-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1355714927425385376415459715731', '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': [0.8090169943749475, -0.5877852522924731], 'a7': [0.0, 0.0], 'a8': [0.8090169943749475, 0.5877852522924731], 'a9': [-0.8090169943749475, 0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9282609234973845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', '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], [-0.30901699437494745, 0.9510565162951535]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '1860.1139', 'coefficient_field': 'CDF', 'conductor': 1860, 'conductor_radical': 930, 'conjugate': '1960203983182128637070971499866', '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], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [-1.8090169943749475, -0.5877852522924731], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [1.3090169943749475, -0.9510565162951535], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [1.118033988749895, -0.36327126400268045], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-1.118033988749895, -1.5388417685876268], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, -1.902113032590307], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [-0.5, 0.36327126400268045], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [-0.5, 1.5388417685876268], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0.6909830056250525, 0.9510565162951535], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0.19098300562505258, 0.5877852522924731], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [1.618033988749895, 1.1755705045849463], [0.30901699437494745, 0.9510565162951535]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-1860-1860.1139-c0-0-2', 'leading_term': '1.179786412992607935218891961310', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1860/1/bt/c/1139/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.179786412992608, 1.1611233439141173, 1.151337939732044, 1.1480595408124457, 1.1482481809694993, 1.1485153880069487, 1.1454093884776138, 1.1356286403760145, 1.116162791279225, 1.0843788016870501, 1.0380734629978194, 0.9755091348493475, 0.8954431585164351, 0.7971559510448912, 0.6804789977889719, 0.54582164804994, 0.39419435701691724, 0.22722543636485878, 0.04716822074613944, -0.14310432688567692, -0.3401202488929037, -0.5398467074752361, -0.7377472754477592, -0.9288594572531234, -1.1078927712440803, -1.2693469339491537, -1.4076488465185488, -1.5173062139337408, -1.5930747540319687, -1.6301351048904469, -1.624274747646196, -1.572069561476432, -1.4710590531370233, -1.3199088894462248, -1.1185541395117138, -0.8683166325873721, -0.5719900799492685, -0.23388711070340684, 0.1401568610195225, 0.5428269893274034, 0.9654223419589302, 1.3980005049161852, 1.8295730211457324, 2.2483494058802154, 2.6420255673498554, 2.9981105330701214, 3.304283512880022, 3.5487715989259043, 3.720736890048322, 3.8106606120765614, 3.8107109597606614, 3.715080975110285, 3.520282853078698, 3.2253856654718582, 2.8321846356858478, 2.3452917773509094, 1.7721399034386596, 1.1228946695897184, 0.4102723636998423, -0.3507355016040289, -1.1432262106144382, -1.9488303201361585, -2.7482249435928785, -3.521700954273779, -4.249766365472353, -4.913765827071658, -5.496494525193239, -5.9827838946375165, -6.360036537597007, -6.618688639258288, -6.752579997690378, -6.7592145183817545, -6.639897598097126, -6.399741132341659, -6.047531780532637, -5.595463432912982, -5.0587403343144555, -4.455062802034603, -3.804012686571137, -3.1263604218488026, -2.4433194631133954, -1.775776904783559, -1.143530929097248, -0.5645663244926354, -0.05439854760643267, 0.37448533912039994, 0.7130640012010305, 0.956077295471409, 1.1021654967395238, 1.1538445342066272, 1.1173166570480415, 1.0021233646314045, 0.8206547533138259, 0.5875362955268199, 0.3189201316872889, 0.03171289961262543, -0.2572243303274398, -0.531866525013506, -0.7777679253057457, -0.9827221021536475, -1.137306390756837, -1.2352834666857389, -1.273839523971546, -1.253646409239105, -1.178743791865452, -1.0562465845425297, -0.8958919107249448, -0.7094484698408604, -0.5100187124763474, -0.3112703760330639, -0.12663827663679858, 0.031460482088347314, 0.15235472416843795, 0.22775001854400675, 0.2522258950814133, 0.22356997353758598, 0.14292803232219553, 