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lfunc_lfunctions • Show schema
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{'Lhash': '1653257702777764815857430584301', 'a10': [0.0, -6.0], 'a2': [-2.0, 0.0], 'a3': [0.0, 1.0], 'a4': [2.0, 0.0], 'a5': [0.0, 3.0], 'a6': [0.0, -2.0], 'a7': [0.0, 2.0], 'a8': [0.0, 0.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.40723705030853014, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, -1.0]]], [17, [[1.0, 0], [-4.0, -1.0]]]], 'bad_primes': [3, 17], 'central_character': '51.16', 'coefficient_field': 'CDF', 'conductor': 51, 'conductor_radical': 51, 'conjugate': '3883310700489247978485687915795', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0, 0], [2.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -3.0], [-5.0, 0]], [[1.0, 0], [0, -2.0], [-7.0, 0]], [[1.0, 0], [0, 5.0], [-11.0, 0]], [[1.0, 0], [1.0, 0], [13.0, 0]], [[1.0, 0], [-4.0, -1.0]], [[1.0, 0], [-5.0, 0], [19.0, 0]], [[1.0, 0], [0, 1.0], [-23.0, 0]], [[1.0, 0], [0, -6.0], [-29.0, 0]], [[1.0, 0], [0, 10.0], [-31.0, 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{'__RealLiteral__': 0, 'data': '-0.211010434811', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30419036797687803621621177953', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.85479155988738852051002926776', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.18842213261785091548349858990', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.40723705030853014, 'bad_primes': [3, 17], 'central_character': '17.16', 'conductor': 51, 'conductor_radical': 51, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/51/2/d/a/16/2'], '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': '2-51-17.16-c1-0-0', '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': '2-51-17.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6381512754108779, 'root_angle': -0.21101043481131537, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30419036797687803621621177953', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1653257702777764815857430584301', 'Lhash_array': ['1653257702777764815857430584301'], 'label': '2-51-17.16-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/51/2/d/a/16/2'}