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lfunc_lfunctions • Show schema
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{'Lhash': '958064155826325426504669518205', 'a10': [-626.0923798911144, -6.944218007208768e-59], 'a2': [4.898979485566356, 2.8284271247461903], 'a3': [-23.657149080546784, 13.013043355832812], 'a4': [16.0, 27.712812921102035], 'a5': [-95.85042891112461, 55.339270933778884], 'a6': [-152.7023328357194, -3.1618897085723896], 'a7': [-163.1690163552285, 282.61702654829287], 'a8': [0.0, 181.01933598375618], 'a9': [390.321405238431, -615.7030133211113], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.140973505157318, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-4.898979485566356, -2.8284271247461903]]], [3, [[1.0, 0], [23.657149080546784, -13.013043355832812]]]], 'bad_primes': [2, 3], 'central_character': '18.11', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '4738840779101790613901071270047', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.898979485566356, -2.8284271247461903]], 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'positive_zeros': ['0.75577935722495958755642441221354', '4.02785149678213105018757182993089', '5.95698820449372778167748373641336', '7.69664809858457341670088372738259', '10.29121891108836585047701171291212', '11.61459622390617229864328116969429', '12.65553618662750616231382745911331', '13.81601456177163850825466937850307', '15.77217395051018090421217787270858', '16.68731846217994426617589859862837'], 'prelabel': '2-18-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0349382067171766, 'root_angle': -0.7645976654346912, 'root_number': '-0.7387798358677096 - 0.6739468481381007*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.382298832717', 'prec': 50}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.75577935722495958755642441221', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.02785149678213105018757182993', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.95698820449372778167748373641', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.140973505157318, 'bad_primes': [2, 3], 'central_character': '9.2', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/7/d/a/11/4'], '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': '2-18-9.2-c6-0-1', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-18-9.2-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0349382067171766, 'root_angle': -0.3822988327173456, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '0.75577935722495958755642441221', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '958064155826325426504669518205', 'Lhash_array': ['958064155826325426504669518205'], 'label': '2-18-9.2-c6-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/7/d/a/11/4'}