Properties

Label 6027.2.a.bo.1.6
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

Related objects

Downloads

Learn more about

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 \(-0.142151\pi\)
0.901929 + 0.431885i \(0.142151\pi\)
\(6\) −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 \(-0.425296\pi\)
0.232542 + 0.972586i \(0.425296\pi\)
\(14\) 0 0
\(15\) 4.03355 1.04146
\(16\) −3.44578 −0.861446
\(17\) −1.53497 −0.372285 −0.186143 0.982523i \(-0.559599\pi\)
−0.186143 + 0.982523i \(0.559599\pi\)
\(18\) −1.32413 −0.312100
\(19\) 4.63220 1.06270 0.531350 0.847152i \(-0.321685\pi\)
0.531350 + 0.847152i \(0.321685\pi\)
\(20\) −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 \(-0.747893\pi\)
−0.702411 + 0.711772i \(0.747893\pi\)
\(32\) −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 \(-0.677524\pi\)
−0.529243 + 0.848470i \(0.677524\pi\)
\(48\) −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 \(-0.355123\pi\)
0.439592 + 0.898198i \(0.355123\pi\)
\(60\) −0.995003 −0.128454
\(61\) −1.19486 −0.152986 −0.0764931 0.997070i \(-0.524372\pi\)
−0.0764931 + 0.997070i \(0.524372\pi\)
\(62\) 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 \(-0.614041\pi\)
−0.350655 + 0.936505i \(0.614041\pi\)
\(74\) −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 \(-0.501544\pi\)
−0.00485021 + 0.999988i \(0.501544\pi\)
\(84\) 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 \(-0.312325\pi\)
0.556028 + 0.831164i \(0.312325\pi\)
\(90\) −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 \(-0.545790\pi\)
−0.143357 + 0.989671i \(0.545790\pi\)
\(98\) 0 0
\(99\) 4.32013 0.434189
\(100\) −2.77998 −0.277998
\(101\) −8.90913 −0.886491 −0.443246 0.896400i \(-0.646173\pi\)
−0.443246 + 0.896400i \(0.646173\pi\)
\(102\) 2.03250 0.201247
\(103\) 13.2664 1.30717 0.653587 0.756852i \(-0.273263\pi\)
0.653587 + 0.756852i \(0.273263\pi\)
\(104\) 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 \(-0.427454\pi\)
0.225941 + 0.974141i \(0.427454\pi\)
\(132\) −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 \(-0.737133\pi\)
−0.677954 + 0.735105i \(0.737133\pi\)
\(140\) 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 \(-0.304434\pi\)
0.576458 + 0.817127i \(0.304434\pi\)
\(158\) −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 \(-0.468577\pi\)
0.0985579 + 0.995131i \(0.468577\pi\)
\(168\) 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 \(-0.484873\pi\)
0.0475039 + 0.998871i \(0.484873\pi\)
\(174\) −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 \(-0.856651\pi\)
−0.900297 + 0.435275i \(0.856651\pi\)
\(182\) 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 \(-0.707216\pi\)
−0.605972 + 0.795486i \(0.707216\pi\)
\(200\) 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 \(-0.735362\pi\)
−0.673854 + 0.738865i \(0.735362\pi\)
\(224\) 0 0
\(225\) 11.2695 0.751300
\(226\) 15.3344 1.02003
\(227\) −7.05161 −0.468032 −0.234016 0.972233i \(-0.575187\pi\)
−0.234016 + 0.972233i \(0.575187\pi\)
\(228\) −1.14268 −0.0756759
\(229\) 15.7618 1.04157 0.520783 0.853689i \(-0.325640\pi\)
0.520783 + 0.853689i \(0.325640\pi\)
\(230\) −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 \(-0.675048\pi\)
−0.522627 + 0.852561i \(0.675048\pi\)
\(242\) −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 \(-0.545071\pi\)
−0.141123 + 0.989992i \(0.545071\pi\)
\(252\) 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 \(-0.648123\pi\)
−0.448730 + 0.893668i \(0.648123\pi\)
\(258\) −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 \(-0.389848\pi\)
