Properties

Label 6008.2.a.b.1.42
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 1.42
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.80582 q^{3} +0.563414 q^{5} -3.54541 q^{7} +4.87261 q^{9} +O(q^{10})\) \(q+2.80582 q^{3} +0.563414 q^{5} -3.54541 q^{7} +4.87261 q^{9} +0.185143 q^{11} +1.50793 q^{13} +1.58084 q^{15} -4.26009 q^{17} -5.87677 q^{19} -9.94777 q^{21} -4.13657 q^{23} -4.68256 q^{25} +5.25420 q^{27} +6.53069 q^{29} -9.18878 q^{31} +0.519478 q^{33} -1.99753 q^{35} +2.36834 q^{37} +4.23098 q^{39} -1.06308 q^{41} +9.99035 q^{43} +2.74530 q^{45} +6.05887 q^{47} +5.56992 q^{49} -11.9530 q^{51} -6.60841 q^{53} +0.104312 q^{55} -16.4891 q^{57} -10.7436 q^{59} +6.98643 q^{61} -17.2754 q^{63} +0.849590 q^{65} -8.95417 q^{67} -11.6065 q^{69} -5.32207 q^{71} -11.7943 q^{73} -13.1384 q^{75} -0.656408 q^{77} -5.38771 q^{79} +0.124498 q^{81} -15.1923 q^{83} -2.40020 q^{85} +18.3239 q^{87} +12.9885 q^{89} -5.34624 q^{91} -25.7820 q^{93} -3.31105 q^{95} +5.71337 q^{97} +0.902131 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) 2.80582 1.61994 0.809970 0.586472i \(-0.199484\pi\)
0.809970 + 0.586472i \(0.199484\pi\)
\(4\) 0 0
\(5\) 0.563414 0.251966 0.125983 0.992032i \(-0.459791\pi\)
0.125983 + 0.992032i \(0.459791\pi\)
\(6\) 0 0
\(7\) −3.54541 −1.34004 −0.670019 0.742344i \(-0.733714\pi\)
−0.670019 + 0.742344i \(0.733714\pi\)
\(8\) 0 0
\(9\) 4.87261 1.62420
\(10\) 0 0
\(11\) 0.185143 0.0558228 0.0279114 0.999610i \(-0.491114\pi\)
0.0279114 + 0.999610i \(0.491114\pi\)
\(12\) 0 0
\(13\) 1.50793 0.418225 0.209113 0.977892i \(-0.432942\pi\)
0.209113 + 0.977892i \(0.432942\pi\)
\(14\) 0 0
\(15\) 1.58084 0.408170
\(16\) 0 0
\(17\) −4.26009 −1.03322 −0.516612 0.856220i \(-0.672807\pi\)
−0.516612 + 0.856220i \(0.672807\pi\)
\(18\) 0 0
\(19\) −5.87677 −1.34822 −0.674111 0.738630i \(-0.735473\pi\)
−0.674111 + 0.738630i \(0.735473\pi\)
\(20\) 0 0
\(21\) −9.94777 −2.17078
\(22\) 0 0
\(23\) −4.13657 −0.862534 −0.431267 0.902224i \(-0.641933\pi\)
−0.431267 + 0.902224i \(0.641933\pi\)
\(24\) 0 0
\(25\) −4.68256 −0.936513
\(26\) 0 0
\(27\) 5.25420 1.01117
\(28\) 0 0
\(29\) 6.53069 1.21272 0.606359 0.795191i \(-0.292629\pi\)
0.606359 + 0.795191i \(0.292629\pi\)
\(30\) 0 0
\(31\) −9.18878 −1.65035 −0.825177 0.564874i \(-0.808925\pi\)
−0.825177 + 0.564874i \(0.808925\pi\)
\(32\) 0 0
\(33\) 0.519478 0.0904295
\(34\) 0 0
\(35\) −1.99753 −0.337645
\(36\) 0 0
\(37\) 2.36834 0.389353 0.194676 0.980868i \(-0.437634\pi\)
0.194676 + 0.980868i \(0.437634\pi\)
\(38\) 0 0
\(39\) 4.23098 0.677499
\(40\) 0 0
\(41\) −1.06308 −0.166025 −0.0830125 0.996549i \(-0.526454\pi\)
−0.0830125 + 0.996549i \(0.526454\pi\)
\(42\) 0 0
\(43\) 9.99035 1.52351 0.761757 0.647862i \(-0.224337\pi\)
0.761757 + 0.647862i \(0.224337\pi\)
\(44\) 0 0
\(45\) 2.74530 0.409245
\(46\) 0 0
\(47\) 6.05887 0.883777 0.441889 0.897070i \(-0.354309\pi\)
0.441889 + 0.897070i \(0.354309\pi\)
\(48\) 0 0
\(49\) 5.56992 0.795703
\(50\) 0 0
\(51\) −11.9530 −1.67376
\(52\) 0 0
\(53\) −6.60841 −0.907735 −0.453868 0.891069i \(-0.649956\pi\)
−0.453868 + 0.891069i \(0.649956\pi\)
\(54\) 0 0
\(55\) 0.104312 0.0140655
\(56\) 0 0
\(57\) −16.4891 −2.18404
\(58\) 0 0
\(59\) −10.7436 −1.39869 −0.699347 0.714782i \(-0.746526\pi\)
−0.699347 + 0.714782i \(0.746526\pi\)
\(60\) 0 0
\(61\) 6.98643 0.894521 0.447260 0.894404i \(-0.352400\pi\)
0.447260 + 0.894404i \(0.352400\pi\)
\(62\) 0 0
\(63\) −17.2754 −2.17649
\(64\) 0 0
\(65\) 0.849590 0.105379
\(66\) 0 0
\(67\) −8.95417 −1.09393 −0.546963 0.837157i \(-0.684216\pi\)
−0.546963 + 0.837157i \(0.684216\pi\)
\(68\) 0 0
\(69\) −11.6065 −1.39725
\(70\) 0 0
\(71\) −5.32207 −0.631614 −0.315807 0.948824i \(-0.602275\pi\)
−0.315807 + 0.948824i \(0.602275\pi\)
\(72\) 0 0
\(73\) −11.7943 −1.38041 −0.690207 0.723612i \(-0.742481\pi\)
−0.690207 + 0.723612i \(0.742481\pi\)
\(74\) 0 0
\(75\) −13.1384 −1.51709
\(76\) 0 0
\(77\) −0.656408 −0.0748047
\(78\) 0 0
\(79\) −5.38771 −0.606165 −0.303083 0.952964i \(-0.598016\pi\)
−0.303083 + 0.952964i \(0.598016\pi\)
\(80\) 0 0
\(81\) 0.124498 0.0138331
