-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1049540313414593404078286947139', 'a10': [-3.7853188626880683, -6.556364593024573], 'a2': [-2.309566616655817, 0.840613502517618], 'a3': [0.0, 0.0], 'a4': [3.0953780099181034, -2.5973305464765435], 'a5': [0.5348820423888605, 3.0334668026399334], 'a6': [0.0, 0.0], 'a7': [-2.0366571837960015, -1.7089582917577828], 'a8': [-2.507841132270207, 4.34370825840306], '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': '729.163', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1240647627120690262291907298893', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.309566616655817, -0.840613502517618], [1.532088886237956, -1.2855752193730787]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5348820423888605, -3.0334668026399334], [-4.698463103929542, 1.7101007166283437]], [[1.0, 0], [2.0366571837960015, 1.7089582917577828], [1.2155372436685123, 6.893654271085456]], [[1.0, 0], [-0.5963670044604346, 3.382165350216336], [-10.336618828644992, -3.762221576582356]], [[1.0, 0], [-3.1422908981555056, -1.1437003543342148], [9.958577760546714, 8.35623892592501]], [[1.0, 0], [-1.2864089518119453, -2.228125663849713], [-8.5, 14.722431864335457]], [[1.0, 0], [-1.0483815613409906, 1.815850129960983], [-9.5, -16.454482671904334]], [[1.0, 0], [0.40940789615652556, -0.34353401466600675], [3.993908086339398, -22.650578319280786]], [[1.0, 0], [-2.3782621988526134, 0.8656166496628391], [22.215288850450364, -18.64084068090964]], [[1.0, 0], [-5.909804014378072, 4.958914368794649], [5.3830935076748405, -30.52904034337845]], [[1.0, 0], [-5.147831404849026, -8.916305541997184], [-18.5, 32.04293994002423]], [[1.0, 0], [4.590404675519445, 1.670770665125483], [31.4078221678781, 26.354291997148113]], [[1.0, 0], [-0.4760547809419095, 2.699840824297943], [-40.406782693794064, -14.706866163003756]], [[1.0, 0], [-4.334276514942988, -3.636889825109008], [8.161464350345726, 46.28596439157378]], [[1.0, 0], [6.426574211857975, 0], [53.0, 0]], [[1.0, 0], [0.2873790047630327, 1.6298073250524185], [-55.44186462636859, 20.179188456214455]], [[1.0, 0], [-11.009750321854222, -9.238277434421816], [10.592538837682751, 60.07327293374469]], [[1.0, 0], [-5.5244363422829, -2.0107303896894293], [51.32497768897153, 43.066769848998135]], [[1.0, 0], [-7.408133900946371, -12.831264305712539], [-35.5, 61.48780366869514]], [[1.0, 0], [0.9406991495700744, -1.6293387216922033], [-36.5, -63.21985447626402]], [[1.0, 0], [16.156594139510325, -5.8805193539015255], [60.51751100639927, -50.780221165236604]], [[1.0, 0], [-3.7294377471601377, 1.3574043305150933], [63.581688778875176, -53.35137160398276]], [[1.0, 0], [-2.549398168735345, 4.4156871569726714], [-44.5, -77.07626093681505]], [[1.0, 0], [1.8462062662099836, -10.470356032820973], [-91.15018421623311, -33.17595390258987]], [[1.0, 0], [4.334347840488123, 3.6369496743476235], [17.538465944359967, 99.46558305423301]], [[1.0, 0], [-1.8008253909262926, -10.212988299866238], [-96.78833994094856, 35.228074762543876]], [[1.0, 0], [-14.245739156793164, 0], [107.0, 0]], [[1.0, 0], [-5.76063657725292, 0], [109.0, 0]], [[1.0, 0], [-1.98248786982509, -11.243247413751673], [-106.18526614880764, 38.64827619580057]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-3e6-27.7-c1-0-8', '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/e/j/163/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6785971055214335, 0.6296514944702517, 0.562361221844021, 0.4757799963831376, 0.36883260847962135, 0.24167024397097844, 0.09684249143484251, -0.05988509499896399, -0.21916165148081185, -0.3681863164944032, -0.4913867212209075, -0.5716553152899342, -0.59211465927106, -0.5383182149955017, -0.400714331440491, -0.1771197933193574, 0.12512003700546528, 0.4876492842946732, 0.8806623711381617, 1.263818418687602, 1.5887073506776654, 1.8028964782920989, 1.855372456833681, 1.7029571442490348, 1.3170479666222774, 0.689850670882081, -0.16082725618619306, -1.1891376160187532, -2.321867577421878, -3.462694775790637, -4.500064304983591, -5.318226074155799, -5.810445844583302, -5.892935055093199, -5.517716059001564, -4.682525512280383, -3.436012320205645, -1.8769259537627747, -0.14669044241975526, 1.5843535125461474, 3.1357955704224083, 4.338959290958475, 5.058862341290757, 5.213225083834403, 4.785563375171172, 3.830027360393802, 2.466706731962419, 0.8674852681502561, -0.7660027450936449, -2.229420893440578, -3.34391792049809, -3.9811821947157306, -4.081370062493384, -3.6608837112043005, -2.8085159117167433, -1.6703616865448163, -0.4258070442070931, 0.7415008650345801, 1.6728296584609115, 2.258683524317211, 2.4540526480387936, 2.2819618517614617, 1.824822422079366, 1.2053774052100585, 0.5610285333630302, 0.016632730838809638, -0.338832461025227, -0.4671144742245252, -0.3841722532565574, -0.15182300756034817, 0.14038843114822339, 0.398882651820772, 0.5498115686133823, 0.5573301984805521, 0.43199510511015504, 0.22714865339918291, 0.023969830247378084, -0.091352175117443, -0.05279272895351622, 0.1643521109771642, 0.5320254150310895, 0.971274573184271, 1.367885478944726, 