Properties

Label 8008.2.a.y.1.14
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{5} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Root \(-3.22058\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.22058 q^{3} -3.58838 q^{5} +1.00000 q^{7} +7.37212 q^{9} +O(q^{10})\) \(q+3.22058 q^{3} -3.58838 q^{5} +1.00000 q^{7} +7.37212 q^{9} -1.00000 q^{11} -1.00000 q^{13} -11.5566 q^{15} -4.82146 q^{17} -7.88691 q^{19} +3.22058 q^{21} +4.80149 q^{23} +7.87644 q^{25} +14.0808 q^{27} +9.62720 q^{29} -5.44581 q^{31} -3.22058 q^{33} -3.58838 q^{35} +0.187963 q^{37} -3.22058 q^{39} +1.50581 q^{41} -9.53445 q^{43} -26.4539 q^{45} -3.00380 q^{47} +1.00000 q^{49} -15.5279 q^{51} -2.34802 q^{53} +3.58838 q^{55} -25.4004 q^{57} -4.59689 q^{59} +5.05035 q^{61} +7.37212 q^{63} +3.58838 q^{65} -12.9657 q^{67} +15.4636 q^{69} -13.4722 q^{71} +12.2013 q^{73} +25.3667 q^{75} -1.00000 q^{77} +11.0938 q^{79} +23.2318 q^{81} -13.8010 q^{83} +17.3012 q^{85} +31.0052 q^{87} -9.44120 q^{89} -1.00000 q^{91} -17.5387 q^{93} +28.3012 q^{95} -0.672558 q^{97} -7.37212 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} + O(q^{10}) \) \( 14q - 3q^{3} - 6q^{5} + 14q^{7} + 21q^{9} - 14q^{11} - 14q^{13} - 6q^{15} - 6q^{17} - 13q^{19} - 3q^{21} - 9q^{23} + 22q^{25} - 18q^{27} + 2q^{29} - 2q^{31} + 3q^{33} - 6q^{35} - q^{37} + 3q^{39} - 16q^{41} - 15q^{43} - 44q^{45} - 8q^{47} + 14q^{49} - 14q^{51} - 6q^{53} + 6q^{55} - 10q^{57} - 36q^{59} - 19q^{61} + 21q^{63} + 6q^{65} - 34q^{67} - q^{69} - 10q^{71} + 9q^{73} - 44q^{75} - 14q^{77} - q^{79} + 42q^{81} - 56q^{83} + 21q^{85} - 5q^{87} - 14q^{89} - 14q^{91} - 20q^{93} + q^{95} - 14q^{97} - 21q^{99} + O(q^{100}) \)

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
\(3\) 3.22058 1.85940 0.929701 0.368316i \(-0.120065\pi\)
0.929701 + 0.368316i \(0.120065\pi\)
\(4\) 0 0
\(5\) −3.58838 −1.60477 −0.802385 0.596806i \(-0.796436\pi\)
−0.802385 + 0.596806i \(0.796436\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 7.37212 2.45737
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −11.5566 −2.98391
\(16\) 0 0
\(17\) −4.82146 −1.16938 −0.584688 0.811258i \(-0.698783\pi\)
−0.584688 + 0.811258i \(0.698783\pi\)
\(18\) 0 0
\(19\) −7.88691 −1.80938 −0.904690 0.426070i \(-0.859898\pi\)
−0.904690 + 0.426070i \(0.859898\pi\)
\(20\) 0 0
\(21\) 3.22058 0.702788
\(22\) 0 0
\(23\) 4.80149 1.00118 0.500590 0.865685i \(-0.333116\pi\)
0.500590 + 0.865685i \(0.333116\pi\)
\(24\) 0 0
\(25\) 7.87644 1.57529
\(26\) 0 0
\(27\) 14.0808 2.70984
\(28\) 0 0
\(29\) 9.62720 1.78773 0.893863 0.448340i \(-0.147985\pi\)
0.893863 + 0.448340i \(0.147985\pi\)
\(30\) 0 0
\(31\) −5.44581 −0.978096 −0.489048 0.872257i \(-0.662656\pi\)
−0.489048 + 0.872257i \(0.662656\pi\)
\(32\) 0 0
\(33\) −3.22058 −0.560631
\(34\) 0 0
\(35\) −3.58838 −0.606546
\(36\) 0 0
\(37\) 0.187963 0.0309009 0.0154504 0.999881i \(-0.495082\pi\)
0.0154504 + 0.999881i \(0.495082\pi\)
\(38\) 0 0
\(39\) −3.22058 −0.515705
\(40\) 0 0
\(41\) 1.50581 0.235169 0.117584 0.993063i \(-0.462485\pi\)
0.117584 + 0.993063i \(0.462485\pi\)
\(42\) 0 0
\(43\) −9.53445 −1.45399 −0.726995 0.686643i \(-0.759084\pi\)
−0.726995 + 0.686643i \(0.759084\pi\)
\(44\) 0 0
\(45\) −26.4539 −3.94352
\(46\) 0 0
\(47\) −3.00380 −0.438150 −0.219075 0.975708i \(-0.570304\pi\)
−0.219075 + 0.975708i \(0.570304\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −15.5279 −2.17434
\(52\) 0 0
\(53\) −2.34802 −0.322526 −0.161263 0.986911i \(-0.551557\pi\)
−0.161263 + 0.986911i \(0.551557\pi\)
\(54\) 0 0
\(55\) 3.58838 0.483857
\(56\) 0 0
\(57\) −25.4004 −3.36436
\(58\) 0 0
\(59\) −4.59689 −0.598464 −0.299232 0.954180i \(-0.596731\pi\)
−0.299232 + 0.954180i \(0.596731\pi\)
\(60\) 0 0
\(61\) 5.05035 0.646632 0.323316 0.946291i \(-0.395202\pi\)
0.323316 + 0.946291i \(0.395202\pi\)
\(62\) 0 0
\(63\) 7.37212 0.928800
\(64\) 0 0
\(65\) 3.58838 0.445083
\(66\) 0 0
\(67\) −12.9657 −1.58401 −0.792006 0.610513i \(-0.790963\pi\)
−0.792006 + 0.610513i \(0.790963\pi\)
\(68\) 0 0
\(69\) 15.4636 1.86160
\(70\) 0 0
\(71\) −13.4722 −1.59886 −0.799430 0.600759i \(-0.794865\pi\)
−0.799430 + 0.600759i \(0.794865\pi\)
