Properties

Label 8015.2.a.l.1.26
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 1.26
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.573704 q^{2} +0.0256257 q^{3} -1.67086 q^{4} -1.00000 q^{5} -0.0147015 q^{6} -1.00000 q^{7} +2.10599 q^{8} -2.99934 q^{9} +O(q^{10})\) \(q-0.573704 q^{2} +0.0256257 q^{3} -1.67086 q^{4} -1.00000 q^{5} -0.0147015 q^{6} -1.00000 q^{7} +2.10599 q^{8} -2.99934 q^{9} +0.573704 q^{10} -2.70525 q^{11} -0.0428170 q^{12} +5.99183 q^{13} +0.573704 q^{14} -0.0256257 q^{15} +2.13351 q^{16} +8.13576 q^{17} +1.72074 q^{18} +1.85406 q^{19} +1.67086 q^{20} -0.0256257 q^{21} +1.55201 q^{22} -4.26254 q^{23} +0.0539674 q^{24} +1.00000 q^{25} -3.43754 q^{26} -0.153737 q^{27} +1.67086 q^{28} +0.728131 q^{29} +0.0147015 q^{30} +1.70095 q^{31} -5.43598 q^{32} -0.0693239 q^{33} -4.66752 q^{34} +1.00000 q^{35} +5.01149 q^{36} +3.17740 q^{37} -1.06368 q^{38} +0.153545 q^{39} -2.10599 q^{40} +5.60644 q^{41} +0.0147015 q^{42} -1.83170 q^{43} +4.52011 q^{44} +2.99934 q^{45} +2.44544 q^{46} -5.42993 q^{47} +0.0546727 q^{48} +1.00000 q^{49} -0.573704 q^{50} +0.208484 q^{51} -10.0115 q^{52} +0.229266 q^{53} +0.0881996 q^{54} +2.70525 q^{55} -2.10599 q^{56} +0.0475114 q^{57} -0.417731 q^{58} +0.971481 q^{59} +0.0428170 q^{60} -14.1581 q^{61} -0.975843 q^{62} +2.99934 q^{63} -1.14838 q^{64} -5.99183 q^{65} +0.0397714 q^{66} -8.03509 q^{67} -13.5937 q^{68} -0.109230 q^{69} -0.573704 q^{70} -8.27354 q^{71} -6.31659 q^{72} -3.33270 q^{73} -1.82289 q^{74} +0.0256257 q^{75} -3.09788 q^{76} +2.70525 q^{77} -0.0880892 q^{78} +10.5865 q^{79} -2.13351 q^{80} +8.99409 q^{81} -3.21644 q^{82} -10.5022 q^{83} +0.0428170 q^{84} -8.13576 q^{85} +1.05086 q^{86} +0.0186588 q^{87} -5.69723 q^{88} +7.41590 q^{89} -1.72074 q^{90} -5.99183 q^{91} +7.12212 q^{92} +0.0435880 q^{93} +3.11517 q^{94} -1.85406 q^{95} -0.139301 q^{96} +12.5611 q^{97} -0.573704 q^{98} +8.11398 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.573704 −0.405670 −0.202835 0.979213i \(-0.565016\pi\)
−0.202835 + 0.979213i \(0.565016\pi\)
\(3\) 0.0256257 0.0147950 0.00739749 0.999973i \(-0.497645\pi\)
0.00739749 + 0.999973i \(0.497645\pi\)
\(4\) −1.67086 −0.835432
\(5\) −1.00000 −0.447214
\(6\) −0.0147015 −0.00600188
\(7\) −1.00000 −0.377964
\(8\) 2.10599 0.744580
\(9\) −2.99934 −0.999781
\(10\) 0.573704 0.181421
\(11\) −2.70525 −0.815664 −0.407832 0.913057i \(-0.633715\pi\)
−0.407832 + 0.913057i \(0.633715\pi\)
\(12\) −0.0428170 −0.0123602
\(13\) 5.99183 1.66184 0.830918 0.556395i \(-0.187816\pi\)
0.830918 + 0.556395i \(0.187816\pi\)
\(14\) 0.573704 0.153329
\(15\) −0.0256257 −0.00661652
\(16\) 2.13351 0.533378
\(17\) 8.13576 1.97321 0.986605 0.163125i \(-0.0521574\pi\)
0.986605 + 0.163125i \(0.0521574\pi\)
\(18\) 1.72074 0.405581
\(19\) 1.85406 0.425350 0.212675 0.977123i \(-0.431782\pi\)
0.212675 + 0.977123i \(0.431782\pi\)
\(20\) 1.67086 0.373616
\(21\) −0.0256257 −0.00559198
\(22\) 1.55201 0.330891
\(23\) −4.26254 −0.888801 −0.444401 0.895828i \(-0.646583\pi\)
−0.444401 + 0.895828i \(0.646583\pi\)
\(24\) 0.0539674 0.0110160
\(25\) 1.00000 0.200000
\(26\) −3.43754 −0.674157
\(27\) −0.153737 −0.0295867
\(28\) 1.67086 0.315764
\(29\) 0.728131 0.135210 0.0676052 0.997712i \(-0.478464\pi\)
0.0676052 + 0.997712i \(0.478464\pi\)
\(30\) 0.0147015 0.00268412
\(31\) 1.70095 0.305500 0.152750 0.988265i \(-0.451187\pi\)
0.152750 + 0.988265i \(0.451187\pi\)
\(32\) −5.43598 −0.960955
\(33\) −0.0693239 −0.0120677
\(34\) −4.66752 −0.800473
\(35\) 1.00000 0.169031
\(36\) 5.01149 0.835249
\(37\) 3.17740 0.522362 0.261181 0.965290i \(-0.415888\pi\)
0.261181 + 0.965290i \(0.415888\pi\)
\(38\) −1.06368 −0.172552
\(39\) 0.153545 0.0245868
\(40\) −2.10599 −0.332986
\(41\) 5.60644 0.875579 0.437789 0.899078i \(-0.355762\pi\)
0.437789 + 0.899078i \(0.355762\pi\)
\(42\) 0.0147015 0.00226850
\(43\) −1.83170 −0.279332 −0.139666 0.990199i \(-0.544603\pi\)
−0.139666 + 0.990199i \(0.544603\pi\)
\(44\) 4.52011 0.681432
\(45\) 2.99934 0.447116
\(46\) 2.44544 0.360560
\(47\) −5.42993 −0.792036 −0.396018 0.918243i \(-0.629608\pi\)
−0.396018 + 0.918243i \(0.629608\pi\)
\(48\) 0.0546727 0.00789132
\(49\) 1.00000 0.142857
\(50\) −0.573704 −0.0811340
\(51\) 0.208484 0.0291936
\(52\) −10.0115 −1.38835
\(53\) 0.229266 0.0314921 0.0157461 0.999876i \(-0.494988\pi\)
0.0157461 + 0.999876i \(0.494988\pi\)
\(54\) 0.0881996 0.0120024
\(55\) 2.70525 0.364776
\(56\) −2.10599 −0.281425
\(57\) 0.0475114 0.00629304
\(58\) −0.417731 −0.0548508
\(59\) 0.971481 0.126476 0.0632380 0.997998i \(-0.479857\pi\)
0.0632380 + 0.997998i \(0.479857\pi\)
\(60\) 0.0428170 0.00552765
\(61\) −14.1581 −1.81276 −0.906380 0.422463i \(-0.861165\pi\)
−0.906380 + 0.422463i \(0.861165\pi\)
\(62\) −0.975843 −0.123932
\(63\) 2.99934 0.377882
\(64\) −1.14838 −0.143547
\(65\) −5.99183 −0.743196
\(66\) 0.0397714 0.00489552
\(67\) −8.03509 −0.981642 −0.490821 0.871260i \(-0.663303\pi\)
−0.490821 + 0.871260i \(0.663303\pi\)
\(68\) −13.5937 −1.64848
\(69\) −0.109230 −0.0131498
\(70\) −0.573704 −0.0685708
\(71\) −8.27354 −0.981889 −0.490944 0.871191i \(-0.663348\pi\)
−0.490944 + 0.871191i \(0.663348\pi\)
\(72\) −6.31659 −0.744417
