Properties

Label 8018.2.a.f.1.1
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -3.31570 q^{3} +1.00000 q^{4} -0.532224 q^{5} +3.31570 q^{6} -2.51205 q^{7} -1.00000 q^{8} +7.99387 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -3.31570 q^{3} +1.00000 q^{4} -0.532224 q^{5} +3.31570 q^{6} -2.51205 q^{7} -1.00000 q^{8} +7.99387 q^{9} +0.532224 q^{10} +6.00144 q^{11} -3.31570 q^{12} +4.31378 q^{13} +2.51205 q^{14} +1.76470 q^{15} +1.00000 q^{16} +2.00033 q^{17} -7.99387 q^{18} -1.00000 q^{19} -0.532224 q^{20} +8.32922 q^{21} -6.00144 q^{22} -2.59430 q^{23} +3.31570 q^{24} -4.71674 q^{25} -4.31378 q^{26} -16.5582 q^{27} -2.51205 q^{28} +10.1254 q^{29} -1.76470 q^{30} +5.47223 q^{31} -1.00000 q^{32} -19.8990 q^{33} -2.00033 q^{34} +1.33697 q^{35} +7.99387 q^{36} -9.44633 q^{37} +1.00000 q^{38} -14.3032 q^{39} +0.532224 q^{40} +0.879606 q^{41} -8.32922 q^{42} +2.40635 q^{43} +6.00144 q^{44} -4.25453 q^{45} +2.59430 q^{46} -2.58783 q^{47} -3.31570 q^{48} -0.689592 q^{49} +4.71674 q^{50} -6.63248 q^{51} +4.31378 q^{52} -11.7756 q^{53} +16.5582 q^{54} -3.19411 q^{55} +2.51205 q^{56} +3.31570 q^{57} -10.1254 q^{58} -14.3370 q^{59} +1.76470 q^{60} +15.3249 q^{61} -5.47223 q^{62} -20.0810 q^{63} +1.00000 q^{64} -2.29590 q^{65} +19.8990 q^{66} -9.80986 q^{67} +2.00033 q^{68} +8.60191 q^{69} -1.33697 q^{70} -2.81792 q^{71} -7.99387 q^{72} +3.87418 q^{73} +9.44633 q^{74} +15.6393 q^{75} -1.00000 q^{76} -15.0759 q^{77} +14.3032 q^{78} -1.12586 q^{79} -0.532224 q^{80} +30.9204 q^{81} -0.879606 q^{82} -13.8218 q^{83} +8.32922 q^{84} -1.06462 q^{85} -2.40635 q^{86} -33.5730 q^{87} -6.00144 q^{88} -10.7320 q^{89} +4.25453 q^{90} -10.8364 q^{91} -2.59430 q^{92} -18.1443 q^{93} +2.58783 q^{94} +0.532224 q^{95} +3.31570 q^{96} +7.84668 q^{97} +0.689592 q^{98} +47.9748 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} + O(q^{10}) \) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} - 7q^{10} + 4q^{11} - 10q^{12} - 5q^{13} + 6q^{14} - 17q^{15} + 34q^{16} + 8q^{17} - 38q^{18} - 34q^{19} + 7q^{20} - 4q^{22} - 24q^{23} + 10q^{24} + 5q^{25} + 5q^{26} - 31q^{27} - 6q^{28} + 24q^{29} + 17q^{30} - 28q^{31} - 34q^{32} - 16q^{33} - 8q^{34} + 2q^{35} + 38q^{36} - 36q^{37} + 34q^{38} - 9q^{39} - 7q^{40} + 9q^{41} - 24q^{43} + 4q^{44} + 22q^{45} + 24q^{46} - 29q^{47} - 10q^{48} + 22q^{49} - 5q^{50} - 21q^{51} - 5q^{52} - 9q^{53} + 31q^{54} - 28q^{55} + 6q^{56} + 10q^{57} - 24q^{58} - 28q^{59} - 17q^{60} + 23q^{61} + 28q^{62} - 27q^{63} + 34q^{64} - 6q^{65} + 16q^{66} - 51q^{67} + 8q^{68} - 17q^{69} - 2q^{70} - 31q^{71} - 38q^{72} - 26q^{73} + 36q^{74} - 109q^{75} - 34q^{76} - 28q^{77} + 9q^{78} - 36q^{79} + 7q^{80} + 6q^{81} - 9q^{82} - 10q^{83} - 32q^{85} + 24q^{86} - 8q^{87} - 4q^{88} - 34q^{89} - 22q^{90} - 41q^{91} - 24q^{92} - 33q^{93} + 29q^{94} - 7q^{95} + 10q^{96} - 56q^{97} - 22q^{98} - 28q^{99} + O(q^{100}) \)

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
\(3\) −3.31570 −1.91432 −0.957160 0.289558i \(-0.906492\pi\)
−0.957160 + 0.289558i \(0.906492\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.532224 −0.238018 −0.119009 0.992893i \(-0.537972\pi\)
−0.119009 + 0.992893i \(0.537972\pi\)
\(6\) 3.31570 1.35363
\(7\) −2.51205 −0.949467 −0.474733 0.880130i \(-0.657455\pi\)
−0.474733 + 0.880130i \(0.657455\pi\)
\(8\) −1.00000 −0.353553
\(9\) 7.99387 2.66462
\(10\) 0.532224 0.168304
\(11\) 6.00144 1.80950 0.904752 0.425940i \(-0.140056\pi\)
0.904752 + 0.425940i \(0.140056\pi\)
\(12\) −3.31570 −0.957160
\(13\) 4.31378 1.19643 0.598213 0.801337i \(-0.295878\pi\)
0.598213 + 0.801337i \(0.295878\pi\)
\(14\) 2.51205 0.671374
\(15\) 1.76470 0.455643
\(16\) 1.00000 0.250000
\(17\) 2.00033 0.485150 0.242575 0.970133i \(-0.422008\pi\)
0.242575 + 0.970133i \(0.422008\pi\)
\(18\) −7.99387 −1.88417
\(19\) −1.00000 −0.229416
\(20\) −0.532224 −0.119009
\(21\) 8.32922 1.81758
\(22\) −6.00144 −1.27951
\(23\) −2.59430 −0.540948 −0.270474 0.962727i \(-0.587180\pi\)
−0.270474 + 0.962727i \(0.587180\pi\)
\(24\) 3.31570 0.676815
\(25\) −4.71674 −0.943348
\(26\) −4.31378 −0.846001
\(27\) −16.5582 −3.18663
\(28\) −2.51205 −0.474733
\(29\) 10.1254 1.88025 0.940124 0.340832i \(-0.110709\pi\)
0.940124 + 0.340832i \(0.110709\pi\)
\(30\) −1.76470 −0.322188
\(31\) 5.47223 0.982841 0.491420 0.870923i \(-0.336478\pi\)
0.491420 + 0.870923i \(0.336478\pi\)
\(32\) −1.00000 −0.176777
\(33\) −19.8990 −3.46397
\(34\) −2.00033 −0.343053
\(35\) 1.33697 0.225990
\(36\) 7.99387 1.33231
\(37\) −9.44633 −1.55297 −0.776484 0.630138i \(-0.782998\pi\)
−0.776484 + 0.630138i \(0.782998\pi\)
\(38\) 1.00000 0.162221
\(39\) −14.3032 −2.29034
\(40\) 0.532224 0.0841520
\(41\) 0.879606 0.137371 0.0686857 0.997638i \(-0.478119\pi\)
0.0686857 + 0.997638i \(0.478119\pi\)
\(42\) −8.32922 −1.28523
\(43\) 2.40635 0.366965 0.183482 0.983023i \(-0.441263\pi\)
0.183482 + 0.983023i \(0.441263\pi\)
\(44\) 6.00144 0.904752
\(45\) −4.25453 −0.634228
\(46\) 2.59430 0.382508
\(47\) −2.58783 −0.377474 −0.188737 0.982028i \(-0.560439\pi\)
−0.188737 + 0.982028i \(0.560439\pi\)
\(48\) −3.31570 −0.478580
\(49\) −0.689592 −0.0985131
\(50\) 4.71674 0.667047
\(51\) −6.63248 −0.928733
\(52\) 4.31378 0.598213
