Properties

Label 6008.2.a.b.1.41
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 1.41
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.62887 q^{3} -0.385949 q^{5} +1.06025 q^{7} +3.91098 q^{9} +O(q^{10})\) \(q+2.62887 q^{3} -0.385949 q^{5} +1.06025 q^{7} +3.91098 q^{9} -3.06623 q^{11} -4.43652 q^{13} -1.01461 q^{15} -2.91886 q^{17} -0.422058 q^{19} +2.78728 q^{21} -0.921411 q^{23} -4.85104 q^{25} +2.39486 q^{27} -8.01261 q^{29} +6.77228 q^{31} -8.06074 q^{33} -0.409204 q^{35} +4.94195 q^{37} -11.6631 q^{39} +7.67152 q^{41} +1.55444 q^{43} -1.50944 q^{45} -4.43923 q^{47} -5.87586 q^{49} -7.67332 q^{51} -9.11898 q^{53} +1.18341 q^{55} -1.10954 q^{57} +1.46728 q^{59} +2.75627 q^{61} +4.14664 q^{63} +1.71227 q^{65} -11.8281 q^{67} -2.42228 q^{69} +8.47433 q^{71} -14.0133 q^{73} -12.7528 q^{75} -3.25099 q^{77} -10.1827 q^{79} -5.43717 q^{81} +13.7930 q^{83} +1.12653 q^{85} -21.0642 q^{87} +2.11756 q^{89} -4.70384 q^{91} +17.8035 q^{93} +0.162893 q^{95} +1.01462 q^{97} -11.9920 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) 2.62887 1.51778 0.758891 0.651218i \(-0.225742\pi\)
0.758891 + 0.651218i \(0.225742\pi\)
\(4\) 0 0
\(5\) −0.385949 −0.172602 −0.0863008 0.996269i \(-0.527505\pi\)
−0.0863008 + 0.996269i \(0.527505\pi\)
\(6\) 0 0
\(7\) 1.06025 0.400738 0.200369 0.979720i \(-0.435786\pi\)
0.200369 + 0.979720i \(0.435786\pi\)
\(8\) 0 0
\(9\) 3.91098 1.30366
\(10\) 0 0
\(11\) −3.06623 −0.924504 −0.462252 0.886749i \(-0.652959\pi\)
−0.462252 + 0.886749i \(0.652959\pi\)
\(12\) 0 0
\(13\) −4.43652 −1.23047 −0.615235 0.788344i \(-0.710939\pi\)
−0.615235 + 0.788344i \(0.710939\pi\)
\(14\) 0 0
\(15\) −1.01461 −0.261971
\(16\) 0 0
\(17\) −2.91886 −0.707928 −0.353964 0.935259i \(-0.615166\pi\)
−0.353964 + 0.935259i \(0.615166\pi\)
\(18\) 0 0
\(19\) −0.422058 −0.0968267 −0.0484134 0.998827i \(-0.515416\pi\)
−0.0484134 + 0.998827i \(0.515416\pi\)
\(20\) 0 0
\(21\) 2.78728 0.608233
\(22\) 0 0
\(23\) −0.921411 −0.192128 −0.0960638 0.995375i \(-0.530625\pi\)
−0.0960638 + 0.995375i \(0.530625\pi\)
\(24\) 0 0
\(25\) −4.85104 −0.970209
\(26\) 0 0
\(27\) 2.39486 0.460890
\(28\) 0 0
\(29\) −8.01261 −1.48791 −0.743953 0.668233i \(-0.767051\pi\)
−0.743953 + 0.668233i \(0.767051\pi\)
\(30\) 0 0
\(31\) 6.77228 1.21634 0.608169 0.793808i \(-0.291904\pi\)
0.608169 + 0.793808i \(0.291904\pi\)
\(32\) 0 0
\(33\) −8.06074 −1.40320
\(34\) 0 0
\(35\) −0.409204 −0.0691681
\(36\) 0 0
\(37\) 4.94195 0.812452 0.406226 0.913773i \(-0.366845\pi\)
0.406226 + 0.913773i \(0.366845\pi\)
\(38\) 0 0
\(39\) −11.6631 −1.86758
\(40\) 0 0
\(41\) 7.67152 1.19809 0.599045 0.800715i \(-0.295547\pi\)
0.599045 + 0.800715i \(0.295547\pi\)
\(42\) 0 0
\(43\) 1.55444 0.237049 0.118525 0.992951i \(-0.462184\pi\)
0.118525 + 0.992951i \(0.462184\pi\)
\(44\) 0 0
\(45\) −1.50944 −0.225014
\(46\) 0 0
\(47\) −4.43923 −0.647528 −0.323764 0.946138i \(-0.604948\pi\)
−0.323764 + 0.946138i \(0.604948\pi\)
\(48\) 0 0
\(49\) −5.87586 −0.839409
\(50\) 0 0
\(51\) −7.67332 −1.07448
\(52\) 0 0
\(53\) −9.11898 −1.25259 −0.626294 0.779587i \(-0.715429\pi\)
−0.626294 + 0.779587i \(0.715429\pi\)
\(54\) 0 0
\(55\) 1.18341 0.159571
\(56\) 0 0
\(57\) −1.10954 −0.146962
\(58\) 0 0
\(59\) 1.46728 0.191024 0.0955121 0.995428i \(-0.469551\pi\)
0.0955121 + 0.995428i \(0.469551\pi\)
\(60\) 0 0
\(61\) 2.75627 0.352904 0.176452 0.984309i \(-0.443538\pi\)
0.176452 + 0.984309i \(0.443538\pi\)
\(62\) 0 0
\(63\) 4.14664 0.522427
\(64\) 0 0
\(65\) 1.71227 0.212381
\(66\) 0 0
\(67\) −11.8281 −1.44503 −0.722516 0.691354i \(-0.757014\pi\)
−0.722516 + 0.691354i \(0.757014\pi\)
\(68\) 0 0
\(69\) −2.42228 −0.291608
\(70\) 0 0
\(71\) 8.47433 1.00572 0.502859 0.864368i \(-0.332281\pi\)
0.502859 + 0.864368i \(0.332281\pi\)
\(72\) 0 0
\(73\) −14.0133 −1.64014 −0.820068 0.572266i \(-0.806064\pi\)
−0.820068 + 0.572266i \(0.806064\pi\)
\(74\) 0 0
\(75\) −12.7528 −1.47256
\(76\) 0 0
\(77\) −3.25099 −0.370484
\(78\) 0 0
\(79\) −10.1827 −1.14564 −0.572822 0.819679i \(-0.694152\pi\)
−0.572822 + 0.819679i \(0.694152\pi\)
\(80\) 0 0
\(81\) −5.43717 −0.604130
