-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2933417255443018180315032750451', 'a10': [0.0, -2.23606797749979], 'a2': [-1.0, 0.0], 'a3': [0.3962086421951157, 0.0], 'a4': [-3.0, 0.0], 'a5': [0.0, 2.23606797749979], 'a6': [-0.3962086421951157, 0.0], 'a7': [0.0, -8.165308177922403], 'a8': [7.0, 0.0], 'a9': [-8.843018711849902, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1335230401434147, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, -2.23606797749979]]], [23, [[1.0, 0], [18.446810069654788, 13.73736504043198]]]], 'bad_primes': [5, 23], 'central_character': '115.91', 'coefficient_field': 'CDF', 'conductor': 115, 'conductor_radical': 115, 'conjugate': '494006132791280948908022588333', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0], [4.0, 0]], [[1.0, 0], [-0.3962086421951157, 0], [9.0, 0]], [[1.0, 0], [0, -2.23606797749979]], [[1.0, 0], [0, 8.165308177922403], [-49.0, 0]], [[1.0, 0], [0, 18.988464727508315], [-121.0, 0]], [[1.0, 0], [18.635435996240133, 0], [169.0, 0]], [[1.0, 0], [0, -5.572056862509578], [-289.0, 0]], [[1.0, 0], [0, 5.251099687076335], [-361.0, 0]], [[1.0, 0], [18.446810069654788, 13.73736504043198]], [[1.0, 0], [-11.622748146829306, 0], [841.0, 0]], [[1.0, 0], [-49.52905613554971, 0], [961.0, 0]], [[1.0, 0], [0, -29.747024220843542], [-1369.0, 0]], [[1.0, 0], [10.459497919065615, 0], [1681.0, 0]], [[1.0, 0], [0, -57.221754301707506], [-1849.0, 0]], [[1.0, 0], [15.270871992480268, 0], [2209.0, 0]], [[1.0, 0], [0, 40.24922359499622], [-2809.0, 0]], [[1.0, 0], [27.787240278619148, 0], [3481.0, 0]], [[1.0, 0], [0, 110.6310256425199], [-3721.0, 0]], [[1.0, 0], [0, -35.062720964170566], [-4489.0, 0]], [[1.0, 0], [70.45949791906561, 0], [5041.0, 0]], [[1.0, 0], [0.3772518531706943, 0], [5329.0, 0]], [[1.0, 0], [0, 102.65748052752937], [-6241.0, 0]], [[1.0, 0], [0, 116.84499685589596], [-6889.0, 0]], [[1.0, 0], [0, 49.6337634184009], [-7921.0, 0]], [[1.0, 0], [0, -69.61069358415583], [-9409.0, 0]], [[1.0, 0], [-146.91899583813122, 0], [10201.0, 0]], [[1.0, 0], [0, -120.01556546592458], [-10609.0, 0]], [[1.0, 0], [0, 191.38583295169488], [-11449.0, 0]], [[1.0, 0], [0, -134.74139594460317], [-11881.0, 0]], [[1.0, 0], [0, 86.96877852255105], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-115-23.22-c2-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/115/3/d/a/91/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.47393412019233216, 0.6124353831217539, 0.7463887045500939, 0.8761319462106134, 1.0011571400190635, 1.11998940817548, 1.23013707592637, 1.3281126184181378, 1.4095220644287425, 1.4692205973190977, 1.501532841067807, 1.5005362950170675, 1.4604047523982064, 1.3758050895733696, 1.2423357865924964, 1.0569894490808662, 0.8186151060112666, 0.5283498938559696, 0.18998468084113554, -0.1897749816241703, -0.6011917236376861, -1.0315594252134759, -1.4654763544682279, -1.8853477251016726, -2.2721226108665307, -2.60625234082472, -2.8688372093318963, -3.042906931056261, -3.114759509776045, -3.0752651258939814, -2.92102849038966, -2.655297029319791, -2.2885051460705226, -1.8383580262848551, -1.329382599238165, -0.7919079621558786, -0.2604812921384662, 0.22822468801846066, 0.6379040766795323, 0.935351056928174, 1.0932323222112015, 1.092667053720625, 0.9253708195581929, 0.5951294559060369, 0.1184025652521829, -0.47608628964537564, -1.1488368603105388, -1.8521062603378193, -2.533355824996489, -3.1393748436040108, -3.6207554358319336, -3.9363262849277767, -4.057119563374426, -3.969452747587392, -3.6767590795783116, -3.19989660965795, -2.5758003713775204, -1.8545045328884087, -1.0947360968285027, -0.35845041399975125, 0.2951784518393789, 0.8157016945560687, 1.1666263222563866, 1.3293187430445939, 1.3050759530271194, 1.1150350820957282, 0.7978214506314342, 0.40509497163596553, -0.0045843230455556395, -0.3729207257540937, -0.6492583993155696, -0.7972698709113728, -0.8000863933096303, -0.6631381955369327, -0.41421542208459683, -0.10058433110026865, 0.2166373347740968, 0.4702716550116379, 0.5961420539242915, 0.5422809296050284, 0.2770643794690664, -0.20488374490853264, -0.8799547352245006, -1.6965569706956587, -2.579960834177922, -3.4405747578531565, -4.184744879858337, -4.726765620184261, -5.000537174146905, -4.969255119825159, -4.631688851616634, -4.023991124497655, -3.2165409914053673, -2.3059890368645277, -1.403358718450132, -0.6196632971953738, -0.05093122206042882, 0.23528049008450794, 0.2099086556007318, -0.11263748070147905, -0.6754712032165182, -1.386304225399325, -2.12982800687718, -2.78380990874175, -3.236692803512951, -3.404165011152424, -3.2422103397096276, -2.75456915566905, -1.9932968335640375, -1.052097266303213, -0.053195548379167935, 0.8704682334311855, 