Properties

Label 6027.2.a.bn.1.15
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.33013 q^{2} -1.00000 q^{3} -0.230742 q^{4} +3.44355 q^{5} -1.33013 q^{6} -2.96719 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.33013 q^{2} -1.00000 q^{3} -0.230742 q^{4} +3.44355 q^{5} -1.33013 q^{6} -2.96719 q^{8} +1.00000 q^{9} +4.58038 q^{10} +2.42981 q^{11} +0.230742 q^{12} +4.50765 q^{13} -3.44355 q^{15} -3.48527 q^{16} +4.56026 q^{17} +1.33013 q^{18} +1.29115 q^{19} -0.794570 q^{20} +3.23197 q^{22} -5.25675 q^{23} +2.96719 q^{24} +6.85802 q^{25} +5.99578 q^{26} -1.00000 q^{27} +6.83526 q^{29} -4.58038 q^{30} -2.39033 q^{31} +1.29849 q^{32} -2.42981 q^{33} +6.06576 q^{34} -0.230742 q^{36} -0.323629 q^{37} +1.71740 q^{38} -4.50765 q^{39} -10.2176 q^{40} +1.00000 q^{41} +3.93668 q^{43} -0.560658 q^{44} +3.44355 q^{45} -6.99219 q^{46} -12.2131 q^{47} +3.48527 q^{48} +9.12209 q^{50} -4.56026 q^{51} -1.04010 q^{52} +5.17996 q^{53} -1.33013 q^{54} +8.36716 q^{55} -1.29115 q^{57} +9.09182 q^{58} +1.20427 q^{59} +0.794570 q^{60} +4.84509 q^{61} -3.17946 q^{62} +8.69771 q^{64} +15.5223 q^{65} -3.23197 q^{66} +3.77777 q^{67} -1.05224 q^{68} +5.25675 q^{69} -5.00281 q^{71} -2.96719 q^{72} -8.20083 q^{73} -0.430471 q^{74} -6.85802 q^{75} -0.297922 q^{76} -5.99578 q^{78} -7.91250 q^{79} -12.0017 q^{80} +1.00000 q^{81} +1.33013 q^{82} -2.47939 q^{83} +15.7035 q^{85} +5.23631 q^{86} -6.83526 q^{87} -7.20969 q^{88} +2.30019 q^{89} +4.58038 q^{90} +1.21295 q^{92} +2.39033 q^{93} -16.2450 q^{94} +4.44614 q^{95} -1.29849 q^{96} +15.4518 q^{97} +2.42981 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + 4q^{10} + 12q^{11} - 32q^{12} + 4q^{15} + 44q^{16} - 8q^{17} + 8q^{18} + 4q^{19} - 28q^{20} + 16q^{22} + 20q^{23} - 24q^{24} + 48q^{25} - 32q^{26} - 24q^{27} + 24q^{29} - 4q^{30} + 4q^{31} + 36q^{32} - 12q^{33} - 16q^{34} + 32q^{36} + 64q^{37} - 20q^{38} + 48q^{40} + 24q^{41} + 20q^{43} + 48q^{44} - 4q^{45} + 28q^{46} - 32q^{47} - 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} - 8q^{54} + 24q^{55} - 4q^{57} + 28q^{58} - 28q^{59} + 28q^{60} + 28q^{61} + 4q^{62} + 48q^{64} + 28q^{65} - 16q^{66} + 44q^{67} + 32q^{68} - 20q^{69} + 20q^{71} + 24q^{72} + 16q^{73} + 44q^{74} - 48q^{75} + 16q^{76} + 32q^{78} + 4q^{79} - 44q^{80} + 24q^{81} + 8q^{82} - 8q^{83} + 28q^{85} + 56q^{86} - 24q^{87} + 60q^{88} - 60q^{89} + 4q^{90} + 60q^{92} - 4q^{93} - 24q^{94} + 28q^{95} - 36q^{96} + 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.33013 0.940547 0.470274 0.882521i \(-0.344155\pi\)
0.470274 + 0.882521i \(0.344155\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.230742 −0.115371
\(5\) 3.44355 1.54000 0.770001 0.638043i \(-0.220256\pi\)
0.770001 + 0.638043i \(0.220256\pi\)
\(6\) −1.33013 −0.543025
\(7\) 0 0
\(8\) −2.96719 −1.04906
\(9\) 1.00000 0.333333
\(10\) 4.58038 1.44844
\(11\) 2.42981 0.732615 0.366307 0.930494i \(-0.380622\pi\)
0.366307 + 0.930494i \(0.380622\pi\)
\(12\) 0.230742 0.0666094
\(13\) 4.50765 1.25020 0.625099 0.780546i \(-0.285059\pi\)
0.625099 + 0.780546i \(0.285059\pi\)
\(14\) 0 0
\(15\) −3.44355 −0.889120
\(16\) −3.48527 −0.871319
\(17\) 4.56026 1.10602 0.553012 0.833173i \(-0.313478\pi\)
0.553012 + 0.833173i \(0.313478\pi\)
\(18\) 1.33013 0.313516
\(19\) 1.29115 0.296210 0.148105 0.988972i \(-0.452683\pi\)
0.148105 + 0.988972i \(0.452683\pi\)
\(20\) −0.794570 −0.177671
\(21\) 0 0
\(22\) 3.23197 0.689059
\(23\) −5.25675 −1.09611 −0.548054 0.836443i \(-0.684631\pi\)
−0.548054 + 0.836443i \(0.684631\pi\)
\(24\) 2.96719 0.605674
\(25\) 6.85802 1.37160
\(26\) 5.99578 1.17587
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 6.83526 1.26928 0.634638 0.772809i \(-0.281149\pi\)
0.634638 + 0.772809i \(0.281149\pi\)
\(30\) −4.58038 −0.836260
\(31\) −2.39033 −0.429316 −0.214658 0.976689i \(-0.568864\pi\)
−0.214658 + 0.976689i \(0.568864\pi\)
\(32\) 1.29849 0.229543
\(33\) −2.42981 −0.422975
\(34\) 6.06576 1.04027
\(35\) 0 0
\(36\) −0.230742 −0.0384569
\(37\) −0.323629 −0.0532043 −0.0266022 0.999646i \(-0.508469\pi\)
−0.0266022 + 0.999646i \(0.508469\pi\)
\(38\) 1.71740 0.278600
\(39\) −4.50765 −0.721802
\(40\) −10.2176 −1.61555
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 3.93668 0.600338 0.300169 0.953886i \(-0.402957\pi\)
0.300169 + 0.953886i \(0.402957\pi\)
\(44\) −0.560658 −0.0845223
\(45\) 3.44355 0.513334
\(46\) −6.99219 −1.03094
\(47\) −12.2131 −1.78146 −0.890730 0.454534i \(-0.849806\pi\)
−0.890730 + 0.454534i \(0.849806\pi\)
\(48\) 3.48527 0.503056
\(49\) 0 0
\(50\) 9.12209 1.29006
\(51\) −4.56026 −0.638564
\(52\) −1.04010 −0.144236
\(53\) 5.17996 0.711522 0.355761 0.934577i \(-0.384222\pi\)
0.355761 + 0.934577i \(0.384222\pi\)
\(54\) −1.33013 −0.181008
\(55\) 8.36716 1.12823
\(56\) 0 0
\(57\) −1.29115 −0.171017
\(58\) 9.09182 1.19381
\(59\) 1.20427 0.156783 0.0783914 0.996923i \(-0.475022\pi\)
0.0783914 + 0.996923i \(0.475022\pi\)
