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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': 0, 'A6': 1, 'A7': -1, 'A8': -1, 'A9': 1, 'Lhash': '1973388663289803752', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.4082482904638631, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1273.2146602293165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1]], [1063, [1, -1]]], 'bad_primes': [2, 3, 5, 1063], 'central_character': '159450.1', 'coefficient_field': '1.1.1.1', 'conductor': 159450, 'conductor_radical': 31890, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1], [1, 1, 7], [1, 2, 11], [1, 0, 13], [1, -3, 17], [1, 8, 19], [1, -4, 23], [1, -9, 29], [1, -4, 31], [1, -4, 37], [1, 0, 41], [1, -12, 43], [1, -8, 47], [1, 5, 53], [1, 3, 59], [1, 1, 61], [1, 12, 67], [1, -9, 71], [1, -17, 73], [1, -10, 79], [1, -14, 83], [1, 1, 89], [1, -7, 97]], 'gamma_factors': [[], [0]], 'index': 6, 'label': '2-159450-1.1-c1-0-6', 'leading_term': '1.37632549651', '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/159450/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.376325496505867, 0.944509348103478, 0.03925454766913645, -0.3604394188765891, 0.4825393467219306, 1.942302540166051, 2.184120279280242, 0.2286121149844922, -2.295134376765778, -2.637232816458732, -0.655105067419232, 0.3308809361281206, -2.080608640399408, -5.204078864897932, -4.17830912317677, 0.876439064917542, 4.040000489866585, 1.685968906487483, -2.037357259327792, -1.361885573889204, 2.241442274539676, 2.629434003518089, -0.9733239938794083, -3.00304290157807, -1.038841504481862, 0.7815707581960099, -0.08213529681732151, -0.2037889727506131, 2.440808597260859, 3.833980628347037, 1.396078041121154, -0.7774992563641572, 0.4206526786388532, 1.222835604796642, -1.292378107559983, -3.009369235384145, -0.7841162442549007, 1.151826723816971, -0.5289224303832633, -1.862607017128447, 0.08082773077514815, 1.508586887579156, 0.2307123572622939, -0.3372470619141018, 0.1612448349280084, -2.213622789467185, -5.647784860208328, -4.229200283754219, -0.07137571256691702, 0.4297007614159212, -0.3262895483086955, 2.572202585102097, 3.872039465248759, -1.072855908781796, -3.482355738889646, 2.755520694192771, 6.714614870333069, 0.3453935416306441, -5.449169784776314, -1.749558458739541, 2.509289970695262, 0.1393422204318592, -1.79296975848436, 0.5154070984870834, 0.8504434717240003, -1.405740350103595, -0.7303350032787612, 1.220375128411956, 0.3615364107531983, -0.1299139709343923, 1.494043406087418, 1.010412386522937, -0.6790833427152759, 1.052402570972317, 3.022137964902443, 1.181101396498563, -0.1022971812940504, 0.9166713334427938, -0.2675412761111967, -0.7923487573512435, 4.681423577870664, 8.690656446498531, 4.271257460455644, -0.03111243895183355, 1.4242759488857, 1.349641047375124, -0.2235995249226798, 3.875663201711105, 7.308729705797851, 2.051680390644125, -2.203933300194802, 1.605948605151917, 3.496918675476287, 0.1199621477410627, -0.3287899303837632, -0.1392138940457203, -4.681781396963171, -5.686201793748424, 0.02855913277633254, 1.264671524028534, -2.878439411422566, -2.440265434342082, 0.4187992786622146, -0.09855612873758365, 1.224473309515724, 4.756791398783569, 2.842301670432972, -1.315903682893245, -0.7412106276601824, 0.1375164447407217, -1.083246082021134, 0.6002614981589011, 2.621636412139099, 0.6798539311590099, -0.3101293986225647, 0.6669158538877642, -0.8793931979801193, -1.404319331966034, 