\(82\) 0 0
\(83\) 13.7930 1.51398 0.756989 0.653427i \(-0.226669\pi\)
0.756989 + 0.653427i \(0.226669\pi\)
\(84\) 0 0
\(85\) 1.12653 0.122189
\(86\) 0 0
\(87\) −21.0642 −2.25831
\(88\) 0 0
\(89\) 2.11756 0.224461 0.112230 0.993682i \(-0.464201\pi\)
0.112230 + 0.993682i \(0.464201\pi\)
\(90\) 0 0
\(91\) −4.70384 −0.493097
\(92\) 0 0
\(93\) 17.8035 1.84613
\(94\) 0 0
\(95\) 0.162893 0.0167124
\(96\) 0 0
\(97\) 1.01462 0.103019 0.0515095 0.998673i \(-0.483597\pi\)
0.0515095 + 0.998673i \(0.483597\pi\)
\(98\) 0 0
\(99\) −11.9920 −1.20524
\(100\) 0 0
\(101\) 13.3078 1.32417 0.662086 0.749428i \(-0.269671\pi\)
0.662086 + 0.749428i \(0.269671\pi\)
\(102\) 0 0
\(103\) −14.9579 −1.47384 −0.736922 0.675977i \(-0.763722\pi\)
−0.736922 + 0.675977i \(0.763722\pi\)
\(104\) 0 0
\(105\) −1.07575 −0.104982
\(106\) 0 0
\(107\) −6.42206 −0.620844 −0.310422 0.950599i \(-0.600470\pi\)
−0.310422 + 0.950599i \(0.600470\pi\)
\(108\) 0 0
\(109\) −14.2439 −1.36432 −0.682158 0.731204i \(-0.738959\pi\)
−0.682158 + 0.731204i \(0.738959\pi\)
\(110\) 0 0
\(111\) 12.9918 1.23312
\(112\) 0 0
\(113\) −19.6439 −1.84794 −0.923970 0.382464i \(-0.875075\pi\)
−0.923970 + 0.382464i \(0.875075\pi\)
\(114\) 0 0
\(115\) 0.355618 0.0331615
\(116\) 0 0
\(117\) −17.3512 −1.60412
\(118\) 0 0
\(119\) −3.09473 −0.283694
\(120\) 0 0
\(121\) −1.59821 −0.145292
\(122\) 0 0
\(123\) 20.1675 1.81844
\(124\) 0 0
\(125\) 3.80200 0.340061
\(126\) 0 0
\(127\) 12.9335 1.14766 0.573832 0.818973i \(-0.305456\pi\)
0.573832 + 0.818973i \(0.305456\pi\)
\(128\) 0 0
\(129\) 4.08642 0.359789
\(130\) 0 0
\(131\) −3.47119 −0.303280 −0.151640 0.988436i \(-0.548455\pi\)
−0.151640 + 0.988436i \(0.548455\pi\)
\(132\) 0 0
\(133\) −0.447489 −0.0388022
\(134\) 0 0
\(135\) −0.924292 −0.0795504
\(136\) 0 0
\(137\) 0.485435 0.0414735 0.0207367 0.999785i \(-0.493399\pi\)
0.0207367 + 0.999785i \(0.493399\pi\)
\(138\) 0 0
\(139\) −3.43389 −0.291259 −0.145629 0.989339i \(-0.546521\pi\)
−0.145629 + 0.989339i \(0.546521\pi\)
\(140\) 0 0
\(141\) −11.6702 −0.982806
\(142\) 0 0
\(143\) 13.6034 1.13757
\(144\) 0 0
\(145\) 3.09246 0.256815
\(146\) 0 0
\(147\) −15.4469 −1.27404
\(148\) 0 0
\(149\) 12.6436 1.03581 0.517903 0.855440i \(-0.326713\pi\)
0.517903 + 0.855440i \(0.326713\pi\)
\(150\) 0 0
\(151\) −6.80235 −0.553568 −0.276784 0.960932i \(-0.589269\pi\)
−0.276784 + 0.960932i \(0.589269\pi\)
\(152\) 0 0
\(153\) −11.4156 −0.922897
\(154\) 0 0
\(155\) −2.61375 −0.209942
\(156\) 0 0
\(157\) −17.1570 −1.36928 −0.684641 0.728881i \(-0.740041\pi\)
−0.684641 + 0.728881i \(0.740041\pi\)
\(158\) 0 0
\(159\) −23.9727 −1.90116
\(160\) 0 0
\(161\) −0.976931 −0.0769929
\(162\) 0 0
\(163\) −5.85431 −0.458545 −0.229272 0.973362i \(-0.573635\pi\)
−0.229272 + 0.973362i \(0.573635\pi\)
\(164\) 0 0
\(165\) 3.11103 0.242194
\(166\) 0 0
\(167\) 6.83009 0.528528 0.264264 0.964450i \(-0.414871\pi\)
0.264264 + 0.964450i \(0.414871\pi\)
\(168\) 0 0
\(169\) 6.68273 0.514056
\(170\) 0 0
\(171\) −1.65066 −0.126229
\(172\) 0 0
\(173\) 7.75144 0.589331 0.294665 0.955600i \(-0.404792\pi\)
0.294665 + 0.955600i \(0.404792\pi\)
\(174\) 0 0
\(175\) −5.14334 −0.388800
\(176\) 0 0
\(177\) 3.85731 0.289933
\(178\) 0 0
\(179\) 12.8904 0.963471 0.481735 0.876317i \(-0.340007\pi\)
0.481735 + 0.876317i \(0.340007\pi\)
\(180\) 0 0
\(181\) 19.7202 1.46579 0.732897 0.680340i \(-0.238168\pi\)
0.732897 + 0.680340i \(0.238168\pi\)
\(182\) 0 0
\(183\) 7.24589 0.535632
\(184\) 0 0
\(185\) −1.90734 −0.140230
\(186\) 0 0
\(187\) 8.94991 0.654482
\(188\) 0 0
\(189\) 2.53916 0.184696
\(190\) 0 0
\(191\) 18.8115 1.36115 0.680576 0.732678i \(-0.261730\pi\)
0.680576 + 0.732678i \(0.261730\pi\)
\(192\) 0 0
\(193\) −10.8869 −0.783659 −0.391829 0.920038i \(-0.628158\pi\)
−0.391829 + 0.920038i \(0.628158\pi\)
\(194\) 0 0
\(195\) 4.50134 0.322348
\(196\) 0 0
\(197\) −10.7351 −0.764846 −0.382423 0.923987i \(-0.624910\pi\)
−0.382423 + 0.923987i \(0.624910\pi\)
\(198\) 0 0
\(199\) 2.49440 0.176823 0.0884115 0.996084i \(-0.471821\pi\)
0.0884115 + 0.996084i \(0.471821\pi\)
\(200\) 0 0
\(201\) −31.0946 −2.19324
