Properties

Label 6008.2.a.b.1.44
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 1.44
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.96541 q^{3} +0.884771 q^{5} -3.59653 q^{7} +5.79365 q^{9} +O(q^{10})\) \(q+2.96541 q^{3} +0.884771 q^{5} -3.59653 q^{7} +5.79365 q^{9} -5.74927 q^{11} -0.730528 q^{13} +2.62371 q^{15} +1.55700 q^{17} -0.000218127 q^{19} -10.6652 q^{21} +5.06130 q^{23} -4.21718 q^{25} +8.28433 q^{27} -2.90584 q^{29} +2.03130 q^{31} -17.0489 q^{33} -3.18211 q^{35} -9.59024 q^{37} -2.16631 q^{39} -5.53604 q^{41} -5.49898 q^{43} +5.12606 q^{45} -4.78525 q^{47} +5.93505 q^{49} +4.61714 q^{51} +6.57420 q^{53} -5.08679 q^{55} -0.000646836 q^{57} -10.1018 q^{59} -0.100718 q^{61} -20.8371 q^{63} -0.646350 q^{65} -13.6515 q^{67} +15.0088 q^{69} -10.7277 q^{71} +12.8733 q^{73} -12.5057 q^{75} +20.6774 q^{77} +12.1717 q^{79} +7.18547 q^{81} +4.78293 q^{83} +1.37759 q^{85} -8.61700 q^{87} -14.9125 q^{89} +2.62737 q^{91} +6.02365 q^{93} -0.000192993 q^{95} +2.87858 q^{97} -33.3093 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) 2.96541 1.71208 0.856040 0.516909i \(-0.172918\pi\)
0.856040 + 0.516909i \(0.172918\pi\)
\(4\) 0 0
\(5\) 0.884771 0.395682 0.197841 0.980234i \(-0.436607\pi\)
0.197841 + 0.980234i \(0.436607\pi\)
\(6\) 0 0
\(7\) −3.59653 −1.35936 −0.679681 0.733508i \(-0.737882\pi\)
−0.679681 + 0.733508i \(0.737882\pi\)
\(8\) 0 0
\(9\) 5.79365 1.93122
\(10\) 0 0
\(11\) −5.74927 −1.73347 −0.866735 0.498769i \(-0.833786\pi\)
−0.866735 + 0.498769i \(0.833786\pi\)
\(12\) 0 0
\(13\) −0.730528 −0.202612 −0.101306 0.994855i \(-0.532302\pi\)
−0.101306 + 0.994855i \(0.532302\pi\)
\(14\) 0 0
\(15\) 2.62371 0.677439
\(16\) 0 0
\(17\) 1.55700 0.377628 0.188814 0.982013i \(-0.439536\pi\)
0.188814 + 0.982013i \(0.439536\pi\)
\(18\) 0 0
\(19\) −0.000218127 0 −5.00418e−5 0 −2.50209e−5 1.00000i \(-0.500008\pi\)
−2.50209e−5 1.00000i \(0.500008\pi\)
\(20\) 0 0
\(21\) −10.6652 −2.32734
\(22\) 0 0
\(23\) 5.06130 1.05535 0.527677 0.849445i \(-0.323063\pi\)
0.527677 + 0.849445i \(0.323063\pi\)
\(24\) 0 0
\(25\) −4.21718 −0.843436
\(26\) 0 0
\(27\) 8.28433 1.59432
\(28\) 0 0
\(29\) −2.90584 −0.539600 −0.269800 0.962916i \(-0.586958\pi\)
−0.269800 + 0.962916i \(0.586958\pi\)
\(30\) 0 0
\(31\) 2.03130 0.364833 0.182417 0.983221i \(-0.441608\pi\)
0.182417 + 0.983221i \(0.441608\pi\)
\(32\) 0 0
\(33\) −17.0489 −2.96784
\(34\) 0 0
\(35\) −3.18211 −0.537875
\(36\) 0 0
\(37\) −9.59024 −1.57663 −0.788313 0.615275i \(-0.789045\pi\)
−0.788313 + 0.615275i \(0.789045\pi\)
\(38\) 0 0
\(39\) −2.16631 −0.346888
\(40\) 0 0
\(41\) −5.53604 −0.864584 −0.432292 0.901734i \(-0.642295\pi\)
−0.432292 + 0.901734i \(0.642295\pi\)
\(42\) 0 0
\(43\) −5.49898 −0.838586 −0.419293 0.907851i \(-0.637722\pi\)
−0.419293 + 0.907851i \(0.637722\pi\)
\(44\) 0 0
\(45\) 5.12606 0.764148
\(46\) 0 0
\(47\) −4.78525 −0.698001 −0.349000 0.937123i \(-0.613479\pi\)
−0.349000 + 0.937123i \(0.613479\pi\)
\(48\) 0 0
\(49\) 5.93505 0.847864
\(50\) 0 0
\(51\) 4.61714 0.646529
\(52\) 0 0
\(53\) 6.57420 0.903036 0.451518 0.892262i \(-0.350883\pi\)
0.451518 + 0.892262i \(0.350883\pi\)
\(54\) 0 0
\(55\) −5.08679 −0.685902
\(56\) 0 0
\(57\) −0.000646836 0 −8.56756e−5 0
\(58\) 0 0
\(59\) −10.1018 −1.31515 −0.657574 0.753390i \(-0.728417\pi\)
−0.657574 + 0.753390i \(0.728417\pi\)
\(60\) 0 0
\(61\) −0.100718 −0.0128956 −0.00644779 0.999979i \(-0.502052\pi\)
−0.00644779 + 0.999979i \(0.502052\pi\)
\(62\) 0 0
\(63\) −20.8371 −2.62522
\(64\) 0 0
\(65\) −0.646350 −0.0801699
\(66\) 0 0
\(67\) −13.6515 −1.66780 −0.833901 0.551914i \(-0.813898\pi\)
−0.833901 + 0.551914i \(0.813898\pi\)
\(68\) 0 0
\(69\) 15.0088 1.80685
\(70\) 0 0
\(71\) −10.7277 −1.27315 −0.636575 0.771215i \(-0.719649\pi\)
−0.636575 + 0.771215i \(0.719649\pi\)
\(72\) 0 0
\(73\) 12.8733 1.50670 0.753350 0.657619i \(-0.228436\pi\)
0.753350 + 0.657619i \(0.228436\pi\)
\(74\) 0 0
\(75\) −12.5057 −1.44403
\(76\) 0 0
\(77\) 20.6774 2.35641
\(78\) 0 0
\(79\) 12.1717 1.36942 0.684712 0.728814i \(-0.259928\pi\)
0.684712 + 0.728814i \(0.259928\pi\)
\(80\) 0 0
\(81\) 7.18547 0.798386
