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lfunc_lfunctions • Show schema
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{'Lhash': '3523740184190184529227231846770', 'a10': [-8.551497596691322, 2.5019787009498267e-60], 'a2': [1.9956279499774783, -1.449908575734793], 'a3': [0.0, 0.0], 'a4': [1.2622620479921216, -3.8848431247064728], 'a5': [-2.8046449443524257, -2.037693828027266], 'a6': [0.0, 0.0], 'a7': [-0.30901699437494745, 0.9510565162951535], 'a8': [-1.5891378427431295, -4.890863376912726], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.533632860074733, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.30901699437494745, -0.9510565162951535]]], [11, [[1.0, 0], [2.919976857587887, 1.57281122552936]]]], 'bad_primes': [3, 7, 11], 'central_character': '693.190', 'coefficient_field': 'CDF', 'conductor': 693, 'conductor_radical': 231, 'conjugate': '919465680591507511676227723422', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.9956279499774783, 1.449908575734793], [0.6180339887498949, 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'data': '3.71409200889205907212782224593', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38249352175883858580943537710', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.533632860074733, 'bad_primes': [3, 7, 11], 'central_character': '11.3', 'conductor': 693, 'conductor_radical': 231, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/693/2/m/g/190/2'], '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': '2-693-11.3-c1-0-29', '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': '2-693-11.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.352367501066688, 'root_angle': 0.48241874894334585, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.77974087146392383975292270184', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3523740184190184529227231846770', 'Lhash_array': ['3523740184190184529227231846770'], 'factors': ['2-693-11.3-c1-0-29'], 'label': '2-693-11.3-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/693/2/m/g/190/2'}