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lfunc_lfunctions • Show schema
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{'Lhash': '1686221457017174576458736951123', 'a10': [-0.0672021906287527, 0.0], 'a2': [-0.0672021906287527, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.9954838655746967, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.4635729955332324, 0.0], 'a8': [0.2685052683884565, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.04123666420414, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 13], 'central_character': '5265.1', 'coefficient_field': 'CDF', 'conductor': 5265, 'conductor_radical': 195, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.0672021906287527, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.4635729955332324, 0], [7.0, 0]], [[1.0, 0], [3.2121435884722325, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-4.776777570568325, 0], [17.0, 0]], [[1.0, 0], [3.9490323461140875, 0], [19.0, 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'5.54411183763990869734194655313001', '6.16707839078175403336969484995340', '7.45696464576134128430086586020491', '7.88786773010059191278322039101087'], 'prelabel': '2-5265-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.483921395591108, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33019418498566178546759213681', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28180131471235831962652773856', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.34547425583030082332063418201', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.04123666420414, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 5265, 'conductor_radical': 195, 'degree': 2, 'index': 151, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5265/2/a/ba/1/6'], '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': '2-5265-1.1-c1-0-151', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-5265-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.483921395591108, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33019418498566178546759213681', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1686221457017174576458736951123', 'Lhash_array': ['1686221457017174576458736951123'], 'label': '2-5265-1.1-c1-0-151', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5265/2/a/ba/1/6'}