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lfunc_lfunctions • Show schema
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{'Lhash': '900163282936668126208116999131', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -2, 'a5': -4, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.934196333374636, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [23, [1, 1]], [29, [1, -1]]], 'bad_primes': [3, 23, 29], 'central_character': '6003.1', 'coefficient_field': '1.1.1.1', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 2, 'euler_factors': [[1, 0, 2], [1], [1, 4, 5], [1, 4, 7], [1, 4, 11], [1, 5, 13], [1, -5, 17], [1, -5, 19], [1, 1], [1, -1], [1, 2, 31], [1, -5, 37], [1, -2, 41], [1, -1, 43], [1, 6, 47], [1, 2, 53], [1, 9, 59], [1, 10, 61], [1, -8, 67], [1, -3, 71], [1, -8, 73], [1, -13, 79], [1, -6, 83], [1, -9, 89], [1, 6, 97], [1, 12, 101], [1, -16, 103], [1, 18, 107], [1, -14, 109], [1, 10, 113]], 'euler_factors_factorization': [[[[1, 0, 2], 1]], [1], [[[1, 4, 5], 1]], [[[1, 4, 7], 1]], [[[1, 4, 11], 1]], [[[1, 5, 13], 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4.5164798117660805, 4.09649554895538, 3.602331441037452, 3.0592525490272062, 2.4936536999075805, 1.9316787571594356, 1.3978723998136091, 0.9139369281786928, 0.4976610373106822, 0.16207822326109553], 'positive_zeros': ['0.71010362222413778805237105454335', '2.82911129067469526207624771854661', '3.28027512672173009491613515873362', '3.92916553362581132715595761506155', '4.87500219121284891311108676007940', '5.28989831531475286198018533996141', '6.35175977066125987796095421756741', '7.39943062113386048368553094077451', '7.71563520178021378819704348044699'], 'prelabel': '2-6003-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.923452630976444, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1750758846918265011, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71010362222413778805237105454', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.82911129067469526207624771855', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.28027512672173009491613515873', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.934196333374636, 'bad_primes': [3, 23, 29], 'central_character': '1.1', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, -2, -4, 0, -4, 0, 0, 0, -4, 0, -5, 0, 0, 4, 5, 0, 5, 8, 0, 0, -1, 0, 11, 0, 0, 8, 1, 0, -2, 0, 0, 0, 16, 0, 5, 0, 0, 0, 2, 0, 1, 8, 0, 0, -6, 0, 9, 0, 0, 10, -2, 0, 16, 0, 0, 0, -9, 0, -10, 0, 0, -8, 20, 0, 8, -10, 0, 0, 3, 0, 8, 0, 0, -10, 16, 0, 13, -16, 0, 0, 6, 0, -20, 0, 0, 0, 9, 0, 20, 2, 0, 0, -20, 0, -6, 0, 0, -22], 'euler11': [1, 4, 11], 'euler13': [1, 5, 13], 'euler17': [1, -5, 17], 'euler19': [1, -5, 19], 'euler2': [1, 0, 2], 'euler23': [1, 1, 0], 'euler29': [1, -1, 0], 'euler3': [1, 0, 0], 'euler31': [1, 2, 31], 'euler37': [1, -5, 37], 'euler41': [1, -2, 41], 'euler43': [1, -1, 43], 'euler47': [1, 6, 47], 'euler5': [1, 4, 5], 'euler53': [1, 2, 53], 'euler59': [1, 9, 59], 'euler61': [1, 10, 61], 'euler67': [1, -8, 67], 'euler7': [1, 4, 7], 'euler71': [1, -3, 71], 'euler73': [1, -8, 73], 'euler79': [1, -13, 79], 'euler83': [1, -6, 83], 'euler89': [1, -9, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 2], [1, 0, 0], [1, 4, 5], [1, 4, 7], [1, 4, 11], [1, 5, 13], [1, -5, 17], [1, -5, 19], [1, 1, 0], [1, -1, 0], [1, 2, 31], [1, -5, 37], [1, -2, 41], [1, -1, 43], [1, 6, 47], [1, 2, 53], [1, 9, 59], [1, 10, 61], [1, -8, 67], [1, -3, 71], [1, -8, 73], [1, -13, 79], [1, -6, 83], [1, -9, 89], [1, 6, 97]], 'index': 71, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6003/a', 'ModularForm/GL2/Q/holomorphic/6003/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/6003/2/a/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-6003-1.1-c1-0-71', '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': '2-6003-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.923452630976444, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1750758846918265011, 'z1': {'__RealLiteral__': 0, 'data': '0.71010362222413778805237105454', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21585801
{'Lhash': '900163282936668126208116999131', 'Lhash_array': ['900163282936668126208116999131'], 'label': '2-6003-1.1-c1-0-71', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6003/2/a/a'}
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id: 24572972
{'Lhash': '900163282936668126208116999131', 'Lhash_array': ['900163282936668126208116999131'], 'label': '2-6003-1.1-c1-0-71', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6003/2/a/a/1/1'}
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id: 42948
{'Lhash': '1750758846918265011', 'Lhash_array': ['1750758846918265011'], 'label': '2-6003-1.1-c1-0-71', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6003/a'}