Properties

Label 6008.2.a.e.1.28
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.28
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.363113 q^{3} +1.56553 q^{5} +3.79058 q^{7} -2.86815 q^{9} +O(q^{10})\) \(q+0.363113 q^{3} +1.56553 q^{5} +3.79058 q^{7} -2.86815 q^{9} -0.247976 q^{11} +4.99282 q^{13} +0.568466 q^{15} +5.01347 q^{17} -8.47134 q^{19} +1.37641 q^{21} +5.06856 q^{23} -2.54911 q^{25} -2.13080 q^{27} +0.226828 q^{29} -3.67858 q^{31} -0.0900433 q^{33} +5.93428 q^{35} +2.82049 q^{37} +1.81296 q^{39} +4.03334 q^{41} +3.40433 q^{43} -4.49018 q^{45} +7.95479 q^{47} +7.36851 q^{49} +1.82046 q^{51} +4.00370 q^{53} -0.388214 q^{55} -3.07606 q^{57} +8.61749 q^{59} -1.44468 q^{61} -10.8720 q^{63} +7.81642 q^{65} +13.6298 q^{67} +1.84046 q^{69} +0.864128 q^{71} -2.13913 q^{73} -0.925615 q^{75} -0.939972 q^{77} -12.9958 q^{79} +7.83072 q^{81} -12.6165 q^{83} +7.84876 q^{85} +0.0823642 q^{87} +11.5379 q^{89} +18.9257 q^{91} -1.33574 q^{93} -13.2622 q^{95} +1.16300 q^{97} +0.711231 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.363113 0.209644 0.104822 0.994491i \(-0.466573\pi\)
0.104822 + 0.994491i \(0.466573\pi\)
\(4\) 0 0
\(5\) 1.56553 0.700128 0.350064 0.936726i \(-0.386160\pi\)
0.350064 + 0.936726i \(0.386160\pi\)
\(6\) 0 0
\(7\) 3.79058 1.43271 0.716353 0.697738i \(-0.245810\pi\)
0.716353 + 0.697738i \(0.245810\pi\)
\(8\) 0 0
\(9\) −2.86815 −0.956050
\(10\) 0 0
\(11\) −0.247976 −0.0747675 −0.0373838 0.999301i \(-0.511902\pi\)
−0.0373838 + 0.999301i \(0.511902\pi\)
\(12\) 0 0
\(13\) 4.99282 1.38476 0.692380 0.721533i \(-0.256562\pi\)
0.692380 + 0.721533i \(0.256562\pi\)
\(14\) 0 0
\(15\) 0.568466 0.146777
\(16\) 0 0
\(17\) 5.01347 1.21595 0.607973 0.793958i \(-0.291983\pi\)
0.607973 + 0.793958i \(0.291983\pi\)
\(18\) 0 0
\(19\) −8.47134 −1.94346 −0.971729 0.236097i \(-0.924132\pi\)
−0.971729 + 0.236097i \(0.924132\pi\)
\(20\) 0 0
\(21\) 1.37641 0.300358
\(22\) 0 0
\(23\) 5.06856 1.05687 0.528434 0.848974i \(-0.322779\pi\)
0.528434 + 0.848974i \(0.322779\pi\)
\(24\) 0 0
\(25\) −2.54911 −0.509821
\(26\) 0 0
\(27\) −2.13080 −0.410073
\(28\) 0 0
\(29\) 0.226828 0.0421209 0.0210604 0.999778i \(-0.493296\pi\)
0.0210604 + 0.999778i \(0.493296\pi\)
\(30\) 0 0
\(31\) −3.67858 −0.660693 −0.330347 0.943860i \(-0.607166\pi\)
−0.330347 + 0.943860i \(0.607166\pi\)
\(32\) 0 0
\(33\) −0.0900433 −0.0156745
\(34\) 0 0
\(35\) 5.93428 1.00308
\(36\) 0 0
\(37\) 2.82049 0.463686 0.231843 0.972753i \(-0.425524\pi\)
0.231843 + 0.972753i \(0.425524\pi\)
\(38\) 0 0
\(39\) 1.81296 0.290306
\(40\) 0 0
\(41\) 4.03334 0.629902 0.314951 0.949108i \(-0.398012\pi\)
0.314951 + 0.949108i \(0.398012\pi\)
\(42\) 0 0
\(43\) 3.40433 0.519155 0.259578 0.965722i \(-0.416417\pi\)
0.259578 + 0.965722i \(0.416417\pi\)
\(44\) 0 0
\(45\) −4.49018 −0.669357
\(46\) 0 0
\(47\) 7.95479 1.16033 0.580163 0.814501i \(-0.302989\pi\)
0.580163 + 0.814501i \(0.302989\pi\)
\(48\) 0 0
\(49\) 7.36851 1.05264
\(50\) 0 0
\(51\) 1.82046 0.254915
\(52\) 0 0
\(53\) 4.00370 0.549950 0.274975 0.961451i \(-0.411330\pi\)
0.274975 + 0.961451i \(0.411330\pi\)
\(54\) 0 0
\(55\) −0.388214 −0.0523468
\(56\) 0 0
\(57\) −3.07606 −0.407434
\(58\) 0 0
\(59\) 8.61749 1.12190 0.560951 0.827849i \(-0.310436\pi\)
0.560951 + 0.827849i \(0.310436\pi\)
\(60\) 0 0
\(61\) −1.44468 −0.184972 −0.0924859 0.995714i \(-0.529481\pi\)
−0.0924859 + 0.995714i \(0.529481\pi\)
\(62\) 0 0
\(63\) −10.8720 −1.36974
\(64\) 0 0
\(65\) 7.81642 0.969508
\(66\) 0 0
\(67\) 13.6298 1.66514 0.832570 0.553920i \(-0.186869\pi\)
0.832570 + 0.553920i \(0.186869\pi\)
\(68\) 0 0
\(69\) 1.84046 0.221566
\(70\) 0 0
\(71\) 0.864128 0.102553 0.0512766 0.998684i \(-0.483671\pi\)
0.0512766 + 0.998684i \(0.483671\pi\)
\(72\) 0 0
\(73\) −2.13913 −0.250366 −0.125183 0.992134i \(-0.539952\pi\)
−0.125183 + 0.992134i \(0.539952\pi\)
\(74\) 0 0
\(75\) −0.925615 −0.106881
\(76\) 0 0
\(77\) −0.939972 −0.107120
\(78\) 0 0
\(79\) −12.9958 −1.46214 −0.731071 0.682302i \(-0.760979\pi\)
−0.731071 + 0.682302i \(0.760979\pi\)
\(80\) 0 0
\(81\) 7.83072 0.870080
\(82\) 0 0
