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lfunc_lfunctions • Show schema
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{'Lhash': '1944131586875596781490894647779', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.123440174278894, -2.712224505258899], 'a6': [0, 0], 'a7': [-3.031502686810599, 3.031502686810599], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.198766312851504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.143', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '709085838275462975435911822597', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.123440174278894, 2.712224505258899], [-3.5355339059327378, -3.5355339059327378]], [[1.0, 0], [3.031502686810599, -3.031502686810599], [0, -7.0]], [[1.0, 0], [-0.6168468814919061, 1.4892001072053092], [-7.7781745930520225, -7.7781745930520225]], [[1.0, 0], [-3.3513254765752944, 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'8.464990520035725974680804236122525', '9.356644786171868302366260139154162', '10.27068112339904580348959213882037'], 'prelabel': '2-1152-96.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': 0.543842708181805, 'root_number': '-0.1373008405173186718167515134881204377227928839084837923 + 0.9905293934019514109434245921887356956474243806857201451*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2719213540909025', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.53364940349144543143533886522', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.02525438056124115437105415440', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62210129396617399131352648310', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.198766312851504, 'bad_primes': [2, 3], 'central_character': '96.59', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/2/w/a/143/7'], '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': '2-1152-96.59-c1-0-12', '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': '2-1152-96.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': 0.2719213540909025, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53364940349144543143533886522', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1944131586875596781490894647779', 'Lhash_array': ['1944131586875596781490894647779'], 'label': '2-1152-96.59-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/w/a/143/7'}