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lfunc_lfunctions • Show schema
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{'Lhash': '423380692091968697527117434375', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.5504683016975498, 0.7720414790871767], 'a4': [-1.939593872070019, 0.4878274402167543], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.4927183450814306, 0.38008930258671747], 'a8': [0.0, 0.0], 'a9': [1.807903909137769, -2.3940516818407187], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.354222026159927, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.5504683016975498, -0.7720414790871767]]], [307, [[1.0, 0], [8.575655376938194, 15.279336859170002]]]], 'bad_primes': [3, 307], 'central_character': '921.116', 'coefficient_field': 'CDF', 'conductor': 921, 'conductor_radical': 921, 'conjugate': '1828371845748503440938666752288', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [1.939593872070019, -0.4878274402167543]], [[1.0, 0], [1.5504683016975498, -0.7720414790871767]], [[1.0, 0], [0, 0], [4.894965861547023, 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'4.51052621974809112907544785339062', '5.55226818243571740001542865924822', '5.95302725131974515022265627854855', '7.20175039970985615067742704559675', '8.084583751671848589744864886100081', '8.806952475791026105504115993271278', '9.927658342001185084960405012372951'], 'prelabel': '2-921-921.116-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7118668894619304, 'root_angle': -0.822342418390166, 'root_number': '-0.8482481371258314 - 0.5295989972257849*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.411171209195', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33398847601676890109862627409', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.60361697090562089731110298643', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51757541748898568988777743338', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.354222026159927, 'bad_primes': [3, 307], 'central_character': '921.116', 'conductor': 921, 'conductor_radical': 921, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/921/2/x/a/116/1'], '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': '2-921-921.116-c1-0-11', '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': '2-921-921.116-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7118668894619304, 'root_angle': -0.411171209195083, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.33398847601676890109862627409', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '423380692091968697527117434375', 'Lhash_array': ['423380692091968697527117434375'], 'label': '2-921-921.116-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/921/2/x/a/116/1'}