-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2200379673399564048778892189202', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.766044443118978, -0.6427876096865394], 'a4': [0.0, 0.0], 'a5': [0.8263518223330697, -0.3007674663608706], 'a6': [0.0, 0.0], 'a7': [-1.0923962654520476, -1.8920858337614448], 'a8': [0.0, 0.0], 'a9': [0.17364817766693036, 0.984807753012208], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.282356664340774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.766044443118978, 0.6427876096865394]]], [19, [[1.0, 0], [2.777188796356143, 3.3596461702676246]]]], 'bad_primes': [2, 3, 19], 'central_character': '912.625', 'coefficient_field': 'CDF', 'conductor': 912, 'conductor_radical': 114, 'conjugate': '572053469766658213297266501925', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.766044443118978, 0.6427876096865394]], [[1.0, 0], [-0.8263518223330697, 0.3007674663608706], [3.83022221559489, -3.2139380484326967]], [[1.0, 0], [1.0923962654520476, 1.8920858337614448], [-3.5, 6.06217782649107]], [[1.0, 0], [0.08125191221488266, -0.14073244016830305], [-5.5, -9.526279441628825]], [[1.0, 0], [-0.5812519122148827, 0.4877282651605968], [2.2574263096700946, -12.802500789158705]], [[1.0, 0], [-0.5393628462133006, 3.058878703906754], [-15.974774553360442, -5.814342436536369]], [[1.0, 0], [2.777188796356143, 3.3596461702676246]], [[1.0, 0], [-1.213011023880231, -0.44149990652917365], [17.619022191736494, 14.784115022790404]], [[1.0, 0], [1.1317591116653483, 6.418524874174379], [-27.251086002791343, 9.918584156444393]], [[1.0, 0], [-0.479055466999209, -0.8297484084862655], [-15.5, 26.846787517317598]], [[1.0, 0], [1.1625038244297654, 0], [37.0, 0]], [[1.0, 0], [8.11721119171466, 6.81114891715586], [7.119575284344144, 40.37711787350053]], [[1.0, 0], [0.16637421769158586, -0.06055526298906265], [32.93991105411605, -27.639867216521193]], [[1.0, 0], [-0.6021964452156737, -3.415225751590062], [-44.16555317693769, 16.07494673630643]], [[1.0, 0], [7.83022221559489, 2.849967814166494], [40.60035548530583, 34.067743313386586]], [[1.0, 0], [-0.48292586026102946, 2.738808651521619], [-55.44186462636859, -20.179188456214455]], [[1.0, 0], [6.7908593693815895, 2.4716706755426525], [46.728711030257664, 39.2100441908789]], [[1.0, 0], [0.18479253090409536, 1.0480105209175399], [-62.95940559265586, 22.915349602819806]], [[1.0, 0], [-4.7771887963561435, 1.7387545253436227], [54.38915546144744, -45.63792028774429]], [[1.0, 0], [-1.722811203643857, -1.445610245565646], [12.676316969685915, 71.89096596989118]], [[1.0, 0], [-4.015014746498985, -3.368997392958639], [13.718206035687498, 77.79981248796443]], [[1.0, 0], [8.556903812500568, 14.820992158730814], [-41.5, 71.88010851410841]], [[1.0, 0], [-11.96837794031034, 10.042661515504701], [15.4546878123568, -87.64789001808651]], [[1.0, 0], [1.6356295049271687, -9.276115874923768], [-91.15018421623311, -33.17595390258987]], [[1.0, 0], [4.83022221559489, -4.053037679609977], [17.538465944359967, -99.46558305423301]], [[1.0, 0], [4.30793350912056, -7.461559713425293], [-51.5, -89.20061658979718]], [[1.0, 0], [6.573977952239538, 11.386463821116486], [-53.5, 92.66471820493493]], [[1.0, 0], [-9.44356301404773, 3.437175842530596], [83.49884429996861, -70.06384945583278]], [[1.0, 0], [-8.04457741294866, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-912-19.17-c1-0-17', '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/912/2/bo/e/625/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.924082250964371, 1.1573878269969267, 1.3839132938752225, 1.6005448629013685, 1.7994686159451194, 1.9683276954854185, 2.091245507106721, 2.1504938270050133, 2.128601188375058, 2.010724568681255, 1.7871010574884962, 1.4553581936929265, 1.0224156341185942, 0.5056820089926334, -0.06674143730257269, -0.6570828216748812, -1.2202717040915072, -1.7076308789666401, -2.071669523785913, -2.2715607860218396, -2.278706979110639, -2.0816670886540494, -1.6896758446638829, -1.13404591879415, -0.4669269352036804, 0.24280849637177498, 0.9163963805309592, 1.4741473594718706, 1.8455554387143789, 1.979239115885191, 1.851244199126327, 1.4702886263730168, 0.8788180269762056, 0.14925557681610271, -0.6244817694822861, -1.3393583302968832, -1.897912960894393, -2.2231393175156726, -2.2711585546362985, -2.0394081275277913, -1.568599814175843, -0.9375987593580626, -0.251526960762647, 0.37538026503064625, 0.8395548627051299, 1.0671842502997175, 1.0290974761051759, 0.748394332452588, 0.2988368854769476, -0.2064206357575079, -0.6343975591089145, -0.8570816567787838, -0.7771182451895973, -0.3495160395973723, 0.40514376677479497, 1.3992217702258773, 2.489443776591753, 3.4999652753997177, 4.253401669882306, 4.604283923796595, 4.46850689018384, 3.842685591482526, 2.808954875164079, 1.5234060011813657, 0.1895746128631004, -0.9784578698753579, -1.796386462860956, -2.145377898010936, -1.9956403519960704, -1.4125531906831066, -0.5434918990341826, 0.41247549480539386, 1.246065373750824, 1.781811902613695, 1.9151559149873512, 1.6342835534427758, 1.021528636979254, 0.23358980725723064, -0.535382575117232, -1.0996986137818006, -1.3265504908705854, -1.1684562358408195, -0.6757209924439381, 0.014593494101358231, 