Properties

Label 8011.2.a.b.1.8
Level 8011
Weight 2
Character 8011.1
Self dual Yes
Analytic conductor 63.968
Analytic rank 0
Dimension 358
CM No

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Newspace parameters

Level: \( N \) = \( 8011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8011.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9681570592\)
Analytic rank: \(0\)
Dimension: \(358\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.69679 q^{2} +2.11156 q^{3} +5.27265 q^{4} -0.515809 q^{5} -5.69442 q^{6} -2.39275 q^{7} -8.82564 q^{8} +1.45867 q^{9} +O(q^{10})\) \(q-2.69679 q^{2} +2.11156 q^{3} +5.27265 q^{4} -0.515809 q^{5} -5.69442 q^{6} -2.39275 q^{7} -8.82564 q^{8} +1.45867 q^{9} +1.39103 q^{10} -5.17864 q^{11} +11.1335 q^{12} -0.224327 q^{13} +6.45273 q^{14} -1.08916 q^{15} +13.2556 q^{16} +6.20189 q^{17} -3.93373 q^{18} +5.80177 q^{19} -2.71968 q^{20} -5.05243 q^{21} +13.9657 q^{22} +6.32260 q^{23} -18.6358 q^{24} -4.73394 q^{25} +0.604962 q^{26} -3.25460 q^{27} -12.6161 q^{28} -7.27997 q^{29} +2.93723 q^{30} -5.90428 q^{31} -18.0961 q^{32} -10.9350 q^{33} -16.7252 q^{34} +1.23420 q^{35} +7.69108 q^{36} -4.47970 q^{37} -15.6461 q^{38} -0.473679 q^{39} +4.55234 q^{40} +3.34952 q^{41} +13.6253 q^{42} +9.61738 q^{43} -27.3051 q^{44} -0.752397 q^{45} -17.0507 q^{46} +2.61442 q^{47} +27.9899 q^{48} -1.27475 q^{49} +12.7664 q^{50} +13.0956 q^{51} -1.18280 q^{52} +13.5061 q^{53} +8.77695 q^{54} +2.67119 q^{55} +21.1176 q^{56} +12.2508 q^{57} +19.6325 q^{58} +3.78788 q^{59} -5.74276 q^{60} -0.220649 q^{61} +15.9226 q^{62} -3.49024 q^{63} +22.2902 q^{64} +0.115710 q^{65} +29.4893 q^{66} -14.0813 q^{67} +32.7004 q^{68} +13.3505 q^{69} -3.32838 q^{70} +4.03732 q^{71} -12.8737 q^{72} -14.7325 q^{73} +12.0808 q^{74} -9.99599 q^{75} +30.5907 q^{76} +12.3912 q^{77} +1.27741 q^{78} -16.4615 q^{79} -6.83733 q^{80} -11.2483 q^{81} -9.03295 q^{82} +4.90642 q^{83} -26.6397 q^{84} -3.19899 q^{85} -25.9360 q^{86} -15.3721 q^{87} +45.7048 q^{88} -0.348917 q^{89} +2.02905 q^{90} +0.536758 q^{91} +33.3369 q^{92} -12.4672 q^{93} -7.05054 q^{94} -2.99260 q^{95} -38.2110 q^{96} +12.5960 q^{97} +3.43772 q^{98} -7.55394 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 358q + 33q^{2} + 11q^{3} + 391q^{4} + 76q^{5} + 32q^{6} + 19q^{7} + 99q^{8} + 451q^{9} + O(q^{10}) \) \( 358q + 33q^{2} + 11q^{3} + 391q^{4} + 76q^{5} + 32q^{6} + 19q^{7} + 99q^{8} + 451q^{9} + 21q^{10} + 70q^{11} + 20q^{12} + 53q^{13} + 69q^{14} + 28q^{15} + 449q^{16} + 88q^{17} + 86q^{18} + 44q^{19} + 136q^{20} + 125q^{21} + 17q^{22} + 104q^{23} + 84q^{24} + 444q^{25} + 100q^{26} + 32q^{27} + 46q^{28} + 373q^{29} + 99q^{30} + 30q^{31} + 221q^{32} + 56q^{33} + 26q^{34} + 164q^{35} + 599q^{36} + 81q^{37} + 66q^{38} + 143q^{39} + 42q^{40} + 182q^{41} + 32q^{42} + 40q^{43} + 184q^{44} + 198q^{45} + 54q^{46} + 66q^{47} + 5q^{48} + 479q^{49} + 184q^{50} + 123q^{51} + 64q^{52} + 221q^{53} + 67q^{54} + 38q^{55} + 174q^{56} + 84q^{57} + 44q^{58} + 127q^{59} + 29q^{60} + 174q^{61} + 86q^{62} + 48q^{63} + 549q^{64} + 202q^{65} + 32q^{66} + 29q^{67} + 172q^{68} + 249q^{69} + 12q^{70} + 185q^{71} + 218q^{72} + 57q^{73} + 272q^{74} + 24q^{75} + 84q^{76} + 384q^{77} + 12q^{78} + 93q^{79} + 215q^{80} + 702q^{81} + 48q^{82} + 121q^{83} + 179q^{84} + 177q^{85} + 209q^{86} + 91q^{87} + 36q^{88} + 186q^{89} + 66q^{90} + 32q^{91} + 272q^{92} + 220q^{93} + 60q^{94} + 170q^{95} + 162q^{96} + 22q^{97} + 196q^{98} + 152q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69679 −1.90692 −0.953458 0.301527i \(-0.902504\pi\)
−0.953458 + 0.301527i \(0.902504\pi\)
\(3\) 2.11156 1.21911 0.609554 0.792744i \(-0.291349\pi\)
0.609554 + 0.792744i \(0.291349\pi\)
\(4\) 5.27265 2.63633
\(5\) −0.515809 −0.230677 −0.115338 0.993326i \(-0.536795\pi\)
−0.115338 + 0.993326i \(0.536795\pi\)
\(6\) −5.69442 −2.32474
\(7\) −2.39275 −0.904374 −0.452187 0.891923i \(-0.649356\pi\)
−0.452187 + 0.891923i \(0.649356\pi\)
\(8\) −8.82564 −3.12034
\(9\) 1.45867 0.486225
\(10\) 1.39103 0.439881
\(11\) −5.17864 −1.56142 −0.780709 0.624895i \(-0.785142\pi\)
−0.780709 + 0.624895i \(0.785142\pi\)
\(12\) 11.1335 3.21397
\(13\) −0.224327 −0.0622171 −0.0311085 0.999516i \(-0.509904\pi\)
−0.0311085 + 0.999516i \(0.509904\pi\)
\(14\) 6.45273 1.72457
\(15\) −1.08916 −0.281220
\(16\) 13.2556 3.31389
\(17\) 6.20189 1.50418 0.752089 0.659061i \(-0.229046\pi\)
0.752089 + 0.659061i \(0.229046\pi\)
\(18\) −3.93373 −0.927189
\(19\) 5.80177 1.33102 0.665508 0.746390i \(-0.268215\pi\)
0.665508 + 0.746390i \(0.268215\pi\)
\(20\) −2.71968 −0.608139
\(21\) −5.05243 −1.10253
\(22\) 13.9657 2.97749
\(23\) 6.32260 1.31835 0.659177 0.751988i \(-0.270905\pi\)
0.659177 + 0.751988i \(0.270905\pi\)
\(24\) −18.6358 −3.80403
\(25\) −4.73394 −0.946788
\(26\) 0.604962 0.118643
\(27\) −3.25460 −0.626348
\(28\) −12.6161 −2.38423
\(29\) −7.27997 −1.35186 −0.675928 0.736968i \(-0.736257\pi\)
−0.675928 + 0.736968i \(0.736257\pi\)
\(30\) 2.93723 0.536263
\(31\) −5.90428 −1.06044 −0.530220 0.847860i \(-0.677891\pi\)
−0.530220 + 0.847860i \(0.677891\pi\)
\(32\) −18.0961 −3.19897
\(33\) −10.9350 −1.90354
\(34\) −16.7252 −2.86834
\(35\) 1.23420 0.208618
\(36\) 7.69108 1.28185
\(37\) −4.47970 −0.736459 −0.368229 0.929735i \(-0.620036\pi\)