0.339187 + 0.940719i \(0.389848\pi\)
\(270\) −5.34094 −0.325039
\(271\) 9.36079 0.568627 0.284314 0.958731i \(-0.408234\pi\)
0.284314 + 0.958731i \(0.408234\pi\)
\(272\) 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 \(-0.827515\pi\)
−0.856742 + 0.515745i \(0.827515\pi\)
\(284\) 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 \(-0.534320\pi\)
−0.107611 + 0.994193i \(0.534320\pi\)
\(294\) 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 \(-0.901774\pi\)
−0.952764 + 0.303711i \(0.901774\pi\)
\(308\) 0 0
\(309\) 13.2664 0.754697
\(310\) 41.7753 2.37268
\(311\) 20.4085 1.15726 0.578629 0.815591i \(-0.303588\pi\)
0.578629 + 0.815591i \(0.303588\pi\)
\(312\) 4.98856 0.282422
\(313\) 11.2547 0.636156 0.318078 0.948065i \(-0.396963\pi\)
0.318078 + 0.948065i \(0.396963\pi\)
\(314\) −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 \(-0.613525\pi\)
−0.349137 + 0.937072i \(0.613525\pi\)
\(350\) 0 0
\(351\) 1.67689 0.0895056
\(352\) −5.99258 −0.319405
\(353\) −5.78886 −0.308110 −0.154055 0.988062i \(-0.549233\pi\)
−0.154055 + 0.988062i \(0.549233\pi\)
\(354\) −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 \(-0.577362\pi\)
−0.240653 + 0.970611i \(0.577362\pi\)
\(368\) −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 \(-0.566681\pi\)
−0.207956 + 0.978138i \(0.566681\pi\)
\(384\) −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 \(-0.440634\pi\)
0.185424 + 0.982659i \(0.440634\pi\)
\(398\) 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 \(-0.350049\pi\)
0.453854 + 0.891076i \(0.350049\pi\)
\(410\) 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 \(-0.698742\pi\)
−0.584583 + 0.811334i \(0.698742\pi\)
\(420\) 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 \(-0.257608\pi\)
0.690007 + 0.723803i \(0.257608\pi\)
\(434\) 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 \(-0.578198\pi\)
−0.243202 + 0.969976i \(0.578198\pi\)
\(440\) 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 \(-0.727791\pi\)
−0.656089 + 0.754683i \(0.727791\pi\)
\(462\) 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 \(-0.548243\pi\)
−0.150979 + 0.988537i \(0.548243\pi\)
\(468\) −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 \(-0.450377\pi\)
0.155266 + 0.987873i \(0.450377\pi\)
\(480\) −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 \(-0.247815\pi\)
0.711944 + 0.702237i \(0.247815\pi\)
\(504\) 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 \(-0.252386\pi\)
0.701787 + 0.712387i \(0.252386\pi\)
\(510\) 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 \(-0.239889\pi\)
0.729207 + 0.684294i \(0.239889\pi\)
\(522\) −8.19809 −0.358821
\(523\) 28.6126 1.25114 0.625570 0.780168i \(-0.284866\pi\)
0.625570 + 0.780168i \(0.284866\pi\)
\(524\) −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 \(-0.669442\pi\)
−0.507531 + 0.861634i \(0.669442\pi\)
\(564\) 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 \(-0.606240\pi\)
−0.327600 + 0.944817i \(0.606240\pi\)
\(578\) 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 \(-0.137728\pi\)
0.907843 + 0.419310i \(0.137728\pi\)
\(588\) 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 \(-0.840090\pi\)
−0.876442 + 0.481507i \(0.840090\pi\)
\(594\) −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 \(-0.218237\pi\)
0.774032 + 0.633146i \(0.218237\pi\)
\(602\) 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 \(-0.868626\pi\)
−0.916031 + 0.401107i \(0.868626\pi\)
