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lfunc_lfunctions • Show schema
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{'Lhash': '2381806186614883412971107422457', 'a10': [-13.5, 7.794228634059948], 'a2': [-1.5, 2.598076211353316], 'a3': [-1.5, 0.8660254037844386], 'a4': [-2.5, -4.330127018922194], 'a5': [4.5, 2.598076211353316], 'a6': [-8.716572796529987e-61, -5.196152422706632], 'a7': [6.5, -2.598076211353316], 'a8': [3.0, 0.0], 'a9': [1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5722085551566236, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.5, -0.8660254037844386]]], [7, [[1.0, 0], [-6.5, 2.598076211353316]]]], 'bad_primes': [3, 7], 'central_character': '21.19', 'coefficient_field': 'CDF', 'conductor': 21, 'conductor_radical': 21, 'conjugate': '6899928624405890032081925951279', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5, -2.598076211353316], [-2.0, -3.4641016151377544]], [[1.0, 0], [1.5, -0.8660254037844386]], [[1.0, 0], [-4.5, -2.598076211353316], [12.5, 21.650635094610966]], [[1.0, 0], 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'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.87891378443402310107045640709', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.38247025637035665847715214257', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.117815582577185859987229594189', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5722085551566236, 'bad_primes': [3, 7], 'central_character': '7.5', 'conductor': 21, 'conductor_radical': 21, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/21/3/f/a/19/1'], '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': '2-21-7.5-c2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-21-7.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7564446808304118, 'root_angle': -0.2903459061078923, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.87891378443402310107045640709', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2381806186614883412971107422457', 'Lhash_array': ['2381806186614883412971107422457'], 'label': '2-21-7.5-c2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/21/3/f/a/19/1'}