-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '309417783750167648736832034473', 'a10': [-180353069069118.0, -104126892976230.45], 'a2': [-15670.866231988806, 9047.578837473353], 'a3': [-8120620.913576591, -1638869.5319840133], 'a4': [-104718090.35940865, 181377052.9740844], 'a5': [5754406501.823263, 9966924428.56258], 'a6': [142084965352.3079, -47789452717.41552], 'a7': [604314495631.8242, 1689588632236.3896], 'a8': [-6.9179380421197455e-56, -13504544516678.07], 'a9': [63258590679152.0, 26617276392105.715], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 111.88388900436998, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '14.5', 'prec': 14}, 'bad_lfactors': [[3, [[1.0, 0], [8120620.913576591, 1638869.5319840133]]], [7, [[1.0, 0], [-604314495631.8242, -1689588632236.3896]]]], 'bad_primes': [3, 7], 'central_character': '21.17', 'coefficient_field': 'CDF', 'conductor': 21, 'conductor_radical': 21, 'conjugate': '1545469804254746174706353373349', 'degree': 2, 'euler_factors': [[[1.0, 0], [15670.866231988806, -9047.578837473353], [268435456.0, -464943848.3449198]], [[1.0, 0], [8120620.913576591, 1638869.5319840133]], [[1.0, 0], [-5754406501.823263, -9966924428.56258], [-93132257461547840000, 161309801746986570000]], [[1.0, 0], [-604314495631.8242, -1689588632236.3896]], [[1.0, 0], [-79720739061067.52, -46026790156903.24], [793154648585745800000000000000, 1373784149609950000000000000000]], [[1.0, 0], [2.034124435022946e-47, -6582225014661993.0], [-201538126434611140000000000000000, 0]], [[1.0, 0], [-320639204126506600, 555363392445557950], [-240984286053375460000000000000000000, -417397027270158300000000000000000000]], [[1.0, 0], [2572642227867414500, -1485315682787850200], [6064910997294611000000000000000000000, -10504733990697496000000000000000000000]], [[1.0, 0], [37109087688161140000, -21424941766141264000], [1545529321546768800000000000000000000000, -2676935309506460000000000000000000000000]], [[1.0, 0], [-1.1036724507653351e-42, -608726675969485200000], [-2567686153161211300000000000000000000000000, 0]], [[1.0, 0], [-1388826546804961300000, -801839380655542900000], [8880943876546949000000000000000000000000000, 15382246013347018000000000000000000000000000]], [[1.0, 0], [-21640971218993763000000, -37483261676432980000000], [-1502519102851267600000000000000000000000000000, 2602439425481203400000000000000000000000000000]], [[1.0, 0], [-71404816045211780000000, 1.4629876582442411e-39], [58983677299744400000000000000000000000000000000, 0]], [[1.0, 0], [-432892554492001250000000, -2.853498295682267e-40], [234738979284454770000000000000000000000000000000, 0]], [[1.0, 0], [-1101922881031612500000000, -1908586415969428500000000], [-1548131632268516000000000000000000000000000000000, 2681442643893607000000000000000000000000000000000]], [[1.0, 0], [-2937980524611644500000000, -1696243846758410700000000], [50462669683385310000000000000000000000000000000000, 87403907777189020000000000000000000000000000000000]], [[1.0, 0], [967065450752809500000000, -1675006494948364000000000], [-1131561967070132700000000000000000000000000000000000, -1959922818878051000000000000000000000000000000000000]], [[1.0, 0], [118196199303068860000000000, -68240607484817470000000000], [2975330537207969000000000000000000000000000000000000, -5153423659755404000000000000000000000000000000000000]], [[1.0, 0], [66173756837955040000000000, -114616308971046530000000000], [-45200088241494824000000000000000000000000000000000000, -78288849340865620000000000000000000000000000000000000]], [[1.0, 0], [-1.8089026023150132e-36, -1145576625513390400000000000], [-485838707624806700000000000000000000000000000000000000, 0]], [[1.0, 0], [-827716774549605500000000000, -477882502598983500000000000], [543666968996610900000000000000000000000000000000000000, 941658812699103600000000000000000000000000000000000000]], [[1.0, 0], [-593814952414513200000000000, -1028517667876032000000000000], [-5372243038238311600000000000000000000000000000000000000, 9304997892836945000000000000000000000000000000000000000]], [[1.0, 0], [-2723769144698678000000000000, 3.6186930054363213e-35], [45005405483997304000000000000000000000000000000000000000, 0]], [[1.0, 0], [9158928988503125000000000000, 15863730351002838000000000000], [-170325705714810440000000000000000000000000000000000000000, 295012776133076370000000000000000000000000000000000000000]], [[1.0, 