\(82\) 0 0
\(83\) −15.1923 −1.66757 −0.833784 0.552091i \(-0.813830\pi\)
−0.833784 + 0.552091i \(0.813830\pi\)
\(84\) 0 0
\(85\) −2.40020 −0.260338
\(86\) 0 0
\(87\) 18.3239 1.96453
\(88\) 0 0
\(89\) 12.9885 1.37678 0.688391 0.725339i \(-0.258317\pi\)
0.688391 + 0.725339i \(0.258317\pi\)
\(90\) 0 0
\(91\) −5.34624 −0.560438
\(92\) 0 0
\(93\) −25.7820 −2.67347
\(94\) 0 0
\(95\) −3.31105 −0.339707
\(96\) 0 0
\(97\) 5.71337 0.580105 0.290053 0.957011i \(-0.406327\pi\)
0.290053 + 0.957011i \(0.406327\pi\)
\(98\) 0 0
\(99\) 0.902131 0.0906675
\(100\) 0 0
\(101\) −2.06265 −0.205241 −0.102621 0.994721i \(-0.532723\pi\)
−0.102621 + 0.994721i \(0.532723\pi\)
\(102\) 0 0
\(103\) 11.9516 1.17763 0.588815 0.808268i \(-0.299595\pi\)
0.588815 + 0.808268i \(0.299595\pi\)
\(104\) 0 0
\(105\) −5.60471 −0.546964
\(106\) 0 0
\(107\) −17.9629 −1.73654 −0.868269 0.496093i \(-0.834767\pi\)
−0.868269 + 0.496093i \(0.834767\pi\)
\(108\) 0 0
\(109\) 10.3465 0.991019 0.495509 0.868603i \(-0.334981\pi\)
0.495509 + 0.868603i \(0.334981\pi\)
\(110\) 0 0
\(111\) 6.64513 0.630728
\(112\) 0 0
\(113\) 1.59788 0.150316 0.0751580 0.997172i \(-0.476054\pi\)
0.0751580 + 0.997172i \(0.476054\pi\)
\(114\) 0 0
\(115\) −2.33060 −0.217330
\(116\) 0 0
\(117\) 7.34757 0.679283
\(118\) 0 0
\(119\) 15.1038 1.38456
\(120\) 0 0
\(121\) −10.9657 −0.996884
\(122\) 0 0
\(123\) −2.98281 −0.268951
\(124\) 0 0
\(125\) −5.45529 −0.487936
\(126\) 0 0
\(127\) −4.73602 −0.420254 −0.210127 0.977674i \(-0.567388\pi\)
−0.210127 + 0.977674i \(0.567388\pi\)
\(128\) 0 0
\(129\) 28.0311 2.46800
\(130\) 0 0
\(131\) −11.1476 −0.973973 −0.486987 0.873409i \(-0.661904\pi\)
−0.486987 + 0.873409i \(0.661904\pi\)
\(132\) 0 0
\(133\) 20.8355 1.80667
\(134\) 0 0
\(135\) 2.96029 0.254781
\(136\) 0 0
\(137\) 4.06554 0.347343 0.173671 0.984804i \(-0.444437\pi\)
0.173671 + 0.984804i \(0.444437\pi\)
\(138\) 0 0
\(139\) 18.8548 1.59925 0.799623 0.600502i \(-0.205033\pi\)
0.799623 + 0.600502i \(0.205033\pi\)
\(140\) 0 0
\(141\) 17.0001 1.43167
\(142\) 0 0
\(143\) 0.279183 0.0233465
\(144\) 0 0
\(145\) 3.67948 0.305564
\(146\) 0 0
\(147\) 15.6282 1.28899
\(148\) 0 0
\(149\) 6.01916 0.493109 0.246554 0.969129i \(-0.420702\pi\)
0.246554 + 0.969129i \(0.420702\pi\)
\(150\) 0 0
\(151\) −14.4902 −1.17920 −0.589600 0.807696i \(-0.700714\pi\)
−0.589600 + 0.807696i \(0.700714\pi\)
\(152\) 0 0
\(153\) −20.7578 −1.67817
\(154\) 0 0
\(155\) −5.17709 −0.415834
\(156\) 0 0
\(157\) −19.5305 −1.55870 −0.779350 0.626589i \(-0.784450\pi\)
−0.779350 + 0.626589i \(0.784450\pi\)
\(158\) 0 0
\(159\) −18.5420 −1.47048
\(160\) 0 0
\(161\) 14.6658 1.15583
\(162\) 0 0
\(163\) 14.5560 1.14012 0.570058 0.821605i \(-0.306921\pi\)
0.570058 + 0.821605i \(0.306921\pi\)
\(164\) 0 0
\(165\) 0.292681 0.0227852
\(166\) 0 0
\(167\) 23.2343 1.79793 0.898964 0.438023i \(-0.144321\pi\)
0.898964 + 0.438023i \(0.144321\pi\)
\(168\) 0 0
\(169\) −10.7261 −0.825088
\(170\) 0 0
\(171\) −28.6352 −2.18979
\(172\) 0 0
\(173\) 9.98314 0.759004 0.379502 0.925191i \(-0.376095\pi\)
0.379502 + 0.925191i \(0.376095\pi\)
\(174\) 0 0
\(175\) 16.6016 1.25496
\(176\) 0 0
\(177\) −30.1445 −2.26580
\(178\) 0 0
\(179\) 12.6134 0.942772 0.471386 0.881927i \(-0.343754\pi\)
0.471386 + 0.881927i \(0.343754\pi\)
\(180\) 0 0
\(181\) 19.5162 1.45063 0.725313 0.688420i \(-0.241695\pi\)
0.725313 + 0.688420i \(0.241695\pi\)
\(182\) 0 0
\(183\) 19.6026 1.44907
\(184\) 0 0
\(185\) 1.33436 0.0981038
\(186\) 0 0
\(187\) −0.788727 −0.0576774
\(188\) 0 0
\(189\) −18.6283 −1.35501
\(190\) 0 0
\(191\) −18.7162 −1.35426 −0.677129 0.735865i \(-0.736776\pi\)
−0.677129 + 0.735865i \(0.736776\pi\)
\(192\) 0 0
\(193\) −15.1270 −1.08886 −0.544432 0.838805i \(-0.683255\pi\)
−0.544432 + 0.838805i \(0.683255\pi\)
\(194\) 0 0
\(195\) 2.38380 0.170707
\(196\) 0 0
\(197\) −18.3602 −1.30811 −0.654054 0.756448i \(-0.726933\pi\)
−0.654054 + 0.756448i \(0.726933\pi\)
\(198\) 0 0
\(199\) 10.7989 0.765513 0.382756 0.923849i \(-0.374975\pi\)
0.382756 + 0.923849i \(0.374975\pi\)
\(200\) 0 0
\(201\) −25.1238 −1.77209
\(202\) 0 0
