Properties

Label 8018.2.a.f.1.20
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(34\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+0.100558 q^{3}\) \(+1.00000 q^{4}\) \(+2.02652 q^{5}\) \(-0.100558 q^{6}\) \(+1.91249 q^{7}\) \(-1.00000 q^{8}\) \(-2.98989 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+0.100558 q^{3}\) \(+1.00000 q^{4}\) \(+2.02652 q^{5}\) \(-0.100558 q^{6}\) \(+1.91249 q^{7}\) \(-1.00000 q^{8}\) \(-2.98989 q^{9}\) \(-2.02652 q^{10}\) \(-3.03504 q^{11}\) \(+0.100558 q^{12}\) \(-1.59215 q^{13}\) \(-1.91249 q^{14}\) \(+0.203783 q^{15}\) \(+1.00000 q^{16}\) \(+4.83109 q^{17}\) \(+2.98989 q^{18}\) \(-1.00000 q^{19}\) \(+2.02652 q^{20}\) \(+0.192316 q^{21}\) \(+3.03504 q^{22}\) \(+2.15761 q^{23}\) \(-0.100558 q^{24}\) \(-0.893223 q^{25}\) \(+1.59215 q^{26}\) \(-0.602332 q^{27}\) \(+1.91249 q^{28}\) \(-1.54555 q^{29}\) \(-0.203783 q^{30}\) \(-3.26259 q^{31}\) \(-1.00000 q^{32}\) \(-0.305197 q^{33}\) \(-4.83109 q^{34}\) \(+3.87569 q^{35}\) \(-2.98989 q^{36}\) \(-11.1692 q^{37}\) \(+1.00000 q^{38}\) \(-0.160103 q^{39}\) \(-2.02652 q^{40}\) \(-0.0525980 q^{41}\) \(-0.192316 q^{42}\) \(+8.48995 q^{43}\) \(-3.03504 q^{44}\) \(-6.05906 q^{45}\) \(-2.15761 q^{46}\) \(+11.3415 q^{47}\) \(+0.100558 q^{48}\) \(-3.34239 q^{49}\) \(+0.893223 q^{50}\) \(+0.485805 q^{51}\) \(-1.59215 q^{52}\) \(-9.77354 q^{53}\) \(+0.602332 q^{54}\) \(-6.15055 q^{55}\) \(-1.91249 q^{56}\) \(-0.100558 q^{57}\) \(+1.54555 q^{58}\) \(+3.74947 q^{59}\) \(+0.203783 q^{60}\) \(+9.52357 q^{61}\) \(+3.26259 q^{62}\) \(-5.71812 q^{63}\) \(+1.00000 q^{64}\) \(-3.22651 q^{65}\) \(+0.305197 q^{66}\) \(+11.6242 q^{67}\) \(+4.83109 q^{68}\) \(+0.216965 q^{69}\) \(-3.87569 q^{70}\) \(-14.7569 q^{71}\) \(+2.98989 q^{72}\) \(+5.61699 q^{73}\) \(+11.1692 q^{74}\) \(-0.0898209 q^{75}\) \(-1.00000 q^{76}\) \(-5.80446 q^{77}\) \(+0.160103 q^{78}\) \(-8.77091 q^{79}\) \(+2.02652 q^{80}\) \(+8.90909 q^{81}\) \(+0.0525980 q^{82}\) \(-4.40132 q^{83}\) \(+0.192316 q^{84}\) \(+9.79029 q^{85}\) \(-8.48995 q^{86}\) \(-0.155417 q^{87}\) \(+3.03504 q^{88}\) \(-12.7448 q^{89}\) \(+6.05906 q^{90}\) \(-3.04496 q^{91}\) \(+2.15761 q^{92}\) \(-0.328080 q^{93}\) \(-11.3415 q^{94}\) \(-2.02652 q^{95}\) \(-0.100558 q^{96}\) \(+17.8613 q^{97}\) \(+3.34239 q^{98}\) \(+9.07442 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut -\mathstrut 7q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 38q^{18} \) \(\mathstrut -\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 31q^{27} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 17q^{30} \) \(\mathstrut -\mathstrut 28q^{31} \) \(\mathstrut -\mathstrut 34q^{32} \) \(\mathstrut -\mathstrut 16q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 36q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 7q^{40} \) \(\mathstrut +\mathstrut 9q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 22q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 29q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 22q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 21q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 9q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 23q^{61} \) \(\mathstrut +\mathstrut 28q^{62} \) \(\mathstrut -\mathstrut 27q^{63} \) \(\mathstrut +\mathstrut 34q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 51q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 17q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut -\mathstrut 38q^{72} \) \(\mathstrut -\mathstrut 26q^{73} \) \(\mathstrut +\mathstrut 36q^{74} \) \(\mathstrut -\mathstrut 109q^{75} \) \(\mathstrut -\mathstrut 34q^{76} \) \(\mathstrut -\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 9q^{78} \) \(\mathstrut -\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 7q^{80} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 9q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 22q^{90} \) \(\mathstrut -\mathstrut 41q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 56q^{97} \) \(\mathstrut -\mathstrut 22q^{98} \) \(\mathstrut -\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.100558 0.0580573 0.0290286 0.999579i \(-0.490759\pi\)
0.0290286 + 0.999579i \(0.490759\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.02652 0.906287 0.453143 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(6\) −0.100558 −0.0410527
\(7\) 1.91249 0.722852 0.361426 0.932401i \(-0.382290\pi\)
0.361426 + 0.932401i \(0.382290\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.98989 −0.996629
\(10\) −2.02652 −0.640841
\(11\) −3.03504 −0.915097 −0.457549 0.889185i \(-0.651272\pi\)
−0.457549 + 0.889185i \(0.651272\pi\)
\(12\) 0.100558 0.0290286
\(13\) −1.59215 −0.441582 −0.220791 0.975321i \(-0.570864\pi\)
−0.220791 + 0.975321i \(0.570864\pi\)
\(14\) −1.91249 −0.511134
\(15\) 0.203783 0.0526165
\(16\) 1.00000 0.250000
\(17\) 4.83109 1.17171 0.585856 0.810415i \(-0.300759\pi\)
0.585856 + 0.810415i \(0.300759\pi\)
\(18\) 2.98989 0.704723
\(19\) −1.00000 −0.229416
\(20\) 2.02652 0.453143
\(21\) 0.192316 0.0419668
\(22\) 3.03504 0.647072
\(23\) 2.15761 0.449893 0.224947 0.974371i \(-0.427779\pi\)
0.224947 + 0.974371i \(0.427779\pi\)
\(24\) −0.100558 −0.0205263
\(25\) −0.893223 −0.178645
\(26\) 1.59215 0.312245
\(27\) −0.602332 −0.115919
\(28\) 1.91249 0.361426
\(29\) −1.54555 −0.287001 −0.143501 0.989650i \(-0.545836\pi\)
−0.143501 + 0.989650i \(0.545836\pi\)
