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lfunc_lfunctions • Show schema
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{'Lhash': '2506038935655129590155085042694', 'a10': [0.4369491948401323, -0.29790691681344306], 'a2': [0.182039975524451, 0.2282709091767509], 'a3': [0.8780587738244413, 2.2372572687051187], 'a4': [0.4260728126251911, -1.8667469629246873], 'a5': [0.13535786119893475, -1.8062251321791698], 'a6': [-0.3508589530935812, 0.6077055330485082], 'a7': [-1.8699199755634235, -3.238796403763803], 'a8': [1.0297970833449244, -0.4959241378609368], 'a9': [-2.035177260594328, 1.888368534865312], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.776924015606564, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [0.2225209339563144, 0.9749279121818236]]], [43, [[1.0, 0], [2.5671336393783277, -6.034055425464054]]]], 'bad_primes': [11, 43], 'central_character': '473.23', 'coefficient_field': 'CDF', 'conductor': 473, 'conductor_radical': 473, 'conjugate': '1401950697686112361128036726985', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'0.9210564556106449 + 0.3894290764413415*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0636638320482', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.97691614330000648598324634088', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.86773499083883697092662610146', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.71074893162472347673717190214', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.776924015606564, 'bad_primes': [11, 43], 'central_character': '43.23', 'conductor': 473, 'conductor_radical': 473, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/473/2/r/a/23/9'], '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': '2-473-43.23-c1-0-22', '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': '2-473-43.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.943430990698297, 'root_angle': 0.06366383204821754, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.97691614330000648598324634088', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2506038935655129590155085042694', 'Lhash_array': ['2506038935655129590155085042694'], 'label': '2-473-43.23-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/473/2/r/a/23/9'}