Properties

Label 6008.2.a.b.1.6
Level 6008
Weight 2
Character 6008.1
Self dual yes
Analytic conductor 47.974
Analytic rank 1
Dimension 44
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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 1.6
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.98092 q^{3} +3.05916 q^{5} +0.297244 q^{7} +5.88586 q^{9} +O(q^{10})\) \(q-2.98092 q^{3} +3.05916 q^{5} +0.297244 q^{7} +5.88586 q^{9} -0.132067 q^{11} +3.60162 q^{13} -9.11910 q^{15} +6.86161 q^{17} -2.04931 q^{19} -0.886059 q^{21} -8.92554 q^{23} +4.35846 q^{25} -8.60250 q^{27} -4.43490 q^{29} -2.21683 q^{31} +0.393681 q^{33} +0.909317 q^{35} -5.90972 q^{37} -10.7361 q^{39} -9.20315 q^{41} +0.709880 q^{43} +18.0058 q^{45} +0.369774 q^{47} -6.91165 q^{49} -20.4539 q^{51} -11.1347 q^{53} -0.404015 q^{55} +6.10883 q^{57} +5.23739 q^{59} +0.397250 q^{61} +1.74954 q^{63} +11.0179 q^{65} -4.96553 q^{67} +26.6063 q^{69} -3.02363 q^{71} -9.74973 q^{73} -12.9922 q^{75} -0.0392562 q^{77} -4.16717 q^{79} +7.98576 q^{81} +4.18223 q^{83} +20.9908 q^{85} +13.2201 q^{87} +10.9084 q^{89} +1.07056 q^{91} +6.60819 q^{93} -6.26918 q^{95} -2.82202 q^{97} -0.777329 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −2.98092 −1.72103 −0.860516 0.509423i \(-0.829859\pi\)
−0.860516 + 0.509423i \(0.829859\pi\)
\(4\) 0 0
\(5\) 3.05916 1.36810 0.684049 0.729436i \(-0.260218\pi\)
0.684049 + 0.729436i \(0.260218\pi\)
\(6\) 0 0
\(7\) 0.297244 0.112348 0.0561738 0.998421i \(-0.482110\pi\)
0.0561738 + 0.998421i \(0.482110\pi\)
\(8\) 0 0
\(9\) 5.88586 1.96195
\(10\) 0 0
\(11\) −0.132067 −0.0398198 −0.0199099 0.999802i \(-0.506338\pi\)
−0.0199099 + 0.999802i \(0.506338\pi\)
\(12\) 0 0
\(13\) 3.60162 0.998909 0.499455 0.866340i \(-0.333534\pi\)
0.499455 + 0.866340i \(0.333534\pi\)
\(14\) 0 0
\(15\) −9.11910 −2.35454
\(16\) 0 0
\(17\) 6.86161 1.66419 0.832093 0.554636i \(-0.187143\pi\)
0.832093 + 0.554636i \(0.187143\pi\)
\(18\) 0 0
\(19\) −2.04931 −0.470145 −0.235072 0.971978i \(-0.575533\pi\)
−0.235072 + 0.971978i \(0.575533\pi\)
\(20\) 0 0
\(21\) −0.886059 −0.193354
\(22\) 0 0
\(23\) −8.92554 −1.86110 −0.930552 0.366161i \(-0.880672\pi\)
−0.930552 + 0.366161i \(0.880672\pi\)
\(24\) 0 0
\(25\) 4.35846 0.871691
\(26\) 0 0
\(27\) −8.60250 −1.65555
\(28\) 0 0
\(29\) −4.43490 −0.823541 −0.411770 0.911288i \(-0.635089\pi\)
−0.411770 + 0.911288i \(0.635089\pi\)
\(30\) 0 0
\(31\) −2.21683 −0.398155 −0.199077 0.979984i \(-0.563795\pi\)
−0.199077 + 0.979984i \(0.563795\pi\)
\(32\) 0 0
\(33\) 0.393681 0.0685311
\(34\) 0 0
\(35\) 0.909317 0.153703
\(36\) 0 0
\(37\) −5.90972 −0.971552 −0.485776 0.874083i \(-0.661463\pi\)
−0.485776 + 0.874083i \(0.661463\pi\)
\(38\) 0 0
\(39\) −10.7361 −1.71916
\(40\) 0 0
\(41\) −9.20315 −1.43729 −0.718645 0.695377i \(-0.755237\pi\)
−0.718645 + 0.695377i \(0.755237\pi\)
\(42\) 0 0
\(43\) 0.709880 0.108256 0.0541278 0.998534i \(-0.482762\pi\)
0.0541278 + 0.998534i \(0.482762\pi\)
\(44\) 0 0
\(45\) 18.0058 2.68414
\(46\) 0 0
\(47\) 0.369774 0.0539370 0.0269685 0.999636i \(-0.491415\pi\)
0.0269685 + 0.999636i \(0.491415\pi\)
\(48\) 0 0
\(49\) −6.91165 −0.987378
\(50\) 0 0
\(51\) −20.4539 −2.86412
\(52\) 0 0
\(53\) −11.1347 −1.52947 −0.764736 0.644344i \(-0.777131\pi\)
−0.764736 + 0.644344i \(0.777131\pi\)
\(54\) 0 0
\(55\) −0.404015 −0.0544773
\(56\) 0 0
\(57\) 6.10883 0.809134
\(58\) 0 0
\(59\) 5.23739 0.681851 0.340925 0.940090i \(-0.389260\pi\)
0.340925 + 0.940090i \(0.389260\pi\)
\(60\) 0 0
\(61\) 0.397250 0.0508626 0.0254313 0.999677i \(-0.491904\pi\)
0.0254313 + 0.999677i \(0.491904\pi\)
\(62\) 0 0
\(63\) 1.74954 0.220421
\(64\) 0 0
\(65\) 11.0179 1.36661
\(66\) 0 0
\(67\) −4.96553 −0.606636 −0.303318 0.952889i \(-0.598094\pi\)
−0.303318 + 0.952889i \(0.598094\pi\)
\(68\) 0 0
\(69\) 26.6063 3.20302
\(70\) 0 0
\(71\) −3.02363 −0.358839 −0.179419 0.983773i \(-0.557422\pi\)
−0.179419 + 0.983773i \(0.557422\pi\)
\(72\) 0 0
\(73\) −9.74973 −1.14112 −0.570560 0.821256i \(-0.693274\pi\)
−0.570560 + 0.821256i \(0.693274\pi\)
\(74\) 0 0
\(75\) −12.9922 −1.50021
\(76\) 0 0
\(77\) −0.0392562 −0.00447366
