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lfunc_lfunctions • Show schema
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{'Lhash': '1562790455566908816640853714155', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 1.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.660888362042632, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-0.8660254037844386, 0.5]]]], 'bad_primes': [2, 13], 'central_character': '3328.1407', 'coefficient_field': 'CDF', 'conductor': 3328, 'conductor_radical': 26, 'conjugate': '1315056689549286863907294537165', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, -1.0], [-1.0, 0]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [-0.5, 0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], 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'3.40111890204301787533385152403635', '4.29752275679114191870030067395746', '4.89141429406323763153044144991211', '5.75561460216029227163854048108215', '6.47910861268353249226663221547703', '7.48668875796155470922828352322251', '8.197726071045382444016678235501575', '8.631418797162020754593382606086054'], 'prelabel': '2-3328-104.3-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2887545778939573, 'root_angle': -0.0010204756962833475, 'root_number': '0.99997944423778784317632110012315 - 0.0064117939677561009901236128827089*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0010204756962833475', 'prec': 74}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23282429344926911721284320887', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.01485939258307213524789821735', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.40111890204301787533385152404', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.660888362042632, 'bad_primes': [2, 13], 'central_character': '104.3', 'conductor': 3328, 'conductor_radical': 26, 'degree': 2, 'index': 3, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3328/1/v/b/1407/2', 'ArtinRepresentation/2.3328.24t65.a.c'], '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': '2-3328-104.3-c0-0-3', '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': '2-3328-104.3-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2887545778939573, 'root_angle': -0.0010204756962833475, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23282429344926911721284320887', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24608316
{'Lhash': '1562790455566908816640853714155', 'Lhash_array': ['1562790455566908816640853714155'], 'factors': ['2-3328-104.3-c0-0-3'], 'label': '2-3328-104.3-c0-0-3', 'type': 'Artin', 'url': 'ArtinRepresentation/2.3328.24t65.a.c'}
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id: 19930493
{'Lhash': '1562790455566908816640853714155', 'Lhash_array': ['1562790455566908816640853714155'], 'factors': ['2-3328-104.3-c0-0-3'], 'label': '2-3328-104.3-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3328/1/v/b/1407/2'}