Properties

Label 6008.2.a.b.1.1
Level 6008
Weight 2
Character 6008.1
Self dual yes
Analytic conductor 47.974
Analytic rank 1
Dimension 44
CM no
Inner twists 1

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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: \(1\)
Dimension: \(44\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.30487 q^{3} +0.148423 q^{5} -4.48376 q^{7} +7.92214 q^{9} +O(q^{10})\) \(q-3.30487 q^{3} +0.148423 q^{5} -4.48376 q^{7} +7.92214 q^{9} -5.76809 q^{11} +2.52864 q^{13} -0.490519 q^{15} -1.39645 q^{17} +6.53547 q^{19} +14.8182 q^{21} -1.51253 q^{23} -4.97797 q^{25} -16.2670 q^{27} -7.16181 q^{29} +4.58421 q^{31} +19.0628 q^{33} -0.665494 q^{35} -3.08289 q^{37} -8.35682 q^{39} +1.44541 q^{41} -0.693289 q^{43} +1.17583 q^{45} +0.309604 q^{47} +13.1041 q^{49} +4.61509 q^{51} +9.64897 q^{53} -0.856119 q^{55} -21.5989 q^{57} +14.8274 q^{59} +14.2407 q^{61} -35.5209 q^{63} +0.375309 q^{65} -6.92913 q^{67} +4.99872 q^{69} +7.49241 q^{71} +1.54792 q^{73} +16.4515 q^{75} +25.8627 q^{77} -9.02035 q^{79} +29.9938 q^{81} -0.305722 q^{83} -0.207266 q^{85} +23.6688 q^{87} -8.31641 q^{89} -11.3378 q^{91} -15.1502 q^{93} +0.970016 q^{95} -14.7898 q^{97} -45.6956 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −3.30487 −1.90806 −0.954032 0.299703i \(-0.903112\pi\)
−0.954032 + 0.299703i \(0.903112\pi\)
\(4\) 0 0
\(5\) 0.148423 0.0663769 0.0331885 0.999449i \(-0.489434\pi\)
0.0331885 + 0.999449i \(0.489434\pi\)
\(6\) 0 0
\(7\) −4.48376 −1.69470 −0.847351 0.531034i \(-0.821804\pi\)
−0.847351 + 0.531034i \(0.821804\pi\)
\(8\) 0 0
\(9\) 7.92214 2.64071
\(10\) 0 0
\(11\) −5.76809 −1.73914 −0.869572 0.493806i \(-0.835605\pi\)
−0.869572 + 0.493806i \(0.835605\pi\)
\(12\) 0 0
\(13\) 2.52864 0.701319 0.350659 0.936503i \(-0.385957\pi\)
0.350659 + 0.936503i \(0.385957\pi\)
\(14\) 0 0
\(15\) −0.490519 −0.126651
\(16\) 0 0
\(17\) −1.39645 −0.338690 −0.169345 0.985557i \(-0.554165\pi\)
−0.169345 + 0.985557i \(0.554165\pi\)
\(18\) 0 0
\(19\) 6.53547 1.49934 0.749670 0.661812i \(-0.230212\pi\)
0.749670 + 0.661812i \(0.230212\pi\)
\(20\) 0 0
\(21\) 14.8182 3.23360
\(22\) 0 0
\(23\) −1.51253 −0.315385 −0.157692 0.987488i \(-0.550405\pi\)
−0.157692 + 0.987488i \(0.550405\pi\)
\(24\) 0 0
\(25\) −4.97797 −0.995594
\(26\) 0 0
\(27\) −16.2670 −3.13058
\(28\) 0 0
\(29\) −7.16181 −1.32991 −0.664957 0.746881i \(-0.731550\pi\)
−0.664957 + 0.746881i \(0.731550\pi\)
\(30\) 0 0
\(31\) 4.58421 0.823348 0.411674 0.911331i \(-0.364944\pi\)
0.411674 + 0.911331i \(0.364944\pi\)
\(32\) 0 0
\(33\) 19.0628 3.31840
\(34\) 0 0
\(35\) −0.665494 −0.112489
\(36\) 0 0
\(37\) −3.08289 −0.506824 −0.253412 0.967358i \(-0.581553\pi\)
−0.253412 + 0.967358i \(0.581553\pi\)
\(38\) 0 0
\(39\) −8.35682 −1.33816
\(40\) 0 0
\(41\) 1.44541 0.225735 0.112868 0.993610i \(-0.463996\pi\)
0.112868 + 0.993610i \(0.463996\pi\)
\(42\) 0 0
\(43\) −0.693289 −0.105726 −0.0528628 0.998602i \(-0.516835\pi\)
−0.0528628 + 0.998602i \(0.516835\pi\)
\(44\) 0 0
\(45\) 1.17583 0.175282
\(46\) 0 0
\(47\) 0.309604 0.0451604 0.0225802 0.999745i \(-0.492812\pi\)
0.0225802 + 0.999745i \(0.492812\pi\)
\(48\) 0 0
\(49\) 13.1041 1.87201
\(50\) 0 0
\(51\) 4.61509 0.646242
\(52\) 0 0
\(53\) 9.64897 1.32539 0.662694 0.748890i \(-0.269413\pi\)
0.662694 + 0.748890i \(0.269413\pi\)
\(54\) 0 0
\(55\) −0.856119 −0.115439
\(56\) 0 0
\(57\) −21.5989 −2.86084
\(58\) 0 0
\(59\) 14.8274 1.93036 0.965179 0.261589i \(-0.0842466\pi\)
0.965179 + 0.261589i \(0.0842466\pi\)
\(60\) 0 0
\(61\) 14.2407 1.82333 0.911666 0.410931i \(-0.134796\pi\)
0.911666 + 0.410931i \(0.134796\pi\)
\(62\) 0 0
\(63\) −35.5209 −4.47522
\(64\) 0 0
\(65\) 0.375309 0.0465514
\(66\) 0 0
\(67\) −6.92913 −0.846527 −0.423264 0.906007i \(-0.639116\pi\)
−0.423264 + 0.906007i \(0.639116\pi\)
\(68\) 0 0
\(69\) 4.99872 0.601775
\(70\) 0 0
\(71\) 7.49241 0.889186 0.444593 0.895733i \(-0.353348\pi\)
0.444593 + 0.895733i \(0.353348\pi\)
\(72\) 0 0
\(73\) 1.54792 0.181171 0.0905853 0.995889i \(-0.471126\pi\)
0.0905853 + 0.995889i \(0.471126\pi\)
\(74\) 0 0
\(75\) 16.4515 1.89966
\(76\) 0 0