\(60\) 0.794570 0.102579
\(61\) 4.84509 0.620350 0.310175 0.950679i \(-0.399612\pi\)
0.310175 + 0.950679i \(0.399612\pi\)
\(62\) −3.17946 −0.403792
\(63\) 0 0
\(64\) 8.69771 1.08721
\(65\) 15.5223 1.92531
\(66\) −3.23197 −0.397828
\(67\) 3.77777 0.461528 0.230764 0.973010i \(-0.425877\pi\)
0.230764 + 0.973010i \(0.425877\pi\)
\(68\) −1.05224 −0.127603
\(69\) 5.25675 0.632839
\(70\) 0 0
\(71\) −5.00281 −0.593725 −0.296862 0.954920i \(-0.595940\pi\)
−0.296862 + 0.954920i \(0.595940\pi\)
\(72\) −2.96719 −0.349686
\(73\) −8.20083 −0.959834 −0.479917 0.877314i \(-0.659333\pi\)
−0.479917 + 0.877314i \(0.659333\pi\)
\(74\) −0.430471 −0.0500412
\(75\) −6.85802 −0.791896
\(76\) −0.297922 −0.0341740
\(77\) 0 0
\(78\) −5.99578 −0.678889
\(79\) −7.91250 −0.890226 −0.445113 0.895474i \(-0.646837\pi\)
−0.445113 + 0.895474i \(0.646837\pi\)
\(80\) −12.0017 −1.34183
\(81\) 1.00000 0.111111
\(82\) 1.33013 0.146889
\(83\) −2.47939 −0.272148 −0.136074 0.990699i \(-0.543448\pi\)
−0.136074 + 0.990699i \(0.543448\pi\)
\(84\) 0 0
\(85\) 15.7035 1.70328
\(86\) 5.23631 0.564646
\(87\) −6.83526 −0.732817
\(88\) −7.20969 −0.768556
\(89\) 2.30019 0.243819 0.121910 0.992541i \(-0.461098\pi\)
0.121910 + 0.992541i \(0.461098\pi\)
\(90\) 4.58038 0.482815
\(91\) 0 0
\(92\) 1.21295 0.126459
\(93\) 2.39033 0.247866
\(94\) −16.2450 −1.67555
\(95\) 4.44614 0.456164
\(96\) −1.29849 −0.132526
\(97\) 15.4518 1.56890 0.784448 0.620195i \(-0.212946\pi\)
0.784448 + 0.620195i \(0.212946\pi\)
\(98\) 0 0
\(99\) 2.42981 0.244205
\(100\) −1.58243 −0.158243
\(101\) −2.10297 −0.209253 −0.104626 0.994512i \(-0.533365\pi\)
−0.104626 + 0.994512i \(0.533365\pi\)
\(102\) −6.06576 −0.600599
\(103\) −9.55463 −0.941445 −0.470723 0.882281i \(-0.656007\pi\)
−0.470723 + 0.882281i \(0.656007\pi\)
\(104\) −13.3750 −1.31153
\(105\) 0 0
\(106\) 6.89004 0.669220
\(107\) −0.434379 −0.0419930 −0.0209965 0.999780i \(-0.506684\pi\)
−0.0209965 + 0.999780i \(0.506684\pi\)
\(108\) 0.230742 0.0222031
\(109\) 11.2038 1.07313 0.536565 0.843859i \(-0.319722\pi\)
0.536565 + 0.843859i \(0.319722\pi\)
\(110\) 11.1294 1.06115
\(111\) 0.323629 0.0307175
\(112\) 0 0
\(113\) 3.07828 0.289580 0.144790 0.989462i \(-0.453749\pi\)
0.144790 + 0.989462i \(0.453749\pi\)
\(114\) −1.71740 −0.160850
\(115\) −18.1019 −1.68801
\(116\) −1.57718 −0.146437
\(117\) 4.50765 0.416732
\(118\) 1.60184 0.147462
\(119\) 0 0
\(120\) 10.2176 0.932739
\(121\) −5.09604 −0.463276
\(122\) 6.44462 0.583469
\(123\) −1.00000 −0.0901670
\(124\) 0.551549 0.0495305
\(125\) 6.39818 0.572271
\(126\) 0 0
\(127\) 5.57946 0.495097 0.247549 0.968875i \(-0.420375\pi\)
0.247549 + 0.968875i \(0.420375\pi\)
\(128\) 8.97216 0.793034
\(129\) −3.93668 −0.346605
\(130\) 20.6468 1.81084
\(131\) −5.67239 −0.495599 −0.247799 0.968811i \(-0.579707\pi\)
−0.247799 + 0.968811i \(0.579707\pi\)
\(132\) 0.560658 0.0487990
\(133\) 0 0
\(134\) 5.02494 0.434089
\(135\) −3.44355 −0.296373
\(136\) −13.5311 −1.16029
\(137\) 20.9994 1.79410 0.897049 0.441931i \(-0.145707\pi\)
0.897049 + 0.441931i \(0.145707\pi\)
\(138\) 6.99219 0.595215
\(139\) 1.80530 0.153124 0.0765618 0.997065i \(-0.475606\pi\)
0.0765618 + 0.997065i \(0.475606\pi\)
\(140\) 0 0
\(141\) 12.2131 1.02853
\(142\) −6.65442 −0.558426
\(143\) 10.9527 0.915913
\(144\) −3.48527 −0.290440
\(145\) 23.5376 1.95469
\(146\) −10.9082 −0.902769
\(147\) 0 0
\(148\) 0.0746748 0.00613823
\(149\) 6.51313 0.533576 0.266788 0.963755i \(-0.414038\pi\)
0.266788 + 0.963755i \(0.414038\pi\)
\(150\) −9.12209 −0.744816
\(151\) 14.5560 1.18455 0.592275 0.805736i \(-0.298230\pi\)
0.592275 + 0.805736i \(0.298230\pi\)
\(152\) −3.83109 −0.310742
\(153\) 4.56026 0.368675
\(154\) 0 0
\(155\) −8.23122 −0.661147
\(156\) 1.04010 0.0832749
\(157\) −0.583942 −0.0466036 −0.0233018 0.999728i \(-0.507418\pi\)
−0.0233018 + 0.999728i \(0.507418\pi\)
\(158\) −10.5247 −0.837300
\(159\) −5.17996 −0.410798
\(160\) 4.47141 0.353496
\(161\) 0 0
\(162\) 1.33013 0.104505
\(163\) 13.7479 1.07682 0.538408 0.842684i \(-0.319026\pi\)
0.538408 + 0.842684i \(0.319026\pi\)
\(164\) −0.230742 −0.0180179
\(165\) −8.36716 −0.651382
\(166\) −3.29792 −0.255968
\(167\) 19.7472 1.52809 0.764043 0.645165i \(-0.223212\pi\)
0.764043 + 0.645165i \(0.223212\pi\)
\(168\) 0 0
\(169\) 7.31891 0.562993
\(170\) 20.8877 1.60201
\(171\) 1.29115 0.0987368
\(172\) −0.908356 −0.0692615
\(173\) −17.4423 −1.32612 −0.663059 0.748567i \(-0.730742\pi\)
−0.663059 + 0.748567i \(0.730742\pi\)
\(174\) −9.09182 −0.689249
\(175\) 0 0
\(176\) −8.46855 −0.638341
\(177\) −1.20427 −0.0905186
\(178\) 3.05956 0.229324
\(179\) −5.51743 −0.412392 −0.206196 0.978511i \(-0.566108\pi\)
−0.206196 + 0.978511i \(0.566108\pi\)
\(180\) −0.794570 −0.0592237
\(181\) 6.26958 0.466014 0.233007 0.972475i \(-0.425143\pi\)
0.233007 + 0.972475i \(0.425143\pi\)
\(182\) 0 0
\(183\) −4.84509 −0.358159
\(184\) 15.5978 1.14988
