Properties

Label 4016.2.a.m.1.3
Level 4016
Weight 2
Character 4016.1
Self dual yes
Analytic conductor 32.068
Analytic rank 0
Dimension 23
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4016 = 2^{4} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0679214517\)
Analytic rank: \(0\)
Dimension: \(23\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 2008)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.15136 q^{3} +4.04418 q^{5} -3.52087 q^{7} +6.93109 q^{9} +O(q^{10})\) \(q-3.15136 q^{3} +4.04418 q^{5} -3.52087 q^{7} +6.93109 q^{9} +5.53748 q^{11} +0.479348 q^{13} -12.7447 q^{15} -7.91995 q^{17} +5.32818 q^{19} +11.0955 q^{21} +3.98503 q^{23} +11.3554 q^{25} -12.3883 q^{27} +4.58479 q^{29} +0.0567383 q^{31} -17.4506 q^{33} -14.2390 q^{35} -1.74446 q^{37} -1.51060 q^{39} +4.51530 q^{41} +11.5560 q^{43} +28.0306 q^{45} -11.2736 q^{47} +5.39651 q^{49} +24.9586 q^{51} +4.14986 q^{53} +22.3946 q^{55} -16.7910 q^{57} +4.02416 q^{59} -12.3346 q^{61} -24.4034 q^{63} +1.93857 q^{65} +5.97615 q^{67} -12.5583 q^{69} -5.10917 q^{71} +2.78681 q^{73} -35.7849 q^{75} -19.4967 q^{77} +2.61228 q^{79} +18.2467 q^{81} -1.48896 q^{83} -32.0297 q^{85} -14.4483 q^{87} -6.81110 q^{89} -1.68772 q^{91} -0.178803 q^{93} +21.5481 q^{95} -5.45770 q^{97} +38.3808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} + O(q^{10}) \) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} - 8q^{11} + 8q^{13} - 7q^{15} + 19q^{17} + 9q^{19} + 9q^{21} - 21q^{23} + 65q^{25} - 5q^{27} + 10q^{29} + 9q^{31} + 34q^{33} - 12q^{35} + 11q^{37} + 9q^{39} + 35q^{41} + 9q^{43} + 29q^{45} - 37q^{47} + 77q^{49} + 17q^{51} + 38q^{53} + 20q^{55} + 51q^{57} - 17q^{59} - 22q^{63} + 41q^{65} - 9q^{67} + 8q^{69} - 13q^{71} + 41q^{73} - 25q^{75} + 36q^{77} + 36q^{79} + 127q^{81} - 29q^{83} + 34q^{85} - 10q^{87} + 36q^{89} + 6q^{91} + 36q^{93} - 25q^{95} + 40q^{97} - 19q^{99} + O(q^{100}) \)

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
\(3\) −3.15136 −1.81944 −0.909720 0.415222i \(-0.863704\pi\)
−0.909720 + 0.415222i \(0.863704\pi\)
\(4\) 0 0
\(5\) 4.04418 1.80861 0.904306 0.426885i \(-0.140389\pi\)
0.904306 + 0.426885i \(0.140389\pi\)
\(6\) 0 0
\(7\) −3.52087 −1.33076 −0.665381 0.746504i \(-0.731731\pi\)
−0.665381 + 0.746504i \(0.731731\pi\)
\(8\) 0 0
\(9\) 6.93109 2.31036
\(10\) 0 0
\(11\) 5.53748 1.66961 0.834806 0.550544i \(-0.185580\pi\)
0.834806 + 0.550544i \(0.185580\pi\)
\(12\) 0 0
\(13\) 0.479348 0.132947 0.0664735 0.997788i \(-0.478825\pi\)
0.0664735 + 0.997788i \(0.478825\pi\)
\(14\) 0 0
\(15\) −12.7447 −3.29066
\(16\) 0 0
\(17\) −7.91995 −1.92087 −0.960435 0.278503i \(-0.910162\pi\)
−0.960435 + 0.278503i \(0.910162\pi\)
\(18\) 0 0
\(19\) 5.32818 1.22237 0.611184 0.791489i \(-0.290694\pi\)
0.611184 + 0.791489i \(0.290694\pi\)
\(20\) 0 0
\(21\) 11.0955 2.42124
\(22\) 0 0
\(23\) 3.98503 0.830936 0.415468 0.909608i \(-0.363618\pi\)
0.415468 + 0.909608i \(0.363618\pi\)
\(24\) 0 0
\(25\) 11.3554 2.27108
\(26\) 0 0
\(27\) −12.3883 −2.38413
\(28\) 0 0
\(29\) 4.58479 0.851375 0.425687 0.904870i \(-0.360032\pi\)
0.425687 + 0.904870i \(0.360032\pi\)
\(30\) 0 0
\(31\) 0.0567383 0.0101905 0.00509525 0.999987i \(-0.498378\pi\)
0.00509525 + 0.999987i \(0.498378\pi\)
\(32\) 0 0
\(33\) −17.4506 −3.03776
\(34\) 0 0
\(35\) −14.2390 −2.40683
\(36\) 0 0
\(37\) −1.74446 −0.286787 −0.143394 0.989666i \(-0.545802\pi\)
−0.143394 + 0.989666i \(0.545802\pi\)
\(38\) 0 0
\(39\) −1.51060 −0.241889
\(40\) 0 0
\(41\) 4.51530 0.705171 0.352586 0.935780i \(-0.385303\pi\)
0.352586 + 0.935780i \(0.385303\pi\)
\(42\) 0 0
\(43\) 11.5560 1.76227 0.881135 0.472864i \(-0.156780\pi\)
0.881135 + 0.472864i \(0.156780\pi\)
\(44\) 0 0
\(45\) 28.0306 4.17855
\(46\) 0 0
\(47\) −11.2736 −1.64442 −0.822212 0.569181i \(-0.807260\pi\)
−0.822212 + 0.569181i \(0.807260\pi\)
\(48\) 0 0
\(49\) 5.39651 0.770929
\(50\) 0 0
\(51\) 24.9586 3.49491
\(52\) 0 0
\(53\) 4.14986 0.570027 0.285014 0.958523i \(-0.408002\pi\)
0.285014 + 0.958523i \(0.408002\pi\)
\(54\) 0 0
\(55\) 22.3946 3.01968
\(56\) 0 0
\(57\) −16.7910 −2.22403
\(58\) 0 0
\(59\) 4.02416 0.523901 0.261951 0.965081i \(-0.415634\pi\)
0.261951 + 0.965081i \(0.415634\pi\)
\(60\) 0 0
