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lfunc_lfunctions • Show schema
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{'Lhash': '506856416108765048157691272409', 'a10': [0, 0], 'a2': [0, -1.0], 'a3': [-1.0, 0], 'a4': [-1.0, 0], 'a5': [0, 0], 'a6': [0, 1.0], 'a7': [0, 2.0], 'a8': [0, 1.0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.570828394149682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-3.0, -2.0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1950.1351', 'coefficient_field': 'CDF', 'conductor': 1950, 'conductor_radical': 390, 'conjugate': '1568132740839419092263937008058', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.0], [-7.0, 0]], [[1.0, 0], [0, 0], [-11.0, 0]], [[1.0, 0], [-3.0, -2.0]], [[1.0, 0], [-2.0, 0], [17.0, 0]], [[1.0, 0], [0, 6.0], [-19.0, 0]], [[1.0, 0], [4.0, 0], [23.0, 0]], [[1.0, 0], [10.0, 0], [29.0, 0]], [[1.0, 0], [0, -10.0], 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'root_number': '0.5547001962252291220183417334569993763463533190531148020 - 0.8320502943378436830275126001854990645195299785796722030*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1564164790945006', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39983921122863822593076142449', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.76108113140118599472720261700', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.67416244534569336265678746531', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.570828394149682, 'bad_primes': [2, 3, 5, 13], 'central_character': '13.12', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1950/2/b/c/1351/1'], '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': '2-1950-13.12-c1-0-4', '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': '2-1950-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': -0.1564164790945006, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.39983921122863822593076142449', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '506856416108765048157691272409', 'Lhash_array': ['506856416108765048157691272409'], 'factors': ['2-1950-13.12-c1-0-4'], 'label': '2-1950-13.12-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/b/c/1351/1'}