-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3747178488850007951849164207674', 'a10': [2.613340798452839, 2.1928533001223154], 'a2': [-1.9396926207859084, 1.6275953626987474], 'a3': [0.6133407984528387, 0.22323779409789932], 'a4': [0.766044443118978, -4.344453923279833], 'a5': [-0.23395555688102196, -1.3268278963378768], 'a6': [-1.5530334192387472, 0.565257937423568], 'a7': [-0.766044443118978, 1.3268278963378768], 'a8': [3.053033419238747, 5.288008999327243], 'a9': [-1.9717815070238645, -1.654521135305906], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.1517157638404328, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[19, [[1.0, 0], [-0.8190778623577252, -4.281251155374501]]]], 'bad_primes': [19], 'central_character': '19.6', 'coefficient_field': 'CDF', 'conductor': 19, 'conductor_radical': 19, 'conjugate': '7327413605299354603837910954701', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.9396926207859084, -1.6275953626987474], [0.3472963553338607, -1.969615506024416]], [[1.0, 0], [-0.6133407984528387, -0.22323779409789932], [2.298133329356934, 1.928362829059618]], [[1.0, 0], [0.23395555688102196, 1.3268278963378768], [-4.698463103929542, 1.7101007166283437]], [[1.0, 0], [0.766044443118978, -1.3268278963378768], [-3.5, -6.06217782649107]], [[1.0, 0], [-0.5923962654520477, -1.0260604299770062], [-5.5, 9.526279441628825]], [[1.0, 0], [2.553033419238747, -0.9292281716897705], [9.958577760546714, -8.35623892592501]], [[1.0, 0], [-2.9717815070238642, 2.493620766483186], [2.952019020337816, -16.741731801207536]], [[1.0, 0], [-0.8190778623577252, -4.281251155374501]], [[1.0, 0], [0.8793852415718167, -4.987241532966372], [-21.612930278075893, -7.866463296490381]], [[1.0, 0], [3.564177772475912, 2.990700254334797], [5.03579715234098, 28.559424837354033]], [[1.0, 0], [-1.9187480877851173, 3.3233691749694514], [-15.5, -26.846787517317598]], [[1.0, 0], [4.106066838477494, 0], [37.0, 0]], [[1.0, 0], [-9.383255634833636, -3.415225751590062], [31.4078221678781, 26.354291997148113]], [[1.0, 0], [1.5111443532371651, 8.570125497331896], [-40.406782693794064, 14.706866163003756]], [[1.0, 0], [-0.4396926207859084, -0.3689459159328274], [8.161464350345726, 46.28596439157378]], [[1.0, 0], [-0.511144353237165, 2.8988436777141864], [-49.803708901653145, -18.127067596260442]], [[1.0, 0], [3.0150147464989856, -2.529897761781359], [10.24524248234889, -58.10365742772028]], [[1.0, 0], [0.7844627563314875, -4.4489093681499625], [-57.32124986794041, -20.863228742865793]], [[1.0, 0], [2.9777112935256698, 2.498596448149811], [11.634427903684333, 65.98211945181794]], [[1.0, 0], [1.2043928904313475, 6.830451503180124], [-66.71817607579949, 24.28343017612248]], [[1.0, 0], [5.758770483143634, 2.0960210418350798], [55.921244347685395, 46.92349550711737]], [[1.0, 0], [9.216881417142051, 3.3546704886009997], [60.51751100639927, 50.780221165236604]], [[1.0, 0], [6.159100257716242, -10.667874575275096], [-41.5, -71.88010851410841]], [[1.0, 0], [-2.2797150161444244, 0.8297484084862655], [68.17795543758905, -57.208097262102]], [[1.0, 0], [-5.645429684690795, 4.737077966261314], [16.843873233692243, -95.52635204218419]], [[1.0, 0], [2.0393628462133004, -0.7422673728900442], [77.37048875501678, -64.92154857834048]], [[1.0, 0], [-6.237825950142843, -10.80423147441901], [-51.5, 89.20061658979718]], [[1.0, 0], [-3.3400223953585164, 5.785088487178854], [-53.5, -92.66471820493493]], [[1.0, 0], [-1.6415592914289743, -9.309745365305671], [-102.42649566566402, 37.28019562249789]], [[1.0, 