-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2464426432896215165964471736928', 'a10': [6.898522423275195, -2.5801305845620365e-60], 'a2': [-1.2852659764207814, 0.41760823063713004], 'a3': [0.0, 0.0], 'a4': [-1.7585559816507996, 1.277665708547521], 'a5': [-4.85484892961012, -1.5774360394655706], 'a6': [0.0, 0.0], 'a7': [10.653067360555045, -7.73990649114906], 'a8': [4.904000687002211, -6.749777883568057], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.6975546171669396, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [4.161510628084335, 10.182427475427513]]]], 'bad_primes': [3, 11], 'central_character': '99.71', 'coefficient_field': 'CDF', 'conductor': 99, 'conductor_radical': 33, 'conjugate': '898978209189957982811964716455', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.2852659764207814, -0.41760823063713004], [3.23606797749979, -2.3511410091698925]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.85484892961012, 1.5774360394655706], [20.225424859373685, 14.694631307311829]], [[1.0, 0], [-10.653067360555045, 7.73990649114906], [15.141832724372424, -46.60176929846253]], [[1.0, 0], [4.161510628084335, 10.182427475427513]], [[1.0, 0], [0.8251585200600016, 2.539576792748563], [-136.72387204936612, 99.33570763742796]], [[1.0, 0], [-16.3734795749745, -5.3200660097764105], [233.8059113743598, 169.86993791252473]], [[1.0, 0], [24.77424179734534, 17.99954026485936], [111.55513496935602, 343.33140238255044]], [[1.0, 0], [0, 15.530904161601788], [-529.0, 0]], [[1.0, 0], [-6.10286569483791, -8.399874005438646], [-259.8832922693308, 799.8385302042242]], [[1.0, 0], [-5.212450624850489, -16.042273476441213], [-777.4653315943244, 564.8616274530667]], [[1.0, 0], [15.169840125965521, -11.021533994556151], [423.04426529930305, -1301.9963708080652]], [[1.0, 0], [7.851726103338049, -10.806973853126069], [-519.4575675442866, -1598.7260038921531]], [[1.0, 0], [-10.535629021420815, 0], [1849.0, 0]], [[1.0, 0], [-48.31976701883838, 66.50645372610843], [-682.6185405742589, -2100.8838444959943]], [[1.0, 0], [59.90218274917809, -19.463399022550984], [2272.528737199227, -1651.088773689557]], [[1.0, 0], [-38.73847371802626, -53.31893485213907], [-1075.688157419192, 3310.6277332234295]], [[1.0, 0], [-11.296479015873484, 34.76698749519953], [-3010.3522360691795, -2187.1489237802925]], [[1.0, 0], [-60.58150159265866, 0], [4489.0, 0]], [[1.0, 0], [-46.78180333893603, -15.200329330114657], [4078.25466864411, 2963.025456806357]], [[1.0, 0], [5.155927399464381, -3.746000527018958], [1646.7515630240948, -5068.180175336874]], [[1.0, 0], [-35.55328949867009, -109.42177378248275], [-5049.0750618940465, 3668.367759557325]], [[1.0, 0], [38.511062444742606, 12.513002711152255], [5573.318074249013, 4049.2526030428476]], [[1.0, 0], [0, 71.1307724555116], [-7921.0, 0]], [[1.0, 0], [-5.768792018971332, -17.75451622617606], [-7612.04090007388, 5530.47143881988]], [[1.0, 0], [44.75924455918823, -14.543160145785805], [8252.78235961884, -5995.997358635518]], [[1.0, 0], [90.15504002384105, -65.50147069134597], [3278.3612933238173, -10089.758581375285]], [[1.0, 0], [-65.17367134430435, 89.7038629290307], [-3537.935568598773, -10888.646055063213]], [[1.0, 0], [-118.33746020796022, 0], [11881.0, 0]], [[1.0, 0], [40.75938171084255, -56.10047607638709], [-3945.8380011737036, -12144.040656572815]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-99-33.5-c2-0-4', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/99/3/l/a/71/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6952728487240455, 0.7787834167966289, 0.8539973837009649, 0.9208247930216614, 0.978325416486909, 1.0247146127741953, 1.0574279704167409, 1.0732385599827905, 1.068420775822214, 1.0389561244165122, 0.980777451880933, 0.8900480013393013, 0.763470004446402, 0.5986144031701603, 0.3942592163408647, 0.15071957224359173, -0.1298518908239674, -0.443219124570206, -0.7828984100190629, -1.1401033321870153, -1.5038247844733914, -1.861067396472945, -2.1972565950131866, -2.496820563328883, -2.7439389322226138, -2.9234356798479655, -3.0217782905504142, -3.0281298667906373, -2.935386974035145, -2.741125050031722, -2.448366784681045, -2.0660884207299173, -1.609385607401026, -1.0992349781606081, -0.5618101289104778, -0.027340511649799715, 0.4714625218347704, 0.9013489741077342, 1.2307393223325007, 1.4320592502145786, 1.4840299085094288, 1.3737246939941525, 1.0981989822109928, 0.66551166652418, 0.09498805668027525, -0.5833776515624616, -1.3304177018273144, -2.1001452042820055, -2.84284719843347, -3.5087157614317115, -4.05174632349874, -4.433580309180446, -4.626942926850423, -4.618332194299764, -4.40965532129387, -4.018583252175976, -3.4774996220695527, -2.831048889226545, -2.1324288033364076, -1.4387108475779025, -0.8055936508754694, -0.2820835902026946, 0.09435917827667635, 0.30168156833910703, 0.3356468325701863, 0.21045947170732413, -0.04255390671038206, -0.37816252207271006, -0.7420869752085576, -1.0770286752972704, -1.3292452506453554, -1.4549412455103896, -1.425719543093989, -1.2324036283808888, -0.8866935414887266, -0.42034767476541535, 0.11813373462274221, 0.6690405333404019, 1.1686235800039695, 1.5570865776731162, 1.7864259652614096, 1.8271050184235431, 1.672635321216448, 1.341352440031626, 