-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1088693349364894006657483645668', 'a10': [0.05767641820117589, -0.02309015473283255], 'a2': [0.17421151262654205, 0.016635182482607862], 'a3': [-0.690079011482112, 0.7237340381050702], 'a4': [-1.9337844726900153, -0.37270640811459305], 'a5': [0.3155380095581082, -0.16267114999903237], 'a6': [-0.1322591562148801, 0.1146032112341771], 'a7': [2.6312810406358955, 0.2763332864315834], 'a8': [-0.6665175882827239, -0.19570722192919443], 'a9': [-0.0475819158237423, -0.998867339183008], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.690079011482112, -0.7237340381050702]]], [7, [[1.0, 0], [-2.6312810406358955, -0.2763332864315834]]], [23, [[1.0, 0], [-4.330544965651198, -2.060674719715139]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.19', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': '1779824427301649985601127429972', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.17421151262654205, -0.016635182482607862], [1.9638573945254134, 0.37850248872082043]], [[1.0, 0], [0.690079011482112, -0.7237340381050702]], [[1.0, 0], [-0.3155380095581082, 0.16267114999903237], [2.900284547855991, -4.072879760251679]], [[1.0, 0], [-2.6312810406358955, -0.2763332864315834]], [[1.0, 0], [-0.13228588745363595, -1.385360489825513], [-10.801215669889773, 2.081763687964512]], [[1.0, 0], [0.39944898882608343, 0.05743209415143143], [12.473408656988466, 3.662523238938586]], [[1.0, 0], [-0.008656187944717937, 0.025010412550762876], [-13.362902610627387, -10.50870276575029]], [[1.0, 0], [-1.8679852786156284, -5.397189011525205], [-14.935008800112962, 11.7450207381915]], [[1.0, 0], [-4.330544965651198, -2.060674719715139]], [[1.0, 0], [-3.1840903543822385, -3.674636155892855], [-4.127130309925269, 28.70482181454705]], [[1.0, 0], [-4.358683640903024, 1.0574052099156912], [27.553898908302628, -14.205022173549722]], [[1.0, 0], [-8.037211175410622, 0.3828595556230944], [36.83246113520413, -3.5170736022547584]], [[1.0, 0], [6.16669957588082, -9.595571841085329], [-17.03201553307734, -37.29491180953525]], [[1.0, 0], [0.19403687411138218, 0.6608289060350941], [-36.17390191174079, 23.247555150590696]], [[1.0, 0], [0.8625705714183675, 0.4980053516034437], [23.5, 40.703193977868615]], [[1.0, 0], [8.036669085739488, 10.219456073740144], [-12.495223581999642, 51.50601312114771]], [[1.0, 0], [2.2170676810913403, 5.537967338655805], [-42.70030824819914, 40.71466167744461]], [[1.0, 0], [-2.7305707002259814, 2.6035939038152622], [2.9024968652482803, -60.93090769016349]], [[1.0, 0], [-3.3925860070972833, -2.415849559243725], [21.91355354226725, 63.31505485388279]], [[1.0, 0], [5.738556624782818, 12.565686240695353], [-46.49511211011524, 53.65821977915234]], [[1.0, 0], [1.4533795698760337, -7.540849268915811], [-67.7708591101733, -27.13135926320391]], [[1.0, 0], [-6.420671950494852, 8.164548553878898], [-18.62495590524475, -76.7731138975598]], [[1.0, 0], [8.459544779375236, -5.4366193143125425], [34.479446079156574, -75.49945561442503]], [[1.0, 0], [-3.105451806157432, 12.800846693568282], [-79.10635493028819, -40.78216043373953]], [[1.0, 0], [-10.040184715961532, -6.45243492051038], [40.295256261182985, 88.23430354938829]], [[1.0, 0], [4.624040810920998, -8.969387833073974], [-58.585747866691015, -82.2721711570839]], [[1.0, 0], [1.6795011229678527, 2.358529316067432], [-33.68800022169443, 97.33508432761086]], [[1.0, 0], [-2.216875693586796, -2.3249923139245334], [-5.091264993140426, 106.87880529258186]], [[1.0, 0], [-6.329026941667193, -2.1904975219044722], [85.67978732696383, 