Properties

Label 8047.2.a.b.1.16
Level 8047
Weight 2
Character 8047.1
Self dual Yes
Analytic conductor 64.256
Analytic rank 1
Dimension 142
CM No

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Newspace parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2556185065\)
Analytic rank: \(1\)
Dimension: \(142\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.41564 q^{2} +2.60884 q^{3} +3.83533 q^{4} +1.90553 q^{5} -6.30203 q^{6} -0.0638029 q^{7} -4.43349 q^{8} +3.80607 q^{9} +O(q^{10})\) \(q-2.41564 q^{2} +2.60884 q^{3} +3.83533 q^{4} +1.90553 q^{5} -6.30203 q^{6} -0.0638029 q^{7} -4.43349 q^{8} +3.80607 q^{9} -4.60307 q^{10} -0.824160 q^{11} +10.0058 q^{12} +1.00000 q^{13} +0.154125 q^{14} +4.97122 q^{15} +3.03908 q^{16} +1.70186 q^{17} -9.19410 q^{18} -3.21690 q^{19} +7.30832 q^{20} -0.166452 q^{21} +1.99088 q^{22} -7.15699 q^{23} -11.5663 q^{24} -1.36897 q^{25} -2.41564 q^{26} +2.10290 q^{27} -0.244705 q^{28} -9.58079 q^{29} -12.0087 q^{30} +1.24948 q^{31} +1.52566 q^{32} -2.15010 q^{33} -4.11107 q^{34} -0.121578 q^{35} +14.5975 q^{36} +2.14765 q^{37} +7.77088 q^{38} +2.60884 q^{39} -8.44814 q^{40} -4.26465 q^{41} +0.402088 q^{42} +10.6940 q^{43} -3.16092 q^{44} +7.25257 q^{45} +17.2887 q^{46} -1.09153 q^{47} +7.92849 q^{48} -6.99593 q^{49} +3.30693 q^{50} +4.43988 q^{51} +3.83533 q^{52} -3.55456 q^{53} -5.07986 q^{54} -1.57046 q^{55} +0.282870 q^{56} -8.39239 q^{57} +23.1438 q^{58} -11.8914 q^{59} +19.0663 q^{60} -12.6040 q^{61} -3.01829 q^{62} -0.242838 q^{63} -9.76360 q^{64} +1.90553 q^{65} +5.19388 q^{66} -13.0800 q^{67} +6.52717 q^{68} -18.6715 q^{69} +0.293690 q^{70} +8.31218 q^{71} -16.8742 q^{72} -5.91273 q^{73} -5.18795 q^{74} -3.57142 q^{75} -12.3379 q^{76} +0.0525838 q^{77} -6.30203 q^{78} +7.96634 q^{79} +5.79105 q^{80} -5.93205 q^{81} +10.3019 q^{82} -5.46635 q^{83} -0.638398 q^{84} +3.24293 q^{85} -25.8329 q^{86} -24.9948 q^{87} +3.65391 q^{88} +7.57667 q^{89} -17.5196 q^{90} -0.0638029 q^{91} -27.4494 q^{92} +3.25969 q^{93} +2.63674 q^{94} -6.12989 q^{95} +3.98020 q^{96} +5.99226 q^{97} +16.8997 q^{98} -3.13681 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41564 −1.70812 −0.854058 0.520177i \(-0.825866\pi\)
−0.854058 + 0.520177i \(0.825866\pi\)
\(3\) 2.60884 1.50622 0.753108 0.657896i \(-0.228554\pi\)
0.753108 + 0.657896i \(0.228554\pi\)
\(4\) 3.83533 1.91766
\(5\) 1.90553 0.852178 0.426089 0.904681i \(-0.359891\pi\)
0.426089 + 0.904681i \(0.359891\pi\)
\(6\) −6.30203 −2.57279
\(7\) −0.0638029 −0.0241152 −0.0120576 0.999927i \(-0.503838\pi\)
−0.0120576 + 0.999927i \(0.503838\pi\)
\(8\) −4.43349 −1.56748
\(9\) 3.80607 1.26869
\(10\) −4.60307 −1.45562
\(11\) −0.824160 −0.248494 −0.124247 0.992251i \(-0.539651\pi\)
−0.124247 + 0.992251i \(0.539651\pi\)
\(12\) 10.0058 2.88842
\(13\) 1.00000 0.277350
\(14\) 0.154125 0.0411917
\(15\) 4.97122 1.28356
\(16\) 3.03908 0.759770
\(17\) 1.70186 0.412761 0.206380 0.978472i \(-0.433832\pi\)
0.206380 + 0.978472i \(0.433832\pi\)
\(18\) −9.19410 −2.16707
\(19\) −3.21690 −0.738008 −0.369004 0.929428i \(-0.620301\pi\)
−0.369004 + 0.929428i \(0.620301\pi\)
\(20\) 7.30832 1.63419
\(21\) −0.166452 −0.0363228
\(22\) 1.99088 0.424456
\(23\) −7.15699 −1.49234 −0.746168 0.665758i \(-0.768108\pi\)
−0.746168 + 0.665758i \(0.768108\pi\)
\(24\) −11.5663 −2.36096
\(25\) −1.36897 −0.273793
\(26\) −2.41564 −0.473746
\(27\) 2.10290 0.404704
\(28\) −0.244705 −0.0462449
\(29\) −9.58079 −1.77911 −0.889554 0.456829i \(-0.848985\pi\)
−0.889554 + 0.456829i \(0.848985\pi\)
\(30\) −12.0087 −2.19248
\(31\) 1.24948 0.224413 0.112206 0.993685i \(-0.464208\pi\)
0.112206 + 0.993685i \(0.464208\pi\)
\(32\) 1.52566 0.269701
\(33\) −2.15010 −0.374285
\(34\) −4.11107 −0.705043
\(35\) −0.121578 −0.0205505
\(36\) 14.5975 2.43292
\(37\) 2.14765 0.353071 0.176536 0.984294i \(-0.443511\pi\)
0.176536 + 0.984294i \(0.443511\pi\)
\(38\) 7.77088 1.26060
\(39\) 2.60884 0.417749
\(40\) −8.44814 −1.33577
\(41\) −4.26465 −0.666026 −0.333013 0.942922i \(-0.608065\pi\)
−0.333013 + 0.942922i \(0.608065\pi\)
\(42\) 0.402088 0.0620436
\(43\) 10.6940 1.63082 0.815412 0.578882i \(-0.196511\pi\)
0.815412 + 0.578882i \(0.196511\pi\)
\(44\) −3.16092 −0.476527
\(45\) 7.25257 1.08115
\(46\) 17.2887 2.54908
\(47\) −1.09153 −0.159216 −0.0796078 0.996826i \(-0.525367\pi\)
−0.0796078 + 0.996826i \(0.525367\pi\)
\(48\) 7.92849 1.14438
\(49\) −6.99593 −0.999418
\(50\) 3.30693 0.467671
\(51\) 4.43988 0.621707
\(52\) 3.83533 0.531864
\(53\) −3.55456 −0.488256 −0.244128 0.969743i \(-0.578502\pi\)
−0.244128 + 0.969743i \(0.578502\pi\)
\(54\) −5.07986 −0.691282
\(55\) −1.57046 −0.211761
\(56\) 0.282870 0.0378001
\(57\) −8.39239 −1.11160
\(58\) 23.1438 3.03893
\(59\) −11.8914 −1.54813 −0.774064 0.633107i \(-0.781779\pi\)
−0.774064 + 0.633107i \(0.781779\pi\)
\(60\) 19.0663 2.46144
\(61\) −12.6040 −1.61377 −0.806887 0.590706i \(-0.798849\pi\)
−0.806887 + 0.590706i \(0.798849\pi\)
\(62\) −3.01829 −0.383323
\(63\) −0.242838 −0.0305947
\(64\) −9.76360 −1.22045
\(65\) 1.90553 0.236352
\(66\) 5.19388 0.639323
\(67\) −13.0800 −1.59798 −0.798990 0.601345i \(-0.794632\pi\)
