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lfunc_lfunctions • Show schema
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{'Lhash': '479232356489535628002203488287', 'a10': [0.09780249739953162, -3.882545162971195], 'a2': [-0.9962321726381689, 1.422766991605567], 'a3': [-1.4482996285104044, 0.949962202435773], 'a4': [-0.34774708395165177, -0.9554272608383542], 'a5': [-1.863396512733312, 1.2360232345442912], 'a6': [0.09126782064342964, -3.0069758142559384], 'a7': [0.9201121538160306, -0.4290553436859051], 'a8': [-1.649603024587059, -0.44200979827003994], 'a9': [1.1951436278867509, -2.751659809773311], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0779804272872857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.4482996285104044, -0.949962202435773]]], [5, [[1.0, 0], [1.863396512733312, -1.2360232345442912]]]], 'bad_primes': [3, 5], 'central_character': '135.68', 'coefficient_field': 'CDF', 'conductor': 135, 'conductor_radical': 15, 'conjugate': '4638222947382522438914627025260', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37804767055153370685503096910', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.27210184511957436274568513730', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.49547972163373573673519659409', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0779804272872857, 'bad_primes': [3, 5], 'central_character': '135.68', 'conductor': 135, 'conductor_radical': 15, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/135/2/q/a/68/4'], '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': '2-135-135.68-c1-0-0', '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': '2-135-135.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0382583624933082, 'root_angle': 0.37511850712776873, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37804767055153370685503096910', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '479232356489535628002203488287', 'Lhash_array': ['479232356489535628002203488287'], 'label': '2-135-135.68-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/135/2/q/a/68/4'}