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lfunc_lfunctions • Show schema
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{'Lhash': '2453414747508476003496685851067', 'a10': [-1.6292880439821893, -2.710243618152562], 'a2': [0.9865009905441763, -1.0133191973190674], 'a3': [0, 0], 'a4': [-0.053631591310718034, -1.9992807837853792], 'a5': [0.5695238092076331, -2.16232343342656], 'a6': [0, 0], 'a7': [0, 4.647621809986332], 'a8': [-2.07881721699332, -1.9179465525222927], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.623843418298286, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9865009905441763, 1.0133191973190674]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.5695238092076331, 2.16232343342656]]]], 'bad_primes': [2, 3, 5], 'central_character': '1080.109', 'coefficient_field': 'CDF', 'conductor': 1080, 'conductor_radical': 30, 'conjugate': '854046226882628421462526079204', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9865009905441763, 1.0133191973190674]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5695238092076331, 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93540297860211649805978723334', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.44325897926375727427385580984', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.99824514251666719118562227499', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.623843418298286, 'bad_primes': [2, 3, 5], 'central_character': '40.29', 'conductor': 1080, 'conductor_radical': 30, 'degree': 2, 'index': 86, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1080/2/d/i/109/15'], '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': '2-1080-40.29-c1-0-86', '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': '2-1080-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.936638114970635, 'root_angle': 0.4095855934417898, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93540297860211649805978723334', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2453414747508476003496685851067', 'Lhash_array': ['2453414747508476003496685851067'], 'label': '2-1080-40.29-c1-0-86', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1080/2/d/i/109/15'}