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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': -1, 'A6': 1, 'A7': 0, 'A8': -1, 'A9': 1, 'Lhash': '2037581289998857060', 'a10': [0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 396.7447074829339, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [7, [1]], [13, [1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '49686.1', 'coefficient_field': '1.1.1.1', 'conductor': 49686, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, 1, 5], [1], [1, 5, 11], [1], [1, -3, 17], [1, 1, 19], [1, -3, 23], [1, -9, 29], [1, -4, 31], [1, -11, 37], [1, 0, 41], [1, 5, 43], [1, 8, 47], [1, 2, 53], [1, -4, 59], [1, -15, 61], [1, -2, 67], [1, -12, 71], [1, -11, 73], [1, -10, 79], [1, 14, 83], [1, -6, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 16, 'label': '2-49686-1.1-c1-0-16', 'leading_term': '1.02671627178', '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/49686/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.026716271775594, 0.71941620142942, 0.002092204589142725, -0.5192832281585182, -0.1171919820003976, 1.349447839084157, 2.918537497494468, 3.076592757881829, 1.286542735277524, -1.020329281115914, -1.531949371347146, 0.3696705358569504, 2.405810056972584, 1.613784153393405, -1.965294185225988, -4.661394066444373, -3.16607663002747, 1.268648309872518, 3.995709235998364, 2.62752933907808, -0.01849256472246303, 0.130272766287055, 2.76090465126495, 3.800043737428715, 1.511043435318114, -0.8964297345243193, -0.1401507549627187, 2.157506258111322, 2.107428018147402, -0.3464970912215417, -1.578478396492491, -0.2788319280184254, 0.7527893415862901, -0.03679470623227684, 0.1000048475537438, 3.218673764133436, 6.14993432478777, 4.920000603907717, 1.196114199549195, -0.3491432113601203, 0.5578324723255162, 0.3104066879710581, -1.527657813484198, -1.667517016165551, 0.2128175683065745, 0.5846308567633416, -0.969875171570208, -0.5907404848674744, 2.115286842393696, 2.396422575174646, -0.6716601829665496, -1.491524335719607, 1.568266482995742, 1.720487235231306, -4.082664731834049, -7.568036620691566, -2.141627554356724, 4.921722355736849, 3.576308236730812, -2.955752725874694, -4.689226791133676, -1.293453140587561, 0.1500831643858236, -1.172395231734531, -0.6502035687206007, 1.180087192378787, 0.4926928693898965, -1.012245291096956, 0.3944967886323267, 2.314591856636341, 0.9710487664838847, -1.095541856944711, -0.5629252055189311, -0.0257390264168924, -1.595275428808666, -1.810710153803549, 0.5343613392383144, 1.051700376686659, -0.6035114288439054, 0.8421774691636162, 4.553744445718252, 3.616342467478139, -1.038207180166017, -1.628525526278805, 1.319138220935079, 1.058432212968085, -0.3571545810210074, 3.149427164431126, 6.440904118016167, 1.445620035574951, -5.874765592104726, -5.351600262151183, -0.5265361954545839, 0.4417147312874777, -0.01353683807841343, 1.839688677866905, 1.079776246278988, -3.548933441369403, -4.017277557761941, 0.8979939841119452, 2.319449882455685, -0.9363442044509879, -1.100422788390413, 1.417633300221569, -0.1724307083468496, -3.592571214348803, -2.573524477197839, 0.07449767792918985, -0.0623675579770538, 0.1954958575742209, 2.280157015222251, 1.68915768851206, -1.086025751076039, -1.077828010154416, 0.1780378662450084, -0.7421528630655894, -0.6988265238831899, 1.227646833168146, -0.1066908543317149, -2.927646313191136, -0.3189306537373125], 'positive_zeros': ['0.5006991723387578', '1.027578762334292', '2.129705153151397', '2.713114363533683', '3.374936753034452', '4.180604557680827', '4.997284440531726', '5.232021463854415', '6.128196480415211', '6.515496568099879', '7.215990861662073', '7.790827303723587', '8.240822559298565', '8.484321175102987', '9.621579832161268', '9.871563038595768', '10.29756009787391', '10.97043688756508', '11.35099274440617', '11.81116797328042', '12.44767753117065', '12.88466206558757', '13.34337416214382', '14.06293597578822', '14.63421627616061', '15.38101121826809', '15.54215061256786', '16.07853973902575', '16.56189276923535', '16.96033195920303', '17.59365919252002', '18.13465484397844', '18.24018797662146', '18.94459917422136', '19.39761663728574', '19.68315742343421'], 'prelabel': '2-49686-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.918451432853256, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2037581289998857060, 'z1': {'__RealLiteral__': 0, 'data': '0.5006991723387578', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.027578762334292', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.129705153151397', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 396.7447074829339, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 49686, 'conductor_radical': 546, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, -1, 1, 0, -1, 1, 1, -5, -1, 0, 0, 1, 1, 3, -1, -1, -1, 0, 5, 3, 1, -4, 0, -1, 0, 9, -1, 4, -1, 5, -3, 0, 1, 11, 1, 0, 1, 0, 0, -5, -5, -1, -3, -8, -1, 0, 4, -3, 0, -2, 1, 5, 0, 1, -9, 4, 1, 15, -4, 0, 1, 0, -5, 2, 3, -3, 0, 12, -1, 11, -11, 4, -1, 0, 0, 10, -1, 1, 0, -14, 0, -3, 5, -9, 5, 6, 1, 0, 3, -4, 8, 1, 1, -14, 0, -5, -4], 'euler11': [1, 5, 11], 'euler13': [1, 0, 0], 'euler17': [1, -3, 17], 'euler19': [1, 1, 19], 'euler2': [1, 1, 0], 'euler23': [1, -3, 23], 'euler29': [1, -9, 29], 'euler3': [1, 1, 0], 'euler31': [1, -4, 31], 'euler37': [1, -11, 37], 'euler41': [1, 0, 41], 'euler43': [1, 5, 43], 'euler47': [1, 8, 47], 'euler5': [1, 1, 5], 'euler53': [1, 2, 53], 'euler59': [1, -4, 59], 'euler61': [1, -15, 61], 'euler67': [1, -2, 67], 'euler7': [1, 0, 0], 'euler71': [1, -12, 71], 'euler73': [1, -11, 73], 'euler79': [1, -10, 79], 'euler83': [1, 14, 83], 'euler89': [1, -6, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 1, 5], [1, 0, 0], [1, 5, 11], [1, 0, 0], [1, -3, 17], [1, 1, 19], [1, -3, 23], [1, -9, 29], [1, -4, 31], [1, -11, 37], [1, 0, 41], [1, 5, 43], [1, 8, 47], [1, 2, 53], [1, -4, 59], [1, -15, 61], [1, -2, 67], [1, -12, 71], [1, -11, 73], [1, -10, 79], [1, 14, 83], [1, -6, 89], [1, 14, 97]], 'index': 16, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/49686/h'], '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': '2-49686-1.1-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': '2-49686-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.918451432853256, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2037581289998857060, 'z1': {'__RealLiteral__': 0, 'data': '0.5006991723387578', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2037581289998857060', 'Lhash_array': ['2037581289998857060'], 'label': '2-49686-1.1-c1-0-16', 'type': 'ECQ', 'url': 'EllipticCurve/Q/49686/h'}