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lfunc_lfunctions • Show schema
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{'Lhash': '3847245117548834079485563210068', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.4226403122993017, -0.9879749702401097], 'a4': [-0.6180339887498949, -1.902113032590307], 'a5': [-1.9494631391585195, -2.6832058193627657], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0478109163581089, 2.8110660404125656], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8985695933724793, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.4226403122993017, 0.9879749702401097]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '363.161', 'coefficient_field': 'CDF', 'conductor': 363, 'conductor_radical': 33, 'conjugate': '375392563872982324970010137541', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.6180339887498949, 1.902113032590307]], [[1.0, 0], [1.4226403122993017, 0.9879749702401097]], [[1.0, 0], [1.9494631391585195, 2.6832058193627657], [-1.545084971874737, 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False, 'root_analytic_conductor': 1.7025186029446138, 'root_angle': -0.8143527248656748, 'root_number': '-0.8346892100294979 - 0.5507212749298258*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.407176362433', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.03494126603669122292874903642', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.86653699915197537433462811456', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.88452191871450324022881804082', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8985695933724793, 'bad_primes': [3, 11], 'central_character': '33.29', 'conductor': 363, 'conductor_radical': 33, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/363/2/f/c/161/1'], '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': '2-363-33.29-c1-0-26', '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': '2-363-33.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7025186029446138, 'root_angle': -0.4071763624328374, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.03494126603669122292874903642', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3847245117548834079485563210068', 'Lhash_array': ['3847245117548834079485563210068'], 'label': '2-363-33.29-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/363/2/f/c/161/1'}