\(83\) −12.6165 −1.38485 −0.692423 0.721492i \(-0.743457\pi\)
−0.692423 + 0.721492i \(0.743457\pi\)
\(84\) 0 0
\(85\) 7.84876 0.851317
\(86\) 0 0
\(87\) 0.0823642 0.00883037
\(88\) 0 0
\(89\) 11.5379 1.22301 0.611506 0.791240i \(-0.290564\pi\)
0.611506 + 0.791240i \(0.290564\pi\)
\(90\) 0 0
\(91\) 18.9257 1.98395
\(92\) 0 0
\(93\) −1.33574 −0.138510
\(94\) 0 0
\(95\) −13.2622 −1.36067
\(96\) 0 0
\(97\) 1.16300 0.118084 0.0590422 0.998255i \(-0.481195\pi\)
0.0590422 + 0.998255i \(0.481195\pi\)
\(98\) 0 0
\(99\) 0.711231 0.0714814
\(100\) 0 0
\(101\) 7.04166 0.700671 0.350336 0.936624i \(-0.386068\pi\)
0.350336 + 0.936624i \(0.386068\pi\)
\(102\) 0 0
\(103\) −19.0516 −1.87721 −0.938603 0.345000i \(-0.887879\pi\)
−0.938603 + 0.345000i \(0.887879\pi\)
\(104\) 0 0
\(105\) 2.15482 0.210289
\(106\) 0 0
\(107\) 15.7332 1.52099 0.760494 0.649344i \(-0.224957\pi\)
0.760494 + 0.649344i \(0.224957\pi\)
\(108\) 0 0
\(109\) −7.16256 −0.686049 −0.343025 0.939326i \(-0.611451\pi\)
−0.343025 + 0.939326i \(0.611451\pi\)
\(110\) 0 0
\(111\) 1.02416 0.0972088
\(112\) 0 0
\(113\) −2.68481 −0.252565 −0.126283 0.991994i \(-0.540305\pi\)
−0.126283 + 0.991994i \(0.540305\pi\)
\(114\) 0 0
\(115\) 7.93500 0.739943
\(116\) 0 0
\(117\) −14.3202 −1.32390
\(118\) 0 0
\(119\) 19.0040 1.74209
\(120\) 0 0
\(121\) −10.9385 −0.994410
\(122\) 0 0
\(123\) 1.46456 0.132055
\(124\) 0 0
\(125\) −11.8184 −1.05707
\(126\) 0 0
\(127\) 17.7521 1.57524 0.787622 0.616159i \(-0.211312\pi\)
0.787622 + 0.616159i \(0.211312\pi\)
\(128\) 0 0
\(129\) 1.23616 0.108838
\(130\) 0 0
\(131\) −9.35653 −0.817483 −0.408742 0.912650i \(-0.634032\pi\)
−0.408742 + 0.912650i \(0.634032\pi\)
\(132\) 0 0
\(133\) −32.1113 −2.78440
\(134\) 0 0
\(135\) −3.33584 −0.287104
\(136\) 0 0
\(137\) −2.29891 −0.196409 −0.0982046 0.995166i \(-0.531310\pi\)
−0.0982046 + 0.995166i \(0.531310\pi\)
\(138\) 0 0
\(139\) 16.2411 1.37755 0.688775 0.724976i \(-0.258149\pi\)
0.688775 + 0.724976i \(0.258149\pi\)
\(140\) 0 0
\(141\) 2.88849 0.243255
\(142\) 0 0
\(143\) −1.23810 −0.103535
\(144\) 0 0
\(145\) 0.355106 0.0294900
\(146\) 0 0
\(147\) 2.67561 0.220680
\(148\) 0 0
\(149\) −9.65723 −0.791151 −0.395576 0.918433i \(-0.629455\pi\)
−0.395576 + 0.918433i \(0.629455\pi\)
\(150\) 0 0
\(151\) −11.5971 −0.943761 −0.471880 0.881663i \(-0.656425\pi\)
−0.471880 + 0.881663i \(0.656425\pi\)
\(152\) 0 0
\(153\) −14.3794 −1.16250
\(154\) 0 0
\(155\) −5.75894 −0.462570
\(156\) 0 0
\(157\) 15.1889 1.21221 0.606103 0.795386i \(-0.292732\pi\)
0.606103 + 0.795386i \(0.292732\pi\)
\(158\) 0 0
\(159\) 1.45380 0.115293
\(160\) 0 0
\(161\) 19.2128 1.51418
\(162\) 0 0
\(163\) 14.2886 1.11917 0.559586 0.828772i \(-0.310960\pi\)
0.559586 + 0.828772i \(0.310960\pi\)
\(164\) 0 0
\(165\) −0.140966 −0.0109742
\(166\) 0 0
\(167\) −3.06504 −0.237180 −0.118590 0.992943i \(-0.537837\pi\)
−0.118590 + 0.992943i \(0.537837\pi\)
\(168\) 0 0
\(169\) 11.9283 0.917558
\(170\) 0 0
\(171\) 24.2971 1.85804
\(172\) 0 0
\(173\) 18.5299 1.40880 0.704400 0.709803i \(-0.251216\pi\)
0.704400 + 0.709803i \(0.251216\pi\)
\(174\) 0 0
\(175\) −9.66260 −0.730424
\(176\) 0 0
\(177\) 3.12913 0.235199
\(178\) 0 0
\(179\) 6.54681 0.489331 0.244666 0.969608i \(-0.421322\pi\)
0.244666 + 0.969608i \(0.421322\pi\)
\(180\) 0 0
\(181\) −0.0903538 −0.00671595 −0.00335797 0.999994i \(-0.501069\pi\)
−0.00335797 + 0.999994i \(0.501069\pi\)
\(182\) 0 0
\(183\) −0.524581 −0.0387781
\(184\) 0 0
\(185\) 4.41557 0.324639
\(186\) 0 0
\(187\) −1.24322 −0.0909132
\(188\) 0 0
\(189\) −8.07698 −0.587514
\(190\) 0 0
\(191\) −21.8064 −1.57786 −0.788930 0.614484i \(-0.789364\pi\)
−0.788930 + 0.614484i \(0.789364\pi\)
\(192\) 0 0
\(193\) 10.0685 0.724747 0.362373 0.932033i \(-0.381967\pi\)
0.362373 + 0.932033i \(0.381967\pi\)
\(194\) 0 0
\(195\) 2.83825 0.203251
\(196\) 0 0
\(197\) −2.03221 −0.144789 −0.0723944 0.997376i \(-0.523064\pi\)
−0.0723944 + 0.997376i \(0.523064\pi\)
\(198\) 0 0
\(199\) 13.7343 0.973601 0.486800 0.873513i \(-0.338164\pi\)
0.486800 + 0.873513i \(0.338164\pi\)
\(200\) 0 0
\(201\) 4.94915 0.349086
\(202\) 0 0
