Properties

Label 8042.2.a.c.1.7
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.59394 q^{3} +1.00000 q^{4} -0.859547 q^{5} +2.59394 q^{6} -3.29568 q^{7} -1.00000 q^{8} +3.72855 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.59394 q^{3} +1.00000 q^{4} -0.859547 q^{5} +2.59394 q^{6} -3.29568 q^{7} -1.00000 q^{8} +3.72855 q^{9} +0.859547 q^{10} -0.214484 q^{11} -2.59394 q^{12} +0.577971 q^{13} +3.29568 q^{14} +2.22962 q^{15} +1.00000 q^{16} +6.01944 q^{17} -3.72855 q^{18} +0.272395 q^{19} -0.859547 q^{20} +8.54880 q^{21} +0.214484 q^{22} +2.84049 q^{23} +2.59394 q^{24} -4.26118 q^{25} -0.577971 q^{26} -1.88982 q^{27} -3.29568 q^{28} +3.81514 q^{29} -2.22962 q^{30} +8.62269 q^{31} -1.00000 q^{32} +0.556360 q^{33} -6.01944 q^{34} +2.83279 q^{35} +3.72855 q^{36} +1.26944 q^{37} -0.272395 q^{38} -1.49922 q^{39} +0.859547 q^{40} -8.40030 q^{41} -8.54880 q^{42} -0.438888 q^{43} -0.214484 q^{44} -3.20486 q^{45} -2.84049 q^{46} +7.89612 q^{47} -2.59394 q^{48} +3.86149 q^{49} +4.26118 q^{50} -15.6141 q^{51} +0.577971 q^{52} +12.2211 q^{53} +1.88982 q^{54} +0.184359 q^{55} +3.29568 q^{56} -0.706577 q^{57} -3.81514 q^{58} -3.37745 q^{59} +2.22962 q^{60} -9.85667 q^{61} -8.62269 q^{62} -12.2881 q^{63} +1.00000 q^{64} -0.496793 q^{65} -0.556360 q^{66} +6.77627 q^{67} +6.01944 q^{68} -7.36806 q^{69} -2.83279 q^{70} +14.8404 q^{71} -3.72855 q^{72} -1.64480 q^{73} -1.26944 q^{74} +11.0533 q^{75} +0.272395 q^{76} +0.706870 q^{77} +1.49922 q^{78} +2.37919 q^{79} -0.859547 q^{80} -6.28357 q^{81} +8.40030 q^{82} -0.683145 q^{83} +8.54880 q^{84} -5.17399 q^{85} +0.438888 q^{86} -9.89626 q^{87} +0.214484 q^{88} -16.0029 q^{89} +3.20486 q^{90} -1.90480 q^{91} +2.84049 q^{92} -22.3668 q^{93} -7.89612 q^{94} -0.234136 q^{95} +2.59394 q^{96} +3.79190 q^{97} -3.86149 q^{98} -0.799715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 86q - 86q^{2} + 12q^{3} + 86q^{4} - 4q^{5} - 12q^{6} + 35q^{7} - 86q^{8} + 72q^{9} + O(q^{10}) \) \( 86q - 86q^{2} + 12q^{3} + 86q^{4} - 4q^{5} - 12q^{6} + 35q^{7} - 86q^{8} + 72q^{9} + 4q^{10} + 13q^{11} + 12q^{12} + 45q^{13} - 35q^{14} + 17q^{15} + 86q^{16} + 5q^{17} - 72q^{18} + 47q^{19} - 4q^{20} + 15q^{21} - 13q^{22} + 6q^{23} - 12q^{24} + 112q^{25} - 45q^{26} + 51q^{27} + 35q^{28} - 14q^{29} - 17q^{30} + 24q^{31} - 86q^{32} + 43q^{33} - 5q^{34} + 42q^{35} + 72q^{36} + 61q^{37} - 47q^{38} + 20q^{39} + 4q^{40} - 16q^{41} - 15q^{42} + 72q^{43} + 13q^{44} + 6q^{45} - 6q^{46} + 11q^{47} + 12q^{48} + 89q^{49} - 112q^{50} + 56q^{51} + 45q^{52} - 7q^{53} - 51q^{54} + 48q^{55} - 35q^{56} + 65q^{57} + 14q^{58} + 24q^{59} + 17q^{60} + 31q^{61} - 24q^{62} + 98q^{63} + 86q^{64} - 9q^{65} - 43q^{66} + 157q^{67} + 5q^{68} + q^{69} - 42q^{70} - 11q^{71} - 72q^{72} + 74q^{73} - 61q^{74} + 76q^{75} + 47q^{76} - 13q^{77} - 20q^{78} + 57q^{79} - 4q^{80} + 34q^{81} + 16q^{82} + 65q^{83} + 15q^{84} + 102q^{85} - 72q^{86} + 49q^{87} - 13q^{88} - 34q^{89} - 6q^{90} + 91q^{91} + 6q^{92} + 57q^{93} - 11q^{94} - 13q^{95} - 12q^{96} + 64q^{97} - 89q^{98} + 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.59394 −1.49761 −0.748807 0.662788i \(-0.769373\pi\)
−0.748807 + 0.662788i \(0.769373\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.859547 −0.384401 −0.192201 0.981356i \(-0.561562\pi\)
−0.192201 + 0.981356i \(0.561562\pi\)
\(6\) 2.59394 1.05897
\(7\) −3.29568 −1.24565 −0.622824 0.782362i \(-0.714015\pi\)
−0.622824 + 0.782362i \(0.714015\pi\)
\(8\) −1.00000 −0.353553
\(9\) 3.72855 1.24285
\(10\) 0.859547 0.271813
\(11\) −0.214484 −0.0646694 −0.0323347 0.999477i \(-0.510294\pi\)
−0.0323347 + 0.999477i \(0.510294\pi\)
\(12\) −2.59394 −0.748807
\(13\) 0.577971 0.160300 0.0801501 0.996783i \(-0.474460\pi\)
0.0801501 + 0.996783i \(0.474460\pi\)
\(14\) 3.29568 0.880807
\(15\) 2.22962 0.575685
\(16\) 1.00000 0.250000
\(17\) 6.01944 1.45993 0.729964 0.683485i \(-0.239537\pi\)
0.729964 + 0.683485i \(0.239537\pi\)
\(18\) −3.72855 −0.878828
\(19\) 0.272395 0.0624917 0.0312458 0.999512i \(-0.490053\pi\)
0.0312458 + 0.999512i \(0.490053\pi\)
\(20\) −0.859547 −0.192201
\(21\) 8.54880 1.86550
\(22\) 0.214484 0.0457282
\(23\) 2.84049 0.592282 0.296141 0.955144i \(-0.404300\pi\)
0.296141 + 0.955144i \(0.404300\pi\)
\(24\) 2.59394 0.529487
\(25\) −4.26118 −0.852236
\(26\) −0.577971 −0.113349
\(27\) −1.88982 −0.363696
\(28\) −3.29568 −0.622824
\(29\) 3.81514 0.708453 0.354227 0.935160i \(-0.384744\pi\)
0.354227 + 0.935160i \(0.384744\pi\)
\(30\) −2.22962 −0.407071
\(31\) 8.62269 1.54868 0.774341 0.632769i \(-0.218082\pi\)
0.774341 + 0.632769i \(0.218082\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.556360 0.0968498
\(34\) −6.01944 −1.03233
\(35\) 2.83279 0.478829
\(36\) 3.72855 0.621425
\(37\) 1.26944 0.208695 0.104347 0.994541i \(-0.466725\pi\)
0.104347 + 0.994541i \(0.466725\pi\)
\(38\) −0.272395 −0.0441883
\(39\) −1.49922 −0.240068
\(40\) 0.859547 0.135906
\(41\) −8.40030 −1.31191 −0.655953 0.754801i \(-0.727733\pi\)
−0.655953 + 0.754801i \(0.727733\pi\)
\(42\) −8.54880 −1.31911
\(43\) −0.438888 −0.0669299 −0.0334649 0.999440i \(-0.510654\pi\)
−0.0334649 + 0.999440i \(0.510654\pi\)
\(44\) −0.214484 −0.0323347
\(45\) −3.20486 −0.477753
\(46\) −2.84049 −0.418807
\(47\) 7.89612 1.15177 0.575884 0.817531i \(-0.304658\pi\)
