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lfunc_lfunctions • Show schema
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{'Lhash': '821716744760819893597494645088', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 3.0], 'a4': [2.0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -1.0], 'a8': [0, 0], 'a9': [-6.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.371202389096482, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 1.0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 7, 11], 'central_character': '1925.1849', 'coefficient_field': 'CDF', 'conductor': 1925, 'conductor_radical': 385, 'conjugate': '2159467835647485339696737909498', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-2.0, 0]], [[1.0, 0], [0, -3.0], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, -4.0], [-13.0, 0]], [[1.0, 0], [0, -2.0], [-17.0, 0]], [[1.0, 0], [-6.0, 0], [19.0, 0]], [[1.0, 0], [0, -5.0], [-23.0, 0]], [[1.0, 0], [10.0, 0], [29.0, 0]], [[1.0, 0], [-1.0, 0], [31.0, 0]], [[1.0, 0], [0, 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'-0.89442719099991587856366946749251049417624734384461028971 - 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.42620819117478337', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64822021510728349110196068581', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.79477473021876510147740357461', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.61945981667518846661467950286', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.371202389096482, 'bad_primes': [5, 7, 11], 'central_character': '5.4', 'conductor': 1925, 'conductor_radical': 385, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1925/2/b/e/1849/2'], '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': '2-1925-5.4-c1-0-20', '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': '2-1925-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.920612501777813, 'root_angle': -0.42620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.64822021510728349110196068581', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '821716744760819893597494645088', 'Lhash_array': ['821716744760819893597494645088'], 'label': '2-1925-5.4-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1925/2/b/e/1849/2'}