\(53\) −11.7756 −1.61750 −0.808750 0.588153i \(-0.799855\pi\)
−0.808750 + 0.588153i \(0.799855\pi\)
\(54\) 16.5582 2.25328
\(55\) −3.19411 −0.430694
\(56\) 2.51205 0.335687
\(57\) 3.31570 0.439175
\(58\) −10.1254 −1.32954
\(59\) −14.3370 −1.86652 −0.933259 0.359203i \(-0.883049\pi\)
−0.933259 + 0.359203i \(0.883049\pi\)
\(60\) 1.76470 0.227821
\(61\) 15.3249 1.96215 0.981074 0.193636i \(-0.0620280\pi\)
0.981074 + 0.193636i \(0.0620280\pi\)
\(62\) −5.47223 −0.694973
\(63\) −20.0810 −2.52997
\(64\) 1.00000 0.125000
\(65\) −2.29590 −0.284771
\(66\) 19.8990 2.44940
\(67\) −9.80986 −1.19847 −0.599233 0.800575i \(-0.704528\pi\)
−0.599233 + 0.800575i \(0.704528\pi\)
\(68\) 2.00033 0.242575
\(69\) 8.60191 1.03555
\(70\) −1.33697 −0.159799
\(71\) −2.81792 −0.334426 −0.167213 0.985921i \(-0.553477\pi\)
−0.167213 + 0.985921i \(0.553477\pi\)
\(72\) −7.99387 −0.942087
\(73\) 3.87418 0.453438 0.226719 0.973960i \(-0.427200\pi\)
0.226719 + 0.973960i \(0.427200\pi\)
\(74\) 9.44633 1.09811
\(75\) 15.6393 1.80587
\(76\) −1.00000 −0.114708
\(77\) −15.0759 −1.71806
\(78\) 14.3032 1.61952
\(79\) −1.12586 −0.126669 −0.0633345 0.997992i \(-0.520174\pi\)
−0.0633345 + 0.997992i \(0.520174\pi\)
\(80\) −0.532224 −0.0595045
\(81\) 30.9204 3.43560
\(82\) −0.879606 −0.0971363
\(83\) −13.8218 −1.51714 −0.758571 0.651591i \(-0.774102\pi\)
−0.758571 + 0.651591i \(0.774102\pi\)
\(84\) 8.32922 0.908792
\(85\) −1.06462 −0.115474
\(86\) −2.40635 −0.259483
\(87\) −33.5730 −3.59940
\(88\) −6.00144 −0.639756
\(89\) −10.7320 −1.13759 −0.568795 0.822480i \(-0.692590\pi\)
−0.568795 + 0.822480i \(0.692590\pi\)
\(90\) 4.25453 0.448467
\(91\) −10.8364 −1.13597
\(92\) −2.59430 −0.270474
\(93\) −18.1443 −1.88147
\(94\) 2.58783 0.266915
\(95\) 0.532224 0.0546050
\(96\) 3.31570 0.338407
\(97\) 7.84668 0.796710 0.398355 0.917231i \(-0.369581\pi\)
0.398355 + 0.917231i \(0.369581\pi\)
\(98\) 0.689592 0.0696593
\(99\) 47.9748 4.82165
\(100\) −4.71674 −0.471674
\(101\) −6.15584 −0.612529 −0.306264 0.951947i \(-0.599079\pi\)
−0.306264 + 0.951947i \(0.599079\pi\)
\(102\) 6.63248 0.656714
\(103\) 16.6328 1.63888 0.819439 0.573166i \(-0.194285\pi\)
0.819439 + 0.573166i \(0.194285\pi\)
\(104\) −4.31378 −0.423001
\(105\) −4.43301 −0.432617
\(106\) 11.7756 1.14375
\(107\) 5.65780 0.546960 0.273480 0.961878i \(-0.411825\pi\)
0.273480 + 0.961878i \(0.411825\pi\)
\(108\) −16.5582 −1.59331
\(109\) −6.51313 −0.623844 −0.311922 0.950108i \(-0.600973\pi\)
−0.311922 + 0.950108i \(0.600973\pi\)
\(110\) 3.19411 0.304547
\(111\) 31.3212 2.97288
\(112\) −2.51205 −0.237367
\(113\) 1.07069 0.100722 0.0503609 0.998731i \(-0.483963\pi\)
0.0503609 + 0.998731i \(0.483963\pi\)
\(114\) −3.31570 −0.310544
\(115\) 1.38075 0.128755
\(116\) 10.1254 0.940124
\(117\) 34.4838 3.18803
\(118\) 14.3370 1.31983
\(119\) −5.02492 −0.460634
\(120\) −1.76470 −0.161094
\(121\) 25.0173 2.27430
\(122\) −15.3249 −1.38745
\(123\) −2.91651 −0.262973
\(124\) 5.47223 0.491420
\(125\) 5.17148 0.462551
\(126\) 20.0810 1.78896
\(127\) −19.5247 −1.73254 −0.866271 0.499575i \(-0.833489\pi\)
−0.866271 + 0.499575i \(0.833489\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −7.97874 −0.702489
\(130\) 2.29590 0.201363
\(131\) 9.05590 0.791218 0.395609 0.918419i \(-0.370534\pi\)
0.395609 + 0.918419i \(0.370534\pi\)
\(132\) −19.8990 −1.73198
\(133\) 2.51205 0.217823
\(134\) 9.80986 0.847443
\(135\) 8.81267 0.758474
\(136\) −2.00033 −0.171527
\(137\) 6.02022 0.514342 0.257171 0.966366i \(-0.417210\pi\)
0.257171 + 0.966366i \(0.417210\pi\)
\(138\) −8.60191 −0.732243
\(139\) −7.63928 −0.647955 −0.323978 0.946065i \(-0.605020\pi\)
−0.323978 + 0.946065i \(0.605020\pi\)
\(140\) 1.33697 0.112995
\(141\) 8.58048 0.722607
\(142\) 2.81792 0.236475
\(143\) 25.8889 2.16494
\(144\) 7.99387 0.666156
\(145\) −5.38901 −0.447533
\(146\) −3.87418 −0.320629
\(147\) 2.28648 0.188586
\(148\) −9.44633 −0.776484
\(149\) −5.91544 −0.484612 −0.242306 0.970200i \(-0.577904\pi\)
−0.242306 + 0.970200i \(0.577904\pi\)
\(150\) −15.6393 −1.27694
\(151\) −5.07937 −0.413353 −0.206676 0.978409i \(-0.566265\pi\)
−0.206676 + 0.978409i \(0.566265\pi\)
\(152\) 1.00000 0.0811107
\(153\) 15.9903 1.29274
\(154\) 15.0759 1.21485
\(155\) −2.91245 −0.233934
\(156\) −14.3032 −1.14517
\(157\) 19.3190 1.54182 0.770911 0.636943i \(-0.219801\pi\)
0.770911 + 0.636943i \(0.219801\pi\)
\(158\) 1.12586 0.0895685
\(159\) 39.0443 3.09641
\(160\) 0.532224 0.0420760
\(161\) 6.51701 0.513612
\(162\) −30.9204 −2.42934
\(163\) −0.564810 −0.0442393 −0.0221197 0.999755i \(-0.507041\pi\)
−0.0221197 + 0.999755i \(0.507041\pi\)
\(164\) 0.879606 0.0686857
\(165\) 10.5907 0.824487
\(166\) 13.8218 1.07278
\(167\) −16.6926 −1.29171 −0.645856 0.763460i \(-0.723499\pi\)
−0.645856 + 0.763460i \(0.723499\pi\)
\(168\) −8.32922 −0.642613
\(169\) 5.60868 0.431437
\(170\) 1.06462 0.0816527
\(171\) −7.99387 −0.611307
\(172\) 2.40635 0.183482
\(173\) −8.32146 −0.632669 −0.316335 0.948648i \(-0.602452\pi\)
−0.316335 + 0.948648i \(0.602452\pi\)
\(174\) 33.5730 2.54516
\(175\) 11.8487 0.895677
\(176\) 6.00144 0.452376
\(177\) 47.5372 3.57312
\(178\) 10.7320 0.804397
\(179\) −0.372786 −0.0278634 −0.0139317 0.999903i \(-0.504435\pi\)
