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lfunc_lfunctions • Show schema
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{'Lhash': '2958932571027217057088655764898', 'a10': [3.2232399678686128, 0.0], 'a2': [0.6446479935737226, 0.0], 'a3': [4.1868741819857815, 0.0], 'a4': [-7.584428964381374, 0.0], 'a5': [5.0, 0.0], 'a6': [2.6990600407627547, 0.0], 'a7': [0.0, 0.0], 'a8': [-10.046470862880659, 0.0], 'a9': [-9.470084584220894, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.455467951406456, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-5.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 7], 'central_character': '245.1', 'coefficient_field': 'CDF', 'conductor': 245, 'conductor_radical': 35, 'conjugate': '2958932571027217057088655764898', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6446479935737226, 0], [8.0, 0]], [[1.0, 0], [-4.1868741819857815, 0], [27.0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [47.70132089019757, 0], [1331.0, 0]], [[1.0, 0], [57.225606049653365, 0], [2197.0, 0]], [[1.0, 0], 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'4.94469303529271725817132153375853', '5.68944064496039057683454108753444', '7.47304804001997634684633106788048', '8.261989211356264678898520734709506', '9.304500247162222158705007652619396', '9.882418110663964405906443525118062', '11.08642909721367743157944652557544'], 'prelabel': '2-245-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.802034712020191, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.33418622646846625690068666008', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.45221942359868514676449935384', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.94469303529271725817132153376', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.455467951406456, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 245, 'conductor_radical': 35, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/245/4/a/o/1/4'], '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': '2-245-1.1-c3-0-34', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-245-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.802034712020191, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.33418622646846625690068666008', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2958932571027217057088655764898', 'Lhash_array': ['2958932571027217057088655764898'], 'label': '2-245-1.1-c3-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/245/4/a/o/1/4'}