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lfunc_lfunctions • Show schema
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{'Lhash': '2148727045864948060117957898223', 'a10': 0, 'a2': 0, 'a3': -113, 'a4': 256, 'a5': 1151, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 6208, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.481164710672401, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[11, [1, -14641]]], 'bad_primes': [11], 'central_character': '11.10', 'coefficient_field': '1.1.1.1', 'conductor': 11, 'conductor_radical': 11, 'degree': 2, 'euler_factors': [[1, 0, -256], [1, 113, 6561], [1, -1151, 390625], [1, 0, -5764801], [1, -14641], [1, 0, -815730721], [1, 0, -6975757441], [1, 0, -16983563041], [1, 531793, 78310985281], [1, 0, -500246412961], [1, 1541233, 852891037441], [1, -716447, 3512479453921], [1, 0, -7984925229121], [1, 0, -11688200277601], [1, 6080638, 23811286661761], [1, 15265438, 62259690411361], [1, 4101553, 146830437604321], [1, 0, -191707312997281], [1, -19806767, 406067677556641], [1, -7043087, 645753531245761], [1, 0, -806460091894081], [1, 0, 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{'__RealLiteral__': 0, 'data': '5.70223112857235470281460369734', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.53233859618543442273249017838', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.481164710672401, 'bad_primes': [11], 'central_character': '11.10', 'conductor': 11, 'conductor_radical': 11, 'degree': 2, 'dirichlet_coefficients': [1, 0, -113, 256, 1151, 0, 0, 0, 6208, 0, 14641, -28928, 0, 0, -130063, 65536, 0, 0, 0, 294656, 0, 0, -531793, 0, 934176, 0, 39889, 0, 0, 0, -1541233, 0, -1654433, 0, 0, 1589248, 716447, 0, 0, 0, 0, 0, 0, 3748096, 7145408, 0, -6080638, -7405568, 5764801, 0, 0, 0, -15265438, 0, 16851791, 0, 0, 0, -4101553, -33296128, 0, 0, 0, 16777216, 0, 0, 19806767, 0, 60092609, 0, 7043087, 0, 0, 0, -105561888, 0, 0, 0, 0, 75431936, -45238145, 0, 0, 0, 0, 0, 0, 0, -84100993, 0, 0, -136139008, 174159329, 0, 0, 0, -81155713, 0, 90891328, 239149056], 'euler11': [1, -14641, 0], 'euler13': [1, 0, -815730721], 'euler17': [1, 0, -6975757441], 'euler19': [1, 0, -16983563041], 'euler2': [1, 0, -256], 'euler23': [1, 531793, 78310985281], 'euler29': [1, 0, -500246412961], 'euler3': [1, 113, 6561], 'euler31': [1, 1541233, 852891037441], 'euler37': [1, -716447, 3512479453921], 'euler41': [1, 0, -7984925229121], 'euler43': [1, 0, -11688200277601], 'euler47': [1, 6080638, 23811286661761], 'euler5': [1, -1151, 390625], 'euler53': [1, 15265438, 62259690411361], 'euler59': [1, 4101553, 146830437604321], 'euler61': [1, 0, -191707312997281], 'euler67': [1, -19806767, 406067677556641], 'euler7': [1, 0, -5764801], 'euler71': [1, -7043087, 645753531245761], 'euler73': [1, 0, -806460091894081], 'euler79': [1, 0, -1517108809906561], 'euler83': [1, 0, -2252292232139041], 'euler89': [1, 84100993, 3936588805702081], 'euler97': [1, 81155713, 7837433594376961], 'euler_factors': [[1, 0, -256], [1, 113, 6561], [1, -1151, 390625], [1, 0, -5764801], [1, -14641, 0], [1, 0, -815730721], [1, 0, -6975757441], [1, 0, -16983563041], [1, 531793, 78310985281], [1, 0, -500246412961], [1, 1541233, 852891037441], [1, -716447, 3512479453921], [1, 0, -7984925229121], [1, 0, -11688200277601], [1, 6080638, 23811286661761], [1, 15265438, 62259690411361], [1, 4101553, 146830437604321], [1, 0, -191707312997281], [1, -19806767, 406067677556641], [1, -7043087, 645753531245761], [1, 0, -806460091894081], [1, 0, -1517108809906561], [1, 0, -2252292232139041], [1, 84100993, 3936588805702081], [1, 81155713, 7837433594376961]], 'index': 2, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/11/9/b/a/10/1', 'ModularForm/GL2/Q/holomorphic/11/9/b/a'], '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': '2-11-11.10-c8-0-2', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-11-11.10-c8-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.11687616800615, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c8-0', 'trace_hash': 815415583487374044, 'z1': {'__RealLiteral__': 0, 'data': '1.69504676247389347822626893512', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10059205
{'Lhash': '2148727045864948060117957898223', 'Lhash_array': ['2148727045864948060117957898223'], 'label': '2-11-11.10-c8-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/11/9/b/a'}
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id: 24549738
{'Lhash': '2148727045864948060117957898223', 'Lhash_array': ['2148727045864948060117957898223'], 'label': '2-11-11.10-c8-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/11/9/b/a/10/1'}