-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1667561565545987963077069132732', 'a10': [0.0, 0.0], 'a2': [-1.618033988749895, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.6180339887498949, 0.0], 'a5': [0.0, 0.0], 'a6': [1.618033988749895, 0.0], 'a7': [2.0, 0.0], 'a8': [2.23606797749979, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.97195037899008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.618033988749895, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, 0], [7.0, 0]], [[1.0, 0], [3.0, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0], [13.0, 0]], [[1.0, 0], [-4.23606797749979, 0], [17.0, 0]], [[1.0, 0], [6.708203932499369, 0], [19.0, 0]], [[1.0, 0], [5.381966011250105, 0], [23.0, 0]], [[1.0, 0], [3.618033988749895, 0], [29.0, 0]], [[1.0, 0], [-8.70820393249937, 0], [31.0, 0]], [[1.0, 0], [-2.0, 0], [37.0, 0]], [[1.0, 0], [9.381966011250105, 0], [41.0, 0]], [[1.0, 0], [-7.381966011250105, 0], [43.0, 0]], [[1.0, 0], [-4.76393202250021, 0], [47.0, 0]], [[1.0, 0], [11.23606797749979, 0], [53.0, 0]], [[1.0, 0], [-3.9442719099991588, 0], [59.0, 0]], [[1.0, 0], [-8.70820393249937, 0], [61.0, 0]], [[1.0, 0], [-13.180339887498949, 0], [67.0, 0]], [[1.0, 0], [-10.090169943749475, 0], [71.0, 0]], [[1.0, 0], [15.70820393249937, 0], [73.0, 0]], [[1.0, 0], [9.145898033750315, 0], [79.0, 0]], [[1.0, 0], [9.0, 0], [83.0, 0]], [[1.0, 0], [11.180339887498949, 0], [89.0, 0]], [[1.0, 0], [3.8541019662496847, 0], [97.0, 0]], [[1.0, 0], [9.381966011250105, 0], [101.0, 0]], [[1.0, 0], [-14.416407864998739, 0], [103.0, 0]], [[1.0, 0], [-1.1458980337503155, 0], [107.0, 0]], [[1.0, 0], [4.145898033750315, 0], [109.0, 0]], [[1.0, 0], [-3.76393202250021, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 40, 'label': '2-1875-1.1-c1-0-40', '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/1875/2/a/b/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-6.660571039585753e-61, 0.07595315621778713, 0.15152427815038658, 0.226307171571812, 0.29984887467459775, 0.37163003758601326, 0.44104950755422107, 0.5074140552709538, 0.5699338659078853, 0.6277241128603853, 0.6798126590705614, 0.7251537044370936, 0.7626470211449167, 0.7911622861509342, 0.8095679211396712, 0.8167637733391722, 0.8117169053091142, 0.7934997006272311, 0.7613294310572357, 0.7146083681568722, 0.6529634598234617, 0.5762845332974397, 0.4847599351693188, 0.3789084810856758, 0.25960656837699914, 0.12810930874311144, -0.013935430089595392, -0.16448112144955532, -0.32108576546951145, -0.48092497949931123, -0.6408156385152936, -0.7972505041558308, -0.9464440402755427, -1.0843893415054464, -1.2069258039571054, -1.3098168499655538, -1.3888366889306714, -1.4398647623284933, -1.4589861922373664, -1.4425962394443395, -1.387506490072078, -1.2910502396363575, -1.1511843413580494, -0.9665846418172344, -0.7367320512411121, -0.461986296255934, -0.14364448662623786, 0.21601820076453185, 0.6137281550556397, 1.045215362947967, 1.5052394788564625, 1.9876410505513928, 2.485418420258911, 2.9908301624570504, 3.4955222136731137, 3.9906781137741048, 4.467190032202195, 4.915847517911271, 5.327540211349773, 5.693470114393729, 6.005368453382615, 6.255711714339809, 6.43793109952312, 6.546609469749196, 6.5776598134075375, 6.52847943274042, 6.398074368213835, 6.187149094836256, 5.898157216628313, 5.535309747673968, 5.10453858477359, 4.6134139261429725, 4.071015645609873, 3.487759959884029, 2.8751840907529953, 2.2456929839482402, 1.6122734589400374, 0.988182384882077, 0.3866165633909794, -0.17962709341179126, -0.6984918101109424, -1.1589919007796294, -1.5515245462390748, -1.868152652408046, -2.102849494761737, -2.251696614928254, -2.313027500634084, -2.2875109304887924, -2.1781694707762904, -1.9903304325906581, -1.7315085850066043, -1.4112220159711464, -1.0407446730296663, -0.63280123184167, -0.20121196004413722, 0.23950290453401818, 0.6745481286701903, 1.0892953679140707, 1.469728565505978, 1.8028789280950588, 2.077235440180935, 2.283117243981469, 2.4129950474474167, 2.461750020407836, 2.42686037059031, 2.308507914190122, 2.1095994106551026, 1.8357001449469224, 1.4948801269544902, 1.0974762414652828, 0.6557766210018036, 