-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3684404216355200974927269051512', 'a10': [0.0, 0.0], 'a2': [0.266044443118978, -1.508813013470978], 'a3': [0.0, 0.0], 'a4': [-1.2660444431189781, -0.46080249255343814], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.766044443118978, -0.6427876096865394], 'a8': [-0.266044443118978, 0.46080249255343814], 'a9': [-0.9396926207859084, 0.3420201433256687], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.12925783827194762, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-0.766044443118978, 0.6427876096865394]]], [37, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [7, 37], 'central_character': '259.181', 'coefficient_field': 'CDF', 'conductor': 259, 'conductor_radical': 259, 'conjugate': '2276963161149157593577417141129', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.266044443118978, 1.508813013470978], [-0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [0, 0], [0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [0, 0], [-0.17364817766693036, 0.984807753012208]], [[1.0, 0], [-0.766044443118978, 0.6427876096865394]], [[1.0, 0], [0.766044443118978, -1.3268278963378768], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.766044443118978, -0.6427876096865394]], [[1.0, 0], [0, 0], [-0.766044443118978, 0.6427876096865394]], [[1.0, 0], [0, 0], [0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [-0.9396926207859084, -1.6275953626987474], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.17364817766693036, -0.3007674663608706], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.766044443118978, -0.6427876096865394]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [1.4396926207859084, 1.2080455471101075], [0.17364817766693036, 0.984807753012208]], [[1.0, 0], [0, 0], [-0.17364817766693036, -0.984807753012208]], [[1.0, 0], [0, 0], [-0.766044443118978, -0.6427876096865394]], [[1.0, 0], [0.766044443118978, -0.6427876096865394], [0.17364817766693036, -0.984807753012208]], [[1.0, 0], [0.17364817766693036, 0.984807753012208], [-0.9396926207859084, 0.3420201433256687]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.4396926207859084, -1.2080455471101075], [0.17364817766693036, -0.984807753012208]], [[1.0, 0], [0, 0], [-0.766044443118978, 0.6427876096865394]], [[1.0, 0], [0, 0], [-0.17364817766693036, -0.984807753012208]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.32635182233306964, 0.11878234922776941], [0.766044443118978, 0.6427876096865394]], [[1.0, 0], [-0.060307379214091614, 0.3420201433256687], [-0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [-0.3472963553338607, 1.969615506024416], [-0.9396926207859084, -0.3420201433256687]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-259-259.181-c0-0-0', 'leading_term': '0.81691728445700321880234826354661', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/259/1/bi/a/181/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.07421875', 'prec': 34}, 'plot_values': [0.8169172844570032, 0.8558994069196061, 0.9145924666455969, 0.9932717419343371, 1.0913226322337928, 1.2075931509568274, 1.340683292393325, 1.4891090278159278, 1.6513567013415325, 1.8258694396476787, 2.0110019561975485, 2.204966955402781, 2.4057855510390422, 2.611247539142134, 2.8188839569865385, 3.025952792445304, 3.229438064325168, 3.4260622529041886, 3.612311954590681, 3.784476539741452, 3.9386994545704357, 4.071041608605213, 4.177556027564196, 4.2543726358466385, 4.297791675814003, 4.304383888348231, 4.271095188429417, 4.195353189736509, 4.075172583555164, 3.909256080054974, 3.6970873946292797, 3.439012628021349, 3.1363063643526776, 2.791218911454637, 2.4070013453054377, 1.9879054029256757, 1.5391557988091709, 1.066893216140827, 0.5780870366365307, 0.08041780608394282, -0.4178695360229212, -0.9081395342640001, -1.3815639406327898, -1.8293388959014198, -2.2429161087287657, -2.614241600471019, -2.9359947619850457, -3.2018198452325506, -3.406541632061197, -3.5463569244421276, -3.618993716028674, -3.623830455316442, -3.5619687048357878, -3.436253733654488, -3.251239131787504, -3.0130933688314014, -2.7294482833562212, -2.4091917173143096, -2.0622088204602544, -1.6990788518574704, -1.3307364992980901, -0.9681087190409795, -0.6217397641133215, -0.3014183211173865, -0.01582142490445307, 0.22781000510850072, 0.423949616251928, 0.5690047791543952, 0.6614649303955029, 0.7019699692438367, 0.6932925244682352, 0.640231321476702, 0.549416636153028, 0.4290327690706124, 0.28846644055151827, 0.13789380725679226, -0.01217775768697641, -0.15139408611337887, -0.2700436353348337, -0.3595294175261026, -0.41280066199184434, -0.4247222318342785, -0.39236173007886527, -0.31517723872840986, -0.19509265919461874, -0.03645252825510265, 0.15414622068127415, 0.36814203563166337, 0.5954063328634931, 0.8247350861442603, 1.044412999138939, 1.2428240133627728, 1.4090781631832918, 1.5336224019766813, 1.608802202101171, 1.6293416191262555, 1.5927121690265997, 1.4993652657697847, 1.3528089795461897, 1.1595172801218645, 