−0.0139317 + 0.999903i \(0.504435\pi\)
\(180\) −4.25453 −0.317114
\(181\) −13.6576 −1.01516 −0.507580 0.861605i \(-0.669460\pi\)
−0.507580 + 0.861605i \(0.669460\pi\)
\(182\) 10.8364 0.803250
\(183\) −50.8126 −3.75618
\(184\) 2.59430 0.191254
\(185\) 5.02756 0.369634
\(186\) 18.1443 1.33040
\(187\) 12.0048 0.877881
\(188\) −2.58783 −0.188737
\(189\) 41.5950 3.02559
\(190\) −0.532224 −0.0386116
\(191\) 6.08193 0.440073 0.220036 0.975492i \(-0.429382\pi\)
0.220036 + 0.975492i \(0.429382\pi\)
\(192\) −3.31570 −0.239290
\(193\) 22.0638 1.58819 0.794094 0.607795i \(-0.207946\pi\)
0.794094 + 0.607795i \(0.207946\pi\)
\(194\) −7.84668 −0.563359
\(195\) 7.61251 0.545143
\(196\) −0.689592 −0.0492565
\(197\) −13.8017 −0.983330 −0.491665 0.870785i \(-0.663611\pi\)
−0.491665 + 0.870785i \(0.663611\pi\)
\(198\) −47.9748 −3.40942
\(199\) −22.9043 −1.62364 −0.811822 0.583905i \(-0.801524\pi\)
−0.811822 + 0.583905i \(0.801524\pi\)
\(200\) 4.71674 0.333524
\(201\) 32.5266 2.29425
\(202\) 6.15584 0.433123
\(203\) −25.4357 −1.78523
\(204\) −6.63248 −0.464367
\(205\) −0.468148 −0.0326969
\(206\) −16.6328 −1.15886
\(207\) −20.7385 −1.44142
\(208\) 4.31378 0.299107
\(209\) −6.00144 −0.415128
\(210\) 4.43301 0.305907
\(211\) −1.00000 −0.0688428
\(212\) −11.7756 −0.808750
\(213\) 9.34339 0.640199
\(214\) −5.65780 −0.386759
\(215\) −1.28072 −0.0873442
\(216\) 16.5582 1.12664
\(217\) −13.7465 −0.933174
\(218\) 6.51313 0.441125
\(219\) −12.8456 −0.868026
\(220\) −3.19411 −0.215347
\(221\) 8.62896 0.580447
\(222\) −31.3212 −2.10214
\(223\) 19.7312 1.32130 0.660651 0.750693i \(-0.270280\pi\)
0.660651 + 0.750693i \(0.270280\pi\)
\(224\) 2.51205 0.167844
\(225\) −37.7050 −2.51367
\(226\) −1.07069 −0.0712211
\(227\) 28.4902 1.89096 0.945481 0.325677i \(-0.105592\pi\)
0.945481 + 0.325677i \(0.105592\pi\)
\(228\) 3.31570 0.219588
\(229\) −22.2398 −1.46965 −0.734823 0.678259i \(-0.762735\pi\)
−0.734823 + 0.678259i \(0.762735\pi\)
\(230\) −1.38075 −0.0910438
\(231\) 49.9873 3.28892
\(232\) −10.1254 −0.664768
\(233\) 8.79219 0.575996 0.287998 0.957631i \(-0.407010\pi\)
0.287998 + 0.957631i \(0.407010\pi\)
\(234\) −34.4838 −2.25428
\(235\) 1.37731 0.0898456
\(236\) −14.3370 −0.933259
\(237\) 3.73301 0.242485
\(238\) 5.02492 0.325717
\(239\) −20.9718 −1.35655 −0.678277 0.734806i \(-0.737273\pi\)
−0.678277 + 0.734806i \(0.737273\pi\)
\(240\) 1.76470 0.113911
\(241\) −24.3204 −1.56661 −0.783306 0.621636i \(-0.786468\pi\)
−0.783306 + 0.621636i \(0.786468\pi\)
\(242\) −25.0173 −1.60817
\(243\) −52.8482 −3.39021
\(244\) 15.3249 0.981074
\(245\) 0.367017 0.0234479
\(246\) 2.91651 0.185950
\(247\) −4.31378 −0.274479
\(248\) −5.47223 −0.347487
\(249\) 45.8290 2.90430
\(250\) −5.17148 −0.327073
\(251\) 6.35992 0.401435 0.200717 0.979649i \(-0.435673\pi\)
0.200717 + 0.979649i \(0.435673\pi\)
\(252\) −20.0810 −1.26499
\(253\) −15.5695 −0.978847
\(254\) 19.5247 1.22509
\(255\) 3.52997 0.221055
\(256\) 1.00000 0.0625000
\(257\) 11.7714 0.734280 0.367140 0.930166i \(-0.380337\pi\)
0.367140 + 0.930166i \(0.380337\pi\)
\(258\) 7.97874 0.496734
\(259\) 23.7297 1.47449
\(260\) −2.29590 −0.142385
\(261\) 80.9416 5.01016
\(262\) −9.05590 −0.559475
\(263\) −2.03361 −0.125397 −0.0626987 0.998032i \(-0.519971\pi\)
−0.0626987 + 0.998032i \(0.519971\pi\)
\(264\) 19.8990 1.22470
\(265\) 6.26725 0.384994
\(266\) −2.51205 −0.154024
\(267\) 35.5841 2.17771
\(268\) −9.80986 −0.599233
\(269\) −1.11148 −0.0677684 −0.0338842 0.999426i \(-0.510788\pi\)
−0.0338842 + 0.999426i \(0.510788\pi\)
\(270\) −8.81267 −0.536322
\(271\) −1.29913 −0.0789168 −0.0394584 0.999221i \(-0.512563\pi\)
−0.0394584 + 0.999221i \(0.512563\pi\)
\(272\) 2.00033 0.121288
\(273\) 35.9304 2.17461
\(274\) −6.02022 −0.363695
\(275\) −28.3072 −1.70699
\(276\) 8.60191 0.517774
\(277\) −7.79030 −0.468074 −0.234037 0.972228i \(-0.575194\pi\)
−0.234037 + 0.972228i \(0.575194\pi\)
\(278\) 7.63928 0.458174
\(279\) 43.7443 2.61890
\(280\) −1.33697 −0.0798995
\(281\) −1.41989 −0.0847037 −0.0423519 0.999103i \(-0.513485\pi\)
−0.0423519 + 0.999103i \(0.513485\pi\)
\(282\) −8.58048 −0.510960
\(283\) 24.0398 1.42902 0.714510 0.699625i \(-0.246650\pi\)
0.714510 + 0.699625i \(0.246650\pi\)
\(284\) −2.81792 −0.167213
\(285\) −1.76470 −0.104532
\(286\) −25.8889 −1.53084
\(287\) −2.20962 −0.130430
\(288\) −7.99387 −0.471043
\(289\) −12.9987 −0.764629
\(290\) 5.38901 0.316453
\(291\) −26.0172 −1.52516
\(292\) 3.87418 0.226719
\(293\) 1.14275 0.0667601 0.0333801 0.999443i \(-0.489373\pi\)
0.0333801 + 0.999443i \(0.489373\pi\)
\(294\) −2.28648 −0.133350
\(295\) 7.63050 0.444265
\(296\) 9.44633 0.549057
\(297\) −99.3730 −5.76621
\(298\) 5.91544 0.342672
\(299\) −11.1912 −0.647205
\(300\) 15.6393 0.902935
\(301\) −6.04488 −0.348421
\(302\) 5.07937 0.292285
\(303\) 20.4109 1.17258
\(304\) −1.00000 −0.0573539
\(305\) −8.15626 −0.467026
\(306\) −15.9903 −0.914107
\(307\) −26.4911 −1.51193 −0.755965 0.654612i \(-0.772832\pi\)
−0.755965 + 0.654612i \(0.772832\pi\)
\(308\) −15.0759 −0.859031
\(309\) −55.1494 −3.13734
\(310\) 2.91245 0.165416
\(311\) −16.7266 −0.948477 −0.474238 0.880397i \(-0.657276\pi\)
