Properties

Label 5077.2.a.c.1.7
Level 5077
Weight 2
Character 5077.1
Self dual Yes
Analytic conductor 40.540
Analytic rank 0
Dimension 216
CM No

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Newspace parameters

Level: \( N \) = \( 5077 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5077.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(40.5400491062\)
Analytic rank: \(0\)
Dimension: \(216\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.65348 q^{2} -0.258723 q^{3} +5.04097 q^{4} -1.45018 q^{5} +0.686516 q^{6} -0.380682 q^{7} -8.06916 q^{8} -2.93306 q^{9} +O(q^{10})\) \(q-2.65348 q^{2} -0.258723 q^{3} +5.04097 q^{4} -1.45018 q^{5} +0.686516 q^{6} -0.380682 q^{7} -8.06916 q^{8} -2.93306 q^{9} +3.84804 q^{10} +3.71187 q^{11} -1.30421 q^{12} -1.35004 q^{13} +1.01013 q^{14} +0.375196 q^{15} +11.3294 q^{16} +6.71319 q^{17} +7.78283 q^{18} +6.09366 q^{19} -7.31033 q^{20} +0.0984910 q^{21} -9.84939 q^{22} +7.60569 q^{23} +2.08768 q^{24} -2.89697 q^{25} +3.58231 q^{26} +1.53502 q^{27} -1.91900 q^{28} +2.33364 q^{29} -0.995575 q^{30} +10.0394 q^{31} -13.9242 q^{32} -0.960346 q^{33} -17.8133 q^{34} +0.552058 q^{35} -14.7855 q^{36} +9.80297 q^{37} -16.1694 q^{38} +0.349287 q^{39} +11.7018 q^{40} +4.45567 q^{41} -0.261344 q^{42} +1.19870 q^{43} +18.7114 q^{44} +4.25348 q^{45} -20.1816 q^{46} +3.67836 q^{47} -2.93118 q^{48} -6.85508 q^{49} +7.68705 q^{50} -1.73685 q^{51} -6.80552 q^{52} +7.76728 q^{53} -4.07314 q^{54} -5.38290 q^{55} +3.07178 q^{56} -1.57657 q^{57} -6.19229 q^{58} -9.70096 q^{59} +1.89135 q^{60} -5.93375 q^{61} -26.6394 q^{62} +1.11656 q^{63} +14.2886 q^{64} +1.95781 q^{65} +2.54826 q^{66} -6.73084 q^{67} +33.8410 q^{68} -1.96776 q^{69} -1.46488 q^{70} -12.6011 q^{71} +23.6674 q^{72} -11.2724 q^{73} -26.0120 q^{74} +0.749511 q^{75} +30.7180 q^{76} -1.41304 q^{77} -0.926826 q^{78} -13.4256 q^{79} -16.4298 q^{80} +8.40204 q^{81} -11.8230 q^{82} -4.18949 q^{83} +0.496490 q^{84} -9.73536 q^{85} -3.18072 q^{86} -0.603767 q^{87} -29.9517 q^{88} +1.66114 q^{89} -11.2865 q^{90} +0.513936 q^{91} +38.3401 q^{92} -2.59742 q^{93} -9.76047 q^{94} -8.83693 q^{95} +3.60249 q^{96} +8.53803 q^{97} +18.1898 q^{98} -10.8872 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65348 −1.87630 −0.938148 0.346235i \(-0.887460\pi\)
−0.938148 + 0.346235i \(0.887460\pi\)
\(3\) −0.258723 −0.149374 −0.0746868 0.997207i \(-0.523796\pi\)
−0.0746868 + 0.997207i \(0.523796\pi\)
\(4\) 5.04097 2.52049
\(5\) −1.45018 −0.648542 −0.324271 0.945964i \(-0.605119\pi\)
−0.324271 + 0.945964i \(0.605119\pi\)
\(6\) 0.686516 0.280269
\(7\) −0.380682 −0.143884 −0.0719420 0.997409i \(-0.522920\pi\)
−0.0719420 + 0.997409i \(0.522920\pi\)
\(8\) −8.06916 −2.85288
\(9\) −2.93306 −0.977688
\(10\) 3.84804 1.21686
\(11\) 3.71187 1.11917 0.559586 0.828772i \(-0.310960\pi\)
0.559586 + 0.828772i \(0.310960\pi\)
\(12\) −1.30421 −0.376494
\(13\) −1.35004 −0.374434 −0.187217 0.982319i \(-0.559947\pi\)
−0.187217 + 0.982319i \(0.559947\pi\)
\(14\) 1.01013 0.269969
\(15\) 0.375196 0.0968751
\(16\) 11.3294 2.83236
\(17\) 6.71319 1.62819 0.814094 0.580733i \(-0.197234\pi\)
0.814094 + 0.580733i \(0.197234\pi\)
\(18\) 7.78283 1.83443
\(19\) 6.09366 1.39798 0.698991 0.715130i \(-0.253633\pi\)
0.698991 + 0.715130i \(0.253633\pi\)
\(20\) −7.31033 −1.63464
\(21\) 0.0984910 0.0214925
\(22\) −9.84939 −2.09990
\(23\) 7.60569 1.58590 0.792948 0.609289i \(-0.208545\pi\)
0.792948 + 0.609289i \(0.208545\pi\)
\(24\) 2.08768 0.426145
\(25\) −2.89697 −0.579393
\(26\) 3.58231 0.702549
\(27\) 1.53502 0.295414
\(28\) −1.91900 −0.362658
\(29\) 2.33364 0.433347 0.216673 0.976244i \(-0.430479\pi\)
0.216673 + 0.976244i \(0.430479\pi\)
\(30\) −0.995575 −0.181766
\(31\) 10.0394 1.80313 0.901566 0.432642i \(-0.142419\pi\)
0.901566 + 0.432642i \(0.142419\pi\)
\(32\) −13.9242 −2.46147
\(33\) −0.960346 −0.167175
\(34\) −17.8133 −3.05496
\(35\) 0.552058 0.0933149
\(36\) −14.7855 −2.46425
\(37\) 9.80297 1.61160 0.805799 0.592189i \(-0.201736\pi\)
0.805799 + 0.592189i \(0.201736\pi\)
\(38\) −16.1694 −2.62303
\(39\) 0.349287 0.0559306
\(40\) 11.7018 1.85021
\(41\) 4.45567 0.695859 0.347929 0.937521i \(-0.386885\pi\)
0.347929 + 0.937521i \(0.386885\pi\)
\(42\) −0.261344 −0.0403263
\(43\) 1.19870 0.182800 0.0913998 0.995814i \(-0.470866\pi\)
0.0913998 + 0.995814i \(0.470866\pi\)
\(44\) 18.7114 2.82086
\(45\) 4.25348 0.634071
\(46\) −20.1816 −2.97561
\(47\) 3.67836 0.536544 0.268272 0.963343i \(-0.413547\pi\)
0.268272 + 0.963343i \(0.413547\pi\)
\(48\) −2.93118 −0.423080
\(49\) −6.85508 −0.979297
\(50\) 7.68705 1.08711
\(51\) −1.73685 −0.243208
\(52\) −6.80552 −0.943756
\(53\) 7.76728 1.06692 0.533459 0.845826i \(-0.320892\pi\)
0.533459 + 0.845826i \(0.320892\pi\)
\(54\) −4.07314 −0.554285
\(55\) −5.38290 −0.725830
\(56\) 3.07178 0.410484
\(57\) −1.57657 −0.208822
\(58\) −6.19229 −0.813087
\(59\) −9.70096 −1.26296 −0.631479 0.775393i \(-0.717552\pi\)
−0.631479 + 0.775393i \(0.717552\pi\)
\(60\) 1.89135 0.244172
\(61\) −5.93375 −0.759739 −0.379870 0.925040i \(-0.624031\pi\)
−0.379870 + 0.925040i \(0.624031\pi\)
\(62\) −26.6394 −3.38321
