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lfunc_lfunctions • Show schema
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{'Lhash': '373313087171983340099544022985', 'a10': [19.79898987322333, -34.292856398964496], 'a2': [-1.0, -1.7320508075688772], 'a3': [0, 0], 'a4': [-2.0, 3.4641016151377544], 'a5': [9.899494936611665, 17.146428199482248], 'a6': [0, 0], 'a7': [0, 0], 'a8': [8.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 52.039684625063245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 1.7320508075688772]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '882.361', 'coefficient_field': 'CDF', 'conductor': 882, 'conductor_radical': 42, 'conjugate': '2031880969553966907793024226248', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-9.899494936611665, -17.146428199482248], [-62.5, 108.25317547305482]], [[1.0, 0], [0, 0]], [[1.0, 0], [7.0, -12.12435565298214], [-665.5, -1152.6798124370878]], [[1.0, 0], 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'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/882/4/g/ba/361/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.020718232016021, 0.8165956879610317, 0.6101790267245205, 0.4042348429589919, 0.20156859870997676, 0.0050035965871823174, -0.18264228323671666, -0.35858264843435944, -0.5200919118347826, -0.6645381574648737, -0.7894196691297183, -0.8924050286422992, -0.9713764679106306, -1.0244759279810383, -1.0501530470866967, -1.0472140770792409, -1.0148705215168567, -0.9527861070512855, -0.8611205500910255, -0.7405684699723006, -0.5923917343305495, -0.41844350751556136, -0.22118231325537327, -0.003674521739291993, 0.23041616906291135, 0.47685346712282245, 0.7308683633319565, 0.9872147416816601, 1.2402409220256416, 1.4839768989231408, 1.7122365679082425, 1.9187337331928078, 2.0972101812788972, 2.24157359792213, 2.346042617442094, 2.4052958406284155, 2.414621258099395, 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'root_analytic_conductor': 7.213853659803701, 'root_angle': -0.7698695708271456, 'root_number': '-0.7498400306039945301714288520225375404802689692146216792 - 0.6616191718079219523819485086349207591460594151595316938*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3849347854135728', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.29449209987734126769555513327', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.34860642810361518569607493128', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.63019114901879984600017364355', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 52.039684625063245, 'bad_primes': [2, 3, 7], 'central_character': '7.4', 'conductor': 882, 'conductor_radical': 42, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/4/g/ba/361/2'], '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': '2-882-7.4-c3-0-8', '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': '2-882-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.213853659803701, 'root_angle': -0.3849347854135728, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.29449209987734126769555513327', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '373313087171983340099544022985', 'Lhash_array': ['373313087171983340099544022985'], 'label': '2-882-7.4-c3-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/4/g/ba/361/2'}