−0.368229 + 0.929735i \(0.620036\pi\)
\(38\) −15.6461 −2.53814
\(39\) −0.473679 −0.0758494
\(40\) 4.55234 0.719789
\(41\) 3.34952 0.523108 0.261554 0.965189i \(-0.415765\pi\)
0.261554 + 0.965189i \(0.415765\pi\)
\(42\) 13.6253 2.10243
\(43\) 9.61738 1.46664 0.733319 0.679885i \(-0.237970\pi\)
0.733319 + 0.679885i \(0.237970\pi\)
\(44\) −27.3051 −4.11641
\(45\) −0.752397 −0.112161
\(46\) −17.0507 −2.51399
\(47\) 2.61442 0.381353 0.190677 0.981653i \(-0.438932\pi\)
0.190677 + 0.981653i \(0.438932\pi\)
\(48\) 27.9899 4.03999
\(49\) −1.27475 −0.182107
\(50\) 12.7664 1.80544
\(51\) 13.0956 1.83376
\(52\) −1.18280 −0.164025
\(53\) 13.5061 1.85521 0.927606 0.373560i \(-0.121863\pi\)
0.927606 + 0.373560i \(0.121863\pi\)
\(54\) 8.77695 1.19439
\(55\) 2.67119 0.360183
\(56\) 21.1176 2.82195
\(57\) 12.2508 1.62265
\(58\) 19.6325 2.57788
\(59\) 3.78788 0.493140 0.246570 0.969125i \(-0.420696\pi\)
0.246570 + 0.969125i \(0.420696\pi\)
\(60\) −5.74276 −0.741387
\(61\) −0.220649 −0.0282512 −0.0141256 0.999900i \(-0.504496\pi\)
−0.0141256 + 0.999900i \(0.504496\pi\)
\(62\) 15.9226 2.02217
\(63\) −3.49024 −0.439729
\(64\) 22.2902 2.78628
\(65\) 0.115710 0.0143520
\(66\) 29.4893 3.62988
\(67\) −14.0813 −1.72031 −0.860154 0.510035i \(-0.829632\pi\)
−0.860154 + 0.510035i \(0.829632\pi\)
\(68\) 32.7004 3.96550
\(69\) 13.3505 1.60722
\(70\) −3.32838 −0.397817
\(71\) 4.03732 0.479141 0.239571 0.970879i \(-0.422993\pi\)
0.239571 + 0.970879i \(0.422993\pi\)
\(72\) −12.8737 −1.51718
\(73\) −14.7325 −1.72430 −0.862152 0.506649i \(-0.830884\pi\)
−0.862152 + 0.506649i \(0.830884\pi\)
\(74\) 12.0808 1.40436
\(75\) −9.99599 −1.15424
\(76\) 30.5907 3.50899
\(77\) 12.3912 1.41211
\(78\) 1.27741 0.144638
\(79\) −16.4615 −1.85206 −0.926032 0.377445i \(-0.876803\pi\)
−0.926032 + 0.377445i \(0.876803\pi\)
\(80\) −6.83733 −0.764437
\(81\) −11.2483 −1.24981
\(82\) −9.03295 −0.997522
\(83\) 4.90642 0.538550 0.269275 0.963063i \(-0.413216\pi\)
0.269275 + 0.963063i \(0.413216\pi\)
\(84\) −26.6397 −2.90663
\(85\) −3.19899 −0.346979
\(86\) −25.9360 −2.79675
\(87\) −15.3721 −1.64806
\(88\) 45.7048 4.87215
\(89\) −0.348917 −0.0369851 −0.0184926 0.999829i \(-0.505887\pi\)
−0.0184926 + 0.999829i \(0.505887\pi\)
\(90\) 2.02905 0.213881
\(91\) 0.536758 0.0562676
\(92\) 33.3369 3.47561
\(93\) −12.4672 −1.29279
\(94\) −7.05054 −0.727208
\(95\) −2.99260 −0.307035
\(96\) −38.2110 −3.89989
\(97\) 12.5960 1.27893 0.639467 0.768819i \(-0.279155\pi\)
0.639467 + 0.768819i \(0.279155\pi\)
\(98\) 3.43772 0.347262
\(99\) −7.55394 −0.759200
\(100\) −24.9604 −2.49604
\(101\) 11.0272 1.09725 0.548623 0.836070i \(-0.315152\pi\)
0.548623 + 0.836070i \(0.315152\pi\)
\(102\) −35.3161 −3.49682
\(103\) −2.79573 −0.275472 −0.137736 0.990469i \(-0.543982\pi\)
−0.137736 + 0.990469i \(0.543982\pi\)
\(104\) 1.97983 0.194138
\(105\) 2.60609 0.254328
\(106\) −36.4232 −3.53773
\(107\) −4.71809 −0.456115 −0.228058 0.973648i \(-0.573237\pi\)
−0.228058 + 0.973648i \(0.573237\pi\)
\(108\) −17.1604 −1.65126
\(109\) −6.38191 −0.611276 −0.305638 0.952148i \(-0.598870\pi\)
−0.305638 + 0.952148i \(0.598870\pi\)
\(110\) −7.20362 −0.686838
\(111\) −9.45915 −0.897823
\(112\) −31.7172 −2.99700
\(113\) 6.51429 0.612813 0.306407 0.951901i \(-0.400873\pi\)
0.306407 + 0.951901i \(0.400873\pi\)
\(114\) −33.0377 −3.09426
\(115\) −3.26126 −0.304114
\(116\) −38.3847 −3.56393
\(117\) −0.327220 −0.0302515
\(118\) −10.2151 −0.940376
\(119\) −14.8396 −1.36034
\(120\) 9.61254 0.877500
\(121\) 15.8183 1.43802
\(122\) 0.595043 0.0538726
\(123\) 7.07271 0.637725
\(124\) −31.1312 −2.79567
\(125\) 5.02085 0.449079
\(126\) 9.41244 0.838526
\(127\) 12.0204 1.06663 0.533317 0.845916i \(-0.320945\pi\)
0.533317 + 0.845916i \(0.320945\pi\)
\(128\) −23.9197 −2.11422
\(129\) 20.3077 1.78799
\(130\) −0.312045 −0.0273681
\(131\) 2.13921 0.186904 0.0934518 0.995624i \(-0.470210\pi\)
0.0934518 + 0.995624i \(0.470210\pi\)
\(132\) −57.6564 −5.01834
\(133\) −13.8822 −1.20374
\(134\) 37.9743 3.28048
\(135\) 1.67875 0.144484
\(136\) −54.7356 −4.69354
\(137\) −16.1226 −1.37745 −0.688725 0.725023i \(-0.741829\pi\)
−0.688725 + 0.725023i \(0.741829\pi\)
\(138\) −36.0035 −3.06483
\(139\) −13.8648 −1.17600 −0.588000 0.808861i \(-0.700084\pi\)
−0.588000 + 0.808861i \(0.700084\pi\)
\(140\) 6.50752 0.549986
\(141\) 5.52051 0.464911
\(142\) −10.8878 −0.913682
\(143\) 1.16171 0.0971468
\(144\) 19.3355 1.61129
\(145\) 3.75507 0.311842
\(146\) 39.7303 3.28810
\(147\) −2.69170 −0.222008
\(148\) −23.6199 −1.94155
\(149\) 17.3222 1.41909 0.709545 0.704660i \(-0.248901\pi\)
0.709545 + 0.704660i \(0.248901\pi\)
\(150\) 26.9570 2.20103
\(151\) −0.847711 −0.0689857 −0.0344929 0.999405i \(-0.510982\pi\)
−0.0344929 + 0.999405i \(0.510982\pi\)
\(152\) −51.2043 −4.15322
\(153\) 9.04653 0.731369
\(154\) −33.4164 −2.69277
\(155\) 3.04548 0.244619
\(156\) −2.49755 −0.199964
\(157\) 15.0637 1.20222 0.601109 0.799167i \(-0.294726\pi\)
0.601109 + 0.799167i \(0.294726\pi\)
\(158\) 44.3932 3.53173
\(159\) 28.5190 2.26170
\(160\) 9.33413 0.737928
\(161\) −15.1284 −1.19229
\(162\) 30.3342 2.38328
\(163\) 22.9414 1.79691 0.898455 0.439065i \(-0.144690\pi\)
0.898455 + 0.439065i \(0.144690\pi\)
\(164\) 17.6609 1.37908
\(165\) 5.64036 0.439102