\(203\) 0.859809 0.0603468
\(204\) 0 0
\(205\) 6.31433 0.441012
\(206\) 0 0
\(207\) −14.5374 −1.01042
\(208\) 0 0
\(209\) 2.10069 0.145308
\(210\) 0 0
\(211\) −20.7374 −1.42762 −0.713810 0.700339i \(-0.753032\pi\)
−0.713810 + 0.700339i \(0.753032\pi\)
\(212\) 0 0
\(213\) 0.313776 0.0214996
\(214\) 0 0
\(215\) 5.32959 0.363475
\(216\) 0 0
\(217\) −13.9440 −0.946579
\(218\) 0 0
\(219\) −0.776747 −0.0524877
\(220\) 0 0
\(221\) 25.0314 1.68379
\(222\) 0 0
\(223\) 15.2223 1.01936 0.509681 0.860363i \(-0.329763\pi\)
0.509681 + 0.860363i \(0.329763\pi\)
\(224\) 0 0
\(225\) 7.31122 0.487415
\(226\) 0 0
\(227\) −20.0482 −1.33064 −0.665322 0.746557i \(-0.731706\pi\)
−0.665322 + 0.746557i \(0.731706\pi\)
\(228\) 0 0
\(229\) 24.2437 1.60207 0.801033 0.598620i \(-0.204284\pi\)
0.801033 + 0.598620i \(0.204284\pi\)
\(230\) 0 0
\(231\) −0.341317 −0.0224570
\(232\) 0 0
\(233\) 0.653982 0.0428438 0.0214219 0.999771i \(-0.493181\pi\)
0.0214219 + 0.999771i \(0.493181\pi\)
\(234\) 0 0
\(235\) 12.4535 0.812376
\(236\) 0 0
\(237\) −4.71895 −0.306529
\(238\) 0 0
\(239\) −5.16420 −0.334044 −0.167022 0.985953i \(-0.553415\pi\)
−0.167022 + 0.985953i \(0.553415\pi\)
\(240\) 0 0
\(241\) 0.716483 0.0461527 0.0230764 0.999734i \(-0.492654\pi\)
0.0230764 + 0.999734i \(0.492654\pi\)
\(242\) 0 0
\(243\) 9.23585 0.592480
\(244\) 0 0
\(245\) 11.5356 0.736985
\(246\) 0 0
\(247\) −42.2959 −2.69122
\(248\) 0 0
\(249\) −4.58123 −0.290324
\(250\) 0 0
\(251\) −19.9941 −1.26202 −0.631010 0.775775i \(-0.717359\pi\)
−0.631010 + 0.775775i \(0.717359\pi\)
\(252\) 0 0
\(253\) −1.25688 −0.0790194
\(254\) 0 0
\(255\) 2.84999 0.178473
\(256\) 0 0
\(257\) 14.8853 0.928520 0.464260 0.885699i \(-0.346320\pi\)
0.464260 + 0.885699i \(0.346320\pi\)
\(258\) 0 0
\(259\) 10.6913 0.664325
\(260\) 0 0
\(261\) −0.650576 −0.0402696
\(262\) 0 0
\(263\) −18.6297 −1.14876 −0.574379 0.818589i \(-0.694756\pi\)
−0.574379 + 0.818589i \(0.694756\pi\)
\(264\) 0 0
\(265\) 6.26792 0.385035
\(266\) 0 0
\(267\) 4.18956 0.256397
\(268\) 0 0
\(269\) 7.10569 0.433241 0.216621 0.976256i \(-0.430497\pi\)
0.216621 + 0.976256i \(0.430497\pi\)
\(270\) 0 0
\(271\) 14.8249 0.900550 0.450275 0.892890i \(-0.351326\pi\)
0.450275 + 0.892890i \(0.351326\pi\)
\(272\) 0 0
\(273\) 6.87217 0.415923
\(274\) 0 0
\(275\) 0.632117 0.0381181
\(276\) 0 0
\(277\) −2.15211 −0.129308 −0.0646539 0.997908i \(-0.520594\pi\)
−0.0646539 + 0.997908i \(0.520594\pi\)
\(278\) 0 0
\(279\) 10.5507 0.631655
\(280\) 0 0
\(281\) −15.9058 −0.948859 −0.474429 0.880294i \(-0.657346\pi\)
−0.474429 + 0.880294i \(0.657346\pi\)
\(282\) 0 0
\(283\) 15.3382 0.911759 0.455880 0.890041i \(-0.349325\pi\)
0.455880 + 0.890041i \(0.349325\pi\)
\(284\) 0 0
\(285\) −4.81567 −0.285256
\(286\) 0 0
\(287\) 15.2887 0.902464
\(288\) 0 0
\(289\) 8.13491 0.478524
\(290\) 0 0
\(291\) 0.422299 0.0247556
\(292\) 0 0
\(293\) −32.0061 −1.86981 −0.934907 0.354892i \(-0.884517\pi\)
−0.934907 + 0.354892i \(0.884517\pi\)
\(294\) 0 0
\(295\) 13.4910 0.785474
\(296\) 0 0
\(297\) 0.528388 0.0306602
\(298\) 0 0
\(299\) 25.3064 1.46351
\(300\) 0 0
\(301\) 12.9044 0.743796
\(302\) 0 0
\(303\) 2.55692 0.146891
\(304\) 0 0
\(305\) −2.26169 −0.129504
\(306\) 0 0
\(307\) −22.8601 −1.30469 −0.652347 0.757920i \(-0.726215\pi\)
−0.652347 + 0.757920i \(0.726215\pi\)
\(308\) 0 0
\(309\) −6.91787 −0.393544
\(310\) 0 0
\(311\) −16.4603 −0.933379 −0.466690 0.884421i \(-0.654554\pi\)
−0.466690 + 0.884421i \(0.654554\pi\)
\(312\) 0 0
\(313\) 18.3332 1.03625 0.518127 0.855304i \(-0.326630\pi\)
0.518127 + 0.855304i \(0.326630\pi\)
\(314\) 0 0
\(315\) −17.0204 −0.958991
\(316\) 0 0
\(317\) −27.6693 −1.55406 −0.777031 0.629463i \(-0.783275\pi\)
−0.777031 + 0.629463i \(0.783275\pi\)
\(318\) 0 0
\(319\) −0.0562478 −0.00314927
\(320\) 0 0
\(321\) 5.71295 0.318866
\(322\) 0 0
\(323\) −42.4708 −2.36314
\(324\) 0 0
\(325\) −12.7272 −0.705980
\(326\) 0 0
\(327\) −2.60082 −0.143826
\(328\) 0 0
\(329\) 30.1533 1.66240
\(330\) 0 0
\(331\) −24.6163 −1.35303 −0.676516 0.736427i \(-0.736511\pi\)
−0.676516 + 0.736427i \(0.736511\pi\)
\(332\) 0 0
