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lfunc_lfunctions • Show schema
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{'Lhash': '1501153645852020427567590820989', 'a10': [3.932411926690262, 0.9319987474485494], 'a2': [-1.1759677622044216, -0.3273530000883308], 'a3': [0.0, 0.0], 'a4': [-0.43659360798328883, -0.26348559237416946], 'a5': [-3.308243759070388, 0.12837492400611963], 'a6': [0.0, 0.0], 'a7': [3.0289894398927752, 0.47372530388624673], 'a8': [2.102530376276705, 2.228552002556967], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.685', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '514780570110058554852986463388', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1759677622044216, 0.3273530000883308], [1.712333799060533, 1.0333987423037259]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.308243759070388, -0.12837492400611963], [4.98496470583896, -0.38746210335965475]], 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'z1': {'__RealLiteral__': 0, 'data': '1.18420142394264700803961027818', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.17418248960914301456749072212', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.50326707855559487089710024522', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '243.103', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/i/a/685/7'], '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': '2-3e6-243.103-c1-0-11', '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': '2-3e6-243.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.3002508931311747, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18420142394264700803961027818', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1501153645852020427567590820989', 'Lhash_array': ['1501153645852020427567590820989'], 'label': '2-3e6-243.103-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/i/a/685/7'}