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lfunc_lfunctions • Show schema
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{'Lhash': '2394069839637900008152220459063', 'a10': [-39.59797974644666, 0.0], 'a2': [-2.0, 0.0], 'a3': [7.0710678118654755, 0.0], 'a4': [4.0, 0.0], 'a5': [19.79898987322333, 0.0], 'a6': [-14.142135623730951, 0.0], 'a7': [0.0, 0.0], 'a8': [-8.0, 0.0], 'a9': [23.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.782187180562583, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [2.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '98.1', 'coefficient_field': 'CDF', 'conductor': 98, 'conductor_radical': 14, 'conjugate': '2394069839637900008152220459063', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0, 0]], [[1.0, 0], [-7.0710678118654755, 0], [27.0, 0]], [[1.0, 0], [-19.79898987322333, 0], [125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [14.0, 0], [1331.0, 0]], [[1.0, 0], [50.91168824543142, 0], [2197.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [4913.0, 0]], [[1.0, 0], 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'10.87355260115927838384521029721234', '12.74715359284140321439404655188334', '13.53666154760026102715186056446815'], 'prelabel': '2-98-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4046178866012338, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.88858810085907637027060777657', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87528667587869975948663621385', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.33526409159283873578687297752', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.782187180562583, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 98, 'conductor_radical': 14, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/98/4/a/g/1/2'], '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': '2-98-1.1-c3-0-3', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-98-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4046178866012338, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.88858810085907637027060777657', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2394069839637900008152220459063', 'Lhash_array': ['2394069839637900008152220459063'], 'label': '2-98-1.1-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/98/4/a/g/1/2'}