Properties

Label 6008.2.a.b.1.38
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 1.38
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.87831 q^{3} -1.46462 q^{5} -0.498105 q^{7} +0.528033 q^{9} +O(q^{10})\) \(q+1.87831 q^{3} -1.46462 q^{5} -0.498105 q^{7} +0.528033 q^{9} +0.602542 q^{11} +3.48030 q^{13} -2.75101 q^{15} -0.975945 q^{17} +1.95948 q^{19} -0.935593 q^{21} -6.22486 q^{23} -2.85487 q^{25} -4.64311 q^{27} -0.238672 q^{29} -1.95329 q^{31} +1.13176 q^{33} +0.729537 q^{35} +0.114676 q^{37} +6.53707 q^{39} -2.20599 q^{41} -4.53861 q^{43} -0.773370 q^{45} +4.00260 q^{47} -6.75189 q^{49} -1.83312 q^{51} +7.59279 q^{53} -0.882497 q^{55} +3.68050 q^{57} -2.21604 q^{59} -11.3328 q^{61} -0.263016 q^{63} -5.09734 q^{65} -9.31589 q^{67} -11.6922 q^{69} -4.58698 q^{71} +6.26713 q^{73} -5.36233 q^{75} -0.300129 q^{77} +3.09141 q^{79} -10.3053 q^{81} +2.87490 q^{83} +1.42939 q^{85} -0.448299 q^{87} +8.49258 q^{89} -1.73356 q^{91} -3.66888 q^{93} -2.86990 q^{95} +13.8132 q^{97} +0.318162 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) 1.87831 1.08444 0.542220 0.840236i \(-0.317584\pi\)
0.542220 + 0.840236i \(0.317584\pi\)
\(4\) 0 0
\(5\) −1.46462 −0.655000 −0.327500 0.944851i \(-0.606206\pi\)
−0.327500 + 0.944851i \(0.606206\pi\)
\(6\) 0 0
\(7\) −0.498105 −0.188266 −0.0941330 0.995560i \(-0.530008\pi\)
−0.0941330 + 0.995560i \(0.530008\pi\)
\(8\) 0 0
\(9\) 0.528033 0.176011
\(10\) 0 0
\(11\) 0.602542 0.181673 0.0908366 0.995866i \(-0.471046\pi\)
0.0908366 + 0.995866i \(0.471046\pi\)
\(12\) 0 0
\(13\) 3.48030 0.965262 0.482631 0.875824i \(-0.339681\pi\)
0.482631 + 0.875824i \(0.339681\pi\)
\(14\) 0 0
\(15\) −2.75101 −0.710308
\(16\) 0 0
\(17\) −0.975945 −0.236701 −0.118351 0.992972i \(-0.537761\pi\)
−0.118351 + 0.992972i \(0.537761\pi\)
\(18\) 0 0
\(19\) 1.95948 0.449535 0.224768 0.974412i \(-0.427838\pi\)
0.224768 + 0.974412i \(0.427838\pi\)
\(20\) 0 0
\(21\) −0.935593 −0.204163
\(22\) 0 0
\(23\) −6.22486 −1.29797 −0.648987 0.760800i \(-0.724807\pi\)
−0.648987 + 0.760800i \(0.724807\pi\)
\(24\) 0 0
\(25\) −2.85487 −0.570975
\(26\) 0 0
\(27\) −4.64311 −0.893567
\(28\) 0 0
\(29\) −0.238672 −0.0443202 −0.0221601 0.999754i \(-0.507054\pi\)
−0.0221601 + 0.999754i \(0.507054\pi\)
\(30\) 0 0
\(31\) −1.95329 −0.350822 −0.175411 0.984495i \(-0.556125\pi\)
−0.175411 + 0.984495i \(0.556125\pi\)
\(32\) 0 0
\(33\) 1.13176 0.197014
\(34\) 0 0
\(35\) 0.729537 0.123314
\(36\) 0 0
\(37\) 0.114676 0.0188526 0.00942629 0.999956i \(-0.496999\pi\)
0.00942629 + 0.999956i \(0.496999\pi\)
\(38\) 0 0
\(39\) 6.53707 1.04677
\(40\) 0 0
\(41\) −2.20599 −0.344518 −0.172259 0.985052i \(-0.555107\pi\)
−0.172259 + 0.985052i \(0.555107\pi\)
\(42\) 0 0
\(43\) −4.53861 −0.692131 −0.346066 0.938210i \(-0.612483\pi\)
−0.346066 + 0.938210i \(0.612483\pi\)
\(44\) 0 0
\(45\) −0.773370 −0.115287
\(46\) 0 0
\(47\) 4.00260 0.583840 0.291920 0.956443i \(-0.405706\pi\)
0.291920 + 0.956443i \(0.405706\pi\)
\(48\) 0 0
\(49\) −6.75189 −0.964556
\(50\) 0 0
\(51\) −1.83312 −0.256689
\(52\) 0 0
\(53\) 7.59279 1.04295 0.521475 0.853266i \(-0.325382\pi\)
0.521475 + 0.853266i \(0.325382\pi\)
\(54\) 0 0
\(55\) −0.882497 −0.118996
\(56\) 0 0
\(57\) 3.68050 0.487494
\(58\) 0 0
\(59\) −2.21604 −0.288504 −0.144252 0.989541i \(-0.546078\pi\)
−0.144252 + 0.989541i \(0.546078\pi\)
\(60\) 0 0
\(61\) −11.3328 −1.45102 −0.725509 0.688212i \(-0.758396\pi\)
−0.725509 + 0.688212i \(0.758396\pi\)
\(62\) 0 0
\(63\) −0.263016 −0.0331369
\(64\) 0 0
\(65\) −5.09734 −0.632247
\(66\) 0 0
\(67\) −9.31589 −1.13812 −0.569059 0.822297i \(-0.692692\pi\)
−0.569059 + 0.822297i \(0.692692\pi\)
\(68\) 0 0
\(69\) −11.6922 −1.40758
\(70\) 0 0
\(71\) −4.58698 −0.544374 −0.272187 0.962244i \(-0.587747\pi\)
−0.272187 + 0.962244i \(0.587747\pi\)
\(72\) 0 0
\(73\) 6.26713 0.733512 0.366756 0.930317i \(-0.380468\pi\)
0.366756 + 0.930317i \(0.380468\pi\)
\(74\) 0 0
\(75\) −5.36233 −0.619188
\(76\) 0 0
\(77\) −0.300129 −0.0342029
\(78\) 0 0
\(79\) 3.09141 0.347811 0.173905 0.984762i \(-0.444361\pi\)
0.173905 + 0.984762i \(0.444361\pi\)
\(80\) 0 0
\(81\) −10.3053 −1.14503