−0.474238 + 0.880397i \(0.657276\pi\)
\(312\) 14.3032 0.809759
\(313\) −2.36264 −0.133544 −0.0667722 0.997768i \(-0.521270\pi\)
−0.0667722 + 0.997768i \(0.521270\pi\)
\(314\) −19.3190 −1.09023
\(315\) 10.6876 0.602179
\(316\) −1.12586 −0.0633345
\(317\) 26.0184 1.46134 0.730670 0.682731i \(-0.239208\pi\)
0.730670 + 0.682731i \(0.239208\pi\)
\(318\) −39.0443 −2.18950
\(319\) 60.7673 3.40232
\(320\) −0.532224 −0.0297522
\(321\) −18.7596 −1.04706
\(322\) −6.51701 −0.363179
\(323\) −2.00033 −0.111301
\(324\) 30.9204 1.71780
\(325\) −20.3470 −1.12865
\(326\) 0.564810 0.0312819
\(327\) 21.5956 1.19424
\(328\) −0.879606 −0.0485681
\(329\) 6.50077 0.358399
\(330\) −10.5907 −0.583000
\(331\) −19.2136 −1.05607 −0.528037 0.849221i \(-0.677072\pi\)
−0.528037 + 0.849221i \(0.677072\pi\)
\(332\) −13.8218 −0.758571
\(333\) −75.5128 −4.13807
\(334\) 16.6926 0.913378
\(335\) 5.22104 0.285256
\(336\) 8.32922 0.454396
\(337\) −5.71500 −0.311316 −0.155658 0.987811i \(-0.549750\pi\)
−0.155658 + 0.987811i \(0.549750\pi\)
\(338\) −5.60868 −0.305072
\(339\) −3.55008 −0.192814
\(340\) −1.06462 −0.0577372
\(341\) 32.8412 1.77845
\(342\) 7.99387 0.432259
\(343\) 19.3167 1.04300
\(344\) −2.40635 −0.129742
\(345\) −4.57814 −0.246479
\(346\) 8.32146 0.447365
\(347\) −11.0469 −0.593031 −0.296516 0.955028i \(-0.595825\pi\)
−0.296516 + 0.955028i \(0.595825\pi\)
\(348\) −33.5730 −1.79970
\(349\) 5.41033 0.289608 0.144804 0.989460i \(-0.453745\pi\)
0.144804 + 0.989460i \(0.453745\pi\)
\(350\) −11.8487 −0.633339
\(351\) −71.4284 −3.81256
\(352\) −6.00144 −0.319878
\(353\) 8.21985 0.437499 0.218749 0.975781i \(-0.429802\pi\)
0.218749 + 0.975781i \(0.429802\pi\)
\(354\) −47.5372 −2.52657
\(355\) 1.49977 0.0795994
\(356\) −10.7320 −0.568795
\(357\) 16.6611 0.881801
\(358\) 0.372786 0.0197024
\(359\) 27.5741 1.45531 0.727653 0.685945i \(-0.240611\pi\)
0.727653 + 0.685945i \(0.240611\pi\)
\(360\) 4.25453 0.224234
\(361\) 1.00000 0.0526316
\(362\) 13.6576 0.717826
\(363\) −82.9499 −4.35374
\(364\) −10.8364 −0.567984
\(365\) −2.06193 −0.107926
\(366\) 50.8126 2.65602
\(367\) −35.1518 −1.83491 −0.917453 0.397843i \(-0.869759\pi\)
−0.917453 + 0.397843i \(0.869759\pi\)
\(368\) −2.59430 −0.135237
\(369\) 7.03146 0.366043
\(370\) −5.02756 −0.261371
\(371\) 29.5809 1.53576
\(372\) −18.1443 −0.940736
\(373\) −21.9794 −1.13805 −0.569025 0.822320i \(-0.692679\pi\)
−0.569025 + 0.822320i \(0.692679\pi\)
\(374\) −12.0048 −0.620755
\(375\) −17.1471 −0.885472
\(376\) 2.58783 0.133457
\(377\) 43.6789 2.24958
\(378\) −41.5950 −2.13942
\(379\) −5.41110 −0.277950 −0.138975 0.990296i \(-0.544381\pi\)
−0.138975 + 0.990296i \(0.544381\pi\)
\(380\) 0.532224 0.0273025
\(381\) 64.7382 3.31664
\(382\) −6.08193 −0.311178
\(383\) 3.51955 0.179841 0.0899204 0.995949i \(-0.471339\pi\)
0.0899204 + 0.995949i \(0.471339\pi\)
\(384\) 3.31570 0.169204
\(385\) 8.02378 0.408930
\(386\) −22.0638 −1.12302
\(387\) 19.2361 0.977824
\(388\) 7.84668 0.398355
\(389\) 9.79046 0.496396 0.248198 0.968709i \(-0.420162\pi\)
0.248198 + 0.968709i \(0.420162\pi\)
\(390\) −7.61251 −0.385474
\(391\) −5.18944 −0.262441
\(392\) 0.689592 0.0348296
\(393\) −30.0267 −1.51464
\(394\) 13.8017 0.695319
\(395\) 0.599209 0.0301495
\(396\) 47.9748 2.41082
\(397\) 13.4179 0.673424 0.336712 0.941608i \(-0.390685\pi\)
0.336712 + 0.941608i \(0.390685\pi\)
\(398\) 22.9043 1.14809
\(399\) −8.32922 −0.416982
\(400\) −4.71674 −0.235837
\(401\) 36.6623 1.83083 0.915413 0.402516i \(-0.131864\pi\)
0.915413 + 0.402516i \(0.131864\pi\)
\(402\) −32.5266 −1.62228
\(403\) 23.6060 1.17590
\(404\) −6.15584 −0.306264
\(405\) −16.4566 −0.817734
\(406\) 25.4357 1.26235
\(407\) −56.6916 −2.81010
\(408\) 6.63248 0.328357
\(409\) −23.9115 −1.18235 −0.591175 0.806544i \(-0.701336\pi\)
−0.591175 + 0.806544i \(0.701336\pi\)
\(410\) 0.468148 0.0231202
\(411\) −19.9613 −0.984616
\(412\) 16.6328 0.819439
\(413\) 36.0153 1.77220
\(414\) 20.7385 1.01924
\(415\) 7.35631 0.361107
\(416\) −4.31378 −0.211500
\(417\) 25.3296 1.24039
\(418\) 6.00144 0.293540
\(419\) −14.7038 −0.718329 −0.359164 0.933274i \(-0.616938\pi\)
−0.359164 + 0.933274i \(0.616938\pi\)
\(420\) −4.43301 −0.216309
\(421\) 11.7662 0.573448 0.286724 0.958013i \(-0.407434\pi\)
0.286724 + 0.958013i \(0.407434\pi\)
\(422\) 1.00000 0.0486792
\(423\) −20.6868 −1.00583
\(424\) 11.7756 0.571873
\(425\) −9.43501 −0.457665
\(426\) −9.34339 −0.452689
\(427\) −38.4969 −1.86299
\(428\) 5.65780 0.273480
\(429\) −85.8398 −4.14439
\(430\) 1.28072 0.0617617
\(431\) −34.5868 −1.66599 −0.832993 0.553283i \(-0.813375\pi\)
−0.832993 + 0.553283i \(0.813375\pi\)
\(432\) −16.5582 −0.796656
\(433\) −25.8068 −1.24020 −0.620098 0.784524i \(-0.712907\pi\)
−0.620098 + 0.784524i \(0.712907\pi\)
\(434\) 13.7465 0.659854
\(435\) 17.8683 0.856721
\(436\) −6.51313 −0.311922
\(437\) 2.59430 0.124102
\(438\) 12.8456 0.613787
\(439\) −15.6198 −0.745491 −0.372745 0.927934i \(-0.621584\pi\)
−0.372745 + 0.927934i \(0.621584\pi\)
\(440\) 3.19411 0.152273
\(441\) −5.51251 −0.262500
\(442\) −8.62896 −0.410438
\(443\) 6.69100 0.317899 0.158949 0.987287i \(-0.449189\pi\)
0.158949 + 0.987287i \(0.449189\pi\)
\(444\) 31.3212 1.48644
\(445\) 5.71183 0.270767
