-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4149141845830644286405098227613', 'a10': [3.0293827925023784, -2.612850209890512], 'a2': [1.6811910563735675, -0.6119035026345316], 'a3': [0.595254507139095, -1.6354483171932537], 'a4': [0.9198885852561076, -0.7718781726125897], 'a5': [2.0906405494526914, -0.7932352065964724], 'a6': [-1.5505513047259005e-60, -3.1137394019039037], 'a7': [-4.265560855233818, 0.7521334666315969], 'a8': [-0.7148926485141319, 1.2382303891839557], 'a9': [-0.022229940583904612, -0.01865313494504721], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.4772324373936878, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-2.0906405494526914, 0.7932352065964724]]], [37, [[1.0, 0], [3.35577998792461, -5.07333624675565]]]], 'bad_primes': [5, 37], 'central_character': '185.104', 'coefficient_field': 'CDF', 'conductor': 185, 'conductor_radical': 185, 'conjugate': '2696744314173676948272720382377', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.6811910563735675, 0.6119035026345316], [1.532088886237956, -1.2855752193730787]], [[1.0, 0], [-0.595254507139095, 1.6354483171932537], [-2.298133329356934, -1.928362829059618]], [[1.0, 0], [-2.0906405494526914, 0.7932352065964724]], [[1.0, 0], [4.265560855233818, -0.7521334666315969], [6.5778483455013586, -2.3941410032796813]], [[1.0, 0], [1.9163359636948898, -3.319191253491016], [-5.5, -9.526279441628825]], [[1.0, 0], [-1.3844758489309767, 1.1617131742118343], [2.2574263096700946, -12.802500789158705]], [[1.0, 0], [-2.5589838989696645, -2.1472424458140433], [2.952019020337816, 16.741731801207536]], [[1.0, 0], [-1.922179179669869, 5.281143892288775], [-14.554844419260583, -12.212964584044247]], [[1.0, 0], [2.833358956504604, 4.907521668746311], [-11.5, 19.91858428704209]], [[1.0, 0], [5.782762231586696, 3.3386793310661798], [14.5, 25.11473670974872]], [[1.0, 0], [0, -4.6538874759372355], [-31.0, 0]], [[1.0, 0], [3.35577998792461, -5.07333624675565]], [[1.0, 0], [3.083606727878424, -2.5874532680585647], [7.119575284344144, -40.37711787350053]], [[1.0, 0], [4.209740819201887, 0], [43.0, 0]], [[1.0, 0], [0.20097654735928627, -0.11603386371868551], [23.5, -40.703193977868615]], [[1.0, 0], [-8.062189947564486, -1.421581611352183], [49.803708901653145, 18.127067596260442]], [[1.0, 0], [4.925938708911486, 0.8685758996973164], [55.44186462636859, 20.179188456214455]], [[1.0, 0], [8.081105584927133, 9.630686612970045], [-10.592538837682751, 60.07327293374469]], [[1.0, 0], [4.204810464889618, -0.7414215337253433], [62.95940559265586, -22.915349602819806]], [[1.0, 0], [-10.880887329914797, -3.960319110493242], [54.38915546144744, 45.63792028774429]], [[1.0, 0], [0, 1.9119654875843357], [-73.0, 0]], [[1.0, 0], [-1.5336107497846119, 0.27041695309156577], [74.23571704208676, -27.01959132272783]], [[1.0, 0], [2.4879794323170534, -2.9650584267643514], [-14.412798746355218, -81.73904350001327]], [[1.0, 0], [-14.586782183190023, -2.5720432606139276], [83.63264324994584, 30.439792755984517]], [[1.0, 0], [-2.442598625495083, -4.230704921855389], [-48.5, 84.00446416709055]], [[1.0, 0], [7.69744675034598, 13.332368860155185], [-50.5, 87.4685657822283]], [[1.0, 0], [-1.0286409761221063, 1.7816584333907324], [-51.5, -89.20061658979718]], [[1.0, 0], [-2.5784008955436843, -3.072818530412314], [-18.580355010361547, 105.37442957230627]], [[1.0, 0], [1.5268313566577523, 4.194934675732441], [-83.49884429996861, 70.06384945583278]], [[1.0, 