\(77\) 25.8627 2.94733
\(78\) 0 0
\(79\) −9.02035 −1.01487 −0.507434 0.861690i \(-0.669406\pi\)
−0.507434 + 0.861690i \(0.669406\pi\)
\(80\) 0 0
\(81\) 29.9938 3.33265
\(82\) 0 0
\(83\) −0.305722 −0.0335574 −0.0167787 0.999859i \(-0.505341\pi\)
−0.0167787 + 0.999859i \(0.505341\pi\)
\(84\) 0 0
\(85\) −0.207266 −0.0224812
\(86\) 0 0
\(87\) 23.6688 2.53756
\(88\) 0 0
\(89\) −8.31641 −0.881537 −0.440769 0.897621i \(-0.645294\pi\)
−0.440769 + 0.897621i \(0.645294\pi\)
\(90\) 0 0
\(91\) −11.3378 −1.18853
\(92\) 0 0
\(93\) −15.1502 −1.57100
\(94\) 0 0
\(95\) 0.970016 0.0995216
\(96\) 0 0
\(97\) −14.7898 −1.50168 −0.750841 0.660483i \(-0.770351\pi\)
−0.750841 + 0.660483i \(0.770351\pi\)
\(98\) 0 0
\(99\) −45.6956 −4.59258
\(100\) 0 0
\(101\) 12.3697 1.23083 0.615413 0.788205i \(-0.288989\pi\)
0.615413 + 0.788205i \(0.288989\pi\)
\(102\) 0 0
\(103\) 3.83180 0.377558 0.188779 0.982020i \(-0.439547\pi\)
0.188779 + 0.982020i \(0.439547\pi\)
\(104\) 0 0
\(105\) 2.19937 0.214636
\(106\) 0 0
\(107\) 9.02224 0.872213 0.436107 0.899895i \(-0.356357\pi\)
0.436107 + 0.899895i \(0.356357\pi\)
\(108\) 0 0
\(109\) −13.7229 −1.31441 −0.657207 0.753710i \(-0.728262\pi\)
−0.657207 + 0.753710i \(0.728262\pi\)
\(110\) 0 0
\(111\) 10.1885 0.967054
\(112\) 0 0
\(113\) 15.5587 1.46364 0.731819 0.681499i \(-0.238671\pi\)
0.731819 + 0.681499i \(0.238671\pi\)
\(114\) 0 0
\(115\) −0.224495 −0.0209343
\(116\) 0 0
\(117\) 20.0322 1.85198
\(118\) 0 0
\(119\) 6.26136 0.573978
\(120\) 0 0
\(121\) 22.2708 2.02462
\(122\) 0 0
\(123\) −4.77688 −0.430717
\(124\) 0 0
\(125\) −1.48096 −0.132461
\(126\) 0 0
\(127\) −0.872690 −0.0774387 −0.0387193 0.999250i \(-0.512328\pi\)
−0.0387193 + 0.999250i \(0.512328\pi\)
\(128\) 0 0
\(129\) 2.29123 0.201731
\(130\) 0 0
\(131\) 5.63571 0.492394 0.246197 0.969220i \(-0.420819\pi\)
0.246197 + 0.969220i \(0.420819\pi\)
\(132\) 0 0
\(133\) −29.3035 −2.54093
\(134\) 0 0
\(135\) −2.41440 −0.207799
\(136\) 0 0
\(137\) 17.8345 1.52370 0.761852 0.647751i \(-0.224290\pi\)
0.761852 + 0.647751i \(0.224290\pi\)
\(138\) 0 0
\(139\) 17.6861 1.50011 0.750057 0.661373i \(-0.230026\pi\)
0.750057 + 0.661373i \(0.230026\pi\)
\(140\) 0 0
\(141\) −1.02320 −0.0861690
\(142\) 0 0
\(143\) −14.5854 −1.21969
\(144\) 0 0
\(145\) −1.06298 −0.0882757
\(146\) 0 0
\(147\) −43.3073 −3.57192
\(148\) 0 0
\(149\) −5.56767 −0.456121 −0.228061 0.973647i \(-0.573238\pi\)
−0.228061 + 0.973647i \(0.573238\pi\)
\(150\) 0 0
\(151\) −9.71377 −0.790496 −0.395248 0.918575i \(-0.629341\pi\)
−0.395248 + 0.918575i \(0.629341\pi\)
\(152\) 0 0
\(153\) −11.0629 −0.894382
\(154\) 0 0
\(155\) 0.680404 0.0546513
\(156\) 0 0
\(157\) −9.10929 −0.727000 −0.363500 0.931594i \(-0.618418\pi\)
−0.363500 + 0.931594i \(0.618418\pi\)
\(158\) 0 0
\(159\) −31.8886 −2.52893
\(160\) 0 0
\(161\) 6.78183 0.534483
\(162\) 0 0
\(163\) −1.64943 −0.129194 −0.0645968 0.997911i \(-0.520576\pi\)
−0.0645968 + 0.997911i \(0.520576\pi\)
\(164\) 0 0
\(165\) 2.82936 0.220265
\(166\) 0 0
\(167\) −5.97735 −0.462541 −0.231271 0.972889i \(-0.574288\pi\)
−0.231271 + 0.972889i \(0.574288\pi\)
\(168\) 0 0
\(169\) −6.60597 −0.508152
\(170\) 0 0
\(171\) 51.7749 3.95932
\(172\) 0 0
\(173\) 7.18636 0.546369 0.273184 0.961962i \(-0.411923\pi\)
0.273184 + 0.961962i \(0.411923\pi\)
\(174\) 0 0
\(175\) 22.3200 1.68723
\(176\) 0 0
\(177\) −49.0024 −3.68325
\(178\) 0 0
\(179\) 2.15011 0.160707 0.0803535 0.996766i \(-0.474395\pi\)
0.0803535 + 0.996766i \(0.474395\pi\)
\(180\) 0 0
\(181\) 8.78730 0.653155 0.326578 0.945170i \(-0.394105\pi\)
0.326578 + 0.945170i \(0.394105\pi\)
\(182\) 0 0
\(183\) −47.0635 −3.47904
\(184\) 0 0
\(185\) −0.457573 −0.0336414
\(186\) 0 0
\(187\) 8.05486 0.589030
\(188\) 0 0
\(189\) 72.9373 5.30541
\(190\) 0 0
\(191\) 2.48682 0.179940 0.0899700 0.995944i \(-0.471323\pi\)
0.0899700 + 0.995944i \(0.471323\pi\)
\(192\) 0 0
\(193\) −12.6742 −0.912307 −0.456153 0.889901i \(-0.650773\pi\)
−0.456153 + 0.889901i \(0.650773\pi\)
\(194\) 0 0
\(195\) −1.24035 −0.0888231
\(196\) 0 0
\(197\) −3.79838 −0.270623 −0.135312 0.990803i \(-0.543204\pi\)
−0.135312 + 0.990803i \(0.543204\pi\)
