-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1978293795400703250466355177338', 'a10': [2727.894098842352, 0.0], 'a2': [8.0, 0.0], 'a3': [27.0, 0.0], 'a4': [64.0, 0.0], 'a5': [340.986762355294, 0.0], 'a6': [216.0, 0.0], 'a7': [1267.120132968389, 0.0], 'a8': [512.0, 0.0], 'a9': [729.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43.10913351680882, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-8.0, 0]]], [3, [[1.0, 0], [-27.0, 0]]], [23, [[1.0, 0], [12167.0, 0]]]], 'bad_primes': [2, 3, 23], 'central_character': '138.1', 'coefficient_field': 'CDF', 'conductor': 138, 'conductor_radical': 138, 'degree': 2, 'euler_factors': [[[1.0, 0], [-8.0, 0]], [[1.0, 0], [-27.0, 0]], [[1.0, 0], [-340.986762355294, 0], [78125.0, 0]], [[1.0, 0], [-1267.120132968389, 0], [823543.0, 0]], [[1.0, 0], [-5101.248820685297, 0], [19487171.0, 0]], [[1.0, 0], [5814.28983804854, 0], [62748517.0, 0]], [[1.0, 0], [-6404.73306369642, 0], [410338673.0, 0]], [[1.0, 0], [38566.62964134202, 0], [893871739.0, 0]], [[1.0, 0], [12167.0, 0]], [[1.0, 0], [208060.75793324015, 0], [17249876309.0, 0]], [[1.0, 0], [-3653.7803457702576, 0], [27512614111.0, 0]], [[1.0, 0], [-23930.89111685147, 0], [94931877133.0, 0]], [[1.0, 0], [1151.5016443235154, 0], [194754273881.0, 0]], [[1.0, 0], [489301.60067708127, 0], [271818611107.0, 0]], [[1.0, 0], [-988906.80466954, 0], [506623120463.0, 0]], [[1.0, 0], [777026.8363088523, 0], [1174711139837.0, 0]], [[1.0, 0], [-1611871.5921234633, 0], [2488651484819.0, 0]], [[1.0, 0], [1040924.8820798283, 0], [3142742836021.0, 0]], [[1.0, 0], [2060657.247262978, 0], [6060711605323.0, 0]], [[1.0, 0], [-3583924.4535363526, 0], [9095120158391.0, 0]], [[1.0, 0], [975849.7945753054, 0], [11047398519097.0, 0]], [[1.0, 0], [-6003586.937030601, 0], [19203908986159.0, 0]], [[1.0, 0], [5402516.366926565, 0], [27136050989627.0, 0]], [[1.0, 0], [4139111.707768844, 0], [44231334895529.0, 0]], [[1.0, 0], [-11884432.861512579, 0], [80798284478113.0, 0]], [[1.0, 0], [-9543269.471617352, 0], [107213535210701.0, 0]], [[1.0, 0], [3123468.0427171453, 0], [122987386542487.0, 0]], [[1.0, 0], [-10246787.393420063, 0], [160578147647843.0, 0]], [[1.0, 0], [12673259.98222413, 0], [182803912081669.0, 0]], [[1.0, 0], [-543321.0055409465, 0], [235260548044817.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-138-1.1-c7-0-19', 'leading_term': '5.93018602536553912800201373293', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/138/8/a/h/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [5.930186025365539, 5.907959948942307, 5.841591469355355, 5.732005846317746, 5.580731905060388, 5.389882208096574, 5.162125465554569, 4.90065136183301, 4.609128037932561, 4.291652537727531, 3.9526946034298738, 3.5970342908549657, 3.2296939685841095, 2.855865365926025, 2.480832441315312, 2.109890953469054, 1.7482657297039468, 1.4010267362168558, 1.0730051603036084, 0.7687108104972312, 0.4922522232216915, 0.2472609293834037, 0.03682137692646712, -0.13659197856344835, -0.27116891765917156, -0.36580758649760686, -0.42014714896203365, -0.43458772423928255, -0.41029653853828574, -0.349199426931123, -0.2539570684562556, -0.12792562251358156, 0.024898246492818805, 0.19994762143909225, 0.392170156561192, 0.5961263833190223, 0.8061000177087303, 1.016218403144178, 1.220580853400503, 1.4133923181745198, 1.589099491683984, 1.7425262345080048, 1.8690049922798357, 1.9645007827934458, 2.0257242952586436, 2.050230709856859, 2.0365010083507564, 1.9840028107517014, 1.8932281395920094, 1.765705979712468, 1.6039880618605955, 1.411606943551746, 1.1930061778557026, 0.9534431339487192, 0.6988658431821019, 0.4357660690373361, 0.1710116143276001, -0.08833834167361758, -0.33523036686380536, -0.5628212246206231, -0.7646840002252359, -0.9350098893526441, -1.0687994261064195, -1.1620369029334856, -1.2118419046495803, -1.2165922519608463, -1.1760132282879794, -1.0912287425984595, -0.9647710483640041, -0.8005467753849713, -0.6037583105236278, -0.38078095195652234, -0.1389977197645498, 0.1134048113897093, 0.36767483309807036, 0.6147615704271511, 0.8456020341903921, 1.0514197229982802, 1.2240258950516083, 1.3561134581553458, 1.4415332655173732, 1.475542683187538, 1.4550167307606097, 1.3786128967011726, 1.2468818869719362, 1.0623180606425087, 0.8293451051641767, 0.5542345599282962, 0.24495704991703543, -0.08903152912799636, -0.4370642066099221, -0.7875904611325772, -1.1285477654813427, -1.4477658135854963, -1.733390369927419, -1.9743123544544265, -2.1605869137746296, -2.283826890658563, -2.337555330264806, -2.3175024752581748, -2.2218341037434977, -2.0513000314273855, -1.8092940869233922, -1.5018198078471647, -1.1373594048134157, -0.7266470907763105, -0.2823515483840837, 