\(333\) −8.08959 −0.443307
\(334\) 0 0
\(335\) 21.3378 1.16581
\(336\) 0 0
\(337\) −0.399526 −0.0217636 −0.0108818 0.999941i \(-0.503464\pi\)
−0.0108818 + 0.999941i \(0.503464\pi\)
\(338\) 0 0
\(339\) −0.974889 −0.0529487
\(340\) 0 0
\(341\) 0.912200 0.0493984
\(342\) 0 0
\(343\) 1.39687 0.0754239
\(344\) 0 0
\(345\) 2.88130 0.155124
\(346\) 0 0
\(347\) −25.9293 −1.39196 −0.695979 0.718062i \(-0.745030\pi\)
−0.695979 + 0.718062i \(0.745030\pi\)
\(348\) 0 0
\(349\) 30.5889 1.63738 0.818692 0.574233i \(-0.194700\pi\)
0.818692 + 0.574233i \(0.194700\pi\)
\(350\) 0 0
\(351\) −10.6387 −0.567853
\(352\) 0 0
\(353\) 5.03394 0.267930 0.133965 0.990986i \(-0.457229\pi\)
0.133965 + 0.990986i \(0.457229\pi\)
\(354\) 0 0
\(355\) 1.35282 0.0718003
\(356\) 0 0
\(357\) 6.90060 0.365218
\(358\) 0 0
\(359\) 6.39274 0.337396 0.168698 0.985668i \(-0.446044\pi\)
0.168698 + 0.985668i \(0.446044\pi\)
\(360\) 0 0
\(361\) 52.7636 2.77703
\(362\) 0 0
\(363\) −3.97192 −0.208472
\(364\) 0 0
\(365\) −3.34888 −0.175288
\(366\) 0 0
\(367\) −20.7256 −1.08187 −0.540933 0.841066i \(-0.681929\pi\)
−0.540933 + 0.841066i \(0.681929\pi\)
\(368\) 0 0
\(369\) −11.5682 −0.602218
\(370\) 0 0
\(371\) 15.1763 0.787916
\(372\) 0 0
\(373\) 28.7957 1.49099 0.745493 0.666513i \(-0.232214\pi\)
0.745493 + 0.666513i \(0.232214\pi\)
\(374\) 0 0
\(375\) −4.29141 −0.221607
\(376\) 0 0
\(377\) 1.13251 0.0583273
\(378\) 0 0
\(379\) 6.36089 0.326737 0.163368 0.986565i \(-0.447764\pi\)
0.163368 + 0.986565i \(0.447764\pi\)
\(380\) 0 0
\(381\) 6.44602 0.330240
\(382\) 0 0
\(383\) −22.1432 −1.13146 −0.565731 0.824590i \(-0.691406\pi\)
−0.565731 + 0.824590i \(0.691406\pi\)
\(384\) 0 0
\(385\) −1.47156 −0.0749975
\(386\) 0 0
\(387\) −9.76412 −0.496338
\(388\) 0 0
\(389\) 20.1533 1.02181 0.510906 0.859637i \(-0.329310\pi\)
0.510906 + 0.859637i \(0.329310\pi\)
\(390\) 0 0
\(391\) 25.4111 1.28509
\(392\) 0 0
\(393\) −3.39748 −0.171380
\(394\) 0 0
\(395\) −20.3453 −1.02369
\(396\) 0 0
\(397\) −7.28166 −0.365456 −0.182728 0.983163i \(-0.558493\pi\)
−0.182728 + 0.983163i \(0.558493\pi\)
\(398\) 0 0
\(399\) −11.6600 −0.583732
\(400\) 0 0
\(401\) 12.1771 0.608096 0.304048 0.952657i \(-0.401662\pi\)
0.304048 + 0.952657i \(0.401662\pi\)
\(402\) 0 0
\(403\) −18.3665 −0.914901
\(404\) 0 0
\(405\) 12.2593 0.609167
\(406\) 0 0
\(407\) −0.699414 −0.0346686
\(408\) 0 0
\(409\) 5.80267 0.286924 0.143462 0.989656i \(-0.454177\pi\)
0.143462 + 0.989656i \(0.454177\pi\)
\(410\) 0 0
\(411\) −0.834765 −0.0411759
\(412\) 0 0
\(413\) 32.6653 1.60735
\(414\) 0 0
\(415\) −19.7516 −0.969568
\(416\) 0 0
\(417\) 5.89735 0.288794
\(418\) 0 0
\(419\) −14.6649 −0.716428 −0.358214 0.933639i \(-0.616614\pi\)
−0.358214 + 0.933639i \(0.616614\pi\)
\(420\) 0 0
\(421\) 19.3955 0.945281 0.472640 0.881255i \(-0.343301\pi\)
0.472640 + 0.881255i \(0.343301\pi\)
\(422\) 0 0
\(423\) −22.8155 −1.10933
\(424\) 0 0
\(425\) −12.7799 −0.619915
\(426\) 0 0
\(427\) −5.47616 −0.265010
\(428\) 0 0
\(429\) −0.449570 −0.0217055
\(430\) 0 0
\(431\) −9.54357 −0.459698 −0.229849 0.973226i \(-0.573823\pi\)
−0.229849 + 0.973226i \(0.573823\pi\)
\(432\) 0 0
\(433\) −30.9789 −1.48875 −0.744374 0.667762i \(-0.767252\pi\)
−0.744374 + 0.667762i \(0.767252\pi\)
\(434\) 0 0
\(435\) 0.128944 0.00618239
\(436\) 0 0
\(437\) −42.9375 −2.05398
\(438\) 0 0
\(439\) 33.0681 1.57825 0.789126 0.614231i \(-0.210534\pi\)
0.789126 + 0.614231i \(0.210534\pi\)
\(440\) 0 0
\(441\) −21.1340 −1.00638
\(442\) 0 0
\(443\) 36.0251 1.71160 0.855802 0.517304i \(-0.173064\pi\)
0.855802 + 0.517304i \(0.173064\pi\)
\(444\) 0 0
\(445\) 18.0629 0.856265
\(446\) 0 0
\(447\) −3.50667 −0.165860
\(448\) 0 0
\(449\) 13.0293 0.614889 0.307445 0.951566i \(-0.400526\pi\)
0.307445 + 0.951566i \(0.400526\pi\)
\(450\) 0 0
\(451\) −1.00017 −0.0470962
\(452\) 0 0
\(453\) −4.21107 −0.197853
\(454\) 0 0
\(455\) 29.6288 1.38902
\(456\) 0 0
\(457\) −2.29899 −0.107542 −0.0537712 0.998553i \(-0.517124\pi\)
−0.0537712 + 0.998553i \(0.517124\pi\)
\(458\) 0 0
\(459\) −10.6827 −0.498627
\(460\) 0 0
\(461\) 7.38626 0.344012 0.172006 0.985096i \(-0.444975\pi\)
