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lfunc_lfunctions • Show schema
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{'Lhash': '3087118637072482517238838831582', 'a10': [3.395780004288959, -1.9605544995849793], 'a2': [-2.4124661677651895, 0.6464183614200879], 'a3': [0.8727365814607602, -1.4961052300490718], 'a4': [3.67008550506175, -2.118924854296345], 'a5': [-1.5164749460998632, 0.40633823714948863], 'a6': [-1.1383375848247874, 4.1734562018491745], 'a7': [-1.7903909005062142, -1.947947746574468], 'a8': [-3.952149568790145, 3.952149568790145], 'a9': [-1.4766617187603719, -2.611411527957182], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.8727365814607602, 1.4961052300490718]]], [7, [[1.0, 0], [1.7903909005062142, 1.947947746574468]]], [13, [[1.0, 0], [1.6780505299158863, -3.1912609449947857]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.44', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': 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-4.478020671973997], 'positive_zeros': ['2.43530720256565477264529270609642', '3.44222794444295657313004394806334', '5.20937237699921499894411444228407', '6.95023055787161743971361045167805', '8.133815109401711714453393233781492', '8.586644593618582116357748338623835', '9.546367102612470075642097299625912', '10.24038833462244127253994826803424', '10.98741075896292239599257187650012', '12.06117582914409201467898546108804'], 'prelabel': '2-273-273.44-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.9718360248553745, 'root_number': '-0.9960882210333976 + 0.08836433623652272*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.485918012428', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.43530720256565477264529270610', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.44222794444295657313004394806', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.20937237699921499894411444228', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '273.44', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/cd/e/44/3'], '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': '2-273-273.44-c1-0-27', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-273-273.44-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': 0.48591801242768723, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.43530720256565477264529270610', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3087118637072482517238838831582', 'Lhash_array': ['3087118637072482517238838831582'], 'label': '2-273-273.44-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/cd/e/44/3'}