Properties

Label 8015.2.a.l.1.56
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.56
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.39193 q^{2} -0.616339 q^{3} +3.72134 q^{4} -1.00000 q^{5} -1.47424 q^{6} -1.00000 q^{7} +4.11733 q^{8} -2.62013 q^{9} +O(q^{10})\) \(q+2.39193 q^{2} -0.616339 q^{3} +3.72134 q^{4} -1.00000 q^{5} -1.47424 q^{6} -1.00000 q^{7} +4.11733 q^{8} -2.62013 q^{9} -2.39193 q^{10} +0.550190 q^{11} -2.29361 q^{12} +3.12576 q^{13} -2.39193 q^{14} +0.616339 q^{15} +2.40569 q^{16} +2.92502 q^{17} -6.26717 q^{18} -7.49240 q^{19} -3.72134 q^{20} +0.616339 q^{21} +1.31602 q^{22} +5.91234 q^{23} -2.53767 q^{24} +1.00000 q^{25} +7.47660 q^{26} +3.46390 q^{27} -3.72134 q^{28} +3.14112 q^{29} +1.47424 q^{30} +1.69415 q^{31} -2.48041 q^{32} -0.339103 q^{33} +6.99644 q^{34} +1.00000 q^{35} -9.75038 q^{36} -0.900002 q^{37} -17.9213 q^{38} -1.92652 q^{39} -4.11733 q^{40} +4.84696 q^{41} +1.47424 q^{42} -7.55186 q^{43} +2.04744 q^{44} +2.62013 q^{45} +14.1419 q^{46} +9.22768 q^{47} -1.48272 q^{48} +1.00000 q^{49} +2.39193 q^{50} -1.80280 q^{51} +11.6320 q^{52} -0.956524 q^{53} +8.28542 q^{54} -0.550190 q^{55} -4.11733 q^{56} +4.61786 q^{57} +7.51336 q^{58} +10.7205 q^{59} +2.29361 q^{60} +8.86504 q^{61} +4.05230 q^{62} +2.62013 q^{63} -10.7443 q^{64} -3.12576 q^{65} -0.811112 q^{66} +0.505435 q^{67} +10.8850 q^{68} -3.64400 q^{69} +2.39193 q^{70} +7.84495 q^{71} -10.7879 q^{72} +7.74262 q^{73} -2.15274 q^{74} -0.616339 q^{75} -27.8818 q^{76} -0.550190 q^{77} -4.60812 q^{78} -0.0674259 q^{79} -2.40569 q^{80} +5.72544 q^{81} +11.5936 q^{82} -10.1691 q^{83} +2.29361 q^{84} -2.92502 q^{85} -18.0635 q^{86} -1.93600 q^{87} +2.26531 q^{88} +11.0915 q^{89} +6.26717 q^{90} -3.12576 q^{91} +22.0018 q^{92} -1.04417 q^{93} +22.0720 q^{94} +7.49240 q^{95} +1.52877 q^{96} -0.0409927 q^{97} +2.39193 q^{98} -1.44157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.39193 1.69135 0.845676 0.533697i \(-0.179198\pi\)
0.845676 + 0.533697i \(0.179198\pi\)
\(3\) −0.616339 −0.355843 −0.177922 0.984045i \(-0.556937\pi\)
−0.177922 + 0.984045i \(0.556937\pi\)
\(4\) 3.72134 1.86067
\(5\) −1.00000 −0.447214
\(6\) −1.47424 −0.601856
\(7\) −1.00000 −0.377964
\(8\) 4.11733 1.45570
\(9\) −2.62013 −0.873376
\(10\) −2.39193 −0.756395
\(11\) 0.550190 0.165888 0.0829442 0.996554i \(-0.473568\pi\)
0.0829442 + 0.996554i \(0.473568\pi\)
\(12\) −2.29361 −0.662107
\(13\) 3.12576 0.866929 0.433464 0.901171i \(-0.357291\pi\)
0.433464 + 0.901171i \(0.357291\pi\)
\(14\) −2.39193 −0.639271
\(15\) 0.616339 0.159138
\(16\) 2.40569 0.601423
\(17\) 2.92502 0.709421 0.354710 0.934976i \(-0.384579\pi\)
0.354710 + 0.934976i \(0.384579\pi\)
\(18\) −6.26717 −1.47718
\(19\) −7.49240 −1.71888 −0.859438 0.511241i \(-0.829186\pi\)
−0.859438 + 0.511241i \(0.829186\pi\)
\(20\) −3.72134 −0.832117
\(21\) 0.616339 0.134496
\(22\) 1.31602 0.280576
\(23\) 5.91234 1.23281 0.616404 0.787430i \(-0.288589\pi\)
0.616404 + 0.787430i \(0.288589\pi\)
\(24\) −2.53767 −0.517999
\(25\) 1.00000 0.200000
\(26\) 7.47660 1.46628
\(27\) 3.46390 0.666628
\(28\) −3.72134 −0.703267
\(29\) 3.14112 0.583292 0.291646 0.956526i \(-0.405797\pi\)
0.291646 + 0.956526i \(0.405797\pi\)
\(30\) 1.47424 0.269158
\(31\) 1.69415 0.304279 0.152139 0.988359i \(-0.451384\pi\)
0.152139 + 0.988359i \(0.451384\pi\)
\(32\) −2.48041 −0.438478
\(33\) −0.339103 −0.0590303
\(34\) 6.99644 1.19988
\(35\) 1.00000 0.169031
\(36\) −9.75038 −1.62506
\(37\) −0.900002 −0.147959 −0.0739797 0.997260i \(-0.523570\pi\)
−0.0739797 + 0.997260i \(0.523570\pi\)
\(38\) −17.9213 −2.90722
\(39\) −1.92652 −0.308491
\(40\) −4.11733 −0.651007
\(41\) 4.84696 0.756968 0.378484 0.925608i \(-0.376446\pi\)
0.378484 + 0.925608i \(0.376446\pi\)
\(42\) 1.47424 0.227480
\(43\) −7.55186 −1.15165 −0.575824 0.817574i \(-0.695319\pi\)
−0.575824 + 0.817574i \(0.695319\pi\)
\(44\) 2.04744 0.308664
\(45\) 2.62013 0.390585
\(46\) 14.1419 2.08511
\(47\) 9.22768 1.34600 0.672998 0.739645i \(-0.265006\pi\)
0.672998 + 0.739645i \(0.265006\pi\)
\(48\) −1.48272 −0.214012
\(49\) 1.00000 0.142857
\(50\) 2.39193 0.338270
\(51\) −1.80280 −0.252443
\(52\) 11.6320 1.61307
\(53\) −0.956524 −0.131389 −0.0656943 0.997840i \(-0.520926\pi\)
−0.0656943 + 0.997840i \(0.520926\pi\)
\(54\) 8.28542 1.12750
\(55\) −0.550190 −0.0741876
\(56\) −4.11733 −0.550201
\(57\) 4.61786 0.611650
\(58\) 7.51336 0.986552
\(59\) 10.7205 1.39570 0.697848 0.716246i \(-0.254141\pi\)
0.697848 + 0.716246i \(0.254141\pi\)
\(60\) 2.29361 0.296103
\(61\) 8.86504 1.13505 0.567526 0.823355i \(-0.307901\pi\)
0.567526 + 0.823355i \(0.307901\pi\)
\(62\) 4.05230 0.514642
\(63\) 2.62013 0.330105
\(64\) −10.7443 −1.34304
\(65\) −3.12576 −0.387702
\(66\) −0.811112 −0.0998410
\(67\) 0.505435 0.0617487 0.0308743 0.999523i \(-0.490171\pi\)
0.0308743 + 0.999523i \(0.490171\pi\)
\(68\) 10.8850 1.32000
\(69\) −3.64400 −0.438686
\(70\) 2.39193 0.285891
\(71\) 7.84495 0.931025 0.465512 0.885041i \(-0.345870\pi\)
0.465512 + 0.885041i \(0.345870\pi\)
\(72\) −10.7879 −1.27137
