-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1987747512205213615943804195213', 'a10': [0.6933523258501898, 0.164327519924088], 'a2': [-1.756613093162628, -0.4889866750796774], 'a3': [0.0, 0.0], 'a4': [1.1342477916043647, 0.6845220493503165], 'a5': [-0.3904916707335955, 0.015152855172175793], 'a6': [0.0, 0.0], 'a7': [-1.3831182079355162, -0.21631574040352147], 'a8': [0.8448773955715326, 0.8955177214373143], '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': '729.685', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '114505660131255109211607215081', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.756613093162628, 0.4889866750796774], [1.712333799060533, 1.0333987423037259]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.3904916707335955, -0.015152855172175793], [4.98496470583896, -0.38746210335965475]], [[1.0, 0], [1.3831182079355162, 0.21631574040352147], [6.665735197368908, 2.1372819838657917]], [[1.0, 0], [-0.14439575770375335, -1.057163976413466], [-10.597079664774684, 2.949898740367011]], [[1.0, 0], [-0.3996646125185677, 0.5827252642349795], [-4.682310422461235, -12.127488161516007]], [[1.0, 0], [-1.1656843830445704, 0.5854287006499114], [10.151696058947365, -13.636094276835744]], [[1.0, 0], [0.11655071640869066, 2.0010985193937634], [-18.871528797096918, 2.2057653683793745]], [[1.0, 0], [0.3957935875071563, -1.0251311027716736], [-17.032512301507104, -15.456180792777015]], [[1.0, 0], [3.8117472694361156, 2.7244732033125287], [9.38828431969131, 27.438296549396764]], [[1.0, 0], [-1.3448109508810857, 1.5409823811101262], [-4.195270292254064, -30.714812504310206]], [[1.0, 0], [-2.7992566146370246, -3.760054170318068], [-10.61171961031034, 35.44561195567309]], [[1.0, 0], [0.19146210445739825, -0.7433015129812465], [-35.89788748338572, -19.80761657116218]], [[1.0, 0], [3.6824493036462305, 3.341644567158525], [4.162867440236701, 42.79802021910613]], [[1.0, 0], [4.9205353000442615, 5.638307896013787], [-6.360571088256162, 46.567618958147726]], [[1.0, 0], [-0.3556183718262779, 2.016812006860421], [-49.803708901653145, -18.127067596260442]], [[1.0, 0], [13.442087440726802, -5.491697020256185], [42.121854338916044, -41.312823518262945]], [[1.0, 0], [9.431536381015132, -5.69196136844363], [28.428654701854867, -53.970469627776126]], [[1.0, 0], [-6.23219298784357, 4.454503825423839], [21.69017411790751, -63.391926510675276]], [[1.0, 0], [1.5754520996847206, 5.262376488530484], [-59.31963461031849, 39.01513744302723]], [[1.0, 0], [4.210477215244248, -0.9979014314685715], [65.23518274360909, -32.76234015463374]], [[1.0, 0], [10.200423700668836, -10.0045050430722], [1.5319152099741253, -78.98514566543162]], [[1.0, 0], [1.5981517068827726, 6.204405749461742], [-72.67133319807354, 40.098345741620996]], [[1.0, 0], [3.4537084192810528, -11.536189508714049], [-74.35841521575134, -48.90629904830174]], [[1.0, 0], [-2.3176780510071975, -0.08993646337363802], [96.70831529327583, 7.516764805177302]], [[1.0, 0], [0.09144160286650076, 4.714705014524337], [-100.92404320292724, 3.9163124969384877]], [[1.0, 0], [9.070984998347585, 7.030543892582504], [25.692437837972072, 99.744165934364]], [[1.0, 0], [15.862438520625119, 5.773455464385157], [81.96675541373065, 68.77827423645971]], [[1.0, 0], [11.13076539410605, -4.051267288054917], [83.49884429996861, -70.06384945583278]], [[1.0, 0], [3.8498629791882992, -3.4935643773753986], [10.939628389459237, -112.46921592462773]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-3e6-243.103-c1-0-16', '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/i/a/685/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.11286087934701272, 0.26924879204200425, 0.4257132987088883, 0.5803366802316399, 0.72830222552572, 0.8613478117912301, 0.9678359398483111, 1.0333965752299197, 1.0420739933589316, 0.9779077284770419, 0.8268635530363603, 0.5789919664147456, 0.2306361556679634, -0.21354670101732012, -0.7390320455425977, -1.3206417963614412, -1.9228044406696494, -2.5010742878194314, -3.0050092679084357, -3.3823508463401417, -3.5842645346897424, -3.5712057450325947, -3.3188002049214598, -2.8230010612073597, -2.1037357026348102, -1.2063081437536276, -0.19999067964329498, 0.8264806901186005, 1.7724191791921586, 2.5351935559358942, 3.0217873060492475, 3.160610772456758, 2.912040016631383, 2.2761194479597413, 1.2960544442595472, 0.056540934439302734, -1.3233997526388463, -2.702659144955625, -3.9341467387467515, -4.88286048423537, -5.4435383885100865, -5.555341189029928, -5.211232412350652, -4.460329484879253, -3.4024411392280873, -2.175161090326136, -0.9350837167946596, 0.164254430137294, 0.994415675429217, 1.4706064584465908, 1.5636390767303385, 1.303169995737746, 0.7714557251341229, 0.08846640101499709, -0.6092601958241549, -1.1924433694927703, -1.561375521559769, -1.6626807408228832, -1.4973735826586563, -1.1186234894005163, -0.619557432561706, -0.11338234899201458, 0.2903082435153902, 0.5083039475682097, 0.500936881073403, 0.2799680129049715, -0.09462534255822777, -0.528478026000282, -0.9144848442084746, -1.1576523753044647, -1.1976437828168096, -1.0237879526687415, -0.6787962450495263, -0.24983792879920708, 0.15151490003482532, 0.4162732304132545, 0.46586114247480753, 