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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 2, 'A3': 0, 'A4': 2, 'A5': 0, 'A6': 0, 'A7': -3, 'A8': 0, 'A9': 0, 'Lhash': '1245170268994980877', 'a10': [0.0, 0], 'a2': [1.414213562373095, 0], 'a3': [0.0, 0], 'a4': [1.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 648.5848904178503, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [19, [1]]], 'bad_primes': [3, 5, 19], 'central_character': '81225.1', 'coefficient_field': '1.1.1.1', 'conductor': 81225, 'conductor_radical': 285, 'degree': 2, 'euler_factors': [[1, -2, 2], [1], [1], [1, 3, 7], [1, 2, 11], [1, 1, 13], [1, 2, 17], [1], [1, 6, 23], [1, -10, 29], [1, -3, 31], [1, 2, 37], [1, 8, 41], [1, -1, 43], [1, 2, 47], [1, 4, 53], [1, 10, 59], [1, -7, 61], [1, -3, 67], [1, 8, 71], [1, 14, 73], [1, 0, 79], [1, 6, 83], [1, 0, 89], [1, 17, 97]], 'gamma_factors': [[], [0]], 'index': 2, 'label': '2-285e2-1.1-c1-0-2', 'leading_term': '1.11462571974', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/81225/bp', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.114625719735474, 0.006680667118447985, -2.843063300500355, -5.909517737915214, -7.016086530992823, -4.856380988753414, -0.4878128478761408, 3.109928187329898, 3.597231908737758, 1.518868420943628, -0.4214693166886747, -0.4663195293738964, 0.4050631111940396, 0.2646167385949692, -0.881713386678639, -1.2309875224723, -0.1139598031971435, 0.8378532279672742, 0.2860418507757723, -0.5451867871493264, 0.1522633582742478, 1.576994504075866, 1.455831652482657, -0.02529854012973942, -0.34527856763253, 0.8999996583371113, 1.134487002899439, -0.1322127930379144, 0.6230448437335556, 4.620969894270283, 6.544313491674336, 1.936855043753459, -4.234211675886424, -3.694308380903906, 1.882024261698185, 2.594983608357442, -3.893733561457389, -8.215325918167872, -4.469146339137084, 0.5510034084495365, -0.3974213481955142, -2.969423298828536, -0.2284465336891874, 4.274572534981366, 2.946217265370381, -2.249011302997108, -3.601038775633587, -0.7322682816079252, 0.7048556724003318, -0.1485974937254065, 0.184125771398789, 1.42534197044439, 0.9459849591681473, -0.07097255056275094, 0.4536951533606672, 0.7158546567980424, -0.489538982837206, -0.3725538627215226, 1.533158614665152, 1.230067967198886, -1.496704645643197, -1.909694959790268, 0.142950320761442, 0.4109152066532695, 0.1003594657368622, 2.590875874584307, 2.975917467177643, -3.590763520742803, -8.55991995141235, -3.010786511099343, 4.270505955635216, 1.806916959033238, -2.822612306239253, 1.801957316312122, 7.978223585249415, 4.240579807130327, -2.075422681247482, -0.1145963297895225, 3.899153906327774, 1.456569540252378, -1.542638527989018, 0.6110245333629842, 1.779931206551643, -1.265490599433397, -2.176806219955615, 0.5431467456124665, 1.210226355350871, -0.3429675450492782, -0.2193212115964351, 0.1975493779353259, -0.9143423366437216, -0.7937431341887468, 0.5904516680417842, 0.1023954787725571, -0.678682737691567, 0.297040937512562, -0.5120268754903525, -3.249236817947608, -2.343895452768416, 0.5049876321480425, -0.86599550806853, -2.137506700802686, 2.183633804402772, 4.263724872311322, -0.4938927745301767, -1.829038751211147, 2.125136903657694, -0.9496074075045097, -8.462860445344566, -5.076180380132207, 3.312564191619759, -0.7915834722117033, -10.24488229379625, -7.830105586215322, 0.1754094481693457, 