Properties

Label 8041.2.a.g.1.16
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.85886 q^{2} +3.31260 q^{3} +1.45535 q^{4} +0.943187 q^{5} -6.15766 q^{6} -1.28029 q^{7} +1.01243 q^{8} +7.97335 q^{9} +O(q^{10})\) \(q-1.85886 q^{2} +3.31260 q^{3} +1.45535 q^{4} +0.943187 q^{5} -6.15766 q^{6} -1.28029 q^{7} +1.01243 q^{8} +7.97335 q^{9} -1.75325 q^{10} -1.00000 q^{11} +4.82099 q^{12} -3.54307 q^{13} +2.37987 q^{14} +3.12440 q^{15} -4.79266 q^{16} +1.00000 q^{17} -14.8213 q^{18} -3.35662 q^{19} +1.37266 q^{20} -4.24108 q^{21} +1.85886 q^{22} +3.29817 q^{23} +3.35378 q^{24} -4.11040 q^{25} +6.58607 q^{26} +16.4747 q^{27} -1.86326 q^{28} -6.51572 q^{29} -5.80782 q^{30} +0.322173 q^{31} +6.88400 q^{32} -3.31260 q^{33} -1.85886 q^{34} -1.20755 q^{35} +11.6040 q^{36} -10.0135 q^{37} +6.23947 q^{38} -11.7368 q^{39} +0.954911 q^{40} -8.39914 q^{41} +7.88356 q^{42} +1.00000 q^{43} -1.45535 q^{44} +7.52036 q^{45} -6.13083 q^{46} +6.51522 q^{47} -15.8762 q^{48} -5.36087 q^{49} +7.64064 q^{50} +3.31260 q^{51} -5.15640 q^{52} +3.17636 q^{53} -30.6242 q^{54} -0.943187 q^{55} -1.29620 q^{56} -11.1191 q^{57} +12.1118 q^{58} +1.42476 q^{59} +4.54710 q^{60} -10.7885 q^{61} -0.598873 q^{62} -10.2082 q^{63} -3.21106 q^{64} -3.34178 q^{65} +6.15766 q^{66} +12.2670 q^{67} +1.45535 q^{68} +10.9255 q^{69} +2.24466 q^{70} -4.14908 q^{71} +8.07246 q^{72} -6.21252 q^{73} +18.6137 q^{74} -13.6161 q^{75} -4.88505 q^{76} +1.28029 q^{77} +21.8170 q^{78} -16.6114 q^{79} -4.52037 q^{80} +30.6542 q^{81} +15.6128 q^{82} -0.588060 q^{83} -6.17224 q^{84} +0.943187 q^{85} -1.85886 q^{86} -21.5840 q^{87} -1.01243 q^{88} +11.0170 q^{89} -13.9793 q^{90} +4.53614 q^{91} +4.79998 q^{92} +1.06723 q^{93} -12.1109 q^{94} -3.16592 q^{95} +22.8040 q^{96} -17.6870 q^{97} +9.96509 q^{98} -7.97335 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.85886 −1.31441 −0.657205 0.753712i \(-0.728261\pi\)
−0.657205 + 0.753712i \(0.728261\pi\)
\(3\) 3.31260 1.91253 0.956267 0.292497i \(-0.0944861\pi\)
0.956267 + 0.292497i \(0.0944861\pi\)
\(4\) 1.45535 0.727674
\(5\) 0.943187 0.421806 0.210903 0.977507i \(-0.432360\pi\)
0.210903 + 0.977507i \(0.432360\pi\)
\(6\) −6.15766 −2.51385
\(7\) −1.28029 −0.483902 −0.241951 0.970288i \(-0.577787\pi\)
−0.241951 + 0.970288i \(0.577787\pi\)
\(8\) 1.01243 0.357948
\(9\) 7.97335 2.65778
\(10\) −1.75325 −0.554426
\(11\) −1.00000 −0.301511
\(12\) 4.82099 1.39170
\(13\) −3.54307 −0.982672 −0.491336 0.870970i \(-0.663491\pi\)
−0.491336 + 0.870970i \(0.663491\pi\)
\(14\) 2.37987 0.636046
\(15\) 3.12440 0.806718
\(16\) −4.79266 −1.19816
\(17\) 1.00000 0.242536
\(18\) −14.8213 −3.49342
\(19\) −3.35662 −0.770061 −0.385031 0.922904i \(-0.625809\pi\)
−0.385031 + 0.922904i \(0.625809\pi\)
\(20\) 1.37266 0.306937
\(21\) −4.24108 −0.925479
\(22\) 1.85886 0.396310
\(23\) 3.29817 0.687716 0.343858 0.939022i \(-0.388266\pi\)
0.343858 + 0.939022i \(0.388266\pi\)
\(24\) 3.35378 0.684588
\(25\) −4.11040 −0.822080
\(26\) 6.58607 1.29163
\(27\) 16.4747 3.17056
\(28\) −1.86326 −0.352123
\(29\) −6.51572 −1.20994 −0.604970 0.796249i \(-0.706815\pi\)
−0.604970 + 0.796249i \(0.706815\pi\)
\(30\) −5.80782 −1.06036
\(31\) 0.322173 0.0578639 0.0289320 0.999581i \(-0.490789\pi\)
0.0289320 + 0.999581i \(0.490789\pi\)
\(32\) 6.88400 1.21693
\(33\) −3.31260 −0.576650
\(34\) −1.85886 −0.318791
\(35\) −1.20755 −0.204113
\(36\) 11.6040 1.93400
\(37\) −10.0135 −1.64621 −0.823106 0.567888i \(-0.807761\pi\)
−0.823106 + 0.567888i \(0.807761\pi\)
\(38\) 6.23947 1.01218
\(39\) −11.7368 −1.87939
\(40\) 0.954911 0.150985
\(41\) −8.39914 −1.31172 −0.655862 0.754880i \(-0.727695\pi\)
−0.655862 + 0.754880i \(0.727695\pi\)
\(42\) 7.88356 1.21646
\(43\) 1.00000 0.152499
\(44\) −1.45535 −0.219402
\(45\) 7.52036 1.12107
\(46\) −6.13083 −0.903941
\(47\) 6.51522 0.950343 0.475171 0.879893i \(-0.342386\pi\)
0.475171 + 0.879893i \(0.342386\pi\)
\(48\) −15.8762 −2.29153
\(49\) −5.36087 −0.765839
\(50\) 7.64064 1.08055
\(51\) 3.31260 0.463857
\(52\) −5.15640 −0.715065
\(53\) 3.17636 0.436307 0.218154 0.975914i \(-0.429997\pi\)
0.218154 + 0.975914i \(0.429997\pi\)
\(54\) −30.6242 −4.16742
\(55\) −0.943187 −0.127179
\(56\) −1.29620 −0.173212
\(57\) −11.1191 −1.47277
\(58\) 12.1118 1.59036
\(59\) 1.42476 0.185487 0.0927437 0.995690i \(-0.470436\pi\)
0.0927437 + 0.995690i \(0.470436\pi\)
\(60\) 4.54710 0.587027
\(61\) −10.7885 −1.38132 −0.690660 0.723180i \(-0.742680\pi\)
−0.690660 + 0.723180i \(0.742680\pi\)
\(62\) −0.598873 −0.0760569
\(63\) −10.2082 −1.28611
\(64\) −3.21106 −0.401382
\(65\) −3.34178 −0.414497
\(66\) 6.15766 0.757955
\(67\) 12.2670 1.49866 0.749328 0.662199i \(-0.230377\pi\)
0.749328 + 0.662199i \(0.230377\pi\)
\(68\) 1.45535 0.176487
\(69\) 10.9255 1.31528
\(70\) 2.24466 0.268288
\(71\) −4.14908 −0.492405 −0.246203 0.969218i \(-0.579183\pi\)
−0.246203 + 0.969218i \(0.579183\pi\)
\(72\) 8.07246 0.951348
\(73\) −6.21252 −0.727120 −0.363560 0.931571i \(-0.618439\pi\)
−0.363560 + 0.931571i \(0.618439\pi\)
\(74\) 18.6137 2.16380