0], [5.880307986883343, -2.140257075543351], [86.56302207244451, -72.63499989457894]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-185-185.104-c1-0-15', '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/185/2/v/a/104/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.1614781018239433, 2.252699115395939, 2.371509463642129, 2.517121586876714, 2.6861620019648567, 2.873062819144268, 3.070506410269074, 3.269830327578814, 3.461381510316659, 3.6348564229003477, 3.7796733698999114, 3.8854104817095227, 3.9423222187527434, 3.9419263654387886, 3.8776351607124733, 3.7453891678279287, 3.544241055330123, 3.276829186355772, 2.9496785886923806, 2.5732703703221014, 2.1618306509602614, 1.732806887351737, 1.3060227551633283, 0.9025314316630203, 0.5432192922876514, 0.24724498132501957, 0.03042916894071441, -0.09626572138550674, -0.12801277506638092, -0.06700169733707974, 0.077213267722872, 0.2880021860599054, 0.542638438357627, 0.8139570833575926, 1.072608486924001, 1.2897475810456536, 1.4399296936583976, 1.5039296992425575, 1.4711711397538336, 1.34145340107431, 1.1257028425352151, 0.8455491289397221, 0.5316376033803808, 0.22072425542310983, -0.04825100124168488, -0.2387708038169534, -0.32155989295013426, -0.279066467553789, -0.1090259230383773, 0.1734326615269173, 0.5355648538308425, 0.9289216531976654, 1.2934064989620646, 1.5632274224323874, 1.6742276394011746, 1.5718458843785832, 1.2187939254312778, 0.6014728801442545, -0.2657972366844921, -1.3394816912389944, -2.5489204747651324, -3.80186833529235, -4.993115244706261, -6.015385616416636, -6.77134578253819, -7.18529988581229, -7.213070803509659, -6.848673177619958, -6.126693964430856, -5.119778462011621, -3.931225702045503, -2.6833529100942437, -1.5029066398365443, -0.5052874688642394, 0.2203647085342152, 0.6231641305478227, 0.6977670743561284, 0.4857191647731881, 0.07039015427413413, -0.4340943749574172, -0.8986363315279562, -1.1976297160058786, -1.227580034035734, -0.9232028659871996, -0.268564979823058, 0.6985531470168322, 1.8899733846111004, 3.1779107795028745, 4.411908495957994, 5.439609628580075, 6.128392564675439, 6.384661389247675, 6.167836922635111, 5.496820209018467, 4.447804008916432, 3.1436278820722676, 1.7362038189139937, 0.38466513598011615, -0.7673815808668069, -1.6119284457702276, -2.090780634245413, -2.20166149856218, -1.9952842623459883, -1.5639757894622661, -1.0238739751731394, -0.49382978879262834, -0.07472308643642239, 0.1671695639116901, 0.209841557741516, 0.07660864908630106, -0.17151441937721187, -0.45054998784868405, -0.6724845894397312, -0.7646376283323202, -0.6855995904481351, -0.43449681336791063, -0.051623670830560464, 0.389806857309945, 0.7992290997441247, 1.0884814313466846, 1.191645692025244, 1.0806817537414175, 0.7732686910238042, 0.3307433628781603, -0.15397471779551558, -0.5764487176399613, -0.8449178476924724, -0.903612080263499, -0.7500118084378335, -0.44177945977214833, -0.09095097212580043, 0.15452653492046955, 0.13916067535551419, -0.2668587615989229, -1.1360355764928067, -2.460212098975297, -4.141003289869114, -5.9971880039142835, -7.78906390231437, -9.256388419513625, -10.163590881689103, -10.344070430727509, -9.735032041309617, -8.395620362995125, -6.503921570481646, -4.332237230671472, -2.2041798911657797, -0.4407873829871998, 0.6947468914051804, 1.0435081836249864, 0.5795903282524956, -0.5846197866571405, -2.2180027384783156, -4.011784927518242, -5.6346301749941325, -6.791462415454983, -7.27494805927116, -6.99996153195742, -6.014688089615494, -4.486631291679249, -2.6667580624614797, -0.839313907127025, 0.732417728756733, 1.8535289569560867, 2.428841964374944, 2.4725307486332464, 2.0950362175581696, 1.471127041769705, 0.7968643383100946, 