\(78\) 0 0
\(79\) −4.16717 −0.468844 −0.234422 0.972135i \(-0.575320\pi\)
−0.234422 + 0.972135i \(0.575320\pi\)
\(80\) 0 0
\(81\) 7.98576 0.887306
\(82\) 0 0
\(83\) 4.18223 0.459059 0.229530 0.973302i \(-0.426281\pi\)
0.229530 + 0.973302i \(0.426281\pi\)
\(84\) 0 0
\(85\) 20.9908 2.27677
\(86\) 0 0
\(87\) 13.2201 1.41734
\(88\) 0 0
\(89\) 10.9084 1.15629 0.578146 0.815933i \(-0.303776\pi\)
0.578146 + 0.815933i \(0.303776\pi\)
\(90\) 0 0
\(91\) 1.07056 0.112225
\(92\) 0 0
\(93\) 6.60819 0.685237
\(94\) 0 0
\(95\) −6.26918 −0.643204
\(96\) 0 0
\(97\) −2.82202 −0.286532 −0.143266 0.989684i \(-0.545761\pi\)
−0.143266 + 0.989684i \(0.545761\pi\)
\(98\) 0 0
\(99\) −0.777329 −0.0781245
\(100\) 0 0
\(101\) 1.34157 0.133491 0.0667457 0.997770i \(-0.478738\pi\)
0.0667457 + 0.997770i \(0.478738\pi\)
\(102\) 0 0
\(103\) 3.83741 0.378111 0.189056 0.981966i \(-0.439457\pi\)
0.189056 + 0.981966i \(0.439457\pi\)
\(104\) 0 0
\(105\) −2.71060 −0.264527
\(106\) 0 0
\(107\) −14.4717 −1.39903 −0.699514 0.714619i \(-0.746600\pi\)
−0.699514 + 0.714619i \(0.746600\pi\)
\(108\) 0 0
\(109\) −16.6270 −1.59258 −0.796290 0.604915i \(-0.793207\pi\)
−0.796290 + 0.604915i \(0.793207\pi\)
\(110\) 0 0
\(111\) 17.6164 1.67207
\(112\) 0 0
\(113\) −9.49624 −0.893331 −0.446666 0.894701i \(-0.647389\pi\)
−0.446666 + 0.894701i \(0.647389\pi\)
\(114\) 0 0
\(115\) −27.3046 −2.54617
\(116\) 0 0
\(117\) 21.1986 1.95981
\(118\) 0 0
\(119\) 2.03957 0.186967
\(120\) 0 0
\(121\) −10.9826 −0.998414
\(122\) 0 0
\(123\) 27.4338 2.47362
\(124\) 0 0
\(125\) −1.96259 −0.175539
\(126\) 0 0
\(127\) 6.61087 0.586620 0.293310 0.956017i \(-0.405243\pi\)
0.293310 + 0.956017i \(0.405243\pi\)
\(128\) 0 0
\(129\) −2.11609 −0.186311
\(130\) 0 0
\(131\) 15.4245 1.34765 0.673824 0.738892i \(-0.264650\pi\)
0.673824 + 0.738892i \(0.264650\pi\)
\(132\) 0 0
\(133\) −0.609146 −0.0528197
\(134\) 0 0
\(135\) −26.3164 −2.26496
\(136\) 0 0
\(137\) −18.1197 −1.54807 −0.774034 0.633144i \(-0.781764\pi\)
−0.774034 + 0.633144i \(0.781764\pi\)
\(138\) 0 0
\(139\) −12.6817 −1.07565 −0.537823 0.843058i \(-0.680753\pi\)
−0.537823 + 0.843058i \(0.680753\pi\)
\(140\) 0 0
\(141\) −1.10226 −0.0928274
\(142\) 0 0
\(143\) −0.475656 −0.0397763
\(144\) 0 0
\(145\) −13.5671 −1.12668
\(146\) 0 0
\(147\) 20.6030 1.69931
\(148\) 0 0
\(149\) 17.8738 1.46428 0.732141 0.681153i \(-0.238521\pi\)
0.732141 + 0.681153i \(0.238521\pi\)
\(150\) 0 0
\(151\) 12.0643 0.981775 0.490888 0.871223i \(-0.336673\pi\)
0.490888 + 0.871223i \(0.336673\pi\)
\(152\) 0 0
\(153\) 40.3865 3.26505
\(154\) 0 0
\(155\) −6.78164 −0.544715
\(156\) 0 0
\(157\) 20.3399 1.62330 0.811651 0.584143i \(-0.198569\pi\)
0.811651 + 0.584143i \(0.198569\pi\)
\(158\) 0 0
\(159\) 33.1917 2.63227
\(160\) 0 0
\(161\) −2.65306 −0.209091
\(162\) 0 0
\(163\) 16.8285 1.31811 0.659056 0.752094i \(-0.270956\pi\)
0.659056 + 0.752094i \(0.270956\pi\)
\(164\) 0 0
\(165\) 1.20433 0.0937573
\(166\) 0 0
\(167\) 15.7134 1.21594 0.607969 0.793960i \(-0.291984\pi\)
0.607969 + 0.793960i \(0.291984\pi\)
\(168\) 0 0
\(169\) −0.0283398 −0.00217999
\(170\) 0 0
\(171\) −12.0620 −0.922402
\(172\) 0 0
\(173\) −7.03141 −0.534588 −0.267294 0.963615i \(-0.586129\pi\)
−0.267294 + 0.963615i \(0.586129\pi\)
\(174\) 0 0
\(175\) 1.29552 0.0979325
\(176\) 0 0
\(177\) −15.6122 −1.17349
\(178\) 0 0
\(179\) 5.47536 0.409248 0.204624 0.978841i \(-0.434403\pi\)
0.204624 + 0.978841i \(0.434403\pi\)
\(180\) 0 0
\(181\) −11.7222 −0.871305 −0.435653 0.900115i \(-0.643482\pi\)
−0.435653 + 0.900115i \(0.643482\pi\)
\(182\) 0 0
\(183\) −1.18417 −0.0875362
\(184\) 0 0
\(185\) −18.0788 −1.32918
\(186\) 0 0
\(187\) −0.906194 −0.0662675
\(188\) 0 0
\(189\) −2.55704 −0.185997
\(190\) 0 0
\(191\) −24.1170 −1.74505 −0.872523 0.488573i \(-0.837517\pi\)
−0.872523 + 0.488573i \(0.837517\pi\)
\(192\) 0 0
\(193\) 8.15585 0.587071 0.293535 0.955948i \(-0.405168\pi\)
0.293535 + 0.955948i \(0.405168\pi\)
\(194\) 0 0
\(195\) −32.8435 −2.35197
\(196\) 0 0
\(197\) −9.76635 −0.695823 −0.347912 0.937527i \(-0.613109\pi\)
−0.347912 + 0.937527i \(0.613109\pi\)
\(198\) 0 0