\(202\) 0 0
\(203\) −8.49541 −0.596261
\(204\) 0 0
\(205\) −2.96081 −0.206792
\(206\) 0 0
\(207\) −3.60362 −0.250469
\(208\) 0 0
\(209\) 1.29413 0.0895167
\(210\) 0 0
\(211\) 14.3338 0.986776 0.493388 0.869809i \(-0.335758\pi\)
0.493388 + 0.869809i \(0.335758\pi\)
\(212\) 0 0
\(213\) 22.2780 1.52646
\(214\) 0 0
\(215\) −0.599932 −0.0409150
\(216\) 0 0
\(217\) 7.18034 0.487433
\(218\) 0 0
\(219\) −36.8393 −2.48937
\(220\) 0 0
\(221\) 12.9496 0.871084
\(222\) 0 0
\(223\) 11.4907 0.769471 0.384736 0.923027i \(-0.374293\pi\)
0.384736 + 0.923027i \(0.374293\pi\)
\(224\) 0 0
\(225\) −18.9723 −1.26482
\(226\) 0 0
\(227\) 28.6613 1.90232 0.951159 0.308703i \(-0.0998949\pi\)
0.951159 + 0.308703i \(0.0998949\pi\)
\(228\) 0 0
\(229\) 25.7970 1.70471 0.852356 0.522962i \(-0.175173\pi\)
0.852356 + 0.522962i \(0.175173\pi\)
\(230\) 0 0
\(231\) −8.54644 −0.562314
\(232\) 0 0
\(233\) −12.5583 −0.822719 −0.411360 0.911473i \(-0.634946\pi\)
−0.411360 + 0.911473i \(0.634946\pi\)
\(234\) 0 0
\(235\) 1.71331 0.111764
\(236\) 0 0
\(237\) −26.7691 −1.73884
\(238\) 0 0
\(239\) −28.1629 −1.82171 −0.910854 0.412730i \(-0.864575\pi\)
−0.910854 + 0.412730i \(0.864575\pi\)
\(240\) 0 0
\(241\) −10.9306 −0.704100 −0.352050 0.935981i \(-0.614515\pi\)
−0.352050 + 0.935981i \(0.614515\pi\)
\(242\) 0 0
\(243\) −21.4782 −1.37783
\(244\) 0 0
\(245\) 2.26778 0.144883
\(246\) 0 0
\(247\) 1.87247 0.119142
\(248\) 0 0
\(249\) 36.2601 2.29789
\(250\) 0 0
\(251\) 21.5941 1.36301 0.681505 0.731814i \(-0.261326\pi\)
0.681505 + 0.731814i \(0.261326\pi\)
\(252\) 0 0
\(253\) 2.82526 0.177623
\(254\) 0 0
\(255\) 2.96151 0.185457
\(256\) 0 0
\(257\) −13.0167 −0.811962 −0.405981 0.913882i \(-0.633070\pi\)
−0.405981 + 0.913882i \(0.633070\pi\)
\(258\) 0 0
\(259\) 5.23973 0.325581
\(260\) 0 0
\(261\) −31.3372 −1.93972
\(262\) 0 0
\(263\) 19.6538 1.21190 0.605952 0.795501i \(-0.292792\pi\)
0.605952 + 0.795501i \(0.292792\pi\)
\(264\) 0 0
\(265\) 3.51946 0.216199
\(266\) 0 0
\(267\) 5.56679 0.340682
\(268\) 0 0
\(269\) 15.1920 0.926272 0.463136 0.886287i \(-0.346724\pi\)
0.463136 + 0.886287i \(0.346724\pi\)
\(270\) 0 0
\(271\) 2.16377 0.131440 0.0657199 0.997838i \(-0.479066\pi\)
0.0657199 + 0.997838i \(0.479066\pi\)
\(272\) 0 0
\(273\) −12.3658 −0.748413
\(274\) 0 0
\(275\) 14.8744 0.896962
\(276\) 0 0
\(277\) −10.4628 −0.628649 −0.314325 0.949316i \(-0.601778\pi\)
−0.314325 + 0.949316i \(0.601778\pi\)
\(278\) 0 0
\(279\) 26.4863 1.58569
\(280\) 0 0
\(281\) −11.7212 −0.699227 −0.349613 0.936894i \(-0.613687\pi\)
−0.349613 + 0.936894i \(0.613687\pi\)
\(282\) 0 0
\(283\) −14.8020 −0.879887 −0.439944 0.898025i \(-0.645002\pi\)
−0.439944 + 0.898025i \(0.645002\pi\)
\(284\) 0 0
\(285\) 0.428225 0.0253658
\(286\) 0 0
\(287\) 8.13376 0.480121
\(288\) 0 0
\(289\) −8.48025 −0.498838
\(290\) 0 0
\(291\) 2.66731 0.156360
\(292\) 0 0
\(293\) 6.91494 0.403975 0.201987 0.979388i \(-0.435260\pi\)
0.201987 + 0.979388i \(0.435260\pi\)
\(294\) 0 0
\(295\) −0.566297 −0.0329711
\(296\) 0 0
\(297\) −7.34319 −0.426095
\(298\) 0 0
\(299\) 4.08786 0.236407
\(300\) 0 0
\(301\) 1.64810 0.0949947
\(302\) 0 0
\(303\) 34.9844 2.00980
\(304\) 0 0
\(305\) −1.06378 −0.0609118
\(306\) 0 0
\(307\) 7.00843 0.399992 0.199996 0.979797i \(-0.435907\pi\)
0.199996 + 0.979797i \(0.435907\pi\)
\(308\) 0 0
\(309\) −39.3224 −2.23697
\(310\) 0 0
\(311\) −18.9854 −1.07656 −0.538282 0.842764i \(-0.680927\pi\)
−0.538282 + 0.842764i \(0.680927\pi\)
\(312\) 0 0
\(313\) −4.91551 −0.277841 −0.138921 0.990304i \(-0.544363\pi\)
−0.138921 + 0.990304i \(0.544363\pi\)
\(314\) 0 0
\(315\) −1.60039 −0.0901717
\(316\) 0 0
\(317\) −27.6581 −1.55343 −0.776716 0.629851i \(-0.783116\pi\)
−0.776716 + 0.629851i \(0.783116\pi\)
\(318\) 0 0
\(319\) 24.5685 1.37557
\(320\) 0 0
\(321\) −16.8828 −0.942305
\(322\) 0 0
\(323\) 1.23193 0.0685463
\(324\) 0 0
\(325\) 21.5218 1.19381
\(326\) 0 0
\(327\) −37.4454 −2.07073
\(328\) 0 0
\(329\) −4.70671 −0.259489
\(330\) 0 0
\(331\) 21.0884 1.15912 0.579562 0.814928i \(-0.303224\pi\)
0.579562 + 0.814928i \(0.303224\pi\)
\(332\) 0 0
\(333\) 19.3279 1.05916
