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lfunc_lfunctions • Show schema
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{'Lhash': '1418403320465389637054179432507', 'a10': [3.4641016151377544, 3.4641016151377544], 'a2': [-1.0, -1.0], 'a3': [0.0, 0.0], 'a4': [0.0, 2.0], 'a5': [-3.4641016151377544, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.7320508075688772, 2.0], 'a8': [2.0, -2.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.024460261872533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 1.0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.7320508075688772, -2.0]]]], 'bad_primes': [2, 3, 7], 'central_character': '504.307', 'coefficient_field': 'CDF', 'conductor': 504, 'conductor_radical': 42, 'conjugate': '740115951123949268095306878611', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.4641016151377544, 0], [5.0, 0]], [[1.0, 0], [1.7320508075688772, -2.0]], [[1.0, 0], [-2.0, 0], [11.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [13.0, 0]], [[1.0, 0], [0, 3.4641016151377544], 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'9.075226766970808952043419831516838', '10.42621698774774783742443779168453', '10.74856997592978381163062032819571'], 'prelabel': '2-504-56.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': 0.47718552582850504, 'root_number': '0.07161243393857311 + 0.9974325337111245*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.238592762914', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11892292735081616892222788900', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.59817122738588803860458302893', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.26034556935623912322598867249', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.024460261872533, 'bad_primes': [2, 3, 7], 'central_character': '56.27', 'conductor': 504, 'conductor_radical': 42, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/504/2/p/b/307/1'], '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': '2-504-56.27-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': '2-504-56.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': 0.23859276291425252, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11892292735081616892222788900', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1418403320465389637054179432507', 'Lhash_array': ['1418403320465389637054179432507'], 'label': '2-504-56.27-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/504/2/p/b/307/1'}