\(61\) −12.3346 −1.57929 −0.789643 0.613566i \(-0.789734\pi\)
−0.789643 + 0.613566i \(0.789734\pi\)
\(62\) 0 0
\(63\) −24.4034 −3.07455
\(64\) 0 0
\(65\) 1.93857 0.240450
\(66\) 0 0
\(67\) 5.97615 0.730103 0.365051 0.930987i \(-0.381051\pi\)
0.365051 + 0.930987i \(0.381051\pi\)
\(68\) 0 0
\(69\) −12.5583 −1.51184
\(70\) 0 0
\(71\) −5.10917 −0.606347 −0.303173 0.952935i \(-0.598046\pi\)
−0.303173 + 0.952935i \(0.598046\pi\)
\(72\) 0 0
\(73\) 2.78681 0.326171 0.163086 0.986612i \(-0.447855\pi\)
0.163086 + 0.986612i \(0.447855\pi\)
\(74\) 0 0
\(75\) −35.7849 −4.13209
\(76\) 0 0
\(77\) −19.4967 −2.22186
\(78\) 0 0
\(79\) 2.61228 0.293904 0.146952 0.989144i \(-0.453054\pi\)
0.146952 + 0.989144i \(0.453054\pi\)
\(80\) 0 0
\(81\) 18.2467 2.02742
\(82\) 0 0
\(83\) −1.48896 −0.163435 −0.0817173 0.996656i \(-0.526040\pi\)
−0.0817173 + 0.996656i \(0.526040\pi\)
\(84\) 0 0
\(85\) −32.0297 −3.47411
\(86\) 0 0
\(87\) −14.4483 −1.54903
\(88\) 0 0
\(89\) −6.81110 −0.721976 −0.360988 0.932571i \(-0.617560\pi\)
−0.360988 + 0.932571i \(0.617560\pi\)
\(90\) 0 0
\(91\) −1.68772 −0.176921
\(92\) 0 0
\(93\) −0.178803 −0.0185410
\(94\) 0 0
\(95\) 21.5481 2.21079
\(96\) 0 0
\(97\) −5.45770 −0.554145 −0.277072 0.960849i \(-0.589364\pi\)
−0.277072 + 0.960849i \(0.589364\pi\)
\(98\) 0 0
\(99\) 38.3808 3.85741
\(100\) 0 0
\(101\) 1.79407 0.178517 0.0892585 0.996008i \(-0.471550\pi\)
0.0892585 + 0.996008i \(0.471550\pi\)
\(102\) 0 0
\(103\) −7.62771 −0.751581 −0.375790 0.926705i \(-0.622629\pi\)
−0.375790 + 0.926705i \(0.622629\pi\)
\(104\) 0 0
\(105\) 44.8723 4.37909
\(106\) 0 0
\(107\) −6.94989 −0.671872 −0.335936 0.941885i \(-0.609053\pi\)
−0.335936 + 0.941885i \(0.609053\pi\)
\(108\) 0 0
\(109\) −13.2310 −1.26730 −0.633650 0.773620i \(-0.718444\pi\)
−0.633650 + 0.773620i \(0.718444\pi\)
\(110\) 0 0
\(111\) 5.49743 0.521793
\(112\) 0 0
\(113\) 16.5091 1.55304 0.776521 0.630092i \(-0.216983\pi\)
0.776521 + 0.630092i \(0.216983\pi\)
\(114\) 0 0
\(115\) 16.1162 1.50284
\(116\) 0 0
\(117\) 3.32240 0.307156
\(118\) 0 0
\(119\) 27.8851 2.55622
\(120\) 0 0
\(121\) 19.6637 1.78761
\(122\) 0 0
\(123\) −14.2293 −1.28302
\(124\) 0 0
\(125\) 25.7023 2.29888
\(126\) 0 0
\(127\) −1.48799 −0.132037 −0.0660187 0.997818i \(-0.521030\pi\)
−0.0660187 + 0.997818i \(0.521030\pi\)
\(128\) 0 0
\(129\) −36.4171 −3.20635
\(130\) 0 0
\(131\) −1.69420 −0.148023 −0.0740116 0.997257i \(-0.523580\pi\)
−0.0740116 + 0.997257i \(0.523580\pi\)
\(132\) 0 0
\(133\) −18.7598 −1.62668
\(134\) 0 0
\(135\) −50.1005 −4.31196
\(136\) 0 0
\(137\) 9.76601 0.834367 0.417183 0.908822i \(-0.363017\pi\)
0.417183 + 0.908822i \(0.363017\pi\)
\(138\) 0 0
\(139\) −7.40302 −0.627916 −0.313958 0.949437i \(-0.601655\pi\)
−0.313958 + 0.949437i \(0.601655\pi\)
\(140\) 0 0
\(141\) 35.5272 2.99193
\(142\) 0 0
\(143\) 2.65438 0.221970
\(144\) 0 0
\(145\) 18.5417 1.53981
\(146\) 0 0
\(147\) −17.0063 −1.40266
\(148\) 0 0
\(149\) 13.2514 1.08560 0.542801 0.839862i \(-0.317364\pi\)
0.542801 + 0.839862i \(0.317364\pi\)
\(150\) 0 0
\(151\) 6.04285 0.491760 0.245880 0.969300i \(-0.420923\pi\)
0.245880 + 0.969300i \(0.420923\pi\)
\(152\) 0 0
\(153\) −54.8939 −4.43791
\(154\) 0 0
\(155\) 0.229460 0.0184307
\(156\) 0 0
\(157\) 6.09159 0.486162 0.243081 0.970006i \(-0.421842\pi\)
0.243081 + 0.970006i \(0.421842\pi\)
\(158\) 0 0
\(159\) −13.0777 −1.03713
\(160\) 0 0
\(161\) −14.0308 −1.10578
\(162\) 0 0
\(163\) 3.28142 0.257021 0.128510 0.991708i \(-0.458980\pi\)
0.128510 + 0.991708i \(0.458980\pi\)
\(164\) 0 0
\(165\) −70.5734 −5.49413
\(166\) 0 0
\(167\) 7.80322 0.603832 0.301916 0.953335i \(-0.402374\pi\)
0.301916 + 0.953335i \(0.402374\pi\)
\(168\) 0 0
\(169\) −12.7702 −0.982325
\(170\) 0 0
\(171\) 36.9301 2.82411
\(172\) 0 0
\(173\) −8.64285 −0.657104 −0.328552 0.944486i \(-0.606561\pi\)
−0.328552 + 0.944486i \(0.606561\pi\)
\(174\) 0 0
\(175\) −39.9808 −3.02226
\(176\) 0 0
\(177\) −12.6816 −0.953207
\(178\) 0 0
\(179\) 15.5814 1.16461 0.582306 0.812970i \(-0.302151\pi\)
0.582306 + 0.812970i \(0.302151\pi\)
\(180\) 0 0
\(181\) 11.2473 0.836008 0.418004 0.908445i \(-0.362730\pi\)
0.418004 + 0.908445i \(0.362730\pi\)
\(182\) 0 0
\(183\) 38.8709 2.87342
