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lfunc_lfunctions • Show schema
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{'A10': 3, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': -3, 'A6': 0, 'A7': -1, 'A8': -1, 'A9': 0, 'Lhash': '1042176345624665892', 'a10': [0.9486832980505138, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-1.3416407864998738, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 308.58986365144034, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [19, [1, -1]], [113, [1, -1]]], 'bad_primes': [2, 3, 19, 113], 'central_character': '38646.1', 'coefficient_field': '1.1.1.1', 'conductor': 38646, 'conductor_radical': 12882, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 3, 5], [1, 1, 7], [1, 0, 11], [1, -5, 13], [1, -3, 17], [1, -1], [1, -3, 23], [1, -6, 29], [1, 7, 31], [1, -2, 37], [1, 0, 41], [1, 10, 43], [1, 0, 47], [1, -12, 53], [1, -3, 59], [1, 1, 61], [1, -8, 67], [1, -9, 71], [1, 4, 73], [1, 10, 79], [1, 12, 83], [1, 18, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 15, 'label': '2-38646-1.1-c1-0-15', 'leading_term': '3.38268039434', '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/38646/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.760776810715118, 1.036540716174183, 0.5453593486233347, -0.4344311068255993, -0.9624366029298997, -0.06465180007561287, 2.19359181474416, 4.287843711174925, 4.317122003725613, 1.915195284986747, -1.023603541497635, -2.047869963393604, -0.8117039304388665, 0.435774772666124, -0.3985912001218696, -2.303565232707476, -2.034667996079697, 1.608915165540842, 5.427277206397607, 5.135194635407357, 0.8201003806653449, -2.637670352755764, -1.400411960303503, 2.561127637976126, 4.222644922146966, 2.133395790260018, -0.1891056022031796, 0.2623503709949836, 1.889077248024565, 1.602738651042925, -0.1923334129845685, -0.6710775464153506, 0.4681992407203065, 0.710683864789477, -0.4710321459221801, -0.3158997482335795, 2.257327791028613, 3.985601914341533, 2.266772686983306, -0.2237610425113687, 0.3709641523077741, 2.731818134110412, 2.681866529717269, 0.3182000721653537, -0.569443539979013, 0.35096508627648, -0.4700205320959101, -3.09290606288877, -3.068430933521712, 0.109749383817718, 0.7323944636714795, -3.123928763893058, -4.665595149451831, 0.6803676504706814, 6.246689452891909, 3.942457378791479, -2.53301426799663, -3.674074132521852, 0.7512396918036508, 2.91997018242278, 0.6748972179353757, -0.7343484720930799, 0.4710449666790556, 0.5667243917896466, -0.957244937034748, -0.7272475531397639, 0.3742552737981387, -1.761844135215786, -5.34202446248367, -4.471529384559152, 0.10645007533038, 2.003014157314843, 0.3341694226365803, -0.1561301469198973, 1.021344330706641, 0.3210337948505333, -1.412612568971469, -0.7901552455060822, 0.5078812315864747, -0.3960775736621602, -0.5186770530491795, 2.569154634370181, 3.880318760865709, 0.5470177780601024, -0.6844122569444707, 3.794114012406022, 5.29023105373859, -1.815414158512177, -8.115251262734875, -5.079202659894514, 0.5745166308028885, 0.6437388446575096, -0.9151255798377947, 0.4666697536765539, 0.2569164752994658, -3.143260948571769, -2.727510050777574, 2.576256150175375, 4.238252378586243, 0.4456639188940858, -0.9804575292055088, 1.499543309127832, 1.646789378088801, -0.4342682214148215, 0.541346148540149, 2.820543006181873, 1.659290302403294, -0.4330866359420777, 0.07140131238358553, 0.3220872522989838, -1.048843288714593, -0.4942194865522536, 1.098482565716851, -0.4994911502706503, -2.362694945011851, -0.1664484438054055, 0.8779182608338001, -3.526913375204696, -5.898295195380851, -1.397976164922082], 'positive_zeros': ['0.8920399354326448', '1.509251574542923', '2.653213738399267', '3.376736482571370', '3.689672708759210', '4.408271178598604', '5.293190745779388', '5.841266724717445', '6.713757240832012', '6.956363422363250', '7.720413770230516', '8.156439405064653', '8.655083811362924', '9.042972641454255', '9.963420379258208', '10.20282592135648', '11.03931482618479', '11.40334502386911', '11.69043234376748', '12.49088185382325', '12.81502213217563', '13.47655914294258', '14.14531424972396', '14.71030294664712', '15.31666046109783', '15.66882029795471', '16.09456427063480', '16.62280824240543', '16.85063618336558', '17.74366692878611', '18.30281240512437', '18.53784610136493', '19.04074604161872', '19.61585488677533', '19.93059719270157'], 'prelabel': '2-38646-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.566726036784438, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1042176345624665892, 'z1': {'__RealLiteral__': 0, 'data': '0.8920399354326448', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.509251574542923', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.653213738399267', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 308.58986365144034, 'bad_primes': [2, 3, 19, 113], 'central_character': '1.1', 'conductor': 38646, 'conductor_radical': 12882, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, -3, 0, -1, -1, 0, 3, 0, 0, 5, 1, 0, 1, 3, 0, 1, -3, 0, 0, 3, 0, 4, -5, 0, -1, 6, 0, -7, -1, 0, -3, 3, 0, 2, -1, 0, 3, 0, 0, -10, 0, 0, -3, 0, 0, -6, -4, 0, 5, 12, 0, 0, 1, 0, -6, 3, 0, -1, 7, 0, 1, -15, 0, 8, 3, 0, -3, 9, 0, -4, -2, 0, 1, 0, 0, -10, -3, 0, 0, -12, 0, -9, 10, 0, 0, -18, 0, -5, 3, 0, 0, -3, 0, 2, 6, 0, 4], 'euler11': [1, 0, 11], 'euler13': [1, -5, 13], 'euler17': [1, -3, 17], 'euler19': [1, -1, 0], 'euler2': [1, 1, 0], 'euler23': [1, -3, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 7, 31], 'euler37': [1, -2, 37], 'euler41': [1, 0, 41], 'euler43': [1, 10, 43], 'euler47': [1, 0, 47], 'euler5': [1, 3, 5], 'euler53': [1, -12, 53], 'euler59': [1, -3, 59], 'euler61': [1, 1, 61], 'euler67': [1, -8, 67], 'euler7': [1, 1, 7], 'euler71': [1, -9, 71], 'euler73': [1, 4, 73], 'euler79': [1, 10, 79], 'euler83': [1, 12, 83], 'euler89': [1, 18, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 3, 5], [1, 1, 7], [1, 0, 11], [1, -5, 13], [1, -3, 17], [1, -1, 0], [1, -3, 23], [1, -6, 29], [1, 7, 31], [1, -2, 37], [1, 0, 41], [1, 10, 43], [1, 0, 47], [1, -12, 53], [1, -3, 59], [1, 1, 61], [1, -8, 67], [1, -9, 71], [1, 4, 73], [1, 10, 79], [1, 12, 83], [1, 18, 89], [1, -2, 97]], 'index': 15, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/38646/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': '2-38646-1.1-c1-0-15', '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': '2-38646-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.566726036784438, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1042176345624665892, 'z1': {'__RealLiteral__': 0, 'data': '0.8920399354326448', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1042176345624665892', 'Lhash_array': ['1042176345624665892'], 'label': '2-38646-1.1-c1-0-15', 'type': 'ECQ', 'url': 'EllipticCurve/Q/38646/b'}