0.575884 + 0.817531i \(0.304658\pi\)
\(48\) −2.59394 −0.374404
\(49\) 3.86149 0.551641
\(50\) 4.26118 0.602622
\(51\) −15.6141 −2.18641
\(52\) 0.577971 0.0801501
\(53\) 12.2211 1.67869 0.839347 0.543596i \(-0.182938\pi\)
0.839347 + 0.543596i \(0.182938\pi\)
\(54\) 1.88982 0.257172
\(55\) 0.184359 0.0248590
\(56\) 3.29568 0.440403
\(57\) −0.706577 −0.0935885
\(58\) −3.81514 −0.500952
\(59\) −3.37745 −0.439706 −0.219853 0.975533i \(-0.570558\pi\)
−0.219853 + 0.975533i \(0.570558\pi\)
\(60\) 2.22962 0.287842
\(61\) −9.85667 −1.26202 −0.631008 0.775776i \(-0.717359\pi\)
−0.631008 + 0.775776i \(0.717359\pi\)
\(62\) −8.62269 −1.09508
\(63\) −12.2881 −1.54815
\(64\) 1.00000 0.125000
\(65\) −0.496793 −0.0616196
\(66\) −0.556360 −0.0684832
\(67\) 6.77627 0.827854 0.413927 0.910310i \(-0.364157\pi\)
0.413927 + 0.910310i \(0.364157\pi\)
\(68\) 6.01944 0.729964
\(69\) −7.36806 −0.887011
\(70\) −2.83279 −0.338583
\(71\) 14.8404 1.76123 0.880617 0.473829i \(-0.157128\pi\)
0.880617 + 0.473829i \(0.157128\pi\)
\(72\) −3.72855 −0.439414
\(73\) −1.64480 −0.192509 −0.0962546 0.995357i \(-0.530686\pi\)
−0.0962546 + 0.995357i \(0.530686\pi\)
\(74\) −1.26944 −0.147569
\(75\) 11.0533 1.27632
\(76\) 0.272395 0.0312458
\(77\) 0.706870 0.0805553
\(78\) 1.49922 0.169754
\(79\) 2.37919 0.267679 0.133840 0.991003i \(-0.457269\pi\)
0.133840 + 0.991003i \(0.457269\pi\)
\(80\) −0.859547 −0.0961003
\(81\) −6.28357 −0.698174
\(82\) 8.40030 0.927658
\(83\) −0.683145 −0.0749849 −0.0374925 0.999297i \(-0.511937\pi\)
−0.0374925 + 0.999297i \(0.511937\pi\)
\(84\) 8.54880 0.932751
\(85\) −5.17399 −0.561198
\(86\) 0.438888 0.0473266
\(87\) −9.89626 −1.06099
\(88\) 0.214484 0.0228641
\(89\) −16.0029 −1.69630 −0.848151 0.529755i \(-0.822284\pi\)
−0.848151 + 0.529755i \(0.822284\pi\)
\(90\) 3.20486 0.337822
\(91\) −1.90480 −0.199678
\(92\) 2.84049 0.296141
\(93\) −22.3668 −2.31933
\(94\) −7.89612 −0.814423
\(95\) −0.234136 −0.0240219
\(96\) 2.59394 0.264743
\(97\) 3.79190 0.385009 0.192505 0.981296i \(-0.438339\pi\)
0.192505 + 0.981296i \(0.438339\pi\)
\(98\) −3.86149 −0.390069
\(99\) −0.799715 −0.0803743
\(100\) −4.26118 −0.426118
\(101\) −7.52717 −0.748981 −0.374491 0.927231i \(-0.622182\pi\)
−0.374491 + 0.927231i \(0.622182\pi\)
\(102\) 15.6141 1.54603
\(103\) −0.884886 −0.0871904 −0.0435952 0.999049i \(-0.513881\pi\)
−0.0435952 + 0.999049i \(0.513881\pi\)
\(104\) −0.577971 −0.0566747
\(105\) −7.34810 −0.717101
\(106\) −12.2211 −1.18702
\(107\) −6.22409 −0.601705 −0.300853 0.953671i \(-0.597271\pi\)
−0.300853 + 0.953671i \(0.597271\pi\)
\(108\) −1.88982 −0.181848
\(109\) −16.8282 −1.61185 −0.805924 0.592020i \(-0.798331\pi\)
−0.805924 + 0.592020i \(0.798331\pi\)
\(110\) −0.184359 −0.0175780
\(111\) −3.29286 −0.312544
\(112\) −3.29568 −0.311412
\(113\) −10.5751 −0.994823 −0.497412 0.867515i \(-0.665716\pi\)
−0.497412 + 0.867515i \(0.665716\pi\)
\(114\) 0.706577 0.0661770
\(115\) −2.44153 −0.227674
\(116\) 3.81514 0.354227
\(117\) 2.15499 0.199229
\(118\) 3.37745 0.310919
\(119\) −19.8381 −1.81856
\(120\) −2.22962 −0.203535
\(121\) −10.9540 −0.995818
\(122\) 9.85667 0.892381
\(123\) 21.7899 1.96473
\(124\) 8.62269 0.774341
\(125\) 7.96042 0.712001
\(126\) 12.2881 1.09471
\(127\) 0.441878 0.0392103 0.0196052 0.999808i \(-0.493759\pi\)
0.0196052 + 0.999808i \(0.493759\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.13845 0.100235
\(130\) 0.496793 0.0435716
\(131\) 11.5681 1.01071 0.505353 0.862913i \(-0.331362\pi\)
0.505353 + 0.862913i \(0.331362\pi\)
\(132\) 0.556360 0.0484249
\(133\) −0.897726 −0.0778427
\(134\) −6.77627 −0.585381
\(135\) 1.62439 0.139805
\(136\) −6.01944 −0.516163
\(137\) −0.498277 −0.0425707 −0.0212853 0.999773i \(-0.506776\pi\)
−0.0212853 + 0.999773i \(0.506776\pi\)
\(138\) 7.36806 0.627211
\(139\) 16.9212 1.43524 0.717619 0.696436i \(-0.245232\pi\)
0.717619 + 0.696436i \(0.245232\pi\)
\(140\) 2.83279 0.239414
\(141\) −20.4821 −1.72490
\(142\) −14.8404 −1.24538
\(143\) −0.123965 −0.0103665
\(144\) 3.72855 0.310712
\(145\) −3.27929 −0.272330
\(146\) 1.64480 0.136125
\(147\) −10.0165 −0.826145
\(148\) 1.26944 0.104347
\(149\) 16.0277 1.31304 0.656520 0.754309i \(-0.272028\pi\)
0.656520 + 0.754309i \(0.272028\pi\)
\(150\) −11.0533 −0.902495
\(151\) 7.91714 0.644288 0.322144 0.946691i \(-0.395597\pi\)
0.322144 + 0.946691i \(0.395597\pi\)
\(152\) −0.272395 −0.0220941
\(153\) 22.4438 1.81447
\(154\) −0.706870 −0.0569612
\(155\) −7.41161 −0.595315
\(156\) −1.49922 −0.120034
\(157\) −5.37384 −0.428879 −0.214440 0.976737i \(-0.568793\pi\)
−0.214440 + 0.976737i \(0.568793\pi\)
\(158\) −2.37919 −0.189278
\(159\) −31.7008 −2.51404
\(160\) 0.859547 0.0679531
\(161\) −9.36132 −0.737776
\(162\) 6.28357 0.493684
\(163\) 12.4404 0.974410 0.487205 0.873288i \(-0.338016\pi\)
0.487205 + 0.873288i \(0.338016\pi\)
\(164\) −8.40030 −0.655953
\(165\) −0.478217 −0.0372292
\(166\) 0.683145 0.0530223
\(167\) −20.0060 −1.54811 −0.774057 0.633116i \(-0.781776\pi\)
−0.774057 + 0.633116i \(0.781776\pi\)
\(168\) −8.54880 −0.659555
\(169\) −12.6660 −0.974304
\(170\) 5.17399 0.396827
\(171\) 1.01564 0.0776678
\(172\) −0.438888 −0.0334649
\(173\) 18.5547 1.41068 0.705342 0.708867i \(-0.250793\pi\)
0.705342 + 0.708867i \(0.250793\pi\)