\(82\) 0 0
\(83\) 2.87490 0.315561 0.157781 0.987474i \(-0.449566\pi\)
0.157781 + 0.987474i \(0.449566\pi\)
\(84\) 0 0
\(85\) 1.42939 0.155039
\(86\) 0 0
\(87\) −0.448299 −0.0480627
\(88\) 0 0
\(89\) 8.49258 0.900212 0.450106 0.892975i \(-0.351386\pi\)
0.450106 + 0.892975i \(0.351386\pi\)
\(90\) 0 0
\(91\) −1.73356 −0.181726
\(92\) 0 0
\(93\) −3.66888 −0.380446
\(94\) 0 0
\(95\) −2.86990 −0.294446
\(96\) 0 0
\(97\) 13.8132 1.40252 0.701261 0.712904i \(-0.252621\pi\)
0.701261 + 0.712904i \(0.252621\pi\)
\(98\) 0 0
\(99\) 0.318162 0.0319765
\(100\) 0 0
\(101\) −2.70228 −0.268887 −0.134443 0.990921i \(-0.542925\pi\)
−0.134443 + 0.990921i \(0.542925\pi\)
\(102\) 0 0
\(103\) 3.79271 0.373707 0.186853 0.982388i \(-0.440171\pi\)
0.186853 + 0.982388i \(0.440171\pi\)
\(104\) 0 0
\(105\) 1.37029 0.133727
\(106\) 0 0
\(107\) −8.04476 −0.777716 −0.388858 0.921298i \(-0.627130\pi\)
−0.388858 + 0.921298i \(0.627130\pi\)
\(108\) 0 0
\(109\) −14.2748 −1.36727 −0.683637 0.729822i \(-0.739603\pi\)
−0.683637 + 0.729822i \(0.739603\pi\)
\(110\) 0 0
\(111\) 0.215396 0.0204445
\(112\) 0 0
\(113\) −15.2185 −1.43163 −0.715817 0.698288i \(-0.753946\pi\)
−0.715817 + 0.698288i \(0.753946\pi\)
\(114\) 0 0
\(115\) 9.11709 0.850173
\(116\) 0 0
\(117\) 1.83771 0.169897
\(118\) 0 0
\(119\) 0.486123 0.0445628
\(120\) 0 0
\(121\) −10.6369 −0.966995
\(122\) 0 0
\(123\) −4.14353 −0.373610
\(124\) 0 0
\(125\) 11.5044 1.02899
\(126\) 0 0
\(127\) 11.5573 1.02555 0.512774 0.858524i \(-0.328618\pi\)
0.512774 + 0.858524i \(0.328618\pi\)
\(128\) 0 0
\(129\) −8.52490 −0.750575
\(130\) 0 0
\(131\) 20.5891 1.79887 0.899437 0.437050i \(-0.143977\pi\)
0.899437 + 0.437050i \(0.143977\pi\)
\(132\) 0 0
\(133\) −0.976026 −0.0846322
\(134\) 0 0
\(135\) 6.80041 0.585286
\(136\) 0 0
\(137\) 6.46955 0.552731 0.276365 0.961053i \(-0.410870\pi\)
0.276365 + 0.961053i \(0.410870\pi\)
\(138\) 0 0
\(139\) −9.44362 −0.800997 −0.400499 0.916297i \(-0.631163\pi\)
−0.400499 + 0.916297i \(0.631163\pi\)
\(140\) 0 0
\(141\) 7.51812 0.633140
\(142\) 0 0
\(143\) 2.09703 0.175362
\(144\) 0 0
\(145\) 0.349565 0.0290298
\(146\) 0 0
\(147\) −12.6821 −1.04600
\(148\) 0 0
\(149\) −19.2603 −1.57787 −0.788933 0.614479i \(-0.789366\pi\)
−0.788933 + 0.614479i \(0.789366\pi\)
\(150\) 0 0
\(151\) 3.39212 0.276046 0.138023 0.990429i \(-0.455925\pi\)
0.138023 + 0.990429i \(0.455925\pi\)
\(152\) 0 0
\(153\) −0.515331 −0.0416620
\(154\) 0 0
\(155\) 2.86084 0.229788
\(156\) 0 0
\(157\) 3.40878 0.272050 0.136025 0.990705i \(-0.456567\pi\)
0.136025 + 0.990705i \(0.456567\pi\)
\(158\) 0 0
\(159\) 14.2616 1.13102
\(160\) 0 0
\(161\) 3.10063 0.244364
\(162\) 0 0
\(163\) −21.5157 −1.68524 −0.842618 0.538511i \(-0.818987\pi\)
−0.842618 + 0.538511i \(0.818987\pi\)
\(164\) 0 0
\(165\) −1.65760 −0.129044
\(166\) 0 0
\(167\) 13.1544 1.01792 0.508958 0.860792i \(-0.330031\pi\)
0.508958 + 0.860792i \(0.330031\pi\)
\(168\) 0 0
\(169\) −0.887489 −0.0682684
\(170\) 0 0
\(171\) 1.03467 0.0791231
\(172\) 0 0
\(173\) 3.10497 0.236067 0.118033 0.993010i \(-0.462341\pi\)
0.118033 + 0.993010i \(0.462341\pi\)
\(174\) 0 0
\(175\) 1.42203 0.107495
\(176\) 0 0
\(177\) −4.16240 −0.312865
\(178\) 0 0
\(179\) −5.81994 −0.435003 −0.217502 0.976060i \(-0.569791\pi\)
−0.217502 + 0.976060i \(0.569791\pi\)
\(180\) 0 0
\(181\) −20.5155 −1.52491 −0.762453 0.647044i \(-0.776005\pi\)
−0.762453 + 0.647044i \(0.776005\pi\)
\(182\) 0 0
\(183\) −21.2865 −1.57354
\(184\) 0 0
\(185\) −0.167957 −0.0123484
\(186\) 0 0
\(187\) −0.588047 −0.0430023
\(188\) 0 0
\(189\) 2.31276 0.168228
\(190\) 0 0
\(191\) 0.847720 0.0613389 0.0306694 0.999530i \(-0.490236\pi\)
0.0306694 + 0.999530i \(0.490236\pi\)
\(192\) 0 0
\(193\) −11.7399 −0.845059 −0.422530 0.906349i \(-0.638858\pi\)
−0.422530 + 0.906349i \(0.638858\pi\)
\(194\) 0 0
\(195\) −9.57436 −0.685634
\(196\) 0 0
\(197\) −6.30965 −0.449544 −0.224772 0.974411i \(-0.572164\pi\)
−0.224772 + 0.974411i \(0.572164\pi\)
\(198\) 0 0
\(199\) −18.7268 −1.32751 −0.663753 0.747952i \(-0.731037\pi\)
−0.663753 + 0.747952i \(0.731037\pi\)
\(200\) 0 0
\(201\) −17.4981 −1.23422