−0.798990 + 0.601345i \(0.794632\pi\)
\(68\) 6.52717 0.791536
\(69\) −18.6715 −2.24778
\(70\) 0.293690 0.0351026
\(71\) 8.31218 0.986474 0.493237 0.869895i \(-0.335814\pi\)
0.493237 + 0.869895i \(0.335814\pi\)
\(72\) −16.8742 −1.98864
\(73\) −5.91273 −0.692033 −0.346016 0.938228i \(-0.612466\pi\)
−0.346016 + 0.938228i \(0.612466\pi\)
\(74\) −5.18795 −0.603087
\(75\) −3.57142 −0.412392
\(76\) −12.3379 −1.41525
\(77\) 0.0525838 0.00599248
\(78\) −6.30203 −0.713565
\(79\) 7.96634 0.896283 0.448142 0.893963i \(-0.352086\pi\)
0.448142 + 0.893963i \(0.352086\pi\)
\(80\) 5.79105 0.647459
\(81\) −5.93205 −0.659117
\(82\) 10.3019 1.13765
\(83\) −5.46635 −0.600010 −0.300005 0.953938i \(-0.596988\pi\)
−0.300005 + 0.953938i \(0.596988\pi\)
\(84\) −0.638398 −0.0696549
\(85\) 3.24293 0.351745
\(86\) −25.8329 −2.78564
\(87\) −24.9948 −2.67972
\(88\) 3.65391 0.389508
\(89\) 7.57667 0.803126 0.401563 0.915831i \(-0.368467\pi\)
0.401563 + 0.915831i \(0.368467\pi\)
\(90\) −17.5196 −1.84673
\(91\) −0.0638029 −0.00668837
\(92\) −27.4494 −2.86180
\(93\) 3.25969 0.338014
\(94\) 2.63674 0.271959
\(95\) −6.12989 −0.628914
\(96\) 3.98020 0.406228
\(97\) 5.99226 0.608422 0.304211 0.952605i \(-0.401607\pi\)
0.304211 + 0.952605i \(0.401607\pi\)
\(98\) 16.8997 1.70712
\(99\) −3.13681 −0.315261
\(100\) −5.25043 −0.525043
\(101\) −6.14079 −0.611032 −0.305516 0.952187i \(-0.598829\pi\)
−0.305516 + 0.952187i \(0.598829\pi\)
\(102\) −10.7252 −1.06195
\(103\) −0.100735 −0.00992568 −0.00496284 0.999988i \(-0.501580\pi\)
−0.00496284 + 0.999988i \(0.501580\pi\)
\(104\) −4.43349 −0.434740
\(105\) −0.317179 −0.0309535
\(106\) 8.58655 0.833999
\(107\) 1.09078 0.105450 0.0527249 0.998609i \(-0.483209\pi\)
0.0527249 + 0.998609i \(0.483209\pi\)
\(108\) 8.06532 0.776086
\(109\) 8.76954 0.839970 0.419985 0.907531i \(-0.362035\pi\)
0.419985 + 0.907531i \(0.362035\pi\)
\(110\) 3.79367 0.361712
\(111\) 5.60288 0.531802
\(112\) −0.193902 −0.0183220
\(113\) 3.23054 0.303904 0.151952 0.988388i \(-0.451444\pi\)
0.151952 + 0.988388i \(0.451444\pi\)
\(114\) 20.2730 1.89874
\(115\) −13.6378 −1.27174
\(116\) −36.7455 −3.41173
\(117\) 3.80607 0.351871
\(118\) 28.7254 2.64439
\(119\) −0.108583 −0.00995382
\(120\) −22.0399 −2.01196
\(121\) −10.3208 −0.938251
\(122\) 30.4467 2.75652
\(123\) −11.1258 −1.00318
\(124\) 4.79215 0.430348
\(125\) −12.1362 −1.08550
\(126\) 0.586610 0.0522594
\(127\) −8.72529 −0.774244 −0.387122 0.922028i \(-0.626531\pi\)
−0.387122 + 0.922028i \(0.626531\pi\)
\(128\) 20.5341 1.81497
\(129\) 27.8990 2.45637
\(130\) −4.60307 −0.403716
\(131\) −9.11276 −0.796186 −0.398093 0.917345i \(-0.630328\pi\)
−0.398093 + 0.917345i \(0.630328\pi\)
\(132\) −8.24635 −0.717753
\(133\) 0.205248 0.0177972
\(134\) 31.5967 2.72954
\(135\) 4.00714 0.344880
\(136\) −7.54517 −0.646993
\(137\) 10.5666 0.902763 0.451382 0.892331i \(-0.350931\pi\)
0.451382 + 0.892331i \(0.350931\pi\)
\(138\) 45.1036 3.83947
\(139\) 16.6761 1.41445 0.707225 0.706989i \(-0.249947\pi\)
0.707225 + 0.706989i \(0.249947\pi\)
\(140\) −0.466292 −0.0394089
\(141\) −2.84762 −0.239813
\(142\) −20.0792 −1.68501
\(143\) −0.824160 −0.0689197
\(144\) 11.5669 0.963912
\(145\) −18.2565 −1.51612
\(146\) 14.2830 1.18207
\(147\) −18.2513 −1.50534
\(148\) 8.23694 0.677072
\(149\) 7.20135 0.589958 0.294979 0.955504i \(-0.404687\pi\)
0.294979 + 0.955504i \(0.404687\pi\)
\(150\) 8.62726 0.704413
\(151\) −12.2610 −0.997784 −0.498892 0.866664i \(-0.666260\pi\)
−0.498892 + 0.866664i \(0.666260\pi\)
\(152\) 14.2621 1.15681
\(153\) 6.47738 0.523665
\(154\) −0.127024 −0.0102359
\(155\) 2.38091 0.191239
\(156\) 10.0058 0.801103
\(157\) 11.5322 0.920371 0.460186 0.887823i \(-0.347783\pi\)
0.460186 + 0.887823i \(0.347783\pi\)
\(158\) −19.2438 −1.53096
\(159\) −9.27330 −0.735420
\(160\) 2.90718 0.229833
\(161\) 0.456637 0.0359880
\(162\) 14.3297 1.12585
\(163\) 13.2058 1.03436 0.517180 0.855877i \(-0.326982\pi\)
0.517180 + 0.855877i \(0.326982\pi\)
\(164\) −16.3563 −1.27721
\(165\) −4.09708 −0.318958
\(166\) 13.2048 1.02489
\(167\) 2.55278 0.197540 0.0987700 0.995110i \(-0.468509\pi\)
0.0987700 + 0.995110i \(0.468509\pi\)
\(168\) 0.737964 0.0569351
\(169\) 1.00000 0.0769231
\(170\) −7.83377 −0.600822
\(171\) −12.2437 −0.936302
\(172\) 41.0151 3.12737
\(173\) −4.61463 −0.350844 −0.175422 0.984493i \(-0.556129\pi\)
−0.175422 + 0.984493i \(0.556129\pi\)
\(174\) 60.3785 4.57728
\(175\) 0.0873440 0.00660259
\(176\) −2.50469 −0.188798
\(177\) −31.0228 −2.33182
\(178\) −18.3025 −1.37183
\(179\) −6.35735 −0.475170 −0.237585 0.971367i \(-0.576356\pi\)
−0.237585 + 0.971367i \(0.576356\pi\)
\(180\) 27.8160 2.07328
\(181\) −21.4995 −1.59804 −0.799021 0.601303i \(-0.794649\pi\)
−0.799021 + 0.601303i \(0.794649\pi\)
\(182\) 0.154125 0.0114245
\(183\) −32.8818 −2.43069
\(184\) 31.7305 2.33920
\(185\) 4.09240 0.300879
\(186\) −7.87424 −0.577367
\(187\) −1.40260 −0.102568
\(188\) −4.18636 −0.305322
\(189\) −0.134171 −0.00975954
\(190\) 14.8076 1.07426
\(191\) 3.29487 0.238408 0.119204 0.992870i \(-0.461966\pi\)
0.119204 + 0.992870i \(0.461966\pi\)
\(192\) −25.4717 −1.83826