\(166\) −13.2316 −1.02697
\(167\) 2.28913 0.177138 0.0885691 0.996070i \(-0.471771\pi\)
0.0885691 + 0.996070i \(0.471771\pi\)
\(168\) 44.5909 3.44026
\(169\) −12.9497 −0.996129
\(170\) 8.62699 0.661660
\(171\) 8.46289 0.647173
\(172\) 50.7091 3.86653
\(173\) −25.6366 −1.94912 −0.974559 0.224133i \(-0.928045\pi\)
−0.974559 + 0.224133i \(0.928045\pi\)
\(174\) 41.4552 3.14271
\(175\) 11.3271 0.856251
\(176\) −68.6457 −5.17436
\(177\) 7.99832 0.601191
\(178\) 0.940955 0.0705275
\(179\) 11.6607 0.871559 0.435780 0.900053i \(-0.356473\pi\)
0.435780 + 0.900053i \(0.356473\pi\)
\(180\) −3.96713 −0.295692
\(181\) −5.67485 −0.421808 −0.210904 0.977507i \(-0.567641\pi\)
−0.210904 + 0.977507i \(0.567641\pi\)
\(182\) −1.44752 −0.107297
\(183\) −0.465913 −0.0344413
\(184\) −55.8010 −4.11371
\(185\) 2.31067 0.169884
\(186\) 33.6215 2.46525
\(187\) −32.1173 −2.34865
\(188\) 13.7850 1.00537
\(189\) 7.78744 0.566453
\(190\) 8.07041 0.585489
\(191\) 13.6240 0.985795 0.492897 0.870087i \(-0.335938\pi\)
0.492897 + 0.870087i \(0.335938\pi\)
\(192\) 47.0671 3.39677
\(193\) 0.404203 0.0290952 0.0145476 0.999894i \(-0.495369\pi\)
0.0145476 + 0.999894i \(0.495369\pi\)
\(194\) −33.9688 −2.43882
\(195\) 0.244328 0.0174967
\(196\) −6.72130 −0.480093
\(197\) −13.2540 −0.944306 −0.472153 0.881517i \(-0.656523\pi\)
−0.472153 + 0.881517i \(0.656523\pi\)
\(198\) 20.3714 1.44773
\(199\) 13.9681 0.990173 0.495086 0.868844i \(-0.335136\pi\)
0.495086 + 0.868844i \(0.335136\pi\)
\(200\) 41.7801 2.95430
\(201\) −29.7335 −2.09724
\(202\) −29.7379 −2.09235
\(203\) 17.4191 1.22258
\(204\) 69.0487 4.83438
\(205\) −1.72771 −0.120669
\(206\) 7.53949 0.525301
\(207\) 9.22262 0.641016
\(208\) −2.97358 −0.206181
\(209\) −30.0452 −2.07827
\(210\) −7.02806 −0.484982
\(211\) 21.3947 1.47287 0.736435 0.676509i \(-0.236508\pi\)
0.736435 + 0.676509i \(0.236508\pi\)
\(212\) 71.2132 4.89094
\(213\) 8.52502 0.584125
\(214\) 12.7237 0.869773
\(215\) −4.96073 −0.338319
\(216\) 28.7239 1.95441
\(217\) 14.1275 0.959036
\(218\) 17.2106 1.16565
\(219\) −31.1084 −2.10211
\(220\) 14.0842 0.949559
\(221\) −1.39125 −0.0935856
\(222\) 25.5093 1.71207
\(223\) −9.87492 −0.661273 −0.330637 0.943758i \(-0.607263\pi\)
−0.330637 + 0.943758i \(0.607263\pi\)
\(224\) 43.2995 2.89307
\(225\) −6.90528 −0.460352
\(226\) −17.5676 −1.16858
\(227\) 6.06544 0.402577 0.201289 0.979532i \(-0.435487\pi\)
0.201289 + 0.979532i \(0.435487\pi\)
\(228\) 64.5940 4.27784
\(229\) 16.8609 1.11420 0.557098 0.830446i \(-0.311915\pi\)
0.557098 + 0.830446i \(0.311915\pi\)
\(230\) 8.79491 0.579919
\(231\) 26.1647 1.72151
\(232\) 64.2504 4.21824
\(233\) 21.1090 1.38289 0.691447 0.722427i \(-0.256974\pi\)
0.691447 + 0.722427i \(0.256974\pi\)
\(234\) 0.882442 0.0576870
\(235\) −1.34854 −0.0879693
\(236\) 19.9722 1.30008
\(237\) −34.7594 −2.25787
\(238\) 40.0191 2.59405
\(239\) 25.5194 1.65071 0.825355 0.564614i \(-0.190975\pi\)
0.825355 + 0.564614i \(0.190975\pi\)
\(240\) −14.4374 −0.931932
\(241\) −4.38295 −0.282331 −0.141165 0.989986i \(-0.545085\pi\)
−0.141165 + 0.989986i \(0.545085\pi\)
\(242\) −42.6585 −2.74219
\(243\) −13.9876 −0.897306
\(244\) −1.16340 −0.0744794
\(245\) 0.657526 0.0420078
\(246\) −19.0736 −1.21609
\(247\) −1.30149 −0.0828120
\(248\) 52.1091 3.30893
\(249\) 10.3602 0.656551
\(250\) −13.5402 −0.856355
\(251\) −15.8248 −0.998855 −0.499428 0.866356i \(-0.666456\pi\)
−0.499428 + 0.866356i \(0.666456\pi\)
\(252\) −18.4028 −1.15927
\(253\) −32.7425 −2.05850
\(254\) −32.4163 −2.03398
\(255\) −6.75485 −0.423005
\(256\) 19.9259 1.24537
\(257\) −15.7477 −0.982312 −0.491156 0.871072i \(-0.663426\pi\)
−0.491156 + 0.871072i \(0.663426\pi\)
\(258\) −54.7654 −3.40954
\(259\) 10.7188 0.666035
\(260\) 0.610098 0.0378366
\(261\) −10.6191 −0.657306
\(262\) −5.76899 −0.356409
\(263\) 16.4156 1.01223 0.506115 0.862466i \(-0.331081\pi\)
0.506115 + 0.862466i \(0.331081\pi\)
\(264\) 96.5083 5.93967
\(265\) −6.96659 −0.427954
\(266\) 37.4373 2.29543
\(267\) −0.736758 −0.0450889
\(268\) −74.2459 −4.53529
\(269\) 19.1499 1.16759 0.583794 0.811902i \(-0.301568\pi\)
0.583794 + 0.811902i \(0.301568\pi\)
\(270\) −4.52723 −0.275518
\(271\) 28.2402 1.71547 0.857734 0.514094i \(-0.171872\pi\)
0.857734 + 0.514094i \(0.171872\pi\)
\(272\) 82.2094 4.98468
\(273\) 1.13340 0.0685962
\(274\) 43.4793 2.62668
\(275\) 24.5154 1.47833
\(276\) 70.3928 4.23715
\(277\) −0.156512 −0.00940391 −0.00470195 0.999989i \(-0.501497\pi\)
−0.00470195 + 0.999989i \(0.501497\pi\)
\(278\) 37.3905 2.24253
\(279\) −8.61243 −0.515613
\(280\) −10.8926 −0.650959
\(281\) −0.0972981 −0.00580432 −0.00290216 0.999996i \(-0.500924\pi\)
−0.00290216 + 0.999996i \(0.500924\pi\)
\(282\) −14.8876 −0.886545
\(283\) −14.5735 −0.866304 −0.433152 0.901321i \(-0.642599\pi\)
−0.433152 + 0.901321i \(0.642599\pi\)
\(284\) 21.2874 1.26317
\(285\) −6.31905 −0.374308
\(286\) −3.13288 −0.185251
\(287\) −8.01457 −0.473085
\(288\) −26.3963 −1.55542
\(289\) 21.4634 1.26255
\(290\) −10.1266 −0.594656
\(291\) 26.5973 1.55916
\(292\) −77.6792 −4.54583
\(293\) 29.6258 1.73076 0.865379 0.501118i \(-0.167078\pi\)
0.865379 + 0.501118i \(0.167078\pi\)
\(294\) 7.25894 0.423350
\(295\) −1.95382 −0.113756
\(296\) 39.5363 2.29800
\(297\) 16.8544 0.977990
