Properties

Label 6008.2.a.b.1.26
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 1.26
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.0368230 q^{3} -3.59158 q^{5} -0.547211 q^{7} -2.99864 q^{9} +O(q^{10})\) \(q-0.0368230 q^{3} -3.59158 q^{5} -0.547211 q^{7} -2.99864 q^{9} +1.30756 q^{11} +0.987833 q^{13} +0.132253 q^{15} +1.11658 q^{17} +5.02241 q^{19} +0.0201500 q^{21} -2.20016 q^{23} +7.89946 q^{25} +0.220888 q^{27} +0.0479181 q^{29} +3.20026 q^{31} -0.0481482 q^{33} +1.96535 q^{35} -6.60748 q^{37} -0.0363750 q^{39} -0.410505 q^{41} -7.81229 q^{43} +10.7699 q^{45} +9.58834 q^{47} -6.70056 q^{49} -0.0411157 q^{51} -1.16958 q^{53} -4.69620 q^{55} -0.184940 q^{57} +7.75541 q^{59} +8.47931 q^{61} +1.64089 q^{63} -3.54788 q^{65} +5.28110 q^{67} +0.0810166 q^{69} +14.7035 q^{71} -10.4830 q^{73} -0.290882 q^{75} -0.715509 q^{77} +5.56063 q^{79} +8.98780 q^{81} -0.439874 q^{83} -4.01027 q^{85} -0.00176449 q^{87} +11.3734 q^{89} -0.540553 q^{91} -0.117843 q^{93} -18.0384 q^{95} -17.5419 q^{97} -3.92090 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −0.0368230 −0.0212598 −0.0106299 0.999944i \(-0.503384\pi\)
−0.0106299 + 0.999944i \(0.503384\pi\)
\(4\) 0 0
\(5\) −3.59158 −1.60620 −0.803102 0.595842i \(-0.796819\pi\)
−0.803102 + 0.595842i \(0.796819\pi\)
\(6\) 0 0
\(7\) −0.547211 −0.206826 −0.103413 0.994638i \(-0.532976\pi\)
−0.103413 + 0.994638i \(0.532976\pi\)
\(8\) 0 0
\(9\) −2.99864 −0.999548
\(10\) 0 0
\(11\) 1.30756 0.394243 0.197122 0.980379i \(-0.436841\pi\)
0.197122 + 0.980379i \(0.436841\pi\)
\(12\) 0 0
\(13\) 0.987833 0.273976 0.136988 0.990573i \(-0.456258\pi\)
0.136988 + 0.990573i \(0.456258\pi\)
\(14\) 0 0
\(15\) 0.132253 0.0341476
\(16\) 0 0
\(17\) 1.11658 0.270809 0.135405 0.990790i \(-0.456767\pi\)
0.135405 + 0.990790i \(0.456767\pi\)
\(18\) 0 0
\(19\) 5.02241 1.15222 0.576110 0.817373i \(-0.304570\pi\)
0.576110 + 0.817373i \(0.304570\pi\)
\(20\) 0 0
\(21\) 0.0201500 0.00439708
\(22\) 0 0
\(23\) −2.20016 −0.458765 −0.229383 0.973336i \(-0.573671\pi\)
−0.229383 + 0.973336i \(0.573671\pi\)
\(24\) 0 0
\(25\) 7.89946 1.57989
\(26\) 0 0
\(27\) 0.220888 0.0425100
\(28\) 0 0
\(29\) 0.0479181 0.00889817 0.00444909 0.999990i \(-0.498584\pi\)
0.00444909 + 0.999990i \(0.498584\pi\)
\(30\) 0 0
\(31\) 3.20026 0.574784 0.287392 0.957813i \(-0.407212\pi\)
0.287392 + 0.957813i \(0.407212\pi\)
\(32\) 0 0
\(33\) −0.0481482 −0.00838153
\(34\) 0 0
\(35\) 1.96535 0.332205
\(36\) 0 0
\(37\) −6.60748 −1.08626 −0.543131 0.839648i \(-0.682761\pi\)
−0.543131 + 0.839648i \(0.682761\pi\)
\(38\) 0 0
\(39\) −0.0363750 −0.00582467
\(40\) 0 0
\(41\) −0.410505 −0.0641101 −0.0320551 0.999486i \(-0.510205\pi\)
−0.0320551 + 0.999486i \(0.510205\pi\)
\(42\) 0 0
\(43\) −7.81229 −1.19136 −0.595682 0.803221i \(-0.703118\pi\)
−0.595682 + 0.803221i \(0.703118\pi\)
\(44\) 0 0
\(45\) 10.7699 1.60548
\(46\) 0 0
\(47\) 9.58834 1.39860 0.699302 0.714827i \(-0.253494\pi\)
0.699302 + 0.714827i \(0.253494\pi\)
\(48\) 0 0
\(49\) −6.70056 −0.957223
\(50\) 0 0
\(51\) −0.0411157 −0.00575735
\(52\) 0 0
\(53\) −1.16958 −0.160655 −0.0803274 0.996769i \(-0.525597\pi\)
−0.0803274 + 0.996769i \(0.525597\pi\)
\(54\) 0 0
\(55\) −4.69620 −0.633235
\(56\) 0 0
\(57\) −0.184940 −0.0244959
\(58\) 0 0
\(59\) 7.75541 1.00967 0.504834 0.863216i \(-0.331554\pi\)
0.504834 + 0.863216i \(0.331554\pi\)
\(60\) 0 0
\(61\) 8.47931 1.08566 0.542832 0.839841i \(-0.317352\pi\)
0.542832 + 0.839841i \(0.317352\pi\)
\(62\) 0 0
\(63\) 1.64089 0.206733
\(64\) 0 0
\(65\) −3.54788 −0.440061
\(66\) 0 0
\(67\) 5.28110 0.645189 0.322594 0.946537i \(-0.395445\pi\)
0.322594 + 0.946537i \(0.395445\pi\)
\(68\) 0 0
\(69\) 0.0810166 0.00975325
\(70\) 0 0
\(71\) 14.7035 1.74498 0.872491 0.488631i \(-0.162504\pi\)
0.872491 + 0.488631i \(0.162504\pi\)
\(72\) 0 0
\(73\) −10.4830 −1.22694 −0.613469 0.789719i \(-0.710227\pi\)
−0.613469 + 0.789719i \(0.710227\pi\)
\(74\) 0 0
\(75\) −0.290882 −0.0335882
\(76\) 0 0
\(77\) −0.715509 −0.0815399
\(78\) 0 0
\(79\) 5.56063 0.625620 0.312810 0.949816i \(-0.398730\pi\)
0.312810 + 0.949816i \(0.398730\pi\)
\(80\) 0 0
\(81\) 8.98780 0.998644
