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lfunc_lfunctions • Show schema
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{'Lhash': '2247321286470693691222154069375', 'a10': [4.400446443635507, 0.0], 'a2': [1.491690613966488, 0.0], 'a3': [0.0, 0.0], 'a4': [0.22514088779571803, 0.0], 'a5': [2.949972603189126, 0.0], 'a6': [0.0, 0.0], 'a7': [1.8942200097312907, 0.0], 'a8': [-2.647540678788021, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.934196333374636, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-1.0, 0]]], [29, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 23, 29], 'central_character': '6003.1', 'coefficient_field': 'CDF', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.491690613966488, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.949972603189126, 0], [5.0, 0]], [[1.0, 0], [-1.8942200097312907, 0], [7.0, 0]], [[1.0, 0], [1.0325982150842856, 0], [11.0, 0]], [[1.0, 0], [6.971824125268009, 0], [13.0, 0]], [[1.0, 0], 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'4.92223542838927568468437479005757', '5.36534956209498960507979523996290', '6.03562783297682240895841055925809', '6.88637409960178889597334486010268', '7.49769003054031013968291212539551'], 'prelabel': '2-6003-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.923452630976444, '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': '1.77282390436772021609839547652', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40200992200332868859356389304', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17041394785760456311830790970', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.934196333374636, 'bad_primes': [3, 23, 29], 'central_character': '1.1', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 2, 'index': 245, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6003/2/a/i/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': '2-6003-1.1-c1-0-245', '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': '2-6003-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.923452630976444, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77282390436772021609839547652', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2247321286470693691222154069375', 'Lhash_array': ['2247321286470693691222154069375'], 'label': '2-6003-1.1-c1-0-245', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6003/2/a/i/1/5'}