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lfunc_lfunctions • Show schema
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{'Lhash': '1841049996484648269389858578701', 'a10': 0, 'a2': -1, 'a3': 1, 'a4': 1, 'a5': 0, 'a6': -1, 'a7': 1, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.958151453981024, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [7, [1, -1]], [11, [1, -1]], [13, [1, -1]]], 'bad_primes': [2, 3, 7, 11, 13], 'central_character': '6006.1', 'coefficient_field': '1.1.1.1', 'conductor': 6006, 'conductor_radical': 6006, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1, 0, 5], [1, -1], [1, -1], [1, -1], [1, 6, 17], [1, 4, 19], [1, 0, 23], [1, -6, 29], [1, -2, 31], [1, 4, 37], [1, 6, 41], [1, 10, 43], [1, -12, 47], [1, -6, 53], [1, 6, 59], [1, 10, 61], [1, 10, 67], [1, 6, 71], [1, -2, 73], [1, 4, 79], [1, 0, 83], [1, 6, 89], [1, 16, 97], [1, 0, 101], [1, 4, 103], [1, 12, 107], [1, -2, 109], [1, -18, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, -1], 1]], [[[1, 0, 5], 1]], [[[1, 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2.245562238425068, 1.7273581156378597, 1.196181365318572, 0.6809521691451227, 0.21058531472333825, -0.18753460610280823, -0.4890351321744235, -0.6739155871875937, -0.727709810936221, -0.6423861955292002, -0.41693183292202457], 'positive_zeros': ['1.45233236678402023597389627869057', '2.16443810714876659809131045445966', '3.02454295717369388295349502843732', '4.07250101882315061852419144352392', '4.62921816402815364000416993243193', '5.76664171057413663377072465216696', '6.56890271020717317917775066153481', '7.04576517766578426769797044951809', '7.939600956213806596881204281900077'], 'prelabel': '2-6006-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.925182413047401, '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': 2183688819471653873, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45233236678402023597389627869', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.16443810714876659809131045446', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.02454295717369388295349502844', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.958151453981024, 'bad_primes': [2, 3, 7, 11, 13], 'central_character': '1.1', 'conductor': 6006, 'conductor_radical': 6006, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, 0, -1, 1, -1, 1, 0, 1, 1, 1, -1, 0, 1, -6, -1, -4, 0, 1, -1, 0, -1, -5, -1, 1, 1, 6, 0, 2, -1, 1, 6, 0, 1, -4, 4, 1, 0, -6, -1, -10, 1, 0, 0, 12, 1, 1, 5, -6, 1, 6, -1, 0, -1, -4, -6, -6, 0, -10, -2, 1, 1, 0, -1, -10, -6, 0, 0, -6, -1, 2, 4, -5, -4, 1, -1, -4, 0, 1, 6, 0, 1, 0, 10, 6, -1, -6, 0, 1, 0, 2, -12, 0, -1, -16, -1, 1, -5], 'euler11': [1, -1, 0], 'euler13': [1, -1, 0], 'euler17': [1, 6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -2, 31], 'euler37': [1, 4, 37], 'euler41': [1, 6, 41], 'euler43': [1, 10, 43], 'euler47': [1, -12, 47], 'euler5': [1, 0, 5], 'euler53': [1, -6, 53], 'euler59': [1, 6, 59], 'euler61': [1, 10, 61], 'euler67': [1, 10, 67], 'euler7': [1, -1, 0], 'euler71': [1, 6, 71], 'euler73': [1, -2, 73], 'euler79': [1, 4, 79], 'euler83': [1, 0, 83], 'euler89': [1, 6, 89], 'euler97': [1, 16, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, 0, 5], [1, -1, 0], [1, -1, 0], [1, -1, 0], [1, 6, 17], [1, 4, 19], [1, 0, 23], [1, -6, 29], [1, -2, 31], [1, 4, 37], [1, 6, 41], [1, 10, 43], [1, -12, 47], [1, -6, 53], [1, 6, 59], [1, 10, 61], [1, 10, 67], [1, 6, 71], [1, -2, 73], [1, 4, 79], [1, 0, 83], [1, 6, 89], [1, 16, 97]], 'index': 101, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6006/p', 'ModularForm/GL2/Q/holomorphic/6006/2/a/p/1/1', 'ModularForm/GL2/Q/holomorphic/6006/2/a/p'], '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': '2-6006-1.1-c1-0-101', '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': '2-6006-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.925182413047401, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2183688819471653873, 'z1': {'__RealLiteral__': 0, 'data': '1.45233236678402023597389627869', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21591057
{'Lhash': '1841049996484648269389858578701', 'Lhash_array': ['1841049996484648269389858578701'], 'label': '2-6006-1.1-c1-0-101', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6006/2/a/p'}
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id: 24572995
{'Lhash': '1841049996484648269389858578701', 'Lhash_array': ['1841049996484648269389858578701'], 'label': '2-6006-1.1-c1-0-101', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6006/2/a/p/1/1'}
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id: 92721
{'Lhash': '2183688819471653873', 'Lhash_array': ['2183688819471653873'], 'label': '2-6006-1.1-c1-0-101', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6006/p'}