\(184\) 0 0
\(185\) −7.05491 −0.518687
\(186\) 0 0
\(187\) −43.8566 −3.20711
\(188\) 0 0
\(189\) 43.6175 3.17271
\(190\) 0 0
\(191\) 1.81146 0.131073 0.0655364 0.997850i \(-0.479124\pi\)
0.0655364 + 0.997850i \(0.479124\pi\)
\(192\) 0 0
\(193\) 9.19667 0.661991 0.330995 0.943632i \(-0.392616\pi\)
0.330995 + 0.943632i \(0.392616\pi\)
\(194\) 0 0
\(195\) −6.10913 −0.437484
\(196\) 0 0
\(197\) 10.9081 0.777169 0.388585 0.921413i \(-0.372964\pi\)
0.388585 + 0.921413i \(0.372964\pi\)
\(198\) 0 0
\(199\) −11.1164 −0.788023 −0.394012 0.919105i \(-0.628913\pi\)
−0.394012 + 0.919105i \(0.628913\pi\)
\(200\) 0 0
\(201\) −18.8330 −1.32838
\(202\) 0 0
\(203\) −16.1424 −1.13298
\(204\) 0 0
\(205\) 18.2607 1.27538
\(206\) 0 0
\(207\) 27.6206 1.91976
\(208\) 0 0
\(209\) 29.5047 2.04088
\(210\) 0 0
\(211\) −12.5194 −0.861868 −0.430934 0.902383i \(-0.641816\pi\)
−0.430934 + 0.902383i \(0.641816\pi\)
\(212\) 0 0
\(213\) 16.1008 1.10321
\(214\) 0 0
\(215\) 46.7345 3.18726
\(216\) 0 0
\(217\) −0.199768 −0.0135611
\(218\) 0 0
\(219\) −8.78225 −0.593449
\(220\) 0 0
\(221\) −3.79641 −0.255374
\(222\) 0 0
\(223\) 12.9011 0.863924 0.431962 0.901892i \(-0.357821\pi\)
0.431962 + 0.901892i \(0.357821\pi\)
\(224\) 0 0
\(225\) 78.7051 5.24701
\(226\) 0 0
\(227\) 12.4519 0.826463 0.413231 0.910626i \(-0.364400\pi\)
0.413231 + 0.910626i \(0.364400\pi\)
\(228\) 0 0
\(229\) −10.6207 −0.701834 −0.350917 0.936407i \(-0.614130\pi\)
−0.350917 + 0.936407i \(0.614130\pi\)
\(230\) 0 0
\(231\) 61.4413 4.04254
\(232\) 0 0
\(233\) 19.6738 1.28887 0.644436 0.764658i \(-0.277092\pi\)
0.644436 + 0.764658i \(0.277092\pi\)
\(234\) 0 0
\(235\) −45.5925 −2.97412
\(236\) 0 0
\(237\) −8.23223 −0.534741
\(238\) 0 0
\(239\) −25.8440 −1.67171 −0.835855 0.548951i \(-0.815028\pi\)
−0.835855 + 0.548951i \(0.815028\pi\)
\(240\) 0 0
\(241\) 10.3953 0.669618 0.334809 0.942286i \(-0.391328\pi\)
0.334809 + 0.942286i \(0.391328\pi\)
\(242\) 0 0
\(243\) −20.3372 −1.30463
\(244\) 0 0
\(245\) 21.8244 1.39431
\(246\) 0 0
\(247\) 2.55405 0.162510
\(248\) 0 0
\(249\) 4.69225 0.297359
\(250\) 0 0
\(251\) 1.00000 0.0631194
\(252\) 0 0
\(253\) 22.0670 1.38734
\(254\) 0 0
\(255\) 100.937 6.32093
\(256\) 0 0
\(257\) −21.1531 −1.31949 −0.659746 0.751489i \(-0.729336\pi\)
−0.659746 + 0.751489i \(0.729336\pi\)
\(258\) 0 0
\(259\) 6.14201 0.381646
\(260\) 0 0
\(261\) 31.7776 1.96699
\(262\) 0 0
\(263\) 23.8106 1.46822 0.734112 0.679028i \(-0.237599\pi\)
0.734112 + 0.679028i \(0.237599\pi\)
\(264\) 0 0
\(265\) 16.7828 1.03096
\(266\) 0 0
\(267\) 21.4643 1.31359
\(268\) 0 0
\(269\) 17.2857 1.05392 0.526962 0.849889i \(-0.323331\pi\)
0.526962 + 0.849889i \(0.323331\pi\)
\(270\) 0 0
\(271\) 28.7163 1.74439 0.872194 0.489159i \(-0.162696\pi\)
0.872194 + 0.489159i \(0.162696\pi\)
\(272\) 0 0
\(273\) 5.31862 0.321897
\(274\) 0 0
\(275\) 62.8802 3.79182
\(276\) 0 0
\(277\) −8.14989 −0.489679 −0.244840 0.969564i \(-0.578735\pi\)
−0.244840 + 0.969564i \(0.578735\pi\)
\(278\) 0 0
\(279\) 0.393259 0.0235438
\(280\) 0 0
\(281\) 29.1216 1.73725 0.868626 0.495469i \(-0.165004\pi\)
0.868626 + 0.495469i \(0.165004\pi\)
\(282\) 0 0
\(283\) 0.474087 0.0281816 0.0140908 0.999901i \(-0.495515\pi\)
0.0140908 + 0.999901i \(0.495515\pi\)
\(284\) 0 0
\(285\) −67.9059 −4.02240
\(286\) 0 0
\(287\) −15.8978 −0.938416
\(288\) 0 0
\(289\) 45.7256 2.68974
\(290\) 0 0
\(291\) 17.1992 1.00823
\(292\) 0 0
\(293\) 28.8082 1.68299 0.841497 0.540261i \(-0.181675\pi\)
0.841497 + 0.540261i \(0.181675\pi\)
\(294\) 0 0
\(295\) 16.2744 0.947533
\(296\) 0 0
\(297\) −68.5999 −3.98057
\(298\) 0 0
\(299\) 1.91021 0.110470
\(300\) 0 0
\(301\) −40.6871 −2.34516
\(302\) 0 0
\(303\) −5.65378 −0.324801
\(304\) 0 0
\(305\) −49.8834 −2.85632
\(306\) 0 0
\(307\) 26.9035 1.53546 0.767732 0.640771i \(-0.221385\pi\)
0.767732 + 0.640771i \(0.221385\pi\)
\(308\) 0 0
\(309\) 24.0377 1.36746
\(310\) 0 0
\(311\) −16.0223 −0.908540 −0.454270 0.890864i \(-0.650100\pi\)
−0.454270 + 0.890864i \(0.650100\pi\)
\(312\) 0 0
\(313\) −16.1881 −0.915004 −0.457502 0.889209i \(-0.651256\pi\)
−0.457502 + 0.889209i \(0.651256\pi\)
\(314\) 0 0
\(315\) −98.6919 −5.56066
\(316\) 0 0
\(317\) 3.76329 0.211367 0.105684 0.994400i \(-0.466297\pi\)
