.904772
\(283\) 15.5041 0.921621 0.460811 0.887498i \(-0.347559\pi\)
0.460811 + 0.887498i \(0.347559\pi\)
\(284\) −2.37465 −0.140910
\(285\) −8.93265 −0.529125
\(286\) 1.06420 0.0629272
\(287\) −56.9760 −3.36319
\(288\) 3.08551 0.181816
\(289\) −12.6954 −0.746786
\(290\) 1.02821 0.0603784
\(291\) 1.85532 0.108761
\(292\) −12.6825 −0.742185
\(293\) −1.81133 −0.105819 −0.0529095 0.998599i \(-0.516849\pi\)
−0.0529095 + 0.998599i \(0.516849\pi\)
\(294\) −45.4434 −2.65031
\(295\) 1.64780 0.0959386
\(296\) −5.96190 −0.346528
\(297\) 0.0435053 0.00252443
\(298\) −8.33167 −0.482641
\(299\) −27.2366 −1.57514
\(300\) 11.4540 0.661294
\(301\) 21.6101 1.24559
\(302\) −1.08744 −0.0625751
\(303\) 10.8794 0.625003
\(304\) 6.06110 0.347628
\(305\) 0.850496 0.0486993
\(306\) 6.40171 0.365961
\(307\) −5.04156 −0.287737 −0.143869 0.989597i \(-0.545954\pi\)
−0.143869 + 0.989597i \(0.545954\pi\)
\(308\) 1.03984 0.0592502
\(309\) −18.4437 −1.04923
\(310\) 0.204166 0.0115958
\(311\) 7.76766 0.440464 0.220232 0.975448i \(-0.429319\pi\)
0.220232 + 0.975448i \(0.429319\pi\)
\(312\) 12.7293 0.720654
\(313\) −6.45761 −0.365006 −0.182503 0.983205i \(-0.558420\pi\)
−0.182503 + 0.983205i \(0.558420\pi\)
\(314\) −13.7631 −0.776699
\(315\) −9.29409 −0.523663
\(316\) 13.0518 0.734219
\(317\) −4.52038 −0.253890 −0.126945 0.991910i \(-0.540517\pi\)
−0.126945 + 0.991910i \(0.540517\pi\)
\(318\) −10.2954 −0.577337
\(319\) −0.354949 −0.0198733
\(320\) 0.597421 0.0333968
\(321\) 7.47817 0.417391
\(322\) −26.6132 −1.48310
\(323\) 12.5754 0.699711
\(324\) −8.73615 −0.485342
\(325\) 23.9587 1.32899
\(326\) 10.4848 0.580701
\(327\) 49.1410 2.71751
\(328\) 11.3004 0.623958
\(329\) 31.0538 1.71205
\(330\) 0.303945 0.0167316
\(331\) −2.88305 −0.158467 −0.0792335 0.996856i \(-0.525247\pi\)
−0.0792335 + 0.996856i \(0.525247\pi\)
\(332\) 4.49973 0.246955
\(333\) −18.3955 −1.00807
\(334\) −3.90386 −0.213610
\(335\) 8.98096 0.490682
\(336\) 12.4379 0.678545
\(337\) −17.2248 −0.938292 −0.469146 0.883121i \(-0.655438\pi\)
−0.469146 + 0.883121i \(0.655438\pi\)
\(338\) 13.6263 0.741176
\(339\) −15.4060 −0.836738
\(340\) 1.23951 0.0672217
\(341\) −0.0704804 −0.00381673
\(342\) 18.7016 1.01127
\(343\) −57.5861 −3.10936
\(344\) −4.28605 −0.231089
\(345\) −7.77905 −0.418810
\(346\) −9.56419 −0.514174
\(347\) −17.4462 −0.936561 −0.468281 0.883580i \(-0.655126\pi\)
−0.468281 + 0.883580i \(0.655126\pi\)
\(348\) −4.24570 −0.227593
\(349\) 17.1132 0.916047 0.458023 0.888940i \(-0.348558\pi\)
0.458023 + 0.888940i \(0.348558\pi\)
\(350\) 23.4103 1.25133
\(351\) 1.08851 0.0581004
\(352\) −0.206237 −0.0109924
\(353\) −14.9818 −0.797401 −0.398701 0.917081i \(-0.630539\pi\)
−0.398701 + 0.917081i \(0.630539\pi\)
\(354\) −6.80413 −0.361635
\(355\) −1.41867 −0.0752950
\(356\) −8.99137 −0.476542
\(357\) 25.8058 1.36579
\(358\) 11.2547 0.594827
\(359\) −11.6614 −0.615465 −0.307733 0.951473i \(-0.599570\pi\)
−0.307733 + 0.951473i \(0.599570\pi\)
\(360\) 1.84335 0.0971530
\(361\) 17.7370 0.933525
\(362\) 25.3725 1.33355
\(363\) 27.0308 1.41875
\(364\) 26.0169 1.36366
\(365\) −7.57676 −0.396586
\(366\) −3.51189 −0.183569
\(367\) 13.2591 0.692119 0.346060 0.938213i \(-0.387520\pi\)
0.346060 + 0.938213i \(0.387520\pi\)
\(368\) 5.27834 0.275153
\(369\) 34.8674 1.81512
\(370\) −3.56176 −0.185167
\(371\) −21.0423 −1.09246
\(372\) −0.843046 −0.0437099