\(73\) −3.33270 −0.390063 −0.195032 0.980797i \(-0.562481\pi\)
−0.195032 + 0.980797i \(0.562481\pi\)
\(74\) −1.82289 −0.211907
\(75\) 0.0256257 0.00295900
\(76\) −3.09788 −0.355351
\(77\) 2.70525 0.308292
\(78\) −0.0880892 −0.00997414
\(79\) 10.5865 1.19108 0.595540 0.803326i \(-0.296938\pi\)
0.595540 + 0.803326i \(0.296938\pi\)
\(80\) −2.13351 −0.238534
\(81\) 8.99409 0.999343
\(82\) −3.21644 −0.355196
\(83\) −10.5022 −1.15276 −0.576381 0.817181i \(-0.695536\pi\)
−0.576381 + 0.817181i \(0.695536\pi\)
\(84\) 0.0428170 0.00467172
\(85\) −8.13576 −0.882447
\(86\) 1.05086 0.113317
\(87\) 0.0186588 0.00200044
\(88\) −5.69723 −0.607327
\(89\) 7.41590 0.786084 0.393042 0.919521i \(-0.371423\pi\)
0.393042 + 0.919521i \(0.371423\pi\)
\(90\) −1.72074 −0.181381
\(91\) −5.99183 −0.628115
\(92\) 7.12212 0.742533
\(93\) 0.0435880 0.00451987
\(94\) 3.11517 0.321305
\(95\) −1.85406 −0.190222
\(96\) −0.139301 −0.0142173
\(97\) 12.5611 1.27538 0.637691 0.770292i \(-0.279890\pi\)
0.637691 + 0.770292i \(0.279890\pi\)
\(98\) −0.573704 −0.0579529
\(99\) 8.11398 0.815486
\(100\) −1.67086 −0.167086
\(101\) −11.9030 −1.18440 −0.592198 0.805792i \(-0.701740\pi\)
−0.592198 + 0.805792i \(0.701740\pi\)
\(102\) −0.119608 −0.0118430
\(103\) −3.14238 −0.309628 −0.154814 0.987944i \(-0.549478\pi\)
−0.154814 + 0.987944i \(0.549478\pi\)
\(104\) 12.6187 1.23737
\(105\) 0.0256257 0.00250081
\(106\) −0.131531 −0.0127754
\(107\) −7.69595 −0.743996 −0.371998 0.928234i \(-0.621327\pi\)
−0.371998 + 0.928234i \(0.621327\pi\)
\(108\) 0.256874 0.0247177
\(109\) 19.0746 1.82702 0.913510 0.406817i \(-0.133361\pi\)
0.913510 + 0.406817i \(0.133361\pi\)
\(110\) −1.55201 −0.147979
\(111\) 0.0814231 0.00772834
\(112\) −2.13351 −0.201598
\(113\) 12.1057 1.13881 0.569404 0.822058i \(-0.307174\pi\)
0.569404 + 0.822058i \(0.307174\pi\)
\(114\) −0.0272575 −0.00255290
\(115\) 4.26254 0.397484
\(116\) −1.21661 −0.112959
\(117\) −17.9716 −1.66147
\(118\) −0.557343 −0.0513076
\(119\) −8.13576 −0.745804
\(120\) −0.0539674 −0.00492652
\(121\) −3.68161 −0.334692
\(122\) 8.12256 0.735382
\(123\) 0.143669 0.0129542
\(124\) −2.84206 −0.255224
\(125\) −1.00000 −0.0894427
\(126\) −1.72074 −0.153295
\(127\) −6.70647 −0.595103 −0.297551 0.954706i \(-0.596170\pi\)
−0.297551 + 0.954706i \(0.596170\pi\)
\(128\) 11.5308 1.01919
\(129\) −0.0469386 −0.00413272
\(130\) 3.43754 0.301492
\(131\) −9.95341 −0.869634 −0.434817 0.900519i \(-0.643187\pi\)
−0.434817 + 0.900519i \(0.643187\pi\)
\(132\) 0.115831 0.0100818
\(133\) −1.85406 −0.160767
\(134\) 4.60976 0.398223
\(135\) 0.153737 0.0132316
\(136\) 17.1338 1.46921
\(137\) 1.72109 0.147043 0.0735213 0.997294i \(-0.476576\pi\)
0.0735213 + 0.997294i \(0.476576\pi\)
\(138\) 0.0626659 0.00533448
\(139\) 1.72410 0.146237 0.0731183 0.997323i \(-0.476705\pi\)
0.0731183 + 0.997323i \(0.476705\pi\)
\(140\) −1.67086 −0.141214
\(141\) −0.139145 −0.0117182
\(142\) 4.74656 0.398323
\(143\) −16.2094 −1.35550
\(144\) −6.39914 −0.533261
\(145\) −0.728131 −0.0604679
\(146\) 1.91199 0.158237
\(147\) 0.0256257 0.00211357
\(148\) −5.30901 −0.436398
\(149\) 3.95468 0.323980 0.161990 0.986792i \(-0.448209\pi\)
0.161990 + 0.986792i \(0.448209\pi\)
\(150\) −0.0147015 −0.00120038
\(151\) 5.03130 0.409441 0.204721 0.978820i \(-0.434371\pi\)
0.204721 + 0.978820i \(0.434371\pi\)
\(152\) 3.90462 0.316707
\(153\) −24.4019 −1.97278
\(154\) −1.55201 −0.125065
\(155\) −1.70095 −0.136624
\(156\) −0.256552 −0.0205406
\(157\) −18.4639 −1.47358 −0.736792 0.676120i \(-0.763660\pi\)
−0.736792 + 0.676120i \(0.763660\pi\)
\(158\) −6.07354 −0.483185
\(159\) 0.00587510 0.000465926 0
\(160\) 5.43598 0.429752
\(161\) 4.26254 0.335935
\(162\) −5.15995 −0.405404
\(163\) −2.56209 −0.200679 −0.100339 0.994953i \(-0.531993\pi\)
−0.100339 + 0.994953i \(0.531993\pi\)
\(164\) −9.36760 −0.731486
\(165\) 0.0693239 0.00539686
\(166\) 6.02513 0.467641
\(167\) 3.82143 0.295711 0.147856 0.989009i \(-0.452763\pi\)
0.147856 + 0.989009i \(0.452763\pi\)
\(168\) −0.0539674 −0.00416367
\(169\) 22.9021 1.76170
\(170\) 4.66752 0.357982
\(171\) −5.56095 −0.425257
\(172\) 3.06053 0.233363
\(173\) 4.36667 0.331992 0.165996 0.986126i \(-0.446916\pi\)
0.165996 + 0.986126i \(0.446916\pi\)
\(174\) −0.0107046 −0.000811517 0
\(175\) −1.00000 −0.0755929
\(176\) −5.77169 −0.435057
\(177\) 0.0248948 0.00187121
\(178\) −4.25453 −0.318891
\(179\) −4.49515 −0.335983 −0.167992 0.985788i \(-0.553728\pi\)
−0.167992 + 0.985788i \(0.553728\pi\)
\(180\) −5.01149 −0.373535
\(181\) 8.85136 0.657916 0.328958 0.944345i \(-0.393303\pi\)
0.328958 + 0.944345i \(0.393303\pi\)
\(182\) 3.43754 0.254807
\(183\) −0.362811 −0.0268197
\(184\) −8.97687 −0.661783
\(185\) −3.17740 −0.233607
\(186\) −0.0250066 −0.00183357
\(187\) −22.0093 −1.60948
\(188\) 9.07267 0.661692
\(189\) 0.153737 0.0111827
\(190\) 1.06368 0.0771675
\(191\) 4.36919 0.316143 0.158072 0.987428i \(-0.449472\pi\)
0.158072 + 0.987428i \(0.449472\pi\)
\(192\) −0.0294280 −0.00212378
\(193\) 11.5196 0.829199 0.414599 0.910004i \(-0.363922\pi\)
0.414599 + 0.910004i \(0.363922\pi\)
\(194\) −7.20633 −0.517384
\(195\) −0.153545 −0.0109956
\(196\) −1.67086 −0.119347
\(197\) −7.38632 −0.526254 −0.263127 0.964761i \(-0.584754\pi\)