0.9766193670622854, -0.1163100055818526, -1.857924962891052], 'positive_zeros': ['0.5119170620021974', '0.9006297709506010', '1.770819519132704', '2.586360607967455', '2.817907482732138', '3.709299029891476', '4.347076083830042', '4.844944790917833', '5.439084455804656', '6.100768531641856', '6.484469646862562', '6.779860492840206', '7.617065602543549', '7.946673922784902', '8.397054474495984', '9.064933805039595', '9.447310247626747', '9.992190544261474', '10.53910813391042', '10.86262481398643', '11.04895598406863', '12.00627777865821', '12.32368295152815', '12.55388384634882', '13.20547473707504', '13.66212839586061', '14.25979464278707', '14.82126682124754', '15.25914338360220', '15.70110177289822', '16.09213337128501', '16.57450622601732', '17.06242476204309', '17.27772976826018', '17.86728817736908', '18.15526385677183', '18.89977349143181', '19.03754259903518', '19.46991045759674', '19.80871186789316'], 'prelabel': '2-159450-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 35.68213362775994, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1973388663289803752, 'z1': {'__RealLiteral__': 0, 'data': '0.5119170620021974', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.9006297709506010', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.770819519132704', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1273.2146602293165, 'bad_primes': [2, 3, 5, 1063], 'central_character': '1.1', 'conductor': 159450, 'conductor_radical': 31890, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, -1, -1, 1, 0, -2, -1, 0, 1, 0, 1, 3, -1, -8, 0, 1, 2, 4, 1, 0, 0, -1, -1, 9, 0, 4, -1, 2, -3, 0, 1, 4, 8, 0, 0, 0, -1, 12, -2, 0, -4, 8, -1, -6, 0, -3, 0, -5, 1, 0, 1, 8, -9, -3, 0, -1, -4, -1, 1, 0, -2, -12, 3, -4, 0, 9, -1, 17, -4, 0, -8, 2, 0, 10, 0, 1, 0, 14, 1, 0, -12, -9, 2, -1, 0, 0, 4, -4, -8, 0, 1, 7, 6, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, 0, 13], 'euler17': [1, -3, 17], 'euler19': [1, 8, 19], 'euler2': [1, 1, 0], 'euler23': [1, -4, 23], 'euler29': [1, -9, 29], 'euler3': [1, 1, 0], 'euler31': [1, -4, 31], 'euler37': [1, -4, 37], 'euler41': [1, 0, 41], 'euler43': [1, -12, 43], 'euler47': [1, -8, 47], 'euler5': [1, 0, 0], 'euler53': [1, 5, 53], 'euler59': [1, 3, 59], 'euler61': [1, 1, 61], 'euler67': [1, 12, 67], 'euler7': [1, 1, 7], 'euler71': [1, -9, 71], 'euler73': [1, -17, 73], 'euler79': [1, -10, 79], 'euler83': [1, -14, 83], 'euler89': [1, 1, 89], 'euler97': [1, -7, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 0, 0], [1, 1, 7], [1, 2, 11], [1, 0, 13], [1, -3, 17], [1, 8, 19], [1, -4, 23], [1, -9, 29], [1, -4, 31], [1, -4, 37], [1, 0, 41], [1, -12, 43], [1, -8, 47], [1, 5, 53], [1, 3, 59], [1, 1, 61], [1, 12, 67], [1, -9, 71], [1, -17, 73], [1, -10, 79], [1, -14, 83], [1, 1, 89], [1, -7, 97]], 'index': 6, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/159450/d'], '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': '2-159450-1.1-c1-0-6', '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': '2-159450-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 35.68213362775994, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1973388663289803752, 'z1': {'__RealLiteral__': 0, 'data': '0.5119170620021974', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1973388663289803752', 'Lhash_array': ['1973388663289803752'], 'label': '2-159450-1.1-c1-0-6', 'type': 'ECQ', 'url': 'EllipticCurve/Q/159450/d'}