1.5951550445085767, 2.0253618930283586, 2.1090122803686486, 1.8463321086790851, 1.290843769514378, 0.5420976038544146, -0.26894745388926017, -0.999786963375327, -1.5184702166624968, -1.7244808004268641, -1.565040910288372, -1.04412901440043, -0.22261190641423192, 0.7906988953466348, 1.8557738055874844, 2.823271407287666, 3.5581080734014647, 3.960827954113216, 3.983206861632662, 3.635433387457163, 2.9835963757201163, 2.137844575202418, 1.2331947533016592, 0.40626623592281086, -0.22802533531471525, -0.595723605078945, -0.67561282528793, -0.5013962527650717, -0.15384927280722804, 0.2556556076745174, 0.6072511449454542, 0.7962175327270364, 0.7537227269964928, 0.46068566762759033, -0.0479882742777741, -0.6897740818748868, -1.3504606762571056, -1.906746156997223, -2.251221240730531, -2.314879756763485, -2.0826284986521237, -1.598492214184988, -0.959119083842031, -0.29644283261353954, 0.247475381695269, 0.5487450498258999, 0.5276010797816145, 0.1667745144550015, -0.48167882272707385, -1.3029367469109425, -2.138639864151473, -2.8155519074081514, -3.1784258665365663, -3.120815940720399, -2.6077347249574707, -1.6854243189910514, -0.4758654841139263, 0.8434383914954788, 2.070953060718441, 3.0180978525578657, 3.544671154226027, 3.5857532062416864, 3.1645971776670425, 2.3886339321129264, 1.4289846671202804, 0.4871640611833438, -0.24469612156377527, -0.6223205266119621, -0.5787506329120334, -0.1387098710279113, 0.5853100991166841, 1.414809171595744, 2.1408347260890404, 2.5664041229711247, 2.5473301207381938, 2.023145328040709, 1.0316834722086807, -0.2959049680381536, -1.7589817256172486, -3.1255067170980584, -4.176807740845483, -4.749994199770546, -4.769362203894926, -4.260330609400733, -3.3430148297092193, -2.2067580113191485, -1.0709167719469643, -0.14009434507165228, 0.43680291705186314, 0.5951131332871651, 0.3646386509771908, -0.14046497113199533, -0.7497533630904988, -1.2762500710802551, -1.5591008820511687, -1.499716329878418, -1.0834508265960838, -0.38209350037893985, 0.46326077614535593, 1.2749822726695366, 1.8798066022505917, 2.1484997154033834, 2.0251930305568635, 1.5396485703028564, 0.7996387929435456, -0.03476274656793837, -0.7889433889456352, -1.3146516893853948, -1.5243008348129128, -1.410404929345299, -1.0453279329362446, -0.5611864592333694, -0.11454324621432552, 0.15567794212915997, 0.16676161805924455, -0.08247697072473405, -0.5064223951346698, -0.9495908685064147, -1.2225804489514316, -1.149105320896008, -0.6131628699892742, 0.4051214056122237, 1.8142105733265488, 3.4211737653888483, 4.965951115127913, 6.173059487383221, 6.809583682496213, 6.736428458975169, 5.940936067809987, 4.542925167080913, 2.7721280486797957, 0.9215501348966432, -0.7130808993108467, -1.8942246385722268, -2.4899715311358324, -2.4971671929950805, -2.034940837217025, -1.310268299450375, -0.5638153968695254, -0.009044113451601275, 0.22074588811621715, 0.10458272485121312, -0.2627223390621902, -0.696822901963311, -0.9735208876234712], 'positive_zeros': ['2.31405819151971534130614912126398', '4.56466438561201244349145874715102', '5.52672603610774314416552750226721', '7.44091616050910172740891091583868', '8.498562252877243683532421923809096', '9.413569887747486527880429154900499', '10.07821953761592870143475109749483', '12.01522109523490172893201210524136', '12.34164426235018446153084098861205', '13.75677672339866887875099155255814'], 'prelabel': '2-115-23.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7701759912910962, 'root_angle': 0.7037505919080503, 'root_number': '-0.5972767408883471 + 0.8020352204197733*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.351875295954', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.31405819151971534130614912126', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.56466438561201244349145874715', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.52672603610774314416552750227', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.1335230401434147, 'bad_primes': [5, 23], 'central_character': '23.22', 'conductor': 115, 'conductor_radical': 115, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/115/3/d/a/91/4'], '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': '2-115-23.22-c2-0-10', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-115-23.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7701759912910962, 'root_angle': 0.35187529595402517, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.31405819151971534130614912126', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2933417255443018180315032750451', 'Lhash_array': ['2933417255443018180315032750451'], 'label': '2-115-23.22-c2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/115/3/d/a/91/4'}