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lfunc_lfunctions • Show schema
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{'Lhash': '566021059272223851223037704117', 'a10': [2.2419776760005403, -2.2419776760005403], 'a2': [0, -1.0], 'a3': [0.7071067811865476, 0.7071067811865476], 'a4': [-1.0, 0], 'a5': [2.2419776760005403, 2.2419776760005403], 'a6': [0.7071067811865476, -0.7071067811865476], 'a7': [-2.7851554542044483, 2.7851554542044483], 'a8': [0, 1.0], 'a9': [0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.959215106787664, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [11, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [17, [[1.0, 0], [3.590744221366142, 2.0264638996847837]]]], 'bad_primes': [2, 3, 11, 17], 'central_character': '1122.727', 'coefficient_field': 'CDF', 'conductor': 1122, 'conductor_radical': 1122, 'conjugate': '2846994414949103998197898953900', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], 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-0.6254421119239972, 'root_number': '-0.3839662719746254456230752949024981829818312378133041825 - 0.9233471189026952078925726485669996299053339475901868048*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3127210559619986', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44651188519164248484920409850', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95202126047662963579418979080', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.32040055289515531219221573354', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.959215106787664, 'bad_primes': [2, 3, 11, 17], 'central_character': '17.13', 'conductor': 1122, 'conductor_radical': 1122, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1122/2/l/f/727/8'], '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': '2-1122-17.13-c1-0-3', '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': '2-1122-17.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9931947993386037, 'root_angle': -0.3127210559619986, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44651188519164248484920409850', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '566021059272223851223037704117', 'Lhash_array': ['566021059272223851223037704117'], 'label': '2-1122-17.13-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1122/2/l/f/727/8'}