\(193\) 8.75016 0.629851 0.314925 0.949116i \(-0.398021\pi\)
0.314925 + 0.949116i \(0.398021\pi\)
\(194\) −14.4752 −1.03926
\(195\) 4.97122 0.355997
\(196\) −26.8317 −1.91655
\(197\) 12.0653 0.859620 0.429810 0.902919i \(-0.358581\pi\)
0.429810 + 0.902919i \(0.358581\pi\)
\(198\) 7.57741 0.538503
\(199\) −3.69665 −0.262049 −0.131024 0.991379i \(-0.541827\pi\)
−0.131024 + 0.991379i \(0.541827\pi\)
\(200\) 6.06930 0.429164
\(201\) −34.1238 −2.40690
\(202\) 14.8340 1.04371
\(203\) 0.611283 0.0429036
\(204\) 17.0284 1.19222
\(205\) −8.12641 −0.567573
\(206\) 0.243339 0.0169542
\(207\) −27.2400 −1.89331
\(208\) 3.03908 0.210722
\(209\) 2.65124 0.183390
\(210\) 0.766190 0.0528721
\(211\) −0.242385 −0.0166865 −0.00834324 0.999965i \(-0.502656\pi\)
−0.00834324 + 0.999965i \(0.502656\pi\)
\(212\) −13.6329 −0.936312
\(213\) 21.6852 1.48584
\(214\) −2.63494 −0.180121
\(215\) 20.3778 1.38975
\(216\) −9.32321 −0.634364
\(217\) −0.0797202 −0.00541176
\(218\) −21.1841 −1.43477
\(219\) −15.4254 −1.04235
\(220\) −6.02323 −0.406086
\(221\) 1.70186 0.114479
\(222\) −13.5346 −0.908380
\(223\) −27.7076 −1.85544 −0.927718 0.373283i \(-0.878232\pi\)
−0.927718 + 0.373283i \(0.878232\pi\)
\(224\) −0.0973414 −0.00650390
\(225\) −5.21037 −0.347358
\(226\) −7.80384 −0.519104
\(227\) −14.4105 −0.956456 −0.478228 0.878236i \(-0.658721\pi\)
−0.478228 + 0.878236i \(0.658721\pi\)
\(228\) −32.1876 −2.13167
\(229\) 0.0125556 0.000829698 0 0.000414849 1.00000i \(-0.499868\pi\)
0.000414849 1.00000i \(0.499868\pi\)
\(230\) 32.9441 2.17227
\(231\) 0.137183 0.00902598
\(232\) 42.4764 2.78871
\(233\) 18.0524 1.18265 0.591327 0.806432i \(-0.298604\pi\)
0.591327 + 0.806432i \(0.298604\pi\)
\(234\) −9.19410 −0.601037
\(235\) −2.07993 −0.135680
\(236\) −45.6074 −2.96879
\(237\) 20.7829 1.35000
\(238\) 0.262299 0.0170023
\(239\) −23.6749 −1.53140 −0.765701 0.643197i \(-0.777608\pi\)
−0.765701 + 0.643197i \(0.777608\pi\)
\(240\) 15.1079 0.975214
\(241\) 22.9441 1.47796 0.738978 0.673729i \(-0.235309\pi\)
0.738978 + 0.673729i \(0.235309\pi\)
\(242\) 24.9313 1.60264
\(243\) −21.7845 −1.39748
\(244\) −48.3404 −3.09468
\(245\) −13.3309 −0.851682
\(246\) 26.8760 1.71355
\(247\) −3.21690 −0.204686
\(248\) −5.53954 −0.351761
\(249\) −14.2609 −0.903746
\(250\) 29.3168 1.85416
\(251\) −26.7989 −1.69153 −0.845764 0.533557i \(-0.820855\pi\)
−0.845764 + 0.533557i \(0.820855\pi\)
\(252\) −0.931364 −0.0586704
\(253\) 5.89850 0.370836
\(254\) 21.0772 1.32250
\(255\) 8.46031 0.529805
\(256\) −30.0757 −1.87973
\(257\) −5.06781 −0.316122 −0.158061 0.987429i \(-0.550524\pi\)
−0.158061 + 0.987429i \(0.550524\pi\)
\(258\) −67.3941 −4.19577
\(259\) −0.137026 −0.00851440
\(260\) 7.30832 0.453243
\(261\) −36.4651 −2.25714
\(262\) 22.0132 1.35998
\(263\) −6.68257 −0.412065 −0.206033 0.978545i \(-0.566055\pi\)
−0.206033 + 0.978545i \(0.566055\pi\)
\(264\) 9.53248 0.586683
\(265\) −6.77331 −0.416081
\(266\) −0.495805 −0.0303998
\(267\) 19.7664 1.20968
\(268\) −50.1662 −3.06439
\(269\) −31.7006 −1.93282 −0.966410 0.257005i \(-0.917264\pi\)
−0.966410 + 0.257005i \(0.917264\pi\)
\(270\) −9.67982 −0.589095
\(271\) 29.6669 1.80213 0.901067 0.433680i \(-0.142785\pi\)
0.901067 + 0.433680i \(0.142785\pi\)
\(272\) 5.17208 0.313603
\(273\) −0.166452 −0.0100741
\(274\) −25.5251 −1.54203
\(275\) 1.12825 0.0680358
\(276\) −71.6112 −4.31049
\(277\) 22.7214 1.36520 0.682599 0.730793i \(-0.260850\pi\)
0.682599 + 0.730793i \(0.260850\pi\)
\(278\) −40.2835 −2.41605
\(279\) 4.75559 0.284710
\(280\) 0.539016 0.0322124
\(281\) −6.85002 −0.408638 −0.204319 0.978904i \(-0.565498\pi\)
−0.204319 + 0.978904i \(0.565498\pi\)
\(282\) 6.87884 0.409629
\(283\) −9.68222 −0.575548 −0.287774 0.957698i \(-0.592915\pi\)
−0.287774 + 0.957698i \(0.592915\pi\)
\(284\) 31.8799 1.89173
\(285\) −15.9919 −0.947280
\(286\) 1.99088 0.117723
\(287\) 0.272097 0.0160614
\(288\) 5.80676 0.342166
\(289\) −14.1037 −0.829629
\(290\) 44.1011 2.58970
\(291\) 15.6329 0.916415
\(292\) −22.6773 −1.32709
\(293\) 22.0201 1.28643 0.643214 0.765687i \(-0.277601\pi\)
0.643214 + 0.765687i \(0.277601\pi\)
\(294\) 44.0886 2.57130
\(295\) −22.6594 −1.31928
\(296\) −9.52159 −0.553431
\(297\) −1.73313 −0.100566
\(298\) −17.3959 −1.00772
\(299\) −7.15699 −0.413899
\(300\) −13.6976 −0.790828
\(301\) −0.682310 −0.0393277
\(302\) 29.6181 1.70433
\(303\) −16.0204 −0.920346
\(304\) −9.77642 −0.560716
\(305\) −24.0172 −1.37522
\(306\) −15.6470 −0.894481
\(307\) 23.2828 1.32882 0.664410 0.747368i \(-0.268683\pi\)
0.664410 + 0.747368i \(0.268683\pi\)
\(308\) 0.201676 0.0114916
\(309\) −0.262801 −0.0149502
\(310\) −5.75143 −0.326659
\(311\) 30.1986 1.71240 0.856202 0.516642i \(-0.172818\pi\)
0.856202 + 0.516642i \(0.172818\pi\)
\(312\) −11.5663 −0.654812
\(313\) −4.73934 −0.267883 −0.133942 0.990989i \(-0.542763\pi\)
−0.133942 + 0.990989i \(0.542763\pi\)
\(314\) −27.8577 −1.57210
\(315\) −0.462735 −0.0260722
\(316\) 30.5535 1.71877
\(317\) 27.4554 1.54205 0.771023 0.636807i \(-0.219745\pi\)
0.771023 + 0.636807i \(0.219745\pi\)
\(318\) 22.4010 1.25618
\(319\) 7.89611 0.442097