\(185\) −1.11443 −0.0819347
\(186\) 3.17946 0.233129
\(187\) 11.0805 0.810290
\(188\) 2.81806 0.205528
\(189\) 0 0
\(190\) 5.91396 0.429044
\(191\) 21.0906 1.52606 0.763030 0.646363i \(-0.223711\pi\)
0.763030 + 0.646363i \(0.223711\pi\)
\(192\) −8.69771 −0.627703
\(193\) −8.97043 −0.645706 −0.322853 0.946449i \(-0.604642\pi\)
−0.322853 + 0.946449i \(0.604642\pi\)
\(194\) 20.5530 1.47562
\(195\) −15.5223 −1.11158
\(196\) 0 0
\(197\) −21.6173 −1.54017 −0.770084 0.637943i \(-0.779786\pi\)
−0.770084 + 0.637943i \(0.779786\pi\)
\(198\) 3.23197 0.229686
\(199\) −6.63970 −0.470676 −0.235338 0.971914i \(-0.575620\pi\)
−0.235338 + 0.971914i \(0.575620\pi\)
\(200\) −20.3490 −1.43889
\(201\) −3.77777 −0.266463
\(202\) −2.79723 −0.196812
\(203\) 0 0
\(204\) 1.05224 0.0736716
\(205\) 3.44355 0.240508
\(206\) −12.7089 −0.885474
\(207\) −5.25675 −0.365370
\(208\) −15.7104 −1.08932
\(209\) 3.13725 0.217008
\(210\) 0 0
\(211\) −26.1364 −1.79931 −0.899653 0.436606i \(-0.856180\pi\)
−0.899653 + 0.436606i \(0.856180\pi\)
\(212\) −1.19523 −0.0820889
\(213\) 5.00281 0.342787
\(214\) −0.577783 −0.0394964
\(215\) 13.5561 0.924521
\(216\) 2.96719 0.201891
\(217\) 0 0
\(218\) 14.9026 1.00933
\(219\) 8.20083 0.554161
\(220\) −1.93065 −0.130165
\(221\) 20.5560 1.38275
\(222\) 0.430471 0.0288913
\(223\) −7.82588 −0.524059 −0.262030 0.965060i \(-0.584392\pi\)
−0.262030 + 0.965060i \(0.584392\pi\)
\(224\) 0 0
\(225\) 6.85802 0.457201
\(226\) 4.09453 0.272364
\(227\) 15.8918 1.05478 0.527389 0.849624i \(-0.323171\pi\)
0.527389 + 0.849624i \(0.323171\pi\)
\(228\) 0.297922 0.0197304
\(229\) −21.6629 −1.43152 −0.715761 0.698345i \(-0.753920\pi\)
−0.715761 + 0.698345i \(0.753920\pi\)
\(230\) −24.0779 −1.58765
\(231\) 0 0
\(232\) −20.2815 −1.33155
\(233\) 10.1366 0.664073 0.332036 0.943267i \(-0.392264\pi\)
0.332036 + 0.943267i \(0.392264\pi\)
\(234\) 5.99578 0.391957
\(235\) −42.0563 −2.74345
\(236\) −0.277876 −0.0180882
\(237\) 7.91250 0.513972
\(238\) 0 0
\(239\) 28.9215 1.87078 0.935389 0.353620i \(-0.115049\pi\)
0.935389 + 0.353620i \(0.115049\pi\)
\(240\) 12.0017 0.774707
\(241\) 1.59730 0.102891 0.0514454 0.998676i \(-0.483617\pi\)
0.0514454 + 0.998676i \(0.483617\pi\)
\(242\) −6.77841 −0.435733
\(243\) −1.00000 −0.0641500
\(244\) −1.11796 −0.0715703
\(245\) 0 0
\(246\) −1.33013 −0.0848063
\(247\) 5.82006 0.370321
\(248\) 7.09256 0.450378
\(249\) 2.47939 0.157125
\(250\) 8.51044 0.538247
\(251\) 15.4326 0.974099 0.487050 0.873374i \(-0.338073\pi\)
0.487050 + 0.873374i \(0.338073\pi\)
\(252\) 0 0
\(253\) −12.7729 −0.803025
\(254\) 7.42144 0.465663
\(255\) −15.7035 −0.983389
\(256\) −5.46125 −0.341328
\(257\) −8.02184 −0.500389 −0.250194 0.968196i \(-0.580495\pi\)
−0.250194 + 0.968196i \(0.580495\pi\)
\(258\) −5.23631 −0.325999
\(259\) 0 0
\(260\) −3.58164 −0.222124
\(261\) 6.83526 0.423092
\(262\) −7.54504 −0.466134
\(263\) 26.1307 1.61129 0.805645 0.592398i \(-0.201819\pi\)
0.805645 + 0.592398i \(0.201819\pi\)
\(264\) 7.20969 0.443726
\(265\) 17.8374 1.09575
\(266\) 0 0
\(267\) −2.30019 −0.140769
\(268\) −0.871689 −0.0532469
\(269\) 14.6818 0.895166 0.447583 0.894243i \(-0.352285\pi\)
0.447583 + 0.894243i \(0.352285\pi\)
\(270\) −4.58038 −0.278753
\(271\) −2.98493 −0.181322 −0.0906609 0.995882i \(-0.528898\pi\)
−0.0906609 + 0.995882i \(0.528898\pi\)
\(272\) −15.8937 −0.963700
\(273\) 0 0
\(274\) 27.9320 1.68743
\(275\) 16.6637 1.00486
\(276\) −1.21295 −0.0730111
\(277\) 5.30104 0.318509 0.159254 0.987238i \(-0.449091\pi\)
0.159254 + 0.987238i \(0.449091\pi\)
\(278\) 2.40129 0.144020
\(279\) −2.39033 −0.143105
\(280\) 0 0
\(281\) −24.6022 −1.46764 −0.733821 0.679343i \(-0.762265\pi\)
−0.733821 + 0.679343i \(0.762265\pi\)
\(282\) 16.2450 0.967377
\(283\) 16.2722 0.967282 0.483641 0.875267i \(-0.339314\pi\)
0.483641 + 0.875267i \(0.339314\pi\)
\(284\) 1.15436 0.0684985
\(285\) −4.44614 −0.263367
\(286\) 14.5686 0.861459
\(287\) 0 0
\(288\) 1.29849 0.0765142
\(289\) 3.79594 0.223291
\(290\) 31.3081 1.83848
\(291\) −15.4518 −0.905803
\(292\) 1.89227 0.110737
\(293\) −23.2890 −1.36056 −0.680279 0.732953i \(-0.738141\pi\)
−0.680279 + 0.732953i \(0.738141\pi\)
\(294\) 0 0
\(295\) 4.14697 0.241446
\(296\) 0.960269 0.0558145
\(297\) −2.42981 −0.140992
\(298\) 8.66334 0.501854
\(299\) −23.6956 −1.37035
\(300\) 1.58243 0.0913617
\(301\) 0 0
\(302\) 19.3614 1.11413
\(303\) 2.10297 0.120812
\(304\) −4.50002 −0.258094
\(305\) 16.6843 0.955340
\(306\) 6.06576 0.346756
\(307\) 23.6521 1.34990 0.674948 0.737865i \(-0.264166\pi\)
0.674948 + 0.737865i \(0.264166\pi\)
\(308\) 0 0
\(309\) 9.55463 0.543544
\(310\) −10.9486 −0.621840
\(311\) −34.3154 −1.94585 −0.972925 0.231121i \(-0.925761\pi\)
−0.972925 + 0.231121i \(0.925761\pi\)
\(312\) 13.3750 0.757213
\(313\) 27.6991 1.56565 0.782824 0.622243i \(-0.213778\pi\)
0.782824 + 0.622243i \(0.213778\pi\)
\(314\) −0.776721 −0.0438329
\(315\) 0 0
