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lfunc_lfunctions • Show schema
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{'A10': 2, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': -2, 'A6': 1, 'A7': -1, 'A8': -1, 'A9': 1, 'Lhash': '2088362889238971004', 'a10': [0.6324555320336759, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.4082482904638631, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2784.5911295273036, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [7, [1, 1]], [19, [1]], [23, [1, -1]]], 'bad_primes': [2, 3, 7, 19, 23], 'central_character': '348726.1', 'coefficient_field': '1.1.1.1', 'conductor': 348726, 'conductor_radical': 18354, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, 2, 5], [1, 1], [1, -4, 11], [1, 2, 13], [1, -6, 17], [1], [1, -1], [1, -2, 29], [1, 4, 31], [1, 6, 37], [1, -6, 41], [1, -12, 43], [1, 12, 47], [1, 6, 53], [1, -4, 59], [1, 10, 61], [1, 4, 67], [1, -16, 71], [1, -2, 73], [1, 8, 79], [1, 16, 83], [1, 6, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 23, 'label': '2-348726-1.1-c1-0-23', 'leading_term': '3.75029357545', '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/348726/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.7477880184932402, 0.5661728128184498, -0.4848831548313509, -1.0879454578154, -0.1612504921228098, 1.111016107874934, 0.09226148634456323, -3.39277128284616, -5.46076282126408, -2.833535269228159, 1.84739391938447, 2.918375875683606, -0.04291943447276099, -1.54443941266088, 0.7142385061703357, 1.852800027981402, -1.317249251035204, -3.663791338993107, -0.3178365465134979, 3.893279917386844, 2.074631051362877, -2.690860386793487, -2.951348532008979, -0.06780608347417484, -0.5436618398906214, -3.325440491018424, -2.779601963220656, -0.1793000049390382, -0.1692786078624539, -0.820239668080083, 1.185811039268322, 2.292382363429121, -0.1371566065185204, -0.9322091927831265, 2.335320237665026, 3.584601904030942, 0.612253052870964, -0.8378658039928054, 0.06134015254471754, -1.629516932225347, -4.024232632481895, -1.988912277353152, 0.8335617737196184, -0.3312816083329334, -1.266748903307599, 0.6853238962078155, 0.7833550014141116, -0.8460687708791895, 0.2060109445324902, 0.7270431645579746, -0.8229279788049437, 4.741502226490494, 16.4301891338831, 16.71903914043733, 3.809164087212731, -2.62401261046456, 1.644394645862968, 1.83049279758171, -2.326176642641993, -0.05473501214974215, 3.9381570973358, 1.42840039070534, -1.144598348395547, 0.4972120707167339, 0.3778761885854703, -1.131584118988517, 0.2061544339301523, 0.7584885164215855, -0.5040290568029783, 1.068390626964217, 2.190822921885159, -1.113548455066402, -2.104287400710359, 1.200319547966705, 1.294755062008215, -0.8831323690081503, -0.1510710536216695, 0.08132165272818855, -0.443501067387893, 2.080788626062464, 1.17580565122526, -5.49515481768667, -5.683402518137425, 0.4447032955903876, 0.06430414631094954, -1.445323707406453, 5.14351490904297, 8.035049092111105, 1.835221950222769, -0.6488692113301233, 0.6341154195057601, -2.029340782936172, -1.920407504522791, 2.061037461176624, -0.001883323625809326, -3.135370328699735, 0.1015430977754393, 1.010388621992998, -0.9628726887092623, 2.998565697315837, 5.635215328034171, 0.8560203748324346, -0.9572219954671635, 0.1515206691475206, -4.086107802170801, -6.309854426922759, -1.659938709755537, 0.6019206165404491, -0.4180727010036267, 0.01248528639712273, -0.4200446355132936, -0.04678834712249169, 2.491908020666326, 0.8273471182019203, -1.854384272482001, 