\(373\) 12.1397 0.628569 0.314285 0.949329i \(-0.398235\pi\)
0.314285 + 0.949329i \(0.398235\pi\)
\(374\) −0.427892 −0.0221258
\(375\) 14.2117 0.733887
\(376\) −6.15907 −0.317630
\(377\) −8.88088 −0.457389
\(378\) 1.06359 0.0547054
\(379\) −0.406652 −0.0208883 −0.0104442 0.999945i \(-0.503325\pi\)
−0.0104442 + 0.999945i \(0.503325\pi\)
\(380\) 3.62103 0.185755
\(381\) 39.0303 1.99958
\(382\) −10.3545 −0.529783
\(383\) −8.16968 −0.417451 −0.208726 0.977974i \(-0.566932\pi\)
−0.208726 + 0.977974i \(0.566932\pi\)
\(384\) −2.46688 −0.125888
\(385\) 0.621220 0.0316603
\(386\) −0.158094 −0.00804676
\(387\) −13.2247 −0.672248
\(388\) −0.752092 −0.0381817
\(389\) −10.1023 −0.512207 −0.256103 0.966649i \(-0.582439\pi\)
−0.256103 + 0.966649i \(0.582439\pi\)
\(390\) 7.60475 0.385081
\(391\) 10.9513 0.553832
\(392\) 18.4214 0.930420
\(393\) 39.3466 1.98477
\(394\) −18.1348 −0.913616
\(395\) 7.79739 0.392329
\(396\) −0.636345 −0.0319776
\(397\) −37.2395 −1.86900 −0.934498 0.355969i \(-0.884151\pi\)
−0.934498 + 0.355969i \(0.884151\pi\)
\(398\) 7.36515 0.369181
\(399\) 75.3876 3.77410
\(400\) −4.64309 −0.232154
\(401\) 27.9160 1.39406 0.697030 0.717042i \(-0.254504\pi\)
0.697030 + 0.717042i \(0.254504\pi\)
\(402\) −37.0844 −1.84960
\(403\) −1.76343 −0.0878427
\(404\) −4.41017 −0.219414
\(405\) −5.21916 −0.259342
\(406\) −8.67760 −0.430662
\(407\) 1.22956 0.0609471
\(408\) −5.11820 −0.253389
\(409\) 14.8891 0.736217 0.368108 0.929783i \(-0.380006\pi\)
0.368108 + 0.929783i \(0.380006\pi\)
\(410\) 6.75107 0.333412
\(411\) −21.6860 −1.06969
\(412\) 7.47654 0.368343
\(413\) −13.9067 −0.684303
\(414\) 16.2864 0.800432
\(415\) 2.68823 0.131960
\(416\) −5.16007 −0.252993
\(417\) −12.3720 −0.605858
\(418\) −1.25002 −0.0611405
\(419\) −15.8049 −0.772122 −0.386061 0.922473i \(-0.626165\pi\)
−0.386061 + 0.922473i \(0.626165\pi\)
\(420\) 7.43068 0.362580
\(421\) 13.5903 0.662352 0.331176 0.943569i \(-0.392555\pi\)
0.331176 + 0.943569i \(0.392555\pi\)
\(422\) 2.54089 0.123689
\(423\) −19.0039 −0.924000
\(424\) 4.17344 0.202680
\(425\) −9.63331 −0.467284
\(426\) 5.85799 0.283821
\(427\) −7.17781 −0.347358
\(428\) −3.03143 −0.146529
\(429\) −2.62525 −0.126748
\(430\) −2.56058 −0.123482
\(431\) −23.9318 −1.15275 −0.576376 0.817184i \(-0.695534\pi\)
−0.576376 + 0.817184i \(0.695534\pi\)
\(432\) −0.210949 −0.0101493
\(433\) 6.08276 0.292319 0.146159 0.989261i \(-0.453309\pi\)
0.146159 + 0.989261i \(0.453309\pi\)
\(434\) −1.72307 −0.0827098
\(435\) −2.53647 −0.121614
\(436\) −19.9203 −0.954009
\(437\) 31.9926 1.53041
\(438\) 31.2861 1.49491
\(439\) 14.7184 0.702470 0.351235 0.936287i \(-0.385762\pi\)
0.351235 + 0.936287i \(0.385762\pi\)
\(440\) −0.123210 −0.00587381
\(441\) 56.8394 2.70664
\(442\) −10.7059 −0.509229
\(443\) 11.2481 0.534412 0.267206 0.963639i \(-0.413900\pi\)
0.267206 + 0.963639i \(0.413900\pi\)
\(444\) 14.7073 0.697978
\(445\) −5.37163 −0.254640
\(446\) −9.24713 −0.437864
\(447\) 20.5533 0.972136
\(448\) −5.04196 −0.238210
\(449\) 32.3736 1.52780 0.763902 0.645332i \(-0.223281\pi\)
0.763902 + 0.645332i \(0.223281\pi\)
\(450\) −14.3263 −0.675349
\(451\) −2.33055 −0.109741
\(452\) 6.24512 0.293746
\(453\) 2.68259 0.126039
\(454\) 9.89379 0.464338
\(455\) 15.5430 0.728668
\(456\) −14.9520 −0.700193
\(457\) −25.1265 −1.17537 −0.587685 0.809090i \(-0.699961\pi\)
−0.587685 + 0.809090i \(0.699961\pi\)
\(458\) −19.8534 −0.927688