\(82\) 0 0
\(83\) 4.78293 0.524995 0.262498 0.964933i \(-0.415454\pi\)
0.262498 + 0.964933i \(0.415454\pi\)
\(84\) 0 0
\(85\) 1.37759 0.149420
\(86\) 0 0
\(87\) −8.61700 −0.923839
\(88\) 0 0
\(89\) −14.9125 −1.58072 −0.790362 0.612640i \(-0.790107\pi\)
−0.790362 + 0.612640i \(0.790107\pi\)
\(90\) 0 0
\(91\) 2.62737 0.275423
\(92\) 0 0
\(93\) 6.02365 0.624623
\(94\) 0 0
\(95\) −0.000192993 0 −1.98006e−5 0
\(96\) 0 0
\(97\) 2.87858 0.292276 0.146138 0.989264i \(-0.453316\pi\)
0.146138 + 0.989264i \(0.453316\pi\)
\(98\) 0 0
\(99\) −33.3093 −3.34771
\(100\) 0 0
\(101\) 4.88531 0.486107 0.243053 0.970013i \(-0.421851\pi\)
0.243053 + 0.970013i \(0.421851\pi\)
\(102\) 0 0
\(103\) 3.42356 0.337334 0.168667 0.985673i \(-0.446054\pi\)
0.168667 + 0.985673i \(0.446054\pi\)
\(104\) 0 0
\(105\) −9.43626 −0.920884
\(106\) 0 0
\(107\) 1.20424 0.116418 0.0582092 0.998304i \(-0.481461\pi\)
0.0582092 + 0.998304i \(0.481461\pi\)
\(108\) 0 0
\(109\) 3.84975 0.368740 0.184370 0.982857i \(-0.440976\pi\)
0.184370 + 0.982857i \(0.440976\pi\)
\(110\) 0 0
\(111\) −28.4390 −2.69931
\(112\) 0 0
\(113\) −0.797629 −0.0750346 −0.0375173 0.999296i \(-0.511945\pi\)
−0.0375173 + 0.999296i \(0.511945\pi\)
\(114\) 0 0
\(115\) 4.47809 0.417584
\(116\) 0 0
\(117\) −4.23243 −0.391288
\(118\) 0 0
\(119\) −5.59980 −0.513333
\(120\) 0 0
\(121\) 22.0541 2.00492
\(122\) 0 0
\(123\) −16.4166 −1.48024
\(124\) 0 0
\(125\) −8.15510 −0.729414
\(126\) 0 0
\(127\) −9.00969 −0.799480 −0.399740 0.916628i \(-0.630900\pi\)
−0.399740 + 0.916628i \(0.630900\pi\)
\(128\) 0 0
\(129\) −16.3067 −1.43573
\(130\) 0 0
\(131\) 2.78116 0.242991 0.121496 0.992592i \(-0.461231\pi\)
0.121496 + 0.992592i \(0.461231\pi\)
\(132\) 0 0
\(133\) 0.000784502 0 6.80249e−5 0
\(134\) 0 0
\(135\) 7.32974 0.630844
\(136\) 0 0
\(137\) −15.7398 −1.34474 −0.672370 0.740215i \(-0.734724\pi\)
−0.672370 + 0.740215i \(0.734724\pi\)
\(138\) 0 0
\(139\) −12.1771 −1.03285 −0.516423 0.856334i \(-0.672737\pi\)
−0.516423 + 0.856334i \(0.672737\pi\)
\(140\) 0 0
\(141\) −14.1902 −1.19503
\(142\) 0 0
\(143\) 4.20000 0.351222
\(144\) 0 0
\(145\) −2.57100 −0.213510
\(146\) 0 0
\(147\) 17.5999 1.45161
\(148\) 0 0
\(149\) 15.7070 1.28677 0.643384 0.765543i \(-0.277530\pi\)
0.643384 + 0.765543i \(0.277530\pi\)
\(150\) 0 0
\(151\) −7.33810 −0.597166 −0.298583 0.954384i \(-0.596514\pi\)
−0.298583 + 0.954384i \(0.596514\pi\)
\(152\) 0 0
\(153\) 9.02071 0.729281
\(154\) 0 0
\(155\) 1.79724 0.144358
\(156\) 0 0
\(157\) 18.3411 1.46378 0.731890 0.681423i \(-0.238638\pi\)
0.731890 + 0.681423i \(0.238638\pi\)
\(158\) 0 0
\(159\) 19.4952 1.54607
\(160\) 0 0
\(161\) −18.2031 −1.43461
\(162\) 0 0
\(163\) −2.92420 −0.229041 −0.114521 0.993421i \(-0.536533\pi\)
−0.114521 + 0.993421i \(0.536533\pi\)
\(164\) 0 0
\(165\) −15.0844 −1.17432
\(166\) 0 0
\(167\) −1.25130 −0.0968286 −0.0484143 0.998827i \(-0.515417\pi\)
−0.0484143 + 0.998827i \(0.515417\pi\)
\(168\) 0 0
\(169\) −12.4663 −0.958948
\(170\) 0 0
\(171\) −0.00126375 −9.66417e−5 0
\(172\) 0 0
\(173\) −14.0554 −1.06861 −0.534306 0.845291i \(-0.679427\pi\)
−0.534306 + 0.845291i \(0.679427\pi\)
\(174\) 0 0
\(175\) 15.1672 1.14653
\(176\) 0 0
\(177\) −29.9561 −2.25164
\(178\) 0 0
\(179\) 21.0259 1.57155 0.785776 0.618512i \(-0.212264\pi\)
0.785776 + 0.618512i \(0.212264\pi\)
\(180\) 0 0
\(181\) 8.45584 0.628518 0.314259 0.949337i \(-0.398244\pi\)
0.314259 + 0.949337i \(0.398244\pi\)
\(182\) 0 0
\(183\) −0.298669 −0.0220783
\(184\) 0 0
\(185\) −8.48517 −0.623842
\(186\) 0 0
\(187\) −8.95160 −0.654606
\(188\) 0 0
\(189\) −29.7949 −2.16726
\(190\) 0 0
\(191\) −14.2503 −1.03112 −0.515559 0.856854i \(-0.672416\pi\)
−0.515559 + 0.856854i \(0.672416\pi\)
\(192\) 0 0
\(193\) −10.3303 −0.743593 −0.371796 0.928314i \(-0.621258\pi\)
−0.371796 + 0.928314i \(0.621258\pi\)
\(194\) 0 0
\(195\) −1.91669 −0.137257
\(196\) 0 0
\(197\) 18.4733 1.31617 0.658083 0.752946i \(-0.271368\pi\)
0.658083 + 0.752946i \(0.271368\pi\)
\(198\) 0 0
\(199\) 2.02675 0.143672 0.0718361 0.997416i \(-0.477114\pi\)
0.0718361 + 0.997416i \(0.477114\pi\)
\(200\) 0 0
\(201\) −40.4824 −2.85541