\(320\) −18.6048 −1.04004
\(321\) 2.84568 0.158830
\(322\) −1.10307 −0.0614718
\(323\) −5.47470 −0.304620
\(324\) −22.7514 −1.26396
\(325\) −1.36897 −0.0759365
\(326\) −31.9005 −1.76681
\(327\) 22.8784 1.26518
\(328\) 18.9073 1.04398
\(329\) 0.0696426 0.00383952
\(330\) 9.89709 0.544817
\(331\) 15.5537 0.854910 0.427455 0.904037i \(-0.359410\pi\)
0.427455 + 0.904037i \(0.359410\pi\)
\(332\) −20.9653 −1.15062
\(333\) 8.17410 0.447938
\(334\) −6.16660 −0.337421
\(335\) −24.9244 −1.36176
\(336\) −0.505861 −0.0275970
\(337\) −31.9426 −1.74002 −0.870011 0.493032i \(-0.835889\pi\)
−0.870011 + 0.493032i \(0.835889\pi\)
\(338\) −2.41564 −0.131394
\(339\) 8.42799 0.457745
\(340\) 12.4377 0.674529
\(341\) −1.02977 −0.0557651
\(342\) 29.5765 1.59931
\(343\) 0.892981 0.0482165
\(344\) −47.4119 −2.55628
\(345\) −35.5790 −1.91551
\(346\) 11.1473 0.599282
\(347\) 3.66600 0.196801 0.0984007 0.995147i \(-0.468627\pi\)
0.0984007 + 0.995147i \(0.468627\pi\)
\(348\) −95.8632 −5.13881
\(349\) −4.73828 −0.253634 −0.126817 0.991926i \(-0.540476\pi\)
−0.126817 + 0.991926i \(0.540476\pi\)
\(350\) −0.210992 −0.0112780
\(351\) 2.10290 0.112245
\(352\) −1.25739 −0.0670189
\(353\) 10.9188 0.581148 0.290574 0.956853i \(-0.406154\pi\)
0.290574 + 0.956853i \(0.406154\pi\)
\(354\) 74.9400 3.98302
\(355\) 15.8391 0.840651
\(356\) 29.0590 1.54012
\(357\) −0.283277 −0.0149926
\(358\) 15.3571 0.811646
\(359\) −2.64298 −0.139491 −0.0697457 0.997565i \(-0.522219\pi\)
−0.0697457 + 0.997565i \(0.522219\pi\)
\(360\) −32.1542 −1.69468
\(361\) −8.65155 −0.455345
\(362\) 51.9350 2.72964
\(363\) −26.9253 −1.41321
\(364\) −0.244705 −0.0128260
\(365\) −11.2669 −0.589735
\(366\) 79.4307 4.15191
\(367\) 18.9646 0.989945 0.494973 0.868909i \(-0.335178\pi\)
0.494973 + 0.868909i \(0.335178\pi\)
\(368\) −21.7507 −1.13383
\(369\) −16.2315 −0.844980
\(370\) −9.88578 −0.513937
\(371\) 0.226791 0.0117744
\(372\) 12.5020 0.648197
\(373\) 11.4200 0.591306 0.295653 0.955295i \(-0.404463\pi\)
0.295653 + 0.955295i \(0.404463\pi\)
\(374\) 3.38818 0.175199
\(375\) −31.6616 −1.63500
\(376\) 4.83928 0.249567
\(377\) −9.58079 −0.493436
\(378\) 0.324110 0.0166704
\(379\) 25.9715 1.33407 0.667034 0.745027i \(-0.267564\pi\)
0.667034 + 0.745027i \(0.267564\pi\)
\(380\) −23.5101 −1.20604
\(381\) −22.7629 −1.16618
\(382\) −7.95922 −0.407229
\(383\) −18.3084 −0.935517 −0.467759 0.883856i \(-0.654938\pi\)
−0.467759 + 0.883856i \(0.654938\pi\)
\(384\) 53.5701 2.73374
\(385\) 0.100200 0.00510666
\(386\) −21.1373 −1.07586
\(387\) 40.7022 2.06901
\(388\) 22.9823 1.16675
\(389\) −21.2237 −1.07609 −0.538043 0.842917i \(-0.680836\pi\)
−0.538043 + 0.842917i \(0.680836\pi\)
\(390\) −12.0087 −0.608084
\(391\) −12.1802 −0.615977
\(392\) 31.0164 1.56657
\(393\) −23.7738 −1.19923
\(394\) −29.1456 −1.46833
\(395\) 15.1801 0.763792
\(396\) −12.0307 −0.604565
\(397\) 1.87919 0.0943137 0.0471568 0.998887i \(-0.484984\pi\)
0.0471568 + 0.998887i \(0.484984\pi\)
\(398\) 8.92978 0.447610
\(399\) 0.535459 0.0268065
\(400\) −4.16039 −0.208020
\(401\) 7.36040 0.367561 0.183780 0.982967i \(-0.441166\pi\)
0.183780 + 0.982967i \(0.441166\pi\)
\(402\) 82.4308 4.11127
\(403\) 1.24948 0.0622408
\(404\) −23.5519 −1.17175
\(405\) −11.3037 −0.561685
\(406\) −1.47664 −0.0732844
\(407\) −1.77001 −0.0877359
\(408\) −19.6842 −0.974511
\(409\) 18.7092 0.925112 0.462556 0.886590i \(-0.346933\pi\)
0.462556 + 0.886590i \(0.346933\pi\)
\(410\) 19.6305 0.969481
\(411\) 27.5665 1.35976
\(412\) −0.386350 −0.0190341
\(413\) 0.758706 0.0373335
\(414\) 65.8021 3.23399
\(415\) −10.4163 −0.511315
\(416\) 1.52566 0.0748015
\(417\) 43.5054 2.13047
\(418\) −6.40445 −0.313252
\(419\) 18.3118 0.894590 0.447295 0.894386i \(-0.352387\pi\)
0.447295 + 0.894386i \(0.352387\pi\)
\(420\) −1.21648 −0.0593583
\(421\) 24.2019 1.17953 0.589764 0.807576i \(-0.299221\pi\)
0.589764 + 0.807576i \(0.299221\pi\)
\(422\) 0.585516 0.0285025
\(423\) −4.15442 −0.201995
\(424\) 15.7591 0.765331
\(425\) −2.32978 −0.113011
\(426\) −52.3836 −2.53799
\(427\) 0.804171 0.0389166
\(428\) 4.18351 0.202217
\(429\) −2.15010 −0.103808
\(430\) −49.2254 −2.37386
\(431\) 13.2485 0.638157 0.319079 0.947728i \(-0.396627\pi\)
0.319079 + 0.947728i \(0.396627\pi\)
\(432\) 6.39089 0.307482
\(433\) −18.3409 −0.881405 −0.440703 0.897653i \(-0.645271\pi\)
−0.440703 + 0.897653i \(0.645271\pi\)
\(434\) 0.192576 0.00924392
\(435\) −47.6283 −2.28360
\(436\) 33.6341 1.61078
\(437\) 23.0233 1.10135
\(438\) 37.2622 1.78046
\(439\) 35.7212 1.70488 0.852440 0.522825i \(-0.175122\pi\)
0.852440 + 0.522825i \(0.175122\pi\)
\(440\) 6.96262 0.331930
\(441\) −26.6270 −1.26795
\(442\) −4.11107 −0.195544
\(443\) 16.8973 0.802816 0.401408 0.915899i \(-0.368521\pi\)
0.401408 + 0.915899i \(0.368521\pi\)
\(444\) 21.4889 1.01982
\(445\) 14.4376 0.684406
\(446\) 66.9315 3.16930
\(447\) 18.7872 0.888604
\(448\) 0.622947 0.0294315
\(449\) −21.7834 −1.02802 −0.514012 0.857783i \(-0.671841\pi\)
−0.514012 + 0.857783i \(0.671841\pi\)
\(450\) 12.5864 0.593329
\(451\) 3.51475 0.165503
\(452\) 12.3902 0.582786
\(453\) −31.9870 −1.50288
\(454\) 34.8105 1.63374
