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lfunc_lfunctions • Show schema
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{'Lhash': '1791274207295088720140390707880', 'a10': [742.1064294964871, 0.0], 'a2': [10.291195104206762, 0.0], 'a3': [0.0, 0.0], 'a4': [73.90869667284922, 0.0], 'a5': [72.11081142491742, 0.0], 'a6': [0.0, 0.0], 'a7': [169.98749685151776, 0.0], 'a8': [431.2905740233121, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 116.9198046436629, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.1', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'euler_factors': [[[1.0, 0], [-10.291195104206762, 0], [32.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-72.11081142491742, 0], [3125.0, 0]], [[1.0, 0], [-169.98749685151776, 0], [16807.0, 0]], [[1.0, 0], [474.9519646831264, 0], [161051.0, 0]], [[1.0, 0], [-556.2840506626065, 0], [371293.0, 0]], [[1.0, 0], [-503.6992245367189, 0], [1419857.0, 0]], [[1.0, 0], [3.0354824932917612, 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'positive_zeros': ['1.41306619266585403636699082594284', '2.17778996931717396108195250883795', '3.13179897405721199852000917752359', '4.40245616122873247531807027331291', '5.22427715009140937986692143487266', '5.69271759059524900453625034768164', '6.56028767232854935232984991216000', '7.67711490978984928993878786063170', '8.565642821376797423137181716904704', '10.05082135586845598369713404861128'], 'prelabel': '2-3e6-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.812946159288083, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41306619266585403636699082594', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.17778996931717396108195250884', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.13179897405721199852000917752', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 116.9198046436629, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 145, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/6/a/e/1/39'], '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': '2-3e6-1.1-c5-0-145', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-3e6-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.812946159288083, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41306619266585403636699082594', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1791274207295088720140390707880', 'Lhash_array': ['1791274207295088720140390707880'], 'label': '2-3e6-1.1-c5-0-145', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/6/a/e/1/39'}