\(30\) −0.203783 −0.0372055
\(31\) −3.26259 −0.585979 −0.292990 0.956116i \(-0.594650\pi\)
−0.292990 + 0.956116i \(0.594650\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.305197 −0.0531280
\(34\) −4.83109 −0.828525
\(35\) 3.87569 0.655111
\(36\) −2.98989 −0.498315
\(37\) −11.1692 −1.83621 −0.918103 0.396341i \(-0.870280\pi\)
−0.918103 + 0.396341i \(0.870280\pi\)
\(38\) 1.00000 0.162221
\(39\) −0.160103 −0.0256370
\(40\) −2.02652 −0.320421
\(41\) −0.0525980 −0.00821442 −0.00410721 0.999992i \(-0.501307\pi\)
−0.00410721 + 0.999992i \(0.501307\pi\)
\(42\) −0.192316 −0.0296750
\(43\) 8.48995 1.29470 0.647352 0.762191i \(-0.275876\pi\)
0.647352 + 0.762191i \(0.275876\pi\)
\(44\) −3.03504 −0.457549
\(45\) −6.05906 −0.903232
\(46\) −2.15761 −0.318123
\(47\) 11.3415 1.65433 0.827167 0.561956i \(-0.189951\pi\)
0.827167 + 0.561956i \(0.189951\pi\)
\(48\) 0.100558 0.0145143
\(49\) −3.34239 −0.477485
\(50\) 0.893223 0.126321
\(51\) 0.485805 0.0680263
\(52\) −1.59215 −0.220791
\(53\) −9.77354 −1.34250 −0.671250 0.741231i \(-0.734242\pi\)
−0.671250 + 0.741231i \(0.734242\pi\)
\(54\) 0.602332 0.0819670
\(55\) −6.15055 −0.829341
\(56\) −1.91249 −0.255567
\(57\) −0.100558 −0.0133192
\(58\) 1.54555 0.202940
\(59\) 3.74947 0.488140 0.244070 0.969758i \(-0.421517\pi\)
0.244070 + 0.969758i \(0.421517\pi\)
\(60\) 0.203783 0.0263083
\(61\) 9.52357 1.21937 0.609684 0.792645i \(-0.291296\pi\)
0.609684 + 0.792645i \(0.291296\pi\)
\(62\) 3.26259 0.414350
\(63\) −5.71812 −0.720416
\(64\) 1.00000 0.125000
\(65\) −3.22651 −0.400199
\(66\) 0.305197 0.0375672
\(67\) 11.6242 1.42012 0.710058 0.704143i \(-0.248669\pi\)
0.710058 + 0.704143i \(0.248669\pi\)
\(68\) 4.83109 0.585856
\(69\) 0.216965 0.0261196
\(70\) −3.87569 −0.463234
\(71\) −14.7569 −1.75132 −0.875658 0.482931i \(-0.839572\pi\)
−0.875658 + 0.482931i \(0.839572\pi\)
\(72\) 2.98989 0.352362
\(73\) 5.61699 0.657419 0.328710 0.944431i \(-0.393386\pi\)
0.328710 + 0.944431i \(0.393386\pi\)
\(74\) 11.1692 1.29839
\(75\) −0.0898209 −0.0103716
\(76\) −1.00000 −0.114708
\(77\) −5.80446 −0.661480
\(78\) 0.160103 0.0181281
\(79\) −8.77091 −0.986805 −0.493402 0.869801i \(-0.664247\pi\)
−0.493402 + 0.869801i \(0.664247\pi\)
\(80\) 2.02652 0.226572
\(81\) 8.90909 0.989899
\(82\) 0.0525980 0.00580847
\(83\) −4.40132 −0.483108 −0.241554 0.970387i \(-0.577657\pi\)
−0.241554 + 0.970387i \(0.577657\pi\)
\(84\) 0.192316 0.0209834
\(85\) 9.79029 1.06191
\(86\) −8.48995 −0.915494
\(87\) −0.155417 −0.0166625
\(88\) 3.03504 0.323536
\(89\) −12.7448 −1.35095 −0.675473 0.737385i \(-0.736061\pi\)
−0.675473 + 0.737385i \(0.736061\pi\)
\(90\) 6.05906 0.638681
\(91\) −3.04496 −0.319198
\(92\) 2.15761 0.224947
\(93\) −0.328080 −0.0340204
\(94\) −11.3415 −1.16979
\(95\) −2.02652 −0.207916
\(96\) −0.100558 −0.0102632
\(97\) 17.8613 1.81354 0.906769 0.421627i \(-0.138541\pi\)
0.906769 + 0.421627i \(0.138541\pi\)
\(98\) 3.34239 0.337633
\(99\) 9.07442 0.912013
\(100\) −0.893223 −0.0893223
\(101\) −14.7941 −1.47207 −0.736035 0.676943i \(-0.763304\pi\)
−0.736035 + 0.676943i \(0.763304\pi\)
\(102\) −0.485805 −0.0481019
\(103\) −1.75592 −0.173016 −0.0865080 0.996251i \(-0.527571\pi\)
−0.0865080 + 0.996251i \(0.527571\pi\)
\(104\) 1.59215 0.156123
\(105\) 0.389732 0.0380340
\(106\) 9.77354 0.949290
\(107\) −13.3976 −1.29520 −0.647598 0.761982i \(-0.724227\pi\)
−0.647598 + 0.761982i \(0.724227\pi\)
\(108\) −0.602332 −0.0579594
\(109\) −6.12159 −0.586342 −0.293171 0.956060i \(-0.594711\pi\)
−0.293171 + 0.956060i \(0.594711\pi\)
\(110\) 6.15055 0.586432
\(111\) −1.12315 −0.106605
\(112\) 1.91249 0.180713
\(113\) 10.1321 0.953147 0.476574 0.879135i \(-0.341879\pi\)
0.476574 + 0.879135i \(0.341879\pi\)
\(114\) 0.100558 0.00941813
\(115\) 4.37244 0.407732
\(116\) −1.54555 −0.143501
\(117\) 4.76034 0.440093
\(118\) −3.74947 −0.345167
\(119\) 9.23940 0.846974
\(120\) −0.203783 −0.0186027
\(121\) −1.78856 −0.162597
\(122\) −9.52357 −0.862223
\(123\) −0.00528915 −0.000476907 0
\(124\) −3.26259 −0.292990
\(125\) −11.9427 −1.06819
\(126\) 5.71812 0.509411
\(127\) −10.1667 −0.902148 −0.451074 0.892487i \(-0.648959\pi\)
−0.451074 + 0.892487i \(0.648959\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.853733 0.0751670
\(130\) 3.22651 0.282984
\(131\) 1.91916 0.167678 0.0838389 0.996479i \(-0.473282\pi\)
0.0838389 + 0.996479i \(0.473282\pi\)
\(132\) −0.305197 −0.0265640
\(133\) −1.91249 −0.165834
\(134\) −11.6242 −1.00417
\(135\) −1.22064 −0.105056
\(136\) −4.83109 −0.414263
\(137\) 0.917951 0.0784258 0.0392129 0.999231i \(-0.487515\pi\)
0.0392129 + 0.999231i \(0.487515\pi\)
\(138\) −0.216965 −0.0184693
\(139\) 11.4651 0.972460 0.486230 0.873831i \(-0.338372\pi\)
0.486230 + 0.873831i \(0.338372\pi\)
\(140\) 3.87569 0.327556
\(141\) 1.14048 0.0960461
\(142\) 14.7569 1.23837
\(143\) 4.83222 0.404090
\(144\) −2.98989 −0.249157
\(145\) −3.13208 −0.260105
\(146\) −5.61699 −0.464866
\(147\) −0.336105 −0.0277215
\(148\) −11.1692 −0.918103
\(149\) −12.1455 −0.994995 −0.497497 0.867466i \(-0.665748\pi\)
−0.497497 + 0.867466i \(0.665748\pi\)
\(150\) 0.0898209 0.00733384
\(151\) −7.48903 −0.609448 −0.304724 0.952441i \(-0.598564\pi\)
−0.304724 + 0.952441i \(0.598564\pi\)
\(152\) 1.00000 0.0811107
\(153\) −14.4444 −1.16776
\(154\) 5.80446 0.467737
\(155\) −6.61171 −0.531065
\(156\) −0.160103 −0.0128185
\(157\) −10.1203 −0.807690 −0.403845 0.914827i \(-0.632326\pi\)
