Properties

Label 6027.2.a.bn.1.6
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 1.6
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.32413 q^{2} -1.00000 q^{3} -0.246682 q^{4} -4.03355 q^{5} +1.32413 q^{6} +2.97490 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.32413 q^{2} -1.00000 q^{3} -0.246682 q^{4} -4.03355 q^{5} +1.32413 q^{6} +2.97490 q^{8} +1.00000 q^{9} +5.34094 q^{10} +4.32013 q^{11} +0.246682 q^{12} -1.67689 q^{13} +4.03355 q^{15} -3.44578 q^{16} +1.53497 q^{17} -1.32413 q^{18} -4.63220 q^{19} +0.995003 q^{20} -5.72040 q^{22} +1.68322 q^{23} -2.97490 q^{24} +11.2695 q^{25} +2.22041 q^{26} -1.00000 q^{27} +6.19131 q^{29} -5.34094 q^{30} +7.82172 q^{31} -1.38713 q^{32} -4.32013 q^{33} -2.03250 q^{34} -0.246682 q^{36} +5.18274 q^{37} +6.13364 q^{38} +1.67689 q^{39} -11.9994 q^{40} +1.00000 q^{41} +4.53487 q^{43} -1.06570 q^{44} -4.03355 q^{45} -2.22881 q^{46} +7.25662 q^{47} +3.44578 q^{48} -14.9223 q^{50} -1.53497 q^{51} +0.413657 q^{52} -1.52553 q^{53} +1.32413 q^{54} -17.4254 q^{55} +4.63220 q^{57} -8.19809 q^{58} -6.75314 q^{59} -0.995003 q^{60} +1.19486 q^{61} -10.3570 q^{62} +8.72831 q^{64} +6.76380 q^{65} +5.72040 q^{66} +3.40655 q^{67} -0.378649 q^{68} -1.68322 q^{69} -16.5966 q^{71} +2.97490 q^{72} +5.99200 q^{73} -6.86262 q^{74} -11.2695 q^{75} +1.14268 q^{76} -2.22041 q^{78} +5.84022 q^{79} +13.8987 q^{80} +1.00000 q^{81} -1.32413 q^{82} +0.0883750 q^{83} -6.19138 q^{85} -6.00475 q^{86} -6.19131 q^{87} +12.8519 q^{88} -10.4911 q^{89} +5.34094 q^{90} -0.415221 q^{92} -7.82172 q^{93} -9.60870 q^{94} +18.6842 q^{95} +1.38713 q^{96} +2.82381 q^{97} +4.32013 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + 4q^{10} + 12q^{11} - 32q^{12} + 4q^{15} + 44q^{16} - 8q^{17} + 8q^{18} + 4q^{19} - 28q^{20} + 16q^{22} + 20q^{23} - 24q^{24} + 48q^{25} - 32q^{26} - 24q^{27} + 24q^{29} - 4q^{30} + 4q^{31} + 36q^{32} - 12q^{33} - 16q^{34} + 32q^{36} + 64q^{37} - 20q^{38} + 48q^{40} + 24q^{41} + 20q^{43} + 48q^{44} - 4q^{45} + 28q^{46} - 32q^{47} - 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} - 8q^{54} + 24q^{55} - 4q^{57} + 28q^{58} - 28q^{59} + 28q^{60} + 28q^{61} + 4q^{62} + 48q^{64} + 28q^{65} - 16q^{66} + 44q^{67} + 32q^{68} - 20q^{69} + 20q^{71} + 24q^{72} + 16q^{73} + 44q^{74} - 48q^{75} + 16q^{76} + 32q^{78} + 4q^{79} - 44q^{80} + 24q^{81} + 8q^{82} - 8q^{83} + 28q^{85} + 56q^{86} - 24q^{87} + 60q^{88} - 60q^{89} + 4q^{90} + 60q^{92} - 4q^{93} - 24q^{94} + 28q^{95} - 36q^{96} + 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.32413 −0.936301 −0.468150 0.883649i \(-0.655079\pi\)
−0.468150 + 0.883649i \(0.655079\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.246682 −0.123341
\(5\) −4.03355 −1.80386 −0.901929 0.431885i \(-0.857849\pi\)
−0.901929 + 0.431885i \(0.857849\pi\)
\(6\) 1.32413 0.540573
\(7\) 0 0
\(8\) 2.97490 1.05178
\(9\) 1.00000 0.333333
\(10\) 5.34094 1.68895
\(11\) 4.32013 1.30257 0.651283 0.758835i \(-0.274231\pi\)
0.651283 + 0.758835i \(0.274231\pi\)
\(12\) 0.246682 0.0712109
\(13\) −1.67689 −0.465085 −0.232542 0.972586i \(-0.574704\pi\)
−0.232542 + 0.972586i \(0.574704\pi\)
\(14\) 0 0
\(15\) 4.03355 1.04146
\(16\) −3.44578 −0.861446
\(17\) 1.53497 0.372285 0.186143 0.982523i \(-0.440401\pi\)
0.186143 + 0.982523i \(0.440401\pi\)
\(18\) −1.32413 −0.312100
\(19\) −4.63220 −1.06270 −0.531350 0.847152i \(-0.678315\pi\)
−0.531350 + 0.847152i \(0.678315\pi\)
\(20\) 0.995003 0.222489
\(21\) 0 0
\(22\) −5.72040 −1.21959
\(23\) 1.68322 0.350977 0.175488 0.984482i \(-0.443850\pi\)
0.175488 + 0.984482i \(0.443850\pi\)
\(24\) −2.97490 −0.607248
\(25\) 11.2695 2.25390
\(26\) 2.22041 0.435459
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 6.19131 1.14970 0.574848 0.818260i \(-0.305061\pi\)
0.574848 + 0.818260i \(0.305061\pi\)
\(30\) −5.34094 −0.975117
\(31\) 7.82172 1.40482 0.702411 0.711772i \(-0.252107\pi\)
0.702411 + 0.711772i \(0.252107\pi\)
\(32\) −1.38713 −0.245212
\(33\) −4.32013 −0.752037
\(34\) −2.03250 −0.348571
\(35\) 0 0
\(36\) −0.246682 −0.0411136
\(37\) 5.18274 0.852038 0.426019 0.904714i \(-0.359916\pi\)
0.426019 + 0.904714i \(0.359916\pi\)
\(38\) 6.13364 0.995007
\(39\) 1.67689 0.268517
\(40\) −11.9994 −1.89727
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 4.53487 0.691561 0.345780 0.938316i \(-0.387614\pi\)
0.345780 + 0.938316i \(0.387614\pi\)
\(44\) −1.06570 −0.160660
\(45\) −4.03355 −0.601286
\(46\) −2.22881 −0.328620
\(47\) 7.25662 1.05849 0.529243 0.848470i \(-0.322476\pi\)
0.529243 + 0.848470i \(0.322476\pi\)
\(48\) 3.44578 0.497356
\(49\) 0 0
\(50\) −14.9223 −2.11033
\(51\) −1.53497 −0.214939
\(52\) 0.413657 0.0573639
\(53\) −1.52553 −0.209547 −0.104774 0.994496i \(-0.533412\pi\)
−0.104774 + 0.994496i \(0.533412\pi\)
\(54\) 1.32413 0.180191
\(55\) −17.4254 −2.34964
\(56\) 0 0
\(57\) 4.63220 0.613550
\(58\) −8.19809 −1.07646