\(199\) −0.217197 −0.0153967 −0.00769834 0.999970i \(-0.502450\pi\)
−0.00769834 + 0.999970i \(0.502450\pi\)
\(200\) 0 0
\(201\) 14.8018 1.04404
\(202\) 0 0
\(203\) −1.31825 −0.0925229
\(204\) 0 0
\(205\) −28.1539 −1.96635
\(206\) 0 0
\(207\) −52.5345 −3.65140
\(208\) 0 0
\(209\) 0.270647 0.0187211
\(210\) 0 0
\(211\) −13.6428 −0.939211 −0.469606 0.882876i \(-0.655604\pi\)
−0.469606 + 0.882876i \(0.655604\pi\)
\(212\) 0 0
\(213\) 9.01319 0.617574
\(214\) 0 0
\(215\) 2.17164 0.148104
\(216\) 0 0
\(217\) −0.658940 −0.0447318
\(218\) 0 0
\(219\) 29.0631 1.96390
\(220\) 0 0
\(221\) 24.7129 1.66237
\(222\) 0 0
\(223\) 24.3483 1.63048 0.815241 0.579121i \(-0.196604\pi\)
0.815241 + 0.579121i \(0.196604\pi\)
\(224\) 0 0
\(225\) 25.6533 1.71022
\(226\) 0 0
\(227\) 12.9318 0.858312 0.429156 0.903230i \(-0.358811\pi\)
0.429156 + 0.903230i \(0.358811\pi\)
\(228\) 0 0
\(229\) 18.9500 1.25225 0.626125 0.779723i \(-0.284640\pi\)
0.626125 + 0.779723i \(0.284640\pi\)
\(230\) 0 0
\(231\) 0.117019 0.00769931
\(232\) 0 0
\(233\) 4.90095 0.321072 0.160536 0.987030i \(-0.448678\pi\)
0.160536 + 0.987030i \(0.448678\pi\)
\(234\) 0 0
\(235\) 1.13120 0.0737911
\(236\) 0 0
\(237\) 12.4220 0.806895
\(238\) 0 0
\(239\) 17.9952 1.16401 0.582006 0.813184i \(-0.302268\pi\)
0.582006 + 0.813184i \(0.302268\pi\)
\(240\) 0 0
\(241\) 6.92465 0.446056 0.223028 0.974812i \(-0.428406\pi\)
0.223028 + 0.974812i \(0.428406\pi\)
\(242\) 0 0
\(243\) 2.00263 0.128469
\(244\) 0 0
\(245\) −21.1438 −1.35083
\(246\) 0 0
\(247\) −7.38085 −0.469632
\(248\) 0 0
\(249\) −12.4669 −0.790056
\(250\) 0 0
\(251\) 25.2014 1.59070 0.795349 0.606152i \(-0.207288\pi\)
0.795349 + 0.606152i \(0.207288\pi\)
\(252\) 0 0
\(253\) 1.17877 0.0741087
\(254\) 0 0
\(255\) −62.5717 −3.91839
\(256\) 0 0
\(257\) −10.7985 −0.673593 −0.336796 0.941578i \(-0.609343\pi\)
−0.336796 + 0.941578i \(0.609343\pi\)
\(258\) 0 0
\(259\) −1.75663 −0.109152
\(260\) 0 0
\(261\) −26.1032 −1.61575
\(262\) 0 0
\(263\) −23.2806 −1.43554 −0.717771 0.696279i \(-0.754838\pi\)
−0.717771 + 0.696279i \(0.754838\pi\)
\(264\) 0 0
\(265\) −34.0629 −2.09247
\(266\) 0 0
\(267\) −32.5171 −1.99002
\(268\) 0 0
\(269\) 13.0946 0.798392 0.399196 0.916866i \(-0.369289\pi\)
0.399196 + 0.916866i \(0.369289\pi\)
\(270\) 0 0
\(271\) −12.5126 −0.760086 −0.380043 0.924969i \(-0.624091\pi\)
−0.380043 + 0.924969i \(0.624091\pi\)
\(272\) 0 0
\(273\) −3.19125 −0.193143
\(274\) 0 0
\(275\) −0.575609 −0.0347105
\(276\) 0 0
\(277\) 20.2064 1.21409 0.607043 0.794669i \(-0.292355\pi\)
0.607043 + 0.794669i \(0.292355\pi\)
\(278\) 0 0
\(279\) −13.0480 −0.781161
\(280\) 0 0
\(281\) −7.31394 −0.436313 −0.218157 0.975914i \(-0.570004\pi\)
−0.218157 + 0.975914i \(0.570004\pi\)
\(282\) 0 0
\(283\) −18.2538 −1.08507 −0.542536 0.840032i \(-0.682536\pi\)
−0.542536 + 0.840032i \(0.682536\pi\)
\(284\) 0 0
\(285\) 18.6879 1.10697
\(286\) 0 0
\(287\) −2.73558 −0.161476
\(288\) 0 0
\(289\) 30.0817 1.76951
\(290\) 0 0
\(291\) 8.41219 0.493132
\(292\) 0 0
\(293\) −14.3113 −0.836077 −0.418038 0.908429i \(-0.637282\pi\)
−0.418038 + 0.908429i \(0.637282\pi\)
\(294\) 0 0
\(295\) 16.0220 0.932838
\(296\) 0 0
\(297\) 1.13611 0.0659237
\(298\) 0 0
\(299\) −32.1464 −1.85907
\(300\) 0 0
\(301\) 0.211008 0.0121623
\(302\) 0 0
\(303\) −3.99912 −0.229743
\(304\) 0 0
\(305\) 1.21525 0.0695850
\(306\) 0 0
\(307\) −6.15472 −0.351268 −0.175634 0.984456i \(-0.556198\pi\)
−0.175634 + 0.984456i \(0.556198\pi\)
\(308\) 0 0
\(309\) −11.4390 −0.650742
\(310\) 0 0
\(311\) −8.08231 −0.458306 −0.229153 0.973390i \(-0.573596\pi\)
−0.229153 + 0.973390i \(0.573596\pi\)
\(312\) 0 0
\(313\) −24.6435 −1.39294 −0.696468 0.717588i \(-0.745246\pi\)
−0.696468 + 0.717588i \(0.745246\pi\)
\(314\) 0 0
\(315\) 5.35211 0.301557
\(316\) 0 0
\(317\) −17.7784 −0.998535 −0.499268 0.866448i \(-0.666398\pi\)
−0.499268 + 0.866448i \(0.666398\pi\)
\(318\) 0 0
\(319\) 0.585705 0.0327932
\(320\) 0 0
\(321\) 43.1388 2.40777
\(322\) 0 0
\(323\) −14.0616 −0.782408
\(324\) 0 0
\(325\) 15.6975 0.870740
\(326\) 0 0
\(327\) 49.5638 2.74088
\(328\) 0 0
\(329\) 0.109913 0.00605970
\(330\) 0 0
