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lfunc_lfunctions • Show schema
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{'Lhash': '2399648001936054426669545668852', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -81.0], 'a4': [0, 0], 'a5': [0, -1783.680949816112], 'a6': [0, 0], 'a7': [-4965.031159162499, 0], 'a8': [0, 0], 'a9': [-6561.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 197.77376108692732, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 81.0]]]], 'bad_primes': [2, 3], 'central_character': '384.193', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '40520667289505221801283360152', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 81.0]], [[1.0, 0], [0, 1783.680949816112], [-1953125.0, 0]], [[1.0, 0], [4965.031159162499, 0], [40353607.0, 0]], [[1.0, 0], [0, 53705.01919483569], [-2357947691.0, 0]], [[1.0, 0], [0, -54228.8675539935], [-10604499373.0, 0]], [[1.0, 0], [554662.4062964966, 0], [118587876497.0, 0]], [[1.0, 0], [0, 650851.7676459906], 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'data': '1.89298849501906818441232844471', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.90586880792400405774988894879', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.71899831566087687934798257446', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 197.77376108692732, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 71, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/10/d/a/193/1'], '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': '2-384-8.5-c9-0-71', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-384-8.5-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.06320593203866, 'root_angle': -0.125, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89298849501906818441232844471', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2399648001936054426669545668852', 'Lhash_array': ['2399648001936054426669545668852'], 'label': '2-384-8.5-c9-0-71', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/10/d/a/193/1'}