\(316\) 1.82574 0.102706
\(317\) −2.07093 −0.116315 −0.0581576 0.998307i \(-0.518523\pi\)
−0.0581576 + 0.998307i \(0.518523\pi\)
\(318\) −6.89004 −0.386375
\(319\) 16.6084 0.929890
\(320\) 29.9510 1.67431
\(321\) 0.434379 0.0242447
\(322\) 0 0
\(323\) 5.88798 0.327616
\(324\) −0.230742 −0.0128190
\(325\) 30.9136 1.71478
\(326\) 18.2865 1.01280
\(327\) −11.2038 −0.619571
\(328\) −2.96719 −0.163835
\(329\) 0 0
\(330\) −11.1294 −0.612656
\(331\) −7.68409 −0.422356 −0.211178 0.977448i \(-0.567730\pi\)
−0.211178 + 0.977448i \(0.567730\pi\)
\(332\) 0.572098 0.0313979
\(333\) −0.323629 −0.0177348
\(334\) 26.2665 1.43724
\(335\) 13.0089 0.710753
\(336\) 0 0
\(337\) 29.8787 1.62760 0.813798 0.581147i \(-0.197396\pi\)
0.813798 + 0.581147i \(0.197396\pi\)
\(338\) 9.73514 0.529522
\(339\) −3.07828 −0.167189
\(340\) −3.62344 −0.196509
\(341\) −5.80804 −0.314523
\(342\) 1.71740 0.0928666
\(343\) 0 0
\(344\) −11.6809 −0.629790
\(345\) 18.1019 0.974572
\(346\) −23.2007 −1.24728
\(347\) 12.4873 0.670355 0.335177 0.942155i \(-0.391204\pi\)
0.335177 + 0.942155i \(0.391204\pi\)
\(348\) 1.57718 0.0845457
\(349\) −30.7391 −1.64543 −0.822714 0.568455i \(-0.807541\pi\)
−0.822714 + 0.568455i \(0.807541\pi\)
\(350\) 0 0
\(351\) −4.50765 −0.240601
\(352\) 3.15508 0.168166
\(353\) −1.52558 −0.0811985 −0.0405993 0.999176i \(-0.512927\pi\)
−0.0405993 + 0.999176i \(0.512927\pi\)
\(354\) −1.60184 −0.0851370
\(355\) −17.2274 −0.914337
\(356\) −0.530749 −0.0281296
\(357\) 0 0
\(358\) −7.33893 −0.387874
\(359\) 29.4597 1.55482 0.777412 0.628992i \(-0.216532\pi\)
0.777412 + 0.628992i \(0.216532\pi\)
\(360\) −10.2176 −0.538517
\(361\) −17.3329 −0.912259
\(362\) 8.33938 0.438308
\(363\) 5.09604 0.267473
\(364\) 0 0
\(365\) −28.2399 −1.47815
\(366\) −6.44462 −0.336866
\(367\) −3.85518 −0.201239 −0.100619 0.994925i \(-0.532082\pi\)
−0.100619 + 0.994925i \(0.532082\pi\)
\(368\) 18.3212 0.955060
\(369\) 1.00000 0.0520579
\(370\) −1.48235 −0.0770635
\(371\) 0 0
\(372\) −0.551549 −0.0285965
\(373\) 5.04932 0.261444 0.130722 0.991419i \(-0.458270\pi\)
0.130722 + 0.991419i \(0.458270\pi\)
\(374\) 14.7386 0.762116
\(375\) −6.39818 −0.330401
\(376\) 36.2385 1.86886
\(377\) 30.8110 1.58685
\(378\) 0 0
\(379\) −30.0604 −1.54410 −0.772048 0.635564i \(-0.780768\pi\)
−0.772048 + 0.635564i \(0.780768\pi\)
\(380\) −1.02591 −0.0526281
\(381\) −5.57946 −0.285845
\(382\) 28.0533 1.43533
\(383\) −23.9341 −1.22298 −0.611488 0.791254i \(-0.709429\pi\)
−0.611488 + 0.791254i \(0.709429\pi\)
\(384\) −8.97216 −0.457858
\(385\) 0 0
\(386\) −11.9319 −0.607317
\(387\) 3.93668 0.200113
\(388\) −3.56538 −0.181005
\(389\) 9.60257 0.486870 0.243435 0.969917i \(-0.421726\pi\)
0.243435 + 0.969917i \(0.421726\pi\)
\(390\) −20.6468 −1.04549
\(391\) −23.9721 −1.21232
\(392\) 0 0
\(393\) 5.67239 0.286134
\(394\) −28.7539 −1.44860
\(395\) −27.2471 −1.37095
\(396\) −0.560658 −0.0281741
\(397\) −4.61217 −0.231478 −0.115739 0.993280i \(-0.536924\pi\)
−0.115739 + 0.993280i \(0.536924\pi\)
\(398\) −8.83169 −0.442693
\(399\) 0 0
\(400\) −23.9021 −1.19510
\(401\) −3.10914 −0.155263 −0.0776315 0.996982i \(-0.524736\pi\)
−0.0776315 + 0.996982i \(0.524736\pi\)
\(402\) −5.02494 −0.250621
\(403\) −10.7748 −0.536730
\(404\) 0.485242 0.0241417
\(405\) 3.44355 0.171111
\(406\) 0 0
\(407\) −0.786357 −0.0389783
\(408\) 13.5311 0.669891
\(409\) 12.4282 0.614535 0.307267 0.951623i \(-0.400585\pi\)
0.307267 + 0.951623i \(0.400585\pi\)
\(410\) 4.58038 0.226209
\(411\) −20.9994 −1.03582
\(412\) 2.20465 0.108615
\(413\) 0 0
\(414\) −6.99219 −0.343647
\(415\) −8.53788 −0.419108
\(416\) 5.85313 0.286973
\(417\) −1.80530 −0.0884060
\(418\) 4.17296 0.204106
\(419\) 4.45355 0.217570 0.108785 0.994065i \(-0.465304\pi\)
0.108785 + 0.994065i \(0.465304\pi\)
\(420\) 0 0
\(421\) 4.19931 0.204662 0.102331 0.994750i \(-0.467370\pi\)
0.102331 + 0.994750i \(0.467370\pi\)
\(422\) −34.7650 −1.69233
\(423\) −12.2131 −0.593820
\(424\) −15.3699 −0.746429
\(425\) 31.2743 1.51703
\(426\) 6.65442 0.322407
\(427\) 0 0
\(428\) 0.100229 0.00484477
\(429\) −10.9527 −0.528802
\(430\) 18.0315 0.869556
\(431\) 21.7632 1.04830 0.524149 0.851626i \(-0.324383\pi\)
0.524149 + 0.851626i \(0.324383\pi\)
\(432\) 3.48527 0.167685
\(433\) 7.84478 0.376996 0.188498 0.982074i \(-0.439638\pi\)
0.188498 + 0.982074i \(0.439638\pi\)
\(434\) 0 0
\(435\) −23.5376 −1.12854
\(436\) −2.58518 −0.123808
\(437\) −6.78726 −0.324679
\(438\) 10.9082 0.521214
\(439\) −12.3744 −0.590600 −0.295300 0.955405i \(-0.595420\pi\)
−0.295300 + 0.955405i \(0.595420\pi\)
\(440\) −24.8269 −1.18358
\(441\) 0 0
\(442\) 27.3423 1.30054
\(443\) 15.3963 0.731502 0.365751 0.930713i \(-0.380812\pi\)
0.365751 + 0.930713i \(0.380812\pi\)
\(444\) −0.0746748 −0.00354391
\(445\) 7.92080 0.375482
\(446\) −10.4095 −0.492903
\(447\) −6.51313 −0.308060
\(448\) 0 0
\(449\) −12.4629 −0.588159 −0.294079 0.955781i \(-0.595013\pi\)