\(75\) −13.6161 −1.57225
\(76\) −4.88505 −0.560353
\(77\) 1.28029 0.145902
\(78\) 21.8170 2.47029
\(79\) −16.6114 −1.86893 −0.934464 0.356059i \(-0.884120\pi\)
−0.934464 + 0.356059i \(0.884120\pi\)
\(80\) −4.52037 −0.505393
\(81\) 30.6542 3.40603
\(82\) 15.6128 1.72414
\(83\) −0.588060 −0.0645480 −0.0322740 0.999479i \(-0.510275\pi\)
−0.0322740 + 0.999479i \(0.510275\pi\)
\(84\) −6.17224 −0.673447
\(85\) 0.943187 0.102303
\(86\) −1.85886 −0.200446
\(87\) −21.5840 −2.31405
\(88\) −1.01243 −0.107925
\(89\) 11.0170 1.16780 0.583902 0.811824i \(-0.301525\pi\)
0.583902 + 0.811824i \(0.301525\pi\)
\(90\) −13.9793 −1.47354
\(91\) 4.53614 0.475517
\(92\) 4.79998 0.500433
\(93\) 1.06723 0.110667
\(94\) −12.1109 −1.24914
\(95\) −3.16592 −0.324816
\(96\) 22.8040 2.32742
\(97\) −17.6870 −1.79584 −0.897919 0.440161i \(-0.854922\pi\)
−0.897919 + 0.440161i \(0.854922\pi\)
\(98\) 9.96509 1.00663
\(99\) −7.97335 −0.801352
\(100\) −5.98206 −0.598206
\(101\) 7.30402 0.726777 0.363389 0.931638i \(-0.381620\pi\)
0.363389 + 0.931638i \(0.381620\pi\)
\(102\) −6.15766 −0.609699
\(103\) −11.4162 −1.12487 −0.562436 0.826841i \(-0.690136\pi\)
−0.562436 + 0.826841i \(0.690136\pi\)
\(104\) −3.58711 −0.351746
\(105\) −4.00013 −0.390373
\(106\) −5.90440 −0.573486
\(107\) 4.24267 0.410154 0.205077 0.978746i \(-0.434255\pi\)
0.205077 + 0.978746i \(0.434255\pi\)
\(108\) 23.9765 2.30714
\(109\) 4.18320 0.400678 0.200339 0.979727i \(-0.435796\pi\)
0.200339 + 0.979727i \(0.435796\pi\)
\(110\) 1.75325 0.167166
\(111\) −33.1708 −3.14844
\(112\) 6.13597 0.579795
\(113\) −8.54508 −0.803854 −0.401927 0.915672i \(-0.631659\pi\)
−0.401927 + 0.915672i \(0.631659\pi\)
\(114\) 20.6689 1.93582
\(115\) 3.11079 0.290083
\(116\) −9.48264 −0.880441
\(117\) −28.2502 −2.61173
\(118\) −2.64842 −0.243807
\(119\) −1.28029 −0.117364
\(120\) 3.16324 0.288763
\(121\) 1.00000 0.0909091
\(122\) 20.0542 1.81562
\(123\) −27.8230 −2.50872
\(124\) 0.468873 0.0421061
\(125\) −8.59281 −0.768564
\(126\) 18.9755 1.69047
\(127\) 3.12850 0.277610 0.138805 0.990320i \(-0.455674\pi\)
0.138805 + 0.990320i \(0.455674\pi\)
\(128\) −7.79911 −0.689350
\(129\) 3.31260 0.291659
\(130\) 6.21189 0.544819
\(131\) 5.20463 0.454730 0.227365 0.973810i \(-0.426989\pi\)
0.227365 + 0.973810i \(0.426989\pi\)
\(132\) −4.82099 −0.419613
\(133\) 4.29743 0.372634
\(134\) −22.8026 −1.96985
\(135\) 15.5388 1.33736
\(136\) 1.01243 0.0868152
\(137\) −16.4360 −1.40422 −0.702111 0.712067i \(-0.747759\pi\)
−0.702111 + 0.712067i \(0.747759\pi\)
\(138\) −20.3090 −1.72882
\(139\) 5.99258 0.508284 0.254142 0.967167i \(-0.418207\pi\)
0.254142 + 0.967167i \(0.418207\pi\)
\(140\) −1.75740 −0.148528
\(141\) 21.5824 1.81756
\(142\) 7.71255 0.647223
\(143\) 3.54307 0.296287
\(144\) −38.2135 −3.18446
\(145\) −6.14554 −0.510359
\(146\) 11.5482 0.955734
\(147\) −17.7584 −1.46469
\(148\) −14.5732 −1.19791
\(149\) −4.15148 −0.340102 −0.170051 0.985435i \(-0.554393\pi\)
−0.170051 + 0.985435i \(0.554393\pi\)
\(150\) 25.3104 2.06659
\(151\) 18.2745 1.48716 0.743578 0.668649i \(-0.233127\pi\)
0.743578 + 0.668649i \(0.233127\pi\)
\(152\) −3.39834 −0.275642
\(153\) 7.97335 0.644607
\(154\) −2.37987 −0.191775
\(155\) 0.303869 0.0244074
\(156\) −17.0811 −1.36758
\(157\) −8.99189 −0.717631 −0.358816 0.933408i \(-0.616819\pi\)
−0.358816 + 0.933408i \(0.616819\pi\)
\(158\) 30.8782 2.45654
\(159\) 10.5220 0.834452
\(160\) 6.49290 0.513309
\(161\) −4.22260 −0.332787
\(162\) −56.9818 −4.47691
\(163\) −4.18972 −0.328164 −0.164082 0.986447i \(-0.552466\pi\)
−0.164082 + 0.986447i \(0.552466\pi\)
\(164\) −12.2237 −0.954508
\(165\) −3.12440 −0.243235
\(166\) 1.09312 0.0848425
\(167\) 9.88467 0.764899 0.382449 0.923976i \(-0.375081\pi\)
0.382449 + 0.923976i \(0.375081\pi\)
\(168\) −4.29380 −0.331274
\(169\) −0.446632 −0.0343563
\(170\) −1.75325 −0.134468
\(171\) −26.7635 −2.04665
\(172\) 1.45535 0.110969
\(173\) −16.0141 −1.21753 −0.608763 0.793352i \(-0.708334\pi\)
−0.608763 + 0.793352i \(0.708334\pi\)
\(174\) 40.1216 3.04161
\(175\) 5.26248 0.397806
\(176\) 4.79266 0.361260
\(177\) 4.71965 0.354751
\(178\) −20.4791 −1.53497
\(179\) 4.67448 0.349387 0.174694 0.984623i \(-0.444107\pi\)
0.174694 + 0.984623i \(0.444107\pi\)
\(180\) 10.9447 0.815772
\(181\) −5.40048 −0.401415 −0.200707 0.979651i \(-0.564324\pi\)
−0.200707 + 0.979651i \(0.564324\pi\)
\(182\) −8.43204 −0.625025
\(183\) −35.7379 −2.64182
\(184\) 3.33917 0.246167
\(185\) −9.44462 −0.694382
\(186\) −1.98383 −0.145461
\(187\) −1.00000 −0.0731272
\(188\) 9.48192 0.691540
\(189\) −21.0924 −1.53424
\(190\) 5.88499 0.426942
\(191\) 21.9393 1.58747 0.793737 0.608261i \(-0.208133\pi\)
0.793737 + 0.608261i \(0.208133\pi\)
\(192\) −10.6370 −0.767657
\(193\) −14.1725 −1.02016 −0.510078 0.860128i \(-0.670383\pi\)
−0.510078 + 0.860128i \(0.670383\pi\)
\(194\) 32.8775 2.36047
\(195\) −11.0700 −0.792739
\(196\) −7.80193 −0.557281
\(197\) −0.784799 −0.0559146 −0.0279573 0.999609i \(-0.508900\pi\)
−0.0279573 + 0.999609i \(0.508900\pi\)
\(198\) 14.8213 1.05330