\(59\) −6.75314 −0.879183 −0.439592 0.898198i \(-0.644877\pi\)
−0.439592 + 0.898198i \(0.644877\pi\)
\(60\) −0.995003 −0.128454
\(61\) 1.19486 0.152986 0.0764931 0.997070i \(-0.475628\pi\)
0.0764931 + 0.997070i \(0.475628\pi\)
\(62\) −10.3570 −1.31534
\(63\) 0 0
\(64\) 8.72831 1.09104
\(65\) 6.76380 0.838946
\(66\) 5.72040 0.704133
\(67\) 3.40655 0.416176 0.208088 0.978110i \(-0.433276\pi\)
0.208088 + 0.978110i \(0.433276\pi\)
\(68\) −0.378649 −0.0459180
\(69\) −1.68322 −0.202636
\(70\) 0 0
\(71\) −16.5966 −1.96965 −0.984825 0.173548i \(-0.944477\pi\)
−0.984825 + 0.173548i \(0.944477\pi\)
\(72\) 2.97490 0.350595
\(73\) 5.99200 0.701310 0.350655 0.936505i \(-0.385959\pi\)
0.350655 + 0.936505i \(0.385959\pi\)
\(74\) −6.86262 −0.797763
\(75\) −11.2695 −1.30129
\(76\) 1.14268 0.131074
\(77\) 0 0
\(78\) −2.22041 −0.251412
\(79\) 5.84022 0.657076 0.328538 0.944491i \(-0.393444\pi\)
0.328538 + 0.944491i \(0.393444\pi\)
\(80\) 13.8987 1.55393
\(81\) 1.00000 0.111111
\(82\) −1.32413 −0.146226
\(83\) 0.0883750 0.00970042 0.00485021 0.999988i \(-0.498456\pi\)
0.00485021 + 0.999988i \(0.498456\pi\)
\(84\) 0 0
\(85\) −6.19138 −0.671549
\(86\) −6.00475 −0.647509
\(87\) −6.19131 −0.663778
\(88\) 12.8519 1.37002
\(89\) −10.4911 −1.11206 −0.556028 0.831164i \(-0.687675\pi\)
−0.556028 + 0.831164i \(0.687675\pi\)
\(90\) 5.34094 0.562984
\(91\) 0 0
\(92\) −0.415221 −0.0432898
\(93\) −7.82172 −0.811074
\(94\) −9.60870 −0.991062
\(95\) 18.6842 1.91696
\(96\) 1.38713 0.141573
\(97\) 2.82381 0.286714 0.143357 0.989671i \(-0.454210\pi\)
0.143357 + 0.989671i \(0.454210\pi\)
\(98\) 0 0
\(99\) 4.32013 0.434189
\(100\) −2.77998 −0.277998
\(101\) 8.90913 0.886491 0.443246 0.896400i \(-0.353827\pi\)
0.443246 + 0.896400i \(0.353827\pi\)
\(102\) 2.03250 0.201247
\(103\) −13.2664 −1.30717 −0.653587 0.756852i \(-0.726737\pi\)
−0.653587 + 0.756852i \(0.726737\pi\)
\(104\) −4.98856 −0.489169
\(105\) 0 0
\(106\) 2.01999 0.196199
\(107\) −5.74268 −0.555166 −0.277583 0.960702i \(-0.589533\pi\)
−0.277583 + 0.960702i \(0.589533\pi\)
\(108\) 0.246682 0.0237370
\(109\) 4.22346 0.404534 0.202267 0.979330i \(-0.435169\pi\)
0.202267 + 0.979330i \(0.435169\pi\)
\(110\) 23.0735 2.19997
\(111\) −5.18274 −0.491924
\(112\) 0 0
\(113\) −11.5807 −1.08942 −0.544712 0.838623i \(-0.683361\pi\)
−0.544712 + 0.838623i \(0.683361\pi\)
\(114\) −6.13364 −0.574468
\(115\) −6.78937 −0.633112
\(116\) −1.52728 −0.141805
\(117\) −1.67689 −0.155028
\(118\) 8.94203 0.823180
\(119\) 0 0
\(120\) 11.9994 1.09539
\(121\) 7.66349 0.696681
\(122\) −1.58215 −0.143241
\(123\) −1.00000 −0.0901670
\(124\) −1.92947 −0.173272
\(125\) −25.2883 −2.26186
\(126\) 0 0
\(127\) −10.8178 −0.959923 −0.479961 0.877290i \(-0.659349\pi\)
−0.479961 + 0.877290i \(0.659349\pi\)
\(128\) −8.78315 −0.776328
\(129\) −4.53487 −0.399273
\(130\) −8.95615 −0.785506
\(131\) −5.17202 −0.451881 −0.225941 0.974141i \(-0.572546\pi\)
−0.225941 + 0.974141i \(0.572546\pi\)
\(132\) 1.06570 0.0927570
\(133\) 0 0
\(134\) −4.51071 −0.389666
\(135\) 4.03355 0.347152
\(136\) 4.56638 0.391564
\(137\) −11.4202 −0.975692 −0.487846 0.872930i \(-0.662217\pi\)
−0.487846 + 0.872930i \(0.662217\pi\)
\(138\) 2.22881 0.189729
\(139\) 15.9859 1.35591 0.677954 0.735105i \(-0.262867\pi\)
0.677954 + 0.735105i \(0.262867\pi\)
\(140\) 0 0
\(141\) −7.25662 −0.611118
\(142\) 21.9760 1.84419
\(143\) −7.24436 −0.605804
\(144\) −3.44578 −0.287149
\(145\) −24.9729 −2.07389
\(146\) −7.93418 −0.656637
\(147\) 0 0
\(148\) −1.27849 −0.105091
\(149\) 0.835425 0.0684407 0.0342203 0.999414i \(-0.489105\pi\)
0.0342203 + 0.999414i \(0.489105\pi\)
\(150\) 14.9223 1.21840
\(151\) −0.560915 −0.0456466 −0.0228233 0.999740i \(-0.507266\pi\)
−0.0228233 + 0.999740i \(0.507266\pi\)
\(152\) −13.7803 −1.11773
\(153\) 1.53497 0.124095
\(154\) 0 0
\(155\) −31.5493 −2.53410
\(156\) −0.413657 −0.0331191
\(157\) −14.4460 −1.15292 −0.576458 0.817127i \(-0.695566\pi\)
−0.576458 + 0.817127i \(0.695566\pi\)
\(158\) −7.73320 −0.615221
\(159\) 1.52553 0.120982
\(160\) 5.59505 0.442328
\(161\) 0 0
\(162\) −1.32413 −0.104033
\(163\) 19.5921 1.53457 0.767286 0.641305i \(-0.221607\pi\)
0.767286 + 0.641305i \(0.221607\pi\)
\(164\) −0.246682 −0.0192626
\(165\) 17.4254 1.35657
\(166\) −0.117020 −0.00908251
\(167\) −2.54730 −0.197116 −0.0985579 0.995131i \(-0.531423\pi\)
−0.0985579 + 0.995131i \(0.531423\pi\)
\(168\) 0 0
\(169\) −10.1881 −0.783696
\(170\) 8.19818 0.628772
\(171\) −4.63220 −0.354234
\(172\) −1.11867 −0.0852977
\(173\) −1.24963 −0.0950079 −0.0475039 0.998871i \(-0.515127\pi\)
−0.0475039 + 0.998871i \(0.515127\pi\)
\(174\) 8.19809 0.621496
\(175\) 0 0
\(176\) −14.8862 −1.12209
\(177\) 6.75314 0.507597
\(178\) 13.8916 1.04122
\(179\) −14.2508 −1.06515 −0.532576 0.846382i \(-0.678776\pi\)
−0.532576 + 0.846382i \(0.678776\pi\)
\(180\) 0.995003 0.0741631
\(181\) 24.2245 1.80059 0.900297 0.435275i \(-0.143349\pi\)
