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lfunc_lfunctions • Show schema
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{'Lhash': '888784779714118201818205737808', 'a10': [0, 0], 'a2': [-22.44994432064365, 0], 'a3': [-67.34983296193094, 45.0], 'a4': [248.0, 0], 'a5': [0, 0], 'a6': [1512.0, -1010.2474944289642], 'a7': [0, 1750.0], 'a8': [179.5995545651492, 0], 'a9': [2511.0, -6061.484966573785], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.553395754584553, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [67.34983296193094, -45.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.74', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '364478030696230876877738610243', 'degree': 2, 'euler_factors': [[[1.0, 0], [22.44994432064365, 0], [256.0, 0]], [[1.0, 0], [67.34983296193094, -45.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1750.0], [-5764801.0, 0]], [[1.0, 0], [0, 6959.482739399531], [-214358881.0, 0]], [[1.0, 0], [0, -25730.0], [-815730721.0, 0]], [[1.0, 0], 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'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.51398480959655594650912759312073', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.553395754584553, 'bad_primes': [3, 5], 'central_character': '15.14', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/9/d/b/74/2'], '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': '2-75-15.14-c8-0-18', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-75-15.14-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.527512619124859, 'root_angle': 0.0824610006306484, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '0.70112756587193685475036515376748', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '888784779714118201818205737808', 'Lhash_array': ['888784779714118201818205737808'], 'label': '2-75-15.14-c8-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/9/d/b/74/2'}