\(199\) −8.61482 −0.610688 −0.305344 0.952242i \(-0.598771\pi\)
−0.305344 + 0.952242i \(0.598771\pi\)
\(200\) −4.16149 −0.294262
\(201\) 40.6358 2.86623
\(202\) −13.5771 −0.955283
\(203\) 8.34198 0.585492
\(204\) 4.82099 0.337537
\(205\) −7.92196 −0.553293
\(206\) 21.2211 1.47854
\(207\) 26.2975 1.82780
\(208\) 16.9807 1.17740
\(209\) 3.35662 0.232182
\(210\) 7.43567 0.513110
\(211\) 28.4532 1.95880 0.979400 0.201928i \(-0.0647207\pi\)
0.979400 + 0.201928i \(0.0647207\pi\)
\(212\) 4.62271 0.317489
\(213\) −13.7443 −0.941742
\(214\) −7.88651 −0.539111
\(215\) 0.943187 0.0643248
\(216\) 16.6795 1.13490
\(217\) −0.412473 −0.0280005
\(218\) −7.77597 −0.526655
\(219\) −20.5796 −1.39064
\(220\) −1.37266 −0.0925450
\(221\) −3.54307 −0.238333
\(222\) 61.6598 4.13834
\(223\) −9.78566 −0.655296 −0.327648 0.944800i \(-0.606256\pi\)
−0.327648 + 0.944800i \(0.606256\pi\)
\(224\) −8.81349 −0.588876
\(225\) −32.7736 −2.18491
\(226\) 15.8841 1.05659
\(227\) 22.7185 1.50788 0.753939 0.656944i \(-0.228151\pi\)
0.753939 + 0.656944i \(0.228151\pi\)
\(228\) −16.1822 −1.07169
\(229\) −3.97620 −0.262754 −0.131377 0.991332i \(-0.541940\pi\)
−0.131377 + 0.991332i \(0.541940\pi\)
\(230\) −5.78251 −0.381288
\(231\) 4.24108 0.279042
\(232\) −6.59671 −0.433095
\(233\) 20.0057 1.31062 0.655308 0.755362i \(-0.272539\pi\)
0.655308 + 0.755362i \(0.272539\pi\)
\(234\) 52.5130 3.43288
\(235\) 6.14507 0.400860
\(236\) 2.07352 0.134974
\(237\) −55.0270 −3.57438
\(238\) 2.37987 0.154264
\(239\) 3.22453 0.208577 0.104289 0.994547i \(-0.466743\pi\)
0.104289 + 0.994547i \(0.466743\pi\)
\(240\) −14.9742 −0.966581
\(241\) −2.86703 −0.184682 −0.0923408 0.995727i \(-0.529435\pi\)
−0.0923408 + 0.995727i \(0.529435\pi\)
\(242\) −1.85886 −0.119492
\(243\) 52.1211 3.34357
\(244\) −15.7010 −1.00515
\(245\) −5.05630 −0.323035
\(246\) 51.7190 3.29748
\(247\) 11.8927 0.756717
\(248\) 0.326177 0.0207123
\(249\) −1.94801 −0.123450
\(250\) 15.9728 1.01021
\(251\) 19.6281 1.23892 0.619458 0.785030i \(-0.287352\pi\)
0.619458 + 0.785030i \(0.287352\pi\)
\(252\) −14.8564 −0.935867
\(253\) −3.29817 −0.207354
\(254\) −5.81543 −0.364893
\(255\) 3.12440 0.195658
\(256\) 20.9195 1.30747
\(257\) −28.8242 −1.79801 −0.899004 0.437941i \(-0.855708\pi\)
−0.899004 + 0.437941i \(0.855708\pi\)
\(258\) −6.15766 −0.383359
\(259\) 12.8202 0.796606
\(260\) −4.86345 −0.301618
\(261\) −51.9521 −3.21575
\(262\) −9.67466 −0.597702
\(263\) −17.5011 −1.07916 −0.539581 0.841933i \(-0.681418\pi\)
−0.539581 + 0.841933i \(0.681418\pi\)
\(264\) −3.35378 −0.206411
\(265\) 2.99590 0.184037
\(266\) −7.98830 −0.489794
\(267\) 36.4951 2.23346
\(268\) 17.8528 1.09053
\(269\) 7.07228 0.431204 0.215602 0.976481i \(-0.430829\pi\)
0.215602 + 0.976481i \(0.430829\pi\)
\(270\) −28.8843 −1.75784
\(271\) −19.4556 −1.18184 −0.590920 0.806730i \(-0.701235\pi\)
−0.590920 + 0.806730i \(0.701235\pi\)
\(272\) −4.79266 −0.290598
\(273\) 15.0265 0.909442
\(274\) 30.5522 1.84572
\(275\) 4.11040 0.247866
\(276\) 15.9005 0.957095
\(277\) 6.25814 0.376015 0.188007 0.982168i \(-0.439797\pi\)
0.188007 + 0.982168i \(0.439797\pi\)
\(278\) −11.1393 −0.668093
\(279\) 2.56880 0.153790
\(280\) −1.22256 −0.0730618
\(281\) −9.10585 −0.543210 −0.271605 0.962409i \(-0.587554\pi\)
−0.271605 + 0.962409i \(0.587554\pi\)
\(282\) −40.1185 −2.38902
\(283\) 3.50582 0.208399 0.104200 0.994556i \(-0.466772\pi\)
0.104200 + 0.994556i \(0.466772\pi\)
\(284\) −6.03836 −0.358311
\(285\) −10.4874 −0.621222
\(286\) −6.58607 −0.389442
\(287\) 10.7533 0.634747
\(288\) 54.8886 3.23434
\(289\) 1.00000 0.0588235
\(290\) 11.4237 0.670822
\(291\) −58.5899 −3.43460
\(292\) −9.04137 −0.529106
\(293\) 5.99704 0.350351 0.175175 0.984537i \(-0.443951\pi\)
0.175175 + 0.984537i \(0.443951\pi\)
\(294\) 33.0104 1.92521
\(295\) 1.34381 0.0782397
\(296\) −10.1380 −0.589259
\(297\) −16.4747 −0.955961
\(298\) 7.71700 0.447034
\(299\) −11.6857 −0.675799
\(300\) −19.8162 −1.14409
\(301\) −1.28029 −0.0737944
\(302\) −33.9696 −1.95473
\(303\) 24.1953 1.38999
\(304\) 16.0871 0.922660
\(305\) −10.1755 −0.582649
\(306\) −14.8213 −0.847278
\(307\) −34.4336 −1.96523 −0.982614 0.185659i \(-0.940558\pi\)
−0.982614 + 0.185659i \(0.940558\pi\)
\(308\) 1.86326 0.106169
\(309\) −37.8174 −2.15135
\(310\) −0.564849 −0.0320813
\(311\) 20.4432 1.15923 0.579615 0.814890i \(-0.303203\pi\)
0.579615 + 0.814890i \(0.303203\pi\)
\(312\) −11.8827 −0.672725
\(313\) 11.8151 0.667827 0.333914 0.942604i \(-0.391631\pi\)
0.333914 + 0.942604i \(0.391631\pi\)
\(314\) 16.7146 0.943262
\(315\) −9.62820 −0.542488
\(316\) −24.1753 −1.35997
\(317\) −30.5989 −1.71861 −0.859303 0.511467i \(-0.829102\pi\)
−0.859303 + 0.511467i \(0.829102\pi\)
\(318\) −19.5590 −1.09681
\(319\) 6.51572 0.364810
\(320\) −3.02863 −0.169305
\(321\) 14.0543 0.784434
\(322\) 7.84921 0.437419
\(323\) −3.35662 −0.186767
\(324\) 44.6126 2.47848
\(325\) 14.5634 0.807835
\(326\) 7.78808 0.431342
\(327\) 13.8573 0.766310
\(328\) −8.50354 −0.469530
\(329\) −8.34134 −0.459873
\(330\) 5.80782 0.319710
\(331\) 13.9574 0.767166 0.383583 0.923506i \(-0.374690\pi\)