0.900297 + 0.435275i \(0.143349\pi\)
\(182\) 0 0
\(183\) −1.19486 −0.0883267
\(184\) 5.00742 0.369152
\(185\) −20.9048 −1.53695
\(186\) 10.3570 0.759409
\(187\) 6.63127 0.484926
\(188\) −1.79008 −0.130555
\(189\) 0 0
\(190\) −24.7403 −1.79485
\(191\) −22.1282 −1.60114 −0.800571 0.599238i \(-0.795470\pi\)
−0.800571 + 0.599238i \(0.795470\pi\)
\(192\) −8.72831 −0.629911
\(193\) −23.9356 −1.72293 −0.861463 0.507821i \(-0.830451\pi\)
−0.861463 + 0.507821i \(0.830451\pi\)
\(194\) −3.73909 −0.268451
\(195\) −6.76380 −0.484366
\(196\) 0 0
\(197\) 23.2050 1.65329 0.826643 0.562727i \(-0.190248\pi\)
0.826643 + 0.562727i \(0.190248\pi\)
\(198\) −5.72040 −0.406531
\(199\) 17.0966 1.21194 0.605972 0.795486i \(-0.292784\pi\)
0.605972 + 0.795486i \(0.292784\pi\)
\(200\) 33.5256 2.37062
\(201\) −3.40655 −0.240279
\(202\) −11.7968 −0.830022
\(203\) 0 0
\(204\) 0.378649 0.0265108
\(205\) −4.03355 −0.281715
\(206\) 17.5664 1.22391
\(207\) 1.68322 0.116992
\(208\) 5.77819 0.400645
\(209\) −20.0117 −1.38424
\(210\) 0 0
\(211\) 20.4613 1.40861 0.704306 0.709897i \(-0.251258\pi\)
0.704306 + 0.709897i \(0.251258\pi\)
\(212\) 0.376319 0.0258457
\(213\) 16.5966 1.13718
\(214\) 7.60405 0.519802
\(215\) −18.2916 −1.24748
\(216\) −2.97490 −0.202416
\(217\) 0 0
\(218\) −5.59240 −0.378765
\(219\) −5.99200 −0.404902
\(220\) 4.29854 0.289807
\(221\) −2.57397 −0.173144
\(222\) 6.86262 0.460589
\(223\) 20.1256 1.34771 0.673854 0.738865i \(-0.264638\pi\)
0.673854 + 0.738865i \(0.264638\pi\)
\(224\) 0 0
\(225\) 11.2695 0.751300
\(226\) 15.3344 1.02003
\(227\) 7.05161 0.468032 0.234016 0.972233i \(-0.424813\pi\)
0.234016 + 0.972233i \(0.424813\pi\)
\(228\) −1.14268 −0.0756759
\(229\) −15.7618 −1.04157 −0.520783 0.853689i \(-0.674360\pi\)
−0.520783 + 0.853689i \(0.674360\pi\)
\(230\) 8.99000 0.592783
\(231\) 0 0
\(232\) 18.4185 1.20923
\(233\) 18.7319 1.22717 0.613583 0.789630i \(-0.289728\pi\)
0.613583 + 0.789630i \(0.289728\pi\)
\(234\) 2.22041 0.145153
\(235\) −29.2699 −1.90936
\(236\) 1.66588 0.108439
\(237\) −5.84022 −0.379363
\(238\) 0 0
\(239\) −16.8693 −1.09119 −0.545593 0.838050i \(-0.683696\pi\)
−0.545593 + 0.838050i \(0.683696\pi\)
\(240\) −13.8987 −0.897159
\(241\) 16.2267 1.04525 0.522627 0.852561i \(-0.324952\pi\)
0.522627 + 0.852561i \(0.324952\pi\)
\(242\) −10.1474 −0.652303
\(243\) −1.00000 −0.0641500
\(244\) −0.294750 −0.0188695
\(245\) 0 0
\(246\) 1.32413 0.0844234
\(247\) 7.76768 0.494246
\(248\) 23.2688 1.47757
\(249\) −0.0883750 −0.00560054
\(250\) 33.4850 2.11778
\(251\) 4.47161 0.282246 0.141123 0.989992i \(-0.454929\pi\)
0.141123 + 0.989992i \(0.454929\pi\)
\(252\) 0 0
\(253\) 7.27174 0.457170
\(254\) 14.3241 0.898776
\(255\) 6.19138 0.387719
\(256\) −5.82659 −0.364162
\(257\) 14.3874 0.897459 0.448730 0.893668i \(-0.351877\pi\)
0.448730 + 0.893668i \(0.351877\pi\)
\(258\) 6.00475 0.373839
\(259\) 0 0
\(260\) −1.66851 −0.103476
\(261\) 6.19131 0.383232
\(262\) 6.84842 0.423097
\(263\) 7.34706 0.453039 0.226520 0.974007i \(-0.427265\pi\)
0.226520 + 0.974007i \(0.427265\pi\)
\(264\) −12.8519 −0.790982
\(265\) 6.15328 0.377993
\(266\) 0 0
\(267\) 10.4911 0.642046
\(268\) −0.840333 −0.0513315
\(269\) −11.1262 −0.678375 −0.339187 0.940719i \(-0.610152\pi\)
−0.339187 + 0.940719i \(0.610152\pi\)
\(270\) −5.34094 −0.325039
\(271\) −9.36079 −0.568627 −0.284314 0.958731i \(-0.591766\pi\)
−0.284314 + 0.958731i \(0.591766\pi\)
\(272\) −5.28918 −0.320703
\(273\) 0 0
\(274\) 15.1218 0.913541
\(275\) 48.6857 2.93586
\(276\) 0.415221 0.0249934
\(277\) 9.20675 0.553180 0.276590 0.960988i \(-0.410796\pi\)
0.276590 + 0.960988i \(0.410796\pi\)
\(278\) −21.1674 −1.26954
\(279\) 7.82172 0.468274
\(280\) 0 0
\(281\) 16.6540 0.993493 0.496747 0.867896i \(-0.334528\pi\)
0.496747 + 0.867896i \(0.334528\pi\)
\(282\) 9.60870 0.572190
\(283\) 28.8253 1.71348 0.856742 0.515745i \(-0.172485\pi\)
0.856742 + 0.515745i \(0.172485\pi\)
\(284\) 4.09407 0.242938
\(285\) −18.6842 −1.10676
\(286\) 9.59247 0.567215
\(287\) 0 0
\(288\) −1.38713 −0.0817374
\(289\) −14.6439 −0.861404
\(290\) 33.0674 1.94178
\(291\) −2.82381 −0.165535
\(292\) −1.47812 −0.0865002
\(293\) 3.68402 0.215223 0.107611 0.994193i \(-0.465680\pi\)
0.107611 + 0.994193i \(0.465680\pi\)
\(294\) 0 0
\(295\) 27.2391 1.58592
\(296\) 15.4181 0.896160
\(297\) −4.32013 −0.250679
\(298\) −1.10621 −0.0640811
\(299\) −2.82258 −0.163234
\(300\) 2.77998 0.160502
\(301\) 0 0
\(302\) 0.742723 0.0427389
\(303\) −8.90913 −0.511816
\(304\) 15.9616 0.915459
\(305\) −4.81953 −0.275965
\(306\) −2.03250 −0.116190
\(307\) 33.3876 1.90553 0.952764 0.303711i \(-0.0982256\pi\)
0.952764 + 0.303711i \(0.0982256\pi\)
\(308\) 0 0
\(309\) 13.2664 0.754697
\(310\) 41.7753 2.37268
\(311\) −20.4085 −1.15726 −0.578629 0.815591i \(-0.696412\pi\)
−0.578629 + 0.815591i \(0.696412\pi\)
\(312\) 4.98856 0.282422
\(313\) −11.2547 −0.636156 −0.318078 0.948065i \(-0.603037\pi\)
