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lfunc_lfunctions • Show schema
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{'Lhash': '1458341610467597007189642798104', 'a10': [4.400807790603425, -1.0462179297285647e-63], 'a2': [-1.0625143657319702, 1.8403288652195924], 'a3': [0.0, 0.0], 'a4': [-1.2578735547736217, -2.178700906365186], 'a5': [-1.035470185754075, -1.7934869714488406], 'a6': [0.0, 0.0], 'a7': [-2.4243363738191146, 4.199073774092001], 'a8': [1.095977425957373, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.487', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '524528070915540546101723243462', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0625143657319702, -1.8403288652195924], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.035470185754075, 1.7934869714488406], [-2.5, 4.330127018922194]], [[1.0, 0], [2.4243363738191146, 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'10.46697662460315926745750134671377'], 'prelabel': '2-3e6-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -4.0033205120149015e-61, 'root_number': '1.0 - 1.2576802310511344e-60*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.000000000000000000000000000000000000000000000000000000000000200166025601', 'prec': 250}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15042868295493676050340453188', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.65357760676528232762852293544', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68178327341010548873269318544', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '9.7', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/c/a/487/2'], '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': '2-3e6-9.7-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': '2-3e6-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -2.0016602560074508e-61, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15042868295493676050340453188', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1458341610467597007189642798104', 'Lhash_array': ['1458341610467597007189642798104'], 'label': '2-3e6-9.7-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/c/a/487/2'}