\(459\) −0.437668 −0.0204286
\(460\) 3.15339 0.147028
\(461\) 16.2603 0.757320 0.378660 0.925536i \(-0.376385\pi\)
0.378660 + 0.925536i \(0.376385\pi\)
\(462\) −2.56516 −0.119342
\(463\) −6.53072 −0.303508 −0.151754 0.988418i \(-0.548492\pi\)
−0.151754 + 0.988418i \(0.548492\pi\)
\(464\) 1.72108 0.0798990
\(465\) −0.503653 −0.0233564
\(466\) −15.2656 −0.707165
\(467\) 18.7351 0.866956 0.433478 0.901164i \(-0.357286\pi\)
0.433478 + 0.901164i \(0.357286\pi\)
\(468\) −15.9215 −0.735970
\(469\) −75.7952 −3.49990
\(470\) −3.67955 −0.169725
\(471\) 33.9521 1.56443
\(472\) 2.75819 0.126956
\(473\) 0.883941 0.0406437
\(474\) −32.1972 −1.47886
\(475\) −28.1422 −1.29125
\(476\) −10.4609 −0.479473
\(477\) 12.8772 0.589606
\(478\) 1.48746 0.0680350
\(479\) −25.3736 −1.15935 −0.579675 0.814848i \(-0.696821\pi\)
−0.579675 + 0.814848i \(0.696821\pi\)
\(480\) −1.47377 −0.0672680
\(481\) 30.7638 1.40271
\(482\) −15.6219 −0.711560
\(483\) 65.6516 2.98725
\(484\) −10.9575 −0.498067
\(485\) −0.449315 −0.0204023
\(486\) 22.1839 1.00628
\(487\) −8.14854 −0.369246 −0.184623 0.982809i \(-0.559106\pi\)
−0.184623 + 0.982809i \(0.559106\pi\)
\(488\) 1.42361 0.0644440
\(489\) −25.8648 −1.16965
\(490\) 11.0053 0.497169
\(491\) −9.49448 −0.428480 −0.214240 0.976781i \(-0.568727\pi\)
−0.214240 + 0.976781i \(0.568727\pi\)
\(492\) −27.8767 −1.25678
\(493\) 3.57083 0.160822
\(494\) −31.2757 −1.40716
\(495\) −0.380166 −0.0170872
\(496\) 0.341745 0.0153448
\(497\) 11.9729 0.537058
\(498\) −11.1003 −0.497416
\(499\) −12.4639 −0.557963 −0.278981 0.960297i \(-0.589997\pi\)
−0.278981 + 0.960297i \(0.589997\pi\)
\(500\) −5.76098 −0.257639
\(501\) 9.63036 0.430253
\(502\) −22.3682 −0.998340
\(503\) −15.7720 −0.703237 −0.351619 0.936143i \(-0.614369\pi\)
−0.351619 + 0.936143i \(0.614369\pi\)
\(504\) −15.5570 −0.692965
\(505\) −2.63473 −0.117244
\(506\) −1.08859 −0.0483936
\(507\) −33.6146 −1.49288
\(508\) −15.8217 −0.701975
\(509\) 16.9849 0.752841 0.376420 0.926449i \(-0.377155\pi\)
0.376420 + 0.926449i \(0.377155\pi\)
\(510\) −3.05772 −0.135398
\(511\) 63.9444 2.82874
\(512\) 1.00000 0.0441942
\(513\) −1.27858 −0.0564507
\(514\) 23.9305 1.05553
\(515\) 4.46664 0.196824
\(516\) 10.5732 0.465459
\(517\) 1.27022 0.0558644
\(518\) 30.0596 1.32074
\(519\) 23.5937 1.03565
\(520\) −3.08273 −0.135187
\(521\) −31.8648 −1.39602 −0.698011 0.716087i \(-0.745931\pi\)
−0.698011 + 0.716087i \(0.745931\pi\)
\(522\) 5.31040 0.232430
\(523\) −24.9166 −1.08953 −0.544764 0.838589i \(-0.683381\pi\)
−0.544764 + 0.838589i \(0.683381\pi\)
\(524\) −15.9499 −0.696775
\(525\) −57.7504 −2.52043
\(526\) −22.0985 −0.963538
\(527\) 0.709041 0.0308863
\(528\) 0.508761 0.0221410
\(529\) 4.86090 0.211344
\(530\) 2.49330 0.108302
\(531\) 8.51043 0.369321
\(532\) −30.5598 −1.32494
\(533\) −58.3107 −2.52572
\(534\) 22.1807 0.959851
\(535\) −1.81104 −0.0782979
\(536\) 15.0329 0.649322
\(537\) −27.7639 −1.19810
\(538\) 2.90026 0.125039
\(539\) −3.79916 −0.163641
\(540\) −0.126025 −0.00542326
\(541\) 4.92452 0.211722 0.105861 0.994381i \(-0.466240\pi\)
0.105861 + 0.994381i \(0.466240\pi\)
\(542\) 30.6715 1.31745
\(543\) −62.5910 −2.68604
\(544\) 2.07476 0.0889547
\(545\) −11.9008 −0.509774
\(546\) −64.1806 −2.74668
\(547\) −17.6702 −0.755525 −0.377763 0.925903i \(-0.623306\pi\)
−0.377763 + 0.925903i \(0.623306\pi\)
\(548\) 8.79086 0.375527
\(549\) 4.39258 0.187471
\(550\) 0.957575 0.0408311