\(202\) 0 0
\(203\) 10.4509 0.733512
\(204\) 0 0
\(205\) −4.89813 −0.342100
\(206\) 0 0
\(207\) 29.3234 2.03812
\(208\) 0 0
\(209\) 0.00125407 8.67460e−5 0
\(210\) 0 0
\(211\) −7.72177 −0.531589 −0.265794 0.964030i \(-0.585634\pi\)
−0.265794 + 0.964030i \(0.585634\pi\)
\(212\) 0 0
\(213\) −31.8122 −2.17973
\(214\) 0 0
\(215\) −4.86534 −0.331813
\(216\) 0 0
\(217\) −7.30565 −0.495940
\(218\) 0 0
\(219\) 38.1745 2.57959
\(220\) 0 0
\(221\) −1.13743 −0.0765119
\(222\) 0 0
\(223\) −24.5669 −1.64512 −0.822560 0.568678i \(-0.807455\pi\)
−0.822560 + 0.568678i \(0.807455\pi\)
\(224\) 0 0
\(225\) −24.4329 −1.62886
\(226\) 0 0
\(227\) −5.27151 −0.349882 −0.174941 0.984579i \(-0.555974\pi\)
−0.174941 + 0.984579i \(0.555974\pi\)
\(228\) 0 0
\(229\) 17.0245 1.12501 0.562506 0.826793i \(-0.309837\pi\)
0.562506 + 0.826793i \(0.309837\pi\)
\(230\) 0 0
\(231\) 61.3171 4.03437
\(232\) 0 0
\(233\) −6.68875 −0.438195 −0.219097 0.975703i \(-0.570311\pi\)
−0.219097 + 0.975703i \(0.570311\pi\)
\(234\) 0 0
\(235\) −4.23385 −0.276186
\(236\) 0 0
\(237\) 36.0941 2.34456
\(238\) 0 0
\(239\) −12.9715 −0.839056 −0.419528 0.907742i \(-0.637804\pi\)
−0.419528 + 0.907742i \(0.637804\pi\)
\(240\) 0 0
\(241\) 3.52989 0.227380 0.113690 0.993516i \(-0.463733\pi\)
0.113690 + 0.993516i \(0.463733\pi\)
\(242\) 0 0
\(243\) −3.54512 −0.227420
\(244\) 0 0
\(245\) 5.25116 0.335484
\(246\) 0 0
\(247\) 0.000159348 0 1.01391e−5 0
\(248\) 0 0
\(249\) 14.1834 0.898834
\(250\) 0 0
\(251\) −9.41803 −0.594461 −0.297230 0.954806i \(-0.596063\pi\)
−0.297230 + 0.954806i \(0.596063\pi\)
\(252\) 0 0
\(253\) −29.0988 −1.82942
\(254\) 0 0
\(255\) 4.08511 0.255820
\(256\) 0 0
\(257\) 8.18963 0.510855 0.255427 0.966828i \(-0.417784\pi\)
0.255427 + 0.966828i \(0.417784\pi\)
\(258\) 0 0
\(259\) 34.4916 2.14320
\(260\) 0 0
\(261\) −16.8354 −1.04209
\(262\) 0 0
\(263\) 19.2938 1.18971 0.594853 0.803835i \(-0.297210\pi\)
0.594853 + 0.803835i \(0.297210\pi\)
\(264\) 0 0
\(265\) 5.81667 0.357315
\(266\) 0 0
\(267\) −44.2217 −2.70633
\(268\) 0 0
\(269\) 15.0549 0.917913 0.458956 0.888459i \(-0.348223\pi\)
0.458956 + 0.888459i \(0.348223\pi\)
\(270\) 0 0
\(271\) −16.6993 −1.01441 −0.507206 0.861825i \(-0.669321\pi\)
−0.507206 + 0.861825i \(0.669321\pi\)
\(272\) 0 0
\(273\) 7.79122 0.471546
\(274\) 0 0
\(275\) 24.2457 1.46207
\(276\) 0 0
\(277\) 0.532678 0.0320055 0.0160028 0.999872i \(-0.494906\pi\)
0.0160028 + 0.999872i \(0.494906\pi\)
\(278\) 0 0
\(279\) 11.7687 0.704572
\(280\) 0 0
\(281\) 11.5228 0.687395 0.343698 0.939080i \(-0.388320\pi\)
0.343698 + 0.939080i \(0.388320\pi\)
\(282\) 0 0
\(283\) 5.49650 0.326733 0.163366 0.986565i \(-0.447765\pi\)
0.163366 + 0.986565i \(0.447765\pi\)
\(284\) 0 0
\(285\) −0.000572302 0 −3.39003e−5 0
\(286\) 0 0
\(287\) 19.9106 1.17528
\(288\) 0 0
\(289\) −14.5758 −0.857397
\(290\) 0 0
\(291\) 8.53618 0.500400
\(292\) 0 0
\(293\) −4.24944 −0.248255 −0.124128 0.992266i \(-0.539613\pi\)
−0.124128 + 0.992266i \(0.539613\pi\)
\(294\) 0 0
\(295\) −8.93782 −0.520380
\(296\) 0 0
\(297\) −47.6289 −2.76371
\(298\) 0 0
\(299\) −3.69742 −0.213827
\(300\) 0 0
\(301\) 19.7772 1.13994
\(302\) 0 0
\(303\) 14.4870 0.832254
\(304\) 0 0
\(305\) −0.0891121 −0.00510255
\(306\) 0 0
\(307\) 30.8981 1.76344 0.881722 0.471768i \(-0.156384\pi\)
0.881722 + 0.471768i \(0.156384\pi\)
\(308\) 0 0
\(309\) 10.1523 0.577542
\(310\) 0 0
\(311\) −21.8983 −1.24174 −0.620869 0.783915i \(-0.713220\pi\)
−0.620869 + 0.783915i \(0.713220\pi\)
\(312\) 0 0
\(313\) 12.1145 0.684753 0.342377 0.939563i \(-0.388768\pi\)
0.342377 + 0.939563i \(0.388768\pi\)
\(314\) 0 0
\(315\) −18.4360 −1.03875
\(316\) 0 0
\(317\) 28.7761 1.61623 0.808114 0.589026i \(-0.200489\pi\)
0.808114 + 0.589026i \(0.200489\pi\)
\(318\) 0 0
\(319\) 16.7064 0.935381
\(320\) 0 0
\(321\) 3.57107 0.199318
\(322\) 0 0
\(323\) −0.000339624 0 −1.88972e−5 0
\(324\) 0 0
\(325\) 3.08077 0.170890
\(326\) 0 0
\(327\) 11.4161 0.631312
\(328\) 0 0
\(329\) 17.2103 0.948835
\(330\) 0 0
\(331\) −30.1988 −1.65988 −0.829938 0.557855i \(-0.811624\pi\)
−0.829938 + 0.557855i \(0.811624\pi\)
\(332\) 0 0