\(82\) 0 0
\(83\) −0.439874 −0.0482824 −0.0241412 0.999709i \(-0.507685\pi\)
−0.0241412 + 0.999709i \(0.507685\pi\)
\(84\) 0 0
\(85\) −4.01027 −0.434975
\(86\) 0 0
\(87\) −0.00176449 −0.000189173 0
\(88\) 0 0
\(89\) 11.3734 1.20558 0.602791 0.797899i \(-0.294055\pi\)
0.602791 + 0.797899i \(0.294055\pi\)
\(90\) 0 0
\(91\) −0.540553 −0.0566654
\(92\) 0 0
\(93\) −0.117843 −0.0122198
\(94\) 0 0
\(95\) −18.0384 −1.85070
\(96\) 0 0
\(97\) −17.5419 −1.78111 −0.890553 0.454880i \(-0.849682\pi\)
−0.890553 + 0.454880i \(0.849682\pi\)
\(98\) 0 0
\(99\) −3.92090 −0.394065
\(100\) 0 0
\(101\) 2.46866 0.245641 0.122821 0.992429i \(-0.460806\pi\)
0.122821 + 0.992429i \(0.460806\pi\)
\(102\) 0 0
\(103\) 17.0932 1.68424 0.842119 0.539291i \(-0.181308\pi\)
0.842119 + 0.539291i \(0.181308\pi\)
\(104\) 0 0
\(105\) −0.0723702 −0.00706261
\(106\) 0 0
\(107\) −13.5655 −1.31143 −0.655714 0.755009i \(-0.727632\pi\)
−0.655714 + 0.755009i \(0.727632\pi\)
\(108\) 0 0
\(109\) 5.90938 0.566016 0.283008 0.959118i \(-0.408668\pi\)
0.283008 + 0.959118i \(0.408668\pi\)
\(110\) 0 0
\(111\) 0.243307 0.0230937
\(112\) 0 0
\(113\) −8.81842 −0.829567 −0.414784 0.909920i \(-0.636143\pi\)
−0.414784 + 0.909920i \(0.636143\pi\)
\(114\) 0 0
\(115\) 7.90205 0.736870
\(116\) 0 0
\(117\) −2.96216 −0.273852
\(118\) 0 0
\(119\) −0.611002 −0.0560105
\(120\) 0 0
\(121\) −9.29029 −0.844572
\(122\) 0 0
\(123\) 0.0151160 0.00136297
\(124\) 0 0
\(125\) −10.4136 −0.931424
\(126\) 0 0
\(127\) −16.1932 −1.43691 −0.718457 0.695571i \(-0.755151\pi\)
−0.718457 + 0.695571i \(0.755151\pi\)
\(128\) 0 0
\(129\) 0.287672 0.0253281
\(130\) 0 0
\(131\) 4.30546 0.376170 0.188085 0.982153i \(-0.439772\pi\)
0.188085 + 0.982153i \(0.439772\pi\)
\(132\) 0 0
\(133\) −2.74831 −0.238309
\(134\) 0 0
\(135\) −0.793338 −0.0682797
\(136\) 0 0
\(137\) −18.2477 −1.55901 −0.779503 0.626399i \(-0.784528\pi\)
−0.779503 + 0.626399i \(0.784528\pi\)
\(138\) 0 0
\(139\) −15.2483 −1.29334 −0.646672 0.762768i \(-0.723840\pi\)
−0.646672 + 0.762768i \(0.723840\pi\)
\(140\) 0 0
\(141\) −0.353072 −0.0297340
\(142\) 0 0
\(143\) 1.29165 0.108013
\(144\) 0 0
\(145\) −0.172102 −0.0142923
\(146\) 0 0
\(147\) 0.246735 0.0203504
\(148\) 0 0
\(149\) 10.5489 0.864199 0.432099 0.901826i \(-0.357773\pi\)
0.432099 + 0.901826i \(0.357773\pi\)
\(150\) 0 0
\(151\) 10.6271 0.864823 0.432411 0.901676i \(-0.357663\pi\)
0.432411 + 0.901676i \(0.357663\pi\)
\(152\) 0 0
\(153\) −3.34821 −0.270687
\(154\) 0 0
\(155\) −11.4940 −0.923220
\(156\) 0 0
\(157\) −17.9067 −1.42911 −0.714556 0.699578i \(-0.753371\pi\)
−0.714556 + 0.699578i \(0.753371\pi\)
\(158\) 0 0
\(159\) 0.0430677 0.00341549
\(160\) 0 0
\(161\) 1.20395 0.0948846
\(162\) 0 0
\(163\) −10.0276 −0.785421 −0.392710 0.919662i \(-0.628463\pi\)
−0.392710 + 0.919662i \(0.628463\pi\)
\(164\) 0 0
\(165\) 0.172928 0.0134625
\(166\) 0 0
\(167\) −17.6913 −1.36899 −0.684497 0.729016i \(-0.739978\pi\)
−0.684497 + 0.729016i \(0.739978\pi\)
\(168\) 0 0
\(169\) −12.0242 −0.924937
\(170\) 0 0
\(171\) −15.0604 −1.15170
\(172\) 0 0
\(173\) 10.3232 0.784857 0.392428 0.919783i \(-0.371635\pi\)
0.392428 + 0.919783i \(0.371635\pi\)
\(174\) 0 0
\(175\) −4.32267 −0.326763
\(176\) 0 0
\(177\) −0.285578 −0.0214653
\(178\) 0 0
\(179\) −0.442138 −0.0330469 −0.0165235 0.999863i \(-0.505260\pi\)
−0.0165235 + 0.999863i \(0.505260\pi\)
\(180\) 0 0
\(181\) 0.333021 0.0247533 0.0123766 0.999923i \(-0.496060\pi\)
0.0123766 + 0.999923i \(0.496060\pi\)
\(182\) 0 0
\(183\) −0.312234 −0.0230810
\(184\) 0 0
\(185\) 23.7313 1.74476
\(186\) 0 0
\(187\) 1.45999 0.106765
\(188\) 0 0
\(189\) −0.120872 −0.00879218
\(190\) 0 0
\(191\) −14.5590 −1.05345 −0.526726 0.850035i \(-0.676581\pi\)
−0.526726 + 0.850035i \(0.676581\pi\)
\(192\) 0 0
\(193\) −23.1033 −1.66301 −0.831504 0.555518i \(-0.812520\pi\)
−0.831504 + 0.555518i \(0.812520\pi\)
\(194\) 0 0
\(195\) 0.130644 0.00935560
\(196\) 0 0
\(197\) 17.1008 1.21838 0.609192 0.793023i \(-0.291494\pi\)
0.609192 + 0.793023i \(0.291494\pi\)
\(198\) 0 0
\(199\) −9.75739 −0.691683 −0.345842 0.938293i \(-0.612407\pi\)
−0.345842 + 0.938293i \(0.612407\pi\)
\(200\) 0 0
