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lfunc_lfunctions • Show schema
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{'Lhash': '350101973440477495289678313516', 'a10': [0, 0], 'a2': [0, 1.4142135623730951], 'a3': [1.7320508075688772, 0], 'a4': [-2.0, 0], 'a5': [0, 0], 'a6': [0, 2.449489742783178], 'a7': [6.631030293135233, -2.242640687119285], 'a8': [0, -2.8284271247461903], 'a9': [3.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.61042775783118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.4142135623730951]]], [3, [[1.0, 0], [-1.7320508075688772, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-6.631030293135233, 2.242640687119285]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.349', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '2055418632782879921948180674543', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.4142135623730951]], [[1.0, 0], [-1.7320508075688772, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-6.631030293135233, 2.242640687119285]], [[1.0, 0], 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'data': '0.27618175968791770979463784608', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.17929225163690731501125354646', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.41792520358083221819932736173', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.61042775783118, 'bad_primes': [2, 3, 5, 7], 'central_character': '35.34', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/3/h/a/349/8'], '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': '2-1050-35.34-c2-0-7', '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': '2-1050-35.34-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': -0.47811302548182344, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.27618175968791770979463784608', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '350101973440477495289678313516', 'Lhash_array': ['350101973440477495289678313516'], 'label': '2-1050-35.34-c2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/3/h/a/349/8'}