-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '939767076474234498698499085537', 'a10': [0, 0], 'a2': [0, 1.0], 'a3': [0, 1.0], 'a4': [-1.0, 0], 'a5': [0, 0], 'a6': [-1.0, 0], 'a7': [0, -4.0], 'a8': [0, -1.0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.36185251542651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [3, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 5, 17], 'central_character': '2550.2449', 'coefficient_field': 'CDF', 'conductor': 2550, 'conductor_radical': 510, 'conjugate': '974990196587309177885763574577', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 4.0], [-7.0, 0]], [[1.0, 0], [2.0, 0], [11.0, 0]], [[1.0, 0], [0, -6.0], [-13.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [4.0, 0], [19.0, 0]], [[1.0, 0], [0, 5.0], [-23.0, 0]], [[1.0, 0], [0, 0], [29.0, 0]], [[1.0, 0], [-10.0, 0], [31.0, 0]], [[1.0, 0], [0, -9.0], [-37.0, 0]], [[1.0, 0], [-11.0, 0], [41.0, 0]], [[1.0, 0], [0, 10.0], [-43.0, 0]], [[1.0, 0], [0, -8.0], [-47.0, 0]], [[1.0, 0], [0, -11.0], [-53.0, 0]], [[1.0, 0], [-15.0, 0], [59.0, 0]], [[1.0, 0], [1.0, 0], [61.0, 0]], [[1.0, 0], [0, 14.0], [-67.0, 0]], [[1.0, 0], [-11.0, 0], [71.0, 0]], [[1.0, 0], [0, 8.0], [-73.0, 0]], [[1.0, 0], [-8.0, 0], [79.0, 0]], [[1.0, 0], [0, -5.0], [-83.0, 0]], [[1.0, 0], [-6.0, 0], [89.0, 0]], [[1.0, 0], [0, -8.0], [-97.0, 0]], [[1.0, 0], [-18.0, 0], [101.0, 0]], [[1.0, 0], [0, 11.0], [-103.0, 0]], [[1.0, 0], [0, -4.0], [-107.0, 0]], [[1.0, 0], [-14.0, 0], [109.0, 0]], [[1.0, 0], [0, -3.0], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 20, 'label': '2-2550-5.4-c1-0-20', 'leading_term': '1.460183495739947453302587342168816884600170134378662174', '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/2550/2/d/e/2449/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.4601834957399475, 1.4319712989911357, 1.3923136596410866, 1.3414591463485785, 1.279564015394083, 1.206725311847666, 1.1230194460302834, 1.0285438731212917, 0.9234594997009371, 0.8080315949715503, 0.6826672493180156, 0.5479477480308018, 0.40465456928548166, 0.25378804127951343, 0.0965779863269377, -0.06551406538396132, -0.23080128903934335, -0.3973866071835447, -0.5631861828274195, -0.7259610131924671, -0.8833561004284157, -1.0329464984263814, -1.1722893529023406, -1.2989808673123409, -1.4107169442249325, -1.505356076596757, -1.5809829032483182, -1.6359707056781942, -1.6690410173607186, -1.6793184498052895, -1.6663788192663633, -1.6302886904603786, -1.5716345440424397, -1.4915399263892084, -1.3916691550248883, -1.2742164303281909, -1.1418795412323663, -0.9978177443858831, -0.8455938351989754, -0.6891009055404431, -0.532474784537996, -0.37999367195004824, -0.2359669822093979, -0.10461590449410221, 0.010051367747253081, 0.10436639356435676, 0.175125567453205, 0.21970964417523606, 0.23619370364396514, 0.22344355594708443, 0.18119471746813356, 0.11011035503590763, 0.01181499796590136, -0.11109864488965476, -0.25509176190615984, -0.4157316297200519, -0.5877742637726225, -0.7652769237593711, -0.9417388714562724, -1.1102677626929731, -1.2637680550221524, -1.3951468631506152, -1.497531831593969, -1.564494854087347, -1.590274886154594, -1.5699927019989741, -1.4998502662286113, -1.3773074458739447, -1.2012290928121754, -0.9719960872956395, -0.6915747472823052, -0.3635400639264195, 0.0069505003437663245, 0.4132344488872448, 0.8472731046948283, 1.2998303439606682, 1.7606979054857346, 2.2189622168348304, 2.663305997879324, 3.0823363615187263, 3.464929793532042, 3.8005833187520204, 4.079760403226455, 4.294219747507351, 4.437315129835463, 4.504254882270476, 4.492310435974481, 4.4009646466157415, 4.231992283777287, 3.989467099621241, 3.6796922264340366, 3.3110532200696956, 2.8937957840050306, 2.439732983724554, 1.9618894931749373, 1.4740929999506152, 0.9905252295673197, 0.5252470315653982, 0.0917135093476989, -0.2977038080968292, -0.6321703247861584, -0.9028000401105759, -1.103009142708441, -1.2287966688035012, -1.2789394865782995, -1.2550915670101506, -1.1617806926203058, -1.0062993376873757, -0.7984903053865253, -0.5504316914416276, -0.27602971100542684, 0.0094682797877611, 0.2900247694443858, 0.5494082966365645, 0.7718137139854816, 0.9424837074348733, 1.0483079552110321, 1.0783763898341276, 1.024464030804682, 0.8814267802888516, 0.6474903777387908, 