\(63\) 1.11656 0.140674
\(64\) 14.2886 1.78608
\(65\) 1.95781 0.242836
\(66\) 2.54826 0.313669
\(67\) −6.73084 −0.822302 −0.411151 0.911567i \(-0.634873\pi\)
−0.411151 + 0.911567i \(0.634873\pi\)
\(68\) 33.8410 4.10382
\(69\) −1.96776 −0.236891
\(70\) −1.46488 −0.175086
\(71\) −12.6011 −1.49547 −0.747735 0.663997i \(-0.768859\pi\)
−0.747735 + 0.663997i \(0.768859\pi\)
\(72\) 23.6674 2.78922
\(73\) −11.2724 −1.31934 −0.659669 0.751556i \(-0.729304\pi\)
−0.659669 + 0.751556i \(0.729304\pi\)
\(74\) −26.0120 −3.02383
\(75\) 0.749511 0.0865461
\(76\) 30.7180 3.52359
\(77\) −1.41304 −0.161031
\(78\) −0.926826 −0.104942
\(79\) −13.4256 −1.51049 −0.755247 0.655440i \(-0.772483\pi\)
−0.755247 + 0.655440i \(0.772483\pi\)
\(80\) −16.4298 −1.83690
\(81\) 8.40204 0.933560
\(82\) −11.8230 −1.30564
\(83\) −4.18949 −0.459856 −0.229928 0.973208i \(-0.573849\pi\)
−0.229928 + 0.973208i \(0.573849\pi\)
\(84\) 0.496490 0.0541715
\(85\) −9.73536 −1.05595
\(86\) −3.18072 −0.342986
\(87\) −0.603767 −0.0647306
\(88\) −29.9517 −3.19286
\(89\) 1.66114 0.176080 0.0880400 0.996117i \(-0.471940\pi\)
0.0880400 + 0.996117i \(0.471940\pi\)
\(90\) −11.2865 −1.18971
\(91\) 0.513936 0.0538751
\(92\) 38.3401 3.99723
\(93\) −2.59742 −0.269340
\(94\) −9.76047 −1.00672
\(95\) −8.83693 −0.906650
\(96\) 3.60249 0.367678
\(97\) 8.53803 0.866906 0.433453 0.901176i \(-0.357295\pi\)
0.433453 + 0.901176i \(0.357295\pi\)
\(98\) 18.1898 1.83745
\(99\) −10.8872 −1.09420
\(100\) −14.6035 −1.46035
\(101\) 4.80589 0.478204 0.239102 0.970995i \(-0.423147\pi\)
0.239102 + 0.970995i \(0.423147\pi\)
\(102\) 4.60871 0.456331
\(103\) −6.35864 −0.626536 −0.313268 0.949665i \(-0.601424\pi\)
−0.313268 + 0.949665i \(0.601424\pi\)
\(104\) 10.8937 1.06822
\(105\) −0.142830 −0.0139388
\(106\) −20.6103 −2.00185
\(107\) 16.5123 1.59630 0.798152 0.602456i \(-0.205811\pi\)
0.798152 + 0.602456i \(0.205811\pi\)
\(108\) 7.73798 0.744588
\(109\) −16.4850 −1.57898 −0.789490 0.613763i \(-0.789655\pi\)
−0.789490 + 0.613763i \(0.789655\pi\)
\(110\) 14.2834 1.36187
\(111\) −2.53625 −0.240730
\(112\) −4.31291 −0.407532
\(113\) 12.2026 1.14793 0.573963 0.818881i \(-0.305405\pi\)
0.573963 + 0.818881i \(0.305405\pi\)
\(114\) 4.18340 0.391811
\(115\) −11.0296 −1.02852
\(116\) 11.7638 1.09224
\(117\) 3.95976 0.366080
\(118\) 25.7413 2.36968
\(119\) −2.55559 −0.234270
\(120\) −3.02751 −0.276373
\(121\) 2.77801 0.252546
\(122\) 15.7451 1.42550
\(123\) −1.15278 −0.103943
\(124\) 50.6084 4.54477
\(125\) 11.4521 1.02430
\(126\) −2.96278 −0.263945
\(127\) 12.2875 1.09034 0.545171 0.838325i \(-0.316465\pi\)
0.545171 + 0.838325i \(0.316465\pi\)
\(128\) −10.0663 −0.889742
\(129\) −0.310130 −0.0273054
\(130\) −5.19501 −0.455633
\(131\) 7.04932 0.615902 0.307951 0.951402i \(-0.400357\pi\)
0.307951 + 0.951402i \(0.400357\pi\)
\(132\) −4.84108 −0.421362
\(133\) −2.31974 −0.201147
\(134\) 17.8602 1.54288
\(135\) −2.22606 −0.191589
\(136\) −54.1698 −4.64502
\(137\) 5.32777 0.455182 0.227591 0.973757i \(-0.426915\pi\)
0.227591 + 0.973757i \(0.426915\pi\)
\(138\) 5.22143 0.444478
\(139\) 15.4878 1.31366 0.656830 0.754039i \(-0.271897\pi\)
0.656830 + 0.754039i \(0.271897\pi\)
\(140\) 2.78291 0.235199
\(141\) −0.951675 −0.0801455
\(142\) 33.4367 2.80594
\(143\) −5.01119 −0.419056
\(144\) −33.2300 −2.76916
\(145\) −3.38421 −0.281044
\(146\) 29.9112 2.47547
\(147\) 1.77357 0.146281
\(148\) 49.4165 4.06201
\(149\) 6.54508 0.536194 0.268097 0.963392i \(-0.413605\pi\)
0.268097 + 0.963392i \(0.413605\pi\)
\(150\) −1.98882 −0.162386
\(151\) 5.76426 0.469089 0.234544 0.972105i \(-0.424640\pi\)
0.234544 + 0.972105i \(0.424640\pi\)
\(152\) −49.1708 −3.98827
\(153\) −19.6902 −1.59186
\(154\) 3.74948 0.302142
\(155\) −14.5590 −1.16941
\(156\) 1.76074 0.140972
\(157\) 14.0415 1.12063 0.560315 0.828279i \(-0.310680\pi\)
0.560315 + 0.828279i \(0.310680\pi\)
\(158\) 35.6245 2.83413
\(159\) −2.00957 −0.159369
\(160\) 20.1926 1.59636
\(161\) −2.89535 −0.228185
\(162\) −22.2947 −1.75164
\(163\) −15.5752 −1.21994 −0.609971 0.792424i \(-0.708819\pi\)
−0.609971 + 0.792424i \(0.708819\pi\)
\(164\) 22.4609 1.75390
\(165\) 1.39268 0.108420
\(166\) 11.1167 0.862826
\(167\) 1.78644 0.138239 0.0691193 0.997608i \(-0.477981\pi\)
0.0691193 + 0.997608i \(0.477981\pi\)
\(168\) −0.794740 −0.0613155
\(169\) −11.1774 −0.859799
\(170\) 25.8326 1.98127
\(171\) −17.8731 −1.36679
\(172\) 6.04260 0.460744
\(173\) −17.4448 −1.32631 −0.663153 0.748484i \(-0.730782\pi\)
−0.663153 + 0.748484i \(0.730782\pi\)
\(174\) 1.60209 0.121454
\(175\) 1.10282 0.0833655
\(176\) 42.0535 3.16990
\(177\) 2.50986 0.188653
\(178\) −4.40780 −0.330378
\(179\) −12.9890 −0.970843 −0.485421 0.874280i \(-0.661334\pi\)
−0.485421 + 0.874280i \(0.661334\pi\)
\(180\) 21.4417 1.59817
\(181\) −4.61727 −0.343199 −0.171600 0.985167i \(-0.554894\pi\)
−0.171600 + 0.985167i \(0.554894\pi\)
\(182\) −1.36372 −0.101086
\(183\) 1.53520 0.113485
\(184\) −61.3715 −4.52437
\(185\) −14.2161 −1.04519
\(186\) 6.89222 0.505362
\(187\) 24.9185 1.82222
\(188\) 18.5425 1.35235
\(189\) −0.584353 −0.0425054
\(190\) 23.4486 1.70114
