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lfunc_lfunctions • Show schema
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{'Lhash': '2346694638732268324036065953738', 'a10': [-3.0632663195665946, 0.0], 'a2': [-2.5070186440929763, 0.0], 'a3': [2.2851424818297854, 0.0], 'a4': [4.285142481829785, 0.0], 'a5': [1.2218761622631908, 0.0], 'a6': [-5.728894806356167, 0.0], 'a7': [-0.778123837736809, 0.0], 'a8': [-5.728894806356167, 0.0], 'a9': [2.221876162263191, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.84418973575603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [11, 13], 'central_character': '1859.1', 'coefficient_field': 'CDF', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.5070186440929763, 0], [2.0, 0]], [[1.0, 0], [-2.2851424818297854, 0], [3.0, 0]], [[1.0, 0], [-1.2218761622631908, 0], [5.0, 0]], [[1.0, 0], [0.778123837736809, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.285142481829785, 0], [17.0, 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'6.61648830143272313699901820048398', '7.77679022687989322394908832576827', '8.283346070774721540305903936989962', '8.833033730251007430788972250219013'], 'prelabel': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, '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': '1.85121565698763246165816699171', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28286188556339518328089312824', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.29501434698583934126098022932', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.84418973575603, 'bad_primes': [11, 13], 'central_character': '1.1', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'index': 108, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1859/2/a/g/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': '2-1859-1.1-c1-0-108', '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': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.85121565698763246165816699171', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2346694638732268324036065953738', 'Lhash_array': ['2346694638732268324036065953738'], 'label': '2-1859-1.1-c1-0-108', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1859/2/a/g/1/1'}