\(198\) 0 0
\(199\) 1.88765 0.133812 0.0669061 0.997759i \(-0.478687\pi\)
0.0669061 + 0.997759i \(0.478687\pi\)
\(200\) 0 0
\(201\) 22.8998 1.61523
\(202\) 0 0
\(203\) 32.1118 2.25381
\(204\) 0 0
\(205\) 0.214533 0.0149836
\(206\) 0 0
\(207\) −11.9825 −0.832841
\(208\) 0 0
\(209\) −37.6972 −2.60757
\(210\) 0 0
\(211\) −20.0694 −1.38163 −0.690816 0.723030i \(-0.742749\pi\)
−0.690816 + 0.723030i \(0.742749\pi\)
\(212\) 0 0
\(213\) −24.7614 −1.69662
\(214\) 0 0
\(215\) −0.102900 −0.00701774
\(216\) 0 0
\(217\) −20.5545 −1.39533
\(218\) 0 0
\(219\) −5.11568 −0.345685
\(220\) 0 0
\(221\) −3.53113 −0.237529
\(222\) 0 0
\(223\) −10.0681 −0.674212 −0.337106 0.941467i \(-0.609448\pi\)
−0.337106 + 0.941467i \(0.609448\pi\)
\(224\) 0 0
\(225\) −39.4362 −2.62908
\(226\) 0 0
\(227\) 5.46529 0.362744 0.181372 0.983415i \(-0.441946\pi\)
0.181372 + 0.983415i \(0.441946\pi\)
\(228\) 0 0
\(229\) 6.35786 0.420139 0.210070 0.977686i \(-0.432631\pi\)
0.210070 + 0.977686i \(0.432631\pi\)
\(230\) 0 0
\(231\) −85.4728 −5.62370
\(232\) 0 0
\(233\) −17.2664 −1.13116 −0.565580 0.824694i \(-0.691348\pi\)
−0.565580 + 0.824694i \(0.691348\pi\)
\(234\) 0 0
\(235\) 0.0459525 0.00299761
\(236\) 0 0
\(237\) 29.8110 1.93644
\(238\) 0 0
\(239\) 11.7402 0.759412 0.379706 0.925107i \(-0.376025\pi\)
0.379706 + 0.925107i \(0.376025\pi\)
\(240\) 0 0
\(241\) −9.45760 −0.609217 −0.304609 0.952478i \(-0.598526\pi\)
−0.304609 + 0.952478i \(0.598526\pi\)
\(242\) 0 0
\(243\) −50.3246 −3.22832
\(244\) 0 0
\(245\) 1.94495 0.124258
\(246\) 0 0
\(247\) 16.5259 1.05152
\(248\) 0 0
\(249\) 1.01037 0.0640297
\(250\) 0 0
\(251\) −23.0926 −1.45759 −0.728795 0.684732i \(-0.759919\pi\)
−0.728795 + 0.684732i \(0.759919\pi\)
\(252\) 0 0
\(253\) 8.72442 0.548500
\(254\) 0 0
\(255\) 0.684987 0.0428956
\(256\) 0 0
\(257\) 7.24364 0.451846 0.225923 0.974145i \(-0.427460\pi\)
0.225923 + 0.974145i \(0.427460\pi\)
\(258\) 0 0
\(259\) 13.8229 0.858916
\(260\) 0 0
\(261\) −56.7368 −3.51192
\(262\) 0 0
\(263\) −0.940250 −0.0579783 −0.0289891 0.999580i \(-0.509229\pi\)
−0.0289891 + 0.999580i \(0.509229\pi\)
\(264\) 0 0
\(265\) 1.43213 0.0879752
\(266\) 0 0
\(267\) 27.4846 1.68203
\(268\) 0 0
\(269\) 26.2956 1.60327 0.801635 0.597814i \(-0.203964\pi\)
0.801635 + 0.597814i \(0.203964\pi\)
\(270\) 0 0
\(271\) −10.0257 −0.609020 −0.304510 0.952509i \(-0.598493\pi\)
−0.304510 + 0.952509i \(0.598493\pi\)
\(272\) 0 0
\(273\) 37.4700 2.26779
\(274\) 0 0
\(275\) 28.7134 1.73148
\(276\) 0 0
\(277\) 15.6662 0.941290 0.470645 0.882323i \(-0.344021\pi\)
0.470645 + 0.882323i \(0.344021\pi\)
\(278\) 0 0
\(279\) 36.3167 2.17423
\(280\) 0 0
\(281\) −27.6006 −1.64651 −0.823256 0.567670i \(-0.807845\pi\)
−0.823256 + 0.567670i \(0.807845\pi\)
\(282\) 0 0
\(283\) −17.3803 −1.03315 −0.516577 0.856241i \(-0.672794\pi\)
−0.516577 + 0.856241i \(0.672794\pi\)
\(284\) 0 0
\(285\) −3.20577 −0.189894
\(286\) 0 0
\(287\) −6.48087 −0.382554
\(288\) 0 0
\(289\) −15.0499 −0.885289
\(290\) 0 0
\(291\) 48.8784 2.86531
\(292\) 0 0
\(293\) −10.9514 −0.639785 −0.319893 0.947454i \(-0.603647\pi\)
−0.319893 + 0.947454i \(0.603647\pi\)
\(294\) 0 0
\(295\) 2.20073 0.128131
\(296\) 0 0
\(297\) 93.8294 5.44454
\(298\) 0 0
\(299\) −3.82465 −0.221185
\(300\) 0 0
\(301\) 3.10854 0.179173
\(302\) 0 0
\(303\) −40.8800 −2.34850
\(304\) 0 0
\(305\) 2.11365 0.121027
\(306\) 0 0
\(307\) 20.6860 1.18061 0.590306 0.807180i \(-0.299007\pi\)
0.590306 + 0.807180i \(0.299007\pi\)
\(308\) 0 0
\(309\) −12.6636 −0.720406
\(310\) 0 0
\(311\) 26.8238 1.52104 0.760519 0.649315i \(-0.224944\pi\)
0.760519 + 0.649315i \(0.224944\pi\)
\(312\) 0 0
\(313\) 26.2321 1.48272 0.741362 0.671105i \(-0.234180\pi\)
0.741362 + 0.671105i \(0.234180\pi\)
\(314\) 0 0
\(315\) −5.27214 −0.297051
\(316\) 0 0
\(317\) −26.9213 −1.51205 −0.756025 0.654542i \(-0.772861\pi\)
−0.756025 + 0.654542i \(0.772861\pi\)
\(318\) 0 0
\(319\) 41.3099 2.31291
\(320\) 0 0
\(321\) −29.8173 −1.66424
\(322\) 0 0
\(323\) −9.12648 −0.507811
\(324\) 0 0
\(325\) −12.5875 −0.698229
\(326\) 0 0
\(327\) 45.3523 2.50799
\(328\) 0 0
\(329\) −1.38819 −0.0765334
\(330\) 0 0
