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lfunc_lfunctions • Show schema
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{'Lhash': '2205850148272197114546537097786', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.5, -2.598076211353316], 'a6': [0, 0], 'a7': [0.5, -2.598076211353316], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.1100711784264, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.5, 2.598076211353316]]]], 'bad_primes': [2, 3, 7], 'central_character': '2268.377', 'coefficient_field': 'CDF', 'conductor': 2268, 'conductor_radical': 42, 'conjugate': '507099561659235133062402400608', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.5, 2.598076211353316], [-2.5, -4.330127018922194]], [[1.0, 0], [-0.5, 2.598076211353316]], [[1.0, 0], [4.5, -2.598076211353316], [5.5, -9.526279441628825]], [[1.0, 0], [3.0, 1.7320508075688772], [6.5, 11.258330249197702]], [[1.0, 0], [-6.0, 0], [17.0, 0]], 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'z1': {'__RealLiteral__': 0, 'data': '1.74010894474790852585693735195', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.88768169706976723533806931641', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06282524784053394291760056659', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.1100711784264, 'bad_primes': [2, 3, 7], 'central_character': '63.41', 'conductor': 2268, 'conductor_radical': 42, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2268/2/x/h/377/1'], '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': '2-2268-63.41-c1-0-29', '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': '2-2268-63.41-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': 0.4191483184698081, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74010894474790852585693735195', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2205850148272197114546537097786', 'Lhash_array': ['2205850148272197114546537097786'], 'label': '2-2268-63.41-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2268/2/x/h/377/1'}