\(201\) −0.194466 −0.0137166
\(202\) 0 0
\(203\) −0.0262213 −0.00184038
\(204\) 0 0
\(205\) 1.47436 0.102974
\(206\) 0 0
\(207\) 6.59750 0.458558
\(208\) 0 0
\(209\) 6.56708 0.454255
\(210\) 0 0
\(211\) −9.30499 −0.640582 −0.320291 0.947319i \(-0.603781\pi\)
−0.320291 + 0.947319i \(0.603781\pi\)
\(212\) 0 0
\(213\) −0.541427 −0.0370979
\(214\) 0 0
\(215\) 28.0585 1.91357
\(216\) 0 0
\(217\) −1.75122 −0.118880
\(218\) 0 0
\(219\) 0.386015 0.0260845
\(220\) 0 0
\(221\) 1.10299 0.0741952
\(222\) 0 0
\(223\) −15.9472 −1.06790 −0.533951 0.845516i \(-0.679293\pi\)
−0.533951 + 0.845516i \(0.679293\pi\)
\(224\) 0 0
\(225\) −23.6877 −1.57918
\(226\) 0 0
\(227\) −22.8186 −1.51453 −0.757263 0.653110i \(-0.773464\pi\)
−0.757263 + 0.653110i \(0.773464\pi\)
\(228\) 0 0
\(229\) −13.3410 −0.881597 −0.440798 0.897606i \(-0.645305\pi\)
−0.440798 + 0.897606i \(0.645305\pi\)
\(230\) 0 0
\(231\) 0.0263472 0.00173352
\(232\) 0 0
\(233\) 5.87184 0.384677 0.192339 0.981329i \(-0.438393\pi\)
0.192339 + 0.981329i \(0.438393\pi\)
\(234\) 0 0
\(235\) −34.4373 −2.24644
\(236\) 0 0
\(237\) −0.204759 −0.0133006
\(238\) 0 0
\(239\) −11.1257 −0.719662 −0.359831 0.933018i \(-0.617166\pi\)
−0.359831 + 0.933018i \(0.617166\pi\)
\(240\) 0 0
\(241\) −23.6564 −1.52384 −0.761921 0.647670i \(-0.775744\pi\)
−0.761921 + 0.647670i \(0.775744\pi\)
\(242\) 0 0
\(243\) −0.993623 −0.0637409
\(244\) 0 0
\(245\) 24.0656 1.53750
\(246\) 0 0
\(247\) 4.96130 0.315680
\(248\) 0 0
\(249\) 0.0161975 0.00102647
\(250\) 0 0
\(251\) 0.674814 0.0425939 0.0212969 0.999773i \(-0.493220\pi\)
0.0212969 + 0.999773i \(0.493220\pi\)
\(252\) 0 0
\(253\) −2.87684 −0.180865
\(254\) 0 0
\(255\) 0.147670 0.00924749
\(256\) 0 0
\(257\) 28.1791 1.75776 0.878881 0.477042i \(-0.158291\pi\)
0.878881 + 0.477042i \(0.158291\pi\)
\(258\) 0 0
\(259\) 3.61568 0.224668
\(260\) 0 0
\(261\) −0.143689 −0.00889415
\(262\) 0 0
\(263\) 25.1677 1.55190 0.775952 0.630792i \(-0.217270\pi\)
0.775952 + 0.630792i \(0.217270\pi\)
\(264\) 0 0
\(265\) 4.20066 0.258044
\(266\) 0 0
\(267\) −0.418805 −0.0256304
\(268\) 0 0
\(269\) −25.5178 −1.55585 −0.777923 0.628359i \(-0.783727\pi\)
−0.777923 + 0.628359i \(0.783727\pi\)
\(270\) 0 0
\(271\) −12.0696 −0.733177 −0.366589 0.930383i \(-0.619474\pi\)
−0.366589 + 0.930383i \(0.619474\pi\)
\(272\) 0 0
\(273\) 0.0199048 0.00120469
\(274\) 0 0
\(275\) 10.3290 0.622862
\(276\) 0 0
\(277\) −5.71005 −0.343084 −0.171542 0.985177i \(-0.554875\pi\)
−0.171542 + 0.985177i \(0.554875\pi\)
\(278\) 0 0
\(279\) −9.59644 −0.574524
\(280\) 0 0
\(281\) −0.212448 −0.0126736 −0.00633680 0.999980i \(-0.502017\pi\)
−0.00633680 + 0.999980i \(0.502017\pi\)
\(282\) 0 0
\(283\) −15.3052 −0.909802 −0.454901 0.890542i \(-0.650325\pi\)
−0.454901 + 0.890542i \(0.650325\pi\)
\(284\) 0 0
\(285\) 0.664228 0.0393455
\(286\) 0 0
\(287\) 0.224633 0.0132597
\(288\) 0 0
\(289\) −15.7533 −0.926662
\(290\) 0 0
\(291\) 0.645944 0.0378659
\(292\) 0 0
\(293\) 23.9617 1.39986 0.699929 0.714212i \(-0.253215\pi\)
0.699929 + 0.714212i \(0.253215\pi\)
\(294\) 0 0
\(295\) −27.8542 −1.62173
\(296\) 0 0
\(297\) 0.288824 0.0167593
\(298\) 0 0
\(299\) −2.17339 −0.125690
\(300\) 0 0
\(301\) 4.27497 0.246405
\(302\) 0 0
\(303\) −0.0909037 −0.00522228
\(304\) 0 0
\(305\) −30.4541 −1.74380
\(306\) 0 0
\(307\) 30.9475 1.76627 0.883133 0.469123i \(-0.155430\pi\)
0.883133 + 0.469123i \(0.155430\pi\)
\(308\) 0 0
\(309\) −0.629422 −0.0358066
\(310\) 0 0
\(311\) −27.8105 −1.57699 −0.788495 0.615041i \(-0.789140\pi\)
−0.788495 + 0.615041i \(0.789140\pi\)
\(312\) 0 0
\(313\) 32.2987 1.82563 0.912814 0.408375i \(-0.133904\pi\)
0.912814 + 0.408375i \(0.133904\pi\)
\(314\) 0 0
\(315\) −5.89339 −0.332055
\(316\) 0 0
\(317\) −32.6102 −1.83157 −0.915787 0.401665i \(-0.868432\pi\)
−0.915787 + 0.401665i \(0.868432\pi\)
\(318\) 0 0
\(319\) 0.0626557 0.00350805
\(320\) 0 0
\(321\) 0.499524 0.0278807
\(322\) 0 0
\(323\) 5.60790 0.312032
\(324\) 0 0
\(325\) 7.80335 0.432852
\(326\) 0 0
\(327\) −0.217601 −0.0120334
\(328\) 0 0
\(329\) −5.24684 −0.289268
\(330\) 0 0
\(331\) −16.4948 −0.906636 −0.453318 0.891349i \(-0.649760\pi\)
−0.453318 + 0.891349i \(0.649760\pi\)
