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lfunc_lfunctions • Show schema
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{'Lhash': '3574015490319932105240436054885', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.5615528128088303, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, -2.5615528128088303], 'a6': [0.0, 0.0], 'a7': [0.0, -4.56155281280883], 'a8': [0.0, 0.0], 'a9': [3.5615528128088303, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8304441810213163, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [3.5615528128088303, 0.5615528128088303]]]], 'bad_primes': [2, 13], 'central_character': '104.25', 'coefficient_field': 'CDF', 'conductor': 104, 'conductor_radical': 26, 'conjugate': '1042397756034953420075156212542', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.5615528128088303, 0], [3.0, 0]], [[1.0, 0], [0, 2.5615528128088303], [-5.0, 0]], [[1.0, 0], [0, 4.56155281280883], [-7.0, 0]], [[1.0, 0], [0, -3.1231056256176606], [-11.0, 0]], [[1.0, 0], [3.5615528128088303, 0.5615528128088303]], 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'10.13985013584147892272852406779424', '11.12304775058398219087056879111135', '11.84270170950207514109985740900077', '12.59468315299087929444429183685867', '14.26437492633309436610098698076237'], 'prelabel': '2-104-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.911287101314024, 'root_angle': 0.27488918491582265, 'root_number': '-0.15574672772794376 + 0.9877970220657875*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.274889184916', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.81940109496769999616361812104', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.17542745090515959892732581799', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.00595867533401268694237966537', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8304441810213163, 'bad_primes': [2, 13], 'central_character': '13.12', 'conductor': 104, 'conductor_radical': 26, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/104/2/f/a/25/1'], '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': '2-104-13.12-c1-0-3', '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': '2-104-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.911287101314024, 'root_angle': 0.27488918491582265, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.81940109496769999616361812104', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3574015490319932105240436054885', 'Lhash_array': ['3574015490319932105240436054885'], 'factors': ['2-104-13.12-c1-0-3'], 'label': '2-104-13.12-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/104/2/f/a/25/1'}