-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1348939196099863646487982708013', 'a10': [2.3788906950626263, -4.120359549501309], 'a2': [-1.433720660577386, 0.8277590093270819], 'a3': [-0.24748844387964705, 0.42866255908570744], 'a4': [0.37036995504430403, -0.6414995797337355], 'a5': [-2.488864212333317, 1.4369464229670665], 'a6': [1.2855630401035072e-60, -0.819443156502871], 'a7': [0.0, 0.0], 'a8': [0.0, -2.084727769020372], 'a9': [1.3774989402920617, 2.385898151958138], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [3.5456158135560742, 0.6546819858993363]]]], 'bad_primes': [7, 13], 'central_character': '637.116', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '280545705359475280863833245870', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.433720660577386, -0.8277590093270819], [1.0, -1.7320508075688772]], [[1.0, 0], [0.24748844387964705, -0.42866255908570744], [-1.5, -2.598076211353316]], [[1.0, 0], [2.488864212333317, -1.4369464229670665], [2.5, -4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.235539065200059, 1.2906890810771783], [5.5, 9.526279441628825]], [[1.0, 0], [3.5456158135560742, 0.6546819858993363]], [[1.0, 0], [-1.1379197927335738, 1.9709348959527961], [-8.5, -14.722431864335457]], [[1.0, 0], [3.8067928246875757, -2.1978528620825077], [9.5, -16.454482671904334]], [[1.0, 0], [3.584630953270238, 6.20876293744811], [-11.5, 19.91858428704209]], [[1.0, 0], [-6.19574081840315, 0], [29.0, 0]], [[1.0, 0], [-5.935768596153957, -3.427017596836814], [15.5, 26.846787517317598]], [[1.0, 0], [-5.10298038635483, 2.946207099731342], [18.5, -32.04293994002423]], [[1.0, 0], [0, 3.980142347739495], [-41.0, 0]], [[1.0, 0], [-1.3142549427650962, 0], [43.0, 0]], [[1.0, 0], [1.170935599979059, -0.6760399838516257], [23.5, -40.703193977868615]], [[1.0, 0], [-4.143888015451211, 7.177424583637262], [-26.5, -45.89934640057525]], [[1.0, 0], [8.323244239863945, 4.805427302416451], [29.5, 51.09549882328188]], [[1.0, 0], [4.77650480826179, 8.273149010506458], [-30.5, 52.827549630850754]], [[1.0, 0], [-13.778062493606987, -7.95476808959548], [33.5, 58.023702053557386]], [[1.0, 0], [0, 4.793956114681034], [-71.0, 0]], [[1.0, 0], [-4.940735287065317, -2.852534847981844], [36.5, 63.21985447626402]], [[1.0, 0], [-1.0071289852477576, -1.7443985722244024], [-39.5, 68.41600689897065]], [[1.0, 0], [0, -3.1179831953320454], [-83.0, 0]], [[1.0, 0], [-11.30887161419432, 6.529180070686008], [44.5, -77.07626093681505]], [[1.0, 0], [0, 14.03820177196362], [-97.0, 0]], [[1.0, 0], [8.724128307605016, -15.110633480521772], [-50.5, -87.4685657822283]], [[1.0, 0], [3.278489104885977, 5.678509701723522], [-51.5, 89.20061658979718]], [[1.0, 0], [7.80101548683376, 13.511755173827732], [-53.5, 92.66471820493493]], [[1.0, 0], [8.675082107252155, 5.0085609898641374], [54.5, 94.39676901250381]], [[1.0, 0], [3.9507386989872733, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-637-91.25-c1-0-21', '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/637/2/r/g/116/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.2339357547516513, 0.3262672814061147, 0.3925176732182383, 0.43185856464966565, 0.4412183089184576, 0.4161137064329317, 0.351835689749111, 0.2447899044072319, 0.09383509085315578, -0.09850725987640103, -0.325092669059389, -0.573570776926411, -0.826310709540469, -1.0609512338124925, -1.2516535075098927, -1.371069797960039, -1.3929548852733973, -1.2952459358829769, -1.063333404429841, -0.6931551263739227, -0.19368498216434576, 0.4116273791338807, 1.0848651599282186, 1.775390544875326, 2.4234425633636487, 2.9654729815199734, 3.3408481575434865, 3.4992881402803477, 3.4081980525749733, 3.0589114017138574, 2.4708463612862204, 1.6926990197864131, 0.8000693447954516, -0.11067868915187029, -0.9320204852700846, -1.557500129239282, -1.8952551512542912, -1.8811387540943765, -1.489575713496559, -0.7403800612195403, 0.2998648882277888, 1.522630069638784, 2.788404122298103, 3.94281419583729, 4.836049284235182, 5.343052187825581, 5.3815933964539155, 4.925408476873675, 4.010104897286986, 2.730485903593639, 1.229183274903033, -0.32214221029083623, -1.7465042147386383, -2.88672350801382, -3.6280832408912387, -3.914800501615727, -3.7574556329798123, -3.2299155654642075, -2.456020047285805, -1.5880812369708377, -0.7807561950090893, -0.16479264423514886, 0.17468988130718438, 0.2114164776665831, -0.01982590702975604, -0.432460222033269, -0.9071859430806034, -1.317205149044549, -1.5546721201634568, -1.553065466972244, -1.3008746400443105, -0.8436556850834949, -0.27384937609663834, 0.28968647941034786, 0.7282292436332383, 0.9501824523418234, 0.9125736164987797, 0.6321216255347073, 0.1830624195432728, -0.3182305463114502, -0.7388198429689852, -0.9595198300647433, -0.9031785138030035, -0.5543068540776845, 0.03487369286857233, 0.7539725039984959, 1.458016753218817, 2.0001531184474626, 2.266114353933551, 2.2022832259584333, 1.8302673935119755, 