-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '915694744918356029845992778225', 'a10': [-38.29552760896586, -18.442154110320924], 'a2': [1.8879375651631616, 2.3673988266981008], 'a3': [-5.8353311839508715, 2.8101473905268257], 'a4': [-0.26010148304682296, 1.139579055838487], 'a5': [-12.647065963183096, 6.090505970253569], 'a6': [-17.669480582530813, -8.509173376059305], 'a7': [-3.941074531545209, 18.096075031254863], 'a8': [18.636297125005854, -8.974767683958536], 'a9': [9.319937019718946, -11.686831372241903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8910935902812915, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [3.941074531545209, -18.096075031254863]]]], 'bad_primes': [7], 'central_character': '49.8', 'coefficient_field': 'CDF', 'conductor': 49, 'conductor_radical': 7, 'conjugate': '5067600629840507738594936257276', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.8879375651631616, -2.3673988266981008], [-1.7801674716505151, 7.799423297454589]], [[1.0, 0], [5.8353311839508715, -2.8101473905268257], [16.834224650185806, -21.109450026636804]], [[1.0, 0], [12.647065963183096, -6.090505970253569], [77.9362252323417, -97.72893530850372]], [[1.0, 0], [3.941074531545209, -18.096075031254863]], [[1.0, 0], [-1.1184202826148024, -1.4024546752364744], [-296.1753630958545, 1297.6290511140073]], [[1.0, 0], [-19.64021146629482, -24.628046202041958], [-488.87849190202274, 2141.9166230634664]], [[1.0, 0], [-3.961387804706063, -17.355973989138594], [-4426.460048004586, 2131.6708102845632]], [[1.0, 0], [-34.80252724864538, 0], [6859.0, 0]], [[1.0, 0], [44.359496149677206, -194.35165131534458], [-10962.088215768734, -5279.06345384333]], [[1.0, 0], [61.33174788977425, 268.7119447933758], [-21973.7297192721, 10581.990513338125]], [[1.0, 0], [-116.66710211725876, 0], [29791.0, 0]], [[1.0, 0], [-7.15720452707436, -31.35776190840896], [-45636.77606586124, 21977.513037521672]], [[1.0, 0], [294.21831562906414, -141.6880731952597], [42971.54063390577, -53884.60760317908]], [[1.0, 0], [-405.9065435042369, -195.47428895953442], [49571.803676382326, 62161.07567658565]], [[1.0, 0], [227.38573620906863, 285.1326945564062], [-23102.79092614643, 101219.94062645348]], [[1.0, 0], [91.3404991818452, -400.18887473519413], [-134133.54214670844, -64595.3094286047]], [[1.0, 0], [-753.6423536919996, -362.9350291964334], [128051.71201594484, 160571.7680378015]], [[1.0, 0], [-1.606003060356582, -7.036359153959192], [-204502.814605359, 98483.36498864245]], [[1.0, 0], [-671.0843320904611, 0], [300763.0, 0]], [[1.0, 0], [159.6897874238483, -699.6466727056616], [-322466.66847982275, -155291.76295130435]], [[1.0, 0], [-341.93107283502513, 428.76800354957874], [-86564.42616488357, -379263.53161323647]], [[1.0, 0], [-195.32267927537396, 0], [493039.0, 0]], [[1.0, 0], [-801.5968567221468, 1005.1706651246652], [-127234.57726407914, -557451.1061227084]], [[1.0, 0], [378.66099044061787, -474.825863432611], [-156870.36029024902, -687293.955322908]], [[1.0, 0], [-665.7672022768272, 0], [912673.0, 0]], [[1.0, 0], [361.7589973230893, -174.21395123606052], [642382.166344855, -805521.7582182935]], [[1.0, 0], [667.6392812097762, -321.5181323495304], [681304.1407156884, -854328.3703428428]], [[1.0, 0], [153.77655213468364, -192.82969723941426], [-272597.7124966453, -1194328.6143229578]], [[1.0, 0], [277.23988157487474, 347.64781551319794], [-288171.0625805119, 1262559.9191849148]], [[1.0, 