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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '547548727507462529', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 308.54195341022756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [7, [1, 1]], [23, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '38640.1', 'coefficient_field': '1.1.1.1', 'conductor': 38640, 'conductor_radical': 4830, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, 1], [1, 0, 11], [1, -2, 13], [1, -6, 17], [1, 4, 19], [1, -1], [1, -6, 29], [1, 4, 31], [1, -2, 37], [1, -10, 41], [1, -8, 43], [1, 4, 47], [1, 6, 53], [1, -4, 59], [1, -2, 61], [1, -8, 67], [1, -8, 71], [1, -10, 73], [1, 0, 79], [1, 12, 83], [1, 2, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 16, 'label': '2-38640-1.1-c1-0-16', 'leading_term': '1.76190198032', '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/38640/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.761901980324132, 1.368618054478532, 0.3777315246557436, -0.5958104829407427, -0.6750993659429347, 0.602424690906569, 2.563181770605047, 3.558601402693027, 2.313124462477832, -0.601996024182299, -2.867412843491898, -2.497238303107498, 0.004982893912264852, 1.968587430183273, 1.433664356279742, -0.5616693650727265, -1.234746687033774, 0.3828752417186795, 2.073071382039175, 1.311899244953363, -1.216707085950612, -2.385405377628609, -0.9072714445918456, 0.8414929892294005, 0.3005656707930395, -1.43395516959531, -1.299859172205583, 0.8061989454618721, 1.542586323217371, -0.7012707182337474, -2.923857026746123, -1.97322653572783, 0.2729897637737633, -0.3980604119752429, -3.629994186790558, -4.532801751919515, -1.29667165289035, 1.618007057489747, 0.2811928701417611, -2.602945906146928, -2.246346594196253, 0.5140155392461665, 1.094125173560584, -0.908405947440445, -1.480352012217974, 0.3003690668749865, 0.6636189970350934, -1.704401168560082, -2.994671773518989, -1.173534731531227, 0.4072430747041354, -0.2874986291000356, 0.3272588276603904, 4.370844186244169, 6.957232216943146, 3.861315732867944, -0.5141961893722934, -0.09179868008005174, 2.557597486710754, 1.165866368003722, -2.791995334600926, -2.940562164236989, 0.4565535249537573, 1.609322533663041, 0.008753626772757823, 0.1788657737713354, 1.991148598193783, 1.315336857537378, -0.7831698341206805, 0.2783988996141183, 2.909385390747649, 1.766949696375207, -1.610344764360555, -1.370108051281136, 1.374669083921205, 1.037982921515872, -1.199537964623372, -0.3713510697818359, 1.318319057465539, -1.113625542152064, -4.040833133245834, -1.172449682672289, 3.7046516399813, 3.100586463618815, -0.5087307718524177, -0.5767423977685383, 0.5190497503045159, -2.37930361532875, -5.511009587628168, -3.451920422416113, 0.06035858937047191, -0.0414609456046824, -0.8247907709667126, 0.6594625469245216, 1.041738139936257, -0.3624590707117133, 1.084227900857071, 4.077881808427101, 1.95040593426454, -3.218976019321633, -3.094535225220339, 0.8209537902979598, 0.6969070315196569, -1.533498358135997, 0.5983793363925831, 3.122531770602565, -0.3972042549002055, -4.716394954155818, -3.001893584156904, 0.1958581459780854, -0.3351475693104025, -0.5887513368916906, 1.591933382646895, 1.409338000328486, -0.8173101231037891, 0.5381536389020108, 3.356408582196706, 1.807643793868476, -0.7447265648681028, 0.5859421456258479, 1.150210593112675], 'positive_zeros': ['0.5854163352028367', '1.159951527527469', '2.201266676701108', '2.999544583482584', '3.677605823595776', '4.205916342005080', '4.882878514308038', '5.605363935757790', '6.042910349417934', '6.659534124525762', '7.190435101284849', '7.956513963752150', '8.206593951434711', '9.082623883591179', '9.522488000038834', '10.19942239611291', '10.64589516249493', '11.21018380530100', '11.58925651325730', '12.38848070058482', '12.67860594162375', '12.96425862647965', '13.95585630068333', '14.25829220328163', '14.82147367588858', '15.46517109282656', '16.00163144771533', '16.22048547515038', '16.88689279909643', '17.22411459007022', '17.87094674173638', '18.36773652855417', '18.85309598243334', '19.28867461986301', '19.67684867624388'], 'prelabel': '2-38640-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.565362319355316, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 547548727507462529, 'z1': {'__RealLiteral__': 0, 'data': '0.5854163352028367', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.159951527527469', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.201266676701108', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 308.54195341022756, 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '1.1', 'conductor': 38640, 'conductor_radical': 4830, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, -1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 6, 0, -4, 0, 1, 0, 1, 0, 1, 0, -1, 0, 6, 0, -4, 0, 0, 0, 1, 0, 2, 0, -2, 0, 10, 0, 8, 0, -1, 0, -4, 0, 1, 0, -6, 0, -6, 0, 0, 0, 4, 0, 4, 0, 2, 0, -1, 0, -2, 0, 8, 0, -1, 0, 8, 0, 10, 0, -1, 0, 0, 0, 0, 0, 1, 0, -12, 0, -6, 0, -6, 0, -2, 0, -2, 0, 4, 0, 4, 0, 6, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, -2, 37], 'euler41': [1, -10, 41], 'euler43': [1, -8, 43], 'euler47': [1, 4, 47], 'euler5': [1, 1, 0], 'euler53': [1, 6, 53], 'euler59': [1, -4, 59], 'euler61': [1, -2, 61], 'euler67': [1, -8, 67], 'euler7': [1, 1, 0], 'euler71': [1, -8, 71], 'euler73': [1, -10, 73], 'euler79': [1, 0, 79], 'euler83': [1, 12, 83], 'euler89': [1, 2, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 1, 0], [1, 0, 11], [1, -2, 13], [1, -6, 17], [1, 4, 19], [1, -1, 0], [1, -6, 29], [1, 4, 31], [1, -2, 37], [1, -10, 41], [1, -8, 43], [1, 4, 47], [1, 6, 53], [1, -4, 59], [1, -2, 61], [1, -8, 67], [1, -8, 71], [1, -10, 73], [1, 0, 79], [1, 12, 83], [1, 2, 89], [1, -6, 97]], 'index': 16, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/38640/j'], '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': '2-38640-1.1-c1-0-16', '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': '2-38640-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.565362319355316, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 547548727507462529, 'z1': {'__RealLiteral__': 0, 'data': '0.5854163352028367', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '547548727507462529', 'Lhash_array': ['547548727507462529'], 'label': '2-38640-1.1-c1-0-16', 'type': 'ECQ', 'url': 'EllipticCurve/Q/38640/j'}