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lfunc_lfunctions • Show schema
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{'Lhash': '1214039293093901270212752883893', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.8660254037844386, 0.5], 'a4': [0.0, 0.0], 'a5': [0.5, -0.8660254037844386], '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': 1.868499407297961, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.8660254037844386, -0.5]]], [13, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 13], 'central_character': '3744.607', 'coefficient_field': 'CDF', 'conductor': 3744, 'conductor_radical': 78, 'conjugate': '1269941322706769304957900571915', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [-0.5, 0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, -1.0], [-1.0, 0]], [[1.0, 0], [-0.5, 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2.120046461647994, 2.4255111167737593, 2.642120609118744, 2.75567148784457], 'positive_zeros': ['0.957708135723932222008143593093185', '2.13136525716493570700301966805390', '3.12353890809117756110062021007983', '3.98815288554879997475912574589187', '5.29556674689736393383725830040773', '5.75614782996802831822082922882078', '6.39697870375717573355845413510317', '7.00527450115587820019037873007413', '7.895196738801804191995937436320766', '8.477996407941092657483313976924344'], 'prelabel': '2-3744-468.139-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3669306519710358, 'root_angle': -0.05351460416298886, 'root_number': '0.98590090587628911565521054446891 - 0.16733022378611853724085320700095*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.02675730208149443', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.957708135723932222008143593093', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.13136525716493570700301966805', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.12353890809117756110062021008', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.868499407297961, 'bad_primes': [2, 3, 13], 'central_character': '468.139', 'conductor': 3744, 'conductor_radical': 78, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3744/1/ck/a/607/1'], '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': '2-3744-468.139-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': '2-3744-468.139-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3669306519710358, 'root_angle': -0.02675730208149443, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.957708135723932222008143593093', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1214039293093901270212752883893', 'Lhash_array': ['1214039293093901270212752883893'], 'label': '2-3744-468.139-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3744/1/ck/a/607/1'}