\(334\) 0 0
\(335\) 4.56504 0.249415
\(336\) 0 0
\(337\) 27.7334 1.51073 0.755366 0.655303i \(-0.227459\pi\)
0.755366 + 0.655303i \(0.227459\pi\)
\(338\) 0 0
\(339\) −51.6413 −2.80477
\(340\) 0 0
\(341\) −20.7654 −1.12451
\(342\) 0 0
\(343\) −13.6517 −0.737122
\(344\) 0 0
\(345\) 0.934874 0.0503319
\(346\) 0 0
\(347\) −17.2013 −0.923414 −0.461707 0.887032i \(-0.652763\pi\)
−0.461707 + 0.887032i \(0.652763\pi\)
\(348\) 0 0
\(349\) 16.0824 0.860871 0.430435 0.902621i \(-0.358360\pi\)
0.430435 + 0.902621i \(0.358360\pi\)
\(350\) 0 0
\(351\) −10.6248 −0.567112
\(352\) 0 0
\(353\) 26.7167 1.42199 0.710993 0.703199i \(-0.248246\pi\)
0.710993 + 0.703199i \(0.248246\pi\)
\(354\) 0 0
\(355\) −3.27066 −0.173588
\(356\) 0 0
\(357\) −8.13567 −0.430585
\(358\) 0 0
\(359\) −24.5985 −1.29826 −0.649130 0.760678i \(-0.724867\pi\)
−0.649130 + 0.760678i \(0.724867\pi\)
\(360\) 0 0
\(361\) −18.8219 −0.990625
\(362\) 0 0
\(363\) −4.20149 −0.220521
\(364\) 0 0
\(365\) 5.40843 0.283090
\(366\) 0 0
\(367\) −27.6065 −1.44105 −0.720524 0.693430i \(-0.756099\pi\)
−0.720524 + 0.693430i \(0.756099\pi\)
\(368\) 0 0
\(369\) 30.0032 1.56190
\(370\) 0 0
\(371\) −9.66844 −0.501960
\(372\) 0 0
\(373\) 30.8027 1.59490 0.797452 0.603382i \(-0.206181\pi\)
0.797452 + 0.603382i \(0.206181\pi\)
\(374\) 0 0
\(375\) 9.99497 0.516138
\(376\) 0 0
\(377\) 35.5481 1.83082
\(378\) 0 0
\(379\) −12.2838 −0.630978 −0.315489 0.948929i \(-0.602169\pi\)
−0.315489 + 0.948929i \(0.602169\pi\)
\(380\) 0 0
\(381\) 34.0006 1.74190
\(382\) 0 0
\(383\) 0.743755 0.0380041 0.0190020 0.999819i \(-0.493951\pi\)
0.0190020 + 0.999819i \(0.493951\pi\)
\(384\) 0 0
\(385\) 1.25471 0.0639462
\(386\) 0 0
\(387\) 6.07937 0.309032
\(388\) 0 0
\(389\) −8.43706 −0.427776 −0.213888 0.976858i \(-0.568613\pi\)
−0.213888 + 0.976858i \(0.568613\pi\)
\(390\) 0 0
\(391\) 2.68947 0.136012
\(392\) 0 0
\(393\) −9.12533 −0.460312
\(394\) 0 0
\(395\) 3.93001 0.197740
\(396\) 0 0
\(397\) 25.4329 1.27644 0.638219 0.769855i \(-0.279671\pi\)
0.638219 + 0.769855i \(0.279671\pi\)
\(398\) 0 0
\(399\) −1.17639 −0.0588933
\(400\) 0 0
\(401\) −22.4850 −1.12285 −0.561425 0.827528i \(-0.689747\pi\)
−0.561425 + 0.827528i \(0.689747\pi\)
\(402\) 0 0
\(403\) −30.0454 −1.49667
\(404\) 0 0
\(405\) 2.09847 0.104274
\(406\) 0 0
\(407\) −15.1532 −0.751115
\(408\) 0 0
\(409\) 20.5185 1.01457 0.507287 0.861777i \(-0.330648\pi\)
0.507287 + 0.861777i \(0.330648\pi\)
\(410\) 0 0
\(411\) 1.27615 0.0629477
\(412\) 0 0
\(413\) 1.55570 0.0765508
\(414\) 0 0
\(415\) −5.32339 −0.261315
\(416\) 0 0
\(417\) −9.02727 −0.442067
\(418\) 0 0
\(419\) 30.2145 1.47607 0.738037 0.674761i \(-0.235753\pi\)
0.738037 + 0.674761i \(0.235753\pi\)
\(420\) 0 0
\(421\) 31.1839 1.51981 0.759905 0.650034i \(-0.225245\pi\)
0.759905 + 0.650034i \(0.225245\pi\)
\(422\) 0 0
\(423\) −17.3617 −0.844156
\(424\) 0 0
\(425\) 14.1595 0.686838
\(426\) 0 0
\(427\) 2.92235 0.141422
\(428\) 0 0
\(429\) 35.7617 1.72659
\(430\) 0 0
\(431\) 3.03702 0.146288 0.0731441 0.997321i \(-0.476697\pi\)
0.0731441 + 0.997321i \(0.476697\pi\)
\(432\) 0 0
\(433\) −31.7544 −1.52602 −0.763010 0.646387i \(-0.776279\pi\)
−0.763010 + 0.646387i \(0.776279\pi\)
\(434\) 0 0
\(435\) 8.12968 0.389789
\(436\) 0 0
\(437\) 0.388889 0.0186031
\(438\) 0 0
\(439\) −20.0020 −0.954643 −0.477321 0.878729i \(-0.658392\pi\)
−0.477321 + 0.878729i \(0.658392\pi\)
\(440\) 0 0
\(441\) −22.9804 −1.09430
\(442\) 0 0
\(443\) −34.8403 −1.65531 −0.827657 0.561234i \(-0.810327\pi\)
−0.827657 + 0.561234i \(0.810327\pi\)
\(444\) 0 0
\(445\) −0.817268 −0.0387422
\(446\) 0 0
\(447\) 33.2385 1.57213
\(448\) 0 0
\(449\) 0.947307 0.0447062 0.0223531 0.999750i \(-0.492884\pi\)
0.0223531 + 0.999750i \(0.492884\pi\)
\(450\) 0 0
\(451\) −23.5227 −1.10764
\(452\) 0 0
\(453\) −17.8825 −0.840195
\(454\) 0 0
\(455\) 1.81544 0.0851092
\(456\) 0 0
\(457\) −37.6267 −1.76010 −0.880052 0.474878i \(-0.842492\pi\)
−0.880052 + 0.474878i \(0.842492\pi\)
\(458\) 0 0
\(459\) −6.99025 −0.326277
\(460\) 0 0
\(461\) 0.853835 0.0397671 0.0198835 0.999802i \(-0.493670\pi\)