−0.403845 + 0.914827i \(0.632326\pi\)
\(158\) 8.77091 0.697776
\(159\) −0.982809 −0.0779418
\(160\) −2.02652 −0.160210
\(161\) 4.12641 0.325206
\(162\) −8.90909 −0.699965
\(163\) 1.50702 0.118039 0.0590195 0.998257i \(-0.481203\pi\)
0.0590195 + 0.998257i \(0.481203\pi\)
\(164\) −0.0525980 −0.00410721
\(165\) −0.618488 −0.0481492
\(166\) 4.40132 0.341609
\(167\) −17.2871 −1.33772 −0.668858 0.743391i \(-0.733216\pi\)
−0.668858 + 0.743391i \(0.733216\pi\)
\(168\) −0.192316 −0.0148375
\(169\) −10.4651 −0.805006
\(170\) −9.79029 −0.750881
\(171\) 2.98989 0.228642
\(172\) 8.48995 0.647352
\(173\) 15.6606 1.19065 0.595327 0.803484i \(-0.297023\pi\)
0.595327 + 0.803484i \(0.297023\pi\)
\(174\) 0.155417 0.0117822
\(175\) −1.70828 −0.129134
\(176\) −3.03504 −0.228774
\(177\) 0.377040 0.0283401
\(178\) 12.7448 0.955263
\(179\) 9.00762 0.673261 0.336631 0.941637i \(-0.390713\pi\)
0.336631 + 0.941637i \(0.390713\pi\)
\(180\) −6.05906 −0.451616
\(181\) −22.7058 −1.68771 −0.843854 0.536573i \(-0.819719\pi\)
−0.843854 + 0.536573i \(0.819719\pi\)
\(182\) 3.04496 0.225707
\(183\) 0.957672 0.0707932
\(184\) −2.15761 −0.159061
\(185\) −22.6346 −1.66413
\(186\) 0.328080 0.0240560
\(187\) −14.6625 −1.07223
\(188\) 11.3415 0.827167
\(189\) −1.15195 −0.0837922
\(190\) 2.02652 0.147019
\(191\) −0.461537 −0.0333956 −0.0166978 0.999861i \(-0.505315\pi\)
−0.0166978 + 0.999861i \(0.505315\pi\)
\(192\) 0.100558 0.00725716
\(193\) −19.0090 −1.36830 −0.684149 0.729342i \(-0.739826\pi\)
−0.684149 + 0.729342i \(0.739826\pi\)
\(194\) −17.8613 −1.28237
\(195\) −0.324452 −0.0232345
\(196\) −3.34239 −0.238742
\(197\) −11.1545 −0.794727 −0.397364 0.917661i \(-0.630075\pi\)
−0.397364 + 0.917661i \(0.630075\pi\)
\(198\) −9.07442 −0.644891
\(199\) −25.3525 −1.79719 −0.898595 0.438779i \(-0.855411\pi\)
−0.898595 + 0.438779i \(0.855411\pi\)
\(200\) 0.893223 0.0631604
\(201\) 1.16890 0.0824481
\(202\) 14.7941 1.04091
\(203\) −2.95584 −0.207459
\(204\) 0.485805 0.0340132
\(205\) −0.106591 −0.00744462
\(206\) 1.75592 0.122341
\(207\) −6.45102 −0.448377
\(208\) −1.59215 −0.110395
\(209\) 3.03504 0.209938
\(210\) −0.389732 −0.0268941
\(211\) −1.00000 −0.0688428
\(212\) −9.77354 −0.671250
\(213\) −1.48392 −0.101677
\(214\) 13.3976 0.915842
\(215\) 17.2050 1.17337
\(216\) 0.602332 0.0409835
\(217\) −6.23967 −0.423576
\(218\) 6.12159 0.414606
\(219\) 0.564834 0.0381680
\(220\) −6.15055 −0.414670
\(221\) −7.69180 −0.517406
\(222\) 1.12315 0.0753812
\(223\) 9.91371 0.663871 0.331935 0.943302i \(-0.392298\pi\)
0.331935 + 0.943302i \(0.392298\pi\)
\(224\) −1.91249 −0.127783
\(225\) 2.67064 0.178043
\(226\) −10.1321 −0.673977
\(227\) −12.3604 −0.820389 −0.410194 0.911998i \(-0.634539\pi\)
−0.410194 + 0.911998i \(0.634539\pi\)
\(228\) −0.100558 −0.00665962
\(229\) 7.65151 0.505626 0.252813 0.967515i \(-0.418644\pi\)
0.252813 + 0.967515i \(0.418644\pi\)
\(230\) −4.37244 −0.288310
\(231\) −0.583686 −0.0384037
\(232\) 1.54555 0.101470
\(233\) 24.2147 1.58635 0.793177 0.608991i \(-0.208425\pi\)
0.793177 + 0.608991i \(0.208425\pi\)
\(234\) −4.76034 −0.311193
\(235\) 22.9838 1.49930
\(236\) 3.74947 0.244070
\(237\) −0.881986 −0.0572912
\(238\) −9.23940 −0.598901
\(239\) −27.6853 −1.79081 −0.895406 0.445250i \(-0.853115\pi\)
−0.895406 + 0.445250i \(0.853115\pi\)
\(240\) 0.203783 0.0131541
\(241\) 5.78747 0.372804 0.186402 0.982474i \(-0.440317\pi\)
0.186402 + 0.982474i \(0.440317\pi\)
\(242\) 1.78856 0.114973
\(243\) 2.70288 0.173390
\(244\) 9.52357 0.609684
\(245\) −6.77342 −0.432738
\(246\) 0.00528915 0.000337224 0
\(247\) 1.59215 0.101306
\(248\) 3.26259 0.207175
\(249\) −0.442588 −0.0280479
\(250\) 11.9427 0.755324
\(251\) −17.4127 −1.09908 −0.549540 0.835467i \(-0.685197\pi\)
−0.549540 + 0.835467i \(0.685197\pi\)
\(252\) −5.71812 −0.360208
\(253\) −6.54843 −0.411696
\(254\) 10.1667 0.637915
\(255\) 0.984493 0.0616514
\(256\) 1.00000 0.0625000
\(257\) 1.30923 0.0816678 0.0408339 0.999166i \(-0.486999\pi\)
0.0408339 + 0.999166i \(0.486999\pi\)
\(258\) −0.853733 −0.0531511
\(259\) −21.3610 −1.32731
\(260\) −3.22651 −0.200100
\(261\) 4.62102 0.286034
\(262\) −1.91916 −0.118566
\(263\) −3.72047 −0.229414 −0.114707 0.993399i \(-0.536593\pi\)
−0.114707 + 0.993399i \(0.536593\pi\)
\(264\) 0.305197 0.0187836
\(265\) −19.8063 −1.21669
\(266\) 1.91249 0.117262
\(267\) −1.28159 −0.0784322
\(268\) 11.6242 0.710058
\(269\) 1.61281 0.0983349 0.0491675 0.998791i \(-0.484343\pi\)
0.0491675 + 0.998791i \(0.484343\pi\)
\(270\) 1.22064 0.0742856
\(271\) −23.8452 −1.44849 −0.724246 0.689541i \(-0.757812\pi\)
−0.724246 + 0.689541i \(0.757812\pi\)
\(272\) 4.83109 0.292928
\(273\) −0.306195 −0.0185318
\(274\) −0.917951 −0.0554554
\(275\) 2.71096 0.163477
\(276\) 0.216965 0.0130598
\(277\) 19.3813 1.16451 0.582254 0.813007i \(-0.302171\pi\)
0.582254 + 0.813007i \(0.302171\pi\)
\(278\) −11.4651 −0.687633
\(279\) 9.75479 0.584004
\(280\) −3.87569 −0.231617
\(281\) 24.9138 1.48623 0.743116 0.669163i \(-0.233347\pi\)
0.743116 + 0.669163i \(0.233347\pi\)
\(282\) −1.14048 −0.0679148
\(283\) 13.9472 0.829075 0.414538 0.910032i \(-0.363943\pi\)
0.414538 + 0.910032i \(0.363943\pi\)
\(284\) −14.7569 −0.875658
\(285\) −0.203783 −0.0120711
\(286\) −4.83222 −0.285735
\(287\) −0.100593 −0.00593781
\(288\) 2.98989 0.176181
\(289\) 6.33943 0.372908
\(290\) 3.13208 0.183922
\(291\) 1.79610 0.105289
\(292\) 5.61699 0.328710