\(174\) 9.89626 0.750233
\(175\) 14.0435 1.06159
\(176\) −0.214484 −0.0161673
\(177\) 8.76091 0.658510
\(178\) 16.0029 1.19947
\(179\) 13.2578 0.990933 0.495466 0.868627i \(-0.334997\pi\)
0.495466 + 0.868627i \(0.334997\pi\)
\(180\) −3.20486 −0.238876
\(181\) −3.73076 −0.277305 −0.138653 0.990341i \(-0.544277\pi\)
−0.138653 + 0.990341i \(0.544277\pi\)
\(182\) 1.90480 0.141193
\(183\) 25.5676 1.89001
\(184\) −2.84049 −0.209403
\(185\) −1.09114 −0.0802224
\(186\) 22.3668 1.64001
\(187\) −1.29107 −0.0944127
\(188\) 7.89612 0.575884
\(189\) 6.22823 0.453037
\(190\) 0.234136 0.0169860
\(191\) 16.8251 1.21742 0.608709 0.793393i \(-0.291688\pi\)
0.608709 + 0.793393i \(0.291688\pi\)
\(192\) −2.59394 −0.187202
\(193\) −2.81052 −0.202306 −0.101153 0.994871i \(-0.532253\pi\)
−0.101153 + 0.994871i \(0.532253\pi\)
\(194\) −3.79190 −0.272242
\(195\) 1.28865 0.0922824
\(196\) 3.86149 0.275820
\(197\) −16.4126 −1.16935 −0.584676 0.811267i \(-0.698778\pi\)
−0.584676 + 0.811267i \(0.698778\pi\)
\(198\) 0.799715 0.0568332
\(199\) 14.8153 1.05023 0.525116 0.851031i \(-0.324022\pi\)
0.525116 + 0.851031i \(0.324022\pi\)
\(200\) 4.26118 0.301311
\(201\) −17.5773 −1.23981
\(202\) 7.52717 0.529610
\(203\) −12.5735 −0.882484
\(204\) −15.6141 −1.09320
\(205\) 7.22045 0.504298
\(206\) 0.884886 0.0616530
\(207\) 10.5909 0.736118
\(208\) 0.577971 0.0400750
\(209\) −0.0584244 −0.00404130
\(210\) 7.34810 0.507067
\(211\) −15.7474 −1.08410 −0.542049 0.840347i \(-0.682351\pi\)
−0.542049 + 0.840347i \(0.682351\pi\)
\(212\) 12.2211 0.839347
\(213\) −38.4952 −2.63765
\(214\) 6.22409 0.425470
\(215\) 0.377245 0.0257279
\(216\) 1.88982 0.128586
\(217\) −28.4176 −1.92911
\(218\) 16.8282 1.13975
\(219\) 4.26652 0.288305
\(220\) 0.184359 0.0124295
\(221\) 3.47906 0.234027
\(222\) 3.29286 0.221002
\(223\) 7.69950 0.515597 0.257798 0.966199i \(-0.417003\pi\)
0.257798 + 0.966199i \(0.417003\pi\)
\(224\) 3.29568 0.220202
\(225\) −15.8880 −1.05920
\(226\) 10.5751 0.703446
\(227\) 12.9742 0.861129 0.430565 0.902560i \(-0.358314\pi\)
0.430565 + 0.902560i \(0.358314\pi\)
\(228\) −0.706577 −0.0467942
\(229\) −4.83978 −0.319822 −0.159911 0.987131i \(-0.551121\pi\)
−0.159911 + 0.987131i \(0.551121\pi\)
\(230\) 2.44153 0.160990
\(231\) −1.83358 −0.120641
\(232\) −3.81514 −0.250476
\(233\) 12.1250 0.794333 0.397166 0.917747i \(-0.369994\pi\)
0.397166 + 0.917747i \(0.369994\pi\)
\(234\) −2.15499 −0.140876
\(235\) −6.78709 −0.442741
\(236\) −3.37745 −0.219853
\(237\) −6.17148 −0.400881
\(238\) 19.8381 1.28591
\(239\) −28.8855 −1.86845 −0.934225 0.356684i \(-0.883907\pi\)
−0.934225 + 0.356684i \(0.883907\pi\)
\(240\) 2.22962 0.143921
\(241\) 14.6062 0.940866 0.470433 0.882436i \(-0.344098\pi\)
0.470433 + 0.882436i \(0.344098\pi\)
\(242\) 10.9540 0.704150
\(243\) 21.9687 1.40929
\(244\) −9.85667 −0.631008
\(245\) −3.31913 −0.212051
\(246\) −21.7899 −1.38927
\(247\) 0.157436 0.0100174
\(248\) −8.62269 −0.547541
\(249\) 1.77204 0.112298
\(250\) −7.96042 −0.503461
\(251\) −29.9159 −1.88827 −0.944137 0.329553i \(-0.893102\pi\)
−0.944137 + 0.329553i \(0.893102\pi\)
\(252\) −12.2881 −0.774077
\(253\) −0.609239 −0.0383025
\(254\) −0.441878 −0.0277259
\(255\) 13.4210 0.840458
\(256\) 1.00000 0.0625000
\(257\) −18.0859 −1.12817 −0.564084 0.825718i \(-0.690770\pi\)
−0.564084 + 0.825718i \(0.690770\pi\)
\(258\) −1.13845 −0.0708769
\(259\) −4.18366 −0.259960
\(260\) −0.496793 −0.0308098
\(261\) 14.2249 0.880501
\(262\) −11.5681 −0.714677
\(263\) −15.2492 −0.940304 −0.470152 0.882585i \(-0.655801\pi\)
−0.470152 + 0.882585i \(0.655801\pi\)
\(264\) −0.556360 −0.0342416
\(265\) −10.5046 −0.645292
\(266\) 0.897726 0.0550431
\(267\) 41.5106 2.54041
\(268\) 6.77627 0.413927
\(269\) −15.9496 −0.972465 −0.486233 0.873829i \(-0.661629\pi\)
−0.486233 + 0.873829i \(0.661629\pi\)
\(270\) −1.62439 −0.0988571
\(271\) 24.3920 1.48171 0.740855 0.671665i \(-0.234420\pi\)
0.740855 + 0.671665i \(0.234420\pi\)
\(272\) 6.01944 0.364982
\(273\) 4.94096 0.299040
\(274\) 0.498277 0.0301020
\(275\) 0.913955 0.0551136
\(276\) −7.36806 −0.443505
\(277\) −6.85269 −0.411738 −0.205869 0.978580i \(-0.566002\pi\)
−0.205869 + 0.978580i \(0.566002\pi\)
\(278\) −16.9212 −1.01487
\(279\) 32.1501 1.92478
\(280\) −2.83279 −0.169291
\(281\) 2.93915 0.175335 0.0876676 0.996150i \(-0.472059\pi\)
0.0876676 + 0.996150i \(0.472059\pi\)
\(282\) 20.4821 1.21969
\(283\) −22.1499 −1.31667 −0.658336 0.752724i \(-0.728740\pi\)
−0.658336 + 0.752724i \(0.728740\pi\)
\(284\) 14.8404 0.880617
\(285\) 0.607336 0.0359755
\(286\) 0.123965 0.00733023
\(287\) 27.6847 1.63418
\(288\) −3.72855 −0.219707
\(289\) 19.2336 1.13139
\(290\) 3.27929 0.192567
\(291\) −9.83598 −0.576595
\(292\) −1.64480 −0.0962546
\(293\) −2.73354 −0.159695 −0.0798476 0.996807i \(-0.525443\pi\)
−0.0798476 + 0.996807i \(0.525443\pi\)
\(294\) 10.0165 0.584173
\(295\) 2.90307 0.169023
\(296\) −1.26944 −0.0737847
\(297\) 0.405336 0.0235200
\(298\) −16.0277 −0.928459
\(299\) 1.64172 0.0949430
\(300\) 11.0533 0.638160
\(301\) 1.44643 0.0833711
\(302\) −7.91714 −0.455580
\(303\) 19.5251 1.12169
\(304\) 0.272395 0.0156229
\(305\) 8.47227 0.485121
\(306\) −22.4438 −1.28303
\(307\) 9.36898 0.534716 0.267358 0.963597i \(-0.413849\pi\)
0.267358 + 0.963597i \(0.413849\pi\)