0.2741128139559285, -0.12230116615792039, -0.6283915467992123, -1.1103431440707843, -1.4264059232929995, -1.4625693220763476, -1.1647038261190932, -0.5590056363114734, 0.24529788410202322, 1.0732751422968447, 1.7193268214547361, 1.993158387323066, 1.7667086375714642, 1.0109633266459395, -0.18695710664555948, -1.632176816526985, -3.0561037431406186, -4.170288551262744, -4.729149141748298, -4.5877029724620355, -3.7406133809107303, -2.3322696366718616, -0.6336960702045069, 1.0104468562774553, 2.254339439426959, 2.827391613774875, 2.5972236386468373, 1.6041609432404618, 0.0580880528784276, -1.7031180051377648, -3.285415266809209, -4.325146464812381, -4.570798887708183, -3.9409951997584365, -2.544816704784225, -0.6591159599187615, 1.3324655000841894, 3.0249096557241333, 4.081828189544899, 4.30897525039364, 3.6940558356934803, 2.4037484946703294, 0.7392763810954692, -0.9380268925748008, -2.292458807407738, -3.0897728447062325, -3.2447299459647416, -2.829553435398059, -2.0427072582920798, -1.1476803205698813, -0.39902842483765816, 0.024209067130104726, 0.06018689190302416, -0.22920010595460882, -0.687137235874607, -1.116418500461724, -1.343000836366853, -1.2697187616776189, -0.90456120591339, -0.3556784972635302, 0.20470562843961032, 0.5959862475972955, 0.6871179612898185, 0.43880732202678213, -0.0832154022768996, -0.7281226900465475, -1.3070781555024755, -1.652857182589212, -1.6731856652300456, -1.3806112534930224, -0.8888116183942513, -0.3757376115118128, -0.024695067214810382, 0.0379892745493909, -0.21178653248381993, -0.6835849426603573, -1.1988880536631215, -1.549762532443493, -1.5721791604412547, -1.2104707770006429, -0.5506643532316547, 0.19106876150295593, 0.7250894188077613, 0.7757947580354551, 0.17461045730629407, -1.0706881515381947, -2.754403892101809, -4.510188406506848, -5.900889403503616, -6.538074422355458, -6.197608509803218, -4.896515606276003, -2.9057043855668803, -0.6907376563844401, 1.206230027688727, 2.3121065909980354, 2.355203276088906, 1.3454531439927684, -0.4225608104238671, -2.4471086207171795, -4.157200546711244, -5.072454213804323, -4.9391550555178885, -3.802743787496286, -1.9949251779547306, -0.03836984418030167, 1.503739387265565, 2.1896007221954186, 1.824836267615143, 0.515936330806142, -1.3640549744739665, -3.2866232000082922, -4.72187415981913, -5.289421863658157, -4.86152573048461, -3.589120232853052, -1.8453157619060168, -0.10613096192346783, 1.1932050300649035, 1.781779170208288, 1.6195627899996325, 0.8893882646707325, -0.07913850106210141, -0.9259525861116472, -1.3775923358036988, -1.3271100411189476, -0.8528837733255874, -0.17377570641528425, 0.44041644867955754, 0.7699064958227911, 0.7214496453928149, 0.3545835593810341, -0.14959383736811732, -0.5635254393620822, -0.7031186142594976, -0.4986820665627159, -0.02063624789619187, 0.5491508114611592, 0.9891645831824971, 1.1257115766061143, 0.9024994275973105, 0.4051976067181295, -0.16942484855063858, -0.5891920016423315, -0.6789393806932337, -0.3941867060566829, 0.1535398212220258, 0.731977699765146, 1.0734584478086233, 0.9799227554943489, 0.4079375852243835, -0.5007189810805057, -1.4587420053667761, -2.133375429042419, -2.2733670288486536, -1.816656843330071, -0.9363724521148638, -0.0024105314764915737, 0.5346715680999665, 0.3017102307706989, -0.8508173827726938, -2.7679101031707534, -5.0086494547985385, -6.965586245043494, -8.050889690487562, -7.889842454723957, -6.45624991822947, -4.100771164378945, -1.4573663177304625, 0.7461531276242316, 1.9139904672927655, 1.7708399451792556, 0.44960111019206594, -1.5526973494079768, -3.5380938857201447, -4.837055147706122, -5.028101163990951, -4.074378423096341, -2.331453297386828, -0.42397987205374255], 'positive_zeros': ['1.56805630182901902516689802959352', '3.27417876410300908781703399341898', '4.38029464139908270906644098268329', '5.85456729089145680988439298557382', '6.64049152824019566675761584315113', '7.65596518636988086222855336556953', '8.221429831874525044859503343785955', '9.199478730196497258495943728875602', '9.716368540807445916115421751724406', '10.58861110218478341872506897261956'], 'prelabel': '2-3e6-243.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.9673628225219343, 'root_number': '-0.9947481244542268 - 0.10235315771776725*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.483681411261', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56805630182901902516689802959', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.27417876410300908781703399342', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38029464139908270906644098268', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '243.103', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/i/a/685/6'], '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': '2-3e6-243.103-c1-0-16', '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': '2-3e6-243.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.48368141126096714, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56805630182901902516689802959', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1987747512205213615943804195213', 'Lhash_array': ['1987747512205213615943804195213'], 'label': '2-3e6-243.103-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/i/a/685/6'}