\(73\) 7.74262 0.906205 0.453103 0.891458i \(-0.350317\pi\)
0.453103 + 0.891458i \(0.350317\pi\)
\(74\) −2.15274 −0.250251
\(75\) −0.616339 −0.0711687
\(76\) −27.8818 −3.19826
\(77\) −0.550190 −0.0627000
\(78\) −4.60812 −0.521766
\(79\) −0.0674259 −0.00758601 −0.00379300 0.999993i \(-0.501207\pi\)
−0.00379300 + 0.999993i \(0.501207\pi\)
\(80\) −2.40569 −0.268964
\(81\) 5.72544 0.636160
\(82\) 11.5936 1.28030
\(83\) −10.1691 −1.11621 −0.558104 0.829771i \(-0.688471\pi\)
−0.558104 + 0.829771i \(0.688471\pi\)
\(84\) 2.29361 0.250253
\(85\) −2.92502 −0.317263
\(86\) −18.0635 −1.94784
\(87\) −1.93600 −0.207561
\(88\) 2.26531 0.241483
\(89\) 11.0915 1.17570 0.587850 0.808970i \(-0.299975\pi\)
0.587850 + 0.808970i \(0.299975\pi\)
\(90\) 6.26717 0.660617
\(91\) −3.12576 −0.327668
\(92\) 22.0018 2.29385
\(93\) −1.04417 −0.108276
\(94\) 22.0720 2.27655
\(95\) 7.49240 0.768704
\(96\) 1.52877 0.156030
\(97\) −0.0409927 −0.00416218 −0.00208109 0.999998i \(-0.500662\pi\)
−0.00208109 + 0.999998i \(0.500662\pi\)
\(98\) 2.39193 0.241622
\(99\) −1.44157 −0.144883
\(100\) 3.72134 0.372134
\(101\) −2.74522 −0.273160 −0.136580 0.990629i \(-0.543611\pi\)
−0.136580 + 0.990629i \(0.543611\pi\)
\(102\) −4.31218 −0.426969
\(103\) 1.11173 0.109542 0.0547710 0.998499i \(-0.482557\pi\)
0.0547710 + 0.998499i \(0.482557\pi\)
\(104\) 12.8698 1.26198
\(105\) −0.616339 −0.0601485
\(106\) −2.28794 −0.222224
\(107\) 15.2749 1.47668 0.738339 0.674430i \(-0.235610\pi\)
0.738339 + 0.674430i \(0.235610\pi\)
\(108\) 12.8904 1.24038
\(109\) 10.2684 0.983538 0.491769 0.870726i \(-0.336350\pi\)
0.491769 + 0.870726i \(0.336350\pi\)
\(110\) −1.31602 −0.125477
\(111\) 0.554706 0.0526504
\(112\) −2.40569 −0.227316
\(113\) 14.2937 1.34464 0.672320 0.740261i \(-0.265298\pi\)
0.672320 + 0.740261i \(0.265298\pi\)
\(114\) 11.0456 1.03452
\(115\) −5.91234 −0.551328
\(116\) 11.6892 1.08531
\(117\) −8.18988 −0.757154
\(118\) 25.6428 2.36061
\(119\) −2.92502 −0.268136
\(120\) 2.53767 0.231656
\(121\) −10.6973 −0.972481
\(122\) 21.2046 1.91977
\(123\) −2.98737 −0.269362
\(124\) 6.30452 0.566162
\(125\) −1.00000 −0.0894427
\(126\) 6.26717 0.558323
\(127\) −8.42042 −0.747191 −0.373596 0.927592i \(-0.621875\pi\)
−0.373596 + 0.927592i \(0.621875\pi\)
\(128\) −20.7389 −1.83308
\(129\) 4.65450 0.409806
\(130\) −7.47660 −0.655741
\(131\) −0.747926 −0.0653466 −0.0326733 0.999466i \(-0.510402\pi\)
−0.0326733 + 0.999466i \(0.510402\pi\)
\(132\) −1.26192 −0.109836
\(133\) 7.49240 0.649674
\(134\) 1.20897 0.104439
\(135\) −3.46390 −0.298125
\(136\) 12.0433 1.03270
\(137\) −22.5558 −1.92707 −0.963536 0.267578i \(-0.913777\pi\)
−0.963536 + 0.267578i \(0.913777\pi\)
\(138\) −8.71621 −0.741973
\(139\) −12.9126 −1.09524 −0.547618 0.836729i \(-0.684465\pi\)
−0.547618 + 0.836729i \(0.684465\pi\)
\(140\) 3.72134 0.314511
\(141\) −5.68737 −0.478963
\(142\) 18.7646 1.57469
\(143\) 1.71976 0.143813
\(144\) −6.30321 −0.525268
\(145\) −3.14112 −0.260856
\(146\) 18.5198 1.53271
\(147\) −0.616339 −0.0508348
\(148\) −3.34921 −0.275304
\(149\) 9.22538 0.755773 0.377886 0.925852i \(-0.376651\pi\)
0.377886 + 0.925852i \(0.376651\pi\)
\(150\) −1.47424 −0.120371
\(151\) 1.41490 0.115143 0.0575715 0.998341i \(-0.481664\pi\)
0.0575715 + 0.998341i \(0.481664\pi\)
\(152\) −30.8487 −2.50216
\(153\) −7.66391 −0.619591
\(154\) −1.31602 −0.106048
\(155\) −1.69415 −0.136078
\(156\) −7.16925 −0.574000
\(157\) 9.70918 0.774877 0.387438 0.921896i \(-0.373360\pi\)
0.387438 + 0.921896i \(0.373360\pi\)
\(158\) −0.161278 −0.0128306
\(159\) 0.589543 0.0467538
\(160\) 2.48041 0.196093
\(161\) −5.91234 −0.465958
\(162\) 13.6949 1.07597
\(163\) −21.3032 −1.66859 −0.834297 0.551315i \(-0.814126\pi\)
−0.834297 + 0.551315i \(0.814126\pi\)
\(164\) 18.0372 1.40847
\(165\) 0.339103 0.0263992
\(166\) −24.3239 −1.88790
\(167\) 23.0846 1.78634 0.893170 0.449720i \(-0.148476\pi\)
0.893170 + 0.449720i \(0.148476\pi\)
\(168\) 2.53767 0.195785
\(169\) −3.22965 −0.248435
\(170\) −6.99644 −0.536603
\(171\) 19.6310 1.50122
\(172\) −28.1030 −2.14284
\(173\) −2.64945 −0.201434 −0.100717 0.994915i \(-0.532114\pi\)
−0.100717 + 0.994915i \(0.532114\pi\)
\(174\) −4.63077 −0.351058
\(175\) −1.00000 −0.0755929
\(176\) 1.32359 0.0997691
\(177\) −6.60749 −0.496649
\(178\) 26.5302 1.98852
\(179\) −12.6460 −0.945206 −0.472603 0.881275i \(-0.656686\pi\)
−0.472603 + 0.881275i \(0.656686\pi\)
\(180\) 9.75038 0.726751
\(181\) 24.5138 1.82210 0.911049 0.412299i \(-0.135274\pi\)
0.911049 + 0.412299i \(0.135274\pi\)
\(182\) −7.47660 −0.554202
\(183\) −5.46387 −0.403901
\(184\) 24.3430 1.79459
\(185\) 0.900002 0.0661695
\(186\) −2.49759 −0.183132
\(187\) 1.60931 0.117685
\(188\) 34.3393 2.50445
\(189\) −3.46390 −0.251962
\(190\) 17.9213 1.30015
\(191\) 11.4174 0.826135 0.413068 0.910700i \(-0.364457\pi\)
0.413068 + 0.910700i \(0.364457\pi\)
\(192\) 6.62216 0.477913
\(193\) 22.5492 1.62313 0.811564 0.584264i \(-0.198617\pi\)
0.811564 + 0.584264i \(0.198617\pi\)
\(194\) −0.0980518 −0.00703971
\(195\) 1.92652 0.137961
\(196\) 3.72134 0.265810
\(197\) −2.24354 −0.159846 −0.0799229 0.996801i \(-0.525467\pi\)