−0.318078 + 0.948065i \(0.603037\pi\)
\(314\) 19.1284 1.07948
\(315\) 0 0
\(316\) −1.44068 −0.0810443
\(317\) 22.7904 1.28004 0.640020 0.768359i \(-0.278926\pi\)
0.640020 + 0.768359i \(0.278926\pi\)
\(318\) −2.01999 −0.113276
\(319\) 26.7472 1.49756
\(320\) −35.2060 −1.96808
\(321\) 5.74268 0.320525
\(322\) 0 0
\(323\) −7.11030 −0.395628
\(324\) −0.246682 −0.0137045
\(325\) −18.8977 −1.04825
\(326\) −25.9425 −1.43682
\(327\) −4.22346 −0.233558
\(328\) 2.97490 0.164261
\(329\) 0 0
\(330\) −23.0735 −1.27016
\(331\) −10.1035 −0.555339 −0.277670 0.960677i \(-0.589562\pi\)
−0.277670 + 0.960677i \(0.589562\pi\)
\(332\) −0.0218005 −0.00119646
\(333\) 5.18274 0.284013
\(334\) 3.37295 0.184560
\(335\) −13.7405 −0.750722
\(336\) 0 0
\(337\) −31.8588 −1.73546 −0.867730 0.497036i \(-0.834422\pi\)
−0.867730 + 0.497036i \(0.834422\pi\)
\(338\) 13.4903 0.733775
\(339\) 11.5807 0.628980
\(340\) 1.52730 0.0828295
\(341\) 33.7908 1.82987
\(342\) 6.13364 0.331669
\(343\) 0 0
\(344\) 13.4908 0.727373
\(345\) 6.78937 0.365527
\(346\) 1.65468 0.0889559
\(347\) 9.88435 0.530620 0.265310 0.964163i \(-0.414526\pi\)
0.265310 + 0.964163i \(0.414526\pi\)
\(348\) 1.52728 0.0818709
\(349\) 13.0448 0.698274 0.349137 0.937072i \(-0.386475\pi\)
0.349137 + 0.937072i \(0.386475\pi\)
\(350\) 0 0
\(351\) 1.67689 0.0895056
\(352\) −5.99258 −0.319405
\(353\) 5.78886 0.308110 0.154055 0.988062i \(-0.450767\pi\)
0.154055 + 0.988062i \(0.450767\pi\)
\(354\) −8.94203 −0.475263
\(355\) 66.9431 3.55297
\(356\) 2.58797 0.137162
\(357\) 0 0
\(358\) 18.8698 0.997302
\(359\) −14.4069 −0.760367 −0.380184 0.924911i \(-0.624139\pi\)
−0.380184 + 0.924911i \(0.624139\pi\)
\(360\) −11.9994 −0.632423
\(361\) 2.45732 0.129333
\(362\) −32.0764 −1.68590
\(363\) −7.66349 −0.402229
\(364\) 0 0
\(365\) −24.1690 −1.26506
\(366\) 1.58215 0.0827003
\(367\) 9.22050 0.481306 0.240653 0.970611i \(-0.422638\pi\)
0.240653 + 0.970611i \(0.422638\pi\)
\(368\) −5.80003 −0.302347
\(369\) 1.00000 0.0520579
\(370\) 27.6807 1.43905
\(371\) 0 0
\(372\) 1.92947 0.100039
\(373\) 28.0620 1.45299 0.726497 0.687170i \(-0.241147\pi\)
0.726497 + 0.687170i \(0.241147\pi\)
\(374\) −8.78065 −0.454037
\(375\) 25.2883 1.30588
\(376\) 21.5877 1.11330
\(377\) −10.3821 −0.534706
\(378\) 0 0
\(379\) 25.2699 1.29803 0.649015 0.760776i \(-0.275181\pi\)
0.649015 + 0.760776i \(0.275181\pi\)
\(380\) −4.60906 −0.236440
\(381\) 10.8178 0.554212
\(382\) 29.3006 1.49915
\(383\) 8.13954 0.415911 0.207956 0.978138i \(-0.433319\pi\)
0.207956 + 0.978138i \(0.433319\pi\)
\(384\) 8.78315 0.448213
\(385\) 0 0
\(386\) 31.6939 1.61318
\(387\) 4.53487 0.230520
\(388\) −0.696583 −0.0353636
\(389\) −17.2736 −0.875805 −0.437902 0.899023i \(-0.644278\pi\)
−0.437902 + 0.899023i \(0.644278\pi\)
\(390\) 8.95615 0.453512
\(391\) 2.58370 0.130663
\(392\) 0 0
\(393\) 5.17202 0.260894
\(394\) −30.7264 −1.54797
\(395\) −23.5568 −1.18527
\(396\) −1.06570 −0.0535533
\(397\) −7.38909 −0.370848 −0.185424 0.982659i \(-0.559366\pi\)
−0.185424 + 0.982659i \(0.559366\pi\)
\(398\) −22.6381 −1.13474
\(399\) 0 0
\(400\) −38.8323 −1.94161
\(401\) 15.2580 0.761948 0.380974 0.924586i \(-0.375589\pi\)
0.380974 + 0.924586i \(0.375589\pi\)
\(402\) 4.51071 0.224974
\(403\) −13.1161 −0.653361
\(404\) −2.19772 −0.109341
\(405\) −4.03355 −0.200429
\(406\) 0 0
\(407\) 22.3901 1.10984
\(408\) −4.56638 −0.226069
\(409\) −18.3573 −0.907709 −0.453854 0.891076i \(-0.649951\pi\)
−0.453854 + 0.891076i \(0.649951\pi\)
\(410\) 5.34094 0.263770
\(411\) 11.4202 0.563316
\(412\) 3.27257 0.161228
\(413\) 0 0
\(414\) −2.22881 −0.109540
\(415\) −0.356465 −0.0174982
\(416\) 2.32606 0.114044
\(417\) −15.9859 −0.782833
\(418\) 26.4981 1.29606
\(419\) 23.9322 1.16917 0.584583 0.811334i \(-0.301258\pi\)
0.584583 + 0.811334i \(0.301258\pi\)
\(420\) 0 0
\(421\) 22.6662 1.10468 0.552341 0.833619i \(-0.313735\pi\)
0.552341 + 0.833619i \(0.313735\pi\)
\(422\) −27.0934 −1.31888
\(423\) 7.25662 0.352829
\(424\) −4.53828 −0.220398
\(425\) 17.2984 0.839093
\(426\) −21.9760 −1.06474
\(427\) 0 0
\(428\) 1.41662 0.0684747
\(429\) 7.24436 0.349761
\(430\) 24.2204 1.16801
\(431\) 35.5576 1.71275 0.856376 0.516353i \(-0.172711\pi\)
0.856376 + 0.516353i \(0.172711\pi\)
\(432\) 3.44578 0.165785
\(433\) −28.7162 −1.38001 −0.690007 0.723803i \(-0.742392\pi\)
−0.690007 + 0.723803i \(0.742392\pi\)
\(434\) 0 0
\(435\) 24.9729 1.19736
\(436\) −1.04185 −0.0498955
\(437\) −7.79704 −0.372983
\(438\) 7.93418 0.379110
\(439\) 10.1913 0.486404 0.243202 0.969976i \(-0.421802\pi\)
0.243202 + 0.969976i \(0.421802\pi\)
\(440\) −51.8389 −2.47132
\(441\) 0 0
\(442\) 3.40827 0.162115
\(443\) −11.5843 −0.550386 −0.275193 0.961389i \(-0.588742\pi\)
−0.275193 + 0.961389i \(0.588742\pi\)
\(444\) 1.27849 0.0606744
\(445\) 42.3164 2.00599
\(446\) −26.6489 −1.26186
\(447\) −0.835425 −0.0395143
\(448\) 0 0
\(449\) −34.2850 −1.61801 −0.809004 0.587803i \(-0.799993\pi\)