0], [-1.0948784856690552e-34, 19192728838526955000000000000], [-4134093490135647000000000000000000000000000000000000000000, 0]], [[1.0, 0], [-49385959337178060000000000000, 85538990752523000000000000000], [-6672519382836167000000000000000000000000000000000000000000, -11557142585560370000000000000000000000000000000000000000000]], [[1.0, 0], [223749125413850000000000000000, -129181617788629650000000000000], [11782827530046894000000000000000000000000000000000000000000, -20408455938862523000000000000000000000000000000000000000000]], [[1.0, 0], [161139751405217970000000000000, -93034078850951980000000000000], [35571285246084250000000000000000000000000000000000000000000, -61611273336743110000000000000000000000000000000000000000000]], [[1.0, 0], [-130471852388000400000000000000, 225983877293643450000000000000], [-60860910408858930000000000000000000000000000000000000000000, -105414189023041200000000000000000000000000000000000000000000]], [[1.0, 0], [2.6747836730388108e-33, -882199776630821600000000000000], [-346158389003024140000000000000000000000000000000000000000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-21-21.17-c29-0-17', 'leading_term': '0.585297642203865493007153770563253343071321564176181835', 'load_key': 'CMFs-workshop', 'motivic_weight': 29, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [29], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/21/30/g/b/17/27', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.5852976422038655, 0.41957667261643594, 0.26218566581631714, 0.11729431360707743, -0.01138880587283995, -0.12070782876610092, -0.20813756774767958, -0.27184606953449036, -0.31074034750917934, -0.32449424656699233, -0.3135577974236992, -0.2791478319906887, -0.22322005108343063, -0.14842315161239125, -0.058036023511170015, 0.044110591755759564, 0.15372623749049852, 0.2661646149675929, 0.3765368657538658, 0.47983171579500944, 0.5710397696148681, 0.6452791376462224, 0.6979195358485067, 0.7247020155453812, 0.7218515626738171, 0.6861799478780584, 0.6151764092955011, 0.5070840043973439, 0.3609597706163189, 0.17671718039546463, -0.04485024254015993, -0.30206487051382946, -0.5923807807659233, -0.9124192875303171, -1.2580236227349695, -1.6243317639559294, -2.0058660002397297, -2.396637446133707, -2.7902633701575925, -3.180094903724425, -3.559352446997649, -3.9212658951370316, -4.259216676449576, -4.5668785264544685, -4.83835392076386, -5.0683031555305655, -5.252063196138386, -5.3857536104985915, -5.466367159060783, -5.491842924415088, -5.461120222891445, -5.374171941479224, -5.232016377365432, -5.036707115301609, -4.791300950136222, -4.499804338071475, -4.167099330217632, -3.798850395557478, -3.40139396749022, -2.981612939166587, -2.546798679012082, -2.1045034312064628, -1.6623861995559952, -1.2280553815010402, -0.8089115176501146, -0.41199354840083663, -0.04383192162675268, 0.28968822559876023, 0.5834507807738643, 0.8332164952532208, 1.0357125024959213, 1.1887014486329517, 1.2910285973182978, 1.3426457392080082, 1.3446112346669459, 1.2990660357718427, 1.2091860591608832, 1.079111803274288, 0.913856610487626, 0.7191954552146012, 0.5015365823610168, 0.2677787163624357, 0.025156900188489633, -0.21891970194487523, -0.45703450159094006, -0.6819310201914758, -0.8866775519561356, -1.0648252836046874, -1.2105563176979415, -1.3188182452562747, -1.385442189039944, -1.4072415858329648, -1.3820893872585616, -1.3089718254593108, -1.1880174024470023, -1.0205003089684808, -0.8088180483371039, -0.5564436201880544, -0.26785319550119824, 0.05156922561128174, 0.3956481508256285, 0.7575514151816626, 1.1299405348094222, 1.5051332734308778, 1.875274800126226, 2.2325135970619048, 2.5691781422716593, 2.877950349091596, 3.152031792371473, 3.385298891909677, 3.5724434533525478, 3.709095281621237, 3.791923975313717, 3.8187174741028174, 3.7884354548034054, 3.701236243878974, 3.5584765217930827, 3.3626837238899516, 3.1175016788423062, 2.827610654224067, 2.498623584548491, 2.1369608256162453, 1.7497062964096772, 1.3444483232645816, 0.9291088792319917, 0.5117652046522765, 0.10046799516090468, -0.29693955508000913, -0.6729975675881161, -1.0207959673552862, -1.334127665417625, -1.607624760026303, -1.8368744741179857, -2.0185120232341163, -2.150288156289316, -2.231109718978502, -2.2610522418731898, -2.241344236844024, -2.1743235798963485, -2.0633670488301634, -1.9127947532317566, -1.7277518253734696, -1.5140703175681194, -1.2781147594582603, -1.0266152542043279, -0.7664923240374617, -0.5046779438282999, -0.24793731932375027, -0.0026959703274809957, 