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lfunc_lfunctions • Show schema
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{'Lhash': '3728356091553347021622841417919', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, -2.0], 'a5': [0.5, -2.179449471770337], 'a6': [0.0, 0.0], 'a7': [-0.6794494717703368, 0.6794494717703368], 'a8': [0.0, 0.0], 'a9': [0.0, 3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.758578819202164, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-0.5, 2.179449471770337]]], [19, [[1.0, 0], [0, 4.358898943540674]]]], 'bad_primes': [5, 19], 'central_character': '95.18', 'coefficient_field': 'CDF', 'conductor': 95, 'conductor_radical': 95, 'conjugate': '2184859050746629932158116107284', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0, 2.0]], [[1.0, 0], [0, 0], [0, -3.0]], [[1.0, 0], [-0.5, 2.179449471770337]], [[1.0, 0], [0.6794494717703368, -0.6794494717703368], [0, -7.0]], [[1.0, 0], [-4.358898943540674, 0], [11.0, 0]], [[1.0, 0], [0, 0], [0, -13.0]], [[1.0, 0], [5.6794494717703365, 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'13.05542375533788608696513465888425', '14.15909926509981515001432653341580'], 'prelabel': '2-95-95.18-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8709643042066443, 'root_angle': 0.24799133773913656, 'root_number': '0.7115547983667889 + 0.7026306063083206*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.12399566887', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.94115436136904689826847043309', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.14979996239562164668399218937', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.56026508530815464094768700367', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.758578819202164, 'bad_primes': [5, 19], 'central_character': '95.18', 'conductor': 95, 'conductor_radical': 95, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/95/2/g/a/18/1'], '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': '2-95-95.18-c1-0-4', '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': '2-95-95.18-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8709643042066443, 'root_angle': 0.12399566886956828, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.94115436136904689826847043309', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3728356091553347021622841417919', 'Lhash_array': ['3728356091553347021622841417919'], 'label': '2-95-95.18-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/95/2/g/a/18/1'}