−0.0799229 + 0.996801i \(0.525467\pi\)
\(198\) −3.44813 −0.245048
\(199\) 12.2650 0.869442 0.434721 0.900565i \(-0.356847\pi\)
0.434721 + 0.900565i \(0.356847\pi\)
\(200\) 4.11733 0.291139
\(201\) −0.311519 −0.0219729
\(202\) −6.56638 −0.462009
\(203\) −3.14112 −0.220464
\(204\) −6.70883 −0.469712
\(205\) −4.84696 −0.338526
\(206\) 2.65918 0.185274
\(207\) −15.4911 −1.07670
\(208\) 7.51960 0.521391
\(209\) −4.12224 −0.285142
\(210\) −1.47424 −0.101732
\(211\) 7.55832 0.520336 0.260168 0.965563i \(-0.416222\pi\)
0.260168 + 0.965563i \(0.416222\pi\)
\(212\) −3.55955 −0.244471
\(213\) −4.83515 −0.331299
\(214\) 36.5365 2.49758
\(215\) 7.55186 0.515032
\(216\) 14.2620 0.970408
\(217\) −1.69415 −0.115007
\(218\) 24.5614 1.66351
\(219\) −4.77208 −0.322467
\(220\) −2.04744 −0.138039
\(221\) 9.14289 0.615017
\(222\) 1.32682 0.0890503
\(223\) 1.94379 0.130166 0.0650830 0.997880i \(-0.479269\pi\)
0.0650830 + 0.997880i \(0.479269\pi\)
\(224\) 2.48041 0.165729
\(225\) −2.62013 −0.174675
\(226\) 34.1896 2.27426
\(227\) 23.9843 1.59190 0.795948 0.605365i \(-0.206973\pi\)
0.795948 + 0.605365i \(0.206973\pi\)
\(228\) 17.1846 1.13808
\(229\) 1.00000 0.0660819
\(230\) −14.1419 −0.932490
\(231\) 0.339103 0.0223114
\(232\) 12.9330 0.849096
\(233\) 3.91088 0.256210 0.128105 0.991761i \(-0.459110\pi\)
0.128105 + 0.991761i \(0.459110\pi\)
\(234\) −19.5896 −1.28061
\(235\) −9.22768 −0.601947
\(236\) 39.8948 2.59693
\(237\) 0.0415572 0.00269943
\(238\) −6.99644 −0.453512
\(239\) 18.7411 1.21226 0.606129 0.795366i \(-0.292722\pi\)
0.606129 + 0.795366i \(0.292722\pi\)
\(240\) 1.48272 0.0957092
\(241\) 15.4978 0.998300 0.499150 0.866515i \(-0.333646\pi\)
0.499150 + 0.866515i \(0.333646\pi\)
\(242\) −25.5872 −1.64481
\(243\) −13.9205 −0.893002
\(244\) 32.9898 2.11196
\(245\) −1.00000 −0.0638877
\(246\) −7.14558 −0.455586
\(247\) −23.4194 −1.49014
\(248\) 6.97538 0.442937
\(249\) 6.26763 0.397195
\(250\) −2.39193 −0.151279
\(251\) 3.82419 0.241381 0.120690 0.992690i \(-0.461489\pi\)
0.120690 + 0.992690i \(0.461489\pi\)
\(252\) 9.75038 0.614216
\(253\) 3.25291 0.204509
\(254\) −20.1411 −1.26376
\(255\) 1.80280 0.112896
\(256\) −28.1174 −1.75734
\(257\) −9.12482 −0.569191 −0.284595 0.958648i \(-0.591859\pi\)
−0.284595 + 0.958648i \(0.591859\pi\)
\(258\) 11.1333 0.693126
\(259\) 0.900002 0.0559234
\(260\) −11.6320 −0.721386
\(261\) −8.23014 −0.509433
\(262\) −1.78899 −0.110524
\(263\) −9.49212 −0.585309 −0.292655 0.956218i \(-0.594539\pi\)
−0.292655 + 0.956218i \(0.594539\pi\)
\(264\) −1.39620 −0.0859301
\(265\) 0.956524 0.0587588
\(266\) 17.9213 1.09883
\(267\) −6.83614 −0.418365
\(268\) 1.88089 0.114894
\(269\) 3.67972 0.224356 0.112178 0.993688i \(-0.464217\pi\)
0.112178 + 0.993688i \(0.464217\pi\)
\(270\) −8.28542 −0.504234
\(271\) −3.83658 −0.233056 −0.116528 0.993187i \(-0.537176\pi\)
−0.116528 + 0.993187i \(0.537176\pi\)
\(272\) 7.03668 0.426662
\(273\) 1.92652 0.116599
\(274\) −53.9520 −3.25936
\(275\) 0.550190 0.0331777
\(276\) −13.5606 −0.816251
\(277\) −6.68087 −0.401415 −0.200707 0.979651i \(-0.564324\pi\)
−0.200707 + 0.979651i \(0.564324\pi\)
\(278\) −30.8862 −1.85243
\(279\) −4.43889 −0.265750
\(280\) 4.11733 0.246057
\(281\) 10.5174 0.627417 0.313709 0.949519i \(-0.398428\pi\)
0.313709 + 0.949519i \(0.398428\pi\)
\(282\) −13.6038 −0.810095
\(283\) −15.5762 −0.925906 −0.462953 0.886383i \(-0.653210\pi\)
−0.462953 + 0.886383i \(0.653210\pi\)
\(284\) 29.1937 1.73233
\(285\) −4.61786 −0.273538
\(286\) 4.11355 0.243239
\(287\) −4.84696 −0.286107
\(288\) 6.49898 0.382956
\(289\) −8.44428 −0.496722
\(290\) −7.51336 −0.441199
\(291\) 0.0252654 0.00148108
\(292\) 28.8129 1.68615
\(293\) 10.2836 0.600773 0.300386 0.953818i \(-0.402884\pi\)
0.300386 + 0.953818i \(0.402884\pi\)
\(294\) −1.47424 −0.0859795
\(295\) −10.7205 −0.624174
\(296\) −3.70560 −0.215384
\(297\) 1.90580 0.110586
\(298\) 22.0665 1.27828
\(299\) 18.4805 1.06876
\(300\) −2.29361 −0.132421
\(301\) 7.55186 0.435282
\(302\) 3.38435 0.194747
\(303\) 1.69199 0.0972020
\(304\) −18.0244 −1.03377
\(305\) −8.86504 −0.507611
\(306\) −18.3316 −1.04795
\(307\) −23.2532 −1.32713 −0.663566 0.748117i \(-0.730958\pi\)
−0.663566 + 0.748117i \(0.730958\pi\)
\(308\) −2.04744 −0.116664
\(309\) −0.685203 −0.0389798
\(310\) −4.05230 −0.230155
\(311\) 5.59117 0.317046 0.158523 0.987355i \(-0.449327\pi\)
0.158523 + 0.987355i \(0.449327\pi\)
\(312\) −7.93213 −0.449069
\(313\) −28.2851 −1.59877 −0.799385 0.600819i \(-0.794841\pi\)
−0.799385 + 0.600819i \(0.794841\pi\)
\(314\) 23.2237 1.31059
\(315\) −2.62013 −0.147627
\(316\) −0.250915 −0.0141151
\(317\) −19.4866 −1.09448 −0.547238 0.836977i \(-0.684321\pi\)
−0.547238 + 0.836977i \(0.684321\pi\)
\(318\) 1.41015 0.0790771
\(319\) 1.72821 0.0967614
\(320\) 10.7443 0.600627
\(321\) −9.41450 −0.525466
\(322\) −14.1419 −0.788098
\(323\) −21.9154 −1.21941
\(324\) 21.3063 1.18368
\(325\) 3.12576 0.173386
\(326\) −50.9558 −2.82218
\(327\) −6.32884 −0.349986
\(328\) 19.9565 1.10191
\(329\) −9.22768 −0.508738
\(330\) 0.811112 0.0446503
