-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2319474204955097488130123575125', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.1667928701453092, -0.6736481776669303], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-0.04125267696479814, -2.6454296846907948], 'a8': [0, 0], 'a9': [-0.5923962654520477, -1.0260604299770062], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.179056282979259, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.04125267696479814, 2.6454296846907948]]]], 'bad_primes': [2, 5, 7], 'central_character': '1400.249', 'coefficient_field': 'CDF', 'conductor': 1400, 'conductor_radical': 70, 'conjugate': '309150918025246845048745511483', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.1667928701453092, 0.6736481776669303], [1.5, 2.598076211353316]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.04125267696479814, 2.6454296846907948]], [[1.0, 0], [0.7057370639048864, -1.222372451467747], [-5.5, -9.526279441628825]], [[1.0, 0], [0, 6.475651900285685], [-13.0, 0]], [[1.0, 0], [-2.248432881444753, -1.2981333293569342], [8.5, 14.722431864335457]], [[1.0, 0], [-0.5812519122148827, -1.0067578439527416], [-9.5, 16.454482671904334]], [[1.0, 0], [1.36310489163605, -0.786988976119769], [11.5, -19.91858428704209]], [[1.0, 0], [6.226681596905678, 0], [29.0, 0]], [[1.0, 0], [2.4927260400246554, -4.317528150672674], [-15.5, -26.846787517317598]], [[1.0, 0], [-7.340129859281255, 4.237825950142843], [18.5, -32.04293994002423]], [[1.0, 0], [-3.573977952239538, 0], [41.0, 0]], [[1.0, 0], [0, 7.248970303380007], [-43.0, 0]], [[1.0, 0], [9.477403578081132, -5.471781507023865], [23.5, -40.703193977868615]], [[1.0, 0], [11.073097486506096, 6.393055814597263], [26.5, 45.89934640057525]], [[1.0, 0], [1.0209445330007911, -1.7683278028670504], [-29.5, -51.09549882328188]], [[1.0, 0], [-0.3079335091205601, -0.5333564831497845], [-30.5, 52.827549630850754]], [[1.0, 0], [-5.268706413302978, -3.0418890660015823], [33.5, 58.023702053557386]], [[1.0, 0], [8.276311449430901, 0], [71.0, 0]], [[1.0, 0], [3.046279835657235, 1.7587704831436335], [36.5, 63.21985447626402]], [[1.0, 0], [-0.4396926207859084, -0.7615699589143088], [-39.5, 68.41600689897065]], [[1.0, 0], [0, 3.9016739480461466], [-83.0, 0]], [[1.0, 0], [-2.9815816867874907, -5.164250968432849], [-44.5, 77.07626093681505]], [[1.0, 0], [0, 3.2344223834293184], [-97.0, 0]], [[1.0, 0], [7.266044443118978, -12.58515814553558], [-50.5, -87.4685657822283]], [[1.0, 0], [13.833536900802336, -7.98679625352285], [51.5, -89.20061658979718]], [[1.0, 0], [15.441829677476818, -8.915344521071594], [53.5, -92.66471820493493]], [[1.0, 0], [-6.117211191714659, 10.595320584678749], [-54.5, -94.39676901250381]], [[1.0, 0], [0, 4.2908593693815895], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 32, 'label': '2-1400-35.4-c1-0-32', 'leading_term': '0.539090662083704501905990281744674774011804661079479774', '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/1400/2/bh/h/249/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.5390906620837045, 0.6752529126503062, 0.813743310718331, 0.9543672868056828, 1.0967855479728732, 1.2404609466722907, 1.3846163861583412, 1.5282057212767264, 1.6698986514577738, 1.8080797847336565, 1.94086144485733, 2.066109401964659, 2.1814804895641253, 2.2844709650856854, 2.37247441591127, 2.4428479588576253, 2.4929853976709273, 2.5203958769459334, 2.522786402803778, 2.4981464012400183, 2.4448322707524532, 2.361649675977879, 2.2479311436053204, 2.1036063800596985, 1.9292626499717322, 1.7261925505718805, 1.4964266023841892, 1.2427482602652824, 0.9686892366750092, 0.6785034229041801, 0.3771181914397639, 0.07006245691084007, -0.2366284472222124, -0.5365302697789063, -0.8229681156868048, -1.0891730637387669, -1.3284538784449993, -1.5343797782456963, -1.7009694999235299, -1.8228812751814059, -1.8955978426278528, -1.9156002876124696, -1.880524361011476, -1.7892929990489896, -1.6422190663783807, -1.4410728834477666, -1.1891098777282112, -0.8910547085161523, -0.5530394387334996, -0.18249473642120204, 0.21200535437579476, 0.6209428759050374, 1.0340957513863593, 1.4408123238977917, 1.8303134461289976, 2.1920134732049705, 2.515850275128534, 2.792613433392985, 3.0142591765962576, 3.1742003918533346, 3.26756025980649, 3.2913787238003085, 3.2447621242662765, 3.1289678951062587, 2.947418198099275, 2.7056387127987627, 2.411121432915091, 2.073113158378148, 1.7023343128852533, 1.310635645940571, 0.9106031748730721, 0.5151242619994669, 0.13692988333525982, -0.21187018564650184, -0.5202414649408125, -0.7786499402118875, -0.9794404308324287, -1.117151366863211, -1.1887510333646472, -1.1937829113196852, -1.1344109697688647, -1.0153595411676963, -0.8437466083640711, -0.6288137870930652, -0.38156082140030295, -0.11429682549357197, 0.15987539756667646, 0.4276220513937638, 0.6759652742257125, 0.8928695163614405, 1.067801590408397, 1.1922387285825957, 1.260100248759299, 1.2680808563682398, 1.215867140388933, 1.1062233521884803, 0.9449379269074831, 0.7406282117807037, 0.5044072565966964, 