0.172006 + 0.985096i \(0.444975\pi\)
\(462\) 0 0
\(463\) −5.79595 −0.269361 −0.134680 0.990889i \(-0.543001\pi\)
−0.134680 + 0.990889i \(0.543001\pi\)
\(464\) 0 0
\(465\) −2.09115 −0.0969748
\(466\) 0 0
\(467\) 1.52157 0.0704100 0.0352050 0.999380i \(-0.488792\pi\)
0.0352050 + 0.999380i \(0.488792\pi\)
\(468\) 0 0
\(469\) 51.6647 2.38565
\(470\) 0 0
\(471\) 5.51529 0.254131
\(472\) 0 0
\(473\) −0.844191 −0.0388159
\(474\) 0 0
\(475\) 21.5944 0.990817
\(476\) 0 0
\(477\) −11.4832 −0.525779
\(478\) 0 0
\(479\) −4.17058 −0.190559 −0.0952794 0.995451i \(-0.530374\pi\)
−0.0952794 + 0.995451i \(0.530374\pi\)
\(480\) 0 0
\(481\) 14.0822 0.642094
\(482\) 0 0
\(483\) 6.97642 0.317438
\(484\) 0 0
\(485\) 1.82071 0.0826741
\(486\) 0 0
\(487\) 36.3937 1.64916 0.824579 0.565747i \(-0.191412\pi\)
0.824579 + 0.565747i \(0.191412\pi\)
\(488\) 0 0
\(489\) 5.18840 0.234627
\(490\) 0 0
\(491\) −15.5397 −0.701295 −0.350648 0.936508i \(-0.614038\pi\)
−0.350648 + 0.936508i \(0.614038\pi\)
\(492\) 0 0
\(493\) 1.13719 0.0512167
\(494\) 0 0
\(495\) 1.11346 0.0500461
\(496\) 0 0
\(497\) 3.27555 0.146928
\(498\) 0 0
\(499\) 38.9248 1.74251 0.871256 0.490829i \(-0.163306\pi\)
0.871256 + 0.490829i \(0.163306\pi\)
\(500\) 0 0
\(501\) −1.11296 −0.0497232
\(502\) 0 0
\(503\) −20.1298 −0.897544 −0.448772 0.893646i \(-0.648139\pi\)
−0.448772 + 0.893646i \(0.648139\pi\)
\(504\) 0 0
\(505\) 11.0239 0.490559
\(506\) 0 0
\(507\) 4.33131 0.192360
\(508\) 0 0
\(509\) −0.0456568 −0.00202370 −0.00101185 0.999999i \(-0.500322\pi\)
−0.00101185 + 0.999999i \(0.500322\pi\)
\(510\) 0 0
\(511\) −8.10855 −0.358701
\(512\) 0 0
\(513\) 18.0508 0.796961
\(514\) 0 0
\(515\) −29.8258 −1.31428
\(516\) 0 0
\(517\) −1.97259 −0.0867546
\(518\) 0 0
\(519\) 6.72844 0.295346
\(520\) 0 0
\(521\) −11.2088 −0.491066 −0.245533 0.969388i \(-0.578963\pi\)
−0.245533 + 0.969388i \(0.578963\pi\)
\(522\) 0 0
\(523\) 0.116293 0.00508516 0.00254258 0.999997i \(-0.499191\pi\)
0.00254258 + 0.999997i \(0.499191\pi\)
\(524\) 0 0
\(525\) −3.50862 −0.153129
\(526\) 0 0
\(527\) −18.4425 −0.803367
\(528\) 0 0
\(529\) 2.69032 0.116970
\(530\) 0 0
\(531\) −24.7162 −1.07259
\(532\) 0 0
\(533\) 20.1378 0.872263
\(534\) 0 0
\(535\) 24.6309 1.06489
\(536\) 0 0
\(537\) 2.37723 0.102585
\(538\) 0 0
\(539\) −1.82721 −0.0787036
\(540\) 0 0
\(541\) 0.0606811 0.00260889 0.00130444 0.999999i \(-0.499585\pi\)
0.00130444 + 0.999999i \(0.499585\pi\)
\(542\) 0 0
\(543\) −0.0328087 −0.00140796
\(544\) 0 0
\(545\) −11.2132 −0.480322
\(546\) 0 0
\(547\) −27.6883 −1.18387 −0.591933 0.805987i \(-0.701635\pi\)
−0.591933 + 0.805987i \(0.701635\pi\)
\(548\) 0 0
\(549\) 4.14354 0.176842
\(550\) 0 0
\(551\) −1.92154 −0.0818602
\(552\) 0 0
\(553\) −49.2616 −2.09482
\(554\) 0 0
\(555\) 1.60335 0.0680586
\(556\) 0 0
\(557\) 42.7445 1.81114 0.905571 0.424194i \(-0.139442\pi\)
0.905571 + 0.424194i \(0.139442\pi\)
\(558\) 0 0
\(559\) 16.9972 0.718905
\(560\) 0 0
\(561\) −0.451430 −0.0190594
\(562\) 0 0
\(563\) 18.5974 0.783787 0.391893 0.920011i \(-0.371820\pi\)
0.391893 + 0.920011i \(0.371820\pi\)
\(564\) 0 0
\(565\) −4.20315 −0.176828
\(566\) 0 0
\(567\) 29.6830 1.24657
\(568\) 0 0
\(569\) −14.4580 −0.606111 −0.303055 0.952973i \(-0.598007\pi\)
−0.303055 + 0.952973i \(0.598007\pi\)
\(570\) 0 0
\(571\) 18.7204 0.783424 0.391712 0.920088i \(-0.371883\pi\)
0.391712 + 0.920088i \(0.371883\pi\)
\(572\) 0 0
\(573\) −7.91821 −0.330788
\(574\) 0 0
\(575\) −12.9203 −0.538814
\(576\) 0 0
\(577\) 41.3729 1.72238 0.861189 0.508285i \(-0.169720\pi\)
0.861189 + 0.508285i \(0.169720\pi\)
\(578\) 0 0
\(579\) 3.65601 0.151939
\(580\) 0 0
\(581\) −47.8240 −1.98407
\(582\) 0 0
\(583\) −0.992820 −0.0411184
\(584\) 0 0
\(585\) −22.4187 −0.926898
\(586\) 0 0
\(587\) 28.3558 1.17037 0.585186 0.810899i \(-0.301022\pi\)
0.585186 + 0.810899i \(0.301022\pi\)
\(588\) 0 0
\(589\) 31.1625 1.28403
\(590\) 0 0
\(591\) −0.737921 −0.0303540
\(592\) 0 0
\(593\) −31.9921 −1.31376 −0.656879 0.753996i \(-0.728124\pi\)
−0.656879 + 0.753996i \(0.728124\pi\)
\(594\) 0 0
\(595\) 29.7514 1.21969
\(596\) 0 0