0.383583 + 0.923506i \(0.374690\pi\)
\(332\) −0.855832 −0.0469699
\(333\) −79.8413 −4.37527
\(334\) −18.3742 −1.00539
\(335\) 11.5701 0.632142
\(336\) 20.3260 1.10888
\(337\) −8.71417 −0.474691 −0.237346 0.971425i \(-0.576277\pi\)
−0.237346 + 0.971425i \(0.576277\pi\)
\(338\) 0.830225 0.0451583
\(339\) −28.3065 −1.53740
\(340\) 1.37266 0.0744432
\(341\) −0.322173 −0.0174466
\(342\) 49.7495 2.69014
\(343\) 15.8254 0.854493
\(344\) 1.01243 0.0545866
\(345\) 10.3048 0.554793
\(346\) 29.7678 1.60033
\(347\) −16.4211 −0.881529 −0.440765 0.897623i \(-0.645293\pi\)
−0.440765 + 0.897623i \(0.645293\pi\)
\(348\) −31.4122 −1.68387
\(349\) −20.5731 −1.10125 −0.550626 0.834752i \(-0.685611\pi\)
−0.550626 + 0.834752i \(0.685611\pi\)
\(350\) −9.78220 −0.522881
\(351\) −58.3712 −3.11562
\(352\) −6.88400 −0.366919
\(353\) 16.8883 0.898872 0.449436 0.893313i \(-0.351625\pi\)
0.449436 + 0.893313i \(0.351625\pi\)
\(354\) −8.77316 −0.466288
\(355\) −3.91336 −0.207700
\(356\) 16.0336 0.849780
\(357\) −4.24108 −0.224462
\(358\) −8.68919 −0.459238
\(359\) −21.3144 −1.12493 −0.562466 0.826820i \(-0.690147\pi\)
−0.562466 + 0.826820i \(0.690147\pi\)
\(360\) 7.61384 0.401284
\(361\) −7.73311 −0.407006
\(362\) 10.0387 0.527623
\(363\) 3.31260 0.173867
\(364\) 6.60167 0.346021
\(365\) −5.85956 −0.306704
\(366\) 66.4316 3.47244
\(367\) 29.0656 1.51721 0.758605 0.651551i \(-0.225881\pi\)
0.758605 + 0.651551i \(0.225881\pi\)
\(368\) −15.8070 −0.823997
\(369\) −66.9692 −3.48628
\(370\) 17.5562 0.912703
\(371\) −4.06665 −0.211130
\(372\) 1.55319 0.0805293
\(373\) 0.918147 0.0475399 0.0237699 0.999717i \(-0.492433\pi\)
0.0237699 + 0.999717i \(0.492433\pi\)
\(374\) 1.85886 0.0961192
\(375\) −28.4646 −1.46990
\(376\) 6.59621 0.340174
\(377\) 23.0857 1.18897
\(378\) 39.2077 2.01662
\(379\) 15.8601 0.814678 0.407339 0.913277i \(-0.366457\pi\)
0.407339 + 0.913277i \(0.366457\pi\)
\(380\) −4.60751 −0.236360
\(381\) 10.3635 0.530937
\(382\) −40.7821 −2.08659
\(383\) −34.9460 −1.78566 −0.892828 0.450398i \(-0.851282\pi\)
−0.892828 + 0.450398i \(0.851282\pi\)
\(384\) −25.8354 −1.31841
\(385\) 1.20755 0.0615423
\(386\) 26.3446 1.34090
\(387\) 7.97335 0.405308
\(388\) −25.7407 −1.30678
\(389\) −24.2776 −1.23092 −0.615460 0.788168i \(-0.711030\pi\)
−0.615460 + 0.788168i \(0.711030\pi\)
\(390\) 20.5775 1.04198
\(391\) 3.29817 0.166796
\(392\) −5.42751 −0.274131
\(393\) 17.2409 0.869687
\(394\) 1.45883 0.0734947
\(395\) −15.6676 −0.788325
\(396\) −11.6040 −0.583123
\(397\) −22.2645 −1.11742 −0.558711 0.829362i \(-0.688704\pi\)
−0.558711 + 0.829362i \(0.688704\pi\)
\(398\) 16.0137 0.802695
\(399\) 14.2357 0.712675
\(400\) 19.6997 0.984987
\(401\) 8.25181 0.412076 0.206038 0.978544i \(-0.433943\pi\)
0.206038 + 0.978544i \(0.433943\pi\)
\(402\) −75.5361 −3.76740
\(403\) −1.14148 −0.0568613
\(404\) 10.6299 0.528857
\(405\) 28.9127 1.43668
\(406\) −15.5065 −0.769577
\(407\) 10.0135 0.496352
\(408\) 3.35378 0.166037
\(409\) 14.9500 0.739229 0.369614 0.929185i \(-0.379490\pi\)
0.369614 + 0.929185i \(0.379490\pi\)
\(410\) 14.7258 0.727254
\(411\) −54.4460 −2.68562
\(412\) −16.6145 −0.818540
\(413\) −1.82409 −0.0897578
\(414\) −48.8832 −2.40248
\(415\) −0.554650 −0.0272267
\(416\) −24.3905 −1.19584
\(417\) 19.8510 0.972109
\(418\) −6.23947 −0.305183
\(419\) 9.64781 0.471326 0.235663 0.971835i \(-0.424274\pi\)
0.235663 + 0.971835i \(0.424274\pi\)
\(420\) −5.82158 −0.284064
\(421\) 18.6504 0.908964 0.454482 0.890756i \(-0.349824\pi\)
0.454482 + 0.890756i \(0.349824\pi\)
\(422\) −52.8905 −2.57467
\(423\) 51.9481 2.52581
\(424\) 3.21585 0.156175
\(425\) −4.11040 −0.199384
\(426\) 25.5486 1.23783
\(427\) 13.8123 0.668424
\(428\) 6.17456 0.298459
\(429\) 11.7368 0.566658
\(430\) −1.75325 −0.0845492
\(431\) −1.02082 −0.0491710 −0.0245855 0.999698i \(-0.507827\pi\)
−0.0245855 + 0.999698i \(0.507827\pi\)
\(432\) −78.9578 −3.79886
\(433\) 37.7907 1.81611 0.908053 0.418854i \(-0.137568\pi\)
0.908053 + 0.418854i \(0.137568\pi\)
\(434\) 0.766728 0.0368041
\(435\) −20.3577 −0.976079
\(436\) 6.08801 0.291563
\(437\) −11.0707 −0.529583
\(438\) 38.2545 1.82787
\(439\) 14.0791 0.671957 0.335978 0.941870i \(-0.390933\pi\)
0.335978 + 0.941870i \(0.390933\pi\)
\(440\) −0.954911 −0.0455236
\(441\) −42.7441 −2.03543
\(442\) 6.58607 0.313267
\(443\) −16.8399 −0.800087 −0.400044 0.916496i \(-0.631005\pi\)
−0.400044 + 0.916496i \(0.631005\pi\)
\(444\) −48.2751 −2.29103
\(445\) 10.3911 0.492586
\(446\) 18.1901 0.861328
\(447\) −13.7522 −0.650457
\(448\) 4.11107 0.194230
\(449\) 24.5218 1.15725 0.578627 0.815592i \(-0.303589\pi\)
0.578627 + 0.815592i \(0.303589\pi\)
\(450\) 60.9215 2.87187
\(451\) 8.39914 0.395500
\(452\) −12.4361 −0.584944
\(453\) 60.5361 2.84424
\(454\) −42.2304 −1.98197
\(455\) 4.27843 0.200576
\(456\) −11.2574 −0.527174
\(457\) 5.13092 0.240014 0.120007 0.992773i \(-0.461708\pi\)
0.120007 + 0.992773i \(0.461708\pi\)
\(458\) 7.39118 0.345367
\(459\) 16.4747 0.768975
\(460\) 4.52728 0.211086