−0.263127 + 0.964761i \(0.584754\pi\)
\(198\) −4.65502 −0.330818
\(199\) 23.5992 1.67290 0.836450 0.548043i \(-0.184627\pi\)
0.836450 + 0.548043i \(0.184627\pi\)
\(200\) 2.10599 0.148916
\(201\) −0.205904 −0.0145234
\(202\) 6.82882 0.480474
\(203\) −0.728131 −0.0511047
\(204\) −0.348349 −0.0243893
\(205\) −5.60644 −0.391571
\(206\) 1.80280 0.125607
\(207\) 12.7848 0.888607
\(208\) 12.7837 0.886387
\(209\) −5.01569 −0.346943
\(210\) −0.0147015 −0.00101450
\(211\) 17.1834 1.18296 0.591478 0.806321i \(-0.298545\pi\)
0.591478 + 0.806321i \(0.298545\pi\)
\(212\) −0.383073 −0.0263095
\(213\) −0.212015 −0.0145270
\(214\) 4.41520 0.301817
\(215\) 1.83170 0.124921
\(216\) −0.323769 −0.0220297
\(217\) −1.70095 −0.115468
\(218\) −10.9432 −0.741167
\(219\) −0.0854027 −0.00577098
\(220\) −4.52011 −0.304746
\(221\) 48.7481 3.27915
\(222\) −0.0467127 −0.00313515
\(223\) 11.7337 0.785746 0.392873 0.919593i \(-0.371481\pi\)
0.392873 + 0.919593i \(0.371481\pi\)
\(224\) 5.43598 0.363207
\(225\) −2.99934 −0.199956
\(226\) −6.94508 −0.461980
\(227\) −6.33583 −0.420524 −0.210262 0.977645i \(-0.567432\pi\)
−0.210262 + 0.977645i \(0.567432\pi\)
\(228\) −0.0793851 −0.00525741
\(229\) 1.00000 0.0660819
\(230\) −2.44544 −0.161247
\(231\) 0.0693239 0.00456118
\(232\) 1.53344 0.100675
\(233\) 19.4515 1.27431 0.637156 0.770735i \(-0.280111\pi\)
0.637156 + 0.770735i \(0.280111\pi\)
\(234\) 10.3104 0.674009
\(235\) 5.42993 0.354209
\(236\) −1.62321 −0.105662
\(237\) 0.271287 0.0176220
\(238\) 4.66752 0.302550
\(239\) 1.98539 0.128424 0.0642121 0.997936i \(-0.479547\pi\)
0.0642121 + 0.997936i \(0.479547\pi\)
\(240\) −0.0546727 −0.00352910
\(241\) −5.48462 −0.353296 −0.176648 0.984274i \(-0.556525\pi\)
−0.176648 + 0.984274i \(0.556525\pi\)
\(242\) 2.11215 0.135774
\(243\) 0.691691 0.0443720
\(244\) 23.6563 1.51444
\(245\) −1.00000 −0.0638877
\(246\) −0.0824233 −0.00525512
\(247\) 11.1092 0.706862
\(248\) 3.58219 0.227469
\(249\) −0.269125 −0.0170551
\(250\) 0.573704 0.0362842
\(251\) 11.6124 0.732966 0.366483 0.930425i \(-0.380562\pi\)
0.366483 + 0.930425i \(0.380562\pi\)
\(252\) −5.01149 −0.315694
\(253\) 11.5312 0.724963
\(254\) 3.84753 0.241415
\(255\) −0.208484 −0.0130558
\(256\) −4.31851 −0.269907
\(257\) −0.596874 −0.0372320 −0.0186160 0.999827i \(-0.505926\pi\)
−0.0186160 + 0.999827i \(0.505926\pi\)
\(258\) 0.0269289 0.00167652
\(259\) −3.17740 −0.197434
\(260\) 10.0115 0.620889
\(261\) −2.18391 −0.135181
\(262\) 5.71031 0.352784
\(263\) −1.63116 −0.100582 −0.0502908 0.998735i \(-0.516015\pi\)
−0.0502908 + 0.998735i \(0.516015\pi\)
\(264\) −0.145995 −0.00898539
\(265\) −0.229266 −0.0140837
\(266\) 1.06368 0.0652184
\(267\) 0.190037 0.0116301
\(268\) 13.4255 0.820095
\(269\) 9.65849 0.588888 0.294444 0.955669i \(-0.404865\pi\)
0.294444 + 0.955669i \(0.404865\pi\)
\(270\) −0.0881996 −0.00536766
\(271\) −16.5250 −1.00382 −0.501911 0.864919i \(-0.667369\pi\)
−0.501911 + 0.864919i \(0.667369\pi\)
\(272\) 17.3577 1.05247
\(273\) −0.153545 −0.00929295
\(274\) −0.987396 −0.0596508
\(275\) −2.70525 −0.163133
\(276\) 0.182509 0.0109858
\(277\) 9.34690 0.561601 0.280800 0.959766i \(-0.409400\pi\)
0.280800 + 0.959766i \(0.409400\pi\)
\(278\) −0.989126 −0.0593238
\(279\) −5.10174 −0.305433
\(280\) 2.10599 0.125857
\(281\) 23.4510 1.39897 0.699485 0.714647i \(-0.253413\pi\)
0.699485 + 0.714647i \(0.253413\pi\)
\(282\) 0.0798283 0.00475371
\(283\) 13.8581 0.823776 0.411888 0.911234i \(-0.364869\pi\)
0.411888 + 0.911234i \(0.364869\pi\)
\(284\) 13.8240 0.820301
\(285\) −0.0475114 −0.00281433
\(286\) 9.29941 0.549886
\(287\) −5.60644 −0.330938
\(288\) 16.3044 0.960745
\(289\) 49.1905 2.89356
\(290\) 0.417731 0.0245300
\(291\) 0.321885 0.0188693
\(292\) 5.56849 0.325871
\(293\) 9.12122 0.532868 0.266434 0.963853i \(-0.414155\pi\)
0.266434 + 0.963853i \(0.414155\pi\)
\(294\) −0.0147015 −0.000857412 0
\(295\) −0.971481 −0.0565618
\(296\) 6.69158 0.388940
\(297\) 0.415898 0.0241328
\(298\) −2.26882 −0.131429
\(299\) −25.5404 −1.47704
\(300\) −0.0428170 −0.00247204
\(301\) 1.83170 0.105578
\(302\) −2.88648 −0.166098
\(303\) −0.305023 −0.0175231
\(304\) 3.95565 0.226872
\(305\) 14.1581 0.810691
\(306\) 13.9995 0.800297
\(307\) −11.0400 −0.630084 −0.315042 0.949078i \(-0.602019\pi\)
−0.315042 + 0.949078i \(0.602019\pi\)
\(308\) −4.52011 −0.257557
\(309\) −0.0805255 −0.00458094
\(310\) 0.975843 0.0554242
\(311\) −21.8088 −1.23666 −0.618331 0.785918i \(-0.712191\pi\)
−0.618331 + 0.785918i \(0.712191\pi\)
\(312\) 0.323364 0.0183069
\(313\) −3.47749 −0.196559 −0.0982795 0.995159i \(-0.531334\pi\)
−0.0982795 + 0.995159i \(0.531334\pi\)
\(314\) 10.5928 0.597789
\(315\) −2.99934 −0.168994
\(316\) −17.6887 −0.995066
\(317\) −20.6682 −1.16084 −0.580421 0.814317i \(-0.697112\pi\)
−0.580421 + 0.814317i \(0.697112\pi\)
\(318\) −0.00337057 −0.000189012 0
\(319\) −1.96978 −0.110286
\(320\) 1.14838 0.0641963
\(321\) −0.197214 −0.0110074
\(322\) −2.44544 −0.136279
\(323\) 15.0842 0.839305
\(324\) −15.0279 −0.834883
\(325\) 5.99183 0.332367
\(326\) 1.46988 0.0814093
\(327\) 0.488800 0.0270307
\(328\) 11.8071 0.651938
\(329\) 5.42993 0.299362
\(330\) −0.0397714 −0.00218934