\(597\) 4.98712 0.204109
\(598\) 0 0
\(599\) −10.0853 −0.412076 −0.206038 0.978544i \(-0.566057\pi\)
−0.206038 + 0.978544i \(0.566057\pi\)
\(600\) 0 0
\(601\) 45.6405 1.86171 0.930856 0.365385i \(-0.119063\pi\)
0.930856 + 0.365385i \(0.119063\pi\)
\(602\) 0 0
\(603\) −39.0922 −1.59196
\(604\) 0 0
\(605\) −17.1246 −0.696214
\(606\) 0 0
\(607\) −44.3535 −1.80025 −0.900126 0.435629i \(-0.856526\pi\)
−0.900126 + 0.435629i \(0.856526\pi\)
\(608\) 0 0
\(609\) 0.312208 0.0126513
\(610\) 0 0
\(611\) 39.7168 1.60677
\(612\) 0 0
\(613\) −34.5779 −1.39659 −0.698295 0.715811i \(-0.746057\pi\)
−0.698295 + 0.715811i \(0.746057\pi\)
\(614\) 0 0
\(615\) 2.29282 0.0924553
\(616\) 0 0
\(617\) 27.6199 1.11193 0.555967 0.831204i \(-0.312348\pi\)
0.555967 + 0.831204i \(0.312348\pi\)
\(618\) 0 0
\(619\) −45.1522 −1.81482 −0.907410 0.420247i \(-0.861943\pi\)
−0.907410 + 0.420247i \(0.861943\pi\)
\(620\) 0 0
\(621\) −10.8001 −0.433393
\(622\) 0 0
\(623\) 43.7353 1.75222
\(624\) 0 0
\(625\) −5.75652 −0.230261
\(626\) 0 0
\(627\) 0.762788 0.0304628
\(628\) 0 0
\(629\) 14.1405 0.563817
\(630\) 0 0
\(631\) 22.6526 0.901787 0.450893 0.892578i \(-0.351105\pi\)
0.450893 + 0.892578i \(0.351105\pi\)
\(632\) 0 0
\(633\) −7.53002 −0.299291
\(634\) 0 0
\(635\) 27.7915 1.10287
\(636\) 0 0
\(637\) 36.7897 1.45766
\(638\) 0 0
\(639\) −2.47845 −0.0980459
\(640\) 0 0
\(641\) 33.3532 1.31737 0.658687 0.752417i \(-0.271112\pi\)
0.658687 + 0.752417i \(0.271112\pi\)
\(642\) 0 0
\(643\) −29.3107 −1.15590 −0.577951 0.816072i \(-0.696147\pi\)
−0.577951 + 0.816072i \(0.696147\pi\)
\(644\) 0 0
\(645\) 1.93524 0.0762002
\(646\) 0 0
\(647\) −1.83563 −0.0721662 −0.0360831 0.999349i \(-0.511488\pi\)
−0.0360831 + 0.999349i \(0.511488\pi\)
\(648\) 0 0
\(649\) −2.13693 −0.0838818
\(650\) 0 0
\(651\) −5.06324 −0.198444
\(652\) 0 0
\(653\) 10.9497 0.428493 0.214247 0.976780i \(-0.431270\pi\)
0.214247 + 0.976780i \(0.431270\pi\)
\(654\) 0 0
\(655\) −14.6479 −0.572343
\(656\) 0 0
\(657\) 6.13534 0.239363
\(658\) 0 0
\(659\) 10.1057 0.393662 0.196831 0.980437i \(-0.436935\pi\)
0.196831 + 0.980437i \(0.436935\pi\)
\(660\) 0 0
\(661\) 22.6395 0.880574 0.440287 0.897857i \(-0.354877\pi\)
0.440287 + 0.897857i \(0.354877\pi\)
\(662\) 0 0
\(663\) 9.08923 0.352996
\(664\) 0 0
\(665\) −50.2713 −1.94944
\(666\) 0 0
\(667\) 1.14969 0.0445162
\(668\) 0 0
\(669\) 5.52743 0.213703
\(670\) 0 0
\(671\) 0.358244 0.0138299
\(672\) 0 0
\(673\) 31.2335 1.20396 0.601982 0.798510i \(-0.294378\pi\)
0.601982 + 0.798510i \(0.294378\pi\)
\(674\) 0 0
\(675\) 5.43165 0.209064
\(676\) 0 0
\(677\) −32.3766 −1.24433 −0.622166 0.782885i \(-0.713747\pi\)
−0.622166 + 0.782885i \(0.713747\pi\)
\(678\) 0 0
\(679\) 4.40843 0.169180
\(680\) 0 0
\(681\) −7.27976 −0.278961
\(682\) 0 0
\(683\) 19.7237 0.754708 0.377354 0.926069i \(-0.376834\pi\)
0.377354 + 0.926069i \(0.376834\pi\)
\(684\) 0 0
\(685\) −3.59902 −0.137512
\(686\) 0 0
\(687\) 8.80320 0.335863
\(688\) 0 0
\(689\) 19.9897 0.761548
\(690\) 0 0
\(691\) 2.90500 0.110511 0.0552557 0.998472i \(-0.482403\pi\)
0.0552557 + 0.998472i \(0.482403\pi\)
\(692\) 0 0
\(693\) 2.69598 0.102412
\(694\) 0 0
\(695\) 25.4259 0.964460
\(696\) 0 0
\(697\) 20.2210 0.765927
\(698\) 0 0
\(699\) 0.237469 0.00898192
\(700\) 0 0
\(701\) −41.3415 −1.56145 −0.780723 0.624878i \(-0.785149\pi\)
−0.780723 + 0.624878i \(0.785149\pi\)
\(702\) 0 0
\(703\) −23.8934 −0.901155
\(704\) 0 0
\(705\) 4.52203 0.170309
\(706\) 0 0
\(707\) 26.6920 1.00386
\(708\) 0 0
\(709\) 25.8126 0.969412 0.484706 0.874677i \(-0.338927\pi\)
0.484706 + 0.874677i \(0.338927\pi\)
\(710\) 0 0
\(711\) 37.2739 1.39788
\(712\) 0 0
\(713\) −18.6451 −0.698266
\(714\) 0 0
\(715\) −1.93828 −0.0724877
\(716\) 0 0
\(717\) −1.87519 −0.0700302
\(718\) 0 0
\(719\) −4.71324 −0.175774 −0.0878872 0.996130i \(-0.528011\pi\)
−0.0878872 + 0.996130i \(0.528011\pi\)
\(720\) 0 0
\(721\) −72.2165 −2.68948
\(722\) 0 0
\(723\) 0.260165 0.00967563
\(724\) 0 0
\(725\) −0.578208 −0.0214741
\(726\) 0 0
\(727\) 15.1640 0.562403 0.281202 0.959649i \(-0.409267\pi\)
0.281202 + 0.959649i \(0.409267\pi\)