\(331\) 9.50558 0.522474 0.261237 0.965275i \(-0.415870\pi\)
0.261237 + 0.965275i \(0.415870\pi\)
\(332\) 0 0
\(333\) −34.7838 −1.90614
\(334\) 0 0
\(335\) −15.1903 −0.829937
\(336\) 0 0
\(337\) −31.2528 −1.70245 −0.851224 0.524803i \(-0.824139\pi\)
−0.851224 + 0.524803i \(0.824139\pi\)
\(338\) 0 0
\(339\) 28.3075 1.53745
\(340\) 0 0
\(341\) 0.292771 0.0158544
\(342\) 0 0
\(343\) −4.13515 −0.223277
\(344\) 0 0
\(345\) 81.3928 4.38204
\(346\) 0 0
\(347\) −28.1380 −1.51053 −0.755264 0.655421i \(-0.772491\pi\)
−0.755264 + 0.655421i \(0.772491\pi\)
\(348\) 0 0
\(349\) 6.77830 0.362834 0.181417 0.983406i \(-0.441932\pi\)
0.181417 + 0.983406i \(0.441932\pi\)
\(350\) 0 0
\(351\) −30.9829 −1.65375
\(352\) 0 0
\(353\) −3.35060 −0.178334 −0.0891672 0.996017i \(-0.528421\pi\)
−0.0891672 + 0.996017i \(0.528421\pi\)
\(354\) 0 0
\(355\) −9.24977 −0.490927
\(356\) 0 0
\(357\) −6.07980 −0.321777
\(358\) 0 0
\(359\) −17.0690 −0.900867 −0.450434 0.892810i \(-0.648731\pi\)
−0.450434 + 0.892810i \(0.648731\pi\)
\(360\) 0 0
\(361\) −14.8003 −0.778964
\(362\) 0 0
\(363\) 32.7381 1.71830
\(364\) 0 0
\(365\) −29.8260 −1.56116
\(366\) 0 0
\(367\) −23.2072 −1.21140 −0.605702 0.795692i \(-0.707108\pi\)
−0.605702 + 0.795692i \(0.707108\pi\)
\(368\) 0 0
\(369\) −54.1684 −2.81990
\(370\) 0 0
\(371\) −3.30973 −0.171833
\(372\) 0 0
\(373\) 18.0032 0.932171 0.466085 0.884740i \(-0.345664\pi\)
0.466085 + 0.884740i \(0.345664\pi\)
\(374\) 0 0
\(375\) 5.85031 0.302109
\(376\) 0 0
\(377\) −15.9728 −0.822643
\(378\) 0 0
\(379\) −21.5805 −1.10852 −0.554259 0.832345i \(-0.686998\pi\)
−0.554259 + 0.832345i \(0.686998\pi\)
\(380\) 0 0
\(381\) −19.7064 −1.00959
\(382\) 0 0
\(383\) −28.4335 −1.45288 −0.726442 0.687227i \(-0.758828\pi\)
−0.726442 + 0.687227i \(0.758828\pi\)
\(384\) 0 0
\(385\) −0.120091 −0.00612040
\(386\) 0 0
\(387\) 4.17825 0.212392
\(388\) 0 0
\(389\) −2.10098 −0.106524 −0.0532619 0.998581i \(-0.516962\pi\)
−0.0532619 + 0.998581i \(0.516962\pi\)
\(390\) 0 0
\(391\) −61.2436 −3.09722
\(392\) 0 0
\(393\) −45.9793 −2.31935
\(394\) 0 0
\(395\) −12.7480 −0.641424
\(396\) 0 0
\(397\) 23.9121 1.20011 0.600056 0.799958i \(-0.295145\pi\)
0.600056 + 0.799958i \(0.295145\pi\)
\(398\) 0 0
\(399\) 1.81581 0.0909044
\(400\) 0 0
\(401\) 11.2924 0.563918 0.281959 0.959426i \(-0.409016\pi\)
0.281959 + 0.959426i \(0.409016\pi\)
\(402\) 0 0
\(403\) −7.98418 −0.397720
\(404\) 0 0
\(405\) 24.4297 1.21392
\(406\) 0 0
\(407\) 0.780480 0.0386870
\(408\) 0 0
\(409\) 9.18638 0.454237 0.227119 0.973867i \(-0.427069\pi\)
0.227119 + 0.973867i \(0.427069\pi\)
\(410\) 0 0
\(411\) 54.0132 2.66427
\(412\) 0 0
\(413\) 1.55678 0.0766043
\(414\) 0 0
\(415\) 12.7941 0.628038
\(416\) 0 0
\(417\) 37.8030 1.85122
\(418\) 0 0
\(419\) −6.50817 −0.317945 −0.158973 0.987283i \(-0.550818\pi\)
−0.158973 + 0.987283i \(0.550818\pi\)
\(420\) 0 0
\(421\) −22.9286 −1.11747 −0.558735 0.829346i \(-0.688713\pi\)
−0.558735 + 0.829346i \(0.688713\pi\)
\(422\) 0 0
\(423\) 2.17644 0.105822
\(424\) 0 0
\(425\) 29.9060 1.45066
\(426\) 0 0
\(427\) 0.118080 0.00571430
\(428\) 0 0
\(429\) 1.41789 0.0684564
\(430\) 0 0
\(431\) 1.03628 0.0499159 0.0249580 0.999689i \(-0.492055\pi\)
0.0249580 + 0.999689i \(0.492055\pi\)
\(432\) 0 0
\(433\) 12.5581 0.603503 0.301751 0.953387i \(-0.402429\pi\)
0.301751 + 0.953387i \(0.402429\pi\)
\(434\) 0 0
\(435\) 40.4423 1.93906
\(436\) 0 0
\(437\) 18.2912 0.874988
\(438\) 0 0
\(439\) −11.2191 −0.535457 −0.267729 0.963494i \(-0.586273\pi\)
−0.267729 + 0.963494i \(0.586273\pi\)
\(440\) 0 0
\(441\) −40.6810 −1.93719
\(442\) 0 0
\(443\) −11.5728 −0.549839 −0.274920 0.961467i \(-0.588651\pi\)
−0.274920 + 0.961467i \(0.588651\pi\)
\(444\) 0 0
\(445\) 33.3706 1.58192
\(446\) 0 0
\(447\) −53.2804 −2.52008
\(448\) 0 0
\(449\) −20.3019 −0.958107 −0.479053 0.877786i \(-0.659020\pi\)
−0.479053 + 0.877786i \(0.659020\pi\)
\(450\) 0 0
\(451\) 1.21543 0.0572326
\(452\) 0 0
\(453\) −35.9625 −1.68967
\(454\) 0 0
\(455\) 3.27501 0.153535
\(456\) 0 0
\(457\) 18.1861 0.850708 0.425354 0.905027i \(-0.360150\pi\)
0.425354 + 0.905027i \(0.360150\pi\)
\(458\) 0 0
\(459\) −59.0270 −2.75515