\(293\) 2.74166 0.160170 0.0800848 0.996788i \(-0.474481\pi\)
0.0800848 + 0.996788i \(0.474481\pi\)
\(294\) 0.336105 0.0196020
\(295\) 7.59838 0.442395
\(296\) 11.1692 0.649197
\(297\) 1.82810 0.106077
\(298\) 12.1455 0.703567
\(299\) −3.43523 −0.198665
\(300\) −0.0898209 −0.00518581
\(301\) 16.2369 0.935880
\(302\) 7.48903 0.430945
\(303\) −1.48767 −0.0854643
\(304\) −1.00000 −0.0573539
\(305\) 19.2997 1.10510
\(306\) 14.4444 0.825732
\(307\) 4.59553 0.262281 0.131140 0.991364i \(-0.458136\pi\)
0.131140 + 0.991364i \(0.458136\pi\)
\(308\) −5.80446 −0.330740
\(309\) −0.176572 −0.0100448
\(310\) 6.61171 0.375520
\(311\) −26.9363 −1.52741 −0.763707 0.645563i \(-0.776623\pi\)
−0.763707 + 0.645563i \(0.776623\pi\)
\(312\) 0.160103 0.00906405
\(313\) −10.1071 −0.571288 −0.285644 0.958336i \(-0.592208\pi\)
−0.285644 + 0.958336i \(0.592208\pi\)
\(314\) 10.1203 0.571123
\(315\) −11.5879 −0.652903
\(316\) −8.77091 −0.493402
\(317\) 21.9768 1.23434 0.617171 0.786829i \(-0.288279\pi\)
0.617171 + 0.786829i \(0.288279\pi\)
\(318\) 0.982809 0.0551132
\(319\) 4.69079 0.262634
\(320\) 2.02652 0.113286
\(321\) −1.34724 −0.0751956
\(322\) −4.12641 −0.229956
\(323\) −4.83109 −0.268809
\(324\) 8.90909 0.494950
\(325\) 1.42214 0.0788862
\(326\) −1.50702 −0.0834661
\(327\) −0.615576 −0.0340414
\(328\) 0.0525980 0.00290424
\(329\) 21.6906 1.19584
\(330\) 0.618488 0.0340466
\(331\) 11.4471 0.629192 0.314596 0.949226i \(-0.398131\pi\)
0.314596 + 0.949226i \(0.398131\pi\)
\(332\) −4.40132 −0.241554
\(333\) 33.3947 1.83002
\(334\) 17.2871 0.945907
\(335\) 23.5566 1.28703
\(336\) 0.192316 0.0104917
\(337\) −3.67206 −0.200030 −0.100015 0.994986i \(-0.531889\pi\)
−0.100015 + 0.994986i \(0.531889\pi\)
\(338\) 10.4651 0.569225
\(339\) 1.01886 0.0553371
\(340\) 9.79029 0.530953
\(341\) 9.90209 0.536228
\(342\) −2.98989 −0.161675
\(343\) −19.7797 −1.06800
\(344\) −8.48995 −0.457747
\(345\) 0.439684 0.0236718
\(346\) −15.6606 −0.841920
\(347\) −0.407595 −0.0218808 −0.0109404 0.999940i \(-0.503483\pi\)
−0.0109404 + 0.999940i \(0.503483\pi\)
\(348\) −0.155417 −0.00833125
\(349\) −27.9617 −1.49676 −0.748378 0.663273i \(-0.769167\pi\)
−0.748378 + 0.663273i \(0.769167\pi\)
\(350\) 1.70828 0.0913113
\(351\) 0.959000 0.0511876
\(352\) 3.03504 0.161768
\(353\) 32.2883 1.71853 0.859267 0.511527i \(-0.170920\pi\)
0.859267 + 0.511527i \(0.170920\pi\)
\(354\) −0.377040 −0.0200395
\(355\) −29.9050 −1.58719
\(356\) −12.7448 −0.675473
\(357\) 0.929096 0.0491730
\(358\) −9.00762 −0.476067
\(359\) −25.7865 −1.36096 −0.680479 0.732767i \(-0.738228\pi\)
−0.680479 + 0.732767i \(0.738228\pi\)
\(360\) 6.05906 0.319341
\(361\) 1.00000 0.0526316
\(362\) 22.7058 1.19339
\(363\) −0.179854 −0.00943991
\(364\) −3.04496 −0.159599
\(365\) 11.3829 0.595810
\(366\) −0.957672 −0.0500583
\(367\) −6.43524 −0.335917 −0.167958 0.985794i \(-0.553717\pi\)
−0.167958 + 0.985794i \(0.553717\pi\)
\(368\) 2.15761 0.112473
\(369\) 0.157262 0.00818673
\(370\) 22.6346 1.17672
\(371\) −18.6918 −0.970428
\(372\) −0.328080 −0.0170102
\(373\) −31.7099 −1.64188 −0.820938 0.571017i \(-0.806549\pi\)
−0.820938 + 0.571017i \(0.806549\pi\)
\(374\) 14.6625 0.758181
\(375\) −1.20094 −0.0620162
\(376\) −11.3415 −0.584895
\(377\) 2.46074 0.126734
\(378\) 1.15195 0.0592500
\(379\) −18.2073 −0.935244 −0.467622 0.883929i \(-0.654889\pi\)
−0.467622 + 0.883929i \(0.654889\pi\)
\(380\) −2.02652 −0.103958
\(381\) −1.02234 −0.0523762
\(382\) 0.461537 0.0236143
\(383\) 33.1960 1.69624 0.848119 0.529806i \(-0.177735\pi\)
0.848119 + 0.529806i \(0.177735\pi\)
\(384\) −0.100558 −0.00513158
\(385\) −11.7629 −0.599491
\(386\) 19.0090 0.967533
\(387\) −25.3840 −1.29034
\(388\) 17.8613 0.906769
\(389\) 31.0290 1.57323 0.786616 0.617442i \(-0.211831\pi\)
0.786616 + 0.617442i \(0.211831\pi\)
\(390\) 0.324452 0.0164293
\(391\) 10.4236 0.527145
\(392\) 3.34239 0.168816
\(393\) 0.192987 0.00973491
\(394\) 11.1545 0.561957
\(395\) −17.7744 −0.894328
\(396\) 9.07442 0.456007
\(397\) 35.5304 1.78322 0.891611 0.452802i \(-0.149576\pi\)
0.891611 + 0.452802i \(0.149576\pi\)
\(398\) 25.3525 1.27081
\(399\) −0.192316 −0.00962785
\(400\) −0.893223 −0.0446612
\(401\) 2.06243 0.102993 0.0514965 0.998673i \(-0.483601\pi\)
0.0514965 + 0.998673i \(0.483601\pi\)
\(402\) −1.16890 −0.0582996
\(403\) 5.19452 0.258758
\(404\) −14.7941 −0.736035
\(405\) 18.0544 0.897133
\(406\) 2.95584 0.146696
\(407\) 33.8989 1.68031
\(408\) −0.485805 −0.0240509
\(409\) −16.3714 −0.809514 −0.404757 0.914424i \(-0.632644\pi\)
−0.404757 + 0.914424i \(0.632644\pi\)
\(410\) 0.106591 0.00526414
\(411\) 0.0923074 0.00455319
\(412\) −1.75592 −0.0865080
\(413\) 7.17082 0.352853
\(414\) 6.45102 0.317050
\(415\) −8.91936 −0.437834
\(416\) 1.59215 0.0780613
\(417\) 1.15291 0.0564584
\(418\) −3.03504 −0.148448
\(419\) 34.3311 1.67718 0.838591 0.544762i \(-0.183380\pi\)
0.838591 + 0.544762i \(0.183380\pi\)
\(420\) 0.389732 0.0190170
\(421\) −0.484634 −0.0236196 −0.0118098 0.999930i \(-0.503759\pi\)
−0.0118098 + 0.999930i \(0.503759\pi\)
\(422\) 1.00000 0.0486792
\(423\) −33.9099 −1.64876
\(424\) 9.77354 0.474645
\(425\) −4.31524 −0.209320
\(426\) 1.48392 0.0718962
\(427\) 18.2137 0.881423
\(428\) −13.3976 −0.647598
\(429\) 0.485919 0.0234604
\(430\) −17.2050 −0.829700
\(431\) 39.1350 1.88507 0.942534 0.334111i \(-0.108436\pi\)
0.942534 + 0.334111i \(0.108436\pi\)
\(432\) −0.602332 −0.0289797
\(433\) 8.60782 0.413665 0.206833 0.978376i \(-0.433684\pi\)