0], [430.4781506291637, -539.8025271193624], [-321074.7880427642, -1406720.5597034167]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-7e2-49.8-c3-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/49/4/e/a/8/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9731712144917091, 0.8045788107791964, 0.6372582588834237, 0.47016007700492096, 0.3023461860127826, 0.13309425355759896, -0.03800629888673262, -0.21096981785395183, -0.3853442474013579, -0.5601577988363189, -0.7338849457950807, -0.9044343267702908, -1.0691612639045405, -1.2249076250582804, -1.3680715352254158, -1.4947088807364806, -1.6006675805986477, -1.6817541997794996, -1.733930665882687, -1.7535366798745564, -1.7375309785851336, -1.6837420446313174, -1.5911163365379768, -1.459949827242846, -1.2920868150305842, -1.091068841293191, -0.8622163453816736, -0.6126266179408413, -0.35107384812056264, -0.08780070021869421, 0.16580408130379723, 0.39764114161412734, 0.5954406404036002, 0.7473903026044015, 0.8428260353116706, 0.8729513816002604, 0.8315446451225258, 0.7156067412547337, 0.5258994410385246, 0.2673233477140596, -0.050911765116567566, -0.4153643576176117, -0.8087150227878026, -1.2104104019066269, -1.5975920797235477, -1.946284453981607, -2.232793458499516, -2.435246320457176, -2.5351830295934414, -2.5190947665478545, -2.3797950080418535, -2.1175070116533212, -1.7405581067987992, -1.2655873482182398, -0.7171985896698988, -0.12702507096013335, 0.4677875051721997, 1.0266272059520456, 1.5078928685742559, 1.8717596107678454, 2.08305351516351, 2.1140296384210573, 1.9468350453363563, 1.575442852410999, 1.0068657841511353, 0.26149853499906095, -0.6275043234862954, -1.615837362350649, -2.650583494180475, -3.6735451791099583, -4.625152938861433, -5.4486722445833475, -6.09438490339664, -6.523401306968322, -6.7107693907789, -6.647586538692054, -6.341890774456311, -5.81820322123612, -5.1157078993548915, -4.285177922067524, -3.3848777558608565, -2.475777409631831, -1.6164946126740802, -0.8584253242260198, -0.24152425795894644, 0.20884763677751655, 0.48368118257756504, 0.5904826821474877, 0.5517988367123957, 0.4022265707155154, 0.1841953726607887, -0.057048592760037514, -0.27872486697984755, -0.4454863391403572, -0.5335032988060044, -0.5331719153724939, -0.45009195240847755, -0.30414350400002166, -0.12670754493500105, 0.04370285941087847, 0.16693021691600265, 0.2071486716292998, 0.1386034565445196, -0.04962466623011483, -0.3504935289433228, -0.7380156936874496, -1.16868821426072, -1.585327295381867, -1.9230011045109092, -2.116473554898533, -2.108344675847511, -1.8569308883588607, -1.3428945549041178, -0.5737182377248449, 0.41467727575801444, 1.5595682625999476, 2.77634076027346, 3.9663045927196348, 5.026653572973425, 5.86150762371627, 6.392776719971827, 6.569535757585956, 6.374709046925356, 5.828128973861258, 4.985431025094401, 3.932733949373913, 2.7775723487703323, 1.6370349524939185, 0.624451145038868, -0.16379418281340744, -0.6596901840876825, -0.8318054646267858, -0.6891548959120365, -0.28012588105322755, 0.31352679106725007, 0.9869746748517008, 1.6256815941760647, 2.1201906313869467, 2.380448795965501, 2.3477954796444402, 2.003000205471405, 1.3692189283982075, 0.5093888427094482, -0.4816834935004894, -1.4895647155393115, -2.395184201362888, -3.090580637623639, -3.4932737558655593, -3.5572800337688117, -3.279222006577364, -2.6986392645779107, -1.8924081992599908, -0.9640068904459407, -0.02910290360726871, 0.8005142201887877, 1.432371474500596, 1.8059020299974928, 1.9003561944307263, 1.7368698533960298, 1.374376125052587, 0.8999565204402525, 0.41506405250015277, 0.019684431994678515, -0.203168152263865, -0.20025442660303927, 0.043759432257935146, 