\(460\) 0 0
\(461\) 16.3340 0.760750 0.380375 0.924832i \(-0.375795\pi\)
0.380375 + 0.924832i \(0.375795\pi\)
\(462\) 0 0
\(463\) −10.0699 −0.467988 −0.233994 0.972238i \(-0.575180\pi\)
−0.233994 + 0.972238i \(0.575180\pi\)
\(464\) 0 0
\(465\) 20.2155 0.937471
\(466\) 0 0
\(467\) −5.21270 −0.241215 −0.120608 0.992700i \(-0.538484\pi\)
−0.120608 + 0.992700i \(0.538484\pi\)
\(468\) 0 0
\(469\) −1.47597 −0.0681541
\(470\) 0 0
\(471\) −60.6316 −2.79376
\(472\) 0 0
\(473\) −0.0937519 −0.00431071
\(474\) 0 0
\(475\) −8.93184 −0.409821
\(476\) 0 0
\(477\) −65.5374 −3.00075
\(478\) 0 0
\(479\) 5.14836 0.235235 0.117617 0.993059i \(-0.462474\pi\)
0.117617 + 0.993059i \(0.462474\pi\)
\(480\) 0 0
\(481\) −21.2846 −0.970493
\(482\) 0 0
\(483\) 7.90856 0.359852
\(484\) 0 0
\(485\) −8.63300 −0.392004
\(486\) 0 0
\(487\) 6.00118 0.271940 0.135970 0.990713i \(-0.456585\pi\)
0.135970 + 0.990713i \(0.456585\pi\)
\(488\) 0 0
\(489\) −50.1645 −2.26851
\(490\) 0 0
\(491\) 14.9781 0.675951 0.337976 0.941155i \(-0.390258\pi\)
0.337976 + 0.941155i \(0.390258\pi\)
\(492\) 0 0
\(493\) −30.4306 −1.37053
\(494\) 0 0
\(495\) −2.37797 −0.106882
\(496\) 0 0
\(497\) −0.898756 −0.0403147
\(498\) 0 0
\(499\) 20.4259 0.914391 0.457195 0.889366i \(-0.348854\pi\)
0.457195 + 0.889366i \(0.348854\pi\)
\(500\) 0 0
\(501\) −46.8403 −2.09267
\(502\) 0 0
\(503\) 13.5387 0.603662 0.301831 0.953361i \(-0.402402\pi\)
0.301831 + 0.953361i \(0.402402\pi\)
\(504\) 0 0
\(505\) 4.10408 0.182629
\(506\) 0 0
\(507\) 0.0844786 0.00375183
\(508\) 0 0
\(509\) 10.3012 0.456594 0.228297 0.973591i \(-0.426684\pi\)
0.228297 + 0.973591i \(0.426684\pi\)
\(510\) 0 0
\(511\) −2.89805 −0.128202
\(512\) 0 0
\(513\) 17.6292 0.778349
\(514\) 0 0
\(515\) 11.7392 0.517293
\(516\) 0 0
\(517\) −0.0488350 −0.00214776
\(518\) 0 0
\(519\) 20.9600 0.920043
\(520\) 0 0
\(521\) 15.8230 0.693220 0.346610 0.938009i \(-0.387333\pi\)
0.346610 + 0.938009i \(0.387333\pi\)
\(522\) 0 0
\(523\) −29.7200 −1.29956 −0.649782 0.760121i \(-0.725140\pi\)
−0.649782 + 0.760121i \(0.725140\pi\)
\(524\) 0 0
\(525\) −3.86185 −0.168545
\(526\) 0 0
\(527\) −15.2110 −0.662603
\(528\) 0 0
\(529\) 56.6652 2.46371
\(530\) 0 0
\(531\) 30.8266 1.33776
\(532\) 0 0
\(533\) −33.1462 −1.43572
\(534\) 0 0
\(535\) −44.2711 −1.91401
\(536\) 0 0
\(537\) −16.3216 −0.704329
\(538\) 0 0
\(539\) 0.912802 0.0393172
\(540\) 0 0
\(541\) −7.91261 −0.340190 −0.170095 0.985428i \(-0.554407\pi\)
−0.170095 + 0.985428i \(0.554407\pi\)
\(542\) 0 0
\(543\) 34.9429 1.49954
\(544\) 0 0
\(545\) −50.8647 −2.17881
\(546\) 0 0
\(547\) 29.2010 1.24855 0.624273 0.781206i \(-0.285395\pi\)
0.624273 + 0.781206i \(0.285395\pi\)
\(548\) 0 0
\(549\) 2.33816 0.0997900
\(550\) 0 0
\(551\) 9.08851 0.387183
\(552\) 0 0
\(553\) −1.23867 −0.0526735
\(554\) 0 0
\(555\) 53.8913 2.28756
\(556\) 0 0
\(557\) −22.1567 −0.938810 −0.469405 0.882983i \(-0.655532\pi\)
−0.469405 + 0.882983i \(0.655532\pi\)
\(558\) 0 0
\(559\) 2.55672 0.108138
\(560\) 0 0
\(561\) 2.70129 0.114049
\(562\) 0 0
\(563\) 0.409756 0.0172692 0.00863458 0.999963i \(-0.497251\pi\)
0.00863458 + 0.999963i \(0.497251\pi\)
\(564\) 0 0
\(565\) −29.0505 −1.22216
\(566\) 0 0
\(567\) 2.37372 0.0996868
\(568\) 0 0
\(569\) −4.87091 −0.204199 −0.102100 0.994774i \(-0.532556\pi\)
−0.102100 + 0.994774i \(0.532556\pi\)
\(570\) 0 0
\(571\) −43.2933 −1.81177 −0.905884 0.423525i \(-0.860793\pi\)
−0.905884 + 0.423525i \(0.860793\pi\)
\(572\) 0 0
\(573\) 71.8908 3.00328
\(574\) 0 0
\(575\) −38.9016 −1.62231
\(576\) 0 0
\(577\) 13.2488 0.551553 0.275776 0.961222i \(-0.411065\pi\)
0.275776 + 0.961222i \(0.411065\pi\)
\(578\) 0 0
\(579\) −24.3119 −1.01037
\(580\) 0 0
\(581\) 1.24314 0.0515742
\(582\) 0 0
\(583\) 1.47053 0.0609032
\(584\) 0 0
\(585\) 64.8500 2.68122
\(586\) 0 0
\(587\) 5.15537 0.212785 0.106392 0.994324i \(-0.466070\pi\)
0.106392 + 0.994324i \(0.466070\pi\)
\(588\) 0 0
\(589\) 4.54298 0.187190
\(590\) 0 0
\(591\) 29.1127 1.19753
\(592\) 0 0
\(593\) 43.3018 1.77819 0.889095 0.457722i \(-0.151335\pi\)
0.889095 + 0.457722i \(0.151335\pi\)
\(594\) 0 0
\(595\) 6.23938 0.255790
