-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2044696275410521450902138478630', 'a10': [0.30901699437494745, 0.9510565162951535], 'a2': [0.30901699437494745, 0.9510565162951535], 'a3': [-0.30901699437494745, 0.9510565162951535], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [1.0, 0.0], 'a6': [-1.0, -5.918439231014134e-61], 'a7': [1.1524502934702743, -0.837304149618413], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [-0.8090169943749475, -0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.426087387979079, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.30901699437494745, -0.9510565162951535]]], [3, [[1.0, 0], [0.30901699437494745, -0.9510565162951535]]], [5, [[1.0, 0], [-1.0, 0]]], [31, [[1.0, 0], [3.9741207981508806, -3.899533803123728]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.841', 'coefficient_field': 'CDF', 'conductor': 930, 'conductor_radical': 930, 'conjugate': '1197910971768657158257074809654', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.1524502934702743, 0.837304149618413], [2.163118960624632, -6.657395614066075]], [[1.0, 0], [-4.352637865941729, 3.1623765186131627], [3.3991869381244215, -10.46162167924669]], [[1.0, 0], [-2.1337239270919075, 6.566927003287695], [-10.517220926874316, -7.641208279802151]], [[1.0, 0], [-0.2466697564297998, -0.17921606841897336], [5.253288904374106, 16.167960777017612]], [[1.0, 0], [1.208804508250163, 3.720317734704755], [-15.371322893124, 11.16791979355699]], [[1.0, 0], [0.9098969444748735, 0.6610788262631281], [7.1073908706237905, 21.874299874788534]], [[1.0, 0], [1.5275184178018646, 4.701218287200789], [-23.461492836873475, 17.04577231648172]], [[1.0, 0], [3.9741207981508806, -3.899533803123728]], [[1.0, 0], [-4.5298075489556275, 0], [37.0, 0]], [[1.0, 0], [-0.9858823893863848, -3.0342339994054797], [-33.16969676937284, 24.099195343991397]], [[1.0, 0], [-0.34440505107293046, -1.0599697558071604], [-34.78773075812274, 25.274765848576344]], [[1.0, 0], [3.466555447257224, -10.668960630728757], [-38.02379873562253, -27.625906857746237]], [[1.0, 0], [0.5090294512016125, 0.369831544305201], [16.377900701872214, 50.405995363643136]], [[1.0, 0], [-3.934871282570737, 12.110288567271631], [-47.7320026681219, -34.67932988525592]], [[1.0, 0], [-1.8541019662496845, 0], [61.0, 0]], [[1.0, 0], [6.259724936419493, 0], [67.0, 0]], [[1.0, 0], [-11.563081590144638, -8.401070530035932], [21.940206600621266, 67.52501265695591]], [[1.0, 0], [13.012720398530007, -9.454294774574919], [22.558240589371163, -69.42712568954622]], [[1.0, 0], [12.78024808562127, 9.285393752662952], [24.412342555620846, 75.13346478731714]], [[1.0, 0], [-4.315677481515348, -13.282289536617744], [-67.14841053312064, 48.78617594027527]], [[1.0, 0], [-10.652517181694622, 7.7395067628089524], [27.502512499370322, -84.64402995026867]], [[1.0, 0], [-5.0796763922399055, 3.6906009274671323], [29.974648454369902, -92.2524820806299]], [[1.0, 0], [3.078704640262302, 2.236809852318008], [31.210716431869688, 96.05670814581052]], [[1.0, 0], [-3.0482296273315326, -9.381486141568116], [-83.32875042061958, 60.54188098612473]], [[1.0, 0], [-15.383672115427197, -11.176892028748055], [33.06481839811937, 101.76304724358143]], [[1.0, 0], [1.6759605312581813, -5.1580761360087966], [-88.18285238686927, -64.06859249987957]], [[1.0, 0], [6.487934120762034, -4.713760057630687], [34.91892036436906, -107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-930-31.4-c1-0-18', '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/930/2/n/a/841/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.8693808232471727, 1.905461397410889, 1.9157353635662446, 1.8972628075168263, 1.844331876609796, 1.7506695045356813, 1.6117126113102087, 1.4265810573933262, 1.1995421800762265, 0.9408403791127441, 0.6667961662283116, 0.3990992325447348, 0.16326108649275806, -0.013733421939637929, -0.10643356335868158, -0.0943288687588859, 0.03472029226754939, 0.2814890701914719, 0.6333307305216204, 1.0635247110446393, 1.5323899467366995, 1.990334142341882, 2.3827540360277752, 2.656407090978428, 2.7665817776058184, 2.6841504601524453, 2.4014463600143148, 1.9359076622550422, 1.330604864687173, 0.651114742623235, -0.021301364223212493, -0.5996740404623176, -1.003328752206163, -1.1702960202433494, -1.0682162526055359, -0.7018141382344403, -0.11533215592815037, 0.6110507153084953, 1.3708955037744779, 2.0463272250550495, 2.5260617221842017, 2.723910325895629, 2.5946453111894825, 2.1442294604804686, 1.4320903322803251, 0.5642991737088294, -0.3219622891939677, -1.0806415989564024, -1.5823303924692504, -1.7386880365653161, -1.5211990799882307, -0.9703277259283238, -0.1925856434498007, 0.6548998049052848, 1.3903839477442637, 1.8399509178626055, 1.8707120018297496, 1.4184661011438566, 0.504130037332502, -0.7649760277372745, -2.210202419434041, -3.611066096280043, -4.744238721714854, -5.424890361536156, -5.542352495087997, -5.082755430340315, -4.133548255416005, -2.8682579760523916, -1.5138371364781937, -0.3066686724653161, 0.5540734758666218, 0.9461038718708431, 0.8482568767071332, 0.3437867975469129, -0.39841284939825744, -1.1610540927165793, -1.7263915809423225, -1.9245029144136099, -1.6712208729752418, -0.9870960818035736, 0.00712341900099573, 1.1177332679795147, 