\(72\) 0 0
\(73\) 12.2013 1.42805 0.714027 0.700118i \(-0.246869\pi\)
0.714027 + 0.700118i \(0.246869\pi\)
\(74\) 0 0
\(75\) 25.3667 2.92909
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 11.0938 1.24815 0.624073 0.781366i \(-0.285477\pi\)
0.624073 + 0.781366i \(0.285477\pi\)
\(80\) 0 0
\(81\) 23.2318 2.58131
\(82\) 0 0
\(83\) −13.8010 −1.51485 −0.757427 0.652920i \(-0.773544\pi\)
−0.757427 + 0.652920i \(0.773544\pi\)
\(84\) 0 0
\(85\) 17.3012 1.87658
\(86\) 0 0
\(87\) 31.0052 3.32410
\(88\) 0 0
\(89\) −9.44120 −1.00077 −0.500383 0.865804i \(-0.666807\pi\)
−0.500383 + 0.865804i \(0.666807\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −17.5387 −1.81867
\(94\) 0 0
\(95\) 28.3012 2.90364
\(96\) 0 0
\(97\) −0.672558 −0.0682879 −0.0341439 0.999417i \(-0.510870\pi\)
−0.0341439 + 0.999417i \(0.510870\pi\)
\(98\) 0 0
\(99\) −7.37212 −0.740926
\(100\) 0 0
\(101\) −16.9285 −1.68445 −0.842223 0.539130i \(-0.818753\pi\)
−0.842223 + 0.539130i \(0.818753\pi\)
\(102\) 0 0
\(103\) −9.87422 −0.972935 −0.486468 0.873699i \(-0.661715\pi\)
−0.486468 + 0.873699i \(0.661715\pi\)
\(104\) 0 0
\(105\) −11.5566 −1.12781
\(106\) 0 0
\(107\) −8.81921 −0.852585 −0.426292 0.904585i \(-0.640181\pi\)
−0.426292 + 0.904585i \(0.640181\pi\)
\(108\) 0 0
\(109\) 19.4616 1.86409 0.932043 0.362347i \(-0.118024\pi\)
0.932043 + 0.362347i \(0.118024\pi\)
\(110\) 0 0
\(111\) 0.605348 0.0574571
\(112\) 0 0
\(113\) −18.4208 −1.73289 −0.866444 0.499275i \(-0.833600\pi\)
−0.866444 + 0.499275i \(0.833600\pi\)
\(114\) 0 0
\(115\) −17.2296 −1.60666
\(116\) 0 0
\(117\) −7.37212 −0.681553
\(118\) 0 0
\(119\) −4.82146 −0.441982
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 4.84959 0.437273
\(124\) 0 0
\(125\) −10.3218 −0.923207
\(126\) 0 0
\(127\) −8.56887 −0.760364 −0.380182 0.924912i \(-0.624139\pi\)
−0.380182 + 0.924912i \(0.624139\pi\)
\(128\) 0 0
\(129\) −30.7064 −2.70355
\(130\) 0 0
\(131\) 10.7365 0.938052 0.469026 0.883184i \(-0.344605\pi\)
0.469026 + 0.883184i \(0.344605\pi\)
\(132\) 0 0
\(133\) −7.88691 −0.683882
\(134\) 0 0
\(135\) −50.5271 −4.34868
\(136\) 0 0
\(137\) −4.31232 −0.368427 −0.184213 0.982886i \(-0.558974\pi\)
−0.184213 + 0.982886i \(0.558974\pi\)
\(138\) 0 0
\(139\) −5.63319 −0.477801 −0.238900 0.971044i \(-0.576787\pi\)
−0.238900 + 0.971044i \(0.576787\pi\)
\(140\) 0 0
\(141\) −9.67398 −0.814696
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −34.5460 −2.86889
\(146\) 0 0
\(147\) 3.22058 0.265629
\(148\) 0 0
\(149\) 17.7571 1.45471 0.727357 0.686259i \(-0.240748\pi\)
0.727357 + 0.686259i \(0.240748\pi\)
\(150\) 0 0
\(151\) −7.42961 −0.604613 −0.302307 0.953211i \(-0.597757\pi\)
−0.302307 + 0.953211i \(0.597757\pi\)
\(152\) 0 0
\(153\) −35.5444 −2.87359
\(154\) 0 0
\(155\) 19.5416 1.56962
\(156\) 0 0
\(157\) −22.8574 −1.82422 −0.912111 0.409944i \(-0.865548\pi\)
−0.912111 + 0.409944i \(0.865548\pi\)
\(158\) 0 0
\(159\) −7.56200 −0.599705
\(160\) 0 0
\(161\) 4.80149 0.378410
\(162\) 0 0
\(163\) −11.0878 −0.868463 −0.434232 0.900801i \(-0.642980\pi\)
−0.434232 + 0.900801i \(0.642980\pi\)
\(164\) 0 0
\(165\) 11.5566 0.899684
\(166\) 0 0
\(167\) −17.3294 −1.34099 −0.670495 0.741914i \(-0.733918\pi\)
−0.670495 + 0.741914i \(0.733918\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −58.1432 −4.44632
\(172\) 0 0
\(173\) 1.42083 0.108024 0.0540118 0.998540i \(-0.482799\pi\)
0.0540118 + 0.998540i \(0.482799\pi\)
\(174\) 0 0
\(175\) 7.87644 0.595403
\(176\) 0 0
\(177\) −14.8046 −1.11279
\(178\) 0 0
\(179\) −8.73218 −0.652674 −0.326337 0.945254i \(-0.605814\pi\)
−0.326337 + 0.945254i \(0.605814\pi\)
\(180\) 0 0
\(181\) −2.81515 −0.209249 −0.104624 0.994512i \(-0.533364\pi\)
−0.104624 + 0.994512i \(0.533364\pi\)
\(182\) 0 0
\(183\) 16.2651 1.20235
\(184\) 0 0
\(185\) −0.674480 −0.0495888
\(186\) 0 0
\(187\) 4.82146 0.352580
\(188\) 0 0
\(189\) 14.0808 1.02422
\(190\) 0 0
\(191\) 26.2757 1.90125 0.950623 0.310349i \(-0.100446\pi\)
0.950623 + 0.310349i \(0.100446\pi\)
\(192\) 0 0
\(193\) 21.2260 1.52788 0.763941 0.645286i \(-0.223262\pi\)
0.763941 + 0.645286i \(0.223262\pi\)
\(194\) 0 0
