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lfunc_lfunctions • Show schema
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{'Lhash': '1924670176733509861020591449142', 'a10': [-546.9515686978926, 0.0], 'a2': [-12.34148714840122, 0.0], 'a3': [-116.11584994607715, 0.0], 'a4': [-359.6876949658475, 0.0], 'a5': [44.3181248840621, 0.0], 'a6': [1433.0422698351956, 0.0], 'a7': [8404.170697961077, 0.0], 'a8': [10757.92248484049, 0.0], 'a9': [-6200.109391300096, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.05632593806331, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[37, [[1.0, 0], [1874161.0, 0]]]], 'bad_primes': [37], 'central_character': '37.1', 'coefficient_field': 'CDF', 'conductor': 37, 'conductor_radical': 37, 'conjugate': '1924670176733509861020591449142', 'degree': 2, 'euler_factors': [[[1.0, 0], [12.34148714840122, 0], [512.0, 0]], [[1.0, 0], [116.11584994607715, 0], [19683.0, 0]], [[1.0, 0], [-44.3181248840621, 0], [1953125.0, 0]], [[1.0, 0], [-8404.170697961077, 0], [40353607.0, 0]], [[1.0, 0], [-77256.91010891755, 0], [2357947691.0, 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{'__RealLiteral__': 0, 'data': '5.49232738074010621646785416268', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.05632593806331, 'bad_primes': [37], 'central_character': '1.1', 'conductor': 37, 'conductor_radical': 37, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/37/10/a/a/1/6'], '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': '2-37-1.1-c9-0-12', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 1, 'prelabel': '2-37-1.1-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.365355190366909, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51829705786988136337311170308', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1924670176733509861020591449142', 'Lhash_array': ['1924670176733509861020591449142'], 'label': '2-37-1.1-c9-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/37/10/a/a/1/6'}