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lfunc_lfunctions • Show schema
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{'Lhash': '4496365718517236188755277178051', 'a10': [-6.618033988749895, -2.7903848909932795e-60], 'a2': [0.5877852522924731, 0.8090169943749475], 'a3': [1.508593032130205, -2.59309603821536], 'a4': [0.9270509831248422, -2.853169548885461], 'a5': [-3.889982777757519, 5.354101966249685], 'a6': [2.9845874989598937, -0.3037062084520608], 'a7': [-2.73606797749979, 8.420751370943494], 'a8': [6.657395614066075, -2.163118960624632], 'a9': [-4.448294126816388, -7.823853229792263], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8991848723889799, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.508593032130205, 2.59309603821536]]], [11, [[1.0, 0], [10.857649092690291, -1.7639320225002102]]]], 'bad_primes': [3, 11], 'central_character': '33.14', 'coefficient_field': 'CDF', 'conductor': 33, 'conductor_radical': 33, 'conjugate': '3605905521516912508292158625689', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.54700713091423210320113727816', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.60554845048805868125646246277', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.62818304482763887511519592706', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8991848723889799, 'bad_primes': [3, 11], 'central_character': '33.14', 'conductor': 33, 'conductor_radical': 33, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/33/3/h/a/14/2'], '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': '2-33-33.14-c2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-33-33.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9482535907598663, 'root_angle': 0.012011626609435352, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '3.54700713091423210320113727816', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4496365718517236188755277178051', 'Lhash_array': ['4496365718517236188755277178051'], 'label': '2-33-33.14-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/33/3/h/a/14/2'}