\(461\) −4.93593 −0.229889 −0.114945 0.993372i \(-0.536669\pi\)
−0.114945 + 0.993372i \(0.536669\pi\)
\(462\) −7.88356 −0.366776
\(463\) −2.36012 −0.109684 −0.0548419 0.998495i \(-0.517465\pi\)
−0.0548419 + 0.998495i \(0.517465\pi\)
\(464\) 31.2276 1.44971
\(465\) 1.00660 0.0466799
\(466\) −37.1877 −1.72269
\(467\) 20.6048 0.953475 0.476738 0.879046i \(-0.341819\pi\)
0.476738 + 0.879046i \(0.341819\pi\)
\(468\) −41.1138 −1.90049
\(469\) −15.7053 −0.725203
\(470\) −11.4228 −0.526895
\(471\) −29.7866 −1.37249
\(472\) 1.44247 0.0663949
\(473\) −1.00000 −0.0459800
\(474\) 102.287 4.69821
\(475\) 13.7970 0.633052
\(476\) −1.86326 −0.0854024
\(477\) 25.3263 1.15961
\(478\) −5.99394 −0.274156
\(479\) 9.43578 0.431132 0.215566 0.976489i \(-0.430840\pi\)
0.215566 + 0.976489i \(0.430840\pi\)
\(480\) 21.5084 0.981720
\(481\) 35.4786 1.61769
\(482\) 5.32940 0.242747
\(483\) −13.9878 −0.636467
\(484\) 1.45535 0.0661522
\(485\) −16.6821 −0.757495
\(486\) −96.8857 −4.39483
\(487\) −28.5570 −1.29404 −0.647020 0.762473i \(-0.723985\pi\)
−0.647020 + 0.762473i \(0.723985\pi\)
\(488\) −10.9226 −0.494441
\(489\) −13.8789 −0.627624
\(490\) 9.39894 0.424601
\(491\) −18.8039 −0.848607 −0.424304 0.905520i \(-0.639481\pi\)
−0.424304 + 0.905520i \(0.639481\pi\)
\(492\) −40.4922 −1.82553
\(493\) −6.51572 −0.293453
\(494\) −22.1069 −0.994637
\(495\) −7.52036 −0.338015
\(496\) −1.54406 −0.0693305
\(497\) 5.31201 0.238276
\(498\) 3.62107 0.162264
\(499\) −12.3897 −0.554640 −0.277320 0.960778i \(-0.589446\pi\)
−0.277320 + 0.960778i \(0.589446\pi\)
\(500\) −12.5055 −0.559264
\(501\) 32.7440 1.46289
\(502\) −36.4859 −1.62844
\(503\) 35.4862 1.58225 0.791126 0.611653i \(-0.209495\pi\)
0.791126 + 0.611653i \(0.209495\pi\)
\(504\) −10.3350 −0.460360
\(505\) 6.88905 0.306559
\(506\) 6.13083 0.272548
\(507\) −1.47951 −0.0657076
\(508\) 4.55306 0.202009
\(509\) 19.5505 0.866560 0.433280 0.901259i \(-0.357356\pi\)
0.433280 + 0.901259i \(0.357356\pi\)
\(510\) −5.80782 −0.257175
\(511\) 7.95379 0.351855
\(512\) −23.2882 −1.02920
\(513\) −55.2994 −2.44153
\(514\) 53.5801 2.36332
\(515\) −10.7676 −0.474478
\(516\) 4.82099 0.212232
\(517\) −6.51522 −0.286539
\(518\) −23.8308 −1.04707
\(519\) −53.0482 −2.32856
\(520\) −3.38332 −0.148368
\(521\) 9.59821 0.420505 0.210253 0.977647i \(-0.432571\pi\)
0.210253 + 0.977647i \(0.432571\pi\)
\(522\) 96.5715 4.22682
\(523\) −21.9654 −0.960478 −0.480239 0.877138i \(-0.659450\pi\)
−0.480239 + 0.877138i \(0.659450\pi\)
\(524\) 7.57454 0.330895
\(525\) 17.4325 0.760818
\(526\) 32.5320 1.41846
\(527\) 0.322173 0.0140341
\(528\) 15.8762 0.690922
\(529\) −12.1221 −0.527047
\(530\) −5.56896 −0.241900
\(531\) 11.3601 0.492985
\(532\) 6.25425 0.271156
\(533\) 29.7588 1.28899
\(534\) −67.8391 −2.93569
\(535\) 4.00163 0.173006
\(536\) 12.4195 0.536441
\(537\) 15.4847 0.668215
\(538\) −13.1464 −0.566779
\(539\) 5.36087 0.230909
\(540\) 22.6143 0.973164
\(541\) 27.0384 1.16247 0.581235 0.813736i \(-0.302570\pi\)
0.581235 + 0.813736i \(0.302570\pi\)
\(542\) 36.1651 1.55342
\(543\) −17.8897 −0.767719
\(544\) 6.88400 0.295149
\(545\) 3.94554 0.169008
\(546\) −27.9320 −1.19538
\(547\) −28.5198 −1.21942 −0.609708 0.792626i \(-0.708713\pi\)
−0.609708 + 0.792626i \(0.708713\pi\)
\(548\) −23.9201 −1.02182
\(549\) −86.0201 −3.67125
\(550\) −7.64064 −0.325798
\(551\) 21.8708 0.931727
\(552\) 11.0613 0.470802
\(553\) 21.2673 0.904378
\(554\) −11.6330 −0.494238
\(555\) −31.2863 −1.32803
\(556\) 8.72128 0.369865
\(557\) 13.1962 0.559142 0.279571 0.960125i \(-0.409808\pi\)
0.279571 + 0.960125i \(0.409808\pi\)
\(558\) −4.77502 −0.202143
\(559\) −3.54307 −0.149856
\(560\) 5.78737 0.244561
\(561\) −3.31260 −0.139858
\(562\) 16.9265 0.714000
\(563\) 33.0690 1.39369 0.696845 0.717222i \(-0.254586\pi\)
0.696845 + 0.717222i \(0.254586\pi\)
\(564\) 31.4098 1.32259
\(565\) −8.05961 −0.339070
\(566\) −6.51681 −0.273922
\(567\) −39.2462 −1.64818
\(568\) −4.20066 −0.176256
\(569\) 18.1691 0.761688 0.380844 0.924639i \(-0.375634\pi\)
0.380844 + 0.924639i \(0.375634\pi\)
\(570\) 19.4946 0.816540
\(571\) 3.24713 0.135888 0.0679442 0.997689i \(-0.478356\pi\)
0.0679442 + 0.997689i \(0.478356\pi\)
\(572\) 5.15640 0.215600
\(573\) 72.6763 3.03610
\(574\) −19.9888 −0.834317
\(575\) −13.5568 −0.565357
\(576\) −25.6029 −1.06679
\(577\) −29.3846 −1.22330 −0.611648 0.791130i \(-0.709493\pi\)
−0.611648 + 0.791130i \(0.709493\pi\)
\(578\) −1.85886 −0.0773182
\(579\) −46.9478 −1.95108
\(580\) −8.94390 −0.371375
\(581\) 0.752884 0.0312349
\(582\) 108.910 4.51447
\(583\) −3.17636 −0.131552
\(584\) −6.28974 −0.260271
\(585\) −26.6452 −1.10164
\(586\) −11.1476 −0.460504
\(587\) −38.9668 −1.60833 −0.804165 0.594406i \(-0.797387\pi\)
−0.804165 + 0.594406i \(0.797387\pi\)
\(588\) −25.8447 −1.06582
\(589\) −1.08141 −0.0445588
\(590\) −2.49795 −0.102839
\(591\) −2.59973 −0.106938
\(592\) 47.9914 1.97243
\(593\) −14.1572 −0.581365 −0.290682 0.956820i \(-0.593882\pi\)
−0.290682 + 0.956820i \(0.593882\pi\)
\(594\) 30.6242 1.25652
\(595\) −1.20755 −0.0495046
\(596\) −6.04184 −0.247484
