-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2335178996977652052440585140866', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.3546091220107779, -0.6142010161500583], 'a4': [0.0, 0.0], 'a5': [-0.5, -0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [3.110788174114542, 0.0], 'a8': [0.0, 0.0], 'a9': [1.2485047411734904, -2.1624736452031166], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.034315276808656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.5, 0.8660254037844386]]], [19, [[1.0, 0], [-4.351618604357759, 0.2518243876343803]]]], 'bad_primes': [2, 5, 19], 'central_character': '380.121', 'coefficient_field': 'CDF', 'conductor': 380, 'conductor_radical': 190, 'conjugate': '1255498032798282632862927204383', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.3546091220107779, 0.6142010161500583], [-1.5, 2.598076211353316]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-3.110788174114542, 0], [7.0, 0]], [[1.0, 0], [3.5292246621576533, 0], [11.0, 0]], [[1.0, 0], [0.20078496504649296, -0.3477697608564669], [-6.5, -11.258330249197702]], [[1.0, 0], [1.7485047411734904, 3.028499048987555], [-8.5, 14.722431864335457]], [[1.0, 0], [-4.351618604357759, 0.2518243876343803]], [[1.0, 0], [-3.6585079502415394, 6.336721649713016], [-11.5, -19.91858428704209]], [[1.0, 0], [-3.9653972961253197, 6.868269589085302], [-14.5, -25.11473670974872]], [[1.0, 0], [-5.735452388526189, 0], [31.0, 0]], [[1.0, 0], [10.529224662157652, 0], [37.0, 0]], [[1.0, 0], [-0.5553940870572708, -0.9619707770065252], [-20.5, 35.50704155516198]], [[1.0, 0], [-4.3038988282307615, -7.454571441131835], [-21.5, 37.239092362730865]], [[1.0, 0], [3.7616218134258075, -6.515320099712874], [-23.5, -40.703193977868615]], [[1.0, 0], [5.2777294033311435, -9.141295475169716], [-26.5, -45.89934640057525]], [[1.0, 0], [-4.2561790521037635, -7.3719183643540624], [-29.5, 51.09549882328188]], [[1.0, 0], [-4.610788174114542, 7.986119380504121], [-30.5, -52.827549630850754]], [[1.0, 0], [4.206227726368537, -7.285400130275227], [-33.5, -58.023702053557386]], [[1.0, 0], [-4.312332107205824, -7.469178308791046], [-35.5, 61.48780366869514]], [[1.0, 0], [0.8707167119161139, 1.5081255840380225], [-36.5, 63.21985447626402]], [[1.0, 0], [-4.505442761322044, -7.803655773203198], [-39.5, 68.41600689897065]], [[1.0, 0], [-4.07857299430387, 0], [83.0, 0]], [[1.0, 0], [-6.616230935436586, 11.459648134785127], [-44.5, -77.07626093681505]], [[1.0, 0], [-3.8516186043577587, -6.6711991141251685], [-48.5, 84.00446416709055]], [[1.0, 0], [8.687732612399193, -15.047594287248494], [-50.5, -87.4685657822283]], [[1.0, 0], [7.126136795975088, 0], [103.0, 0]], [[1.0, 0], [-0.7354523885261899, 0], [107.0, 0]], [[1.0, 0], [-8.004683793277254, -13.864519028479373], [-54.5, 94.39676901250381]], [[1.0, 0], [-4.349231080293751, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-380-19.7-c1-0-5', '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/380/2/i/c/121/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3038947874117142, 1.4077777885964213, 1.5115471079333862, 1.6132678602426591, 1.7077847973476832, 1.7872300171977038, 1.841792958723262, 1.8606235598117384, 1.83280745298383, 1.7483945351730843, 1.5994668566080896, 1.3812110183559807, 1.092930370671766, 0.7389048480263702, 0.3289881259146422, -0.12117302315720331, -0.5904013133039175, -1.052809663907311, -1.4792116862642788, -1.8390946223652447, -2.1030584935301735, -2.2455529284693747, -2.2476759999248785, -2.0997471164156187, -1.8033384466039264, -1.3724551624683006, -0.8335999654564771, -0.2245437971087595, 0.4082510259431834, 1.0134560032724729, 1.5396840282900066, 1.9408527975229672, 2.1815455727265203, 2.241730329805447, 2.1201888666952162, 1.836081980671345, 1.428238609165298, 0.9519971522524141, 0.4737246028940248, 0.06346040731410334, -0.21356476544445047, -0.3055457230918932, -0.181732965949401, 0.1620369316843069, 0.7008569067916085, 1.3819349005971167, 2.1296236323301168, 2.853942835446388, 3.4617086010923104, 3.868923074428628, 4.012766974263352, 3.8614420839024906, 3.4202699417348676, 2.732869856601681, 1.8768768667246454, 0.9544414914347732, 0.07856934890425366, -0.6429165641368667, -1.123500226963511, -1.3117048270010931, -1.2001468154164932, -0.8282029489563034, -0.27748294154322467, 0.3395947931518965, 0.8966855518500816, 1.2734313951938077, 1.3753212925205647, 1.1502304435336774, 0.5987274008485218, -0.22388443067207703, -1.2145380197918172, -2.2376339898989834, -3.146315050617306, -3.806400580382239, -4.118959787886225, -4.0375419476154795, -3.576839196842474, -2.810940271859347, -1.8611285215552862, -0.8750783804761246, -0.0009634183179470347, 0.6389202022569282, 0.9701291165641279, 0.9793901015746626, 0.7164752797480461, 0.28393291254693137, -0.18370682061674806, -0.5475103239302829, -0.6932704580481857, -0.5564229813805589, -0.13757332604682265, 0.49488830018333224, 1.2161589238434818, 1.8686693039383067, 2.293710699961175, 