\(203\) −23.1539 −1.62509
\(204\) 0 0
\(205\) −0.598954 −0.0418328
\(206\) 0 0
\(207\) −20.1559 −1.40093
\(208\) 0 0
\(209\) −1.08804 −0.0752615
\(210\) 0 0
\(211\) −0.667536 −0.0459551 −0.0229775 0.999736i \(-0.507315\pi\)
−0.0229775 + 0.999736i \(0.507315\pi\)
\(212\) 0 0
\(213\) −14.9328 −1.02318
\(214\) 0 0
\(215\) 5.62871 0.383875
\(216\) 0 0
\(217\) 32.5780 2.21154
\(218\) 0 0
\(219\) −33.0925 −2.23619
\(220\) 0 0
\(221\) −6.42393 −0.432120
\(222\) 0 0
\(223\) 18.2574 1.22261 0.611305 0.791395i \(-0.290645\pi\)
0.611305 + 0.791395i \(0.290645\pi\)
\(224\) 0 0
\(225\) −22.8163 −1.52109
\(226\) 0 0
\(227\) −6.12774 −0.406712 −0.203356 0.979105i \(-0.565185\pi\)
−0.203356 + 0.979105i \(0.565185\pi\)
\(228\) 0 0
\(229\) 0.462703 0.0305763 0.0152881 0.999883i \(-0.495133\pi\)
0.0152881 + 0.999883i \(0.495133\pi\)
\(230\) 0 0
\(231\) −1.84176 −0.121179
\(232\) 0 0
\(233\) 9.40114 0.615889 0.307944 0.951404i \(-0.400359\pi\)
0.307944 + 0.951404i \(0.400359\pi\)
\(234\) 0 0
\(235\) 3.41365 0.222682
\(236\) 0 0
\(237\) −15.1169 −0.981951
\(238\) 0 0
\(239\) −1.91341 −0.123768 −0.0618839 0.998083i \(-0.519711\pi\)
−0.0618839 + 0.998083i \(0.519711\pi\)
\(240\) 0 0
\(241\) −8.37616 −0.539556 −0.269778 0.962923i \(-0.586950\pi\)
−0.269778 + 0.962923i \(0.586950\pi\)
\(242\) 0 0
\(243\) −15.4133 −0.988763
\(244\) 0 0
\(245\) 3.13817 0.200490
\(246\) 0 0
\(247\) −8.86177 −0.563861
\(248\) 0 0
\(249\) −42.6267 −2.70136
\(250\) 0 0
\(251\) −14.0673 −0.887923 −0.443961 0.896046i \(-0.646427\pi\)
−0.443961 + 0.896046i \(0.646427\pi\)
\(252\) 0 0
\(253\) −0.765857 −0.0481490
\(254\) 0 0
\(255\) −6.73451 −0.421731
\(256\) 0 0
\(257\) 10.4083 0.649250 0.324625 0.945843i \(-0.394762\pi\)
0.324625 + 0.945843i \(0.394762\pi\)
\(258\) 0 0
\(259\) −8.39673 −0.521748
\(260\) 0 0
\(261\) 31.8215 1.96970
\(262\) 0 0
\(263\) 3.42163 0.210987 0.105493 0.994420i \(-0.466358\pi\)
0.105493 + 0.994420i \(0.466358\pi\)
\(264\) 0 0
\(265\) −3.72327 −0.228719
\(266\) 0 0
\(267\) 36.4435 2.23030
\(268\) 0 0
\(269\) 12.2543 0.747157 0.373579 0.927599i \(-0.378131\pi\)
0.373579 + 0.927599i \(0.378131\pi\)
\(270\) 0 0
\(271\) −0.885159 −0.0537696 −0.0268848 0.999639i \(-0.508559\pi\)
−0.0268848 + 0.999639i \(0.508559\pi\)
\(272\) 0 0
\(273\) −15.0006 −0.907875
\(274\) 0 0
\(275\) −0.866945 −0.0522787
\(276\) 0 0
\(277\) 17.7964 1.06928 0.534641 0.845079i \(-0.320447\pi\)
0.534641 + 0.845079i \(0.320447\pi\)
\(278\) 0 0
\(279\) −44.7734 −2.68051
\(280\) 0 0
\(281\) 10.7704 0.642511 0.321256 0.946993i \(-0.395895\pi\)
0.321256 + 0.946993i \(0.395895\pi\)
\(282\) 0 0
\(283\) 26.2740 1.56183 0.780914 0.624639i \(-0.214754\pi\)
0.780914 + 0.624639i \(0.214754\pi\)
\(284\) 0 0
\(285\) −9.29021 −0.550305
\(286\) 0 0
\(287\) 3.76905 0.222480
\(288\) 0 0
\(289\) 1.14837 0.0675509
\(290\) 0 0
\(291\) 16.0307 0.939735
\(292\) 0 0
\(293\) 0.392479 0.0229288 0.0114644 0.999934i \(-0.496351\pi\)
0.0114644 + 0.999934i \(0.496351\pi\)
\(294\) 0 0
\(295\) −6.05308 −0.352424
\(296\) 0 0
\(297\) 0.972780 0.0564464
\(298\) 0 0
\(299\) −6.23766 −0.360733
\(300\) 0 0
\(301\) −35.4199 −2.04157
\(302\) 0 0
\(303\) −5.78742 −0.332478
\(304\) 0 0
\(305\) 3.93625 0.225389
\(306\) 0 0
\(307\) 3.29287 0.187934 0.0939670 0.995575i \(-0.470045\pi\)
0.0939670 + 0.995575i \(0.470045\pi\)
\(308\) 0 0
\(309\) 33.5341 1.90769
\(310\) 0 0
\(311\) 13.6513 0.774091 0.387046 0.922061i \(-0.373496\pi\)
0.387046 + 0.922061i \(0.373496\pi\)
\(312\) 0 0
\(313\) −26.0662 −1.47335 −0.736675 0.676247i \(-0.763605\pi\)
−0.736675 + 0.676247i \(0.763605\pi\)
\(314\) 0 0
\(315\) −9.73320 −0.548404
\(316\) 0 0
\(317\) −6.80146 −0.382008 −0.191004 0.981589i \(-0.561174\pi\)
−0.191004 + 0.981589i \(0.561174\pi\)
\(318\) 0 0
\(319\) 1.20911 0.0676973
\(320\) 0 0
\(321\) −50.4006 −2.81309
\(322\) 0 0
\(323\) 25.0356 1.39302
\(324\) 0 0
\(325\) −7.06099 −0.391673
\(326\) 0 0
\(327\) 29.0305 1.60539
\(328\) 0 0
\(329\) −21.4812 −1.18430
\(330\) 0 0
\(331\) −5.06329 −0.278304 −0.139152 0.990271i \(-0.544438\pi\)
−0.139152 + 0.990271i \(0.544438\pi\)
\(332\) 0 0
