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lfunc_lfunctions • Show schema
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{'Lhash': '803467690288054289629908420243', 'a10': [-0.8851311228909179, 0.425599888370698], 'a2': [0.4296267388675286, 0.09131998241518634], 'a3': [0.33573897382963086, 1.6991996178942093], 'a4': [-1.650851119723564, -0.7350062736746473], 'a5': [-1.7697124412518819, 1.3667910869179327], 'a6': [-0.010928438788835674, 0.7606812677070544], 'a7': [-0.8880662624061638, 1.5381758869752704], 'a8': [-1.3528097682975038, -0.9828738289692148], 'a9': [-2.774558682903653, 1.1409750720870053], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.33573897382963086, -1.6991996178942093]]], [5, [[1.0, 0], [1.7697124412518819, -1.3667910869179327]]]], 'bad_primes': [3, 5], 'central_character': '225.106', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '3847618518847377459514592263751', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'root_number': '-0.7582862007345796 - 0.6519218034208679*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.386981514409', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63382424947647006242713611932', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.09266965104391091818712969343', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.25972730310862628328875707065', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'bad_primes': [3, 5], 'central_character': '225.106', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/q/a/106/18'], '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': '2-15e2-225.106-c1-0-3', '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': '2-15e2-225.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': -0.38698151440929424, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.63382424947647006242713611932', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '803467690288054289629908420243', 'Lhash_array': ['803467690288054289629908420243'], 'label': '2-15e2-225.106-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/q/a/106/18'}