\(331\) −30.8683 −1.69668 −0.848339 0.529453i \(-0.822397\pi\)
−0.848339 + 0.529453i \(0.822397\pi\)
\(332\) −37.8428 −2.07689
\(333\) 2.35812 0.129224
\(334\) 55.2168 3.02133
\(335\) −0.505435 −0.0276148
\(336\) 1.48272 0.0808890
\(337\) −18.9961 −1.03478 −0.517391 0.855749i \(-0.673097\pi\)
−0.517391 + 0.855749i \(0.673097\pi\)
\(338\) −7.72510 −0.420190
\(339\) −8.80977 −0.478481
\(340\) −10.8850 −0.590321
\(341\) 0.932105 0.0504763
\(342\) 46.9561 2.53910
\(343\) −1.00000 −0.0539949
\(344\) −31.0935 −1.67645
\(345\) 3.64400 0.196187
\(346\) −6.33732 −0.340696
\(347\) 10.8780 0.583960 0.291980 0.956424i \(-0.405686\pi\)
0.291980 + 0.956424i \(0.405686\pi\)
\(348\) −7.20450 −0.386202
\(349\) −19.3947 −1.03817 −0.519086 0.854722i \(-0.673728\pi\)
−0.519086 + 0.854722i \(0.673728\pi\)
\(350\) −2.39193 −0.127854
\(351\) 10.8273 0.577919
\(352\) −1.36470 −0.0727385
\(353\) 23.8929 1.27169 0.635845 0.771817i \(-0.280652\pi\)
0.635845 + 0.771817i \(0.280652\pi\)
\(354\) −15.8047 −0.840008
\(355\) −7.84495 −0.416367
\(356\) 41.2753 2.18759
\(357\) 1.80280 0.0954143
\(358\) −30.2484 −1.59868
\(359\) −6.96980 −0.367852 −0.183926 0.982940i \(-0.558881\pi\)
−0.183926 + 0.982940i \(0.558881\pi\)
\(360\) 10.7879 0.568573
\(361\) 37.1361 1.95453
\(362\) 58.6354 3.08181
\(363\) 6.59315 0.346051
\(364\) −11.6320 −0.609682
\(365\) −7.74262 −0.405267
\(366\) −13.0692 −0.683138
\(367\) −35.2206 −1.83850 −0.919251 0.393673i \(-0.871204\pi\)
−0.919251 + 0.393673i \(0.871204\pi\)
\(368\) 14.2233 0.741439
\(369\) −12.6996 −0.661117
\(370\) 2.15274 0.111916
\(371\) 0.956524 0.0496603
\(372\) −3.88572 −0.201465
\(373\) 2.73361 0.141541 0.0707706 0.997493i \(-0.477454\pi\)
0.0707706 + 0.997493i \(0.477454\pi\)
\(374\) 3.84937 0.199046
\(375\) 0.616339 0.0318276
\(376\) 37.9934 1.95936
\(377\) 9.81839 0.505673
\(378\) −8.28542 −0.426156
\(379\) −10.9491 −0.562416 −0.281208 0.959647i \(-0.590735\pi\)
−0.281208 + 0.959647i \(0.590735\pi\)
\(380\) 27.8818 1.43031
\(381\) 5.18983 0.265883
\(382\) 27.3097 1.39728
\(383\) 20.4432 1.04460 0.522299 0.852763i \(-0.325075\pi\)
0.522299 + 0.852763i \(0.325075\pi\)
\(384\) 12.7822 0.652289
\(385\) 0.550190 0.0280403
\(386\) 53.9362 2.74528
\(387\) 19.7868 1.00582
\(388\) −0.152548 −0.00774444
\(389\) 3.12924 0.158659 0.0793294 0.996848i \(-0.474722\pi\)
0.0793294 + 0.996848i \(0.474722\pi\)
\(390\) 4.60812 0.233341
\(391\) 17.2937 0.874579
\(392\) 4.11733 0.207956
\(393\) 0.460976 0.0232532
\(394\) −5.36640 −0.270355
\(395\) 0.0674259 0.00339257
\(396\) −5.36456 −0.269579
\(397\) 25.3923 1.27440 0.637201 0.770698i \(-0.280092\pi\)
0.637201 + 0.770698i \(0.280092\pi\)
\(398\) 29.3370 1.47053
\(399\) −4.61786 −0.231182
\(400\) 2.40569 0.120285
\(401\) −21.5201 −1.07466 −0.537331 0.843371i \(-0.680567\pi\)
−0.537331 + 0.843371i \(0.680567\pi\)
\(402\) −0.745132 −0.0371638
\(403\) 5.29551 0.263788
\(404\) −10.2159 −0.508260
\(405\) −5.72544 −0.284500
\(406\) −7.51336 −0.372882
\(407\) −0.495172 −0.0245448
\(408\) −7.42272 −0.367480
\(409\) −2.02546 −0.100152 −0.0500762 0.998745i \(-0.515946\pi\)
−0.0500762 + 0.998745i \(0.515946\pi\)
\(410\) −11.5936 −0.572567
\(411\) 13.9020 0.685736
\(412\) 4.13713 0.203822
\(413\) −10.7205 −0.527524
\(414\) −37.0536 −1.82109
\(415\) 10.1691 0.499183
\(416\) −7.75315 −0.380129
\(417\) 7.95856 0.389732
\(418\) −9.86013 −0.482275
\(419\) −33.7393 −1.64827 −0.824137 0.566390i \(-0.808340\pi\)
−0.824137 + 0.566390i \(0.808340\pi\)
\(420\) −2.29361 −0.111917
\(421\) −34.9060 −1.70121 −0.850606 0.525803i \(-0.823765\pi\)
−0.850606 + 0.525803i \(0.823765\pi\)
\(422\) 18.0790 0.880072
\(423\) −24.1777 −1.17556
\(424\) −3.93832 −0.191262
\(425\) 2.92502 0.141884
\(426\) −11.5653 −0.560343
\(427\) −8.86504 −0.429009
\(428\) 56.8430 2.74761
\(429\) −1.05995 −0.0511751
\(430\) 18.0635 0.871101
\(431\) 18.7058 0.901028 0.450514 0.892769i \(-0.351241\pi\)
0.450514 + 0.892769i \(0.351241\pi\)
\(432\) 8.33308 0.400925
\(433\) 3.18617 0.153117 0.0765587 0.997065i \(-0.475607\pi\)
0.0765587 + 0.997065i \(0.475607\pi\)
\(434\) −4.05230 −0.194516
\(435\) 1.93600 0.0928239
\(436\) 38.2124 1.83004
\(437\) −44.2976 −2.11904
\(438\) −11.4145 −0.545405
\(439\) 27.2791 1.30196 0.650981 0.759094i \(-0.274358\pi\)
0.650981 + 0.759094i \(0.274358\pi\)
\(440\) −2.26531 −0.107995
\(441\) −2.62013 −0.124768
\(442\) 21.8692 1.04021
\(443\) −34.8478 −1.65567 −0.827834 0.560974i \(-0.810427\pi\)
−0.827834 + 0.560974i \(0.810427\pi\)
\(444\) 2.06425 0.0979650
\(445\) −11.0915 −0.525789
\(446\) 4.64942 0.220156
\(447\) −5.68596 −0.268937
\(448\) 10.7443 0.507623
\(449\) −17.2330 −0.813275 −0.406638 0.913590i \(-0.633299\pi\)
−0.406638 + 0.913590i \(0.633299\pi\)
\(450\) −6.26717 −0.295437
\(451\) 2.66675 0.125572
\(452\) 53.1918 2.50193
\(453\) −0.872059 −0.0409729
\(454\) 57.3689 2.69246
\(455\) 3.12576 0.146538
\(456\) 19.0132 0.890377
\(457\) 17.7944 0.832385 0.416192 0.909277i \(-0.363364\pi\)
0.416192 + 0.909277i \(0.363364\pi\)
\(458\) 2.39193 0.111768
\(459\) 10.1320 0.472920