\(298\) −46.7142 −2.70608
\(299\) −1.41833 −0.0820242
\(300\) −52.7054 −3.04295
\(301\) −23.0120 −1.32639
\(302\) 2.28609 0.131550
\(303\) 23.2845 1.33766
\(304\) 76.9057 4.41084
\(305\) 0.113813 0.00651689
\(306\) −24.3966 −1.39466
\(307\) 5.04627 0.288006 0.144003 0.989577i \(-0.454003\pi\)
0.144003 + 0.989577i \(0.454003\pi\)
\(308\) 65.3344 3.72277
\(309\) −5.90335 −0.335830
\(310\) −8.21301 −0.466468
\(311\) −23.2867 −1.32047 −0.660235 0.751059i \(-0.729543\pi\)
−0.660235 + 0.751059i \(0.729543\pi\)
\(312\) 4.18052 0.236675
\(313\) −8.02511 −0.453606 −0.226803 0.973941i \(-0.572827\pi\)
−0.226803 + 0.973941i \(0.572827\pi\)
\(314\) −40.6237 −2.29253
\(315\) 1.80030 0.101435
\(316\) −86.7958 −4.88265
\(317\) −15.7717 −0.885829 −0.442915 0.896564i \(-0.646056\pi\)
−0.442915 + 0.896564i \(0.646056\pi\)
\(318\) −76.9096 −4.31288
\(319\) 37.7003 2.11081
\(320\) −11.4975 −0.642729
\(321\) −9.96253 −0.556054
\(322\) 40.7981 2.27359
\(323\) 35.9819 2.00209
\(324\) −59.3083 −3.29491
\(325\) 1.06195 0.0589064
\(326\) −61.8681 −3.42656
\(327\) −13.4758 −0.745212
\(328\) −29.5617 −1.63227
\(329\) −6.25566 −0.344886
\(330\) −15.2109 −0.837330
\(331\) −18.0566 −0.992480 −0.496240 0.868185i \(-0.665286\pi\)
−0.496240 + 0.868185i \(0.665286\pi\)
\(332\) 25.8699 1.41979
\(333\) −6.53443 −0.358085
\(334\) −6.17329 −0.337788
\(335\) 7.26327 0.396835
\(336\) −66.9727 −3.65366
\(337\) 32.1742 1.75264 0.876320 0.481730i \(-0.159991\pi\)
0.876320 + 0.481730i \(0.159991\pi\)
\(338\) 34.9225 1.89953
\(339\) 13.7553 0.747085
\(340\) −16.8672 −0.914750
\(341\) 30.5761 1.65579
\(342\) −22.8226 −1.23410
\(343\) 19.7994 1.06907
\(344\) −84.8796 −4.57640
\(345\) −6.88633 −0.370747
\(346\) 69.1365 3.71680
\(347\) −11.2239 −0.602530 −0.301265 0.953541i \(-0.597409\pi\)
−0.301265 + 0.953541i \(0.597409\pi\)
\(348\) −81.0516 −4.34482
\(349\) 3.74787 0.200619 0.100309 0.994956i \(-0.468017\pi\)
0.100309 + 0.994956i \(0.468017\pi\)
\(350\) −30.5469 −1.63280
\(351\) 0.730094 0.0389695
\(352\) 93.7131 4.99493
\(353\) −12.1360 −0.645935 −0.322968 0.946410i \(-0.604681\pi\)
−0.322968 + 0.946410i \(0.604681\pi\)
\(354\) −21.5698 −1.14642
\(355\) −2.08248 −0.110527
\(356\) −1.83972 −0.0975049
\(357\) −31.3346 −1.65840
\(358\) −31.4463 −1.66199
\(359\) 9.90402 0.522714 0.261357 0.965242i \(-0.415830\pi\)
0.261357 + 0.965242i \(0.415830\pi\)
\(360\) 6.64039 0.349979
\(361\) 14.6605 0.771606
\(362\) 15.3039 0.804353
\(363\) 33.4012 1.75311
\(364\) 2.83014 0.148340
\(365\) 7.59914 0.397757
\(366\) 1.25647 0.0656766
\(367\) 25.4116 1.32648 0.663238 0.748409i \(-0.269182\pi\)
0.663238 + 0.748409i \(0.269182\pi\)
\(368\) 83.8096 4.36888
\(369\) 4.88586 0.254348
\(370\) −6.23139 −0.323954
\(371\) −32.3168 −1.67781
\(372\) −65.7354 −3.40822
\(373\) 20.5130 1.06212 0.531061 0.847333i \(-0.321793\pi\)
0.531061 + 0.847333i \(0.321793\pi\)
\(374\) 86.6135 4.47868
\(375\) 10.6018 0.547476
\(376\) −23.0740 −1.18995
\(377\) 1.63309 0.0841086
\(378\) −21.0011 −1.08018
\(379\) 16.4816 0.846603 0.423302 0.905989i \(-0.360871\pi\)
0.423302 + 0.905989i \(0.360871\pi\)
\(380\) −15.7790 −0.809443
\(381\) 25.3817 1.30034
\(382\) −36.7409 −1.87983
\(383\) −25.2852 −1.29201 −0.646006 0.763332i \(-0.723562\pi\)
−0.646006 + 0.763332i \(0.723562\pi\)
\(384\) −50.5078 −2.57747
\(385\) −6.39148 −0.325740
\(386\) −1.09005 −0.0554820
\(387\) 14.0286 0.713115
\(388\) 66.4145 3.37169
\(389\) 31.3025 1.58710 0.793550 0.608505i \(-0.208231\pi\)
0.793550 + 0.608505i \(0.208231\pi\)
\(390\) −0.658900 −0.0333647
\(391\) 39.2121 1.98304
\(392\) 11.2505 0.568234
\(393\) 4.51706 0.227856
\(394\) 35.7431 1.80071
\(395\) 8.49099 0.427228
\(396\) −39.8293 −2.00150
\(397\) −5.26773 −0.264380 −0.132190 0.991224i \(-0.542201\pi\)
−0.132190 + 0.991224i \(0.542201\pi\)
\(398\) −37.6690 −1.88818
\(399\) −29.3130 −1.46749
\(400\) −62.7510 −3.13755
\(401\) 3.46063 0.172816 0.0864078 0.996260i \(-0.472461\pi\)
0.0864078 + 0.996260i \(0.472461\pi\)
\(402\) 80.1849 3.99926
\(403\) 1.32449 0.0659775
\(404\) 58.1425 2.89270
\(405\) 5.80197 0.288302
\(406\) −46.9757 −2.33136
\(407\) 23.1988 1.14992
\(408\) −115.577 −5.72193
\(409\) 37.0125 1.83015 0.915076 0.403282i \(-0.132131\pi\)
0.915076 + 0.403282i \(0.132131\pi\)
\(410\) 4.65928 0.230105
\(411\) −34.0439 −1.67926
\(412\) −14.7409 −0.726233
\(413\) −9.06345 −0.445983
\(414\) −24.8714 −1.22236
\(415\) −2.53078 −0.124231
\(416\) 4.05944 0.199031
\(417\) −29.2764 −1.43367
\(418\) 81.0256 3.96309
\(419\) −17.5965 −0.859644 −0.429822 0.902914i \(-0.641424\pi\)
−0.429822 + 0.902914i \(0.641424\pi\)
\(420\) 13.7410 0.670492
\(421\) −16.9729 −0.827208 −0.413604 0.910457i \(-0.635730\pi\)
−0.413604 + 0.910457i \(0.635730\pi\)
\(422\) −57.6968 −2.80864
\(423\) 3.81359 0.185423
\(424\) −119.200 −5.78888
\(425\) −29.3594 −1.42414
\(426\) −22.9902 −1.11388
\(427\) 0.527958 0.0255497
\(428\) −24.8769 −1.20247
\(429\) 2.45301 0.118433
\(430\) 13.3780 0.645146
\(431\) 19.8086 0.954149 0.477075 0.878863i \(-0.341697\pi\)
0.477075 + 0.878863i \(0.341697\pi\)
\(432\) −43.1415 −2.07565
\(433\) 27.0156 1.29829 0.649143 0.760666i \(-0.275128\pi\)
0.649143 + 0.760666i \(0.275128\pi\)
\(434\) −38.0988 −1.82880
\(435\) 7.92905 0.380169
\(436\) −33.6496 −1.61152
