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lfunc_lfunctions • Show schema
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{'Lhash': '1707072190097514482092728940574', 'a10': [-2.6493634178027374, 0.0], 'a2': [1.5784042159256992, 0.0], 'a3': [0.0, 0.0], 'a4': [0.49135986885202165, 0.0], 'a5': [-1.678507565471082, 0.0], 'a6': [0.0, 0.0], 'a7': [2.779281892026434, 0.0], 'a8': [-2.381243943318669, 0.0], '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': '729.1', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1707072190097514482092728940574', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.5784042159256992, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.678507565471082, 0], [5.0, 0]], [[1.0, 0], [-2.779281892026434, 0], [7.0, 0]], [[1.0, 0], [-4.1512221195495895, 0], [11.0, 0]], [[1.0, 0], [-6.876045014708415, 0], [13.0, 0]], [[1.0, 0], [0.9765512449100223, 0], [17.0, 0]], 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'5.89226550628940752819413040867726', '6.54011047749795226117728967444461', '7.87751280807879778726118249212679', '8.578901176151904908375190160624689', '9.361097737216377301684157927361241', '10.81842899596414765729474117144110'], 'prelabel': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34664251315794041929588163134', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21596947489960235244913463399', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.07878727395895045298731739855', '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': '1.1', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/a/e/1/4'], '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': '2-3e6-1.1-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': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34664251315794041929588163134', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1707072190097514482092728940574', 'Lhash_array': ['1707072190097514482092728940574'], 'label': '2-3e6-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/a/e/1/4'}