\(597\) −28.5375 −1.16796
\(598\) 21.7220 0.888277
\(599\) −6.92580 −0.282981 −0.141490 0.989940i \(-0.545189\pi\)
−0.141490 + 0.989940i \(0.545189\pi\)
\(600\) −13.7854 −0.562786
\(601\) −20.9555 −0.854794 −0.427397 0.904064i \(-0.640569\pi\)
−0.427397 + 0.904064i \(0.640569\pi\)
\(602\) 2.37987 0.0969961
\(603\) 97.8093 3.98310
\(604\) 26.5957 1.08216
\(605\) 0.943187 0.0383460
\(606\) −44.9756 −1.82701
\(607\) 31.8935 1.29452 0.647259 0.762270i \(-0.275915\pi\)
0.647259 + 0.762270i \(0.275915\pi\)
\(608\) −23.1070 −0.937112
\(609\) 27.6337 1.11977
\(610\) 18.9148 0.765840
\(611\) −23.0839 −0.933875
\(612\) 11.6040 0.469064
\(613\) −38.2938 −1.54667 −0.773337 0.633996i \(-0.781414\pi\)
−0.773337 + 0.633996i \(0.781414\pi\)
\(614\) 64.0071 2.58312
\(615\) −26.2423 −1.05819
\(616\) 1.29620 0.0522254
\(617\) 45.6248 1.83679 0.918393 0.395669i \(-0.129487\pi\)
0.918393 + 0.395669i \(0.129487\pi\)
\(618\) 70.2970 2.82776
\(619\) −3.29046 −0.132255 −0.0661273 0.997811i \(-0.521064\pi\)
−0.0661273 + 0.997811i \(0.521064\pi\)
\(620\) 0.442235 0.0177606
\(621\) 54.3365 2.18045
\(622\) −38.0011 −1.52370
\(623\) −14.1049 −0.565103
\(624\) 56.2505 2.25182
\(625\) 12.4474 0.497895
\(626\) −21.9625 −0.877799
\(627\) 11.1191 0.444056
\(628\) −13.0863 −0.522201
\(629\) −10.0135 −0.399265
\(630\) 17.8974 0.713051
\(631\) 30.0293 1.19545 0.597723 0.801703i \(-0.296072\pi\)
0.597723 + 0.801703i \(0.296072\pi\)
\(632\) −16.8179 −0.668979
\(633\) 94.2543 3.74627
\(634\) 56.8790 2.25895
\(635\) 2.95076 0.117097
\(636\) 15.3132 0.607209
\(637\) 18.9940 0.752568
\(638\) −12.1118 −0.479510
\(639\) −33.0821 −1.30871
\(640\) −7.35602 −0.290772
\(641\) 5.08003 0.200649 0.100325 0.994955i \(-0.468012\pi\)
0.100325 + 0.994955i \(0.468012\pi\)
\(642\) −26.1249 −1.03107
\(643\) 34.5575 1.36282 0.681408 0.731904i \(-0.261368\pi\)
0.681408 + 0.731904i \(0.261368\pi\)
\(644\) −6.14535 −0.242161
\(645\) 3.12440 0.123023
\(646\) 6.23947 0.245489
\(647\) 45.1815 1.77627 0.888135 0.459583i \(-0.152001\pi\)
0.888135 + 0.459583i \(0.152001\pi\)
\(648\) 31.0353 1.21918
\(649\) −1.42476 −0.0559266
\(650\) −27.0714 −1.06183
\(651\) −1.36636 −0.0535519
\(652\) −6.09749 −0.238796
\(653\) 6.68020 0.261417 0.130708 0.991421i \(-0.458275\pi\)
0.130708 + 0.991421i \(0.458275\pi\)
\(654\) −25.7587 −1.00725
\(655\) 4.90894 0.191808
\(656\) 40.2542 1.57166
\(657\) −49.5346 −1.93253
\(658\) 15.5054 0.604462
\(659\) −37.0358 −1.44271 −0.721354 0.692566i \(-0.756480\pi\)
−0.721354 + 0.692566i \(0.756480\pi\)
\(660\) −4.54710 −0.176995
\(661\) 34.3829 1.33734 0.668670 0.743559i \(-0.266864\pi\)
0.668670 + 0.743559i \(0.266864\pi\)
\(662\) −25.9447 −1.00837
\(663\) −11.7368 −0.455820
\(664\) −0.595370 −0.0231048
\(665\) 4.05328 0.157179
\(666\) 148.413 5.75090
\(667\) −21.4900 −0.832095
\(668\) 14.3856 0.556597
\(669\) −32.4160 −1.25328
\(670\) −21.5071 −0.830894
\(671\) 10.7885 0.416484
\(672\) −29.1956 −1.12624
\(673\) 37.4467 1.44346 0.721732 0.692173i \(-0.243346\pi\)
0.721732 + 0.692173i \(0.243346\pi\)
\(674\) 16.1984 0.623939
\(675\) −67.7177 −2.60646
\(676\) −0.650005 −0.0250002
\(677\) −31.3125 −1.20344 −0.601720 0.798707i \(-0.705517\pi\)
−0.601720 + 0.798707i \(0.705517\pi\)
\(678\) 52.6177 2.02077
\(679\) 22.6443 0.869010
\(680\) 0.954911 0.0366192
\(681\) 75.2573 2.88387
\(682\) 0.598873 0.0229320
\(683\) 30.8163 1.17915 0.589576 0.807713i \(-0.299295\pi\)
0.589576 + 0.807713i \(0.299295\pi\)
\(684\) −38.9502 −1.48930
\(685\) −15.5022 −0.592309
\(686\) −29.4172 −1.12315
\(687\) −13.1716 −0.502527
\(688\) −4.79266 −0.182718
\(689\) −11.2541 −0.428747
\(690\) −19.1552 −0.729225
\(691\) −3.22077 −0.122524 −0.0612619 0.998122i \(-0.519512\pi\)
−0.0612619 + 0.998122i \(0.519512\pi\)
\(692\) −23.3060 −0.885962
\(693\) 10.2082 0.387776
\(694\) 30.5244 1.15869
\(695\) 5.65212 0.214397
\(696\) −21.8523 −0.828309
\(697\) −8.39914 −0.318140
\(698\) 38.2424 1.44750
\(699\) 66.2709 2.50660
\(700\) 7.65874 0.289473
\(701\) −31.0900 −1.17425 −0.587127 0.809495i \(-0.699741\pi\)
−0.587127 + 0.809495i \(0.699741\pi\)
\(702\) 108.504 4.09521
\(703\) 33.6116 1.26768
\(704\) 3.21106 0.121021
\(705\) 20.3562 0.766659
\(706\) −31.3929 −1.18149
\(707\) −9.35123 −0.351689
\(708\) 6.86874 0.258143
\(709\) −12.1758 −0.457273 −0.228636 0.973512i \(-0.573427\pi\)
−0.228636 + 0.973512i \(0.573427\pi\)
\(710\) 7.27437 0.273002
\(711\) −132.448 −4.96720
\(712\) 11.1540 0.418013
\(713\) 1.06258 0.0397940
\(714\) 7.88356 0.295035
\(715\) 3.34178 0.124975
\(716\) 6.80300 0.254240
\(717\) 10.6816 0.398911
\(718\) 39.6205 1.47862
\(719\) 7.71558 0.287742 0.143871 0.989596i \(-0.454045\pi\)
0.143871 + 0.989596i \(0.454045\pi\)
\(720\) −36.0425 −1.34322
\(721\) 14.6160 0.544328
\(722\) 14.3747 0.534973
\(723\) −9.49734 −0.353210
\(724\) −7.85958 −0.292099
\(725\) 26.7822 0.994666
\(726\) −6.15766 −0.228532
\(727\) 18.5549 0.688163 0.344082 0.938940i \(-0.388190\pi\)
0.344082 + 0.938940i \(0.388190\pi\)
\(728\) 4.59253 0.170210
\(729\) 80.6940 2.98867