\(596\) 0 0
\(597\) 0.647446 0.0264982
\(598\) 0 0
\(599\) 12.2368 0.499983 0.249992 0.968248i \(-0.419572\pi\)
0.249992 + 0.968248i \(0.419572\pi\)
\(600\) 0 0
\(601\) −25.2617 −1.03045 −0.515224 0.857056i \(-0.672291\pi\)
−0.515224 + 0.857056i \(0.672291\pi\)
\(602\) 0 0
\(603\) −29.2264 −1.19019
\(604\) 0 0
\(605\) −33.5974 −1.36593
\(606\) 0 0
\(607\) −16.9595 −0.688365 −0.344182 0.938903i \(-0.611844\pi\)
−0.344182 + 0.938903i \(0.611844\pi\)
\(608\) 0 0
\(609\) 3.92959 0.159235
\(610\) 0 0
\(611\) 1.33178 0.0538782
\(612\) 0 0
\(613\) 28.3245 1.14402 0.572008 0.820248i \(-0.306165\pi\)
0.572008 + 0.820248i \(0.306165\pi\)
\(614\) 0 0
\(615\) 83.9244 3.38416
\(616\) 0 0
\(617\) 47.8076 1.92466 0.962331 0.271881i \(-0.0876456\pi\)
0.962331 + 0.271881i \(0.0876456\pi\)
\(618\) 0 0
\(619\) 34.9193 1.40353 0.701763 0.712411i \(-0.252397\pi\)
0.701763 + 0.712411i \(0.252397\pi\)
\(620\) 0 0
\(621\) 76.7820 3.08115
\(622\) 0 0
\(623\) 3.24247 0.129907
\(624\) 0 0
\(625\) −27.7961 −1.11185
\(626\) 0 0
\(627\) −0.806776 −0.0322195
\(628\) 0 0
\(629\) −40.5502 −1.61684
\(630\) 0 0
\(631\) 12.9559 0.515766 0.257883 0.966176i \(-0.416975\pi\)
0.257883 + 0.966176i \(0.416975\pi\)
\(632\) 0 0
\(633\) 40.6681 1.61641
\(634\) 0 0
\(635\) 20.2237 0.802553
\(636\) 0 0
\(637\) −24.8931 −0.986301
\(638\) 0 0
\(639\) −17.7967 −0.704025
\(640\) 0 0
\(641\) −6.61478 −0.261268 −0.130634 0.991431i \(-0.541701\pi\)
−0.130634 + 0.991431i \(0.541701\pi\)
\(642\) 0 0
\(643\) −2.03171 −0.0801227 −0.0400613 0.999197i \(-0.512755\pi\)
−0.0400613 + 0.999197i \(0.512755\pi\)
\(644\) 0 0
\(645\) −6.47346 −0.254892
\(646\) 0 0
\(647\) −22.8630 −0.898839 −0.449420 0.893321i \(-0.648369\pi\)
−0.449420 + 0.893321i \(0.648369\pi\)
\(648\) 0 0
\(649\) −0.691688 −0.0271511
\(650\) 0 0
\(651\) 1.96424 0.0769848
\(652\) 0 0
\(653\) −6.75304 −0.264267 −0.132133 0.991232i \(-0.542183\pi\)
−0.132133 + 0.991232i \(0.542183\pi\)
\(654\) 0 0
\(655\) 47.1861 1.84371
\(656\) 0 0
\(657\) −57.3855 −2.23882
\(658\) 0 0
\(659\) −4.72239 −0.183958 −0.0919790 0.995761i \(-0.529319\pi\)
−0.0919790 + 0.995761i \(0.529319\pi\)
\(660\) 0 0
\(661\) 47.4057 1.84387 0.921934 0.387346i \(-0.126608\pi\)
0.921934 + 0.387346i \(0.126608\pi\)
\(662\) 0 0
\(663\) −73.6671 −2.86099
\(664\) 0 0
\(665\) −1.86348 −0.0722625
\(666\) 0 0
\(667\) 39.5839 1.53269
\(668\) 0 0
\(669\) −72.5802 −2.80611
\(670\) 0 0
\(671\) −0.0524637 −0.00202534
\(672\) 0 0
\(673\) 11.4380 0.440902 0.220451 0.975398i \(-0.429247\pi\)
0.220451 + 0.975398i \(0.429247\pi\)
\(674\) 0 0
\(675\) −37.4936 −1.44313
\(676\) 0 0
\(677\) 9.02734 0.346949 0.173475 0.984838i \(-0.444501\pi\)
0.173475 + 0.984838i \(0.444501\pi\)
\(678\) 0 0
\(679\) −0.838828 −0.0321912
\(680\) 0 0
\(681\) −38.5485 −1.47718
\(682\) 0 0
\(683\) 13.4228 0.513610 0.256805 0.966463i \(-0.417330\pi\)
0.256805 + 0.966463i \(0.417330\pi\)
\(684\) 0 0
\(685\) −55.4309 −2.11791
\(686\) 0 0
\(687\) −56.4883 −2.15516
\(688\) 0 0
\(689\) −40.1030 −1.52780
\(690\) 0 0
\(691\) 36.9348 1.40506 0.702532 0.711652i \(-0.252053\pi\)
0.702532 + 0.711652i \(0.252053\pi\)
\(692\) 0 0
\(693\) −0.231056 −0.00877711
\(694\) 0 0
\(695\) −38.7953 −1.47159
\(696\) 0 0
\(697\) −63.1484 −2.39192
\(698\) 0 0
\(699\) −14.6093 −0.552576
\(700\) 0 0
\(701\) 45.7399 1.72757 0.863785 0.503860i \(-0.168087\pi\)
0.863785 + 0.503860i \(0.168087\pi\)
\(702\) 0 0
\(703\) 12.1109 0.456770
\(704\) 0 0
\(705\) −3.37200 −0.126997
\(706\) 0 0
\(707\) 0.398774 0.0149975
\(708\) 0 0
\(709\) −10.9620 −0.411687 −0.205843 0.978585i \(-0.565994\pi\)
−0.205843 + 0.978585i \(0.565994\pi\)
\(710\) 0 0
\(711\) −24.5274 −0.919849
\(712\) 0 0
\(713\) 19.7864 0.741007
\(714\) 0 0
\(715\) −1.45511 −0.0544179
\(716\) 0 0
\(717\) −53.6422 −2.00330
\(718\) 0 0
\(719\) 46.8983 1.74901 0.874506 0.485015i \(-0.161186\pi\)
0.874506 + 0.485015i \(0.161186\pi\)
\(720\) 0 0
\(721\) 1.14065 0.0424799
\(722\) 0 0
\(723\) −20.6418 −0.767677
\(724\) 0 0
\(725\) −19.3293 −0.717873
\(726\) 0 0
\(727\) −47.1700 −1.74944 −0.874719 0.484631i \(-0.838954\pi\)
−0.874719 + 0.484631i \(0.838954\pi\)
