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lfunc_lfunctions • Show schema
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{'Lhash': '389095826610725102490376410236', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [-1.2426406871192852, -0.7174389352143008], 'a6': [0.0, 0.0], 'a7': [-1.7426406871192852, -6.7796167617053715], 'a8': [0.0, 0.0], 'a9': [1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.155336882505978, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.5, -0.8660254037844386]]], [7, [[1.0, 0], [1.7426406871192852, 6.7796167617053715]]]], 'bad_primes': [2, 3, 7], 'central_character': '336.145', 'coefficient_field': 'CDF', 'conductor': 336, 'conductor_radical': 42, 'conjugate': '2094589585703328016218449130790', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.5, -0.8660254037844386]], [[1.0, 0], [1.2426406871192852, 0.7174389352143008], [12.5, 21.650635094610966]], [[1.0, 0], [1.7426406871192852, 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'11.14052378801537224038014951444207'], 'prelabel': '2-336-7.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0257787233216473, 'root_angle': -0.7064058083209576, 'root_number': '-0.6039461471509299 - 0.7970251259160827*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.35320290416', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.30694248599785445817418134248', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.35070845570825123393360283764', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68878024531006319202674696792', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.155336882505978, 'bad_primes': [2, 3, 7], 'central_character': '7.5', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/3/bh/e/145/1'], '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': '2-336-7.5-c2-0-2', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-336-7.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0257787233216473, 'root_angle': -0.3532029041604788, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.30694248599785445817418134248', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '389095826610725102490376410236', 'Lhash_array': ['389095826610725102490376410236'], 'label': '2-336-7.5-c2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/3/bh/e/145/1'}