\(730\) 10.8921 0.403134
\(731\) 1.00000 0.0369863
\(732\) −52.0110 −1.92238
\(733\) 19.8352 0.732629 0.366315 0.930491i \(-0.380619\pi\)
0.366315 + 0.930491i \(0.380619\pi\)
\(734\) −54.0287 −1.99424
\(735\) −16.7495 −0.617816
\(736\) 22.7046 0.836903
\(737\) −12.2670 −0.451862
\(738\) 124.486 4.58240
\(739\) −1.56707 −0.0576456 −0.0288228 0.999585i \(-0.509176\pi\)
−0.0288228 + 0.999585i \(0.509176\pi\)
\(740\) −13.7452 −0.505284
\(741\) 39.3960 1.44725
\(742\) 7.55932 0.277511
\(743\) −0.973473 −0.0357133 −0.0178566 0.999841i \(-0.505684\pi\)
−0.0178566 + 0.999841i \(0.505684\pi\)
\(744\) 1.08050 0.0396129
\(745\) −3.91562 −0.143457
\(746\) −1.70670 −0.0624869
\(747\) −4.68881 −0.171554
\(748\) −1.45535 −0.0532128
\(749\) −5.43183 −0.198475
\(750\) 52.9116 1.93206
\(751\) 27.3002 0.996199 0.498099 0.867120i \(-0.334031\pi\)
0.498099 + 0.867120i \(0.334031\pi\)
\(752\) −31.2252 −1.13867
\(753\) 65.0202 2.36947
\(754\) −42.9130 −1.56280
\(755\) 17.2363 0.627291
\(756\) −30.6967 −1.11643
\(757\) −13.6539 −0.496260 −0.248130 0.968727i \(-0.579816\pi\)
−0.248130 + 0.968727i \(0.579816\pi\)
\(758\) −29.4816 −1.07082
\(759\) −10.9255 −0.396572
\(760\) −3.20527 −0.116267
\(761\) −45.0451 −1.63288 −0.816442 0.577427i \(-0.804057\pi\)
−0.816442 + 0.577427i \(0.804057\pi\)
\(762\) −19.2642 −0.697869
\(763\) −5.35569 −0.193889
\(764\) 31.9294 1.15516
\(765\) 7.52036 0.271899
\(766\) 64.9595 2.34708
\(767\) −5.04802 −0.182273
\(768\) 69.2982 2.50058
\(769\) −36.2208 −1.30615 −0.653077 0.757291i \(-0.726522\pi\)
−0.653077 + 0.757291i \(0.726522\pi\)
\(770\) −2.24466 −0.0808919
\(771\) −95.4833 −3.43875
\(772\) −20.6259 −0.742341
\(773\) −7.92742 −0.285130 −0.142565 0.989785i \(-0.545535\pi\)
−0.142565 + 0.989785i \(0.545535\pi\)
\(774\) −14.8213 −0.532741
\(775\) −1.32426 −0.0475688
\(776\) −17.9068 −0.642817
\(777\) 42.4681 1.52354
\(778\) 45.1285 1.61793
\(779\) 28.1927 1.01011
\(780\) −16.1107 −0.576855
\(781\) 4.14908 0.148466
\(782\) −6.13083 −0.219238
\(783\) −107.345 −3.83619
\(784\) 25.6928 0.917601
\(785\) −8.48103 −0.302701
\(786\) −32.0483 −1.14313
\(787\) 46.3341 1.65163 0.825817 0.563938i \(-0.190714\pi\)
0.825817 + 0.563938i \(0.190714\pi\)
\(788\) −1.14215 −0.0406876
\(789\) −57.9742 −2.06393
\(790\) 29.1239 1.03618
\(791\) 10.9401 0.388987
\(792\) −8.07246 −0.286842
\(793\) 38.2243 1.35738
\(794\) 41.3865 1.46875
\(795\) 9.92424 0.351977
\(796\) −12.5376 −0.444382
\(797\) −43.0850 −1.52615 −0.763075 0.646310i \(-0.776311\pi\)
−0.763075 + 0.646310i \(0.776311\pi\)
\(798\) −26.4621 −0.936748
\(799\) 6.51522 0.230492
\(800\) −28.2960 −1.00041
\(801\) 87.8426 3.10377
\(802\) −15.3389 −0.541637
\(803\) 6.21252 0.219235
\(804\) 59.1392 2.08568
\(805\) −3.98270 −0.140372
\(806\) 2.12185 0.0747390
\(807\) 23.4277 0.824693
\(808\) 7.39481 0.260149
\(809\) −26.3872 −0.927723 −0.463861 0.885908i \(-0.653536\pi\)
−0.463861 + 0.885908i \(0.653536\pi\)
\(810\) −53.7445 −1.88839
\(811\) −46.8754 −1.64602 −0.823009 0.568028i \(-0.807706\pi\)
−0.823009 + 0.568028i \(0.807706\pi\)
\(812\) 12.1405 0.426047
\(813\) −64.4485 −2.26031
\(814\) −18.6137 −0.652410
\(815\) −3.95168 −0.138421
\(816\) −15.8762 −0.555778
\(817\) −3.35662 −0.117433
\(818\) −27.7899 −0.971650
\(819\) 36.1683 1.26382
\(820\) −11.5292 −0.402617
\(821\) −50.4348 −1.76019 −0.880093 0.474801i \(-0.842520\pi\)
−0.880093 + 0.474801i \(0.842520\pi\)
\(822\) 101.207 3.53001
\(823\) 28.2008 0.983017 0.491508 0.870873i \(-0.336446\pi\)
0.491508 + 0.870873i \(0.336446\pi\)
\(824\) −11.5581 −0.402646
\(825\) 13.6161 0.474053
\(826\) 3.39073 0.117979
\(827\) −17.5382 −0.609864 −0.304932 0.952374i \(-0.598634\pi\)
−0.304932 + 0.952374i \(0.598634\pi\)
\(828\) 38.2719 1.33004
\(829\) 49.5341 1.72039 0.860196 0.509964i \(-0.170341\pi\)
0.860196 + 0.509964i \(0.170341\pi\)
\(830\) 1.03102 0.0357871
\(831\) 20.7307 0.719141
\(832\) 11.3770 0.394427
\(833\) −5.36087 −0.185743
\(834\) −36.9002 −1.27775
\(835\) 9.32309 0.322639
\(836\) 4.88505 0.168953
\(837\) 5.30771 0.183461
\(838\) −17.9339 −0.619516
\(839\) −48.7441 −1.68283 −0.841416 0.540387i \(-0.818278\pi\)
−0.841416 + 0.540387i \(0.818278\pi\)
\(840\) −4.04985 −0.139733
\(841\) 13.4546 0.463952
\(842\) −34.6684 −1.19475
\(843\) −30.1641 −1.03891
\(844\) 41.4093 1.42537
\(845\) −0.421257 −0.0144917
\(846\) −96.5641 −3.31994
\(847\) −1.28029 −0.0439911
\(848\) −15.2232 −0.522768
\(849\) 11.6134 0.398570
\(850\) 7.64064 0.262072
\(851\) −33.0263 −1.13213
\(852\) −20.0027 −0.685281
\(853\) 21.3435 0.730787 0.365393 0.930853i \(-0.380934\pi\)
0.365393 + 0.930853i \(0.380934\pi\)
\(854\) −25.6751 −0.878583
\(855\) −25.2430 −0.863291
\(856\) 4.29541 0.146814
\(857\) 29.3366 1.00212 0.501060 0.865413i \(-0.332944\pi\)
0.501060 + 0.865413i \(0.332944\pi\)
\(858\) −21.8170 −0.744821
\(859\) −32.3320 −1.10315 −0.551577 0.834124i \(-0.685974\pi\)
−0.551577 + 0.834124i \(0.685974\pi\)
\(860\) 1.37266 0.0468075
\(861\) 35.6214 1.21397
\(862\) 1.89755 0.0646309
\(863\) −10.6727 −0.363302 −0.181651 0.983363i \(-0.558144\pi\)