\(331\) 34.1535 1.87725 0.938624 0.344943i \(-0.112102\pi\)
0.938624 + 0.344943i \(0.112102\pi\)
\(332\) 0 0
\(333\) −24.4231 −1.33838
\(334\) 0 0
\(335\) −1.02844 −0.0561899
\(336\) 0 0
\(337\) −3.46160 −0.188565 −0.0942826 0.995545i \(-0.530056\pi\)
−0.0942826 + 0.995545i \(0.530056\pi\)
\(338\) 0 0
\(339\) −51.4194 −2.79272
\(340\) 0 0
\(341\) −26.4421 −1.43192
\(342\) 0 0
\(343\) −27.3693 −1.47780
\(344\) 0 0
\(345\) 0.741926 0.0399440
\(346\) 0 0
\(347\) 19.8963 1.06809 0.534045 0.845456i \(-0.320671\pi\)
0.534045 + 0.845456i \(0.320671\pi\)
\(348\) 0 0
\(349\) −31.7447 −1.69925 −0.849627 0.527385i \(-0.823173\pi\)
−0.849627 + 0.527385i \(0.823173\pi\)
\(350\) 0 0
\(351\) −41.1334 −2.19554
\(352\) 0 0
\(353\) −25.3293 −1.34814 −0.674072 0.738665i \(-0.735456\pi\)
−0.674072 + 0.738665i \(0.735456\pi\)
\(354\) 0 0
\(355\) 1.11205 0.0590214
\(356\) 0 0
\(357\) −20.6930 −1.09519
\(358\) 0 0
\(359\) −12.7839 −0.674706 −0.337353 0.941378i \(-0.609532\pi\)
−0.337353 + 0.941378i \(0.609532\pi\)
\(360\) 0 0
\(361\) 23.7124 1.24802
\(362\) 0 0
\(363\) −73.6021 −3.86311
\(364\) 0 0
\(365\) 0.229748 0.0120256
\(366\) 0 0
\(367\) −18.0515 −0.942279 −0.471140 0.882059i \(-0.656157\pi\)
−0.471140 + 0.882059i \(0.656157\pi\)
\(368\) 0 0
\(369\) 11.4507 0.596101
\(370\) 0 0
\(371\) −43.2637 −2.24614
\(372\) 0 0
\(373\) 6.21241 0.321666 0.160833 0.986982i \(-0.448582\pi\)
0.160833 + 0.986982i \(0.448582\pi\)
\(374\) 0 0
\(375\) 4.89439 0.252745
\(376\) 0 0
\(377\) −18.1096 −0.932694
\(378\) 0 0
\(379\) 32.9698 1.69355 0.846773 0.531955i \(-0.178542\pi\)
0.846773 + 0.531955i \(0.178542\pi\)
\(380\) 0 0
\(381\) 2.88412 0.147758
\(382\) 0 0
\(383\) −20.5101 −1.04802 −0.524008 0.851713i \(-0.675564\pi\)
−0.524008 + 0.851713i \(0.675564\pi\)
\(384\) 0 0
\(385\) 3.83863 0.195635
\(386\) 0 0
\(387\) −5.49233 −0.279191
\(388\) 0 0
\(389\) −2.55097 −0.129339 −0.0646697 0.997907i \(-0.520599\pi\)
−0.0646697 + 0.997907i \(0.520599\pi\)
\(390\) 0 0
\(391\) 2.11218 0.106818
\(392\) 0 0
\(393\) −18.6253 −0.939520
\(394\) 0 0
\(395\) −1.33883 −0.0673639
\(396\) 0 0
\(397\) −39.1921 −1.96699 −0.983497 0.180923i \(-0.942091\pi\)
−0.983497 + 0.180923i \(0.942091\pi\)
\(398\) 0 0
\(399\) 96.8440 4.84827
\(400\) 0 0
\(401\) −3.38811 −0.169194 −0.0845971 0.996415i \(-0.526960\pi\)
−0.0845971 + 0.996415i \(0.526960\pi\)
\(402\) 0 0
\(403\) 11.5918 0.577430
\(404\) 0 0
\(405\) 4.45178 0.221211
\(406\) 0 0
\(407\) 17.7824 0.881440
\(408\) 0 0
\(409\) −30.7071 −1.51837 −0.759185 0.650875i \(-0.774402\pi\)
−0.759185 + 0.650875i \(0.774402\pi\)
\(410\) 0 0
\(411\) −58.9406 −2.90733
\(412\) 0 0
\(413\) −66.4823 −3.27138
\(414\) 0 0
\(415\) −0.0453763 −0.00222744
\(416\) 0 0
\(417\) −58.4501 −2.86231
\(418\) 0 0
\(419\) −27.3851 −1.33785 −0.668924 0.743331i \(-0.733245\pi\)
−0.668924 + 0.743331i \(0.733245\pi\)
\(420\) 0 0
\(421\) 8.24185 0.401683 0.200842 0.979624i \(-0.435632\pi\)
0.200842 + 0.979624i \(0.435632\pi\)
\(422\) 0 0
\(423\) 2.45272 0.119256
\(424\) 0 0
\(425\) 6.95150 0.337197
\(426\) 0 0
\(427\) −63.8518 −3.09000
\(428\) 0 0
\(429\) 48.2029 2.32726
\(430\) 0 0
\(431\) 40.8702 1.96865 0.984325 0.176365i \(-0.0564338\pi\)
0.984325 + 0.176365i \(0.0564338\pi\)
\(432\) 0 0
\(433\) −21.7992 −1.04760 −0.523800 0.851841i \(-0.675486\pi\)
−0.523800 + 0.851841i \(0.675486\pi\)
\(434\) 0 0
\(435\) 3.51300 0.168436
\(436\) 0 0
\(437\) −9.88511 −0.472869
\(438\) 0 0
\(439\) −14.8708 −0.709744 −0.354872 0.934915i \(-0.615476\pi\)
−0.354872 + 0.934915i \(0.615476\pi\)
\(440\) 0 0
\(441\) 103.812 4.94345
\(442\) 0 0
\(443\) 1.70472 0.0809936 0.0404968 0.999180i \(-0.487106\pi\)
0.0404968 + 0.999180i \(0.487106\pi\)
\(444\) 0 0
\(445\) −1.23435 −0.0585138
\(446\) 0 0
\(447\) 18.4004 0.870309
\(448\) 0 0
\(449\) −38.6971 −1.82623 −0.913114 0.407704i \(-0.866330\pi\)
−0.913114 + 0.407704i \(0.866330\pi\)
\(450\) 0 0
\(451\) −8.33725 −0.392586
\(452\) 0 0
\(453\) 32.1027 1.50832
\(454\) 0 0
\(455\) −1.68280 −0.0788907
\(456\) 0 0
\(457\) 0.532922 0.0249291 0.0124645 0.999922i \(-0.496032\pi\)
0.0124645 + 0.999922i \(0.496032\pi\)