\(333\) 11.5400 0.632388
\(334\) 0 0
\(335\) −5.04491 −0.275633
\(336\) 0 0
\(337\) 6.36868 0.346924 0.173462 0.984841i \(-0.444505\pi\)
0.173462 + 0.984841i \(0.444505\pi\)
\(338\) 0 0
\(339\) 4.48336 0.243503
\(340\) 0 0
\(341\) −1.70124 −0.0921274
\(342\) 0 0
\(343\) 5.07023 0.273766
\(344\) 0 0
\(345\) −6.53924 −0.352061
\(346\) 0 0
\(347\) −0.546503 −0.0293378 −0.0146689 0.999892i \(-0.504669\pi\)
−0.0146689 + 0.999892i \(0.504669\pi\)
\(348\) 0 0
\(349\) −16.7935 −0.898934 −0.449467 0.893297i \(-0.648386\pi\)
−0.449467 + 0.893297i \(0.648386\pi\)
\(350\) 0 0
\(351\) 7.92298 0.422897
\(352\) 0 0
\(353\) −28.1421 −1.49785 −0.748926 0.662654i \(-0.769430\pi\)
−0.748926 + 0.662654i \(0.769430\pi\)
\(354\) 0 0
\(355\) −2.99853 −0.159145
\(356\) 0 0
\(357\) 42.3784 2.24290
\(358\) 0 0
\(359\) 4.25359 0.224496 0.112248 0.993680i \(-0.464195\pi\)
0.112248 + 0.993680i \(0.464195\pi\)
\(360\) 0 0
\(361\) 15.5364 0.817704
\(362\) 0 0
\(363\) −30.7678 −1.61489
\(364\) 0 0
\(365\) −6.64506 −0.347818
\(366\) 0 0
\(367\) 5.28010 0.275619 0.137810 0.990459i \(-0.455994\pi\)
0.137810 + 0.990459i \(0.455994\pi\)
\(368\) 0 0
\(369\) −5.17997 −0.269659
\(370\) 0 0
\(371\) 23.4295 1.21640
\(372\) 0 0
\(373\) 10.1093 0.523442 0.261721 0.965144i \(-0.415710\pi\)
0.261721 + 0.965144i \(0.415710\pi\)
\(374\) 0 0
\(375\) −15.3066 −0.790427
\(376\) 0 0
\(377\) 9.84783 0.507189
\(378\) 0 0
\(379\) −0.500870 −0.0257279 −0.0128640 0.999917i \(-0.504095\pi\)
−0.0128640 + 0.999917i \(0.504095\pi\)
\(380\) 0 0
\(381\) −13.2884 −0.680786
\(382\) 0 0
\(383\) −23.2575 −1.18840 −0.594201 0.804317i \(-0.702532\pi\)
−0.594201 + 0.804317i \(0.702532\pi\)
\(384\) 0 0
\(385\) −0.369830 −0.0188483
\(386\) 0 0
\(387\) 48.6791 2.47450
\(388\) 0 0
\(389\) −34.4111 −1.74471 −0.872357 0.488870i \(-0.837409\pi\)
−0.872357 + 0.488870i \(0.837409\pi\)
\(390\) 0 0
\(391\) 17.6221 0.891190
\(392\) 0 0
\(393\) −31.2782 −1.57778
\(394\) 0 0
\(395\) −3.03551 −0.152733
\(396\) 0 0
\(397\) 1.19491 0.0599706 0.0299853 0.999550i \(-0.490454\pi\)
0.0299853 + 0.999550i \(0.490454\pi\)
\(398\) 0 0
\(399\) 58.4607 2.92670
\(400\) 0 0
\(401\) 26.1871 1.30772 0.653860 0.756616i \(-0.273149\pi\)
0.653860 + 0.756616i \(0.273149\pi\)
\(402\) 0 0
\(403\) −13.8561 −0.690220
\(404\) 0 0
\(405\) 0.0701437 0.00348547
\(406\) 0 0
\(407\) 0.438482 0.0217348
\(408\) 0 0
\(409\) −22.9639 −1.13549 −0.567746 0.823204i \(-0.692184\pi\)
−0.567746 + 0.823204i \(0.692184\pi\)
\(410\) 0 0
\(411\) 11.4072 0.562674
\(412\) 0 0
\(413\) 38.0904 1.87430
\(414\) 0 0
\(415\) −8.55954 −0.420171
\(416\) 0 0
\(417\) 52.9032 2.59068
\(418\) 0 0
\(419\) 6.19193 0.302495 0.151248 0.988496i \(-0.451671\pi\)
0.151248 + 0.988496i \(0.451671\pi\)
\(420\) 0 0
\(421\) −39.5190 −1.92604 −0.963020 0.269431i \(-0.913165\pi\)
−0.963020 + 0.269431i \(0.913165\pi\)
\(422\) 0 0
\(423\) 29.5225 1.43543
\(424\) 0 0
\(425\) 19.9481 0.967627
\(426\) 0 0
\(427\) −24.7697 −1.19869
\(428\) 0 0
\(429\) 0.783338 0.0378199
\(430\) 0 0
\(431\) 25.6442 1.23524 0.617618 0.786478i \(-0.288098\pi\)
0.617618 + 0.786478i \(0.288098\pi\)
\(432\) 0 0
\(433\) 25.6835 1.23427 0.617136 0.786856i \(-0.288293\pi\)
0.617136 + 0.786856i \(0.288293\pi\)
\(434\) 0 0
\(435\) 10.3240 0.494996
\(436\) 0 0
\(437\) 24.3096 1.16289
\(438\) 0 0
\(439\) 21.4263 1.02262 0.511311 0.859396i \(-0.329160\pi\)
0.511311 + 0.859396i \(0.329160\pi\)
\(440\) 0 0
\(441\) 27.1400 1.29238
\(442\) 0 0
\(443\) −36.1179 −1.71601 −0.858006 0.513639i \(-0.828297\pi\)
−0.858006 + 0.513639i \(0.828297\pi\)
\(444\) 0 0
\(445\) 7.31793 0.346903
\(446\) 0 0
\(447\) 16.8887 0.798807
\(448\) 0 0
\(449\) 3.03763 0.143355 0.0716773 0.997428i \(-0.477165\pi\)
0.0716773 + 0.997428i \(0.477165\pi\)
\(450\) 0 0
\(451\) −0.196822 −0.00926798
\(452\) 0 0
\(453\) −40.6570 −1.91023
\(454\) 0 0
\(455\) −3.01214 −0.141212
\(456\) 0 0
\(457\) 25.3760 1.18704 0.593519 0.804820i \(-0.297738\pi\)
0.593519 + 0.804820i \(0.297738\pi\)
\(458\) 0 0
\(459\) −22.3834 −1.04477
\(460\) 0 0
\(461\) 33.1125 1.54220 0.771101 0.636713i \(-0.219706\pi\)