\(333\) −55.5625 −3.04481
\(334\) 0 0
\(335\) −12.0785 −0.659919
\(336\) 0 0
\(337\) 16.1502 0.879756 0.439878 0.898058i \(-0.355022\pi\)
0.439878 + 0.898058i \(0.355022\pi\)
\(338\) 0 0
\(339\) −2.36530 −0.128465
\(340\) 0 0
\(341\) −11.6785 −0.632427
\(342\) 0 0
\(343\) 3.83013 0.206808
\(344\) 0 0
\(345\) 13.2794 0.714937
\(346\) 0 0
\(347\) −33.2301 −1.78389 −0.891943 0.452148i \(-0.850658\pi\)
−0.891943 + 0.452148i \(0.850658\pi\)
\(348\) 0 0
\(349\) 22.0847 1.18216 0.591082 0.806611i \(-0.298701\pi\)
0.591082 + 0.806611i \(0.298701\pi\)
\(350\) 0 0
\(351\) −6.05194 −0.323028
\(352\) 0 0
\(353\) −22.9292 −1.22040 −0.610199 0.792248i \(-0.708910\pi\)
−0.610199 + 0.792248i \(0.708910\pi\)
\(354\) 0 0
\(355\) −9.49160 −0.503762
\(356\) 0 0
\(357\) −16.6057 −0.878866
\(358\) 0 0
\(359\) −8.19210 −0.432363 −0.216181 0.976353i \(-0.569360\pi\)
−0.216181 + 0.976353i \(0.569360\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 0 0
\(363\) 65.3994 3.43258
\(364\) 0 0
\(365\) 11.3899 0.596174
\(366\) 0 0
\(367\) −6.26701 −0.327135 −0.163568 0.986532i \(-0.552300\pi\)
−0.163568 + 0.986532i \(0.552300\pi\)
\(368\) 0 0
\(369\) −32.0739 −1.66970
\(370\) 0 0
\(371\) −23.6443 −1.22755
\(372\) 0 0
\(373\) −33.1365 −1.71574 −0.857871 0.513864i \(-0.828213\pi\)
−0.857871 + 0.513864i \(0.828213\pi\)
\(374\) 0 0
\(375\) −24.1832 −1.24882
\(376\) 0 0
\(377\) 2.12280 0.109330
\(378\) 0 0
\(379\) −6.35013 −0.326184 −0.163092 0.986611i \(-0.552147\pi\)
−0.163092 + 0.986611i \(0.552147\pi\)
\(380\) 0 0
\(381\) −26.7174 −1.36877
\(382\) 0 0
\(383\) 10.1163 0.516919 0.258460 0.966022i \(-0.416785\pi\)
0.258460 + 0.966022i \(0.416785\pi\)
\(384\) 0 0
\(385\) 18.2948 0.932390
\(386\) 0 0
\(387\) −31.8592 −1.61949
\(388\) 0 0
\(389\) 25.8793 1.31213 0.656066 0.754703i \(-0.272219\pi\)
0.656066 + 0.754703i \(0.272219\pi\)
\(390\) 0 0
\(391\) 7.88043 0.398531
\(392\) 0 0
\(393\) 8.24729 0.416021
\(394\) 0 0
\(395\) 10.7692 0.541856
\(396\) 0 0
\(397\) −19.6261 −0.985003 −0.492502 0.870311i \(-0.663917\pi\)
−0.492502 + 0.870311i \(0.663917\pi\)
\(398\) 0 0
\(399\) 0.00232637 0.000116464 0
\(400\) 0 0
\(401\) −3.92229 −0.195870 −0.0979349 0.995193i \(-0.531224\pi\)
−0.0979349 + 0.995193i \(0.531224\pi\)
\(402\) 0 0
\(403\) −1.48392 −0.0739196
\(404\) 0 0
\(405\) 6.35750 0.315907
\(406\) 0 0
\(407\) 55.1369 2.73303
\(408\) 0 0
\(409\) 33.5096 1.65694 0.828471 0.560031i \(-0.189211\pi\)
0.828471 + 0.560031i \(0.189211\pi\)
\(410\) 0 0
\(411\) −46.6749 −2.30230
\(412\) 0 0
\(413\) 36.3316 1.78776
\(414\) 0 0
\(415\) 4.23180 0.207731
\(416\) 0 0
\(417\) −36.1100 −1.76831
\(418\) 0 0
\(419\) −9.71141 −0.474433 −0.237217 0.971457i \(-0.576235\pi\)
−0.237217 + 0.971457i \(0.576235\pi\)
\(420\) 0 0
\(421\) −10.7693 −0.524865 −0.262433 0.964950i \(-0.584525\pi\)
−0.262433 + 0.964950i \(0.584525\pi\)
\(422\) 0 0
\(423\) −27.7241 −1.34799
\(424\) 0 0
\(425\) −6.56614 −0.318505
\(426\) 0 0
\(427\) 0.362235 0.0175298
\(428\) 0 0
\(429\) 12.4547 0.601320
\(430\) 0 0
\(431\) 3.37426 0.162533 0.0812663 0.996692i \(-0.474104\pi\)
0.0812663 + 0.996692i \(0.474104\pi\)
\(432\) 0 0
\(433\) 17.5334 0.842600 0.421300 0.906921i \(-0.361574\pi\)
0.421300 + 0.906921i \(0.361574\pi\)
\(434\) 0 0
\(435\) −7.62407 −0.365546
\(436\) 0 0
\(437\) −0.00110401 −5.28118e−5 0
\(438\) 0 0
\(439\) 2.57771 0.123027 0.0615136 0.998106i \(-0.480407\pi\)
0.0615136 + 0.998106i \(0.480407\pi\)
\(440\) 0 0
\(441\) 34.3856 1.63741
\(442\) 0 0
\(443\) 22.5113 1.06955 0.534773 0.844996i \(-0.320397\pi\)
0.534773 + 0.844996i \(0.320397\pi\)
\(444\) 0 0
\(445\) −13.1942 −0.625464
\(446\) 0 0
\(447\) 46.5777 2.20305
\(448\) 0 0
\(449\) −5.51994 −0.260502 −0.130251 0.991481i \(-0.541578\pi\)
−0.130251 + 0.991481i \(0.541578\pi\)
\(450\) 0 0
\(451\) 31.8282 1.49873
\(452\) 0 0
\(453\) −21.7605 −1.02240
\(454\) 0 0
\(455\) 2.32462 0.108980
\(456\) 0 0
\(457\) 24.1526 1.12981 0.564907 0.825155i \(-0.308912\pi\)
0.564907 + 0.825155i \(0.308912\pi\)
\(458\) 0 0
\(459\) 12.8987 0.602059
\(460\) 0 0
\(461\) 28.7937 1.34106 0.670529 0.741884i \(-0.266067\pi\)