0.18132402976038092, 0.6491123887699743, 1.1052080080561473, 1.5338303544421892, 1.9198045241466937, 2.249137723864008, 2.5095693450925967, 2.6910725413831393, 2.786286259294125, 2.790858599830472, 2.703685160690396, 2.527029556451218, 2.2665175237379236, 1.9310007482105151, 1.5322916279155088, 1.0847754183119889, 0.6049113774973517, 0.1106394277062185, -0.37928674557392783, -0.8460155282062019, -1.271334692959293, -1.6384009581582772, -1.932431923590763, -2.1413311203274756, -2.256218767406838, -2.2718439082405757, -2.1868578182867373, -2.0039337947294262, -1.7297244705703216, -1.3746544080186889, -0.952552652489243, -0.48013687721048115, 0.023632584997438415, 0.5383044457222174, 1.0427643188728049, 1.5161050830214031, 1.9385033884937972, 2.292064763889435, 2.561600219747564, 2.735299352478749, 2.805268678289581, 2.767909157511551, 2.6241134138318736, 2.3792707522202448, 2.043076417619976, 1.6291502521161392, 1.1544786096887028, 0.6387016706297404, 0.10327576430318487, -0.42945341330787695, -0.937226040052439, -1.3988482415274115, -1.7951323696872719, -2.1097539270978234, -2.3299847255278867, -2.4472669970016834, -2.457600091048603, -2.3617198052326365, -2.1650599367941603, -1.8774958747849237, -1.5128804910406857, -1.0883927271453688, -0.6237286060849031, -0.14017244044509078, 0.3404076662209579, 0.796591677274745, 1.2084165758038026, 1.5583127145815467, 1.8319209417847848, 2.0187493662068126, 2.1126362920214214, 2.1119953545572434, 2.019829774738907, 1.8435143866819794, 1.5943560878118193, 1.2869549922154981, 0.9383992170685607, 0.5673353160602271, 0.1929633778348602, -0.16598968591517765, -0.49226342366883036, -0.770969689836142, -0.990361216877548, -1.1424200308645724, -1.2232322445273847, -1.2331271828186472, -1.1765716394854486, -1.061823653916117, -0.9003638011682454, -0.7061348496234223, -0.4946320258711001, -0.28189536302922463, -0.0834621260608747, 0.08665932848543952, 0.21693295972413462, 0.2990979836291134, 0.32878057569460434, 0.3058736109717904, 0.23465636227692097, 0.1236406653288183, -0.01485419278031484, -0.16537957086061772, -0.3102548595344322, -0.4306365873234138, -0.5077001875337697, -0.5238669901425108, -0.46400431772948136, -0.3165259517210379, -0.07432385199325894, 0.2645302238270582, 0.696362971431648, 1.2117925856945737, 1.7959541833859238, 2.4290562802113698, 3.087247587541406, 3.7437545916966393, 4.370233302110177, 4.938264254278588, 5.42090924953334, 5.794242138801656, 6.038764707279025, 6.140622613384941, 6.092545305386986, 5.8944475093548485, 5.553647591815545, 5.0846789313487974, 4.508693255984869, 3.8524784374557615, 3.1471361193445704, 2.4264854328515195, 1.7252766394908838, 1.077311710666906, 0.5135767152317127, 0.060492832608943704, -0.2616114305612132, -0.43971457995887264, -0.46892677218558115, -0.352869323924023, -0.10357822781923781, 0.25907224864136214, 0.7084020263627768, 1.2123628936046298, 1.7353059686245822, 2.2399828482479176, 2.689668914246274, 3.050288106531161, 3.2924162561007355, 3.3930450780726744, 3.3370010034196675, 3.1179315944492876], 'positive_zeros': ['1.56059863423290988715566080698940', '2.23926123181204487153841145198481', '3.98357776240550575233263389674544', '5.10143329624921625261834535948440', '6.23944945264349408458013697014042', '7.49614518543419847573736020138066', '8.734478099354739517834966058416669', '9.770194926669081462566953831750069', '10.91194919498731904894536438943432', '11.97344765259626577689863020120001'], 'prelabel': '2-138-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.565754603761004, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56059863423290988715566080699', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23926123181204487153841145198', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.98357776240550575233263389675', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 43.10913351680882, 'bad_primes': [2, 3, 23], 'central_character': '1.1', 'conductor': 138, 'conductor_radical': 138, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/138/8/a/h/1/3'], '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': '2-138-1.1-c7-0-19', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-138-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.565754603761004, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56059863423290988715566080699', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1978293795400703250466355177338', 'Lhash_array': ['1978293795400703250466355177338'], 'label': '2-138-1.1-c7-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/138/8/a/h/1/3'}