\(460\) −22.0018 −1.02584
\(461\) −7.73559 −0.360282 −0.180141 0.983641i \(-0.557655\pi\)
−0.180141 + 0.983641i \(0.557655\pi\)
\(462\) 0.811112 0.0377364
\(463\) 26.9467 1.25232 0.626160 0.779695i \(-0.284626\pi\)
0.626160 + 0.779695i \(0.284626\pi\)
\(464\) 7.55657 0.350805
\(465\) 1.04417 0.0484223
\(466\) 9.35456 0.433342
\(467\) 27.5082 1.27293 0.636464 0.771307i \(-0.280396\pi\)
0.636464 + 0.771307i \(0.280396\pi\)
\(468\) −30.4773 −1.40881
\(469\) −0.505435 −0.0233388
\(470\) −22.0720 −1.01810
\(471\) −5.98414 −0.275735
\(472\) 44.1400 2.03171
\(473\) −4.15496 −0.191045
\(474\) 0.0994020 0.00456569
\(475\) −7.49240 −0.343775
\(476\) −10.8850 −0.498912
\(477\) 2.50621 0.114752
\(478\) 44.8273 2.05035
\(479\) 24.6571 1.12661 0.563306 0.826248i \(-0.309529\pi\)
0.563306 + 0.826248i \(0.309529\pi\)
\(480\) −1.52877 −0.0697786
\(481\) −2.81319 −0.128270
\(482\) 37.0697 1.68848
\(483\) 3.64400 0.165808
\(484\) −39.8083 −1.80947
\(485\) 0.0409927 0.00186138
\(486\) −33.2969 −1.51038
\(487\) −10.3641 −0.469644 −0.234822 0.972038i \(-0.575451\pi\)
−0.234822 + 0.972038i \(0.575451\pi\)
\(488\) 36.5003 1.65229
\(489\) 13.1300 0.593758
\(490\) −2.39193 −0.108056
\(491\) 16.6841 0.752943 0.376471 0.926428i \(-0.377137\pi\)
0.376471 + 0.926428i \(0.377137\pi\)
\(492\) −11.1170 −0.501194
\(493\) 9.18784 0.413800
\(494\) −56.0177 −2.52035
\(495\) 1.44157 0.0647936
\(496\) 4.07561 0.183000
\(497\) −7.84495 −0.351894
\(498\) 14.9918 0.671797
\(499\) −20.9392 −0.937367 −0.468683 0.883366i \(-0.655271\pi\)
−0.468683 + 0.883366i \(0.655271\pi\)
\(500\) −3.72134 −0.166423
\(501\) −14.2279 −0.635657
\(502\) 9.14720 0.408259
\(503\) 11.2573 0.501937 0.250968 0.967995i \(-0.419251\pi\)
0.250968 + 0.967995i \(0.419251\pi\)
\(504\) 10.7879 0.480532
\(505\) 2.74522 0.122161
\(506\) 7.78074 0.345896
\(507\) 1.99056 0.0884038
\(508\) −31.3352 −1.39028
\(509\) −15.3245 −0.679245 −0.339623 0.940562i \(-0.610299\pi\)
−0.339623 + 0.940562i \(0.610299\pi\)
\(510\) 4.31218 0.190946
\(511\) −7.74262 −0.342513
\(512\) −25.7771 −1.13920
\(513\) −25.9530 −1.14585
\(514\) −21.8260 −0.962702
\(515\) −1.11173 −0.0489887
\(516\) 17.3210 0.762514
\(517\) 5.07697 0.223285
\(518\) 2.15274 0.0945861
\(519\) 1.63296 0.0716791
\(520\) −12.8698 −0.564376
\(521\) 13.9781 0.612394 0.306197 0.951968i \(-0.400943\pi\)
0.306197 + 0.951968i \(0.400943\pi\)
\(522\) −19.6859 −0.861630
\(523\) −43.8496 −1.91741 −0.958705 0.284402i \(-0.908205\pi\)
−0.958705 + 0.284402i \(0.908205\pi\)
\(524\) −2.78329 −0.121588
\(525\) 0.616339 0.0268992
\(526\) −22.7045 −0.989964
\(527\) 4.95542 0.215862
\(528\) −0.815778 −0.0355022
\(529\) 11.9557 0.519815
\(530\) 2.28794 0.0993818
\(531\) −28.0892 −1.21897
\(532\) 27.8818 1.20883
\(533\) 15.1504 0.656237
\(534\) −16.3516 −0.707602
\(535\) −15.2749 −0.660390
\(536\) 2.08104 0.0898873
\(537\) 7.79422 0.336345
\(538\) 8.80164 0.379465
\(539\) 0.550190 0.0236984
\(540\) −12.8904 −0.554713
\(541\) 44.3227 1.90558 0.952791 0.303626i \(-0.0981972\pi\)
0.952791 + 0.303626i \(0.0981972\pi\)
\(542\) −9.17684 −0.394179
\(543\) −15.1088 −0.648381
\(544\) −7.25523 −0.311066
\(545\) −10.2684 −0.439852
\(546\) 4.60812 0.197209
\(547\) 30.3468 1.29754 0.648768 0.760986i \(-0.275285\pi\)
0.648768 + 0.760986i \(0.275285\pi\)
\(548\) −83.9378 −3.58565
\(549\) −23.2275 −0.991327
\(550\) 1.31602 0.0561151
\(551\) −23.5346 −1.00261
\(552\) −15.0036 −0.638594
\(553\) 0.0674259 0.00286724
\(554\) −15.9802 −0.678934
\(555\) −0.554706 −0.0235460
\(556\) −48.0523 −2.03787
\(557\) 20.7732 0.880190 0.440095 0.897951i \(-0.354945\pi\)
0.440095 + 0.897951i \(0.354945\pi\)
\(558\) −10.6175 −0.449476
\(559\) −23.6053 −0.998396
\(560\) 2.40569 0.101659
\(561\) −0.991883 −0.0418773
\(562\) 25.1570 1.06118
\(563\) 28.0941 1.18403 0.592013 0.805929i \(-0.298334\pi\)
0.592013 + 0.805929i \(0.298334\pi\)
\(564\) −21.1647 −0.891193
\(565\) −14.2937 −0.601341
\(566\) −37.2571 −1.56603
\(567\) −5.72544 −0.240446
\(568\) 32.3002 1.35529
\(569\) −14.8752 −0.623603 −0.311801 0.950147i \(-0.600932\pi\)
−0.311801 + 0.950147i \(0.600932\pi\)
\(570\) −11.0456 −0.462650
\(571\) 16.6643 0.697380 0.348690 0.937238i \(-0.386627\pi\)
0.348690 + 0.937238i \(0.386627\pi\)
\(572\) 6.39981 0.267589
\(573\) −7.03700 −0.293975
\(574\) −11.5936 −0.483907
\(575\) 5.91234 0.246562
\(576\) 28.1516 1.17298
\(577\) 23.0203 0.958349 0.479174 0.877720i \(-0.340936\pi\)
0.479174 + 0.877720i \(0.340936\pi\)
\(578\) −20.1981 −0.840132
\(579\) −13.8980 −0.577579
\(580\) −11.6892 −0.485367
\(581\) 10.1691 0.421887
\(582\) 0.0604331 0.00250503
\(583\) −0.526270 −0.0217959
\(584\) 31.8789 1.31916
\(585\) 8.18988 0.338610
\(586\) 24.5976 1.01612
\(587\) −36.5714 −1.50946 −0.754731 0.656034i \(-0.772233\pi\)
−0.754731 + 0.656034i \(0.772233\pi\)
\(588\) −2.29361 −0.0945867
\(589\) −12.6933 −0.523017
\(590\) −25.6428 −1.05570
\(591\) 1.38278 0.0568801
\(592\) −2.16513 −0.0889861
\(593\) 20.7365 0.851547 0.425773 0.904830i \(-0.360002\pi\)
0.425773 + 0.904830i \(0.360002\pi\)
\(594\) 4.55855 0.187040