0.670529 + 0.741884i \(0.266067\pi\)
\(462\) 0 0
\(463\) 42.1961 1.96102 0.980509 0.196475i \(-0.0629495\pi\)
0.980509 + 0.196475i \(0.0629495\pi\)
\(464\) 0 0
\(465\) 5.32955 0.247152
\(466\) 0 0
\(467\) −19.8438 −0.918260 −0.459130 0.888369i \(-0.651839\pi\)
−0.459130 + 0.888369i \(0.651839\pi\)
\(468\) 0 0
\(469\) 49.0982 2.26715
\(470\) 0 0
\(471\) 54.3889 2.50611
\(472\) 0 0
\(473\) 31.6151 1.45366
\(474\) 0 0
\(475\) 0.000919882 0 4.22071e−5 0
\(476\) 0 0
\(477\) 38.0887 1.74396
\(478\) 0 0
\(479\) −2.44800 −0.111852 −0.0559259 0.998435i \(-0.517811\pi\)
−0.0559259 + 0.998435i \(0.517811\pi\)
\(480\) 0 0
\(481\) 7.00594 0.319443
\(482\) 0 0
\(483\) −53.9797 −2.45616
\(484\) 0 0
\(485\) 2.54689 0.115648
\(486\) 0 0
\(487\) 26.8878 1.21840 0.609201 0.793016i \(-0.291490\pi\)
0.609201 + 0.793016i \(0.291490\pi\)
\(488\) 0 0
\(489\) −8.67145 −0.392137
\(490\) 0 0
\(491\) 18.0058 0.812591 0.406295 0.913742i \(-0.366820\pi\)
0.406295 + 0.913742i \(0.366820\pi\)
\(492\) 0 0
\(493\) −4.52438 −0.203768
\(494\) 0 0
\(495\) −29.4711 −1.32463
\(496\) 0 0
\(497\) 38.5827 1.73067
\(498\) 0 0
\(499\) 4.67645 0.209347 0.104673 0.994507i \(-0.466620\pi\)
0.104673 + 0.994507i \(0.466620\pi\)
\(500\) 0 0
\(501\) −3.71062 −0.165778
\(502\) 0 0
\(503\) −6.26549 −0.279364 −0.139682 0.990196i \(-0.544608\pi\)
−0.139682 + 0.990196i \(0.544608\pi\)
\(504\) 0 0
\(505\) 4.32238 0.192344
\(506\) 0 0
\(507\) −36.9678 −1.64180
\(508\) 0 0
\(509\) 10.8597 0.481346 0.240673 0.970606i \(-0.422632\pi\)
0.240673 + 0.970606i \(0.422632\pi\)
\(510\) 0 0
\(511\) −46.2991 −2.04815
\(512\) 0 0
\(513\) −0.00180704 −7.97827e−5 0
\(514\) 0 0
\(515\) 3.02907 0.133477
\(516\) 0 0
\(517\) 27.5117 1.20996
\(518\) 0 0
\(519\) −41.6800 −1.82955
\(520\) 0 0
\(521\) 12.9623 0.567891 0.283945 0.958840i \(-0.408357\pi\)
0.283945 + 0.958840i \(0.408357\pi\)
\(522\) 0 0
\(523\) 10.6615 0.466193 0.233097 0.972454i \(-0.425114\pi\)
0.233097 + 0.972454i \(0.425114\pi\)
\(524\) 0 0
\(525\) 44.9770 1.96296
\(526\) 0 0
\(527\) 3.16274 0.137771
\(528\) 0 0
\(529\) 2.61673 0.113771
\(530\) 0 0
\(531\) −58.5266 −2.53984
\(532\) 0 0
\(533\) 4.04423 0.175175
\(534\) 0 0
\(535\) 1.06548 0.0460646
\(536\) 0 0
\(537\) 62.3505 2.69062
\(538\) 0 0
\(539\) −34.1222 −1.46975
\(540\) 0 0
\(541\) −21.5182 −0.925140 −0.462570 0.886583i \(-0.653073\pi\)
−0.462570 + 0.886583i \(0.653073\pi\)
\(542\) 0 0
\(543\) 25.0750 1.07607
\(544\) 0 0
\(545\) 3.40615 0.145904
\(546\) 0 0
\(547\) 34.3330 1.46797 0.733986 0.679164i \(-0.237658\pi\)
0.733986 + 0.679164i \(0.237658\pi\)
\(548\) 0 0
\(549\) −0.583524 −0.0249042
\(550\) 0 0
\(551\) 0.000633842 0 2.70026e−5 0
\(552\) 0 0
\(553\) −43.7760 −1.86154
\(554\) 0 0
\(555\) −25.1620 −1.06807
\(556\) 0 0
\(557\) 20.1350 0.853148 0.426574 0.904453i \(-0.359720\pi\)
0.426574 + 0.904453i \(0.359720\pi\)
\(558\) 0 0
\(559\) 4.01716 0.169908
\(560\) 0 0
\(561\) −26.5452 −1.12074
\(562\) 0 0
\(563\) 40.9515 1.72590 0.862951 0.505288i \(-0.168614\pi\)
0.862951 + 0.505288i \(0.168614\pi\)
\(564\) 0 0
\(565\) −0.705719 −0.0296898
\(566\) 0 0
\(567\) −25.8428 −1.08530
\(568\) 0 0
\(569\) −32.0053 −1.34173 −0.670867 0.741578i \(-0.734078\pi\)
−0.670867 + 0.741578i \(0.734078\pi\)
\(570\) 0 0
\(571\) −40.4408 −1.69240 −0.846198 0.532869i \(-0.821114\pi\)
−0.846198 + 0.532869i \(0.821114\pi\)
\(572\) 0 0
\(573\) −42.2581 −1.76536
\(574\) 0 0
\(575\) −21.3444 −0.890123
\(576\) 0 0
\(577\) −18.2538 −0.759917 −0.379959 0.925004i \(-0.624062\pi\)
−0.379959 + 0.925004i \(0.624062\pi\)
\(578\) 0 0
\(579\) −30.6336 −1.27309
\(580\) 0 0
\(581\) −17.2020 −0.713658
\(582\) 0 0
\(583\) −37.7969 −1.56539
\(584\) 0 0
\(585\) −3.74473 −0.154826
\(586\) 0 0
\(587\) 1.68219 0.0694314 0.0347157 0.999397i \(-0.488947\pi\)
0.0347157 + 0.999397i \(0.488947\pi\)
\(588\) 0 0
\(589\) −0.000443083 0 −1.82569e−5 0
\(590\) 0 0
\(591\) 54.7808 2.25338
\(592\) 0 0
\(593\) −41.4684 −1.70290 −0.851452 0.524433i \(-0.824277\pi\)
−0.851452 + 0.524433i \(0.824277\pi\)
\(594\) 0 0
\(595\) −4.95454 −0.203116
\(596\) 0 0
\(597\) 6.01013 0.245978
\(598\) 0 0