\(202\) 0 0
\(203\) 0.118884 0.00834399
\(204\) 0 0
\(205\) 3.23095 0.225660
\(206\) 0 0
\(207\) −3.28693 −0.228457
\(208\) 0 0
\(209\) 1.18067 0.0816685
\(210\) 0 0
\(211\) −25.9126 −1.78390 −0.891949 0.452137i \(-0.850662\pi\)
−0.891949 + 0.452137i \(0.850662\pi\)
\(212\) 0 0
\(213\) −8.61575 −0.590342
\(214\) 0 0
\(215\) 6.64736 0.453346
\(216\) 0 0
\(217\) 0.972945 0.0660478
\(218\) 0 0
\(219\) 11.7716 0.795450
\(220\) 0 0
\(221\) −3.39658 −0.228479
\(222\) 0 0
\(223\) −7.48609 −0.501306 −0.250653 0.968077i \(-0.580645\pi\)
−0.250653 + 0.968077i \(0.580645\pi\)
\(224\) 0 0
\(225\) −1.50747 −0.100498
\(226\) 0 0
\(227\) −12.3558 −0.820086 −0.410043 0.912066i \(-0.634486\pi\)
−0.410043 + 0.912066i \(0.634486\pi\)
\(228\) 0 0
\(229\) 5.69215 0.376148 0.188074 0.982155i \(-0.439776\pi\)
0.188074 + 0.982155i \(0.439776\pi\)
\(230\) 0 0
\(231\) −0.563734 −0.0370910
\(232\) 0 0
\(233\) −10.8469 −0.710606 −0.355303 0.934751i \(-0.615622\pi\)
−0.355303 + 0.934751i \(0.615622\pi\)
\(234\) 0 0
\(235\) −5.86231 −0.382415
\(236\) 0 0
\(237\) 5.80661 0.377180
\(238\) 0 0
\(239\) 3.09267 0.200048 0.100024 0.994985i \(-0.468108\pi\)
0.100024 + 0.994985i \(0.468108\pi\)
\(240\) 0 0
\(241\) 2.39728 0.154422 0.0772112 0.997015i \(-0.475398\pi\)
0.0772112 + 0.997015i \(0.475398\pi\)
\(242\) 0 0
\(243\) −5.42713 −0.348151
\(244\) 0 0
\(245\) 9.88899 0.631784
\(246\) 0 0
\(247\) 6.81958 0.433920
\(248\) 0 0
\(249\) 5.39994 0.342208
\(250\) 0 0
\(251\) −18.2555 −1.15228 −0.576139 0.817352i \(-0.695441\pi\)
−0.576139 + 0.817352i \(0.695441\pi\)
\(252\) 0 0
\(253\) −3.75074 −0.235807
\(254\) 0 0
\(255\) 2.68484 0.168131
\(256\) 0 0
\(257\) −3.00317 −0.187333 −0.0936664 0.995604i \(-0.529859\pi\)
−0.0936664 + 0.995604i \(0.529859\pi\)
\(258\) 0 0
\(259\) −0.0571206 −0.00354930
\(260\) 0 0
\(261\) −0.126026 −0.00780084
\(262\) 0 0
\(263\) −16.2256 −1.00051 −0.500256 0.865878i \(-0.666761\pi\)
−0.500256 + 0.865878i \(0.666761\pi\)
\(264\) 0 0
\(265\) −11.1206 −0.683132
\(266\) 0 0
\(267\) 15.9517 0.976226
\(268\) 0 0
\(269\) 18.1857 1.10880 0.554400 0.832250i \(-0.312948\pi\)
0.554400 + 0.832250i \(0.312948\pi\)
\(270\) 0 0
\(271\) 19.7670 1.20076 0.600380 0.799715i \(-0.295016\pi\)
0.600380 + 0.799715i \(0.295016\pi\)
\(272\) 0 0
\(273\) −3.25615 −0.197071
\(274\) 0 0
\(275\) −1.72018 −0.103731
\(276\) 0 0
\(277\) −24.4874 −1.47130 −0.735652 0.677359i \(-0.763124\pi\)
−0.735652 + 0.677359i \(0.763124\pi\)
\(278\) 0 0
\(279\) −1.03140 −0.0617485
\(280\) 0 0
\(281\) −1.40921 −0.0840666 −0.0420333 0.999116i \(-0.513384\pi\)
−0.0420333 + 0.999116i \(0.513384\pi\)
\(282\) 0 0
\(283\) −27.7300 −1.64838 −0.824188 0.566317i \(-0.808368\pi\)
−0.824188 + 0.566317i \(0.808368\pi\)
\(284\) 0 0
\(285\) −5.39055 −0.319309
\(286\) 0 0
\(287\) 1.09882 0.0648611
\(288\) 0 0
\(289\) −16.0475 −0.943972
\(290\) 0 0
\(291\) 25.9455 1.52095
\(292\) 0 0
\(293\) 27.4625 1.60438 0.802188 0.597072i \(-0.203669\pi\)
0.802188 + 0.597072i \(0.203669\pi\)
\(294\) 0 0
\(295\) 3.24567 0.188970
\(296\) 0 0
\(297\) −2.79767 −0.162337
\(298\) 0 0
\(299\) −21.6644 −1.25289
\(300\) 0 0
\(301\) 2.26070 0.130305
\(302\) 0 0
\(303\) −5.07570 −0.291592
\(304\) 0 0
\(305\) 16.5983 0.950417
\(306\) 0 0
\(307\) −0.0884198 −0.00504638 −0.00252319 0.999997i \(-0.500803\pi\)
−0.00252319 + 0.999997i \(0.500803\pi\)
\(308\) 0 0
\(309\) 7.12387 0.405263
\(310\) 0 0
\(311\) 19.8893 1.12782 0.563908 0.825838i \(-0.309297\pi\)
0.563908 + 0.825838i \(0.309297\pi\)
\(312\) 0 0
\(313\) −8.05293 −0.455179 −0.227589 0.973757i \(-0.573084\pi\)
−0.227589 + 0.973757i \(0.573084\pi\)
\(314\) 0 0
\(315\) 0.385219 0.0217046
\(316\) 0 0
\(317\) 21.1117 1.18575 0.592876 0.805294i \(-0.297992\pi\)
0.592876 + 0.805294i \(0.297992\pi\)
\(318\) 0 0
\(319\) −0.143810 −0.00805180
\(320\) 0 0
\(321\) −15.1105 −0.843387
\(322\) 0 0
\(323\) −1.91234 −0.106406
\(324\) 0 0
\(325\) −9.93583 −0.551141
\(326\) 0 0
\(327\) −26.8124 −1.48273
\(328\) 0 0
\(329\) −1.99372 −0.109917
\(330\) 0 0
\(331\) −0.586105 −0.0322152 −0.0161076 0.999870i \(-0.505127\pi\)
−0.0161076 + 0.999870i \(0.505127\pi\)
