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lfunc_lfunctions • Show schema
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{'Lhash': '1934915201216824967599106799618', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-3.414213562373095, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.390407277702577, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1176.1', 'coefficient_field': 'CDF', 'conductor': 1176, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.414213562373095, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.82842712474619, 0], [11.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [13.0, 0]], [[1.0, 0], [-6.242640687119285, 0], [17.0, 0]], [[1.0, 0], [1.17157287525381, 0], [19.0, 0]], [[1.0, 0], [0.8284271247461901, 0], [23.0, 0]], [[1.0, 0], 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'8.531280241852026142832813155333251', '9.321555432034374677952770044322728'], 'prelabel': '2-1176-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0643771435158853, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52637895715780074710635560934', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.53488641975581685815856522423', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.88346124659252457747948510552', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.390407277702577, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1176, 'conductor_radical': 42, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1176/2/a/j/1/1'], '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': '2-1176-1.1-c1-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1176-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0643771435158853, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52637895715780074710635560934', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1934915201216824967599106799618', 'Lhash_array': ['1934915201216824967599106799618'], 'label': '2-1176-1.1-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1176/2/a/j/1/1'}