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lfunc_lfunctions • Show schema
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{'Lhash': '593957794234357023720028851487,1896017188975392808212625587714', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8644315128125628, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, -2, 1]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1', 'coefficient_field': '1.1.1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, -1, 0, 1], [1, 2, 3, 2, 1], [1, 0, 2, 0, 1], [1, 3, 4, 3, 1], [1, 0, -1, 0, 1], [1, -2, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 3, 4, 3, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, -3, 4, -3, 1], [1, 0, 2, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 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'4.99497728007132371328790400022963', '5.17710922816259131839983574731379', '5.71516146990152639360945575936486', '6.34826758260039717661456176860879', '6.52321417514903310232637302741560', '6.91681211065318024499585023461559', '7.43020527753381586090306463394336', '7.53189804481116670919883617896641', '7.81681491718672206284192146433846', '8.537485418341376265690210624144291', '8.995895180678542776277115577398736', '9.441745388027253689956561372729972'], 'prelabel': '4-2736e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1685212341091173, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e2-0', 'trace_hash': 2242233715256600882, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46855008322279034826699165570', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.49569383600972657544422535565', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.29035475215703533085928477681', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8644315128125628, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 2, 0, 1], 'euler13': [1, 3, 4, 3, 1], 'euler17': [1, 0, -1, 0, 1], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -1, 0, 1], 'euler29': [1, 0, 1, 0, 1], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 1, 0, 1], 'euler37': [1, 0, 1, 0, 1], 'euler41': [1, 0, 1, 0, 1], 'euler43': [1, 1, 0, 1, 1], 'euler47': [1, 0, -1, 0, 1], 'euler5': [1, 0, -1, 0, 1], 'euler53': [1, 0, 1, 0, 1], 'euler59': [1, 0, 1, 0, 1], 'euler61': [1, 1, 0, 1, 1], 'euler67': [1, 3, 4, 3, 1], 'euler7': [1, 2, 3, 2, 1], 'euler71': [1, 0, 1, 0, 1], 'euler73': [1, -1, 0, -1, 1], 'euler79': [1, -3, 4, -3, 1], 'euler83': [1, 0, 2, 0, 1], 'euler89': [1, 0, 1, 0, 1], 'euler97': [1, 0, 1, 0, 1], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -1, 0, 1], [1, 2, 3, 2, 1], [1, 0, 2, 0, 1], [1, 3, 4, 3, 1], [1, 0, -1, 0, 1], [1, -2, 1, 0, 0], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 3, 4, 3, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, -3, 4, -3, 1], [1, 0, 2, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/1/cd/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '4-2736e2-1.1-c0e2-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-2736e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1685212341091173, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 2242233715256600882, 'z1': {'__RealLiteral__': 0, 'data': '0.46855008322279034826699165570', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '593957794234357023720028851487,1896017188975392808212625587714', 'Lhash_array': ['593957794234357023720028851487', '1896017188975392808212625587714'], 'label': '4-2736e2-1.1-c0e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/1/cd/a'}