\(551\) 10.4316 0.444402
\(552\) −13.0211 −0.554213
\(553\) −65.8064 −2.79837
\(554\) 12.1559 0.516453
\(555\) 8.78645 0.372964
\(556\) 5.01522 0.212693
\(557\) −41.4217 −1.75509 −0.877547 0.479491i \(-0.840821\pi\)
−0.877547 + 0.479491i \(0.840821\pi\)
\(558\) 1.05446 0.0446388
\(559\) 22.1164 0.935422
\(560\) −3.01217 −0.127287
\(561\) 1.05556 0.0445658
\(562\) −5.51172 −0.232498
\(563\) 16.3116 0.687452 0.343726 0.939070i \(-0.388311\pi\)
0.343726 + 0.939070i \(0.388311\pi\)
\(564\) 15.1937 0.639770
\(565\) 3.73097 0.156963
\(566\) 15.5041 0.651685
\(567\) 44.0473 1.84981
\(568\) −2.37465 −0.0996383
\(569\) 23.9703 1.00489 0.502443 0.864611i \(-0.332435\pi\)
0.502443 + 0.864611i \(0.332435\pi\)
\(570\) −8.93265 −0.374148
\(571\) −21.2922 −0.891052 −0.445526 0.895269i \(-0.646983\pi\)
−0.445526 + 0.895269i \(0.646983\pi\)
\(572\) 1.06420 0.0444963
\(573\) 25.5434 1.06709
\(574\) −56.9760 −2.37813
\(575\) −24.5078 −1.02205
\(576\) 3.08551 0.128563
\(577\) 13.7511 0.572466 0.286233 0.958160i \(-0.407597\pi\)
0.286233 + 0.958160i \(0.407597\pi\)
\(578\) −12.6954 −0.528057
\(579\) 0.389999 0.0162078
\(580\) 1.02821 0.0426940
\(581\) −22.6874 −0.941234
\(582\) 1.85532 0.0769056
\(583\) −0.860716 −0.0356472
\(584\) −12.6825 −0.524804
\(585\) −9.51181 −0.393265
\(586\) −1.81133 −0.0748254
\(587\) −35.9089 −1.48212 −0.741059 0.671440i \(-0.765676\pi\)
−0.741059 + 0.671440i \(0.765676\pi\)
\(588\) −45.4434 −1.87405
\(589\) 2.07135 0.0853486
\(590\) 1.64780 0.0678388
\(591\) 44.7363 1.84021
\(592\) −5.96190 −0.245032
\(593\) −13.4816 −0.553623 −0.276812 0.960924i \(-0.589278\pi\)
−0.276812 + 0.960924i \(0.589278\pi\)
\(594\) 0.0435053 0.00178504
\(595\) −6.24954 −0.256206
\(596\) −8.33167 −0.341279
\(597\) −18.1690 −0.743606
\(598\) −27.2366 −1.11379
\(599\) −25.7308 −1.05133 −0.525667 0.850691i \(-0.676184\pi\)
−0.525667 + 0.850691i \(0.676184\pi\)
\(600\) 11.4540 0.467606
\(601\) −42.6246 −1.73869 −0.869346 0.494204i \(-0.835460\pi\)
−0.869346 + 0.494204i \(0.835460\pi\)
\(602\) 21.6101 0.880763
\(603\) 46.3842 1.88891
\(604\) −1.08744 −0.0442473
\(605\) −6.54622 −0.266142
\(606\) 10.8794 0.441944
\(607\) −39.8783 −1.61861 −0.809305 0.587389i \(-0.800156\pi\)
−0.809305 + 0.587389i \(0.800156\pi\)
\(608\) 6.06110 0.245810
\(609\) 21.4066 0.867440
\(610\) 0.850496 0.0344356
\(611\) 31.7812 1.28573
\(612\) 6.40171 0.258774
\(613\) −28.8520 −1.16532 −0.582662 0.812715i \(-0.697989\pi\)
−0.582662 + 0.812715i \(0.697989\pi\)
\(614\) −5.04156 −0.203461
\(615\) −16.6541 −0.671558
\(616\) 1.03984 0.0418962
\(617\) 1.17852 0.0474455 0.0237228 0.999719i \(-0.492448\pi\)
0.0237228 + 0.999719i \(0.492448\pi\)
\(618\) −18.4437 −0.741916
\(619\) 6.78632 0.272765 0.136383 0.990656i \(-0.456452\pi\)
0.136383 + 0.990656i \(0.456452\pi\)
\(620\) 0.204166 0.00819949
\(621\) −1.11346 −0.0446816
\(622\) 7.76766 0.311455
\(623\) 45.3341 1.81627
\(624\) 12.7293 0.509580
\(625\) 19.7737 0.790949
\(626\) −6.45761 −0.258098
\(627\) 3.08366 0.123149
\(628\) −13.7631 −0.549209
\(629\) −12.3695 −0.493205
\(630\) −9.29409 −0.370286
\(631\) 24.0116 0.955886 0.477943 0.878391i \(-0.341383\pi\)
0.477943 + 0.878391i \(0.341383\pi\)
\(632\) 13.0518 0.519171
\(633\) −6.26808 −0.249134
\(634\) −4.52038 −0.179527
\(635\) −9.45222 −0.375100
\(636\) −10.2954 −0.408239
\(637\) −95.0556 −3.76624
\(638\) −0.354949 −0.0140526
