-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2029858159137477030214229089979', 'a10': [0.0, 0.0], 'a2': [-0.20777831824803336, -0.036636923513358274], 'a3': [-0.051355851720933224, 0.061203520789157716], 'a4': [-1.8375556762023595, -0.6688155699445626], 'a5': [0.0, 0.0], 'a6': [0.012912941212671478, -0.010835244208966538], 'a7': [1.4611820265430262, -0.843613836359659], 'a8': [0.7227352563797171, 0.4172713948236629], 'a9': [0.5198360855497847, 2.94813694115973], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-4.349329933084061, 0.28866785962243513]]]], 'bad_primes': [5, 19], 'central_character': '475.74', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '867632918362155331443934717901', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.20777831824803336, 0.036636923513358274], [1.8793852415718169, 0.6840402866513374]], [[1.0, 0], [0.051355851720933224, -0.061203520789157716], [-0.520944533000791, -2.9544232590366244]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.4611820265430262, 0.843613836359659], [3.5, -6.06217782649107]], [[1.0, 0], [-1.4433916420381614, 2.500027659230365], [-5.5, -9.526279441628825]], [[1.0, 0], [4.156271098853463, 4.953251013854099], [-2.2574263096700946, 12.802500789158705]], [[1.0, 0], [2.9411151723273705, 0.5185979582523419], [15.974774553360442, 5.814342436536369]], [[1.0, 0], [-4.349329933084061, 0.28866785962243513]], [[1.0, 0], [-2.824243737725459, 7.759545896436822], [-17.619022191736494, -14.784115022790404]], [[1.0, 0], [1.260211241595882, 7.147013103340586], [-27.251086002791343, 9.918584156444393]], [[1.0, 0], [2.028002051498473, 3.5126025910492698], [-15.5, 26.846787517317598]], [[1.0, 0], [0, 7.96989197046181], [-37.0, 0]], [[1.0, 0], [-4.179499967010023, -3.507016880823564], [7.119575284344144, 40.37711787350053]], [[1.0, 0], [-1.8235292548198005, -5.010105451332316], [-32.93991105411605, 27.639867216521193]], [[1.0, 0], [-1.624549206908562, 0.28645185666651807], [44.16555317693769, -16.07494673630643]], [[1.0, 0], [-0.6539209775041043, 1.7966331198002206], [-40.60035548530583, -34.067743313386586]], [[1.0, 0], [0.6169306689813824, -3.498787686958705], [-55.44186462636859, -20.179188456214455]], [[1.0, 0], [-7.423701870201714, -2.7020065088197622], [46.728711030257664, 39.2100441908789]], [[1.0, 0], [-2.2309145234686407, 0.39337042214188933], [62.95940559265586, -22.915349602819806]], [[1.0, 0], [9.793893979472314, -3.5646858860868873], [54.38915546144744, -45.63792028774429]], [[1.0, 0], [0.9075285660930463, -1.08155042902326], [-12.676316969685915, -71.89096596989118]], [[1.0, 0], [-1.8467503367658087, -1.5496075264567077], [13.718206035687498, 77.79981248796443]], [[1.0, 0], [9.87319194840199, -5.700290029170735], [41.5, -71.88010851410841]], [[1.0, 0], [-7.749383241314208, 6.502504619638146], [15.4546878123568, -87.64789001808651]], [[1.0, 0], [-9.718282562458246, -1.7135954219099867], [91.15018421623311, 33.17595390258987]], [[1.0, 0], [-3.194212947848911, 2.6802629064417136], [17.538465944359967, -99.46558305423301]], [[1.0, 0], [-10.880402651434004, -6.28180339969694], [51.5, 89.20061658979718]], [[1.0, 0], [12.940424845897448, -7.471157768207013], [53.5, -92.66471820493493]], [[1.0, 0], [-4.891063242318802, 1.7802014341175858], [83.49884429996861, -70.06384945583278]], [[1.0, 0], [0, -8.570643363046084], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-475-95.74-c1-0-18', '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/475/2/u/b/74/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9613047167347071, 1.0826468260495437, 1.1955155298224263, 1.297878633159568, 1.3842916898195365, 1.4463717467636803, 1.473645657535998, 1.4546247877970502, 1.3780149364019976, 1.2340098140168048, 1.0156201275133014, 0.7199679852225048, 0.34944475099921934, -0.08739673731669795, -0.5753585181284463, -1.09266030152822, -1.6116596008502244, -2.100290518992095, -2.524212364266128, -2.8495736001712886, -3.0462036202892664, -3.09095547411656, -2.9708498847292426, -2.6856281700332056, -2.2493211850382253, -1.6904919398696183, -1.0509144771880434, -0.38260715365779613, 0.2566671703897706, 0.8091081834581707, 1.2232606661422303, 1.4603726772204808, 1.499929680706602, 1.343559169002615, 1.0166051684825497, 0.5668902036048158, 0.060500054324717695, -0.4251871648358591, -0.8105980367707187, -1.0241848468088108, -1.0124920517970866, -0.7486645646005612, -0.23805991541062907, 0.48010164980129355, 1.3356516917503969, 2.2349478443608835, 3.0722281739274746, 3.7435215089553426, 4.161280765324282, 4.267629536091745, 4.044137858772704, 3.5163999670724824, 2.7523521954245167, 1.854166052181829, 0.9445552265068716, 0.14928959326681118, -0.42155051269466437, -0.6906654217760338, -0.6261341077861208, -0.24724088348895235, 0.3777569414124672, 1.1419238606423459, 1.9166297951171072, 2.572615583598899, 3.001675652742484, 3.135195046214157, 2.9561367913939285, 2.5020755082531556, 1.8583776410806006, 1.1423950953196234, 0.48125533562188094, -0.012830678983533584, -0.2651426757952786, -0.25446510997699423, -0.019121416873698928, 0.3486420611612237, 0.719408984870902, 0.9517499580105858, 0.9212326649969312, 