\(332\) 0 0
\(333\) 19.8135 1.08577
\(334\) 0 0
\(335\) −18.9675 −1.03630
\(336\) 0 0
\(337\) −2.05633 −0.112015 −0.0560077 0.998430i \(-0.517837\pi\)
−0.0560077 + 0.998430i \(0.517837\pi\)
\(338\) 0 0
\(339\) 0.324721 0.0176364
\(340\) 0 0
\(341\) 4.18453 0.226605
\(342\) 0 0
\(343\) 7.49709 0.404805
\(344\) 0 0
\(345\) −0.290978 −0.0156657
\(346\) 0 0
\(347\) −11.7232 −0.629334 −0.314667 0.949202i \(-0.601893\pi\)
−0.314667 + 0.949202i \(0.601893\pi\)
\(348\) 0 0
\(349\) 9.49831 0.508433 0.254217 0.967147i \(-0.418182\pi\)
0.254217 + 0.967147i \(0.418182\pi\)
\(350\) 0 0
\(351\) 0.218201 0.0116467
\(352\) 0 0
\(353\) 28.6099 1.52275 0.761377 0.648310i \(-0.224524\pi\)
0.761377 + 0.648310i \(0.224524\pi\)
\(354\) 0 0
\(355\) −52.8087 −2.80280
\(356\) 0 0
\(357\) 0.0224990 0.00119077
\(358\) 0 0
\(359\) 9.76360 0.515303 0.257651 0.966238i \(-0.417051\pi\)
0.257651 + 0.966238i \(0.417051\pi\)
\(360\) 0 0
\(361\) 6.22456 0.327609
\(362\) 0 0
\(363\) 0.342097 0.0179554
\(364\) 0 0
\(365\) 37.6504 1.97071
\(366\) 0 0
\(367\) −12.7863 −0.667437 −0.333719 0.942673i \(-0.608304\pi\)
−0.333719 + 0.942673i \(0.608304\pi\)
\(368\) 0 0
\(369\) 1.23096 0.0640812
\(370\) 0 0
\(371\) 0.640009 0.0332276
\(372\) 0 0
\(373\) 24.6501 1.27633 0.638166 0.769899i \(-0.279693\pi\)
0.638166 + 0.769899i \(0.279693\pi\)
\(374\) 0 0
\(375\) 0.383462 0.0198019
\(376\) 0 0
\(377\) 0.0473351 0.00243788
\(378\) 0 0
\(379\) 14.3795 0.738626 0.369313 0.929305i \(-0.379593\pi\)
0.369313 + 0.929305i \(0.379593\pi\)
\(380\) 0 0
\(381\) 0.596283 0.0305485
\(382\) 0 0
\(383\) −25.9455 −1.32575 −0.662877 0.748728i \(-0.730665\pi\)
−0.662877 + 0.748728i \(0.730665\pi\)
\(384\) 0 0
\(385\) 2.56981 0.130970
\(386\) 0 0
\(387\) 23.4263 1.19082
\(388\) 0 0
\(389\) −31.0273 −1.57314 −0.786572 0.617498i \(-0.788146\pi\)
−0.786572 + 0.617498i \(0.788146\pi\)
\(390\) 0 0
\(391\) −2.45665 −0.124238
\(392\) 0 0
\(393\) −0.158540 −0.00799730
\(394\) 0 0
\(395\) −19.9715 −1.00487
\(396\) 0 0
\(397\) 9.06988 0.455204 0.227602 0.973754i \(-0.426911\pi\)
0.227602 + 0.973754i \(0.426911\pi\)
\(398\) 0 0
\(399\) 0.101201 0.00506640
\(400\) 0 0
\(401\) −30.2787 −1.51204 −0.756022 0.654546i \(-0.772860\pi\)
−0.756022 + 0.654546i \(0.772860\pi\)
\(402\) 0 0
\(403\) 3.16133 0.157477
\(404\) 0 0
\(405\) −32.2804 −1.60403
\(406\) 0 0
\(407\) −8.63966 −0.428252
\(408\) 0 0
\(409\) −3.15860 −0.156183 −0.0780913 0.996946i \(-0.524883\pi\)
−0.0780913 + 0.996946i \(0.524883\pi\)
\(410\) 0 0
\(411\) 0.671935 0.0331441
\(412\) 0 0
\(413\) −4.24384 −0.208826
\(414\) 0 0
\(415\) 1.57984 0.0775514
\(416\) 0 0
\(417\) 0.561489 0.0274962
\(418\) 0 0
\(419\) −14.9861 −0.732117 −0.366058 0.930592i \(-0.619293\pi\)
−0.366058 + 0.930592i \(0.619293\pi\)
\(420\) 0 0
\(421\) 22.3764 1.09056 0.545279 0.838255i \(-0.316424\pi\)
0.545279 + 0.838255i \(0.316424\pi\)
\(422\) 0 0
\(423\) −28.7520 −1.39797
\(424\) 0 0
\(425\) 8.82035 0.427850
\(426\) 0 0
\(427\) −4.63997 −0.224544
\(428\) 0 0
\(429\) −0.0475624 −0.00229634
\(430\) 0 0
\(431\) 23.3150 1.12304 0.561522 0.827462i \(-0.310216\pi\)
0.561522 + 0.827462i \(0.310216\pi\)
\(432\) 0 0
\(433\) 31.8072 1.52856 0.764278 0.644887i \(-0.223096\pi\)
0.764278 + 0.644887i \(0.223096\pi\)
\(434\) 0 0
\(435\) 0.00633731 0.000303851 0
\(436\) 0 0
\(437\) −11.0501 −0.528598
\(438\) 0 0
\(439\) 25.9005 1.23616 0.618081 0.786115i \(-0.287911\pi\)
0.618081 + 0.786115i \(0.287911\pi\)
\(440\) 0 0
\(441\) 20.0926 0.956790
\(442\) 0 0
\(443\) −14.0153 −0.665887 −0.332943 0.942947i \(-0.608042\pi\)
−0.332943 + 0.942947i \(0.608042\pi\)
\(444\) 0 0
\(445\) −40.8486 −1.93641
\(446\) 0 0
\(447\) −0.388442 −0.0183727
\(448\) 0 0
\(449\) 35.2077 1.66155 0.830776 0.556607i \(-0.187897\pi\)
0.830776 + 0.556607i \(0.187897\pi\)
\(450\) 0 0
\(451\) −0.536759 −0.0252750
\(452\) 0 0
\(453\) −0.391323 −0.0183860
\(454\) 0 0
\(455\) 1.94144 0.0910161
\(456\) 0 0
\(457\) −10.5389 −0.492991 −0.246495 0.969144i \(-0.579279\pi\)
−0.246495 + 0.969144i \(0.579279\pi\)
\(458\) 0 0
\(459\) 0.246639 0.0115121
\(460\) 0 0
\(461\) 12.3500 0.575199 0.287599 0.957751i \(-0.407143\pi\)
