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lfunc_lfunctions • Show schema
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{'Lhash': '2318734488837157540530876157979', 'a10': [1.7957603914657794, -8.978818078285203e-61], 'a2': [1.4171720101115104, -0.8182046415258836], 'a3': [0.0, 0.0], 'a4': [0.3389176708289994, -0.5870226254587313], 'a5': [0.9503576728793562, 0.5486892582633226], 'a6': [0.0, 0.0], 'a7': [2.7794159312133186, -1.6046965360759438], 'a8': [0.0, 2.1636025206338187], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8027491109469427, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.3751363890642383, 3.333016638343014]]]], 'bad_primes': [3, 13], 'central_character': '351.64', 'coefficient_field': 'CDF', 'conductor': 351, 'conductor_radical': 39, 'conjugate': '2342118308110772866128791296107', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4171720101115104, 0.8182046415258836], [1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.9503576728793562, -0.5486892582633226], 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'11.59233586519771921965868061267453'], 'prelabel': '2-351-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6741413055494876, 'root_angle': 0.0783411598889475, 'root_number': '0.8812802129851066 + 0.47259410301116234*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0783411598889', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.82915898783126019069910290989', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.62965845432739858250991193976', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.98249132345931705729535927056', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8027491109469427, 'bad_primes': [3, 13], 'central_character': '117.103', 'conductor': 351, 'conductor_radical': 39, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/351/2/t/c/64/8'], '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': '2-351-117.103-c1-0-8', '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': '2-351-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6741413055494876, 'root_angle': 0.0783411598889475, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.82915898783126019069910290989', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2318734488837157540530876157979', 'Lhash_array': ['2318734488837157540530876157979'], 'factors': ['2-351-117.103-c1-0-8'], 'label': '2-351-117.103-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/351/2/t/c/64/8'}