\(458\) 0 0
\(459\) 22.7161 1.06030
\(460\) 0 0
\(461\) 34.6301 1.61288 0.806442 0.591313i \(-0.201390\pi\)
0.806442 + 0.591313i \(0.201390\pi\)
\(462\) 0 0
\(463\) −25.4364 −1.18213 −0.591065 0.806624i \(-0.701292\pi\)
−0.591065 + 0.806624i \(0.701292\pi\)
\(464\) 0 0
\(465\) −2.24864 −0.104278
\(466\) 0 0
\(467\) 0.501459 0.0232048 0.0116024 0.999933i \(-0.496307\pi\)
0.0116024 + 0.999933i \(0.496307\pi\)
\(468\) 0 0
\(469\) 31.0685 1.43461
\(470\) 0 0
\(471\) 30.1050 1.38716
\(472\) 0 0
\(473\) 3.99895 0.183872
\(474\) 0 0
\(475\) −32.5334 −1.49273
\(476\) 0 0
\(477\) 76.4405 3.49997
\(478\) 0 0
\(479\) 8.29956 0.379217 0.189608 0.981860i \(-0.439278\pi\)
0.189608 + 0.981860i \(0.439278\pi\)
\(480\) 0 0
\(481\) −7.79553 −0.355446
\(482\) 0 0
\(483\) −22.4130 −1.01983
\(484\) 0 0
\(485\) −2.19516 −0.0996770
\(486\) 0 0
\(487\) −31.4129 −1.42346 −0.711728 0.702455i \(-0.752087\pi\)
−0.711728 + 0.702455i \(0.752087\pi\)
\(488\) 0 0
\(489\) 5.45116 0.246510
\(490\) 0 0
\(491\) −13.5894 −0.613282 −0.306641 0.951825i \(-0.599205\pi\)
−0.306641 + 0.951825i \(0.599205\pi\)
\(492\) 0 0
\(493\) 10.0011 0.450428
\(494\) 0 0
\(495\) −6.78229 −0.304841
\(496\) 0 0
\(497\) −33.5942 −1.50690
\(498\) 0 0
\(499\) −44.0750 −1.97307 −0.986535 0.163551i \(-0.947705\pi\)
−0.986535 + 0.163551i \(0.947705\pi\)
\(500\) 0 0
\(501\) 19.7543 0.882558
\(502\) 0 0
\(503\) 9.64921 0.430237 0.215119 0.976588i \(-0.430986\pi\)
0.215119 + 0.976588i \(0.430986\pi\)
\(504\) 0 0
\(505\) 1.83594 0.0816985
\(506\) 0 0
\(507\) 21.8318 0.969586
\(508\) 0 0
\(509\) −14.2454 −0.631415 −0.315708 0.948857i \(-0.602242\pi\)
−0.315708 + 0.948857i \(0.602242\pi\)
\(510\) 0 0
\(511\) −6.94051 −0.307030
\(512\) 0 0
\(513\) −106.312 −4.69381
\(514\) 0 0
\(515\) 0.568729 0.0250612
\(516\) 0 0
\(517\) −1.78582 −0.0785404
\(518\) 0 0
\(519\) −23.7500 −1.04251
\(520\) 0 0
\(521\) −29.8294 −1.30685 −0.653425 0.756991i \(-0.726669\pi\)
−0.653425 + 0.756991i \(0.726669\pi\)
\(522\) 0 0
\(523\) −22.7909 −0.996575 −0.498287 0.867012i \(-0.666038\pi\)
−0.498287 + 0.867012i \(0.666038\pi\)
\(524\) 0 0
\(525\) −73.7647 −3.21935
\(526\) 0 0
\(527\) −6.40164 −0.278860
\(528\) 0 0
\(529\) −20.7122 −0.900532
\(530\) 0 0
\(531\) 117.464 5.09752
\(532\) 0 0
\(533\) 3.65492 0.158312
\(534\) 0 0
\(535\) 1.33911 0.0578948
\(536\) 0 0
\(537\) −7.10583 −0.306639
\(538\) 0 0
\(539\) −75.5855 −3.25570
\(540\) 0 0
\(541\) −26.6036 −1.14378 −0.571888 0.820332i \(-0.693789\pi\)
−0.571888 + 0.820332i \(0.693789\pi\)
\(542\) 0 0
\(543\) −29.0408 −1.24626
\(544\) 0 0
\(545\) −2.03680 −0.0872468
\(546\) 0 0
\(547\) 6.86528 0.293538 0.146769 0.989171i \(-0.453113\pi\)
0.146769 + 0.989171i \(0.453113\pi\)
\(548\) 0 0
\(549\) 112.817 4.81490
\(550\) 0 0
\(551\) −46.8058 −1.99399
\(552\) 0 0
\(553\) 40.4451 1.71990
\(554\) 0 0
\(555\) 1.51222 0.0641901
\(556\) 0 0
\(557\) 34.0133 1.44119 0.720596 0.693356i \(-0.243868\pi\)
0.720596 + 0.693356i \(0.243868\pi\)
\(558\) 0 0
\(559\) −1.75308 −0.0741473
\(560\) 0 0
\(561\) −26.6202 −1.12391
\(562\) 0 0
\(563\) −28.3031 −1.19284 −0.596418 0.802674i \(-0.703410\pi\)
−0.596418 + 0.802674i \(0.703410\pi\)
\(564\) 0 0
\(565\) 2.30927 0.0971519
\(566\) 0 0
\(567\) −134.485 −5.64784
\(568\) 0 0
\(569\) 6.45557 0.270632 0.135316 0.990803i \(-0.456795\pi\)
0.135316 + 0.990803i \(0.456795\pi\)
\(570\) 0 0
\(571\) 27.4735 1.14973 0.574865 0.818248i \(-0.305055\pi\)
0.574865 + 0.818248i \(0.305055\pi\)
\(572\) 0 0
\(573\) −8.21860 −0.343337
\(574\) 0 0
\(575\) 7.52934 0.313995
\(576\) 0 0
\(577\) −12.6039 −0.524706 −0.262353 0.964972i \(-0.584499\pi\)
−0.262353 + 0.964972i \(0.584499\pi\)
\(578\) 0 0
\(579\) 41.8864 1.74074
\(580\) 0 0
\(581\) 1.37079 0.0568698
\(582\) 0 0
\(583\) −55.6561 −2.30504
\(584\) 0 0
\(585\) 2.97325 0.122929
\(586\) 0 0
\(587\) −22.3671 −0.923190 −0.461595 0.887091i \(-0.652723\pi\)
−0.461595 + 0.887091i \(0.652723\pi\)
\(588\) 0 0
\(589\) 29.9600 1.23448
\(590\) 0 0
\(591\) 12.5531 0.516367
\(592\) 0 0
\(593\) 42.8316 1.75888 0.879442 0.476007i \(-0.157916\pi\)
0.879442 + 0.476007i \(0.157916\pi\)
\(594\) 0 0