\(332\) 0 0
\(333\) 0.0605526 0.00331826
\(334\) 0 0
\(335\) 13.6443 0.745467
\(336\) 0 0
\(337\) −16.8242 −0.916474 −0.458237 0.888830i \(-0.651519\pi\)
−0.458237 + 0.888830i \(0.651519\pi\)
\(338\) 0 0
\(339\) −28.5850 −1.55252
\(340\) 0 0
\(341\) −1.17694 −0.0637350
\(342\) 0 0
\(343\) 6.84988 0.369859
\(344\) 0 0
\(345\) 17.1247 0.921962
\(346\) 0 0
\(347\) −3.49786 −0.187775 −0.0938876 0.995583i \(-0.529929\pi\)
−0.0938876 + 0.995583i \(0.529929\pi\)
\(348\) 0 0
\(349\) 0.897813 0.0480588 0.0240294 0.999711i \(-0.492350\pi\)
0.0240294 + 0.999711i \(0.492350\pi\)
\(350\) 0 0
\(351\) −16.1594 −0.862527
\(352\) 0 0
\(353\) 2.56450 0.136495 0.0682473 0.997668i \(-0.478259\pi\)
0.0682473 + 0.997668i \(0.478259\pi\)
\(354\) 0 0
\(355\) 6.71820 0.356565
\(356\) 0 0
\(357\) 0.913087 0.0483257
\(358\) 0 0
\(359\) 18.5733 0.980259 0.490130 0.871650i \(-0.336949\pi\)
0.490130 + 0.871650i \(0.336949\pi\)
\(360\) 0 0
\(361\) −15.1604 −0.797918
\(362\) 0 0
\(363\) −19.9794 −1.04865
\(364\) 0 0
\(365\) −9.17899 −0.480450
\(366\) 0 0
\(367\) −5.41854 −0.282846 −0.141423 0.989949i \(-0.545168\pi\)
−0.141423 + 0.989949i \(0.545168\pi\)
\(368\) 0 0
\(369\) −1.16484 −0.0606390
\(370\) 0 0
\(371\) −3.78201 −0.196352
\(372\) 0 0
\(373\) 4.81215 0.249164 0.124582 0.992209i \(-0.460241\pi\)
0.124582 + 0.992209i \(0.460241\pi\)
\(374\) 0 0
\(375\) 21.6089 1.11588
\(376\) 0 0
\(377\) −0.830650 −0.0427807
\(378\) 0 0
\(379\) 19.7484 1.01441 0.507204 0.861826i \(-0.330679\pi\)
0.507204 + 0.861826i \(0.330679\pi\)
\(380\) 0 0
\(381\) 21.7082 1.11214
\(382\) 0 0
\(383\) −30.3952 −1.55312 −0.776561 0.630043i \(-0.783037\pi\)
−0.776561 + 0.630043i \(0.783037\pi\)
\(384\) 0 0
\(385\) 0.439576 0.0224029
\(386\) 0 0
\(387\) −2.39653 −0.121823
\(388\) 0 0
\(389\) 34.6896 1.75883 0.879417 0.476051i \(-0.157932\pi\)
0.879417 + 0.476051i \(0.157932\pi\)
\(390\) 0 0
\(391\) 6.07512 0.307232
\(392\) 0 0
\(393\) 38.6725 1.95077
\(394\) 0 0
\(395\) −4.52775 −0.227816
\(396\) 0 0
\(397\) 7.18192 0.360450 0.180225 0.983625i \(-0.442317\pi\)
0.180225 + 0.983625i \(0.442317\pi\)
\(398\) 0 0
\(399\) −1.83328 −0.0917786
\(400\) 0 0
\(401\) 10.4454 0.521621 0.260810 0.965390i \(-0.416010\pi\)
0.260810 + 0.965390i \(0.416010\pi\)
\(402\) 0 0
\(403\) −6.79806 −0.338635
\(404\) 0 0
\(405\) 15.0934 0.749995
\(406\) 0 0
\(407\) 0.0690969 0.00342501
\(408\) 0 0
\(409\) −11.1123 −0.549466 −0.274733 0.961520i \(-0.588590\pi\)
−0.274733 + 0.961520i \(0.588590\pi\)
\(410\) 0 0
\(411\) 12.1518 0.599403
\(412\) 0 0
\(413\) 1.10382 0.0543154
\(414\) 0 0
\(415\) −4.21065 −0.206693
\(416\) 0 0
\(417\) −17.7380 −0.868634
\(418\) 0 0
\(419\) 33.1323 1.61862 0.809309 0.587383i \(-0.199842\pi\)
0.809309 + 0.587383i \(0.199842\pi\)
\(420\) 0 0
\(421\) 36.0960 1.75921 0.879605 0.475704i \(-0.157807\pi\)
0.879605 + 0.475704i \(0.157807\pi\)
\(422\) 0 0
\(423\) 2.11351 0.102762
\(424\) 0 0
\(425\) 2.78620 0.135151
\(426\) 0 0
\(427\) 5.64493 0.273177
\(428\) 0 0
\(429\) 3.93886 0.190170
\(430\) 0 0
\(431\) −32.8845 −1.58399 −0.791996 0.610526i \(-0.790958\pi\)
−0.791996 + 0.610526i \(0.790958\pi\)
\(432\) 0 0
\(433\) 11.5043 0.552860 0.276430 0.961034i \(-0.410849\pi\)
0.276430 + 0.961034i \(0.410849\pi\)
\(434\) 0 0
\(435\) 0.656589 0.0314810
\(436\) 0 0
\(437\) −12.1975 −0.583485
\(438\) 0 0
\(439\) 20.5543 0.981004 0.490502 0.871440i \(-0.336813\pi\)
0.490502 + 0.871440i \(0.336813\pi\)
\(440\) 0 0
\(441\) −3.56522 −0.169772
\(442\) 0 0
\(443\) 31.3136 1.48775 0.743877 0.668317i \(-0.232985\pi\)
0.743877 + 0.668317i \(0.232985\pi\)
\(444\) 0 0
\(445\) −12.4384 −0.589639
\(446\) 0 0
\(447\) −36.1767 −1.71110
\(448\) 0 0
\(449\) −27.3467 −1.29057 −0.645286 0.763941i \(-0.723262\pi\)
−0.645286 + 0.763941i \(0.723262\pi\)
\(450\) 0 0
\(451\) −1.32920 −0.0625897
\(452\) 0 0
\(453\) 6.37143 0.299356
\(454\) 0 0
\(455\) 2.53901 0.119031
\(456\) 0 0
\(457\) 35.3735 1.65470 0.827350 0.561686i \(-0.189847\pi\)
0.827350 + 0.561686i \(0.189847\pi\)
\(458\) 0 0
\(459\) 4.53142 0.211509
\(460\) 0 0
\(461\) 2.86418 0.133398 0.0666991 0.997773i \(-0.478753\pi\)