0.711171732587003, 1.215124138122829, 1.3698217224121314, 1.1016778762424662, 0.44144195505379574, -0.47999119035986637, -1.461119047444704, -2.2782065039789945, -2.7409667958793786, -2.741686412078573, -2.285019360459537, -1.4900751490792645, -0.563173583848023, 0.25288124035389925, 0.7408409566687372, 0.7667449959820822, 0.3181664133753601, -0.48778915969505027, -1.4300634405637498, -2.237501502313949, -2.6580550423840354, -2.5258459318910895, -1.8084591560945178, -0.6213410790395475, 0.7956575875842256, 2.134754410907635, 3.095998128730447, 3.4630443367423234, 3.1590708350278702, 2.2676681786957587, 1.0124733907388197, -0.2998056367559276, -1.358399002565433, -1.9287091863847476, -1.9122541983283212, -1.369976545300877, -0.5023674780247638, 0.40833039003187765, 1.0779937491129115, 1.3003643255266353, 1.0042582063502454, 0.27196371201944786, -0.6865575035807794, -1.596418570301801, -2.199484218847052, -2.331213086501376, -1.9699880092556765, -1.2440229097593105, -0.39326378326731526, 0.302936781780297, 0.6111411301601868, 0.4165721415886933, -0.23905015490680065, -1.1668530955404286, -2.08556493714755, -2.706013781803654, -2.8201960286042187, -2.3676420407569068, -1.4580028096850872, -0.3416401066706477, 0.6642060234541073, 1.272136752412678, 1.3148997261778832, 0.8010188635256567, -0.08268741639615353, -1.0242670291742109, -1.680842563131227, -1.7859985041102102, -1.2374492562292643, -0.13710542975559192, 1.2305136147059108, 2.4769480466445177, 3.2232026283880457, 3.214187043392327, 2.3992691647828277, 0.9535919228048644, -0.767538929969052, -2.3284710086946565, -3.3376482870427275, -3.559172553661418, -2.977621630781946, -1.7965321053677792, -0.3714970063191635, 0.9007856882833977, 1.702442008342917, 1.8856338646677735, 1.5067980626789026, 0.7942122515465918, 0.060904962924152733, -0.40726838520198483, -0.45055959107565746, -0.08798674619510159, 0.49387080950158835, 1.0118053883850195, 1.1919866560025754, 0.874033983138598, 0.07630173238291187, -1.0016358782632884, -2.041915195661117, -2.716535467936338, -2.804131269900449, -2.2745756162562882, -1.3104432606257297, -0.25521212451944053, 0.49689764272406334, 0.6338479955118482, 0.036756339860890115, -1.1698346033334546, -2.647695006658398, -3.94730406408271, -4.650634005743098, -4.50746556524078, -3.519404986457095, -1.9424573491834756, -0.20600703343025928, 1.225669082092136, 2.003363233089167, 2.0039225109190397, 1.3645804617897226, 0.4288504654510986, -0.3775287924878944, -0.6978772281186014, -0.3706910802502659, 0.5133574376225408, 1.6436384185063742, 2.5999983698492244, 3.002886155077046, 2.650431542311115, 1.5939925001053081, 0.1251082813725497, -1.3220329617742903, -2.318560090710292, -2.58722976182486, -2.0954125837779, -1.0619693305739981, 0.12404838380483932, 1.0433543416433653, 1.3944781084086253, 1.0965486404735345, 0.3100483109245751, -0.6311499019738229, -1.350520282732703, -1.5732650909047154, -1.2301138988819258, -0.48139937556873386, 0.34786327554195756, 0.8974868338149727, 0.9168990838018579, 0.36927793137197146, -0.5463817108256084, -1.4661000000916828, -2.000033456890726, -1.8882883920097924, -1.1137348908015188, 0.0735013706321057, 1.2331753064841717, 1.8889273310775698, 1.704472485930558, 0.6170024895221657, -1.1234078609726572, -3.026301066093703, -4.522284521483934, -5.157109331074044, -4.748835259180272, -3.4507782469744352, -1.6965619445380182, -0.04643672025147152, 1.0097305757018065, 1.2213361208684734, 0.6566455115521143, -0.3349651857623748, -1.2626741225012073, -1.6825689146133065], 'positive_zeros': ['1.73579350098789440633448833991126', '3.08223815905244983724436294722662', '4.14915968120378601622293514389176', '5.29755353569939446277988069588748', '6.07353418931826029497743160913276', '6.68899501514532183507347488275570', '8.018627475202872402148117456347968', '8.820668859858642979862119661850164', '9.661225502356515891832788680432277', '10.37249278918257437919959794780510'], 'prelabel': '2-912-19.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': 0.7295966302278072, 'root_number': '-0.6603607762077092 + 0.7509484970664445*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.364798315114', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.73579350098789440633448833991', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08223815905244983724436294723', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.14915968120378601622293514389', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.282356664340774, 'bad_primes': [2, 3, 19], 'central_character': '19.17', 'conductor': 912, 'conductor_radical': 114, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/912/2/bo/e/625/1'], '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': '2-912-19.17-c1-0-17', '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': '2-912-19.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': 0.3647983151139036, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.73579350098789440633448833991', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2200379673399564048778892189202', 'Lhash_array': ['2200379673399564048778892189202'], 'label': '2-912-19.17-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/912/2/bo/e/625/1'}