\(331\) −5.62875 −0.309384 −0.154692 0.987963i \(-0.549438\pi\)
−0.154692 + 0.987963i \(0.549438\pi\)
\(332\) 17.5477 0.963054
\(333\) −9.53013 −0.522248
\(334\) −2.19237 −0.119961
\(335\) 8.03509 0.439004
\(336\) −0.0546727 −0.00298264
\(337\) 11.9241 0.649547 0.324774 0.945792i \(-0.394712\pi\)
0.324774 + 0.945792i \(0.394712\pi\)
\(338\) −13.1390 −0.714668
\(339\) 0.310216 0.0168486
\(340\) 13.5937 0.737224
\(341\) −4.60151 −0.249185
\(342\) 3.19034 0.172514
\(343\) −1.00000 −0.0539949
\(344\) −3.85755 −0.207985
\(345\) 0.109230 0.00588077
\(346\) −2.50518 −0.134679
\(347\) −13.8236 −0.742091 −0.371046 0.928615i \(-0.621001\pi\)
−0.371046 + 0.928615i \(0.621001\pi\)
\(348\) −0.0311763 −0.00167123
\(349\) 2.55384 0.136704 0.0683520 0.997661i \(-0.478226\pi\)
0.0683520 + 0.997661i \(0.478226\pi\)
\(350\) 0.573704 0.0306658
\(351\) −0.921167 −0.0491683
\(352\) 14.7057 0.783817
\(353\) −16.0711 −0.855377 −0.427688 0.903926i \(-0.640672\pi\)
−0.427688 + 0.903926i \(0.640672\pi\)
\(354\) −0.0142823 −0.000759094 0
\(355\) 8.27354 0.439114
\(356\) −12.3910 −0.656719
\(357\) −0.208484 −0.0110341
\(358\) 2.57888 0.136298
\(359\) −33.2961 −1.75730 −0.878651 0.477465i \(-0.841556\pi\)
−0.878651 + 0.477465i \(0.841556\pi\)
\(360\) 6.31659 0.332913
\(361\) −15.5625 −0.819078
\(362\) −5.07806 −0.266897
\(363\) −0.0943437 −0.00495176
\(364\) 10.0115 0.524747
\(365\) 3.33270 0.174442
\(366\) 0.208146 0.0108800
\(367\) 23.8343 1.24414 0.622069 0.782962i \(-0.286292\pi\)
0.622069 + 0.782962i \(0.286292\pi\)
\(368\) −9.09418 −0.474067
\(369\) −16.8156 −0.875387
\(370\) 1.82289 0.0947675
\(371\) −0.229266 −0.0119029
\(372\) −0.0728296 −0.00377604
\(373\) −12.9984 −0.673032 −0.336516 0.941678i \(-0.609249\pi\)
−0.336516 + 0.941678i \(0.609249\pi\)
\(374\) 12.6268 0.652917
\(375\) −0.0256257 −0.00132330
\(376\) −11.4354 −0.589734
\(377\) 4.36284 0.224698
\(378\) −0.0881996 −0.00453650
\(379\) 26.8152 1.37740 0.688701 0.725045i \(-0.258181\pi\)
0.688701 + 0.725045i \(0.258181\pi\)
\(380\) 3.09788 0.158918
\(381\) −0.171858 −0.00880453
\(382\) −2.50662 −0.128250
\(383\) 30.2377 1.54507 0.772536 0.634971i \(-0.218988\pi\)
0.772536 + 0.634971i \(0.218988\pi\)
\(384\) 0.295484 0.0150789
\(385\) −2.70525 −0.137872
\(386\) −6.60884 −0.336381
\(387\) 5.49391 0.279271
\(388\) −20.9878 −1.06549
\(389\) 37.6725 1.91007 0.955035 0.296493i \(-0.0958171\pi\)
0.955035 + 0.296493i \(0.0958171\pi\)
\(390\) 0.0880892 0.00446057
\(391\) −34.6790 −1.75379
\(392\) 2.10599 0.106369
\(393\) −0.255063 −0.0128662
\(394\) 4.23756 0.213485
\(395\) −10.5865 −0.532667
\(396\) −13.5574 −0.681283
\(397\) −6.22080 −0.312213 −0.156106 0.987740i \(-0.549894\pi\)
−0.156106 + 0.987740i \(0.549894\pi\)
\(398\) −13.5389 −0.678646
\(399\) −0.0475114 −0.00237855
\(400\) 2.13351 0.106676
\(401\) −5.79352 −0.289315 −0.144657 0.989482i \(-0.546208\pi\)
−0.144657 + 0.989482i \(0.546208\pi\)
\(402\) 0.118128 0.00589170
\(403\) 10.1918 0.507691
\(404\) 19.8884 0.989483
\(405\) −8.99409 −0.446920
\(406\) 0.417731 0.0207317
\(407\) −8.59568 −0.426072
\(408\) 0.439065 0.0217370
\(409\) 6.08364 0.300817 0.150408 0.988624i \(-0.451941\pi\)
0.150408 + 0.988624i \(0.451941\pi\)
\(410\) 3.21644 0.158849
\(411\) 0.0441040 0.00217549
\(412\) 5.25048 0.258673
\(413\) −0.971481 −0.0478035
\(414\) −7.33471 −0.360481
\(415\) 10.5022 0.515531
\(416\) −32.5715 −1.59695
\(417\) 0.0441813 0.00216357
\(418\) 2.87752 0.140744
\(419\) −12.3288 −0.602300 −0.301150 0.953577i \(-0.597371\pi\)
−0.301150 + 0.953577i \(0.597371\pi\)
\(420\) −0.0428170 −0.00208925
\(421\) −14.1263 −0.688471 −0.344236 0.938883i \(-0.611862\pi\)
−0.344236 + 0.938883i \(0.611862\pi\)
\(422\) −9.85821 −0.479890
\(423\) 16.2862 0.791863
\(424\) 0.482832 0.0234484
\(425\) 8.13576 0.394642
\(426\) 0.121634 0.00589318
\(427\) 14.1581 0.685159
\(428\) 12.8589 0.621558
\(429\) −0.415377 −0.0200546
\(430\) −1.05086 −0.0506768
\(431\) 31.3917 1.51208 0.756041 0.654524i \(-0.227131\pi\)
0.756041 + 0.654524i \(0.227131\pi\)
\(432\) −0.328000 −0.0157809
\(433\) 15.0572 0.723605 0.361802 0.932255i \(-0.382161\pi\)
0.361802 + 0.932255i \(0.382161\pi\)
\(434\) 0.975843 0.0468420
\(435\) −0.0186588 −0.000894622 0
\(436\) −31.8711 −1.52635
\(437\) −7.90299 −0.378051
\(438\) 0.0489959 0.00234111
\(439\) −30.7506 −1.46765 −0.733824 0.679340i \(-0.762266\pi\)
−0.733824 + 0.679340i \(0.762266\pi\)
\(440\) 5.69723 0.271605
\(441\) −2.99934 −0.142826
\(442\) −27.9670 −1.33025
\(443\) 27.9663 1.32872 0.664360 0.747412i \(-0.268704\pi\)
0.664360 + 0.747412i \(0.268704\pi\)
\(444\) −0.136047 −0.00645650
\(445\) −7.41590 −0.351547
\(446\) −6.73166 −0.318754
\(447\) 0.101341 0.00479328
\(448\) 1.14838 0.0542558
\(449\) 17.6662 0.833720 0.416860 0.908971i \(-0.363130\pi\)
0.416860 + 0.908971i \(0.363130\pi\)
\(450\) 1.72074 0.0811163
\(451\) −15.1668 −0.714178
\(452\) −20.2270 −0.951396
\(453\) 0.128930 0.00605768
\(454\) 3.63489 0.170594
\(455\) 5.99183 0.280902
\(456\) 0.100059 0.00468567
\(457\) −14.2243 −0.665387 −0.332693 0.943035i \(-0.607957\pi\)
−0.332693 + 0.943035i \(0.607957\pi\)
\(458\) −0.573704 −0.0268074
\(459\) −1.25077 −0.0583808