0.0666991 + 0.997773i \(0.478753\pi\)
\(462\) 0 0
\(463\) −0.335522 −0.0155930 −0.00779651 0.999970i \(-0.502482\pi\)
−0.00779651 + 0.999970i \(0.502482\pi\)
\(464\) 0 0
\(465\) 5.37354 0.249192
\(466\) 0 0
\(467\) −5.19806 −0.240538 −0.120269 0.992741i \(-0.538376\pi\)
−0.120269 + 0.992741i \(0.538376\pi\)
\(468\) 0 0
\(469\) 4.64029 0.214269
\(470\) 0 0
\(471\) 6.40273 0.295022
\(472\) 0 0
\(473\) −2.73470 −0.125742
\(474\) 0 0
\(475\) −5.59407 −0.256673
\(476\) 0 0
\(477\) 4.00924 0.183571
\(478\) 0 0
\(479\) 1.45623 0.0665370 0.0332685 0.999446i \(-0.489408\pi\)
0.0332685 + 0.999446i \(0.489408\pi\)
\(480\) 0 0
\(481\) 0.399107 0.0181977
\(482\) 0 0
\(483\) 5.82394 0.264998
\(484\) 0 0
\(485\) −20.2312 −0.918652
\(486\) 0 0
\(487\) 13.6526 0.618658 0.309329 0.950955i \(-0.399896\pi\)
0.309329 + 0.950955i \(0.399896\pi\)
\(488\) 0 0
\(489\) −40.4130 −1.82754
\(490\) 0 0
\(491\) −20.5999 −0.929660 −0.464830 0.885400i \(-0.653885\pi\)
−0.464830 + 0.885400i \(0.653885\pi\)
\(492\) 0 0
\(493\) 0.232930 0.0104907
\(494\) 0 0
\(495\) −0.465987 −0.0209446
\(496\) 0 0
\(497\) 2.28480 0.102487
\(498\) 0 0
\(499\) −21.5332 −0.963958 −0.481979 0.876183i \(-0.660082\pi\)
−0.481979 + 0.876183i \(0.660082\pi\)
\(500\) 0 0
\(501\) 24.7079 1.10387
\(502\) 0 0
\(503\) −40.8753 −1.82254 −0.911270 0.411810i \(-0.864897\pi\)
−0.911270 + 0.411810i \(0.864897\pi\)
\(504\) 0 0
\(505\) 3.95782 0.176121
\(506\) 0 0
\(507\) −1.66698 −0.0740330
\(508\) 0 0
\(509\) −20.2908 −0.899372 −0.449686 0.893187i \(-0.648464\pi\)
−0.449686 + 0.893187i \(0.648464\pi\)
\(510\) 0 0
\(511\) −3.12169 −0.138095
\(512\) 0 0
\(513\) −9.09808 −0.401690
\(514\) 0 0
\(515\) −5.55490 −0.244778
\(516\) 0 0
\(517\) 2.41174 0.106068
\(518\) 0 0
\(519\) 5.83209 0.256000
\(520\) 0 0
\(521\) 15.2044 0.666117 0.333059 0.942906i \(-0.391919\pi\)
0.333059 + 0.942906i \(0.391919\pi\)
\(522\) 0 0
\(523\) 21.8582 0.955793 0.477896 0.878416i \(-0.341399\pi\)
0.477896 + 0.878416i \(0.341399\pi\)
\(524\) 0 0
\(525\) 2.67100 0.116572
\(526\) 0 0
\(527\) 1.90631 0.0830401
\(528\) 0 0
\(529\) 15.7489 0.684736
\(530\) 0 0
\(531\) −1.17014 −0.0507798
\(532\) 0 0
\(533\) −7.67753 −0.332551
\(534\) 0 0
\(535\) 11.7826 0.509404
\(536\) 0 0
\(537\) −10.9316 −0.471735
\(538\) 0 0
\(539\) −4.06830 −0.175234
\(540\) 0 0
\(541\) 23.3644 1.00452 0.502258 0.864718i \(-0.332503\pi\)
0.502258 + 0.864718i \(0.332503\pi\)
\(542\) 0 0
\(543\) −38.5344 −1.65367
\(544\) 0 0
\(545\) 20.9072 0.895565
\(546\) 0 0
\(547\) 16.2811 0.696130 0.348065 0.937470i \(-0.386839\pi\)
0.348065 + 0.937470i \(0.386839\pi\)
\(548\) 0 0
\(549\) −5.98410 −0.255395
\(550\) 0 0
\(551\) −0.467672 −0.0199235
\(552\) 0 0
\(553\) −1.53985 −0.0654809
\(554\) 0 0
\(555\) −0.315475 −0.0133911
\(556\) 0 0
\(557\) 10.6940 0.453120 0.226560 0.973997i \(-0.427252\pi\)
0.226560 + 0.973997i \(0.427252\pi\)
\(558\) 0 0
\(559\) −15.7957 −0.668088
\(560\) 0 0
\(561\) −1.10453 −0.0466334
\(562\) 0 0
\(563\) −2.76883 −0.116692 −0.0583461 0.998296i \(-0.518583\pi\)
−0.0583461 + 0.998296i \(0.518583\pi\)
\(564\) 0 0
\(565\) 22.2894 0.937721
\(566\) 0 0
\(567\) 5.13311 0.215570
\(568\) 0 0
\(569\) 40.5177 1.69859 0.849296 0.527917i \(-0.177027\pi\)
0.849296 + 0.527917i \(0.177027\pi\)
\(570\) 0 0
\(571\) −17.9082 −0.749436 −0.374718 0.927139i \(-0.622260\pi\)
−0.374718 + 0.927139i \(0.622260\pi\)
\(572\) 0 0
\(573\) 1.59228 0.0665184
\(574\) 0 0
\(575\) 17.7712 0.741110
\(576\) 0 0
\(577\) 32.4904 1.35259 0.676296 0.736630i \(-0.263584\pi\)
0.676296 + 0.736630i \(0.263584\pi\)
\(578\) 0 0
\(579\) −22.0512 −0.916416
\(580\) 0 0
\(581\) −1.43200 −0.0594095
\(582\) 0 0
\(583\) 4.57497 0.189476
\(584\) 0 0
\(585\) −2.69156 −0.111282
\(586\) 0 0
\(587\) −6.16993 −0.254660 −0.127330 0.991860i \(-0.540641\pi\)
−0.127330 + 0.991860i \(0.540641\pi\)
\(588\) 0 0
\(589\) −3.82744 −0.157707
\(590\) 0 0
\(591\) −11.8515 −0.487504
\(592\) 0 0
\(593\) 8.13388 0.334018 0.167009 0.985955i \(-0.446589\pi\)
0.167009 + 0.985955i \(0.446589\pi\)
\(594\) 0 0
\(595\) −0.711987 −0.0291886
\(596\) 0 0
\(597\) −35.1746 −1.43960