0.105684 + 0.994400i \(0.466297\pi\)
\(318\) 0 0
\(319\) 25.3882 1.42147
\(320\) 0 0
\(321\) 21.9016 1.22243
\(322\) 0 0
\(323\) −42.1989 −2.34801
\(324\) 0 0
\(325\) 5.44317 0.301933
\(326\) 0 0
\(327\) 41.6957 2.30578
\(328\) 0 0
\(329\) 39.6929 2.18834
\(330\) 0 0
\(331\) −26.1622 −1.43800 −0.719001 0.695009i \(-0.755401\pi\)
−0.719001 + 0.695009i \(0.755401\pi\)
\(332\) 0 0
\(333\) −12.0910 −0.662583
\(334\) 0 0
\(335\) 24.1686 1.32047
\(336\) 0 0
\(337\) 15.6236 0.851070 0.425535 0.904942i \(-0.360086\pi\)
0.425535 + 0.904942i \(0.360086\pi\)
\(338\) 0 0
\(339\) −52.0260 −2.82567
\(340\) 0 0
\(341\) 0.314187 0.0170142
\(342\) 0 0
\(343\) 5.64569 0.304839
\(344\) 0 0
\(345\) −50.7879 −2.73433
\(346\) 0 0
\(347\) −27.7409 −1.48921 −0.744604 0.667506i \(-0.767362\pi\)
−0.744604 + 0.667506i \(0.767362\pi\)
\(348\) 0 0
\(349\) −22.9806 −1.23012 −0.615062 0.788479i \(-0.710869\pi\)
−0.615062 + 0.788479i \(0.710869\pi\)
\(350\) 0 0
\(351\) −5.93830 −0.316963
\(352\) 0 0
\(353\) −6.88236 −0.366311 −0.183155 0.983084i \(-0.558631\pi\)
−0.183155 + 0.983084i \(0.558631\pi\)
\(354\) 0 0
\(355\) −20.6624 −1.09665
\(356\) 0 0
\(357\) −87.8761 −4.65089
\(358\) 0 0
\(359\) 14.9320 0.788083 0.394041 0.919093i \(-0.371077\pi\)
0.394041 + 0.919093i \(0.371077\pi\)
\(360\) 0 0
\(361\) 9.38949 0.494184
\(362\) 0 0
\(363\) −61.9674 −3.25244
\(364\) 0 0
\(365\) 11.2704 0.589917
\(366\) 0 0
\(367\) 9.32339 0.486677 0.243338 0.969941i \(-0.421757\pi\)
0.243338 + 0.969941i \(0.421757\pi\)
\(368\) 0 0
\(369\) 31.2959 1.62920
\(370\) 0 0
\(371\) −14.6111 −0.758571
\(372\) 0 0
\(373\) 20.1887 1.04533 0.522665 0.852538i \(-0.324938\pi\)
0.522665 + 0.852538i \(0.324938\pi\)
\(374\) 0 0
\(375\) −80.9972 −4.18268
\(376\) 0 0
\(377\) 2.19771 0.113188
\(378\) 0 0
\(379\) 19.1073 0.981477 0.490739 0.871307i \(-0.336727\pi\)
0.490739 + 0.871307i \(0.336727\pi\)
\(380\) 0 0
\(381\) 4.68919 0.240234
\(382\) 0 0
\(383\) 4.05445 0.207173 0.103586 0.994620i \(-0.466968\pi\)
0.103586 + 0.994620i \(0.466968\pi\)
\(384\) 0 0
\(385\) −78.8482 −4.01848
\(386\) 0 0
\(387\) 80.0956 4.07149
\(388\) 0 0
\(389\) −10.3037 −0.522419 −0.261209 0.965282i \(-0.584121\pi\)
−0.261209 + 0.965282i \(0.584121\pi\)
\(390\) 0 0
\(391\) −31.5612 −1.59612
\(392\) 0 0
\(393\) 5.33905 0.269319
\(394\) 0 0
\(395\) 10.5645 0.531558
\(396\) 0 0
\(397\) 37.7089 1.89256 0.946278 0.323353i \(-0.104810\pi\)
0.946278 + 0.323353i \(0.104810\pi\)
\(398\) 0 0
\(399\) 59.1190 2.95965
\(400\) 0 0
\(401\) 14.4754 0.722867 0.361434 0.932398i \(-0.382287\pi\)
0.361434 + 0.932398i \(0.382287\pi\)
\(402\) 0 0
\(403\) 0.0271974 0.00135480
\(404\) 0 0
\(405\) 73.7931 3.66681
\(406\) 0 0
\(407\) −9.65991 −0.478824
\(408\) 0 0
\(409\) 12.5803 0.622054 0.311027 0.950401i \(-0.399327\pi\)
0.311027 + 0.950401i \(0.399327\pi\)
\(410\) 0 0
\(411\) −30.7763 −1.51808
\(412\) 0 0
\(413\) −14.1685 −0.697188
\(414\) 0 0
\(415\) −6.02162 −0.295590
\(416\) 0 0
\(417\) 23.3296 1.14246
\(418\) 0 0
\(419\) −4.00486 −0.195650 −0.0978251 0.995204i \(-0.531189\pi\)
−0.0978251 + 0.995204i \(0.531189\pi\)
\(420\) 0 0
\(421\) 6.98847 0.340597 0.170299 0.985392i \(-0.445527\pi\)
0.170299 + 0.985392i \(0.445527\pi\)
\(422\) 0 0
\(423\) −78.1384 −3.79922
\(424\) 0 0
\(425\) −89.9340 −4.36244
\(426\) 0 0
\(427\) 43.4286 2.10166
\(428\) 0 0
\(429\) −8.36491 −0.403862
\(430\) 0 0
\(431\) 12.3992 0.597248 0.298624 0.954371i \(-0.403472\pi\)
0.298624 + 0.954371i \(0.403472\pi\)
\(432\) 0 0
\(433\) 20.9395 1.00629 0.503143 0.864203i \(-0.332177\pi\)
0.503143 + 0.864203i \(0.332177\pi\)
\(434\) 0 0
\(435\) −58.4317 −2.80159
\(436\) 0 0
\(437\) 21.2329 1.01571
\(438\) 0 0
\(439\) −8.17498 −0.390170 −0.195085 0.980786i \(-0.562498\pi\)
−0.195085 + 0.980786i \(0.562498\pi\)
\(440\) 0 0
\(441\) 37.4037 1.78113
\(442\) 0 0
\(443\) 4.88162 0.231933 0.115966 0.993253i \(-0.463004\pi\)
0.115966 + 0.993253i \(0.463004\pi\)
\(444\) 0 0
\(445\) −27.5453 −1.30577
\(446\) 0 0
\(447\) −41.7601 −1.97519
\(448\) 0 0
\(449\) −3.88168 −0.183188 −0.0915940 0.995796i \(-0.529196\pi\)
−0.0915940 + 0.995796i \(0.529196\pi\)
\(450\) 0 0
\(451\) 25.0034 1.17736
\(452\) 0 0