2.364911357638492, 2.0167588304570603, 1.2620561397645453, 0.1941876655729955, -1.0269887124898727, -2.203475610209752, -3.136503215070199, -3.6656302640461633, -3.7016037827766466, -3.245970285100041, -2.392917297619019, -1.3123715955138748, -0.2172810165663901, 0.6785599291313715, 1.2035734946855914, 1.263332699779001, 0.8598226212495973, 0.09064380954367363, -0.8720114610530647, -1.818392577750015, -2.5464215622195248, -2.9053347908030753, -2.8280923428161375, -2.3452160589937234, -1.5767366290270057, -0.7038109447264589, 0.0737704013563119, 0.5846044123040952, 0.7263983540991824, 0.4907932238680023, -0.033816465914341405, -0.6825484403648273, -1.2530461701783477, -1.5543515752736394, -1.454174010815457, -0.9131734810550417, 0.002318118831321252, 1.1327643738174937, 2.2607329732381407, 3.1611085381369537, 3.654435469530217, 3.650524930599679, 3.171473361170209, 2.347970569124705, 1.3891537352949854, 0.5327742563625485, -0.01251658890975992, -0.11868734704292068, 0.229268504311743, 0.9285546127078128, 1.7832679674181584, 2.5530877925925495, 3.0143028518867645, 3.0180973049770845, 2.5312898203689578, 1.648744071052958, 0.5735395009162891, -0.4309473368538438, -1.1056641675310395, -1.2612798853947593, -0.827825361180299, 0.12435326614517851, 1.3982616006085848, 2.7157877180015393, 3.7841558620587357, 4.366811796175987, 4.3408348314539555, 3.7261601382608376, 2.6789594407354813, 1.4507060860568757, 0.32337803884943567, -0.46242668401011244, -0.7676957591105295, -0.587712209484263, -0.04864771708882882, 0.6309832606954394, 1.2035693873521887, 1.463139643855425, 1.304191876192595, 0.7522831970059247, -0.042352795765681434, -0.8467733345287575, -1.41157432831455, -1.5431535193074024, -1.161711713932474, -0.3283224654604158, 0.7672495419653163, 1.855432804733026, 2.659487034042282, 2.9719474354775177, 2.7133868023816294, 1.9564970998331725, 0.9079000450434146, -0.14811276006046117, -0.9288146126612608, -1.2332744433763478, -1.0007941358555383, -0.33041577567337915, 0.5449629675666819, 1.323543380176114, 1.7210301961271666, 1.5543196091683653, 0.7985008500890719, -0.3997493304362283, -1.7572521063228486, -2.9290552534767667, -3.60249291428168, -3.584366730537782, -2.856529746629448, -1.5837502968227612, -0.07108789660938698, 1.3176453952145049, 2.257567990788166, 2.5490258661681335, 2.1681211858218608, 1.2673282242671888, 0.12647096971541835, -0.9312488061219731, -1.6333186673285036, -1.8343532022987075, -1.5525227878071888, -0.9556357321260613, -0.3017286513049783, 0.1471803720820718, 0.21130385274500502, -0.14768341652997008, -0.8131422795240468, -1.5503738881338032, -2.0828945238377012, -2.184504028848362, -1.7581377417407935, -0.8759865585255934, 0.23310353483657398, 1.2467818278676173, 1.8448407678340815, 1.8086420285139249, 1.0935853452431472, -0.1486467386561748, -1.6064713935722796, -2.893993664810321, -3.661048917473156, -3.694919090336535, -2.9828576234773236, -1.7160267516471541, -0.23310120880975246, 1.0797414939658294, 1.902167483447476, 2.071746508261412, 1.626465125451859, 0.7846753023423166, -0.13106475618952698, -0.8021510120839733, -1.0197457818187345, -0.7543905148876072, -0.1667974462463424, 0.44425236207646557, 0.7408980461980531, 0.4608276313504817, -0.489177372569657, -1.9913299718994373, -3.7410869647816205, -5.33120796141337], 'positive_zeros': ['1.84213141740888498894496777582906', '3.41937975074693589557824707093499', '4.89827486425458345349048421788813', '5.32531640845324913121052485520767', '7.01216042936862670405579627019511', '7.80636194875614772006068489193207', '8.594068927210827818089321642359841', '10.00015561887179724818012301001393', '10.69957960919140263787281294738267', '11.28028638652935778823611564417656'], 'prelabel': '2-380-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': 0.3826868258440707, 'root_number': '0.36026336989765034 + 0.9328506334403106*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.191343412922', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84213141740888498894496777583', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.41937975074693589557824707093', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.89827486425458345349048421789', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.034315276808656, 'bad_primes': [2, 5, 19], 'central_character': '19.7', 'conductor': 380, 'conductor_radical': 190, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/380/2/i/c/121/2'], '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': '2-380-19.7-c1-0-5', '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': '2-380-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': 0.19134341292203536, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84213141740888498894496777583', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2335178996977652052440585140866', 'Lhash_array': ['2335178996977652052440585140866'], 'label': '2-380-19.7-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/380/2/i/c/121/2'}