\(608\) −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 \(-0.293542\pi\)
0.604076 + 0.796927i \(0.293542\pi\)
\(620\) 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 \(-0.471345\pi\)
0.0899007 + 0.995951i \(0.471345\pi\)
\(644\) 0 0
\(645\) 18.2916 0.720231
\(646\) 9.41495 0.370426
\(647\) 27.0812 1.06467 0.532335 0.846534i \(-0.321315\pi\)
0.532335 + 0.846534i \(0.321315\pi\)
\(648\) 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 \(-0.648929\pi\)
−0.450989 + 0.892529i \(0.648929\pi\)
\(662\) 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 \(-0.171426\pi\)
0.858454 + 0.512891i \(0.171426\pi\)
\(678\) 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 \(-0.312506\pi\)
0.555555 + 0.831480i \(0.312506\pi\)
\(692\) −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 \(-0.738577\pi\)
−0.681282 + 0.732021i \(0.738577\pi\)
\(720\) −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 \(-0.112416\pi\)
0.938282 + 0.345870i \(0.112416\pi\)
\(728\) 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 \(-0.448827\pi\)
0.160075 + 0.987105i \(0.448827\pi\)
\(734\) 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 \(-0.396606\pi\)
0.319140 + 0.947707i \(0.396606\pi\)
\(762\) 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 \(-0.658805\pi\)
−0.478460 + 0.878109i \(0.658805\pi\)
\(770\) 0 0
\(771\) −14.3874 −0.518148
\(772\) 5.90449 0.212507
\(773\) 26.1052 0.938940 0.469470 0.882949i \(-0.344445\pi\)
0.469470 + 0.882949i \(0.344445\pi\)
\(774\) −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 \(-0.531779\pi\)
−0.0996701 + 0.995021i \(0.531779\pi\)
\(788\) −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 \(-0.924003\pi\)
−0.971634 + 0.236489i \(0.924003\pi\)
\(798\) 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 \(-0.567411\pi\)
−0.210197 + 0.977659i \(0.567411\pi\)
\(812\) 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 \(-0.404570\pi\)
0.295332 + 0.955395i \(0.404570\pi\)
\(830\) 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 \(-0.346176\pi\)
0.464662 + 0.885488i \(0.346176\pi\)
\(840\) 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 \(-0.362863\pi\)
0.417623 + 0.908620i \(0.362863\pi\)
\(854\) 0 0
\(855\) 18.6842 0.638987
\(856\) −17.0839 −0.583915
\(857\) 31.1527 1.06416 0.532078 0.846695i \(-0.321411\pi\)
0.532078 + 0.846695i \(0.321411\pi\)
\(858\) −9.59247 −0.327481
\(859\) −51.4913 −1.75686 −0.878430 0.477871i \(-0.841409\pi\)
−0.878430 + 0.477871i \(0.841409\pi\)
\(860\) −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 \(-0.495999\pi\)
0.0125697 + 0.999921i \(0.495999\pi\)
\(882\) 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 \(-0.618704\pi\)
−0.364335 + 0.931268i \(0.618704\pi\)
\(888\) 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 \(-0.704192\pi\)
−0.598388 + 0.801207i \(0.704192\pi\)
\(930\) 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 \(-0.712069\pi\)
−0.618029 + 0.786155i \(0.712069\pi\)
\(938\) 0 0
\(939\) 11.2547 0.367285
\(940\) 7.22036 0.235502
\(941\) −41.6898 −1.35905 −0.679524 0.733653i \(-0.737814\pi\)
−0.679524 + 0.733653i \(0.737814\pi\)
\(942\) −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 \(-0.731133\pi\)
−0.663977 + 0.747753i \(0.731133\pi\)
\(972\) −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 \(-0.207916\pi\)
0.794151 + 0.607721i \(0.207916\pi\)
\(984\) −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 \(-0.519763\pi\)
−0.0620481 + 0.998073i \(0.519763\pi\)
\(998\) 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 \(a_p\))