0.8749947182805796, 0.33409038900449706, -0.20941835954485538, -0.6814897345845167, -1.016097308921938, -1.164826118307634, -1.1046147655439962, -0.8424733929269358, -0.41634372606724346, 0.1082586724810748, 0.6456238609725984, 1.1004860377878782, 1.3806596059542213, 1.4100548113915654, 1.1403010472764326, 0.5592902240846803, -0.304720557540522, -1.3842686200518335, -2.5792405978492154, -3.7682064701204547, -4.823210762480508, -5.626140893805575, -6.0844722520019054, -6.144167697763268, -5.797806593550112, -5.08660999125048, -4.095843906289885, -2.9440136517278597, -1.7671772554480478, -0.7004680329218448, 0.14059627018740234, 0.6763145600837037, 0.8740827837383408, 0.7529706717943039, 0.38075424583833556, -0.13633059150342614, -0.669741343882393, -1.0883803047332021, -1.2790208322271486, -1.164301971173222, -0.715478248485032, 0.042146451910398994, 1.0320820220973232, 2.137516243093777, 3.2186172458483924, 4.1336595120514446, 4.760697940807778, 5.01636523202334, 4.868770259150823, 4.34237979753346, 3.5140382213970804, 2.5007186388858815, 1.4409684542347585, 0.4730802423375782, -0.28640370800223575, -0.7602689418920341, -0.921341211262517, -0.7945417648733556, -0.44997956363606245, 0.011660902352246826, 0.47880790202429996, 0.8502120538623504, 1.0538160690589626, 1.0598088695537582, 0.8854144480466126, 0.5904637486143839, 0.26450657904766856, 0.007831321756545453, -0.09002882045307357, 0.02984806794723402, 0.3815101228900116, 0.9284656864576094, 1.58805767733348, 2.245429706696405, 2.774755563664898, 3.0638951902394913, 3.0378061466547446, 2.676067726846877, 2.0207970239754744, 1.1729147556183184, 0.2768651766108726, -0.5038818901315446, -1.016341057748065, -1.1471712089806252, -0.8459417551726052, -0.13783332624413808, 0.8770967851235003, 2.038527156750279, 3.152193759958164, 4.023449142155327, 4.492049992616503, 4.461716148788664, 3.918774657767743, 2.9360881553199314, 1.6611440205377885, 0.29015990258551805, -0.9672241206394148, -1.926181482471645, -2.460660208539427, -2.526522638209966, -2.1692610009183335, -1.5145742531366027, -0.7433845629920326, -0.055933421715959525, 0.3681817893137865, 0.4062500454448824, 0.017782467787492574, -0.7462146716041582, -1.7520942170835008, -2.809052579871363, -3.7064183036650156, -4.255494759829974, -4.327693513039291, -3.881323037305599, -2.9715700971306194, -1.7415146642788133, -0.3958010169719142, 0.8379153634396567, 1.7521316651314234, 2.1986922800263273, 2.116211166268961, 1.5402987529028942, 0.594674517618983, -0.53484347093146, -1.6379784744786405, -2.521414099395897, -3.0454342797177216, -3.148325597807612, -2.853763377434138, -2.260094717240852, -1.5143415146725756, -0.7770253208249127, -0.18584318029261024, 0.17363187202729619, 0.2837325281101983, 0.19361067232004972, 0.0018421987883632024, -0.1729171986763153, -0.22604248891525186, -0.09744746292305395, 0.20912618304410055, 0.6231029357549559, 1.0216142601949576, 1.2586548382288651, 1.2023006992645284, 0.7712469769930355, -0.0382778526667268, -1.1422668524874828, -2.3787805406971922, -3.536740432982793, -4.398048601655501, -4.78406383997073, -4.596064579175718, -3.840269724348786, -2.631136824231038, -1.1713631242862663, 0.2877524933682655, 1.4973577546095937, 2.262441445616185, 2.482119224758526, 2.169575449601868, 1.446823600512734, 0.5150751825817752, -0.39289860411788696, -1.0677588313567266, -1.373369593972421, -1.2797073177903957, -0.87091831716021, -0.32612443186158985, 0.1231401335656392, 0.24944265432514448, -0.1129835636516245, -1.0230928201384808], 'positive_zeros': ['1.94408966670509740213623702319946', '4.38155643112180013974818082943244', '5.51860395411650914308709761683927', '7.71304089494360157426984110530069', '8.232068082585866043272303368150388', '9.473316217747080047383069207041981', '10.70080370248364341462973143191229', '11.60014726872879623687770099792412', '12.45988791751742686976778018546198', '14.22584382391783977476661619967022'], 'prelabel': '2-99-33.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6424233976557139, 'root_angle': 0.38698120690138604, 'root_number': '0.3476456952588144 + 0.9376259758389885*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.193490603451', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.94408966670509740213623702320', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.38155643112180013974818082943', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.51860395411650914308709761684', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.6975546171669396, 'bad_primes': [3, 11], 'central_character': '33.5', 'conductor': 99, 'conductor_radical': 33, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/99/3/l/a/71/3'], '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': '2-99-33.5-c2-0-4', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-99-33.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6424233976557139, 'root_angle': 0.19349060345069302, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.94408966670509740213623702320', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2464426432896215165964471736928', 'Lhash_array': ['2464426432896215165964471736928'], 'label': '2-99-33.5-c2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/99/3/l/a/71/3'}