\(599\) 6.30022 0.257420 0.128710 0.991682i \(-0.458916\pi\)
0.128710 + 0.991682i \(0.458916\pi\)
\(600\) 0 0
\(601\) 2.92182 0.119183 0.0595917 0.998223i \(-0.481020\pi\)
0.0595917 + 0.998223i \(0.481020\pi\)
\(602\) 0 0
\(603\) −79.0924 −3.22089
\(604\) 0 0
\(605\) 19.5128 0.793310
\(606\) 0 0
\(607\) 3.18809 0.129401 0.0647003 0.997905i \(-0.479391\pi\)
0.0647003 + 0.997905i \(0.479391\pi\)
\(608\) 0 0
\(609\) 30.9913 1.25583
\(610\) 0 0
\(611\) 3.49576 0.141423
\(612\) 0 0
\(613\) 5.67680 0.229284 0.114642 0.993407i \(-0.463428\pi\)
0.114642 + 0.993407i \(0.463428\pi\)
\(614\) 0 0
\(615\) −14.5250 −0.585703
\(616\) 0 0
\(617\) 27.0567 1.08926 0.544630 0.838676i \(-0.316670\pi\)
0.544630 + 0.838676i \(0.316670\pi\)
\(618\) 0 0
\(619\) 24.1115 0.969124 0.484562 0.874757i \(-0.338979\pi\)
0.484562 + 0.874757i \(0.338979\pi\)
\(620\) 0 0
\(621\) 41.9295 1.68257
\(622\) 0 0
\(623\) 53.6334 2.14878
\(624\) 0 0
\(625\) 13.8705 0.554820
\(626\) 0 0
\(627\) 0.00371884 0.000148516 0
\(628\) 0 0
\(629\) −14.9320 −0.595377
\(630\) 0 0
\(631\) −6.09867 −0.242784 −0.121392 0.992605i \(-0.538736\pi\)
−0.121392 + 0.992605i \(0.538736\pi\)
\(632\) 0 0
\(633\) −22.8982 −0.910122
\(634\) 0 0
\(635\) −7.97151 −0.316340
\(636\) 0 0
\(637\) −4.33572 −0.171787
\(638\) 0 0
\(639\) −62.1529 −2.45873
\(640\) 0 0
\(641\) −32.0752 −1.26690 −0.633448 0.773785i \(-0.718361\pi\)
−0.633448 + 0.773785i \(0.718361\pi\)
\(642\) 0 0
\(643\) 10.4495 0.412090 0.206045 0.978543i \(-0.433941\pi\)
0.206045 + 0.978543i \(0.433941\pi\)
\(644\) 0 0
\(645\) −14.4277 −0.568091
\(646\) 0 0
\(647\) 31.5311 1.23962 0.619808 0.784754i \(-0.287211\pi\)
0.619808 + 0.784754i \(0.287211\pi\)
\(648\) 0 0
\(649\) 58.0782 2.27977
\(650\) 0 0
\(651\) −21.6643 −0.849089
\(652\) 0 0
\(653\) −8.28625 −0.324266 −0.162133 0.986769i \(-0.551837\pi\)
−0.162133 + 0.986769i \(0.551837\pi\)
\(654\) 0 0
\(655\) 2.46069 0.0961472
\(656\) 0 0
\(657\) 74.5832 2.90977
\(658\) 0 0
\(659\) −10.2273 −0.398398 −0.199199 0.979959i \(-0.563834\pi\)
−0.199199 + 0.979959i \(0.563834\pi\)
\(660\) 0 0
\(661\) 23.2710 0.905135 0.452568 0.891730i \(-0.350508\pi\)
0.452568 + 0.891730i \(0.350508\pi\)
\(662\) 0 0
\(663\) −3.37295 −0.130994
\(664\) 0 0
\(665\) 0.000694105 0 2.69162e−5 0
\(666\) 0 0
\(667\) −14.7073 −0.569469
\(668\) 0 0
\(669\) −72.8509 −2.81658
\(670\) 0 0
\(671\) 0.579053 0.0223541
\(672\) 0 0
\(673\) 13.5258 0.521380 0.260690 0.965423i \(-0.416050\pi\)
0.260690 + 0.965423i \(0.416050\pi\)
\(674\) 0 0
\(675\) −34.9365 −1.34471
\(676\) 0 0
\(677\) −24.1791 −0.929278 −0.464639 0.885500i \(-0.653816\pi\)
−0.464639 + 0.885500i \(0.653816\pi\)
\(678\) 0 0
\(679\) −10.3529 −0.397309
\(680\) 0 0
\(681\) −15.6322 −0.599027
\(682\) 0 0
\(683\) −29.8626 −1.14266 −0.571330 0.820721i \(-0.693572\pi\)
−0.571330 + 0.820721i \(0.693572\pi\)
\(684\) 0 0
\(685\) −13.9261 −0.532089
\(686\) 0 0
\(687\) 50.4847 1.92611
\(688\) 0 0
\(689\) −4.80264 −0.182966
\(690\) 0 0
\(691\) 13.3803 0.509011 0.254505 0.967071i \(-0.418087\pi\)
0.254505 + 0.967071i \(0.418087\pi\)
\(692\) 0 0
\(693\) 119.798 4.55075
\(694\) 0 0
\(695\) −10.7739 −0.408678
\(696\) 0 0
\(697\) −8.61961 −0.326491
\(698\) 0 0
\(699\) −19.8349 −0.750225
\(700\) 0 0
\(701\) −15.2061 −0.574325 −0.287163 0.957882i \(-0.592712\pi\)
−0.287163 + 0.957882i \(0.592712\pi\)
\(702\) 0 0
\(703\) 0.00209189 7.88972e−5 0
\(704\) 0 0
\(705\) −12.5551 −0.472853
\(706\) 0 0
\(707\) −17.5702 −0.660795
\(708\) 0 0
\(709\) −5.67741 −0.213220 −0.106610 0.994301i \(-0.534000\pi\)
−0.106610 + 0.994301i \(0.534000\pi\)
\(710\) 0 0
\(711\) 70.5187 2.64466
\(712\) 0 0
\(713\) 10.2810 0.385028
\(714\) 0 0
\(715\) 3.71604 0.138972
\(716\) 0 0
\(717\) −38.4658 −1.43653
\(718\) 0 0
\(719\) 32.6468 1.21752 0.608759 0.793355i \(-0.291668\pi\)
0.608759 + 0.793355i \(0.291668\pi\)
\(720\) 0 0
\(721\) −12.3130 −0.458558
\(722\) 0 0
\(723\) 10.4676 0.389293
\(724\) 0 0
\(725\) 12.2544 0.455118
\(726\) 0 0
\(727\) −40.6212 −1.50656 −0.753279 0.657701i \(-0.771529\pi\)
−0.753279 + 0.657701i \(0.771529\pi\)
\(728\) 0 0
\(729\) −32.0692 −1.18775
