-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '999757137277741585713398805159', 'a10': [3.7691356246584387, -4.113789598314548], 'a2': [-1.1634409490959048, 0.8039932574137798], 'a3': [-0.2225209339563144, -0.9749279121818236], 'a4': [0.7071896840663591, -1.870797356944392], 'a5': [-3.8463129139438186, 0.877895823070239], 'a6': [1.0427254344545214, 0.9553657249146159], 'a7': [-2.229817019413922, 1.424049177497748], 'a8': [0.6813350237498139, 2.7451379902314272], 'a9': [-0.9009688679024191, 0.4338837391175581], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.6952036388512886, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.1634409490959048, -0.8039932574137798]]], [3, [[1.0, 0], [0.2225209339563144, 0.9749279121818236]]], [7, [[1.0, 0], [2.229817019413922, -1.424049177497748]]]], 'bad_primes': [2, 3, 7], 'central_character': '588.559', 'coefficient_field': 'CDF', 'conductor': 588, 'conductor_radical': 42, 'conjugate': '794593604482768366646729987217', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1634409490959048, -0.8039932574137798]], [[1.0, 0], [0.2225209339563144, 0.9749279121818236]], [[1.0, 0], [3.8463129139438186, -0.877895823070239], [4.504844339512096, -2.1694186955877908]], [[1.0, 0], [2.229817019413922, -1.424049177497748]], [[1.0, 0], [0.211161456405496, -0.4384812823573891], [-6.858387820446069, -8.600146307148329]], [[1.0, 0], [-1.8056613279843543, 3.749494382522731], [-8.105367424163536, -10.163809272084388]], [[1.0, 0], [-3.8776966100254993, -3.0923598566548445], [3.782855877257345, 16.573774507091002]], [[1.0, 0], [1.2624705594587238, 0], [19.0, 0]], [[1.0, 0], [1.0175576983702497, -0.811475186102702], [5.1179814809952315, -22.42334198018194]], [[1.0, 0], [-3.8483847765219292, 4.825721873823448], [-6.453107084733118, -28.272909453272884]], [[1.0, 0], [1.4686367529679851, 0], [31.0, 0]], [[1.0, 0], [-5.945966861669847, 7.456006613590769], [-8.233274556383632, -36.072332750727476]], [[1.0, 0], [0.7856903665882727, -0.17932869906497795], [36.93972358399918, -17.789233303819884]], [[1.0, 0], [-9.958707537793371, -2.2730100088613345], [38.741661319804024, 18.657000782055]], [[1.0, 0], [7.290980271676799, 3.511151045065966], [29.304020687360477, 36.7460796759974]], [[1.0, 0], [-4.0209224049046135, -5.04207721656972], [-11.793609499684663, 51.67117934563665]], [[1.0, 0], [-0.24693905186819773, 1.081910676868204], [-53.15716320624273, -25.59914060793593]], [[1.0, 0], [-4.527278696615834, -3.6103842846053418], [13.573776971335178, 59.47060264309124]], [[1.0, 0], [0, 5.765794828665429], [-67.0, 0]], [[1.0, 0], [-3.1414774624399655, 2.5052446780696944], [15.798986310898323, -69.21988176490947]], [[1.0, 0], [-6.3563244913772685, -13.199043809901672], [-45.51475553568755, 57.07369822016618]], [[1.0, 0], [0, -17.297277306955067], [-79.0, 0]], [[1.0, 0], [-4.954989428297538, 2.386197145127721], [51.749653554274886, -64.89201304484648]], [[1.0, 0], [6.1938534725267, 12.86166926293556], [-55.49059236542728, 69.58300193965465]], [[1.0, 0], [0, -3.59515477962454], [-97.0, 0]], [[1.0, 0], [9.20206356523109, -2.100310959687354], [90.99785565814433, -43.82225765087337]], [[1.0, 0], [3.1318925807324303, 13.721717955357194], [-92.79979339394917, 44.690025129108484]], [[1.0, 0], [-7.501120907081467, -15.576238061830761], [-66.71340879888449, 83.6559686240792]], [[1.0, 0], [1.6035744294669343, 0.7722407446000391], [67.96038840260195, 85.21963158901525]], [[1.0, 0], [-13.698203028312514, 