\(191\) 0.0907224 0.00656444 0.00328222 0.999995i \(-0.498955\pi\)
0.00328222 + 0.999995i \(0.498955\pi\)
\(192\) −3.69679 −0.266793
\(193\) 1.58024 0.113748 0.0568741 0.998381i \(-0.481887\pi\)
0.0568741 + 0.998381i \(0.481887\pi\)
\(194\) −22.6555 −1.62657
\(195\) −0.506530 −0.0362733
\(196\) −34.5563 −2.46830
\(197\) 3.04036 0.216617 0.108308 0.994117i \(-0.465457\pi\)
0.108308 + 0.994117i \(0.465457\pi\)
\(198\) 28.8889 2.05304
\(199\) −10.2417 −0.726012 −0.363006 0.931787i \(-0.618250\pi\)
−0.363006 + 0.931787i \(0.618250\pi\)
\(200\) 23.3761 1.65294
\(201\) 1.74142 0.122830
\(202\) −12.7523 −0.897251
\(203\) −0.888375 −0.0623517
\(204\) −8.75543 −0.613003
\(205\) −6.46154 −0.451293
\(206\) 16.8725 1.17557
\(207\) −22.3080 −1.55051
\(208\) −15.2952 −1.06053
\(209\) 22.6189 1.56458
\(210\) 0.378997 0.0261533
\(211\) 10.3043 0.709375 0.354687 0.934985i \(-0.384587\pi\)
0.354687 + 0.934985i \(0.384587\pi\)
\(212\) 39.1546 2.68915
\(213\) 3.26018 0.223384
\(214\) −43.8151 −2.99514
\(215\) −1.73833 −0.118553
\(216\) −12.3863 −0.842782
\(217\) −3.82182 −0.259442
\(218\) 43.7428 2.96263
\(219\) 2.91643 0.197074
\(220\) −27.1350 −1.82944
\(221\) −9.06309 −0.609649
\(222\) 6.72990 0.451681
\(223\) 14.0899 0.943529 0.471764 0.881725i \(-0.343617\pi\)
0.471764 + 0.881725i \(0.343617\pi\)
\(224\) 5.30067 0.354166
\(225\) 8.49699 0.566466
\(226\) −32.3795 −2.15385
\(227\) 6.84089 0.454046 0.227023 0.973889i \(-0.427101\pi\)
0.227023 + 0.973889i \(0.427101\pi\)
\(228\) −7.94744 −0.526332
\(229\) 18.4901 1.22186 0.610929 0.791686i \(-0.290796\pi\)
0.610929 + 0.791686i \(0.290796\pi\)
\(230\) 29.2670 1.92981
\(231\) 0.365586 0.0240538
\(232\) −18.8306 −1.23629
\(233\) 7.78140 0.509777 0.254888 0.966970i \(-0.417961\pi\)
0.254888 + 0.966970i \(0.417961\pi\)
\(234\) −10.5071 −0.686874
\(235\) −5.33430 −0.347971
\(236\) −48.9022 −3.18326
\(237\) 3.47350 0.225628
\(238\) 6.78121 0.439560
\(239\) 20.7955 1.34515 0.672576 0.740028i \(-0.265188\pi\)
0.672576 + 0.740028i \(0.265188\pi\)
\(240\) 4.25076 0.274385
\(241\) 21.8046 1.40455 0.702277 0.711904i \(-0.252167\pi\)
0.702277 + 0.711904i \(0.252167\pi\)
\(242\) −7.37140 −0.473851
\(243\) −6.77885 −0.434864
\(244\) −29.9119 −1.91491
\(245\) 9.94113 0.635115
\(246\) 3.05889 0.195028
\(247\) −8.22670 −0.523452
\(248\) −81.0096 −5.14412
\(249\) 1.08392 0.0686904
\(250\) −30.3878 −1.92189
\(251\) −25.9723 −1.63935 −0.819677 0.572826i \(-0.805847\pi\)
−0.819677 + 0.572826i \(0.805847\pi\)
\(252\) 5.62856 0.354566
\(253\) 28.2314 1.77489
\(254\) −32.6048 −2.04580
\(255\) 2.51876 0.157731
\(256\) −1.86652 −0.116658
\(257\) 13.5900 0.847721 0.423861 0.905727i \(-0.360675\pi\)
0.423861 + 0.905727i \(0.360675\pi\)
\(258\) 0.822925 0.0512331
\(259\) −3.73181 −0.231883
\(260\) 9.86926 0.612065
\(261\) −6.84473 −0.423678
\(262\) −18.7053 −1.15561
\(263\) −1.90884 −0.117704 −0.0588519 0.998267i \(-0.518744\pi\)
−0.0588519 + 0.998267i \(0.518744\pi\)
\(264\) 7.74919 0.476930
\(265\) −11.2640 −0.691941
\(266\) 6.15540 0.377412
\(267\) −0.429774 −0.0263017
\(268\) −33.9299 −2.07260
\(269\) −5.37022 −0.327428 −0.163714 0.986508i \(-0.552347\pi\)
−0.163714 + 0.986508i \(0.552347\pi\)
\(270\) 5.90681 0.359477
\(271\) −20.3577 −1.23664 −0.618321 0.785926i \(-0.712187\pi\)
−0.618321 + 0.785926i \(0.712187\pi\)
\(272\) 76.0567 4.61161
\(273\) −0.132967 −0.00804753
\(274\) −14.1371 −0.854056
\(275\) −10.7532 −0.648441
\(276\) −9.91944 −0.597080
\(277\) 24.5615 1.47576 0.737878 0.674934i \(-0.235828\pi\)
0.737878 + 0.674934i \(0.235828\pi\)
\(278\) −41.0967 −2.46481
\(279\) −29.4462 −1.76290
\(280\) −4.45465 −0.266216
\(281\) 7.66906 0.457498 0.228749 0.973485i \(-0.426537\pi\)
0.228749 + 0.973485i \(0.426537\pi\)
\(282\) 2.52525 0.150377
\(283\) −32.7910 −1.94922 −0.974612 0.223899i \(-0.928121\pi\)
−0.974612 + 0.223899i \(0.928121\pi\)
\(284\) −63.5215 −3.76931
\(285\) 2.28632 0.135430
\(286\) 13.2971 0.786274
\(287\) −1.69619 −0.100123
\(288\) 40.8404 2.40654
\(289\) 28.0669 1.65099
\(290\) 8.97995 0.527321
\(291\) −2.20898 −0.129493
\(292\) −56.8240 −3.32537
\(293\) −3.74366 −0.218707 −0.109353 0.994003i \(-0.534878\pi\)
−0.109353 + 0.994003i \(0.534878\pi\)
\(294\) −4.70613 −0.274467
\(295\) 14.0682 0.819081
\(296\) −79.1017 −4.59769
\(297\) 5.69779 0.330620
\(298\) −17.3673 −1.00606
\(299\) −10.2680 −0.593814
\(300\) 3.77826 0.218138
\(301\) −0.456322 −0.0263019
\(302\) −15.2954 −0.880149
\(303\) −1.24339 −0.0714310
\(304\) 69.0378 3.95959
\(305\) 8.60503 0.492723
\(306\) 52.2476 2.98680
\(307\) −15.8895 −0.906859 −0.453430 0.891292i \(-0.649800\pi\)
−0.453430 + 0.891292i \(0.649800\pi\)
\(308\) −7.12310 −0.405876
\(309\) 1.64513 0.0935879
\(310\) 38.6320 2.19415
\(311\) 3.58626 0.203358 0.101679 0.994817i \(-0.467579\pi\)
0.101679 + 0.994817i \(0.467579\pi\)
\(312\) −2.81845 −0.159563
\(313\) 21.1462 1.19525 0.597626 0.801775i \(-0.296111\pi\)
0.597626 + 0.801775i \(0.296111\pi\)
\(314\) −37.2588 −2.10263
\(315\) −1.61922 −0.0912328
\(316\) −67.6779 −3.80718
\(317\) 29.8655 1.67741 0.838707 0.544583i \(-0.183312\pi\)
0.838707 + 0.544583i \(0.183312\pi\)