1.097297685963436, 2.276120864880361, -0.2322611293859284, 0.7701661393548755, 0.0474366472941726], 'positive_zeros': ['0.6446124021159075', '1.276171012874049', '1.758663401815196', '2.643576308900133', '3.246693677582704', '3.688009427152086', '4.168998844837145', '4.764934817534973', '5.351250052520131', '6.009142594848970', '6.188853632949923', '7.030622032257700', '7.212130189435335', '7.633173313708557', '8.237825690055798', '8.590921724538121', '9.302031965539909', '9.713085606551284', '9.808825887949783', '10.64112595280067', '10.96241740368680', '11.42005078507404', '11.85255670757569', '12.22307665989001', '12.59618232116738', '12.84546789488880', '13.83585655633182', '14.16906748555918', '14.59803257870640', '15.00257843148590', '15.58879424414226', '15.93753468371881', '16.29840153670949', '16.72380765587778', '17.12823006061998', '17.39139140722985', '17.92871488340761', '18.41023220366869', '18.87570571719350', '19.27846176059660', '19.51902353791940', '19.81747224066184'], 'prelabel': '2-348726-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 52.76922521249771, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2088362889238971004, 'z1': {'__RealLiteral__': 0, 'data': '0.6446124021159075', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.276171012874049', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.758663401815196', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2784.5911295273036, 'bad_primes': [2, 3, 7, 19, 23], 'central_character': '1.1', 'conductor': 348726, 'conductor_radical': 18354, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, -2, 1, -1, -1, 1, 2, 4, -1, -2, 1, 2, 1, 6, -1, 0, -2, 1, -4, 1, 1, -1, 2, -1, -1, 2, -2, -4, -1, -4, -6, 2, 1, -6, 0, 2, 2, 6, -1, 12, 4, -2, -1, -12, -1, 1, 1, -6, -2, -6, 1, -8, 1, 0, -2, 4, 2, -10, 4, -1, 1, 4, 4, -4, 6, -1, -2, 16, -1, 2, 6, 1, 0, -4, -2, -8, -2, 1, -6, -16, 1, -12, -12, -2, -4, -6, 2, 2, 1, 4, 12, 0, 1, 2, -1, 4, -1], 'euler11': [1, -4, 11], 'euler13': [1, 2, 13], 'euler17': [1, -6, 17], 'euler19': [1, 0, 0], 'euler2': [1, 1, 0], 'euler23': [1, -1, 0], 'euler29': [1, -2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 6, 37], 'euler41': [1, -6, 41], 'euler43': [1, -12, 43], 'euler47': [1, 12, 47], 'euler5': [1, 2, 5], 'euler53': [1, 6, 53], 'euler59': [1, -4, 59], 'euler61': [1, 10, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 0], 'euler71': [1, -16, 71], 'euler73': [1, -2, 73], 'euler79': [1, 8, 79], 'euler83': [1, 16, 83], 'euler89': [1, 6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 2, 5], [1, 1, 0], [1, -4, 11], [1, 2, 13], [1, -6, 17], [1, 0, 0], [1, -1, 0], [1, -2, 29], [1, 4, 31], [1, 6, 37], [1, -6, 41], [1, -12, 43], [1, 12, 47], [1, 6, 53], [1, -4, 59], [1, 10, 61], [1, 4, 67], [1, -16, 71], [1, -2, 73], [1, 8, 79], [1, 16, 83], [1, 6, 89], [1, -2, 97]], 'index': 23, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/348726/b'], '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': '2-348726-1.1-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': '2-348726-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 52.76922521249771, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2088362889238971004, 'z1': {'__RealLiteral__': 0, 'data': '0.6446124021159075', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2088362889238971004', 'Lhash_array': ['2088362889238971004'], 'factors': ['2-348726-1.1-c1-0-23'], 'label': '2-348726-1.1-c1-0-23', 'type': 'ECQ', 'url': 'EllipticCurve/Q/348726/b'}