0.206833 + 0.978376i \(0.433684\pi\)
\(434\) 6.23967 0.299514
\(435\) −0.314956 −0.0151010
\(436\) −6.12159 −0.293171
\(437\) −2.15761 −0.103213
\(438\) −0.564834 −0.0269888
\(439\) −26.2639 −1.25351 −0.626753 0.779218i \(-0.715616\pi\)
−0.626753 + 0.779218i \(0.715616\pi\)
\(440\) 6.15055 0.293216
\(441\) 9.99338 0.475875
\(442\) 7.69180 0.365861
\(443\) 30.9679 1.47133 0.735664 0.677347i \(-0.236870\pi\)
0.735664 + 0.677347i \(0.236870\pi\)
\(444\) −1.12315 −0.0533025
\(445\) −25.8276 −1.22434
\(446\) −9.91371 −0.469428
\(447\) −1.22132 −0.0577667
\(448\) 1.91249 0.0903565
\(449\) 5.98084 0.282253 0.141127 0.989992i \(-0.454928\pi\)
0.141127 + 0.989992i \(0.454928\pi\)
\(450\) −2.67064 −0.125895
\(451\) 0.159637 0.00751700
\(452\) 10.1321 0.476574
\(453\) −0.753082 −0.0353829
\(454\) 12.3604 0.580103
\(455\) −6.17066 −0.289285
\(456\) 0.100558 0.00470906
\(457\) −13.5583 −0.634230 −0.317115 0.948387i \(-0.602714\pi\)
−0.317115 + 0.948387i \(0.602714\pi\)
\(458\) −7.65151 −0.357531
\(459\) −2.90992 −0.135823
\(460\) 4.37244 0.203866
\(461\) 4.14128 0.192879 0.0964394 0.995339i \(-0.469255\pi\)
0.0964394 + 0.995339i \(0.469255\pi\)
\(462\) 0.583686 0.0271555
\(463\) −18.9491 −0.880638 −0.440319 0.897841i \(-0.645135\pi\)
−0.440319 + 0.897841i \(0.645135\pi\)
\(464\) −1.54555 −0.0717503
\(465\) −0.664861 −0.0308322
\(466\) −24.2147 −1.12172
\(467\) −16.8398 −0.779255 −0.389628 0.920972i \(-0.627396\pi\)
−0.389628 + 0.920972i \(0.627396\pi\)
\(468\) 4.76034 0.220047
\(469\) 22.2310 1.02653
\(470\) −22.9838 −1.06017
\(471\) −1.01768 −0.0468922
\(472\) −3.74947 −0.172584
\(473\) −25.7673 −1.18478
\(474\) 0.881986 0.0405110
\(475\) 0.893223 0.0409839
\(476\) 9.23940 0.423487
\(477\) 29.2218 1.33797
\(478\) 27.6853 1.26630
\(479\) −29.7128 −1.35761 −0.678807 0.734317i \(-0.737503\pi\)
−0.678807 + 0.734317i \(0.737503\pi\)
\(480\) −0.203783 −0.00930137
\(481\) 17.7830 0.810835
\(482\) −5.78747 −0.263612
\(483\) 0.414944 0.0188806
\(484\) −1.78856 −0.0812983
\(485\) 36.1962 1.64359
\(486\) −2.70288 −0.122605
\(487\) −14.5662 −0.660058 −0.330029 0.943971i \(-0.607059\pi\)
−0.330029 + 0.943971i \(0.607059\pi\)
\(488\) −9.52357 −0.431112
\(489\) 0.151543 0.00685302
\(490\) 6.77342 0.305992
\(491\) 30.5166 1.37719 0.688597 0.725144i \(-0.258227\pi\)
0.688597 + 0.725144i \(0.258227\pi\)
\(492\) −0.00528915 −0.000238453 0
\(493\) −7.46668 −0.336283
\(494\) −1.59215 −0.0716340
\(495\) 18.3895 0.826545
\(496\) −3.26259 −0.146495
\(497\) −28.2223 −1.26594
\(498\) 0.442588 0.0198329
\(499\) −31.5212 −1.41108 −0.705540 0.708670i \(-0.749296\pi\)
−0.705540 + 0.708670i \(0.749296\pi\)
\(500\) −11.9427 −0.534095
\(501\) −1.73836 −0.0776641
\(502\) 17.4127 0.777167
\(503\) 1.84738 0.0823708 0.0411854 0.999152i \(-0.486887\pi\)
0.0411854 + 0.999152i \(0.486887\pi\)
\(504\) 5.71812 0.254705
\(505\) −29.9806 −1.33412
\(506\) 6.54843 0.291113
\(507\) −1.05235 −0.0467364
\(508\) −10.1667 −0.451074
\(509\) −12.9404 −0.573571 −0.286786 0.957995i \(-0.592587\pi\)
−0.286786 + 0.957995i \(0.592587\pi\)
\(510\) −0.984493 −0.0435941
\(511\) 10.7424 0.475217
\(512\) −1.00000 −0.0441942
\(513\) 0.602332 0.0265936
\(514\) −1.30923 −0.0577478
\(515\) −3.55840 −0.156802
\(516\) 0.853733 0.0375835
\(517\) −34.4220 −1.51388
\(518\) 21.3610 0.938547
\(519\) 1.57480 0.0691261
\(520\) 3.22651 0.141492
\(521\) 3.52182 0.154294 0.0771470 0.997020i \(-0.475419\pi\)
0.0771470 + 0.997020i \(0.475419\pi\)
\(522\) −4.62102 −0.202256
\(523\) −21.6922 −0.948534 −0.474267 0.880381i \(-0.657287\pi\)
−0.474267 + 0.880381i \(0.657287\pi\)
\(524\) 1.91916 0.0838389
\(525\) −0.171781 −0.00749715
\(526\) 3.72047 0.162220
\(527\) −15.7619 −0.686599
\(528\) −0.305197 −0.0132820
\(529\) −18.3447 −0.797596
\(530\) 19.8063 0.860329
\(531\) −11.2105 −0.486495
\(532\) −1.91249 −0.0829168
\(533\) 0.0837436 0.00362734
\(534\) 1.28159 0.0554599
\(535\) −27.1505 −1.17382
\(536\) −11.6242 −0.502087
\(537\) 0.905789 0.0390877
\(538\) −1.61281 −0.0695333
\(539\) 10.1443 0.436945
\(540\) −1.22064 −0.0525278
\(541\) 10.6975 0.459921 0.229960 0.973200i \(-0.426140\pi\)
0.229960 + 0.973200i \(0.426140\pi\)
\(542\) 23.8452 1.02424
\(543\) −2.28325 −0.0979837
\(544\) −4.83109 −0.207131
\(545\) −12.4055 −0.531394
\(546\) 0.306195 0.0131039
\(547\) −18.0029 −0.769748 −0.384874 0.922969i \(-0.625755\pi\)
−0.384874 + 0.922969i \(0.625755\pi\)
\(548\) 0.917951 0.0392129
\(549\) −28.4744 −1.21526
\(550\) −2.71096 −0.115596
\(551\) 1.54555 0.0658426
\(552\) −0.216965 −0.00923466
\(553\) −16.7743 −0.713314
\(554\) −19.3813 −0.823432
\(555\) −2.27609 −0.0966148
\(556\) 11.4651 0.486230
\(557\) 1.26638 0.0536584 0.0268292 0.999640i \(-0.491459\pi\)
0.0268292 + 0.999640i \(0.491459\pi\)
\(558\) −9.75479 −0.412953
\(559\) −13.5172 −0.571718
\(560\) 3.87569 0.163778
\(561\) −1.47444 −0.0622507
\(562\) −24.9138 −1.05092
\(563\) 12.0579 0.508179 0.254090 0.967181i \(-0.418224\pi\)
0.254090 + 0.967181i \(0.418224\pi\)
\(564\) 1.14048 0.0480230
\(565\) 20.5329 0.863824
\(566\) −13.9472 −0.586245
\(567\) 17.0385 0.715551
\(568\) 14.7569 0.619184
\(569\) −4.47378 −0.187551 −0.0937753 0.995593i \(-0.529894\pi\)
−0.0937753 + 0.995593i \(0.529894\pi\)
\(570\) 0.203783 0.00853552
\(571\) 1.27084 0.0531829 0.0265914 0.999646i \(-0.491535\pi\)
0.0265914 + 0.999646i \(0.491535\pi\)
\(572\) 4.83222 0.202045
\(573\) −0.0464113 −0.00193886
