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lfunc_lfunctions • Show schema
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{'Lhash': '312649086995364244189545523033', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 2.0], 'a8': [0, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.1640964851073, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '2400.49', 'coefficient_field': 'CDF', 'conductor': 2400, 'conductor_radical': 30, 'conjugate': '2004499953094110587814471310951', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.0], [-7.0, 0]], [[1.0, 0], [0, -4.0], [-11.0, 0]], [[1.0, 0], [0, 0], [13.0, 0]], [[1.0, 0], [0, -6.0], [-17.0, 0]], [[1.0, 0], [0, 4.0], [-19.0, 0]], [[1.0, 0], [0, -4.0], [-23.0, 0]], [[1.0, 0], [0, 6.0], [-29.0, 0]], [[1.0, 0], [10.0, 0], [31.0, 0]], [[1.0, 0], [4.0, 0], [37.0, 0]], 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'root_number': '-0.94868329805051379959966806332981556011586654179756504806 - 0.3162277660168379331998893544432718533719555139325216827*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.44879180882521663', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.24663664178368590765317991110', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.36093322532895384015085682539', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.87314781687839045679315728058', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.1640964851073, 'bad_primes': [2, 3, 5], 'central_character': '40.29', 'conductor': 2400, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2400/2/d/a/49/2'], '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': '2-2400-40.29-c1-0-1', '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': '2-2400-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.377681633594122, 'root_angle': -0.44879180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.24663664178368590765317991110', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '312649086995364244189545523033', 'Lhash_array': ['312649086995364244189545523033'], 'label': '2-2400-40.29-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2400/2/d/a/49/2'}