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lfunc_lfunctions • Show schema
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{'Lhash': '797351821415485205404320777553', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-3.23606797749979, 0], 'a4': [0, 0], 'a5': [0, 2.23606797749979], 'a6': [0, 0], 'a7': [0, -0.7639320225002103], 'a8': [0, 0], 'a9': [7.47213595499958, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.220851458723894, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, -2.23606797749979]]]], 'bad_primes': [2, 5], 'central_character': '1280.129', 'coefficient_field': 'CDF', 'conductor': 1280, 'conductor_radical': 10, 'conjugate': '1044156278958192618317703111214', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.23606797749979, 0], [3.0, 0]], [[1.0, 0], [0, -2.23606797749979]], [[1.0, 0], [0, 0.7639320225002103], [-7.0, 0]], [[1.0, 0], [0, 0], [-11.0, 0]], [[1.0, 0], [0, 0], [13.0, 0]], [[1.0, 0], [0, 0], [-17.0, 0]], [[1.0, 0], [0, 0], [-19.0, 0]], [[1.0, 0], [0, 5.708203932499369], [-23.0, 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'2-1280-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.197006640394088, 'root_angle': -0.25, 'root_number': '0.7071067811865475244008443621048490392848359376884740366 - 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.125', 'prec': 20}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62899967962144220574872994114', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.75874994722527744116461720097', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79899227438733933686813987936', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.220851458723894, 'bad_primes': [2, 5], 'central_character': '40.29', 'conductor': 1280, 'conductor_radical': 10, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1280/2/f/g/129/2'], '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': '2-1280-40.29-c1-0-11', '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': '2-1280-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.197006640394088, 'root_angle': -0.125, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62899967962144220574872994114', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '797351821415485205404320777553', 'Lhash_array': ['797351821415485205404320777553'], 'label': '2-1280-40.29-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1280/2/f/g/129/2'}