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lfunc_lfunctions • Show schema
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{'Lhash': '2732087104265559752944391345099', 'a10': [2.432458234887408, 2.020679820141834], 'a2': [1.411074343794321, -0.09417641045095253], 'a3': [-1.6812233022910785, 0.4165191566224544], 'a4': [1.9822616074291475, -0.265779833155965], 'a5': [1.621039517734604, 1.5402048181793104], 'a6': [-2.3331047889973444, 0.7460710713850643], 'a7': [-0.36198928490127213, -0.36198928490127213], 'a8': [2.7720883062748785, -0.5617173864267297], 'a9': [2.6530235843330385, -1.4005234239285955], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.411074343794321, 0.09417641045095253]]], [3, [[1.0, 0], [1.6812233022910785, -0.4165191566224544]]], [5, [[1.0, 0], [-1.621039517734604, -1.5402048181793104]]]], 'bad_primes': [2, 3, 5], 'central_character': '120.77', 'coefficient_field': 'CDF', 'conductor': 120, 'conductor_radical': 30, 'conjugate': 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'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.07528829236962344, 'root_number': '0.9721580908050338 - 0.2343259406943918*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0376441461848', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.15523670621358233049512183517', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.58305846880449325612744215944', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.35488946864313463135466148459', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'bad_primes': [2, 3, 5], 'central_character': '120.77', 'conductor': 120, 'conductor_radical': 30, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/120/2/w/c/77/16'], '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': '2-120-120.77-c1-0-7', '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': '2-120-120.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.03764414618481172, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.15523670621358233049512183517', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2732087104265559752944391345099', 'Lhash_array': ['2732087104265559752944391345099'], 'label': '2-120-120.77-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/120/2/w/c/77/16'}