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lfunc_lfunctions • Show schema
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{'Lhash': '1508846903436820593546690478366', 'a10': 0, 'a2': 1, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': -1, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.067265720149466, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '1386.1', 'coefficient_field': '1.1.1.1', 'conductor': 1386, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, 0, 5], [1, 1], [1, -1], [1, -6, 13], [1, 4, 17], [1, -6, 19], [1, -4, 23], [1, 6, 29], [1, 2, 31], [1, -10, 37], [1, -4, 41], [1, -8, 43], [1, -6, 47], [1, -10, 53], [1, 0, 59], [1, 2, 61], [1, 4, 67], [1, 16, 71], [1, -12, 73], [1, 16, 79], [1, -2, 83], [1, -6, 89], [1, 6, 97], [1, -14, 101], [1, 14, 103], [1, 8, 107], [1, 14, 109], [1, -2, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [1], [[[1, 0, 5], 1]], [[[1, 1], 1]], [[[1, -1], 1]], [[[1, 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2.2444228691633668, 2.4000981685603016, 2.45057553830741, 2.3875892652849044, 2.210237971496544, 1.9252201652782395, 1.5465380017947779, 1.0946806923342933, 0.5953361002344457, 0.07771343729212274, -0.427410858423879, -0.8897901968379627, -1.2818012894044686, -1.5803848743869213, -1.768692638550014], 'positive_zeros': ['1.19027033408509088196634720414303', '2.59024020521701587582121097787336', '3.66659975798484481234060481750698', '4.27334010758862108959056723897475', '5.61371504482077087781349905589476', '6.04478799301580802001339575092304', '7.05017713754858032134757992630421', '7.76942870316508074151045948134844', '8.939866287033108653082236334370007', '9.421165170395764700270395716860811'], 'prelabel': '2-1386-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.326750023694216, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1457624846876464821, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19027033408509088196634720414', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59024020521701587582121097787', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.66659975798484481234060481751', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.067265720149466, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 1386, 'conductor_radical': 462, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, -1, 1, 0, 0, 1, 0, 6, -1, 0, 1, -4, 0, 6, 0, 0, 1, 4, 0, -5, 6, 0, -1, -6, 0, -2, 1, 0, -4, 0, 0, 10, 6, 0, 0, 4, 0, 8, 1, 0, 4, 6, 0, 1, -5, 0, 6, 10, 0, 0, -1, 0, -6, 0, 0, -2, -2, 0, 1, 0, 0, -4, -4, 0, 0, -16, 0, 12, 10, 0, 6, -1, 0, -16, 0, 0, 4, 2, 0, 0, 8, 0, 1, 6, 0, -6, 4, 0, 6, 0, 0, -6, 1, 0, -5], 'euler11': [1, -1, 0], 'euler13': [1, -6, 13], 'euler17': [1, 4, 17], 'euler19': [1, -6, 19], 'euler2': [1, -1, 0], 'euler23': [1, -4, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 2, 31], 'euler37': [1, -10, 37], 'euler41': [1, -4, 41], 'euler43': [1, -8, 43], 'euler47': [1, -6, 47], 'euler5': [1, 0, 5], 'euler53': [1, -10, 53], 'euler59': [1, 0, 59], 'euler61': [1, 2, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 0], 'euler71': [1, 16, 71], 'euler73': [1, -12, 73], 'euler79': [1, 16, 79], 'euler83': [1, -2, 83], 'euler89': [1, -6, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 0, 5], [1, 1, 0], [1, -1, 0], [1, -6, 13], [1, 4, 17], [1, -6, 19], [1, -4, 23], [1, 6, 29], [1, 2, 31], [1, -10, 37], [1, -4, 41], [1, -8, 43], [1, -6, 47], [1, -10, 53], [1, 0, 59], [1, 2, 61], [1, 4, 67], [1, 16, 71], [1, -12, 73], [1, 16, 79], [1, -2, 83], [1, -6, 89], [1, 6, 97]], 'index': 12, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1386/j', 'ModularForm/GL2/Q/holomorphic/1386/2/a/j/1/1', 'ModularForm/GL2/Q/holomorphic/1386/2/a/j'], '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': '2-1386-1.1-c1-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1386-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.326750023694216, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1457624846876464821, 'z1': {'__RealLiteral__': 0, 'data': '1.19027033408509088196634720414', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20704703
{'Lhash': '1508846903436820593546690478366', 'Lhash_array': ['1508846903436820593546690478366'], 'label': '2-1386-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1386/2/a/j'}
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id: 24552915
{'Lhash': '1508846903436820593546690478366', 'Lhash_array': ['1508846903436820593546690478366'], 'label': '2-1386-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1386/2/a/j/1/1'}
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id: 92390
{'Lhash': '1457624846876464821', 'Lhash_array': ['1457624846876464821'], 'label': '2-1386-1.1-c1-0-12', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1386/j'}