−0.294079 + 0.955781i \(0.595013\pi\)
\(450\) 9.12209 0.430019
\(451\) 2.42981 0.114415
\(452\) −0.710287 −0.0334091
\(453\) −14.5560 −0.683901
\(454\) 21.1383 0.992069
\(455\) 0 0
\(456\) 3.83109 0.179407
\(457\) −18.2640 −0.854354 −0.427177 0.904168i \(-0.640492\pi\)
−0.427177 + 0.904168i \(0.640492\pi\)
\(458\) −28.8145 −1.34641
\(459\) −4.56026 −0.212855
\(460\) 4.17686 0.194747
\(461\) 36.6943 1.70902 0.854512 0.519432i \(-0.173856\pi\)
0.854512 + 0.519432i \(0.173856\pi\)
\(462\) 0 0
\(463\) 6.66895 0.309932 0.154966 0.987920i \(-0.450473\pi\)
0.154966 + 0.987920i \(0.450473\pi\)
\(464\) −23.8228 −1.10594
\(465\) 8.23122 0.381713
\(466\) 13.4831 0.624592
\(467\) −38.6299 −1.78758 −0.893789 0.448488i \(-0.851963\pi\)
−0.893789 + 0.448488i \(0.851963\pi\)
\(468\) −1.04010 −0.0480788
\(469\) 0 0
\(470\) −55.9405 −2.58034
\(471\) 0.583942 0.0269066
\(472\) −3.57330 −0.164474
\(473\) 9.56537 0.439816
\(474\) 10.5247 0.483415
\(475\) 8.85474 0.406283
\(476\) 0 0
\(477\) 5.17996 0.237174
\(478\) 38.4695 1.75956
\(479\) 23.6927 1.08255 0.541274 0.840846i \(-0.317942\pi\)
0.541274 + 0.840846i \(0.317942\pi\)
\(480\) −4.47141 −0.204091
\(481\) −1.45881 −0.0665159
\(482\) 2.12462 0.0967737
\(483\) 0 0
\(484\) 1.17587 0.0534485
\(485\) 53.2091 2.41610
\(486\) −1.33013 −0.0603361
\(487\) −3.45210 −0.156429 −0.0782147 0.996937i \(-0.524922\pi\)
−0.0782147 + 0.996937i \(0.524922\pi\)
\(488\) −14.3763 −0.650784
\(489\) −13.7479 −0.621700
\(490\) 0 0
\(491\) 41.9801 1.89453 0.947267 0.320447i \(-0.103833\pi\)
0.947267 + 0.320447i \(0.103833\pi\)
\(492\) 0.230742 0.0104026
\(493\) 31.1706 1.40385
\(494\) 7.74146 0.348305
\(495\) 8.36716 0.376076
\(496\) 8.33096 0.374071
\(497\) 0 0
\(498\) 3.29792 0.147783
\(499\) −31.7195 −1.41996 −0.709981 0.704221i \(-0.751296\pi\)
−0.709981 + 0.704221i \(0.751296\pi\)
\(500\) −1.47633 −0.0660233
\(501\) −19.7472 −0.882241
\(502\) 20.5275 0.916186
\(503\) 22.9497 1.02328 0.511639 0.859201i \(-0.329039\pi\)
0.511639 + 0.859201i \(0.329039\pi\)
\(504\) 0 0
\(505\) −7.24166 −0.322250
\(506\) −16.9897 −0.755283
\(507\) −7.31891 −0.325044
\(508\) −1.28741 −0.0571198
\(509\) 32.5353 1.44210 0.721051 0.692882i \(-0.243659\pi\)
0.721051 + 0.692882i \(0.243659\pi\)
\(510\) −20.8877 −0.924924
\(511\) 0 0
\(512\) −25.2085 −1.11407
\(513\) −1.29115 −0.0570057
\(514\) −10.6701 −0.470639
\(515\) −32.9018 −1.44983
\(516\) 0.908356 0.0399881
\(517\) −29.6754 −1.30512
\(518\) 0 0
\(519\) 17.4423 0.765634
\(520\) −46.0576 −2.01976
\(521\) −42.0823 −1.84366 −0.921829 0.387597i \(-0.873305\pi\)
−0.921829 + 0.387597i \(0.873305\pi\)
\(522\) 9.09182 0.397938
\(523\) −13.2249 −0.578283 −0.289141 0.957286i \(-0.593370\pi\)
−0.289141 + 0.957286i \(0.593370\pi\)
\(524\) 1.30886 0.0571776
\(525\) 0 0
\(526\) 34.7574 1.51549
\(527\) −10.9005 −0.474834
\(528\) 8.46855 0.368546
\(529\) 4.63346 0.201455
\(530\) 23.7262 1.03060
\(531\) 1.20427 0.0522610
\(532\) 0 0
\(533\) 4.50765 0.195248
\(534\) −3.05956 −0.132400
\(535\) −1.49581 −0.0646693
\(536\) −11.2093 −0.484170
\(537\) 5.51743 0.238095
\(538\) 19.5288 0.841945
\(539\) 0 0
\(540\) 0.794570 0.0341928
\(541\) −23.1355 −0.994672 −0.497336 0.867558i \(-0.665688\pi\)
−0.497336 + 0.867558i \(0.665688\pi\)
\(542\) −3.97036 −0.170542
\(543\) −6.26958 −0.269053
\(544\) 5.92144 0.253880
\(545\) 38.5808 1.65262
\(546\) 0 0
\(547\) −30.8794 −1.32031 −0.660154 0.751130i \(-0.729509\pi\)
−0.660154 + 0.751130i \(0.729509\pi\)
\(548\) −4.84543 −0.206987
\(549\) 4.84509 0.206783
\(550\) 22.1649 0.945115
\(551\) 8.82536 0.375973
\(552\) −15.5978 −0.663885
\(553\) 0 0
\(554\) 7.05110 0.299573
\(555\) 1.11443 0.0473050
\(556\) −0.416558 −0.0176660
\(557\) −44.7665 −1.89682 −0.948408 0.317051i \(-0.897307\pi\)
−0.948408 + 0.317051i \(0.897307\pi\)
\(558\) −3.17946 −0.134597
\(559\) 17.7452 0.750541
\(560\) 0 0
\(561\) −11.0805 −0.467821
\(562\) −32.7242 −1.38039
\(563\) −26.7582 −1.12772 −0.563861 0.825869i \(-0.690685\pi\)
−0.563861 + 0.825869i \(0.690685\pi\)
\(564\) −2.81806 −0.118662
\(565\) 10.6002 0.445954
\(566\) 21.6442 0.909774
\(567\) 0 0
\(568\) 14.8443 0.622852
\(569\) −42.2545 −1.77140 −0.885701 0.464257i \(-0.846322\pi\)
−0.885701 + 0.464257i \(0.846322\pi\)
\(570\) −5.91396 −0.247709
\(571\) 25.9438 1.08571 0.542857 0.839825i \(-0.317343\pi\)
0.542857 + 0.839825i \(0.317343\pi\)
\(572\) −2.52725 −0.105670
\(573\) −21.0906 −0.881072
\(574\) 0 0
\(575\) −36.0509 −1.50343
\(576\) 8.69771 0.362405
\(577\) −25.1709 −1.04788 −0.523940 0.851755i \(-0.675538\pi\)
−0.523940 + 0.851755i \(0.675538\pi\)
\(578\) 5.04912 0.210016
\(579\) 8.97043 0.372798
\(580\) −5.43109 −0.225514
\(581\) 0 0
\(582\) −20.5530 −0.851950
\(583\) 12.5863 0.521272
\(584\) 24.3334 1.00692
\(585\) 15.5223 0.641769
\(586\) −30.9775 −1.27967
\(587\) −37.6709 −1.55484 −0.777422 0.628979i \(-0.783473\pi\)
−0.777422 + 0.628979i \(0.783473\pi\)
\(588\) 0 0