0.22512343302189197, 0.430250259054045, 0.6081972427308593, 0.7553705060287471, 0.8691553544598816, 0.9479755447100653, 0.9913243947143195, 0.9997668325321005, 0.9749122360460347, 0.9193586826649198, 0.8366099871598838, 0.7309676367174348, 0.6074004158966888, 0.4713951320051706, 0.3287923864576821, 0.18561177484409244, 0.047871224906064526, -0.07859461270304463, -0.18831192824350626, -0.276336332710583, -0.33840770139531323, -0.3710868445753092, -0.37187000726255137, -0.3392777515916851, -0.272915427292474, -0.17350317197247092, -0.042874185357904555, 0.11605913014526485, 0.29937069811472855, 0.5022166284978574, 0.7189592215707578, 0.9433161222360151, 1.1685308942612525, 1.3875606357593857, 1.5932757167114613, 1.7786663030272623, 1.9370500528877843, 2.0622752398290647, 2.1489135793401033, 2.1924372137723753, 2.189374642055973, 2.137440859871185, 2.035637592226016, 1.8843202396383307, 1.685229003528398, 1.4414825850311892, 1.1575338406049438, 0.8390878018283573, 0.49298349850224066, 0.12704203574466574, -0.2501156606409681, -0.629277127686958, -1.0008675868209165, -1.3551943484008289, -1.682700124064465, -1.9742186125127326, -2.221225538691284, -2.4160783224242146, -2.552237733752615, -2.6244652569023947, -2.628990426260761, -2.563643104323824, -2.427946526893882, -2.2231679240800557, -1.9523246122274818, -1.6201446138239124, -1.2329820691935607, -0.7986889230968723, -0.32644556800945285, 0.17344572935740554, 0.6897997331057897, 1.2108136475866298, 1.7243524064349542, 2.2182465874316213, 2.680595259000708, 3.1000658273482715, 3.466182929687446, 3.7695986125234087, 4.002336442444614, 4.158002812102616, 4.23195951196985, 4.221452619335702, 4.125693884973448, 3.9458920455818327, 3.6852328232884424, 3.348807756104833, 2.9434933972228077, 2.4777837875350572, 1.961580406063356, 1.405944999717372, 0.8228217520321276, 0.22473613873838938, -0.3755214908864754, -0.9652190957960911, -1.5320041396644928, -2.064214060513022, -2.5511675253711803, -2.9834284773627187, -3.3530357084834823, -3.653691629143341, -3.8809050304602355, -4.0320839167582365, -4.106575888239589, -4.1056550379145955, -4.032455850260503, -3.8918561077586156, -3.690312281057318, -3.435652255574558], 'positive_zeros': ['0.24408759298063652829737978682373', '0.911224151780741100383830928015809', '1.86313948220835734923449889397740', '4.13283672832054147832057156083527', '5.13142670574873024846872651555168', '6.17775929481258074672713459588908', '7.890549531547156033376971019833281', '9.250709858957552521080990913074205', '10.33536424433220480136612013656175', '10.95543844205767122281673804193529'], 'prelabel': '2-21-21.17-c29-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.577518092840588, 'root_angle': 0.7470393568093906, 'root_number': '-0.7004993943805647631879101817430294267096077343171453175 + 0.7136529958407391089044326303874521387537019056029428007*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3735196784046953', 'prec': 60}, 'spectral_label': 'c29-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.24408759298063652829737978682', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.911224151780741100383830928016', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.86313948220835734923449889398', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 111.88388900436998, 'bad_primes': [3, 7], 'central_character': '21.17', 'conductor': 21, 'conductor_radical': 21, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/21/30/g/b/17/27'], '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': '2-21-21.17-c29-0-17', 'motivic_weight': 29, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [29], 'order_of_vanishing': 0, 'prelabel': '2-21-21.17-c29-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.577518092840588, 'root_angle': 0.3735196784046953, 'self_dual': False, 'spectral_label': 'c29-0', 'z1': {'__RealLiteral__': 0, 'data': '0.24408759298063652829737978682', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '309417783750167648736832034473', 'Lhash_array': ['309417783750167648736832034473'], 'label': '2-21-21.17-c29-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/21/30/g/b/17/27'}