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lfunc_lfunctions • Show schema
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{'Lhash': '2330138805576141223707487603574', 'a10': [0.0, 0.0], 'a2': [1.5636629649360596, 0.0], 'a3': [0.0, 0.0], 'a4': [1.445041867912629, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.8019377358048383, 0.0], 'a8': [0.6958954867009434, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.001623480354436, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [223, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 223], 'central_character': '2007.1783', 'coefficient_field': 'CDF', 'conductor': 2007, 'conductor_radical': 669, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.5636629649360596, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.8019377358048383, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.9498558243636472, 0], [1.0, 0]], [[1.0, 0], [0.4450418679126288, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.001623480354436, 'bad_primes': [3, 223], 'central_character': '223.222', 'conductor': 2007, 'conductor_radical': 669, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2007/1/d/c/1783/5'], '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': '2-2007-223.222-c0-0-8', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2007-223.222-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.000811410983326, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.83815540745740199642200787035', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2330138805576141223707487603574', 'Lhash_array': ['2330138805576141223707487603574'], 'label': '2-2007-223.222-c0-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2007/1/d/c/1783/5'}