\(595\) 0.929332 0.0380989
\(596\) 0 0
\(597\) −6.23844 −0.255322
\(598\) 0 0
\(599\) 8.45315 0.345386 0.172693 0.984976i \(-0.444753\pi\)
0.172693 + 0.984976i \(0.444753\pi\)
\(600\) 0 0
\(601\) −3.33543 −0.136055 −0.0680275 0.997683i \(-0.521671\pi\)
−0.0680275 + 0.997683i \(0.521671\pi\)
\(602\) 0 0
\(603\) −54.8935 −2.23543
\(604\) 0 0
\(605\) 3.30551 0.134388
\(606\) 0 0
\(607\) 40.6823 1.65124 0.825622 0.564223i \(-0.190824\pi\)
0.825622 + 0.564223i \(0.190824\pi\)
\(608\) 0 0
\(609\) −106.125 −4.30041
\(610\) 0 0
\(611\) 0.782878 0.0316718
\(612\) 0 0
\(613\) 24.7532 0.999774 0.499887 0.866091i \(-0.333375\pi\)
0.499887 + 0.866091i \(0.333375\pi\)
\(614\) 0 0
\(615\) −0.709001 −0.0285897
\(616\) 0 0
\(617\) 21.6587 0.871945 0.435972 0.899960i \(-0.356405\pi\)
0.435972 + 0.899960i \(0.356405\pi\)
\(618\) 0 0
\(619\) 12.7606 0.512891 0.256446 0.966559i \(-0.417449\pi\)
0.256446 + 0.966559i \(0.417449\pi\)
\(620\) 0 0
\(621\) 24.6044 0.987339
\(622\) 0 0
\(623\) 37.2888 1.49394
\(624\) 0 0
\(625\) 24.6700 0.986802
\(626\) 0 0
\(627\) 124.584 4.97541
\(628\) 0 0
\(629\) 4.30511 0.171656
\(630\) 0 0
\(631\) −7.34600 −0.292440 −0.146220 0.989252i \(-0.546711\pi\)
−0.146220 + 0.989252i \(0.546711\pi\)
\(632\) 0 0
\(633\) 66.3266 2.63624
\(634\) 0 0
\(635\) −0.129528 −0.00514014
\(636\) 0 0
\(637\) 33.1356 1.31288
\(638\) 0 0
\(639\) 59.3559 2.34808
\(640\) 0 0
\(641\) 38.0218 1.50177 0.750885 0.660433i \(-0.229627\pi\)
0.750885 + 0.660433i \(0.229627\pi\)
\(642\) 0 0
\(643\) 6.02505 0.237605 0.118802 0.992918i \(-0.462095\pi\)
0.118802 + 0.992918i \(0.462095\pi\)
\(644\) 0 0
\(645\) 0.340071 0.0133903
\(646\) 0 0
\(647\) −31.4833 −1.23774 −0.618869 0.785495i \(-0.712409\pi\)
−0.618869 + 0.785495i \(0.712409\pi\)
\(648\) 0 0
\(649\) −85.5255 −3.35717
\(650\) 0 0
\(651\) 67.9298 2.66238
\(652\) 0 0
\(653\) 1.16063 0.0454191 0.0227096 0.999742i \(-0.492771\pi\)
0.0227096 + 0.999742i \(0.492771\pi\)
\(654\) 0 0
\(655\) 0.836471 0.0326836
\(656\) 0 0
\(657\) 12.2629 0.478420
\(658\) 0 0
\(659\) −6.08026 −0.236853 −0.118427 0.992963i \(-0.537785\pi\)
−0.118427 + 0.992963i \(0.537785\pi\)
\(660\) 0 0
\(661\) 8.29926 0.322804 0.161402 0.986889i \(-0.448398\pi\)
0.161402 + 0.986889i \(0.448398\pi\)
\(662\) 0 0
\(663\) 11.6699 0.453222
\(664\) 0 0
\(665\) −4.34932 −0.168659
\(666\) 0 0
\(667\) 10.8325 0.419435
\(668\) 0 0
\(669\) 33.2738 1.28644
\(670\) 0 0
\(671\) −82.1415 −3.17104
\(672\) 0 0
\(673\) −8.31993 −0.320710 −0.160355 0.987059i \(-0.551264\pi\)
−0.160355 + 0.987059i \(0.551264\pi\)
\(674\) 0 0
\(675\) 80.9766 3.11679
\(676\) 0 0
\(677\) 44.2891 1.70217 0.851083 0.525030i \(-0.175946\pi\)
0.851083 + 0.525030i \(0.175946\pi\)
\(678\) 0 0
\(679\) 66.3141 2.54490
\(680\) 0 0
\(681\) −18.0620 −0.692139
\(682\) 0 0
\(683\) 4.78069 0.182928 0.0914641 0.995808i \(-0.470845\pi\)
0.0914641 + 0.995808i \(0.470845\pi\)
\(684\) 0 0
\(685\) 2.64706 0.101139
\(686\) 0 0
\(687\) −21.0119 −0.801653
\(688\) 0 0
\(689\) 24.3988 0.929520
\(690\) 0 0
\(691\) 31.3183 1.19140 0.595702 0.803205i \(-0.296874\pi\)
0.595702 + 0.803205i \(0.296874\pi\)
\(692\) 0 0
\(693\) 204.888 7.78305
\(694\) 0 0
\(695\) 2.62503 0.0995729
\(696\) 0 0
\(697\) −2.01845 −0.0764541
\(698\) 0 0
\(699\) 57.0631 2.15833
\(700\) 0 0
\(701\) 16.7524 0.632729 0.316365 0.948638i \(-0.397538\pi\)
0.316365 + 0.948638i \(0.397538\pi\)
\(702\) 0 0
\(703\) −20.1482 −0.759902
\(704\) 0 0
\(705\) −0.151867 −0.00571963
\(706\) 0 0
\(707\) −55.4625 −2.08588
\(708\) 0 0
\(709\) −13.4759 −0.506099 −0.253050 0.967453i \(-0.581434\pi\)
−0.253050 + 0.967453i \(0.581434\pi\)
\(710\) 0 0
\(711\) −71.4604 −2.67998
\(712\) 0 0
\(713\) −6.93377 −0.259672
\(714\) 0 0
\(715\) −2.16482 −0.0809596
\(716\) 0 0
\(717\) −38.7999 −1.44901
\(718\) 0 0
\(719\) 10.0649 0.375356 0.187678 0.982231i \(-0.439904\pi\)
0.187678 + 0.982231i \(0.439904\pi\)
\(720\) 0 0
\(721\) −17.1809 −0.639849
\(722\) 0 0
\(723\) 31.2561 1.16243
\(724\) 0 0
\(725\) 35.6513 1.32406
\(726\) 0 0
\(727\) 3.58010 0.132779 0.0663893 0.997794i \(-0.478852\pi\)
0.0663893 + 0.997794i \(0.478852\pi\)
