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lfunc_lfunctions • Show schema
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{'Lhash': '1203556250009518562407200014090', 'a10': [-6.298643202609351, 0.0], 'a2': [0.0, 1.4142135623730951], 'a3': [0.4689266436393547, 1.6673655276768589], 'a4': [-2.0, 0.0], 'a5': [0.0, 4.453813320839625], 'a6': [-2.3580109426739857, 0.6631624191928707], 'a7': [0.0, 0.0], 'a8': [0.0, -2.8284271247461903], 'a9': [-2.560215605770259, 1.563744241226942], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.7787939903405587, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.4142135623730951]]], [3, [[1.0, 0], [-0.4689266436393547, -1.6673655276768589]]], [29, [[1.0, 0], [0, -5.385164807134504]]]], 'bad_primes': [2, 3, 29], 'central_character': '348.347', 'coefficient_field': 'CDF', 'conductor': 348, 'conductor_radical': 174, 'conjugate': '4112670618769519796979009301128', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.4142135623730951]], [[1.0, 0], [-0.4689266436393547, -1.6673655276768589]], [[1.0, 0], [0, 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'7.58713988792562171158175920510142', '8.383586163771274376880456968602271', '9.163715096449820835362403331424173', '9.813016759901623193364487557786956', '11.45086863992764398526656356806898'], 'prelabel': '2-348-348.347-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6669715025580247, 'root_angle': 0.9127333123456217, 'root_number': '-0.9626539362417368 + 0.27073492393536924*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.456366656173', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.949438472866915211484016234343', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.88521682338592601522507627047', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68710274946788999886720858811', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.7787939903405587, 'bad_primes': [2, 3, 29], 'central_character': '348.347', 'conductor': 348, 'conductor_radical': 174, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/348/2/b/b/347/10'], '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': '2-348-348.347-c1-0-14', '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': '2-348-348.347-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6669715025580247, 'root_angle': 0.45636665617281086, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.949438472866915211484016234343', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1203556250009518562407200014090', 'Lhash_array': ['1203556250009518562407200014090'], 'label': '2-348-348.347-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/348/2/b/b/347/10'}