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lfunc_lfunctions • Show schema
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{'Lhash': '2327164473656895915498519882266', 'a10': -3, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': 3, 'a6': 0, 'a7': -3, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.354727167426075, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [79, [1, -1]]], 'bad_primes': [2, 3, 79], 'central_character': '1422.1', 'coefficient_field': '1.1.1.1', 'conductor': 1422, 'conductor_radical': 474, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, -3, 5], [1, 3, 7], [1, -2, 11], [1, 5, 13], [1, 6, 17], [1, 0, 19], [1, -2, 23], [1, 6, 29], [1, 10, 31], [1, 10, 37], [1, 2, 41], [1, -4, 43], [1, -3, 47], [1, -12, 53], [1, -1, 59], [1, -12, 61], [1, 8, 67], [1, -3, 71], [1, 6, 73], [1, -1], [1, 14, 83], [1, -7, 89], [1, 11, 97], [1, 3, 101], [1, -13, 103], [1, -1, 107], [1, -2, 109], [1, 12, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [[[1, -3, 5], 1]], [[[1, 3, 7], 1]], [[[1, -2, 11], 1]], [[[1, 5, 13], 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0.755510555566172, 1.3476002053944034, 1.8030974042350305, 2.0944630548258116, 2.204221269285762, 2.126100960009783, 1.8654648479499962, 1.4389947109671695, 0.8736504928113421, 0.20496887480456263], 'positive_zeros': ['1.83580907328715839320391152738213', '2.56149928245518451776775111666383', '3.80933035482911494201207656756737', '5.22641373981494590954939993298539', '5.95900466730196271449972715731919', '6.93717508441912222809183241427513', '7.17450713167885343099030707176680', '8.820853343801771743435698779759973', '9.174675330538307822169019064371729'], 'prelabel': '2-1422-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.3696776058587674, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1609562742758957343, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.83580907328715839320391152738', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56149928245518451776775111666', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.80933035482911494201207656757', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.354727167426075, 'bad_primes': [2, 3, 79], 'central_character': '1.1', 'conductor': 1422, 'conductor_radical': 474, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 3, 0, -3, -1, 0, -3, 2, 0, -5, 3, 0, 1, -6, 0, 0, 3, 0, -2, 2, 0, 4, 5, 0, -3, -6, 0, -10, -1, 0, 6, -9, 0, -10, 0, 0, -3, -2, 0, 4, 2, 0, -2, 3, 0, 2, -4, 0, -5, 12, 0, 6, 3, 0, 6, 1, 0, 12, 10, 0, 1, -15, 0, -8, -6, 0, 9, 3, 0, -6, 10, 0, 0, -6, 0, 1, 3, 0, 2, -14, 0, -18, -4, 0, -2, 7, 0, 15, 2, 0, -3, 0, 0, -11, -2, 0, 4], 'euler11': [1, -2, 11], 'euler13': [1, 5, 13], 'euler17': [1, 6, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 0], 'euler23': [1, -2, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 10, 31], 'euler37': [1, 10, 37], 'euler41': [1, 2, 41], 'euler43': [1, -4, 43], 'euler47': [1, -3, 47], 'euler5': [1, -3, 5], 'euler53': [1, -12, 53], 'euler59': [1, -1, 59], 'euler61': [1, -12, 61], 'euler67': [1, 8, 67], 'euler7': [1, 3, 7], 'euler71': [1, -3, 71], 'euler73': [1, 6, 73], 'euler79': [1, -1, 0], 'euler83': [1, 14, 83], 'euler89': [1, -7, 89], 'euler97': [1, 11, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, -3, 5], [1, 3, 7], [1, -2, 11], [1, 5, 13], [1, 6, 17], [1, 0, 19], [1, -2, 23], [1, 6, 29], [1, 10, 31], [1, 10, 37], [1, 2, 41], [1, -4, 43], [1, -3, 47], [1, -12, 53], [1, -1, 59], [1, -12, 61], [1, 8, 67], [1, -3, 71], [1, 6, 73], [1, -1, 0], [1, 14, 83], [1, -7, 89], [1, 11, 97]], 'index': 23, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1422/c', 'ModularForm/GL2/Q/holomorphic/1422/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/1422/2/a/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-1422-1.1-c1-0-23', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1422-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.3696776058587674, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1609562742758957343, 'z1': {'__RealLiteral__': 0, 'data': '1.83580907328715839320391152738', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20591979
{'Lhash': '2327164473656895915498519882266', 'Lhash_array': ['2327164473656895915498519882266'], 'label': '2-1422-1.1-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1422/2/a/c'}
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id: 24553055
{'Lhash': '2327164473656895915498519882266', 'Lhash_array': ['2327164473656895915498519882266'], 'label': '2-1422-1.1-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1422/2/a/c/1/1'}
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id: 42597
{'Lhash': '1609562742758957343', 'Lhash_array': ['1609562742758957343'], 'label': '2-1422-1.1-c1-0-23', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1422/c'}