0.014758937129230062, -0.1534058830407349, -0.3513876570270961, -0.5669486776937097, -0.7865125522770321, -0.9959766422529143, -1.181570762014232, -1.330712393252022, -1.4328076239663026, -1.4799488906028597, -1.4674653793935082, -1.3942894502053271, -1.2631123392054682, -1.0803141791749598, -0.8556664223803532, -0.6018183361071018, -0.3335925808741779, -0.0671271753713119, 0.18108836985558513, 0.3952269986914894, 0.5611274946605971, 0.6672252633023674, 0.7053507753975841, 0.6713419496177644, 0.5654262577305623, 0.3923408904850856, 0.1611742860939178, -0.11507111814498835, -0.42017784154223886, -0.735640117406722, -1.0417691267353246, -1.3189143801454875, -1.5487292298453383, -1.715402846543657, -1.806779906824587, -1.8152929615399849, -1.738640967800171, -1.5801604438061894, -1.3488525367411963, -1.0590491059936797, -0.7297226233472923, -0.3834670219777184, -0.04519823844486091, 0.2593572753323216, 0.5053016310463776, 0.6702360813375453, 0.7358607656908713, 0.6894010858223009, 0.524764255511368, 0.2433418352581588, -0.14560798894107196, -0.625041859943358, -1.1706935375004104, -1.752105603364283, -2.3340901727263152, -2.8785504891091613, -3.3465705982812453, -3.700660275186334, -3.9070284204811503, -3.9377513331355236, -3.7727032851038977, -3.4011258976575056, -2.8227296819507792, -2.048245003920853, -1.09936945008251, -0.00809248941938902, 1.1845854835406904, 2.4304863134384216, 3.676551796399916, 4.867488261990546, 5.948616519960067, 6.868769666424231, 7.583074268691305, 8.055453170923398, 8.260700674204635, 8.186002628310005, 7.831803921681569, 7.211962326606522, 6.35316855611151, 5.293655297963367, 4.081260307281923, 2.770947738782491, 1.4219253034597676, 0.09452036973977525, -1.1530059249253442, -2.2675222775342254, -3.2037902819934136, -3.9267657250703536, -4.413304013668383, -4.653171268278822, -4.649304619273833, -4.417311019281409, -3.984240565806752, -3.3867149452166214, -2.668531288713451, -1.877893884681431, -1.0644486917253075, -0.27630692280585745, 0.44275667900464244, 1.0557578988433944, 1.5344603369498504, 1.8607203830247454, 2.0271454093013483, 2.0370365844797167, 1.9036353256934355, 1.6487385684586549, 1.3007896229197224, 0.8925855650431794, 0.4587665365134561, 0.03326530339049211, -0.3531039643458743, -0.6747505475455904, -0.9129619696412838, -1.056998488764545, -1.1045581967291815, -1.0615895690444639, -0.9414757947868408, -0.7636608659258047, -0.5518279471467453, -0.33177304420118925, -0.12913906034678813, 0.032814673109756914, 0.13523517582049413, 0.16533429166303565, 0.1175535116758945, -0.005857180415555991, -0.19489465731029038, -0.43249240836100605, -0.6957965567934155, -0.9579348257511724, -1.1901465965274447, -1.364113198619196, -1.4543103785559792, -1.4402009293293485, -1.308095174658188, -1.0525298287482057, -0.6770501431949855, -0.19432377423764763, 0.37443569394329523, 1.0007057909856933], 'positive_zeros': ['1.06947050487042783174678019420610', '2.20519177403856578838694642963732', '3.43040812018609698711606768303056', '4.92870687516810184692643415484224', '5.57279402041584039770696279141980', '6.49119982247709318411973322592020', '6.86117299035637665850889405461244', '7.86683741671395288550662338481829', '8.414033423555046015373566840060079', '9.324599310834984565141929940021986'], 'prelabel': '2-1860-1860.1139-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9634629850167491, 'root_angle': -0.04163573119880574, 'root_number': '0.96597611554792523011321450188259 - 0.25863129004616089667100837730026*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.04163573119880573', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06947050487042783174678019421', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.20519177403856578838694642964', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43040812018609698711606768303', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.9282609234973845, 'bad_primes': [2, 3, 5, 31], 'central_character': '1860.1139', 'conductor': 1860, 'conductor_radical': 930, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1860/1/bt/c/1139/1'], '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': '2-1860-1860.1139-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1860-1860.1139-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9634629850167491, 'root_angle': -0.04163573119880574, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06947050487042783174678019421', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1355714927425385376415459715731', 'Lhash_array': ['1355714927425385376415459715731'], 'factors': ['2-1860-1860.1139-c0-0-2'], 'label': '2-1860-1860.1139-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1860/1/bt/c/1139/1'}