\(308\) 0.706870 0.0402777
\(309\) 2.29535 0.130578
\(310\) 7.41161 0.420951
\(311\) −25.2611 −1.43242 −0.716211 0.697883i \(-0.754125\pi\)
−0.716211 + 0.697883i \(0.754125\pi\)
\(312\) 1.49922 0.0848768
\(313\) −4.99421 −0.282289 −0.141145 0.989989i \(-0.545078\pi\)
−0.141145 + 0.989989i \(0.545078\pi\)
\(314\) 5.37384 0.303263
\(315\) 10.5622 0.595112
\(316\) 2.37919 0.133840
\(317\) 13.3623 0.750503 0.375251 0.926923i \(-0.377556\pi\)
0.375251 + 0.926923i \(0.377556\pi\)
\(318\) 31.7008 1.77769
\(319\) −0.818286 −0.0458152
\(320\) −0.859547 −0.0480501
\(321\) 16.1449 0.901123
\(322\) 9.36132 0.521686
\(323\) 1.63966 0.0912334
\(324\) −6.28357 −0.349087
\(325\) −2.46284 −0.136614
\(326\) −12.4404 −0.689012
\(327\) 43.6514 2.41393
\(328\) 8.40030 0.463829
\(329\) −26.0231 −1.43470
\(330\) 0.478217 0.0263250
\(331\) −16.1125 −0.885624 −0.442812 0.896614i \(-0.646019\pi\)
−0.442812 + 0.896614i \(0.646019\pi\)
\(332\) −0.683145 −0.0374925
\(333\) 4.73317 0.259376
\(334\) 20.0060 1.09468
\(335\) −5.82452 −0.318228
\(336\) 8.54880 0.466375
\(337\) −0.830310 −0.0452299 −0.0226149 0.999744i \(-0.507199\pi\)
−0.0226149 + 0.999744i \(0.507199\pi\)
\(338\) 12.6660 0.688937
\(339\) 27.4313 1.48986
\(340\) −5.17399 −0.280599
\(341\) −1.84943 −0.100152
\(342\) −1.01564 −0.0549194
\(343\) 10.3435 0.558498
\(344\) 0.438888 0.0236633
\(345\) 6.33320 0.340968
\(346\) −18.5547 −0.997505
\(347\) −5.79706 −0.311202 −0.155601 0.987820i \(-0.549731\pi\)
−0.155601 + 0.987820i \(0.549731\pi\)
\(348\) −9.89626 −0.530495
\(349\) 13.0665 0.699432 0.349716 0.936856i \(-0.386278\pi\)
0.349716 + 0.936856i \(0.386278\pi\)
\(350\) −14.0435 −0.750655
\(351\) −1.09226 −0.0583005
\(352\) 0.214484 0.0114320
\(353\) 28.8089 1.53334 0.766672 0.642038i \(-0.221911\pi\)
0.766672 + 0.642038i \(0.221911\pi\)
\(354\) −8.76091 −0.465637
\(355\) −12.7560 −0.677020
\(356\) −16.0029 −0.848151
\(357\) 51.4590 2.72350
\(358\) −13.2578 −0.700695
\(359\) 17.9892 0.949432 0.474716 0.880139i \(-0.342551\pi\)
0.474716 + 0.880139i \(0.342551\pi\)
\(360\) 3.20486 0.168911
\(361\) −18.9258 −0.996095
\(362\) 3.73076 0.196084
\(363\) 28.4141 1.49135
\(364\) −1.90480 −0.0998389
\(365\) 1.41378 0.0740008
\(366\) −25.5676 −1.33644
\(367\) −12.6204 −0.658778 −0.329389 0.944194i \(-0.606843\pi\)
−0.329389 + 0.944194i \(0.606843\pi\)
\(368\) 2.84049 0.148071
\(369\) −31.3209 −1.63050
\(370\) 1.09114 0.0567258
\(371\) −40.2767 −2.09106
\(372\) −22.3668 −1.15966
\(373\) 31.7521 1.64406 0.822031 0.569443i \(-0.192841\pi\)
0.822031 + 0.569443i \(0.192841\pi\)
\(374\) 1.29107 0.0667598
\(375\) −20.6489 −1.06630
\(376\) −7.89612 −0.407212
\(377\) 2.20504 0.113565
\(378\) −6.22823 −0.320346
\(379\) −36.0652 −1.85254 −0.926272 0.376855i \(-0.877006\pi\)
−0.926272 + 0.376855i \(0.877006\pi\)
\(380\) −0.234136 −0.0120109
\(381\) −1.14621 −0.0587220
\(382\) −16.8251 −0.860845
\(383\) −30.2081 −1.54356 −0.771781 0.635889i \(-0.780634\pi\)
−0.771781 + 0.635889i \(0.780634\pi\)
\(384\) 2.59394 0.132372
\(385\) −0.607588 −0.0309656
\(386\) 2.81052 0.143052
\(387\) −1.63642 −0.0831838
\(388\) 3.79190 0.192505
\(389\) 20.5431 1.04158 0.520789 0.853686i \(-0.325638\pi\)
0.520789 + 0.853686i \(0.325638\pi\)
\(390\) −1.28865 −0.0652535
\(391\) 17.0981 0.864690
\(392\) −3.86149 −0.195034
\(393\) −30.0069 −1.51365
\(394\) 16.4126 0.826856
\(395\) −2.04502 −0.102896
\(396\) −0.799715 −0.0401872
\(397\) 21.4893 1.07852 0.539258 0.842141i \(-0.318705\pi\)
0.539258 + 0.842141i \(0.318705\pi\)
\(398\) −14.8153 −0.742626
\(399\) 2.32865 0.116578
\(400\) −4.26118 −0.213059
\(401\) −37.0212 −1.84875 −0.924376 0.381483i \(-0.875413\pi\)
−0.924376 + 0.381483i \(0.875413\pi\)
\(402\) 17.5773 0.876675
\(403\) 4.98366 0.248254
\(404\) −7.52717 −0.374491
\(405\) 5.40102 0.268379
\(406\) 12.5735 0.624010
\(407\) −0.272275 −0.0134962
\(408\) 15.6141 0.773013
\(409\) −20.3727 −1.00736 −0.503682 0.863889i \(-0.668022\pi\)
−0.503682 + 0.863889i \(0.668022\pi\)
\(410\) −7.22045 −0.356593
\(411\) 1.29250 0.0637545
\(412\) −0.884886 −0.0435952
\(413\) 11.1310 0.547719
\(414\) −10.5909 −0.520514
\(415\) 0.587195 0.0288243
\(416\) −0.577971 −0.0283373
\(417\) −43.8927 −2.14943
\(418\) 0.0584244 0.00285763
\(419\) 28.1112 1.37332 0.686661 0.726978i \(-0.259076\pi\)
0.686661 + 0.726978i \(0.259076\pi\)
\(420\) −7.34810 −0.358550
\(421\) −0.202907 −0.00988910 −0.00494455 0.999988i \(-0.501574\pi\)
−0.00494455 + 0.999988i \(0.501574\pi\)
\(422\) 15.7474 0.766573
\(423\) 29.4411 1.43147
\(424\) −12.2211 −0.593508
\(425\) −25.6499 −1.24420
\(426\) 38.4952 1.86510
\(427\) 32.4844 1.57203
\(428\) −6.22409 −0.300853
\(429\) 0.321560 0.0155250
\(430\) −0.377245 −0.0181924
\(431\) 12.4226 0.598376 0.299188 0.954194i \(-0.403284\pi\)
0.299188 + 0.954194i \(0.403284\pi\)
\(432\) −1.88982 −0.0909239
\(433\) 31.2682 1.50266 0.751328 0.659929i \(-0.229414\pi\)
0.751328 + 0.659929i \(0.229414\pi\)
\(434\) 28.4176 1.36409
\(435\) 8.50630 0.407846
\(436\) −16.8282 −0.805924
\(437\) 0.773734 0.0370127
\(438\) −4.26652 −0.203862
\(439\) 20.9378 0.999304 0.499652 0.866226i \(-0.333461\pi\)
0.499652 + 0.866226i \(0.333461\pi\)
\(440\) −0.184359 −0.00878898
\(441\) 14.3977 0.685607
\(442\) −3.47906 −0.165482