\(460\) −7.12212 −0.332071
\(461\) −1.08513 −0.0505397 −0.0252699 0.999681i \(-0.508045\pi\)
−0.0252699 + 0.999681i \(0.508045\pi\)
\(462\) −0.0397714 −0.00185033
\(463\) −21.1005 −0.980624 −0.490312 0.871547i \(-0.663117\pi\)
−0.490312 + 0.871547i \(0.663117\pi\)
\(464\) 1.55348 0.0721183
\(465\) −0.0435880 −0.00202135
\(466\) −11.1594 −0.516950
\(467\) 12.4222 0.574832 0.287416 0.957806i \(-0.407204\pi\)
0.287416 + 0.957806i \(0.407204\pi\)
\(468\) 30.0280 1.38805
\(469\) 8.03509 0.371026
\(470\) −3.11517 −0.143692
\(471\) −0.473151 −0.0218016
\(472\) 2.04593 0.0941715
\(473\) 4.95522 0.227841
\(474\) −0.155639 −0.00714872
\(475\) 1.85406 0.0850700
\(476\) 13.5937 0.623068
\(477\) −0.687648 −0.0314853
\(478\) −1.13903 −0.0520978
\(479\) 12.3409 0.563868 0.281934 0.959434i \(-0.409024\pi\)
0.281934 + 0.959434i \(0.409024\pi\)
\(480\) 0.139301 0.00635818
\(481\) 19.0385 0.868080
\(482\) 3.14655 0.143321
\(483\) 0.109230 0.00497016
\(484\) 6.15147 0.279612
\(485\) −12.5611 −0.570368
\(486\) −0.396826 −0.0180004
\(487\) 23.2029 1.05142 0.525711 0.850663i \(-0.323799\pi\)
0.525711 + 0.850663i \(0.323799\pi\)
\(488\) −29.8168 −1.34974
\(489\) −0.0656553 −0.00296904
\(490\) 0.573704 0.0259173
\(491\) −25.3593 −1.14445 −0.572225 0.820097i \(-0.693919\pi\)
−0.572225 + 0.820097i \(0.693919\pi\)
\(492\) −0.240051 −0.0108223
\(493\) 5.92389 0.266799
\(494\) −6.37339 −0.286753
\(495\) −8.11398 −0.364696
\(496\) 3.62900 0.162947
\(497\) 8.27354 0.371119
\(498\) 0.154398 0.00691874
\(499\) 21.1509 0.946845 0.473422 0.880836i \(-0.343018\pi\)
0.473422 + 0.880836i \(0.343018\pi\)
\(500\) 1.67086 0.0747233
\(501\) 0.0979267 0.00437504
\(502\) −6.66206 −0.297342
\(503\) −10.9351 −0.487574 −0.243787 0.969829i \(-0.578390\pi\)
−0.243787 + 0.969829i \(0.578390\pi\)
\(504\) 6.31659 0.281363
\(505\) 11.9030 0.529678
\(506\) −6.61553 −0.294096
\(507\) 0.586881 0.0260643
\(508\) 11.2056 0.497168
\(509\) −23.7692 −1.05355 −0.526775 0.850005i \(-0.676599\pi\)
−0.526775 + 0.850005i \(0.676599\pi\)
\(510\) 0.119608 0.00529634
\(511\) 3.33270 0.147430
\(512\) −20.5840 −0.909695
\(513\) −0.285037 −0.0125847
\(514\) 0.342429 0.0151039
\(515\) 3.14238 0.138470
\(516\) 0.0784280 0.00345260
\(517\) 14.6893 0.646036
\(518\) 1.82289 0.0800932
\(519\) 0.111899 0.00491182
\(520\) −12.6187 −0.553368
\(521\) 1.63322 0.0715528 0.0357764 0.999360i \(-0.488610\pi\)
0.0357764 + 0.999360i \(0.488610\pi\)
\(522\) 1.25292 0.0548388
\(523\) 34.0006 1.48674 0.743372 0.668879i \(-0.233225\pi\)
0.743372 + 0.668879i \(0.233225\pi\)
\(524\) 16.6308 0.726520
\(525\) −0.0256257 −0.00111840
\(526\) 0.935803 0.0408029
\(527\) 13.8385 0.602816
\(528\) −0.147903 −0.00643667
\(529\) −4.83074 −0.210032
\(530\) 0.131531 0.00571334
\(531\) −2.91381 −0.126448
\(532\) 3.09788 0.134310
\(533\) 33.5929 1.45507
\(534\) −0.109025 −0.00471798
\(535\) 7.69595 0.332725
\(536\) −16.9218 −0.730911
\(537\) −0.115191 −0.00497086
\(538\) −5.54111 −0.238894
\(539\) −2.70525 −0.116523
\(540\) −0.256874 −0.0110541
\(541\) −32.5894 −1.40113 −0.700563 0.713590i \(-0.747068\pi\)
−0.700563 + 0.713590i \(0.747068\pi\)
\(542\) 9.48046 0.407221
\(543\) 0.226822 0.00973386
\(544\) −44.2258 −1.89617
\(545\) −19.0746 −0.817068
\(546\) 0.0880892 0.00376987
\(547\) −18.9662 −0.810937 −0.405468 0.914109i \(-0.632892\pi\)
−0.405468 + 0.914109i \(0.632892\pi\)
\(548\) −2.87571 −0.122844
\(549\) 42.4650 1.81236
\(550\) 1.55201 0.0661781
\(551\) 1.35000 0.0575117
\(552\) −0.230038 −0.00979107
\(553\) −10.5865 −0.450186
\(554\) −5.36235 −0.227825
\(555\) −0.0814231 −0.00345622
\(556\) −2.88074 −0.122171
\(557\) 37.4245 1.58573 0.792864 0.609398i \(-0.208589\pi\)
0.792864 + 0.609398i \(0.208589\pi\)
\(558\) 2.92689 0.123905
\(559\) −10.9753 −0.464204
\(560\) 2.13351 0.0901574
\(561\) −0.564002 −0.0238122
\(562\) −13.4539 −0.567520
\(563\) −11.3656 −0.479005 −0.239502 0.970896i \(-0.576984\pi\)
−0.239502 + 0.970896i \(0.576984\pi\)
\(564\) 0.232493 0.00978973
\(565\) −12.1057 −0.509290
\(566\) −7.95043 −0.334181
\(567\) −8.99409 −0.377716
\(568\) −17.4240 −0.731094
\(569\) 29.5516 1.23887 0.619433 0.785050i \(-0.287363\pi\)
0.619433 + 0.785050i \(0.287363\pi\)
\(570\) 0.0272575 0.00114169
\(571\) −11.0866 −0.463958 −0.231979 0.972721i \(-0.574520\pi\)
−0.231979 + 0.972721i \(0.574520\pi\)
\(572\) 27.0837 1.13243
\(573\) 0.111963 0.00467734
\(574\) 3.21644 0.134252
\(575\) −4.26254 −0.177760
\(576\) 3.44438 0.143516
\(577\) 43.5675 1.81374 0.906868 0.421414i \(-0.138466\pi\)
0.906868 + 0.421414i \(0.138466\pi\)
\(578\) −28.2208 −1.17383
\(579\) 0.295197 0.0122680
\(580\) 1.21661 0.0505168
\(581\) 10.5022 0.435703
\(582\) −0.184667 −0.00765469
\(583\) −0.620223 −0.0256870
\(584\) −7.01864 −0.290433
\(585\) 17.9716 0.743033
\(586\) −5.23288 −0.216168
\(587\) −8.21387 −0.339023 −0.169511 0.985528i \(-0.554219\pi\)
−0.169511 + 0.985528i \(0.554219\pi\)
\(588\) −0.0428170 −0.00176574
\(589\) 3.15366 0.129944
\(590\) 0.557343 0.0229454
\(591\) −0.189279 −0.00778592
\(592\) 6.77903 0.278616
\(593\) 11.9303 0.489918 0.244959 0.969533i \(-0.421226\pi\)
0.244959 + 0.969533i \(0.421226\pi\)
\(594\) −0.238602 −0.00978997
\(595\) 8.13576 0.333534
