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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1111698591999407998', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1391.31340481879, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]], [11, [1]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '174240.1', 'coefficient_field': '1.1.1.1', 'conductor': 174240, 'conductor_radical': 330, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, 0, 7], [1], [1, 2, 13], [1, 2, 17], [1, -8, 19], [1, -4, 23], [1, 6, 29], [1, 0, 31], [1, -2, 37], [1, 6, 41], [1, -4, 43], [1, 12, 47], [1, -6, 53], [1, -12, 59], [1, 14, 61], [1, -12, 67], [1, 0, 71], [1, 2, 73], [1, 8, 79], [1, -4, 83], [1, 2, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 22, 'label': '2-174240-1.1-c1-0-22', 'leading_term': '2.21407512629', '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/174240/dk', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.214075126292151, 1.381938358871581, -0.5788962676955955, -2.211004825681144, -2.073524741208414, -0.3215549842914663, 0.9968193246478645, 0.1094190467697627, -2.035289621811236, -2.608828097437134, -0.6873078698072358, 1.134502656739763, 0.3159997062802888, -1.576437153239755, -0.9082357273463684, 2.168433015391095, 3.263520336737207, 0.3724096487826085, -2.625342285027407, -1.83410451303563, 0.6267639086721545, 0.6651285164023863, -0.5342966145315067, 0.9685318056573256, 3.926920568231373, 3.461060021798905, -0.01036394442649375, -1.121413486783667, 0.7434171801591785, 0.5760719984670688, -2.220649778043192, -2.329817978804114, 0.8246976086527295, 1.113378643186623, -2.686137287181499, -4.077251543374049, -0.9124348569607081, 1.073630549531385, -0.1463910036194834, 0.05953958047582955, 1.894303496810886, 0.254727303912018, -3.485278989940042, -2.770018565158461, 0.9817353469308129, 1.080295460906538, -0.7802428583219535, 1.175506814901268, 3.64648375308624, 1.033613012280009, -2.033239301267829, 0.05493094539139682, 2.408766642660873, 0.6233747207194089, -0.240663050581839, 1.900475257331931, 1.136329899124044, -2.41489241983315, -2.071544782729708, 0.4373492562620274, -0.9699754388497692, -2.268883716951331, 1.714508304521554, 4.569523254677006, 1.680703569793516, 0.09146932473813432, 2.388419824751403, 1.513903617941926, -2.116791650555628, -1.486195764004964, 0.6459453142305553, -1.283597843330608, -2.435471387030649, 0.1296572361150912, -0.02559543579106567, -2.440345610237815, 0.2797162856941612, 4.275642122222904, 1.957122298412025, -0.9289695874775725, 1.130927053077651, 1.353435335607932, -1.934003610747202, -1.42686156976984, 0.6360048156032918, -2.110383543534903, -3.969753091082023, -0.6109892898467784, 0.638903084480825, -1.340077895237168, -0.1021182274809281, 0.9757709150648758, -2.011875460437298, -1.041669604708494, 4.829230004388415, 4.537642815988134, -0.8584295199165667, -1.367742935611414, 0.33793223763761, -0.2493244413838822, 2.171535642663149, 5.683906835929202, 2.592482453890045, -1.483414445565987, -0.180011445654576, -0.4238706967485403, -3.268311368438773, -1.300961177257252, 1.225734575183611, -1.109930803922511, -0.5584033256392475, 3.305446513586802, 0.6952559090835471, -3.998648303171387, -1.755675407165888, 0.945474533362972, -0.2063428016662059, 0.5132587953205555, 0.1925958363008064, -4.474899719188171, -4.512944026864728], 'positive_zeros': ['0.4313945754370202', '1.292128867160636', '1.763870156754951', '2.571015882611497', '3.038275113622561', '3.581227655967067', '4.273883918211775', '4.923228225448355', '5.362972455382673', '5.655384579351261', '6.499164485270929', '6.906691917312347', '7.308183220090842', '7.934023749413206', '8.336753487761255', '9.068026372595026', '9.473650009081061', '9.741375982526167', '10.26645700692467', '10.92459943512418', '11.36660033633941', '11.65888050990962', '12.30980050097132', '12.74622968392792', '13.32005691089401', '13.53877036114510', '14.07808368506528', '14.68136486747911', '14.90691545212761', '15.41624259731077', '16.17366411086215', '16.22359355231941', '16.84611794657301', '17.38202501842944', '17.63567009213175', '18.23654621764677', '18.49748722296011', '18.98629490177211', '19.61949602061575', '19.89994820988681'], 'prelabel': '2-174240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 37.30031373619785, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1111698591999407998, 'z1': {'__RealLiteral__': 0, 'data': '0.4313945754370202', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.292128867160636', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.763870156754951', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1391.31340481879, 'bad_primes': [2, 3, 5, 11], 'central_character': '1.1', 'conductor': 174240, 'conductor_radical': 330, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 8, 0, 0, 0, 4, 0, 1, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -6, 0, 4, 0, 0, 0, -12, 0, -7, 0, 0, 0, 6, 0, 0, 0, 0, 0, 12, 0, -14, 0, 0, 0, -2, 0, 12, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -8, 0, 0, 0, 4, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 8, 0, -14, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 2, 13], 'euler17': [1, 2, 17], 'euler19': [1, -8, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, -2, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 12, 47], 'euler5': [1, -1, 0], 'euler53': [1, -6, 53], 'euler59': [1, -12, 59], 'euler61': [1, 14, 61], 'euler67': [1, -12, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, 2, 73], 'euler79': [1, 8, 79], 'euler83': [1, -4, 83], 'euler89': [1, 2, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, 0, 7], [1, 0, 0], [1, 2, 13], [1, 2, 17], [1, -8, 19], [1, -4, 23], [1, 6, 29], [1, 0, 31], [1, -2, 37], [1, 6, 41], [1, -4, 43], [1, 12, 47], [1, -6, 53], [1, -12, 59], [1, 14, 61], [1, -12, 67], [1, 0, 71], [1, 2, 73], [1, 8, 79], [1, -4, 83], [1, 2, 89], [1, 14, 97]], 'index': 22, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/174240/dk'], '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': '2-174240-1.1-c1-0-22', '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': '2-174240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 37.30031373619785, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1111698591999407998, 'z1': {'__RealLiteral__': 0, 'data': '0.4313945754370202', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1111698591999407998', 'Lhash_array': ['1111698591999407998'], 'factors': ['2-174240-1.1-c1-0-22'], 'label': '2-174240-1.1-c1-0-22', 'type': 'ECQ', 'url': 'EllipticCurve/Q/174240/dk'}