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lfunc_lfunctions • Show schema
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{'Lhash': '2401080125822568232751055761993', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.5, -0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6467882563723711, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1296.703', 'coefficient_field': 'CDF', 'conductor': 1296, 'conductor_radical': 6, 'conjugate': '728767306839397247050491456908', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [1.5, 0.8660254037844386], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-1.0, 0]], 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'6.01671241690362663200240029679695', '6.67904247366919260201388449221324', '7.56187268558252173153700921642822', '8.669060831731531756725945666177553', '9.311455163150950780164805280022367', '9.919836076926915501974594132397871'], 'prelabel': '2-6e4-36.7-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.804231469399433, 'root_angle': 0.5555555555555556, 'root_number': '-0.17364817766693034885171662676923 + 0.98480775301220805936674302458979*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2777777777777778', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89411824156457209905851467830', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.06804887972638879037669248962', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86408416361333946066487271286', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6467882563723711, 'bad_primes': [2, 3], 'central_character': '36.7', 'conductor': 1296, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1296/1/o/a/703/1'], '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': '2-6e4-36.7-c0-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-6e4-36.7-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.804231469399433, 'root_angle': 0.2777777777777778, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89411824156457209905851467830', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2401080125822568232751055761993', 'Lhash_array': ['2401080125822568232751055761993'], 'label': '2-6e4-36.7-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1296/1/o/a/703/1'}