0.24942301954484328, -0.009713351682255676, -0.2575876936202019, -0.4787039695310601, -0.6582349469996912, -0.7827683353862873, -0.8410131590708672, -0.8244316104942746, -0.7277637641171735, -0.5494163124002975, -0.29169180042067644, 0.03915850062315562, 0.4330671913184923, 0.8764694164529327, 1.3527993308411521, 1.843147233461953, 2.32705187547662, 2.7833949839523884, 3.1913588904121015, 3.5314036700381224, 3.786217674377703, 3.9415949832321835, 3.987195215721565, 3.9171453220904033, 3.730449307745229, 3.431180086529911, 3.0284374815691963, 2.536067355044108, 1.9721484428315512, 1.3582651328670114, 0.7185955681200705, 0.07885449041587272, -0.5348613816353746, -1.0972714158029986, -1.5850948541620444, -1.9781617352039174, -2.260394443289647, -2.420608411484792, -2.4530883220095463, -2.357906435832899, -2.140961981671902, -1.813734264733268, -1.392756640866215, -0.8988330030225654, -0.3560321789025022, 0.20949210911745386, 0.770798012918426, 1.3015040833880493, 1.7771205747874526, 2.1762941160909475, 2.4818995883704758, 2.6819199114398162, 2.7700646440642447, 2.746091373377218, 2.615809172316412, 2.3907601586330918, 2.087592512128109, 1.7271552581587581, 1.3333607591637007, 0.9318742731327028, 0.5487003391303157, 0.20874248340322465, -0.06558465724681145, -0.25561346640678145, -0.3474805439187505, -0.3329220374121111, -0.20976006984495507, 0.01794996995609412, 0.34012268148264957, 0.7411880529155646, 1.200950942416905, 1.6957181882727814, 2.1996308829434197, 2.6861266892788813, 3.1294485857480314, 3.506112685394673, 3.79624909804231, 3.9847362222782885, 4.062060086325478, 4.024845834849976, 3.876027344502351, 3.624642182769021, 3.2852614744819237, 2.8770863835667604, 2.4227635109723717, 1.9469892722228683, 1.4749871107314694, 1.0309503023879225, 0.636546467160587, 0.30957740344526147, 0.06287953264064394, -0.09646352261727967, -0.16754316482834838, -0.15565190303434306, -0.07190680300757522, 0.06751084263348117, 0.24245612910675737, 0.4301955546653664, 0.6069718764094904, 0.7496605448374292, 0.8374117045891369, 0.8531705753144168, 0.7849746554032421, 0.6269384220739883, 0.37985440955874455, 0.05136271276957258, -0.3443322743260474, -0.7871903428567518, -1.2524727187157134, -1.712224373022121, -2.137013894081367, -2.4978246898495042, -2.7679789458323887, -2.9249707539758703, -2.9520876519531227, -2.839710475481181, -2.586199429549194, -2.1982986421459527, -1.6910207558228132, -1.0870055639993579, -0.41538028851602393, 0.28981832161468485, 0.9915704430688849, 1.6520342212599828, 2.2348099117059492, 2.70716618853913, 3.04208713076874, 3.2200069486836616, 3.230116814053061, 3.0711532684415204, 2.751609132583457, 2.2893437082067623, 1.7106071032840493, 1.0485312841400656, 0.34117549212655185, -0.3707563823450547, -1.0463860529008957, -1.647164234478691, -2.1392484654806294, -2.4956026760315995, -2.697681914097393, -2.7365908838317146, -2.6136378229545865, -2.340243691331203, -1.9372081973904987, -1.4333761396694387, -0.8637871035421254, -0.2674260593684808, 0.31528051311806193, 0.8450606058229891, 1.28631529824339, 1.6093946834181476, 1.7924810248156227, 1.8229545080868894, 1.698150981711504, 1.4254614798637135, 1.021767406063469, 0.5122500560374053], 'positive_zeros': ['1.82974252095766487049261586765414', '2.89855879607238860123546997373870', '4.24106487890555426269089305836726', '5.00491088672665662345798804705187', '5.85715452668463860137371012455419', '6.43895498302419907766892484176790', '7.62452904173808063070361231286926', '8.415892154183163666253427895848832', '9.417973122673130304374725509449409', '9.722723754912989411968001492900757'], 'prelabel': '2-1400-35.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.343509575727167, 'root_angle': -0.9657073015361034, 'root_number': '-0.99420233689317800544329764408723767821630261247338523230 - 0.1075254077701813891202439803621822909573050586264800017*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4828536507680517', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.82974252095766487049261586765', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.89855879607238860123546997374', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.24106487890555426269089305837', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 11.179056282979259, 'bad_primes': [2, 5, 7], 'central_character': '35.4', 'conductor': 1400, 'conductor_radical': 70, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1400/2/bh/h/249/2'], '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': '2-1400-35.4-c1-0-32', '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': '2-1400-35.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.343509575727167, 'root_angle': -0.4828536507680517, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.82974252095766487049261586765', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2319474204955097488130123575125', 'Lhash_array': ['2319474204955097488130123575125'], 'label': '2-1400-35.4-c1-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1400/2/bh/h/249/2'}