0.771101 + 0.636713i \(0.219706\pi\)
\(462\) 0 0
\(463\) −36.7838 −1.70949 −0.854743 0.519052i \(-0.826285\pi\)
−0.854743 + 0.519052i \(0.826285\pi\)
\(464\) 0 0
\(465\) −14.5260 −0.673626
\(466\) 0 0
\(467\) −40.4712 −1.87278 −0.936392 0.350957i \(-0.885856\pi\)
−0.936392 + 0.350957i \(0.885856\pi\)
\(468\) 0 0
\(469\) 31.7462 1.46590
\(470\) 0 0
\(471\) −54.7989 −2.52500
\(472\) 0 0
\(473\) 1.84965 0.0850468
\(474\) 0 0
\(475\) 27.5183 1.26263
\(476\) 0 0
\(477\) −32.2002 −1.47435
\(478\) 0 0
\(479\) 31.9838 1.46138 0.730689 0.682711i \(-0.239199\pi\)
0.730689 + 0.682711i \(0.239199\pi\)
\(480\) 0 0
\(481\) 3.57130 0.162837
\(482\) 0 0
\(483\) 41.1496 1.87237
\(484\) 0 0
\(485\) 3.21900 0.146167
\(486\) 0 0
\(487\) 9.00976 0.408271 0.204136 0.978943i \(-0.434562\pi\)
0.204136 + 0.978943i \(0.434562\pi\)
\(488\) 0 0
\(489\) 40.8415 1.84692
\(490\) 0 0
\(491\) −34.2768 −1.54689 −0.773444 0.633864i \(-0.781468\pi\)
−0.773444 + 0.633864i \(0.781468\pi\)
\(492\) 0 0
\(493\) −27.8213 −1.25301
\(494\) 0 0
\(495\) 0.508273 0.0228452
\(496\) 0 0
\(497\) 18.8689 0.846386
\(498\) 0 0
\(499\) 7.43029 0.332625 0.166313 0.986073i \(-0.446814\pi\)
0.166313 + 0.986073i \(0.446814\pi\)
\(500\) 0 0
\(501\) 65.1913 2.91253
\(502\) 0 0
\(503\) 18.2073 0.811822 0.405911 0.913913i \(-0.366954\pi\)
0.405911 + 0.913913i \(0.366954\pi\)
\(504\) 0 0
\(505\) −1.16213 −0.0517139
\(506\) 0 0
\(507\) −30.0956 −1.33659
\(508\) 0 0
\(509\) −9.01717 −0.399679 −0.199840 0.979829i \(-0.564042\pi\)
−0.199840 + 0.979829i \(0.564042\pi\)
\(510\) 0 0
\(511\) 41.8155 1.84981
\(512\) 0 0
\(513\) −30.8777 −1.36328
\(514\) 0 0
\(515\) 6.73372 0.296723
\(516\) 0 0
\(517\) 1.12176 0.0493349
\(518\) 0 0
\(519\) 28.0109 1.22954
\(520\) 0 0
\(521\) 26.2630 1.15060 0.575301 0.817942i \(-0.304885\pi\)
0.575301 + 0.817942i \(0.304885\pi\)
\(522\) 0 0
\(523\) 0.996034 0.0435535 0.0217768 0.999763i \(-0.493068\pi\)
0.0217768 + 0.999763i \(0.493068\pi\)
\(524\) 0 0
\(525\) 46.5811 2.03296
\(526\) 0 0
\(527\) 39.1450 1.70518
\(528\) 0 0
\(529\) −5.88881 −0.256035
\(530\) 0 0
\(531\) −52.3493 −2.27176
\(532\) 0 0
\(533\) −1.60305 −0.0694359
\(534\) 0 0
\(535\) −10.1205 −0.437550
\(536\) 0 0
\(537\) 35.3910 1.52723
\(538\) 0 0
\(539\) 1.03123 0.0444183
\(540\) 0 0
\(541\) −7.66813 −0.329679 −0.164839 0.986320i \(-0.552711\pi\)
−0.164839 + 0.986320i \(0.552711\pi\)
\(542\) 0 0
\(543\) 54.7588 2.34992
\(544\) 0 0
\(545\) 5.82939 0.249704
\(546\) 0 0
\(547\) 2.71041 0.115889 0.0579445 0.998320i \(-0.481545\pi\)
0.0579445 + 0.998320i \(0.481545\pi\)
\(548\) 0 0
\(549\) 34.0422 1.45288
\(550\) 0 0
\(551\) −38.3793 −1.63501
\(552\) 0 0
\(553\) 19.1016 0.812285
\(554\) 0 0
\(555\) 3.74396 0.158922
\(556\) 0 0
\(557\) 21.9636 0.930627 0.465313 0.885146i \(-0.345942\pi\)
0.465313 + 0.885146i \(0.345942\pi\)
\(558\) 0 0
\(559\) 15.0648 0.637172
\(560\) 0 0
\(561\) −2.21302 −0.0934339
\(562\) 0 0
\(563\) −34.4192 −1.45059 −0.725297 0.688436i \(-0.758298\pi\)
−0.725297 + 0.688436i \(0.758298\pi\)
\(564\) 0 0
\(565\) 0.900269 0.0378746
\(566\) 0 0
\(567\) −0.441395 −0.0185368
\(568\) 0 0
\(569\) −12.3584 −0.518089 −0.259045 0.965865i \(-0.583408\pi\)
−0.259045 + 0.965865i \(0.583408\pi\)
\(570\) 0 0
\(571\) −20.2648 −0.848055 −0.424028 0.905649i \(-0.639384\pi\)
−0.424028 + 0.905649i \(0.639384\pi\)
\(572\) 0 0
\(573\) −52.5142 −2.19381
\(574\) 0 0
\(575\) 19.3697 0.807774
\(576\) 0 0
\(577\) 21.9941 0.915626 0.457813 0.889049i \(-0.348633\pi\)
0.457813 + 0.889049i \(0.348633\pi\)
\(578\) 0 0
\(579\) −42.4435 −1.76389
\(580\) 0 0
\(581\) 53.8628 2.23460
\(582\) 0 0
\(583\) −1.22350 −0.0506723
\(584\) 0 0
\(585\) 4.13972 0.171156
\(586\) 0 0
\(587\) −18.0891 −0.746617 −0.373309 0.927707i \(-0.621777\pi\)
−0.373309 + 0.927707i \(0.621777\pi\)
\(588\) 0 0
\(589\) 54.0003 2.22505
\(590\) 0 0
\(591\) −51.5153 −2.11906
\(592\) 0 0
\(593\) −42.8224 −1.75851 −0.879254 0.476354i \(-0.841958\pi\)
−0.879254 + 0.476354i \(0.841958\pi\)
\(594\) 0 0
\(595\) 8.50967 0.348862
\(596\) 0 0
\(597\) 30.2997 1.24008
\(598\) 0 0