0], [-1.3104597289088415, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-19-19.6-c1-0-0', '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/19/2/e/a/6/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.36433983732007563, 0.35823512627319415, 0.36468282743860675, 0.3814339446480068, 0.40610881230504287, 0.4363138680683493, 0.4696049160491784, 0.5033550442447313, 0.5345987583662634, 0.5598967002901389, 0.5752417775773802, 0.5760167921639537, 0.5570109179942321, 0.5125024275632434, 0.43641502319311676, 0.322553741396009, 0.16492320764474433, -0.04187408009602619, -0.3021686644692313, -0.618701880797649, -0.9920775182351578, -1.420224163470037, -1.8979140104281738, -2.4163910646651794, -2.9631656483877395, -3.522031598002465, -4.073356348243155, -4.594681334909575, -5.06165045049531, -5.449257980639956, -5.733375715624903, -5.8924838946376354, -5.909495360980175, -5.773530645781589, -5.481478045748742, -5.039161616328347, -4.4619454312526345, -3.7746274691859996, -3.0105223812019033, -2.2096981935585593, -1.4164140465669164, -0.6758978737044564, -0.030695386158971057, 0.48309623566893156, 0.8393369462540974, 1.0246961108704733, 1.040467545482518, 0.9030329539415135, 0.6427748023400072, 0.30139743614798836, -0.07219806815026215, -0.4271440460702658, -0.7164198608402716, -0.9025895362925498, -0.9627338233785557, -0.8918650264900078, -0.7042299158899039, -0.4321207411061769, -0.12211089735778502, 0.17102022040423706, 0.39205207096107186, 0.49384214421148986, 0.44544451542630925, 0.238594095788237, -0.10858340128778594, -0.551499804209612, -1.023093898685123, -1.4417432743457277, -1.7223489349191343, -1.7892706849023046, -1.589352216099443, -1.1030551986422605, -0.351784191675348, 0.6001457462367223, 1.6497904519600364, 2.6661266915633095, 3.505917757655777, 4.033014065095864, 4.138481940524532, 3.7585697875736535, 2.8875789727144876, 1.5832438674826363, -0.03679883332856422, -1.8075765162189081, -3.53708028497415, -5.031663685038649, -6.12290499109136, -6.691825735534656, -6.686540804928282, -6.130272920488332, -5.118098622853193, -3.8025941673036785, -2.370424604525595, -1.0135376786353891, 0.10032228371340757, 0.8528031070812394, 1.1914826592744763, 1.134846603594125, 0.7648343839374666, 0.20835697499830252, -0.38872262431255156, -0.8901706503438935, -1.1949897495099333, -1.2550355537817286, -1.0811709958931641, -0.7367894192410032, -0.3201572649231999, 0.06057002671576901, 0.31413977418120625, 0.3887491485076025, 0.2850695562714546, 0.05645343777075542, -0.2041501498464372, -0.38796687198184043, -0.39959501127914804, -0.18476655073853382, 0.250303631957295, 0.8334449423911031, 1.4374963400839649, 1.906543867526143, 2.092513735732095, 1.8943000619171442, 1.2902920135837501, 0.35587478201627126, -0.7397881281516965, -1.7590976696676377, -2.4399224940061437, -2.549937733581896, -1.9402095956357175, -0.5860869302695175, 1.3946289656106179, 3.75194468040433, 6.142168898087245, 8.18820524894009, 9.550044266456709, 9.991012198025786, 9.425593464077796, 7.9381046434748095, 5.767517451008559, 3.261029997105058, 0.8059311452768312, -1.2457348723391617, -2.6434405297465133, -3.28107655386374, -3.2074761813529986, -2.6030141781595155, -1.7286033967692676, -0.8597983359743937, -0.22203891299271128, 0.05752686453370646, -0.029392464312485406, -0.38317238106887047, -0.8345271705739357, -1.198934115247227, -1.332075848282568, -1.1711686681618232, -0.7511202257805807, -0.19153667705941824, 0.34121332624881784, 0.6856102805269281, 0.7350536051896207, 0.471504301977396, -0.027564208396193952, -0.6114683272436696, -1.1017691417372366, -1.347638764525139, -1.274419292014727, -0.9100156453786135, -0.3797841368789319, 