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lfunc_lfunctions • Show schema
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{'Lhash': '1612007551282593490399840732669', 'a10': [0.38051430420034116, 0.0], 'a2': [-2.0888064486103306, 0.0], 'a3': [0.0, 0.0], 'a4': [2.3631123797561018, 0.0], 'a5': [-0.18216829254500572, 0.0], 'a6': [0.0, 0.0], 'a7': [1.6559296772239391, 0.0], 'a8': [-0.7584714804047891, 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], [2.0888064486103306, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.18216829254500572, 0], [5.0, 0]], [[1.0, 0], [-1.6559296772239391, 0], [7.0, 0]], [[1.0, 0], [-1.2483424265768945, 0], [11.0, 0]], [[1.0, 0], [-4.5791077441796935, 0], [13.0, 0]], [[1.0, 0], 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'4.68703163180846966530287816312814', '5.88459252836118794588632784349038', '6.54503199742563935103218451752170', '7.18888405236233803289809018043092', '8.094607209093613879611223635750710'], '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': '1.27164973612789331083023278094', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.84724171333059420109396472169', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.96864378348622951996328049665', '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': 180, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6003/2/a/k/1/3'], '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-c1-0-180', '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': '1.27164973612789331083023278094', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1612007551282593490399840732669', 'Lhash_array': ['1612007551282593490399840732669'], 'label': '2-6003-1.1-c1-0-180', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6003/2/a/k/1/3'}