\(728\) 0 0
\(729\) −20.1385 −0.745871
\(730\) 0 0
\(731\) 17.0675 0.631264
\(732\) 0 0
\(733\) 5.96043 0.220153 0.110077 0.993923i \(-0.464890\pi\)
0.110077 + 0.993923i \(0.464890\pi\)
\(734\) 0 0
\(735\) 4.18875 0.154504
\(736\) 0 0
\(737\) −3.37985 −0.124498
\(738\) 0 0
\(739\) 9.23179 0.339597 0.169798 0.985479i \(-0.445688\pi\)
0.169798 + 0.985479i \(0.445688\pi\)
\(740\) 0 0
\(741\) −15.3582 −0.564198
\(742\) 0 0
\(743\) −51.0084 −1.87132 −0.935658 0.352909i \(-0.885193\pi\)
−0.935658 + 0.352909i \(0.885193\pi\)
\(744\) 0 0
\(745\) −15.1187 −0.553907
\(746\) 0 0
\(747\) 36.1861 1.32398
\(748\) 0 0
\(749\) 59.6381 2.17913
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −7.26014 −0.264574
\(754\) 0 0
\(755\) −18.1557 −0.660753
\(756\) 0 0
\(757\) 40.4183 1.46903 0.734514 0.678594i \(-0.237410\pi\)
0.734514 + 0.678594i \(0.237410\pi\)
\(758\) 0 0
\(759\) −0.456390 −0.0165659
\(760\) 0 0
\(761\) −30.5931 −1.10900 −0.554500 0.832184i \(-0.687090\pi\)
−0.554500 + 0.832184i \(0.687090\pi\)
\(762\) 0 0
\(763\) −27.1503 −0.982906
\(764\) 0 0
\(765\) −22.5114 −0.813901
\(766\) 0 0
\(767\) 43.0256 1.55356
\(768\) 0 0
\(769\) −40.7009 −1.46771 −0.733855 0.679306i \(-0.762281\pi\)
−0.733855 + 0.679306i \(0.762281\pi\)
\(770\) 0 0
\(771\) 5.40506 0.194658
\(772\) 0 0
\(773\) −29.2149 −1.05079 −0.525393 0.850859i \(-0.676082\pi\)
−0.525393 + 0.850859i \(0.676082\pi\)
\(774\) 0 0
\(775\) 9.37710 0.336836
\(776\) 0 0
\(777\) 3.88216 0.139272
\(778\) 0 0
\(779\) −34.1678 −1.22419
\(780\) 0 0
\(781\) −0.214283 −0.00766764
\(782\) 0 0
\(783\) −0.483325 −0.0172726
\(784\) 0 0
\(785\) 23.7787 0.848699
\(786\) 0 0
\(787\) −16.2828 −0.580420 −0.290210 0.956963i \(-0.593725\pi\)
−0.290210 + 0.956963i \(0.593725\pi\)
\(788\) 0 0
\(789\) −6.76470 −0.240830
\(790\) 0 0
\(791\) −10.1770 −0.361852
\(792\) 0 0
\(793\) −7.21300 −0.256141
\(794\) 0 0
\(795\) 2.27596 0.0807202
\(796\) 0 0
\(797\) −26.7775 −0.948509 −0.474254 0.880388i \(-0.657282\pi\)
−0.474254 + 0.880388i \(0.657282\pi\)
\(798\) 0 0
\(799\) 39.8811 1.41089
\(800\) 0 0
\(801\) −33.0923 −1.16926
\(802\) 0 0
\(803\) 0.530452 0.0187193
\(804\) 0 0
\(805\) 30.0783 1.06012
\(806\) 0 0
\(807\) 2.58017 0.0908263
\(808\) 0 0
\(809\) −14.0495 −0.493955 −0.246978 0.969021i \(-0.579437\pi\)
−0.246978 + 0.969021i \(0.579437\pi\)
\(810\) 0 0
\(811\) 10.3335 0.362859 0.181430 0.983404i \(-0.441928\pi\)
0.181430 + 0.983404i \(0.441928\pi\)
\(812\) 0 0
\(813\) 5.38313 0.188795
\(814\) 0 0
\(815\) 22.3693 0.783563
\(816\) 0 0
\(817\) −28.8392 −1.00896
\(818\) 0 0
\(819\) −54.2817 −1.89676
\(820\) 0 0
\(821\) 19.9187 0.695169 0.347584 0.937649i \(-0.387002\pi\)
0.347584 + 0.937649i \(0.387002\pi\)
\(822\) 0 0
\(823\) −15.8346 −0.551961 −0.275980 0.961163i \(-0.589002\pi\)
−0.275980 + 0.961163i \(0.589002\pi\)
\(824\) 0 0
\(825\) 0.229530 0.00799121
\(826\) 0 0
\(827\) −40.6275 −1.41275 −0.706377 0.707835i \(-0.749672\pi\)
−0.706377 + 0.707835i \(0.749672\pi\)
\(828\) 0 0
\(829\) −17.3777 −0.603552 −0.301776 0.953379i \(-0.597580\pi\)
−0.301776 + 0.953379i \(0.597580\pi\)
\(830\) 0 0
\(831\) −0.781460 −0.0271086
\(832\) 0 0
\(833\) 36.9418 1.27996
\(834\) 0 0
\(835\) −4.79842 −0.166056
\(836\) 0 0
\(837\) 7.83834 0.270933
\(838\) 0 0
\(839\) −42.7478 −1.47582 −0.737910 0.674900i \(-0.764187\pi\)
−0.737910 + 0.674900i \(0.764187\pi\)
\(840\) 0 0
\(841\) −28.9485 −0.998226
\(842\) 0 0
\(843\) −5.77560 −0.198922
\(844\) 0 0
\(845\) 18.6741 0.642408
\(846\) 0 0
\(847\) −41.4633 −1.42470
\(848\) 0 0
\(849\) 5.56949 0.191145
\(850\) 0 0
\(851\) 14.2958 0.490055
\(852\) 0 0
\(853\) −36.7516 −1.25835 −0.629176 0.777263i \(-0.716608\pi\)
−0.629176 + 0.777263i \(0.716608\pi\)
\(854\) 0 0
\(855\) 38.0379 1.30087
\(856\) 0 0
\(857\) 2.70706 0.0924714 0.0462357 0.998931i \(-0.485277\pi\)
0.0462357 + 0.998931i \(0.485277\pi\)
\(858\) 0 0
\(859\) −45.4054 −1.54921 −0.774605 0.632445i \(-0.782051\pi\)
−0.774605 + 0.632445i \(0.782051\pi\)
\(860\) 0 0
\(861\) 5.55154 0.189196
\(862\) 0 0
\(863\) −47.1118 −1.60370 −0.801852 0.597522i \(-0.796152\pi\)
