Formats: - HTML - YAML - JSON - 2026-03-12T08:31:57.245090
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '1790236468094789436477189467357', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-3.8541019662496847, 0.0], 'a6': [0.0, 0.0], 'a7': [0.2360679774997897, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.594278373489917, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 11], 'central_character': '1452.1', 'coefficient_field': 'CDF', 'conductor': 1452, 'conductor_radical': 66, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.8541019662496847, 0], [5.0, 0]], [[1.0, 0], [-0.2360679774997897, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-6.23606797749979, 0], [13.0, 0]], [[1.0, 0], [2.381966011250105, 0], [17.0, 0]], [[1.0, 0], [-5.0901699437494745, 0], [19.0, 0]], [[1.0, 0], [0.2360679774997897, 0], [23.0, 0]], [[1.0, 0], [4.47213595499958, 0], [29.0, 0]], [[1.0, 0], [6.381966011250105, 0], [31.0, 0]], [[1.0, 0], [3.76393202250021, 0], [37.0, 0]], [[1.0, 0], [9.47213595499958, 0], [41.0, 0]], [[1.0, 0], [9.47213595499958, 0], [43.0, 0]], [[1.0, 0], [-3.618033988749895, 0], [47.0, 0]], [[1.0, 0], [-6.562305898749053, 0], [53.0, 0]], [[1.0, 0], [-2.1458980337503153, 0], [59.0, 0]], [[1.0, 0], [-2.618033988749895, 0], [61.0, 0]], [[1.0, 0], [0.14589803375031546, 0], [67.0, 0]], [[1.0, 0], [1.381966011250105, 0], [71.0, 0]], [[1.0, 0], [3.23606797749979, 0], [73.0, 0]], [[1.0, 0], [14.23606797749979, 0], [79.0, 0]], [[1.0, 0], [15.47213595499958, 0], [83.0, 0]], [[1.0, 0], [-1.0, 0], [89.0, 0]], [[1.0, 0], [5.0901699437494745, 0], [97.0, 0]], [[1.0, 0], [-5.944271909999159, 0], [101.0, 0]], [[1.0, 0], [-12.47213595499958, 0], [103.0, 0]], [[1.0, 0], [6.52786404500042, 0], [107.0, 0]], [[1.0, 0], [-8.0, 0], [109.0, 0]], [[1.0, 0], [-12.23606797749979, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 20328406, 'index': 10, 'label': '2-1452-1.1-c1-0-10', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1452/2/a/i/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-7.912466691186725e-61, 0.1025231225143682, 0.20481330082083163, 0.3066058372073509, 0.4075741042528963, 0.5073024003950283, 0.6052630666963315, 0.7007988026646444, 0.7931108026664793, 0.881253031869422, 0.9641326998686476, 1.0405167858122233, 1.1090443227073743, 1.1682440528231155, 1.2165570075120713, 1.252363528774842, 1.2740142234111411, 1.2798643137095242, 1.2683108150673015, 1.2378319279185075, 1.1870279789519362, 1.1146631870062451, 1.0197074658189151, 0.9013774133695208, 0.7591755806296541, 0.5929270658549008, 0.4028124486399048, 0.18939606491421745, -0.04635136653715924, -0.30303672063990916, -0.578835937855418, -0.871493791913441, -1.1783326328942998, -1.496270634518497, -1.8218498957954468, -2.1512745425852655, -2.4804587473526674, -2.8050843396228333, -3.120667420495773, -3.4226331280049416, -3.7063974328407734, -3.9674545833475556, -4.20146857255201, -4.404366776374208, -4.57243371924008, -4.7024027690091215, -4.7915434549611025, -4.837742047357759, -4.839573040645763, -4.796359249301227, -4.708218358763763, -4.5760939753038175, -4.401769487562015, -4.18786338641899, -3.937805084205058, -3.655790722296514, -3.346718949004868, -3.0161071764654177, -2.669989373248226, -2.3147970043291313, -1.9572252762766857, -1.6040873665489679, -1.2621597947234677, -0.9380225134254936, -0.6378976413802446, -0.36749101523294664, -0.13184088710134267, 0.06482186996548309, 0.2191977747934204, 0.32902291243910653, 0.3931495608433678, 0.411600035993974, 0.3855911187858831, 0.31752713455706383, 0.21096056002326286, 0.0705199132158501, -0.09819438239701765, -0.28874450372874344, -0.4940174822219946, -0.7064116477906207, -0.9180428266456835, -1.120965069960821, -1.3074000230643135, -1.4699685249635261, -1.6019176798828212, -1.697336486348487, -1.7513531603258226, -1.7603075562552475, -1.7218925762419235, -1.6352591587857903, -1.5010803426480288, -1.3215709897450818, -1.1004609972250312, -0.8429212003445978, -0.5554426257433861, -0.24567125558931807, 0.07779804048568688, 