\(446\) −19.7312 −0.934301
\(447\) 19.6138 0.927702
\(448\) −2.51205 −0.118683
\(449\) 10.4379 0.492595 0.246297 0.969194i \(-0.420786\pi\)
0.246297 + 0.969194i \(0.420786\pi\)
\(450\) 37.7050 1.77743
\(451\) 5.27891 0.248574
\(452\) 1.07069 0.0503609
\(453\) 16.8417 0.791290
\(454\) −28.4902 −1.33711
\(455\) 5.76741 0.270381
\(456\) −3.31570 −0.155272
\(457\) 21.5202 1.00667 0.503336 0.864091i \(-0.332106\pi\)
0.503336 + 0.864091i \(0.332106\pi\)
\(458\) 22.2398 1.03920
\(459\) −33.1218 −1.54599
\(460\) 1.38075 0.0643777
\(461\) 38.6757 1.80131 0.900654 0.434538i \(-0.143088\pi\)
0.900654 + 0.434538i \(0.143088\pi\)
\(462\) −49.9873 −2.32562
\(463\) −3.68622 −0.171313 −0.0856566 0.996325i \(-0.527299\pi\)
−0.0856566 + 0.996325i \(0.527299\pi\)
\(464\) 10.1254 0.470062
\(465\) 9.65681 0.447824
\(466\) −8.79219 −0.407290
\(467\) 7.66542 0.354713 0.177357 0.984147i \(-0.443245\pi\)
0.177357 + 0.984147i \(0.443245\pi\)
\(468\) 34.4838 1.59401
\(469\) 24.6429 1.13790
\(470\) −1.37731 −0.0635304
\(471\) −64.0560 −2.95154
\(472\) 14.3370 0.659914
\(473\) 14.4416 0.664024
\(474\) −3.73301 −0.171463
\(475\) 4.71674 0.216419
\(476\) −5.02492 −0.230317
\(477\) −94.1325 −4.31003
\(478\) 20.9718 0.959229
\(479\) 12.8827 0.588625 0.294313 0.955709i \(-0.404909\pi\)
0.294313 + 0.955709i \(0.404909\pi\)
\(480\) −1.76470 −0.0805470
\(481\) −40.7494 −1.85801
\(482\) 24.3204 1.10776
\(483\) −21.6085 −0.983219
\(484\) 25.0173 1.13715
\(485\) −4.17619 −0.189631
\(486\) 52.8482 2.39724
\(487\) −36.9578 −1.67472 −0.837359 0.546654i \(-0.815901\pi\)
−0.837359 + 0.546654i \(0.815901\pi\)
\(488\) −15.3249 −0.693724
\(489\) 1.87274 0.0846883
\(490\) −0.367017 −0.0165802
\(491\) −12.0707 −0.544743 −0.272371 0.962192i \(-0.587808\pi\)
−0.272371 + 0.962192i \(0.587808\pi\)
\(492\) −2.91651 −0.131487
\(493\) 20.2542 0.912203
\(494\) 4.31378 0.194086
\(495\) −25.5333 −1.14764
\(496\) 5.47223 0.245710
\(497\) 7.07877 0.317526
\(498\) −45.8290 −2.05365
\(499\) −21.9071 −0.980697 −0.490349 0.871526i \(-0.663131\pi\)
−0.490349 + 0.871526i \(0.663131\pi\)
\(500\) 5.17148 0.231276
\(501\) 55.3476 2.47275
\(502\) −6.35992 −0.283857
\(503\) 24.4459 1.08999 0.544994 0.838440i \(-0.316532\pi\)
0.544994 + 0.838440i \(0.316532\pi\)
\(504\) 20.0810 0.894480
\(505\) 3.27628 0.145793
\(506\) 15.5695 0.692150
\(507\) −18.5967 −0.825909
\(508\) −19.5247 −0.866271
\(509\) 33.3226 1.47700 0.738499 0.674254i \(-0.235535\pi\)
0.738499 + 0.674254i \(0.235535\pi\)
\(510\) −3.52997 −0.156310
\(511\) −9.73214 −0.430524
\(512\) −1.00000 −0.0441942
\(513\) 16.5582 0.731062
\(514\) −11.7714 −0.519214
\(515\) −8.85238 −0.390082
\(516\) −7.97874 −0.351244
\(517\) −15.5307 −0.683041
\(518\) −23.7297 −1.04262
\(519\) 27.5915 1.21113
\(520\) 2.29590 0.100682
\(521\) −20.9988 −0.919975 −0.459987 0.887925i \(-0.652146\pi\)
−0.459987 + 0.887925i \(0.652146\pi\)
\(522\) −80.9416 −3.54272
\(523\) −5.03035 −0.219962 −0.109981 0.993934i \(-0.535079\pi\)
−0.109981 + 0.993934i \(0.535079\pi\)
\(524\) 9.05590 0.395609
\(525\) −39.2867 −1.71461
\(526\) 2.03361 0.0886694
\(527\) 10.9462 0.476825
\(528\) −19.8990 −0.865992
\(529\) −16.2696 −0.707375
\(530\) −6.26725 −0.272232
\(531\) −114.608 −4.97357
\(532\) 2.51205 0.108911
\(533\) 3.79443 0.164355
\(534\) −35.5841 −1.53987
\(535\) −3.01122 −0.130186
\(536\) 9.80986 0.423721
\(537\) 1.23605 0.0533394
\(538\) 1.11148 0.0479195
\(539\) −4.13854 −0.178260
\(540\) 8.81267 0.379237
\(541\) −25.3594 −1.09028 −0.545142 0.838344i \(-0.683524\pi\)
−0.545142 + 0.838344i \(0.683524\pi\)
\(542\) 1.29913 0.0558026
\(543\) 45.2844 1.94334
\(544\) −2.00033 −0.0857633
\(545\) 3.46644 0.148486
\(546\) −35.9304 −1.53768
\(547\) 13.5467 0.579213 0.289607 0.957146i \(-0.406476\pi\)
0.289607 + 0.957146i \(0.406476\pi\)
\(548\) 6.02022 0.257171
\(549\) 122.505 5.22838
\(550\) 28.3072 1.20702
\(551\) −10.1254 −0.431359
\(552\) −8.60191 −0.366122
\(553\) 2.82822 0.120268
\(554\) 7.79030 0.330978
\(555\) −16.6699 −0.707598
\(556\) −7.63928 −0.323978
\(557\) −10.8735 −0.460725 −0.230363 0.973105i \(-0.573991\pi\)
−0.230363 + 0.973105i \(0.573991\pi\)
\(558\) −43.7443 −1.85184
\(559\) 10.3805 0.439047
\(560\) 1.33697 0.0564975
\(561\) −39.8045 −1.68055
\(562\) 1.41989 0.0598946
\(563\) −27.5105 −1.15943 −0.579714 0.814820i \(-0.696836\pi\)
−0.579714 + 0.814820i \(0.696836\pi\)
\(564\) 8.58048 0.361303
\(565\) −0.569846 −0.0239736
\(566\) −24.0398 −1.01047
\(567\) −77.6736 −3.26199
\(568\) 2.81792 0.118237
\(569\) −24.9055 −1.04409 −0.522047 0.852916i \(-0.674832\pi\)
−0.522047 + 0.852916i \(0.674832\pi\)
\(570\) 1.76470 0.0739150
\(571\) −5.55007 −0.232263 −0.116132 0.993234i \(-0.537049\pi\)
−0.116132 + 0.993234i \(0.537049\pi\)
\(572\) 25.8889 1.08247
\(573\) −20.1659 −0.842441
\(574\) 2.20962 0.0922277
\(575\) 12.2366 0.510302
\(576\) 7.99387 0.333078
\(577\) 18.4253 0.767057 0.383528 0.923529i \(-0.374709\pi\)
0.383528 + 0.923529i \(0.374709\pi\)
\(578\) 12.9987 0.540675
\(579\) −73.1570 −3.04030
\(580\) −5.38901 −0.223766
\(581\) 34.7211 1.44048
\(582\) 26.0172 1.07845
\(583\) −70.6705 −2.92687
\(584\) −3.87418 −0.160315
\(585\) −18.3531 −0.758808
\(586\) −1.14275 −0.0472065
