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lfunc_lfunctions • Show schema
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{'Lhash': '2124555725154047509284997337885', 'a10': [2.0, 0.0], 'a2': [2.732050807568877, 0.0], 'a3': [0.0, 0.0], 'a4': [5.464101615137754, 0.0], 'a5': [0.7320508075688773, 0.0], 'a6': [0.0, 0.0], 'a7': [3.732050807568877, 0.0], 'a8': [9.464101615137755, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.087126340352313, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '3267.1', 'coefficient_field': 'CDF', 'conductor': 3267, 'conductor_radical': 33, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.732050807568877, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.7320508075688773, 0], [5.0, 0]], [[1.0, 0], [-3.732050807568877, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.2679491924311227, 0], [13.0, 0]], [[1.0, 0], [4.196152422706632, 0], [17.0, 0]], [[1.0, 0], [-5.196152422706632, 0], [19.0, 0]], [[1.0, 0], 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'5.38271612213209932829614683742538', '6.13112834876282934301004446392203', '6.85981541718734233847150399030463', '7.76962570671786487152308430723640', '8.200926429652364122672091042867470'], 'prelabel': '2-3267-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.107555808833841, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67597895253750507910167912655', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.11601101881608347878569705749', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.31658559922733930064782479692', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.087126340352313, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 3267, 'conductor_radical': 33, 'degree': 2, 'index': 126, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3267/2/a/q/1/2'], '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': '2-3267-1.1-c1-0-126', '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': '2-3267-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.107555808833841, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.67597895253750507910167912655', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2124555725154047509284997337885', 'Lhash_array': ['2124555725154047509284997337885'], 'label': '2-3267-1.1-c1-0-126', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3267/2/a/q/1/2'}