1.243745373650162, 0.5873917901145542, 0.022047712271453256, -0.3160613881162286, -0.3522729348168521, -0.09707982449351599, 0.3505350874220715, 0.8224259463209663, 1.120251436443634, 1.0659696156080047, 0.5522548327199748, -0.4196877251827566, -1.7253651707992623, -3.130979443094492, -4.335318060130805, -5.03192892410728, -4.978511991837269, -4.057780546424652, -2.314961461441728, 0.038371768635179826, 2.6571755246960693, 5.127150357262541, 7.047320927417861, 8.1130988007013, 8.181045224346358, 7.300070081698197, 5.7010886189353, 3.746603428483343, 1.8510796951180553, 0.390052688115317, -0.3811479347413454, -0.38019033818726294, 0.2902031589979256, 1.373500950017778, 2.5260479661353648, 3.4027465982091187, 3.740713668288069, 3.420532726907461, 2.490462689538038, 1.148390255009917, -0.3129652444253799, -1.58282666030036, -2.4109545321839976, -2.667794894063208, -2.371111784469877, -1.673162345877051, -0.8130756098102486, -0.048317103889274376, 0.41553786224093664, 0.47748493271967085, 0.16228133141083964, -0.3946924645339709, -0.9933920488420118, -1.4317261578289702, -1.5661705270236277, -1.3526645302794154, -0.8561891350573919, -0.2269157105753488, 0.34911167871839827, 0.7091424152161514, 0.7641960170031101, 0.5250582973471222, 0.09565296165051931, -0.364081993862389, -0.6939152311708262, -0.7895369068396303, -0.6405657659177171, -0.3370228668898713, -0.04081009396417939, 0.06986859892316027, -0.13416958425994252, -0.6795936901587144, -1.4679935622539089, -2.294529919492943, -2.905378055761607, -3.078722689938668, -2.7051781732534654, -1.8416177399573501, -0.7185544306468057, 0.305959667651959, 0.8369960577732664, 0.5546890085861486, -0.6841024446742643, -2.7852314215017127, -5.418570533657544, -8.0850953120702, -10.234672850697738, -11.403979963257422, -11.336744528692199, -10.052073227139854, -7.840379726738764, -5.18665134411116, -2.641693605445283, -0.6773682060738492, 0.43304999165871483, 0.6752151801555765, 0.27776581240993586, -0.3743976668024428, -0.8709848880807122, -0.9113778009827743, -0.4025469149293233, 0.5103385273627292, 1.4902752358228804, 2.1177818630384095, 2.0296755690602906, 1.0442568079626962, -0.7663782679742631, -3.080288506754222, -5.406045971837035, -7.216183299507341, -8.094005029830445, -7.849812909144144, -6.57190075140514, -4.59762701745348, -2.414241401382569, -0.5203033379972123, 0.7101110525926027, 1.1201294480601232, 0.793861658198, 0.007531567267221509, -0.8730148602000173, -1.513402416808451, -1.7111345465844598, -1.4446159822010025, -0.8583948091293574, -0.19395559622151307, 0.3067959858406013, 0.4902345794070878, 0.34111280666590976, -0.021846127589307953, -0.40069905459660365, -0.6011077670928491, -0.5112140498880053, -0.1465554741020558, 0.35597770192922573, 0.7928604390436954, 0.9765028189385292, 0.8138847374107439, 0.3502544348421179, -0.24061190676886746, -0.7182184759827652, -0.8677755009050436, -0.5889812458368622, 0.05357909641333416, 0.8405854575876225, 1.4692865273697338, 1.663532842237498, 1.2840641534605444, 0.3977753229791762, -0.7231035232218364, -1.6773663386566733, -2.0651077868407515, -1.6293512706036026, -0.35953704253556296, 1.4822694229863678, 3.4267190742870475, 4.937031005118651, 5.57932972177738, 5.166534518200341, 3.825261603234263, 1.9595491917167351, 0.11979037708439551, -1.1815965107386495, -1.6461501971242372, -1.2959003997245513, -0.4710667309683792], 'positive_zeros': ['1.06412539532344239366578673529559', '2.54210843681061690195040549495119', '4.10944822711233307152791515753180', '4.96672642830003722511841037287341', '6.34866017776290604503727695000189', '7.67264209921175912831277713954663', '7.992587679360477991603418900476672', '9.058888894922869220921364292793725', '9.795425368206420947395434537570978', '10.49352175276716041285100483229675'], 'prelabel': '2-637-91.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.20166868473218383, 'root_number': '0.8059245289044025 + 0.5920182883241166*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.100834342366', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06412539532344239366578673530', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54210843681061690195040549495', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.10944822711233307152791515753', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '91.25', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/r/g/116/3'], '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': '2-637-91.25-c1-0-21', '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': '2-637-91.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.10083434236609191, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06412539532344239366578673530', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1348939196099863646487982708013', 'Lhash_array': ['1348939196099863646487982708013'], 'label': '2-637-91.25-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/r/g/116/3'}