\(453\) −19.0432 −0.894728
\(454\) 0 0
\(455\) −6.82544 −0.319981
\(456\) 0 0
\(457\) −35.5909 −1.66487 −0.832435 0.554123i \(-0.813054\pi\)
−0.832435 + 0.554123i \(0.813054\pi\)
\(458\) 0 0
\(459\) 98.1147 4.57960
\(460\) 0 0
\(461\) 20.6008 0.959475 0.479738 0.877412i \(-0.340732\pi\)
0.479738 + 0.877412i \(0.340732\pi\)
\(462\) 0 0
\(463\) −16.5277 −0.768108 −0.384054 0.923311i \(-0.625472\pi\)
−0.384054 + 0.923311i \(0.625472\pi\)
\(464\) 0 0
\(465\) −0.723112 −0.0335335
\(466\) 0 0
\(467\) 12.4680 0.576950 0.288475 0.957487i \(-0.406852\pi\)
0.288475 + 0.957487i \(0.406852\pi\)
\(468\) 0 0
\(469\) −21.0412 −0.971594
\(470\) 0 0
\(471\) −19.1968 −0.884542
\(472\) 0 0
\(473\) 63.9910 2.94231
\(474\) 0 0
\(475\) 60.5035 2.77609
\(476\) 0 0
\(477\) 28.7631 1.31697
\(478\) 0 0
\(479\) −16.9698 −0.775370 −0.387685 0.921792i \(-0.626725\pi\)
−0.387685 + 0.921792i \(0.626725\pi\)
\(480\) 0 0
\(481\) −0.836203 −0.0381276
\(482\) 0 0
\(483\) 44.2160 2.01190
\(484\) 0 0
\(485\) −22.0719 −1.00223
\(486\) 0 0
\(487\) −17.2328 −0.780893 −0.390446 0.920626i \(-0.627679\pi\)
−0.390446 + 0.920626i \(0.627679\pi\)
\(488\) 0 0
\(489\) −10.3409 −0.467634
\(490\) 0 0
\(491\) 18.7874 0.847865 0.423933 0.905694i \(-0.360649\pi\)
0.423933 + 0.905694i \(0.360649\pi\)
\(492\) 0 0
\(493\) −36.3113 −1.63538
\(494\) 0 0
\(495\) 155.219 6.97656
\(496\) 0 0
\(497\) 17.9887 0.806904
\(498\) 0 0
\(499\) −36.7584 −1.64553 −0.822765 0.568381i \(-0.807570\pi\)
−0.822765 + 0.568381i \(0.807570\pi\)
\(500\) 0 0
\(501\) −24.5908 −1.09864
\(502\) 0 0
\(503\) 17.0001 0.757996 0.378998 0.925397i \(-0.376269\pi\)
0.378998 + 0.925397i \(0.376269\pi\)
\(504\) 0 0
\(505\) 7.25555 0.322868
\(506\) 0 0
\(507\) 40.2436 1.78728
\(508\) 0 0
\(509\) 11.0726 0.490783 0.245391 0.969424i \(-0.421084\pi\)
0.245391 + 0.969424i \(0.421084\pi\)
\(510\) 0 0
\(511\) −9.81198 −0.434057
\(512\) 0 0
\(513\) −66.0070 −2.91428
\(514\) 0 0
\(515\) −30.8478 −1.35932
\(516\) 0 0
\(517\) −62.4273 −2.74555
\(518\) 0 0
\(519\) 27.2368 1.19556
\(520\) 0 0
\(521\) −0.0217845 −0.000954397 0 −0.000477198 1.00000i \(-0.500152\pi\)
−0.000477198 1.00000i \(0.500152\pi\)
\(522\) 0 0
\(523\) 33.5812 1.46840 0.734201 0.678932i \(-0.237557\pi\)
0.734201 + 0.678932i \(0.237557\pi\)
\(524\) 0 0
\(525\) 125.994 5.49883
\(526\) 0 0
\(527\) −0.449365 −0.0195746
\(528\) 0 0
\(529\) −7.11956 −0.309546
\(530\) 0 0
\(531\) 27.8918 1.21040
\(532\) 0 0
\(533\) 2.16440 0.0937505
\(534\) 0 0
\(535\) −28.1066 −1.21515
\(536\) 0 0
\(537\) −49.1028 −2.11894
\(538\) 0 0
\(539\) 29.8830 1.28715
\(540\) 0 0
\(541\) −13.5095 −0.580817 −0.290409 0.956903i \(-0.593791\pi\)
−0.290409 + 0.956903i \(0.593791\pi\)
\(542\) 0 0
\(543\) −35.4444 −1.52107
\(544\) 0 0
\(545\) −53.5085 −2.29205
\(546\) 0 0
\(547\) −16.1666 −0.691233 −0.345617 0.938376i \(-0.612330\pi\)
−0.345617 + 0.938376i \(0.612330\pi\)
\(548\) 0 0
\(549\) −85.4924 −3.64873
\(550\) 0 0
\(551\) 24.4286 1.04069
\(552\) 0 0
\(553\) −9.19748 −0.391117
\(554\) 0 0
\(555\) 22.2326 0.943720
\(556\) 0 0
\(557\) −41.9289 −1.77659 −0.888293 0.459278i \(-0.848108\pi\)
−0.888293 + 0.459278i \(0.848108\pi\)
\(558\) 0 0
\(559\) 5.53933 0.234289
\(560\) 0 0
\(561\) 138.208 5.83515
\(562\) 0 0
\(563\) −5.70801 −0.240564 −0.120282 0.992740i \(-0.538380\pi\)
−0.120282 + 0.992740i \(0.538380\pi\)
\(564\) 0 0
\(565\) 66.7656 2.80885
\(566\) 0 0
\(567\) −64.2444 −2.69801
\(568\) 0 0
\(569\) 24.7184 1.03625 0.518125 0.855305i \(-0.326630\pi\)
0.518125 + 0.855305i \(0.326630\pi\)
\(570\) 0 0
\(571\) 37.8063 1.58214 0.791072 0.611723i \(-0.209523\pi\)
0.791072 + 0.611723i \(0.209523\pi\)
\(572\) 0 0
\(573\) −5.70858 −0.238479
\(574\) 0 0
\(575\) 45.2515 1.88712
\(576\) 0 0
\(577\) −37.7099 −1.56988 −0.784942 0.619569i \(-0.787307\pi\)
−0.784942 + 0.619569i \(0.787307\pi\)
\(578\) 0 0
\(579\) −28.9820 −1.20445
\(580\) 0 0
\(581\) 5.24243 0.217493
\(582\) 0 0
\(583\) 22.9798 0.951725
\(584\) 0 0
\(585\) 13.4364 0.555526
\(586\) 0 0
\(587\) −1.98185 −0.0817998 −0.0408999 0.999163i \(-0.513022\pi\)
−0.0408999 + 0.999163i \(0.513022\pi\)
\(588\) 0 0
\(589\) 0.302312 0.0124566
\(590\) 0 0
\(591\) −34.3754 −1.41401
\(592\) 0 0
