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lfunc_lfunctions • Show schema
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{'Lhash': '2429348711613973028432632864338', 'a10': [2.922946987117368, -3.6911967713690057], 'a2': [0, -2.1056377985999144], 'a3': [0, -1.901418344232104], 'a4': [-2.433710538892694, 0], 'a5': [1.7530065112923812, 1.3881527910739921], 'a6': [-4.003698336566382, 0], 'a7': [0, 0.11691745349104785], 'a8': [0, 0.9132373043435952], 'a9': [-0.6153917197823561, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.344367011223804, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.7530065112923812, -1.3881527910739921]]], [11, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.419', 'coefficient_field': 'CDF', 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': '869419436118530800647381156627', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.1056377985999144], [-2.0, 0]], [[1.0, 0], [0, 1.901418344232104], [-3.0, 0]], [[1.0, 0], [-1.7530065112923812, 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-1.157724470889173, -1.195204528531862], 'positive_zeros': ['1.91641822374129751858341839473404', '3.79408300276939846175958784529438', '4.62381543608843741901469030010331', '5.37058905911035458048787823332333', '6.07374469333326601225010825667530', '6.92437582597120393079902217117312', '8.030325823400093357872308162659515', '8.750212147267396093222911084311614', '9.350938443961441208013208628240396', '10.18014590496560498456925690703524'], 'prelabel': '2-1045-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.888661802846398, 'root_angle': -0.7868075733296355, 'root_number': '-0.7839683448499034272014735049190253830979682602851170997 - 0.6208008007995019480261086354198953555470199956167047571*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.39340378666481773', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91641822374129751858341839473', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.79408300276939846175958784529', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.62381543608843741901469030010', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.344367011223804, 'bad_primes': [5, 11, 19], 'central_character': '5.4', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 2, 'index': 75, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1045/2/b/b/419/2'], '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': '2-1045-5.4-c1-0-75', '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': '2-1045-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.888661802846398, 'root_angle': -0.39340378666481773, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91641822374129751858341839473', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2429348711613973028432632864338', 'Lhash_array': ['2429348711613973028432632864338'], 'label': '2-1045-5.4-c1-0-75', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1045/2/b/b/419/2'}