-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2582447144493040818018557589246', 'a10': [1.9664975294901614, 1.0643718647677096], 'a2': [0.8660254037844386, -0.5], 'a3': [0.25881904510252074, -0.9659258262890683], 'a4': [0.5, -0.8660254037844386], 'a5': [1.1708508846339634, 1.9050218387073323], 'a6': [-0.25881904510252074, -0.9659258262890683], 'a7': [1.9722033576591307, -3.4159564183235487], 'a8': [0.0, -1.0], 'a9': [-0.8660254037844386, -0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, 0.5]]], [3, [[1.0, 0], [-0.25881904510252074, 0.9659258262890683]]], [5, [[1.0, 0], [-1.1708508846339634, -1.9050218387073323]]], [13, [[1.0, 0], [-0.7306850585765756, 3.5307363743520908]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.223', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '1955250998246960490837380605340', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [-0.25881904510252074, 0.9659258262890683]], [[1.0, 0], [-1.1708508846339634, -1.9050218387073323]], [[1.0, 0], [-1.9722033576591307, 3.4159564183235487], [-3.5, -6.06217782649107]], [[1.0, 0], [1.4898414478641724, -5.56016397865107], [-9.526279441628825, -5.5]], [[1.0, 0], [-0.7306850585765756, 3.5307363743520908]], [[1.0, 0], [-3.8593527471454045, 1.034110451904446], [14.722431864335457, -8.5]], [[1.0, 0], [2.0850644470070585, -0.5586913347423867], [16.454482671904334, -9.5]], [[1.0, 0], [4.182206312830559, 1.1206188041032916], [19.91858428704209, 11.5]], [[1.0, 0], [-5.045144145388551, 2.912815330440544], [14.5, -25.11473670974872]], [[1.0, 0], [2.831912836647098, -2.831912836647098], [0, -31.0]], [[1.0, 0], [1.8249412292493967, 3.1608909298871573], [-18.5, 32.04293994002423]], [[1.0, 0], [0.05773282056122802, 0.015469462646151965], [35.50704155516198, 20.5]], [[1.0, 0], [-2.763644231631584, -10.314060686493722], [-37.239092362730865, 21.5]], [[1.0, 0], [13.45561428894878, 0], [47.0, 0]], [[1.0, 0], [-4.1506205598068915, -4.1506205598068915], [0, 53.0]], [[1.0, 0], [-0.50900756689173, -1.89964210107695], [-51.09549882328188, 29.5]], [[1.0, 0], [1.4294783095337387, -2.4759290604301056], [-30.5, -52.827549630850754]], [[1.0, 0], [2.359776840450982, -1.362417794061819], [33.5, -58.023702053557386]], [[1.0, 0], [-3.3129023532341106, -12.363919902784197], [-61.48780366869514, 35.5]], [[1.0, 0], [0, -4.598153381812209], [-73.0, 0]], [[1.0, 0], [0, 2.4995352423507304], [-79.0, 0]], [[1.0, 0], [-12.012539983786889, 0], [83.0, 0]], [[1.0, 0], [8.00536929275773, 2.1450322371073414], [77.07626093681505, 44.5]], [[1.0, 0], [-8.26098205578059, -4.769480213675592], [48.5, 84.00446416709055]], [[1.0, 0], [5.668419390852424, -3.2726634611883414], [50.5, -87.4685657822283]], [[1.0, 0], [-5.761943461724443, 5.761943461724443], [0, -103.0]], [[1.0, 0], [12.048118509534465, 3.2282836249442215], [92.66471820493493, 53.5]], [[1.0, 0], [1.0778815381437858, 1.0778815381437858], [0, 109.0]], [[1.0, 0], [8.172385883010072, -2.1897841975880565], [97.86087062764156, -56.5]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-390-65.28-c1-0-9', '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/390/2/bd/b/223/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.225409380887143, 2.3209239908305515, 2.4265391328585295, 2.538472130007003, 2.6490920547434036, 2.7477258109699174, 2.821684865284317, 2.8573586718844903, 2.8413207944119003, 2.7614476947911886, 2.6080517303627926, 2.375001121395925, 2.060762730322837, 1.6692721197499316, 1.2105164140591858, 0.7007123255057651, 0.16197595826766611, -0.37858694360201556, -0.890392894364199, -1.3414548662470716, -1.7009079748691591, -1.941803597842958, -2.0439243442089756, -1.9963253398546263, -1.7992875307121843, -1.4653840830066567, -1.0194162843600445, -0.4970709255035254, 0.05771821517225984, 0.5965675091939542, 1.0712998106955762, 1.439011548419332, 1.6669888307538134, 1.7368547194541946, 1.6473480380151346, 1.4152359238084011, 1.0740465672170945, 0.6705617160263704, 0.25930473446399654, -0.10443704084159619, -0.3722502557983146, -0.5099022997969935, -0.5032585601767564, -0.3618307500784601, -0.11920943466142654, 0.1699944995034314, 0.43660219895261054, 0.6061016946045837, 0.609572125793253, 0.3948334601161258, -0.06383035612451655, -0.7589808615770061, -1.647672378076326, -2.654204754487569, -3.678033526617223, -4.606090802020057, -5.328008505708763, -5.752138914247439, -5.819950960436872, -5.516426107994411, -4.87451442774544, -3.972506686606463, -2.9242341723906082, -1.8631721834192596, -0.9226088144838458, -0.21485566878181883, 0.18714293952114425, 0.2626053657019672, 0.04763477137067683, -0.36940813676618195, -0.8616432025258832, -1.2846940790689472, -1.501786488318223, -1.408791943119812, -0.9548339238700436, -0.15458247723702556, 0.9104002072871991, 2.1021077024331953, 3.247113133824242, 4.164979445272585, 4.699354682549586, 4.7463091983079275, 4.274688476561154, 3.3344505708800605, 2.0509665382301683, 