\(599\) −6.99757 −0.285913 −0.142956 0.989729i \(-0.545661\pi\)
−0.142956 + 0.989729i \(0.545661\pi\)
\(600\) 0 0
\(601\) 26.9500 1.09931 0.549656 0.835391i \(-0.314759\pi\)
0.549656 + 0.835391i \(0.314759\pi\)
\(602\) 0 0
\(603\) −43.6302 −1.77676
\(604\) 0 0
\(605\) −6.17824 −0.251181
\(606\) 0 0
\(607\) −26.3474 −1.06941 −0.534705 0.845039i \(-0.679577\pi\)
−0.534705 + 0.845039i \(0.679577\pi\)
\(608\) 0 0
\(609\) −64.9657 −2.63254
\(610\) 0 0
\(611\) 9.13637 0.369618
\(612\) 0 0
\(613\) −26.3344 −1.06364 −0.531818 0.846859i \(-0.678491\pi\)
−0.531818 + 0.846859i \(0.678491\pi\)
\(614\) 0 0
\(615\) −1.68056 −0.0677665
\(616\) 0 0
\(617\) 36.6486 1.47542 0.737709 0.675118i \(-0.235907\pi\)
0.737709 + 0.675118i \(0.235907\pi\)
\(618\) 0 0
\(619\) −42.9610 −1.72675 −0.863373 0.504565i \(-0.831653\pi\)
−0.863373 + 0.504565i \(0.831653\pi\)
\(620\) 0 0
\(621\) −21.7344 −0.872170
\(622\) 0 0
\(623\) −46.0497 −1.84494
\(624\) 0 0
\(625\) 20.3392 0.813569
\(626\) 0 0
\(627\) −3.05285 −0.121919
\(628\) 0 0
\(629\) −10.0893 −0.402288
\(630\) 0 0
\(631\) −18.9436 −0.754133 −0.377067 0.926186i \(-0.623067\pi\)
−0.377067 + 0.926186i \(0.623067\pi\)
\(632\) 0 0
\(633\) −1.87298 −0.0744444
\(634\) 0 0
\(635\) −2.66834 −0.105890
\(636\) 0 0
\(637\) 8.39906 0.332783
\(638\) 0 0
\(639\) −25.9324 −1.02587
\(640\) 0 0
\(641\) 25.3769 1.00233 0.501164 0.865352i \(-0.332905\pi\)
0.501164 + 0.865352i \(0.332905\pi\)
\(642\) 0 0
\(643\) −3.86051 −0.152244 −0.0761219 0.997099i \(-0.524254\pi\)
−0.0761219 + 0.997099i \(0.524254\pi\)
\(644\) 0 0
\(645\) 15.7931 0.621854
\(646\) 0 0
\(647\) −10.4831 −0.412132 −0.206066 0.978538i \(-0.566066\pi\)
−0.206066 + 0.978538i \(0.566066\pi\)
\(648\) 0 0
\(649\) −1.98910 −0.0780790
\(650\) 0 0
\(651\) 91.4079 3.58256
\(652\) 0 0
\(653\) 0.672990 0.0263361 0.0131681 0.999913i \(-0.495808\pi\)
0.0131681 + 0.999913i \(0.495808\pi\)
\(654\) 0 0
\(655\) −6.28073 −0.245409
\(656\) 0 0
\(657\) −57.4688 −2.24207
\(658\) 0 0
\(659\) 50.3465 1.96122 0.980610 0.195971i \(-0.0627859\pi\)
0.980610 + 0.195971i \(0.0627859\pi\)
\(660\) 0 0
\(661\) −44.8856 −1.74585 −0.872923 0.487858i \(-0.837778\pi\)
−0.872923 + 0.487858i \(0.837778\pi\)
\(662\) 0 0
\(663\) −18.0244 −0.700008
\(664\) 0 0
\(665\) 11.7390 0.455220
\(666\) 0 0
\(667\) −27.0146 −1.04601
\(668\) 0 0
\(669\) 51.2271 1.98055
\(670\) 0 0
\(671\) 1.29349 0.0499346
\(672\) 0 0
\(673\) 48.2054 1.85818 0.929092 0.369849i \(-0.120591\pi\)
0.929092 + 0.369849i \(0.120591\pi\)
\(674\) 0 0
\(675\) −24.6031 −0.946975
\(676\) 0 0
\(677\) −29.0608 −1.11690 −0.558449 0.829539i \(-0.688603\pi\)
−0.558449 + 0.829539i \(0.688603\pi\)
\(678\) 0 0
\(679\) −20.2562 −0.777363
\(680\) 0 0
\(681\) −17.1933 −0.658849
\(682\) 0 0
\(683\) 16.9263 0.647667 0.323834 0.946114i \(-0.395028\pi\)
0.323834 + 0.946114i \(0.395028\pi\)
\(684\) 0 0
\(685\) 2.29058 0.0875187
\(686\) 0 0
\(687\) 1.29826 0.0495317
\(688\) 0 0
\(689\) −9.96504 −0.379638
\(690\) 0 0
\(691\) −31.4757 −1.19739 −0.598697 0.800976i \(-0.704315\pi\)
−0.598697 + 0.800976i \(0.704315\pi\)
\(692\) 0 0
\(693\) −3.19842 −0.121498
\(694\) 0 0
\(695\) 10.6231 0.402957
\(696\) 0 0
\(697\) 4.52881 0.171541
\(698\) 0 0
\(699\) 26.3779 0.997703
\(700\) 0 0
\(701\) 47.2629 1.78510 0.892548 0.450953i \(-0.148916\pi\)
0.892548 + 0.450953i \(0.148916\pi\)
\(702\) 0 0
\(703\) −13.9182 −0.524934
\(704\) 0 0
\(705\) 9.57809 0.360732
\(706\) 0 0
\(707\) 7.31293 0.275031
\(708\) 0 0
\(709\) −11.0724 −0.415832 −0.207916 0.978147i \(-0.566668\pi\)
−0.207916 + 0.978147i \(0.566668\pi\)
\(710\) 0 0
\(711\) −26.2522 −0.984536
\(712\) 0 0
\(713\) 38.0100 1.42349
\(714\) 0 0
\(715\) 0.157296 0.00588253
\(716\) 0 0
\(717\) −5.36866 −0.200496
\(718\) 0 0
\(719\) −44.0986 −1.64460 −0.822300 0.569055i \(-0.807309\pi\)
−0.822300 + 0.569055i \(0.807309\pi\)
\(720\) 0 0
\(721\) −42.3734 −1.57807
\(722\) 0 0
\(723\) −23.5020 −0.874047
\(724\) 0 0
\(725\) −30.5804 −1.13573
\(726\) 0 0
\(727\) 14.1669 0.525421 0.262711 0.964875i \(-0.415384\pi\)
0.262711 + 0.964875i \(0.415384\pi\)
\(728\) 0 0
\(729\) −43.6204 −1.61557