\(195\) 11.5566 0.827589
\(196\) 0 0
\(197\) −3.19961 −0.227963 −0.113982 0.993483i \(-0.536360\pi\)
−0.113982 + 0.993483i \(0.536360\pi\)
\(198\) 0 0
\(199\) 6.44127 0.456609 0.228305 0.973590i \(-0.426682\pi\)
0.228305 + 0.973590i \(0.426682\pi\)
\(200\) 0 0
\(201\) −41.7570 −2.94532
\(202\) 0 0
\(203\) 9.62720 0.675697
\(204\) 0 0
\(205\) −5.40342 −0.377392
\(206\) 0 0
\(207\) 35.3972 2.46027
\(208\) 0 0
\(209\) 7.88691 0.545549
\(210\) 0 0
\(211\) −4.29768 −0.295864 −0.147932 0.988998i \(-0.547262\pi\)
−0.147932 + 0.988998i \(0.547262\pi\)
\(212\) 0 0
\(213\) −43.3884 −2.97292
\(214\) 0 0
\(215\) 34.2132 2.33332
\(216\) 0 0
\(217\) −5.44581 −0.369686
\(218\) 0 0
\(219\) 39.2952 2.65532
\(220\) 0 0
\(221\) 4.82146 0.324326
\(222\) 0 0
\(223\) 17.0231 1.13995 0.569974 0.821662i \(-0.306953\pi\)
0.569974 + 0.821662i \(0.306953\pi\)
\(224\) 0 0
\(225\) 58.0661 3.87107
\(226\) 0 0
\(227\) 8.75499 0.581089 0.290545 0.956861i \(-0.406164\pi\)
0.290545 + 0.956861i \(0.406164\pi\)
\(228\) 0 0
\(229\) −2.48184 −0.164005 −0.0820023 0.996632i \(-0.526131\pi\)
−0.0820023 + 0.996632i \(0.526131\pi\)
\(230\) 0 0
\(231\) −3.22058 −0.211898
\(232\) 0 0
\(233\) −28.5143 −1.86804 −0.934018 0.357225i \(-0.883723\pi\)
−0.934018 + 0.357225i \(0.883723\pi\)
\(234\) 0 0
\(235\) 10.7788 0.703130
\(236\) 0 0
\(237\) 35.7283 2.32080
\(238\) 0 0
\(239\) 24.4973 1.58460 0.792300 0.610131i \(-0.208883\pi\)
0.792300 + 0.610131i \(0.208883\pi\)
\(240\) 0 0
\(241\) −16.3070 −1.05042 −0.525212 0.850971i \(-0.676014\pi\)
−0.525212 + 0.850971i \(0.676014\pi\)
\(242\) 0 0
\(243\) 32.5776 2.08985
\(244\) 0 0
\(245\) −3.58838 −0.229253
\(246\) 0 0
\(247\) 7.88691 0.501832
\(248\) 0 0
\(249\) −44.4471 −2.81672
\(250\) 0 0
\(251\) −15.5380 −0.980750 −0.490375 0.871511i \(-0.663140\pi\)
−0.490375 + 0.871511i \(0.663140\pi\)
\(252\) 0 0
\(253\) −4.80149 −0.301867
\(254\) 0 0
\(255\) 55.7199 3.48931
\(256\) 0 0
\(257\) −2.16513 −0.135057 −0.0675285 0.997717i \(-0.521511\pi\)
−0.0675285 + 0.997717i \(0.521511\pi\)
\(258\) 0 0
\(259\) 0.187963 0.0116794
\(260\) 0 0
\(261\) 70.9729 4.39311
\(262\) 0 0
\(263\) −24.7513 −1.52623 −0.763117 0.646261i \(-0.776332\pi\)
−0.763117 + 0.646261i \(0.776332\pi\)
\(264\) 0 0
\(265\) 8.42560 0.517580
\(266\) 0 0
\(267\) −30.4061 −1.86083
\(268\) 0 0
\(269\) −8.63021 −0.526193 −0.263097 0.964769i \(-0.584744\pi\)
−0.263097 + 0.964769i \(0.584744\pi\)
\(270\) 0 0
\(271\) 15.5050 0.941860 0.470930 0.882171i \(-0.343918\pi\)
0.470930 + 0.882171i \(0.343918\pi\)
\(272\) 0 0
\(273\) −3.22058 −0.194918
\(274\) 0 0
\(275\) −7.87644 −0.474967
\(276\) 0 0
\(277\) −4.26881 −0.256488 −0.128244 0.991743i \(-0.540934\pi\)
−0.128244 + 0.991743i \(0.540934\pi\)
\(278\) 0 0
\(279\) −40.1472 −2.40355
\(280\) 0 0
\(281\) 30.5752 1.82397 0.911983 0.410228i \(-0.134551\pi\)
0.911983 + 0.410228i \(0.134551\pi\)
\(282\) 0 0
\(283\) 9.50838 0.565215 0.282607 0.959236i \(-0.408801\pi\)
0.282607 + 0.959236i \(0.408801\pi\)
\(284\) 0 0
\(285\) 91.1462 5.39903
\(286\) 0 0
\(287\) 1.50581 0.0888853
\(288\) 0 0
\(289\) 6.24647 0.367439
\(290\) 0 0
\(291\) −2.16602 −0.126975
\(292\) 0 0
\(293\) 9.94798 0.581167 0.290584 0.956850i \(-0.406151\pi\)
0.290584 + 0.956850i \(0.406151\pi\)
\(294\) 0 0
\(295\) 16.4954 0.960398
\(296\) 0 0
\(297\) −14.0808 −0.817048
\(298\) 0 0
\(299\) −4.80149 −0.277677
\(300\) 0 0
\(301\) −9.53445 −0.549556
\(302\) 0 0
\(303\) −54.5194 −3.13206
\(304\) 0 0
\(305\) −18.1226 −1.03770
\(306\) 0 0
\(307\) 1.51711 0.0865863 0.0432931 0.999062i \(-0.486215\pi\)
0.0432931 + 0.999062i \(0.486215\pi\)
\(308\) 0 0
\(309\) −31.8007 −1.80908
\(310\) 0 0
\(311\) −24.5405 −1.39156 −0.695781 0.718254i \(-0.744942\pi\)
−0.695781 + 0.718254i \(0.744942\pi\)
\(312\) 0 0
\(313\) −16.8630 −0.953152 −0.476576 0.879133i \(-0.658122\pi\)
−0.476576 + 0.879133i \(0.658122\pi\)
\(314\) 0 0
\(315\) −26.4539 −1.49051
\(316\) 0 0
\(317\) −4.33688 −0.243583 −0.121792 0.992556i \(-0.538864\pi\)
−0.121792 + 0.992556i \(0.538864\pi\)
\(318\) 0 0
\(319\) −9.62720 −0.539020
\(320\) 0 0
\(321\) −28.4029 −1.58530
\(322\) 0 0
\(323\) 38.0264 2.11585