0.5041109369928546, 1.1200436036434636, 1.8045729263112518, 2.458387104228608, 2.9856822752000216, 3.309400997736731, 3.3834130678973127, 3.199647657109364, 2.788988679478209, 2.215758481979192, 1.5666774223698756, 0.9361244514055541, 0.41017719270795483, 0.05216179259651979, -0.10776151364954538, -0.07709166732830221, 0.1013438997669066, 0.3582771192918613, 0.6120140001896915, 0.7851880321738413, 0.8212847044849122, 0.6978841143762249, 0.434013173394599, 0.08992031380674716, -0.24115340971294832, -0.4482341556523803, -0.42263171572279495, -0.07946284963402755, 0.6230328860220077, 1.6699479498609948, 2.9847230855201863, 4.434223542033802, 5.843756092270517, 7.0202240707501256, 7.78015062210434, 7.97830845184799, 7.532366838497802, 6.439388107275491, 4.781137290644773, 2.716849498592579, 0.4640694787667261, -1.7298818271090082, -3.6216733761672795, -5.005867751275595, -5.7437218466523134, -5.782353557694637, -5.16121119121113, -4.0047791742274095, -2.502655313273994, -0.8801747915137629, 0.6357120647183252, 1.8498430565014996, 2.6262155838020966, 2.9050579077944927, 2.7070948172791995, 2.1246831999025364, 1.3017148008809438, 0.4060586459349163, -0.4004848454175385, -0.9894330065508827, -1.2854150126204729, -1.2753031348639114, -1.0054817939551433, -0.568252441264397, -0.08035368230519879, 0.34202502690861225, 0.6068005529026389, 0.6635752535237709, 0.511944047223969, 0.19911659539750814, -0.19241364036179537, -0.564430842980701, -0.825619910420043, -0.9124693644880141, -0.8040213740430749, -0.5272877590752565, -0.1520655775434739, 0.22391192022536754, 0.49650407970121246, 0.5789097364184227, 0.4225801212219186, 0.0306846240185125, -0.5390763991442937, -1.183400541019687, -1.7727261957741878, -2.1774293527895634, -2.2957287851211525, -2.0775620994501534, -1.5392543348869165, -0.7654413396859436, 0.10285920287547301], 'positive_zeros': ['0.72235578538241783759695500100516', '3.66744826637582117436631560894519', '4.98130365391546669877365438641961', '6.90149556713670426348559776895107', '8.163663568533916155584562340106684', '10.56099652145871230109118189775029', '11.34530476694917110731729148948630', '12.34072261043912725198630574049679', '12.84861920644446549030998567341804', '14.20043683791754679431528162349064'], 'prelabel': '2-7e2-49.8-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.700321613778197, 'root_angle': -0.9043010585922612, 'root_number': '-0.9551450605766628 - 0.29613833466135914*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.452150529296', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.72235578538241783759695500101', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.66744826637582117436631560895', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.98130365391546669877365438642', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.8910935902812915, 'bad_primes': [7], 'central_character': '49.8', 'conductor': 49, 'conductor_radical': 7, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/4/e/a/8/10'], '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': '2-7e2-49.8-c3-0-2', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-7e2-49.8-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.700321613778197, 'root_angle': -0.4521505292961306, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.72235578538241783759695500101', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '915694744918356029845992778225', 'Lhash_array': ['915694744918356029845992778225'], 'label': '2-7e2-49.8-c3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/4/e/a/8/10'}