0.13028693268155286, 0.43259916896793543, 0.4022266536535517, 0.026697413351386316, -0.5755650635775297, -1.176805168720392, -1.498807831926986, -1.2949687111479709, -0.433327108729202, 1.0438987909469761, 2.904008258019139, 4.759698042449324, 6.1519474665720715, 6.661089169961961, 6.018021337838819, 4.185592049442712, 1.3865127166573863, -1.9326194505816308, -5.194876889859473, -7.822117951068495, -9.367409034453999, -9.616779594337126, -8.633876068366126, -6.736003107511499, -4.4083173236164805, -2.179489311654838, -0.4922880358439194, 0.3966491314920603, 0.4623758364413531, -0.10711687047689093, -0.985306941901971, -1.8131210271836848, -2.3043677729207337, -2.3201310528908023, -1.89229001206323, -1.19265116056249, -0.4610553850018307, 0.08198731001651967, 0.3088336530455913, 0.22086954129792893, -0.06296094394128164, -0.359123360941107, -0.4937514566343931, -0.37094629246360417, -0.010244238108143063, 0.4605582146903629, 0.8549901876608875, 1.0021175390948054, 0.8179855021079167, 0.34680313654934336, -0.24580307051484523, -0.7284386198150138, -0.8914443820102733, -0.6361600238236987, -0.032683599350069495, 0.6786894817824661, 1.1492828852633954, 1.0323030013979426, 0.10838621256739434, -1.6151583630976853, -3.867922647816026, -6.16151090877813, -7.9095271531507345, -8.590780141977346, -7.9077435159009655, -5.8905738056274926, -2.911186574158363, 0.40179962559337373, 3.3259915601328927, 5.239831337963033, 5.791511542312241, 4.991401534643537, 3.1999007397328594, 1.0145375126585094, -0.9088513496542192, -2.04586603671223, -2.146482456960921, -1.2890668413109967, 0.1677757138578613, 1.7161003301677031, 2.867132805775873, 3.3018621429858412, 2.9563199694210494, 2.0177469482486208, 0.838623627508704, -0.197130303118247, -0.8069088285434824, -0.8951557747636211], 'positive_zeros': ['2.95600261473892036517366115513459', '7.39209480653299014951293223244839', '8.755142049334680624551706331763280', '10.26542560881370856685877618345513', '11.20109023371604474172051081790074', '12.72471086044817483942803291073476', '14.41031108850262875564062938710493', '16.50519445136723328310599643141587', '17.46286449521392914520972112469938', '18.77735995923535259005713061412057'], 'prelabel': '2-19-19.6-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3895070780363725, 'root_angle': -0.3331255714153264, 'root_number': '0.5005651511066537 - 0.8656988676771923*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.166562785708', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.95600261473892036517366115513', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '7.39209480653299014951293223245', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.755142049334680624551706331763', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.1517157638404328, 'bad_primes': [19], 'central_character': '19.6', 'conductor': 19, 'conductor_radical': 19, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/19/2/e/a/6/1'], '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': '2-19-19.6-c1-0-0', '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': '2-19-19.6-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3895070780363725, 'root_angle': -0.1665627857076632, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.95600261473892036517366115513', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3747178488850007951849164207674', 'Lhash_array': ['3747178488850007951849164207674'], 'label': '2-19-19.6-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/19/2/e/a/6/1'}