\(598\) 0 0
\(599\) 34.9323 1.42730 0.713648 0.700504i \(-0.247041\pi\)
0.713648 + 0.700504i \(0.247041\pi\)
\(600\) 0 0
\(601\) 22.1604 0.903940 0.451970 0.892033i \(-0.350721\pi\)
0.451970 + 0.892033i \(0.350721\pi\)
\(602\) 0 0
\(603\) −4.91910 −0.200321
\(604\) 0 0
\(605\) 15.5791 0.633382
\(606\) 0 0
\(607\) −24.7350 −1.00396 −0.501981 0.864878i \(-0.667395\pi\)
−0.501981 + 0.864878i \(0.667395\pi\)
\(608\) 0 0
\(609\) 0.223300 0.00904856
\(610\) 0 0
\(611\) 13.9303 0.563559
\(612\) 0 0
\(613\) 23.6945 0.957013 0.478506 0.878084i \(-0.341178\pi\)
0.478506 + 0.878084i \(0.341178\pi\)
\(614\) 0 0
\(615\) 6.06872 0.244714
\(616\) 0 0
\(617\) −0.640308 −0.0257778 −0.0128889 0.999917i \(-0.504103\pi\)
−0.0128889 + 0.999917i \(0.504103\pi\)
\(618\) 0 0
\(619\) −33.8745 −1.36153 −0.680766 0.732501i \(-0.738353\pi\)
−0.680766 + 0.732501i \(0.738353\pi\)
\(620\) 0 0
\(621\) 28.9027 1.15983
\(622\) 0 0
\(623\) −4.23020 −0.169479
\(624\) 0 0
\(625\) −2.57532 −0.103013
\(626\) 0 0
\(627\) 2.21766 0.0885646
\(628\) 0 0
\(629\) −0.111917 −0.00446243
\(630\) 0 0
\(631\) 12.6706 0.504410 0.252205 0.967674i \(-0.418844\pi\)
0.252205 + 0.967674i \(0.418844\pi\)
\(632\) 0 0
\(633\) −48.6718 −1.93453
\(634\) 0 0
\(635\) −16.9271 −0.671733
\(636\) 0 0
\(637\) −23.4986 −0.931050
\(638\) 0 0
\(639\) −2.42208 −0.0958158
\(640\) 0 0
\(641\) 19.6854 0.777528 0.388764 0.921337i \(-0.372902\pi\)
0.388764 + 0.921337i \(0.372902\pi\)
\(642\) 0 0
\(643\) 39.5123 1.55821 0.779106 0.626892i \(-0.215673\pi\)
0.779106 + 0.626892i \(0.215673\pi\)
\(644\) 0 0
\(645\) 12.4858 0.491627
\(646\) 0 0
\(647\) −29.0648 −1.14266 −0.571328 0.820722i \(-0.693572\pi\)
−0.571328 + 0.820722i \(0.693572\pi\)
\(648\) 0 0
\(649\) −1.33526 −0.0524134
\(650\) 0 0
\(651\) 1.82749 0.0716249
\(652\) 0 0
\(653\) 42.6203 1.66786 0.833930 0.551870i \(-0.186086\pi\)
0.833930 + 0.551870i \(0.186086\pi\)
\(654\) 0 0
\(655\) −30.1552 −1.17826
\(656\) 0 0
\(657\) 3.30925 0.129106
\(658\) 0 0
\(659\) −34.2649 −1.33477 −0.667385 0.744713i \(-0.732586\pi\)
−0.667385 + 0.744713i \(0.732586\pi\)
\(660\) 0 0
\(661\) 49.4331 1.92272 0.961361 0.275289i \(-0.0887737\pi\)
0.961361 + 0.275289i \(0.0887737\pi\)
\(662\) 0 0
\(663\) −6.37982 −0.247772
\(664\) 0 0
\(665\) 1.42951 0.0554341
\(666\) 0 0
\(667\) 1.48570 0.0575265
\(668\) 0 0
\(669\) −14.0612 −0.543636
\(670\) 0 0
\(671\) −6.82850 −0.263611
\(672\) 0 0
\(673\) 15.3737 0.592612 0.296306 0.955093i \(-0.404245\pi\)
0.296306 + 0.955093i \(0.404245\pi\)
\(674\) 0 0
\(675\) 13.2555 0.510204
\(676\) 0 0
\(677\) 43.5481 1.67369 0.836844 0.547441i \(-0.184398\pi\)
0.836844 + 0.547441i \(0.184398\pi\)
\(678\) 0 0
\(679\) −6.88044 −0.264047
\(680\) 0 0
\(681\) −23.2081 −0.889335
\(682\) 0 0
\(683\) −17.3400 −0.663498 −0.331749 0.943368i \(-0.607639\pi\)
−0.331749 + 0.943368i \(0.607639\pi\)
\(684\) 0 0
\(685\) −9.47546 −0.362039
\(686\) 0 0
\(687\) 10.6916 0.407910
\(688\) 0 0
\(689\) 26.4252 1.00672
\(690\) 0 0
\(691\) 22.8687 0.869966 0.434983 0.900439i \(-0.356754\pi\)
0.434983 + 0.900439i \(0.356754\pi\)
\(692\) 0 0
\(693\) −0.158478 −0.00602008
\(694\) 0 0
\(695\) 13.8314 0.524653
\(696\) 0 0
\(697\) 2.15293 0.0815480
\(698\) 0 0
\(699\) −20.3739 −0.770610
\(700\) 0 0
\(701\) 21.2294 0.801822 0.400911 0.916117i \(-0.368694\pi\)
0.400911 + 0.916117i \(0.368694\pi\)
\(702\) 0 0
\(703\) 0.224705 0.00847490
\(704\) 0 0
\(705\) −11.0112 −0.414706
\(706\) 0 0
\(707\) 1.34602 0.0506222
\(708\) 0 0
\(709\) 7.50721 0.281939 0.140970 0.990014i \(-0.454978\pi\)
0.140970 + 0.990014i \(0.454978\pi\)
\(710\) 0 0
\(711\) 1.63236 0.0612185
\(712\) 0 0
\(713\) 12.1590 0.455358
\(714\) 0 0
\(715\) −3.07136 −0.114862
\(716\) 0 0
\(717\) 5.80897 0.216940
\(718\) 0 0
\(719\) 12.2603 0.457232 0.228616 0.973517i \(-0.426580\pi\)
0.228616 + 0.973517i \(0.426580\pi\)
\(720\) 0 0
\(721\) −1.88917 −0.0703563
\(722\) 0 0
\(723\) 4.50283 0.167462
\(724\) 0 0
\(725\) 0.681378 0.0253057
\(726\) 0 0
\(727\) 33.5974 1.24606 0.623029 0.782198i \(-0.285902\pi\)
0.623029 + 0.782198i \(0.285902\pi\)
\(728\) 0 0
\(729\) 20.7220 0.767482