\(587\) 31.6993 1.30837 0.654185 0.756334i \(-0.273012\pi\)
0.654185 + 0.756334i \(0.273012\pi\)
\(588\) 2.28648 0.0942928
\(589\) −5.47223 −0.225479
\(590\) −7.63050 −0.314143
\(591\) 45.7623 1.88241
\(592\) −9.44633 −0.388242
\(593\) −5.01929 −0.206118 −0.103059 0.994675i \(-0.532863\pi\)
−0.103059 + 0.994675i \(0.532863\pi\)
\(594\) 99.3730 4.07732
\(595\) 2.67439 0.109639
\(596\) −5.91544 −0.242306
\(597\) 75.9439 3.10818
\(598\) 11.1912 0.457643
\(599\) 18.2729 0.746609 0.373305 0.927709i \(-0.378225\pi\)
0.373305 + 0.927709i \(0.378225\pi\)
\(600\) −15.6393 −0.638471
\(601\) −21.3508 −0.870919 −0.435460 0.900208i \(-0.643414\pi\)
−0.435460 + 0.900208i \(0.643414\pi\)
\(602\) 6.04488 0.246371
\(603\) −78.4188 −3.19346
\(604\) −5.07937 −0.206676
\(605\) −13.3148 −0.541324
\(606\) −20.4109 −0.829137
\(607\) −22.7582 −0.923728 −0.461864 0.886951i \(-0.652819\pi\)
−0.461864 + 0.886951i \(0.652819\pi\)
\(608\) 1.00000 0.0405554
\(609\) 84.3370 3.41751
\(610\) 8.15626 0.330237
\(611\) −11.1633 −0.451620
\(612\) 15.9903 0.646372
\(613\) 0.0618928 0.00249983 0.00124991 0.999999i \(-0.499602\pi\)
0.00124991 + 0.999999i \(0.499602\pi\)
\(614\) 26.4911 1.06910
\(615\) 1.55224 0.0625923
\(616\) 15.0759 0.607427
\(617\) 14.1077 0.567953 0.283977 0.958831i \(-0.408346\pi\)
0.283977 + 0.958831i \(0.408346\pi\)
\(618\) 55.1494 2.21843
\(619\) 22.2558 0.894535 0.447268 0.894400i \(-0.352397\pi\)
0.447268 + 0.894400i \(0.352397\pi\)
\(620\) −2.91245 −0.116967
\(621\) 42.9569 1.72380
\(622\) 16.7266 0.670674
\(623\) 26.9593 1.08010
\(624\) −14.3032 −0.572586
\(625\) 20.8313 0.833252
\(626\) 2.36264 0.0944301
\(627\) 19.8990 0.794689
\(628\) 19.3190 0.770911
\(629\) −18.8957 −0.753422
\(630\) −10.6876 −0.425805
\(631\) 3.89365 0.155004 0.0775019 0.996992i \(-0.475306\pi\)
0.0775019 + 0.996992i \(0.475306\pi\)
\(632\) 1.12586 0.0447843
\(633\) 3.31570 0.131787
\(634\) −26.0184 −1.03332
\(635\) 10.3915 0.412376
\(636\) 39.0443 1.54821
\(637\) −2.97475 −0.117864
\(638\) −60.7673 −2.40580
\(639\) −22.5261 −0.891120
\(640\) 0.532224 0.0210380
\(641\) −21.4135 −0.845781 −0.422891 0.906181i \(-0.638985\pi\)
−0.422891 + 0.906181i \(0.638985\pi\)
\(642\) 18.7596 0.740381
\(643\) −28.1090 −1.10851 −0.554256 0.832347i \(-0.686997\pi\)
−0.554256 + 0.832347i \(0.686997\pi\)
\(644\) 6.51701 0.256806
\(645\) 4.24648 0.167205
\(646\) 2.00033 0.0787018
\(647\) −18.1515 −0.713610 −0.356805 0.934179i \(-0.616134\pi\)
−0.356805 + 0.934179i \(0.616134\pi\)
\(648\) −30.9204 −1.21467
\(649\) −86.0427 −3.37747
\(650\) 20.3470 0.798073
\(651\) 45.5793 1.78640
\(652\) −0.564810 −0.0221197
\(653\) 5.18457 0.202888 0.101444 0.994841i \(-0.467654\pi\)
0.101444 + 0.994841i \(0.467654\pi\)
\(654\) −21.5956 −0.844454
\(655\) −4.81977 −0.188324
\(656\) 0.879606 0.0343429
\(657\) 30.9697 1.20824
\(658\) −6.50077 −0.253426
\(659\) −33.7893 −1.31624 −0.658122 0.752911i \(-0.728649\pi\)
−0.658122 + 0.752911i \(0.728649\pi\)
\(660\) 10.5907 0.412243
\(661\) −39.7254 −1.54514 −0.772569 0.634930i \(-0.781029\pi\)
−0.772569 + 0.634930i \(0.781029\pi\)
\(662\) 19.2136 0.746757
\(663\) −28.6111 −1.11116
\(664\) 13.8218 0.536391
\(665\) −1.33697 −0.0518457
\(666\) 75.5128 2.92606
\(667\) −26.2684 −1.01712
\(668\) −16.6926 −0.645856
\(669\) −65.4229 −2.52939
\(670\) −5.22104 −0.201707
\(671\) 91.9713 3.55051
\(672\) −8.32922 −0.321306
\(673\) −25.0815 −0.966821 −0.483410 0.875394i \(-0.660602\pi\)
−0.483410 + 0.875394i \(0.660602\pi\)
\(674\) 5.71500 0.220133
\(675\) 78.1006 3.00609
\(676\) 5.60868 0.215719
\(677\) 31.4916 1.21032 0.605161 0.796103i \(-0.293109\pi\)
0.605161 + 0.796103i \(0.293109\pi\)
\(678\) 3.55008 0.136340
\(679\) −19.7113 −0.756449
\(680\) 1.06462 0.0408264
\(681\) −94.4650 −3.61991
\(682\) −32.8412 −1.25756
\(683\) 10.2390 0.391786 0.195893 0.980625i \(-0.437239\pi\)
0.195893 + 0.980625i \(0.437239\pi\)
\(684\) −7.99387 −0.305653
\(685\) −3.20411 −0.122423
\(686\) −19.3167 −0.737513
\(687\) 73.7404 2.81337
\(688\) 2.40635 0.0917412
\(689\) −50.7972 −1.93522
\(690\) 4.57814 0.174287
\(691\) 35.4416 1.34826 0.674131 0.738612i \(-0.264518\pi\)
0.674131 + 0.738612i \(0.264518\pi\)
\(692\) −8.32146 −0.316335
\(693\) −120.515 −4.57799
\(694\) 11.0469 0.419336
\(695\) 4.06581 0.154225
\(696\) 33.5730 1.27258
\(697\) 1.75950 0.0666458
\(698\) −5.41033 −0.204784
\(699\) −29.1523 −1.10264
\(700\) 11.8487 0.447838
\(701\) −47.9520 −1.81112 −0.905561 0.424216i \(-0.860550\pi\)
−0.905561 + 0.424216i \(0.860550\pi\)
\(702\) 71.4284 2.69589
\(703\) 9.44633 0.356275
\(704\) 6.00144 0.226188
\(705\) −4.56674 −0.171993
\(706\) −8.21985 −0.309358
\(707\) 15.4638 0.581575
\(708\) 47.5372 1.78656
\(709\) 24.7691 0.930224 0.465112 0.885252i \(-0.346014\pi\)
0.465112 + 0.885252i \(0.346014\pi\)
\(710\) −1.49977 −0.0562853
\(711\) −8.99997 −0.337525
\(712\) 10.7320 0.402198
\(713\) −14.1966 −0.531666
\(714\) −16.6611 −0.623528
\(715\) −13.7787 −0.515294
\(716\) −0.372786 −0.0139317
\(717\) 69.5363 2.59688
\(718\) −27.5741 −1.02906
\(719\) −0.289733 −0.0108052 −0.00540262 0.999985i \(-0.501720\pi\)
−0.00540262 + 0.999985i \(0.501720\pi\)
\(720\) −4.25453 −0.158557