\(595\) 2.92502 0.119914
\(596\) 34.3308 1.40624
\(597\) −7.55939 −0.309385
\(598\) 44.2042 1.80764
\(599\) −28.7457 −1.17452 −0.587259 0.809399i \(-0.699793\pi\)
−0.587259 + 0.809399i \(0.699793\pi\)
\(600\) −2.53767 −0.103600
\(601\) 16.6934 0.680938 0.340469 0.940256i \(-0.389414\pi\)
0.340469 + 0.940256i \(0.389414\pi\)
\(602\) 18.0635 0.736215
\(603\) −1.32430 −0.0539298
\(604\) 5.26533 0.214243
\(605\) 10.6973 0.434907
\(606\) 4.04712 0.164403
\(607\) −21.9168 −0.889574 −0.444787 0.895636i \(-0.646721\pi\)
−0.444787 + 0.895636i \(0.646721\pi\)
\(608\) 18.5842 0.753690
\(609\) 1.93600 0.0784505
\(610\) −21.2046 −0.858548
\(611\) 28.8435 1.16688
\(612\) −28.5200 −1.15285
\(613\) −33.5060 −1.35329 −0.676647 0.736308i \(-0.736567\pi\)
−0.676647 + 0.736308i \(0.736567\pi\)
\(614\) −55.6202 −2.24465
\(615\) 2.98737 0.120462
\(616\) −2.26531 −0.0912720
\(617\) 16.8600 0.678760 0.339380 0.940649i \(-0.389783\pi\)
0.339380 + 0.940649i \(0.389783\pi\)
\(618\) −1.63896 −0.0659286
\(619\) −28.4173 −1.14219 −0.571094 0.820885i \(-0.693481\pi\)
−0.571094 + 0.820885i \(0.693481\pi\)
\(620\) −6.30452 −0.253195
\(621\) 20.4798 0.821824
\(622\) 13.3737 0.536237
\(623\) −11.0915 −0.444373
\(624\) −4.63462 −0.185533
\(625\) 1.00000 0.0400000
\(626\) −67.6561 −2.70408
\(627\) 2.54070 0.101466
\(628\) 36.1311 1.44179
\(629\) −2.63252 −0.104965
\(630\) −6.26717 −0.249690
\(631\) 21.9706 0.874636 0.437318 0.899307i \(-0.355928\pi\)
0.437318 + 0.899307i \(0.355928\pi\)
\(632\) −0.277615 −0.0110429
\(633\) −4.65849 −0.185158
\(634\) −46.6106 −1.85114
\(635\) 8.42042 0.334154
\(636\) 2.19389 0.0869934
\(637\) 3.12576 0.123847
\(638\) 4.13377 0.163658
\(639\) −20.5548 −0.813134
\(640\) 20.7389 0.819778
\(641\) 40.9895 1.61899 0.809493 0.587129i \(-0.199742\pi\)
0.809493 + 0.587129i \(0.199742\pi\)
\(642\) −22.5188 −0.888748
\(643\) −26.8360 −1.05831 −0.529155 0.848525i \(-0.677491\pi\)
−0.529155 + 0.848525i \(0.677491\pi\)
\(644\) −22.0018 −0.866993
\(645\) −4.65450 −0.183271
\(646\) −52.4202 −2.06244
\(647\) 25.9958 1.02200 0.510999 0.859581i \(-0.329275\pi\)
0.510999 + 0.859581i \(0.329275\pi\)
\(648\) 23.5735 0.926056
\(649\) 5.89834 0.231530
\(650\) 7.47660 0.293256
\(651\) 1.04417 0.0409243
\(652\) −79.2764 −3.10470
\(653\) 3.24324 0.126918 0.0634590 0.997984i \(-0.479787\pi\)
0.0634590 + 0.997984i \(0.479787\pi\)
\(654\) −15.1382 −0.591949
\(655\) 0.747926 0.0292239
\(656\) 11.6603 0.455258
\(657\) −20.2866 −0.791457
\(658\) −22.0720 −0.860455
\(659\) −7.65698 −0.298273 −0.149137 0.988817i \(-0.547649\pi\)
−0.149137 + 0.988817i \(0.547649\pi\)
\(660\) 1.26192 0.0491201
\(661\) 15.9221 0.619296 0.309648 0.950851i \(-0.399789\pi\)
0.309648 + 0.950851i \(0.399789\pi\)
\(662\) −73.8350 −2.86968
\(663\) −5.63512 −0.218850
\(664\) −41.8697 −1.62486
\(665\) −7.49240 −0.290543
\(666\) 5.64046 0.218563
\(667\) 18.5714 0.719087
\(668\) 85.9056 3.32379
\(669\) −1.19803 −0.0463187
\(670\) −1.20897 −0.0467064
\(671\) 4.87746 0.188292
\(672\) −1.52877 −0.0589736
\(673\) −32.5199 −1.25355 −0.626774 0.779201i \(-0.715625\pi\)
−0.626774 + 0.779201i \(0.715625\pi\)
\(674\) −45.4373 −1.75018
\(675\) 3.46390 0.133326
\(676\) −12.0186 −0.462255
\(677\) 3.77986 0.145272 0.0726359 0.997359i \(-0.476859\pi\)
0.0726359 + 0.997359i \(0.476859\pi\)
\(678\) −21.0724 −0.809280
\(679\) 0.0409927 0.00157316
\(680\) −12.0433 −0.461838
\(681\) −14.7825 −0.566466
\(682\) 2.22953 0.0853732
\(683\) −24.8965 −0.952639 −0.476319 0.879272i \(-0.658029\pi\)
−0.476319 + 0.879272i \(0.658029\pi\)
\(684\) 73.0538 2.79328
\(685\) 22.5558 0.861813
\(686\) −2.39193 −0.0913244
\(687\) −0.616339 −0.0235148
\(688\) −18.1674 −0.692627
\(689\) −2.98986 −0.113905
\(690\) 8.71621 0.331820
\(691\) 23.9413 0.910768 0.455384 0.890295i \(-0.349502\pi\)
0.455384 + 0.890295i \(0.349502\pi\)
\(692\) −9.85952 −0.374803
\(693\) 1.44157 0.0547606
\(694\) 26.0194 0.987682
\(695\) 12.9126 0.489804
\(696\) −7.97113 −0.302145
\(697\) 14.1774 0.537009
\(698\) −46.3907 −1.75591
\(699\) −2.41043 −0.0911708
\(700\) −3.72134 −0.140653
\(701\) −3.94347 −0.148943 −0.0744715 0.997223i \(-0.523727\pi\)
−0.0744715 + 0.997223i \(0.523727\pi\)
\(702\) 25.8982 0.977464
\(703\) 6.74318 0.254324
\(704\) −5.91143 −0.222795
\(705\) 5.68737 0.214199
\(706\) 57.1501 2.15087
\(707\) 2.74522 0.103245
\(708\) −24.5887 −0.924100
\(709\) −47.3665 −1.77889 −0.889443 0.457046i \(-0.848907\pi\)
−0.889443 + 0.457046i \(0.848907\pi\)
\(710\) −18.7646 −0.704223
\(711\) 0.176664 0.00662543
\(712\) 45.6675 1.71146
\(713\) 10.0164 0.375117
\(714\) 4.31218 0.161379
\(715\) −1.71976 −0.0643153
\(716\) −47.0601 −1.75872
\(717\) −11.5508 −0.431374
\(718\) −16.6713 −0.622167
\(719\) −19.5578 −0.729384 −0.364692 0.931128i \(-0.618826\pi\)
−0.364692 + 0.931128i \(0.618826\pi\)
\(720\) 6.30321 0.234907
\(721\) −1.11173 −0.0414030
\(722\) 88.8271 3.30580
\(723\) −9.55189 −0.355239
\(724\) 91.2242 3.39032
\(725\) 3.14112 0.116658
\(726\) 15.7704 0.585294
\(727\) −27.7183 −1.02802 −0.514008 0.857785i \(-0.671840\pi\)
−0.514008 + 0.857785i \(0.671840\pi\)
