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lfunc_lfunctions • Show schema
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{'Lhash': '32272314446513667148944749584', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -1.0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -4.783386116752813], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 59.88780151596032, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '7500.1249', 'coefficient_field': 'CDF', 'conductor': 7500, 'conductor_radical': 30, 'conjugate': '1339462585712112209533894935051', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 4.783386116752813], [-7.0, 0]], [[1.0, 0], [-1.9562952014676114, 0], [11.0, 0]], [[1.0, 0], [0, 1.0798526403528974], [-13.0, 0]], [[1.0, 0], [0, 3.8057267116178424], [-17.0, 0]], [[1.0, 0], [4.250851615652939, 0], [19.0, 0]], [[1.0, 0], [0, -5.8632387571057105], [-23.0, 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'3.47814905809631509290057666656339', '4.05100581319490161457262371488519', '4.95688359385561982292891527987477', '5.71127211088971478867350439781098', '6.09971862224137383727377690032882', '6.88312780240574909073712609673452', '7.904986851678708353476873316845610'], 'prelabel': '2-7500-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.738720922475517, 'root_angle': -0.5, 'root_number': '0.e-55 - 1.0000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.02545836718785390804262432021', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95514384798287765140330418212', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.25195397208124724303182785650', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 59.88780151596032, 'bad_primes': [2, 3, 5], 'central_character': '5.4', 'conductor': 7500, 'conductor_radical': 30, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7500/2/d/d/1249/1'], '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': '2-7500-5.4-c1-0-0', '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': '2-7500-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.738720922475517, 'root_angle': -0.25, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.02545836718785390804262432021', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '32272314446513667148944749584', 'Lhash_array': ['32272314446513667148944749584'], 'label': '2-7500-5.4-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7500/2/d/d/1249/1'}