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lfunc_lfunctions • Show schema
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{'Lhash': '2074666893934435777642262115133', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.7052991752005642, 1.2216140059838], 'a6': [0, 0], 'a7': [-0.779537239024697, -2.5283041140206515], '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], [0.779537239024697, 2.5283041140206515]]]], 'bad_primes': [2, 3, 7], 'central_character': '2268.2053', 'coefficient_field': 'CDF', 'conductor': 2268, 'conductor_radical': 42, 'conjugate': '501461151448610492522300520179', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.7052991752005642, -1.2216140059838], [-2.5, 4.330127018922194]], [[1.0, 0], [0.779537239024697, 2.5283041140206515]], [[1.0, 0], [-2.4848364142252612, 4.303862917935417], [-5.5, -9.526279441628825]], [[1.0, 0], 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'9.254477503216846982105001721967101'], 'prelabel': '2-2268-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': 0.6624059665370973, 'root_number': '-0.4883634719146790065984419412854518591985470892284000417 + 0.8726403149634106430984279671821796607927854459202022336*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.33120298326854863', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.63662360398118389407164648494', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24516427811096969173137832563', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.67157241957804061921286432986', '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': '63.58', 'conductor': 2268, 'conductor_radical': 42, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2268/2/i/l/2053/3'], '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': '2-2268-63.58-c1-0-27', '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': '2-2268-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': 0.33120298326854863, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.63662360398118389407164648494', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2074666893934435777642262115133', 'Lhash_array': ['2074666893934435777642262115133'], 'label': '2-2268-63.58-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2268/2/i/l/2053/3'}