\(721\) −41.7825 −1.55606
\(722\) −1.00000 −0.0372161
\(723\) 80.6390 2.99900
\(724\) −13.6576 −0.507580
\(725\) −47.7591 −1.77373
\(726\) 82.9499 3.07856
\(727\) 51.4476 1.90808 0.954042 0.299673i \(-0.0968775\pi\)
0.954042 + 0.299673i \(0.0968775\pi\)
\(728\) 10.8364 0.401625
\(729\) 82.4676 3.05436
\(730\) 2.06193 0.0763155
\(731\) 4.81348 0.178033
\(732\) −50.8126 −1.87809
\(733\) 27.8290 1.02789 0.513943 0.857824i \(-0.328184\pi\)
0.513943 + 0.857824i \(0.328184\pi\)
\(734\) 35.1518 1.29747
\(735\) −1.21692 −0.0448868
\(736\) 2.59430 0.0956270
\(737\) −58.8733 −2.16863
\(738\) −7.03146 −0.258832
\(739\) −29.1854 −1.07360 −0.536802 0.843709i \(-0.680368\pi\)
−0.536802 + 0.843709i \(0.680368\pi\)
\(740\) 5.02756 0.184817
\(741\) 14.3032 0.525441
\(742\) −29.5809 −1.08595
\(743\) 34.3759 1.26113 0.630564 0.776137i \(-0.282824\pi\)
0.630564 + 0.776137i \(0.282824\pi\)
\(744\) 18.1443 0.665201
\(745\) 3.14834 0.115346
\(746\) 21.9794 0.804723
\(747\) −110.490 −4.04261
\(748\) 12.0048 0.438940
\(749\) −14.2127 −0.519320
\(750\) 17.1471 0.626123
\(751\) −21.7340 −0.793085 −0.396542 0.918016i \(-0.629790\pi\)
−0.396542 + 0.918016i \(0.629790\pi\)
\(752\) −2.58783 −0.0943685
\(753\) −21.0876 −0.768475
\(754\) −43.6789 −1.59069
\(755\) 2.70336 0.0983854
\(756\) 41.5950 1.51280
\(757\) 23.7135 0.861881 0.430941 0.902380i \(-0.358182\pi\)
0.430941 + 0.902380i \(0.358182\pi\)
\(758\) 5.41110 0.196540
\(759\) 51.6239 1.87383
\(760\) −0.532224 −0.0193058
\(761\) 39.4330 1.42945 0.714723 0.699408i \(-0.246553\pi\)
0.714723 + 0.699408i \(0.246553\pi\)
\(762\) −64.7382 −2.34522
\(763\) 16.3613 0.592319
\(764\) 6.08193 0.220036
\(765\) −8.51045 −0.307696
\(766\) −3.51955 −0.127167
\(767\) −61.8467 −2.23315
\(768\) −3.31570 −0.119645
\(769\) 16.5387 0.596401 0.298200 0.954503i \(-0.403614\pi\)
0.298200 + 0.954503i \(0.403614\pi\)
\(770\) −8.02378 −0.289157
\(771\) −39.0304 −1.40565
\(772\) 22.0638 0.794094
\(773\) 10.4349 0.375319 0.187659 0.982234i \(-0.439910\pi\)
0.187659 + 0.982234i \(0.439910\pi\)
\(774\) −19.2361 −0.691426
\(775\) −25.8110 −0.927160
\(776\) −7.84668 −0.281679
\(777\) −78.6805 −2.82265
\(778\) −9.79046 −0.351005
\(779\) −0.879606 −0.0315152
\(780\) 7.61251 0.272571
\(781\) −16.9116 −0.605145
\(782\) 5.18944 0.185574
\(783\) −167.659 −5.99165
\(784\) −0.689592 −0.0246283
\(785\) −10.2820 −0.366981
\(786\) 30.0267 1.07102
\(787\) 15.4677 0.551362 0.275681 0.961249i \(-0.411097\pi\)
0.275681 + 0.961249i \(0.411097\pi\)
\(788\) −13.8017 −0.491665
\(789\) 6.74283 0.240051
\(790\) −0.599209 −0.0213189
\(791\) −2.68962 −0.0956320
\(792\) −47.9748 −1.70471
\(793\) 66.1080 2.34757
\(794\) −13.4179 −0.476182
\(795\) −20.7803 −0.737002
\(796\) −22.9043 −0.811822
\(797\) 5.17864 0.183437 0.0917184 0.995785i \(-0.470764\pi\)
0.0917184 + 0.995785i \(0.470764\pi\)
\(798\) 8.32922 0.294851
\(799\) −5.17651 −0.183132
\(800\) 4.71674 0.166762
\(801\) −85.7902 −3.03125
\(802\) −36.6623 −1.29459
\(803\) 23.2506 0.820498
\(804\) 32.5266 1.14712
\(805\) −3.46851 −0.122249
\(806\) −23.6060 −0.831485
\(807\) 3.68535 0.129730
\(808\) 6.15584 0.216562
\(809\) −2.47229 −0.0869211 −0.0434605 0.999055i \(-0.513838\pi\)
−0.0434605 + 0.999055i \(0.513838\pi\)
\(810\) 16.4566 0.578225
\(811\) −44.9503 −1.57842 −0.789209 0.614124i \(-0.789509\pi\)
−0.789209 + 0.614124i \(0.789509\pi\)
\(812\) −25.4357 −0.892617
\(813\) 4.30754 0.151072
\(814\) 56.6916 1.98704
\(815\) 0.300606 0.0105298
\(816\) −6.63248 −0.232183
\(817\) −2.40635 −0.0841875
\(818\) 23.9115 0.836047
\(819\) −86.6251 −3.02693
\(820\) −0.468148 −0.0163484
\(821\) 0.446654 0.0155883 0.00779417 0.999970i \(-0.497519\pi\)
0.00779417 + 0.999970i \(0.497519\pi\)
\(822\) 19.9613 0.696229
\(823\) −39.7433 −1.38536 −0.692681 0.721244i \(-0.743571\pi\)
−0.692681 + 0.721244i \(0.743571\pi\)
\(824\) −16.6328 −0.579431
\(825\) 93.8583 3.26773
\(826\) −36.0153 −1.25313
\(827\) −33.8125 −1.17578 −0.587888 0.808942i \(-0.700040\pi\)
−0.587888 + 0.808942i \(0.700040\pi\)
\(828\) −20.7385 −0.720712
\(829\) −11.4591 −0.397990 −0.198995 0.980001i \(-0.563768\pi\)
−0.198995 + 0.980001i \(0.563768\pi\)
\(830\) −7.35631 −0.255341
\(831\) 25.8303 0.896043
\(832\) 4.31378 0.149553
\(833\) −1.37941 −0.0477937
\(834\) −25.3296 −0.877091
\(835\) 8.88420 0.307450
\(836\) −6.00144 −0.207564
\(837\) −90.6101 −3.13194
\(838\) 14.7038 0.507935
\(839\) 17.5795 0.606913 0.303456 0.952845i \(-0.401859\pi\)
0.303456 + 0.952845i \(0.401859\pi\)
\(840\) 4.43301 0.152953
\(841\) 73.5247 2.53534
\(842\) −11.7662 −0.405489
\(843\) 4.70794 0.162150
\(844\) −1.00000 −0.0344214
\(845\) −2.98508 −0.102690
\(846\) 20.6868 0.711227
\(847\) −62.8448 −2.15937
\(848\) −11.7756 −0.404375
\(849\) −79.7089 −2.73560
\(850\) 9.43501 0.323618
\(851\) 24.5066 0.840075
\(852\) 9.34339 0.320099
\(853\) 27.7700 0.950827 0.475414 0.879762i \(-0.342298\pi\)
0.475414 + 0.879762i \(0.342298\pi\)
\(854\) 38.4969 1.31734
\(855\) 4.25453 0.145502
\(856\) −5.65780 −0.193380
\(857\) 26.3289 0.899379 0.449689 0.893185i \(-0.351535\pi\)
0.449689 + 0.893185i \(0.351535\pi\)
\(858\) 85.8398 2.93052
\(859\) 38.2165 1.30393 0.651965 0.758249i \(-0.273945\pi\)
