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lfunc_lfunctions • Show schema
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{'Lhash': '1249050195562457835562174522249', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.97649665038542, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [7, [1, -1]], [19, [1, -1]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '6384.1', 'coefficient_field': '1.1.1.1', 'conductor': 6384, 'conductor_radical': 798, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -2, 5], [1, -1], [1, -4, 11], [1, 6, 13], [1, -2, 17], [1, -1], [1, -4, 23], [1, -6, 29], [1, 4, 31], [1, -2, 37], [1, -10, 41], [1, 12, 43], [1, 4, 47], [1, -14, 53], [1, -4, 59], [1, -6, 61], [1, 4, 67], [1, -8, 71], [1, 6, 73], [1, -12, 79], [1, 12, 83], [1, 6, 89], [1, -2, 97], [1, -18, 101], [1, 4, 103], [1, 4, 107], [1, -18, 109], [1, -2, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, -2, 5], 1]], [[[1, -1], 1]], [[[1, -4, 11], 1]], [[[1, 6, 13], 1]], [[[1, -2, 17], 1]], [[[1, -1], 1]], [[[1, -4, 23], 1]], [[[1, -6, 29], 1]], [[[1, 4, 31], 1]], [[[1, -2, 37], 1]], [[[1, -10, 41], 1]], [[[1, 12, 43], 1]], [[[1, 4, 47], 1]], [[[1, -14, 53], 1]], [[[1, -4, 59], 1]], [[[1, -6, 61], 1]], [[[1, 4, 67], 1]], [[[1, -8, 71], 1]], [[[1, 6, 73], 1]], [[[1, -12, 79], 1]], [[[1, 12, 83], 1]], [[[1, 6, 89], 1]], [[[1, -2, 97], 1]], [[[1, -18, 101], 1]], [[[1, 4, 103], 1]], [[[1, 4, 107], 1]], [[[1, -18, 109], 1]], [[[1, -2, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 54, 'label': '2-6384-1.1-c1-0-54', 'leading_term': '3.45594602442958238939169710648690000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/6384/2/a/bg', 'plot_delta': {'__RealLiteral__': 0, 'data': 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2.8455370978052095, 2.6766676823517503, 2.3738612397616294, 1.9556659113911066, 1.4479846033551542, 0.8823734318719388, 0.2939869665596936, -0.28069686611798633, -0.8062248943595842, -1.2504376138696796, -1.5865117660669883, -1.794644224926395, -1.8632684040455136, -1.7897252455904558, -1.5803469761243836], 'positive_zeros': ['0.985326867937882310957049618848392', '1.94435285936221864504020005068292', '2.61946596669972812099801775138407', '3.54125722323614090063054391624252', '4.47077941170628328261013401344900', '5.13286708747725914438118767082837', '5.86954646759091444473031262846810', '6.80274783066483389766425361700356', '7.22871495038663873112013199388112', '8.050882121400679747355536858475960'], 'prelabel': '2-6384-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.139782675290994, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 700113249264416821, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.985326867937882310957049618848', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.94435285936221864504020005068', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.61946596669972812099801775138', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 50.97649665038542, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 6384, 'conductor_radical': 798, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 4, 0, -6, 0, 2, 0, 2, 0, 1, 0, 1, 0, 4, 0, -1, 0, 1, 0, 6, 0, -4, 0, 4, 0, 2, 0, 2, 0, -6, 0, 10, 0, -12, 0, 2, 0, -4, 0, 1, 0, 2, 0, 14, 0, 8, 0, 1, 0, 4, 0, 6, 0, 1, 0, -12, 0, -4, 0, 4, 0, 8, 0, -6, 0, -1, 0, 4, 0, 12, 0, 1, 0, -12, 0, 4, 0, 6, 0, -6, 0, -6, 0, -4, 0, 2, 0, 2, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 6, 13], 'euler17': [1, -2, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, -2, 37], 'euler41': [1, -10, 41], 'euler43': [1, 12, 43], 'euler47': [1, 4, 47], 'euler5': [1, -2, 5], 'euler53': [1, -14, 53], 'euler59': [1, -4, 59], 'euler61': [1, -6, 61], 'euler67': [1, 4, 67], 'euler7': [1, -1, 0], 'euler71': [1, -8, 71], 'euler73': [1, 6, 73], 'euler79': [1, -12, 79], 'euler83': [1, 12, 83], 'euler89': [1, 6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -2, 5], [1, -1, 0], [1, -4, 11], [1, 6, 13], [1, -2, 17], [1, -1, 0], [1, -4, 23], [1, -6, 29], [1, 4, 31], [1, -2, 37], [1, -10, 41], [1, 12, 43], [1, 4, 47], [1, -14, 53], [1, -4, 59], [1, -6, 61], [1, 4, 67], [1, -8, 71], [1, 6, 73], [1, -12, 79], [1, 12, 83], [1, 6, 89], [1, -2, 97]], 'index': 54, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6384/bg', 'ModularForm/GL2/Q/holomorphic/6384/2/a/bg/1/1', 'ModularForm/GL2/Q/holomorphic/6384/2/a/bg'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-6384-1.1-c1-0-54', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-6384-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.139782675290994, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 700113249264416821, 'z1': {'__RealLiteral__': 0, 'data': '0.985326867937882310957049618848', 'prec': 107}}
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lfunc_instances • Show schema
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id: 21646652
{'Lhash': '1249050195562457835562174522249', 'Lhash_array': ['1249050195562457835562174522249'], 'label': '2-6384-1.1-c1-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6384/2/a/bg'}
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id: 24574764
{'Lhash': '1249050195562457835562174522249', 'Lhash_array': ['1249050195562457835562174522249'], 'label': '2-6384-1.1-c1-0-54', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6384/2/a/bg/1/1'}
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id: 30704
{'Lhash': '700113249264416821', 'Lhash_array': ['700113249264416821'], 'label': '2-6384-1.1-c1-0-54', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6384/bg'}