\(318\) 5.33236 0.299024
\(319\) 8.66220 0.484990
\(320\) −20.7211 −1.15835
\(321\) −4.27211 −0.238446
\(322\) 7.68275 0.428143
\(323\) 40.9079 2.27618
\(324\) 42.3545 2.35303
\(325\) 3.91103 0.216945
\(326\) 41.3284 2.28897
\(327\) 4.26505 0.235858
\(328\) −35.9535 −1.98520
\(329\) −1.40028 −0.0772001
\(330\) −3.69545 −0.203428
\(331\) −15.4579 −0.849644 −0.424822 0.905277i \(-0.639663\pi\)
−0.424822 + 0.905277i \(0.639663\pi\)
\(332\) −21.1191 −1.15906
\(333\) −28.7527 −1.57564
\(334\) −4.74028 −0.259377
\(335\) 9.76095 0.533298
\(336\) 1.11585 0.0608745
\(337\) 6.24131 0.339986 0.169993 0.985445i \(-0.445626\pi\)
0.169993 + 0.985445i \(0.445626\pi\)
\(338\) 29.6590 1.61324
\(339\) −3.15710 −0.171470
\(340\) −49.0757 −2.66150
\(341\) 37.2650 2.01801
\(342\) 47.4259 2.56450
\(343\) 5.27437 0.284789
\(344\) −9.67248 −0.521505
\(345\) 2.85362 0.153634
\(346\) 46.2896 2.48854
\(347\) −2.08629 −0.111998 −0.0559990 0.998431i \(-0.517834\pi\)
−0.0559990 + 0.998431i \(0.517834\pi\)
\(348\) −3.04357 −0.163153
\(349\) 0.137009 0.00733393 0.00366697 0.999993i \(-0.498833\pi\)
0.00366697 + 0.999993i \(0.498833\pi\)
\(350\) −2.92632 −0.156418
\(351\) −2.07234 −0.110613
\(352\) −51.6847 −2.75480
\(353\) −9.08273 −0.483425 −0.241713 0.970348i \(-0.577709\pi\)
−0.241713 + 0.970348i \(0.577709\pi\)
\(354\) −6.65987 −0.353968
\(355\) 18.2738 0.969875
\(356\) 8.37374 0.443807
\(357\) 0.661188 0.0349938
\(358\) 34.4661 1.82159
\(359\) −20.9067 −1.10341 −0.551707 0.834038i \(-0.686023\pi\)
−0.551707 + 0.834038i \(0.686023\pi\)
\(360\) −34.3220 −1.80893
\(361\) 18.1327 0.954354
\(362\) 12.2519 0.643943
\(363\) −0.718734 −0.0377237
\(364\) 2.59074 0.135791
\(365\) 16.3471 0.855646
\(366\) −4.07362 −0.212931
\(367\) 4.30378 0.224656 0.112328 0.993671i \(-0.464169\pi\)
0.112328 + 0.993671i \(0.464169\pi\)
\(368\) 86.1682 4.49183
\(369\) −13.0688 −0.680332
\(370\) 37.7222 1.96108
\(371\) −2.95686 −0.153512
\(372\) −13.0935 −0.678868
\(373\) −28.8018 −1.49130 −0.745650 0.666338i \(-0.767861\pi\)
−0.745650 + 0.666338i \(0.767861\pi\)
\(374\) −66.1208 −3.41903
\(375\) −2.96291 −0.153004
\(376\) −29.6813 −1.53070
\(377\) −3.15052 −0.162260
\(378\) 1.55057 0.0797528
\(379\) 13.7141 0.704448 0.352224 0.935916i \(-0.385426\pi\)
0.352224 + 0.935916i \(0.385426\pi\)
\(380\) −44.5467 −2.28520
\(381\) −3.17906 −0.162868
\(382\) −0.240730 −0.0123168
\(383\) −4.61563 −0.235848 −0.117924 0.993023i \(-0.537624\pi\)
−0.117924 + 0.993023i \(0.537624\pi\)
\(384\) 2.60438 0.132904
\(385\) 2.04917 0.104435
\(386\) −4.19314 −0.213425
\(387\) −3.51585 −0.178721
\(388\) 43.0400 2.18502
\(389\) −20.9676 −1.06310 −0.531550 0.847027i \(-0.678390\pi\)
−0.531550 + 0.847027i \(0.678390\pi\)
\(390\) 1.34407 0.0680595
\(391\) 51.0584 2.58214
\(392\) 55.3148 2.79382
\(393\) −1.82382 −0.0919995
\(394\) −8.06754 −0.406437
\(395\) 19.4695 0.979619
\(396\) −54.8818 −2.75792
\(397\) −27.7210 −1.39127 −0.695637 0.718393i \(-0.744878\pi\)
−0.695637 + 0.718393i \(0.744878\pi\)
\(398\) 27.1761 1.36221
\(399\) 0.600171 0.0300461
\(400\) −32.8210 −1.64105
\(401\) 22.2959 1.11340 0.556701 0.830713i \(-0.312067\pi\)
0.556701 + 0.830713i \(0.312067\pi\)
\(402\) −4.62083 −0.230466
\(403\) −13.5536 −0.675154
\(404\) 24.2263 1.20531
\(405\) −12.1845 −0.605453
\(406\) 2.35729 0.116990
\(407\) 36.3874 1.80366
\(408\) 14.0150 0.693844
\(409\) −21.3442 −1.05540 −0.527701 0.849430i \(-0.676946\pi\)
−0.527701 + 0.849430i \(0.676946\pi\)
\(410\) 17.1456 0.846760
\(411\) −1.37842 −0.0679922
\(412\) −32.0537 −1.57917
\(413\) 3.69298 0.181719
\(414\) 59.1938 2.90922
\(415\) 6.07553 0.298236
\(416\) 18.7982 0.921657
\(417\) −4.00705 −0.196226
\(418\) −60.0189 −2.93562
\(419\) 36.4555 1.78097 0.890485 0.455013i \(-0.150365\pi\)
0.890485 + 0.455013i \(0.150365\pi\)
\(420\) −0.720002 −0.0351325
\(421\) −17.7023 −0.862755 −0.431378 0.902172i \(-0.641972\pi\)
−0.431378 + 0.902172i \(0.641972\pi\)
\(422\) −27.3422 −1.33100
\(423\) −10.7889 −0.524572
\(424\) −62.6754 −3.04379
\(425\) −19.4479 −0.943361
\(426\) −8.65083 −0.419134
\(427\) 2.25887 0.109314
\(428\) 83.2380 4.02346
\(429\) 1.29651 0.0625960
\(430\) 4.61263 0.222441
\(431\) −5.46445 −0.263213 −0.131607 0.991302i \(-0.542014\pi\)
−0.131607 + 0.991302i \(0.542014\pi\)
\(432\) 17.3909 0.836720
\(433\) −33.2146 −1.59619 −0.798096 0.602531i \(-0.794159\pi\)
−0.798096 + 0.602531i \(0.794159\pi\)
\(434\) 10.1411 0.486790
\(435\) 0.875573 0.0419805
\(436\) −83.1006 −3.97980
\(437\) 46.3465 2.21705
\(438\) −7.73871 −0.369770
\(439\) 13.1244 0.626393 0.313197 0.949688i \(-0.398600\pi\)
0.313197 + 0.949688i \(0.398600\pi\)
\(440\) 43.4355 2.07071
\(441\) 20.1064 0.957447
\(442\) 24.0487 1.14388
\(443\) 30.5879 1.45327 0.726637 0.687021i \(-0.241082\pi\)
0.726637 + 0.687021i \(0.241082\pi\)
\(444\) −12.7852 −0.606757
\(445\) −2.40895 −0.114195
\(446\) −37.3873 −1.77034
\(447\) −1.69336 −0.0800933
\(448\) −5.43941 −0.256988
\(449\) 12.8196 0.604997 0.302498 0.953150i \(-0.402179\pi\)
0.302498 + 0.953150i \(0.402179\pi\)
\(450\) −22.5466 −1.06286
\(451\) 16.5389 0.778785
\(452\) 61.5131 2.89333