\(437\) 36.6823 1.75475
\(438\) 83.8928 4.00855
\(439\) 26.7073 1.27467 0.637335 0.770587i \(-0.280037\pi\)
0.637335 + 0.770587i \(0.280037\pi\)
\(440\) −23.5749 −1.12389
\(441\) −1.85944 −0.0885448
\(442\) 3.75190 0.178460
\(443\) 34.6713 1.64728 0.823642 0.567110i \(-0.191938\pi\)
0.823642 + 0.567110i \(0.191938\pi\)
\(444\) −49.8748 −2.36695
\(445\) 0.179975 0.00853161
\(446\) 26.6305 1.26099
\(447\) 36.5768 1.73002
\(448\) −53.3349 −2.51984
\(449\) −0.0390835 −0.00184446 −0.000922231 1.00000i \(-0.500294\pi\)
−0.000922231 1.00000i \(0.500294\pi\)
\(450\) 18.6221 0.877852
\(451\) −17.3460 −0.816790
\(452\) 34.3476 1.61558
\(453\) −1.78999 −0.0841011
\(454\) −16.3572 −0.767681
\(455\) −0.276865 −0.0129796
\(456\) −108.121 −5.06322
\(457\) 29.0480 1.35881 0.679405 0.733764i \(-0.262238\pi\)
0.679405 + 0.733764i \(0.262238\pi\)
\(458\) −45.4701 −2.12468
\(459\) −20.1846 −0.942138
\(460\) −17.1955 −0.801743
\(461\) −1.53698 −0.0715843 −0.0357922 0.999359i \(-0.511395\pi\)
−0.0357922 + 0.999359i \(0.511395\pi\)
\(462\) −70.5606 −3.28277
\(463\) −20.0754 −0.932983 −0.466492 0.884526i \(-0.654482\pi\)
−0.466492 + 0.884526i \(0.654482\pi\)
\(464\) −96.5000 −4.47990
\(465\) 6.43071 0.298217
\(466\) −56.9263 −2.63706
\(467\) −12.4858 −0.577774 −0.288887 0.957363i \(-0.593285\pi\)
−0.288887 + 0.957363i \(0.593285\pi\)
\(468\) −1.72532 −0.0797528
\(469\) 33.6931 1.55580
\(470\) 3.63673 0.167750
\(471\) 31.8079 1.46563
\(472\) −33.4305 −1.53876
\(473\) −49.8049 −2.29003
\(474\) 93.7387 4.30556
\(475\) −27.4652 −1.26019
\(476\) −78.2439 −3.58630
\(477\) 19.7011 0.902050
\(478\) −68.8202 −3.14776
\(479\) 23.2505 1.06234 0.531172 0.847264i \(-0.321752\pi\)
0.531172 + 0.847264i \(0.321752\pi\)
\(480\) 19.7096 0.899614
\(481\) 1.00492 0.0458203
\(482\) 11.8199 0.538381
\(483\) −31.9445 −1.45353
\(484\) 83.4042 3.79110
\(485\) −6.49715 −0.295020
\(486\) 37.7216 1.71109
\(487\) −27.8564 −1.26229 −0.631146 0.775664i \(-0.717415\pi\)
−0.631146 + 0.775664i \(0.717415\pi\)
\(488\) 1.94737 0.0881532
\(489\) 48.4421 2.19063
\(490\) −1.77321 −0.0801053
\(491\) 11.8873 0.536466 0.268233 0.963354i \(-0.413560\pi\)
0.268233 + 0.963354i \(0.413560\pi\)
\(492\) 37.2919 1.68125
\(493\) −45.1495 −2.03343
\(494\) 3.50985 0.157915
\(495\) 3.89639 0.175130
\(496\) −78.2646 −3.51418
\(497\) −9.66029 −0.433323
\(498\) −27.9392 −1.25199
\(499\) −7.62190 −0.341203 −0.170602 0.985340i \(-0.554571\pi\)
−0.170602 + 0.985340i \(0.554571\pi\)
\(500\) 26.4732 1.18392
\(501\) 4.83363 0.215951
\(502\) 42.6762 1.90473
\(503\) 36.2809 1.61769 0.808843 0.588024i \(-0.200094\pi\)
0.808843 + 0.588024i \(0.200094\pi\)
\(504\) 30.8036 1.37210
\(505\) −5.68792 −0.253109
\(506\) 88.2994 3.92539
\(507\) −27.3440 −1.21439
\(508\) 63.3791 2.81199
\(509\) 43.0078 1.90629 0.953144 0.302516i \(-0.0978264\pi\)
0.953144 + 0.302516i \(0.0978264\pi\)
\(510\) 18.2164 0.806635
\(511\) 35.2511 1.55942
\(512\) −5.89643 −0.260588
\(513\) −18.8824 −0.833679
\(514\) 42.4681 1.87319
\(515\) 1.44206 0.0635449
\(516\) 107.075 4.71372
\(517\) −13.5392 −0.595451
\(518\) −28.9063 −1.27007
\(519\) −54.1332 −2.37618
\(520\) −1.02121 −0.0447832
\(521\) 0.764581 0.0334969 0.0167485 0.999860i \(-0.494669\pi\)
0.0167485 + 0.999860i \(0.494669\pi\)
\(522\) 28.6374 1.25343
\(523\) 5.53840 0.242177 0.121089 0.992642i \(-0.461361\pi\)
0.121089 + 0.992642i \(0.461361\pi\)
\(524\) 11.2793 0.492739
\(525\) 23.9179 1.04386
\(526\) −44.2694 −1.93024
\(527\) −36.6177 −1.59509
\(528\) −144.949 −6.30811
\(529\) 16.9753 0.738058
\(530\) 18.7874 0.816073
\(531\) 5.52528 0.239777
\(532\) −73.1959 −3.17344
\(533\) −0.751388 −0.0325462
\(534\) 1.98688 0.0859807
\(535\) 2.43364 0.105215
\(536\) 124.277 5.36793
\(537\) 24.6222 1.06253
\(538\) −51.6431 −2.22649
\(539\) 6.60145 0.284345
\(540\) 8.85147 0.380907
\(541\) −17.1790 −0.738582 −0.369291 0.929314i \(-0.620399\pi\)
−0.369291 + 0.929314i \(0.620399\pi\)
\(542\) −76.1577 −3.27125
\(543\) −11.9828 −0.514230
\(544\) −112.230 −4.81182
\(545\) 3.29185 0.141007
\(546\) −3.05653 −0.130807
\(547\) 12.9001 0.551570 0.275785 0.961219i \(-0.411062\pi\)
0.275785 + 0.961219i \(0.411062\pi\)
\(548\) −85.0091 −3.63141
\(549\) −0.321855 −0.0137364
\(550\) −66.1127 −2.81905
\(551\) −42.2367 −1.79934
\(552\) −117.827 −5.01505
\(553\) 39.3883 1.67496
\(554\) 0.422080 0.0179325
\(555\) 4.87912 0.207107
\(556\) −73.1044 −3.10032
\(557\) 40.6292 1.72152 0.860758 0.509015i \(-0.169990\pi\)
0.860758 + 0.509015i \(0.169990\pi\)
\(558\) 23.2259 0.983230
\(559\) −2.15744 −0.0912499
\(560\) 16.3600 0.691337
\(561\) −67.8175 −2.86326
\(562\) 0.262392 0.0110683
\(563\) −39.8268 −1.67850 −0.839249 0.543748i \(-0.817005\pi\)
−0.839249 + 0.543748i \(0.817005\pi\)
\(564\) 29.1077 1.22566
\(565\) −3.36013 −0.141362
\(566\) 39.3016 1.65197
\(567\) 26.9144 1.13030
\(568\) −35.6319 −1.49508
\(569\) 12.4856 0.523424 0.261712 0.965146i \(-0.415713\pi\)
0.261712 + 0.965146i \(0.415713\pi\)
\(570\) 17.0411 0.713775
\(571\) 21.7663 0.910892 0.455446 0.890263i \(-0.349480\pi\)
0.455446 + 0.890263i \(0.349480\pi\)
\(572\) 6.12528 0.256111
\(573\) 28.7678 1.20179
\(574\) 21.6136 0.902134
\(575\) −29.9308 −1.24820
\(576\) 32.5142 1.35476
\(577\) 25.4640 1.06008 0.530040 0.847972i \(-0.322177\pi\)