\(455\) −0.121578 −0.00569968
\(456\) 37.2076 1.74241
\(457\) 7.03014 0.328856 0.164428 0.986389i \(-0.447422\pi\)
0.164428 + 0.986389i \(0.447422\pi\)
\(458\) −0.0303299 −0.00141722
\(459\) 3.57884 0.167046
\(460\) −52.3056 −2.43876
\(461\) −2.44003 −0.113644 −0.0568219 0.998384i \(-0.518097\pi\)
−0.0568219 + 0.998384i \(0.518097\pi\)
\(462\) −0.331385 −0.0154174
\(463\) −12.6006 −0.585601 −0.292801 0.956173i \(-0.594587\pi\)
−0.292801 + 0.956173i \(0.594587\pi\)
\(464\) −29.1168 −1.35171
\(465\) 6.21143 0.288048
\(466\) −43.6082 −2.02011
\(467\) −33.4221 −1.54659 −0.773295 0.634046i \(-0.781393\pi\)
−0.773295 + 0.634046i \(0.781393\pi\)
\(468\) 14.5975 0.674770
\(469\) 0.834544 0.0385357
\(470\) 5.02438 0.231757
\(471\) 30.0858 1.38628
\(472\) 52.7205 2.42666
\(473\) −8.81358 −0.405249
\(474\) −50.2041 −2.30595
\(475\) 4.40382 0.202061
\(476\) −0.416453 −0.0190881
\(477\) −13.5289 −0.619446
\(478\) 57.1901 2.61581
\(479\) 8.98724 0.410637 0.205319 0.978695i \(-0.434177\pi\)
0.205319 + 0.978695i \(0.434177\pi\)
\(480\) 7.58439 0.346178
\(481\) 2.14765 0.0979244
\(482\) −55.4246 −2.52452
\(483\) 1.19129 0.0542058
\(484\) −39.5835 −1.79925
\(485\) 11.4184 0.518484
\(486\) 52.6236 2.38705
\(487\) 15.7344 0.712995 0.356498 0.934296i \(-0.383971\pi\)
0.356498 + 0.934296i \(0.383971\pi\)
\(488\) 55.8797 2.52955
\(489\) 34.4519 1.55797
\(490\) 32.2028 1.45477
\(491\) −8.82120 −0.398095 −0.199047 0.979990i \(-0.563785\pi\)
−0.199047 + 0.979990i \(0.563785\pi\)
\(492\) −42.6711 −1.92376
\(493\) −16.3051 −0.734346
\(494\) 7.77088 0.349628
\(495\) −5.97727 −0.268658
\(496\) 3.79726 0.170502
\(497\) −0.530341 −0.0237891
\(498\) 34.4491 1.54370
\(499\) −2.48821 −0.111387 −0.0556937 0.998448i \(-0.517737\pi\)
−0.0556937 + 0.998448i \(0.517737\pi\)
\(500\) −46.5464 −2.08162
\(501\) 6.65980 0.297538
\(502\) 64.7364 2.88933
\(503\) −26.3041 −1.17284 −0.586421 0.810007i \(-0.699464\pi\)
−0.586421 + 0.810007i \(0.699464\pi\)
\(504\) 1.07662 0.0479566
\(505\) −11.7014 −0.520708
\(506\) −14.2487 −0.633431
\(507\) 2.60884 0.115863
\(508\) −33.4643 −1.48474
\(509\) −32.1102 −1.42326 −0.711630 0.702554i \(-0.752043\pi\)
−0.711630 + 0.702554i \(0.752043\pi\)
\(510\) −20.4371 −0.904969
\(511\) 0.377250 0.0166885
\(512\) 31.5841 1.39583
\(513\) −6.76483 −0.298675
\(514\) 12.2420 0.539973
\(515\) −0.191953 −0.00845845
\(516\) 107.002 4.71050
\(517\) 0.899593 0.0395640
\(518\) 0.331007 0.0145436
\(519\) −12.0388 −0.528446
\(520\) −8.44814 −0.370476
\(521\) −21.9410 −0.961252 −0.480626 0.876926i \(-0.659590\pi\)
−0.480626 + 0.876926i \(0.659590\pi\)
\(522\) 88.0867 3.85545
\(523\) 23.8296 1.04200 0.520999 0.853557i \(-0.325560\pi\)
0.520999 + 0.853557i \(0.325560\pi\)
\(524\) −34.9504 −1.52682
\(525\) 0.227867 0.00994493
\(526\) 16.1427 0.703855
\(527\) 2.12643 0.0926287
\(528\) −6.53434 −0.284371
\(529\) 28.2225 1.22707
\(530\) 16.3619 0.710716
\(531\) −45.2595 −1.96409
\(532\) 0.787192 0.0341291
\(533\) −4.26465 −0.184722
\(534\) −47.7484 −2.06628
\(535\) 2.07852 0.0898621
\(536\) 57.9902 2.50480
\(537\) −16.5853 −0.715709
\(538\) 76.5773 3.30148
\(539\) 5.76576 0.248349
\(540\) 15.3687 0.661363
\(541\) 22.7653 0.978757 0.489378 0.872072i \(-0.337224\pi\)
0.489378 + 0.872072i \(0.337224\pi\)
\(542\) −71.6645 −3.07826
\(543\) −56.0888 −2.40700
\(544\) 2.59645 0.111322
\(545\) 16.7106 0.715804
\(546\) 0.402088 0.0172078
\(547\) 43.5915 1.86384 0.931919 0.362667i \(-0.118134\pi\)
0.931919 + 0.362667i \(0.118134\pi\)
\(548\) 40.5263 1.73120
\(549\) −47.9716 −2.04738
\(550\) −2.72544 −0.116213
\(551\) 30.8205 1.31300
\(552\) 82.7798 3.52334
\(553\) −0.508276 −0.0216141
\(554\) −54.8868 −2.33192
\(555\) 10.6764 0.453190
\(556\) 63.9584 2.71244
\(557\) −12.4726 −0.528479 −0.264240 0.964457i \(-0.585121\pi\)
−0.264240 + 0.964457i \(0.585121\pi\)
\(558\) −11.4878 −0.486318
\(559\) 10.6940 0.452309
\(560\) −0.369486 −0.0156136
\(561\) −3.65917 −0.154490
\(562\) 16.5472 0.698001
\(563\) −34.5936 −1.45795 −0.728973 0.684543i \(-0.760002\pi\)
−0.728973 + 0.684543i \(0.760002\pi\)
\(564\) −10.9216 −0.459881
\(565\) 6.15589 0.258980
\(566\) 23.3888 0.983104
\(567\) 0.378482 0.0158948
\(568\) −36.8520 −1.54627
\(569\) 12.0678 0.505908 0.252954 0.967478i \(-0.418598\pi\)
0.252954 + 0.967478i \(0.418598\pi\)
\(570\) 38.6308 1.61807
\(571\) −35.3249 −1.47830 −0.739151 0.673540i \(-0.764773\pi\)
−0.739151 + 0.673540i \(0.764773\pi\)
\(572\) −3.16092 −0.132165
\(573\) 8.59580 0.359095
\(574\) −0.657289 −0.0274347
\(575\) 9.79767 0.408591
\(576\) −37.1609 −1.54837
\(577\) −12.0527 −0.501759 −0.250879 0.968018i \(-0.580720\pi\)
−0.250879 + 0.968018i \(0.580720\pi\)
\(578\) 34.0695 1.41710
\(579\) 22.8278 0.948692
\(580\) −70.0195 −2.90740
\(581\) 0.348769 0.0144694
\(582\) −37.7634 −1.56534
\(583\) 2.92953 0.121329
\(584\) 26.2141 1.08475
\(585\) 7.25257 0.299857
\(586\) −53.1927 −2.19737
\(587\) −24.2889 −1.00251 −0.501255 0.865300i \(-0.667128\pi\)
−0.501255 + 0.865300i \(0.667128\pi\)
\(588\) −69.9997 −2.88674
\(589\) −4.01944 −0.165618
\(590\) 54.7370 2.25349
\(591\) 31.4766 1.29477
