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lfunc_lfunctions • Show schema
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{'Lhash': '4635165242466239353870002204701', 'a10': [0.5830022605485444, 0.08787345195304898], 'a2': [-1.164382338400933, -0.3591643851291789], 'a3': [0.6711203973600696, -1.709986884625432], 'a4': [-0.4256903741971857, -0.2902307828731507], 'a5': [-0.47845204063908425, 0.07211504182741678], 'a6': [-1.3956071256221347, 1.7500359824896077], 'a7': [1.9019551926443536, -1.8391754797118136], 'a8': [1.9108924603267416, 2.3961833547884357], 'a9': [-0.27449694234877386, -0.25469594166789644], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.39126696990427406, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-1.9019551926443536, 1.8391754797118136]]]], 'bad_primes': [7], 'central_character': '49.2', 'coefficient_field': 'CDF', 'conductor': 49, 'conductor_radical': 7, 'conjugate': '2223932724111482206781135048622', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.164382338400933, 0.3591643851291789], [1.6524775486319898, 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[-74.78041603590079, -36.01235034675732]], [[1.0, 0], [1.3812884664751115, 1.281648398971518], [6.650978329191759, 88.75113794912504]], [[1.0, 0], [0.10465735438841782, 0], [97.0, 0]], [[1.0, 0], [1.5896081168684215, -4.050255426942058], [-74.03823905481246, -68.69744651486286]], [[1.0, 0], [-5.1216534254029025, 0.7719650448247896], [98.4239989959725, -30.359782964323134]], [[1.0, 0], [7.5175809655690795, 6.975295778185646], [7.996120013747396, 106.70080629838628]], [[1.0, 0], [0.5351564223846653, -0.49655259462125556], [8.145580200920243, -108.69521389274864]], [[1.0, 0], [1.2216342653371555, -5.352329430671672], [-101.80948207297337, -49.028862520284065]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-7e2-49.2-c1-0-2', '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': 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.200919271093', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.65650064902088824725966133784', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.38275838685264699006622450397', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.84182407115337564183952520071', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.39126696990427406, 'bad_primes': [7], 'central_character': '49.2', 'conductor': 49, 'conductor_radical': 7, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/2/g/a/2/2'], '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': '2-7e2-49.2-c1-0-2', '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': '2-7e2-49.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.625513365088448, 'root_angle': 0.2009192710926527, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.65650064902088824725966133784', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4635165242466239353870002204701', 'Lhash_array': ['4635165242466239353870002204701'], 'label': '2-7e2-49.2-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/2/g/a/2/2'}