\(453\) −1.49134 −0.0700695
\(454\) −18.1522 −0.851924
\(455\) −0.745302 −0.0349403
\(456\) 12.7216 0.595743
\(457\) −22.0826 −1.03298 −0.516490 0.856293i \(-0.672762\pi\)
−0.516490 + 0.856293i \(0.672762\pi\)
\(458\) −49.0630 −2.29257
\(459\) 10.3049 0.480990
\(460\) −55.6001 −2.59237
\(461\) 23.8680 1.11165 0.555823 0.831301i \(-0.312403\pi\)
0.555823 + 0.831301i \(0.312403\pi\)
\(462\) −0.970076 −0.0451320
\(463\) 7.84127 0.364415 0.182207 0.983260i \(-0.441676\pi\)
0.182207 + 0.983260i \(0.441676\pi\)
\(464\) 26.4389 1.22739
\(465\) 3.76674 0.174679
\(466\) −20.6478 −0.956492
\(467\) −3.93530 −0.182104 −0.0910519 0.995846i \(-0.529023\pi\)
−0.0910519 + 0.995846i \(0.529023\pi\)
\(468\) 19.9610 0.922699
\(469\) 2.56230 0.118316
\(470\) 14.1545 0.652897
\(471\) −3.63284 −0.167393
\(472\) 78.2786 3.60306
\(473\) 4.44941 0.204584
\(474\) −9.21687 −0.423345
\(475\) −17.6531 −0.809982
\(476\) −12.8826 −0.590475
\(477\) −22.7819 −1.04311
\(478\) −55.1806 −2.52390
\(479\) −0.949575 −0.0433872 −0.0216936 0.999765i \(-0.506906\pi\)
−0.0216936 + 0.999765i \(0.506906\pi\)
\(480\) −5.22428 −0.238455
\(481\) −13.2344 −0.603437
\(482\) −57.8580 −2.63536
\(483\) 0.749092 0.0340849
\(484\) 14.0039 0.636539
\(485\) −12.3817 −0.562225
\(486\) 17.9876 0.815933
\(487\) −27.7112 −1.25571 −0.627857 0.778329i \(-0.716068\pi\)
−0.627857 + 0.778329i \(0.716068\pi\)
\(488\) 47.8804 2.16744
\(489\) 4.02965 0.182227
\(490\) −26.3786 −1.19166
\(491\) −26.6067 −1.20074 −0.600371 0.799722i \(-0.704980\pi\)
−0.600371 + 0.799722i \(0.704980\pi\)
\(492\) −5.81114 −0.261987
\(493\) 15.6662 0.705570
\(494\) 21.8294 0.982152
\(495\) 15.7884 0.709635
\(496\) 113.741 5.10712
\(497\) 4.79699 0.215174
\(498\) −2.87615 −0.128883
\(499\) 9.19984 0.411841 0.205921 0.978569i \(-0.433981\pi\)
0.205921 + 0.978569i \(0.433981\pi\)
\(500\) 57.7295 2.58174
\(501\) −0.462192 −0.0206492
\(502\) 68.9169 3.07591
\(503\) 4.42759 0.197416 0.0987082 0.995116i \(-0.468529\pi\)
0.0987082 + 0.995116i \(0.468529\pi\)
\(504\) −9.00973 −0.401325
\(505\) −6.96942 −0.310135
\(506\) −74.9114 −3.33022
\(507\) 2.89184 0.128431
\(508\) 61.9411 2.74819
\(509\) 16.3034 0.722634 0.361317 0.932443i \(-0.382327\pi\)
0.361317 + 0.932443i \(0.382327\pi\)
\(510\) −6.68348 −0.295950
\(511\) 4.29121 0.189832
\(512\) 25.0853 1.10863
\(513\) 9.35388 0.412984
\(514\) −36.0608 −1.59058
\(515\) 9.22120 0.406335
\(516\) −1.56336 −0.0688230
\(517\) 13.6536 0.600485
\(518\) 9.90229 0.435082
\(519\) 4.51338 0.198115
\(520\) −15.7979 −0.692783
\(521\) −25.5523 −1.11947 −0.559734 0.828672i \(-0.689097\pi\)
−0.559734 + 0.828672i \(0.689097\pi\)
\(522\) 18.1624 0.794945
\(523\) 34.6595 1.51555 0.757777 0.652514i \(-0.226286\pi\)
0.757777 + 0.652514i \(0.226286\pi\)
\(524\) 35.5354 1.55237
\(525\) −0.285325 −0.0124526
\(526\) 5.06506 0.220847
\(527\) 67.3965 2.93584
\(528\) −10.8802 −0.473499
\(529\) 34.8465 1.51507
\(530\) 29.8888 1.29829
\(531\) 28.4535 1.23478
\(532\) −11.6938 −0.506989
\(533\) −6.01534 −0.260553
\(534\) 1.14040 0.0493498
\(535\) −23.9459 −1.03527
\(536\) 54.3122 2.34593
\(537\) 3.36055 0.145018
\(538\) 14.2498 0.614352
\(539\) −25.4452 −1.09600
\(540\) −11.2215 −0.482896
\(541\) −17.8441 −0.767179 −0.383589 0.923504i \(-0.625312\pi\)
−0.383589 + 0.923504i \(0.625312\pi\)
\(542\) 54.0188 2.32031
\(543\) 1.19459 0.0512649
\(544\) −93.4755 −4.00773
\(545\) 23.9063 1.02403
\(546\) 0.352825 0.0150995
\(547\) 32.5133 1.39017 0.695084 0.718928i \(-0.255367\pi\)
0.695084 + 0.718928i \(0.255367\pi\)
\(548\) 26.8571 1.14728
\(549\) 17.4041 0.742787
\(550\) 28.5334 1.21667
\(551\) 14.2204 0.605811
\(552\) 15.8782 0.675822
\(553\) 5.11087 0.217336
\(554\) −65.1734 −2.76895
\(555\) 3.67803 0.156124
\(556\) 78.0736 3.31106
\(557\) 23.3170 0.987971 0.493986 0.869470i \(-0.335540\pi\)
0.493986 + 0.869470i \(0.335540\pi\)
\(558\) 78.1350 3.30772
\(559\) −1.61829 −0.0684464
\(560\) 6.25451 0.264301
\(561\) −6.44699 −0.272192
\(562\) −20.3497 −0.858401
\(563\) −24.0641 −1.01418 −0.507091 0.861892i \(-0.669279\pi\)
−0.507091 + 0.861892i \(0.669279\pi\)
\(564\) −4.79737 −0.202006
\(565\) −17.6961 −0.744478
\(566\) 87.0104 3.65732
\(567\) −3.19850 −0.134324
\(568\) 101.680 4.26640
\(569\) −19.0905 −0.800314 −0.400157 0.916447i \(-0.631044\pi\)
−0.400157 + 0.916447i \(0.631044\pi\)
\(570\) −6.06670 −0.254106
\(571\) −10.1892 −0.426406 −0.213203 0.977008i \(-0.568390\pi\)
−0.213203 + 0.977008i \(0.568390\pi\)
\(572\) −25.2612 −1.05623
\(573\) −0.0234719 −0.000980554 0
\(574\) 4.50081 0.187860
\(575\) −22.0334 −0.918858
\(576\) −41.9094 −1.74622
\(577\) −9.03063 −0.375950 −0.187975 0.982174i \(-0.560192\pi\)
−0.187975 + 0.982174i \(0.560192\pi\)
\(578\) −74.4751 −3.09775
\(579\) −0.408844 −0.0169910
\(580\) −17.0597 −0.708366
\(581\) 1.59486 0.0661660
\(582\) 5.86150 0.242967
\(583\) 28.8311 1.19406
\(584\) 90.9591 3.76391
\(585\) −5.74238 −0.237418
\(586\) 9.93374 0.410359
\(587\) −20.2191 −0.834531 −0.417265 0.908785i \(-0.637011\pi\)
−0.417265 + 0.908785i \(0.637011\pi\)
\(588\) 8.94049 0.368700
\(589\) 61.1768 2.52075
\(590\) −37.3297 −1.53684