−0.809004 + 0.587803i \(0.799993\pi\)
\(450\) −14.9223 −0.703443
\(451\) 4.32013 0.203427
\(452\) 2.85676 0.134371
\(453\) 0.560915 0.0263541
\(454\) −9.33725 −0.438219
\(455\) 0 0
\(456\) 13.7803 0.645323
\(457\) 1.34031 0.0626970 0.0313485 0.999509i \(-0.490020\pi\)
0.0313485 + 0.999509i \(0.490020\pi\)
\(458\) 20.8706 0.975219
\(459\) −1.53497 −0.0716463
\(460\) 1.67481 0.0780885
\(461\) 28.1737 1.31218 0.656089 0.754683i \(-0.272209\pi\)
0.656089 + 0.754683i \(0.272209\pi\)
\(462\) 0 0
\(463\) −25.4603 −1.18324 −0.591620 0.806217i \(-0.701512\pi\)
−0.591620 + 0.806217i \(0.701512\pi\)
\(464\) −21.3339 −0.990402
\(465\) 31.5493 1.46306
\(466\) −24.8034 −1.14900
\(467\) 6.52537 0.301958 0.150979 0.988537i \(-0.451757\pi\)
0.150979 + 0.988537i \(0.451757\pi\)
\(468\) 0.413657 0.0191213
\(469\) 0 0
\(470\) 38.7572 1.78773
\(471\) 14.4460 0.665637
\(472\) −20.0899 −0.924712
\(473\) 19.5912 0.900804
\(474\) 7.73320 0.355198
\(475\) −52.2026 −2.39522
\(476\) 0 0
\(477\) −1.52553 −0.0698490
\(478\) 22.3372 1.02168
\(479\) −6.79632 −0.310532 −0.155266 0.987873i \(-0.549623\pi\)
−0.155266 + 0.987873i \(0.549623\pi\)
\(480\) −5.59505 −0.255378
\(481\) −8.69087 −0.396270
\(482\) −21.4863 −0.978673
\(483\) 0 0
\(484\) −1.89044 −0.0859292
\(485\) −11.3900 −0.517192
\(486\) 1.32413 0.0600637
\(487\) 4.67769 0.211967 0.105983 0.994368i \(-0.466201\pi\)
0.105983 + 0.994368i \(0.466201\pi\)
\(488\) 3.55459 0.160909
\(489\) −19.5921 −0.885986
\(490\) 0 0
\(491\) 30.9925 1.39867 0.699336 0.714793i \(-0.253479\pi\)
0.699336 + 0.714793i \(0.253479\pi\)
\(492\) 0.246682 0.0111213
\(493\) 9.50347 0.428015
\(494\) −10.2854 −0.462763
\(495\) −17.4254 −0.783215
\(496\) −26.9519 −1.21018
\(497\) 0 0
\(498\) 0.117020 0.00524379
\(499\) −15.1164 −0.676702 −0.338351 0.941020i \(-0.609869\pi\)
−0.338351 + 0.941020i \(0.609869\pi\)
\(500\) 6.23817 0.278980
\(501\) 2.54730 0.113805
\(502\) −5.92099 −0.264267
\(503\) −31.9345 −1.42389 −0.711944 0.702237i \(-0.752185\pi\)
−0.711944 + 0.702237i \(0.752185\pi\)
\(504\) 0 0
\(505\) −35.9354 −1.59910
\(506\) −9.62873 −0.428049
\(507\) 10.1881 0.452467
\(508\) 2.66855 0.118398
\(509\) −31.6661 −1.40357 −0.701787 0.712387i \(-0.747614\pi\)
−0.701787 + 0.712387i \(0.747614\pi\)
\(510\) −8.19818 −0.363022
\(511\) 0 0
\(512\) 25.2815 1.11729
\(513\) 4.63220 0.204517
\(514\) −19.0507 −0.840292
\(515\) 53.5105 2.35795
\(516\) 1.11867 0.0492467
\(517\) 31.3495 1.37875
\(518\) 0 0
\(519\) 1.24963 0.0548528
\(520\) 20.1216 0.882391
\(521\) −33.2889 −1.45841 −0.729207 0.684294i \(-0.760111\pi\)
−0.729207 + 0.684294i \(0.760111\pi\)
\(522\) −8.19809 −0.358821
\(523\) −28.6126 −1.25114 −0.625570 0.780168i \(-0.715134\pi\)
−0.625570 + 0.780168i \(0.715134\pi\)
\(524\) 1.27584 0.0557354
\(525\) 0 0
\(526\) −9.72846 −0.424181
\(527\) 12.0061 0.522994
\(528\) 14.8862 0.647840
\(529\) −20.1668 −0.876815
\(530\) −8.14774 −0.353915
\(531\) −6.75314 −0.293061
\(532\) 0 0
\(533\) −1.67689 −0.0726340
\(534\) −13.8916 −0.601148
\(535\) 23.1634 1.00144
\(536\) 10.1341 0.437727
\(537\) 14.2508 0.614966
\(538\) 14.7325 0.635163
\(539\) 0 0
\(540\) −0.995003 −0.0428181
\(541\) −26.4485 −1.13711 −0.568554 0.822646i \(-0.692497\pi\)
−0.568554 + 0.822646i \(0.692497\pi\)
\(542\) 12.3949 0.532406
\(543\) −24.2245 −1.03957
\(544\) −2.12920 −0.0912889
\(545\) −17.0355 −0.729721
\(546\) 0 0
\(547\) 25.0439 1.07080 0.535401 0.844598i \(-0.320161\pi\)
0.535401 + 0.844598i \(0.320161\pi\)
\(548\) 2.81715 0.120343
\(549\) 1.19486 0.0509954
\(550\) −64.4661 −2.74884
\(551\) −28.6794 −1.22178
\(552\) −5.00742 −0.213130
\(553\) 0 0
\(554\) −12.1909 −0.517943
\(555\) 20.9048 0.887361
\(556\) −3.94343 −0.167239
\(557\) −9.72009 −0.411853 −0.205927 0.978567i \(-0.566021\pi\)
−0.205927 + 0.978567i \(0.566021\pi\)
\(558\) −10.3570 −0.438445
\(559\) −7.60446 −0.321634
\(560\) 0 0
\(561\) −6.63127 −0.279972
\(562\) −22.0520 −0.930208
\(563\) 24.0850 1.01506 0.507531 0.861634i \(-0.330558\pi\)
0.507531 + 0.861634i \(0.330558\pi\)
\(564\) 1.79008 0.0753758
\(565\) 46.7115 1.96517
\(566\) −38.1684 −1.60434
\(567\) 0 0
\(568\) −49.3731 −2.07165
\(569\) −17.7779 −0.745289 −0.372644 0.927974i \(-0.621549\pi\)
−0.372644 + 0.927974i \(0.621549\pi\)
\(570\) 24.7403 1.03626
\(571\) −39.5045 −1.65321 −0.826607 0.562780i \(-0.809732\pi\)
−0.826607 + 0.562780i \(0.809732\pi\)
\(572\) 1.78705 0.0747204
\(573\) 22.1282 0.924419
\(574\) 0 0
\(575\) 18.9691 0.791066
\(576\) 8.72831 0.363680
\(577\) 15.7384 0.655200 0.327600 0.944817i \(-0.393760\pi\)
0.327600 + 0.944817i \(0.393760\pi\)
\(578\) 19.3904 0.806533
\(579\) 23.9356 0.994732
\(580\) 6.16037 0.255795
\(581\) 0 0
\(582\) 3.73909 0.154990
\(583\) −6.59046 −0.272949
\(584\) 17.8256 0.737627
\(585\) 6.76380 0.279649
\(586\) −4.87812 −0.201513
\(587\) −43.9906 −1.81569 −0.907843 0.419310i \(-0.862272\pi\)