67.37932949804596]], [[1.0, 0], [6.524118059023805, -2.979464884872416], [73.99926293581721, -85.39970190203118]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-483-161.19-c1-0-9', '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/483/2/bf/a/19/17', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1490029017850691, 1.0554814782505588, 0.9460656425845613, 0.8151806650093412, 0.6563218620008365, 0.46353088143469895, 0.23275142445131214, -0.03704564138067898, -0.3430043662476014, -0.6778138593922695, -1.0294638101122715, -1.3813813865813136, -1.7130089724546453, -2.0008647453285655, -2.22009064906106, -2.346439041029378, -2.358586329361978, -2.2405969579668943, -1.984303154574344, -1.5913246545966586, -1.0744376180453326, -0.4580210702735364, 0.22263270957029074, 0.9232599194846715, 1.5938033011519734, 2.182655635925627, 2.6416361087605815, 2.9312199126595075, 3.02543224344677, 2.9157687640392593, 2.6135334808373867, 2.150101412431969, 1.574815876639787, 0.9505040091673911, 0.3469113144044638, -0.16732265707740687, -0.5332465363805625, -0.7096475592669208, -0.6794234117018121, -0.453231084020267, -0.06963731764956511, 0.4085869177301771, 0.9018626372762262, 1.3241635032165207, 1.5950980369659253, 1.6520848631793716, 1.460815207486114, 1.0222816434475046, 0.37501660852498697, -0.40819770394176724, -1.2290864101580212, -1.9771730699641523, -2.5458657415330057, -2.848998695490443, -2.835218926932132, -2.497743383359855, -1.8775761940957352, -1.059211168662242, -0.1590284710597561, 0.692156030635746, 1.3698268319762374, 1.7764786961603218, 1.8587575820942175, 1.6178641770901903, 1.111017162413821, 0.44320619089837954, -0.24985647476050987, -0.8250383673042092, -1.1575029419212388, -1.1643181135671221, -0.8215413780011913, -0.17129796360591995, 0.6829861405699623, 1.5929352229187095, 2.3907120983560075, 2.919336942108314, 3.0623770974544766, 2.767373165477198, 2.0582683304167064, 1.0339794292704705, -0.14721725789609963, -1.2950756680969144, -2.2217282028032552, -2.776599204227164, -2.875108809431735, -2.5153494564178907, -1.7790909032676425, -0.8164792152438717, 0.18293549695762557, 1.0273423539771211, 1.5606383887577653, 1.693486528464678, 1.420940514697018, 0.8227469625894336, 0.045986251202708134, -0.7265396342922934, -1.3156254384640158, -1.5843183631066153, -1.4674909291076639, -0.9857127468527586, -0.2401321906858053, 0.6107490262531561, 1.38741748056532, 1.930706067206511, 2.1387092389553835, 1.9905702014235875, 1.5512710304929016, 0.9558454126384016, 0.3762541834027821, -0.021594643829037516, -0.12056504662238388, 0.11569507401008598, 0.629737193325719, 1.2803322751233133, 1.8741552428157249, 2.212426404733526, 2.141836614511109, 1.5975103744320562, 0.6270779556789126, -0.6110457545518464, -1.8761882421012253, -2.895353113013348, -3.4237606189444922, -3.3021628616934726, -2.4972796205239676, -1.1151818479843203, 0.6164794891608125, 2.3942217233924574, 3.90252401754865, 4.881178042099605, 5.180541399390016, 4.791655245923993, 3.844048615684711, 2.5717912746164293, 1.2560921266512581, 0.1585323321244523, -0.5386318604126025, -0.7704297019208888, -0.5962472190257286, -0.17477345837898595, 0.28609588366447103, 0.5907554771845679, 0.6121017493726114, 0.3271210454920867, -0.17800380474363559, -0.7348876277145848, -1.1448075310101535, -1.2411277074821467, -0.944639406113853, -0.2956064691383809, 0.547726261195177, 1.3453892536035812, 1.8382433882088842, 1.8206381692385991, 1.203413006022181, 