\(593\) −33.4131 −1.37211 −0.686055 0.727550i \(-0.740659\pi\)
−0.686055 + 0.727550i \(0.740659\pi\)
\(594\) 0 0
\(595\) 112.772 4.62321
\(596\) 0 0
\(597\) 35.0319 1.43376
\(598\) 0 0
\(599\) −24.4120 −0.997447 −0.498723 0.866761i \(-0.666198\pi\)
−0.498723 + 0.866761i \(0.666198\pi\)
\(600\) 0 0
\(601\) −0.535645 −0.0218494 −0.0109247 0.999940i \(-0.503478\pi\)
−0.0109247 + 0.999940i \(0.503478\pi\)
\(602\) 0 0
\(603\) 41.4212 1.68680
\(604\) 0 0
\(605\) 79.5234 3.23309
\(606\) 0 0
\(607\) 38.4095 1.55899 0.779497 0.626406i \(-0.215475\pi\)
0.779497 + 0.626406i \(0.215475\pi\)
\(608\) 0 0
\(609\) 50.8707 2.06139
\(610\) 0 0
\(611\) −5.40397 −0.218621
\(612\) 0 0
\(613\) −10.0723 −0.406815 −0.203407 0.979094i \(-0.565202\pi\)
−0.203407 + 0.979094i \(0.565202\pi\)
\(614\) 0 0
\(615\) −57.5460 −2.32048
\(616\) 0 0
\(617\) −22.1667 −0.892396 −0.446198 0.894934i \(-0.647222\pi\)
−0.446198 + 0.894934i \(0.647222\pi\)
\(618\) 0 0
\(619\) −31.1859 −1.25347 −0.626734 0.779233i \(-0.715609\pi\)
−0.626734 + 0.779233i \(0.715609\pi\)
\(620\) 0 0
\(621\) −49.3677 −1.98106
\(622\) 0 0
\(623\) 23.9810 0.960778
\(624\) 0 0
\(625\) 47.1677 1.88671
\(626\) 0 0
\(627\) −92.9800 −3.71326
\(628\) 0 0
\(629\) 13.8160 0.550882
\(630\) 0 0
\(631\) −0.787730 −0.0313590 −0.0156795 0.999877i \(-0.504991\pi\)
−0.0156795 + 0.999877i \(0.504991\pi\)
\(632\) 0 0
\(633\) 39.4531 1.56812
\(634\) 0 0
\(635\) −6.01768 −0.238804
\(636\) 0 0
\(637\) 2.58680 0.102493
\(638\) 0 0
\(639\) −35.4121 −1.40088
\(640\) 0 0
\(641\) −38.1821 −1.50810 −0.754051 0.656816i \(-0.771903\pi\)
−0.754051 + 0.656816i \(0.771903\pi\)
\(642\) 0 0
\(643\) −24.7804 −0.977243 −0.488622 0.872496i \(-0.662500\pi\)
−0.488622 + 0.872496i \(0.662500\pi\)
\(644\) 0 0
\(645\) −147.277 −5.79904
\(646\) 0 0
\(647\) 44.2350 1.73906 0.869528 0.493883i \(-0.164423\pi\)
0.869528 + 0.493883i \(0.164423\pi\)
\(648\) 0 0
\(649\) 22.2837 0.874712
\(650\) 0 0
\(651\) 0.629542 0.0246737
\(652\) 0 0
\(653\) −6.69132 −0.261852 −0.130926 0.991392i \(-0.541795\pi\)
−0.130926 + 0.991392i \(0.541795\pi\)
\(654\) 0 0
\(655\) −6.85166 −0.267716
\(656\) 0 0
\(657\) 19.3156 0.753574
\(658\) 0 0
\(659\) 19.5366 0.761040 0.380520 0.924773i \(-0.375745\pi\)
0.380520 + 0.924773i \(0.375745\pi\)
\(660\) 0 0
\(661\) −48.5989 −1.89028 −0.945139 0.326668i \(-0.894074\pi\)
−0.945139 + 0.326668i \(0.894074\pi\)
\(662\) 0 0
\(663\) 11.9639 0.464638
\(664\) 0 0
\(665\) −75.8680 −2.94204
\(666\) 0 0
\(667\) 18.2705 0.707438
\(668\) 0 0
\(669\) −40.6562 −1.57186
\(670\) 0 0
\(671\) −68.3027 −2.63680
\(672\) 0 0
\(673\) 12.2954 0.473954 0.236977 0.971515i \(-0.423843\pi\)
0.236977 + 0.971515i \(0.423843\pi\)
\(674\) 0 0
\(675\) −140.674 −5.41454
\(676\) 0 0
\(677\) 18.3173 0.703989 0.351995 0.936002i \(-0.385504\pi\)
0.351995 + 0.936002i \(0.385504\pi\)
\(678\) 0 0
\(679\) 19.2158 0.737435
\(680\) 0 0
\(681\) −39.2405 −1.50370
\(682\) 0 0
\(683\) −3.01922 −0.115527 −0.0577637 0.998330i \(-0.518397\pi\)
−0.0577637 + 0.998330i \(0.518397\pi\)
\(684\) 0 0
\(685\) 39.4955 1.50905
\(686\) 0 0
\(687\) 33.4696 1.27694
\(688\) 0 0
\(689\) 1.98923 0.0757834
\(690\) 0 0
\(691\) 42.6494 1.62246 0.811229 0.584728i \(-0.198799\pi\)
0.811229 + 0.584728i \(0.198799\pi\)
\(692\) 0 0
\(693\) −135.134 −5.13330
\(694\) 0 0
\(695\) −29.9391 −1.13566
\(696\) 0 0
\(697\) −35.7610 −1.35454
\(698\) 0 0
\(699\) −61.9992 −2.34503
\(700\) 0 0
\(701\) −32.4132 −1.22423 −0.612115 0.790769i \(-0.709681\pi\)
−0.612115 + 0.790769i \(0.709681\pi\)
\(702\) 0 0
\(703\) −9.29480 −0.350560
\(704\) 0 0
\(705\) 143.678 5.41124
\(706\) 0 0
\(707\) −6.31670 −0.237564
\(708\) 0 0
\(709\) −42.2051 −1.58505 −0.792524 0.609841i \(-0.791233\pi\)
−0.792524 + 0.609841i \(0.791233\pi\)
\(710\) 0 0
\(711\) 18.1059 0.679025
\(712\) 0 0
\(713\) 0.226104 0.00846766
\(714\) 0 0
\(715\) 10.7348 0.401458
\(716\) 0 0
\(717\) 81.4438 3.04158
\(718\) 0 0
\(719\) −14.1237 −0.526725 −0.263363 0.964697i \(-0.584832\pi\)
−0.263363 + 0.964697i \(0.584832\pi\)
\(720\) 0 0
\(721\) 26.8562 1.00018
\(722\) 0 0
\(723\) −32.7592 −1.21833
\(724\) 0 0
\(725\) 52.0621 1.93354
\(726\) 0 0
\(727\) −7.03623 −0.260959 −0.130480 0.991451i \(-0.541652\pi\)