6.5967069017077336], [70.45434761003689, -88.34695751888736]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-588-196.167-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/588/2/x/a/559/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5156631808110286, 0.5247303479359908, 0.5061725369158754, 0.4564966881129608, 0.3703461085839324, 0.24165709845717953, 0.06498897146686847, -0.16314576050959875, -0.443065969659472, -0.7709095283408616, -1.137914321799363, -1.5300938469388632, -1.9284101444331085, -2.309528801577051, -2.647199634574497, -2.914243754367657, -3.0850482214167365, -3.138381937845081, -3.060262217537105, -2.8465340258872844, -2.5047871910938184, -2.0552436290246066, -1.530305893898521, -0.9725734390078253, -0.4312994025083644, 0.042534730291492025, 0.4021285799571776, 0.6111508501318641, 0.6496390802760262, 0.5186627870884627, 0.24292698730209156, -0.12935816054345428, -0.5297434232790859, -0.8759668826648883, -1.0811220598185238, -1.0646961317197765, -0.7642112150357439, -0.14593392748692924, 0.7869603935598375, 1.9902312106952977, 3.3794944104139906, 4.836685931426693, 6.221775399228656, 7.38863120568776, 8.203202284199799, 8.56164217643036, 8.405768472692305, 7.7333993542856385, 6.601658540115878, 5.122245370198654, 3.448817599500422, 1.7578659738640523, 0.22557503169185147, -0.996034071682431, -1.8000595891290765, -2.139406654712532, -2.032670939704849, -1.55999881938486, -0.849311370761598, -0.054916570742434036, 0.668087802946887, 1.1893641781180098, 1.4244417386958388, 1.3476284480034775, 0.9943371606863733, 0.45229701636559855, -0.1568359796970638, -0.7021123147582161, -1.069532776532377, -1.1848383735773496, -1.0283264971530826, -0.638635507696487, -0.10457253974533844, 0.4535368189437379, 0.9093029458758457, 1.1573354220709007, 1.1362251239270091, 0.8424435669963187, 0.3319427501603554, -0.29120769861488016, -0.8970014491395231, -1.3578890862519424, -1.5772269984715506, -1.5113752926207817, -1.1802203837859295, -0.6633237149422379, -0.08208687136616376, 0.42841104833588206, 0.7516544615349827, 0.8184835375576521, 0.6253296690664495, 0.23691394604261595, -0.22812384660180138, -0.6261573865958403, -0.8258444599398944, -0.7450347144153749, -0.3780525667002637, 0.19427280481781897, 0.8158568370956113, 1.287059608509417, 1.4109671850831422, 1.0443523483559594, 0.14143046046821398, -1.2207758732283187, -2.8432358818667236, -4.434127063439896, -5.662255938565034, -6.224520591705576, -5.913262047056795, -4.668391133019839, -2.601665264129907, 0.013951429277511015, 2.7894113901497932, 5.290972974305571, 7.1233831352919665, 8.00719468604899, 7.833323425103628, 6.682639359773845, 4.806032015001964, 2.569275125832509, 0.37506259104946055, -1.4201482747723642, -2.5756934588034635, -3.0071733930520366, -2.789390689896926, -2.122400502402535, -1.2702467220725913, -0.48849249899643205, 0.040865210379766974, 0.25073977314025003, 0.19660890996473135, 0.029490232281780968, -0.05755122145750311, 0.10587232143126599, 0.6097247414608468, 1.4290792476483998, 2.4228998240664623, 3.3669358755085854, 4.012154212726335, 4.152922992338315, 3.6861923372974323, 2.6450713072378425, 1.1969729471775872, -0.3939050932633773, -1.8301897833607832, -2.8541622167996406, -3.3102307085659994, -3.18018131391041, -2.5817880713488117, -1.7315190288282776, -0.8820933534631477, -0.2526745071010672, 0.02852680798781041, -0.04684465926047908, -0.37459492216801943, -0.7785408050239151, -1.0715043066841166, -1.1177968589075344, -0.8777560420052785, -0.42029474245710513, 0.1007907755737847, 0.4996987855717749, 0.6242153611661179, 0.41298127678006624, -0.07475925556544234, -0.6681788014653106, -1.132086319109745, -1.239573662186419, -0.8484987985874127, 