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lfunc_lfunctions • Show schema
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{'Lhash': '562916952262253714415634600942', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.9462317888958511, -3.3709723416732795], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.2568327496616, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '5292.1549', 'coefficient_field': 'CDF', 'conductor': 5292, 'conductor_radical': 42, 'conjugate': '1246704856888156498179050613141', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.9462317888958511, 3.3709723416732795], [-2.5, 4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.1877839004173762, 3.7893528715041045], [-5.5, -9.526279441628825]], [[1.0, 0], [-0.7922006102176441, 1.3721317066840277], [-6.5, -11.258330249197702]], [[1.0, 0], 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'primitive': True, 'rational': False, 'root_analytic_conductor': 6.500525574879434, 'root_angle': -0.1089721470600091, 'root_number': '0.9419696787569735156905324269744584882607642612132992697 - 0.3356979658897028791585649433244209427516379820749905598*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.05448607353000455', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44406317652585455440987757337', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.10848546674755461557628197823', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.75569540362913728004244454367', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.2568327496616, 'bad_primes': [2, 3, 7], 'central_character': '63.58', 'conductor': 5292, 'conductor_radical': 42, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5292/2/i/j/1549/1'], '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': '2-5292-63.58-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': '2-5292-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.500525574879434, 'root_angle': -0.05448607353000455, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44406317652585455440987757337', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '562916952262253714415634600942', 'Lhash_array': ['562916952262253714415634600942'], 'label': '2-5292-63.58-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5292/2/i/j/1549/1'}