\(639\) −7.32702 −0.289853
\(640\) 0.597421 0.0236151
\(641\) −45.2640 −1.78782 −0.893911 0.448245i \(-0.852049\pi\)
−0.893911 + 0.448245i \(0.852049\pi\)
\(642\) 7.47817 0.295140
\(643\) 7.84867 0.309521 0.154761 0.987952i \(-0.450539\pi\)
0.154761 + 0.987952i \(0.450539\pi\)
\(644\) −26.6132 −1.04871
\(645\) 6.31665 0.248718
\(646\) 12.5754 0.494771
\(647\) −0.373408 −0.0146802 −0.00734009 0.999973i \(-0.502336\pi\)
−0.00734009 + 0.999973i \(0.502336\pi\)
\(648\) −8.73615 −0.343188
\(649\) −0.568839 −0.0223289
\(650\) 23.9587 0.939736
\(651\) 4.25060 0.166594
\(652\) 10.4848 0.410618
\(653\) −34.5048 −1.35028 −0.675138 0.737691i \(-0.735916\pi\)
−0.675138 + 0.737691i \(0.735916\pi\)
\(654\) 49.1410 1.92157
\(655\) −9.52881 −0.372321
\(656\) 11.3004 0.441205
\(657\) −39.1319 −1.52668
\(658\) 31.0538 1.21060
\(659\) 34.5659 1.34650 0.673249 0.739416i \(-0.264898\pi\)
0.673249 + 0.739416i \(0.264898\pi\)
\(660\) 0.303945 0.0118310
\(661\) −16.4279 −0.638970 −0.319485 0.947591i \(-0.603510\pi\)
−0.319485 + 0.947591i \(0.603510\pi\)
\(662\) −2.88305 −0.112053
\(663\) 26.4103 1.02569
\(664\) 4.49973 0.174623
\(665\) −18.2571 −0.707979
\(666\) −18.3955 −0.712811
\(667\) 9.08443 0.351751
\(668\) −3.90386 −0.151045
\(669\) 22.8116 0.881947
\(670\) 8.98096 0.346965
\(671\) −0.293601 −0.0113343
\(672\) 12.4379 0.479803
\(673\) −14.9764 −0.577298 −0.288649 0.957435i \(-0.593206\pi\)
−0.288649 + 0.957435i \(0.593206\pi\)
\(674\) −17.2248 −0.663473
\(675\) 0.979453 0.0376992
\(676\) 13.6263 0.524090
\(677\) −29.9056 −1.14936 −0.574682 0.818377i \(-0.694874\pi\)
−0.574682 + 0.818377i \(0.694874\pi\)
\(678\) −15.4060 −0.591663
\(679\) 3.79202 0.145524
\(680\) 1.23951 0.0475329
\(681\) −24.4068 −0.935271
\(682\) −0.0704804 −0.00269883
\(683\) −27.5849 −1.05551 −0.527753 0.849398i \(-0.676965\pi\)
−0.527753 + 0.849398i \(0.676965\pi\)
\(684\) 18.7016 0.715074
\(685\) 5.25184 0.200663
\(686\) −57.5861 −2.19865
\(687\) 48.9760 1.86855
\(688\) −4.28605 −0.163404
\(689\) −21.5352 −0.820428
\(690\) −7.77905 −0.296143
\(691\) 10.0637 0.382840 0.191420 0.981508i \(-0.438691\pi\)
0.191420 + 0.981508i \(0.438691\pi\)
\(692\) −9.56419 −0.363576
\(693\) 3.20843 0.121878
\(694\) −17.4462 −0.662249
\(695\) 2.99620 0.113652
\(696\) −4.24570 −0.160933
\(697\) 23.4456 0.888064
\(698\) 17.1132 0.647743
\(699\) 37.6584 1.42437
\(700\) 23.4103 0.884825
\(701\) 13.2993 0.502309 0.251154 0.967947i \(-0.419190\pi\)
0.251154 + 0.967947i \(0.419190\pi\)
\(702\) 1.08851 0.0410832
\(703\) −36.1357 −1.36288
\(704\) −0.206237 −0.00777283
\(705\) 9.07703 0.341861
\(706\) −14.9818 −0.563848
\(707\) 22.2359 0.836267
\(708\) −6.80413 −0.255715
\(709\) 0.846722 0.0317993 0.0158997 0.999874i \(-0.494939\pi\)
0.0158997 + 0.999874i \(0.494939\pi\)
\(710\) −1.41867 −0.0532416
\(711\) 40.2713 1.51029
\(712\) −8.99137 −0.336966
\(713\) 1.80385 0.0675547
\(714\) 25.8058 0.965756
\(715\) 0.635772 0.0237765
\(716\) 11.2547 0.420606
\(717\) −3.66940 −0.137036
\(718\) −11.6614 −0.435200
\(719\) −12.0419 −0.449086 −0.224543 0.974464i \(-0.572089\pi\)
−0.224543 + 0.974464i \(0.572089\pi\)
\(720\) 1.84335 0.0686976
\(721\) −37.6964 −1.40389
\(722\) 17.7370 0.660102
\(723\) 38.5375 1.43323
\(724\) 25.3725 0.942962
\(725\) −7.99111 −0.296782
\(726\) 27.0308 1.00321
\(727\) 5.85243 0.217055 0.108527 0.994093i \(-0.465387\pi\)
0.108527 + 0.994093i \(0.465387\pi\)