−0.907843 + 0.419310i \(0.862272\pi\)
\(588\) 0 0
\(589\) −36.2318 −1.49290
\(590\) −36.0681 −1.48490
\(591\) −23.2050 −0.954525
\(592\) −17.8586 −0.733984
\(593\) 42.6855 1.75288 0.876442 0.481507i \(-0.159910\pi\)
0.876442 + 0.481507i \(0.159910\pi\)
\(594\) 5.72040 0.234711
\(595\) 0 0
\(596\) −0.206084 −0.00844154
\(597\) −17.0966 −0.699716
\(598\) 3.73746 0.152836
\(599\) 43.1503 1.76307 0.881537 0.472114i \(-0.156509\pi\)
0.881537 + 0.472114i \(0.156509\pi\)
\(600\) −33.5256 −1.36868
\(601\) −37.9513 −1.54806 −0.774032 0.633146i \(-0.781763\pi\)
−0.774032 + 0.633146i \(0.781763\pi\)
\(602\) 0 0
\(603\) 3.40655 0.138725
\(604\) 0.138367 0.00563009
\(605\) −30.9110 −1.25671
\(606\) 11.7968 0.479214
\(607\) 45.1372 1.83206 0.916031 0.401107i \(-0.131374\pi\)
0.916031 + 0.401107i \(0.131374\pi\)
\(608\) 6.42547 0.260587
\(609\) 0 0
\(610\) 6.38168 0.258387
\(611\) −12.1685 −0.492286
\(612\) −0.378649 −0.0153060
\(613\) −0.969393 −0.0391534 −0.0195767 0.999808i \(-0.506232\pi\)
−0.0195767 + 0.999808i \(0.506232\pi\)
\(614\) −44.2094 −1.78415
\(615\) 4.03355 0.162648
\(616\) 0 0
\(617\) 47.4830 1.91160 0.955798 0.294025i \(-0.0949951\pi\)
0.955798 + 0.294025i \(0.0949951\pi\)
\(618\) −17.5664 −0.706623
\(619\) −30.0585 −1.20815 −0.604076 0.796927i \(-0.706458\pi\)
−0.604076 + 0.796927i \(0.706458\pi\)
\(620\) 7.78263 0.312558
\(621\) −1.68322 −0.0675455
\(622\) 27.0235 1.08354
\(623\) 0 0
\(624\) −5.77819 −0.231313
\(625\) 45.6542 1.82617
\(626\) 14.9027 0.595633
\(627\) 20.0117 0.799191
\(628\) 3.56357 0.142202
\(629\) 7.95536 0.317201
\(630\) 0 0
\(631\) 35.9101 1.42956 0.714780 0.699350i \(-0.246527\pi\)
0.714780 + 0.699350i \(0.246527\pi\)
\(632\) 17.3740 0.691103
\(633\) −20.4613 −0.813262
\(634\) −30.1775 −1.19850
\(635\) 43.6340 1.73156
\(636\) −0.376319 −0.0149220
\(637\) 0 0
\(638\) −35.4168 −1.40216
\(639\) −16.5966 −0.656550
\(640\) 35.4272 1.40038
\(641\) 24.6578 0.973924 0.486962 0.873423i \(-0.338105\pi\)
0.486962 + 0.873423i \(0.338105\pi\)
\(642\) −7.60405 −0.300108
\(643\) −4.55930 −0.179801 −0.0899007 0.995951i \(-0.528655\pi\)
−0.0899007 + 0.995951i \(0.528655\pi\)
\(644\) 0 0
\(645\) 18.2916 0.720231
\(646\) 9.41495 0.370426
\(647\) −27.0812 −1.06467 −0.532335 0.846534i \(-0.678685\pi\)
−0.532335 + 0.846534i \(0.678685\pi\)
\(648\) 2.97490 0.116865
\(649\) −29.1744 −1.14520
\(650\) 25.0230 0.981481
\(651\) 0 0
\(652\) −4.83302 −0.189276
\(653\) 38.7977 1.51827 0.759136 0.650932i \(-0.225622\pi\)
0.759136 + 0.650932i \(0.225622\pi\)
\(654\) 5.59240 0.218680
\(655\) 20.8616 0.815129
\(656\) −3.44578 −0.134535
\(657\) 5.99200 0.233770
\(658\) 0 0
\(659\) −46.7303 −1.82035 −0.910176 0.414222i \(-0.864054\pi\)
−0.910176 + 0.414222i \(0.864054\pi\)
\(660\) −4.29854 −0.167320
\(661\) 23.1898 0.901978 0.450989 0.892529i \(-0.351071\pi\)
0.450989 + 0.892529i \(0.351071\pi\)
\(662\) 13.3784 0.519965
\(663\) 2.57397 0.0999647
\(664\) 0.262907 0.0102028
\(665\) 0 0
\(666\) −6.86262 −0.265921
\(667\) 10.4214 0.403517
\(668\) 0.628372 0.0243125
\(669\) −20.1256 −0.778100
\(670\) 18.1941 0.702901
\(671\) 5.16195 0.199275
\(672\) 0 0
\(673\) 28.4829 1.09794 0.548968 0.835844i \(-0.315021\pi\)
0.548968 + 0.835844i \(0.315021\pi\)
\(674\) 42.1852 1.62491
\(675\) −11.2695 −0.433763
\(676\) 2.51321 0.0966618
\(677\) −44.6726 −1.71691 −0.858454 0.512891i \(-0.828574\pi\)
−0.858454 + 0.512891i \(0.828574\pi\)
\(678\) −15.3344 −0.588914
\(679\) 0 0
\(680\) −18.4187 −0.706325
\(681\) −7.05161 −0.270218
\(682\) −44.7434 −1.71331
\(683\) 11.0672 0.423473 0.211736 0.977327i \(-0.432088\pi\)
0.211736 + 0.977327i \(0.432088\pi\)
\(684\) 1.14268 0.0436915
\(685\) 46.0638 1.76001
\(686\) 0 0
\(687\) 15.7618 0.601349
\(688\) −15.6262 −0.595742
\(689\) 2.55813 0.0974571
\(690\) −8.99000 −0.342243
\(691\) −29.2076 −1.11111 −0.555555 0.831480i \(-0.687494\pi\)
−0.555555 + 0.831480i \(0.687494\pi\)
\(692\) 0.308262 0.0117184
\(693\) 0 0
\(694\) −13.0882 −0.496819
\(695\) −64.4799 −2.44586
\(696\) −18.4185 −0.698151
\(697\) 1.53497 0.0581412
\(698\) −17.2730 −0.653795
\(699\) −18.7319 −0.708505
\(700\) 0 0
\(701\) 16.9978 0.641999 0.321000 0.947079i \(-0.395981\pi\)
0.321000 + 0.947079i \(0.395981\pi\)
\(702\) −2.22041 −0.0838041
\(703\) −24.0075 −0.905461
\(704\) 37.7074 1.42115
\(705\) 29.2699 1.10237
\(706\) −7.66519 −0.288483
\(707\) 0 0
\(708\) −1.66588 −0.0626074
\(709\) 44.0489 1.65429 0.827145 0.561988i \(-0.189963\pi\)
0.827145 + 0.561988i \(0.189963\pi\)
\(710\) −88.6413 −3.32665
\(711\) 5.84022 0.219025
\(712\) −31.2100 −1.16964
\(713\) 13.1657 0.493059
\(714\) 0 0
\(715\) 29.2205 1.09278
\(716\) 3.51540 0.131377
\(717\) 16.8693 0.629997
\(718\) 19.0766 0.711933
\(719\) 36.5360 1.36256 0.681282 0.732021i \(-0.261423\pi\)
0.681282 + 0.732021i \(0.261423\pi\)
\(720\) 13.8987 0.517975
\(721\) 0 0
\(722\) −3.25381 −0.121094
\(723\) −16.2267 −0.603478