−0.801852 + 0.597522i \(0.796152\pi\)
\(864\) 0 0
\(865\) 29.0091 0.986339
\(866\) 0 0
\(867\) 2.95389 0.100319
\(868\) 0 0
\(869\) 3.22264 0.109321
\(870\) 0 0
\(871\) 68.0509 2.30582
\(872\) 0 0
\(873\) −3.33565 −0.112894
\(874\) 0 0
\(875\) −44.7985 −1.51447
\(876\) 0 0
\(877\) −45.6039 −1.53993 −0.769967 0.638084i \(-0.779727\pi\)
−0.769967 + 0.638084i \(0.779727\pi\)
\(878\) 0 0
\(879\) −11.6218 −0.391995
\(880\) 0 0
\(881\) −48.3132 −1.62771 −0.813857 0.581066i \(-0.802636\pi\)
−0.813857 + 0.581066i \(0.802636\pi\)
\(882\) 0 0
\(883\) 39.0276 1.31338 0.656691 0.754160i \(-0.271956\pi\)
0.656691 + 0.754160i \(0.271956\pi\)
\(884\) 0 0
\(885\) 4.89875 0.164670
\(886\) 0 0
\(887\) 53.8234 1.80721 0.903607 0.428362i \(-0.140909\pi\)
0.903607 + 0.428362i \(0.140909\pi\)
\(888\) 0 0
\(889\) 67.2908 2.25686
\(890\) 0 0
\(891\) −1.94183 −0.0650537
\(892\) 0 0
\(893\) −67.3877 −2.25504
\(894\) 0 0
\(895\) 10.2492 0.342594
\(896\) 0 0
\(897\) 9.18910 0.306815
\(898\) 0 0
\(899\) −0.834405 −0.0278290
\(900\) 0 0
\(901\) 20.0724 0.668709
\(902\) 0 0
\(903\) 4.68575 0.155932
\(904\) 0 0
\(905\) −0.141452 −0.00470202
\(906\) 0 0
\(907\) −25.7716 −0.855731 −0.427866 0.903842i \(-0.640734\pi\)
−0.427866 + 0.903842i \(0.640734\pi\)
\(908\) 0 0
\(909\) −20.1965 −0.669876
\(910\) 0 0
\(911\) −19.1198 −0.633468 −0.316734 0.948514i \(-0.602586\pi\)
−0.316734 + 0.948514i \(0.602586\pi\)
\(912\) 0 0
\(913\) 3.12860 0.103541
\(914\) 0 0
\(915\) −0.821249 −0.0271496
\(916\) 0 0
\(917\) −35.4667 −1.17121
\(918\) 0 0
\(919\) −40.5991 −1.33924 −0.669620 0.742704i \(-0.733543\pi\)
−0.669620 + 0.742704i \(0.733543\pi\)
\(920\) 0 0
\(921\) −8.30080 −0.273521
\(922\) 0 0
\(923\) 4.31444 0.142011
\(924\) 0 0
\(925\) −7.18974 −0.236397
\(926\) 0 0
\(927\) 54.6427 1.79470
\(928\) 0 0
\(929\) 44.6533 1.46503 0.732514 0.680752i \(-0.238347\pi\)
0.732514 + 0.680752i \(0.238347\pi\)
\(930\) 0 0
\(931\) −62.4212 −2.04577
\(932\) 0 0
\(933\) −5.97696 −0.195677
\(934\) 0 0
\(935\) −1.94630 −0.0636509
\(936\) 0 0
\(937\) −43.8615 −1.43289 −0.716447 0.697642i \(-0.754233\pi\)
−0.716447 + 0.697642i \(0.754233\pi\)
\(938\) 0 0
\(939\) 6.65703 0.217244
\(940\) 0 0
\(941\) 26.7665 0.872564 0.436282 0.899810i \(-0.356295\pi\)
0.436282 + 0.899810i \(0.356295\pi\)
\(942\) 0 0
\(943\) 20.4432 0.665724
\(944\) 0 0
\(945\) −12.6448 −0.411335
\(946\) 0 0
\(947\) 52.4011 1.70281 0.851404 0.524510i \(-0.175752\pi\)
0.851404 + 0.524510i \(0.175752\pi\)
\(948\) 0 0
\(949\) −10.6803 −0.346697
\(950\) 0 0
\(951\) −10.0471 −0.325799
\(952\) 0 0
\(953\) −27.5861 −0.893600 −0.446800 0.894634i \(-0.647436\pi\)
−0.446800 + 0.894634i \(0.647436\pi\)
\(954\) 0 0
\(955\) −34.1387 −1.10470
\(956\) 0 0
\(957\) −0.0204243 −0.000660225 0
\(958\) 0 0
\(959\) −8.71421 −0.281397
\(960\) 0 0
\(961\) −17.4680 −0.563484
\(962\) 0 0
\(963\) −45.1252 −1.45414
\(964\) 0 0
\(965\) 15.7626 0.507415
\(966\) 0 0
\(967\) −25.3095 −0.813899 −0.406949 0.913451i \(-0.633407\pi\)
−0.406949 + 0.913451i \(0.633407\pi\)
\(968\) 0 0
\(969\) −15.4217 −0.495417
\(970\) 0 0
\(971\) −12.5560 −0.402941 −0.201471 0.979495i \(-0.564572\pi\)
−0.201471 + 0.979495i \(0.564572\pi\)
\(972\) 0 0
\(973\) 61.5631 1.97362
\(974\) 0 0
\(975\) −4.62143 −0.148004
\(976\) 0 0
\(977\) −37.4838 −1.19921 −0.599606 0.800295i \(-0.704676\pi\)
−0.599606 + 0.800295i \(0.704676\pi\)
\(978\) 0 0
\(979\) −2.86111 −0.0914416
\(980\) 0 0
\(981\) 20.5433 0.655897
\(982\) 0 0
\(983\) −37.2078 −1.18674 −0.593372 0.804929i \(-0.702204\pi\)
−0.593372 + 0.804929i \(0.702204\pi\)
\(984\) 0 0
\(985\) −3.18149 −0.101371
\(986\) 0 0
\(987\) 10.9491 0.348512
\(988\) 0 0
\(989\) 17.2550 0.548678
\(990\) 0 0
\(991\) −41.9488 −1.33255 −0.666274 0.745707i \(-0.732112\pi\)
−0.666274 + 0.745707i \(0.732112\pi\)
\(992\) 0 0
\(993\) −8.93850 −0.283655
\(994\) 0 0
\(995\) 21.5015 0.681645
\(996\) 0 0
\(997\) 19.4934 0.617361 0.308681 0.951166i \(-0.400113\pi\)
0.308681 + 0.951166i \(0.400113\pi\)
\(998\) 0 0
\(999\) −6.00991 −0.190145
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 \(a_p\))