0.0198835 + 0.999802i \(0.493670\pi\)
\(462\) 0 0
\(463\) 11.3267 0.526397 0.263199 0.964742i \(-0.415223\pi\)
0.263199 + 0.964742i \(0.415223\pi\)
\(464\) 0 0
\(465\) −6.87123 −0.318646
\(466\) 0 0
\(467\) −41.3143 −1.91180 −0.955899 0.293696i \(-0.905115\pi\)
−0.955899 + 0.293696i \(0.905115\pi\)
\(468\) 0 0
\(469\) −12.5408 −0.579080
\(470\) 0 0
\(471\) −45.1037 −2.07827
\(472\) 0 0
\(473\) −4.76626 −0.219153
\(474\) 0 0
\(475\) 2.04742 0.0939422
\(476\) 0 0
\(477\) −35.6642 −1.63295
\(478\) 0 0
\(479\) 24.2435 1.10772 0.553858 0.832611i \(-0.313155\pi\)
0.553858 + 0.832611i \(0.313155\pi\)
\(480\) 0 0
\(481\) −21.9251 −0.999698
\(482\) 0 0
\(483\) −2.56823 −0.116858
\(484\) 0 0
\(485\) −0.391591 −0.0177812
\(486\) 0 0
\(487\) −17.2489 −0.781621 −0.390811 0.920471i \(-0.627805\pi\)
−0.390811 + 0.920471i \(0.627805\pi\)
\(488\) 0 0
\(489\) −15.3902 −0.695971
\(490\) 0 0
\(491\) 1.32041 0.0595892 0.0297946 0.999556i \(-0.490515\pi\)
0.0297946 + 0.999556i \(0.490515\pi\)
\(492\) 0 0
\(493\) 23.3877 1.05333
\(494\) 0 0
\(495\) 4.62829 0.208026
\(496\) 0 0
\(497\) 8.98495 0.403030
\(498\) 0 0
\(499\) −4.79336 −0.214580 −0.107290 0.994228i \(-0.534217\pi\)
−0.107290 + 0.994228i \(0.534217\pi\)
\(500\) 0 0
\(501\) 17.9554 0.802190
\(502\) 0 0
\(503\) −12.3724 −0.551657 −0.275829 0.961207i \(-0.588952\pi\)
−0.275829 + 0.961207i \(0.588952\pi\)
\(504\) 0 0
\(505\) −5.13611 −0.228554
\(506\) 0 0
\(507\) 17.5681 0.780225
\(508\) 0 0
\(509\) 38.2590 1.69580 0.847901 0.530155i \(-0.177866\pi\)
0.847901 + 0.530155i \(0.177866\pi\)
\(510\) 0 0
\(511\) −14.8577 −0.657266
\(512\) 0 0
\(513\) −1.01077 −0.0446265
\(514\) 0 0
\(515\) 5.77298 0.254388
\(516\) 0 0
\(517\) 13.6117 0.598642
\(518\) 0 0
\(519\) 20.3776 0.894475
\(520\) 0 0
\(521\) −15.4874 −0.678514 −0.339257 0.940694i \(-0.610176\pi\)
−0.339257 + 0.940694i \(0.610176\pi\)
\(522\) 0 0
\(523\) 26.0329 1.13834 0.569170 0.822220i \(-0.307265\pi\)
0.569170 + 0.822220i \(0.307265\pi\)
\(524\) 0 0
\(525\) −13.5212 −0.590113
\(526\) 0 0
\(527\) −19.7673 −0.861079
\(528\) 0 0
\(529\) −22.1510 −0.963087
\(530\) 0 0
\(531\) 5.73852 0.249031
\(532\) 0 0
\(533\) −34.0349 −1.47421
\(534\) 0 0
\(535\) 2.47859 0.107159
\(536\) 0 0
\(537\) 33.8871 1.46234
\(538\) 0 0
\(539\) 18.0168 0.776037
\(540\) 0 0
\(541\) 35.8172 1.53990 0.769952 0.638102i \(-0.220280\pi\)
0.769952 + 0.638102i \(0.220280\pi\)
\(542\) 0 0
\(543\) 51.8420 2.22475
\(544\) 0 0
\(545\) 5.49741 0.235483
\(546\) 0 0
\(547\) 7.76624 0.332060 0.166030 0.986121i \(-0.446905\pi\)
0.166030 + 0.986121i \(0.446905\pi\)
\(548\) 0 0
\(549\) 10.7797 0.460067
\(550\) 0 0
\(551\) 3.38179 0.144069
\(552\) 0 0
\(553\) −10.7963 −0.459104
\(554\) 0 0
\(555\) −5.01416 −0.212839
\(556\) 0 0
\(557\) 38.1611 1.61694 0.808470 0.588538i \(-0.200296\pi\)
0.808470 + 0.588538i \(0.200296\pi\)
\(558\) 0 0
\(559\) −6.89629 −0.291682
\(560\) 0 0
\(561\) 23.5282 0.993361
\(562\) 0 0
\(563\) −5.95868 −0.251129 −0.125564 0.992085i \(-0.540074\pi\)
−0.125564 + 0.992085i \(0.540074\pi\)
\(564\) 0 0
\(565\) 7.58153 0.318957
\(566\) 0 0
\(567\) −5.76478 −0.242098
\(568\) 0 0
\(569\) 40.1828 1.68455 0.842275 0.539048i \(-0.181216\pi\)
0.842275 + 0.539048i \(0.181216\pi\)
\(570\) 0 0
\(571\) 21.1336 0.884416 0.442208 0.896913i \(-0.354195\pi\)
0.442208 + 0.896913i \(0.354195\pi\)
\(572\) 0 0
\(573\) 49.4530 2.06593
\(574\) 0 0
\(575\) 4.46981 0.186404
\(576\) 0 0
\(577\) 19.8944 0.828213 0.414107 0.910228i \(-0.364094\pi\)
0.414107 + 0.910228i \(0.364094\pi\)
\(578\) 0 0
\(579\) −28.6204 −1.18942
\(580\) 0 0
\(581\) 14.6241 0.606710
\(582\) 0 0
\(583\) 27.9609 1.15802
\(584\) 0 0
\(585\) 6.69666 0.276873
\(586\) 0 0
\(587\) 5.59029 0.230736 0.115368 0.993323i \(-0.463195\pi\)
0.115368 + 0.993323i \(0.463195\pi\)
\(588\) 0 0
\(589\) −2.85830 −0.117774
\(590\) 0 0
\(591\) −28.2213 −1.16087
\(592\) 0 0
\(593\) 16.9966 0.697967 0.348984 0.937129i \(-0.386527\pi\)
0.348984 + 0.937129i \(0.386527\pi\)
\(594\) 0 0
\(595\) 1.19441 0.0489660
\(596\) 0 0
\(597\) 6.55745 0.268379
\(598\) 0 0
