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lfunc_lfunctions • Show schema
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{'Lhash': '2122364864992228174336065643614', 'a10': [3.0, 5.196152422706632], 'a2': [-0.42534943004813686, 2.4122764896167532], 'a3': [0.0, 0.0], 'a4': [-3.7587704831436337, -1.3680805733026749], 'a5': [1.8764180059359885, -1.5745016567152952], 'a6': [0.0, 0.0], 'a7': [-1.8793852415718169, 0.6840402866513374], 'a8': [2.449489742783178, -4.242640687119285], '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': '729.649', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '496735208288547151831469313411', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.42534943004813686, -2.4122764896167532], [-1.8793852415718169, -0.6840402866513374]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.8764180059359885, 1.5745016567152952], [0.8682408883346517, -4.924038765061041]], [[1.0, 0], 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['1.67425066860703962612759841841246', '2.55284369076679863162709418970130', '3.53644016501746653482806567517109', '4.53976462552000741644412006268055', '5.98901889903242688264675901852875', '6.86393422021330070506602330635424', '8.203345128394665397791655164256112', '9.167433575749506248188879348840879', '9.893661370661692994535946131478021', '10.52560638576943268439683311849773'], 'prelabel': '2-3e6-27.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.07407407407407408, 'root_number': '0.9730448705798238 + 0.2306158707424402*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.037037037037', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67425066860703962612759841841', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.55284369076679863162709418970', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53644016501746653482806567517', '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': '27.25', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/p/649/1'], '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': '2-3e6-27.25-c1-0-21', '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': '2-3e6-27.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.03703703703703704, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.67425066860703962612759841841', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2122364864992228174336065643614', 'Lhash_array': ['2122364864992228174336065643614'], 'label': '2-3e6-27.25-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/p/649/1'}