-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1663070528514924405816899980994', 'a10': [-3.369803996897514, -1.9455572447250564], 'a2': [-0.8660254037844386, -0.5], 'a3': [0, 0], 'a4': [0.5, 0.8660254037844386], 'a5': [3.891114489450113, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, -1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.1284163748308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, 0.5]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '2646.2285', 'coefficient_field': 'CDF', 'conductor': 2646, 'conductor_radical': 42, 'conjugate': '1043049668819825100675433411127', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.891114489450113, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.9446195473019814], [-11.0, 0]], [[1.0, 0], [-2.4668677372776555, -1.4242467521724573], [6.5, 11.258330249197702]], [[1.0, 0], [-0.3710584631965526, 0.6426921108348554], [-8.5, -14.722431864335457]], [[1.0, 0], [1.5456283704547138, -0.8923689557491516], [9.5, -16.454482671904334]], [[1.0, 0], [0, 6.2531100448542185], [-23.0, 0]], [[1.0, 0], [-2.500788584724784, 1.4438309625771972], [14.5, -25.11473670974872]], [[1.0, 0], [3.0412517220942243, -1.7558675004245132], [15.5, -26.846787517317598]], [[1.0, 0], [1.500788584724784, 2.5994420801627145], [-18.5, 32.04293994002423]], [[1.0, 0], [-5.247053115604284, 9.088162586239193], [-20.5, -35.50704155516198]], [[1.0, 0], [-0.47152118892620665, -0.8166986560654733], [-21.5, 37.239092362730865]], [[1.0, 0], [1.0926260039204017, -1.892483752461087], [-23.5, -40.703193977868615]], [[1.0, 0], [0, 0], [26.5, 45.89934640057525]], [[1.0, 0], [0.010567303870706729, 0.018303107203083313], [-29.5, 51.09549882328188]], [[1.0, 0], [-2.138315462474366, -1.2345570078719141], [30.5, 52.827549630850754]], [[1.0, 0], [6.724631233780425, 11.64740295907228], [-33.5, 58.023702053557386]], [[1.0, 0], [0, -1.9430423778524133], [-71.0, 0]], [[1.0, 0], [4.204432130499085, 2.4274300223331586], [36.5, 63.21985447626402]], [[1.0, 0], [1.818064524874872, -3.148980128521849], [-39.5, -68.41600689897065]], [[1.0, 0], [-4.0299770199528595, -6.980124951893368], [-41.5, 71.88010851410841]], [[1.0, 0], [4.633231415843218, 8.024992215464739], [-44.5, 77.07626093681505]], [[1.0, 0], [-16.298253858789025, 9.409801252692699], [48.5, -84.00446416709055]], [[1.0, 0], [-8.281582668728818, 0], [101.0, 0]], [[1.0, 0], [0, -17.04869181058666], [-103.0, 0]], [[1.0, 0], [12.416140736228188, -7.1684621963576225], [53.5, -92.66471820493493]], [[1.0, 0], [5.639983385283829, -9.768737777155907], [-54.5, -94.39676901250381]], [[1.0, 0], [-8.515005532306288, -4.916140736228188], [56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 30, 'label': '2-2646-63.59-c1-0-30', 'leading_term': '1.936322365036661109520745496152955248713919987485911505', '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/2646/2/t/a/2285/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.9363223650366612, 2.00420583499324, 2.06142307487387, 2.107368964849172, 2.1412204446220007, 2.1619620650034173, 2.1684341751798337, 2.1594002637683674, 2.1336289458158983, 2.0899855949548702, 2.027528561059805, 1.9456051436831276, 1.8439428686400745, 1.7227320335653722, 1.5826958895945615, 1.4251451949953182, 1.2520142274784891, 1.065875706186092, 0.8699324873700613, 0.6679843907926304, 0.4643691090749156, 0.2638768603949978, 0.07163926494548324, -0.10700615523118145, -0.2666734581081732, -0.4021043111630145, -0.508358091240928, -0.5810105760678141, -0.6163548385767167, -0.611597187992183, -0.5650404283822312, -0.476246374356821, -0.3461695175761985, -0.17725401159135834, 0.026513239274109333, 0.25959962697196026, 0.5149789349802998, 0.78424173171387, 1.0577653507399296, 1.3249425388061788, 1.5744654678072716, 1.7946593287665003, 1.9738572514326884, 2.1008059284575222, 2.165089180190421, 2.157554887768894, 2.070729357135249, 1.8992023540629073, 1.6399658543363747, 1.2926900475823875, 0.8599213562681117, 0.34718919198283743, -0.2369891543533714, -0.8812127613266234, -1.571413844474082, -2.2911860917502853, -3.022219006238597, -3.7448279874092867, -4.438565278018869, -5.082892615868753, -5.657892672671726, -6.144993342666541, -6.527676849174227, -6.792144626668643, -6.927909128766252, -6.928285180657255, -6.790756254853079, -6.517195058882673, -6.113922977824303, -5.591599046970435, -4.964936016499245, -4.252248436096041, -3.4748452177283697, -2.6562864861350852, -1.8215313433298772, -0.9960091041070279, -0.20465127486298645, 0.529075241221254, 1.1840917555105008, 1.7425466867840818, 2.190530593618174, 2.5186325486039443, 2.722309234489445, 2.8020459372170055, 2.7632977136485906, 2.6162090311475024, 2.3751206542193404, 2.0578829858661813, 1.6850049314328444, 1.278676117736237, 0.8617074791234376, 0.4564403831739591, 0.08367726587196037, -0.23831305863652025, -0.4946647664381092, -0.6746136265975801, -0.77198711178801, -0.7854582078996162, -0.7185467862191597, -0.5793652703870048, -0.3801187480899089, -0.13638294079132487, 