\(443\) 12.4567 0.591836 0.295918 0.955213i \(-0.404375\pi\)
0.295918 + 0.955213i \(0.404375\pi\)
\(444\) −3.29286 −0.156272
\(445\) 13.7552 0.652060
\(446\) −7.69950 −0.364582
\(447\) −41.5749 −1.96643
\(448\) −3.29568 −0.155706
\(449\) 5.45129 0.257262 0.128631 0.991693i \(-0.458942\pi\)
0.128631 + 0.991693i \(0.458942\pi\)
\(450\) 15.8880 0.748968
\(451\) 1.80173 0.0848402
\(452\) −10.5751 −0.497412
\(453\) −20.5366 −0.964895
\(454\) −12.9742 −0.608910
\(455\) 1.63727 0.0767563
\(456\) 0.706577 0.0330885
\(457\) 36.5002 1.70741 0.853703 0.520760i \(-0.174351\pi\)
0.853703 + 0.520760i \(0.174351\pi\)
\(458\) 4.83978 0.226148
\(459\) −11.3756 −0.530970
\(460\) −2.44153 −0.113837
\(461\) 16.5147 0.769167 0.384583 0.923090i \(-0.374345\pi\)
0.384583 + 0.923090i \(0.374345\pi\)
\(462\) 1.83358 0.0853060
\(463\) 12.7582 0.592923 0.296461 0.955045i \(-0.404193\pi\)
0.296461 + 0.955045i \(0.404193\pi\)
\(464\) 3.81514 0.177113
\(465\) 19.2253 0.891552
\(466\) −12.1250 −0.561678
\(467\) 5.22843 0.241943 0.120971 0.992656i \(-0.461399\pi\)
0.120971 + 0.992656i \(0.461399\pi\)
\(468\) 2.15499 0.0996145
\(469\) −22.3324 −1.03121
\(470\) 6.78709 0.313065
\(471\) 13.9394 0.642296
\(472\) 3.37745 0.155460
\(473\) 0.0941346 0.00432831
\(474\) 6.17148 0.283465
\(475\) −1.16072 −0.0532577
\(476\) −19.8381 −0.909279
\(477\) 45.5669 2.08636
\(478\) 28.8855 1.32119
\(479\) −0.185788 −0.00848889 −0.00424445 0.999991i \(-0.501351\pi\)
−0.00424445 + 0.999991i \(0.501351\pi\)
\(480\) −2.22962 −0.101768
\(481\) 0.733699 0.0334538
\(482\) −14.6062 −0.665293
\(483\) 24.2828 1.10490
\(484\) −10.9540 −0.497909
\(485\) −3.25932 −0.147998
\(486\) −21.9687 −0.996519
\(487\) −5.11940 −0.231982 −0.115991 0.993250i \(-0.537004\pi\)
−0.115991 + 0.993250i \(0.537004\pi\)
\(488\) 9.85667 0.446190
\(489\) −32.2698 −1.45929
\(490\) 3.31913 0.149943
\(491\) 18.1467 0.818951 0.409476 0.912321i \(-0.365712\pi\)
0.409476 + 0.912321i \(0.365712\pi\)
\(492\) 21.7899 0.982365
\(493\) 22.9650 1.03429
\(494\) −0.157436 −0.00708339
\(495\) 0.687392 0.0308960
\(496\) 8.62269 0.387170
\(497\) −48.9092 −2.19388
\(498\) −1.77204 −0.0794070
\(499\) −20.2236 −0.905335 −0.452667 0.891679i \(-0.649528\pi\)
−0.452667 + 0.891679i \(0.649528\pi\)
\(500\) 7.96042 0.356001
\(501\) 51.8946 2.31848
\(502\) 29.9159 1.33521
\(503\) 11.2702 0.502513 0.251257 0.967920i \(-0.419156\pi\)
0.251257 + 0.967920i \(0.419156\pi\)
\(504\) 12.2881 0.547355
\(505\) 6.46995 0.287909
\(506\) 0.609239 0.0270840
\(507\) 32.8548 1.45913
\(508\) 0.441878 0.0196052
\(509\) −11.5245 −0.510814 −0.255407 0.966834i \(-0.582209\pi\)
−0.255407 + 0.966834i \(0.582209\pi\)
\(510\) −13.4210 −0.594294
\(511\) 5.42073 0.239799
\(512\) −1.00000 −0.0441942
\(513\) −0.514777 −0.0227280
\(514\) 18.0859 0.797735
\(515\) 0.760601 0.0335161
\(516\) 1.13845 0.0501176
\(517\) −1.69359 −0.0744841
\(518\) 4.18366 0.183820
\(519\) −48.1298 −2.11266
\(520\) 0.496793 0.0217858
\(521\) 31.5858 1.38380 0.691900 0.721993i \(-0.256774\pi\)
0.691900 + 0.721993i \(0.256774\pi\)
\(522\) −14.2249 −0.622608
\(523\) −4.78787 −0.209359 −0.104679 0.994506i \(-0.533382\pi\)
−0.104679 + 0.994506i \(0.533382\pi\)
\(524\) 11.5681 0.505353
\(525\) −36.4280 −1.58985
\(526\) 15.2492 0.664896
\(527\) 51.9038 2.26096
\(528\) 0.556360 0.0242125
\(529\) −14.9316 −0.649202
\(530\) 10.5046 0.456290
\(531\) −12.5930 −0.546489
\(532\) −0.897726 −0.0389213
\(533\) −4.85513 −0.210299
\(534\) −41.5106 −1.79634
\(535\) 5.34990 0.231296
\(536\) −6.77627 −0.292690
\(537\) −34.3899 −1.48404
\(538\) 15.9496 0.687637
\(539\) −0.828227 −0.0356743
\(540\) 1.62439 0.0699025
\(541\) 6.62763 0.284944 0.142472 0.989799i \(-0.454495\pi\)
0.142472 + 0.989799i \(0.454495\pi\)
\(542\) −24.3920 −1.04773
\(543\) 9.67738 0.415296
\(544\) −6.01944 −0.258081
\(545\) 14.4646 0.619596
\(546\) −4.94096 −0.211453
\(547\) 32.1201 1.37335 0.686677 0.726962i \(-0.259068\pi\)
0.686677 + 0.726962i \(0.259068\pi\)
\(548\) −0.498277 −0.0212853
\(549\) −36.7511 −1.56850
\(550\) −0.913955 −0.0389712
\(551\) 1.03922 0.0442724
\(552\) 7.36806 0.313606
\(553\) −7.84103 −0.333435
\(554\) 6.85269 0.291143
\(555\) 2.83037 0.120142
\(556\) 16.9212 0.717619
\(557\) 33.9454 1.43831 0.719157 0.694848i \(-0.244528\pi\)
0.719157 + 0.694848i \(0.244528\pi\)
\(558\) −32.1501 −1.36102
\(559\) −0.253665 −0.0107289
\(560\) 2.83279 0.119707
\(561\) 3.34897 0.141394
\(562\) −2.93915 −0.123981
\(563\) −16.5135 −0.695961 −0.347981 0.937502i \(-0.613132\pi\)
−0.347981 + 0.937502i \(0.613132\pi\)
\(564\) −20.4821 −0.862452
\(565\) 9.08981 0.382411
\(566\) 22.1499 0.931028
\(567\) 20.7086 0.869680
\(568\) −14.8404 −0.622690
\(569\) −31.1502 −1.30588 −0.652942 0.757408i \(-0.726465\pi\)
−0.652942 + 0.757408i \(0.726465\pi\)
\(570\) −0.607336 −0.0254385
\(571\) −15.4768 −0.647684 −0.323842 0.946111i \(-0.604975\pi\)
−0.323842 + 0.946111i \(0.604975\pi\)
\(572\) −0.123965 −0.00518326
\(573\) −43.6433 −1.82322
\(574\) −27.6847 −1.15554
\(575\) −12.1038 −0.504764
\(576\) 3.72855 0.155356
\(577\) 24.4444 1.01763 0.508817 0.860875i \(-0.330083\pi\)
0.508817 + 0.860875i \(0.330083\pi\)
\(578\) −19.2336 −0.800014
\(579\) 7.29033 0.302976
\(580\) −3.27929 −0.136165
\(581\) 2.25142 0.0934048
\(582\) 9.83598 0.407714
