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lfunc_lfunctions • Show schema
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{'Lhash': '1592984856258042019658732928647', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-23.926067865247944, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 127.44412561239979, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-5.0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '2160.1', 'coefficient_field': 'CDF', 'conductor': 2160, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [23.926067865247944, 0], [343.0, 0]], [[1.0, 0], [-57.94057833502963, 0], [1331.0, 0]], [[1.0, 0], [8.162374739285791, 0], [2197.0, 0]], [[1.0, 0], [-50.08844260453374, 0], [4913.0, 0]], [[1.0, 0], [69.77820359574383, 0], [6859.0, 0]], [[1.0, 0], [-4.926067865247945, 0], [12167.0, 0]], 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'6.07736387890552511899348628238331', '6.72296317108167638162863543011141', '7.31858737809018870030372597318455', '8.586073635541684526636636617397437'], 'prelabel': '2-2160-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.289115360044816, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25664347571108240023114863116', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.32885282283661426561726151817', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51203911652305220053848828474', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 127.44412561239979, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 2160, 'conductor_radical': 30, 'degree': 2, 'index': 74, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2160/4/a/bn/1/1'], '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': '2-2160-1.1-c3-0-74', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-2160-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.289115360044816, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25664347571108240023114863116', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1592984856258042019658732928647', 'Lhash_array': ['1592984856258042019658732928647'], 'label': '2-2160-1.1-c3-0-74', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2160/4/a/bn/1/1'}