\(728\) 0 0
\(729\) −29.9270 −1.10841
\(730\) 0 0
\(731\) 4.87092 0.180157
\(732\) 0 0
\(733\) 50.1170 1.85111 0.925557 0.378609i \(-0.123597\pi\)
0.925557 + 0.378609i \(0.123597\pi\)
\(734\) 0 0
\(735\) 63.0280 2.32482
\(736\) 0 0
\(737\) 0.655783 0.0241561
\(738\) 0 0
\(739\) 35.1130 1.29165 0.645827 0.763484i \(-0.276513\pi\)
0.645827 + 0.763484i \(0.276513\pi\)
\(740\) 0 0
\(741\) 22.0017 0.808252
\(742\) 0 0
\(743\) −46.4629 −1.70456 −0.852280 0.523087i \(-0.824780\pi\)
−0.852280 + 0.523087i \(0.824780\pi\)
\(744\) 0 0
\(745\) 54.6789 2.00328
\(746\) 0 0
\(747\) 24.6160 0.900653
\(748\) 0 0
\(749\) −4.30161 −0.157177
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −75.1232 −2.73764
\(754\) 0 0
\(755\) 36.9065 1.34316
\(756\) 0 0
\(757\) 24.7374 0.899097 0.449548 0.893256i \(-0.351585\pi\)
0.449548 + 0.893256i \(0.351585\pi\)
\(758\) 0 0
\(759\) −3.51382 −0.127543
\(760\) 0 0
\(761\) −2.95100 −0.106974 −0.0534869 0.998569i \(-0.517034\pi\)
−0.0534869 + 0.998569i \(0.517034\pi\)
\(762\) 0 0
\(763\) −4.94229 −0.178923
\(764\) 0 0
\(765\) 123.549 4.46691
\(766\) 0 0
\(767\) 18.8631 0.681107
\(768\) 0 0
\(769\) 7.49197 0.270167 0.135084 0.990834i \(-0.456870\pi\)
0.135084 + 0.990834i \(0.456870\pi\)
\(770\) 0 0
\(771\) 32.1894 1.15927
\(772\) 0 0
\(773\) 35.3565 1.27169 0.635843 0.771819i \(-0.280653\pi\)
0.635843 + 0.771819i \(0.280653\pi\)
\(774\) 0 0
\(775\) −9.66196 −0.347068
\(776\) 0 0
\(777\) 5.23636 0.187853
\(778\) 0 0
\(779\) 18.8601 0.675735
\(780\) 0 0
\(781\) 0.399323 0.0142889
\(782\) 0 0
\(783\) 38.1513 1.36342
\(784\) 0 0
\(785\) 62.2230 2.22084
\(786\) 0 0
\(787\) −30.3186 −1.08074 −0.540372 0.841427i \(-0.681716\pi\)
−0.540372 + 0.841427i \(0.681716\pi\)
\(788\) 0 0
\(789\) 69.3975 2.47062
\(790\) 0 0
\(791\) −2.82270 −0.100364
\(792\) 0 0
\(793\) 1.43074 0.0508071
\(794\) 0 0
\(795\) 101.539 3.60120
\(796\) 0 0
\(797\) −49.6831 −1.75987 −0.879933 0.475099i \(-0.842412\pi\)
−0.879933 + 0.475099i \(0.842412\pi\)
\(798\) 0 0
\(799\) 2.53724 0.0897612
\(800\) 0 0
\(801\) 64.2055 2.26859
\(802\) 0 0
\(803\) 1.28762 0.0454391
\(804\) 0 0
\(805\) −8.11614 −0.286056
\(806\) 0 0
\(807\) −39.0339 −1.37406
\(808\) 0 0
\(809\) 29.6256 1.04158 0.520791 0.853685i \(-0.325637\pi\)
0.520791 + 0.853685i \(0.325637\pi\)
\(810\) 0 0
\(811\) −52.0726 −1.82852 −0.914258 0.405134i \(-0.867225\pi\)
−0.914258 + 0.405134i \(0.867225\pi\)
\(812\) 0 0
\(813\) 37.2990 1.30813
\(814\) 0 0
\(815\) 51.4812 1.80331
\(816\) 0 0
\(817\) −1.45477 −0.0508958
\(818\) 0 0
\(819\) 6.30116 0.220180
\(820\) 0 0
\(821\) −24.0722 −0.840124 −0.420062 0.907495i \(-0.637992\pi\)
−0.420062 + 0.907495i \(0.637992\pi\)
\(822\) 0 0
\(823\) −54.7874 −1.90977 −0.954884 0.296980i \(-0.904020\pi\)
−0.954884 + 0.296980i \(0.904020\pi\)
\(824\) 0 0
\(825\) 1.71584 0.0597380
\(826\) 0 0
\(827\) 16.2267 0.564257 0.282128 0.959377i \(-0.408960\pi\)
0.282128 + 0.959377i \(0.408960\pi\)
\(828\) 0 0
\(829\) −24.2588 −0.842544 −0.421272 0.906934i \(-0.638416\pi\)
−0.421272 + 0.906934i \(0.638416\pi\)
\(830\) 0 0
\(831\) −60.2337 −2.08948
\(832\) 0 0
\(833\) −47.4250 −1.64318
\(834\) 0 0
\(835\) 48.0698 1.66352
\(836\) 0 0
\(837\) 19.0703 0.659166
\(838\) 0 0
\(839\) 41.6871 1.43920 0.719599 0.694390i \(-0.244326\pi\)
0.719599 + 0.694390i \(0.244326\pi\)
\(840\) 0 0
\(841\) −9.33163 −0.321780
\(842\) 0 0
\(843\) 21.8022 0.750909
\(844\) 0 0
\(845\) −0.0866960 −0.00298243
\(846\) 0 0
\(847\) −3.26450 −0.112170
\(848\) 0 0
\(849\) 54.4129 1.86745
\(850\) 0 0
\(851\) 52.7474 1.80816
\(852\) 0 0
\(853\) 2.71850 0.0930798 0.0465399 0.998916i \(-0.485181\pi\)
0.0465399 + 0.998916i \(0.485181\pi\)
\(854\) 0 0
\(855\) −36.8995 −1.26194
\(856\) 0 0
\(857\) −1.75359 −0.0599015 −0.0299507 0.999551i \(-0.509535\pi\)
−0.0299507 + 0.999551i \(0.509535\pi\)
\(858\) 0 0
\(859\) 13.7566 0.469369 0.234685 0.972072i \(-0.424594\pi\)
0.234685 + 0.972072i \(0.424594\pi\)
\(860\) 0 0
\(861\) 8.15454 0.277906
\(862\) 0 0
\(863\) 9.16644 0.312029 0.156015 0.987755i \(-0.450135\pi\)
0.156015 + 0.987755i \(0.450135\pi\)
\(864\) 0 0