\(574\) 0.100593 0.00419867
\(575\) −1.92723 −0.0803710
\(576\) −2.98989 −0.124579
\(577\) −3.27565 −0.136367 −0.0681836 0.997673i \(-0.521720\pi\)
−0.0681836 + 0.997673i \(0.521720\pi\)
\(578\) −6.33943 −0.263686
\(579\) −1.91151 −0.0794397
\(580\) −3.13208 −0.130053
\(581\) −8.41747 −0.349215
\(582\) −1.79610 −0.0744506
\(583\) 29.6630 1.22852
\(584\) −5.61699 −0.232433
\(585\) 9.64691 0.398851
\(586\) −2.74166 −0.113257
\(587\) 6.38985 0.263737 0.131869 0.991267i \(-0.457902\pi\)
0.131869 + 0.991267i \(0.457902\pi\)
\(588\) −0.336105 −0.0138607
\(589\) 3.26259 0.134433
\(590\) −7.59838 −0.312820
\(591\) −1.12168 −0.0461397
\(592\) −11.1692 −0.459052
\(593\) 4.34937 0.178607 0.0893036 0.996004i \(-0.471536\pi\)
0.0893036 + 0.996004i \(0.471536\pi\)
\(594\) −1.82810 −0.0750078
\(595\) 18.7238 0.767601
\(596\) −12.1455 −0.497497
\(597\) −2.54940 −0.104340
\(598\) 3.43523 0.140477
\(599\) −15.4381 −0.630785 −0.315392 0.948961i \(-0.602136\pi\)
−0.315392 + 0.948961i \(0.602136\pi\)
\(600\) 0.0898209 0.00366692
\(601\) −36.6882 −1.49654 −0.748271 0.663393i \(-0.769116\pi\)
−0.748271 + 0.663393i \(0.769116\pi\)
\(602\) −16.2369 −0.661767
\(603\) −34.7549 −1.41533
\(604\) −7.48903 −0.304724
\(605\) −3.62455 −0.147359
\(606\) 1.48767 0.0604324
\(607\) 28.4521 1.15483 0.577417 0.816449i \(-0.304061\pi\)
0.577417 + 0.816449i \(0.304061\pi\)
\(608\) 1.00000 0.0405554
\(609\) −0.297234 −0.0120445
\(610\) −19.2997 −0.781422
\(611\) −18.0574 −0.730524
\(612\) −14.4444 −0.583881
\(613\) −41.7708 −1.68711 −0.843554 0.537045i \(-0.819540\pi\)
−0.843554 + 0.537045i \(0.819540\pi\)
\(614\) −4.59553 −0.185461
\(615\) −0.0107186 −0.000432214 0
\(616\) 5.80446 0.233869
\(617\) 25.5161 1.02724 0.513620 0.858018i \(-0.328304\pi\)
0.513620 + 0.858018i \(0.328304\pi\)
\(618\) 0.176572 0.00710277
\(619\) 19.2877 0.775239 0.387620 0.921819i \(-0.373297\pi\)
0.387620 + 0.921819i \(0.373297\pi\)
\(620\) −6.61171 −0.265533
\(621\) −1.29960 −0.0521511
\(622\) 26.9363 1.08005
\(623\) −24.3743 −0.976534
\(624\) −0.160103 −0.00640925
\(625\) −19.7360 −0.789441
\(626\) 10.1071 0.403962
\(627\) 0.305197 0.0121884
\(628\) −10.1203 −0.403845
\(629\) −53.9594 −2.15150
\(630\) 11.5879 0.461672
\(631\) −17.7784 −0.707746 −0.353873 0.935293i \(-0.615136\pi\)
−0.353873 + 0.935293i \(0.615136\pi\)
\(632\) 8.77091 0.348888
\(633\) −0.100558 −0.00399683
\(634\) −21.9768 −0.872812
\(635\) −20.6030 −0.817604
\(636\) −0.982809 −0.0389709
\(637\) 5.32158 0.210849
\(638\) −4.69079 −0.185710
\(639\) 44.1213 1.74541
\(640\) −2.02652 −0.0801052
\(641\) 27.6669 1.09278 0.546389 0.837532i \(-0.316002\pi\)
0.546389 + 0.837532i \(0.316002\pi\)
\(642\) 1.34724 0.0531713
\(643\) −5.88810 −0.232204 −0.116102 0.993237i \(-0.537040\pi\)
−0.116102 + 0.993237i \(0.537040\pi\)
\(644\) 4.12641 0.162603
\(645\) 1.73011 0.0681228
\(646\) 4.83109 0.190077
\(647\) −39.8685 −1.56739 −0.783697 0.621143i \(-0.786669\pi\)
−0.783697 + 0.621143i \(0.786669\pi\)
\(648\) −8.90909 −0.349982
\(649\) −11.3798 −0.446696
\(650\) −1.42214 −0.0557810
\(651\) −0.627449 −0.0245917
\(652\) 1.50702 0.0590195
\(653\) −1.54468 −0.0604481 −0.0302240 0.999543i \(-0.509622\pi\)
−0.0302240 + 0.999543i \(0.509622\pi\)
\(654\) 0.615576 0.0240709
\(655\) 3.88921 0.151964
\(656\) −0.0525980 −0.00205361
\(657\) −16.7942 −0.655203
\(658\) −21.6906 −0.845586
\(659\) 4.85462 0.189109 0.0945547 0.995520i \(-0.469857\pi\)
0.0945547 + 0.995520i \(0.469857\pi\)
\(660\) −0.618488 −0.0240746
\(661\) 26.0039 1.01143 0.505717 0.862700i \(-0.331228\pi\)
0.505717 + 0.862700i \(0.331228\pi\)
\(662\) −11.4471 −0.444906
\(663\) −0.773472 −0.0300392
\(664\) 4.40132 0.170804
\(665\) −3.87569 −0.150293
\(666\) −33.3947 −1.29402
\(667\) −3.33469 −0.129120
\(668\) −17.2871 −0.668858
\(669\) 0.996904 0.0385425
\(670\) −23.5566 −0.910069
\(671\) −28.9044 −1.11584
\(672\) −0.192316 −0.00741875
\(673\) −35.8428 −1.38164 −0.690820 0.723027i \(-0.742750\pi\)
−0.690820 + 0.723027i \(0.742750\pi\)
\(674\) 3.67206 0.141442
\(675\) 0.538017 0.0207083
\(676\) −10.4651 −0.402503
\(677\) −14.4793 −0.556484 −0.278242 0.960511i \(-0.589752\pi\)
−0.278242 + 0.960511i \(0.589752\pi\)
\(678\) −1.01886 −0.0391292
\(679\) 34.1595 1.31092
\(680\) −9.79029 −0.375441
\(681\) −1.24294 −0.0476295
\(682\) −9.90209 −0.379171
\(683\) 27.4785 1.05143 0.525717 0.850659i \(-0.323797\pi\)
0.525717 + 0.850659i \(0.323797\pi\)
\(684\) 2.98989 0.114321
\(685\) 1.86024 0.0710763
\(686\) 19.7797 0.755192
\(687\) 0.769421 0.0293552
\(688\) 8.48995 0.323676
\(689\) 15.5609 0.592823
\(690\) −0.439684 −0.0167385
\(691\) 5.39570 0.205262 0.102631 0.994719i \(-0.467274\pi\)
0.102631 + 0.994719i \(0.467274\pi\)
\(692\) 15.6606 0.595327
\(693\) 17.3547 0.659251
\(694\) 0.407595 0.0154721
\(695\) 23.2343 0.881328
\(696\) 0.155417 0.00589108
\(697\) −0.254106 −0.00962493
\(698\) 27.9617 1.05837
\(699\) 2.43498 0.0920994
\(700\) −1.70828 −0.0645668
\(701\) −6.60945 −0.249635 −0.124818 0.992180i \(-0.539835\pi\)
−0.124818 + 0.992180i \(0.539835\pi\)
\(702\) −0.959000 −0.0361951
\(703\) 11.1692 0.421255
\(704\) −3.03504 −0.114387
\(705\) 2.31121 0.0870453
\(706\) −32.2883 −1.21519
\(707\) −28.2936 −1.06409
\(708\) 0.377040 0.0141700
\(709\) 13.5222 0.507837 0.253918 0.967226i \(-0.418281\pi\)
0.253918 + 0.967226i \(0.418281\pi\)
\(710\) 29.9050 1.12232
\(711\) 26.2240 0.983478
\(712\) 12.7448 0.477632
\(713\) −7.03941 −0.263628