\(596\) −6.60773 −0.270663
\(597\) 0.604744 0.0247505
\(598\) 14.6527 0.599192
\(599\) −19.7455 −0.806781 −0.403390 0.915028i \(-0.632168\pi\)
−0.403390 + 0.915028i \(0.632168\pi\)
\(600\) 0.0539674 0.00220321
\(601\) 27.2731 1.11249 0.556246 0.831017i \(-0.312241\pi\)
0.556246 + 0.831017i \(0.312241\pi\)
\(602\) −1.05086 −0.0428297
\(603\) 24.1000 0.981427
\(604\) −8.40661 −0.342060
\(605\) 3.68161 0.149679
\(606\) 0.174993 0.00710861
\(607\) −25.4004 −1.03097 −0.515485 0.856898i \(-0.672388\pi\)
−0.515485 + 0.856898i \(0.672388\pi\)
\(608\) −10.0786 −0.408742
\(609\) −0.0186588 −0.000756094 0
\(610\) −8.12256 −0.328873
\(611\) −32.5352 −1.31623
\(612\) 40.7723 1.64812
\(613\) −11.1609 −0.450786 −0.225393 0.974268i \(-0.572367\pi\)
−0.225393 + 0.974268i \(0.572367\pi\)
\(614\) 6.33367 0.255606
\(615\) −0.143669 −0.00579328
\(616\) 5.69723 0.229548
\(617\) −16.1275 −0.649268 −0.324634 0.945840i \(-0.605241\pi\)
−0.324634 + 0.945840i \(0.605241\pi\)
\(618\) 0.0461978 0.00185835
\(619\) 18.2800 0.734737 0.367369 0.930075i \(-0.380259\pi\)
0.367369 + 0.930075i \(0.380259\pi\)
\(620\) 2.84206 0.114140
\(621\) 0.655311 0.0262967
\(622\) 12.5118 0.501676
\(623\) −7.41590 −0.297112
\(624\) 0.327589 0.0131141
\(625\) 1.00000 0.0400000
\(626\) 1.99505 0.0797381
\(627\) −0.128530 −0.00513301
\(628\) 30.8507 1.23108
\(629\) 25.8506 1.03073
\(630\) 1.72074 0.0685557
\(631\) −27.9539 −1.11283 −0.556414 0.830905i \(-0.687823\pi\)
−0.556414 + 0.830905i \(0.687823\pi\)
\(632\) 22.2952 0.886854
\(633\) 0.440337 0.0175018
\(634\) 11.8574 0.470919
\(635\) 6.70647 0.266138
\(636\) −0.00981649 −0.000389249 0
\(637\) 5.99183 0.237405
\(638\) 1.13007 0.0447399
\(639\) 24.8152 0.981674
\(640\) −11.5308 −0.455795
\(641\) −4.85896 −0.191917 −0.0959587 0.995385i \(-0.530592\pi\)
−0.0959587 + 0.995385i \(0.530592\pi\)
\(642\) 0.113142 0.00446537
\(643\) 33.8416 1.33458 0.667292 0.744796i \(-0.267453\pi\)
0.667292 + 0.744796i \(0.267453\pi\)
\(644\) −7.12212 −0.280651
\(645\) 0.0469386 0.00184821
\(646\) −8.65384 −0.340481
\(647\) 4.08747 0.160695 0.0803474 0.996767i \(-0.474397\pi\)
0.0803474 + 0.996767i \(0.474397\pi\)
\(648\) 18.9415 0.744091
\(649\) −2.62810 −0.103162
\(650\) −3.43754 −0.134831
\(651\) −0.0435880 −0.00170835
\(652\) 4.28091 0.167653
\(653\) 4.51998 0.176880 0.0884402 0.996081i \(-0.471812\pi\)
0.0884402 + 0.996081i \(0.471812\pi\)
\(654\) −0.280427 −0.0109656
\(655\) 9.95341 0.388912
\(656\) 11.9614 0.467015
\(657\) 9.99592 0.389978
\(658\) −3.11517 −0.121442
\(659\) 5.03050 0.195961 0.0979803 0.995188i \(-0.468762\pi\)
0.0979803 + 0.995188i \(0.468762\pi\)
\(660\) −0.115831 −0.00450871
\(661\) 27.4597 1.06806 0.534030 0.845466i \(-0.320677\pi\)
0.534030 + 0.845466i \(0.320677\pi\)
\(662\) 3.22923 0.125508
\(663\) 1.24920 0.0485150
\(664\) −22.1174 −0.858323
\(665\) 1.85406 0.0718972
\(666\) 5.46747 0.211860
\(667\) −3.10369 −0.120175
\(668\) −6.38509 −0.247047
\(669\) 0.300683 0.0116251
\(670\) −4.60976 −0.178091
\(671\) 38.3013 1.47860
\(672\) 0.139301 0.00537364
\(673\) 0.470371 0.0181315 0.00906574 0.999959i \(-0.497114\pi\)
0.00906574 + 0.999959i \(0.497114\pi\)
\(674\) −6.84090 −0.263502
\(675\) −0.153737 −0.00591734
\(676\) −38.2662 −1.47178
\(677\) 8.90707 0.342327 0.171163 0.985243i \(-0.445247\pi\)
0.171163 + 0.985243i \(0.445247\pi\)
\(678\) −0.177972 −0.00683498
\(679\) −12.5611 −0.482049
\(680\) −17.1338 −0.657052
\(681\) −0.162360 −0.00622164
\(682\) 2.63990 0.101087
\(683\) 7.61638 0.291433 0.145716 0.989326i \(-0.453451\pi\)
0.145716 + 0.989326i \(0.453451\pi\)
\(684\) 9.29159 0.355273
\(685\) −1.72109 −0.0657594
\(686\) 0.573704 0.0219041
\(687\) 0.0256257 0.000977680 0
\(688\) −3.90796 −0.148990
\(689\) 1.37373 0.0523348
\(690\) −0.0626659 −0.00238565
\(691\) −39.0306 −1.48479 −0.742396 0.669961i \(-0.766311\pi\)
−0.742396 + 0.669961i \(0.766311\pi\)
\(692\) −7.29612 −0.277357
\(693\) −8.11398 −0.308225
\(694\) 7.93067 0.301044
\(695\) −1.72410 −0.0653990
\(696\) 0.0392953 0.00148948
\(697\) 45.6126 1.72770
\(698\) −1.46515 −0.0554567
\(699\) 0.498458 0.0188534
\(700\) 1.67086 0.0631527
\(701\) −8.26912 −0.312320 −0.156160 0.987732i \(-0.549912\pi\)
−0.156160 + 0.987732i \(0.549912\pi\)
\(702\) 0.528477 0.0199461
\(703\) 5.89109 0.222187
\(704\) 3.10665 0.117086
\(705\) 0.139145 0.00524052
\(706\) 9.22004 0.347001
\(707\) 11.9030 0.447660
\(708\) −0.0415959 −0.00156327
\(709\) −26.6261 −0.999965 −0.499983 0.866035i \(-0.666660\pi\)
−0.499983 + 0.866035i \(0.666660\pi\)
\(710\) −4.74656 −0.178135
\(711\) −31.7527 −1.19082
\(712\) 15.6178 0.585302
\(713\) −7.25038 −0.271529
\(714\) 0.119608 0.00447622
\(715\) 16.2094 0.606198
\(716\) 7.51078 0.280691
\(717\) 0.0508769 0.00190003
\(718\) 19.1021 0.712885
\(719\) −10.0375 −0.374335 −0.187168 0.982328i \(-0.559931\pi\)
−0.187168 + 0.982328i \(0.559931\pi\)
\(720\) 6.39914 0.238482
\(721\) 3.14238 0.117028
\(722\) 8.92825 0.332275
\(723\) −0.140547 −0.00522700
\(724\) −14.7894 −0.549644
\(725\) 0.728131 0.0270421
\(726\) 0.0541253 0.00200878
\(727\) 21.5768 0.800240 0.400120 0.916463i \(-0.368969\pi\)
0.400120 + 0.916463i \(0.368969\pi\)
\(728\) −12.6187 −0.467682