\(592\) 6.52688 0.268253
\(593\) −23.8610 −0.979853 −0.489927 0.871764i \(-0.662976\pi\)
−0.489927 + 0.871764i \(0.662976\pi\)
\(594\) 4.18662 0.171779
\(595\) −0.206909 −0.00848243
\(596\) 27.6195 1.13134
\(597\) −9.64398 −0.394702
\(598\) 17.2887 0.706989
\(599\) 43.7740 1.78856 0.894278 0.447511i \(-0.147690\pi\)
0.894278 + 0.447511i \(0.147690\pi\)
\(600\) 15.8339 0.646414
\(601\) 14.2337 0.580603 0.290302 0.956935i \(-0.406244\pi\)
0.290302 + 0.956935i \(0.406244\pi\)
\(602\) 1.64822 0.0671763
\(603\) −49.7835 −2.02734
\(604\) −47.0249 −1.91341
\(605\) −19.6665 −0.799557
\(606\) 38.6995 1.57206
\(607\) −7.01723 −0.284821 −0.142410 0.989808i \(-0.545485\pi\)
−0.142410 + 0.989808i \(0.545485\pi\)
\(608\) −4.90789 −0.199041
\(609\) 1.59474 0.0646222
\(610\) 58.0170 2.34904
\(611\) −1.09153 −0.0441584
\(612\) 24.8429 1.00421
\(613\) 38.3264 1.54799 0.773995 0.633192i \(-0.218256\pi\)
0.773995 + 0.633192i \(0.218256\pi\)
\(614\) −56.2429 −2.26978
\(615\) −21.2005 −0.854888
\(616\) −0.233130 −0.00939308
\(617\) −7.24688 −0.291748 −0.145874 0.989303i \(-0.546599\pi\)
−0.145874 + 0.989303i \(0.546599\pi\)
\(618\) 0.634833 0.0255367
\(619\) 1.00000 0.0401934
\(620\) 9.13157 0.366733
\(621\) −15.0505 −0.603954
\(622\) −72.9489 −2.92499
\(623\) −0.483414 −0.0193676
\(624\) 7.92849 0.317393
\(625\) −16.2811 −0.651244
\(626\) 11.4485 0.457576
\(627\) 6.91667 0.276225
\(628\) 44.2298 1.76496
\(629\) 3.65499 0.145734
\(630\) 1.11780 0.0445343
\(631\) 12.8226 0.510459 0.255229 0.966881i \(-0.417849\pi\)
0.255229 + 0.966881i \(0.417849\pi\)
\(632\) −35.3187 −1.40490
\(633\) −0.632345 −0.0251335
\(634\) −66.3223 −2.63400
\(635\) −16.6263 −0.659794
\(636\) −35.5661 −1.41029
\(637\) −6.99593 −0.277189
\(638\) −19.0742 −0.755153
\(639\) 31.6367 1.25153
\(640\) 39.1282 1.54668
\(641\) 33.5471 1.32503 0.662515 0.749049i \(-0.269489\pi\)
0.662515 + 0.749049i \(0.269489\pi\)
\(642\) −6.87415 −0.271301
\(643\) 26.8806 1.06007 0.530034 0.847977i \(-0.322179\pi\)
0.530034 + 0.847977i \(0.322179\pi\)
\(644\) 1.75135 0.0690129
\(645\) 53.1624 2.09327
\(646\) 13.2249 0.520327
\(647\) −21.3863 −0.840784 −0.420392 0.907343i \(-0.638107\pi\)
−0.420392 + 0.907343i \(0.638107\pi\)
\(648\) 26.2997 1.03315
\(649\) 9.80042 0.384700
\(650\) 3.30693 0.129708
\(651\) −0.207978 −0.00815129
\(652\) 50.6486 1.98355
\(653\) 13.6991 0.536087 0.268044 0.963407i \(-0.413623\pi\)
0.268044 + 0.963407i \(0.413623\pi\)
\(654\) −55.2660 −2.16107
\(655\) −17.3646 −0.678492
\(656\) −12.9606 −0.506027
\(657\) −22.5042 −0.877974
\(658\) −0.168232 −0.00655835
\(659\) 31.4603 1.22552 0.612760 0.790269i \(-0.290059\pi\)
0.612760 + 0.790269i \(0.290059\pi\)
\(660\) −15.7137 −0.611653
\(661\) 4.31046 0.167658 0.0838288 0.996480i \(-0.473285\pi\)
0.0838288 + 0.996480i \(0.473285\pi\)
\(662\) −37.5722 −1.46029
\(663\) 4.43988 0.172431
\(664\) 24.2350 0.940502
\(665\) 0.391105 0.0151664
\(666\) −19.7457 −0.765130
\(667\) 68.5696 2.65503
\(668\) 9.79074 0.378815
\(669\) −72.2847 −2.79469
\(670\) 60.2083 2.32605
\(671\) 10.3877 0.401013
\(672\) −0.253949 −0.00979628
\(673\) 0.398047 0.0153436 0.00767180 0.999971i \(-0.497558\pi\)
0.00767180 + 0.999971i \(0.497558\pi\)
\(674\) 77.1618 2.97216
\(675\) −2.87880 −0.110805
\(676\) 3.83533 0.147513
\(677\) −33.2389 −1.27747 −0.638737 0.769425i \(-0.720543\pi\)
−0.638737 + 0.769425i \(0.720543\pi\)
\(678\) −20.3590 −0.781883
\(679\) −0.382324 −0.0146722
\(680\) −14.3775 −0.551353
\(681\) −37.5947 −1.44063
\(682\) 2.48755 0.0952533
\(683\) −12.5541 −0.480368 −0.240184 0.970727i \(-0.577208\pi\)
−0.240184 + 0.970727i \(0.577208\pi\)
\(684\) −46.9587 −1.79551
\(685\) 20.1349 0.769315
\(686\) −2.15712 −0.0823594
\(687\) 0.0327556 0.00124971
\(688\) 32.5000 1.23905
\(689\) −3.55456 −0.135418
\(690\) 85.9461 3.27191
\(691\) −32.7263 −1.24497 −0.622483 0.782633i \(-0.713876\pi\)
−0.622483 + 0.782633i \(0.713876\pi\)
\(692\) −17.6986 −0.672800
\(693\) 0.200138 0.00760260
\(694\) −8.85575 −0.336160
\(695\) 31.7768 1.20536
\(696\) 110.814 4.20040
\(697\) −7.25782 −0.274909
\(698\) 11.4460 0.433237
\(699\) 47.0960 1.78133
\(700\) 0.334993 0.0126615
\(701\) 50.0423 1.89007 0.945035 0.326968i \(-0.106027\pi\)
0.945035 + 0.326968i \(0.106027\pi\)
\(702\) −5.07986 −0.191727
\(703\) −6.90877 −0.260569
\(704\) 8.04677 0.303274
\(705\) −5.42622 −0.204363
\(706\) −26.3759 −0.992669
\(707\) 0.391801 0.0147352
\(708\) −118.983 −4.47164
\(709\) −37.0940 −1.39309 −0.696547 0.717511i \(-0.745281\pi\)
−0.696547 + 0.717511i \(0.745281\pi\)
\(710\) −38.2616 −1.43593
\(711\) 30.3204 1.13710
\(712\) −33.5911 −1.25888
\(713\) −8.94249 −0.334899
\(714\) 0.684296 0.0256091
\(715\) −1.57046 −0.0587318
\(716\) −24.3825 −0.911217
\(717\) −61.7641 −2.30662
\(718\) 6.38450 0.238268
\(719\) −35.2256 −1.31369 −0.656847 0.754023i \(-0.728110\pi\)
−0.656847 + 0.754023i \(0.728110\pi\)
\(720\) 22.0411 0.821424
\(721\) 0.00642717 0.000239360 0
\(722\) 20.8991 0.777782
\(723\) 59.8575 2.22612
\(724\) −82.4575 −3.06451
\(725\) 13.1158 0.487108
\(726\) 65.0418 2.41393
\(727\) −3.97574 −0.147452 −0.0737261 0.997279i \(-0.523489\pi\)