\(730\) 0 0
\(731\) −42.5598 −1.57413
\(732\) 0 0
\(733\) −11.6254 −0.429392 −0.214696 0.976681i \(-0.568876\pi\)
−0.214696 + 0.976681i \(0.568876\pi\)
\(734\) 0 0
\(735\) 8.80513 0.324782
\(736\) 0 0
\(737\) −1.65780 −0.0610660
\(738\) 0 0
\(739\) −35.3222 −1.29935 −0.649674 0.760213i \(-0.725094\pi\)
−0.649674 + 0.760213i \(0.725094\pi\)
\(740\) 0 0
\(741\) −24.8645 −0.913420
\(742\) 0 0
\(743\) 12.9680 0.475751 0.237876 0.971296i \(-0.423549\pi\)
0.237876 + 0.971296i \(0.423549\pi\)
\(744\) 0 0
\(745\) 3.39128 0.124247
\(746\) 0 0
\(747\) −74.0260 −2.70847
\(748\) 0 0
\(749\) 63.6858 2.32703
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −39.4704 −1.43838
\(754\) 0 0
\(755\) −8.16401 −0.297119
\(756\) 0 0
\(757\) 13.6843 0.497363 0.248682 0.968585i \(-0.420003\pi\)
0.248682 + 0.968585i \(0.420003\pi\)
\(758\) 0 0
\(759\) −2.14886 −0.0779985
\(760\) 0 0
\(761\) 19.4331 0.704448 0.352224 0.935916i \(-0.385426\pi\)
0.352224 + 0.935916i \(0.385426\pi\)
\(762\) 0 0
\(763\) −36.6827 −1.32800
\(764\) 0 0
\(765\) −11.6952 −0.422841
\(766\) 0 0
\(767\) −16.2006 −0.584969
\(768\) 0 0
\(769\) 16.8085 0.606131 0.303066 0.952970i \(-0.401990\pi\)
0.303066 + 0.952970i \(0.401990\pi\)
\(770\) 0 0
\(771\) 29.2037 1.05175
\(772\) 0 0
\(773\) 43.9213 1.57974 0.789869 0.613276i \(-0.210148\pi\)
0.789869 + 0.613276i \(0.210148\pi\)
\(774\) 0 0
\(775\) 43.0271 1.54558
\(776\) 0 0
\(777\) −23.5597 −0.845199
\(778\) 0 0
\(779\) 6.24747 0.223839
\(780\) 0 0
\(781\) −0.985345 −0.0352584
\(782\) 0 0
\(783\) 34.3135 1.22627
\(784\) 0 0
\(785\) −11.0037 −0.392740
\(786\) 0 0
\(787\) −33.0207 −1.17706 −0.588530 0.808475i \(-0.700293\pi\)
−0.588530 + 0.808475i \(0.700293\pi\)
\(788\) 0 0
\(789\) 9.60046 0.341785
\(790\) 0 0
\(791\) −5.66514 −0.201429
\(792\) 0 0
\(793\) 10.5351 0.374111
\(794\) 0 0
\(795\) −10.4468 −0.370511
\(796\) 0 0
\(797\) 36.5728 1.29547 0.647737 0.761864i \(-0.275715\pi\)
0.647737 + 0.761864i \(0.275715\pi\)
\(798\) 0 0
\(799\) −25.8113 −0.913140
\(800\) 0 0
\(801\) 63.2881 2.23618
\(802\) 0 0
\(803\) −2.18363 −0.0770585
\(804\) 0 0
\(805\) 8.26293 0.291230
\(806\) 0 0
\(807\) 34.3833 1.21035
\(808\) 0 0
\(809\) −29.3319 −1.03126 −0.515628 0.856813i \(-0.672441\pi\)
−0.515628 + 0.856813i \(0.672441\pi\)
\(810\) 0 0
\(811\) 37.1117 1.30317 0.651583 0.758577i \(-0.274105\pi\)
0.651583 + 0.758577i \(0.274105\pi\)
\(812\) 0 0
\(813\) −2.48359 −0.0871035
\(814\) 0 0
\(815\) 8.20107 0.287271
\(816\) 0 0
\(817\) −58.7110 −2.05404
\(818\) 0 0
\(819\) −26.0501 −0.910265
\(820\) 0 0
\(821\) −5.39651 −0.188339 −0.0941697 0.995556i \(-0.530020\pi\)
−0.0941697 + 0.995556i \(0.530020\pi\)
\(822\) 0 0
\(823\) 28.2770 0.985675 0.492838 0.870121i \(-0.335960\pi\)
0.492838 + 0.870121i \(0.335960\pi\)
\(824\) 0 0
\(825\) −2.43249 −0.0846884
\(826\) 0 0
\(827\) 2.97846 0.103571 0.0517855 0.998658i \(-0.483509\pi\)
0.0517855 + 0.998658i \(0.483509\pi\)
\(828\) 0 0
\(829\) 56.9304 1.97727 0.988637 0.150324i \(-0.0480316\pi\)
0.988637 + 0.150324i \(0.0480316\pi\)
\(830\) 0 0
\(831\) 49.9335 1.73217
\(832\) 0 0
\(833\) −23.7283 −0.822139
\(834\) 0 0
\(835\) 13.0906 0.453017
\(836\) 0 0
\(837\) −48.2797 −1.66879
\(838\) 0 0
\(839\) 36.1406 1.24771 0.623856 0.781540i \(-0.285565\pi\)
0.623856 + 0.781540i \(0.285565\pi\)
\(840\) 0 0
\(841\) 13.6499 0.470685
\(842\) 0 0
\(843\) 30.2199 1.04083
\(844\) 0 0
\(845\) −6.04326 −0.207894
\(846\) 0 0
\(847\) 38.8780 1.33586
\(848\) 0 0
\(849\) 73.7201 2.53007
\(850\) 0 0
\(851\) −9.79680 −0.335830
\(852\) 0 0
\(853\) 25.5692 0.875474 0.437737 0.899103i \(-0.355780\pi\)
0.437737 + 0.899103i \(0.355780\pi\)
\(854\) 0 0
\(855\) −16.1335 −0.551753
\(856\) 0 0
\(857\) 56.8797 1.94297 0.971486 0.237097i \(-0.0761959\pi\)
0.971486 + 0.237097i \(0.0761959\pi\)
\(858\) 0 0
\(859\) −29.0594 −0.991495 −0.495747 0.868467i \(-0.665106\pi\)
−0.495747 + 0.868467i \(0.665106\pi\)
\(860\) 0 0
\(861\) 10.5753 0.360404
\(862\) 0 0
\(863\) −16.8374 −0.573152 −0.286576 0.958058i \(-0.592517\pi\)
−0.286576 + 0.958058i \(0.592517\pi\)
\(864\) 0 0
