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lfunc_lfunctions • Show schema
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{'Lhash': '787543376447981062555203921530', 'a10': [311.8051520288439, -302.497984158318], 'a2': [0, -7.771280115946437], 'a3': [0, 16.51070448165288], 'a4': [-28.392794640504466, 0], 'a5': [38.92511653744164, 40.122752928314725], 'a6': [128.30930943853673, 0], 'a7': [0, -7.310090836743977], 'a8': [0, -28.032603284383065], 'a9': [-29.603362480472462, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.444139278492777, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-38.92511653744164, -40.122752928314725]]], [23, [[1.0, 0], [0, -529.0]]]], 'bad_primes': [5, 23], 'central_character': '115.24', 'coefficient_field': 'CDF', 'conductor': 115, 'conductor_radical': 115, 'conjugate': '2206948938745842500678875176221', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 7.771280115946437], [-32.0, 0]], [[1.0, 0], [0, -16.51070448165288], [-243.0, 0]], [[1.0, 0], [-38.92511653744164, -40.122752928314725]], [[1.0, 0], [0, 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'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62126218084556640989897666572', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40238050959137791906522817291', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.16077727678530791163660610043', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.444139278492777, 'bad_primes': [5, 23], 'central_character': '5.4', 'conductor': 115, 'conductor_radical': 115, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/115/6/b/a/24/10'], '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': '2-115-5.4-c5-0-11', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-115-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.294664047221014, 'root_angle': -0.12258886393314125, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62126218084556640989897666572', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '787543376447981062555203921530', 'Lhash_array': ['787543376447981062555203921530'], 'label': '2-115-5.4-c5-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/115/6/b/a/24/10'}