\(728\) 26.0169 0.964250
\(729\) −28.5167 −1.05617
\(730\) −7.57676 −0.280429
\(731\) −8.89255 −0.328903
\(732\) −3.51189 −0.129803
\(733\) −23.7870 −0.878594 −0.439297 0.898342i \(-0.644773\pi\)
−0.439297 + 0.898342i \(0.644773\pi\)
\(734\) 13.2591 0.489402
\(735\) −27.1488 −1.00140
\(736\) 5.27834 0.194562
\(737\) −3.10033 −0.114202
\(738\) 34.8674 1.28349
\(739\) −24.3102 −0.894265 −0.447132 0.894468i \(-0.647555\pi\)
−0.447132 + 0.894468i \(0.647555\pi\)
\(740\) −3.56176 −0.130933
\(741\) 77.1536 2.83431
\(742\) −21.0423 −0.772488
\(743\) 51.2362 1.87968 0.939838 0.341622i \(-0.110976\pi\)
0.939838 + 0.341622i \(0.110976\pi\)
\(744\) −0.843046 −0.0309076
\(745\) −4.97751 −0.182362
\(746\) 12.1397 0.444466
\(747\) 13.8840 0.507988
\(748\) −0.427892 −0.0156453
\(749\) 15.2843 0.558477
\(750\) 14.2117 0.518937
\(751\) 40.8744 1.49153 0.745764 0.666211i \(-0.232085\pi\)
0.745764 + 0.666211i \(0.232085\pi\)
\(752\) −6.15907 −0.224598
\(753\) 55.1797 2.01086
\(754\) −8.88088 −0.323423
\(755\) −0.649659 −0.0236435
\(756\) 1.06359 0.0386826
\(757\) 17.6936 0.643086 0.321543 0.946895i \(-0.395799\pi\)
0.321543 + 0.946895i \(0.395799\pi\)
\(758\) −0.406652 −0.0147703
\(759\) 2.68542 0.0974745
\(760\) 3.62103 0.131349
\(761\) 28.4541 1.03146 0.515729 0.856752i \(-0.327521\pi\)
0.515729 + 0.856752i \(0.327521\pi\)
\(762\) 39.0303 1.41392
\(763\) 100.437 3.63608
\(764\) −10.3545 −0.374613
\(765\) 3.82451 0.138276
\(766\) −8.16968 −0.295183
\(767\) −14.2325 −0.513904
\(768\) −2.46688 −0.0890160
\(769\) 33.6460 1.21330 0.606652 0.794967i \(-0.292512\pi\)
0.606652 + 0.794967i \(0.292512\pi\)
\(770\) 0.621220 0.0223872
\(771\) −59.0337 −2.12605
\(772\) −0.158094 −0.00568992
\(773\) 14.4416 0.519430 0.259715 0.965685i \(-0.416371\pi\)
0.259715 + 0.965685i \(0.416371\pi\)
\(774\) −13.2247 −0.475351
\(775\) −1.58675 −0.0569979
\(776\) −0.752092 −0.0269985
\(777\) −74.1536 −2.66025
\(778\) −10.1023 −0.362185
\(779\) 68.4926 2.45400
\(780\) 7.60475 0.272294
\(781\) 0.489740 0.0175243
\(782\) 10.9513 0.391618
\(783\) −0.363059 −0.0129747
\(784\) 18.4214 0.657906
\(785\) −8.22239 −0.293470
\(786\) 39.3466 1.40345
\(787\) 32.3128 1.15183 0.575914 0.817510i \(-0.304646\pi\)
0.575914 + 0.817510i \(0.304646\pi\)
\(788\) −18.1348 −0.646024
\(789\) 54.5143 1.94076
\(790\) 7.79739 0.277419
\(791\) −31.4877 −1.11957
\(792\) −0.636345 −0.0226115
\(793\) −7.34595 −0.260862
\(794\) −37.2395 −1.32158
\(795\) −6.15068 −0.218142
\(796\) 7.36515 0.261051
\(797\) −44.6368 −1.58112 −0.790559 0.612386i \(-0.790210\pi\)
−0.790559 + 0.612386i \(0.790210\pi\)
\(798\) 75.3876 2.66869
\(799\) −12.7786 −0.452075
\(800\) −4.64309 −0.164158
\(801\) −27.7430 −0.980250
\(802\) 27.9160 0.985750
\(803\) 2.61559 0.0923020
\(804\) −37.0844 −1.30787
\(805\) −15.8993 −0.560376
\(806\) −1.76343 −0.0621142
\(807\) −7.15461 −0.251854
\(808\) −4.41017 −0.155149
\(809\) −35.2167 −1.23815 −0.619077 0.785330i \(-0.712493\pi\)
−0.619077 + 0.785330i \(0.712493\pi\)
\(810\) −5.21916 −0.183383
\(811\) 19.5063 0.684960 0.342480 0.939525i \(-0.388733\pi\)
0.342480 + 0.939525i \(0.388733\pi\)
\(812\) −8.67760 −0.304524
\(813\) −75.6630 −2.65362
\(814\) 1.22956 0.0430961
\(815\) 6.26385 0.219413
\(816\) −5.11820 −0.179173
\(817\) −25.9782 −0.908863
\(818\) 14.8891 0.520584
\(819\) 80.2754 2.80505
\(820\) 6.75107 0.235758
\(821\) −15.9704 −0.557370 −0.278685 0.960383i \(-0.589899\pi\)
