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lfunc_lfunctions • Show schema
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{'Lhash': '657469398282365764069087722512', 'a10': [20.0, 0], 'a2': [-2.0, 3.4641016151377544], 'a3': [0, 0], 'a4': [-4.0, -6.928203230275509], 'a5': [-2.5, -4.330127018922194], 'a6': [0, 0], 'a7': [-3.0, 5.196152422706632], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.89577355232496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.5, 4.330127018922194]]]], 'bad_primes': [3, 5], 'central_character': '405.136', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '1319712650941082588025807713154', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0, -3.4641016151377544], [-4.0, -6.928203230275509]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.5, 4.330127018922194]], [[1.0, 0], [3.0, -5.196152422706632], [-171.5, -297.04671349806245]], [[1.0, 0], [-16.0, 27.712812921102035], [-665.5, -1152.6798124370878]], [[1.0, 0], [-19.0, 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{'__RealLiteral__': 0, 'data': '-0.3888888888888889', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.51865190468414100090190551256', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.85873732817549221747354452230', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.11680274847789275431131654342', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.89577355232496, 'bad_primes': [3, 5], 'central_character': '9.7', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/e/c/136/1'], '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': '2-405-9.7-c3-0-12', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-405-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': -0.3888888888888889, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.51865190468414100090190551256', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '657469398282365764069087722512', 'Lhash_array': ['657469398282365764069087722512'], 'label': '2-405-9.7-c3-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/e/c/136/1'}