0.24536588713750593, -0.06882259853325444, -0.10921709315055318, 0.08285473288861758, 0.40716437276963974, 0.7367303869131855, 0.9547767392047116, 0.9871141629064593, 0.8218623698709574, 0.5116913242598214, 0.1581953982547888, -0.11744600603807835, -0.2098344414656055, -0.061414533605319704, 0.3174145591642687, 0.8458993585199311, 1.389588117253838, 1.792505712494655, 1.9171760684585903, 1.6824942866502202, 1.0895755475628097, 0.2283371254534254, -0.7378673094434935, -1.6068201113438583, -2.183525823622384, -2.3268969563805397, -1.985510676151065, -1.2131564655188805, -0.15955619603916874, 0.9623612360824622, 1.9253603985723629, 2.541410600679766, 2.706684462897343, 2.4265954169924084, 1.8140415342045635, 1.060533893840023, 0.3867282108379331, -0.01566378943096447, -0.035965758018173935, 0.3230284212172193, 0.9414719094618246, 1.6099435078189672, 2.0823484038092084, 2.1418394593184487, 1.6634359894279531, 0.6570480649412821, -0.7212407852994344, -2.194389097985611, -3.4219513746475267, -4.077539513804592, -3.9282294181125117, -2.8966452732304173, -1.0898591235887403, 1.2133172505727214, 3.6153031805120777, 5.681882006112287, 7.035060567676485, 7.435180382925408, 6.832916730077221, 5.378658583114895, 3.3867704033468207, 1.262986149776192, -0.5879605562811134, -1.8526134869437165, -2.3756801169974446, -2.187994869710849, -1.4895897112398229, -0.5928894324591482, 0.15928218498731914, 0.4802644909822238, 0.20934019269259324, -0.6519955366497558, -1.9452566428326363, -3.3990541024705596, -4.6997046857288085, -5.56966328536282, -5.8336851943986865, -5.456456538943129, -4.543384968053632, -3.306136012181635, -2.0036645637364505, -0.8754920529140202, -0.0852761578496421, 0.31092583719470795, 0.36476390205997794, 0.20625778095461736, -0.004615273066851147, -0.13008728333467937], 'positive_zeros': ['3.27309579239234185876298762183864', '3.69127673350003551678930985477081', '5.47518076944089825424705001080654', '6.05367134106707346256760365250200', '7.21503398305356972807206195484221', '9.205989660536644901773167570243520', '9.768072502076648390153123479894304', '10.53861154263794006755812089267384', '12.16378004878882865430171262120653', '13.27953382741595388790145110668989'], 'prelabel': '2-185-185.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2154145125814846, 'root_angle': 0.1754983164404566, 'root_number': '0.4511985246280309 + 0.8924236053430502*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17549831644', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.27309579239234185876298762184', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.69127673350003551678930985477', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.47518076944089825424705001081', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.4772324373936878, 'bad_primes': [5, 37], 'central_character': '185.104', 'conductor': 185, 'conductor_radical': 185, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/185/2/v/a/104/14'], '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': '2-185-185.104-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': 0, 'prelabel': '2-185-185.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2154145125814846, 'root_angle': 0.1754983164404566, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.27309579239234185876298762184', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4149141845830644286405098227613', 'Lhash_array': ['4149141845830644286405098227613'], 'factors': ['2-185-185.104-c1-0-15'], 'label': '2-185-185.104-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/185/2/v/a/104/14'}