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lfunc_lfunctions • Show schema
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{'Lhash': '2408118349484742860097032198582', 'a10': [2.14106117772978, 0.0], 'a2': [0.5300178381558639, 0.0], 'a3': [3.237094296290708, 0.0], 'a4': [-1.7190810912365846, 0.0], 'a5': [4.039602110712644, 0.0], 'a6': [1.7157177208266785, 0.0], 'a7': [0.37770693125793003, 0.0], 'a8': [-1.9711793199035657, 0.0], 'a9': [7.478779483077833, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.380047121500306, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [1.0, 0]]], [47, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [17, 47], 'central_character': '799.1', 'coefficient_field': 'CDF', 'conductor': 799, 'conductor_radical': 799, 'conjugate': '2408118349484742860097032198582', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5300178381558639, 0], [2.0, 0]], [[1.0, 0], [-3.237094296290708, 0], [3.0, 0]], [[1.0, 0], [-4.039602110712644, 0], [5.0, 0]], [[1.0, 0], [-0.37770693125793003, 0], [7.0, 0]], [[1.0, 0], [0.3396827082375669, 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'3.75995733684252975706860719126774', '4.71478160719479798369943156256527', '5.72433314568185472341404949343607', '6.85348958251307790262668867156132', '7.962603948857564845227666216613540', '8.843660393338515887121263472477600', '9.326631010884181284792706307710480', '9.857512007152383067113503578175363'], 'prelabel': '2-799-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.525875515836104, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89967042105386312037316816052', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51233920797145294415684445820', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.75995733684252975706860719127', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.380047121500306, 'bad_primes': [17, 47], 'central_character': '1.1', 'conductor': 799, 'conductor_radical': 799, 'degree': 2, 'index': 43, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/799/2/a/g/1/11'], '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': '2-799-1.1-c1-0-43', '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': '2-799-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.525875515836104, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89967042105386312037316816052', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2408118349484742860097032198582', 'Lhash_array': ['2408118349484742860097032198582'], 'label': '2-799-1.1-c1-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/799/2/a/g/1/11'}