0.530040 + 0.847972i \(0.322177\pi\)
\(578\) −57.8822 −2.40758
\(579\) 0.853498 0.0354702
\(580\) 19.7992 0.822117
\(581\) −11.7398 −0.487051
\(582\) −71.7271 −2.97318
\(583\) −69.9434 −2.89676
\(584\) 130.023 5.38041
\(585\) 0.168783 0.00697832
\(586\) −79.8945 −3.30041
\(587\) −34.7678 −1.43502 −0.717509 0.696549i \(-0.754718\pi\)
−0.717509 + 0.696549i \(0.754718\pi\)
\(588\) −14.1924 −0.585285
\(589\) −34.2553 −1.41146
\(590\) 5.26904 0.216923
\(591\) −27.9865 −1.15121
\(592\) −59.3810 −2.44054
\(593\) −38.3282 −1.57395 −0.786975 0.616985i \(-0.788354\pi\)
−0.786975 + 0.616985i \(0.788354\pi\)
\(594\) −45.4526 −1.86494
\(595\) 7.65438 0.313799
\(596\) 91.3339 3.74118
\(597\) 29.4945 1.20713
\(598\) 3.82493 0.156413
\(599\) 36.5774 1.49451 0.747257 0.664535i \(-0.231371\pi\)
0.747257 + 0.664535i \(0.231371\pi\)
\(600\) 88.2210 3.60161
\(601\) 14.1086 0.575502 0.287751 0.957705i \(-0.407093\pi\)
0.287751 + 0.957705i \(0.407093\pi\)
\(602\) 62.0584 2.52931
\(603\) −20.5401 −0.836456
\(604\) −4.46968 −0.181869
\(605\) −8.15920 −0.331719
\(606\) −62.7934 −2.55081
\(607\) 9.07298 0.368261 0.184131 0.982902i \(-0.441053\pi\)
0.184131 + 0.982902i \(0.441053\pi\)
\(608\) −104.989 −4.25788
\(609\) 36.7815 1.49046
\(610\) −0.306928 −0.0124272
\(611\) −0.586486 −0.0237267
\(612\) 47.6992 1.92813
\(613\) 34.5623 1.39596 0.697980 0.716118i \(-0.254083\pi\)
0.697980 + 0.716118i \(0.254083\pi\)
\(614\) −13.6087 −0.549203
\(615\) −3.64817 −0.147108
\(616\) −109.360 −4.40624
\(617\) 11.7161 0.471674 0.235837 0.971793i \(-0.424217\pi\)
0.235837 + 0.971793i \(0.424217\pi\)
\(618\) 15.9201 0.640399
\(619\) −0.105246 −0.00423018 −0.00211509 0.999998i \(-0.500673\pi\)
−0.00211509 + 0.999998i \(0.500673\pi\)
\(620\) 16.0578 0.644896
\(621\) −20.5775 −0.825748
\(622\) 62.7994 2.51802
\(623\) 0.834871 0.0334484
\(624\) −6.27888 −0.251356
\(625\) 21.0799 0.843196
\(626\) 21.6420 0.864989
\(627\) −63.4422 −2.53364
\(628\) 79.4258 3.16944
\(629\) −27.7826 −1.10777
\(630\) −4.85502 −0.193429
\(631\) −0.640391 −0.0254936 −0.0127468 0.999919i \(-0.504058\pi\)
−0.0127468 + 0.999919i \(0.504058\pi\)
\(632\) 145.283 5.77906
\(633\) 45.1761 1.79559
\(634\) 42.5330 1.68920
\(635\) −6.20020 −0.246048
\(636\) 150.371 5.96259
\(637\) 0.285960 0.0113302
\(638\) −101.670 −4.02514
\(639\) 5.88913 0.232970
\(640\) 12.3380 0.487702
\(641\) −12.2307 −0.483085 −0.241542 0.970390i \(-0.577653\pi\)
−0.241542 + 0.970390i \(0.577653\pi\)
\(642\) 26.8668 1.06035
\(643\) 14.9933 0.591279 0.295639 0.955300i \(-0.404467\pi\)
0.295639 + 0.955300i \(0.404467\pi\)
\(644\) −79.7668 −3.14325
\(645\) −10.4749 −0.412448
\(646\) −97.0355 −3.81781
\(647\) −37.7829 −1.48540 −0.742699 0.669625i \(-0.766455\pi\)
−0.742699 + 0.669625i \(0.766455\pi\)
\(648\) 99.2734 3.89983
\(649\) −19.6160 −0.769997
\(650\) −2.86385 −0.112330
\(651\) 29.8310 1.16917
\(652\) 120.962 4.73724
\(653\) −31.0438 −1.21484 −0.607419 0.794382i \(-0.707795\pi\)
−0.607419 + 0.794382i \(0.707795\pi\)
\(654\) 36.3413 1.42106
\(655\) −1.10342 −0.0431143
\(656\) 44.3998 1.73352
\(657\) −21.4899 −0.838399
\(658\) 16.8702 0.657668
\(659\) −7.74599 −0.301741 −0.150870 0.988554i \(-0.548208\pi\)
−0.150870 + 0.988554i \(0.548208\pi\)
\(660\) 29.7397 1.15762
\(661\) 14.5962 0.567725 0.283863 0.958865i \(-0.408384\pi\)
0.283863 + 0.958865i \(0.408384\pi\)
\(662\) 48.6948 1.89258
\(663\) −2.93770 −0.114091
\(664\) −43.3023 −1.68046
\(665\) 7.16055 0.277674
\(666\) 17.6220 0.682837
\(667\) −46.0284 −1.78223
\(668\) 12.0698 0.466994
\(669\) −20.8514 −0.806164
\(670\) −19.5875 −0.756731
\(671\) 1.14266 0.0441119
\(672\) 91.4293 3.52696
\(673\) −21.7037 −0.836617 −0.418308 0.908305i \(-0.637377\pi\)
−0.418308 + 0.908305i \(0.637377\pi\)
\(674\) −86.7669 −3.34213
\(675\) 15.4071 0.593019
\(676\) −68.2791 −2.62612
\(677\) 47.0155 1.80695 0.903477 0.428638i \(-0.141006\pi\)
0.903477 + 0.428638i \(0.141006\pi\)
\(678\) −37.0951 −1.42463
\(679\) −30.1392 −1.15663
\(680\) 28.2331 1.08269
\(681\) 12.8075 0.490785
\(682\) −82.4573 −3.15745
\(683\) −30.9907 −1.18583 −0.592913 0.805266i \(-0.702022\pi\)
−0.592913 + 0.805266i \(0.702022\pi\)
\(684\) 44.6219 1.70616
\(685\) 8.31620 0.317746
\(686\) −53.3947 −2.03862
\(687\) 35.6027 1.35833
\(688\) 127.484 4.86027
\(689\) −3.02979 −0.115426
\(690\) 18.5710 0.706984
\(691\) −2.81786 −0.107197 −0.0535983 0.998563i \(-0.517069\pi\)
−0.0535983 + 0.998563i \(0.517069\pi\)
\(692\) −135.173 −5.13851
\(693\) 18.0747 0.686601
\(694\) 30.2684 1.14897
\(695\) 7.15160 0.271276
\(696\) 135.668 5.14250
\(697\) 20.7734 0.786847
\(698\) −10.1072 −0.382563
\(699\) 44.5728 1.68590
\(700\) 59.7241 2.25736
\(701\) 1.20300 0.0454366 0.0227183 0.999742i \(-0.492768\pi\)
0.0227183 + 0.999742i \(0.492768\pi\)
\(702\) −1.96891 −0.0743116
\(703\) −25.9902 −0.980239
\(704\) −115.433 −4.35054
\(705\) −2.84753 −0.107244
\(706\) 32.7283 1.23174
\(707\) −26.3853 −0.992321
\(708\) 42.1724 1.58494
\(709\) −44.9216 −1.68707 −0.843533 0.537078i \(-0.819528\pi\)
−0.843533 + 0.537078i \(0.819528\pi\)
\(710\) 5.61601 0.210765
\(711\) −24.0120 −0.900520
\(712\) 3.07942 0.115406
\(713\) −37.3305 −1.39804
\(714\) 84.5027 3.16243
\(715\) −0.599219 −0.0224095
\(716\) 61.4827 2.29771
