-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1688542745909189930333339956293', 'a10': -2250, 'a2': -18, 'a3': 0, 'a4': 196, 'a5': 125, 'a6': 0, 'a7': 343, 'a8': -1224, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 98.4012830274984, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -125]], [7, [1, -343]]], 'bad_primes': [3, 5, 7], 'central_character': '315.1', 'coefficient_field': '1.1.1.1', 'conductor': 315, 'conductor_radical': 105, 'degree': 2, 'euler_factors': [[1, 18, 128], [1], [1, -125], [1, -343], [1, -8016, 19487171], [1, 1786, 62748517], [1, 8358, 410338673], [1, 5884, 893871739], [1, -77700, 3404825447], [1, 155742, 17249876309], [1, 310000, 27512614111], [1, 433618, 94931877133], [1, 357942, 194754273881], [1, 724492, 271818611107], [1, 175320, 506623120463], [1, 132198, 1174711139837], [1, 2648628, 2488651484819], [1, -835478, 3142742836021], [1, -3486308, 6060711605323], [1, -2872260, 9095120158391], [1, -5951882, 11047398519097], [1, 1680904, 19203908986159], [1, 3577524, 27136050989627], [1, -6254826, 44231334895529], [1, 5257054, 80798284478113], [1, 15024954, 107213535210701], [1, 16006576, 122987386542487], [1, 5301048, 160578147647843], [1, 6463402, 182803912081669], [1, -14833302, 235260548044817]], 'euler_factors_factorization': [[[[1, 18, 128], 1]], [1], [[[1, -125], 1]], [[[1, -343], 1]], [[[1, -8016, 19487171], 1]], [[[1, 1786, 62748517], 1]], [[[1, 8358, 410338673], 1]], [[[1, 5884, 893871739], 1]], [[[1, -77700, 3404825447], 1]], [[[1, 155742, 17249876309], 1]], [[[1, 310000, 27512614111], 1]], [[[1, 433618, 94931877133], 1]], [[[1, 357942, 194754273881], 1]], [[[1, 724492, 271818611107], 1]], [[[1, 175320, 506623120463], 1]], [[[1, 132198, 1174711139837], 1]], [[[1, 2648628, 2488651484819], 1]], [[[1, -835478, 3142742836021], 1]], [[[1, -3486308, 6060711605323], 1]], [[[1, -2872260, 9095120158391], 1]], [[[1, -5951882, 11047398519097], 1]], [[[1, 1680904, 19203908986159], 1]], [[[1, 3577524, 27136050989627], 1]], [[[1, -6254826, 44231334895529], 1]], [[[1, 5257054, 80798284478113], 1]], [[[1, 15024954, 107213535210701], 1]], [[[1, 16006576, 122987386542487], 1]], [[[1, 5301048, 160578147647843], 1]], [[[1, 6463402, 182803912081669], 1]], [[[1, -14833302, 235260548044817], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 59, 'label': '2-315-1.1-c7-0-59', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/315/8/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-7.365521989030961e-61, 0.1542649407782024, 0.3053138172424251, 0.44999889092468714, 0.5853079209720696, 0.708429040316918, 0.8168122199039263, 0.9082262425565812, 0.9808101589089316, 1.0331182617724595, 1.0641576925188663, 1.0734178836497592, 1.0608911457075403, 1.0270838239286493, 0.973017580230647, 0.9002204987019179, 0.8107078668908154, 0.7069526497155145, 0.5918458462324078, 0.46864709993236253, 0.3409261184174951, 0.21249564559654702, 0.08733691590018075, -0.03048129791400171, -0.13688875770293077, -0.22790350577382193, -0.299723689590797, -0.34881974538252486, -0.3720251191651367, -0.36662363070438175, -0.3304315453425687, -0.2618724139220167, -0.16004277527844618, -0.0247668913756113, 0.14336119620807428, 0.3429498372163514, 0.5717975135882285, 0.8268972439427972, 1.1044584562308823, 1.39994680716178, 1.7081420688786435, 2.023213818842587, 2.3388142649270267, 2.6481871222978492, 2.9442910406666702, 3.219935669632992, 3.467928056342569, 3.681226704215581, 3.8531002947873665, 3.977287797345549, 4.04815647317678, 4.060854132231275, 4.0114519281812955, 3.897073990121725, 3.716010290798018, 3.4678093455704637, 3.1533476244777865, 2.77487294051983, 2.3360195468957863, 1.8417932280714158, 1.2985252952540622, 0.7137950846230084, 0.09632129257273278, -0.5441767498445642, -1.197145979170739, -1.851392018029488, -2.495293699255234, -3.1170355823732887, -3.70485371513236, -4.247289348127323, -4.733444874682139, -5.153235958693586, -5.497633645200666, -5.758890234115081, -5.930742845295238, -6.008588917367394, -5.989628363340362, -5.872967748352384, -5.659682649195831, -5.352835287084737, -4.957445575234377, -4.480414867555165, -3.93040290649069, -3.317659715740169, -2.653815433651361, -1.9516323000360072, -1.2247241568383214, -0.4872498655349471, 