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lfunc_lfunctions • Show schema
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{'Lhash': '1565675506276257199616178945808', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.5, 0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.1482223087520017, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [3, 11], 'central_character': '297.10', 'coefficient_field': 'CDF', 'conductor': 297, 'conductor_radical': 33, 'conjugate': '3396253391737290884239675410477', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5, -0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 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'4.80518956208838619905369878598622', '5.61229297238830216896924244977574', '6.84159616035865893324531911569784', '8.279897436479740655662250885709236', '8.946546214429717118093823632695982', '9.796016467305744821634256055647919', '10.94443428055690846751617338560828', '11.71818531332266187221612733754415'], 'prelabel': '2-297-99.76-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.38499650485686454, 'root_angle': -0.38888888888888895, 'root_number': '0.34202014332566873304409961468239 - 0.93969262078590838405410927732446*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.19444444444444445', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23510019716345420483302233806', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.56493651180833204370871519282', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.80518956208838619905369878599', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.1482223087520017, 'bad_primes': [3, 11], 'central_character': '99.76', 'conductor': 297, 'conductor_radical': 33, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/297/1/h/a/10/1', 'ArtinRepresentation/2.297.12t18.b.a'], 'is_instance_Artin': True, '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': '2-297-99.76-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-297-99.76-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.38499650485686454, 'root_angle': -0.19444444444444448, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23510019716345420483302233806', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24603040
{'Lhash': '1565675506276257199616178945808', 'Lhash_array': ['1565675506276257199616178945808'], 'label': '2-297-99.76-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.297.12t18.b.a'}
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id: 19805737
{'Lhash': '1565675506276257199616178945808', 'Lhash_array': ['1565675506276257199616178945808'], 'label': '2-297-99.76-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/297/1/h/a/10/1'}