−0.278685 + 0.960383i \(0.589899\pi\)
\(822\) −21.6860 −0.756387
\(823\) 12.4569 0.434221 0.217110 0.976147i \(-0.430337\pi\)
0.217110 + 0.976147i \(0.430337\pi\)
\(824\) 7.47654 0.260458
\(825\) −2.36222 −0.0822421
\(826\) −13.9067 −0.483875
\(827\) −30.7970 −1.07092 −0.535459 0.844561i \(-0.679861\pi\)
−0.535459 + 0.844561i \(0.679861\pi\)
\(828\) 16.2864 0.565991
\(829\) −12.0695 −0.419190 −0.209595 0.977788i \(-0.567215\pi\)
−0.209595 + 0.977788i \(0.567215\pi\)
\(830\) 2.68823 0.0933098
\(831\) −29.9871 −1.04024
\(832\) −5.16007 −0.178893
\(833\) 38.2200 1.32424
\(834\) −12.3720 −0.428406
\(835\) −2.33225 −0.0807107
\(836\) −1.25002 −0.0432329
\(837\) −0.0720907 −0.00249182
\(838\) −15.8049 −0.545973
\(839\) 45.2808 1.56327 0.781634 0.623737i \(-0.214387\pi\)
0.781634 + 0.623737i \(0.214387\pi\)
\(840\) 7.43068 0.256383
\(841\) −26.0379 −0.897858
\(842\) 13.5903 0.468353
\(843\) 13.5968 0.468298
\(844\) 2.54089 0.0874610
\(845\) 8.14066 0.280047
\(846\) −19.0039 −0.653367
\(847\) 55.2471 1.89831
\(848\) 4.17344 0.143316
\(849\) −38.2467 −1.31262
\(850\) −9.63331 −0.330420
\(851\) −31.4689 −1.07874
\(852\) 5.85799 0.200692
\(853\) 44.2305 1.51442 0.757211 0.653170i \(-0.226561\pi\)
0.757211 + 0.653170i \(0.226561\pi\)
\(854\) −7.17781 −0.245619
\(855\) 11.1727 0.382099
\(856\) −3.03143 −0.103612
\(857\) −16.7000 −0.570462 −0.285231 0.958459i \(-0.592070\pi\)
−0.285231 + 0.958459i \(0.592070\pi\)
\(858\) −2.62525 −0.0896244
\(859\) 21.8236 0.744613 0.372307 0.928110i \(-0.378567\pi\)
0.372307 + 0.928110i \(0.378567\pi\)
\(860\) −2.56058 −0.0873150
\(861\) 140.553 4.79004
\(862\) −23.9318 −0.815119
\(863\) 12.7166 0.432878 0.216439 0.976296i \(-0.430556\pi\)
0.216439 + 0.976296i \(0.430556\pi\)
\(864\) −0.210949 −0.00717662
\(865\) −5.71384 −0.194276
\(866\) 6.08276 0.206701
\(867\) 31.3180 1.06361
\(868\) −1.72307 −0.0584847
\(869\) −2.69175 −0.0913113
\(870\) −2.53647 −0.0859943
\(871\) −77.5708 −2.62839
\(872\) −19.9203 −0.674586
\(873\) −2.32059 −0.0785400
\(874\) 31.9926 1.08217
\(875\) 29.0466 0.981956
\(876\) 31.2861 1.05706
\(877\) 19.1714 0.647371 0.323685 0.946165i \(-0.395078\pi\)
0.323685 + 0.946165i \(0.395078\pi\)
\(878\) 14.7184 0.496721
\(879\) 4.46834 0.150713
\(880\) −0.123210 −0.00415341
\(881\) 39.2349 1.32186 0.660929 0.750449i \(-0.270163\pi\)
0.660929 + 0.750449i \(0.270163\pi\)
\(882\) 56.8394 1.91388
\(883\) 55.3914 1.86407 0.932034 0.362371i \(-0.118033\pi\)
0.932034 + 0.362371i \(0.118033\pi\)
\(884\) −10.7059 −0.360079
\(885\) −4.06493 −0.136641
\(886\) 11.2481 0.377887
\(887\) 57.1384 1.91852 0.959259 0.282528i \(-0.0911730\pi\)
0.959259 + 0.282528i \(0.0911730\pi\)
\(888\) 14.7073 0.493545
\(889\) 79.7725 2.67548
\(890\) −5.37163 −0.180057
\(891\) 1.80171 0.0603597
\(892\) −9.24713 −0.309617
\(893\) −37.3307 −1.24923
\(894\) 20.5533 0.687404
\(895\) 6.72376 0.224751
\(896\) −5.04196 −0.168440
\(897\) 67.1896 2.24340
\(898\) 32.3736 1.08032
\(899\) 0.588170 0.0196166
\(900\) −14.3263 −0.477544
\(901\) 8.65890 0.288470
\(902\) −2.33055 −0.0775987
\(903\) −53.3096 −1.77403
\(904\) 6.24512 0.207710
\(905\) 15.1581 0.503871
\(906\) 2.68259 0.0891230
\(907\) 1.27361 0.0422896 0.0211448 0.999776i \(-0.493269\pi\)
0.0211448 + 0.999776i \(0.493269\pi\)
\(908\) 9.89379 0.328337
\(909\) −13.6076 −0.451337
\(910\) 15.5430 0.515246