0.651965 + 0.758249i \(0.273945\pi\)
\(860\) −1.28072 −0.0436721
\(861\) 7.32643 0.249684
\(862\) 34.5868 1.17803
\(863\) −44.0262 −1.49867 −0.749335 0.662191i \(-0.769627\pi\)
−0.749335 + 0.662191i \(0.769627\pi\)
\(864\) 16.5582 0.563321
\(865\) 4.42888 0.150587
\(866\) 25.8068 0.876951
\(867\) 43.0998 1.46375
\(868\) −13.7465 −0.466587
\(869\) −6.75678 −0.229208
\(870\) −17.8683 −0.605793
\(871\) −42.3176 −1.43388
\(872\) 6.51313 0.220562
\(873\) 62.7254 2.12293
\(874\) −2.59430 −0.0877534
\(875\) −12.9910 −0.439177
\(876\) −12.8456 −0.434013
\(877\) 12.6840 0.428307 0.214154 0.976800i \(-0.431301\pi\)
0.214154 + 0.976800i \(0.431301\pi\)
\(878\) 15.6198 0.527142
\(879\) −3.78901 −0.127800
\(880\) −3.19411 −0.107674
\(881\) −39.1519 −1.31906 −0.659530 0.751678i \(-0.729245\pi\)
−0.659530 + 0.751678i \(0.729245\pi\)
\(882\) 5.51251 0.185616
\(883\) 29.2904 0.985701 0.492851 0.870114i \(-0.335955\pi\)
0.492851 + 0.870114i \(0.335955\pi\)
\(884\) 8.62896 0.290223
\(885\) −25.3005 −0.850465
\(886\) −6.69100 −0.224788
\(887\) −32.2916 −1.08425 −0.542123 0.840299i \(-0.682379\pi\)
−0.542123 + 0.840299i \(0.682379\pi\)
\(888\) −31.3212 −1.05107
\(889\) 49.0472 1.64499
\(890\) −5.71183 −0.191461
\(891\) 185.567 6.21673
\(892\) 19.7312 0.660651
\(893\) 2.58783 0.0865985
\(894\) −19.6138 −0.655984
\(895\) 0.198406 0.00663198
\(896\) 2.51205 0.0839218
\(897\) 37.1067 1.23896
\(898\) −10.4379 −0.348317
\(899\) 55.4087 1.84798
\(900\) −37.7050 −1.25683
\(901\) −23.5550 −0.784730
\(902\) −5.27891 −0.175768
\(903\) 20.0430 0.666990
\(904\) −1.07069 −0.0356105
\(905\) 7.26889 0.241626
\(906\) −16.8417 −0.559527
\(907\) −11.0212 −0.365954 −0.182977 0.983117i \(-0.558573\pi\)
−0.182977 + 0.983117i \(0.558573\pi\)
\(908\) 28.4902 0.945481
\(909\) −49.2090 −1.63216
\(910\) −5.76741 −0.191188
\(911\) 12.8298 0.425072 0.212536 0.977153i \(-0.431828\pi\)
0.212536 + 0.977153i \(0.431828\pi\)
\(912\) 3.31570 0.109794
\(913\) −82.9509 −2.74527
\(914\) −21.5202 −0.711825
\(915\) 27.0437 0.894038
\(916\) −22.2398 −0.734823
\(917\) −22.7489 −0.751235
\(918\) 33.1218 1.09318
\(919\) 13.1128 0.432550 0.216275 0.976333i \(-0.430609\pi\)
0.216275 + 0.976333i \(0.430609\pi\)
\(920\) −1.38075 −0.0455219
\(921\) 87.8367 2.89432
\(922\) −38.6757 −1.27372
\(923\) −12.1559 −0.400116
\(924\) 49.9873 1.64446
\(925\) 44.5559 1.46499
\(926\) 3.68622 0.121137
\(927\) 132.960 4.36700
\(928\) −10.1254 −0.332384
\(929\) −31.7158 −1.04056 −0.520281 0.853995i \(-0.674173\pi\)
−0.520281 + 0.853995i \(0.674173\pi\)
\(930\) −9.65681 −0.316659
\(931\) 0.689592 0.0226005
\(932\) 8.79219 0.287998
\(933\) 55.4603 1.81569
\(934\) −7.66542 −0.250820
\(935\) −6.38926 −0.208951
\(936\) −34.4838 −1.12714
\(937\) −40.8118 −1.33326 −0.666631 0.745388i \(-0.732264\pi\)
−0.666631 + 0.745388i \(0.732264\pi\)
\(938\) −24.6429 −0.804619
\(939\) 7.83381 0.255647
\(940\) 1.37731 0.0449228
\(941\) 41.1901 1.34276 0.671379 0.741114i \(-0.265702\pi\)
0.671379 + 0.741114i \(0.265702\pi\)
\(942\) 64.0560 2.08706
\(943\) −2.28196 −0.0743108
\(944\) −14.3370 −0.466630
\(945\) −22.1379 −0.720145
\(946\) −14.4416 −0.469536
\(947\) −11.1139 −0.361154 −0.180577 0.983561i \(-0.557796\pi\)
−0.180577 + 0.983561i \(0.557796\pi\)
\(948\) 3.73301 0.121243
\(949\) 16.7123 0.542505
\(950\) −4.71674 −0.153031
\(951\) −86.2692 −2.79747
\(952\) 5.02492 0.162859
\(953\) −52.8313 −1.71137 −0.855687 0.517493i \(-0.826865\pi\)
−0.855687 + 0.517493i \(0.826865\pi\)
\(954\) 94.1325 3.04765
\(955\) −3.23695 −0.104745
\(956\) −20.9718 −0.678277
\(957\) −201.486 −6.51312
\(958\) −12.8827 −0.416221
\(959\) −15.1231 −0.488351
\(960\) 1.76470 0.0569553
\(961\) −1.05475 −0.0340242
\(962\) 40.7494 1.31381
\(963\) 45.2277 1.45744
\(964\) −24.3204 −0.783306
\(965\) −11.7429 −0.378017
\(966\) 21.6085 0.695241
\(967\) 35.4337 1.13947 0.569735 0.821829i \(-0.307046\pi\)
0.569735 + 0.821829i \(0.307046\pi\)
\(968\) −25.0173 −0.804087
\(969\) 6.63248 0.213066
\(970\) 4.17619 0.134089
\(971\) 27.7189 0.889541 0.444771 0.895644i \(-0.353285\pi\)
0.444771 + 0.895644i \(0.353285\pi\)
\(972\) −52.8482 −1.69511
\(973\) 19.1903 0.615212
\(974\) 36.9578 1.18420
\(975\) 67.4644 2.16059
\(976\) 15.3249 0.490537
\(977\) 0.472769 0.0151252 0.00756261 0.999971i \(-0.497593\pi\)
0.00756261 + 0.999971i \(0.497593\pi\)
\(978\) −1.87274 −0.0598837
\(979\) −64.4074 −2.05847
\(980\) 0.367017 0.0117239
\(981\) −52.0651 −1.66231
\(982\) 12.0707 0.385191
\(983\) 37.5753 1.19847 0.599234 0.800574i \(-0.295472\pi\)
0.599234 + 0.800574i \(0.295472\pi\)
\(984\) 2.91651 0.0929750
\(985\) 7.34559 0.234050
\(986\) −20.2542 −0.645025
\(987\) −21.5546 −0.686091
\(988\) −4.31378 −0.137240
\(989\) −6.24279 −0.198509
\(990\) 25.5333 0.811502
\(991\) −22.5540 −0.716451 −0.358226 0.933635i \(-0.616618\pi\)
−0.358226 + 0.933635i \(0.616618\pi\)
\(992\) −5.47223 −0.173743
\(993\) 63.7065 2.02166
\(994\) −7.07877 −0.224525
\(995\) 12.1902 0.386456
\(996\) 45.8290 1.45215
\(997\) −10.3390 −0.327440 −0.163720 0.986507i \(-0.552349\pi\)
−0.163720 + 0.986507i \(0.552349\pi\)
\(998\) 21.9071 0.693458
\(999\) 156.414 4.94872
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 \(a_p\))