0.7160613324095237, -0.987242108574252, 1.047083689012641, 0.7150112090332462, -2.350812900593159, -1.562309698277307], 'positive_zeros': ['0.2507789513562879', '1.527226441004306', '2.423619705878697', '2.876686863580175', '3.315603432259092', '4.020389186732739', '4.565338120992652', '4.972706144194703', '5.745170988448954', '6.084081774216017', '6.719119310018445', '6.928235001322288', '7.818065960084459', '8.413714479053771', '8.868355083223294', '9.704110686067549', '9.968633830123795', '10.51107201511329', '11.13865514248895', '11.81975438675018', '12.20599103287209', '12.46113689171048', '13.20988445668809', '13.36208525939968', '13.90610926264404', '14.30458364778595', '14.86550602342482', '15.47964423584368', '15.87554194066895', '15.97025884511950', '16.63687570943984', '17.33201755820974', '17.82078505214264', '18.19181098406541', '18.89077148405336', '19.25548453910590', '19.83304416803463'], 'prelabel': '2-285e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 25.467329864315385, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1245170268994980877, 'z1': {'__RealLiteral__': 0, 'data': '0.2507789513562879', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.527226441004306', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.423619705878697', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 648.5848904178503, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 81225, 'conductor_radical': 285, 'degree': 2, 'dirichlet_coefficients': [1, 2, 0, 2, 0, 0, -3, 0, 0, 0, -2, 0, -1, -6, 0, -4, -2, 0, 0, 0, 0, -4, -6, 0, 0, -2, 0, -6, 10, 0, 3, -8, 0, -4, 0, 0, -2, 0, 0, 0, -8, 0, 1, -4, 0, -12, -2, 0, 2, 0, 0, -2, -4, 0, 0, 0, 0, 20, -10, 0, 7, 6, 0, -8, 0, 0, 3, -4, 0, 0, -8, 0, -14, -4, 0, 0, 6, 0, 0, 0, 0, -16, -6, 0, 0, 2, 0, 0, 0, 0, 3, -12, 0, -4, 0, 0, -17, 4, 0, 0], 'euler11': [1, 2, 11], 'euler13': [1, 1, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 0], 'euler2': [1, -2, 2], 'euler23': [1, 6, 23], 'euler29': [1, -10, 29], 'euler3': [1, 0, 0], 'euler31': [1, -3, 31], 'euler37': [1, 2, 37], 'euler41': [1, 8, 41], 'euler43': [1, -1, 43], 'euler47': [1, 2, 47], 'euler5': [1, 0, 0], 'euler53': [1, 4, 53], 'euler59': [1, 10, 59], 'euler61': [1, -7, 61], 'euler67': [1, -3, 67], 'euler7': [1, 3, 7], 'euler71': [1, 8, 71], 'euler73': [1, 14, 73], 'euler79': [1, 0, 79], 'euler83': [1, 6, 83], 'euler89': [1, 0, 89], 'euler97': [1, 17, 97], 'euler_factors': [[1, -2, 2], [1, 0, 0], [1, 0, 0], [1, 3, 7], [1, 2, 11], [1, 1, 13], [1, 2, 17], [1, 0, 0], [1, 6, 23], [1, -10, 29], [1, -3, 31], [1, 2, 37], [1, 8, 41], [1, -1, 43], [1, 2, 47], [1, 4, 53], [1, 10, 59], [1, -7, 61], [1, -3, 67], [1, 8, 71], [1, 14, 73], [1, 0, 79], [1, 6, 83], [1, 0, 89], [1, 17, 97]], 'index': 2, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/81225/bp'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, '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': '2-285e2-1.1-c1-0-2', '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': '2-285e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 25.467329864315385, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1245170268994980877, 'z1': {'__RealLiteral__': 0, 'data': '0.2507789513562879', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1245170268994980877', 'Lhash_array': ['1245170268994980877'], 'label': '2-285e2-1.1-c1-0-2', 'type': 'ECQ', 'url': 'EllipticCurve/Q/81225/bp'}