\(599\) 37.0485 1.51376 0.756881 0.653553i \(-0.226722\pi\)
0.756881 + 0.653553i \(0.226722\pi\)
\(600\) 0 0
\(601\) −6.79139 −0.277027 −0.138513 0.990361i \(-0.544232\pi\)
−0.138513 + 0.990361i \(0.544232\pi\)
\(602\) 0 0
\(603\) −46.2595 −1.88383
\(604\) 0 0
\(605\) 0.616827 0.0250776
\(606\) 0 0
\(607\) 23.5147 0.954432 0.477216 0.878786i \(-0.341646\pi\)
0.477216 + 0.878786i \(0.341646\pi\)
\(608\) 0 0
\(609\) −22.3334 −0.904994
\(610\) 0 0
\(611\) 19.6947 0.796763
\(612\) 0 0
\(613\) −34.4466 −1.39129 −0.695643 0.718388i \(-0.744880\pi\)
−0.695643 + 0.718388i \(0.744880\pi\)
\(614\) 0 0
\(615\) −7.78361 −0.313865
\(616\) 0 0
\(617\) 2.77501 0.111718 0.0558589 0.998439i \(-0.482210\pi\)
0.0558589 + 0.998439i \(0.482210\pi\)
\(618\) 0 0
\(619\) −35.8593 −1.44131 −0.720653 0.693295i \(-0.756158\pi\)
−0.720653 + 0.693295i \(0.756158\pi\)
\(620\) 0 0
\(621\) −2.20665 −0.0885497
\(622\) 0 0
\(623\) 2.24515 0.0899500
\(624\) 0 0
\(625\) 22.7878 0.911514
\(626\) 0 0
\(627\) 3.40210 0.135867
\(628\) 0 0
\(629\) −14.4249 −0.575157
\(630\) 0 0
\(631\) −29.2138 −1.16298 −0.581491 0.813553i \(-0.697530\pi\)
−0.581491 + 0.813553i \(0.697530\pi\)
\(632\) 0 0
\(633\) 37.6816 1.49771
\(634\) 0 0
\(635\) −4.99168 −0.198089
\(636\) 0 0
\(637\) 26.0684 1.03287
\(638\) 0 0
\(639\) 33.1430 1.31112
\(640\) 0 0
\(641\) −0.769270 −0.0303843 −0.0151922 0.999885i \(-0.504836\pi\)
−0.0151922 + 0.999885i \(0.504836\pi\)
\(642\) 0 0
\(643\) −31.0795 −1.22566 −0.612829 0.790216i \(-0.709968\pi\)
−0.612829 + 0.790216i \(0.709968\pi\)
\(644\) 0 0
\(645\) −1.57715 −0.0621001
\(646\) 0 0
\(647\) 24.1262 0.948498 0.474249 0.880391i \(-0.342720\pi\)
0.474249 + 0.880391i \(0.342720\pi\)
\(648\) 0 0
\(649\) −4.49904 −0.176603
\(650\) 0 0
\(651\) 18.8762 0.739817
\(652\) 0 0
\(653\) −19.6172 −0.767681 −0.383841 0.923399i \(-0.625399\pi\)
−0.383841 + 0.923399i \(0.625399\pi\)
\(654\) 0 0
\(655\) 1.33970 0.0523465
\(656\) 0 0
\(657\) −54.8059 −2.13818
\(658\) 0 0
\(659\) −13.2915 −0.517761 −0.258881 0.965909i \(-0.583354\pi\)
−0.258881 + 0.965909i \(0.583354\pi\)
\(660\) 0 0
\(661\) 39.7632 1.54661 0.773306 0.634034i \(-0.218602\pi\)
0.773306 + 0.634034i \(0.218602\pi\)
\(662\) 0 0
\(663\) 34.0429 1.32211
\(664\) 0 0
\(665\) 0.172708 0.00669732
\(666\) 0 0
\(667\) 7.38291 0.285868
\(668\) 0 0
\(669\) 30.2075 1.16789
\(670\) 0 0
\(671\) −8.45137 −0.326262
\(672\) 0 0
\(673\) −27.3955 −1.05602 −0.528009 0.849238i \(-0.677061\pi\)
−0.528009 + 0.849238i \(0.677061\pi\)
\(674\) 0 0
\(675\) −11.6176 −0.447160
\(676\) 0 0
\(677\) 29.2926 1.12580 0.562902 0.826523i \(-0.309685\pi\)
0.562902 + 0.826523i \(0.309685\pi\)
\(678\) 0 0
\(679\) 1.07575 0.0412836
\(680\) 0 0
\(681\) 75.3470 2.88730
\(682\) 0 0
\(683\) 7.05739 0.270043 0.135022 0.990843i \(-0.456890\pi\)
0.135022 + 0.990843i \(0.456890\pi\)
\(684\) 0 0
\(685\) −0.187353 −0.00715839
\(686\) 0 0
\(687\) 67.8170 2.58738
\(688\) 0 0
\(689\) 40.4566 1.54127
\(690\) 0 0
\(691\) −49.9069 −1.89855 −0.949275 0.314448i \(-0.898181\pi\)
−0.949275 + 0.314448i \(0.898181\pi\)
\(692\) 0 0
\(693\) −12.7146 −0.482986
\(694\) 0 0
\(695\) 1.32531 0.0502717
\(696\) 0 0
\(697\) −22.3921 −0.848161
\(698\) 0 0
\(699\) −33.0141 −1.24871
\(700\) 0 0
\(701\) −4.71795 −0.178195 −0.0890973 0.996023i \(-0.528398\pi\)
−0.0890973 + 0.996023i \(0.528398\pi\)
\(702\) 0 0
\(703\) −2.08579 −0.0786671
\(704\) 0 0
\(705\) 4.50409 0.169634
\(706\) 0 0
\(707\) 14.1096 0.530647
\(708\) 0 0
\(709\) 13.7207 0.515292 0.257646 0.966239i \(-0.417053\pi\)
0.257646 + 0.966239i \(0.417053\pi\)
\(710\) 0 0
\(711\) −39.8244 −1.49353
\(712\) 0 0
\(713\) −6.24006 −0.233692
\(714\) 0 0
\(715\) −5.25022 −0.196347
\(716\) 0 0
\(717\) −74.0368 −2.76495
\(718\) 0 0
\(719\) −1.45561 −0.0542850 −0.0271425 0.999632i \(-0.508641\pi\)
−0.0271425 + 0.999632i \(0.508641\pi\)
\(720\) 0 0
\(721\) −15.8592 −0.590626
\(722\) 0 0
\(723\) −28.7351 −1.06867
\(724\) 0 0
\(725\) 38.8695 1.44358
\(726\) 0 0
\(727\) 36.8028 1.36494 0.682471 0.730913i \(-0.260906\pi\)
0.682471 + 0.730913i \(0.260906\pi\)
\(728\) 0 0
\(729\) −40.1520 −1.48711
\(730\) 0 0