\(583\) −2.62123 −0.108560
\(584\) 1.64480 0.0680623
\(585\) −1.85232 −0.0765839
\(586\) 2.73354 0.112922
\(587\) 32.8941 1.35769 0.678843 0.734283i \(-0.262482\pi\)
0.678843 + 0.734283i \(0.262482\pi\)
\(588\) −10.0165 −0.413073
\(589\) 2.34878 0.0967797
\(590\) −2.90307 −0.119518
\(591\) 42.5735 1.75124
\(592\) 1.26944 0.0521737
\(593\) −5.82300 −0.239122 −0.119561 0.992827i \(-0.538149\pi\)
−0.119561 + 0.992827i \(0.538149\pi\)
\(594\) −0.405336 −0.0166311
\(595\) 17.0518 0.699055
\(596\) 16.0277 0.656520
\(597\) −38.4302 −1.57284
\(598\) −1.64172 −0.0671348
\(599\) −27.9900 −1.14364 −0.571820 0.820379i \(-0.693762\pi\)
−0.571820 + 0.820379i \(0.693762\pi\)
\(600\) −11.0533 −0.451248
\(601\) −10.4177 −0.424947 −0.212474 0.977167i \(-0.568152\pi\)
−0.212474 + 0.977167i \(0.568152\pi\)
\(602\) −1.44643 −0.0589523
\(603\) 25.2657 1.02890
\(604\) 7.91714 0.322144
\(605\) 9.41547 0.382793
\(606\) −19.5251 −0.793151
\(607\) 34.1311 1.38534 0.692670 0.721255i \(-0.256434\pi\)
0.692670 + 0.721255i \(0.256434\pi\)
\(608\) −0.272395 −0.0110471
\(609\) 32.6149 1.32162
\(610\) −8.47227 −0.343032
\(611\) 4.56373 0.184629
\(612\) 22.4438 0.907236
\(613\) 47.1809 1.90562 0.952810 0.303567i \(-0.0981776\pi\)
0.952810 + 0.303567i \(0.0981776\pi\)
\(614\) −9.36898 −0.378101
\(615\) −18.7295 −0.755245
\(616\) −0.706870 −0.0284806
\(617\) 0.729747 0.0293785 0.0146893 0.999892i \(-0.495324\pi\)
0.0146893 + 0.999892i \(0.495324\pi\)
\(618\) −2.29535 −0.0923324
\(619\) 3.58031 0.143905 0.0719524 0.997408i \(-0.477077\pi\)
0.0719524 + 0.997408i \(0.477077\pi\)
\(620\) −7.41161 −0.297657
\(621\) −5.36800 −0.215410
\(622\) 25.2611 1.01288
\(623\) 52.7403 2.11300
\(624\) −1.49922 −0.0600170
\(625\) 14.4635 0.578542
\(626\) 4.99421 0.199609
\(627\) 0.151550 0.00605231
\(628\) −5.37384 −0.214440
\(629\) 7.64132 0.304679
\(630\) −10.5622 −0.420808
\(631\) −3.61541 −0.143927 −0.0719636 0.997407i \(-0.522927\pi\)
−0.0719636 + 0.997407i \(0.522927\pi\)
\(632\) −2.37919 −0.0946390
\(633\) 40.8480 1.62356
\(634\) −13.3623 −0.530686
\(635\) −0.379815 −0.0150725
\(636\) −31.7008 −1.25702
\(637\) 2.23182 0.0884281
\(638\) 0.818286 0.0323963
\(639\) 55.3332 2.18895
\(640\) 0.859547 0.0339766
\(641\) −25.7428 −1.01678 −0.508389 0.861128i \(-0.669759\pi\)
−0.508389 + 0.861128i \(0.669759\pi\)
\(642\) −16.1449 −0.637190
\(643\) 36.3175 1.43222 0.716110 0.697987i \(-0.245921\pi\)
0.716110 + 0.697987i \(0.245921\pi\)
\(644\) −9.36132 −0.368888
\(645\) −0.978553 −0.0385305
\(646\) −1.63966 −0.0645117
\(647\) 0.676228 0.0265853 0.0132926 0.999912i \(-0.495769\pi\)
0.0132926 + 0.999912i \(0.495769\pi\)
\(648\) 6.28357 0.246842
\(649\) 0.724408 0.0284355
\(650\) 2.46284 0.0966004
\(651\) 73.7137 2.88907
\(652\) 12.4404 0.487205
\(653\) −35.6870 −1.39654 −0.698269 0.715835i \(-0.746046\pi\)
−0.698269 + 0.715835i \(0.746046\pi\)
\(654\) −43.6514 −1.70690
\(655\) −9.94328 −0.388516
\(656\) −8.40030 −0.327977
\(657\) −6.13272 −0.239260
\(658\) 26.0231 1.01449
\(659\) 36.3846 1.41734 0.708672 0.705538i \(-0.249295\pi\)
0.708672 + 0.705538i \(0.249295\pi\)
\(660\) −0.478217 −0.0186146
\(661\) −4.21235 −0.163841 −0.0819207 0.996639i \(-0.526105\pi\)
−0.0819207 + 0.996639i \(0.526105\pi\)
\(662\) 16.1125 0.626231
\(663\) −9.02448 −0.350482
\(664\) 0.683145 0.0265112
\(665\) 0.771637 0.0299228
\(666\) −4.73317 −0.183407
\(667\) 10.8368 0.419604
\(668\) −20.0060 −0.774057
\(669\) −19.9721 −0.772165
\(670\) 5.82452 0.225021
\(671\) 2.11410 0.0816138
\(672\) −8.54880 −0.329777
\(673\) 40.4786 1.56033 0.780167 0.625571i \(-0.215134\pi\)
0.780167 + 0.625571i \(0.215134\pi\)
\(674\) 0.830310 0.0319824
\(675\) 8.05285 0.309954
\(676\) −12.6660 −0.487152
\(677\) −7.86358 −0.302222 −0.151111 0.988517i \(-0.548285\pi\)
−0.151111 + 0.988517i \(0.548285\pi\)
\(678\) −27.4313 −1.05349
\(679\) −12.4969 −0.479586
\(680\) 5.17399 0.198413
\(681\) −33.6544 −1.28964
\(682\) 1.84943 0.0708183
\(683\) 15.3894 0.588858 0.294429 0.955673i \(-0.404871\pi\)
0.294429 + 0.955673i \(0.404871\pi\)
\(684\) 1.01564 0.0388339
\(685\) 0.428292 0.0163642
\(686\) −10.3435 −0.394918
\(687\) 12.5541 0.478969
\(688\) −0.438888 −0.0167325
\(689\) 7.06342 0.269095
\(690\) −6.33320 −0.241101
\(691\) −15.2466 −0.580007 −0.290004 0.957026i \(-0.593657\pi\)
−0.290004 + 0.957026i \(0.593657\pi\)
\(692\) 18.5547 0.705342
\(693\) 2.63560 0.100118
\(694\) 5.79706 0.220053
\(695\) −14.5446 −0.551707
\(696\) 9.89626 0.375117
\(697\) −50.5651 −1.91529
\(698\) −13.0665 −0.494573
\(699\) −31.4515 −1.18960
\(700\) 14.0435 0.530793
\(701\) 40.4465 1.52764 0.763822 0.645427i \(-0.223321\pi\)
0.763822 + 0.645427i \(0.223321\pi\)
\(702\) 1.09226 0.0412247
\(703\) 0.345789 0.0130417
\(704\) −0.214484 −0.00808367
\(705\) 17.6053 0.663055
\(706\) −28.8089 −1.08424
\(707\) 24.8071 0.932967
\(708\) 8.76091 0.329255
\(709\) −27.7344 −1.04159 −0.520794 0.853683i \(-0.674364\pi\)
−0.520794 + 0.853683i \(0.674364\pi\)
\(710\) 12.7560 0.478726
\(711\) 8.87092 0.332685
\(712\) 16.0029 0.599733
\(713\) 24.4926 0.917256
\(714\) −51.4590 −1.92580
\(715\) 0.106554 0.00398490
\(716\) 13.2578 0.495466
\(717\) 74.9275 2.79822
\(718\) −17.9892 −0.671350
\(719\) −42.3104 −1.57791 −0.788956 0.614450i \(-0.789378\pi\)
