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lfunc_lfunctions • Show schema
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{'Lhash': '1103591291880733745720098048339', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.5503972941549735, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.11613287362019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '8280.1', 'coefficient_field': 'CDF', 'conductor': 8280, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.5503972941549735, 0], [7.0, 0]], [[1.0, 0], [-2.7231350832001016, 0], [11.0, 0]], [[1.0, 0], [-7.1263733748284475, 0], [13.0, 0]], [[1.0, 0], [0.9240103570218376, 0], [17.0, 0]], [[1.0, 0], [-7.516232145055794, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 43, 'label': '2-8280-1.1-c1-0-43', 'leading_term': '2.61183399429902911357824508712', '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/8280/2/a/bs/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [2.611833994299029, 2.6030847591125927, 2.5768264368371603, 2.5330338340121457, 2.471686684163908, 2.39280064358709, 2.2964676599788545, 2.182903014825694, 2.052495976344123, 1.9058608537083142, 1.74388529330152, 1.5677728664644714, 1.3790773226054691, 1.1797262808645776, 0.9720325746434283, 0.7586919227608646, 0.5427660645729668, 0.32765095715400455, 0.11703008820788571, -0.08518659161732522, -0.27493716943092683, -0.44809432054833104, -0.6005621024838304, -0.7283807832936539, -0.8278371217025151, -0.8955771843785768, 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'6.28003771821467296351035427080516', '6.99810823511478750310205297496884', '7.74151651941721753376528805423613'], 'prelabel': '2-8280-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.870580025507061478568019292232', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.56441827587576104151232641959', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.86847756713323311857326493321', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 66.11613287362019, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 8280, 'conductor_radical': 690, 'degree': 2, 'index': 43, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8280/2/a/bs/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': '2-8280-1.1-c1-0-43', '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': '2-8280-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.870580025507061478568019292232', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1103591291880733745720098048339', 'Lhash_array': ['1103591291880733745720098048339'], 'label': '2-8280-1.1-c1-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8280/2/a/bs/1/2'}