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lfunc_lfunctions • Show schema
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{'Lhash': '2230952488538948506716895863711', 'a10': [-1.1140882523277726, -1.9296574571473177], 'a2': [-1.3168175819515011, -2.280794956239994], 'a3': [0.0, 0.0], 'a4': [-2.468017088273197, 4.27473099083738], 'a5': [0.8460460033323012, 0.0], 'a6': [0.0, 0.0], 'a7': [0.24105417720350455, -0.4175180822931813], 'a8': [7.732442849773578, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.81497924188321, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [67, [[1.0, 0], [0.5654272885938315, 8.165800143360933]]]], 'bad_primes': [3, 67], 'central_character': '603.37', 'coefficient_field': 'CDF', 'conductor': 603, 'conductor_radical': 201, 'conjugate': '297599082079678099228110383798', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3168175819515011, 2.280794956239994], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.8460460033323012, 0], [5.0, 0]], [[1.0, 0], 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'10.21369895947212313352921799064116', '10.62063868562327168200823981795975'], 'prelabel': '2-603-67.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.194306095758568, 'root_angle': -0.7216050692020485, 'root_number': '-0.6413011622532956 - 0.7672892670255282*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.360802534601', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.75991119961390388403687073943', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.94141600833506152948019720157', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.40709415127408539822577270713', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.81497924188321, 'bad_primes': [3, 67], 'central_character': '67.37', 'conductor': 603, 'conductor_radical': 201, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/603/2/g/f/37/1'], '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': '2-603-67.37-c1-0-17', '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': '2-603-67.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.194306095758568, 'root_angle': -0.36080253460102424, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.75991119961390388403687073943', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2230952488538948506716895863711', 'Lhash_array': ['2230952488538948506716895863711'], 'label': '2-603-67.37-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/603/2/g/f/37/1'}