\(731\) −4.53718 −0.167814
\(732\) 0 0
\(733\) −44.4744 −1.64270 −0.821350 0.570425i \(-0.806778\pi\)
−0.821350 + 0.570425i \(0.806778\pi\)
\(734\) 0 0
\(735\) 5.96171 0.219901
\(736\) 0 0
\(737\) 36.2677 1.33594
\(738\) 0 0
\(739\) −18.5303 −0.681650 −0.340825 0.940127i \(-0.610706\pi\)
−0.340825 + 0.940127i \(0.610706\pi\)
\(740\) 0 0
\(741\) 4.92249 0.180832
\(742\) 0 0
\(743\) −34.1551 −1.25303 −0.626515 0.779409i \(-0.715519\pi\)
−0.626515 + 0.779409i \(0.715519\pi\)
\(744\) 0 0
\(745\) −4.87979 −0.178782
\(746\) 0 0
\(747\) 53.9442 1.97371
\(748\) 0 0
\(749\) −6.80902 −0.248796
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 56.7682 2.06875
\(754\) 0 0
\(755\) 2.62536 0.0955466
\(756\) 0 0
\(757\) −23.5644 −0.856463 −0.428231 0.903669i \(-0.640863\pi\)
−0.428231 + 0.903669i \(0.640863\pi\)
\(758\) 0 0
\(759\) 7.42726 0.269593
\(760\) 0 0
\(761\) 54.8766 1.98928 0.994638 0.103417i \(-0.0329777\pi\)
0.994638 + 0.103417i \(0.0329777\pi\)
\(762\) 0 0
\(763\) −15.1021 −0.546734
\(764\) 0 0
\(765\) 4.40584 0.159293
\(766\) 0 0
\(767\) −6.50964 −0.235050
\(768\) 0 0
\(769\) 9.01166 0.324969 0.162484 0.986711i \(-0.448049\pi\)
0.162484 + 0.986711i \(0.448049\pi\)
\(770\) 0 0
\(771\) −34.2194 −1.23238
\(772\) 0 0
\(773\) −24.4863 −0.880712 −0.440356 0.897823i \(-0.645148\pi\)
−0.440356 + 0.897823i \(0.645148\pi\)
\(774\) 0 0
\(775\) −32.8526 −1.18010
\(776\) 0 0
\(777\) 13.7746 0.494160
\(778\) 0 0
\(779\) −3.23783 −0.116007
\(780\) 0 0
\(781\) −25.9843 −0.929791
\(782\) 0 0
\(783\) −19.1891 −0.685761
\(784\) 0 0
\(785\) 6.62174 0.236340
\(786\) 0 0
\(787\) −12.3100 −0.438804 −0.219402 0.975635i \(-0.570411\pi\)
−0.219402 + 0.975635i \(0.570411\pi\)
\(788\) 0 0
\(789\) 51.6674 1.83941
\(790\) 0 0
\(791\) −20.8275 −0.740541
\(792\) 0 0
\(793\) −12.2283 −0.434238
\(794\) 0 0
\(795\) 9.25221 0.328142
\(796\) 0 0
\(797\) 54.1894 1.91949 0.959744 0.280877i \(-0.0906253\pi\)
0.959744 + 0.280877i \(0.0906253\pi\)
\(798\) 0 0
\(799\) 12.9575 0.458403
\(800\) 0 0
\(801\) 8.28172 0.292620
\(802\) 0 0
\(803\) 42.9681 1.51631
\(804\) 0 0
\(805\) 0.377045 0.0132891
\(806\) 0 0
\(807\) 39.9378 1.40588
\(808\) 0 0
\(809\) −7.73276 −0.271869 −0.135935 0.990718i \(-0.543404\pi\)
−0.135935 + 0.990718i \(0.543404\pi\)
\(810\) 0 0
\(811\) −14.8591 −0.521774 −0.260887 0.965369i \(-0.584015\pi\)
−0.260887 + 0.965369i \(0.584015\pi\)
\(812\) 0 0
\(813\) 5.68829 0.199497
\(814\) 0 0
\(815\) 2.25946 0.0791455
\(816\) 0 0
\(817\) −0.656062 −0.0229527
\(818\) 0 0
\(819\) −18.3966 −0.642831
\(820\) 0 0
\(821\) −9.73848 −0.339875 −0.169938 0.985455i \(-0.554357\pi\)
−0.169938 + 0.985455i \(0.554357\pi\)
\(822\) 0 0
\(823\) 18.3051 0.638075 0.319038 0.947742i \(-0.396640\pi\)
0.319038 + 0.947742i \(0.396640\pi\)
\(824\) 0 0
\(825\) 39.1030 1.36139
\(826\) 0 0
\(827\) −32.4200 −1.12735 −0.563677 0.825995i \(-0.690614\pi\)
−0.563677 + 0.825995i \(0.690614\pi\)
\(828\) 0 0
\(829\) −11.7075 −0.406617 −0.203309 0.979115i \(-0.565169\pi\)
−0.203309 + 0.979115i \(0.565169\pi\)
\(830\) 0 0
\(831\) −27.5054 −0.954152
\(832\) 0 0
\(833\) 17.1508 0.594241
\(834\) 0 0
\(835\) −2.63606 −0.0912247
\(836\) 0 0
\(837\) 16.2186 0.560598
\(838\) 0 0
\(839\) 9.03241 0.311833 0.155917 0.987770i \(-0.450167\pi\)
0.155917 + 0.987770i \(0.450167\pi\)
\(840\) 0 0
\(841\) 35.2020 1.21386
\(842\) 0 0
\(843\) −30.8135 −1.06127
\(844\) 0 0
\(845\) −2.57919 −0.0887269
\(846\) 0 0
\(847\) −1.69451 −0.0582240
\(848\) 0 0
\(849\) −38.9126 −1.33548
\(850\) 0 0
\(851\) −4.55357 −0.156094
\(852\) 0 0
\(853\) −55.0552 −1.88506 −0.942528 0.334128i \(-0.891558\pi\)
−0.942528 + 0.334128i \(0.891558\pi\)
\(854\) 0 0
\(855\) 0.637070 0.0217874
\(856\) 0 0
\(857\) 9.95859 0.340179 0.170089 0.985429i \(-0.445594\pi\)
0.170089 + 0.985429i \(0.445594\pi\)
\(858\) 0 0
\(859\) 2.52496 0.0861506 0.0430753 0.999072i \(-0.486284\pi\)
0.0430753 + 0.999072i \(0.486284\pi\)
\(860\) 0 0
\(861\) 21.3826 0.728718
\(862\) 0 0
\(863\) −6.27195 −0.213500 −0.106750 0.994286i \(-0.534044\pi\)
−0.106750 + 0.994286i \(0.534044\pi\)
\(864\) 0 0