\(865\) −21.5102 −0.731369
\(866\) 0 0
\(867\) −89.6711 −3.04539
\(868\) 0 0
\(869\) 0.550347 0.0186692
\(870\) 0 0
\(871\) −17.8839 −0.605974
\(872\) 0 0
\(873\) −16.6100 −0.562163
\(874\) 0 0
\(875\) −0.583368 −0.0197214
\(876\) 0 0
\(877\) 4.39218 0.148313 0.0741567 0.997247i \(-0.476374\pi\)
0.0741567 + 0.997247i \(0.476374\pi\)
\(878\) 0 0
\(879\) 42.6609 1.43892
\(880\) 0 0
\(881\) −12.9220 −0.435352 −0.217676 0.976021i \(-0.569848\pi\)
−0.217676 + 0.976021i \(0.569848\pi\)
\(882\) 0 0
\(883\) −40.8403 −1.37438 −0.687192 0.726476i \(-0.741157\pi\)
−0.687192 + 0.726476i \(0.741157\pi\)
\(884\) 0 0
\(885\) −47.7603 −1.60544
\(886\) 0 0
\(887\) −29.7519 −0.998972 −0.499486 0.866322i \(-0.666478\pi\)
−0.499486 + 0.866322i \(0.666478\pi\)
\(888\) 0 0
\(889\) 1.96504 0.0659054
\(890\) 0 0
\(891\) −1.05466 −0.0353323
\(892\) 0 0
\(893\) −0.757782 −0.0253582
\(894\) 0 0
\(895\) 16.7500 0.559891
\(896\) 0 0
\(897\) 95.8257 3.19953
\(898\) 0 0
\(899\) 9.83144 0.327897
\(900\) 0 0
\(901\) −76.4022 −2.54533
\(902\) 0 0
\(903\) −0.628996 −0.0209317
\(904\) 0 0
\(905\) −35.8601 −1.19203
\(906\) 0 0
\(907\) 26.8703 0.892214 0.446107 0.894980i \(-0.352810\pi\)
0.446107 + 0.894980i \(0.352810\pi\)
\(908\) 0 0
\(909\) 7.89631 0.261904
\(910\) 0 0
\(911\) −0.290314 −0.00961854 −0.00480927 0.999988i \(-0.501531\pi\)
−0.00480927 + 0.999988i \(0.501531\pi\)
\(912\) 0 0
\(913\) −0.552335 −0.0182796
\(914\) 0 0
\(915\) −3.62256 −0.119758
\(916\) 0 0
\(917\) 4.58485 0.151405
\(918\) 0 0
\(919\) 20.2476 0.667908 0.333954 0.942589i \(-0.391617\pi\)
0.333954 + 0.942589i \(0.391617\pi\)
\(920\) 0 0
\(921\) 18.3467 0.604544
\(922\) 0 0
\(923\) −10.8900 −0.358448
\(924\) 0 0
\(925\) −25.7573 −0.846893
\(926\) 0 0
\(927\) 22.5864 0.741836
\(928\) 0 0
\(929\) 5.86011 0.192264 0.0961320 0.995369i \(-0.469353\pi\)
0.0961320 + 0.995369i \(0.469353\pi\)
\(930\) 0 0
\(931\) 14.1641 0.464211
\(932\) 0 0
\(933\) 24.0927 0.788759
\(934\) 0 0
\(935\) −2.77219 −0.0906604
\(936\) 0 0
\(937\) −33.8764 −1.10670 −0.553348 0.832950i \(-0.686650\pi\)
−0.553348 + 0.832950i \(0.686650\pi\)
\(938\) 0 0
\(939\) 73.4603 2.39729
\(940\) 0 0
\(941\) 53.5147 1.74453 0.872265 0.489033i \(-0.162650\pi\)
0.872265 + 0.489033i \(0.162650\pi\)
\(942\) 0 0
\(943\) 82.1431 2.67495
\(944\) 0 0
\(945\) −7.82240 −0.254463
\(946\) 0 0
\(947\) −47.2206 −1.53446 −0.767231 0.641371i \(-0.778366\pi\)
−0.767231 + 0.641371i \(0.778366\pi\)
\(948\) 0 0
\(949\) −35.1148 −1.13987
\(950\) 0 0
\(951\) 52.9960 1.71851
\(952\) 0 0
\(953\) −39.3831 −1.27574 −0.637872 0.770142i \(-0.720185\pi\)
−0.637872 + 0.770142i \(0.720185\pi\)
\(954\) 0 0
\(955\) −73.7778 −2.38739
\(956\) 0 0
\(957\) −1.74594 −0.0564382
\(958\) 0 0
\(959\) −5.38596 −0.173922
\(960\) 0 0
\(961\) −26.0857 −0.841473
\(962\) 0 0
\(963\) −85.1781 −2.74483
\(964\) 0 0
\(965\) 24.9500 0.803170
\(966\) 0 0
\(967\) −5.23083 −0.168212 −0.0841061 0.996457i \(-0.526803\pi\)
−0.0841061 + 0.996457i \(0.526803\pi\)
\(968\) 0 0
\(969\) 41.9164 1.34655
\(970\) 0 0
\(971\) 49.7138 1.59539 0.797697 0.603059i \(-0.206052\pi\)
0.797697 + 0.603059i \(0.206052\pi\)
\(972\) 0 0
\(973\) −3.76955 −0.120846
\(974\) 0 0
\(975\) −46.7929 −1.49857
\(976\) 0 0
\(977\) 16.7627 0.536286 0.268143 0.963379i \(-0.413590\pi\)
0.268143 + 0.963379i \(0.413590\pi\)
\(978\) 0 0
\(979\) −1.44065 −0.0460433
\(980\) 0 0
\(981\) −97.8643 −3.12457
\(982\) 0 0
\(983\) −2.31366 −0.0737942 −0.0368971 0.999319i \(-0.511747\pi\)
−0.0368971 + 0.999319i \(0.511747\pi\)
\(984\) 0 0
\(985\) −29.8768 −0.951954
\(986\) 0 0
\(987\) −0.327641 −0.0104289
\(988\) 0 0
\(989\) −6.33606 −0.201475
\(990\) 0 0
\(991\) −27.7561 −0.881702 −0.440851 0.897580i \(-0.645323\pi\)
−0.440851 + 0.897580i \(0.645323\pi\)
\(992\) 0 0
\(993\) −28.3353 −0.899194
\(994\) 0 0
\(995\) −0.664440 −0.0210642
\(996\) 0 0
\(997\) 38.8153 1.22929 0.614646 0.788803i \(-0.289299\pi\)
0.614646 + 0.788803i \(0.289299\pi\)
\(998\) 0 0
\(999\) 50.8384 1.60846
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.1.6 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.6 44 1.1 even 1 trivial