\(728\) −12.8698 −0.476985
\(729\) −8.59657 −0.318392
\(730\) −18.5198 −0.685449
\(731\) −22.0893 −0.817003
\(732\) −20.3329 −0.751526
\(733\) 1.21768 0.0449759 0.0224879 0.999747i \(-0.492841\pi\)
0.0224879 + 0.999747i \(0.492841\pi\)
\(734\) −84.2453 −3.10955
\(735\) 0.616339 0.0227340
\(736\) −14.6650 −0.540560
\(737\) 0.278085 0.0102434
\(738\) −30.3767 −1.11818
\(739\) −16.8351 −0.619289 −0.309645 0.950852i \(-0.600210\pi\)
−0.309645 + 0.950852i \(0.600210\pi\)
\(740\) 3.34921 0.123120
\(741\) 14.4343 0.530257
\(742\) 2.28794 0.0839929
\(743\) −17.5584 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(744\) −4.29920 −0.157616
\(745\) −9.22538 −0.337992
\(746\) 6.53862 0.239396
\(747\) 26.6444 0.974869
\(748\) 5.98881 0.218972
\(749\) −15.2749 −0.558132
\(750\) 1.47424 0.0538317
\(751\) −1.79226 −0.0654005 −0.0327002 0.999465i \(-0.510411\pi\)
−0.0327002 + 0.999465i \(0.510411\pi\)
\(752\) 22.1989 0.809512
\(753\) −2.35699 −0.0858937
\(754\) 23.4849 0.855270
\(755\) −1.41490 −0.0514935
\(756\) −12.8904 −0.468818
\(757\) −10.0318 −0.364614 −0.182307 0.983242i \(-0.558356\pi\)
−0.182307 + 0.983242i \(0.558356\pi\)
\(758\) −26.1894 −0.951243
\(759\) −2.00489 −0.0727730
\(760\) 30.8487 1.11900
\(761\) −22.4129 −0.812467 −0.406233 0.913769i \(-0.633158\pi\)
−0.406233 + 0.913769i \(0.633158\pi\)
\(762\) 12.4137 0.449702
\(763\) −10.2684 −0.371743
\(764\) 42.4881 1.53716
\(765\) 7.66391 0.277089
\(766\) 48.8987 1.76678
\(767\) 33.5098 1.20997
\(768\) 17.3299 0.625338
\(769\) −52.1271 −1.87975 −0.939876 0.341516i \(-0.889060\pi\)
−0.939876 + 0.341516i \(0.889060\pi\)
\(770\) 1.31602 0.0474260
\(771\) 5.62398 0.202543
\(772\) 83.9133 3.02011
\(773\) −15.2613 −0.548910 −0.274455 0.961600i \(-0.588497\pi\)
−0.274455 + 0.961600i \(0.588497\pi\)
\(774\) 47.3287 1.70120
\(775\) 1.69415 0.0608557
\(776\) −0.168780 −0.00605886
\(777\) −0.554706 −0.0199000
\(778\) 7.48493 0.268348
\(779\) −36.3154 −1.30113
\(780\) 7.16925 0.256700
\(781\) 4.31621 0.154446
\(782\) 41.3653 1.47922
\(783\) 10.8805 0.388839
\(784\) 2.40569 0.0859175
\(785\) −9.70918 −0.346535
\(786\) 1.10262 0.0393293
\(787\) −46.0429 −1.64125 −0.820626 0.571466i \(-0.806375\pi\)
−0.820626 + 0.571466i \(0.806375\pi\)
\(788\) −8.34898 −0.297420
\(789\) 5.85036 0.208278
\(790\) 0.161278 0.00573802
\(791\) −14.2937 −0.508226
\(792\) −5.93540 −0.210905
\(793\) 27.7100 0.984010
\(794\) 60.7366 2.15546
\(795\) −0.589543 −0.0209089
\(796\) 45.6422 1.61774
\(797\) 25.6399 0.908212 0.454106 0.890948i \(-0.349959\pi\)
0.454106 + 0.890948i \(0.349959\pi\)
\(798\) −11.0456 −0.391010
\(799\) 26.9911 0.954877
\(800\) −2.48041 −0.0876957
\(801\) −29.0612 −1.02683
\(802\) −51.4746 −1.81763
\(803\) 4.25991 0.150329
\(804\) −1.15927 −0.0408842
\(805\) 5.91234 0.208383
\(806\) 12.6665 0.446158
\(807\) −2.26795 −0.0798357
\(808\) −11.3030 −0.397637
\(809\) 24.0710 0.846290 0.423145 0.906062i \(-0.360926\pi\)
0.423145 + 0.906062i \(0.360926\pi\)
\(810\) −13.6949 −0.481189
\(811\) 24.2997 0.853279 0.426639 0.904422i \(-0.359697\pi\)
0.426639 + 0.904422i \(0.359697\pi\)
\(812\) −11.6892 −0.410210
\(813\) 2.36463 0.0829313
\(814\) −1.18442 −0.0415138
\(815\) 21.3032 0.746218
\(816\) −4.33698 −0.151825
\(817\) 56.5816 1.97954
\(818\) −4.84476 −0.169393
\(819\) 8.18988 0.286177
\(820\) −18.0372 −0.629886
\(821\) −34.0864 −1.18962 −0.594812 0.803865i \(-0.702773\pi\)
−0.594812 + 0.803865i \(0.702773\pi\)
\(822\) 33.2527 1.15982
\(823\) 23.5838 0.822080 0.411040 0.911617i \(-0.365166\pi\)
0.411040 + 0.911617i \(0.365166\pi\)
\(824\) 4.57736 0.159460
\(825\) −0.339103 −0.0118061
\(826\) −25.6428 −0.892228
\(827\) −37.8637 −1.31665 −0.658324 0.752735i \(-0.728734\pi\)
−0.658324 + 0.752735i \(0.728734\pi\)
\(828\) −57.6476 −2.00339
\(829\) 7.22183 0.250825 0.125412 0.992105i \(-0.459975\pi\)
0.125412 + 0.992105i \(0.459975\pi\)
\(830\) 24.3239 0.844295
\(831\) 4.11768 0.142841
\(832\) −33.5842 −1.16432
\(833\) 2.92502 0.101346
\(834\) 19.0363 0.659174
\(835\) −23.0846 −0.798875
\(836\) −15.3403 −0.530554
\(837\) 5.86838 0.202841
\(838\) −80.7022 −2.78781
\(839\) 1.18128 0.0407822 0.0203911 0.999792i \(-0.493509\pi\)
0.0203911 + 0.999792i \(0.493509\pi\)
\(840\) −2.53767 −0.0875579
\(841\) −19.1333 −0.659770
\(842\) −83.4927 −2.87735
\(843\) −6.48230 −0.223262
\(844\) 28.1271 0.968174
\(845\) 3.22965 0.111103
\(846\) −57.8314 −1.98828
\(847\) 10.6973 0.367563
\(848\) −2.30110 −0.0790201
\(849\) 9.60019 0.329478
\(850\) 6.99644 0.239976
\(851\) −5.32112 −0.182406
\(852\) −17.9932 −0.616438
\(853\) 23.9614 0.820424 0.410212 0.911990i \(-0.365455\pi\)
0.410212 + 0.911990i \(0.365455\pi\)
\(854\) −21.2046 −0.725606
\(855\) −19.6310 −0.671368
\(856\) 62.8917 2.14959
\(857\) 44.5191 1.52074 0.760372 0.649488i \(-0.225017\pi\)
0.760372 + 0.649488i \(0.225017\pi\)
\(858\) −2.53534 −0.0865550
\(859\) 21.3146 0.727244 0.363622 0.931547i \(-0.381540\pi\)
0.363622 + 0.931547i \(0.381540\pi\)
\(860\) 28.1030 0.958305
\(861\) 2.98737 0.101809
\(862\) 44.7431 1.52395