\(589\) −3.08628 −0.127168
\(590\) 5.51603 0.227091
\(591\) 21.6173 0.889216
\(592\) 1.12794 0.0463579
\(593\) 31.0474 1.27496 0.637482 0.770465i \(-0.279976\pi\)
0.637482 + 0.770465i \(0.279976\pi\)
\(594\) −3.23197 −0.132609
\(595\) 0 0
\(596\) −1.50285 −0.0615591
\(597\) 6.63970 0.271745
\(598\) −31.5184 −1.28888
\(599\) 8.37484 0.342187 0.171093 0.985255i \(-0.445270\pi\)
0.171093 + 0.985255i \(0.445270\pi\)
\(600\) 20.3490 0.830746
\(601\) −3.05224 −0.124503 −0.0622517 0.998060i \(-0.519828\pi\)
−0.0622517 + 0.998060i \(0.519828\pi\)
\(602\) 0 0
\(603\) 3.77777 0.153843
\(604\) −3.35868 −0.136663
\(605\) −17.5484 −0.713446
\(606\) 2.79723 0.113630
\(607\) 39.8725 1.61838 0.809188 0.587550i \(-0.199908\pi\)
0.809188 + 0.587550i \(0.199908\pi\)
\(608\) 1.67654 0.0679929
\(609\) 0 0
\(610\) 22.1924 0.898543
\(611\) −55.0522 −2.22718
\(612\) −1.05224 −0.0425343
\(613\) 6.31640 0.255117 0.127559 0.991831i \(-0.459286\pi\)
0.127559 + 0.991831i \(0.459286\pi\)
\(614\) 31.4605 1.26964
\(615\) −3.44355 −0.138857
\(616\) 0 0
\(617\) −24.1061 −0.970477 −0.485238 0.874382i \(-0.661267\pi\)
−0.485238 + 0.874382i \(0.661267\pi\)
\(618\) 12.7089 0.511229
\(619\) −22.4446 −0.902127 −0.451063 0.892492i \(-0.648955\pi\)
−0.451063 + 0.892492i \(0.648955\pi\)
\(620\) 1.89928 0.0762771
\(621\) 5.25675 0.210946
\(622\) −45.6442 −1.83016
\(623\) 0 0
\(624\) 15.7104 0.628919
\(625\) −12.2577 −0.490307
\(626\) 36.8436 1.47257
\(627\) −3.13725 −0.125290
\(628\) 0.134740 0.00537670
\(629\) −1.47583 −0.0588453
\(630\) 0 0
\(631\) 9.22009 0.367046 0.183523 0.983015i \(-0.441250\pi\)
0.183523 + 0.983015i \(0.441250\pi\)
\(632\) 23.4779 0.933900
\(633\) 26.1364 1.03883
\(634\) −2.75462 −0.109400
\(635\) 19.2132 0.762451
\(636\) 1.19523 0.0473941
\(637\) 0 0
\(638\) 22.0914 0.874606
\(639\) −5.00281 −0.197908
\(640\) 30.8960 1.22127
\(641\) −39.9640 −1.57848 −0.789241 0.614084i \(-0.789526\pi\)
−0.789241 + 0.614084i \(0.789526\pi\)
\(642\) 0.577783 0.0228033
\(643\) −26.3406 −1.03877 −0.519385 0.854540i \(-0.673839\pi\)
−0.519385 + 0.854540i \(0.673839\pi\)
\(644\) 0 0
\(645\) −13.5561 −0.533772
\(646\) 7.83181 0.308138
\(647\) −40.3248 −1.58533 −0.792667 0.609655i \(-0.791308\pi\)
−0.792667 + 0.609655i \(0.791308\pi\)
\(648\) −2.96719 −0.116562
\(649\) 2.92615 0.114861
\(650\) 41.1192 1.61283
\(651\) 0 0
\(652\) −3.17221 −0.124233
\(653\) 34.7576 1.36017 0.680084 0.733134i \(-0.261943\pi\)
0.680084 + 0.733134i \(0.261943\pi\)
\(654\) −14.9026 −0.582736
\(655\) −19.5331 −0.763223
\(656\) −3.48527 −0.136077
\(657\) −8.20083 −0.319945
\(658\) 0 0
\(659\) 3.55366 0.138431 0.0692154 0.997602i \(-0.477950\pi\)
0.0692154 + 0.997602i \(0.477950\pi\)
\(660\) 1.93065 0.0751505
\(661\) −26.4437 −1.02854 −0.514270 0.857628i \(-0.671937\pi\)
−0.514270 + 0.857628i \(0.671937\pi\)
\(662\) −10.2209 −0.397246
\(663\) −20.5560 −0.798331
\(664\) 7.35680 0.285499
\(665\) 0 0
\(666\) −0.430471 −0.0166804
\(667\) −35.9313 −1.39127
\(668\) −4.55651 −0.176297
\(669\) 7.82588 0.302566
\(670\) 17.3036 0.668497
\(671\) 11.7726 0.454478
\(672\) 0 0
\(673\) 31.8563 1.22797 0.613985 0.789318i \(-0.289566\pi\)
0.613985 + 0.789318i \(0.289566\pi\)
\(674\) 39.7427 1.53083
\(675\) −6.85802 −0.263965
\(676\) −1.68878 −0.0649530
\(677\) −11.1442 −0.428306 −0.214153 0.976800i \(-0.568699\pi\)
−0.214153 + 0.976800i \(0.568699\pi\)
\(678\) −4.09453 −0.157249
\(679\) 0 0
\(680\) −46.5951 −1.78684
\(681\) −15.8918 −0.608976
\(682\) −7.72548 −0.295824
\(683\) −47.9051 −1.83304 −0.916519 0.399992i \(-0.869013\pi\)
−0.916519 + 0.399992i \(0.869013\pi\)
\(684\) −0.297922 −0.0113913
\(685\) 72.3123 2.76291
\(686\) 0 0
\(687\) 21.6629 0.826489
\(688\) −13.7204 −0.523086
\(689\) 23.3495 0.889543
\(690\) 24.0779 0.916631
\(691\) 6.92965 0.263616 0.131808 0.991275i \(-0.457922\pi\)
0.131808 + 0.991275i \(0.457922\pi\)
\(692\) 4.02468 0.152995
\(693\) 0 0
\(694\) 16.6098 0.630500
\(695\) 6.21664 0.235811
\(696\) 20.2815 0.768768
\(697\) 4.56026 0.172732
\(698\) −40.8872 −1.54760
\(699\) −10.1366 −0.383403
\(700\) 0 0
\(701\) −20.9178 −0.790053 −0.395026 0.918670i \(-0.629265\pi\)
−0.395026 + 0.918670i \(0.629265\pi\)
\(702\) −5.99578 −0.226296
\(703\) −0.417854 −0.0157597
\(704\) 21.1338 0.796509
\(705\) 42.0563 1.58393
\(706\) −2.02923 −0.0763710
\(707\) 0 0
\(708\) 0.277876 0.0104432
\(709\) −17.1067 −0.642455 −0.321228 0.947002i \(-0.604095\pi\)
−0.321228 + 0.947002i \(0.604095\pi\)
\(710\) −22.9148 −0.859977
\(711\) −7.91250 −0.296742
\(712\) −6.82509 −0.255781
\(713\) 12.5654 0.470577
\(714\) 0 0
\(715\) 37.7162 1.41051
\(716\) 1.27310 0.0475780
\(717\) −28.9215 −1.08009
\(718\) 39.1854 1.46239
\(719\) 0.652683 0.0243410 0.0121705 0.999926i \(-0.496126\pi\)
0.0121705 + 0.999926i \(0.496126\pi\)
\(720\) −12.0017 −0.447277
\(721\) 0 0
\(722\) −23.0551 −0.858023
\(723\) −1.59730 −0.0594041
\(724\) −1.44665 −0.0537644