\(730\) 0 0
\(731\) 4.42943 0.163828
\(732\) 0 0
\(733\) 7.39520 0.273148 0.136574 0.990630i \(-0.456391\pi\)
0.136574 + 0.990630i \(0.456391\pi\)
\(734\) 0 0
\(735\) 18.5745 0.685132
\(736\) 0 0
\(737\) −5.61321 −0.206765
\(738\) 0 0
\(739\) 8.78108 0.323017 0.161509 0.986871i \(-0.448364\pi\)
0.161509 + 0.986871i \(0.448364\pi\)
\(740\) 0 0
\(741\) 12.8093 0.470560
\(742\) 0 0
\(743\) −16.3641 −0.600342 −0.300171 0.953885i \(-0.597044\pi\)
−0.300171 + 0.953885i \(0.597044\pi\)
\(744\) 0 0
\(745\) 28.2091 1.03350
\(746\) 0 0
\(747\) 1.51804 0.0555422
\(748\) 0 0
\(749\) 4.00713 0.146418
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −34.2895 −1.24958
\(754\) 0 0
\(755\) −4.96818 −0.180810
\(756\) 0 0
\(757\) −45.0818 −1.63853 −0.819263 0.573418i \(-0.805617\pi\)
−0.819263 + 0.573418i \(0.805617\pi\)
\(758\) 0 0
\(759\) −7.04504 −0.255719
\(760\) 0 0
\(761\) 24.6919 0.895080 0.447540 0.894264i \(-0.352300\pi\)
0.447540 + 0.894264i \(0.352300\pi\)
\(762\) 0 0
\(763\) 7.11033 0.257411
\(764\) 0 0
\(765\) 0.754766 0.0272886
\(766\) 0 0
\(767\) −7.71249 −0.278482
\(768\) 0 0
\(769\) −45.9969 −1.65869 −0.829346 0.558736i \(-0.811287\pi\)
−0.829346 + 0.558736i \(0.811287\pi\)
\(770\) 0 0
\(771\) −5.64088 −0.203151
\(772\) 0 0
\(773\) −25.5026 −0.917266 −0.458633 0.888626i \(-0.651661\pi\)
−0.458633 + 0.888626i \(0.651661\pi\)
\(774\) 0 0
\(775\) 5.57641 0.200311
\(776\) 0 0
\(777\) −0.107290 −0.00384900
\(778\) 0 0
\(779\) −4.32260 −0.154873
\(780\) 0 0
\(781\) −2.76385 −0.0988982
\(782\) 0 0
\(783\) 1.10818 0.0396031
\(784\) 0 0
\(785\) −4.99258 −0.178193
\(786\) 0 0
\(787\) −40.2584 −1.43506 −0.717528 0.696530i \(-0.754726\pi\)
−0.717528 + 0.696530i \(0.754726\pi\)
\(788\) 0 0
\(789\) −30.4766 −1.08499
\(790\) 0 0
\(791\) 7.58040 0.269528
\(792\) 0 0
\(793\) −39.4416 −1.40061
\(794\) 0 0
\(795\) −20.8879 −0.740816
\(796\) 0 0
\(797\) 33.5588 1.18871 0.594357 0.804201i \(-0.297407\pi\)
0.594357 + 0.804201i \(0.297407\pi\)
\(798\) 0 0
\(799\) −3.90632 −0.138196
\(800\) 0 0
\(801\) 4.48436 0.158447
\(802\) 0 0
\(803\) 3.77621 0.133259
\(804\) 0 0
\(805\) −4.54127 −0.160059
\(806\) 0 0
\(807\) 34.1583 1.20243
\(808\) 0 0
\(809\) −30.7743 −1.08197 −0.540983 0.841034i \(-0.681948\pi\)
−0.540983 + 0.841034i \(0.681948\pi\)
\(810\) 0 0
\(811\) −12.3081 −0.432195 −0.216097 0.976372i \(-0.569333\pi\)
−0.216097 + 0.976372i \(0.569333\pi\)
\(812\) 0 0
\(813\) 37.1285 1.30215
\(814\) 0 0
\(815\) 31.5124 1.10383
\(816\) 0 0
\(817\) −8.89331 −0.311138
\(818\) 0 0
\(819\) −0.915374 −0.0319858
\(820\) 0 0
\(821\) 1.58104 0.0551785 0.0275893 0.999619i \(-0.491217\pi\)
0.0275893 + 0.999619i \(0.491217\pi\)
\(822\) 0 0
\(823\) −1.92788 −0.0672016 −0.0336008 0.999435i \(-0.510697\pi\)
−0.0336008 + 0.999435i \(0.510697\pi\)
\(824\) 0 0
\(825\) −3.23103 −0.112490
\(826\) 0 0
\(827\) −10.3693 −0.360575 −0.180287 0.983614i \(-0.557703\pi\)
−0.180287 + 0.983614i \(0.557703\pi\)
\(828\) 0 0
\(829\) 41.8729 1.45431 0.727154 0.686475i \(-0.240843\pi\)
0.727154 + 0.686475i \(0.240843\pi\)
\(830\) 0 0
\(831\) −45.9948 −1.59554
\(832\) 0 0
\(833\) 6.58947 0.228312
\(834\) 0 0
\(835\) −19.2662 −0.666735
\(836\) 0 0
\(837\) 9.06936 0.313483
\(838\) 0 0
\(839\) −43.3683 −1.49724 −0.748620 0.662999i \(-0.769283\pi\)
−0.748620 + 0.662999i \(0.769283\pi\)
\(840\) 0 0
\(841\) −28.9430 −0.998036
\(842\) 0 0
\(843\) −2.64693 −0.0911652
\(844\) 0 0
\(845\) 1.29984 0.0447158
\(846\) 0 0
\(847\) 5.29831 0.182052
\(848\) 0 0
\(849\) −52.0854 −1.78756
\(850\) 0 0
\(851\) −0.713841 −0.0244702
\(852\) 0 0
\(853\) −23.6270 −0.808972 −0.404486 0.914544i \(-0.632550\pi\)
−0.404486 + 0.914544i \(0.632550\pi\)
\(854\) 0 0
\(855\) −1.51540 −0.0518256
\(856\) 0 0
\(857\) 35.0946 1.19881 0.599405 0.800446i \(-0.295404\pi\)
0.599405 + 0.800446i \(0.295404\pi\)
\(858\) 0 0
\(859\) 5.17267 0.176489 0.0882446 0.996099i \(-0.471874\pi\)
0.0882446 + 0.996099i \(0.471874\pi\)
\(860\) 0 0
\(861\) 2.06391 0.0703380
\(862\) 0 0
\(863\) −55.3885 −1.88545 −0.942723 0.333575i \(-0.891745\pi\)
−0.942723 + 0.333575i \(0.891745\pi\)
\(864\) 0 0