\(591\) −0.786610 −0.0323568
\(592\) 111.062 4.56463
\(593\) 31.0560 1.27532 0.637658 0.770319i \(-0.279903\pi\)
0.637658 + 0.770319i \(0.279903\pi\)
\(594\) −15.1190 −0.620340
\(595\) 3.70607 0.151934
\(596\) 32.9936 1.35147
\(597\) 2.64975 0.108447
\(598\) 27.2460 1.11417
\(599\) 14.8953 0.608604 0.304302 0.952576i \(-0.401577\pi\)
0.304302 + 0.952576i \(0.401577\pi\)
\(600\) −6.04793 −0.246906
\(601\) −37.9245 −1.54697 −0.773487 0.633812i \(-0.781489\pi\)
−0.773487 + 0.633812i \(0.781489\pi\)
\(602\) 1.21084 0.0493502
\(603\) 19.7420 0.803955
\(604\) 29.0574 1.18233
\(605\) −4.02862 −0.163787
\(606\) 3.29932 0.134026
\(607\) 8.03416 0.326097 0.163048 0.986618i \(-0.447867\pi\)
0.163048 + 0.986618i \(0.447867\pi\)
\(608\) −84.8491 −3.44108
\(609\) 0.229843 0.00931371
\(610\) −22.8333 −0.924493
\(611\) −4.96594 −0.200900
\(612\) −99.2577 −4.01226
\(613\) 36.3990 1.47014 0.735071 0.677990i \(-0.237149\pi\)
0.735071 + 0.677990i \(0.237149\pi\)
\(614\) 42.1624 1.70154
\(615\) 1.67175 0.0674113
\(616\) 11.4021 0.459402
\(617\) −3.81701 −0.153667 −0.0768335 0.997044i \(-0.524481\pi\)
−0.0768335 + 0.997044i \(0.524481\pi\)
\(618\) −4.36531 −0.175599
\(619\) 44.7561 1.79890 0.899449 0.437025i \(-0.143968\pi\)
0.899449 + 0.437025i \(0.143968\pi\)
\(620\) −73.3914 −2.94747
\(621\) 11.6749 0.468496
\(622\) −9.51607 −0.381560
\(623\) −0.632364 −0.0253351
\(624\) 3.95722 0.158416
\(625\) −2.12275 −0.0849099
\(626\) −56.1110 −2.24265
\(627\) −5.85203 −0.233707
\(628\) 70.7826 2.82453
\(629\) 65.8092 2.62398
\(630\) 4.29658 0.171180
\(631\) −43.1509 −1.71781 −0.858905 0.512136i \(-0.828855\pi\)
−0.858905 + 0.512136i \(0.828855\pi\)
\(632\) 108.333 4.30926
\(633\) −2.66595 −0.105962
\(634\) −79.2476 −3.14732
\(635\) −17.8192 −0.707133
\(636\) −10.1302 −0.401688
\(637\) 9.25465 0.366683
\(638\) −22.9850 −0.909984
\(639\) 36.9597 1.46210
\(640\) 14.5980 0.577035
\(641\) 16.3213 0.644652 0.322326 0.946629i \(-0.395535\pi\)
0.322326 + 0.946629i \(0.395535\pi\)
\(642\) 11.3360 0.447395
\(643\) 48.4018 1.90878 0.954390 0.298562i \(-0.0965071\pi\)
0.954390 + 0.298562i \(0.0965071\pi\)
\(644\) −14.5953 −0.575137
\(645\) 0.449746 0.0177087
\(646\) −108.548 −4.27078
\(647\) −34.3404 −1.35006 −0.675030 0.737790i \(-0.735869\pi\)
−0.675030 + 0.737790i \(0.735869\pi\)
\(648\) −67.7974 −2.66334
\(649\) −36.0087 −1.41347
\(650\) −10.3778 −0.407053
\(651\) 0.988791 0.0387538
\(652\) −78.5140 −3.07484
\(653\) −24.1910 −0.946665 −0.473333 0.880884i \(-0.656949\pi\)
−0.473333 + 0.880884i \(0.656949\pi\)
\(654\) −11.3172 −0.442539
\(655\) −10.2228 −0.399438
\(656\) 50.4802 1.97092
\(657\) 33.0627 1.28990
\(658\) 3.71563 0.144850
\(659\) −20.5280 −0.799659 −0.399829 0.916590i \(-0.630931\pi\)
−0.399829 + 0.916590i \(0.630931\pi\)
\(660\) 7.02045 0.273271
\(661\) 3.60535 0.140232 0.0701160 0.997539i \(-0.477663\pi\)
0.0701160 + 0.997539i \(0.477663\pi\)
\(662\) 41.0173 1.59418
\(663\) 2.34483 0.0910655
\(664\) 33.8057 1.31191
\(665\) 3.36406 0.130453
\(666\) 76.2948 2.95636
\(667\) 17.7490 0.687243
\(668\) 9.00537 0.348428
\(669\) −3.64537 −0.140938
\(670\) −25.9005 −1.00062
\(671\) −22.0253 −0.850279
\(672\) −1.37140 −0.0529030
\(673\) −23.6906 −0.913204 −0.456602 0.889671i \(-0.650934\pi\)
−0.456602 + 0.889671i \(0.650934\pi\)
\(674\) −16.5612 −0.637913
\(675\) −4.44690 −0.171161
\(676\) −56.3449 −2.16711
\(677\) −44.9389 −1.72714 −0.863571 0.504228i \(-0.831777\pi\)
−0.863571 + 0.504228i \(0.831777\pi\)
\(678\) 8.37730 0.321728
\(679\) −3.25027 −0.124734
\(680\) 78.5562 3.01249
\(681\) −1.76989 −0.0678225
\(682\) −98.8821 −3.78639
\(683\) 3.17352 0.121432 0.0607158 0.998155i \(-0.480662\pi\)
0.0607158 + 0.998155i \(0.480662\pi\)
\(684\) −90.0977 −3.44497
\(685\) −7.72625 −0.295205
\(686\) −13.9955 −0.534349
\(687\) −4.78380 −0.182513
\(688\) 13.5806 0.517754
\(689\) −10.4861 −0.399490
\(690\) −7.57203 −0.288262
\(691\) −24.8283 −0.944512 −0.472256 0.881461i \(-0.656560\pi\)
−0.472256 + 0.881461i \(0.656560\pi\)
\(692\) −87.9389 −3.34294
\(693\) 4.14454 0.157438
\(694\) 5.53594 0.210141
\(695\) −22.4602 −0.851963
\(696\) 4.87189 0.184669
\(697\) 29.9117 1.13299
\(698\) −0.363551 −0.0137606
\(699\) −2.01323 −0.0761472
\(700\) 5.55929 0.210121
\(701\) 8.20127 0.309758 0.154879 0.987933i \(-0.450501\pi\)
0.154879 + 0.987933i \(0.450501\pi\)
\(702\) 5.49892 0.207543
\(703\) 59.7360 2.25298
\(704\) 53.0375 1.99893
\(705\) 1.38010 0.0519777
\(706\) 24.1009 0.907048
\(707\) −1.82951 −0.0688059
\(708\) 12.6521 0.475496
\(709\) 0.670226 0.0251709 0.0125854 0.999921i \(-0.495994\pi\)
0.0125854 + 0.999921i \(0.495994\pi\)
\(710\) −48.4893 −1.81977
\(711\) 39.3780 1.47679
\(712\) −13.4040 −0.502335
\(713\) 76.3566 2.85958
\(714\) −1.75445 −0.0656587
\(715\) 7.26714 0.271776
\(716\) −65.4771 −2.44699
\(717\) −5.38028 −0.200930
\(718\) 55.4756 2.07033
\(719\) −19.3352 −0.721082 −0.360541 0.932743i \(-0.617408\pi\)
−0.360541 + 0.932743i \(0.617408\pi\)
\(720\) 48.1895 1.79592
\(721\) 2.42062 0.0901485
\(722\) −48.1149 −1.79065
\(723\) −5.64133 −0.209803
\(724\) −23.2755 −0.865028