0.287599 + 0.957751i \(0.407143\pi\)
\(462\) 0 0
\(463\) −25.1695 −1.16972 −0.584862 0.811133i \(-0.698851\pi\)
−0.584862 + 0.811133i \(0.698851\pi\)
\(464\) 0 0
\(465\) 0.423244 0.0196275
\(466\) 0 0
\(467\) 10.6410 0.492407 0.246203 0.969218i \(-0.420817\pi\)
0.246203 + 0.969218i \(0.420817\pi\)
\(468\) 0 0
\(469\) −2.88987 −0.133442
\(470\) 0 0
\(471\) 0.659380 0.0303826
\(472\) 0 0
\(473\) −10.2150 −0.469687
\(474\) 0 0
\(475\) 39.6743 1.82038
\(476\) 0 0
\(477\) 3.50717 0.160582
\(478\) 0 0
\(479\) 27.1910 1.24239 0.621193 0.783657i \(-0.286648\pi\)
0.621193 + 0.783657i \(0.286648\pi\)
\(480\) 0 0
\(481\) −6.52709 −0.297610
\(482\) 0 0
\(483\) −0.0443331 −0.00201723
\(484\) 0 0
\(485\) 63.0030 2.86082
\(486\) 0 0
\(487\) −13.2201 −0.599061 −0.299531 0.954087i \(-0.596830\pi\)
−0.299531 + 0.954087i \(0.596830\pi\)
\(488\) 0 0
\(489\) 0.369246 0.0166979
\(490\) 0 0
\(491\) 41.1468 1.85693 0.928464 0.371422i \(-0.121130\pi\)
0.928464 + 0.371422i \(0.121130\pi\)
\(492\) 0 0
\(493\) 0.0535042 0.00240971
\(494\) 0 0
\(495\) 14.0822 0.632949
\(496\) 0 0
\(497\) −8.04590 −0.360908
\(498\) 0 0
\(499\) 33.7054 1.50886 0.754430 0.656380i \(-0.227913\pi\)
0.754430 + 0.656380i \(0.227913\pi\)
\(500\) 0 0
\(501\) 0.651447 0.0291045
\(502\) 0 0
\(503\) −43.2694 −1.92929 −0.964645 0.263554i \(-0.915105\pi\)
−0.964645 + 0.263554i \(0.915105\pi\)
\(504\) 0 0
\(505\) −8.86641 −0.394550
\(506\) 0 0
\(507\) 0.442767 0.0196640
\(508\) 0 0
\(509\) 13.3195 0.590375 0.295188 0.955439i \(-0.404618\pi\)
0.295188 + 0.955439i \(0.404618\pi\)
\(510\) 0 0
\(511\) 5.73639 0.253763
\(512\) 0 0
\(513\) 1.10939 0.0489808
\(514\) 0 0
\(515\) −61.3915 −2.70523
\(516\) 0 0
\(517\) 12.5373 0.551390
\(518\) 0 0
\(519\) −0.380131 −0.0166859
\(520\) 0 0
\(521\) 10.5245 0.461087 0.230544 0.973062i \(-0.425950\pi\)
0.230544 + 0.973062i \(0.425950\pi\)
\(522\) 0 0
\(523\) −42.6580 −1.86531 −0.932653 0.360775i \(-0.882512\pi\)
−0.932653 + 0.360775i \(0.882512\pi\)
\(524\) 0 0
\(525\) 0.159174 0.00694691
\(526\) 0 0
\(527\) 3.57334 0.155657
\(528\) 0 0
\(529\) −18.1593 −0.789535
\(530\) 0 0
\(531\) −23.2557 −1.00921
\(532\) 0 0
\(533\) −0.405511 −0.0175646
\(534\) 0 0
\(535\) 48.7217 2.10642
\(536\) 0 0
\(537\) 0.0162809 0.000702571 0
\(538\) 0 0
\(539\) −8.76137 −0.377379
\(540\) 0 0
\(541\) −24.8753 −1.06947 −0.534737 0.845018i \(-0.679589\pi\)
−0.534737 + 0.845018i \(0.679589\pi\)
\(542\) 0 0
\(543\) −0.0122629 −0.000526250 0
\(544\) 0 0
\(545\) −21.2240 −0.909137
\(546\) 0 0
\(547\) 38.4320 1.64323 0.821616 0.570041i \(-0.193073\pi\)
0.821616 + 0.570041i \(0.193073\pi\)
\(548\) 0 0
\(549\) −25.4264 −1.08517
\(550\) 0 0
\(551\) 0.240664 0.0102526
\(552\) 0 0
\(553\) −3.04284 −0.129395
\(554\) 0 0
\(555\) −0.873859 −0.0370932
\(556\) 0 0
\(557\) 6.34246 0.268739 0.134369 0.990931i \(-0.457099\pi\)
0.134369 + 0.990931i \(0.457099\pi\)
\(558\) 0 0
\(559\) −7.71724 −0.326405
\(560\) 0 0
\(561\) −0.0537612 −0.00226980
\(562\) 0 0
\(563\) 16.2363 0.684280 0.342140 0.939649i \(-0.388848\pi\)
0.342140 + 0.939649i \(0.388848\pi\)
\(564\) 0 0
\(565\) 31.6721 1.33245
\(566\) 0 0
\(567\) −4.91822 −0.206546
\(568\) 0 0
\(569\) −6.88953 −0.288824 −0.144412 0.989518i \(-0.546129\pi\)
−0.144412 + 0.989518i \(0.546129\pi\)
\(570\) 0 0
\(571\) 14.1366 0.591597 0.295798 0.955250i \(-0.404414\pi\)
0.295798 + 0.955250i \(0.404414\pi\)
\(572\) 0 0
\(573\) 0.536106 0.0223962
\(574\) 0 0
\(575\) −17.3801 −0.724799
\(576\) 0 0
\(577\) 6.91701 0.287959 0.143979 0.989581i \(-0.454010\pi\)
0.143979 + 0.989581i \(0.454010\pi\)
\(578\) 0 0
\(579\) 0.850732 0.0353552
\(580\) 0 0
\(581\) 0.240704 0.00998607
\(582\) 0 0
\(583\) −1.52930 −0.0633371
\(584\) 0 0
\(585\) 10.6388 0.439862
\(586\) 0 0
\(587\) 29.4326 1.21481 0.607407 0.794391i \(-0.292210\pi\)
0.607407 + 0.794391i \(0.292210\pi\)
\(588\) 0 0
\(589\) 16.0730 0.662277
\(590\) 0 0
\(591\) −0.629705 −0.0259026
\(592\) 0 0
\(593\) −24.5283 −1.00725 −0.503627 0.863921i \(-0.668002\pi\)
−0.503627 + 0.863921i \(0.668002\pi\)
\(594\) 0 0
\(595\) 2.19446 0.0899643
\(596\) 0 0
\(597\) 0.359297 0.0147050
\(598\) 0 0