\(324\) 0 0
\(325\) −7.87644 −0.436906
\(326\) 0 0
\(327\) 62.6777 3.46609
\(328\) 0 0
\(329\) −3.00380 −0.165605
\(330\) 0 0
\(331\) 5.17809 0.284613 0.142307 0.989823i \(-0.454548\pi\)
0.142307 + 0.989823i \(0.454548\pi\)
\(332\) 0 0
\(333\) 1.38568 0.0759350
\(334\) 0 0
\(335\) 46.5258 2.54198
\(336\) 0 0
\(337\) 14.9945 0.816801 0.408401 0.912803i \(-0.366087\pi\)
0.408401 + 0.912803i \(0.366087\pi\)
\(338\) 0 0
\(339\) −59.3258 −3.22213
\(340\) 0 0
\(341\) 5.44581 0.294907
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −55.4891 −2.98743
\(346\) 0 0
\(347\) 11.8587 0.636607 0.318303 0.947989i \(-0.396887\pi\)
0.318303 + 0.947989i \(0.396887\pi\)
\(348\) 0 0
\(349\) 2.50061 0.133854 0.0669272 0.997758i \(-0.478680\pi\)
0.0669272 + 0.997758i \(0.478680\pi\)
\(350\) 0 0
\(351\) −14.0808 −0.751575
\(352\) 0 0
\(353\) −2.57532 −0.137071 −0.0685353 0.997649i \(-0.521833\pi\)
−0.0685353 + 0.997649i \(0.521833\pi\)
\(354\) 0 0
\(355\) 48.3434 2.56580
\(356\) 0 0
\(357\) −15.5279 −0.821823
\(358\) 0 0
\(359\) −27.7361 −1.46386 −0.731928 0.681382i \(-0.761379\pi\)
−0.731928 + 0.681382i \(0.761379\pi\)
\(360\) 0 0
\(361\) 43.2033 2.27386
\(362\) 0 0
\(363\) 3.22058 0.169036
\(364\) 0 0
\(365\) −43.7828 −2.29170
\(366\) 0 0
\(367\) −2.26063 −0.118004 −0.0590019 0.998258i \(-0.518792\pi\)
−0.0590019 + 0.998258i \(0.518792\pi\)
\(368\) 0 0
\(369\) 11.1010 0.577897
\(370\) 0 0
\(371\) −2.34802 −0.121903
\(372\) 0 0
\(373\) 15.5037 0.802750 0.401375 0.915914i \(-0.368532\pi\)
0.401375 + 0.915914i \(0.368532\pi\)
\(374\) 0 0
\(375\) −33.2420 −1.71661
\(376\) 0 0
\(377\) −9.62720 −0.495826
\(378\) 0 0
\(379\) 18.4062 0.945462 0.472731 0.881207i \(-0.343268\pi\)
0.472731 + 0.881207i \(0.343268\pi\)
\(380\) 0 0
\(381\) −27.5967 −1.41382
\(382\) 0 0
\(383\) 21.6395 1.10573 0.552864 0.833272i \(-0.313535\pi\)
0.552864 + 0.833272i \(0.313535\pi\)
\(384\) 0 0
\(385\) 3.58838 0.182881
\(386\) 0 0
\(387\) −70.2891 −3.57300
\(388\) 0 0
\(389\) −18.7136 −0.948816 −0.474408 0.880305i \(-0.657338\pi\)
−0.474408 + 0.880305i \(0.657338\pi\)
\(390\) 0 0
\(391\) −23.1502 −1.17076
\(392\) 0 0
\(393\) 34.5777 1.74422
\(394\) 0 0
\(395\) −39.8086 −2.00299
\(396\) 0 0
\(397\) −8.96224 −0.449802 −0.224901 0.974382i \(-0.572206\pi\)
−0.224901 + 0.974382i \(0.572206\pi\)
\(398\) 0 0
\(399\) −25.4004 −1.27161
\(400\) 0 0
\(401\) 31.1663 1.55637 0.778186 0.628034i \(-0.216140\pi\)
0.778186 + 0.628034i \(0.216140\pi\)
\(402\) 0 0
\(403\) 5.44581 0.271275
\(404\) 0 0
\(405\) −83.3645 −4.14241
\(406\) 0 0
\(407\) −0.187963 −0.00931696
\(408\) 0 0
\(409\) 22.9295 1.13379 0.566896 0.823789i \(-0.308144\pi\)
0.566896 + 0.823789i \(0.308144\pi\)
\(410\) 0 0
\(411\) −13.8882 −0.685053
\(412\) 0 0
\(413\) −4.59689 −0.226198
\(414\) 0 0
\(415\) 49.5231 2.43099
\(416\) 0 0
\(417\) −18.1421 −0.888423
\(418\) 0 0
\(419\) 8.40201 0.410465 0.205233 0.978713i \(-0.434205\pi\)
0.205233 + 0.978713i \(0.434205\pi\)
\(420\) 0 0
\(421\) 26.9322 1.31260 0.656298 0.754502i \(-0.272122\pi\)
0.656298 + 0.754502i \(0.272122\pi\)
\(422\) 0 0
\(423\) −22.1444 −1.07670
\(424\) 0 0
\(425\) −37.9760 −1.84210
\(426\) 0 0
\(427\) 5.05035 0.244404
\(428\) 0 0
\(429\) 3.22058 0.155491
\(430\) 0 0
\(431\) −37.7147 −1.81665 −0.908326 0.418263i \(-0.862639\pi\)
−0.908326 + 0.418263i \(0.862639\pi\)
\(432\) 0 0
\(433\) 2.03235 0.0976686 0.0488343 0.998807i \(-0.484449\pi\)
0.0488343 + 0.998807i \(0.484449\pi\)
\(434\) 0 0
\(435\) −111.258 −5.33442
\(436\) 0 0
\(437\) −37.8689 −1.81152
\(438\) 0 0
\(439\) 34.1673 1.63072 0.815358 0.578957i \(-0.196540\pi\)
0.815358 + 0.578957i \(0.196540\pi\)
\(440\) 0 0
\(441\) 7.37212 0.351053
\(442\) 0 0
\(443\) −13.1136 −0.623045 −0.311522 0.950239i \(-0.600839\pi\)
−0.311522 + 0.950239i \(0.600839\pi\)
\(444\) 0 0
\(445\) 33.8786 1.60600
\(446\) 0 0
\(447\) 57.1880 2.70490
\(448\) 0 0
\(449\) −19.2230 −0.907189 −0.453595 0.891208i \(-0.649859\pi\)
−0.453595 + 0.891208i \(0.649859\pi\)
\(450\) 0 0
\(451\) −1.50581 −0.0709060
\(452\) 0 0
\(453\) −23.9276 −1.12422
\(454\) 0 0
\(455\) 3.58838 0.168226
\(456\) 0 0
