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lfunc_lfunctions • Show schema
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{'Lhash': '1059189782190775780553053214707', 'a10': [-4.457031096226368, 0.0], 'a2': [-1.5011035075721875, 0.0], 'a3': [0.0, 0.0], 'a4': [0.2533117404455243, 0.0], 'a5': [2.969169729964162, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [2.6219598730523828, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.888306657226465, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [127, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 127], 'central_character': '8001.1', 'coefficient_field': 'CDF', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5011035075721875, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.969169729964162, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-5.032351435094014, 0], [11.0, 0]], [[1.0, 0], [-5.284676497833294, 0], [13.0, 0]], [[1.0, 0], [5.698465794312862, 0], [17.0, 0]], [[1.0, 0], 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'2.26279284051159451349896384077148', '3.55552599857023131933832064517418', '4.17917791015809780411925829455873', '5.16600664755390087290792799957741', '6.02872492913727404104627875352284', '6.50973227213435968487330919008999', '7.05510872778782738447022430798404', '8.107820414498848624351119866099636'], 'prelabel': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.835553410379861710934801858461', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.54309086288284631217664457038', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.26279284051159451349896384077', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.888306657226465, 'bad_primes': [3, 7, 127], 'central_character': '1.1', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'index': 118, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8001/2/a/s/1/5'], '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': '2-8001-1.1-c1-0-118', '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': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.835553410379861710934801858461', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1059189782190775780553053214707', 'Lhash_array': ['1059189782190775780553053214707'], 'factors': ['2-8001-1.1-c1-0-118'], 'label': '2-8001-1.1-c1-0-118', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8001/2/a/s/1/5'}