\(725\) 46.8764 1.74094
\(726\) 6.77841 0.251571
\(727\) 53.3784 1.97969 0.989847 0.142134i \(-0.0453963\pi\)
0.989847 + 0.142134i \(0.0453963\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −37.5629 −1.39027
\(731\) 17.9523 0.663988
\(732\) 1.11796 0.0413212
\(733\) 21.9700 0.811479 0.405740 0.913989i \(-0.367014\pi\)
0.405740 + 0.913989i \(0.367014\pi\)
\(734\) −5.12790 −0.189274
\(735\) 0 0
\(736\) −6.82583 −0.251604
\(737\) 9.17925 0.338122
\(738\) 1.33013 0.0489629
\(739\) 36.2447 1.33328 0.666642 0.745378i \(-0.267731\pi\)
0.666642 + 0.745378i \(0.267731\pi\)
\(740\) 0.257146 0.00945288
\(741\) −5.82006 −0.213805
\(742\) 0 0
\(743\) 37.3789 1.37130 0.685650 0.727931i \(-0.259518\pi\)
0.685650 + 0.727931i \(0.259518\pi\)
\(744\) −7.09256 −0.260026
\(745\) 22.4283 0.821708
\(746\) 6.71628 0.245901
\(747\) −2.47939 −0.0907160
\(748\) −2.55674 −0.0934838
\(749\) 0 0
\(750\) −8.51044 −0.310757
\(751\) 3.40592 0.124284 0.0621420 0.998067i \(-0.480207\pi\)
0.0621420 + 0.998067i \(0.480207\pi\)
\(752\) 42.5659 1.55222
\(753\) −15.4326 −0.562396
\(754\) 40.9828 1.49250
\(755\) 50.1243 1.82421
\(756\) 0 0
\(757\) 24.9914 0.908327 0.454163 0.890918i \(-0.349938\pi\)
0.454163 + 0.890918i \(0.349938\pi\)
\(758\) −39.9843 −1.45230
\(759\) 12.7729 0.463627
\(760\) −13.1925 −0.478543
\(761\) 47.9442 1.73798 0.868988 0.494834i \(-0.164771\pi\)
0.868988 + 0.494834i \(0.164771\pi\)
\(762\) −7.42144 −0.268850
\(763\) 0 0
\(764\) −4.86648 −0.176063
\(765\) 15.7035 0.567760
\(766\) −31.8356 −1.15027
\(767\) 5.42844 0.196010
\(768\) 5.46125 0.197066
\(769\) −50.4114 −1.81788 −0.908940 0.416926i \(-0.863107\pi\)
−0.908940 + 0.416926i \(0.863107\pi\)
\(770\) 0 0
\(771\) 8.02184 0.288900
\(772\) 2.06985 0.0744956
\(773\) −1.16820 −0.0420172 −0.0210086 0.999779i \(-0.506688\pi\)
−0.0210086 + 0.999779i \(0.506688\pi\)
\(774\) 5.23631 0.188215
\(775\) −16.3929 −0.588851
\(776\) −45.8485 −1.64586
\(777\) 0 0
\(778\) 12.7727 0.457924
\(779\) 1.29115 0.0462603
\(780\) 3.58164 0.128243
\(781\) −12.1559 −0.434971
\(782\) −31.8862 −1.14025
\(783\) −6.83526 −0.244272
\(784\) 0 0
\(785\) −2.01083 −0.0717696
\(786\) 7.54504 0.269123
\(787\) −39.1683 −1.39620 −0.698100 0.716001i \(-0.745971\pi\)
−0.698100 + 0.716001i \(0.745971\pi\)
\(788\) 4.98801 0.177690
\(789\) −26.1307 −0.930279
\(790\) −36.2423 −1.28944
\(791\) 0 0
\(792\) −7.20969 −0.256185
\(793\) 21.8400 0.775560
\(794\) −6.13481 −0.217716
\(795\) −17.8374 −0.632629
\(796\) 1.53205 0.0543022
\(797\) −33.5386 −1.18800 −0.593999 0.804465i \(-0.702452\pi\)
−0.593999 + 0.804465i \(0.702452\pi\)
\(798\) 0 0
\(799\) −55.6947 −1.97034
\(800\) 8.90506 0.314841
\(801\) 2.30019 0.0812731
\(802\) −4.13557 −0.146032
\(803\) −19.9264 −0.703189
\(804\) 0.871689 0.0307421
\(805\) 0 0
\(806\) −14.3319 −0.504820
\(807\) −14.6818 −0.516824
\(808\) 6.23989 0.219519
\(809\) −44.6359 −1.56932 −0.784658 0.619929i \(-0.787161\pi\)
−0.784658 + 0.619929i \(0.787161\pi\)
\(810\) 4.58038 0.160938
\(811\) 36.6559 1.28716 0.643582 0.765377i \(-0.277448\pi\)
0.643582 + 0.765377i \(0.277448\pi\)
\(812\) 0 0
\(813\) 2.98493 0.104686
\(814\) −1.04596 −0.0366609
\(815\) 47.3415 1.65830
\(816\) 15.8937 0.556393
\(817\) 5.08285 0.177826
\(818\) 16.5312 0.577999
\(819\) 0 0
\(820\) −0.794570 −0.0277476
\(821\) −33.6318 −1.17376 −0.586878 0.809675i \(-0.699643\pi\)
−0.586878 + 0.809675i \(0.699643\pi\)
\(822\) −27.9320 −0.974240
\(823\) −7.53917 −0.262799 −0.131399 0.991330i \(-0.541947\pi\)
−0.131399 + 0.991330i \(0.541947\pi\)
\(824\) 28.3504 0.987632
\(825\) −16.6637 −0.580154
\(826\) 0 0
\(827\) −16.7185 −0.581360 −0.290680 0.956820i \(-0.593882\pi\)
−0.290680 + 0.956820i \(0.593882\pi\)
\(828\) 1.21295 0.0421530
\(829\) 54.9115 1.90716 0.953578 0.301146i \(-0.0973690\pi\)
0.953578 + 0.301146i \(0.0973690\pi\)
\(830\) −11.3565 −0.394191
\(831\) −5.30104 −0.183891
\(832\) 39.2063 1.35923
\(833\) 0 0
\(834\) −2.40129 −0.0831500
\(835\) 68.0005 2.35325
\(836\) −0.723894 −0.0250364
\(837\) 2.39033 0.0826219
\(838\) 5.92383 0.204635
\(839\) −8.62503 −0.297769 −0.148885 0.988855i \(-0.547568\pi\)
−0.148885 + 0.988855i \(0.547568\pi\)
\(840\) 0 0
\(841\) 17.7208 0.611063
\(842\) 5.58565 0.192494
\(843\) 24.6022 0.847343
\(844\) 6.03076 0.207587
\(845\) 25.2030 0.867011
\(846\) −16.2450 −0.558515
\(847\) 0 0
\(848\) −18.0536 −0.619963
\(849\) −16.2722 −0.558460
\(850\) 41.5991 1.42684
\(851\) 1.70124 0.0583177
\(852\) −1.15436 −0.0395476
\(853\) −9.03717 −0.309427 −0.154713 0.987959i \(-0.549445\pi\)
−0.154713 + 0.987959i \(0.549445\pi\)
\(854\) 0 0
\(855\) 4.44614 0.152055
\(856\) 1.28888 0.0440532
\(857\) −35.6635 −1.21824 −0.609121 0.793077i \(-0.708478\pi\)
−0.609121 + 0.793077i \(0.708478\pi\)
\(858\) −14.5686 −0.497364
\(859\) −20.3978 −0.695965 −0.347982 0.937501i \(-0.613133\pi\)
−0.347982 + 0.937501i \(0.613133\pi\)
\(860\) −3.12797 −0.106663