−0.788956 + 0.614450i \(0.789378\pi\)
\(720\) −3.20486 −0.119438
\(721\) 2.91630 0.108609
\(722\) 18.9258 0.704345
\(723\) −37.8876 −1.40906
\(724\) −3.73076 −0.138653
\(725\) −16.2570 −0.603769
\(726\) −28.4141 −1.05454
\(727\) −44.2633 −1.64164 −0.820818 0.571190i \(-0.806482\pi\)
−0.820818 + 0.571190i \(0.806482\pi\)
\(728\) 1.90480 0.0705967
\(729\) −38.1348 −1.41240
\(730\) −1.41378 −0.0523264
\(731\) −2.64186 −0.0977128
\(732\) 25.5676 0.945007
\(733\) 14.1990 0.524451 0.262226 0.965007i \(-0.415544\pi\)
0.262226 + 0.965007i \(0.415544\pi\)
\(734\) 12.6204 0.465826
\(735\) 8.60963 0.317571
\(736\) −2.84049 −0.104702
\(737\) −1.45340 −0.0535368
\(738\) 31.3209 1.15294
\(739\) 41.2777 1.51842 0.759212 0.650843i \(-0.225584\pi\)
0.759212 + 0.650843i \(0.225584\pi\)
\(740\) −1.09114 −0.0401112
\(741\) −0.408381 −0.0150022
\(742\) 40.2767 1.47860
\(743\) −19.6006 −0.719075 −0.359537 0.933131i \(-0.617066\pi\)
−0.359537 + 0.933131i \(0.617066\pi\)
\(744\) 22.3668 0.820006
\(745\) −13.7766 −0.504734
\(746\) −31.7521 −1.16253
\(747\) −2.54714 −0.0931950
\(748\) −1.29107 −0.0472063
\(749\) 20.5126 0.749514
\(750\) 20.6489 0.753991
\(751\) 39.8357 1.45363 0.726813 0.686835i \(-0.241001\pi\)
0.726813 + 0.686835i \(0.241001\pi\)
\(752\) 7.89612 0.287942
\(753\) 77.6002 2.82791
\(754\) −2.20504 −0.0803027
\(755\) −6.80515 −0.247665
\(756\) 6.22823 0.226519
\(757\) 14.5589 0.529151 0.264575 0.964365i \(-0.414768\pi\)
0.264575 + 0.964365i \(0.414768\pi\)
\(758\) 36.0652 1.30995
\(759\) 1.58033 0.0573624
\(760\) 0.234136 0.00849301
\(761\) −49.5646 −1.79671 −0.898357 0.439266i \(-0.855239\pi\)
−0.898357 + 0.439266i \(0.855239\pi\)
\(762\) 1.14621 0.0415227
\(763\) 55.4602 2.00780
\(764\) 16.8251 0.608709
\(765\) −19.2915 −0.697485
\(766\) 30.2081 1.09146
\(767\) −1.95206 −0.0704850
\(768\) −2.59394 −0.0936009
\(769\) 50.9074 1.83577 0.917885 0.396847i \(-0.129896\pi\)
0.917885 + 0.396847i \(0.129896\pi\)
\(770\) 0.607588 0.0218960
\(771\) 46.9138 1.68956
\(772\) −2.81052 −0.101153
\(773\) −42.4254 −1.52594 −0.762968 0.646436i \(-0.776259\pi\)
−0.762968 + 0.646436i \(0.776259\pi\)
\(774\) 1.63642 0.0588198
\(775\) −36.7428 −1.31984
\(776\) −3.79190 −0.136121
\(777\) 10.8522 0.389320
\(778\) −20.5431 −0.736507
\(779\) −2.28820 −0.0819833
\(780\) 1.28865 0.0461412
\(781\) −3.18303 −0.113898
\(782\) −17.0981 −0.611428
\(783\) −7.20992 −0.257661
\(784\) 3.86149 0.137910
\(785\) 4.61907 0.164862
\(786\) 30.0069 1.07031
\(787\) 8.75741 0.312168 0.156084 0.987744i \(-0.450113\pi\)
0.156084 + 0.987744i \(0.450113\pi\)
\(788\) −16.4126 −0.584676
\(789\) 39.5555 1.40821
\(790\) 2.04502 0.0727586
\(791\) 34.8522 1.23920
\(792\) 0.799715 0.0284166
\(793\) −5.69686 −0.202302
\(794\) −21.4893 −0.762626
\(795\) 27.2483 0.966398
\(796\) 14.8153 0.525116
\(797\) 2.31530 0.0820123 0.0410061 0.999159i \(-0.486944\pi\)
0.0410061 + 0.999159i \(0.486944\pi\)
\(798\) −2.32865 −0.0824333
\(799\) 47.5302 1.68150
\(800\) 4.26118 0.150655
\(801\) −59.6675 −2.10825
\(802\) 37.0212 1.30726
\(803\) 0.352783 0.0124495
\(804\) −17.5773 −0.619903
\(805\) 8.04650 0.283602
\(806\) −4.98366 −0.175542
\(807\) 41.3724 1.45638
\(808\) 7.52717 0.264805
\(809\) 52.1642 1.83399 0.916997 0.398893i \(-0.130606\pi\)
0.916997 + 0.398893i \(0.130606\pi\)
\(810\) −5.40102 −0.189772
\(811\) −44.2360 −1.55334 −0.776668 0.629910i \(-0.783092\pi\)
−0.776668 + 0.629910i \(0.783092\pi\)
\(812\) −12.5735 −0.441242
\(813\) −63.2716 −2.21903
\(814\) 0.272275 0.00954322
\(815\) −10.6931 −0.374564
\(816\) −15.6141 −0.546602
\(817\) −0.119551 −0.00418256
\(818\) 20.3727 0.712314
\(819\) −7.10216 −0.248169
\(820\) 7.22045 0.252149
\(821\) 28.3011 0.987714 0.493857 0.869543i \(-0.335587\pi\)
0.493857 + 0.869543i \(0.335587\pi\)
\(822\) −1.29250 −0.0450812
\(823\) 16.7863 0.585134 0.292567 0.956245i \(-0.405490\pi\)
0.292567 + 0.956245i \(0.405490\pi\)
\(824\) 0.884886 0.0308265
\(825\) −2.37075 −0.0825389
\(826\) −11.1310 −0.387296
\(827\) 34.8798 1.21289 0.606445 0.795126i \(-0.292595\pi\)
0.606445 + 0.795126i \(0.292595\pi\)
\(828\) 10.5909 0.368059
\(829\) 28.2720 0.981927 0.490964 0.871180i \(-0.336645\pi\)
0.490964 + 0.871180i \(0.336645\pi\)
\(830\) −0.587195 −0.0203818
\(831\) 17.7755 0.616625
\(832\) 0.577971 0.0200375
\(833\) 23.2440 0.805356
\(834\) 43.8927 1.51988
\(835\) 17.1961 0.595097
\(836\) −0.0584244 −0.00202065
\(837\) −16.2953 −0.563249
\(838\) −28.1112 −0.971085
\(839\) −33.8765 −1.16955 −0.584773 0.811197i \(-0.698816\pi\)
−0.584773 + 0.811197i \(0.698816\pi\)
\(840\) 7.34810 0.253533
\(841\) −14.4447 −0.498094
\(842\) 0.202907 0.00699265
\(843\) −7.62400 −0.262584
\(844\) −15.7474 −0.542049
\(845\) 10.8870 0.374523
\(846\) −29.4411 −1.01221
\(847\) 36.1008 1.24044
\(848\) 12.2211 0.419673
\(849\) 57.4555 1.97187
\(850\) 25.6499 0.879784
\(851\) 3.60583 0.123606
\(852\) −38.4952 −1.31882
\(853\) 16.7073 0.572049 0.286024 0.958222i \(-0.407666\pi\)
0.286024 + 0.958222i \(0.407666\pi\)
\(854\) −32.4844 −1.11159
\(855\) −0.872989 −0.0298556
\(856\) 6.22409 0.212735
\(857\) −35.9797 −1.22904 −0.614522 0.788900i \(-0.710651\pi\)
−0.614522 + 0.788900i \(0.710651\pi\)
\(858\) −0.321560 −0.0109779
\(859\) −26.9581 −0.919800 −0.459900 0.887971i \(-0.652115\pi\)