0.4056633063566335, 0.7281865960019227, 1.0354867442358788, 1.3178452062685233, 1.5660156194643557, 1.7715272777485052, 1.9269725526820407, 2.026268464212645, 2.064883107089806, 2.0400184733432862, 1.9507423628512894, 1.7980635169408494, 1.584945806851572, 1.316259211816797, 0.9986673731033534, 0.6404536453957109, 0.25128971433338176, -0.15804706585964137, -0.5759995136137438, -0.9905898041145395, -1.3898007071310217, -1.7619664807032303, -2.0961603112773095, -2.382564917167916, -2.6128131228127334, -2.7802858768120298, -2.880356320963133, -2.910570096728466, -2.870754058831632, -2.763047895439658, -2.5918557580421795, -2.363717796036205, -2.087104375164186, -1.7721386321508368, -1.4302557733788606, -1.0738100567933428, -0.7156426013660657, -0.3686249537709933, -0.04519462617984645, 0.2431004629717938, 0.48603160788813743, 0.6750764879872148, 0.8037485573306093, 0.8678550976134467, 0.8656727312943909, 0.7980320361255794, 0.6683061485870887, 0.4823017794264743, 0.24805476234442778, -0.02446402121632853, -0.32372289602320187, -0.6370710421591108, -0.9512318196364942, -1.2528296426595147, -1.5289305121414867, -1.7675752794297996, -1.9582844716138637, -2.09251409303578, -2.164043230572005, -2.1692765007311197, -2.1074473204818633, -1.980711565337876, -1.7941252732073456, -1.555504511835785, -1.2751701828669872, -0.9655852049459726, -0.6408960139845412, -0.3163944540642435, -0.007919729791117162, 0.26877701085692657, 0.4986808323782656, 0.6681481573092442, 0.7655030494921935, 0.7815697270076899, 0.71011837725644, 0.5482043101810026, 0.29638433625978294, -0.04120114169456784, -0.4568866501878706, -0.9396815417823566, -1.4756063018532715, -2.0481546460887277, -2.6388654445486277, -3.2279837025939635, -3.795185776332726, -4.320340887611388, -4.784278983268952, -5.169534165187804, -5.461033363135222, -5.646701640732842, -5.717958471275735, -5.670083396106733, -5.502434534630186, -5.218509256985967, -4.825842724708531, -4.335746688986972, -3.762897629556787, -3.1247897322654596, -2.441074058211492, -1.732810288613218, -1.02166140413106, -0.32906438354578116, 0.3245886563426664, 0.9207245924830085, 1.443286037481665, 1.879321099963083, 2.2194409740462926, 2.458125730121198, 2.5938651712044414, 2.629128767072173, 2.5701661725664446, 2.4266473458894207, 2.2111584693192174, 1.9385764088875153, 1.625350024986146, 1.2887209945423117, 0.9459197104760432, 0.6133731311107482, 0.30596107733177325, 0.036355411058014445, -0.18552715433959355, -0.35293301546696493, -0.46252122338572116, -0.5144428016113917, -0.5122460473535704, -0.4626123168644822, -0.37493497105730916, -0.2607618275204857, -0.13312825687492089, -0.005813637003071794, 0.10744204852642937, 0.19372233174323936, 0.24167948040220993, 0.24220263155224128, 0.18897397282647682, 0.07888318210098995, -0.08772304564457246, -0.30697168916888223, -0.5715808602154305, -0.8711613502616112, -1.1926903169944034, -1.5211363135294385, -1.8402068737868138, -2.1331831465922586, -2.383800974662094, -2.5771346262803925, -2.700438303278935, -2.743901665885279, -2.7012789240521817, -2.570356428983285, -2.3532309360523063, -2.0563794834480014, -1.6905117393985067, -1.2702062498382145, -0.8133427598665106, -0.3403531593361766, 0.12667690488865466, 0.5650155877448378, 0.9523550965729186, 1.267893990057752], 'positive_zeros': ['1.41224756078092261457138151205206', '3.38439668111259848109782356332337', '3.83075727509495184414864371534871', '4.86290527847168790090088235763126', '5.76966136436514785605235865344244', '6.86299248002417109606322716944921', '7.40973026357062656699246483417003', '8.380270746556061855414968287280874', '8.830341188319842416553234282663125'], 'prelabel': '2-1452-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4050372058892275, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41224756078092261457138151205', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.38439668111259848109782356332', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83075727509495184414864371535', 'prec': 103}}