\(599\) −32.5940 −1.33176 −0.665878 0.746061i \(-0.731943\pi\)
−0.665878 + 0.746061i \(0.731943\pi\)
\(600\) 0 0
\(601\) 18.3281 0.747618 0.373809 0.927506i \(-0.378052\pi\)
0.373809 + 0.927506i \(0.378052\pi\)
\(602\) 0 0
\(603\) −15.8361 −0.644897
\(604\) 0 0
\(605\) 33.3668 1.35656
\(606\) 0 0
\(607\) −36.6995 −1.48959 −0.744794 0.667294i \(-0.767452\pi\)
−0.744794 + 0.667294i \(0.767452\pi\)
\(608\) 0 0
\(609\) 0.000965548 0 3.91260e−5 0
\(610\) 0 0
\(611\) 9.47168 0.383183
\(612\) 0 0
\(613\) 31.1587 1.25849 0.629245 0.777207i \(-0.283364\pi\)
0.629245 + 0.777207i \(0.283364\pi\)
\(614\) 0 0
\(615\) −0.0542905 −0.00218920
\(616\) 0 0
\(617\) 9.30996 0.374805 0.187402 0.982283i \(-0.439993\pi\)
0.187402 + 0.982283i \(0.439993\pi\)
\(618\) 0 0
\(619\) −6.72625 −0.270351 −0.135175 0.990822i \(-0.543160\pi\)
−0.135175 + 0.990822i \(0.543160\pi\)
\(620\) 0 0
\(621\) −0.485990 −0.0195021
\(622\) 0 0
\(623\) −6.22367 −0.249346
\(624\) 0 0
\(625\) −2.09586 −0.0838346
\(626\) 0 0
\(627\) −0.241820 −0.00965736
\(628\) 0 0
\(629\) −7.37775 −0.294170
\(630\) 0 0
\(631\) 10.1334 0.403405 0.201702 0.979447i \(-0.435353\pi\)
0.201702 + 0.979447i \(0.435353\pi\)
\(632\) 0 0
\(633\) 0.342638 0.0136186
\(634\) 0 0
\(635\) 58.1592 2.30798
\(636\) 0 0
\(637\) −6.61904 −0.262256
\(638\) 0 0
\(639\) −44.0905 −1.74419
\(640\) 0 0
\(641\) −7.01212 −0.276962 −0.138481 0.990365i \(-0.544222\pi\)
−0.138481 + 0.990365i \(0.544222\pi\)
\(642\) 0 0
\(643\) −35.7876 −1.41133 −0.705663 0.708547i \(-0.749351\pi\)
−0.705663 + 0.708547i \(0.749351\pi\)
\(644\) 0 0
\(645\) −1.03320 −0.0406821
\(646\) 0 0
\(647\) 0.566397 0.0222674 0.0111337 0.999938i \(-0.496456\pi\)
0.0111337 + 0.999938i \(0.496456\pi\)
\(648\) 0 0
\(649\) 10.1406 0.398055
\(650\) 0 0
\(651\) 0.0644851 0.00252737
\(652\) 0 0
\(653\) −29.1741 −1.14167 −0.570836 0.821064i \(-0.693381\pi\)
−0.570836 + 0.821064i \(0.693381\pi\)
\(654\) 0 0
\(655\) −15.4634 −0.604206
\(656\) 0 0
\(657\) 31.4347 1.22638
\(658\) 0 0
\(659\) −35.5997 −1.38677 −0.693383 0.720569i \(-0.743881\pi\)
−0.693383 + 0.720569i \(0.743881\pi\)
\(660\) 0 0
\(661\) −17.7417 −0.690071 −0.345035 0.938590i \(-0.612133\pi\)
−0.345035 + 0.938590i \(0.612133\pi\)
\(662\) 0 0
\(663\) −0.0406155 −0.00157738
\(664\) 0 0
\(665\) 9.87079 0.382773
\(666\) 0 0
\(667\) −0.105428 −0.00408217
\(668\) 0 0
\(669\) 0.587223 0.0227034
\(670\) 0 0
\(671\) 11.0872 0.428016
\(672\) 0 0
\(673\) 15.9294 0.614034 0.307017 0.951704i \(-0.400669\pi\)
0.307017 + 0.951704i \(0.400669\pi\)
\(674\) 0 0
\(675\) 1.74490 0.0671611
\(676\) 0 0
\(677\) 18.3273 0.704377 0.352188 0.935929i \(-0.385438\pi\)
0.352188 + 0.935929i \(0.385438\pi\)
\(678\) 0 0
\(679\) 9.59909 0.368379
\(680\) 0 0
\(681\) 0.840252 0.0321985
\(682\) 0 0
\(683\) 13.9610 0.534205 0.267102 0.963668i \(-0.413934\pi\)
0.267102 + 0.963668i \(0.413934\pi\)
\(684\) 0 0
\(685\) 65.5381 2.50408
\(686\) 0 0
\(687\) 0.491255 0.0187426
\(688\) 0 0
\(689\) −1.15535 −0.0440155
\(690\) 0 0
\(691\) 12.3418 0.469504 0.234752 0.972055i \(-0.424572\pi\)
0.234752 + 0.972055i \(0.424572\pi\)
\(692\) 0 0
\(693\) 2.14556 0.0815030
\(694\) 0 0
\(695\) 54.7655 2.07737
\(696\) 0 0
\(697\) −0.458360 −0.0173616
\(698\) 0 0
\(699\) −0.216219 −0.00817816
\(700\) 0 0
\(701\) 41.7980 1.57869 0.789345 0.613950i \(-0.210420\pi\)
0.789345 + 0.613950i \(0.210420\pi\)
\(702\) 0 0
\(703\) −33.1854 −1.25161
\(704\) 0 0
\(705\) 1.26809 0.0477589
\(706\) 0 0
\(707\) −1.35088 −0.0508051
\(708\) 0 0
\(709\) 5.58664 0.209811 0.104905 0.994482i \(-0.466546\pi\)
0.104905 + 0.994482i \(0.466546\pi\)
\(710\) 0 0
\(711\) −16.6744 −0.625338
\(712\) 0 0
\(713\) −7.04109 −0.263691
\(714\) 0 0
\(715\) −4.63906 −0.173491
\(716\) 0 0
\(717\) 0.409682 0.0152999
\(718\) 0 0
\(719\) −32.2923 −1.20430 −0.602150 0.798383i \(-0.705689\pi\)
−0.602150 + 0.798383i \(0.705689\pi\)
\(720\) 0 0
\(721\) −9.35356 −0.348345
\(722\) 0 0
\(723\) 0.871100 0.0323966
\(724\) 0 0
\(725\) 0.378527 0.0140581
\(726\) 0 0
\(727\) −22.9665 −0.851779 −0.425890 0.904775i \(-0.640039\pi\)
−0.425890 + 0.904775i \(0.640039\pi\)
\(728\) 0 0
\(729\) −26.9268 −0.997289