\(714\) −0.929096 −0.0347706
\(715\) 9.79258 0.366222
\(716\) 9.00762 0.336631
\(717\) −2.78398 −0.103970
\(718\) 25.7865 0.962343
\(719\) −26.4079 −0.984850 −0.492425 0.870355i \(-0.663889\pi\)
−0.492425 + 0.870355i \(0.663889\pi\)
\(720\) −6.05906 −0.225808
\(721\) −3.35817 −0.125065
\(722\) −1.00000 −0.0372161
\(723\) 0.581977 0.0216440
\(724\) −22.7058 −0.843854
\(725\) 1.38052 0.0512712
\(726\) 0.179854 0.00667502
\(727\) −26.8667 −0.996429 −0.498215 0.867054i \(-0.666011\pi\)
−0.498215 + 0.867054i \(0.666011\pi\)
\(728\) 3.04496 0.112854
\(729\) −26.4555 −0.979833
\(730\) −11.3829 −0.421302
\(731\) 41.0157 1.51702
\(732\) 0.957672 0.0353966
\(733\) 23.6822 0.874724 0.437362 0.899286i \(-0.355913\pi\)
0.437362 + 0.899286i \(0.355913\pi\)
\(734\) 6.43524 0.237529
\(735\) −0.681123 −0.0251236
\(736\) −2.15761 −0.0795306
\(737\) −35.2797 −1.29955
\(738\) −0.157262 −0.00578890
\(739\) 2.28553 0.0840747 0.0420373 0.999116i \(-0.486615\pi\)
0.0420373 + 0.999116i \(0.486615\pi\)
\(740\) −22.6346 −0.832065
\(741\) 0.160103 0.00588153
\(742\) 18.6918 0.686197
\(743\) 40.4110 1.48253 0.741267 0.671210i \(-0.234225\pi\)
0.741267 + 0.671210i \(0.234225\pi\)
\(744\) 0.328080 0.0120280
\(745\) −24.6130 −0.901750
\(746\) 31.7099 1.16098
\(747\) 13.1595 0.481479
\(748\) −14.6625 −0.536115
\(749\) −25.6228 −0.936236
\(750\) 1.20094 0.0438521
\(751\) −32.2569 −1.17707 −0.588535 0.808471i \(-0.700295\pi\)
−0.588535 + 0.808471i \(0.700295\pi\)
\(752\) 11.3415 0.413584
\(753\) −1.75099 −0.0638096
\(754\) −2.46074 −0.0896148
\(755\) −15.1767 −0.552335
\(756\) −1.15195 −0.0418961
\(757\) 14.3136 0.520236 0.260118 0.965577i \(-0.416238\pi\)
0.260118 + 0.965577i \(0.416238\pi\)
\(758\) 18.2073 0.661317
\(759\) −0.658498 −0.0239019
\(760\) 2.02652 0.0735095
\(761\) −6.01324 −0.217980 −0.108990 0.994043i \(-0.534762\pi\)
−0.108990 + 0.994043i \(0.534762\pi\)
\(762\) 1.02234 0.0370356
\(763\) −11.7075 −0.423839
\(764\) −0.461537 −0.0166978
\(765\) −29.2719 −1.05833
\(766\) −33.1960 −1.19942
\(767\) −5.96971 −0.215554
\(768\) 0.100558 0.00362858
\(769\) −18.0939 −0.652482 −0.326241 0.945287i \(-0.605782\pi\)
−0.326241 + 0.945287i \(0.605782\pi\)
\(770\) 11.7629 0.423904
\(771\) 0.131654 0.00474141
\(772\) −19.0090 −0.684149
\(773\) −27.4909 −0.988781 −0.494390 0.869240i \(-0.664609\pi\)
−0.494390 + 0.869240i \(0.664609\pi\)
\(774\) 25.3840 0.912409
\(775\) 2.91423 0.104682
\(776\) −17.8613 −0.641183
\(777\) −2.14802 −0.0770597
\(778\) −31.0290 −1.11244
\(779\) 0.0525980 0.00188452
\(780\) −0.324452 −0.0116172
\(781\) 44.7876 1.60263
\(782\) −10.4236 −0.372748
\(783\) 0.930933 0.0332688
\(784\) −3.34239 −0.119371
\(785\) −20.5090 −0.731998
\(786\) −0.192987 −0.00688362
\(787\) −5.79504 −0.206571 −0.103285 0.994652i \(-0.532936\pi\)
−0.103285 + 0.994652i \(0.532936\pi\)
\(788\) −11.1545 −0.397364
\(789\) −0.374124 −0.0133192
\(790\) 17.7744 0.632385
\(791\) 19.3775 0.688984
\(792\) −9.07442 −0.322445
\(793\) −15.1629 −0.538451
\(794\) −35.5304 −1.26093
\(795\) −1.99168 −0.0706376
\(796\) −25.3525 −0.898595
\(797\) −22.7299 −0.805136 −0.402568 0.915390i \(-0.631882\pi\)
−0.402568 + 0.915390i \(0.631882\pi\)
\(798\) 0.192316 0.00680791
\(799\) 54.7920 1.93840
\(800\) 0.893223 0.0315802
\(801\) 38.1055 1.34639
\(802\) −2.06243 −0.0728270
\(803\) −17.0478 −0.601603
\(804\) 1.16890 0.0412240
\(805\) 8.36224 0.294730
\(806\) −5.19452 −0.182969
\(807\) 0.162181 0.00570906
\(808\) 14.7941 0.520455
\(809\) 1.42641 0.0501499 0.0250750 0.999686i \(-0.492018\pi\)
0.0250750 + 0.999686i \(0.492018\pi\)
\(810\) −18.0544 −0.634368
\(811\) −9.03760 −0.317353 −0.158677 0.987331i \(-0.550723\pi\)
−0.158677 + 0.987331i \(0.550723\pi\)
\(812\) −2.95584 −0.103730
\(813\) −2.39783 −0.0840955
\(814\) −33.8989 −1.18816
\(815\) 3.05400 0.106977
\(816\) 0.485805 0.0170066
\(817\) −8.48995 −0.297026
\(818\) 16.3714 0.572413
\(819\) 9.10408 0.318122
\(820\) −0.106591 −0.00372231
\(821\) −29.3903 −1.02573 −0.512864 0.858470i \(-0.671415\pi\)
−0.512864 + 0.858470i \(0.671415\pi\)
\(822\) −0.0923074 −0.00321959
\(823\) −1.10514 −0.0385227 −0.0192613 0.999814i \(-0.506131\pi\)
−0.0192613 + 0.999814i \(0.506131\pi\)
\(824\) 1.75592 0.0611704
\(825\) 0.272609 0.00949104
\(826\) −7.17082 −0.249505
\(827\) 5.12870 0.178342 0.0891711 0.996016i \(-0.471578\pi\)
0.0891711 + 0.996016i \(0.471578\pi\)
\(828\) −6.45102 −0.224188
\(829\) −5.21821 −0.181236 −0.0906180 0.995886i \(-0.528884\pi\)
−0.0906180 + 0.995886i \(0.528884\pi\)
\(830\) 8.91936 0.309595
\(831\) 1.94895 0.0676082
\(832\) −1.59215 −0.0551977
\(833\) −16.1474 −0.559474
\(834\) −1.15291 −0.0399221
\(835\) −35.0326 −1.21235
\(836\) 3.03504 0.104969
\(837\) 1.96516 0.0679260
\(838\) −34.3311 −1.18595
\(839\) 16.7022 0.576625 0.288312 0.957536i \(-0.406906\pi\)
0.288312 + 0.957536i \(0.406906\pi\)
\(840\) −0.389732 −0.0134470
\(841\) −26.6113 −0.917630
\(842\) 0.484634 0.0167016
\(843\) 2.50528 0.0862865
\(844\) −1.00000 −0.0344214
\(845\) −21.2077 −0.729566
\(846\) 33.9099 1.16585
\(847\) −3.42060 −0.117533
\(848\) −9.77354 −0.335625
\(849\) 1.40250 0.0481338
\(850\) 4.31524 0.148012
\(851\) −24.0988 −0.826097
\(852\) −1.48392 −0.0508383
\(853\) 45.7580 1.56672 0.783362 0.621566i \(-0.213503\pi\)
0.783362 + 0.621566i \(0.213503\pi\)
\(854\) −18.2137 −0.623260
\(855\) 6.05906 0.207216
\(856\) 13.3976 0.457921
\(857\) 32.0857 1.09603 0.548013 0.836470i \(-0.315385\pi\)