−0.459900 + 0.887971i \(0.652115\pi\)
\(860\) 0.377245 0.0128640
\(861\) −71.8125 −2.44736
\(862\) −12.4226 −0.423116
\(863\) −13.0122 −0.442940 −0.221470 0.975167i \(-0.571085\pi\)
−0.221470 + 0.975167i \(0.571085\pi\)
\(864\) 1.88982 0.0642929
\(865\) −15.9486 −0.542269
\(866\) −31.2682 −1.06254
\(867\) −49.8910 −1.69439
\(868\) −28.4176 −0.964556
\(869\) −0.510298 −0.0173107
\(870\) −8.50630 −0.288391
\(871\) 3.91649 0.132705
\(872\) 16.8282 0.569874
\(873\) 14.1383 0.478508
\(874\) −0.773734 −0.0261719
\(875\) −26.2350 −0.886904
\(876\) 4.26652 0.144152
\(877\) 43.3050 1.46231 0.731153 0.682213i \(-0.238983\pi\)
0.731153 + 0.682213i \(0.238983\pi\)
\(878\) −20.9378 −0.706615
\(879\) 7.09065 0.239162
\(880\) 0.184359 0.00621474
\(881\) −9.17571 −0.309137 −0.154569 0.987982i \(-0.549399\pi\)
−0.154569 + 0.987982i \(0.549399\pi\)
\(882\) −14.3977 −0.484797
\(883\) −50.5421 −1.70088 −0.850438 0.526076i \(-0.823663\pi\)
−0.850438 + 0.526076i \(0.823663\pi\)
\(884\) 3.47906 0.117013
\(885\) −7.53041 −0.253132
\(886\) −12.4567 −0.418491
\(887\) −9.05723 −0.304112 −0.152056 0.988372i \(-0.548589\pi\)
−0.152056 + 0.988372i \(0.548589\pi\)
\(888\) 3.29286 0.110501
\(889\) −1.45629 −0.0488423
\(890\) −13.7552 −0.461076
\(891\) 1.34772 0.0451505
\(892\) 7.69950 0.257798
\(893\) 2.15086 0.0719759
\(894\) 41.5749 1.39047
\(895\) −11.3957 −0.380916
\(896\) 3.29568 0.110101
\(897\) −4.25852 −0.142188
\(898\) −5.45129 −0.181912
\(899\) 32.8968 1.09717
\(900\) −15.8880 −0.529601
\(901\) 73.5640 2.45077
\(902\) −1.80173 −0.0599911
\(903\) −3.75197 −0.124858
\(904\) 10.5751 0.351723
\(905\) 3.20676 0.106596
\(906\) 20.5366 0.682284
\(907\) −35.2174 −1.16937 −0.584687 0.811259i \(-0.698783\pi\)
−0.584687 + 0.811259i \(0.698783\pi\)
\(908\) 12.9742 0.430565
\(909\) −28.0654 −0.930871
\(910\) −1.63727 −0.0542749
\(911\) 48.0050 1.59048 0.795238 0.606297i \(-0.207346\pi\)
0.795238 + 0.606297i \(0.207346\pi\)
\(912\) −0.706577 −0.0233971
\(913\) 0.146524 0.00484923
\(914\) −36.5002 −1.20732
\(915\) −21.9766 −0.726524
\(916\) −4.83978 −0.159911
\(917\) −38.1246 −1.25898
\(918\) 11.3756 0.375452
\(919\) −40.4524 −1.33440 −0.667200 0.744878i \(-0.732507\pi\)
−0.667200 + 0.744878i \(0.732507\pi\)
\(920\) 2.44153 0.0804949
\(921\) −24.3026 −0.800799
\(922\) −16.5147 −0.543883
\(923\) 8.57733 0.282326
\(924\) −1.83358 −0.0603204
\(925\) −5.40931 −0.177857
\(926\) −12.7582 −0.419260
\(927\) −3.29934 −0.108365
\(928\) −3.81514 −0.125238
\(929\) −4.72986 −0.155182 −0.0775909 0.996985i \(-0.524723\pi\)
−0.0775909 + 0.996985i \(0.524723\pi\)
\(930\) −19.2253 −0.630422
\(931\) 1.05185 0.0344730
\(932\) 12.1250 0.397166
\(933\) 65.5258 2.14522
\(934\) −5.22843 −0.171079
\(935\) 1.10974 0.0362923
\(936\) −2.15499 −0.0704381
\(937\) 40.5497 1.32470 0.662350 0.749195i \(-0.269559\pi\)
0.662350 + 0.749195i \(0.269559\pi\)
\(938\) 22.3324 0.729179
\(939\) 12.9547 0.422761
\(940\) −6.78709 −0.221370
\(941\) −19.6747 −0.641378 −0.320689 0.947184i \(-0.603914\pi\)
−0.320689 + 0.947184i \(0.603914\pi\)
\(942\) −13.9394 −0.454172
\(943\) −23.8609 −0.777019
\(944\) −3.37745 −0.109926
\(945\) −5.35345 −0.174148
\(946\) −0.0941346 −0.00306058
\(947\) −22.7788 −0.740212 −0.370106 0.928989i \(-0.620679\pi\)
−0.370106 + 0.928989i \(0.620679\pi\)
\(948\) −6.17148 −0.200440
\(949\) −0.950646 −0.0308593
\(950\) 1.16072 0.0376588
\(951\) −34.6611 −1.12396
\(952\) 19.8381 0.642957
\(953\) 2.67313 0.0865913 0.0432957 0.999062i \(-0.486214\pi\)
0.0432957 + 0.999062i \(0.486214\pi\)
\(954\) −45.5669 −1.47528
\(955\) −14.4619 −0.467977
\(956\) −28.8855 −0.934225
\(957\) 2.12259 0.0686136
\(958\) 0.185788 0.00600255
\(959\) 1.64216 0.0530281
\(960\) 2.22962 0.0719606
\(961\) 43.3508 1.39841
\(962\) −0.733699 −0.0236554
\(963\) −23.2068 −0.747830
\(964\) 14.6062 0.470433
\(965\) 2.41577 0.0777665
\(966\) −24.2828 −0.781285
\(967\) 59.0292 1.89825 0.949126 0.314896i \(-0.101970\pi\)
0.949126 + 0.314896i \(0.101970\pi\)
\(968\) 10.9540 0.352075
\(969\) −4.25320 −0.136632
\(970\) 3.25932 0.104650
\(971\) −38.8931 −1.24814 −0.624069 0.781369i \(-0.714522\pi\)
−0.624069 + 0.781369i \(0.714522\pi\)
\(972\) 21.9687 0.704646
\(973\) −55.7668 −1.78780
\(974\) 5.11940 0.164036
\(975\) 6.38846 0.204594
\(976\) −9.85667 −0.315504
\(977\) −32.4213 −1.03725 −0.518625 0.855002i \(-0.673556\pi\)
−0.518625 + 0.855002i \(0.673556\pi\)
\(978\) 32.2698 1.03187
\(979\) 3.43236 0.109699
\(980\) −3.31913 −0.106026
\(981\) −62.7447 −2.00328
\(982\) −18.1467 −0.579086
\(983\) 47.4266 1.51267 0.756337 0.654182i \(-0.226987\pi\)
0.756337 + 0.654182i \(0.226987\pi\)
\(984\) −21.7899 −0.694637
\(985\) 14.1074 0.449500
\(986\) −22.9650 −0.731354
\(987\) 67.5024 2.14863
\(988\) 0.157436 0.00500871
\(989\) −1.24666 −0.0396414
\(990\) −0.687392 −0.0218468
\(991\) 19.9541 0.633863 0.316931 0.948448i \(-0.397348\pi\)
0.316931 + 0.948448i \(0.397348\pi\)
\(992\) −8.62269 −0.273771
\(993\) 41.7950 1.32632
\(994\) 48.9092 1.55131
\(995\) −12.7345 −0.403710
\(996\) 1.77204 0.0561492
\(997\) −36.4276 −1.15367 −0.576836 0.816860i \(-0.695713\pi\)
−0.576836 + 0.816860i \(0.695713\pi\)
\(998\) 20.2236 0.640168
\(999\) −2.39901 −0.0759013
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 \(a_p\))