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lfunc_lfunctions • Show schema
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{'A10': 2, 'A2': -1, 'A3': 0, 'A4': -1, 'A5': -2, 'A6': 0, 'A7': 0, 'A8': 3, 'A9': 0, 'Lhash': '1622357917798821623', 'a10': [0.6324555320336759, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [1.0606601717798212, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1123.3274705951708, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1]], [11, [1, -1]], [29, [1, -1]]], 'bad_primes': [3, 7, 11, 29], 'central_character': '140679.1', 'coefficient_field': '1.1.1.1', 'conductor': 140679, 'conductor_radical': 6699, 'degree': 2, 'euler_factors': [[1, 1, 2], [1], [1, 2, 5], [1], [1, -1], [1, -2, 13], [1, 2, 17], [1, 0, 19], [1, 4, 23], [1, -1], [1, -8, 31], [1, -6, 37], [1, 10, 41], [1, -8, 43], [1, -8, 47], [1, -10, 53], [1, 0, 59], [1, -14, 61], [1, 4, 67], [1, 12, 71], [1, 6, 73], [1, -12, 79], [1, -12, 83], [1, 10, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 23, 'label': '2-140679-1.1-c1-0-23', 'leading_term': '3.5436631985', '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': 1, 'origin': 'EllipticCurve/Q/140679/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.7478890443642656, 0.7791324795645901, -0.02192522806489018, -0.7527775364586569, -0.116974406287702, 1.915183179855382, 3.335112095554699, 1.996056275296647, -1.345717873163313, -2.981922894146015, -0.4522381490999783, 3.860356208892175, 5.184896173621745, 2.458127471635753, -0.4024155363804634, -0.3631558342835411, 0.3807777184422602, -1.350873206355988, -3.557838025253494, -1.810789214714012, 2.648101364236524, 3.421615040046695, -1.089078829213311, -4.343622611767774, -1.60939891843821, 2.553770100688461, 1.886891874639211, -1.609277750604739, -1.969347417004412, 0.5588800403394985, 1.27818579213513, -0.03066256255801256, 0.03432865308122616, 1.076539898728651, 0.3643970931482944, -0.6248133963221016, 0.8884996259050224, 2.44088586321918, 0.770053288880618, -1.138416919063372, 0.1971557513751268, 1.316971032208978, -1.063772508098661, -2.486513152785995, 0.4687507003181946, 2.579221193658531, 0.4849384133277613, -0.0975953963968522, 3.14762736504618, 2.802541914098021, -3.212797040980117, -5.795434151152979, -1.83369811285586, 0.3793961088740541, -1.14060686811163, 1.188169361848133, 6.458933792834805, 5.563835757872072, 0.3894170767149941, 0.6309536447270814, 4.251943677963325, 2.744043574826976, -1.103853072562965, -0.709907940437802, 0.1280002622208361, -2.565002012902509, -3.299527703342504, 0.07153688267246068, 1.240844938302204, -0.5994888435721076, -0.1551549374850708, 1.136163316846407, -0.657670596355866, -1.963899168061529, -0.2165224918006064, 0.3146248187620602, -0.6290404812644902, 0.8021067620736414, 1.819717689014428, -0.1965275387231011, 0.3778472450874899, 3.441121761864894, 0.2892012024898825, -5.645279685271846, -2.315279070590972, 5.253690934848525, 4.077053506492145, -0.6913569512598865, 0.7264646828107548, 2.170293564753912, -1.000538116106925, -1.043349268313413, 2.091867661574525, 0.925840633452286, -0.4770051696348117, 2.41455320363972, 0.8228631496070578, -6.466187589282216, -6.798477610984766, -0.4408686735864572, 0.6467693526563991, -1.289493384669144, 1.623335787230662, 3.882153392458312, 1.131253882762141, -0.3172744086549311, 0.6033711742396719, -0.08244693881735, 0.1378739746426197, 2.066389830775339, 1.368092082245019, -0.0953967972117062, 0.1458265965511156, -2.100402568847261, -4.386082778048643, -0.6557889641443345, 1.402890947265595, -3.728781751835997, -3.747370563030344, 4.456887078716567], 'positive_zeros': ['0.7444902331239467', '1.268606567756548', '2.151753277471134', '2.776223322531337', '3.695842190934766', '4.078323685406493', '4.352197264710560', '5.100966216974453', '5.699197796761858', '6.331867226958451', '6.879343836798267', '7.443612840899927', '7.992859257158702', '8.241837842405254', '8.810267932951510', '9.148137202261560', '9.821584864376138', '10.22803309059514', '10.66395672540812', '11.21952437455855', '11.80158033233486', '12.01157884974960', '12.62696410482236', '13.37835090959933', '13.57728258557002', '13.93590088844163', '14.78145223697161', '14.94822392570759', '15.65791921177604', '16.09899862087860', '16.27300774000549', '16.99470758528813', '17.41429453260650', '17.77067289104784', '18.18640729770582', '18.77987779892776', '19.06982128876514', '19.40698834798852', '19.97526426863904'], 'prelabel': '2-140679-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.5160777925337, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1622357917798821623, 'z1': {'__RealLiteral__': 0, 'data': '0.7444902331239467', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.268606567756548', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.151753277471134', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1123.3274705951708, 'bad_primes': [3, 7, 11, 29], 'central_character': '1.1', 'conductor': 140679, 'conductor_radical': 6699, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, -1, -2, 0, 0, 3, 0, 2, 1, 0, 2, 0, 0, -1, -2, 0, 0, 2, 0, -1, -4, 0, -1, -2, 0, 0, 1, 0, 8, -5, 0, 2, 0, 0, 6, 0, 0, -6, -10, 0, 8, -1, 0, 4, 8, 0, 0, 1, 0, -2, 10, 0, -2, 0, 0, -1, 0, 0, 14, -8, 0, 7, -4, 0, -4, 2, 0, 0, -12, 0, -6, -6, 0, 0, 0, 0, 12, 2, 0, 10, 12, 0, 4, -8, 0, 3, -10, 0, 0, 4, 0, -8, 0, 0, 6, 0, 0, 1], 'euler11': [1, -1, 0], 'euler13': [1, -2, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 2], 'euler23': [1, 4, 23], 'euler29': [1, -1, 0], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, -6, 37], 'euler41': [1, 10, 41], 'euler43': [1, -8, 43], 'euler47': [1, -8, 47], 'euler5': [1, 2, 5], 'euler53': [1, -10, 53], 'euler59': [1, 0, 59], 'euler61': [1, -14, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 12, 71], 'euler73': [1, 6, 73], 'euler79': [1, -12, 79], 'euler83': [1, -12, 83], 'euler89': [1, 10, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 1, 2], [1, 0, 0], [1, 2, 5], [1, 0, 0], [1, -1, 0], [1, -2, 13], [1, 2, 17], [1, 0, 19], [1, 4, 23], [1, -1, 0], [1, -8, 31], [1, -6, 37], [1, 10, 41], [1, -8, 43], [1, -8, 47], [1, -10, 53], [1, 0, 59], [1, -14, 61], [1, 4, 67], [1, 12, 71], [1, 6, 73], [1, -12, 79], [1, -12, 83], [1, 10, 89], [1, -6, 97]], 'index': 23, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/140679/i'], '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': '2-140679-1.1-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': '2-140679-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.5160777925337, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1622357917798821623, 'z1': {'__RealLiteral__': 0, 'data': '0.7444902331239467', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1622357917798821623', 'Lhash_array': ['1622357917798821623'], 'label': '2-140679-1.1-c1-0-23', 'type': 'ECQ', 'url': 'EllipticCurve/Q/140679/i'}