-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1341581544460981424628000719430', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.532088886237956, 1.2855752193730787], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.064177772475912, -2.5711504387461575], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.163', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1043991077373241332752501660139', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [1.532088886237956, -1.2855752193730787]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-4.698463103929542, 1.7101007166283437]], [[1.0, 0], [3.064177772475912, 2.5711504387461575], [1.2155372436685123, 6.893654271085456]], [[1.0, 0], [0, 0], [-10.336618828644992, -3.762221576582356]], [[1.0, 0], [-6.5778483455013586, -2.3941410032796813], [9.958577760546714, 8.35623892592501]], [[1.0, 0], [0, 0], [-8.5, 14.722431864335457]], [[1.0, 0], [-0.5, 0.8660254037844386], [-9.5, -16.454482671904334]], [[1.0, 0], [0, 0], [3.993908086339398, -22.650578319280786]], [[1.0, 0], [0, 0], [22.215288850450364, -18.64084068090964]], [[1.0, 0], [-8.426488874308758, 7.070663706551932], [5.3830935076748405, -30.52904034337845]], [[1.0, 0], [-5.0, -8.660254037844387], [-18.5, 32.04293994002423]], [[1.0, 0], [0, 0], [31.4078221678781, 26.354291997148113]], [[1.0, 0], [-0.8682408883346517, 4.924038765061041], [-40.406782693794064, -14.706866163003756]], [[1.0, 0], [0, 0], [8.161464350345726, 46.28596439157378]], [[1.0, 0], [0, 0], [53.0, 0]], [[1.0, 0], [0, 0], [-55.44186462636859, 20.179188456214455]], [[1.0, 0], [0.766044443118978, 0.6427876096865394], [10.592538837682751, 60.07327293374469]], [[1.0, 0], [4.698463103929542, 1.7101007166283437], [51.32497768897153, 43.066769848998135]], [[1.0, 0], [0, 0], [-35.5, 61.48780366869514]], [[1.0, 0], [-3.5, 6.06217782649107], [-36.5, -63.21985447626402]], [[1.0, 0], [-12.216004070216808, 4.446261863233693], [60.51751100639927, -50.780221165236604]], [[1.0, 0], [0, 0], [63.581688778875176, -53.35137160398276]], [[1.0, 0], [0, 0], [-44.5, -77.07626093681505]], [[1.0, 0], [-0.8682408883346517, 4.924038765061041], [-91.15018421623311, -33.17595390258987]], [[1.0, 0], [0, 0], [17.538465944359967, 99.46558305423301]], [[1.0, 0], [2.2574263096700946, 12.802500789158705], [-96.78833994094856, 35.228074762543876]], [[1.0, 0], [0, 0], [107.0, 0]], [[1.0, 0], [19.0, 0], [109.0, 0]], [[1.0, 0], [0, 0], [-106.18526614880764, 38.64827619580057]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-3e6-27.7-c1-0-13', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/729/2/e/e/163/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1442740542825522, 1.170936796038706, 1.1681780866486242, 1.1312062823745315, 1.0524718041986871, 0.923302358363223, 0.7357723019356583, 0.484549902861925, 0.16855701627306496, -0.2076802310263496, -0.633110114996234, -1.089795785148996, -1.5532485311150612, -1.9935553011619431, -2.377340157316747, -2.6705087016295175, -2.841613957425202, -2.865565311701823, -2.72729602764355, -2.42492853107637, -1.9719487181089002, -1.3979360758964854, -0.7475040287248991, -0.0772837327804167, 0.5489777861659607, 1.0668620198490024, 1.4186507987576427, 1.5607806502972277, 1.470390527783237, 1.149952961209502, 0.6291064277772405, -0.03691159229156545, -0.7724147516529672, -1.4896779566045812, -2.0997539927980005, -2.524372086198586, -2.7072678030535067, -2.6231877551510725, -2.282975941936828, -1.7335917368005236, -1.0525962515258014, -0.3374901921128054, 0.30883146264279915, 0.7944719805031437, 1.0542252868258493, 1.0618901519772224, 0.8368464130194446, 0.4432972456861224, -0.018294716962345317, -0.42672762656358515, -0.6603848119525065, -0.6191680429968375, -0.24427960107202973, 0.46783968542134646, 1.4603588694001186, 2.6212738591901683, 3.7988024452955123, 4.824879540612209, 5.543022333022113, 5.835755762389872, 5.64654103119505, 4.991852310294904, 3.9606401632776893, 2.7006618705095495, 1.3936545256523036, 0.2235970797830839, -0.6561211546461867, -1.1503045499284752, -1.2387489884448497, -0.9785753258873805, -0.49122019298228964, 0.06367949779475619, 0.5224567428010345, 0.7526883336994036, 0.6821013079979319, 0.31469730348581776, -0.26981955934518026, -0.9337404506988857, -1.5128421287031815, -1.8551143564341455, -1.8582378752413142, -1.4971968294700977, -0.8352182702485386, -0.014683297876164857, 0.7709400676198294, 1.3186857892898987, 1.4623500703870664, 1.113033530352423, 0.2843548837381313, -0.904227243683997, -2.247817582389933, -3.496648482697141, -4.408409492411722, -4.800849897037554, -4.592621659937921, -3.8226017192102937, -2.642609680122976, -1.284512072165548, -0.008779794538925275, 0.9538266744922067, 1.4538104209488891, 