\(725\) −6.76049 −0.251078
\(726\) 1.90715 0.0707809
\(727\) 17.4601 0.647560 0.323780 0.946132i \(-0.395046\pi\)
0.323780 + 0.946132i \(0.395046\pi\)
\(728\) −4.14703 −0.153699
\(729\) −23.4523 −0.868603
\(730\) −43.3767 −1.60544
\(731\) 8.04708 0.297632
\(732\) 7.73888 0.286037
\(733\) 7.29128 0.269309 0.134655 0.990893i \(-0.457007\pi\)
0.134655 + 0.990893i \(0.457007\pi\)
\(734\) −11.4200 −0.421520
\(735\) −2.57200 −0.0948695
\(736\) −105.903 −3.90363
\(737\) −24.9840 −0.920298
\(738\) 34.6777 1.27650
\(739\) 43.5724 1.60284 0.801419 0.598103i \(-0.204079\pi\)
0.801419 + 0.598103i \(0.204079\pi\)
\(740\) −71.6630 −2.63438
\(741\) 2.12843 0.0781900
\(742\) 7.84597 0.288035
\(743\) 1.38325 0.0507465 0.0253732 0.999678i \(-0.491923\pi\)
0.0253732 + 0.999678i \(0.491923\pi\)
\(744\) 20.9590 0.768396
\(745\) −9.49158 −0.347744
\(746\) 76.4250 2.79812
\(747\) 12.2880 0.449596
\(748\) 125.613 4.59288
\(749\) −6.28593 −0.229683
\(750\) 7.86202 0.287080
\(751\) 45.9369 1.67626 0.838132 0.545468i \(-0.183648\pi\)
0.838132 + 0.545468i \(0.183648\pi\)
\(752\) 41.6738 1.51969
\(753\) 6.71961 0.244876
\(754\) 8.35985 0.304448
\(755\) −8.35923 −0.304224
\(756\) −2.94571 −0.107134
\(757\) −14.9228 −0.542379 −0.271189 0.962526i \(-0.587417\pi\)
−0.271189 + 0.962526i \(0.587417\pi\)
\(758\) −36.3902 −1.32175
\(759\) −7.30409 −0.265122
\(760\) 71.3066 2.58656
\(761\) 26.8310 0.972623 0.486312 0.873785i \(-0.338342\pi\)
0.486312 + 0.873785i \(0.338342\pi\)
\(762\) 8.43559 0.305589
\(763\) 6.27555 0.227190
\(764\) 0.457329 0.0165456
\(765\) 28.5544 1.03239
\(766\) 12.2475 0.442520
\(767\) 13.0967 0.472894
\(768\) 0.482912 0.0174256
\(769\) 29.6147 1.06793 0.533966 0.845506i \(-0.320701\pi\)
0.533966 + 0.845506i \(0.320701\pi\)
\(770\) −5.43744 −0.195952
\(771\) −3.51604 −0.126627
\(772\) 7.96595 0.286701
\(773\) 3.36259 0.120944 0.0604720 0.998170i \(-0.480739\pi\)
0.0604720 + 0.998170i \(0.480739\pi\)
\(774\) 9.32926 0.335333
\(775\) −29.0838 −1.04472
\(776\) −68.8948 −2.47318
\(777\) 0.965504 0.0346372
\(778\) 55.6372 1.99469
\(779\) 27.1513 0.972798
\(780\) −2.55340 −0.0914264
\(781\) −46.7735 −1.67369
\(782\) −135.483 −4.84485
\(783\) 3.58219 0.128017
\(784\) −77.6642 −2.77372
\(785\) −20.3627 −0.726776
\(786\) 4.83947 0.172618
\(787\) −14.6321 −0.521578 −0.260789 0.965396i \(-0.583983\pi\)
−0.260789 + 0.965396i \(0.583983\pi\)
\(788\) 15.3264 0.545979
\(789\) 0.493859 0.0175819
\(790\) −51.6621 −1.83805
\(791\) −4.64531 −0.165168
\(792\) 87.8502 3.12162
\(793\) 8.01082 0.284472
\(794\) 73.5571 2.61044
\(795\) 2.91425 0.103358
\(796\) −51.6279 −1.82990
\(797\) −11.4026 −0.403899 −0.201950 0.979396i \(-0.564728\pi\)
−0.201950 + 0.979396i \(0.564728\pi\)
\(798\) −1.59254 −0.0563754
\(799\) 24.6935 0.873594
\(800\) 40.3378 1.42616
\(801\) −4.87222 −0.172151
\(802\) −59.1617 −2.08907
\(803\) −41.8418 −1.47657
\(804\) 8.77845 0.309592
\(805\) 4.19878 0.147988
\(806\) 35.9643 1.26679
\(807\) 1.38940 0.0489091
\(808\) −38.7795 −1.36426
\(809\) 11.1093 0.390581 0.195291 0.980745i \(-0.437435\pi\)
0.195291 + 0.980745i \(0.437435\pi\)
\(810\) 32.3314 1.13601
\(811\) 32.0357 1.12492 0.562462 0.826823i \(-0.309854\pi\)
0.562462 + 0.826823i \(0.309854\pi\)
\(812\) −4.47827 −0.157157
\(813\) 5.26700 0.184722
\(814\) −96.5533 −3.38419
\(815\) 22.5869 0.791183
\(816\) −19.6776 −0.688854
\(817\) 7.30446 0.255551
\(818\) 56.6365 1.98025
\(819\) −1.50741 −0.0526731
\(820\) −32.5724 −1.13748
\(821\) −33.9899 −1.18625 −0.593127 0.805109i \(-0.702107\pi\)
−0.593127 + 0.805109i \(0.702107\pi\)
\(822\) 3.65760 0.127573
\(823\) −25.2151 −0.878942 −0.439471 0.898257i \(-0.644834\pi\)
−0.439471 + 0.898257i \(0.644834\pi\)
\(824\) 51.3089 1.78743
\(825\) 2.78209 0.0968600
\(826\) −9.79925 −0.340959
\(827\) −43.9644 −1.52879 −0.764397 0.644746i \(-0.776963\pi\)
−0.764397 + 0.644746i \(0.776963\pi\)
\(828\) −112.454 −3.90804
\(829\) −9.72078 −0.337617 −0.168808 0.985649i \(-0.553992\pi\)
−0.168808 + 0.985649i \(0.553992\pi\)
\(830\) −16.1213 −0.559579
\(831\) −6.35461 −0.220439
\(832\) −19.2902 −0.668768
\(833\) −46.0195 −1.59448
\(834\) 10.6326 0.368178
\(835\) −2.59066 −0.0896535
\(836\) 114.021 3.94351
\(837\) 15.4107 0.532671
\(838\) −96.7342 −3.34163
\(839\) 27.1608 0.937695 0.468847 0.883279i \(-0.344669\pi\)
0.468847 + 0.883279i \(0.344669\pi\)
\(840\) 1.15252 0.0397657
\(841\) −23.5541 −0.812210
\(842\) 46.9726 1.61878
\(843\) −1.98416 −0.0683381
\(844\) 51.9435 1.78797
\(845\) 16.2093 0.557616
\(846\) 28.6281 0.984253
\(847\) −1.05754 −0.0363374
\(848\) 87.9989 3.02189
\(849\) 8.48379 0.291163
\(850\) 51.6046 1.77002
\(851\) 74.5583 2.55583
\(852\) 16.4345 0.563036
\(853\) −6.90287 −0.236350 −0.118175 0.992993i \(-0.537704\pi\)
−0.118175 + 0.992993i \(0.537704\pi\)
\(854\) −5.99387 −0.205106
\(855\) 25.9193 0.886420
\(856\) −133.240 −4.55406
\(857\) 1.18637 0.0405257 0.0202629 0.999795i \(-0.493550\pi\)
0.0202629 + 0.999795i \(0.493550\pi\)
\(858\) −3.44026 −0.117449
\(859\) −1.34963 −0.0460486 −0.0230243 0.999735i \(-0.507330\pi\)
−0.0230243 + 0.999735i \(0.507330\pi\)
\(860\) −8.76287 −0.298812