\(865\) −2.99166 −0.101719
\(866\) 0 0
\(867\) −22.2935 −0.757128
\(868\) 0 0
\(869\) 31.2226 1.05915
\(870\) 0 0
\(871\) 52.4756 1.77807
\(872\) 0 0
\(873\) 3.96815 0.134302
\(874\) 0 0
\(875\) 4.03108 0.136276
\(876\) 0 0
\(877\) 29.7100 1.00324 0.501618 0.865089i \(-0.332738\pi\)
0.501618 + 0.865089i \(0.332738\pi\)
\(878\) 0 0
\(879\) 18.1785 0.613146
\(880\) 0 0
\(881\) 7.83415 0.263939 0.131970 0.991254i \(-0.457870\pi\)
0.131970 + 0.991254i \(0.457870\pi\)
\(882\) 0 0
\(883\) −32.7670 −1.10270 −0.551349 0.834275i \(-0.685887\pi\)
−0.551349 + 0.834275i \(0.685887\pi\)
\(884\) 0 0
\(885\) −1.48872 −0.0500429
\(886\) 0 0
\(887\) −35.7445 −1.20018 −0.600092 0.799931i \(-0.704869\pi\)
−0.600092 + 0.799931i \(0.704869\pi\)
\(888\) 0 0
\(889\) 13.7128 0.459914
\(890\) 0 0
\(891\) 16.6716 0.558521
\(892\) 0 0
\(893\) 1.87361 0.0626980
\(894\) 0 0
\(895\) −4.97502 −0.166297
\(896\) 0 0
\(897\) 10.7465 0.358814
\(898\) 0 0
\(899\) −54.2637 −1.80980
\(900\) 0 0
\(901\) 26.6170 0.886742
\(902\) 0 0
\(903\) 4.33264 0.144181
\(904\) 0 0
\(905\) −7.61100 −0.252998
\(906\) 0 0
\(907\) −48.3106 −1.60413 −0.802063 0.597239i \(-0.796264\pi\)
−0.802063 + 0.597239i \(0.796264\pi\)
\(908\) 0 0
\(909\) 52.0464 1.72627
\(910\) 0 0
\(911\) −44.3628 −1.46981 −0.734903 0.678172i \(-0.762772\pi\)
−0.734903 + 0.678172i \(0.762772\pi\)
\(912\) 0 0
\(913\) −42.2926 −1.39968
\(914\) 0 0
\(915\) −2.79654 −0.0924508
\(916\) 0 0
\(917\) −3.68035 −0.121536
\(918\) 0 0
\(919\) −27.7212 −0.914438 −0.457219 0.889354i \(-0.651154\pi\)
−0.457219 + 0.889354i \(0.651154\pi\)
\(920\) 0 0
\(921\) 18.4243 0.607100
\(922\) 0 0
\(923\) −37.5966 −1.23751
\(924\) 0 0
\(925\) −23.9736 −0.788248
\(926\) 0 0
\(927\) −58.5000 −1.92139
\(928\) 0 0
\(929\) −14.2627 −0.467943 −0.233972 0.972243i \(-0.575172\pi\)
−0.233972 + 0.972243i \(0.575172\pi\)
\(930\) 0 0
\(931\) 2.47995 0.0812772
\(932\) 0 0
\(933\) −49.9103 −1.63399
\(934\) 0 0
\(935\) −3.45421 −0.112965
\(936\) 0 0
\(937\) 54.7211 1.78766 0.893831 0.448404i \(-0.148007\pi\)
0.893831 + 0.448404i \(0.148007\pi\)
\(938\) 0 0
\(939\) −12.9223 −0.421702
\(940\) 0 0
\(941\) −19.7531 −0.643932 −0.321966 0.946751i \(-0.604344\pi\)
−0.321966 + 0.946751i \(0.604344\pi\)
\(942\) 0 0
\(943\) −7.06863 −0.230186
\(944\) 0 0
\(945\) −0.979984 −0.0318789
\(946\) 0 0
\(947\) −16.5516 −0.537856 −0.268928 0.963160i \(-0.586669\pi\)
−0.268928 + 0.963160i \(0.586669\pi\)
\(948\) 0 0
\(949\) 62.1704 2.01814
\(950\) 0 0
\(951\) −72.7096 −2.35777
\(952\) 0 0
\(953\) 43.4666 1.40802 0.704011 0.710189i \(-0.251391\pi\)
0.704011 + 0.710189i \(0.251391\pi\)
\(954\) 0 0
\(955\) −7.26027 −0.234937
\(956\) 0 0
\(957\) 64.5876 2.08782
\(958\) 0 0
\(959\) 0.514684 0.0166200
\(960\) 0 0
\(961\) 14.8638 0.479478
\(962\) 0 0
\(963\) −25.1166 −0.809370
\(964\) 0 0
\(965\) 4.20180 0.135261
\(966\) 0 0
\(967\) 54.4228 1.75012 0.875059 0.484015i \(-0.160822\pi\)
0.875059 + 0.484015i \(0.160822\pi\)
\(968\) 0 0
\(969\) 3.23859 0.104038
\(970\) 0 0
\(971\) −15.6010 −0.500660 −0.250330 0.968161i \(-0.580539\pi\)
−0.250330 + 0.968161i \(0.580539\pi\)
\(972\) 0 0
\(973\) −3.64080 −0.116719
\(974\) 0 0
\(975\) 56.5780 1.81195
\(976\) 0 0
\(977\) −32.6341 −1.04406 −0.522029 0.852928i \(-0.674825\pi\)
−0.522029 + 0.852928i \(0.674825\pi\)
\(978\) 0 0
\(979\) −6.49292 −0.207515
\(980\) 0 0
\(981\) −55.7076 −1.77861
\(982\) 0 0
\(983\) 19.6891 0.627984 0.313992 0.949426i \(-0.398333\pi\)
0.313992 + 0.949426i \(0.398333\pi\)
\(984\) 0 0
\(985\) 4.14321 0.132014
\(986\) 0 0
\(987\) −12.3733 −0.393848
\(988\) 0 0
\(989\) −1.43227 −0.0455437
\(990\) 0 0
\(991\) −33.6329 −1.06838 −0.534192 0.845363i \(-0.679384\pi\)
−0.534192 + 0.845363i \(0.679384\pi\)
\(992\) 0 0
\(993\) 55.4388 1.75930
\(994\) 0 0
\(995\) −0.962709 −0.0305199
\(996\) 0 0
\(997\) 13.5851 0.430244 0.215122 0.976587i \(-0.430985\pi\)
0.215122 + 0.976587i \(0.430985\pi\)
\(998\) 0 0
\(999\) 11.8353 0.374451
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.1.41 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.41 44 1.1 even 1 trivial