\(717\) 53.8856 2.01239
\(718\) −26.7090 −0.996772
\(719\) 26.4077 0.984839 0.492420 0.870358i \(-0.336113\pi\)
0.492420 + 0.870358i \(0.336113\pi\)
\(720\) −9.97344 −0.371688
\(721\) 6.68949 0.249129
\(722\) −39.5362 −1.47139
\(723\) −9.25486 −0.344192
\(724\) −29.9215 −1.11202
\(725\) 34.4629 1.27992
\(726\) −90.0758 −3.34303
\(727\) −11.9846 −0.444485 −0.222243 0.974991i \(-0.571338\pi\)
−0.222243 + 0.974991i \(0.571338\pi\)
\(728\) −4.73724 −0.175574
\(729\) 4.20921 0.155897
\(730\) −20.4932 −0.758489
\(731\) 59.6459 2.20608
\(732\) −2.45660 −0.0907984
\(733\) 31.5747 1.16624 0.583120 0.812386i \(-0.301832\pi\)
0.583120 + 0.812386i \(0.301832\pi\)
\(734\) −68.5297 −2.52948
\(735\) 1.38840 0.0512121
\(736\) −114.415 −4.21738
\(737\) 72.9220 2.68612
\(738\) −13.1761 −0.485020
\(739\) −48.3469 −1.77847 −0.889235 0.457452i \(-0.848762\pi\)
−0.889235 + 0.457452i \(0.848762\pi\)
\(740\) 12.1834 0.447869
\(741\) −2.74818 −0.100957
\(742\) 87.1516 3.19944
\(743\) −17.0693 −0.626211 −0.313105 0.949718i \(-0.601369\pi\)
−0.313105 + 0.949718i \(0.601369\pi\)
\(744\) 110.031 4.03394
\(745\) −8.93494 −0.327351
\(746\) −55.3191 −2.02538
\(747\) 7.15687 0.261856
\(748\) −169.343 −6.19181
\(749\) 11.2892 0.412499
\(750\) −28.5908 −1.04399
\(751\) −22.5332 −0.822248 −0.411124 0.911579i \(-0.634864\pi\)
−0.411124 + 0.911579i \(0.634864\pi\)
\(752\) 34.6556 1.26376
\(753\) −33.4151 −1.21771
\(754\) −4.40410 −0.160388
\(755\) 0.437257 0.0159134
\(756\) 41.0605 1.49335
\(757\) 44.8893 1.63153 0.815764 0.578385i \(-0.196317\pi\)
0.815764 + 0.578385i \(0.196317\pi\)
\(758\) −44.4473 −1.61440
\(759\) −69.1376 −2.50954
\(760\) 26.4116 0.958051
\(761\) 48.1043 1.74378 0.871890 0.489702i \(-0.162894\pi\)
0.871890 + 0.489702i \(0.162894\pi\)
\(762\) −68.4489 −2.47964
\(763\) 15.2703 0.552823
\(764\) 71.8344 2.59888
\(765\) −4.66628 −0.168710
\(766\) 68.1887 2.46376
\(767\) −0.849723 −0.0306817
\(768\) 42.0746 1.51824
\(769\) −12.3315 −0.444687 −0.222343 0.974968i \(-0.571371\pi\)
−0.222343 + 0.974968i \(0.571371\pi\)
\(770\) 17.2365 0.621159
\(771\) −33.2521 −1.19754
\(772\) 2.13122 0.0767044
\(773\) −34.8763 −1.25441 −0.627206 0.778854i \(-0.715802\pi\)
−0.627206 + 0.778854i \(0.715802\pi\)
\(774\) −37.8322 −1.35985
\(775\) 27.9505 1.00401
\(776\) −111.168 −3.99070
\(777\) 22.6334 0.811968
\(778\) −84.4161 −3.02646
\(779\) 19.4332 0.696265
\(780\) 1.28826 0.0461270
\(781\) −20.9078 −0.748140
\(782\) −105.747 −3.78149
\(783\) 23.6934 0.846732
\(784\) −16.8975 −0.603482
\(785\) −7.77001 −0.277324
\(786\) −12.1815 −0.434501
\(787\) −17.7712 −0.633476 −0.316738 0.948513i \(-0.602588\pi\)
−0.316738 + 0.948513i \(0.602588\pi\)
\(788\) −69.8836 −2.48950
\(789\) 34.6625 1.23402
\(790\) −22.8984 −0.814688
\(791\) −15.5871 −0.554213
\(792\) 66.6684 2.36896
\(793\) 0.0494975 0.00175771
\(794\) 14.2059 0.504150
\(795\) −14.7104 −0.521723
\(796\) 73.6490 2.61042
\(797\) −16.0438 −0.568302 −0.284151 0.958780i \(-0.591712\pi\)
−0.284151 + 0.958780i \(0.591712\pi\)
\(798\) 79.0509 2.79837
\(799\) 16.2144 0.573623
\(800\) 85.6659 3.02875
\(801\) −0.508956 −0.0179831
\(802\) −9.33258 −0.329545
\(803\) 76.2941 2.69236
\(804\) −156.774 −5.52901
\(805\) 7.80337 0.275033
\(806\) −3.57187 −0.125814
\(807\) 40.4360 1.42342
\(808\) −97.3219 −3.42377
\(809\) 1.92763 0.0677719 0.0338859 0.999426i \(-0.489212\pi\)
0.0338859 + 0.999426i \(0.489212\pi\)
\(810\) −15.6467 −0.549768
\(811\) −26.5886 −0.933653 −0.466827 0.884349i \(-0.654603\pi\)
−0.466827 + 0.884349i \(0.654603\pi\)
\(812\) 91.8451 3.22313
\(813\) 59.6307 2.09134
\(814\) −62.5621 −2.19280
\(815\) −11.8334 −0.414506
\(816\) 173.590 6.07686
\(817\) 55.7978 1.95212
\(818\) −99.8148 −3.48994
\(819\) 0.782955 0.0273587
\(820\) −9.10964 −0.318122
\(821\) 17.0590 0.595364 0.297682 0.954665i \(-0.403787\pi\)
0.297682 + 0.954665i \(0.403787\pi\)
\(822\) 91.8090 3.20221
\(823\) −0.409230 −0.0142649 −0.00713243 0.999975i \(-0.502270\pi\)
−0.00713243 + 0.999975i \(0.502270\pi\)
\(824\) 24.6741 0.859564
\(825\) 51.7656 1.80225
\(826\) 24.4422 0.850452
\(827\) −27.3826 −0.952188 −0.476094 0.879394i \(-0.657948\pi\)
−0.476094 + 0.879394i \(0.657948\pi\)
\(828\) 48.6277 1.68993
\(829\) −8.84670 −0.307259 −0.153629 0.988129i \(-0.549096\pi\)
−0.153629 + 0.988129i \(0.549096\pi\)
\(830\) 6.82496 0.236898
\(831\) −0.330484 −0.0114644
\(832\) −5.00029 −0.173354
\(833\) −7.90584 −0.273921
\(834\) 78.9521 2.73389
\(835\) −1.18075 −0.0408617
\(836\) −158.418 −5.47900
\(837\) 19.2161 0.664205
\(838\) 47.4539 1.63927
\(839\) 4.03553 0.139322 0.0696610 0.997571i \(-0.477808\pi\)
0.0696610 + 0.997571i \(0.477808\pi\)
\(840\) −23.0004 −0.793589
\(841\) 23.9979 0.827515
\(842\) 45.7723 1.57742
\(843\) −0.205450 −0.00707609
\(844\) 112.807 3.88296
\(845\) 6.67956 0.229784
\(846\) −10.2844 −0.353586
\(847\) −37.8492 −1.30051
\(848\) 179.031 6.14797
\(849\) −30.7727 −1.05612
\(850\) 79.1759 2.71571
\(851\) −28.3234 −0.970914
\(852\) 44.9495 1.53994
\(853\) −42.0223 −1.43881 −0.719407 0.694589i \(-0.755586\pi\)
−0.719407 + 0.694589i \(0.755586\pi\)
\(854\) −1.42379 −0.0487210
\(855\) −4.36523 −0.149288
\(856\) 41.6402 1.42323
\(857\) −33.1310 −1.13173 −0.565867 0.824496i \(-0.691459\pi\)
−0.565867 + 0.824496i \(0.691459\pi\)
