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lfunc_lfunctions • Show schema
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{'Lhash': '479975113250372266757369108208', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -16.40898913515887], 'a6': [0, 0], 'a7': [0, 34.50097855786378], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.21833784702655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-26.087016402151434, 65.05741752662706]]]], 'bad_primes': [2, 3, 17], 'central_character': '1224.577', 'coefficient_field': 'CDF', 'conductor': 1224, 'conductor_radical': 102, 'conjugate': '1265589606195918382606525387216', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 16.40898913515887], [-125.0, 0]], [[1.0, 0], [0, -34.50097855786378], [-343.0, 0]], [[1.0, 0], [0, 7.428433924520426], [-1331.0, 0]], [[1.0, 0], [42.02422510163667, 0], [2197.0, 0]], [[1.0, 0], [-26.087016402151434, 65.05741752662706]], [[1.0, 0], 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0.5143724099705766], 'positive_zeros': ['0.37863360232224632427328326646801', '1.81384800321726783740177026813331', '3.12084868486201143830074568822279', '3.79947096307179180012324277696107', '4.75479679321924159304888383871206', '6.10626747339216986922584868544001', '6.84484229930173712330510145004011', '7.53695143728848176700852797219895', '7.926090550668766691802219685719098', '9.651439359520051932792329855300203'], 'prelabel': '2-1224-17.16-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.498137316319768, 'root_angle': -0.3786109968250222, 'root_number': '0.372178284025227542671148430468363124931214168653593692 - 0.928161260180598712385915610102767760670606743633924415*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.18930549841251113', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37863360232224632427328326647', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.81384800321726783740177026813', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.12084868486201143830074568822', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 72.21833784702655, 'bad_primes': [2, 3, 17], 'central_character': '17.16', 'conductor': 1224, 'conductor_radical': 102, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1224/4/c/e/577/2'], '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': '2-1224-17.16-c3-0-16', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1224-17.16-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.498137316319768, 'root_angle': -0.1893054984125111, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37863360232224632427328326647', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '479975113250372266757369108208', 'Lhash_array': ['479975113250372266757369108208'], 'label': '2-1224-17.16-c3-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1224/4/c/e/577/2'}