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lfunc_lfunctions • Show schema
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{'Lhash': '1067123158200476473446050347435', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.0, 0], 'a6': [0, 0], 'a7': [0, -1.361006317734144], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.11613287362019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [-4.0866416987312855, 2.5098525108441483]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '8280.1241', 'coefficient_field': 'CDF', 'conductor': 8280, 'conductor_radical': 690, 'conjugate': '1187911112338342755533137223813', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 1.361006317734144], [-7.0, 0]], [[1.0, 0], [-2.32854650342509, 0], [11.0, 0]], [[1.0, 0], [-6.175959499327967, 0], [13.0, 0]], [[1.0, 0], [-6.918384234344838, 0], [17.0, 0]], [[1.0, 0], [0, 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'2.83239218578612341046043972213529', '3.61068747214337867205938940715141', '4.03010119291472939314796648969232', '5.16837963698793847402340678139925', '5.77460425228865525179849124814903', '6.32292873013087836039888948869924', '7.24793767077458799013214576011966', '7.75206500948964582000565968147241'], 'prelabel': '2-8280-69.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.020598895064517012, 'root_number': '0.997906822620639164078548226873954833636558966242885248467 + 0.06466817893817796340193702451171641234308946332319947085*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.010299447532258506', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.841811740560332858064412689915', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.58563840841336419320746446099', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.83239218578612341046043972214', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 66.11613287362019, 'bad_primes': [2, 3, 5, 23], 'central_character': '69.68', 'conductor': 8280, 'conductor_radical': 690, 'degree': 2, 'index': 56, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8280/2/p/a/1241/19'], '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': '2-8280-69.68-c1-0-56', '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': '2-8280-69.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.010299447532258506, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.841811740560332858064412689915', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1067123158200476473446050347435', 'Lhash_array': ['1067123158200476473446050347435'], 'label': '2-8280-69.68-c1-0-56', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8280/2/p/a/1241/19'}