\(729\) −26.9645 −0.998687
\(730\) −1.91199 −0.0707657
\(731\) −14.9023 −0.551181
\(732\) 0.606207 0.0224061
\(733\) −6.01690 −0.222239 −0.111120 0.993807i \(-0.535444\pi\)
−0.111120 + 0.993807i \(0.535444\pi\)
\(734\) −13.6738 −0.504710
\(735\) −0.0256257 −0.000945217 0
\(736\) 23.1711 0.854098
\(737\) 21.7369 0.800690
\(738\) 9.64720 0.355118
\(739\) −22.7156 −0.835608 −0.417804 0.908537i \(-0.637200\pi\)
−0.417804 + 0.908537i \(0.637200\pi\)
\(740\) 5.30901 0.195163
\(741\) 0.284681 0.0104580
\(742\) 0.131531 0.00482865
\(743\) −18.6872 −0.685567 −0.342784 0.939414i \(-0.611370\pi\)
−0.342784 + 0.939414i \(0.611370\pi\)
\(744\) 0.0917959 0.00336540
\(745\) −3.95468 −0.144888
\(746\) 7.45724 0.273029
\(747\) 31.4996 1.15251
\(748\) 36.7745 1.34461
\(749\) 7.69595 0.281204
\(750\) 0.0147015 0.000536825 0
\(751\) 21.6241 0.789074 0.394537 0.918880i \(-0.370905\pi\)
0.394537 + 0.918880i \(0.370905\pi\)
\(752\) −11.5848 −0.422455
\(753\) 0.297575 0.0108442
\(754\) −2.50298 −0.0911531
\(755\) −5.03130 −0.183108
\(756\) −0.256874 −0.00934241
\(757\) 35.4901 1.28991 0.644955 0.764221i \(-0.276876\pi\)
0.644955 + 0.764221i \(0.276876\pi\)
\(758\) −15.3840 −0.558771
\(759\) 0.295496 0.0107258
\(760\) −3.90462 −0.141636
\(761\) 27.7046 1.00429 0.502145 0.864784i \(-0.332544\pi\)
0.502145 + 0.864784i \(0.332544\pi\)
\(762\) 0.0985954 0.00357174
\(763\) −19.0746 −0.690548
\(764\) −7.30032 −0.264116
\(765\) 24.4019 0.882254
\(766\) −17.3475 −0.626789
\(767\) 5.82095 0.210182
\(768\) −0.110665 −0.00399327
\(769\) 14.7571 0.532154 0.266077 0.963952i \(-0.414272\pi\)
0.266077 + 0.963952i \(0.414272\pi\)
\(770\) 1.55201 0.0559307
\(771\) −0.0152953 −0.000550846 0
\(772\) −19.2477 −0.692739
\(773\) −19.3129 −0.694637 −0.347319 0.937747i \(-0.612908\pi\)
−0.347319 + 0.937747i \(0.612908\pi\)
\(774\) −3.15188 −0.113292
\(775\) 1.70095 0.0611000
\(776\) 26.4535 0.949624
\(777\) −0.0814231 −0.00292104
\(778\) −21.6129 −0.774858
\(779\) 10.3947 0.372427
\(780\) 0.256552 0.00918604
\(781\) 22.3820 0.800892
\(782\) 19.8955 0.711461
\(783\) −0.111941 −0.00400043
\(784\) 2.13351 0.0761969
\(785\) 18.4639 0.659007
\(786\) 0.146331 0.00521944
\(787\) 25.1730 0.897322 0.448661 0.893702i \(-0.351901\pi\)
0.448661 + 0.893702i \(0.351901\pi\)
\(788\) 12.3415 0.439649
\(789\) −0.0417995 −0.00148810
\(790\) 6.07354 0.216087
\(791\) −12.1057 −0.430429
\(792\) 17.0880 0.607194
\(793\) −84.8330 −3.01251
\(794\) 3.56890 0.126655
\(795\) −0.00587510 −0.000208368 0
\(796\) −39.4310 −1.39759
\(797\) 0.0867245 0.00307194 0.00153597 0.999999i \(-0.499511\pi\)
0.00153597 + 0.999999i \(0.499511\pi\)
\(798\) 0.0272575 0.000964905 0
\(799\) −44.1766 −1.56285
\(800\) −5.43598 −0.192191
\(801\) −22.2428 −0.785912
\(802\) 3.32377 0.117366
\(803\) 9.01580 0.318161
\(804\) 0.344038 0.0121333
\(805\) −4.26254 −0.150235
\(806\) −5.84709 −0.205955
\(807\) 0.247505 0.00871259
\(808\) −25.0677 −0.881878
\(809\) 29.8078 1.04798 0.523992 0.851723i \(-0.324442\pi\)
0.523992 + 0.851723i \(0.324442\pi\)
\(810\) 5.15995 0.181302
\(811\) 56.4317 1.98158 0.990792 0.135390i \(-0.0432289\pi\)
0.990792 + 0.135390i \(0.0432289\pi\)
\(812\) 1.21661 0.0426945
\(813\) −0.423464 −0.0148515
\(814\) 4.93138 0.172845
\(815\) 2.56209 0.0897462
\(816\) 0.444803 0.0155712
\(817\) −3.39608 −0.118814
\(818\) −3.49021 −0.122032
\(819\) 17.9716 0.627977
\(820\) 9.36760 0.327131
\(821\) 40.7588 1.42249 0.711246 0.702944i \(-0.248131\pi\)
0.711246 + 0.702944i \(0.248131\pi\)
\(822\) −0.0253027 −0.000882532 0
\(823\) 43.8388 1.52813 0.764063 0.645142i \(-0.223202\pi\)
0.764063 + 0.645142i \(0.223202\pi\)
\(824\) −6.61781 −0.230543
\(825\) −0.0693239 −0.00241355
\(826\) 0.557343 0.0193924
\(827\) 20.9241 0.727604 0.363802 0.931476i \(-0.381479\pi\)
0.363802 + 0.931476i \(0.381479\pi\)
\(828\) −21.3617 −0.742370
\(829\) 35.8915 1.24656 0.623282 0.781997i \(-0.285799\pi\)
0.623282 + 0.781997i \(0.285799\pi\)
\(830\) −6.02513 −0.209135
\(831\) 0.239520 0.00830887
\(832\) −6.88089 −0.238552
\(833\) 8.13576 0.281887
\(834\) −0.0253470 −0.000877695 0
\(835\) −3.82143 −0.132246
\(836\) 8.38054 0.289847
\(837\) −0.261499 −0.00903874
\(838\) 7.07307 0.244335
\(839\) −15.2752 −0.527359 −0.263679 0.964610i \(-0.584936\pi\)
−0.263679 + 0.964610i \(0.584936\pi\)
\(840\) 0.0539674 0.00186205
\(841\) −28.4698 −0.981718
\(842\) 8.10429 0.279292
\(843\) 0.600948 0.0206977
\(844\) −28.7112 −0.988280
\(845\) −22.9021 −0.787855
\(846\) −9.34347 −0.321235
\(847\) 3.68161 0.126502
\(848\) 0.489142 0.0167972
\(849\) 0.355122 0.0121878
\(850\) −4.66752 −0.160095
\(851\) −13.5438 −0.464276
\(852\) 0.354248 0.0121363
\(853\) 5.53483 0.189509 0.0947545 0.995501i \(-0.469793\pi\)
0.0947545 + 0.995501i \(0.469793\pi\)
\(854\) −8.12256 −0.277948
\(855\) 5.56095 0.190181
\(856\) −16.2076 −0.553964
\(857\) 14.5243 0.496141 0.248070 0.968742i \(-0.420204\pi\)
0.248070 + 0.968742i \(0.420204\pi\)
\(858\) 0.238304 0.00813555
\(859\) 12.0888 0.412465 0.206232 0.978503i \(-0.433880\pi\)
0.206232 + 0.978503i \(0.433880\pi\)
\(860\) −3.06053 −0.104363
\(861\) −0.143669 −0.00489622
\(862\) −18.0095 −0.613407
\(863\) 38.0136 1.29400 0.646999 0.762491i \(-0.276024\pi\)