\(911\) −39.1594 −1.29741 −0.648704 0.761041i \(-0.724689\pi\)
−0.648704 + 0.761041i \(0.724689\pi\)
\(912\) −14.9520 −0.495111
\(913\) −0.928008 −0.0307126
\(914\) −25.1265 −0.831112
\(915\) −2.09808 −0.0693602
\(916\) −19.8534 −0.655974
\(917\) 80.4189 2.65566
\(918\) −0.437668 −0.0144452
\(919\) 15.8221 0.521923 0.260961 0.965349i \(-0.415961\pi\)
0.260961 + 0.965349i \(0.415961\pi\)
\(920\) 3.15339 0.103964
\(921\) 12.4369 0.409811
\(922\) 16.2603 0.535506
\(923\) 12.2534 0.403325
\(924\) −2.56516 −0.0843874
\(925\) 27.6816 0.910166
\(926\) −6.53072 −0.214613
\(927\) 23.0690 0.757684
\(928\) 1.72108 0.0564971
\(929\) 28.7555 0.943438 0.471719 0.881749i \(-0.343634\pi\)
0.471719 + 0.881749i \(0.343634\pi\)
\(930\) −0.503653 −0.0165154
\(931\) 111.654 3.65931
\(932\) −15.2656 −0.500041
\(933\) −19.1619 −0.627333
\(934\) 18.7351 0.613030
\(935\) −0.255632 −0.00836005
\(936\) −15.9215 −0.520409
\(937\) −8.72414 −0.285005 −0.142503 0.989794i \(-0.545515\pi\)
−0.142503 + 0.989794i \(0.545515\pi\)
\(938\) −75.7952 −2.47480
\(939\) 15.9302 0.519862
\(940\) −3.67955 −0.120014
\(941\) −0.494092 −0.0161069 −0.00805347 0.999968i \(-0.502564\pi\)
−0.00805347 + 0.999968i \(0.502564\pi\)
\(942\) 33.9521 1.10622
\(943\) 59.6472 1.94238
\(944\) 2.75819 0.0897714
\(945\) 0.635413 0.0206700
\(946\) 0.883941 0.0287394
\(947\) −28.9003 −0.939135 −0.469567 0.882897i \(-0.655590\pi\)
−0.469567 + 0.882897i \(0.655590\pi\)
\(948\) −32.1972 −1.04571
\(949\) 65.4424 2.12435
\(950\) −28.1422 −0.913055
\(951\) 11.1513 0.361604
\(952\) −10.4609 −0.339039
\(953\) −23.3354 −0.755907 −0.377953 0.925825i \(-0.623372\pi\)
−0.377953 + 0.925825i \(0.623372\pi\)
\(954\) 12.8772 0.416915
\(955\) −6.18600 −0.200174
\(956\) 1.48746 0.0481080
\(957\) 0.875618 0.0283047
\(958\) −25.3736 −0.819785
\(959\) −44.3232 −1.43127
\(960\) −1.47377 −0.0475656
\(961\) −30.8832 −0.996233
\(962\) 30.7638 0.991865
\(963\) −9.35350 −0.301412
\(964\) −15.6219 −0.503149
\(965\) −0.0944485 −0.00304041
\(966\) 65.6516 2.11231
\(967\) 5.03580 0.161940 0.0809701 0.996717i \(-0.474198\pi\)
0.0809701 + 0.996717i \(0.474198\pi\)
\(968\) −10.9575 −0.352186
\(969\) −31.0219 −0.996568
\(970\) −0.449315 −0.0144266
\(971\) 8.70491 0.279354 0.139677 0.990197i \(-0.455394\pi\)
0.139677 + 0.990197i \(0.455394\pi\)
\(972\) 22.1839 0.711549
\(973\) −25.2866 −0.810650
\(974\) −8.14854 −0.261096
\(975\) −59.1032 −1.89282
\(976\) 1.42361 0.0455688
\(977\) −5.99496 −0.191796 −0.0958979 0.995391i \(-0.530572\pi\)
−0.0958979 + 0.995391i \(0.530572\pi\)
\(978\) −25.8648 −0.827067
\(979\) 1.85435 0.0592653
\(980\) 11.0053 0.351552
\(981\) −61.4643 −1.96240
\(982\) −9.49448 −0.302981
\(983\) 15.0752 0.480824 0.240412 0.970671i \(-0.422717\pi\)
0.240412 + 0.970671i \(0.422717\pi\)
\(984\) −27.8767 −0.888676
\(985\) −10.8341 −0.345202
\(986\) 3.57083 0.113718
\(987\) −76.6060 −2.43840
\(988\) −31.2757 −0.995014
\(989\) −22.6233 −0.719378
\(990\) −0.380166 −0.0120825
\(991\) 25.8087 0.819839 0.409920 0.912122i \(-0.365557\pi\)
0.409920 + 0.912122i \(0.365557\pi\)
\(992\) 0.341745 0.0108504
\(993\) 7.11216 0.225698
\(994\) 11.9729 0.379758
\(995\) 4.40009 0.139492
\(996\) −11.1003 −0.351726
\(997\) 25.1232 0.795660 0.397830 0.917459i \(-0.369763\pi\)
0.397830 + 0.917459i \(0.369763\pi\)
\(998\) −12.4639 −0.394539
\(999\) 1.25765 0.0397904
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 \(a_p\))