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lfunc_lfunctions • Show schema
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{'Lhash': '1270146349661510000396609658121', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [3.0, 0.0], 'a4': [0.0, 0.0], 'a5': [11.432199927986446, 0.0], 'a6': [0.0, 0.0], 'a7': [11.254298618329436, 0.0], 'a8': [0.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 147.26876737432863, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-3.0, 0]]], [13, [[1.0, 0], [13.0, 0]]]], 'bad_primes': [2, 3, 13], 'central_character': '2496.1', 'coefficient_field': 'CDF', 'conductor': 2496, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [-11.432199927986446, 0], [125.0, 0]], [[1.0, 0], [-11.254298618329436, 0], [343.0, 0]], [[1.0, 0], [-25.87850024451619, 0], [1331.0, 0]], [[1.0, 0], [13.0, 0]], [[1.0, 0], [20.32760184222742, 0], [4913.0, 0]], [[1.0, 0], [-154.711898042221, 0], [6859.0, 0]], [[1.0, 0], [-180.4183923430361, 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'2.72171525885113310138879275239221', '3.60379449808299288755236797722688', '4.71538932789604488522874336504663', '5.40921095693756550761939167578503', '6.20716719136986701666707093458186', '7.29711911009943972386174297876842', '7.59420983018327530720123366028337', '8.928801382316524640591042804738063'], 'prelabel': '2-2496-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.135434371060997, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00196879915714256045522685230', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.75476383729905286427139137374', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.72171525885113310138879275239', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 147.26876737432863, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 2496, 'conductor_radical': 78, 'degree': 2, 'index': 81, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2496/4/a/bp/1/3'], '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': '2-2496-1.1-c3-0-81', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-2496-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.135434371060997, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00196879915714256045522685230', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1270146349661510000396609658121', 'Lhash_array': ['1270146349661510000396609658121'], 'label': '2-2496-1.1-c3-0-81', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2496/4/a/bp/1/3'}