\(730\) 0 0
\(731\) −8.56190 −0.316673
\(732\) 0 0
\(733\) 16.1738 0.597393 0.298697 0.954348i \(-0.403448\pi\)
0.298697 + 0.954348i \(0.403448\pi\)
\(734\) 0 0
\(735\) 15.5718 0.574376
\(736\) 0 0
\(737\) 78.4864 2.89108
\(738\) 0 0
\(739\) 18.7220 0.688701 0.344351 0.938841i \(-0.388099\pi\)
0.344351 + 0.938841i \(0.388099\pi\)
\(740\) 0 0
\(741\) 0.000472532 0 1.73589e−5 0
\(742\) 0 0
\(743\) −14.6138 −0.536130 −0.268065 0.963401i \(-0.586384\pi\)
−0.268065 + 0.963401i \(0.586384\pi\)
\(744\) 0 0
\(745\) 13.8971 0.509151
\(746\) 0 0
\(747\) 27.7107 1.01388
\(748\) 0 0
\(749\) −4.33109 −0.158255
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −27.9283 −1.01776
\(754\) 0 0
\(755\) −6.49254 −0.236288
\(756\) 0 0
\(757\) −35.2551 −1.28137 −0.640685 0.767804i \(-0.721349\pi\)
−0.640685 + 0.767804i \(0.721349\pi\)
\(758\) 0 0
\(759\) −86.2898 −3.13212
\(760\) 0 0
\(761\) 7.90506 0.286558 0.143279 0.989682i \(-0.454235\pi\)
0.143279 + 0.989682i \(0.454235\pi\)
\(762\) 0 0
\(763\) −13.8458 −0.501251
\(764\) 0 0
\(765\) 7.98127 0.288563
\(766\) 0 0
\(767\) 7.37967 0.266465
\(768\) 0 0
\(769\) 25.3906 0.915610 0.457805 0.889053i \(-0.348636\pi\)
0.457805 + 0.889053i \(0.348636\pi\)
\(770\) 0 0
\(771\) 24.2856 0.874625
\(772\) 0 0
\(773\) −23.8211 −0.856784 −0.428392 0.903593i \(-0.640920\pi\)
−0.428392 + 0.903593i \(0.640920\pi\)
\(774\) 0 0
\(775\) −8.56638 −0.307713
\(776\) 0 0
\(777\) 102.282 3.66934
\(778\) 0 0
\(779\) 0.00120756 4.32654e−5 0
\(780\) 0 0
\(781\) 61.6767 2.20697
\(782\) 0 0
\(783\) −24.0729 −0.860296
\(784\) 0 0
\(785\) 16.2277 0.579191
\(786\) 0 0
\(787\) −15.5537 −0.554429 −0.277215 0.960808i \(-0.589411\pi\)
−0.277215 + 0.960808i \(0.589411\pi\)
\(788\) 0 0
\(789\) 57.2140 2.03687
\(790\) 0 0
\(791\) 2.86870 0.101999
\(792\) 0 0
\(793\) 0.0735771 0.00261280
\(794\) 0 0
\(795\) 17.2488 0.611752
\(796\) 0 0
\(797\) 45.2809 1.60393 0.801965 0.597371i \(-0.203788\pi\)
0.801965 + 0.597371i \(0.203788\pi\)
\(798\) 0 0
\(799\) −7.45063 −0.263584
\(800\) 0 0
\(801\) −86.3980 −3.05272
\(802\) 0 0
\(803\) −74.0118 −2.61182
\(804\) 0 0
\(805\) −16.1056 −0.567648
\(806\) 0 0
\(807\) 44.6439 1.57154
\(808\) 0 0
\(809\) 54.7084 1.92344 0.961722 0.274026i \(-0.0883556\pi\)
0.961722 + 0.274026i \(0.0883556\pi\)
\(810\) 0 0
\(811\) −36.2104 −1.27152 −0.635760 0.771887i \(-0.719313\pi\)
−0.635760 + 0.771887i \(0.719313\pi\)
\(812\) 0 0
\(813\) −49.5203 −1.73675
\(814\) 0 0
\(815\) −2.58725 −0.0906274
\(816\) 0 0
\(817\) 0.00119948 4.19644e−5 0
\(818\) 0 0
\(819\) 15.2221 0.531902
\(820\) 0 0
\(821\) 43.3898 1.51431 0.757157 0.653233i \(-0.226588\pi\)
0.757157 + 0.653233i \(0.226588\pi\)
\(822\) 0 0
\(823\) −2.93738 −0.102391 −0.0511953 0.998689i \(-0.516303\pi\)
−0.0511953 + 0.998689i \(0.516303\pi\)
\(824\) 0 0
\(825\) 71.8984 2.50318
\(826\) 0 0
\(827\) −5.97460 −0.207757 −0.103879 0.994590i \(-0.533125\pi\)
−0.103879 + 0.994590i \(0.533125\pi\)
\(828\) 0 0
\(829\) 3.61085 0.125410 0.0627050 0.998032i \(-0.480027\pi\)
0.0627050 + 0.998032i \(0.480027\pi\)
\(830\) 0 0
\(831\) 1.57961 0.0547960
\(832\) 0 0
\(833\) 9.24086 0.320177
\(834\) 0 0
\(835\) −1.10712 −0.0383133
\(836\) 0 0
\(837\) 16.8280 0.581661
\(838\) 0 0
\(839\) −48.4527 −1.67277 −0.836387 0.548139i \(-0.815336\pi\)
−0.836387 + 0.548139i \(0.815336\pi\)
\(840\) 0 0
\(841\) −20.5561 −0.708831
\(842\) 0 0
\(843\) 34.1700 1.17688
\(844\) 0 0
\(845\) −11.0299 −0.379438
\(846\) 0 0
\(847\) −79.3183 −2.72541
\(848\) 0 0
\(849\) 16.2994 0.559393
\(850\) 0 0
\(851\) −48.5390 −1.66390
\(852\) 0 0
\(853\) −3.50534 −0.120021 −0.0600103 0.998198i \(-0.519113\pi\)
−0.0600103 + 0.998198i \(0.519113\pi\)
\(854\) 0 0
\(855\) −0.00111813 −3.82393e−5 0
\(856\) 0 0
\(857\) 4.14627 0.141634 0.0708170 0.997489i \(-0.477439\pi\)
0.0708170 + 0.997489i \(0.477439\pi\)
\(858\) 0 0
\(859\) −26.4830 −0.903587 −0.451794 0.892122i \(-0.649216\pi\)
−0.451794 + 0.892122i \(0.649216\pi\)
\(860\) 0 0
\(861\) 59.0430 2.01218
\(862\) 0 0
\(863\) 37.1738 1.26541 0.632706 0.774392i \(-0.281944\pi\)
0.632706 + 0.774392i \(0.281944\pi\)
\(864\) 0 0
