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lfunc_lfunctions • Show schema
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{'Lhash': '1777024752876186514124571347121', 'a10': [-2.414213562373095, -1.2203761727102424e-60], 'a2': [0.7460330188237685, 2.296053540223068], 'a3': [2.288245611270737, 1.6625077511098136], 'a4': [-3.0972626056456845, 2.250293003402287], 'a5': [-0.30901699437494745, 0.9510565162951535], 'a6': [-2.110100026397432, 6.494220113036444], 'a7': [1.618033988749895, -1.1755705045849463], 'a8': [-3.571173788760211, -2.5946096324323262], 'a9': [1.545084971874737, 4.755282581475768], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.8309493222874655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.30901699437494745, -0.9510565162951535]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 11], 'central_character': '605.511', 'coefficient_field': 'CDF', 'conductor': 605, 'conductor_radical': 55, 'conjugate': '3474955349755266956830135000990', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7460330188237685, -2.296053540223068], 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17181241437760277068652452318', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.8309493222874655, 'bad_primes': [5, 11], 'central_character': '11.5', 'conductor': 605, 'conductor_radical': 55, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/605/2/g/f/511/2'], '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': '2-605-11.5-c1-0-13', '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': '2-605-11.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1979420652709356, 'root_angle': 0.4924325257956566, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40182535515405329537560141060', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1777024752876186514124571347121', 'Lhash_array': ['1777024752876186514124571347121'], 'label': '2-605-11.5-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/605/2/g/f/511/2'}