0.18363632260505808, -0.3039640363880197, -0.7914027895160081, -1.2629291728763536, -1.703185704551338, -2.0977232423887213, -2.4334908487159157, -2.699283106740541, -2.886128688400909, -2.9876057439877144, -3.000072022716729, -2.922800470284234, -2.7580142927486198, -2.510819015836679, -2.1890327800568885, -1.802919859318931, -1.364836032943191, -0.8887978364911404, -0.38999072946753427, 0.11576627787515789, 0.6125801100543022, 1.0850466154859382, 1.5187960397156812, 1.9010003562882922, 2.220823029244748, 2.4697937605602034, 2.642093473525126, 2.7347381080837367, 2.7476536376542264, 2.68363891635314, 2.5482173695579213, 2.3493829755082984, 2.09725027153844, 1.803622077432418, 1.4814920911750027, 1.144502326223687, 0.8063773947714166, 0.48035879807330756, 0.17866259698564338, -0.08801692415912182, -0.3109367064338278, -0.4836492084780783, -0.6022467082279429, -0.665494896745427, -0.6748496802026207, -0.6343560675228292, -0.5504331025621629, -0.43155378298027547, -0.2878335742709427, -0.13054526679884232, 0.028418655556954293, 0.17711242878839467, 0.30410697206435644, 0.39903774212034476, 0.4531055321351232, 0.45950710957206714, 0.4137754962812388, 0.31401356008077747, 0.16100925357854134, -0.04177389327167419, -0.2883317739317412, -0.5703751751473559, -0.8776950580657464, -1.1986217588923533, -1.5205576331258108, -1.8305589583194832, -2.1159402665694538, -2.3648728445398097, -2.566949007682753, -2.7136849594115917, -2.7989375563772776, -2.819214026447946, -2.7738584756238547, -2.665104668967947, -2.497990827899475, -2.2801387659582435, -2.021406279031938, -1.7334279973767006, -1.4290655855337622, -1.121792954172227, -0.8250457729159996, -0.5515668426884432, -0.312779657962243, -0.11822169063220243, 0.024933440213746137, 0.11223960614118043, 0.1422075030472754, 0.11638587739741127, 0.039287980273862384, -0.0818357792958686, -0.23737024226902137, -0.4158367119750219, -0.6044998280508854, -0.7900510639829329, -0.9593352270511518, -1.1000833324632717, -1.201613986179402, -1.255466054085471, -1.2559279387554712, -1.2004331545659528, -1.0897979193128136, -0.9282839096207037, -0.7234778243264673, -0.4859885671158265, -0.22897225389733725, 0.032495596109548525, 0.28217288361910137, 0.5034936806813147, 0.6804601020574664, 0.7985386655779627, 0.845514838368612, 0.8122600950489964, 0.6933687836665682, 0.4876273273486043, 0.19828558986425115, -0.1668907035505426, -0.5957971761664382, -1.0723970292423242, -1.5773440514035448, -2.0887987862625788, -2.5834036833901033, -3.037373891794805, -3.427653081844353, -3.733078726236615, -3.9354989541643577, -4.020783612532783, -3.9796755839679725, -3.8084346388859704, -3.509234909064355, -3.0902880967940254, -2.5656772879860483, -1.9549001293496056, -1.2821344943090989, -0.575253892218742, 0.13536694497891175, 0.8182043229441885, 1.4420344368733666, 1.9774110699152414, 2.398101092550508, 2.682406857448436, 2.8143082480850685, 2.7843642347157247, 2.590324050404691, 2.237411088525773, 1.7382577586334276, 1.1124861143300075], 'positive_zeros': ['1.31547412610837567590861068192543', '2.35690279268179068067664243478613', '3.99519401965184691281326075170385', '4.79664998334316709565876199899452', '5.65594596680013671733621745766315', '6.58991687120145699479680631187894', '7.59955912095787795792560832279126', '8.166569710710947018397642450710543', '8.623243488503016890669362104947909'], 'prelabel': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 1.0, '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': '1.31547412610837567590861068193', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.35690279268179068067664243479', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.99519401965184691281326075170', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.97195037899008, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/a/b/1/1'], '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': '2-1875-1.1-c1-0-40', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31547412610837567590861068193', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1667561565545987963077069132732', 'Lhash_array': ['1667561565545987963077069132732'], 'label': '2-1875-1.1-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/a/b/1/1'}