\(728\) 0 0
\(729\) 76.3344 2.82720
\(730\) 0 0
\(731\) 0.968145 0.0358081
\(732\) 0 0
\(733\) −17.6416 −0.651608 −0.325804 0.945437i \(-0.605635\pi\)
−0.325804 + 0.945437i \(0.605635\pi\)
\(734\) 0 0
\(735\) −6.42781 −0.237093
\(736\) 0 0
\(737\) 39.9678 1.47223
\(738\) 0 0
\(739\) −1.28656 −0.0473269 −0.0236635 0.999720i \(-0.507533\pi\)
−0.0236635 + 0.999720i \(0.507533\pi\)
\(740\) 0 0
\(741\) −54.6158 −2.00636
\(742\) 0 0
\(743\) 7.44654 0.273187 0.136594 0.990627i \(-0.456385\pi\)
0.136594 + 0.990627i \(0.456385\pi\)
\(744\) 0 0
\(745\) −0.826372 −0.0302759
\(746\) 0 0
\(747\) −2.42197 −0.0886154
\(748\) 0 0
\(749\) −40.4536 −1.47814
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 76.3178 2.78118
\(754\) 0 0
\(755\) −1.44175 −0.0524707
\(756\) 0 0
\(757\) −33.3750 −1.21303 −0.606517 0.795070i \(-0.707434\pi\)
−0.606517 + 0.795070i \(0.707434\pi\)
\(758\) 0 0
\(759\) −28.8330 −1.04657
\(760\) 0 0
\(761\) 13.8705 0.502805 0.251403 0.967883i \(-0.419108\pi\)
0.251403 + 0.967883i \(0.419108\pi\)
\(762\) 0 0
\(763\) 61.5301 2.22754
\(764\) 0 0
\(765\) −1.64199 −0.0593663
\(766\) 0 0
\(767\) 37.4931 1.35380
\(768\) 0 0
\(769\) 7.08639 0.255542 0.127771 0.991804i \(-0.459218\pi\)
0.127771 + 0.991804i \(0.459218\pi\)
\(770\) 0 0
\(771\) −23.9392 −0.862151
\(772\) 0 0
\(773\) 23.5465 0.846908 0.423454 0.905917i \(-0.360817\pi\)
0.423454 + 0.905917i \(0.360817\pi\)
\(774\) 0 0
\(775\) −22.8201 −0.819721
\(776\) 0 0
\(777\) −45.6830 −1.63887
\(778\) 0 0
\(779\) 9.44643 0.338454
\(780\) 0 0
\(781\) −43.2169 −1.54642
\(782\) 0 0
\(783\) 116.501 4.16341
\(784\) 0 0
\(785\) −1.35203 −0.0482561
\(786\) 0 0
\(787\) −38.8167 −1.38367 −0.691833 0.722057i \(-0.743197\pi\)
−0.691833 + 0.722057i \(0.743197\pi\)
\(788\) 0 0
\(789\) 3.10740 0.110626
\(790\) 0 0
\(791\) −69.7614 −2.48043
\(792\) 0 0
\(793\) 36.0096 1.27874
\(794\) 0 0
\(795\) −4.73301 −0.167862
\(796\) 0 0
\(797\) −10.3686 −0.367274 −0.183637 0.982994i \(-0.558787\pi\)
−0.183637 + 0.982994i \(0.558787\pi\)
\(798\) 0 0
\(799\) −0.432348 −0.0152954
\(800\) 0 0
\(801\) −65.8837 −2.32789
\(802\) 0 0
\(803\) −8.92856 −0.315082
\(804\) 0 0
\(805\) 1.00658 0.0354774
\(806\) 0 0
\(807\) −86.9033 −3.05914
\(808\) 0 0
\(809\) −43.6326 −1.53404 −0.767020 0.641624i \(-0.778261\pi\)
−0.767020 + 0.641624i \(0.778261\pi\)
\(810\) 0 0
\(811\) 39.1932 1.37626 0.688130 0.725587i \(-0.258432\pi\)
0.688130 + 0.725587i \(0.258432\pi\)
\(812\) 0 0
\(813\) 33.1337 1.16205
\(814\) 0 0
\(815\) −0.244814 −0.00857548
\(816\) 0 0
\(817\) −4.53097 −0.158519
\(818\) 0 0
\(819\) −89.8197 −3.13856
\(820\) 0 0
\(821\) −18.8792 −0.658890 −0.329445 0.944175i \(-0.606862\pi\)
−0.329445 + 0.944175i \(0.606862\pi\)
\(822\) 0 0
\(823\) −50.7060 −1.76750 −0.883750 0.467959i \(-0.844989\pi\)
−0.883750 + 0.467959i \(0.844989\pi\)
\(824\) 0 0
\(825\) −94.8938 −3.30378
\(826\) 0 0
\(827\) −2.32122 −0.0807167 −0.0403583 0.999185i \(-0.512850\pi\)
−0.0403583 + 0.999185i \(0.512850\pi\)
\(828\) 0 0
\(829\) 43.9550 1.52662 0.763311 0.646032i \(-0.223573\pi\)
0.763311 + 0.646032i \(0.223573\pi\)
\(830\) 0 0
\(831\) −51.7747 −1.79604
\(832\) 0 0
\(833\) −18.2993 −0.634032
\(834\) 0 0
\(835\) −0.887178 −0.0307021
\(836\) 0 0
\(837\) −74.5713 −2.57756
\(838\) 0 0
\(839\) −18.6031 −0.642251 −0.321125 0.947037i \(-0.604061\pi\)
−0.321125 + 0.947037i \(0.604061\pi\)
\(840\) 0 0
\(841\) 22.2915 0.768673
\(842\) 0 0
\(843\) 91.2162 3.14165
\(844\) 0 0
\(845\) −0.980480 −0.0337296
\(846\) 0 0
\(847\) −99.8570 −3.43113
\(848\) 0 0
\(849\) 57.4396 1.97132
\(850\) 0 0
\(851\) 4.66298 0.159845
\(852\) 0 0
\(853\) 19.1768 0.656600 0.328300 0.944574i \(-0.393524\pi\)
0.328300 + 0.944574i \(0.393524\pi\)
\(854\) 0 0
\(855\) 7.68460 0.262808
\(856\) 0 0
\(857\) 57.3100 1.95767 0.978836 0.204645i \(-0.0656039\pi\)
0.978836 + 0.204645i \(0.0656039\pi\)
\(858\) 0 0
\(859\) 24.4731 0.835010 0.417505 0.908675i \(-0.362905\pi\)
0.417505 + 0.908675i \(0.362905\pi\)
\(860\) 0 0
\(861\) 21.4184 0.729937
\(862\) 0 0
\(863\) −2.07967 −0.0707929 −0.0353965 0.999373i \(-0.511269\pi\)
−0.0353965 + 0.999373i \(0.511269\pi\)
