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lfunc_lfunctions • Show schema
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{'Lhash': '2474896848589634552642616139862', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.5, -0.8660254037844386], 'a4': [-2.0, 0.0], 'a5': [0.5, 0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.7130436939895395, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [5, [[1.0, 0], [-0.5, -0.8660254037844386]]], [31, [[1.0, 0], [-0.21221445044902618, 5.563718632984653]]]], 'bad_primes': [3, 5, 31], 'central_character': '465.346', 'coefficient_field': 'CDF', 'conductor': 465, 'conductor_radical': 465, 'conjugate': '688865570134401956954704520315', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [2.0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-3.5, -6.06217782649107]], [[1.0, 0], [2.212214450449026, 3.8316678254157757], 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1.9269259700334986, 'root_angle': 0.3199086308809497, 'root_number': '-0.42525977007585114 + 0.9050713385999107*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.319908630881', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.95234936830704850753151687512', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.64899686367562349721175876404', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.72381833816772949957870296050', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.7130436939895395, 'bad_primes': [3, 5, 31], 'central_character': '31.5', 'conductor': 465, 'conductor_radical': 465, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/465/2/i/b/346/1'], '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': '2-465-31.5-c1-0-15', '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': '2-465-31.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9269259700334986, 'root_angle': 0.3199086308809497, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.95234936830704850753151687512', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2474896848589634552642616139862', 'Lhash_array': ['2474896848589634552642616139862'], 'factors': ['2-465-31.5-c1-0-15'], 'label': '2-465-31.5-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/465/2/i/b/346/1'}