\(457\) −1.52855 −0.0715024 −0.0357512 0.999361i \(-0.511382\pi\)
−0.0357512 + 0.999361i \(0.511382\pi\)
\(458\) 0 0
\(459\) −67.8898 −3.16882
\(460\) 0 0
\(461\) 5.36243 0.249753 0.124877 0.992172i \(-0.460147\pi\)
0.124877 + 0.992172i \(0.460147\pi\)
\(462\) 0 0
\(463\) 12.2844 0.570906 0.285453 0.958393i \(-0.407856\pi\)
0.285453 + 0.958393i \(0.407856\pi\)
\(464\) 0 0
\(465\) 62.9353 2.91855
\(466\) 0 0
\(467\) −17.8548 −0.826221 −0.413111 0.910681i \(-0.635558\pi\)
−0.413111 + 0.910681i \(0.635558\pi\)
\(468\) 0 0
\(469\) −12.9657 −0.598700
\(470\) 0 0
\(471\) −73.6141 −3.39196
\(472\) 0 0
\(473\) 9.53445 0.438394
\(474\) 0 0
\(475\) −62.1208 −2.85030
\(476\) 0 0
\(477\) −17.3099 −0.792567
\(478\) 0 0
\(479\) 24.1782 1.10473 0.552365 0.833602i \(-0.313725\pi\)
0.552365 + 0.833602i \(0.313725\pi\)
\(480\) 0 0
\(481\) −0.187963 −0.00857036
\(482\) 0 0
\(483\) 15.4636 0.703617
\(484\) 0 0
\(485\) 2.41339 0.109586
\(486\) 0 0
\(487\) 20.1691 0.913950 0.456975 0.889480i \(-0.348933\pi\)
0.456975 + 0.889480i \(0.348933\pi\)
\(488\) 0 0
\(489\) −35.7091 −1.61482
\(490\) 0 0
\(491\) −33.2466 −1.50040 −0.750199 0.661212i \(-0.770042\pi\)
−0.750199 + 0.661212i \(0.770042\pi\)
\(492\) 0 0
\(493\) −46.4172 −2.09052
\(494\) 0 0
\(495\) 26.4539 1.18902
\(496\) 0 0
\(497\) −13.4722 −0.604312
\(498\) 0 0
\(499\) 16.2438 0.727174 0.363587 0.931560i \(-0.381552\pi\)
0.363587 + 0.931560i \(0.381552\pi\)
\(500\) 0 0
\(501\) −55.8107 −2.49344
\(502\) 0 0
\(503\) −5.01690 −0.223692 −0.111846 0.993726i \(-0.535676\pi\)
−0.111846 + 0.993726i \(0.535676\pi\)
\(504\) 0 0
\(505\) 60.7457 2.70315
\(506\) 0 0
\(507\) 3.22058 0.143031
\(508\) 0 0
\(509\) 4.55308 0.201812 0.100906 0.994896i \(-0.467826\pi\)
0.100906 + 0.994896i \(0.467826\pi\)
\(510\) 0 0
\(511\) 12.2013 0.539753
\(512\) 0 0
\(513\) −111.054 −4.90314
\(514\) 0 0
\(515\) 35.4324 1.56134
\(516\) 0 0
\(517\) 3.00380 0.132107
\(518\) 0 0
\(519\) 4.57589 0.200859
\(520\) 0 0
\(521\) −0.492144 −0.0215612 −0.0107806 0.999942i \(-0.503432\pi\)
−0.0107806 + 0.999942i \(0.503432\pi\)
\(522\) 0 0
\(523\) −25.6861 −1.12317 −0.561587 0.827418i \(-0.689809\pi\)
−0.561587 + 0.827418i \(0.689809\pi\)
\(524\) 0 0
\(525\) 25.3667 1.10709
\(526\) 0 0
\(527\) 26.2568 1.14376
\(528\) 0 0
\(529\) 0.0543117 0.00236138
\(530\) 0 0
\(531\) −33.8888 −1.47065
\(532\) 0 0
\(533\) −1.50581 −0.0652240
\(534\) 0 0
\(535\) 31.6466 1.36820
\(536\) 0 0
\(537\) −28.1227 −1.21358
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) −22.1339 −0.951612 −0.475806 0.879550i \(-0.657844\pi\)
−0.475806 + 0.879550i \(0.657844\pi\)
\(542\) 0 0
\(543\) −9.06642 −0.389077
\(544\) 0 0
\(545\) −69.8357 −2.99143
\(546\) 0 0
\(547\) −3.06333 −0.130979 −0.0654893 0.997853i \(-0.520861\pi\)
−0.0654893 + 0.997853i \(0.520861\pi\)
\(548\) 0 0
\(549\) 37.2318 1.58902
\(550\) 0 0
\(551\) −75.9288 −3.23468
\(552\) 0 0
\(553\) 11.0938 0.471755
\(554\) 0 0
\(555\) −2.17222 −0.0922055
\(556\) 0 0
\(557\) −29.2576 −1.23969 −0.619843 0.784726i \(-0.712804\pi\)
−0.619843 + 0.784726i \(0.712804\pi\)
\(558\) 0 0
\(559\) 9.53445 0.403264
\(560\) 0 0
\(561\) 15.5279 0.655588
\(562\) 0 0
\(563\) 13.6837 0.576701 0.288350 0.957525i \(-0.406893\pi\)
0.288350 + 0.957525i \(0.406893\pi\)
\(564\) 0 0
\(565\) 66.1009 2.78089
\(566\) 0 0
\(567\) 23.2318 0.975644
\(568\) 0 0
\(569\) 33.2646 1.39452 0.697261 0.716817i \(-0.254402\pi\)
0.697261 + 0.716817i \(0.254402\pi\)
\(570\) 0 0
\(571\) −9.90886 −0.414673 −0.207336 0.978270i \(-0.566479\pi\)
−0.207336 + 0.978270i \(0.566479\pi\)
\(572\) 0 0
\(573\) 84.6231 3.53518
\(574\) 0 0
\(575\) 37.8187 1.57715
\(576\) 0 0
\(577\) 12.2505 0.509996 0.254998 0.966942i \(-0.417925\pi\)
0.254998 + 0.966942i \(0.417925\pi\)
\(578\) 0 0
\(579\) 68.3600 2.84095
\(580\) 0 0
\(581\) −13.8010 −0.572561
\(582\) 0 0
\(583\) 2.34802 0.0972452
\(584\) 0 0
\(585\) 26.4539 1.09374
\(586\) 0 0
\(587\) −34.6030 −1.42822 −0.714110 0.700034i \(-0.753168\pi\)
−0.714110 + 0.700034i \(0.753168\pi\)
\(588\) 0 0
\(589\) 42.9506 1.76975
\(590\) 0 0
\(591\) −10.3046 −0.423875
\(592\) 0 0
\(593\) 21.5812 0.886234 0.443117 0.896464i \(-0.353873\pi\)