2.1220159992058547, 2.818871411525013, 3.0743785239397727, 2.851546675797572, 2.217131838283042, 1.323826311788686, 0.3721034017141889, -0.4389466554853377, -0.959608109732412, -1.1243284710811468, -0.9644808228719377, -0.5958156109402399, -0.18383866882887737, 0.10380923422936202, 0.14529426403197823, -0.10015830121331355, -0.5795707864268143, -1.1600414568508002, -1.6658733236770609, -1.9292227895631053, -1.8403747912241175, -1.3833268026310952, -0.6459172659411186, 0.19953111215545355, 0.9408879848347166, 1.3846147021962423, 1.411753318717386, 1.0151748272599908, 0.30620239800214943, -0.5131716491800901, -1.2065771352585215, -1.5735664473318831, -1.5144158355607227, -1.070154780684056, -0.42429944916539625, 0.13724999306404198, 0.3000296320137806, -0.1897082013595628, -1.4441710596395254, -3.3848775171171313, -5.741161222144281, -8.100169028058946, -9.998284795803364, -11.032021558962246, -10.95998019277748, -9.768535325843343, -7.682526989044986, -5.116332402729787, -2.576557824038261, -0.5408704576786911, 0.6556012338198816, 0.8964477018951621, 0.3027256394508354, -0.8102217384217962, -2.0254315836690426, -2.9404582801074666, -3.274650569036277, -2.938076332263313, -2.043851381337633, -0.8620869026345291, 0.26943608844165723, 1.0503885481802842, 1.3071640424366502, 1.0399387741218125, 0.41433725729226617, -0.29838941443268036, -0.8129621771987235, -0.9240790754698337, -0.5729493188026661, 0.13467542610654254, 0.9645222650358731, 1.632133138590151, 1.8981459308523083, 1.649549424870418, 0.9402506123960493, -0.022747611297709237, -0.9437112274039424, -1.5327062959140043, -1.5997924472283556, -1.1180505964334944, -0.23437292115081426, 0.7762331467234737, 1.5985753059027332, 1.9790708922630535, 1.8080430642051581, 1.155124340213107, 0.24554339471387265, -0.615415139767088, -1.1450524449552943, -1.1787979782809326, -0.7262944710221068, 0.031534804096406854, 0.8043098904148522, 1.29270918555446, 1.293825238523146, 0.7750985667247564, -0.10948379591423094, -1.067991877114623, -1.768819835556762, -1.9558598719277693, -1.5410023840751017, -0.6410417854767537, 0.45565958478064866, 1.3834539662231917, 1.8238331347205359, 1.6176588195676997, 0.8256511010219504, -0.2857681765365513, -1.3309750256620703, -1.9363786785326291, -1.8721821511023262, -1.1386537888247574, 0.024937296620703306, 1.2147762490012317, 1.9975371668026078, 2.061187389776975, 1.3295306011937027, -0.0009266420867094323, -1.5177872259747225, -2.7273398224546654, -3.2234099003823404, -2.8334765948300844, -1.6907439010979963, -0.20443570955375143, 1.0655207723688669, 1.590416528479934, 1.0518188736313834, -0.5424273767842342, -2.8457096319848714, -5.270229111799785, -7.164489045833813, -8.013467927266591, -7.596238451246141, -6.049743178185807, -3.818738911382121, -1.509926536868097, 0.3000298564227916, 1.2383859140731084, 1.2354618647708517, 0.5192313591680698, -0.4879349714314738, -1.3303209974906751, -1.6791688307967718, -1.4363125593905723, -0.747606521078548, 0.07366711752467225, 0.6805946179053702, 0.8311306744849362, 0.47902725836040166, -0.21542397540891503, -0.9560442319440169, -1.4328669413947932, -1.4466197575148614, -0.9865876797589859, -0.23188342079762514, 0.5233412275008438, 0.9901234431138348, 1.0018255474485174, 0.5809649114780328, -0.07135597668034672, -0.659407399338177, -0.9163264516367744, -0.7166589422764933, -0.13094315075789598, 0.6020142210937226, 1.1763054031658577, 1.353967154514201, 1.0786175084705454, 0.5185419658037704, 0.016493652217033906, -0.03961953204931793, 0.6220895758959558, 2.0275471504408924, 3.9126055825169823, 5.788705485371355], 'positive_zeros': ['1.61298095472237521362769035245632', '1.97550393562791628741911943565199', '3.74584826357178766240441445599759', '4.52107907244601068525278703509458', '5.70357535120753290635538751672219', '6.52837189146723365800859728365080', '7.30303566476071964589850077761471', '8.663123787808629849024554091688818', '9.185738540749537990109442581667552', '9.999181881263967004866723416314456'], 'prelabel': '2-930-31.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': -0.13497320687326256, 'root_number': '0.9114379118419031 - 0.41143764151724277*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0674866034366', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.61298095472237521362769035246', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.97550393562791628741911943565', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.74584826357178766240441445600', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.426087387979079, 'bad_primes': [2, 3, 5, 31], 'central_character': '31.4', 'conductor': 930, 'conductor_radical': 930, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/2/n/a/841/1'], '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': '2-930-31.4-c1-0-18', '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': '2-930-31.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': -0.06748660343663128, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.61298095472237521362769035246', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2044696275410521450902138478630', 'Lhash_array': ['2044696275410521450902138478630'], 'label': '2-930-31.4-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/n/a/841/1'}