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lfunc_lfunctions • Show schema
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{'Lhash': '2657388602824560531691947981997', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.0193554789367, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, -1]], [23, [1, -1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '1380.1', 'coefficient_field': '1.1.1.1', 'conductor': 1380, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1], [1, 3, 7], [1, 2, 11], [1, 2, 13], [1, 7, 17], [1, 6, 19], [1, -1], [1, 9, 29], [1, -9, 31], [1, 7, 37], [1, -5, 41], [1, 0, 43], [1, -8, 47], [1, 11, 53], [1, -9, 59], [1, 0, 61], [1, 3, 67], [1, -3, 71], [1, 6, 73], [1, 8, 79], [1, -5, 83], [1, 0, 89], [1, 10, 97], [1, -3, 101], [1, -8, 103], [1, -5, 107], [1, -10, 109], [1, -21, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, -1], 1]], [[[1, 3, 7], 1]], [[[1, 2, 11], 1]], [[[1, 2, 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2.1836491616072364, 2.5886088069031823, 2.8810221952211643, 3.046132433713895, 3.07751131720966, 2.977551318031687, 2.757352976669047, 2.4360071618700463, 2.039313903377239], 'positive_zeros': ['2.09630997874818263004859828457186', '2.77431282556833018538797503915444', '3.94385539988496915567759022760129', '4.84828956114251062555624822681950', '6.05722317603077213338585769718767', '6.69307252699898801657576735237241', '7.50086256368661123062194361771083', '8.608402893779175259110116582323337', '9.114626272342420246330424630098351'], 'prelabel': '2-1380-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.3195414561256347, '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': 1279016157879757911, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.09630997874818263004859828457', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.77431282556833018538797503915', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.94385539988496915567759022760', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.0193554789367, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 1380, 'conductor_radical': 690, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, -3, 0, 1, 0, -2, 0, -2, 0, 1, 0, -7, 0, -6, 0, -3, 0, 1, 0, 1, 0, 1, 0, -9, 0, 9, 0, -2, 0, -3, 0, -7, 0, -2, 0, 5, 0, 0, 0, 1, 0, 8, 0, 2, 0, -7, 0, -11, 0, -2, 0, -6, 0, 9, 0, 0, 0, -3, 0, -2, 0, -3, 0, 1, 0, 3, 0, -6, 0, 1, 0, 6, 0, -8, 0, 1, 0, 5, 0, -7, 0, -9, 0, 0, 0, 6, 0, 9, 0, -6, 0, -10, 0, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, 2, 13], 'euler17': [1, 7, 17], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, 9, 29], 'euler3': [1, -1, 0], 'euler31': [1, -9, 31], 'euler37': [1, 7, 37], 'euler41': [1, -5, 41], 'euler43': [1, 0, 43], 'euler47': [1, -8, 47], 'euler5': [1, -1, 0], 'euler53': [1, 11, 53], 'euler59': [1, -9, 59], 'euler61': [1, 0, 61], 'euler67': [1, 3, 67], 'euler7': [1, 3, 7], 'euler71': [1, -3, 71], 'euler73': [1, 6, 73], 'euler79': [1, 8, 79], 'euler83': [1, -5, 83], 'euler89': [1, 0, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -1, 0], [1, 3, 7], [1, 2, 11], [1, 2, 13], [1, 7, 17], [1, 6, 19], [1, -1, 0], [1, 9, 29], [1, -9, 31], [1, 7, 37], [1, -5, 41], [1, 0, 43], [1, -8, 47], [1, 11, 53], [1, -9, 59], [1, 0, 61], [1, 3, 67], [1, -3, 71], [1, 6, 73], [1, 8, 79], [1, -5, 83], [1, 0, 89], [1, 10, 97]], 'index': 15, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1380/e', 'ModularForm/GL2/Q/holomorphic/1380/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/1380/2/a/e'], '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': '2-1380-1.1-c1-0-15', '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': '2-1380-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.3195414561256347, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1279016157879757911, 'z1': {'__RealLiteral__': 0, 'data': '2.09630997874818263004859828457', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20617372
{'Lhash': '2657388602824560531691947981997', 'Lhash_array': ['2657388602824560531691947981997'], 'label': '2-1380-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1380/2/a/e'}
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id: 24552901
{'Lhash': '2657388602824560531691947981997', 'Lhash_array': ['2657388602824560531691947981997'], 'label': '2-1380-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1380/2/a/e/1/1'}
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id: 41717
{'Lhash': '1279016157879757911', 'Lhash_array': ['1279016157879757911'], 'label': '2-1380-1.1-c1-0-15', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1380/e'}