0.443117 + 0.896464i \(0.353873\pi\)
\(594\) 0 0
\(595\) 17.3012 0.709280
\(596\) 0 0
\(597\) 20.7446 0.849020
\(598\) 0 0
\(599\) 7.49682 0.306312 0.153156 0.988202i \(-0.451056\pi\)
0.153156 + 0.988202i \(0.451056\pi\)
\(600\) 0 0
\(601\) 42.9034 1.75007 0.875034 0.484062i \(-0.160839\pi\)
0.875034 + 0.484062i \(0.160839\pi\)
\(602\) 0 0
\(603\) −95.5847 −3.89251
\(604\) 0 0
\(605\) −3.58838 −0.145888
\(606\) 0 0
\(607\) −18.2793 −0.741934 −0.370967 0.928646i \(-0.620974\pi\)
−0.370967 + 0.928646i \(0.620974\pi\)
\(608\) 0 0
\(609\) 31.0052 1.25639
\(610\) 0 0
\(611\) 3.00380 0.121521
\(612\) 0 0
\(613\) −13.1318 −0.530387 −0.265193 0.964195i \(-0.585436\pi\)
−0.265193 + 0.964195i \(0.585436\pi\)
\(614\) 0 0
\(615\) −17.4021 −0.701722
\(616\) 0 0
\(617\) −28.6665 −1.15407 −0.577035 0.816719i \(-0.695791\pi\)
−0.577035 + 0.816719i \(0.695791\pi\)
\(618\) 0 0
\(619\) −8.00413 −0.321713 −0.160856 0.986978i \(-0.551426\pi\)
−0.160856 + 0.986978i \(0.551426\pi\)
\(620\) 0 0
\(621\) 67.6086 2.71304
\(622\) 0 0
\(623\) −9.44120 −0.378254
\(624\) 0 0
\(625\) −2.34385 −0.0937541
\(626\) 0 0
\(627\) 25.4004 1.01439
\(628\) 0 0
\(629\) −0.906254 −0.0361347
\(630\) 0 0
\(631\) −2.94503 −0.117240 −0.0586198 0.998280i \(-0.518670\pi\)
−0.0586198 + 0.998280i \(0.518670\pi\)
\(632\) 0 0
\(633\) −13.8410 −0.550131
\(634\) 0 0
\(635\) 30.7483 1.22021
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −99.3189 −3.92900
\(640\) 0 0
\(641\) 6.80551 0.268802 0.134401 0.990927i \(-0.457089\pi\)
0.134401 + 0.990927i \(0.457089\pi\)
\(642\) 0 0
\(643\) −5.83786 −0.230223 −0.115111 0.993353i \(-0.536722\pi\)
−0.115111 + 0.993353i \(0.536722\pi\)
\(644\) 0 0
\(645\) 110.186 4.33858
\(646\) 0 0
\(647\) 25.5786 1.00560 0.502800 0.864403i \(-0.332303\pi\)
0.502800 + 0.864403i \(0.332303\pi\)
\(648\) 0 0
\(649\) 4.59689 0.180444
\(650\) 0 0
\(651\) −17.5387 −0.687394
\(652\) 0 0
\(653\) −13.7271 −0.537183 −0.268592 0.963254i \(-0.586558\pi\)
−0.268592 + 0.963254i \(0.586558\pi\)
\(654\) 0 0
\(655\) −38.5266 −1.50536
\(656\) 0 0
\(657\) 89.9494 3.50926
\(658\) 0 0
\(659\) 16.9970 0.662109 0.331054 0.943612i \(-0.392596\pi\)
0.331054 + 0.943612i \(0.392596\pi\)
\(660\) 0 0
\(661\) −14.9076 −0.579839 −0.289920 0.957051i \(-0.593629\pi\)
−0.289920 + 0.957051i \(0.593629\pi\)
\(662\) 0 0
\(663\) 15.5279 0.603053
\(664\) 0 0
\(665\) 28.3012 1.09747
\(666\) 0 0
\(667\) 46.2249 1.78984
\(668\) 0 0
\(669\) 54.8241 2.11962
\(670\) 0 0
\(671\) −5.05035 −0.194967
\(672\) 0 0
\(673\) 43.1293 1.66251 0.831256 0.555889i \(-0.187622\pi\)
0.831256 + 0.555889i \(0.187622\pi\)
\(674\) 0 0
\(675\) 110.906 4.26879
\(676\) 0 0
\(677\) −22.9025 −0.880213 −0.440107 0.897946i \(-0.645059\pi\)
−0.440107 + 0.897946i \(0.645059\pi\)
\(678\) 0 0
\(679\) −0.672558 −0.0258104
\(680\) 0 0
\(681\) 28.1961 1.08048
\(682\) 0 0
\(683\) 30.1717 1.15449 0.577245 0.816571i \(-0.304128\pi\)
0.577245 + 0.816571i \(0.304128\pi\)
\(684\) 0 0
\(685\) 15.4742 0.591240
\(686\) 0 0
\(687\) −7.99296 −0.304950
\(688\) 0 0
\(689\) 2.34802 0.0894526
\(690\) 0 0
\(691\) −43.3464 −1.64897 −0.824487 0.565881i \(-0.808536\pi\)
−0.824487 + 0.565881i \(0.808536\pi\)
\(692\) 0 0
\(693\) −7.37212 −0.280044
\(694\) 0 0
\(695\) 20.2140 0.766760
\(696\) 0 0
\(697\) −7.26022 −0.275000
\(698\) 0 0
\(699\) −91.8326 −3.47343
\(700\) 0 0
\(701\) 20.2983 0.766655 0.383327 0.923613i \(-0.374778\pi\)
0.383327 + 0.923613i \(0.374778\pi\)
\(702\) 0 0
\(703\) −1.48244 −0.0559114
\(704\) 0 0
\(705\) 34.7139 1.30740
\(706\) 0 0
\(707\) −16.9285 −0.636661
\(708\) 0 0
\(709\) −35.3039 −1.32587 −0.662933 0.748679i \(-0.730689\pi\)
−0.662933 + 0.748679i \(0.730689\pi\)
\(710\) 0 0
\(711\) 81.7846 3.06716
\(712\) 0 0
\(713\) −26.1480 −0.979250
\(714\) 0 0
\(715\) −3.58838 −0.134198
\(716\) 0 0
\(717\) 78.8956 2.94641
\(718\) 0 0
\(719\) −8.25158 −0.307732 −0.153866 0.988092i \(-0.549172\pi\)
−0.153866 + 0.988092i \(0.549172\pi\)
\(720\) 0 0
\(721\) −9.87422 −0.367735
\(722\) 0 0
\(723\) −52.5178 −1.95316
\(724\) 0 0
\(725\) 75.8281 2.81619
\(726\) 0 0
\(727\) 22.8606 0.847852 0.423926 0.905697i \(-0.360652\pi\)
