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lfunc_lfunctions • Show schema
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{'Lhash': '1990972607956240888907830756954', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.2360679774997898, 0.0], 'a4': [0.0, 0.0], 'a5': [3.23606797749979, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.4721359549995794, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7886490052766815, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7], 'central_character': '224.1', 'coefficient_field': 'CDF', 'conductor': 224, 'conductor_radical': 14, 'conjugate': '1990972607956240888907830756954', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.2360679774997898, 0], [3.0, 0]], [[1.0, 0], [-3.23606797749979, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-6.47213595499958, 0], [11.0, 0]], [[1.0, 0], [-0.7639320225002103, 0], [13.0, 0]], [[1.0, 0], [-4.47213595499958, 0], [17.0, 0]], [[1.0, 0], [-1.2360679774997898, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-224-1.1-c1-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/224/2/a/d/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2281312289952444, 1.22975111486166, 1.2333693820812015, 1.2354372823347535, 1.230563574004541, 1.2121307848503822, 1.1729377247599144, 1.1058080446762364, 1.0041622091662898, 0.8625731700708569, 0.6773198050569642, 0.44693254189551074, 0.17270433520771372, -0.14087697447478592, -0.4858298318972713, -0.8505726343612253, -1.2200656537437171, -1.5762462402686293, -1.8987840789378425, -2.1661580045258577, -2.3570248567207113, -2.4518161852164475, -2.434463278801406, -2.2941187221511417, -2.026717688313139, -1.6362087441532887, -1.1352859459131528, -0.5454743037169988, 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'11.47458123413300220597019137644520', '12.05972195931707119663777641651720'], 'prelabel': '2-224-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3374038302908666, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57060045378259883863154228778', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.48053718942393294634255816722', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.23651453418504227026658067374', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7886490052766815, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 224, 'conductor_radical': 14, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/224/2/a/d/1/1'], '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': '2-224-1.1-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': '2-224-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3374038302908666, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.57060045378259883863154228778', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1990972607956240888907830756954', 'Lhash_array': ['1990972607956240888907830756954'], 'label': '2-224-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/224/2/a/d/1/1'}