\(864\) 0 0
\(865\) 1.06662 0.0362663
\(866\) 0 0
\(867\) 49.7380 1.68919
\(868\) 0 0
\(869\) 52.0302 1.76500
\(870\) 0 0
\(871\) −17.5213 −0.593686
\(872\) 0 0
\(873\) −117.167 −3.96551
\(874\) 0 0
\(875\) 6.64028 0.224483
\(876\) 0 0
\(877\) 45.3804 1.53239 0.766194 0.642610i \(-0.222148\pi\)
0.766194 + 0.642610i \(0.222148\pi\)
\(878\) 0 0
\(879\) 36.1928 1.22075
\(880\) 0 0
\(881\) 10.4651 0.352578 0.176289 0.984338i \(-0.443591\pi\)
0.176289 + 0.984338i \(0.443591\pi\)
\(882\) 0 0
\(883\) 27.4005 0.922099 0.461049 0.887375i \(-0.347473\pi\)
0.461049 + 0.887375i \(0.347473\pi\)
\(884\) 0 0
\(885\) −7.27311 −0.244483
\(886\) 0 0
\(887\) −45.8910 −1.54087 −0.770435 0.637519i \(-0.779961\pi\)
−0.770435 + 0.637519i \(0.779961\pi\)
\(888\) 0 0
\(889\) 3.91293 0.131235
\(890\) 0 0
\(891\) −173.007 −5.79595
\(892\) 0 0
\(893\) 2.02341 0.0677108
\(894\) 0 0
\(895\) 0.319127 0.0106672
\(896\) 0 0
\(897\) 12.6400 0.422036
\(898\) 0 0
\(899\) −32.8312 −1.09498
\(900\) 0 0
\(901\) −13.4743 −0.448895
\(902\) 0 0
\(903\) −10.2733 −0.341874
\(904\) 0 0
\(905\) 1.30424 0.0433544
\(906\) 0 0
\(907\) −3.41092 −0.113258 −0.0566290 0.998395i \(-0.518035\pi\)
−0.0566290 + 0.998395i \(0.518035\pi\)
\(908\) 0 0
\(909\) 97.9940 3.25026
\(910\) 0 0
\(911\) 22.2029 0.735616 0.367808 0.929902i \(-0.380108\pi\)
0.367808 + 0.929902i \(0.380108\pi\)
\(912\) 0 0
\(913\) 1.76343 0.0583611
\(914\) 0 0
\(915\) −6.98533 −0.230928
\(916\) 0 0
\(917\) −25.2692 −0.834461
\(918\) 0 0
\(919\) −29.8312 −0.984042 −0.492021 0.870583i \(-0.663742\pi\)
−0.492021 + 0.870583i \(0.663742\pi\)
\(920\) 0 0
\(921\) −68.3644 −2.25268
\(922\) 0 0
\(923\) 18.9456 0.623603
\(924\) 0 0
\(925\) 15.3465 0.504591
\(926\) 0 0
\(927\) 30.3560 0.997023
\(928\) 0 0
\(929\) 10.6696 0.350057 0.175029 0.984563i \(-0.443998\pi\)
0.175029 + 0.984563i \(0.443998\pi\)
\(930\) 0 0
\(931\) 85.6414 2.80678
\(932\) 0 0
\(933\) −88.6491 −2.90224
\(934\) 0 0
\(935\) 1.19553 0.0390980
\(936\) 0 0
\(937\) −2.29449 −0.0749578 −0.0374789 0.999297i \(-0.511933\pi\)
−0.0374789 + 0.999297i \(0.511933\pi\)
\(938\) 0 0
\(939\) −86.6935 −2.82913
\(940\) 0 0
\(941\) 15.9868 0.521155 0.260578 0.965453i \(-0.416087\pi\)
0.260578 + 0.965453i \(0.416087\pi\)
\(942\) 0 0
\(943\) −2.18623 −0.0711934
\(944\) 0 0
\(945\) 10.8256 0.352157
\(946\) 0 0
\(947\) −25.0989 −0.815606 −0.407803 0.913070i \(-0.633705\pi\)
−0.407803 + 0.913070i \(0.633705\pi\)
\(948\) 0 0
\(949\) 3.91414 0.127058
\(950\) 0 0
\(951\) 88.9713 2.88509
\(952\) 0 0
\(953\) −6.77623 −0.219504 −0.109752 0.993959i \(-0.535006\pi\)
−0.109752 + 0.993959i \(0.535006\pi\)
\(954\) 0 0
\(955\) 0.369102 0.0119439
\(956\) 0 0
\(957\) −136.524 −4.41319
\(958\) 0 0
\(959\) −79.9656 −2.58222
\(960\) 0 0
\(961\) −9.98502 −0.322097
\(962\) 0 0
\(963\) 71.4754 2.30326
\(964\) 0 0
\(965\) −1.88114 −0.0605561
\(966\) 0 0
\(967\) 41.8228 1.34493 0.672465 0.740129i \(-0.265236\pi\)
0.672465 + 0.740129i \(0.265236\pi\)
\(968\) 0 0
\(969\) 30.1618 0.968936
\(970\) 0 0
\(971\) 17.8551 0.572999 0.286499 0.958080i \(-0.407508\pi\)
0.286499 + 0.958080i \(0.407508\pi\)
\(972\) 0 0
\(973\) −79.3001 −2.54224
\(974\) 0 0
\(975\) 41.6000 1.33227
\(976\) 0 0
\(977\) 56.8503 1.81880 0.909401 0.415920i \(-0.136540\pi\)
0.909401 + 0.415920i \(0.136540\pi\)
\(978\) 0 0
\(979\) 47.9698 1.53312
\(980\) 0 0
\(981\) −108.715 −3.47099
\(982\) 0 0
\(983\) −39.0293 −1.24484 −0.622421 0.782682i \(-0.713851\pi\)
−0.622421 + 0.782682i \(0.713851\pi\)
\(984\) 0 0
\(985\) −0.563768 −0.0179631
\(986\) 0 0
\(987\) 4.58778 0.146031
\(988\) 0 0
\(989\) 1.04862 0.0333442
\(990\) 0 0
\(991\) 32.4204 1.02987 0.514933 0.857230i \(-0.327817\pi\)
0.514933 + 0.857230i \(0.327817\pi\)
\(992\) 0 0
\(993\) −112.873 −3.58191
\(994\) 0 0
\(995\) 0.280172 0.00888205
\(996\) 0 0
\(997\) −35.9083 −1.13723 −0.568614 0.822605i \(-0.692520\pi\)
−0.568614 + 0.822605i \(0.692520\pi\)
\(998\) 0 0
\(999\) 50.1494 1.58666
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 6008.2.a.b.1.1 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.1 44 1.1 even 1 trivial