−0.0737261 + 0.997279i \(0.523489\pi\)
\(728\) 0.282870 0.0104839
\(729\) −39.0362 −1.44579
\(730\) 27.2167 1.00734
\(731\) 18.1997 0.673140
\(732\) −126.113 −4.66125
\(733\) 34.4535 1.27257 0.636284 0.771455i \(-0.280471\pi\)
0.636284 + 0.771455i \(0.280471\pi\)
\(734\) −45.8117 −1.69094
\(735\) −34.7783 −1.28282
\(736\) −10.9191 −0.402484
\(737\) 10.7800 0.397088
\(738\) 39.2096 1.44333
\(739\) 34.4317 1.26659 0.633295 0.773911i \(-0.281702\pi\)
0.633295 + 0.773911i \(0.281702\pi\)
\(740\) 15.6957 0.576986
\(741\) −8.39239 −0.308302
\(742\) −0.547847 −0.0201121
\(743\) 3.83161 0.140568 0.0702840 0.997527i \(-0.477609\pi\)
0.0702840 + 0.997527i \(0.477609\pi\)
\(744\) −14.4518 −0.529829
\(745\) 13.7224 0.502749
\(746\) −27.5867 −1.01002
\(747\) −20.8053 −0.761227
\(748\) −5.37944 −0.196692
\(749\) −0.0695951 −0.00254295
\(750\) 76.4830 2.79276
\(751\) 33.3080 1.21542 0.607712 0.794157i \(-0.292087\pi\)
0.607712 + 0.794157i \(0.292087\pi\)
\(752\) −3.31724 −0.120967
\(753\) −69.9140 −2.54781
\(754\) 23.1438 0.842846
\(755\) −23.3636 −0.850290
\(756\) −0.514591 −0.0187155
\(757\) 26.2595 0.954418 0.477209 0.878790i \(-0.341649\pi\)
0.477209 + 0.878790i \(0.341649\pi\)
\(758\) −62.7379 −2.27874
\(759\) 15.3883 0.558559
\(760\) 27.1768 0.985807
\(761\) −13.9212 −0.504644 −0.252322 0.967643i \(-0.581194\pi\)
−0.252322 + 0.967643i \(0.581194\pi\)
\(762\) 54.9871 1.99197
\(763\) −0.559523 −0.0202561
\(764\) 12.6369 0.457187
\(765\) 12.3428 0.446256
\(766\) 44.2266 1.59797
\(767\) −11.8914 −0.429374
\(768\) −78.4629 −2.83129
\(769\) −35.3297 −1.27402 −0.637010 0.770855i \(-0.719829\pi\)
−0.637010 + 0.770855i \(0.719829\pi\)
\(770\) −0.242047 −0.00872277
\(771\) −13.2211 −0.476148
\(772\) 33.5597 1.20784
\(773\) −38.5076 −1.38502 −0.692511 0.721407i \(-0.743496\pi\)
−0.692511 + 0.721407i \(0.743496\pi\)
\(774\) −98.3219 −3.53411
\(775\) −1.71049 −0.0614426
\(776\) −26.5666 −0.953687
\(777\) −0.357480 −0.0128245
\(778\) 51.2689 1.83808
\(779\) 13.7190 0.491532
\(780\) 19.0663 0.682682
\(781\) −6.85056 −0.245132
\(782\) 29.4229 1.05216
\(783\) −20.1475 −0.720012
\(784\) −21.2612 −0.759328
\(785\) 21.9750 0.784320
\(786\) 57.4289 2.04842
\(787\) −15.0643 −0.536983 −0.268491 0.963282i \(-0.586525\pi\)
−0.268491 + 0.963282i \(0.586525\pi\)
\(788\) 46.2745 1.64846
\(789\) −17.4338 −0.620659
\(790\) −36.6696 −1.30465
\(791\) −0.206118 −0.00732872
\(792\) 13.9070 0.494164
\(793\) −12.6040 −0.447580
\(794\) −4.53944 −0.161099
\(795\) −17.6705 −0.626709
\(796\) −14.1779 −0.502521
\(797\) −10.7848 −0.382018 −0.191009 0.981588i \(-0.561176\pi\)
−0.191009 + 0.981588i \(0.561176\pi\)
\(798\) −1.29348 −0.0457886
\(799\) −1.85762 −0.0657179
\(800\) −2.08857 −0.0738422
\(801\) 28.8373 1.01892
\(802\) −17.7801 −0.627837
\(803\) 4.87304 0.171966
\(804\) −130.876 −4.61563
\(805\) 0.870134 0.0306682
\(806\) −3.01829 −0.106315
\(807\) −82.7019 −2.91125
\(808\) 27.2252 0.957778
\(809\) 47.5574 1.67203 0.836014 0.548708i \(-0.184880\pi\)
0.836014 + 0.548708i \(0.184880\pi\)
\(810\) 27.3057 0.959424
\(811\) −7.70241 −0.270468 −0.135234 0.990814i \(-0.543179\pi\)
−0.135234 + 0.990814i \(0.543179\pi\)
\(812\) 2.34447 0.0822747
\(813\) 77.3962 2.71440
\(814\) 4.27570 0.149863
\(815\) 25.1640 0.881458
\(816\) 13.4931 0.472354
\(817\) −34.4016 −1.20356
\(818\) −45.1948 −1.58020
\(819\) −0.242838 −0.00848546
\(820\) −31.1674 −1.08841
\(821\) 30.2128 1.05443 0.527216 0.849731i \(-0.323236\pi\)
0.527216 + 0.849731i \(0.323236\pi\)
\(822\) −66.5909 −2.32262
\(823\) 21.9309 0.764463 0.382231 0.924067i \(-0.375156\pi\)
0.382231 + 0.924067i \(0.375156\pi\)
\(824\) 0.446607 0.0155583
\(825\) 2.94342 0.102477
\(826\) −1.83276 −0.0637700
\(827\) 44.9479 1.56299 0.781496 0.623911i \(-0.214457\pi\)
0.781496 + 0.623911i \(0.214457\pi\)
\(828\) −104.474 −3.63073
\(829\) −14.0334 −0.487402 −0.243701 0.969850i \(-0.578361\pi\)
−0.243701 + 0.969850i \(0.578361\pi\)
\(830\) 25.1620 0.873387
\(831\) 59.2766 2.05628
\(832\) −9.76360 −0.338492
\(833\) −11.9061 −0.412521
\(834\) −105.093 −3.63909
\(835\) 4.86439 0.168339
\(836\) 10.1684 0.351681
\(837\) 2.62753 0.0908207
\(838\) −44.2348 −1.52806
\(839\) 14.2638 0.492442 0.246221 0.969214i \(-0.420811\pi\)
0.246221 + 0.969214i \(0.420811\pi\)
\(840\) 1.40621 0.0485188
\(841\) 62.7916 2.16523
\(842\) −58.4631 −2.01477
\(843\) −17.8706 −0.615497
\(844\) −0.929627 −0.0319991
\(845\) 1.90553 0.0655521
\(846\) 10.0356 0.345031
\(847\) 0.658495 0.0226262
\(848\) −10.8026 −0.370963
\(849\) −25.2594 −0.866900
\(850\) 5.62792 0.193036
\(851\) −15.3707 −0.526901
\(852\) 83.1697 2.84935
\(853\) −31.0187 −1.06206 −0.531030 0.847353i \(-0.678195\pi\)
−0.531030 + 0.847353i \(0.678195\pi\)
\(854\) −1.94259 −0.0664740
\(855\) −23.3308 −0.797896
\(856\) −4.83598 −0.165290
\(857\) −5.04435 −0.172312 −0.0861559 0.996282i \(-0.527458\pi\)
−0.0861559 + 0.996282i \(0.527458\pi\)
\(858\) 5.19388 0.177316
\(859\) 21.1328 0.721041 0.360520 0.932751i \(-0.382599\pi\)
0.360520 + 0.932751i \(0.382599\pi\)
\(860\) 78.1553 2.66508
\(861\) 0.709859 0.0241919
\(862\) −32.0036 −1.09005