1.455372585287912, 1.0417012042694813, 0.3915225308528265, -0.26765160852583525, -0.7182603503405963, -0.8088641236726044, -0.49353563795037014, 0.15579543496261422, 0.9676337740625317, 1.7156426641767435, 2.1786596520310137, 2.200606350477819, 1.7345259319743578, 0.8587341673165797, -0.2398957470411556, -1.3119183397866563, -2.109077162123716, -2.4492585595628134, -2.265237171851758, -1.623645759843498, -0.7082259474132272, 0.22908837137259846, 0.9368419619939545, 1.2342777071972912, 1.0638705426296984, 0.5111393091945451, -0.21483058544628322, -0.8361459925647133, -1.0822910973032698, -0.7675056771016573, 0.15189725748995492, 1.556719533309425, 3.1875097565286348, 4.705853802598772, 5.778787133672309, 6.164039058504388, 5.773068955914097, 4.694487554203892, 3.171063018653686, 1.5362319243497249, 0.12732610762222366, -0.8006466012874306, -1.1368536987242406, -0.9351099490111583, -0.3877143187963297, 0.23920207669794533, 0.6894918970917698, 0.795002398588091, 0.5244695223061513, -0.011406182331549386, -0.6002624176635728, -1.00148308176249, -1.0300576456254538, -0.624536367193982, 0.12299842270775099, 0.9858493244320168, 1.6665455398305238, 1.8875173358653903, 1.4814727157618224, 0.4533346779984218, -1.006804910477998, -2.56608678941251, -3.836382365956172, -4.482545561505454, -4.319926683813842, -3.3718451005551406, -1.8688566617301736, -0.1885965273967707, 1.2472898666932795, 2.0894928700917696, 2.1566327805468624, 1.481934466062556, 0.2973249823753973, -1.0398646628825323, -2.1549984930822537, -2.7658703884938336, -2.7605615213727197, -2.2200066798974833, -1.3793389374446743, -0.5414962074655884, 0.028237468146754558, 0.1920248914598117, -0.015997882036122475, -0.4052586808445634, -0.6993435227396083, -0.6382264470579379, -0.07774789373734398, 0.9478104087469472, 2.222614431542677, 3.4088197312549826, 4.151032329173599, 4.1923755763702975, 3.4639188270429204, 2.1168575063361197, 0.48483702767809816, -1.0135072263474159, -2.0017597652205197, -2.2620939781905256, -1.8027959986819815, -0.8541348642630827, 0.2071644058934256, 0.9811269026889924, 1.1756195592418146, 0.7023424328231893, -0.2942572568320139, -1.4853134081861896, -2.4677472085559993, -2.900210334264874, -2.619636926096119, -1.6992769426385754, -0.42827726255118276, 0.7810162116358009, 1.5275618315280577, 1.5532045481183328, 0.827353476606367, -0.4435833720729122, -1.8849803132535412, -3.0774612301761217, -3.6929616020762164, -3.597128153443719, -2.88358113993717, -1.8293306215652168, -0.7882009865983184, -0.06085830589590563, 0.21175115362469923, 0.09310440960892657, -0.18232634221228503, -0.3086278979517198, -0.0377490079629758, 0.7094786253934168, 1.7931192563485854, 2.886146723546967, 3.5806823123858584, 3.533016269093253, 2.596471253985419, 0.8934882477423671, -1.201870514280103, -3.169093191154411, -4.501191672623906, -4.866386643298961, -4.216371847365349, -2.8032810034721107, -1.0983207521057192, 0.3611933453014971, 1.144827759272044, 1.0634616072465588, 0.2200191309246837, -1.0393329557904494, -2.2545321804929346, -3.014554257288992, -3.095884098284408, -2.528237705261006, -1.5663239232072852, -0.5809636260608074, 0.08776055166656252, 0.25925876603805464], 'positive_zeros': ['1.05832123159129290306861063710949', '2.88971687724150994353734800155575', '3.86852740133365889913321318730350', '5.18741081629584981848113567263551', '5.99499604486112861398323860844438', '6.54964488385060639079402672366754', '8.152597809530267041362975953676546', '8.860207680636327589962838723665566', '9.446314362089780396250193881313145', '10.37719194985201615781198833003095'], 'prelabel': '2-3e6-27.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.07407407407407408, 'root_number': '0.9730448705798238 + 0.2306158707424402*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.037037037037', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05832123159129290306861063711', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.88971687724150994353734800156', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86852740133365889913321318730', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.7', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/e/163/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-3e6-27.7-c1-0-13', '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': '2-3e6-27.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.03703703703703704, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05832123159129290306861063711', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1341581544460981424628000719430', 'Lhash_array': ['1341581544460981424628000719430'], 'label': '2-3e6-27.7-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/e/163/1'}