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lfunc_lfunctions • Show schema
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{'Lhash': '3834306643414654958291667901571', 'a10': [-1.0792783165441513, -0.519753043876981], 'a2': [0.5218447333914755, 0.6543725980910784], 'a3': [5.780231544006704, -2.7836128024242814], 'a4': [1.6242859002864676, -7.116461509475537], 'a5': [-1.2895004599533488, 0.6209906924541668], 'a6': [4.83790333062514, 2.329811452273475], 'a7': [-17.355664986656922, -6.463814111724671], 'a8': [11.537142356160274, -5.555994932296077], 'a9': [8.828351818323961, -11.070403027110661], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8910935902812915, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [17.355664986656922, 6.463814111724671]]]], 'bad_primes': [7], 'central_character': '49.8', 'coefficient_field': 'CDF', 'conductor': 49, 'conductor_radical': 7, 'conjugate': '2381308323912164868424892587606', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5218447333914755, -0.6543725980910784], [-1.7801674716505151, 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'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.02473460961902403442396022372', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.78891441160254439427118816650', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.34237739097525762374957921302', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8910935902812915, 'bad_primes': [7], 'central_character': '49.8', 'conductor': 49, 'conductor_radical': 7, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/4/e/a/8/8'], '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': '2-7e2-49.8-c3-0-11', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-7e2-49.8-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.700321613778197, 'root_angle': 0.093074988006742, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.02473460961902403442396022372', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3834306643414654958291667901571', 'Lhash_array': ['3834306643414654958291667901571'], 'label': '2-7e2-49.8-c3-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/4/e/a/8/8'}