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lfunc_lfunctions • Show schema
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{'Lhash': '467614628641945747492434351825', 'a10': [0.0, 0.0], 'a2': [-2.5778927034576733, 0.0], 'a3': [-1.0, 0.0], 'a4': [4.645530790540312, 0.0], 'a5': [0.0, 0.0], 'a6': [2.5778927034576733, 0.0], 'a7': [-4.698673596590328, 0.0], 'a8': [-6.819894521706482, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.367462439628493, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 29], 'central_character': '2175.1', 'coefficient_field': 'CDF', 'conductor': 2175, 'conductor_radical': 435, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.5778927034576733, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.698673596590328, 0], [7.0, 0]], [[1.0, 0], [3.1150322748036823, 0], [11.0, 0]], [[1.0, 0], [-5.07944942953584, 0], [13.0, 0]], [[1.0, 0], [1.400201826212531, 0], [17.0, 0]], [[1.0, 0], 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'2.92319217425504110822603056912108', '3.90458636026905220803120738911910', '5.58634779304436625833057777723950', '6.39905280928136446165861319993271', '6.65948518864007495867065960066833', '7.67458491261962899226467640778282', '8.464313309952598701659844387715038', '9.084181927340036589792838591765722'], 'prelabel': '2-2175-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.167428756395062, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.36888289924507259664087467196', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.80901281345292221085470937463', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92319217425504110822603056912', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.367462439628493, 'bad_primes': [3, 5, 29], 'central_character': '1.1', 'conductor': 2175, 'conductor_radical': 435, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2175/2/a/bc/1/2'], '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': '2-2175-1.1-c1-0-1', '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': '2-2175-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.167428756395062, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.36888289924507259664087467196', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '467614628641945747492434351825', 'Lhash_array': ['467614628641945747492434351825'], 'factors': ['2-2175-1.1-c1-0-1'], 'label': '2-2175-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2175/2/a/bc/1/2'}