\(858\) −6.61525 −0.225841
\(859\) −18.1779 −0.620223 −0.310111 0.950700i \(-0.600366\pi\)
−0.310111 + 0.950700i \(0.600366\pi\)
\(860\) −26.1562 −0.891920
\(861\) −16.9232 −0.576742
\(862\) −53.4197 −1.81948
\(863\) −6.66000 −0.226709 −0.113354 0.993555i \(-0.536160\pi\)
−0.113354 + 0.993555i \(0.536160\pi\)
\(864\) 58.8956 2.00367
\(865\) 13.2236 0.449616
\(866\) −72.8552 −2.47572
\(867\) 45.3212 1.53919
\(868\) 74.4893 2.52833
\(869\) 85.2482 2.89185
\(870\) −21.3830 −0.724950
\(871\) 3.15882 0.107033
\(872\) 56.3245 1.90739
\(873\) 18.3735 0.621849
\(874\) −98.9242 −3.34616
\(875\) −12.0136 −0.406135
\(876\) −164.024 −5.54186
\(877\) −52.9491 −1.78796 −0.893982 0.448102i \(-0.852100\pi\)
−0.893982 + 0.448102i \(0.852100\pi\)
\(878\) −72.0238 −2.43069
\(879\) 62.5566 2.10998
\(880\) 35.4081 1.19361
\(881\) 31.5753 1.06380 0.531899 0.846808i \(-0.321479\pi\)
0.531899 + 0.846808i \(0.321479\pi\)
\(882\) 5.01451 0.168847
\(883\) 7.48814 0.251996 0.125998 0.992030i \(-0.459787\pi\)
0.125998 + 0.992030i \(0.459787\pi\)
\(884\) −7.33558 −0.246722
\(885\) −4.12561 −0.138681
\(886\) −93.5011 −3.14123
\(887\) −5.76105 −0.193437 −0.0967186 0.995312i \(-0.530835\pi\)
−0.0967186 + 0.995312i \(0.530835\pi\)
\(888\) 83.4831 2.80151
\(889\) −28.7617 −0.964636
\(890\) −0.485353 −0.0162691
\(891\) 58.2508 1.95148
\(892\) −52.0670 −1.74333
\(893\) 15.1683 0.507587
\(894\) −98.6398 −3.29901
\(895\) −6.01468 −0.201049
\(896\) 57.2339 1.91205
\(897\) −2.99489 −0.0999963
\(898\) 0.105400 0.00351723
\(899\) 42.9830 1.43356
\(900\) −36.4091 −1.21364
\(901\) 83.7636 2.79057
\(902\) 46.7783 1.55755
\(903\) −48.5911 −1.61701
\(904\) −57.4928 −1.91218
\(905\) 2.92714 0.0973014
\(906\) 4.82722 0.160374
\(907\) 25.9246 0.860812 0.430406 0.902635i \(-0.358370\pi\)
0.430406 + 0.902635i \(0.358370\pi\)
\(908\) 31.9810 1.06133
\(909\) 16.0851 0.533508
\(910\) 0.746645 0.0247510
\(911\) −12.0988 −0.400852 −0.200426 0.979709i \(-0.564233\pi\)
−0.200426 + 0.979709i \(0.564233\pi\)
\(912\) 162.391 5.37729
\(913\) −25.4086 −0.840901
\(914\) −78.3363 −2.59113
\(915\) 0.240322 0.00794480
\(916\) 88.9014 2.93739
\(917\) −5.11859 −0.169031
\(918\) 54.4337 1.79658
\(919\) 49.8232 1.64352 0.821759 0.569836i \(-0.192993\pi\)
0.821759 + 0.569836i \(0.192993\pi\)
\(920\) 28.7827 0.948937
\(921\) 10.6555 0.351110
\(922\) 4.14491 0.136505
\(923\) −0.905679 −0.0298108
\(924\) 137.957 4.53846
\(925\) 21.2067 0.697271
\(926\) 54.1391 1.77912
\(927\) −4.07806 −0.133941
\(928\) 131.739 4.32455
\(929\) 24.6707 0.809419 0.404709 0.914445i \(-0.367373\pi\)
0.404709 + 0.914445i \(0.367373\pi\)
\(930\) −17.3422 −0.568675
\(931\) −7.39579 −0.242387
\(932\) 111.300 3.64576
\(933\) −49.1713 −1.60980
\(934\) 33.6716 1.10177
\(935\) 16.5664 0.541779
\(936\) 2.88793 0.0943948
\(937\) −34.0952 −1.11384 −0.556920 0.830566i \(-0.688017\pi\)
−0.556920 + 0.830566i \(0.688017\pi\)
\(938\) −90.8630 −2.96678
\(939\) −16.9455 −0.552995
\(940\) −7.11040 −0.231916
\(941\) −9.09520 −0.296495 −0.148247 0.988950i \(-0.547363\pi\)
−0.148247 + 0.988950i \(0.547363\pi\)
\(942\) −85.7792 −2.79484
\(943\) 21.1777 0.689641
\(944\) 50.2104 1.63421
\(945\) −4.01683 −0.130668
\(946\) 134.313 4.36690
\(947\) 23.8356 0.774553 0.387276 0.921964i \(-0.373416\pi\)
0.387276 + 0.921964i \(0.373416\pi\)
\(948\) −183.274 −5.95247
\(949\) 3.30489 0.107281
\(950\) 74.0678 2.40308
\(951\) −33.3029 −1.07992
\(952\) 130.969 4.24472
\(953\) 8.72912 0.282764 0.141382 0.989955i \(-0.454845\pi\)
0.141382 + 0.989955i \(0.454845\pi\)
\(954\) −53.1296 −1.72013
\(955\) −7.02736 −0.227400
\(956\) 134.555 4.35181
\(957\) 79.6064 2.57331
\(958\) −62.7017 −2.02580
\(959\) 38.5774 1.24573
\(960\) −24.2776 −0.783556
\(961\) 3.86058 0.124535
\(962\) −2.71005 −0.0873755
\(963\) −6.88216 −0.221775
\(964\) −23.1098 −0.744316
\(965\) −0.208492 −0.00671158
\(966\) 86.1475 2.77175
\(967\) 23.0298 0.740590 0.370295 0.928914i \(-0.379257\pi\)
0.370295 + 0.928914i \(0.379257\pi\)
\(968\) −139.606 −4.48712
\(969\) 75.9778 2.44076
\(970\) 17.5214 0.562579
\(971\) 5.76075 0.184871 0.0924356 0.995719i \(-0.470535\pi\)
0.0924356 + 0.995719i \(0.470535\pi\)
\(972\) −73.7519 −2.36559
\(973\) 33.1751 1.06354
\(974\) 75.1226 2.40708
\(975\) 2.24237 0.0718133
\(976\) −2.92482 −0.0936213
\(977\) −30.9862 −0.991336 −0.495668 0.868512i \(-0.665077\pi\)
−0.495668 + 0.868512i \(0.665077\pi\)
\(978\) −130.638 −4.17734
\(979\) 1.80691 0.0577492
\(980\) 3.46691 0.110746
\(981\) −9.30913 −0.297218
\(982\) −32.0575 −1.02300
\(983\) 18.7002 0.596444 0.298222 0.954496i \(-0.403606\pi\)
0.298222 + 0.954496i \(0.403606\pi\)
\(984\) −62.4212 −1.98992
\(985\) 6.83652 0.217830
\(986\) 121.759 3.87758
\(987\) −13.2092 −0.420453
\(988\) −6.86232 −0.218319
\(989\) 60.8069 1.93355
\(990\) −10.5077 −0.333958
\(991\) −26.8174 −0.851883 −0.425942 0.904751i \(-0.640057\pi\)
−0.425942 + 0.904751i \(0.640057\pi\)
\(992\) 106.845 3.39232
\(993\) −38.1275 −1.20994
\(994\) 26.0517 0.826311
\(995\) −7.20487 −0.228410
\(996\) 54.6257 1.73088
\(997\) 30.9455 0.980054 0.490027 0.871707i \(-0.336987\pi\)
0.490027 + 0.871707i \(0.336987\pi\)
\(998\) 20.5546 0.650646
\(999\) 14.5796 0.461279
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 \(a_p\))