\(863\) 33.1210 1.12745 0.563726 0.825962i \(-0.309367\pi\)
0.563726 + 0.825962i \(0.309367\pi\)
\(864\) 3.20831 0.109149
\(865\) −8.79330 −0.298981
\(866\) 44.3049 1.50554
\(867\) −36.7943 −1.24960
\(868\) −0.305753 −0.0103779
\(869\) −6.56554 −0.222721
\(870\) 115.053 3.90066
\(871\) −13.0800 −0.443200
\(872\) −38.8797 −1.31663
\(873\) 22.8069 0.771898
\(874\) −55.6161 −1.88124
\(875\) 0.774328 0.0261771
\(876\) −59.1614 −1.99888
\(877\) −51.9908 −1.75561 −0.877803 0.479022i \(-0.840992\pi\)
−0.877803 + 0.479022i \(0.840992\pi\)
\(878\) −86.2897 −2.91214
\(879\) 57.4470 1.93764
\(880\) −4.77275 −0.160889
\(881\) 22.7015 0.764834 0.382417 0.923990i \(-0.375092\pi\)
0.382417 + 0.923990i \(0.375092\pi\)
\(882\) 64.3212 2.16581
\(883\) 42.8551 1.44219 0.721095 0.692836i \(-0.243639\pi\)
0.721095 + 0.692836i \(0.243639\pi\)
\(884\) 6.52717 0.219533
\(885\) −59.1148 −1.98712
\(886\) −40.8179 −1.37130
\(887\) −31.9804 −1.07380 −0.536898 0.843647i \(-0.680404\pi\)
−0.536898 + 0.843647i \(0.680404\pi\)
\(888\) −24.8403 −0.833587
\(889\) 0.556699 0.0186711
\(890\) −34.8760 −1.16905
\(891\) 4.88896 0.163786
\(892\) −106.268 −3.55810
\(893\) 3.51133 0.117502
\(894\) −45.3832 −1.51784
\(895\) −12.1141 −0.404930
\(896\) −1.31013 −0.0437685
\(897\) −18.6715 −0.623422
\(898\) 52.6210 1.75599
\(899\) −11.9710 −0.399254
\(900\) −19.9835 −0.666116
\(901\) −6.04935 −0.201533
\(902\) −8.49039 −0.282699
\(903\) −1.78004 −0.0592360
\(904\) −14.3226 −0.476363
\(905\) −40.9678 −1.36182
\(906\) 77.2691 2.56709
\(907\) 19.4615 0.646209 0.323105 0.946363i \(-0.395273\pi\)
0.323105 + 0.946363i \(0.395273\pi\)
\(908\) −55.2689 −1.83416
\(909\) −23.3723 −0.775209
\(910\) 0.293690 0.00973571
\(911\) −22.6628 −0.750851 −0.375425 0.926853i \(-0.622503\pi\)
−0.375425 + 0.926853i \(0.622503\pi\)
\(912\) −25.5051 −0.844560
\(913\) 4.50515 0.149099
\(914\) −16.9823 −0.561724
\(915\) −62.6572 −2.07138
\(916\) 0.0481549 0.00159108
\(917\) 0.581421 0.0192002
\(918\) −8.64520 −0.285334
\(919\) 37.0287 1.22146 0.610732 0.791838i \(-0.290875\pi\)
0.610732 + 0.791838i \(0.290875\pi\)
\(920\) 60.4633 1.99342
\(921\) 60.7412 2.00149
\(922\) 5.89425 0.194117
\(923\) 8.31218 0.273599
\(924\) 0.526142 0.0173088
\(925\) −2.94006 −0.0966685
\(926\) 30.4386 1.00028
\(927\) −0.383403 −0.0125926
\(928\) −14.6170 −0.479827
\(929\) 2.38453 0.0782338 0.0391169 0.999235i \(-0.487546\pi\)
0.0391169 + 0.999235i \(0.487546\pi\)
\(930\) −15.0046 −0.492020
\(931\) 22.5052 0.737578
\(932\) 69.2370 2.26793
\(933\) 78.7833 2.57925
\(934\) 80.7359 2.64176
\(935\) −2.67270 −0.0874065
\(936\) −16.8742 −0.551550
\(937\) 35.7596 1.16822 0.584108 0.811676i \(-0.301444\pi\)
0.584108 + 0.811676i \(0.301444\pi\)
\(938\) −2.01596 −0.0658234
\(939\) −12.3642 −0.403490
\(940\) −7.97723 −0.260188
\(941\) −37.9116 −1.23588 −0.617941 0.786225i \(-0.712033\pi\)
−0.617941 + 0.786225i \(0.712033\pi\)
\(942\) −72.6764 −2.36793
\(943\) 30.5221 0.993935
\(944\) −36.1389 −1.17622
\(945\) −0.255667 −0.00831686
\(946\) 21.2905 0.692213
\(947\) −15.9966 −0.519818 −0.259909 0.965633i \(-0.583693\pi\)
−0.259909 + 0.965633i \(0.583693\pi\)
\(948\) 79.7093 2.58884
\(949\) −5.91273 −0.191935
\(950\) −10.6381 −0.345144
\(951\) 71.6267 2.32266
\(952\) 0.481404 0.0156024
\(953\) −7.55234 −0.244644 −0.122322 0.992490i \(-0.539034\pi\)
−0.122322 + 0.992490i \(0.539034\pi\)
\(954\) 32.6810 1.05809
\(955\) 6.27846 0.203166
\(956\) −90.8010 −2.93671
\(957\) 20.5997 0.665894
\(958\) −21.7100 −0.701417
\(959\) −0.674178 −0.0217704
\(960\) −48.5371 −1.56653
\(961\) −29.4388 −0.949639
\(962\) −5.18795 −0.167266
\(963\) 4.15159 0.133783
\(964\) 87.9980 2.83422
\(965\) 16.6737 0.536745
\(966\) −2.87774 −0.0925898
\(967\) −53.1304 −1.70856 −0.854280 0.519813i \(-0.826002\pi\)
−0.854280 + 0.519813i \(0.826002\pi\)
\(968\) 45.7570 1.47069
\(969\) −14.2826 −0.458825
\(970\) −27.5828 −0.885630
\(971\) −36.8637 −1.18301 −0.591506 0.806301i \(-0.701466\pi\)
−0.591506 + 0.806301i \(0.701466\pi\)
\(972\) −83.5507 −2.67989
\(973\) −1.06399 −0.0341098
\(974\) −38.0088 −1.21788
\(975\) −3.57142 −0.114377
\(976\) −38.3045 −1.22610
\(977\) −17.3645 −0.555538 −0.277769 0.960648i \(-0.589595\pi\)
−0.277769 + 0.960648i \(0.589595\pi\)
\(978\) −83.2235 −2.66119
\(979\) −6.24439 −0.199572
\(980\) −51.1285 −1.63324
\(981\) 33.3775 1.06566
\(982\) 21.3089 0.679993
\(983\) 8.82194 0.281376 0.140688 0.990054i \(-0.455069\pi\)
0.140688 + 0.990054i \(0.455069\pi\)
\(984\) 49.3262 1.57246
\(985\) 22.9908 0.732549
\(986\) 39.3874 1.25435
\(987\) 0.181687 0.00578315
\(988\) −12.3379 −0.392520
\(989\) −76.5370 −2.43374
\(990\) 14.4390 0.458900
\(991\) −50.2499 −1.59624 −0.798121 0.602497i \(-0.794173\pi\)
−0.798121 + 0.602497i \(0.794173\pi\)
\(992\) 1.90627 0.0605242
\(993\) 40.5772 1.28768
\(994\) 1.28111 0.0406345
\(995\) −7.04407 −0.223312
\(996\) −54.6951 −1.73308
\(997\) 40.8540 1.29386 0.646930 0.762550i \(-0.276053\pi\)
0.646930 + 0.762550i \(0.276053\pi\)
\(998\) 6.01062 0.190263
\(999\) 4.51630 0.142889
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 \(a_p\))