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lfunc_lfunctions • Show schema
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{'Lhash': '106291662262083010758743535023', 'a10': [-14.954451150103322, -25.901869191285787], 'a2': [-1.0, 1.7320508075688772], 'a3': [-1.5, 2.598076211353316], 'a4': [-2.0, -3.4641016151377544], 'a5': [-7.477225575051661, 12.950934595642893], 'a6': [-3.0, -5.196152422706632], 'a7': [-1.9544511501033224, 0.0], 'a8': [8.0, 0.0], 'a9': [-4.5, -7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.726217740654433, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, -1.7320508075688772]]], [3, [[1.0, 0], [1.5, -2.598076211353316]]], [19, [[1.0, 0], [36.863353450309965, 74.16261303647222]]]], 'bad_primes': [2, 3, 19], 'central_character': '114.49', 'coefficient_field': 'CDF', 'conductor': 114, 'conductor_radical': 114, 'conjugate': '3892637346615392091591514357433', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, -1.7320508075688772]], [[1.0, 0], [1.5, -2.598076211353316]], [[1.0, 0], 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'7.00550698654492706744932185444753', '8.205030494884371724329535182566898', '9.052904658701444145559051562528957', '10.32510806563894141076763904972076', '11.71184860315393602110670309649087', '12.16679598420530775764760089514478'], 'prelabel': '2-114-19.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5934952748471383, 'root_angle': 0.6187456799589093, 'root_number': '-0.3644578615740214 + 0.9312198811971808*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.309372839979', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.083849336909512863229023824573', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.75737904508269653157245272937', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.92139843528388033715301749766', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.726217740654433, 'bad_primes': [2, 3, 19], 'central_character': '19.11', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/4/e/c/49/1'], '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': '2-114-19.11-c3-0-1', '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': '2-114-19.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5934952748471383, 'root_angle': 0.30937283997945464, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.083849336909512863229023824573', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '106291662262083010758743535023', 'Lhash_array': ['106291662262083010758743535023'], 'label': '2-114-19.11-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/4/e/c/49/1'}