\(724\) −5.97575 −0.222087
\(725\) 69.7729 2.59130
\(726\) 10.1474 0.376607
\(727\) −50.5977 −1.87656 −0.938282 0.345870i \(-0.887584\pi\)
−0.938282 + 0.345870i \(0.887584\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 32.0029 1.18448
\(731\) 6.96089 0.257458
\(732\) 0.294750 0.0108943
\(733\) −8.66771 −0.320149 −0.160075 0.987105i \(-0.551173\pi\)
−0.160075 + 0.987105i \(0.551173\pi\)
\(734\) −12.2091 −0.450647
\(735\) 0 0
\(736\) −2.33485 −0.0860638
\(737\) 14.7167 0.542097
\(738\) −1.32413 −0.0487419
\(739\) −6.55816 −0.241246 −0.120623 0.992698i \(-0.538489\pi\)
−0.120623 + 0.992698i \(0.538489\pi\)
\(740\) 5.15684 0.189569
\(741\) −7.76768 −0.285353
\(742\) 0 0
\(743\) 31.3630 1.15060 0.575298 0.817944i \(-0.304886\pi\)
0.575298 + 0.817944i \(0.304886\pi\)
\(744\) −23.2688 −0.853076
\(745\) −3.36973 −0.123457
\(746\) −37.1577 −1.36044
\(747\) 0.0883750 0.00323347
\(748\) −1.63581 −0.0598112
\(749\) 0 0
\(750\) −33.4850 −1.22270
\(751\) 35.9531 1.31195 0.655973 0.754785i \(-0.272259\pi\)
0.655973 + 0.754785i \(0.272259\pi\)
\(752\) −25.0047 −0.911829
\(753\) −4.47161 −0.162955
\(754\) 13.7473 0.500646
\(755\) 2.26248 0.0823399
\(756\) 0 0
\(757\) 16.1675 0.587617 0.293808 0.955864i \(-0.405077\pi\)
0.293808 + 0.955864i \(0.405077\pi\)
\(758\) −33.4607 −1.21535
\(759\) −7.27174 −0.263947
\(760\) 55.5836 2.01623
\(761\) −17.6078 −0.638281 −0.319140 0.947707i \(-0.603394\pi\)
−0.319140 + 0.947707i \(0.603394\pi\)
\(762\) −14.3241 −0.518909
\(763\) 0 0
\(764\) 5.45863 0.197486
\(765\) −6.19138 −0.223850
\(766\) −10.7778 −0.389418
\(767\) 11.3242 0.408895
\(768\) 5.82659 0.210249
\(769\) 26.5362 0.956920 0.478460 0.878109i \(-0.341195\pi\)
0.478460 + 0.878109i \(0.341195\pi\)
\(770\) 0 0
\(771\) −14.3874 −0.518148
\(772\) 5.90449 0.212507
\(773\) −26.1052 −0.938940 −0.469470 0.882949i \(-0.655555\pi\)
−0.469470 + 0.882949i \(0.655555\pi\)
\(774\) −6.00475 −0.215836
\(775\) 88.1468 3.16633
\(776\) 8.40054 0.301562
\(777\) 0 0
\(778\) 22.8724 0.820017
\(779\) −4.63220 −0.165966
\(780\) 1.66851 0.0597421
\(781\) −71.6993 −2.56560
\(782\) −3.42115 −0.122340
\(783\) −6.19131 −0.221259
\(784\) 0 0
\(785\) 58.2686 2.07970
\(786\) −6.84842 −0.244275
\(787\) 5.59220 0.199340 0.0996701 0.995021i \(-0.468221\pi\)
0.0996701 + 0.995021i \(0.468221\pi\)
\(788\) −5.72424 −0.203918
\(789\) −7.34706 −0.261562
\(790\) 31.1922 1.10977
\(791\) 0 0
\(792\) 12.8519 0.456673
\(793\) −2.00365 −0.0711516
\(794\) 9.78411 0.347225
\(795\) −6.15328 −0.218234
\(796\) −4.21741 −0.149482
\(797\) 54.8608 1.94327 0.971634 0.236489i \(-0.0759968\pi\)
0.971634 + 0.236489i \(0.0759968\pi\)
\(798\) 0 0
\(799\) 11.1387 0.394059
\(800\) −15.6323 −0.552684
\(801\) −10.4911 −0.370685
\(802\) −20.2036 −0.713412
\(803\) 25.8862 0.913503
\(804\) 0.840333 0.0296363
\(805\) 0 0
\(806\) 17.3674 0.611742
\(807\) 11.1262 0.391660
\(808\) 26.5037 0.932398
\(809\) −54.6666 −1.92197 −0.960987 0.276593i \(-0.910795\pi\)
−0.960987 + 0.276593i \(0.910795\pi\)
\(810\) 5.34094 0.187661
\(811\) 11.9720 0.420394 0.210197 0.977659i \(-0.432589\pi\)
0.210197 + 0.977659i \(0.432589\pi\)
\(812\) 0 0
\(813\) 9.36079 0.328297
\(814\) −29.6474 −1.03914
\(815\) −79.0257 −2.76815
\(816\) 5.28918 0.185158
\(817\) −21.0064 −0.734922
\(818\) 24.3074 0.849888
\(819\) 0 0
\(820\) 0.995003 0.0347470
\(821\) −9.62125 −0.335784 −0.167892 0.985805i \(-0.553696\pi\)
−0.167892 + 0.985805i \(0.553696\pi\)
\(822\) −15.1218 −0.527433
\(823\) −44.0763 −1.53640 −0.768201 0.640209i \(-0.778848\pi\)
−0.768201 + 0.640209i \(0.778848\pi\)
\(824\) −39.4661 −1.37487
\(825\) −48.6857 −1.69502
\(826\) 0 0
\(827\) 15.7234 0.546758 0.273379 0.961906i \(-0.411859\pi\)
0.273379 + 0.961906i \(0.411859\pi\)
\(828\) −0.415221 −0.0144299
\(829\) −17.0066 −0.590664 −0.295332 0.955395i \(-0.595430\pi\)
−0.295332 + 0.955395i \(0.595430\pi\)
\(830\) 0.472005 0.0163835
\(831\) −9.20675 −0.319379
\(832\) −14.6364 −0.507425
\(833\) 0 0
\(834\) 21.1674 0.732967
\(835\) 10.2746 0.355569
\(836\) 4.93652 0.170733
\(837\) −7.82172 −0.270358
\(838\) −31.6893 −1.09469
\(839\) −26.9183 −0.929325 −0.464662 0.885488i \(-0.653824\pi\)
−0.464662 + 0.885488i \(0.653824\pi\)
\(840\) 0 0
\(841\) 9.33227 0.321803
\(842\) −30.0129 −1.03431
\(843\) −16.6540 −0.573593
\(844\) −5.04742 −0.173739
\(845\) 41.0940 1.41368
\(846\) −9.60870 −0.330354
\(847\) 0 0
\(848\) 5.25663 0.180513
\(849\) −28.8253 −0.989281
\(850\) −22.9053 −0.785644
\(851\) 8.72372 0.299045
\(852\) −4.09407 −0.140261
\(853\) −24.3943 −0.835246 −0.417623 0.908620i \(-0.637137\pi\)
−0.417623 + 0.908620i \(0.637137\pi\)
\(854\) 0 0
\(855\) 18.6842 0.638987
\(856\) −17.0839 −0.583915
\(857\) −31.1527 −1.06416 −0.532078 0.846695i \(-0.678589\pi\)
−0.532078 + 0.846695i \(0.678589\pi\)
\(858\) −9.59247 −0.327481
\(859\) 51.4913 1.75686 0.878430 0.477871i \(-0.158591\pi\)
0.878430 + 0.477871i \(0.158591\pi\)
