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lfunc_lfunctions • Show schema
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{'Lhash': '1558331867253231934432464849467', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.3660254037844386, 1.3660254037844386], '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': 1.660888362042632, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [2, 13], 'central_character': '3328.769', 'coefficient_field': 'CDF', 'conductor': 3328, 'conductor_radical': 26, 'conjugate': '582583576891416935507068512349', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [1.3660254037844386, -1.3660254037844386], [0, -1.0]], [[1.0, 0], [0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], 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-0.12291326173985428, 0.15125013823374484], 'positive_zeros': ['1.22930708743613414738356180838241', '2.31211019636281966164021052760271', '3.78798766434395178226370928749506', '4.35290587035079328923646873531594', '4.87504889333634073026327322011935', '5.72968425538747699846814100810663', '7.10340501780488681799603617843538', '7.37418147350973145143368214829215', '8.339796126360831945034308972325167', '8.733561479069540471978973292330538'], 'prelabel': '2-3328-13.2-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2887545778939573, 'root_angle': 0.17077128475646636, 'root_number': '0.47750134200661327652224315510493 + 0.87863101947397881473299313880284*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17077128475646636', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22930708743613414738356180838', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.31211019636281966164021052760', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.78798766434395178226370928750', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.660888362042632, 'bad_primes': [2, 13], 'central_character': '13.2', 'conductor': 3328, 'conductor_radical': 26, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3328/1/bl/a/769/1'], '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': '2-3328-13.2-c0-0-0', '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': '2-3328-13.2-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2887545778939573, 'root_angle': 0.17077128475646636, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22930708743613414738356180838', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1558331867253231934432464849467', 'Lhash_array': ['1558331867253231934432464849467'], 'factors': ['2-3328-13.2-c0-0-0'], 'label': '2-3328-13.2-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3328/1/bl/a/769/1'}