0.5477064393462077, -0.18469671212890995, -1.2192673941439194, -2.4324592343784555, -3.6533026930691865, -4.693353023491734, -5.381731280964118, -5.598493620304652, -5.299551724548158, -4.5277476237484, -3.4072545047802043, -2.121763560409906, -0.8802762780546128, 0.12295222604764733, 0.7462915751032339, 0.9285527834570104, 0.7006822666335842, 0.17846668670424476, -0.4626734994804299, -1.0258492644637818, -1.3359181124669224, -1.2784931148315328, -0.8261226930075354, -0.0455792444481647, 0.915800859935232, 1.8621698558249042, 2.592847853175125, 2.9480271901021817, 2.8461424282444687, 2.3041276656282124, 1.4354378419445581, 0.42568243661242006, -0.5090898132930014, -1.172207704826644, -1.432845918738178, -1.2580986121425086, -0.7226333039152947, 0.007068887402546934, 0.7109527757274248, 1.1677254792023521, 1.2092569717990873, 0.7641066769506702, -0.12059960546777934, -1.2848920915822062, -2.4888050900383774, -3.4653539563232423, -3.9816013523389624, -3.8934894179245694, -3.1812387318712028, -1.956480924147423, -0.43892643437906326, 1.0922966051634115, 2.3612570944293716, 3.1568492063506435, 3.378561465448157, 3.0552854514908687, 2.332675015374245, 1.4324090641651082, 0.5938128638498945, 0.012819400756279915, -0.20601710083804328, -0.07207802894135851, 0.29995396945475294, 0.7274508879904558, 1.0157389014595888, 1.0172390091584405, 0.6774381071743539, 0.05458976527025608, -0.6930006413864832, -1.3494310507667489, -1.7023793601990607, -1.606408518519702, -1.0306179022008328, -0.07653118248323779, 1.0401916914125475, 2.0408778364974536, 2.655256847250831, 2.6945231753663483, 2.106191362859573, 0.9950847730415143, -0.39656221806770375, -1.7460440087243638, -2.7301429959326766, -3.1074173771928137, -2.780915818855112, -1.824164562127066, -0.4628424505679582, 0.9835580413065548, 2.1848186346208203, 2.885580944429643, 2.970212393856596, 2.4891929696983333, 1.6397574664521806, 0.706214118967311, -0.023293914475021174, -0.3400499052094871, -0.17433318273136547, 0.3858354073595085, 1.122319620245429, 1.753063269102317, 2.0177597028021874, 1.7579761634394997, 0.9679882090639599, -0.19917452300959285, -1.473021339736531, -2.542832396782815, -3.1485619117937924, -3.1586344140028135, -2.611179940169964, -1.7056098093269854, -0.7459147726416352, -0.05146828087820916, 0.1388450619409982, -0.2592269275028188, -1.1454751579718598, -2.259627394521903, -3.2539798136975047, -3.793810274347319, -3.6564632732749294, -2.7998468967630585, -1.3796522308970987, 0.2905116703457621, 1.825035464788191, 2.8734817996397717, 3.2177094847874246, 2.8304634090128067, 1.8783432940180702, 0.6686833905902207, -0.443290392654394, -1.1587468631132483, -1.3193991715878801, -0.9463255514886273, -0.2224362813785993, 0.5748431469256345, 1.1685531632006352, 1.3741191579046659, 1.158589530655525, 0.6481317118914802, 0.08146473081814311, -0.2754597627320629, -0.22534803125677852, 0.286029156827292, 1.1424414482579222, 2.087330699551469, 2.803193021925649, 3.0153979920853646, 2.5867970819728385, 1.571418800200123, 0.20792709804635054, -1.147415812468211, -2.128812728455402, -2.4765587683396775, -2.1232217648867704, -1.221700421194701, -0.10432453603256907, 0.816022379258669, 1.172942841231913, 0.7622182567968586, -0.39056910723880667, -2.0325814471544437, -3.756559414608105, -5.121715826762623, -5.784960136567761, -5.601197836430671, -4.661197885620243, -3.255530534031446, -1.7769276658985773, -0.5933384340295587, 0.06663381491467879, 0.1785135904464004, -0.08376619390066121, -0.4211750987133831, -0.5248236113548395, -0.1932242988122926, 0.5891754292946794, 1.63994845626394, 2.6382809247348917, 3.2366645375472096], 'positive_zeros': ['1.60127574488744676595221073298108', '3.44838584825343328351714520647464', '4.51488577720407451635484500954300', '5.29506729523980776421904938716859', '6.90271994002840149522202113147585', '7.42938525587918503525013019449233', '8.870841417286212413752992840434225', '9.257361711618021740200068319557010', '9.973322179095170274025413038667003', '11.48209174002271199826962909366022'], 'prelabel': '2-475-95.74-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.4474630848348322, 'root_number': '0.16430124404440627 + 0.986410209398433*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.223731542417', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60127574488744676595221073298', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.44838584825343328351714520647', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.51488577720407451635484500954', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '95.74', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/u/b/74/3'], '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': '2-475-95.74-c1-0-18', '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': '2-475-95.74-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.2237315424174161, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60127574488744676595221073298', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2029858159137477030214229089979', 'Lhash_array': ['2029858159137477030214229089979'], 'label': '2-475-95.74-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/u/b/74/3'}