−0.130480 + 0.991451i \(0.541652\pi\)
\(728\) 0 0
\(729\) 9.34978 0.346288
\(730\) 0 0
\(731\) −91.5228 −3.38509
\(732\) 0 0
\(733\) −12.5438 −0.463315 −0.231657 0.972797i \(-0.574415\pi\)
−0.231657 + 0.972797i \(0.574415\pi\)
\(734\) 0 0
\(735\) −68.7767 −2.53687
\(736\) 0 0
\(737\) 33.0928 1.21899
\(738\) 0 0
\(739\) −15.0521 −0.553700 −0.276850 0.960913i \(-0.589291\pi\)
−0.276850 + 0.960913i \(0.589291\pi\)
\(740\) 0 0
\(741\) −8.04874 −0.295678
\(742\) 0 0
\(743\) −43.8186 −1.60755 −0.803774 0.594935i \(-0.797178\pi\)
−0.803774 + 0.594935i \(0.797178\pi\)
\(744\) 0 0
\(745\) 53.5912 1.96343
\(746\) 0 0
\(747\) −10.3201 −0.377593
\(748\) 0 0
\(749\) 24.4697 0.894102
\(750\) 0 0
\(751\) −46.5683 −1.69930 −0.849650 0.527346i \(-0.823187\pi\)
−0.849650 + 0.527346i \(0.823187\pi\)
\(752\) 0 0
\(753\) −3.15136 −0.114842
\(754\) 0 0
\(755\) 24.4384 0.889403
\(756\) 0 0
\(757\) 30.6548 1.11417 0.557083 0.830457i \(-0.311920\pi\)
0.557083 + 0.830457i \(0.311920\pi\)
\(758\) 0 0
\(759\) −69.5412 −2.52418
\(760\) 0 0
\(761\) 25.2379 0.914873 0.457437 0.889242i \(-0.348768\pi\)
0.457437 + 0.889242i \(0.348768\pi\)
\(762\) 0 0
\(763\) 46.5846 1.68648
\(764\) 0 0
\(765\) −222.001 −8.02645
\(766\) 0 0
\(767\) 1.92897 0.0696511
\(768\) 0 0
\(769\) 7.00969 0.252776 0.126388 0.991981i \(-0.459662\pi\)
0.126388 + 0.991981i \(0.459662\pi\)
\(770\) 0 0
\(771\) 66.6610 2.40074
\(772\) 0 0
\(773\) 20.9877 0.754873 0.377437 0.926035i \(-0.376806\pi\)
0.377437 + 0.926035i \(0.376806\pi\)
\(774\) 0 0
\(775\) 0.644285 0.0231434
\(776\) 0 0
\(777\) −19.3557 −0.694382
\(778\) 0 0
\(779\) 24.0583 0.861979
\(780\) 0 0
\(781\) −28.2919 −1.01236
\(782\) 0 0
\(783\) −56.7978 −2.02979
\(784\) 0 0
\(785\) 24.6355 0.879278
\(786\) 0 0
\(787\) −34.8551 −1.24245 −0.621225 0.783632i \(-0.713365\pi\)
−0.621225 + 0.783632i \(0.713365\pi\)
\(788\) 0 0
\(789\) −75.0359 −2.67135
\(790\) 0 0
\(791\) −58.1262 −2.06673
\(792\) 0 0
\(793\) −5.91257 −0.209962
\(794\) 0 0
\(795\) −52.8886 −1.87577
\(796\) 0 0
\(797\) −37.7830 −1.33834 −0.669171 0.743109i \(-0.733351\pi\)
−0.669171 + 0.743109i \(0.733351\pi\)
\(798\) 0 0
\(799\) 89.2864 3.15873
\(800\) 0 0
\(801\) −47.2084 −1.66803
\(802\) 0 0
\(803\) 15.4319 0.544580
\(804\) 0 0
\(805\) −56.7429 −1.99992
\(806\) 0 0
\(807\) −54.4734 −1.91755
\(808\) 0 0
\(809\) 5.97233 0.209976 0.104988 0.994473i \(-0.466520\pi\)
0.104988 + 0.994473i \(0.466520\pi\)
\(810\) 0 0
\(811\) −15.0374 −0.528035 −0.264017 0.964518i \(-0.585048\pi\)
−0.264017 + 0.964518i \(0.585048\pi\)
\(812\) 0 0
\(813\) −90.4954 −3.17381
\(814\) 0 0
\(815\) 13.2706 0.464850
\(816\) 0 0
\(817\) 61.5723 2.15414
\(818\) 0 0
\(819\) −11.6977 −0.408752
\(820\) 0 0
\(821\) 7.73076 0.269805 0.134903 0.990859i \(-0.456928\pi\)
0.134903 + 0.990859i \(0.456928\pi\)
\(822\) 0 0
\(823\) 40.1506 1.39956 0.699782 0.714357i \(-0.253281\pi\)
0.699782 + 0.714357i \(0.253281\pi\)
\(824\) 0 0
\(825\) −198.158 −6.89898
\(826\) 0 0
\(827\) 51.3430 1.78537 0.892686 0.450680i \(-0.148818\pi\)
0.892686 + 0.450680i \(0.148818\pi\)
\(828\) 0 0
\(829\) 16.3083 0.566411 0.283205 0.959059i \(-0.408602\pi\)
0.283205 + 0.959059i \(0.408602\pi\)
\(830\) 0 0
\(831\) 25.6833 0.890942
\(832\) 0 0
\(833\) −42.7401 −1.48086
\(834\) 0 0
\(835\) 31.5576 1.09210
\(836\) 0 0
\(837\) −0.702891 −0.0242955
\(838\) 0 0
\(839\) −22.5986 −0.780191 −0.390096 0.920774i \(-0.627558\pi\)
−0.390096 + 0.920774i \(0.627558\pi\)
\(840\) 0 0
\(841\) −7.97967 −0.275161
\(842\) 0 0
\(843\) −91.7729 −3.16083
\(844\) 0 0
\(845\) −51.6451 −1.77664
\(846\) 0 0
\(847\) −69.2332 −2.37888
\(848\) 0 0
\(849\) −1.49402 −0.0512747
\(850\) 0 0
\(851\) −6.95172 −0.238302
\(852\) 0 0
\(853\) 44.4187 1.52087 0.760434 0.649416i \(-0.224986\pi\)
0.760434 + 0.649416i \(0.224986\pi\)
\(854\) 0 0
\(855\) 149.352 5.10773
\(856\) 0 0
\(857\) −34.4871 −1.17806 −0.589028 0.808113i \(-0.700489\pi\)
−0.589028 + 0.808113i \(0.700489\pi\)
\(858\) 0 0
\(859\) 10.7049 0.365247 0.182624 0.983183i \(-0.441541\pi\)
0.182624 + 0.983183i \(0.441541\pi\)
\(860\) 0 0
\(861\) 50.0996 1.70739
\(862\) 0 0
\(863\) −23.1619 −0.788439 −0.394220 0.919016i \(-0.628985\pi\)