\(861\) 0 0
\(862\) 28.9481 0.985975
\(863\) 9.46480 0.322185 0.161093 0.986939i \(-0.448498\pi\)
0.161093 + 0.986939i \(0.448498\pi\)
\(864\) −1.29849 −0.0441755
\(865\) −60.0636 −2.04222
\(866\) 10.4346 0.354582
\(867\) −3.79594 −0.128917
\(868\) 0 0
\(869\) −19.2259 −0.652193
\(870\) −31.3081 −1.06144
\(871\) 17.0289 0.577001
\(872\) −33.2438 −1.12578
\(873\) 15.4518 0.522965
\(874\) −9.02797 −0.305376
\(875\) 0 0
\(876\) −1.89227 −0.0639340
\(877\) 13.8614 0.468066 0.234033 0.972229i \(-0.424808\pi\)
0.234033 + 0.972229i \(0.424808\pi\)
\(878\) −16.4597 −0.555487
\(879\) 23.2890 0.785519
\(880\) −29.1618 −0.983046
\(881\) −48.5099 −1.63434 −0.817170 0.576396i \(-0.804458\pi\)
−0.817170 + 0.576396i \(0.804458\pi\)
\(882\) 0 0
\(883\) 16.6693 0.560966 0.280483 0.959859i \(-0.409505\pi\)
0.280483 + 0.959859i \(0.409505\pi\)
\(884\) −4.74314 −0.159529
\(885\) −4.14697 −0.139399
\(886\) 20.4792 0.688012
\(887\) −12.2497 −0.411303 −0.205652 0.978625i \(-0.565931\pi\)
−0.205652 + 0.978625i \(0.565931\pi\)
\(888\) −0.960269 −0.0322245
\(889\) 0 0
\(890\) 10.5357 0.353159
\(891\) 2.42981 0.0814016
\(892\) 1.80576 0.0604612
\(893\) −15.7689 −0.527687
\(894\) −8.66334 −0.289745
\(895\) −18.9995 −0.635084
\(896\) 0 0
\(897\) 23.6956 0.791173
\(898\) −16.5773 −0.553191
\(899\) −16.3385 −0.544921
\(900\) −1.58243 −0.0527477
\(901\) 23.6219 0.786961
\(902\) 3.23197 0.107613
\(903\) 0 0
\(904\) −9.13383 −0.303787
\(905\) 21.5896 0.717662
\(906\) −19.3614 −0.643241
\(907\) 26.9564 0.895071 0.447536 0.894266i \(-0.352302\pi\)
0.447536 + 0.894266i \(0.352302\pi\)
\(908\) −3.66691 −0.121691
\(909\) −2.10297 −0.0697510
\(910\) 0 0
\(911\) −24.3767 −0.807636 −0.403818 0.914839i \(-0.632317\pi\)
−0.403818 + 0.914839i \(0.632317\pi\)
\(912\) 4.50002 0.149010
\(913\) −6.02443 −0.199380
\(914\) −24.2936 −0.803561
\(915\) −16.6843 −0.551566
\(916\) 4.99852 0.165156
\(917\) 0 0
\(918\) −6.06576 −0.200200
\(919\) −7.40854 −0.244385 −0.122193 0.992506i \(-0.538993\pi\)
−0.122193 + 0.992506i \(0.538993\pi\)
\(920\) 53.7117 1.77082
\(921\) −23.6521 −0.779363
\(922\) 48.8084 1.60742
\(923\) −22.5509 −0.742273
\(924\) 0 0
\(925\) −2.21946 −0.0729753
\(926\) 8.87060 0.291506
\(927\) −9.55463 −0.313815
\(928\) 8.87551 0.291353
\(929\) −6.32793 −0.207613 −0.103806 0.994598i \(-0.533102\pi\)
−0.103806 + 0.994598i \(0.533102\pi\)
\(930\) 10.9486 0.359020
\(931\) 0 0
\(932\) −2.33894 −0.0766146
\(933\) 34.3154 1.12344
\(934\) −51.3830 −1.68130
\(935\) 38.1564 1.24785
\(936\) −13.3750 −0.437177
\(937\) 55.1940 1.80311 0.901555 0.432665i \(-0.142427\pi\)
0.901555 + 0.432665i \(0.142427\pi\)
\(938\) 0 0
\(939\) −27.6991 −0.903927
\(940\) 9.70414 0.316514
\(941\) 8.57076 0.279399 0.139699 0.990194i \(-0.455386\pi\)
0.139699 + 0.990194i \(0.455386\pi\)
\(942\) 0.776721 0.0253069
\(943\) −5.25675 −0.171183
\(944\) −4.19722 −0.136608
\(945\) 0 0
\(946\) 12.7232 0.413668
\(947\) −19.0572 −0.619275 −0.309638 0.950855i \(-0.600208\pi\)
−0.309638 + 0.950855i \(0.600208\pi\)
\(948\) −1.82574 −0.0592974
\(949\) −36.9665 −1.19998
\(950\) 11.7780 0.382129
\(951\) 2.07093 0.0671546
\(952\) 0 0
\(953\) 48.0117 1.55525 0.777626 0.628727i \(-0.216424\pi\)
0.777626 + 0.628727i \(0.216424\pi\)
\(954\) 6.89004 0.223073
\(955\) 72.6264 2.35014
\(956\) −6.67340 −0.215833
\(957\) −16.6084 −0.536873
\(958\) 31.5145 1.01819
\(959\) 0 0
\(960\) −29.9510 −0.966664
\(961\) −25.2863 −0.815688
\(962\) −1.94041 −0.0625614
\(963\) −0.434379 −0.0139977
\(964\) −0.368563 −0.0118706
\(965\) −30.8901 −0.994388
\(966\) 0 0
\(967\) −29.7309 −0.956081 −0.478040 0.878338i \(-0.658653\pi\)
−0.478040 + 0.878338i \(0.658653\pi\)
\(968\) 15.1209 0.486004
\(969\) −5.88798 −0.189149
\(970\) 70.7753 2.27246
\(971\) −39.3323 −1.26223 −0.631117 0.775688i \(-0.717403\pi\)
−0.631117 + 0.775688i \(0.717403\pi\)
\(972\) 0.230742 0.00740104
\(973\) 0 0
\(974\) −4.59175 −0.147129
\(975\) −30.9136 −0.990026
\(976\) −16.8865 −0.540523
\(977\) −43.9645 −1.40655 −0.703275 0.710918i \(-0.748280\pi\)
−0.703275 + 0.710918i \(0.748280\pi\)
\(978\) −18.2865 −0.584739
\(979\) 5.58901 0.178626
\(980\) 0 0
\(981\) 11.2038 0.357710
\(982\) 55.8391 1.78190
\(983\) −16.4200 −0.523716 −0.261858 0.965106i \(-0.584335\pi\)
−0.261858 + 0.965106i \(0.584335\pi\)
\(984\) 2.96719 0.0945905
\(985\) −74.4401 −2.37186
\(986\) 41.4610 1.32039
\(987\) 0 0
\(988\) −1.34293 −0.0427243
\(989\) −20.6941 −0.658036
\(990\) 11.1294 0.353717
\(991\) 46.0055 1.46141 0.730707 0.682691i \(-0.239191\pi\)
0.730707 + 0.682691i \(0.239191\pi\)
\(992\) −3.10382 −0.0985463
\(993\) 7.68409 0.243847
\(994\) 0 0
\(995\) −22.8641 −0.724841
\(996\) −0.572098 −0.0181276
\(997\) −49.3335 −1.56241 −0.781205 0.624275i \(-0.785394\pi\)
−0.781205 + 0.624275i \(0.785394\pi\)
\(998\) −42.1913 −1.33554
\(999\) 0.323629 0.0102392
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 \(a_p\))