\(865\) −4.54762 −0.154624
\(866\) 0 0
\(867\) −30.1422 −1.02368
\(868\) 0 0
\(869\) 1.86270 0.0631879
\(870\) 0 0
\(871\) −32.4221 −1.09858
\(872\) 0 0
\(873\) 7.29384 0.246859
\(874\) 0 0
\(875\) −5.73042 −0.193724
\(876\) 0 0
\(877\) 22.7533 0.768323 0.384161 0.923266i \(-0.374491\pi\)
0.384161 + 0.923266i \(0.374491\pi\)
\(878\) 0 0
\(879\) 51.5829 1.73985
\(880\) 0 0
\(881\) −28.8757 −0.972848 −0.486424 0.873723i \(-0.661699\pi\)
−0.486424 + 0.873723i \(0.661699\pi\)
\(882\) 0 0
\(883\) 21.1280 0.711013 0.355507 0.934674i \(-0.384308\pi\)
0.355507 + 0.934674i \(0.384308\pi\)
\(884\) 0 0
\(885\) 6.09635 0.204927
\(886\) 0 0
\(887\) 30.3497 1.01904 0.509522 0.860458i \(-0.329822\pi\)
0.509522 + 0.860458i \(0.329822\pi\)
\(888\) 0 0
\(889\) −5.75676 −0.193076
\(890\) 0 0
\(891\) −6.20936 −0.208021
\(892\) 0 0
\(893\) 7.84302 0.262457
\(894\) 0 0
\(895\) 8.52403 0.284927
\(896\) 0 0
\(897\) −40.6924 −1.35868
\(898\) 0 0
\(899\) 0.466196 0.0155485
\(900\) 0 0
\(901\) −7.41015 −0.246868
\(902\) 0 0
\(903\) 4.24629 0.141308
\(904\) 0 0
\(905\) 30.0475 0.998813
\(906\) 0 0
\(907\) 59.5499 1.97732 0.988660 0.150169i \(-0.0479819\pi\)
0.988660 + 0.150169i \(0.0479819\pi\)
\(908\) 0 0
\(909\) −1.42689 −0.0473270
\(910\) 0 0
\(911\) −14.8283 −0.491283 −0.245642 0.969361i \(-0.578999\pi\)
−0.245642 + 0.969361i \(0.578999\pi\)
\(912\) 0 0
\(913\) 1.73225 0.0573290
\(914\) 0 0
\(915\) 31.1767 1.03067
\(916\) 0 0
\(917\) −10.2555 −0.338667
\(918\) 0 0
\(919\) −45.0890 −1.48735 −0.743674 0.668542i \(-0.766919\pi\)
−0.743674 + 0.668542i \(0.766919\pi\)
\(920\) 0 0
\(921\) −0.166079 −0.00547250
\(922\) 0 0
\(923\) −15.9641 −0.525464
\(924\) 0 0
\(925\) −0.327385 −0.0107644
\(926\) 0 0
\(927\) 2.00267 0.0657765
\(928\) 0 0
\(929\) 5.36673 0.176077 0.0880383 0.996117i \(-0.471940\pi\)
0.0880383 + 0.996117i \(0.471940\pi\)
\(930\) 0 0
\(931\) −13.2302 −0.433602
\(932\) 0 0
\(933\) 37.3581 1.22305
\(934\) 0 0
\(935\) 0.861269 0.0281665
\(936\) 0 0
\(937\) −0.517479 −0.0169053 −0.00845265 0.999964i \(-0.502691\pi\)
−0.00845265 + 0.999964i \(0.502691\pi\)
\(938\) 0 0
\(939\) −15.1259 −0.493614
\(940\) 0 0
\(941\) 20.9991 0.684552 0.342276 0.939599i \(-0.388802\pi\)
0.342276 + 0.939599i \(0.388802\pi\)
\(942\) 0 0
\(943\) 13.7320 0.447176
\(944\) 0 0
\(945\) −3.38732 −0.110189
\(946\) 0 0
\(947\) −23.4674 −0.762587 −0.381293 0.924454i \(-0.624521\pi\)
−0.381293 + 0.924454i \(0.624521\pi\)
\(948\) 0 0
\(949\) 21.8115 0.708031
\(950\) 0 0
\(951\) 39.6543 1.28588
\(952\) 0 0
\(953\) 11.5154 0.373019 0.186510 0.982453i \(-0.440282\pi\)
0.186510 + 0.982453i \(0.440282\pi\)
\(954\) 0 0
\(955\) −1.24159 −0.0401770
\(956\) 0 0
\(957\) −0.270119 −0.00873170
\(958\) 0 0
\(959\) −3.22251 −0.104060
\(960\) 0 0
\(961\) −27.1846 −0.876924
\(962\) 0 0
\(963\) −4.24790 −0.136887
\(964\) 0 0
\(965\) 17.1946 0.553514
\(966\) 0 0
\(967\) 45.9435 1.47744 0.738722 0.674010i \(-0.235429\pi\)
0.738722 + 0.674010i \(0.235429\pi\)
\(968\) 0 0
\(969\) −3.59197 −0.115391
\(970\) 0 0
\(971\) 24.3784 0.782340 0.391170 0.920318i \(-0.372070\pi\)
0.391170 + 0.920318i \(0.372070\pi\)
\(972\) 0 0
\(973\) 4.70391 0.150800
\(974\) 0 0
\(975\) −18.6625 −0.597679
\(976\) 0 0
\(977\) −6.75204 −0.216017 −0.108008 0.994150i \(-0.534447\pi\)
−0.108008 + 0.994150i \(0.534447\pi\)
\(978\) 0 0
\(979\) 5.11714 0.163544
\(980\) 0 0
\(981\) −7.53754 −0.240655
\(982\) 0 0
\(983\) 16.2737 0.519051 0.259525 0.965736i \(-0.416434\pi\)
0.259525 + 0.965736i \(0.416434\pi\)
\(984\) 0 0
\(985\) 9.24127 0.294451
\(986\) 0 0
\(987\) −3.74481 −0.119199
\(988\) 0 0
\(989\) 28.2522 0.898368
\(990\) 0 0
\(991\) −30.7447 −0.976637 −0.488319 0.872665i \(-0.662390\pi\)
−0.488319 + 0.872665i \(0.662390\pi\)
\(992\) 0 0
\(993\) −1.10088 −0.0349355
\(994\) 0 0
\(995\) 27.4277 0.869516
\(996\) 0 0
\(997\) −59.8157 −1.89438 −0.947191 0.320670i \(-0.896092\pi\)
−0.947191 + 0.320670i \(0.896092\pi\)
\(998\) 0 0
\(999\) −0.532452 −0.0168460
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.1.38 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.38 44 1.1 even 1 trivial