0.9286684117552317, 0.6717182119365135, 0.4018235779519444, 0.1331404018678533, -0.11997138334162584, -0.3437959859182271, -0.526118262443423, -0.657040582300621, -0.7297115032214422, -0.7409198071000114, -0.6915122647417066, -0.5866009413254955, -0.4355356658265048, -0.2516290615233831, -0.05163472758861725, 0.1450068851747671, 0.3171263920213641, 0.44294547893982233, 0.5013056660205517, 0.47294320763193376, 0.3417412112151166, 0.09588729494809835, -0.27113375592534955, -0.7597776704687914, -1.363964841454882, -2.070934162427203, -2.8614536865583906, -3.710396726145411, -4.587671995586513, -5.4594759532410535, -6.289815773090902, -7.042233551746104, -7.68164755945309, -8.176215588274982, -8.499119566184428, -8.630170179329566, -8.557135572092491, -8.276709247359216, -7.795048699551214, -7.127837377032719, -6.299847274943701, -5.344006526036441, -4.3000043067836256, -3.2124926090269623, -2.1289693142410715, -1.0974479866476259, -0.1640354779076641, 0.6294523257642697, 1.2477042786209198, 1.6638305566702942, 1.8608685176524908, 1.8327845519256332, 1.5849049615005728, 1.1337399408309539, 0.5061987682748715, -0.2617706060716559, -1.1270503617456369, -2.0416318988823825, -2.955181347254492, -3.817748678292653, -4.5824668324689135, -5.208085545018858, -5.661192196556092, -5.917988780212121, -5.965519127974956, -5.8022724916027, -5.438126567313861, -4.893632857971145, -4.198687415746565, -3.3906679553478987, -2.5121516098390377, -1.6083540036282533, -0.7244480280459485, 0.09707155514128286, 0.8188144349867774, 1.4105622017328372, 1.8508504059990283, 2.1279703840302266, 2.2403340734752266, 2.196187021449641, 2.0126978866453133, 1.7144940501861505, 1.3317496422832538, 0.8979618049818792, 0.44757124646348156, 0.013592617008797164, -0.3745817978992062, -0.6930550628509387, -0.9248493322424703, -1.0607874558812362, -1.0997792517609637, -1.0485027793385353, -0.9205151906982251, -0.7348694675506537, -0.5143494830539509, -0.28346364269102386, -0.06635471987981686, 0.11521097955513561, 0.24361883606393167, 0.30680803841411475, 0.29919258457411013, 0.22203109291415252, 0.08321898048712147, -0.10347745456113275, -0.3196807268635759, -0.544051251819446, -0.7541893209576374, -0.9286319279906093, -1.0487773483190783, -1.1005747111227326, -1.0758334210711915, -0.9730370113199455, -0.7975856732072724, -0.5614382974361593, -0.2821747353176884, 0.018451847543780944, 0.31635823581934397, 0.5872198438417857, 0.8086303591823013, 0.9621476190888274, 1.0350458974158163, 1.0216148934365459, 0.9238798013687755, 0.7516624846173009, 0.5219575404595123, 0.2576547009549935, -0.01430410120931518, -0.265193332178647, -0.4670171189564704, -0.5950586370318177, -0.6302461314598472, -0.5611232090306817, -0.3852363165127547, -0.10979430752250662, 0.24848917454263297, 0.6643942316748637, 1.1059877273876493, 1.5370951963069, 1.9202737127076381, 2.220057679073015, 2.4062162692356495, 2.456748331668898, 2.360349804151095, 2.118120233965039, 1.7443271307556196, 1.2661161373823901, 0.7221363849497648, 0.16013771539108956, -0.3663171970004841, -0.8018044992764385, -1.0933697109827551, -1.1949092163826376, -1.0712564057265561, -0.7016349880132414, -0.08217824535757987, 0.772725257230421, 1.8304158275516098], 'positive_zeros': ['2.90648244531407647026125572368246', '4.75444078955722594782466586453779', '5.63446707641871008442846432134968', '6.32369882085248349778769295928048', '7.68274010415847466723106456206381', '8.479994183587036104658490220723993', '9.002440935745606874020215538541869', '10.85015582352279559529404503395711', '11.47985130075925360745009186684849', '12.83064793335296590416286406616785'], 'prelabel': '2-259-259.181-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.35952446129845966, 'root_angle': 0.6224783321846376, 'root_number': '-0.37535247788354456926709536255636 + 0.92688214857482457880951714038894*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3112391660923188', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.90648244531407647026125572368', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.75444078955722594782466586454', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.63446707641871008442846432135', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.12925783827194762, 'bad_primes': [7, 37], 'central_character': '259.181', 'conductor': 259, 'conductor_radical': 259, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/259/1/bi/a/181/1'], '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': '2-259-259.181-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-259-259.181-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.35952446129845966, 'root_angle': 0.3112391660923188, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.90648244531407647026125572368', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3684404216355200974927269051512', 'Lhash_array': ['3684404216355200974927269051512'], 'label': '2-259-259.181-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/259/1/bi/a/181/1'}