1.5988022528935915, 1.563406025228815, 1.212050621792878, 0.5643545276535176, -0.2882618460652494, -1.1977746208039155, -1.990159850089999, -2.5049926185862805, -2.6348287618844024, -2.354436964120455, -1.7316713296022925, -0.9157137854141603, -0.10377196018272328, 0.5071328853580611, 0.7722900916545153, 0.642360338623454, 0.18550895384507401, -0.4190611114892247, -0.9173620813857389, -1.0404853620515127, -0.5754304858151991, 0.5696467630887535, 2.3224611341916117, 4.438651866630232, 6.534234418288903, 8.154550567847231, 8.866790065192925, 8.35659182875335, 6.506890863723691, 3.4398924122938865, -0.4895317237854853, -4.750151659268797, -8.730168873943647, -11.852839171278164, -13.687134760499182, -14.029176854610652, -12.936420646960059, -10.707191285736917, -7.810674111044297, -4.783844859995584, -2.1192902917939547, -0.16955211498199865, 0.910908803845346, 1.1746519800921662, 0.8418938424660216, 0.22542546553696535, -0.3592982665286068, -0.6752807602384495, -0.6161704183590742, -0.21800321790505245, 0.36961119240613166, 0.9419537273181583, 1.308768696501822, 1.3541927091813695, 1.070008593157681, 0.5536752665431824, -0.02669310120231836, -0.4884107942709971, -0.6933397720235837, -0.5915004334555841, -0.23574435847065264, 0.23677011321587033, 0.6501339005475868, 0.84762756945414, 0.7434880020805071, 0.3518503707626486, -0.2166005568927039, -0.7894673098226895, -1.1880120316575418, -1.2853105669596783, -1.0482289349449117, -0.5491746833832122, 0.05681535067199402, 0.5827591206597484, 0.8718775091485642, 0.8505493557608597, 0.5537664713304593, 0.11334966862044119, -0.2885680126844973, -0.4862384715503864, -0.39479671969045066, -0.04943529474229667, 0.3968298844687184, 0.719876151501239, 0.7036642062151778, 0.22758607701920155, -0.667589872092332, -1.7606271802067093, -2.690142303840044, -3.048685915556967, -2.5068316975986957, -0.9313381441684492, 1.5404568924115252, 4.4980517602957715, 7.3356984102213625, 9.395893144917961, 10.14258807814591, 9.316621847745578, 7.027624857593096, 3.7520858404767075, 0.2324957025497036, -2.699526279206428, -4.330659214337488, -4.248155459932272, -2.4467796925835064, 0.6696625177293559, 4.393156677817187, 7.893879315695224, 10.429747883738195, 11.525616628718076, 11.07418567174737, 9.334035484186998, 6.830274471955624, 4.191033028833213, 1.9701638964739105, 0.5080613386478847, -0.13160406558670296, -0.13646166016936265, 0.15358774750412968, 0.38202401715040024, 0.3017737252609208, -0.1485799145958285, -0.8400517938757379, -1.516715118971809, -1.9014147870880864, -1.8047121508835144, -1.198652144484517, -0.23060731795056313, 0.825861870178496, 1.664134683205802, 2.047837040405569, 1.8879121976934032, 1.2672654187692007, 0.40597821737136675, -0.4187322390506245, -0.9680265547130502, -1.1180933502379184, -0.8915441284528721, -0.4345144532459121, 0.04929200140915813, 0.38070680028742254, 0.47116417282358597, 0.34759874741786284, 0.1277157340732214, -0.0428839846127947, -0.06472690241617349, 0.06231224513477361, 0.2307247776104137, 0.2682371791915365, 0.016747287784894413, -0.5841472522116882, -1.4451673887426995, -2.333395735245185, -2.941652832905313, -3.0013017170650524, -2.3988530568354745, -1.2506137745619672, 0.09940846036985419, 1.1677835911663197, 1.4841715525840355, 0.7599199407735969, -0.9862766162067372, -3.3949962852565676, -5.846005514418709, -7.634344809112524, -8.190460797108532, -7.273070203160342, -5.067858866278596, -2.153017068962305, 0.6644371872386543, 2.5937469613172768, 3.109515698696047, 2.122901978386824, 0.016119500711838895], 'positive_zeros': ['0.827941321706180592468378860994832', '1.95172902905279583450110084672196', '3.22846924641458681058021220027176', '4.76041583772071595565836404731903', '5.94069746172615853232536741140886', '7.04370181594678233216808848010041', '8.129546232797252600093077810214647', '8.690517327928718673868271329806230', '9.518049377496882699348167625960783', '9.791664719901709372373678373841970'], 'prelabel': '2-3e6-27.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.37037037037037035, 'root_number': '0.3960797660391569 - 0.918216106880274*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.185185185185', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.827941321706180592468378860995', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.95172902905279583450110084672', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.22846924641458681058021220027', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.7', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/j/163/1'], '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': '2-3e6-27.7-c1-0-8', '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': '2-3e6-27.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.18518518518518517, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.827941321706180592468378860995', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1049540313414593404078286947139', 'Lhash_array': ['1049540313414593404078286947139'], 'label': '2-3e6-27.7-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/j/163/1'}