0.6057549880015337, -0.79334697122455, -1.9474849695075254, -2.701246629037882, -2.969889299424997, -2.75409146782395, -2.139184526883101, -1.2786984265813255, -0.3650708283052949, 0.4070669555344605, 0.8780330167988205, 0.953431651476718, 0.621648710072785, -0.04507801107023405, -0.9063495300520207, -1.7829917653795564, -2.4942148458027193, -2.8949277982688417, -2.905449796409321, -2.527351844077865, -1.8420210167438578, -0.9921902710651264, -0.15035374148930583, 0.5191104701697642, 0.895820618330969, 0.92931892752439, 0.6492032896487888, 0.15708956249551062, -0.3978859859134643, -0.8545285897424888, -1.0779027386004671, -0.9915954926036423, -0.5962673192456507, 0.03008796225036005, 0.7505091797195806, 1.4019517249112703, 1.8349885489351436, 1.9507751508211575, 1.7261244378636704, 1.2201781538474419, 0.5604923559005093, -0.08861196334638938, -0.5680495505440807, -0.7660461082285855, -0.6495478093387769, -0.2764219731981086, 0.21565124480321193, 0.6419995712961482, 0.8182998240424104, 0.6111557133066561, -0.020856861519489896, -1.006810223703556, -2.170322422024998, -3.263902788590697, -4.024056182606757, -4.234861761978201, -3.7848748701511297, -2.7029226420571333, -1.1626897494727155, 0.546960336205048, 2.080813134331102, 3.112833247883494, 3.4113033231454386, 2.8957820871724227, 1.6616883110960006, -0.034499813693226335, -1.8272964198259627, -3.3204453116159125, -4.173756105014158, -4.178515571449834, -3.303808085610347, -1.702766032009149, 0.32277111643987866, 2.3907714790130594, 4.12432199037704, 5.233387205761494, 5.573716471234543, 5.169443782946814, 4.195106352655498, 2.9229978847181144, 1.6503573690436817, 0.6256550793723976, -0.007060582120242337, -0.2320595170015428, -0.14920307908638836, 0.07025036165387466, 0.245641625178014, 0.24835934640054108, 0.044823362880036494, -0.29147239802578895, -0.6023697010124213, -0.6954222521024019, -0.40752540609039856, 0.337018631252767, 1.491575015988698, 2.8866391525793578, 4.26524228236654, 5.345495553775331, 5.89340022207772, 5.785637268482831, 5.044373689611209, 3.8336483209490324, 2.4175829614063575, 1.0915027146379697, 0.10492432755348811, -0.4020537094995615, -0.43100767188948474, -0.11696927164976166, 0.31777513999542206, 0.6343005125694248, 0.6512348774717183, 0.3004325711158248, -0.35270059326431075, -1.1306862036237284, -1.801193055571982, -2.152952127949686, -2.067203854862586, -1.5622371145691591, -0.7961280260992617, -0.02510131060952814, 0.4715411537141425, 0.4782921034172299, -0.08404748696389754, -1.1231451645908015, -2.3898440547134476, -3.540919140116577, -4.23346452733227, -4.224310265841325, -3.445257390150548, -2.0309429286771112, -0.28930809628300147, 1.3787454522269715, 2.588712674146258, 3.0798304462309973, 2.789089463684661, 1.8695820906807208, 0.6467188917981176, -0.47596384929429125, -1.1345391362639654, -1.1116046066555925, -0.4005950980621535, 0.792177220680711, 2.10919743712337, 3.1495774199230078, 3.5913936617385294, 3.292042519747854, 2.3361446996953124, 1.0157936959345708, -0.2520032526523612, -1.0469709333885893, -1.0705941360339069, -0.23742734267941526, 1.2946884393457199, 3.164866309550575, 4.908326601746845, 6.085419132410373, 6.402694523904623, 5.790819628397765, 4.417327942853622, 2.631912320799831, 0.8621390999878644, -0.5081012710812939, -1.2407794196917832, -1.2969414602048535, -0.8273560679973698, -0.10684241713562194, 0.5641160086521556, 0.9574705098420925, 0.9838535258586638, 0.7070256548660918, 0.30442996036538444, -0.010109655258360233], 'positive_zeros': ['2.03719159209019725168882966549692', '3.48701843591205211040111524354711', '4.83628829609406952031614747578199', '5.55235827169119234455021638056303', '6.23594271116808041835373887181295', '8.179344246988656383274327991868156', '8.517098717709533836481278996798093', '9.394871423616443413495804267125962', '10.67753946158799259015789737739590', '11.67956796682066051777785972183387'], 'prelabel': '2-390-65.28-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.32395562139325845, 'root_number': '0.52529327008613 + 0.8509212539372959*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.161977810697', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.03719159209019725168882966550', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.48701843591205211040111524355', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.83628829609406952031614747578', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.28', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bd/b/223/4'], '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': '2-390-65.28-c1-0-9', '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': '2-390-65.28-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.16197781069662923, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.03719159209019725168882966550', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2582447144493040818018557589246', 'Lhash_array': ['2582447144493040818018557589246'], 'label': '2-390-65.28-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bd/b/223/4'}