\(861\) 0.438843 0.0149557
\(862\) 14.4998 0.493866
\(863\) 13.3655 0.454969 0.227484 0.973782i \(-0.426950\pi\)
0.227484 + 0.973782i \(0.426950\pi\)
\(864\) −21.3738 −0.727152
\(865\) 25.2982 0.860165
\(866\) 88.1344 2.99493
\(867\) −7.26155 −0.246615
\(868\) −19.2657 −0.653920
\(869\) −49.8340 −1.69050
\(870\) −2.32332 −0.0787679
\(871\) 9.08691 0.307898
\(872\) 133.020 4.50464
\(873\) −25.0426 −0.847563
\(874\) −122.980 −4.15985
\(875\) −4.35959 −0.147381
\(876\) 14.7017 0.496723
\(877\) 21.6659 0.731605 0.365802 0.930693i \(-0.380795\pi\)
0.365802 + 0.930693i \(0.380795\pi\)
\(878\) −34.8254 −1.17530
\(879\) 0.968570 0.0326691
\(880\) −60.9852 −2.05581
\(881\) −17.1146 −0.576607 −0.288304 0.957539i \(-0.593091\pi\)
−0.288304 + 0.957539i \(0.593091\pi\)
\(882\) −53.3519 −1.79645
\(883\) 47.3580 1.59372 0.796861 0.604163i \(-0.206492\pi\)
0.796861 + 0.604163i \(0.206492\pi\)
\(884\) −45.6868 −1.53661
\(885\) −3.63976 −0.122349
\(886\) −81.1644 −2.72677
\(887\) 25.0244 0.840236 0.420118 0.907469i \(-0.361989\pi\)
0.420118 + 0.907469i \(0.361989\pi\)
\(888\) 20.4654 0.686774
\(889\) −4.67764 −0.156883
\(890\) 6.39211 0.214264
\(891\) 31.1873 1.04481
\(892\) 71.0267 2.37815
\(893\) 22.4147 0.750079
\(894\) 4.49331 0.150279
\(895\) 18.8364 0.629632
\(896\) 3.83205 0.128020
\(897\) 2.65657 0.0887001
\(898\) −34.0167 −1.13515
\(899\) 23.4284 0.781382
\(900\) 42.8330 1.42777
\(901\) 52.1432 1.73714
\(902\) −43.8856 −1.46123
\(903\) 0.118061 0.00392882
\(904\) −98.4650 −3.27490
\(905\) 6.69589 0.222579
\(906\) 3.95726 0.131471
\(907\) −25.3179 −0.840667 −0.420334 0.907370i \(-0.638087\pi\)
−0.420334 + 0.907370i \(0.638087\pi\)
\(908\) 34.4847 1.14442
\(909\) −14.0960 −0.467534
\(910\) 1.97765 0.0655583
\(911\) 3.81822 0.126503 0.0632517 0.997998i \(-0.479853\pi\)
0.0632517 + 0.997998i \(0.479853\pi\)
\(912\) −17.8616 −0.591458
\(913\) −15.5509 −0.514658
\(914\) 58.5958 1.93818
\(915\) −2.22632 −0.0735998
\(916\) 93.2078 3.07967
\(917\) −2.68355 −0.0886185
\(918\) −27.3438 −0.902479
\(919\) 27.3638 0.902649 0.451324 0.892360i \(-0.350952\pi\)
0.451324 + 0.892360i \(0.350952\pi\)
\(920\) 89.0000 2.93424
\(921\) 4.11096 0.135461
\(922\) −63.3335 −2.08578
\(923\) 17.0120 0.559955
\(924\) 1.84291 0.0606272
\(925\) −28.3989 −0.933749
\(926\) −20.8067 −0.683750
\(927\) 18.6503 0.612556
\(928\) −32.4940 −1.06667
\(929\) −56.4287 −1.85137 −0.925683 0.378299i \(-0.876509\pi\)
−0.925683 + 0.378299i \(0.876509\pi\)
\(930\) −9.99499 −0.327749
\(931\) −41.7726 −1.36904
\(932\) 39.2258 1.28488
\(933\) −0.927846 −0.0303763
\(934\) 10.4422 0.341681
\(935\) −36.1364 −1.18179
\(936\) −31.9519 −1.04438
\(937\) 6.00281 0.196103 0.0980517 0.995181i \(-0.468739\pi\)
0.0980517 + 0.995181i \(0.468739\pi\)
\(938\) −6.79903 −0.221996
\(939\) −5.47100 −0.178539
\(940\) −26.8900 −0.877056
\(941\) −32.8721 −1.07160 −0.535801 0.844344i \(-0.679990\pi\)
−0.535801 + 0.844344i \(0.679990\pi\)
\(942\) 9.63969 0.314078
\(943\) 33.8884 1.10356
\(944\) −109.906 −3.57715
\(945\) 0.847419 0.0275666
\(946\) −11.8064 −0.383860
\(947\) −39.6640 −1.28891 −0.644453 0.764644i \(-0.722915\pi\)
−0.644453 + 0.764644i \(0.722915\pi\)
\(948\) 17.5098 0.568692
\(949\) 15.2183 0.494005
\(950\) 46.8423 1.51976
\(951\) −7.72689 −0.250561
\(952\) 20.6214 0.668345
\(953\) 10.9335 0.354170 0.177085 0.984196i \(-0.443333\pi\)
0.177085 + 0.984196i \(0.443333\pi\)
\(954\) 60.4514 1.95719
\(955\) −0.131564 −0.00425731
\(956\) 104.830 3.39044
\(957\) −2.24111 −0.0724447
\(958\) 2.51968 0.0814072
\(959\) −2.02818 −0.0654935
\(960\) 5.36102 0.173026
\(961\) 69.7898 2.25128
\(962\) 35.1173 1.13223
\(963\) −48.4316 −1.56069
\(964\) 109.916 3.54016
\(965\) −2.29164 −0.0737705
\(966\) −1.98770 −0.0639533
\(967\) −26.5962 −0.855276 −0.427638 0.903950i \(-0.640654\pi\)
−0.427638 + 0.903950i \(0.640654\pi\)
\(968\) −22.4162 −0.720484
\(969\) −10.5838 −0.340001
\(970\) 32.8547 1.05490
\(971\) 17.8997 0.574427 0.287214 0.957867i \(-0.407271\pi\)
0.287214 + 0.957867i \(0.407271\pi\)
\(972\) −34.1720 −1.09607
\(973\) −5.89593 −0.189015
\(974\) 73.5312 2.35609
\(975\) −1.01187 −0.0324058
\(976\) −67.2261 −2.15185
\(977\) 51.7978 1.65716 0.828579 0.559872i \(-0.189150\pi\)
0.828579 + 0.559872i \(0.189150\pi\)
\(978\) −10.6926 −0.341912
\(979\) 6.16593 0.197064
\(980\) 50.1129 1.60080
\(981\) 48.3517 1.54375
\(982\) 70.6003 2.25295
\(983\) 21.5592 0.687631 0.343816 0.939037i \(-0.388280\pi\)
0.343816 + 0.939037i \(0.388280\pi\)
\(984\) 9.30199 0.296537
\(985\) −4.40908 −0.140485
\(986\) −41.5700 −1.32386
\(987\) 0.362285 0.0115317
\(988\) −41.4706 −1.31935
\(989\) 9.11692 0.289901
\(990\) −41.8942 −1.33148
\(991\) 17.3628 0.551547 0.275773 0.961223i \(-0.411066\pi\)
0.275773 + 0.961223i \(0.411066\pi\)
\(992\) −139.790 −4.43835
\(993\) 3.99932 0.126914
\(994\) −12.7287 −0.403731
\(995\) 14.8523 0.470849
\(996\) 5.46399 0.173133
\(997\) −48.6764 −1.54160 −0.770798 0.637080i \(-0.780142\pi\)
−0.770798 + 0.637080i \(0.780142\pi\)
\(998\) −24.4116 −0.772736
\(999\) 15.0477 0.476089
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 \(a_p\))