\(860\) 4.51220 0.153865
\(861\) 0 0
\(862\) −47.0829 −1.60365
\(863\) −31.1056 −1.05885 −0.529424 0.848358i \(-0.677592\pi\)
−0.529424 + 0.848358i \(0.677592\pi\)
\(864\) 1.38713 0.0471911
\(865\) 5.04046 0.171381
\(866\) 38.0240 1.29211
\(867\) 14.6439 0.497332
\(868\) 0 0
\(869\) 25.2305 0.855885
\(870\) −33.0674 −1.12109
\(871\) −5.71239 −0.193557
\(872\) 12.5643 0.425482
\(873\) 2.82381 0.0955715
\(874\) 10.3243 0.349224
\(875\) 0 0
\(876\) 1.47812 0.0499409
\(877\) 22.9723 0.775720 0.387860 0.921718i \(-0.373214\pi\)
0.387860 + 0.921718i \(0.373214\pi\)
\(878\) −13.4946 −0.455421
\(879\) −3.68402 −0.124259
\(880\) 60.0443 2.02409
\(881\) −0.746180 −0.0251394 −0.0125697 0.999921i \(-0.504001\pi\)
−0.0125697 + 0.999921i \(0.504001\pi\)
\(882\) 0 0
\(883\) −15.0939 −0.507951 −0.253976 0.967211i \(-0.581738\pi\)
−0.253976 + 0.967211i \(0.581738\pi\)
\(884\) 0.634952 0.0213557
\(885\) −27.2391 −0.915632
\(886\) 15.3391 0.515327
\(887\) 21.7017 0.728670 0.364335 0.931268i \(-0.381296\pi\)
0.364335 + 0.931268i \(0.381296\pi\)
\(888\) −15.4181 −0.517398
\(889\) 0 0
\(890\) −56.0324 −1.87821
\(891\) 4.32013 0.144730
\(892\) −4.96461 −0.166227
\(893\) −33.6141 −1.12485
\(894\) 1.10621 0.0369972
\(895\) 57.4811 1.92138
\(896\) 0 0
\(897\) 2.82258 0.0942431
\(898\) 45.3978 1.51494
\(899\) 48.4266 1.61512
\(900\) −2.77998 −0.0926660
\(901\) −2.34164 −0.0780112
\(902\) −5.72040 −0.190469
\(903\) 0 0
\(904\) −34.4515 −1.14584
\(905\) −97.7108 −3.24802
\(906\) −0.742723 −0.0246753
\(907\) 25.6962 0.853227 0.426613 0.904434i \(-0.359707\pi\)
0.426613 + 0.904434i \(0.359707\pi\)
\(908\) −1.73950 −0.0577275
\(909\) 8.90913 0.295497
\(910\) 0 0
\(911\) −5.86146 −0.194199 −0.0970994 0.995275i \(-0.530956\pi\)
−0.0970994 + 0.995275i \(0.530956\pi\)
\(912\) −15.9616 −0.528541
\(913\) 0.381791 0.0126354
\(914\) −1.77474 −0.0587033
\(915\) 4.81953 0.159329
\(916\) 3.88814 0.128468
\(917\) 0 0
\(918\) 2.03250 0.0670825
\(919\) −32.8094 −1.08228 −0.541141 0.840932i \(-0.682008\pi\)
−0.541141 + 0.840932i \(0.682008\pi\)
\(920\) −20.1977 −0.665897
\(921\) −33.3876 −1.10016
\(922\) −37.3056 −1.22859
\(923\) 27.8306 0.916054
\(924\) 0 0
\(925\) 58.4069 1.92041
\(926\) 33.7127 1.10787
\(927\) −13.2664 −0.435724
\(928\) −8.58815 −0.281920
\(929\) 36.4771 1.19678 0.598388 0.801207i \(-0.295808\pi\)
0.598388 + 0.801207i \(0.295808\pi\)
\(930\) −41.7753 −1.36987
\(931\) 0 0
\(932\) −4.62081 −0.151360
\(933\) 20.4085 0.668143
\(934\) −8.64043 −0.282723
\(935\) −26.7475 −0.874738
\(936\) −4.98856 −0.163056
\(937\) 37.8363 1.23606 0.618029 0.786155i \(-0.287931\pi\)
0.618029 + 0.786155i \(0.287931\pi\)
\(938\) 0 0
\(939\) 11.2547 0.367285
\(940\) 7.22036 0.235502
\(941\) 41.6898 1.35905 0.679524 0.733653i \(-0.262186\pi\)
0.679524 + 0.733653i \(0.262186\pi\)
\(942\) −19.1284 −0.623236
\(943\) 1.68322 0.0548133
\(944\) 23.2699 0.757369
\(945\) 0 0
\(946\) −25.9413 −0.843423
\(947\) 14.2571 0.463293 0.231646 0.972800i \(-0.425589\pi\)
0.231646 + 0.972800i \(0.425589\pi\)
\(948\) 1.44068 0.0467910
\(949\) −10.0479 −0.326169
\(950\) 69.1230 2.24265
\(951\) −22.7904 −0.739031
\(952\) 0 0
\(953\) −2.06503 −0.0668930 −0.0334465 0.999441i \(-0.510648\pi\)
−0.0334465 + 0.999441i \(0.510648\pi\)
\(954\) 2.01999 0.0653997
\(955\) 89.2552 2.88823
\(956\) 4.16136 0.134588
\(957\) −26.7472 −0.864615
\(958\) 8.99921 0.290751
\(959\) 0 0
\(960\) 35.2060 1.13627
\(961\) 30.1792 0.973524
\(962\) 11.5078 0.371027
\(963\) −5.74268 −0.185055
\(964\) −4.00284 −0.128923
\(965\) 96.5456 3.10791
\(966\) 0 0
\(967\) −23.1249 −0.743645 −0.371823 0.928304i \(-0.621267\pi\)
−0.371823 + 0.928304i \(0.621267\pi\)
\(968\) 22.7981 0.732758
\(969\) 7.11030 0.228416
\(970\) 15.0818 0.484247
\(971\) 41.3802 1.32795 0.663977 0.747753i \(-0.268867\pi\)
0.663977 + 0.747753i \(0.268867\pi\)
\(972\) 0.246682 0.00791232
\(973\) 0 0
\(974\) −6.19387 −0.198464
\(975\) 18.8977 0.605210
\(976\) −4.11723 −0.131789
\(977\) −14.3806 −0.460076 −0.230038 0.973182i \(-0.573885\pi\)
−0.230038 + 0.973182i \(0.573885\pi\)
\(978\) 25.9425 0.829549
\(979\) −45.3229 −1.44853
\(980\) 0 0
\(981\) 4.22346 0.134845
\(982\) −41.0381 −1.30958
\(983\) −49.7977 −1.58830 −0.794151 0.607721i \(-0.792084\pi\)
−0.794151 + 0.607721i \(0.792084\pi\)
\(984\) −2.97490 −0.0948363
\(985\) −93.5983 −2.98229
\(986\) −12.5838 −0.400751
\(987\) 0 0
\(988\) −1.91615 −0.0609607
\(989\) 7.63320 0.242722
\(990\) 23.0735 0.733325
\(991\) 29.1147 0.924860 0.462430 0.886656i \(-0.346978\pi\)
0.462430 + 0.886656i \(0.346978\pi\)
\(992\) −10.8497 −0.344480
\(993\) 10.1035 0.320625
\(994\) 0 0
\(995\) −68.9598 −2.18617
\(996\) 0.0218005 0.000690775 0
\(997\) 3.91838 0.124096 0.0620481 0.998073i \(-0.480237\pi\)
0.0620481 + 0.998073i \(0.480237\pi\)
\(998\) 20.0161 0.633597
\(999\) −5.18274 −0.163975
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 \(a_p\))