0.423926 + 0.905697i \(0.360652\pi\)
\(728\) 0 0
\(729\) 35.2232 1.30456
\(730\) 0 0
\(731\) 45.9700 1.70026
\(732\) 0 0
\(733\) 9.50689 0.351145 0.175572 0.984467i \(-0.443822\pi\)
0.175572 + 0.984467i \(0.443822\pi\)
\(734\) 0 0
\(735\) −11.5566 −0.426273
\(736\) 0 0
\(737\) 12.9657 0.477598
\(738\) 0 0
\(739\) −19.9610 −0.734277 −0.367139 0.930166i \(-0.619663\pi\)
−0.367139 + 0.930166i \(0.619663\pi\)
\(740\) 0 0
\(741\) 25.4004 0.933107
\(742\) 0 0
\(743\) 0.175889 0.00645274 0.00322637 0.999995i \(-0.498973\pi\)
0.00322637 + 0.999995i \(0.498973\pi\)
\(744\) 0 0
\(745\) −63.7190 −2.33448
\(746\) 0 0
\(747\) −101.742 −3.72256
\(748\) 0 0
\(749\) −8.81921 −0.322247
\(750\) 0 0
\(751\) 1.57364 0.0574228 0.0287114 0.999588i \(-0.490860\pi\)
0.0287114 + 0.999588i \(0.490860\pi\)
\(752\) 0 0
\(753\) −50.0414 −1.82361
\(754\) 0 0
\(755\) 26.6602 0.970266
\(756\) 0 0
\(757\) 50.0158 1.81785 0.908927 0.416955i \(-0.136903\pi\)
0.908927 + 0.416955i \(0.136903\pi\)
\(758\) 0 0
\(759\) −15.4636 −0.561292
\(760\) 0 0
\(761\) −16.8031 −0.609110 −0.304555 0.952495i \(-0.598508\pi\)
−0.304555 + 0.952495i \(0.598508\pi\)
\(762\) 0 0
\(763\) 19.4616 0.704558
\(764\) 0 0
\(765\) 127.547 4.61146
\(766\) 0 0
\(767\) 4.59689 0.165984
\(768\) 0 0
\(769\) 35.5212 1.28093 0.640463 0.767989i \(-0.278742\pi\)
0.640463 + 0.767989i \(0.278742\pi\)
\(770\) 0 0
\(771\) −6.97297 −0.251125
\(772\) 0 0
\(773\) −16.8047 −0.604422 −0.302211 0.953241i \(-0.597725\pi\)
−0.302211 + 0.953241i \(0.597725\pi\)
\(774\) 0 0
\(775\) −42.8936 −1.54078
\(776\) 0 0
\(777\) 0.605348 0.0217167
\(778\) 0 0
\(779\) −11.8762 −0.425509
\(780\) 0 0
\(781\) 13.4722 0.482074
\(782\) 0 0
\(783\) 135.558 4.84446
\(784\) 0 0
\(785\) 82.0210 2.92746
\(786\) 0 0
\(787\) −42.6983 −1.52203 −0.761015 0.648734i \(-0.775299\pi\)
−0.761015 + 0.648734i \(0.775299\pi\)
\(788\) 0 0
\(789\) −79.7136 −2.83788
\(790\) 0 0
\(791\) −18.4208 −0.654970
\(792\) 0 0
\(793\) −5.05035 −0.179343
\(794\) 0 0
\(795\) 27.1353 0.962389
\(796\) 0 0
\(797\) 54.5422 1.93198 0.965992 0.258573i \(-0.0832523\pi\)
0.965992 + 0.258573i \(0.0832523\pi\)
\(798\) 0 0
\(799\) 14.4827 0.512361
\(800\) 0 0
\(801\) −69.6017 −2.45926
\(802\) 0 0
\(803\) −12.2013 −0.430574
\(804\) 0 0
\(805\) −17.2296 −0.607262
\(806\) 0 0
\(807\) −27.7943 −0.978405
\(808\) 0 0
\(809\) −20.7298 −0.728822 −0.364411 0.931238i \(-0.618730\pi\)
−0.364411 + 0.931238i \(0.618730\pi\)
\(810\) 0 0
\(811\) 17.3286 0.608490 0.304245 0.952594i \(-0.401596\pi\)
0.304245 + 0.952594i \(0.401596\pi\)
\(812\) 0 0
\(813\) 49.9350 1.75130
\(814\) 0 0
\(815\) 39.7872 1.39368
\(816\) 0 0
\(817\) 75.1973 2.63082
\(818\) 0 0
\(819\) −7.37212 −0.257603
\(820\) 0 0
\(821\) −23.2760 −0.812337 −0.406169 0.913798i \(-0.633135\pi\)
−0.406169 + 0.913798i \(0.633135\pi\)
\(822\) 0 0
\(823\) −21.3793 −0.745237 −0.372618 0.927985i \(-0.621540\pi\)
−0.372618 + 0.927985i \(0.621540\pi\)
\(824\) 0 0
\(825\) −25.3667 −0.883155
\(826\) 0 0
\(827\) 3.61740 0.125789 0.0628947 0.998020i \(-0.479967\pi\)
0.0628947 + 0.998020i \(0.479967\pi\)
\(828\) 0 0
\(829\) 32.0455 1.11299 0.556493 0.830852i \(-0.312147\pi\)
0.556493 + 0.830852i \(0.312147\pi\)
\(830\) 0 0
\(831\) −13.7480 −0.476914
\(832\) 0 0
\(833\) −4.82146 −0.167054
\(834\) 0 0
\(835\) 62.1844 2.15198
\(836\) 0 0
\(837\) −76.6811 −2.65049
\(838\) 0 0
\(839\) 19.9950 0.690305 0.345152 0.938547i \(-0.387827\pi\)
0.345152 + 0.938547i \(0.387827\pi\)
\(840\) 0 0
\(841\) 63.6830 2.19597
\(842\) 0 0
\(843\) 98.4699 3.39148
\(844\) 0 0
\(845\) −3.58838 −0.123444
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 30.6225 1.05096
\(850\) 0 0
\(851\) 0.902501 0.0309373
\(852\) 0 0
\(853\) −2.80987 −0.0962080 −0.0481040 0.998842i \(-0.515318\pi\)
−0.0481040 + 0.998842i \(0.515318\pi\)
\(854\) 0 0
\(855\) 208.640 7.13533
\(856\) 0 0
\(857\) −50.6433 −1.72994 −0.864971 0.501822i \(-0.832663\pi\)
−0.864971 + 0.501822i \(0.832663\pi\)
\(858\) 0 0
\(859\) −29.6529 −1.01174 −0.505871 0.862609i \(-0.668829\pi\)
−0.505871 + 0.862609i \(0.668829\pi\)
\(860\) 0 0
\(861\) 4.84959 0.165274
\(862\) 0 0