\(730\) 0 0
\(731\) −8.72302 −0.322632
\(732\) 0 0
\(733\) −45.3379 −1.67460 −0.837298 0.546747i \(-0.815866\pi\)
−0.837298 + 0.546747i \(0.815866\pi\)
\(734\) 0 0
\(735\) −0.886169 −0.0326868
\(736\) 0 0
\(737\) 6.90534 0.254361
\(738\) 0 0
\(739\) −15.5760 −0.572974 −0.286487 0.958084i \(-0.592487\pi\)
−0.286487 + 0.958084i \(0.592487\pi\)
\(740\) 0 0
\(741\) −0.182690 −0.00671129
\(742\) 0 0
\(743\) −4.24312 −0.155665 −0.0778326 0.996966i \(-0.524800\pi\)
−0.0778326 + 0.996966i \(0.524800\pi\)
\(744\) 0 0
\(745\) −37.8872 −1.38808
\(746\) 0 0
\(747\) 1.31902 0.0482606
\(748\) 0 0
\(749\) 7.42320 0.271238
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −0.0248487 −0.000905537 0
\(754\) 0 0
\(755\) −38.1682 −1.38908
\(756\) 0 0
\(757\) 43.9764 1.59835 0.799174 0.601099i \(-0.205270\pi\)
0.799174 + 0.601099i \(0.205270\pi\)
\(758\) 0 0
\(759\) 0.105934 0.00384515
\(760\) 0 0
\(761\) 8.95905 0.324765 0.162383 0.986728i \(-0.448082\pi\)
0.162383 + 0.986728i \(0.448082\pi\)
\(762\) 0 0
\(763\) −3.23367 −0.117067
\(764\) 0 0
\(765\) 12.0254 0.434779
\(766\) 0 0
\(767\) 7.66106 0.276625
\(768\) 0 0
\(769\) −40.5452 −1.46210 −0.731049 0.682325i \(-0.760969\pi\)
−0.731049 + 0.682325i \(0.760969\pi\)
\(770\) 0 0
\(771\) −1.03764 −0.0373696
\(772\) 0 0
\(773\) 19.1455 0.688615 0.344307 0.938857i \(-0.388114\pi\)
0.344307 + 0.938857i \(0.388114\pi\)
\(774\) 0 0
\(775\) 25.2803 0.908096
\(776\) 0 0
\(777\) −0.133140 −0.00477639
\(778\) 0 0
\(779\) −2.06172 −0.0738689
\(780\) 0 0
\(781\) 19.2256 0.687947
\(782\) 0 0
\(783\) 0.0105846 0.000378261 0
\(784\) 0 0
\(785\) 64.3135 2.29545
\(786\) 0 0
\(787\) 27.6116 0.984247 0.492124 0.870525i \(-0.336221\pi\)
0.492124 + 0.870525i \(0.336221\pi\)
\(788\) 0 0
\(789\) −0.926750 −0.0329932
\(790\) 0 0
\(791\) 4.82554 0.171576
\(792\) 0 0
\(793\) 8.37614 0.297446
\(794\) 0 0
\(795\) −0.154681 −0.00548597
\(796\) 0 0
\(797\) 41.2018 1.45944 0.729721 0.683745i \(-0.239650\pi\)
0.729721 + 0.683745i \(0.239650\pi\)
\(798\) 0 0
\(799\) 10.7061 0.378755
\(800\) 0 0
\(801\) −34.1049 −1.20504
\(802\) 0 0
\(803\) −13.7071 −0.483712
\(804\) 0 0
\(805\) −4.32409 −0.152404
\(806\) 0 0
\(807\) 0.939642 0.0330770
\(808\) 0 0
\(809\) −50.1610 −1.76357 −0.881783 0.471655i \(-0.843657\pi\)
−0.881783 + 0.471655i \(0.843657\pi\)
\(810\) 0 0
\(811\) 19.6046 0.688411 0.344206 0.938894i \(-0.388148\pi\)
0.344206 + 0.938894i \(0.388148\pi\)
\(812\) 0 0
\(813\) 0.444440 0.0155872
\(814\) 0 0
\(815\) 36.0149 1.26155
\(816\) 0 0
\(817\) −39.2365 −1.37271
\(818\) 0 0
\(819\) 1.62093 0.0566397
\(820\) 0 0
\(821\) 12.5097 0.436593 0.218297 0.975882i \(-0.429950\pi\)
0.218297 + 0.975882i \(0.429950\pi\)
\(822\) 0 0
\(823\) 22.4157 0.781363 0.390682 0.920526i \(-0.372239\pi\)
0.390682 + 0.920526i \(0.372239\pi\)
\(824\) 0 0
\(825\) −0.380345 −0.0132419
\(826\) 0 0
\(827\) −6.43398 −0.223731 −0.111866 0.993723i \(-0.535683\pi\)
−0.111866 + 0.993723i \(0.535683\pi\)
\(828\) 0 0
\(829\) 44.2022 1.53520 0.767602 0.640927i \(-0.221450\pi\)
0.767602 + 0.640927i \(0.221450\pi\)
\(830\) 0 0
\(831\) 0.210262 0.00729389
\(832\) 0 0
\(833\) −7.48169 −0.259225
\(834\) 0 0
\(835\) 63.5397 2.19888
\(836\) 0 0
\(837\) 0.706900 0.0244340
\(838\) 0 0
\(839\) 31.3849 1.08353 0.541763 0.840531i \(-0.317757\pi\)
0.541763 + 0.840531i \(0.317757\pi\)
\(840\) 0 0
\(841\) −28.9977 −0.999921
\(842\) 0 0
\(843\) 0.00782299 0.000269438 0
\(844\) 0 0
\(845\) 43.1858 1.48564
\(846\) 0 0
\(847\) 5.08375 0.174680
\(848\) 0 0
\(849\) 0.563585 0.0193422
\(850\) 0 0
\(851\) 14.5375 0.498339
\(852\) 0 0
\(853\) −19.7815 −0.677305 −0.338653 0.940911i \(-0.609971\pi\)
−0.338653 + 0.940911i \(0.609971\pi\)
\(854\) 0 0
\(855\) 54.0907 1.84986
\(856\) 0 0
\(857\) −28.0193 −0.957122 −0.478561 0.878054i \(-0.658842\pi\)
−0.478561 + 0.878054i \(0.658842\pi\)
\(858\) 0 0
\(859\) 16.4600 0.561606 0.280803 0.959765i \(-0.409399\pi\)
0.280803 + 0.959765i \(0.409399\pi\)
\(860\) 0 0
\(861\) −0.00827166 −0.000281897 0
\(862\) 0 0
\(863\) −4.60626 −0.156799 −0.0783995 0.996922i \(-0.524981\pi\)
−0.0783995 + 0.996922i \(0.524981\pi\)
\(864\) 0 0
