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lfunc_lfunctions • Show schema
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{'Lhash': '623828516466483336442941559120', 'a10': [0.5, 0.8660254037844386], 'a2': [-0.5, -0.8660254037844386], 'a3': [1.0, 0.0], 'a4': [-0.5, 0.8660254037844386], 'a5': [-1.0, 0.0], 'a6': [-0.5, -0.8660254037844386], 'a7': [-1.0, 1.7320508075688772], 'a8': [1.0, 0.0], 'a9': [-2.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.349976935425788, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [5, [[1.0, 0], [1.0, 0]]], [67, [[1.0, 0], [7.223110997362451, 3.850541198296886]]]], 'bad_primes': [2, 5, 67], 'central_character': '670.171', 'coefficient_field': 'CDF', 'conductor': 670, 'conductor_radical': 670, 'conjugate': '2146651442176889492607499667258', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-1.0, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, -1.7320508075688772], [-3.5, -6.06217782649107]], [[1.0, 0], [0, 0], [-5.5, 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.188517831673', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49211392820243091364537608345', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59723595317743128717502856547', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.72325213058338458500796496860', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.349976935425788, 'bad_primes': [2, 5, 67], 'central_character': '67.37', 'conductor': 670, 'conductor_radical': 670, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/670/2/e/e/171/2'], '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': '2-670-67.37-c1-0-2', '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': '2-670-67.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3130017153962052, 'root_angle': -0.18851783167280714, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.49211392820243091364537608345', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '623828516466483336442941559120', 'Lhash_array': ['623828516466483336442941559120'], 'label': '2-670-67.37-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/670/2/e/e/171/2'}