\(865\) 5.62464 0.191244
\(866\) 0 0
\(867\) 3.22211 0.109428
\(868\) 0 0
\(869\) −0.997499 −0.0338378
\(870\) 0 0
\(871\) −13.5023 −0.457508
\(872\) 0 0
\(873\) 27.8390 0.942209
\(874\) 0 0
\(875\) 19.3412 0.653853
\(876\) 0 0
\(877\) −32.4101 −1.09441 −0.547206 0.836998i \(-0.684308\pi\)
−0.547206 + 0.836998i \(0.684308\pi\)
\(878\) 0 0
\(879\) 1.10122 0.0371433
\(880\) 0 0
\(881\) −11.9685 −0.403229 −0.201615 0.979465i \(-0.564619\pi\)
−0.201615 + 0.979465i \(0.564619\pi\)
\(882\) 0 0
\(883\) 41.5811 1.39931 0.699657 0.714479i \(-0.253336\pi\)
0.699657 + 0.714479i \(0.253336\pi\)
\(884\) 0 0
\(885\) −16.9838 −0.570906
\(886\) 0 0
\(887\) −38.3551 −1.28784 −0.643919 0.765094i \(-0.722692\pi\)
−0.643919 + 0.765094i \(0.722692\pi\)
\(888\) 0 0
\(889\) 16.7911 0.563156
\(890\) 0 0
\(891\) 0.0230499 0.000772200 0
\(892\) 0 0
\(893\) −35.6066 −1.19153
\(894\) 0 0
\(895\) 7.10658 0.237547
\(896\) 0 0
\(897\) −17.5017 −0.584366
\(898\) 0 0
\(899\) −60.0091 −2.00141
\(900\) 0 0
\(901\) 28.1524 0.937893
\(902\) 0 0
\(903\) −99.3817 −3.30722
\(904\) 0 0
\(905\) 10.9957 0.365509
\(906\) 0 0
\(907\) 27.3732 0.908914 0.454457 0.890769i \(-0.349833\pi\)
0.454457 + 0.890769i \(0.349833\pi\)
\(908\) 0 0
\(909\) −10.0505 −0.333353
\(910\) 0 0
\(911\) 24.1659 0.800653 0.400327 0.916373i \(-0.368897\pi\)
0.400327 + 0.916373i \(0.368897\pi\)
\(912\) 0 0
\(913\) −2.81274 −0.0930882
\(914\) 0 0
\(915\) 11.0444 0.365117
\(916\) 0 0
\(917\) 39.5229 1.30516
\(918\) 0 0
\(919\) 46.2457 1.52550 0.762752 0.646691i \(-0.223848\pi\)
0.762752 + 0.646691i \(0.223848\pi\)
\(920\) 0 0
\(921\) 9.23919 0.304442
\(922\) 0 0
\(923\) −8.02532 −0.264157
\(924\) 0 0
\(925\) −11.0899 −0.364634
\(926\) 0 0
\(927\) 58.2357 1.91271
\(928\) 0 0
\(929\) −30.3557 −0.995938 −0.497969 0.867195i \(-0.665921\pi\)
−0.497969 + 0.867195i \(0.665921\pi\)
\(930\) 0 0
\(931\) −32.7331 −1.07278
\(932\) 0 0
\(933\) 38.3029 1.25398
\(934\) 0 0
\(935\) −0.444380 −0.0145328
\(936\) 0 0
\(937\) −33.0604 −1.08003 −0.540017 0.841654i \(-0.681582\pi\)
−0.540017 + 0.841654i \(0.681582\pi\)
\(938\) 0 0
\(939\) −73.1370 −2.38674
\(940\) 0 0
\(941\) 33.8658 1.10399 0.551996 0.833847i \(-0.313866\pi\)
0.551996 + 0.833847i \(0.313866\pi\)
\(942\) 0 0
\(943\) 4.39750 0.143202
\(944\) 0 0
\(945\) −10.4954 −0.341417
\(946\) 0 0
\(947\) −16.2165 −0.526966 −0.263483 0.964664i \(-0.584871\pi\)
−0.263483 + 0.964664i \(0.584871\pi\)
\(948\) 0 0
\(949\) −17.7850 −0.577324
\(950\) 0 0
\(951\) −19.0837 −0.618830
\(952\) 0 0
\(953\) −51.9589 −1.68311 −0.841557 0.540168i \(-0.818361\pi\)
−0.841557 + 0.540168i \(0.818361\pi\)
\(954\) 0 0
\(955\) −10.5450 −0.341227
\(956\) 0 0
\(957\) 3.39255 0.109665
\(958\) 0 0
\(959\) −14.4140 −0.465452
\(960\) 0 0
\(961\) 53.4337 1.72367
\(962\) 0 0
\(963\) −87.5262 −2.82049
\(964\) 0 0
\(965\) −8.52275 −0.274357
\(966\) 0 0
\(967\) 10.6519 0.342541 0.171271 0.985224i \(-0.445213\pi\)
0.171271 + 0.985224i \(0.445213\pi\)
\(968\) 0 0
\(969\) 70.2452 2.25660
\(970\) 0 0
\(971\) −24.5157 −0.786746 −0.393373 0.919379i \(-0.628692\pi\)
−0.393373 + 0.919379i \(0.628692\pi\)
\(972\) 0 0
\(973\) −66.8481 −2.14305
\(974\) 0 0
\(975\) −19.8118 −0.634487
\(976\) 0 0
\(977\) −30.4904 −0.975473 −0.487737 0.872991i \(-0.662177\pi\)
−0.487737 + 0.872991i \(0.662177\pi\)
\(978\) 0 0
\(979\) 2.40474 0.0768558
\(980\) 0 0
\(981\) 50.4147 1.60962
\(982\) 0 0
\(983\) −29.7225 −0.948001 −0.474001 0.880525i \(-0.657191\pi\)
−0.474001 + 0.880525i \(0.657191\pi\)
\(984\) 0 0
\(985\) −10.3444 −0.329599
\(986\) 0 0
\(987\) −60.2723 −1.91849
\(988\) 0 0
\(989\) −41.3258 −1.31408
\(990\) 0 0
\(991\) 53.3128 1.69354 0.846769 0.531961i \(-0.178545\pi\)
0.846769 + 0.531961i \(0.178545\pi\)
\(992\) 0 0
\(993\) −14.2067 −0.450835
\(994\) 0 0
\(995\) 6.08425 0.192884
\(996\) 0 0
\(997\) 16.2008 0.513084 0.256542 0.966533i \(-0.417417\pi\)
0.256542 + 0.966533i \(0.417417\pi\)
\(998\) 0 0
\(999\) 12.4437 0.393702
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.1.42 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.42 44 1.1 even 1 trivial