−0.181651 + 0.983363i \(0.558144\pi\)
\(864\) 113.412 3.85836
\(865\) −15.1042 −0.513560
\(866\) −70.2476 −2.38711
\(867\) 3.31260 0.112502
\(868\) −0.600292 −0.0203752
\(869\) 16.6114 0.563503
\(870\) 37.8421 1.28297
\(871\) −43.4630 −1.47269
\(872\) 4.23520 0.143422
\(873\) −141.024 −4.77295
\(874\) 20.5788 0.696090
\(875\) 11.0012 0.371910
\(876\) −29.9505 −1.01193
\(877\) −7.10112 −0.239788 −0.119894 0.992787i \(-0.538255\pi\)
−0.119894 + 0.992787i \(0.538255\pi\)
\(878\) −26.1709 −0.883226
\(879\) 19.8658 0.670057
\(880\) 4.52037 0.152382
\(881\) 37.4879 1.26300 0.631499 0.775376i \(-0.282440\pi\)
0.631499 + 0.775376i \(0.282440\pi\)
\(882\) 79.4551 2.67539
\(883\) 41.8715 1.40909 0.704544 0.709660i \(-0.251151\pi\)
0.704544 + 0.709660i \(0.251151\pi\)
\(884\) −5.15640 −0.173429
\(885\) 4.45152 0.149636
\(886\) 31.3029 1.05164
\(887\) −20.6477 −0.693282 −0.346641 0.937998i \(-0.612678\pi\)
−0.346641 + 0.937998i \(0.612678\pi\)
\(888\) −33.5831 −1.12698
\(889\) −4.00537 −0.134336
\(890\) −19.3156 −0.647460
\(891\) −30.6542 −1.02696
\(892\) −14.2415 −0.476842
\(893\) −21.8691 −0.731822
\(894\) 25.5634 0.854967
\(895\) 4.40891 0.147374
\(896\) 9.98508 0.333578
\(897\) −38.7100 −1.29249
\(898\) −45.5825 −1.52111
\(899\) −2.09919 −0.0700118
\(900\) −47.6970 −1.58990
\(901\) 3.17636 0.105820
\(902\) −15.6128 −0.519849
\(903\) −4.24108 −0.141134
\(904\) −8.65130 −0.287738
\(905\) −5.09366 −0.169319
\(906\) −112.528 −3.73849
\(907\) −47.5322 −1.57828 −0.789140 0.614214i \(-0.789473\pi\)
−0.789140 + 0.614214i \(0.789473\pi\)
\(908\) 33.0633 1.09724
\(909\) 58.2375 1.93162
\(910\) −7.95299 −0.263639
\(911\) 9.03738 0.299422 0.149711 0.988730i \(-0.452166\pi\)
0.149711 + 0.988730i \(0.452166\pi\)
\(912\) 53.2903 1.76462
\(913\) 0.588060 0.0194619
\(914\) −9.53765 −0.315477
\(915\) −33.7075 −1.11434
\(916\) −5.78675 −0.191200
\(917\) −6.66341 −0.220045
\(918\) −30.6242 −1.01075
\(919\) −9.72750 −0.320881 −0.160440 0.987046i \(-0.551291\pi\)
−0.160440 + 0.987046i \(0.551291\pi\)
\(920\) 3.14946 0.103835
\(921\) −114.065 −3.75856
\(922\) 9.17518 0.302169
\(923\) 14.7005 0.483873
\(924\) 6.17224 0.203052
\(925\) 41.1596 1.35332
\(926\) 4.38712 0.144170
\(927\) −91.0253 −2.98966
\(928\) −44.8542 −1.47241
\(929\) 22.3297 0.732613 0.366306 0.930494i \(-0.380622\pi\)
0.366306 + 0.930494i \(0.380622\pi\)
\(930\) −1.87112 −0.0613565
\(931\) 17.9944 0.589742
\(932\) 29.1152 0.953701
\(933\) 67.7204 2.21707
\(934\) −38.3013 −1.25326
\(935\) −0.943187 −0.0308455
\(936\) −28.6013 −0.934863
\(937\) 1.41138 0.0461077 0.0230538 0.999734i \(-0.492661\pi\)
0.0230538 + 0.999734i \(0.492661\pi\)
\(938\) 29.1939 0.953214
\(939\) 39.1387 1.27724
\(940\) 8.94322 0.291696
\(941\) −9.34919 −0.304775 −0.152387 0.988321i \(-0.548696\pi\)
−0.152387 + 0.988321i \(0.548696\pi\)
\(942\) 55.3690 1.80402
\(943\) −27.7018 −0.902094
\(944\) −6.82837 −0.222245
\(945\) −19.8940 −0.647153
\(946\) 1.85886 0.0604366
\(947\) 22.9351 0.745291 0.372646 0.927974i \(-0.378451\pi\)
0.372646 + 0.927974i \(0.378451\pi\)
\(948\) −80.0834 −2.60099
\(949\) 22.0114 0.714520
\(950\) −25.6467 −0.832089
\(951\) −101.362 −3.28689
\(952\) −1.29620 −0.0420101
\(953\) 9.55768 0.309604 0.154802 0.987946i \(-0.450526\pi\)
0.154802 + 0.987946i \(0.450526\pi\)
\(954\) −47.0779 −1.52420
\(955\) 20.6929 0.669606
\(956\) 4.69281 0.151776
\(957\) 21.5840 0.697712
\(958\) −17.5398 −0.566684
\(959\) 21.0428 0.679506
\(960\) −10.0326 −0.323802
\(961\) −30.8962 −0.996652
\(962\) −65.9497 −2.12630
\(963\) 33.8283 1.09010
\(964\) −4.17253 −0.134388
\(965\) −13.3673 −0.430308
\(966\) 26.0013 0.836579
\(967\) −20.7944 −0.668703 −0.334352 0.942448i \(-0.608517\pi\)
−0.334352 + 0.942448i \(0.608517\pi\)
\(968\) 1.01243 0.0325407
\(969\) −11.1191 −0.357199
\(970\) 31.0096 0.995659
\(971\) −55.6084 −1.78456 −0.892280 0.451482i \(-0.850895\pi\)
−0.892280 + 0.451482i \(0.850895\pi\)
\(972\) 75.8544 2.43303
\(973\) −7.67221 −0.245960
\(974\) 53.0834 1.70090
\(975\) 48.2429 1.54501
\(976\) 51.7054 1.65505
\(977\) −41.0713 −1.31399 −0.656994 0.753896i \(-0.728172\pi\)
−0.656994 + 0.753896i \(0.728172\pi\)
\(978\) 25.7988 0.824956
\(979\) −11.0170 −0.352106
\(980\) −7.35868 −0.235064
\(981\) 33.3541 1.06491
\(982\) 34.9537 1.11542
\(983\) −57.0873 −1.82080 −0.910400 0.413729i \(-0.864226\pi\)
−0.910400 + 0.413729i \(0.864226\pi\)
\(984\) −28.1689 −0.897991
\(985\) −0.740212 −0.0235851
\(986\) 12.1118 0.385718
\(987\) −27.6316 −0.879523
\(988\) 17.3081 0.550643
\(989\) 3.29817 0.104876
\(990\) 13.9793 0.444290
\(991\) −8.28906 −0.263311 −0.131655 0.991296i \(-0.542029\pi\)
−0.131655 + 0.991296i \(0.542029\pi\)
\(992\) 2.21784 0.0704164
\(993\) 46.2352 1.46723
\(994\) −9.87426 −0.313193
\(995\) −8.12538 −0.257592
\(996\) −2.83503 −0.0898314
\(997\) 10.5266 0.333382 0.166691 0.986009i \(-0.446692\pi\)
0.166691 + 0.986009i \(0.446692\pi\)
\(998\) 23.0307 0.729025
\(999\) −164.970 −5.21942
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 \(a_p\))