0.042318931008124824, 1.276467248672832, 2.5710350466333427, 3.5893161187648652, 4.0357923996751355, 3.7460323224098127, 2.7440233457830856, 1.2477134318598122, -0.3819156266188858, -1.7361826245468535, -2.4724339474616754, -2.4133430389528057, -1.6017103006853561, -0.2926095806677644, 1.11736351996123, 2.205219843555538, 2.6485494206357676, 2.3269629894533357, 1.3667696254747026, 0.11336473243031439, -0.9632851097145166, -1.4046370052124268, -0.9024830259281008, 0.5998895318564335, 2.8750802276989296, 5.459063014579028, 7.767264808269007, 9.247577250917793, 9.52747399295802, 8.513659797387872, 6.416123398362267, 3.69020157296317, 0.9138542405730842, -1.3642315272786958, -2.7623332784324552, -3.1509606889323285, -2.663861251152315, -1.635428687747176, -0.48685624513408976, 0.40238379345089664, 0.7985685542413105, 0.6636730914918191, 0.14005894086150827, -0.5201162654279221, -1.0537175932497447, -1.2790445929130014, -1.1513002022037027, -0.7646805209569931, -0.3037720734896603, 0.03549571733108819, 0.12506690686129895, -0.04528833436695592, -0.3654299315857152, -0.6501764624885213, -0.7151807700424184, -0.45448578468145334, 0.1101980306614777, 0.8285475178023816, 1.4715308703720145, 1.8156742091718643, 1.7315831096532042, 1.243494459182654, 0.5355441409844252, -0.10135736691953959, -0.3668063623212753, -0.06015564565077933, 0.8367464698255812, 2.134685235234178, 3.4827894580312275, 4.4734174454531646, 4.773470697200494, 4.238451385590564, 2.9693605448120066, 1.2903669357139045, -0.34854735932025865, -1.513830283987362, -1.9288036959254906, -1.5645580359771396, -0.6489421106414267, 0.41158342237548173, 1.1725853649839433, 1.3077835419525685, 0.7268238938347393, -0.3875354604753619, -1.638415552360447, -2.5526231461294056, -2.7518601477435416, -2.098651633674459], 'positive_zeros': ['0.78866932031408659354502187800832', '3.11262028758199367096506515437338', '3.83385182867525040135041120095407', '4.64757461432863378656715045789767', '6.52054108609485274936907860968793', '7.38379412765693043210611083515999', '8.217621313760752346759137986882754', '9.022969452647833698503584299110497', '9.817783008876043014661909713869672', '10.76825281128217491010744977459007'], 'prelabel': '2-588-196.167-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.166841858293145, 'root_angle': 0.018525756100900844, 'root_number': '0.9983068359430881 + 0.05816752796277402*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00926287805045', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78866932031408659354502187801', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.11262028758199367096506515437', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83385182867525040135041120095', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.6952036388512886, 'bad_primes': [2, 3, 7], 'central_character': '196.167', 'conductor': 588, 'conductor_radical': 42, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/588/2/x/a/559/6'], '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': '2-588-196.167-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': '2-588-196.167-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.166841858293145, 'root_angle': 0.009262878050450422, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78866932031408659354502187801', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '999757137277741585713398805159', 'Lhash_array': ['999757137277741585713398805159'], 'label': '2-588-196.167-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/588/2/x/a/559/6'}