0.049223114780827686, -1.4310550454770576, -2.921946328115861, -4.077288001682416, -4.606081246413233, -4.348002955095755, -3.3182804186451507, -1.7091813539042082, 0.15340236972745108, 1.8878598653946315, 3.149432971529575, 3.7134007358175087, 3.5270423541300415, 2.7167369167022564, 1.5485754709279973, 0.35344215347862534, -0.5628172997277501, -0.9995098809622753, -0.9096889093080783, -0.40436130021069533, 0.2879802581864067, 0.8941211572186305, 1.1796717539161892, 1.018941728377101, 0.4308363554407158, -0.42943941916216355, -1.3199568284203622, -1.9876880023288896, -2.2471009248020235, -2.0376652051807915, -1.4424831510068605, -0.662009595281128, 0.04941510233113933, 0.4648658915515543, 0.45870998822873266, 0.049558160322799076, -0.6021449557343298, -1.2425435651477699, -1.6050693055830958, -1.499100017407199, -0.8788753785954188, 0.1299542792798452, 1.2565081946784968, 2.1580378538909266, 2.5201401310141307, 2.1544084365198892, 1.0637125096911257, -0.5460068645995707, -2.3131213754920363, -3.8149275775053466, -4.682993153256449, -4.705816428186988, -3.8883855491224453, -2.450491733739336, -0.7636504363965265, 0.7551577369172904, 1.7616010358076084, 2.078877165854301, 1.7411625109872082, 0.9730095818893946, 0.11164440981432397, -0.5033297719423883, -0.6382581397384324, -0.23788319389093399, 0.5607060865115241, 1.4767754023869033, 2.1815379689251166, 2.40982503709244, 2.0516595823614168, 1.1937187219785808, 0.09652700738991066, -0.8861781736673537, -1.4206766861297182, -1.3029461362895722, -0.5292418675659621, 0.6958995381662337, 2.017889032393876, 3.038935183532547, 3.440054310352014, 3.079552299427817, 2.03651424696241, 0.5853131396007524, -0.8907010819139797, -2.018522710161073, -2.54931466077564, -2.4300690339920714, -1.8103153661682738, -0.9825235735027237, -0.27680283414123713, 0.05432387627879221, -0.07798812227996507, -0.5711720372064427, -1.1713305221681132, -1.5674367994898293, -1.5072299329502086, -0.8944859422416775, 0.16685183913196516, 1.3984521283160805, 2.4362055484801477, 2.95267413292333, 2.7719529014730133, 1.9370146092357836], 'positive_zeros': ['0.858827621088085544003775552556329', '2.70993106258771137026918041977282', '4.33087522470062627318713995895188', '5.01933473400907088972330441013992', '6.06166165627952665946827247611936', '7.27227131513178537487373108832758', '8.203808553435417088154951859399438', '8.901922699268405635254338073946312', '9.984649534150190680391497350931780', '10.97632749667301317401493527937608'], 'prelabel': '2-483-161.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.30435358101462195, 'root_number': '0.5766655515003061 - 0.8169803190486585*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.152176790507', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.858827621088085544003775552556', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.70993106258771137026918041977', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.33087522470062627318713995895', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.19', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/bf/a/19/17'], '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': '2-483-161.19-c1-0-9', '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': '2-483-161.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.15217679050731098, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.858827621088085544003775552556', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1088693349364894006657483645668', 'Lhash_array': ['1088693349364894006657483645668'], 'label': '2-483-161.19-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/bf/a/19/17'}