\(865\) −12.4358 −0.422830
\(866\) 0 0
\(867\) −43.2231 −1.46793
\(868\) 0 0
\(869\) −69.9784 −2.37386
\(870\) 0 0
\(871\) 9.97284 0.337917
\(872\) 0 0
\(873\) 16.6775 0.564449
\(874\) 0 0
\(875\) 29.3301 0.991537
\(876\) 0 0
\(877\) −43.4592 −1.46751 −0.733757 0.679412i \(-0.762235\pi\)
−0.733757 + 0.679412i \(0.762235\pi\)
\(878\) 0 0
\(879\) −12.6013 −0.425033
\(880\) 0 0
\(881\) 16.1099 0.542757 0.271378 0.962473i \(-0.412521\pi\)
0.271378 + 0.962473i \(0.412521\pi\)
\(882\) 0 0
\(883\) −14.7298 −0.495699 −0.247849 0.968799i \(-0.579724\pi\)
−0.247849 + 0.968799i \(0.579724\pi\)
\(884\) 0 0
\(885\) −26.5043 −0.890932
\(886\) 0 0
\(887\) 2.85611 0.0958987 0.0479493 0.998850i \(-0.484731\pi\)
0.0479493 + 0.998850i \(0.484731\pi\)
\(888\) 0 0
\(889\) 32.4036 1.08678
\(890\) 0 0
\(891\) −41.3112 −1.38398
\(892\) 0 0
\(893\) 0.00104379 3.49292e−5 0
\(894\) 0 0
\(895\) 18.6031 0.621834
\(896\) 0 0
\(897\) −10.9644 −0.366089
\(898\) 0 0
\(899\) −5.90264 −0.196864
\(900\) 0 0
\(901\) 10.2360 0.341011
\(902\) 0 0
\(903\) 58.6476 1.95167
\(904\) 0 0
\(905\) 7.48149 0.248693
\(906\) 0 0
\(907\) 22.6681 0.752681 0.376341 0.926481i \(-0.377182\pi\)
0.376341 + 0.926481i \(0.377182\pi\)
\(908\) 0 0
\(909\) 28.3038 0.938778
\(910\) 0 0
\(911\) −46.8935 −1.55365 −0.776825 0.629716i \(-0.783171\pi\)
−0.776825 + 0.629716i \(0.783171\pi\)
\(912\) 0 0
\(913\) −27.4984 −0.910064
\(914\) 0 0
\(915\) −0.264254 −0.00873597
\(916\) 0 0
\(917\) −10.0025 −0.330313
\(918\) 0 0
\(919\) −27.8026 −0.917123 −0.458561 0.888663i \(-0.651635\pi\)
−0.458561 + 0.888663i \(0.651635\pi\)
\(920\) 0 0
\(921\) 91.6254 3.01916
\(922\) 0 0
\(923\) 7.83692 0.257955
\(924\) 0 0
\(925\) 40.4438 1.32978
\(926\) 0 0
\(927\) 19.8349 0.651465
\(928\) 0 0
\(929\) 9.53731 0.312909 0.156454 0.987685i \(-0.449994\pi\)
0.156454 + 0.987685i \(0.449994\pi\)
\(930\) 0 0
\(931\) −0.00129460 −4.24287e−5 0
\(932\) 0 0
\(933\) −64.9374 −2.12595
\(934\) 0 0
\(935\) −7.92012 −0.259016
\(936\) 0 0
\(937\) −44.1291 −1.44164 −0.720818 0.693124i \(-0.756234\pi\)
−0.720818 + 0.693124i \(0.756234\pi\)
\(938\) 0 0
\(939\) 35.9245 1.17235
\(940\) 0 0
\(941\) 3.33713 0.108787 0.0543936 0.998520i \(-0.482677\pi\)
0.0543936 + 0.998520i \(0.482677\pi\)
\(942\) 0 0
\(943\) −28.0196 −0.912442
\(944\) 0 0
\(945\) −26.3616 −0.857544
\(946\) 0 0
\(947\) −49.6351 −1.61292 −0.806462 0.591286i \(-0.798620\pi\)
−0.806462 + 0.591286i \(0.798620\pi\)
\(948\) 0 0
\(949\) −9.40428 −0.305276
\(950\) 0 0
\(951\) 85.3330 2.76711
\(952\) 0 0
\(953\) 4.48661 0.145335 0.0726677 0.997356i \(-0.476849\pi\)
0.0726677 + 0.997356i \(0.476849\pi\)
\(954\) 0 0
\(955\) −12.6083 −0.407995
\(956\) 0 0
\(957\) 49.5414 1.60145
\(958\) 0 0
\(959\) 56.6086 1.82799
\(960\) 0 0
\(961\) −26.8738 −0.866897
\(962\) 0 0
\(963\) 6.97695 0.224829
\(964\) 0 0
\(965\) −9.13997 −0.294226
\(966\) 0 0
\(967\) 5.37328 0.172793 0.0863965 0.996261i \(-0.472465\pi\)
0.0863965 + 0.996261i \(0.472465\pi\)
\(968\) 0 0
\(969\) −0.00100712 −3.23535e−5 0
\(970\) 0 0
\(971\) −48.4014 −1.55327 −0.776637 0.629948i \(-0.783076\pi\)
−0.776637 + 0.629948i \(0.783076\pi\)
\(972\) 0 0
\(973\) 43.7952 1.40401
\(974\) 0 0
\(975\) 9.13574 0.292578
\(976\) 0 0
\(977\) −54.1392 −1.73207 −0.866033 0.499986i \(-0.833338\pi\)
−0.866033 + 0.499986i \(0.833338\pi\)
\(978\) 0 0
\(979\) 85.7361 2.74014
\(980\) 0 0
\(981\) 22.3042 0.712117
\(982\) 0 0
\(983\) −53.3702 −1.70225 −0.851123 0.524966i \(-0.824078\pi\)
−0.851123 + 0.524966i \(0.824078\pi\)
\(984\) 0 0
\(985\) 16.3446 0.520783
\(986\) 0 0
\(987\) 51.0356 1.62448
\(988\) 0 0
\(989\) −27.8320 −0.885005
\(990\) 0 0
\(991\) −19.4152 −0.616744 −0.308372 0.951266i \(-0.599784\pi\)
−0.308372 + 0.951266i \(0.599784\pi\)
\(992\) 0 0
\(993\) −89.5518 −2.84184
\(994\) 0 0
\(995\) 1.79321 0.0568485
\(996\) 0 0
\(997\) −20.4541 −0.647787 −0.323893 0.946094i \(-0.604992\pi\)
−0.323893 + 0.946094i \(0.604992\pi\)
\(998\) 0 0
\(999\) −79.4487 −2.51365
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.1.44 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.44 44 1.1 even 1 trivial