\(863\) −42.5305 −1.44776 −0.723878 0.689928i \(-0.757642\pi\)
−0.723878 + 0.689928i \(0.757642\pi\)
\(864\) 0 0
\(865\) −5.09847 −0.173353
\(866\) 0 0
\(867\) 20.1172 0.683217
\(868\) 0 0
\(869\) −11.0938 −0.376330
\(870\) 0 0
\(871\) 12.9657 0.439326
\(872\) 0 0
\(873\) −4.95818 −0.167809
\(874\) 0 0
\(875\) −10.3218 −0.348939
\(876\) 0 0
\(877\) 21.2810 0.718610 0.359305 0.933220i \(-0.383014\pi\)
0.359305 + 0.933220i \(0.383014\pi\)
\(878\) 0 0
\(879\) 32.0383 1.08062
\(880\) 0 0
\(881\) −12.6285 −0.425466 −0.212733 0.977110i \(-0.568236\pi\)
−0.212733 + 0.977110i \(0.568236\pi\)
\(882\) 0 0
\(883\) 37.7754 1.27124 0.635621 0.772001i \(-0.280744\pi\)
0.635621 + 0.772001i \(0.280744\pi\)
\(884\) 0 0
\(885\) 53.1247 1.78577
\(886\) 0 0
\(887\) −6.70061 −0.224984 −0.112492 0.993653i \(-0.535883\pi\)
−0.112492 + 0.993653i \(0.535883\pi\)
\(888\) 0 0
\(889\) −8.56887 −0.287391
\(890\) 0 0
\(891\) −23.2318 −0.778295
\(892\) 0 0
\(893\) 23.6907 0.792779
\(894\) 0 0
\(895\) 31.3343 1.04739
\(896\) 0 0
\(897\) −15.4636 −0.516314
\(898\) 0 0
\(899\) −52.4279 −1.74857
\(900\) 0 0
\(901\) 11.3209 0.377154
\(902\) 0 0
\(903\) −30.7064 −1.02185
\(904\) 0 0
\(905\) 10.1018 0.335796
\(906\) 0 0
\(907\) −37.0193 −1.22920 −0.614602 0.788837i \(-0.710683\pi\)
−0.614602 + 0.788837i \(0.710683\pi\)
\(908\) 0 0
\(909\) −124.799 −4.13931
\(910\) 0 0
\(911\) −5.08133 −0.168352 −0.0841760 0.996451i \(-0.526826\pi\)
−0.0841760 + 0.996451i \(0.526826\pi\)
\(912\) 0 0
\(913\) 13.8010 0.456745
\(914\) 0 0
\(915\) −58.3652 −1.92949
\(916\) 0 0
\(917\) 10.7365 0.354550
\(918\) 0 0
\(919\) −2.40857 −0.0794514 −0.0397257 0.999211i \(-0.512648\pi\)
−0.0397257 + 0.999211i \(0.512648\pi\)
\(920\) 0 0
\(921\) 4.88599 0.160999
\(922\) 0 0
\(923\) 13.4722 0.443444
\(924\) 0 0
\(925\) 1.48048 0.0486778
\(926\) 0 0
\(927\) −72.7939 −2.39087
\(928\) 0 0
\(929\) 49.1507 1.61258 0.806291 0.591519i \(-0.201471\pi\)
0.806291 + 0.591519i \(0.201471\pi\)
\(930\) 0 0
\(931\) −7.88691 −0.258483
\(932\) 0 0
\(933\) −79.0345 −2.58747
\(934\) 0 0
\(935\) −17.3012 −0.565810
\(936\) 0 0
\(937\) 19.9279 0.651016 0.325508 0.945539i \(-0.394465\pi\)
0.325508 + 0.945539i \(0.394465\pi\)
\(938\) 0 0
\(939\) −54.3086 −1.77229
\(940\) 0 0
\(941\) 18.6058 0.606531 0.303266 0.952906i \(-0.401923\pi\)
0.303266 + 0.952906i \(0.401923\pi\)
\(942\) 0 0
\(943\) 7.23015 0.235446
\(944\) 0 0
\(945\) −50.5271 −1.64365
\(946\) 0 0
\(947\) 24.0457 0.781380 0.390690 0.920522i \(-0.372236\pi\)
0.390690 + 0.920522i \(0.372236\pi\)
\(948\) 0 0
\(949\) −12.2013 −0.396071
\(950\) 0 0
\(951\) −13.9672 −0.452919
\(952\) 0 0
\(953\) −11.8193 −0.382865 −0.191432 0.981506i \(-0.561313\pi\)
−0.191432 + 0.981506i \(0.561313\pi\)
\(954\) 0 0
\(955\) −94.2872 −3.05106
\(956\) 0 0
\(957\) −31.0052 −1.00225
\(958\) 0 0
\(959\) −4.31232 −0.139252
\(960\) 0 0
\(961\) −1.34315 −0.0433276
\(962\) 0 0
\(963\) −65.0163 −2.09512
\(964\) 0 0
\(965\) −76.1669 −2.45190
\(966\) 0 0
\(967\) −2.52709 −0.0812657 −0.0406329 0.999174i \(-0.512937\pi\)
−0.0406329 + 0.999174i \(0.512937\pi\)
\(968\) 0 0
\(969\) 122.467 3.93421
\(970\) 0 0
\(971\) −24.9102 −0.799407 −0.399703 0.916645i \(-0.630887\pi\)
−0.399703 + 0.916645i \(0.630887\pi\)
\(972\) 0 0
\(973\) −5.63319 −0.180592
\(974\) 0 0
\(975\) −25.3667 −0.812385
\(976\) 0 0
\(977\) 18.1903 0.581960 0.290980 0.956729i \(-0.406019\pi\)
0.290980 + 0.956729i \(0.406019\pi\)
\(978\) 0 0
\(979\) 9.44120 0.301742
\(980\) 0 0
\(981\) 143.474 4.58076
\(982\) 0 0
\(983\) −41.7039 −1.33015 −0.665074 0.746778i \(-0.731600\pi\)
−0.665074 + 0.746778i \(0.731600\pi\)
\(984\) 0 0
\(985\) 11.4814 0.365828
\(986\) 0 0
\(987\) −9.67398 −0.307926
\(988\) 0 0
\(989\) −45.7796 −1.45571
\(990\) 0 0
\(991\) 47.8239 1.51918 0.759589 0.650404i \(-0.225400\pi\)
0.759589 + 0.650404i \(0.225400\pi\)
\(992\) 0 0
\(993\) 16.6764 0.529210
\(994\) 0 0
\(995\) −23.1137 −0.732753
\(996\) 0 0
\(997\) −16.8654 −0.534134 −0.267067 0.963678i \(-0.586055\pi\)
−0.267067 + 0.963678i \(0.586055\pi\)
\(998\) 0 0
\(999\) 2.64666 0.0837365
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 \(a_p\))