\(863\) 49.0682 1.67030 0.835150 0.550023i \(-0.185381\pi\)
0.835150 + 0.550023i \(0.185381\pi\)
\(864\) −8.59189 −0.292302
\(865\) 2.64945 0.0900842
\(866\) 7.62110 0.258975
\(867\) 5.20454 0.176755
\(868\) −6.30452 −0.213989
\(869\) −0.0370971 −0.00125843
\(870\) 4.63077 0.156998
\(871\) 1.57987 0.0535317
\(872\) 42.2785 1.43173
\(873\) 0.107406 0.00363514
\(874\) −105.957 −3.58405
\(875\) 1.00000 0.0338062
\(876\) −17.7585 −0.600005
\(877\) 36.6965 1.23915 0.619577 0.784936i \(-0.287304\pi\)
0.619577 + 0.784936i \(0.287304\pi\)
\(878\) 65.2498 2.20208
\(879\) −6.33817 −0.213781
\(880\) −1.32359 −0.0446181
\(881\) 20.1719 0.679609 0.339804 0.940496i \(-0.389639\pi\)
0.339804 + 0.940496i \(0.389639\pi\)
\(882\) −6.26717 −0.211026
\(883\) 36.3932 1.22473 0.612364 0.790576i \(-0.290219\pi\)
0.612364 + 0.790576i \(0.290219\pi\)
\(884\) 34.0238 1.14434
\(885\) 6.60749 0.222108
\(886\) −83.3535 −2.80032
\(887\) 13.4073 0.450173 0.225087 0.974339i \(-0.427734\pi\)
0.225087 + 0.974339i \(0.427734\pi\)
\(888\) 2.28391 0.0766429
\(889\) 8.42042 0.282412
\(890\) −26.5302 −0.889294
\(891\) 3.15008 0.105532
\(892\) 7.23351 0.242196
\(893\) −69.1375 −2.31360
\(894\) −13.6004 −0.454867
\(895\) 12.6460 0.422709
\(896\) 20.7389 0.692839
\(897\) −11.3903 −0.380310
\(898\) −41.2201 −1.37553
\(899\) 5.32154 0.177483
\(900\) −9.75038 −0.325013
\(901\) −2.79785 −0.0932098
\(902\) 6.37868 0.212387
\(903\) −4.65450 −0.154892
\(904\) 58.8519 1.95739
\(905\) −24.5138 −0.814867
\(906\) −2.08591 −0.0692996
\(907\) 3.03808 0.100878 0.0504389 0.998727i \(-0.483938\pi\)
0.0504389 + 0.998727i \(0.483938\pi\)
\(908\) 89.2539 2.96199
\(909\) 7.19283 0.238571
\(910\) 7.47660 0.247847
\(911\) −38.0329 −1.26008 −0.630042 0.776561i \(-0.716963\pi\)
−0.630042 + 0.776561i \(0.716963\pi\)
\(912\) 11.1091 0.367860
\(913\) −5.59496 −0.185166
\(914\) 42.5629 1.40786
\(915\) 5.46387 0.180630
\(916\) 3.72134 0.122957
\(917\) 0.747926 0.0246987
\(918\) 24.2350 0.799874
\(919\) 6.74653 0.222547 0.111274 0.993790i \(-0.464507\pi\)
0.111274 + 0.993790i \(0.464507\pi\)
\(920\) −24.3430 −0.802566
\(921\) 14.3319 0.472251
\(922\) −18.5030 −0.609364
\(923\) 24.5214 0.807132
\(924\) 1.26192 0.0415141
\(925\) −0.900002 −0.0295919
\(926\) 64.4547 2.11811
\(927\) −2.91288 −0.0956714
\(928\) −7.79127 −0.255761
\(929\) −13.6534 −0.447952 −0.223976 0.974595i \(-0.571904\pi\)
−0.223976 + 0.974595i \(0.571904\pi\)
\(930\) 2.49759 0.0818991
\(931\) −7.49240 −0.245554
\(932\) 14.5537 0.476723
\(933\) −3.44606 −0.112819
\(934\) 65.7977 2.15297
\(935\) −1.60931 −0.0526302
\(936\) −33.7204 −1.10219
\(937\) 15.0556 0.491844 0.245922 0.969290i \(-0.420909\pi\)
0.245922 + 0.969290i \(0.420909\pi\)
\(938\) −1.20897 −0.0394741
\(939\) 17.4332 0.568912
\(940\) −34.3393 −1.12003
\(941\) −15.7266 −0.512673 −0.256336 0.966588i \(-0.582515\pi\)
−0.256336 + 0.966588i \(0.582515\pi\)
\(942\) −14.3137 −0.466364
\(943\) 28.6569 0.933196
\(944\) 25.7903 0.839403
\(945\) 3.46390 0.112681
\(946\) −9.93837 −0.323124
\(947\) −2.48662 −0.0808043 −0.0404021 0.999184i \(-0.512864\pi\)
−0.0404021 + 0.999184i \(0.512864\pi\)
\(948\) 0.154648 0.00502275
\(949\) 24.2015 0.785615
\(950\) −17.9213 −0.581444
\(951\) 12.0103 0.389462
\(952\) −12.0433 −0.390324
\(953\) −5.51985 −0.178806 −0.0894028 0.995996i \(-0.528496\pi\)
−0.0894028 + 0.995996i \(0.528496\pi\)
\(954\) 5.99469 0.194085
\(955\) −11.4174 −0.369459
\(956\) 69.7418 2.25561
\(957\) −1.06517 −0.0344319
\(958\) 58.9782 1.90550
\(959\) 22.5558 0.728365
\(960\) −6.62216 −0.213729
\(961\) −28.1298 −0.907414
\(962\) −6.72895 −0.216950
\(963\) −40.0221 −1.28969
\(964\) 57.6725 1.85751
\(965\) −22.5492 −0.725885
\(966\) 8.71621 0.280439
\(967\) 40.2357 1.29389 0.646946 0.762535i \(-0.276046\pi\)
0.646946 + 0.762535i \(0.276046\pi\)
\(968\) −44.0443 −1.41564
\(969\) 13.5073 0.433917
\(970\) 0.0980518 0.00314825
\(971\) −19.9989 −0.641796 −0.320898 0.947114i \(-0.603985\pi\)
−0.320898 + 0.947114i \(0.603985\pi\)
\(972\) −51.8030 −1.66158
\(973\) 12.9126 0.413960
\(974\) −24.7903 −0.794333
\(975\) −1.92652 −0.0616982
\(976\) 21.3265 0.682646
\(977\) −38.7449 −1.23956 −0.619780 0.784776i \(-0.712778\pi\)
−0.619780 + 0.784776i \(0.712778\pi\)
\(978\) 31.4060 1.00425
\(979\) 6.10245 0.195035
\(980\) −3.72134 −0.118874
\(981\) −26.9046 −0.858998
\(982\) 39.9072 1.27349
\(983\) −24.9431 −0.795562 −0.397781 0.917480i \(-0.630220\pi\)
−0.397781 + 0.917480i \(0.630220\pi\)
\(984\) −12.3000 −0.392109
\(985\) 2.24354 0.0714852
\(986\) 21.9767 0.699880
\(987\) 5.68737 0.181031
\(988\) −87.1516 −2.77266
\(989\) −44.6491 −1.41976
\(990\) 3.44813 0.109589
\(991\) 40.9624 1.30121 0.650607 0.759414i \(-0.274514\pi\)
0.650607 + 0.759414i \(0.274514\pi\)
\(992\) −4.20219 −0.133420
\(993\) 19.0254 0.603752
\(994\) −18.7646 −0.595177
\(995\) −12.2650 −0.388826
\(996\) 23.3240 0.739049
\(997\) 40.7070 1.28920 0.644602 0.764518i \(-0.277023\pi\)
0.644602 + 0.764518i \(0.277023\pi\)
\(998\) −50.0851 −1.58542
\(999\) −3.11752 −0.0986339
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 \(a_p\))