\(865\) −37.0765 −1.26064
\(866\) 0 0
\(867\) 0.580083 0.0197006
\(868\) 0 0
\(869\) 7.27085 0.246647
\(870\) 0 0
\(871\) 5.21684 0.176766
\(872\) 0 0
\(873\) 52.6018 1.78030
\(874\) 0 0
\(875\) 5.69845 0.192643
\(876\) 0 0
\(877\) 46.1424 1.55812 0.779059 0.626951i \(-0.215697\pi\)
0.779059 + 0.626951i \(0.215697\pi\)
\(878\) 0 0
\(879\) −0.882343 −0.0297607
\(880\) 0 0
\(881\) 5.07723 0.171056 0.0855280 0.996336i \(-0.472742\pi\)
0.0855280 + 0.996336i \(0.472742\pi\)
\(882\) 0 0
\(883\) −54.4257 −1.83157 −0.915786 0.401668i \(-0.868431\pi\)
−0.915786 + 0.401668i \(0.868431\pi\)
\(884\) 0 0
\(885\) 1.02568 0.0344777
\(886\) 0 0
\(887\) −20.9554 −0.703613 −0.351806 0.936073i \(-0.614432\pi\)
−0.351806 + 0.936073i \(0.614432\pi\)
\(888\) 0 0
\(889\) 8.86109 0.297191
\(890\) 0 0
\(891\) 11.7521 0.393709
\(892\) 0 0
\(893\) 48.1565 1.61150
\(894\) 0 0
\(895\) 1.58797 0.0530801
\(896\) 0 0
\(897\) 0.0800309 0.00267215
\(898\) 0 0
\(899\) 0.153351 0.00511453
\(900\) 0 0
\(901\) −1.30593 −0.0435068
\(902\) 0 0
\(903\) −0.157417 −0.00523852
\(904\) 0 0
\(905\) −1.19607 −0.0397588
\(906\) 0 0
\(907\) −46.8048 −1.55413 −0.777063 0.629422i \(-0.783292\pi\)
−0.777063 + 0.629422i \(0.783292\pi\)
\(908\) 0 0
\(909\) −7.40265 −0.245530
\(910\) 0 0
\(911\) −35.9833 −1.19218 −0.596090 0.802917i \(-0.703280\pi\)
−0.596090 + 0.802917i \(0.703280\pi\)
\(912\) 0 0
\(913\) −0.575160 −0.0190350
\(914\) 0 0
\(915\) 1.12141 0.0370728
\(916\) 0 0
\(917\) −2.35600 −0.0778018
\(918\) 0 0
\(919\) −51.3043 −1.69237 −0.846186 0.532888i \(-0.821107\pi\)
−0.846186 + 0.532888i \(0.821107\pi\)
\(920\) 0 0
\(921\) −1.13958 −0.0375504
\(922\) 0 0
\(923\) 14.5246 0.478082
\(924\) 0 0
\(925\) −52.1955 −1.71618
\(926\) 0 0
\(927\) −51.2563 −1.68348
\(928\) 0 0
\(929\) 38.2441 1.25475 0.627374 0.778718i \(-0.284130\pi\)
0.627374 + 0.778718i \(0.284130\pi\)
\(930\) 0 0
\(931\) −33.6529 −1.10293
\(932\) 0 0
\(933\) 1.02407 0.0335265
\(934\) 0 0
\(935\) −5.24366 −0.171486
\(936\) 0 0
\(937\) −55.3953 −1.80969 −0.904843 0.425746i \(-0.860012\pi\)
−0.904843 + 0.425746i \(0.860012\pi\)
\(938\) 0 0
\(939\) −1.18934 −0.0388125
\(940\) 0 0
\(941\) −1.61479 −0.0526406 −0.0263203 0.999654i \(-0.508379\pi\)
−0.0263203 + 0.999654i \(0.508379\pi\)
\(942\) 0 0
\(943\) 0.903177 0.0294115
\(944\) 0 0
\(945\) 0.434123 0.0141220
\(946\) 0 0
\(947\) −27.3784 −0.889677 −0.444839 0.895611i \(-0.646739\pi\)
−0.444839 + 0.895611i \(0.646739\pi\)
\(948\) 0 0
\(949\) −10.3554 −0.336151
\(950\) 0 0
\(951\) 1.20081 0.0389389
\(952\) 0 0
\(953\) −43.3160 −1.40314 −0.701572 0.712599i \(-0.747518\pi\)
−0.701572 + 0.712599i \(0.747518\pi\)
\(954\) 0 0
\(955\) 52.2898 1.69206
\(956\) 0 0
\(957\) −0.00230717 −7.45803e−5 0
\(958\) 0 0
\(959\) 9.98533 0.322443
\(960\) 0 0
\(961\) −20.7583 −0.669624
\(962\) 0 0
\(963\) 40.6782 1.31084
\(964\) 0 0
\(965\) 82.9772 2.67113
\(966\) 0 0
\(967\) −3.91608 −0.125933 −0.0629664 0.998016i \(-0.520056\pi\)
−0.0629664 + 0.998016i \(0.520056\pi\)
\(968\) 0 0
\(969\) −0.206500 −0.00663373
\(970\) 0 0
\(971\) 27.4920 0.882260 0.441130 0.897443i \(-0.354578\pi\)
0.441130 + 0.897443i \(0.354578\pi\)
\(972\) 0 0
\(973\) 8.34403 0.267497
\(974\) 0 0
\(975\) −0.287343 −0.00920234
\(976\) 0 0
\(977\) −20.7942 −0.665265 −0.332632 0.943057i \(-0.607937\pi\)
−0.332632 + 0.943057i \(0.607937\pi\)
\(978\) 0 0
\(979\) 14.8714 0.475293
\(980\) 0 0
\(981\) −17.7201 −0.565760
\(982\) 0 0
\(983\) −11.2392 −0.358474 −0.179237 0.983806i \(-0.557363\pi\)
−0.179237 + 0.983806i \(0.557363\pi\)
\(984\) 0 0
\(985\) −61.4190 −1.95697
\(986\) 0 0
\(987\) 0.193205 0.00614977
\(988\) 0 0
\(989\) 17.1883 0.546556
\(990\) 0 0
\(991\) 51.4475 1.63428 0.817142 0.576436i \(-0.195557\pi\)
0.817142 + 0.576436i \(0.195557\pi\)
\(992\) 0 0
\(993\) 0.607388 0.0192749
\(994\) 0 0
\(995\) 35.0445 1.11098
\(996\) 0 0
\(997\) −49.3824 −1.56396 −0.781979 0.623305i \(-0.785789\pi\)
−0.781979 + 0.623305i \(0.785789\pi\)
\(998\) 0 0
\(999\) −1.45952 −0.0461770
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.1.26 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.26 44 1.1 even 1 trivial