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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': -1, 'A9': 0, 'Lhash': '570922141057568806', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 578.5161626441767, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1]], [7, [1, 1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '72450.1', 'coefficient_field': '1.1.1.1', 'conductor': 72450, 'conductor_radical': 4830, 'degree': 2, 'euler_factors': [[1, 1], [1], [1], [1, 1], [1, 2, 11], [1, 2, 13], [1, -2, 17], [1, 4, 19], [1, 1], [1, -2, 29], [1, 8, 31], [1, 4, 37], [1, 12, 41], [1, 2, 43], [1, 8, 47], [1, 10, 53], [1, -4, 59], [1, -2, 61], [1, 2, 67], [1, -6, 71], [1, 4, 73], [1, 12, 79], [1, 4, 83], [1, 6, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 130, 'label': '2-72450-1.1-c1-0-130', 'leading_term': '7.70206927939', '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': 2, 'origin': 'EllipticCurve/Q/72450/k', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, -0.4587447212773104, -1.555260928532557, -2.480364474073289, -2.298058642840489, -0.844161254803551, 0.7529739301862816, 0.9300990194437601, -0.5409045293826455, -1.90920334148223, -1.253182702994524, 0.9602626674561907, 1.996294296945188, 0.2918243440765866, -1.909976185863234, -0.9017946956934554, 3.340409731161628, 6.209981187630425, 4.067714930880173, -0.6296055290910839, -2.245898290301133, 0.4224065715270143, 2.603970401061226, 0.6302183632362548, -2.727515307104324, -2.731472489810785, 0.04164966033400079, 1.051402013776058, -0.697726373154656, -1.445504464452853, 0.5164185754358074, 1.931793502596891, 0.517559489236482, -0.9832854844851603, 0.04486703995235453, 1.205201266092598, -0.3911959213501532, -2.515529959733225, -1.763455542127942, 0.215443110927777, 0.06889653396411713, -0.7687653880077903, 0.7168000001037445, 2.411694090244329, 0.8177315015350887, -1.33354414709365, 0.5778769526440022, 3.81313024513578, 2.612974387882956, -0.8755661566958223, -0.4498101258275713, 2.028736010634289, 0.277347973739654, -3.093503869464865, -0.4083436460001083, 5.75609084576848, 5.749003973718437, 0.1516712807284212, -1.41893248596974, 2.130883574460043, 2.813752126927268, -0.3273051788655545, -0.4989092361608299, 2.465000307017262, 2.420976110817729, -0.160888978735939, -0.003879568658004758, 1.549933492297674, 0.2113951252295654, -1.435601678402767, 0.1957938489763599, 1.396899411479834, -0.8743893061119385, -2.231649769990492, -0.3130947874441806, 0.4725630659779342, -0.8239193082186663, 0.1240642753954398, 2.282625115254169, 1.108026556182775, -0.6422720914366921, 1.355208576836396, 2.608928296381948, -0.5274739932663279, -1.72728795984824, 1.83787596036261, 2.464237593616203, -1.294042629659718, -0.7470405201562859, 3.306884672361712, 0.7004403760816624, -5.985087979224462, -5.184617660137289, 0.4476747484637218, 0.5358993434330597, -1.714912628635471, 0.9431143426417403, 2.846394018436181, -1.133941168543393, -3.384503040015033, 0.0380267711661656, 1.808369751836419, -0.06525423778089617, -0.05634817167017632, 0.6625926054215387, -1.647868555129251, -2.724887918895184, -0.08064643572124881, 0.7492266946565113, -0.8848357417483358, 0.1203403482923646, 1.511369128464456, -0.9619862891572668, -2.555279191399916, -0.374318084346757, -0.1222950473101244, -2.107712306848378, -0.8890477702870773, 0.5557745131327515, -1.7970114627766, -1.844545186293681], 'positive_zeros': ['1.368409995642201', '1.924696681635766', '2.645484584937226', '3.277571528518989', '3.813672838397534', '4.712500099085165', '5.219442342887051', '5.792639631916627', '6.495990353083944', '6.916100594080059', '7.447465849167627', '8.060277912494638', '8.493827577891492', '8.961609420472137', '9.710919110710429', '10.01460652416003', '10.41988992261632', '11.07067357997010', '11.45919921539619', '12.17253390536359', '12.54027842735706', '13.01721398881188', '13.51659926213193', '14.25772325014356', '14.61302344246187', '15.22131218344651', '15.54714942323336', '16.22905363997124', '16.50054750138803', '17.02128928998110', '17.48018065451942', '17.92476447395492', '18.53798261624091', '18.84505482299998', '19.23704472149236', '19.86052261317539'], 'prelabel': '2-72450-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.052362932655424, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 570922141057568806, 'z1': {'__RealLiteral__': 0, 'data': '1.368409995642201', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.924696681635766', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.645484584937226', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 578.5161626441767, 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '1.1', 'conductor': 72450, 'conductor_radical': 4830, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 0, 0, -1, -1, 0, 0, -2, 0, -2, 1, 0, 1, 2, 0, -4, 0, 0, 2, -1, 0, 0, 2, 0, -1, 2, 0, -8, -1, 0, -2, 0, 0, -4, 4, 0, 0, -12, 0, -2, -2, 0, 1, -8, 0, 1, 0, 0, -2, -10, 0, 0, 1, 0, -2, 4, 0, 2, 8, 0, 1, 0, 0, -2, 2, 0, 0, 6, 0, -4, 4, 0, -4, 2, 0, -12, 0, 0, 12, -4, 0, 0, 2, 0, 2, -6, 0, 2, -1, 0, 8, 0, 0, 2, -1, 0, 0], 'euler11': [1, 2, 11], 'euler13': [1, 2, 13], 'euler17': [1, -2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 1, 0], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, 4, 37], 'euler41': [1, 12, 41], 'euler43': [1, 2, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, 10, 53], 'euler59': [1, -4, 59], 'euler61': [1, -2, 61], 'euler67': [1, 2, 67], 'euler7': [1, 1, 0], 'euler71': [1, -6, 71], 'euler73': [1, 4, 73], 'euler79': [1, 12, 79], 'euler83': [1, 4, 83], 'euler89': [1, 6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 0, 0], [1, 1, 0], [1, 2, 11], [1, 2, 13], [1, -2, 17], [1, 4, 19], [1, 1, 0], [1, -2, 29], [1, 8, 31], [1, 4, 37], [1, 12, 41], [1, 2, 43], [1, 8, 47], [1, 10, 53], [1, -4, 59], [1, -2, 61], [1, 2, 67], [1, -6, 71], [1, 4, 73], [1, 12, 79], [1, 4, 83], [1, 6, 89], [1, -2, 97]], 'index': 130, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/72450/k'], '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': '2-72450-1.1-c1-0-130', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 2, 'prelabel': '2-72450-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.052362932655424, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 570922141057568806, 'z1': {'__RealLiteral__': 0, 'data': '1.368409995642201', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '570922141057568806', 'Lhash_array': ['570922141057568806'], 'label': '2-72450-1.1-c1-0-130', 'type': 'ECQ', 'url': 'EllipticCurve/Q/72450/k'}