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lfunc_lfunctions • Show schema
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{'Lhash': '52815301900653481916883909153', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.6485916500658324, -0.6828690202723073], 'a6': [0, 0], 'a7': [-2.5126996736491347, -2.5126996736491347], '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': '1152.431', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '2284841941173494759373874357537', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.6485916500658324, 0.6828690202723073], [3.5355339059327378, -3.5355339059327378]], [[1.0, 0], [2.5126996736491347, 2.5126996736491347], [0, 7.0]], [[1.0, 0], [2.6909673531838845, -1.1146351735919953], [7.7781745930520225, -7.7781745930520225]], [[1.0, 0], [1.7605720588535974, 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'7.85429723979613120434340289556498', '8.759555097531386212823798467402647', '9.438885761201487741505958165693755'], 'prelabel': '2-1152-96.35-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.8690565352221996, 'root_number': '-0.9165734568813188767632178654594571238176652859421224486 - 0.3998663503479995074308853383617374820393863229068805631*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4345282676110998', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.04166392686687053106278310055', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.35239434693976971673587698389', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.73181790151061910907677970449', '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': '96.35', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/2/w/a/431/6'], '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': '2-1152-96.35-c1-0-0', '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': '2-1152-96.35-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.4345282676110998, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.04166392686687053106278310055', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '52815301900653481916883909153', 'Lhash_array': ['52815301900653481916883909153'], 'label': '2-1152-96.35-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/w/a/431/6'}