−0.394220 + 0.919016i \(0.628985\pi\)
\(864\) 0 0
\(865\) −34.9532 −1.18844
\(866\) 0 0
\(867\) −144.098 −4.89383
\(868\) 0 0
\(869\) 14.4654 0.490706
\(870\) 0 0
\(871\) 2.86465 0.0970650
\(872\) 0 0
\(873\) −37.8278 −1.28028
\(874\) 0 0
\(875\) −90.4943 −3.05927
\(876\) 0 0
\(877\) 43.4215 1.46624 0.733119 0.680100i \(-0.238064\pi\)
0.733119 + 0.680100i \(0.238064\pi\)
\(878\) 0 0
\(879\) −90.7852 −3.06211
\(880\) 0 0
\(881\) 5.13169 0.172891 0.0864454 0.996257i \(-0.472449\pi\)
0.0864454 + 0.996257i \(0.472449\pi\)
\(882\) 0 0
\(883\) −23.4895 −0.790486 −0.395243 0.918577i \(-0.629340\pi\)
−0.395243 + 0.918577i \(0.629340\pi\)
\(884\) 0 0
\(885\) −51.2866 −1.72398
\(886\) 0 0
\(887\) 14.5715 0.489263 0.244632 0.969616i \(-0.421333\pi\)
0.244632 + 0.969616i \(0.421333\pi\)
\(888\) 0 0
\(889\) 5.23900 0.175711
\(890\) 0 0
\(891\) 101.041 3.38500
\(892\) 0 0
\(893\) −60.0678 −2.01009
\(894\) 0 0
\(895\) 63.0141 2.10633
\(896\) 0 0
\(897\) −6.01978 −0.200994
\(898\) 0 0
\(899\) 0.260134 0.00867594
\(900\) 0 0
\(901\) −32.8667 −1.09495
\(902\) 0 0
\(903\) 128.220 4.26689
\(904\) 0 0
\(905\) 45.4862 1.51201
\(906\) 0 0
\(907\) 13.5526 0.450006 0.225003 0.974358i \(-0.427761\pi\)
0.225003 + 0.974358i \(0.427761\pi\)
\(908\) 0 0
\(909\) 12.4349 0.412439
\(910\) 0 0
\(911\) 23.1056 0.765522 0.382761 0.923847i \(-0.374973\pi\)
0.382761 + 0.923847i \(0.374973\pi\)
\(912\) 0 0
\(913\) −8.24508 −0.272872
\(914\) 0 0
\(915\) 157.201 5.19690
\(916\) 0 0
\(917\) 5.96506 0.196984
\(918\) 0 0
\(919\) 28.0667 0.925834 0.462917 0.886402i \(-0.346803\pi\)
0.462917 + 0.886402i \(0.346803\pi\)
\(920\) 0 0
\(921\) −84.7827 −2.79369
\(922\) 0 0
\(923\) −2.44907 −0.0806121
\(924\) 0 0
\(925\) −19.8090 −0.651316
\(926\) 0 0
\(927\) −52.8684 −1.73642
\(928\) 0 0
\(929\) 11.0125 0.361309 0.180654 0.983547i \(-0.442178\pi\)
0.180654 + 0.983547i \(0.442178\pi\)
\(930\) 0 0
\(931\) 28.7535 0.942359
\(932\) 0 0
\(933\) 50.4920 1.65303
\(934\) 0 0
\(935\) −177.364 −5.80042
\(936\) 0 0
\(937\) 37.1633 1.21407 0.607037 0.794674i \(-0.292358\pi\)
0.607037 + 0.794674i \(0.292358\pi\)
\(938\) 0 0
\(939\) 51.0145 1.66480
\(940\) 0 0
\(941\) 15.3274 0.499660 0.249830 0.968290i \(-0.419625\pi\)
0.249830 + 0.968290i \(0.419625\pi\)
\(942\) 0 0
\(943\) 17.9936 0.585952
\(944\) 0 0
\(945\) 176.397 5.73820
\(946\) 0 0
\(947\) −0.476399 −0.0154809 −0.00774045 0.999970i \(-0.502464\pi\)
−0.00774045 + 0.999970i \(0.502464\pi\)
\(948\) 0 0
\(949\) 1.33585 0.0433635
\(950\) 0 0
\(951\) −11.8595 −0.384570
\(952\) 0 0
\(953\) 48.8116 1.58116 0.790581 0.612357i \(-0.209778\pi\)
0.790581 + 0.612357i \(0.209778\pi\)
\(954\) 0 0
\(955\) 7.32588 0.237060
\(956\) 0 0
\(957\) −80.0074 −2.58627
\(958\) 0 0
\(959\) −34.3848 −1.11034
\(960\) 0 0
\(961\) −30.9968 −0.999896
\(962\) 0 0
\(963\) −48.1703 −1.55227
\(964\) 0 0
\(965\) 37.1930 1.19728
\(966\) 0 0
\(967\) −10.1506 −0.326421 −0.163211 0.986591i \(-0.552185\pi\)
−0.163211 + 0.986591i \(0.552185\pi\)
\(968\) 0 0
\(969\) 132.984 4.27207
\(970\) 0 0
\(971\) 23.7954 0.763631 0.381815 0.924239i \(-0.375299\pi\)
0.381815 + 0.924239i \(0.375299\pi\)
\(972\) 0 0
\(973\) 26.0651 0.835607
\(974\) 0 0
\(975\) −17.1534 −0.549349
\(976\) 0 0
\(977\) −3.16766 −0.101342 −0.0506712 0.998715i \(-0.516136\pi\)
−0.0506712 + 0.998715i \(0.516136\pi\)
\(978\) 0 0
\(979\) −37.7163 −1.20542
\(980\) 0 0
\(981\) −91.7053 −2.92792
\(982\) 0 0
\(983\) −55.7595 −1.77845 −0.889227 0.457467i \(-0.848757\pi\)
−0.889227 + 0.457467i \(0.848757\pi\)
\(984\) 0 0
\(985\) 44.1143 1.40560
\(986\) 0 0
\(987\) −125.087 −3.98155
\(988\) 0 0
\(989\) 46.0509 1.46433
\(990\) 0 0
\(991\) −45.3174 −1.43956 −0.719778 0.694204i \(-0.755756\pi\)
−0.719778 + 0.694204i \(0.755756\pi\)
\(992\) 0 0
\(993\) 82.4465 2.61636
\(994\) 0 0
\(995\) −44.9569 −1.42523
\(996\) 0 0
\(997\) 36.1146 1.14376 0.571880 0.820337i \(-0.306214\pi\)
0.571880 + 0.820337i \(0.306214\pi\)
\(998\) 0 0
\(999\) 21.6109 0.683738
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4016.2.a.m.1.3 23
4.3 odd 2 2008.2.a.d.1.21 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2008.2.a.d.1.21 23 4.3 odd 2
4016.2.a.m.1.3 23 1.1 even 1 trivial