0.1338041699916772, 0.4109904588624383, 0.6754423396059168, 0.9083010399851592, 1.0926988822547363, 1.2147728124930766, 1.264516758478393, 1.2364221120308703, 1.1298664031939956, 0.9492235499996398, 0.703684254202033, 0.4067913635660741, 0.07571143774758261, -0.2697206017622381, -0.6081329147011328, -0.917862075422545, -1.1782420189239518, -1.3708621254553186, -1.4807200169117334, -1.4971990555510652, -1.4148091941235186, -1.2336423401511003, -0.9595091360621719, -0.6037421766315412, -0.18267016963716654, 0.28321273728677404, 0.7703394742503856, 1.2533647700480224, 1.7065889704681716, 2.1054284813741266, 2.4278457837967258, 2.655652589173928, 2.7756056303248675, 2.7802255968186147, 2.6682852772361954, 2.4449322197580314, 2.121433063092233, 1.7145498218234976, 1.2455814128019105, 0.7391251268053177, 0.2216311844569599, -0.28016228167688545, -0.7408175203979736, -1.1377094292878143, -1.4523657892960289, -1.6715489972189304, -1.7880081463990933, -1.8008505558691288, -1.7155058292784748, -1.5432817584048333, -1.3005382016018103, -1.007530707815065, -0.6869983911591578, -0.3625888016174618, -0.05722494979262259, 0.20847475554105666, 0.41761466379417295, 0.5581783460403601, 0.6238398003146812, 0.6143681553802737, 0.5355916949632263, 0.3989171112697766, 0.22043102335540712, 0.019640848300656537, -0.18206101553229104, -0.3631039978128318, -0.5034965240034986, -0.5865060114402321, -0.6001360390239301, -0.5382858264732203, -0.40149639391008185, -0.19721437714032483, 0.060463175497393946, 0.3515636816769415, 0.6514969577323269, 0.9327236200920597, 1.1667292914820406, 1.3261741414172306, 1.3870697855590635, 1.3308278821251411, 1.1460277763301119, 0.8297644161658588, 0.3884618985739159, -0.16192893261330776, -0.7963904357480003, -1.4819529319112177, -2.1794158080477186, -2.8455825146883846, -3.4358779207997743, -3.907185184682993, -4.22071822682879, -4.344736854292218, -4.256915605604945, -3.9461945953591298, -3.413970251251118, -2.6745241710317256, -1.7546368956359955, -0.6923870578742104, 0.46480846694769085, 1.662804911237331, 2.843835140455793, 3.949917667056787, 4.926349424989116, 5.725054913954713, 6.307568137327373, 6.647444083689462, 6.731931277606549, 6.562784040479122, 6.156149522746874, 5.541526529771715, 4.7598564224049795, 3.860866501207461, 2.8998389807747964, 1.9340200689569196, 1.0189106555748244, 0.20469052860001383, -0.4669791366737082, -0.9655547914676239, -1.2734311856421217, -1.386857427510542, -1.3158852662047489, -1.0833546523294544, -0.7229901095922802, -0.2767452285783936, 0.20841301339999768, 0.6840474652821178, 1.1038645666098492, 1.4271359024550334, 1.621678191564988, 1.6661741475772007, 1.5516646803233782, 1.282103762514657, 0.8739365776868303, 0.3547342041174583, -0.23901132092025895, -0.8647644804115839, -1.4772781679490459, -2.0321269309182184, -2.489172492625047, -2.815696750944372, -2.988961859420996, -2.9979998553458773, -2.8444924936616016, -2.5426711533369866, -2.118241690592198, -1.6064142065828566, -1.0491870953125781, -0.4920930404827679, 0.019342758587742398, 0.44315835736944703, 0.744248654439519, 0.8971396568007813, 0.8880254412081645, 0.7159062082839035, 0.39273514149598315], 'positive_zeros': ['1.31193132257066979281342803833909', '1.98505041682540053778321448037142', '3.02389206454463496470898039212969', '4.46894029643891157811209139768824', '5.40488662847417654745005540304025', '5.94800049423874703560853248000444', '6.69261515115478587822429676228059', '7.40630440162840917049432950555852', '8.345786725413239434302239792432863', '9.152408421795020274813558105588056'], 'prelabel': '2-2646-63.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.596565715273828, 'root_angle': 0.3504377740266223, 'root_number': '0.4527646626678014667292343713163541502186948077812539777 + 0.8916300579496588196099008560428946489324333209198170065*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17521888701331115', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.31193132257066979281342803834', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.98505041682540053778321448037', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.02389206454463496470898039213', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 21.1284163748308, 'bad_primes': [2, 3, 7], 'central_character': '63.59', 'conductor': 2646, 'conductor_radical': 42, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2646/2/t/a/2285/4'], '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': '2-2646-63.59-c1-0-30', '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': '2-2646-63.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.596565715273828, 'root_angle': 0.17521888701331115, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31193132257066979281342803834', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1663070528514924405816899980994', 'Lhash_array': ['1663070528514924405816899980994'], 'label': '2-2646-63.59-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2646/2/t/a/2285/4'}