0.646999 + 0.762491i \(0.276024\pi\)
\(864\) 0.835712 0.0284315
\(865\) −4.36667 −0.148471
\(866\) −8.63840 −0.293545
\(867\) 1.26054 0.0428102
\(868\) 2.84206 0.0964658
\(869\) −28.6393 −0.971521
\(870\) 0.0107046 0.000362921 0
\(871\) −48.1449 −1.63133
\(872\) 40.1710 1.36036
\(873\) −37.6749 −1.27510
\(874\) 4.53398 0.153364
\(875\) 1.00000 0.0338062
\(876\) 0.142696 0.00482126
\(877\) −26.4480 −0.893087 −0.446543 0.894762i \(-0.647345\pi\)
−0.446543 + 0.894762i \(0.647345\pi\)
\(878\) 17.6418 0.595381
\(879\) 0.233737 0.00788376
\(880\) 5.77169 0.194564
\(881\) −8.00267 −0.269617 −0.134808 0.990872i \(-0.543042\pi\)
−0.134808 + 0.990872i \(0.543042\pi\)
\(882\) 1.72074 0.0579402
\(883\) 5.05367 0.170069 0.0850347 0.996378i \(-0.472900\pi\)
0.0850347 + 0.996378i \(0.472900\pi\)
\(884\) −81.4514 −2.73951
\(885\) −0.0248948 −0.000836831 0
\(886\) −16.0444 −0.539022
\(887\) 21.5520 0.723644 0.361822 0.932247i \(-0.382155\pi\)
0.361822 + 0.932247i \(0.382155\pi\)
\(888\) 0.171476 0.00575436
\(889\) 6.70647 0.224928
\(890\) 4.25453 0.142612
\(891\) −24.3313 −0.815129
\(892\) −19.6054 −0.656437
\(893\) −10.0674 −0.336893
\(894\) −0.0581399 −0.00194449
\(895\) 4.49515 0.150256
\(896\) −11.5308 −0.385217
\(897\) −0.654491 −0.0218528
\(898\) −10.1352 −0.338215
\(899\) 1.23852 0.0413068
\(900\) 5.01149 0.167050
\(901\) 1.86525 0.0621406
\(902\) 8.70128 0.289721
\(903\) 0.0469386 0.00156202
\(904\) 25.4944 0.847933
\(905\) −8.85136 −0.294229
\(906\) −0.0739679 −0.00245742
\(907\) −16.0121 −0.531674 −0.265837 0.964018i \(-0.585648\pi\)
−0.265837 + 0.964018i \(0.585648\pi\)
\(908\) 10.5863 0.351319
\(909\) 35.7013 1.18414
\(910\) −3.43754 −0.113953
\(911\) 23.6372 0.783137 0.391568 0.920149i \(-0.371933\pi\)
0.391568 + 0.920149i \(0.371933\pi\)
\(912\) 0.101366 0.00335657
\(913\) 28.4110 0.940267
\(914\) 8.16056 0.269927
\(915\) 0.362811 0.0119942
\(916\) −1.67086 −0.0552069
\(917\) 9.95341 0.328691
\(918\) 0.717571 0.0236834
\(919\) 54.5150 1.79828 0.899142 0.437657i \(-0.144191\pi\)
0.899142 + 0.437657i \(0.144191\pi\)
\(920\) 8.97687 0.295959
\(921\) −0.282906 −0.00932208
\(922\) 0.622546 0.0205025
\(923\) −49.5737 −1.63174
\(924\) −0.115831 −0.00381055
\(925\) 3.17740 0.104472
\(926\) 12.1054 0.397810
\(927\) 9.42507 0.309560
\(928\) −3.95811 −0.129931
\(929\) −37.4833 −1.22979 −0.614893 0.788610i \(-0.710801\pi\)
−0.614893 + 0.788610i \(0.710801\pi\)
\(930\) 0.0250066 0.000820000 0
\(931\) 1.85406 0.0607643
\(932\) −32.5009 −1.06460
\(933\) −0.558864 −0.0182964
\(934\) −7.12668 −0.233192
\(935\) 22.0093 0.719780
\(936\) −37.8479 −1.23710
\(937\) −17.8078 −0.581756 −0.290878 0.956760i \(-0.593947\pi\)
−0.290878 + 0.956760i \(0.593947\pi\)
\(938\) −4.60976 −0.150514
\(939\) −0.0891128 −0.00290809
\(940\) −9.07267 −0.295918
\(941\) −8.44558 −0.275318 −0.137659 0.990480i \(-0.543958\pi\)
−0.137659 + 0.990480i \(0.543958\pi\)
\(942\) 0.271449 0.00884427
\(943\) −23.8977 −0.778216
\(944\) 2.07267 0.0674596
\(945\) −0.153737 −0.00500107
\(946\) −2.84283 −0.0924284
\(947\) 21.4313 0.696422 0.348211 0.937416i \(-0.386789\pi\)
0.348211 + 0.937416i \(0.386789\pi\)
\(948\) −0.453284 −0.0147220
\(949\) −19.9690 −0.648221
\(950\) −1.06368 −0.0345103
\(951\) −0.529636 −0.0171746
\(952\) −17.1338 −0.555310
\(953\) −11.2938 −0.365841 −0.182920 0.983128i \(-0.558555\pi\)
−0.182920 + 0.983128i \(0.558555\pi\)
\(954\) 0.394507 0.0127726
\(955\) −4.36919 −0.141384
\(956\) −3.31731 −0.107290
\(957\) −0.0504768 −0.00163168
\(958\) −7.08000 −0.228744
\(959\) −1.72109 −0.0555769
\(960\) 0.0294280 0.000949783 0
\(961\) −28.1068 −0.906670
\(962\) −10.9225 −0.352154
\(963\) 23.0828 0.743833
\(964\) 9.16405 0.295154
\(965\) −11.5196 −0.370829
\(966\) −0.0626659 −0.00201624
\(967\) −39.6780 −1.27596 −0.637980 0.770053i \(-0.720230\pi\)
−0.637980 + 0.770053i \(0.720230\pi\)
\(968\) −7.75343 −0.249205
\(969\) 0.386541 0.0124175
\(970\) 7.20633 0.231381
\(971\) 48.2778 1.54931 0.774653 0.632386i \(-0.217924\pi\)
0.774653 + 0.632386i \(0.217924\pi\)
\(972\) −1.15572 −0.0370698
\(973\) −1.72410 −0.0552722
\(974\) −13.3116 −0.426530
\(975\) 0.153545 0.00491737
\(976\) −30.2065 −0.966886
\(977\) −13.4981 −0.431843 −0.215922 0.976411i \(-0.569276\pi\)
−0.215922 + 0.976411i \(0.569276\pi\)
\(978\) 0.0376667 0.00120445
\(979\) −20.0619 −0.641180
\(980\) 1.67086 0.0533738
\(981\) −57.2114 −1.82662
\(982\) 14.5487 0.464269
\(983\) −5.82233 −0.185704 −0.0928518 0.995680i \(-0.529598\pi\)
−0.0928518 + 0.995680i \(0.529598\pi\)
\(984\) 0.302565 0.00964541
\(985\) 7.38632 0.235348
\(986\) −3.39856 −0.108232
\(987\) 0.139145 0.00442905
\(988\) −18.5620 −0.590535
\(989\) 7.80771 0.248271
\(990\) 4.65502 0.147946
\(991\) 39.4377 1.25278 0.626391 0.779509i \(-0.284532\pi\)
0.626391 + 0.779509i \(0.284532\pi\)
\(992\) −9.24635 −0.293572
\(993\) −0.144240 −0.00457733
\(994\) −4.74656 −0.150552
\(995\) −23.5992 −0.748144
\(996\) 0.449671 0.0142484
\(997\) −10.0796 −0.319225 −0.159612 0.987180i \(-0.551024\pi\)
−0.159612 + 0.987180i \(0.551024\pi\)
\(998\) −12.1344 −0.384107
\(999\) −0.488485 −0.0154550
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 \(a_p\))