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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': -2, 'Lhash': '2202175222871258682', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'algebraic': True, 'analytic_conductor': 355.55787012035745, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [11, [1]], [23, [1, -1]]], 'bad_primes': [2, 11, 23], 'central_character': '44528.1', 'coefficient_field': '1.1.1.1', 'conductor': 44528, 'conductor_radical': 506, 'degree': 2, 'euler_factors': [[1], [1, -1, 3], [1, 2, 5], [1, 4, 7], [1], [1, 7, 13], [1, -4, 17], [1, 6, 19], [1, -1], [1, 5, 29], [1, 3, 31], [1, -2, 37], [1, -9, 41], [1, -8, 43], [1, -1, 47], [1, 6, 53], [1, -8, 59], [1, -10, 61], [1, 2, 67], [1, -13, 71], [1, -3, 73], [1, -6, 79], [1, 0, 83], [1, 4, 89], [1, 8, 97]], 'gamma_factors': [[], [0]], 'index': 10, 'label': '2-44528-1.1-c1-0-10', 'leading_term': '3.15398537957', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/44528/r', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.650361397939707, 0.5018112873569216, -0.976584611069823, -3.530517262118543, -5.876568549944955, -6.400832552729949, -4.545007543404719, -1.581679040715606, 0.3244499774214514, 0.1647288460058281, -0.9039389822054773, -0.9620354622636008, 0.2922812501247051, 1.180966826694656, 0.4541596521523454, -0.5984043887325293, 0.4181157276120975, 3.419531150650574, 5.13137129631722, 3.064432881507245, -0.7511077151402393, -1.874845160520135, 0.7211195883719727, 3.104421947375033, 1.750861319690329, -1.532544696069845, -2.330052123691868, -0.04447732783999725, 1.617180349082957, 0.6693500005536719, -0.2773735373094473, 1.151924058231302, 2.733653910690178, 1.306645361754678, -1.594122945709283, -1.966435277450445, 0.05458520760474801, 0.6888438480616978, -0.5147025392397998, 0.2908551044878846, 3.854460364276737, 5.25029832677067, 1.879851877847302, -1.3336392428632, 0.5189192709467124, 4.224504053201915, 3.830075057956934, 0.3761543851074855, -0.7583577885038959, 0.5522536306928213, 0.1862050295650289, -1.31013631845874, 0.4981230087482664, 4.603200118250408, 4.946836553764827, 0.8745142493776579, -1.64308261164983, -0.4624915188822479, 0.09232593263520165, -1.405025308968081, -0.9991911033006201, 1.677775118702387, 1.751825912214646, -1.184261173755242, -1.716691832394037, 0.8284453149760188, 1.139761556120244, -0.8660380798494935, 0.5109217028812066, 4.039665945973585, 1.470654959766757, -7.012410549341229, -10.88283256756556, -6.13047830416, -0.6502698346474167, 0.103573487340085, -0.4283609591680183, 0.1374959882874006, -0.1983852161685311, -0.317692009119348, 2.381499723007036, 4.19195352928456, 1.137065235449421, -1.377005889018134, 2.413265449627274, 6.680222655063757, 4.216140109473849, -0.1975659671179494, 0.3077431040816014, 2.067042667203012, 0.4488344555428753, -0.3655443170622317, 2.052887887156186, 2.086143193348177, -1.206191236181562, -0.7895392016525229, 3.291991519541138, 2.797457355984701, -2.124169807331147, -3.219225260769214, -0.4043224747332506, -0.02208036576541128, -1.026371680566269, 0.6079346778308007, 1.563679485689217, -0.6928890671596055, -1.040592694415712, 1.650512777703349, 1.15673179728771, -1.871501699797054, -0.5021091143377449, 2.616813164727719, 0.05724936402506947, -3.812033571282742, -1.398317544515049, 2.173686218887694, 0.4211978160550616, -1.34540235831256, 0.424234291604407, -0.6694340962395241], 'positive_zeros': ['0.6143075373678353', '2.180699208346766', '2.540196707508551', '3.199535163940220', '3.835142738851802', '4.200554674084508', '5.194853058251125', '5.696074329475715', '6.378737024956694', '7.004165644802579', '7.615562485513774', '7.843818560998189', '8.605951592982335', '9.242919860413263', '9.643962959906735', '9.970377590470358', '10.86111540046859', '11.21564762363361', '12.03388450867082', '12.39738422428329', '12.77718943097416', '13.21566067125431', '14.05367636929852', '14.57964980303043', '14.77303010873679', '15.34639808413442', '15.90182793589297', '16.42026413304786', '16.88210196954033', '17.21247696079036', '17.79927888722309', '18.81983094213472', '19.03123870188141', '19.43787077222780', '19.68927378027292'], 'prelabel': '2-44528-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 18.856242205708895, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2202175222871258682, 'z1': {'__RealLiteral__': 0, 'data': '0.6143075373678353', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '2.180699208346766', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.540196707508551', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 355.55787012035745, 'bad_primes': [2, 11, 23], 'central_character': '1.1', 'conductor': 44528, 'conductor_radical': 506, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -2, 0, -4, 0, -2, 0, 0, 0, -7, 0, -2, 0, 4, 0, -6, 0, -4, 0, 1, 0, -1, 0, -5, 0, -5, 0, -3, 0, 0, 0, 8, 0, 2, 0, -7, 0, 9, 0, 8, 0, 4, 0, 1, 0, 9, 0, 4, 0, -6, 0, 0, 0, -6, 0, 8, 0, 10, 0, 8, 0, 14, 0, -2, 0, 1, 0, 13, 0, 3, 0, -1, 0, 0, 0, 6, 0, 1, 0, 0, 0, -8, 0, -5, 0, -4, 0, 28, 0, -3, 0, 12, 0, -8, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 7, 13], 'euler17': [1, -4, 17], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, 5, 29], 'euler3': [1, -1, 3], 'euler31': [1, 3, 31], 'euler37': [1, -2, 37], 'euler41': [1, -9, 41], 'euler43': [1, -8, 43], 'euler47': [1, -1, 47], 'euler5': [1, 2, 5], 'euler53': [1, 6, 53], 'euler59': [1, -8, 59], 'euler61': [1, -10, 61], 'euler67': [1, 2, 67], 'euler7': [1, 4, 7], 'euler71': [1, -13, 71], 'euler73': [1, -3, 73], 'euler79': [1, -6, 79], 'euler83': [1, 0, 83], 'euler89': [1, 4, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 0, 0], [1, -1, 3], [1, 2, 5], [1, 4, 7], [1, 0, 0], [1, 7, 13], [1, -4, 17], [1, 6, 19], [1, -1, 0], [1, 5, 29], [1, 3, 31], [1, -2, 37], [1, -9, 41], [1, -8, 43], [1, -1, 47], [1, 6, 53], [1, -8, 59], [1, -10, 61], [1, 2, 67], [1, -13, 71], [1, -3, 73], [1, -6, 79], [1, 0, 83], [1, 4, 89], [1, 8, 97]], 'index': 10, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/44528/r'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-44528-1.1-c1-0-10', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-44528-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 18.856242205708895, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2202175222871258682, 'z1': {'__RealLiteral__': 0, 'data': '0.6143075373678353', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2202175222871258682', 'Lhash_array': ['2202175222871258682'], 'factors': ['2-44528-1.1-c1-0-10'], 'label': '2-44528-1.1-c1-0-10', 'type': 'ECQ', 'url': 'EllipticCurve/Q/44528/r'}