0.548013 + 0.836470i \(0.315385\pi\)
\(858\) −0.485919 −0.0165890
\(859\) −12.9492 −0.441822 −0.220911 0.975294i \(-0.570903\pi\)
−0.220911 + 0.975294i \(0.570903\pi\)
\(860\) 17.2050 0.586687
\(861\) −0.0101154 −0.000344733 0
\(862\) −39.1350 −1.33294
\(863\) 18.9698 0.645740 0.322870 0.946443i \(-0.395352\pi\)
0.322870 + 0.946443i \(0.395352\pi\)
\(864\) 0.602332 0.0204917
\(865\) 31.7365 1.07907
\(866\) −8.60782 −0.292506
\(867\) 0.637481 0.0216500
\(868\) −6.23967 −0.211788
\(869\) 26.6200 0.903022
\(870\) 0.314956 0.0106780
\(871\) −18.5073 −0.627097
\(872\) 6.12159 0.207303
\(873\) −53.4032 −1.80743
\(874\) 2.15761 0.0729823
\(875\) −22.8403 −0.772143
\(876\) 0.564834 0.0190840
\(877\) 9.83788 0.332202 0.166101 0.986109i \(-0.446882\pi\)
0.166101 + 0.986109i \(0.446882\pi\)
\(878\) 26.2639 0.886362
\(879\) 0.275696 0.00929900
\(880\) −6.15055 −0.207335
\(881\) 38.5919 1.30019 0.650097 0.759851i \(-0.274728\pi\)
0.650097 + 0.759851i \(0.274728\pi\)
\(882\) −9.99338 −0.336495
\(883\) 39.8138 1.33984 0.669920 0.742433i \(-0.266328\pi\)
0.669920 + 0.742433i \(0.266328\pi\)
\(884\) −7.69180 −0.258703
\(885\) 0.764079 0.0256842
\(886\) −30.9679 −1.04039
\(887\) 13.0985 0.439805 0.219902 0.975522i \(-0.429426\pi\)
0.219902 + 0.975522i \(0.429426\pi\)
\(888\) 1.12315 0.0376906
\(889\) −19.4437 −0.652119
\(890\) 25.8276 0.865742
\(891\) −27.0394 −0.905854
\(892\) 9.91371 0.331935
\(893\) −11.3415 −0.379530
\(894\) 1.22132 0.0408472
\(895\) 18.2541 0.610167
\(896\) −1.91249 −0.0638917
\(897\) −0.345440 −0.0115339
\(898\) −5.98084 −0.199583
\(899\) 5.04250 0.168177
\(900\) 2.67064 0.0890213
\(901\) −47.2169 −1.57302
\(902\) −0.159637 −0.00531532
\(903\) 1.63275 0.0543346
\(904\) −10.1321 −0.336988
\(905\) −46.0137 −1.52955
\(906\) 0.753082 0.0250195
\(907\) −42.6908 −1.41753 −0.708763 0.705447i \(-0.750746\pi\)
−0.708763 + 0.705447i \(0.750746\pi\)
\(908\) −12.3604 −0.410194
\(909\) 44.2328 1.46711
\(910\) 6.17066 0.204555
\(911\) −24.0607 −0.797168 −0.398584 0.917132i \(-0.630498\pi\)
−0.398584 + 0.917132i \(0.630498\pi\)
\(912\) −0.100558 −0.00332981
\(913\) 13.3582 0.442091
\(914\) 13.5583 0.448468
\(915\) 1.94074 0.0641589
\(916\) 7.65151 0.252813
\(917\) 3.67037 0.121206
\(918\) 2.90992 0.0960416
\(919\) −10.1936 −0.336257 −0.168128 0.985765i \(-0.553772\pi\)
−0.168128 + 0.985765i \(0.553772\pi\)
\(920\) −4.37244 −0.144155
\(921\) 0.462118 0.0152273
\(922\) −4.14128 −0.136386
\(923\) 23.4951 0.773349
\(924\) −0.583686 −0.0192019
\(925\) 9.97660 0.328029
\(926\) 18.9491 0.622705
\(927\) 5.25000 0.172433
\(928\) 1.54555 0.0507351
\(929\) −38.2130 −1.25373 −0.626864 0.779129i \(-0.715662\pi\)
−0.626864 + 0.779129i \(0.715662\pi\)
\(930\) 0.664861 0.0218016
\(931\) 3.34239 0.109543
\(932\) 24.2147 0.793177
\(933\) −2.70866 −0.0886775
\(934\) 16.8398 0.551017
\(935\) −29.7139 −0.971748
\(936\) −4.76034 −0.155596
\(937\) 38.7253 1.26510 0.632550 0.774520i \(-0.282008\pi\)
0.632550 + 0.774520i \(0.282008\pi\)
\(938\) −22.2310 −0.725869
\(939\) −1.01635 −0.0331674
\(940\) 22.9838 0.749650
\(941\) −5.42669 −0.176905 −0.0884525 0.996080i \(-0.528192\pi\)
−0.0884525 + 0.996080i \(0.528192\pi\)
\(942\) 1.01768 0.0331578
\(943\) −0.113486 −0.00369561
\(944\) 3.74947 0.122035
\(945\) −2.33445 −0.0759397
\(946\) 25.7673 0.837767
\(947\) 36.2026 1.17643 0.588213 0.808706i \(-0.299832\pi\)
0.588213 + 0.808706i \(0.299832\pi\)
\(948\) −0.881986 −0.0286456
\(949\) −8.94307 −0.290304
\(950\) −0.893223 −0.0289800
\(951\) 2.20995 0.0716625
\(952\) −9.23940 −0.299451
\(953\) −40.2095 −1.30251 −0.651257 0.758857i \(-0.725758\pi\)
−0.651257 + 0.758857i \(0.725758\pi\)
\(954\) −29.2218 −0.946091
\(955\) −0.935313 −0.0302660
\(956\) −27.6853 −0.895406
\(957\) 0.471697 0.0152478
\(958\) 29.7128 0.959978
\(959\) 1.75557 0.0566903
\(960\) 0.203783 0.00657706
\(961\) −20.3555 −0.656628
\(962\) −17.7830 −0.573347
\(963\) 40.0574 1.29083
\(964\) 5.78747 0.186402
\(965\) −38.5221 −1.24007
\(966\) −0.414944 −0.0133506
\(967\) −23.4551 −0.754264 −0.377132 0.926160i \(-0.623090\pi\)
−0.377132 + 0.926160i \(0.623090\pi\)
\(968\) 1.78856 0.0574866
\(969\) −0.485805 −0.0156063
\(970\) −36.1962 −1.16219
\(971\) 3.10786 0.0997360 0.0498680 0.998756i \(-0.484120\pi\)
0.0498680 + 0.998756i \(0.484120\pi\)
\(972\) 2.70288 0.0866948
\(973\) 21.9269 0.702945
\(974\) 14.5662 0.466732
\(975\) 0.143008 0.00457992
\(976\) 9.52357 0.304842
\(977\) 21.0039 0.671973 0.335987 0.941867i \(-0.390930\pi\)
0.335987 + 0.941867i \(0.390930\pi\)
\(978\) −0.151543 −0.00484582
\(979\) 38.6809 1.23625
\(980\) −6.77342 −0.216369
\(981\) 18.3029 0.584366
\(982\) −30.5166 −0.973823
\(983\) −55.7287 −1.77747 −0.888734 0.458423i \(-0.848414\pi\)
−0.888734 + 0.458423i \(0.848414\pi\)
\(984\) 0.00528915 0.000168612 0
\(985\) −22.6049 −0.720251
\(986\) 7.46668 0.237788
\(987\) 2.18116 0.0694271
\(988\) 1.59215 0.0506529
\(989\) 18.3180 0.582479
\(990\) −18.3895 −0.584456
\(991\) −12.2353 −0.388667 −0.194333 0.980936i \(-0.562254\pi\)
−0.194333 + 0.980936i \(0.562254\pi\)
\(992\) 3.26259 0.103587
\(993\) 1.15110 0.0365291
\(994\) 28.2223 0.895157
\(995\) −51.3773 −1.62877
\(996\) −0.442588 −0.0140240
\(997\) 34.5312 1.09361 0.546807 0.837259i \(-0.315843\pi\)
0.546807 + 0.837259i \(0.315843\pi\)
\(998\) 31.5212 0.997785
\(999\) 6.72757 0.212851
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 \(a_p\))