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lfunc_lfunctions • Show schema
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{'Lhash': '2253374337016999099692790096506', 'a10': [1.744504247435824, 0.0], 'a2': [1.1583137130210224, 0.0], 'a3': [1.7256693847671212, 0.0], 'a4': [-0.6583093422274525, 0.0], 'a5': [1.5060723427731386, 0.0], 'a6': [1.9988665125163076, 0.0], 'a7': [-1.444187158737528, 0.0], 'a8': [-3.0791561645539525, 0.0], 'a9': [-0.022065174477465203, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.833625618948815, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [0, 0]]], [31, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [13, 31], 'central_character': '5239.1', 'coefficient_field': 'CDF', 'conductor': 5239, 'conductor_radical': 403, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.1583137130210224, 0], [2.0, 0]], [[1.0, 0], [-1.7256693847671212, 0], [3.0, 0]], [[1.0, 0], [-1.5060723427731386, 0], [5.0, 0]], [[1.0, 0], [1.444187158737528, 0], [7.0, 0]], [[1.0, 0], [-3.5261371045592704, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 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'4.70348501121305233802658272931520', '5.78840837706648811782099386107014', '6.22053736593625287779339634182240', '6.92516403801949084400048582036872', '7.996296960497969345502934721711011'], 'prelabel': '2-5239-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.467891899139071, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.77759891930102724066042348704', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56923004963298503325693733436', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.40224467738708735445291690128', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.833625618948815, 'bad_primes': [13, 31], 'central_character': '1.1', 'conductor': 5239, 'conductor_radical': 403, 'degree': 2, 'index': 358, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5239/2/a/m/1/13'], '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': '2-5239-1.1-c1-0-358', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-5239-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.467891899139071, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77759891930102724066042348704', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2253374337016999099692790096506', 'Lhash_array': ['2253374337016999099692790096506'], 'label': '2-5239-1.1-c1-0-358', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5239/2/a/m/1/13'}