0.32441831286151573, -0.08245121514867784, -0.5643043780972583, -1.109086736558492, -1.701868738772075, -2.3253309369503428, -2.9603531135008696, -3.586686944610078, -4.183687945384847, -4.731079421523788, -5.209719150093625, -5.602338642191626, -5.894225175470108, -6.0738183489426385, -6.133195679457421, -6.068425650236317, -5.879771508169492, -5.571734812766383, -5.152934049727298, -4.63582028713614, -4.036238600227055, -3.3728505373372575, -2.6664389606379504, -1.9391218983998142, -1.2135063433589677, -0.5118160129609769, 0.1449712125640218, 0.737940248045149, 1.250975557098896, 1.6713859448076351, 1.990389905305322, 2.2034395901377737, 2.3103680765781816, 2.3153520250795556, 2.2266897123442932, 2.056402471732366, 1.819675411090125, 1.5341605549405322, 1.2191719350772636, 0.8948073249793851, 0.5810350203514395, 0.2967861121510313, 0.059092952563490425, -0.11768706957739743, -0.2225267141494878, -0.24823237632946218, -0.19177176865093326, -0.05440945682124618, 0.15835745397392498, 0.43706205690769, 0.7687181769600254, 1.13743922209556, 1.525197799759094, 1.9126916400884928, 2.2802759760271094, 2.608918936323693, 2.881134912662662, 3.0818513780617103, 3.1991672726589577, 3.2249657458932197, 3.155350561974864, 2.9908835567493286, 2.736609815633929, 2.4018672959480303, 1.9998879684383377, 1.5472077042187267, 1.0629115870433183, 0.56774961392569, 0.08316443537295115, -0.3697224736144547, -0.7711172929064144, -1.103503911566144, -1.352490740519226, -1.5075120657319219, -1.5623484693302543, -1.515439433518044, -1.3699712696583017, -1.1337345009951376, -0.8187562341508731, -0.4407243132883409, -0.018230591191552802, 0.42813006996754854, 0.8767609268367018, 1.3061150987287027, 1.6957455010525564, 2.0273002700543534, 2.2854133969236874, 2.458445304155373, 2.5390354843410745, 2.524438728525941, 2.4166274345106364, 2.2221544532585416, 1.9517832911451312, 1.6199045946020236, 1.2437690627671973, 0.842576661513807, 0.43646971720104194, 0.045482718761021224, -0.3114958552068327, -0.6176948062731867, -0.8593130802050295, -1.026208886809099, -1.1123883904668457, -1.1162679891776646, -1.0406963957290556, -0.8927357769528633, -0.6832143937291684, -0.42607579480156427, -0.13756095157261078, 0.16473086165075682, 0.4628496816572679, 0.7395141268954029, 0.9790845518893195, 1.1684346134073547, 1.2976712268623118, 1.3606612287053115, 1.3553338550380007, 1.283740823375911, 1.1518696725388273, 0.9692203047166102, 0.7481685759965362, 0.5031534964860906, 0.2497353808252734, 0.003580482790367893, -0.220567262480364, -0.40986512723278473, -0.5542408214650033, -0.6470973115228568, -0.6858073215327272, -0.6719633245668936, -0.6113627846308616, -0.5137238414960955, -0.3921426708439566, -0.2623194804028283, -0.14159459434120072, -0.04784845927517076], 'positive_zeros': ['0.74134550664436845406359186340575', '2.22956103492190910402914332489397', '2.64596247974211042143188680007504', '3.65534335159504863052349560232184', '4.98796752048631405859558859072281', '5.63503650627466803185498972448834', '6.18577458303303873598219905120156', '7.45324991615617745713253489974821', '8.292336160259142959544631054070209', '8.546008060917776011503918865748415'], 'prelabel': '2-2550-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.512410942658759, 'root_angle': -0.35241638234956674, 'root_number': '0.447213595499957939281834733746255247088123671922305145 - 0.894427190999915878563669467492510494176247343844610290*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17620819117478337', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74134550664436845406359186341', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22956103492190910402914332489', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.64596247974211042143188680008', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 20.36185251542651, 'bad_primes': [2, 3, 5, 17], 'central_character': '5.4', 'conductor': 2550, 'conductor_radical': 510, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2550/2/d/e/2449/2'], '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': '2-2550-5.4-c1-0-20', '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': '2-2550-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.512410942658759, 'root_angle': -0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74134550664436845406359186341', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '939767076474234498698499085537', 'Lhash_array': ['939767076474234498698499085537'], 'label': '2-2550-5.4-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2550/2/d/e/2449/2'}