0.24641205320503384, 0.9619995212783468, 1.6457051794996844, 2.2845079652525326, 2.8664890537760503, 3.3811234147136333, 3.819538682836434, 4.174733743783971, 4.441750380901745, 4.6177924984685, 4.702288802688643, 4.696896350399987, 4.605444025622866, 4.433816729466063, 4.189782818871226, 3.8827690507872212, 3.52358892600676, 3.1241318270153773, 2.69702165510419, 2.25525474616187, 1.8118276403954028, 1.3793657647078819, 0.9697642325833552, 0.5938517603321022, 0.26108813683266896, -0.020695225396653954, -0.2455033667900543, -0.4093277265479177, -0.5102329846625242, -0.5483778125374087, -0.5259686684326276, -0.4471479680055784, -0.3178201515312699, -0.1454212828224429, 0.06136022439512977, 0.2929024206844693, 0.5389973981614189, 0.7892157563072986, 1.0332753806046278, 1.2614016873433593, 1.4646666673501711, 1.6352946954792669, 1.766924149404675, 1.8548153719592049, 1.8959973712956073, 1.8893478228588931, 1.8356033436596475, 1.7372995687570196, 1.5986431801392849, 1.4253206222910193, 1.2242506881626347, 1.0032903777718756, 0.7709053290599147, 0.535817616403865, 0.30664473902323125, 0.09154412831064505, -0.10212254245372286, -0.26809157211487333, -0.4014534588502702, -0.4988523147800758, -0.5586197942508144, -0.5808374071360928, -0.5673239343037194, -0.5215477017783856, -0.44846658485104707, -0.35430167854488875, -0.24625345970363702, -0.13217185504611267, -0.020193803781811077, 0.0816364388051821, 0.16574795254260627, 0.22540805751389215, 0.25505507294032825, 0.250583535267761, 0.2095681704237276, 0.1314152378640298, 0.017432740852802497, -0.129185676593696, -0.30346467808784483, -0.49883673694846886, -0.7074110587570649, -0.9203120959232013, -1.1280744407021328, -1.3210779645179975, -1.4900047612530487, -1.6262978712235878, -1.7226010047247844, -1.7731586110856552, -1.774156677009894, -1.7239865740720317, -1.6234170577628984, -1.4756630590321587, -1.286344077320648, -1.063329623031944, -0.8164740822859828, -0.5572483832707567, -0.2982807159553026, -0.05282307743638063, 0.16583562705978938, 0.34498599678647124, 0.47311785590855376, 0.5405158612058666, 0.5398035154724176, 0.4664092443713597, 0.3189305301533107, 0.0993755711453914, -0.1867335571249797, -0.5304068824407291, -0.9193862481795917, -1.3384968606795837, -1.770142120845105, -2.194926651244593, -2.5923862971830833, -2.9417984343576418, -3.223041418670536, -3.4174686954900486, -3.508761132697636, -3.4837206877381526, -3.332969636231466, -3.051522284930706, -2.639200302531753, -2.1008683972055247, -1.4464738538635447, -0.6908811626064145, 0.14649868125535023, 1.0422759871196527, 1.9698305082258047, 2.900215016221755, 3.803182118852948, 4.64829598537396, 5.40608595725474, 6.049196036485963, 6.553483138486474, 6.8990178720233555, 7.070944481168691, 7.060161383186432, 6.863790303613328, 6.485410105689355, 5.935040721928217, 5.228872745433094, 4.388748805359574, 3.4414133835707346, 2.417557767445804, 1.3506959274475412, 0.27591483941830436, -0.7714512261866179, -1.757168950702445, -2.6494215175193334, -3.4200368591222468, -4.045576992526627, -4.508242116269063, -4.796550510999375, -4.905764448881854, -4.8380428951625465, -4.602313328525357, -4.213867014035191, -3.69369400306279, -3.0675854727213263, -2.365041236384376, -1.618028883653899, -0.8596476357431412, -0.12275430987961457, 0.5613894441736731, 1.1643903448455108, 1.661862323327574, 2.0343822013732784, 2.268221603624902, 2.3558245836038045, 2.2960119319945034], 'positive_zeros': ['1.33202535904229649704791322437660', '1.94298647854702915529021799916715', '3.64173694804000630406893618965624', '5.13646523835169714366678375839039', '6.61636499852554801866918111058061', '7.13188360919454764319842406103573', '8.405675446409159131043949560335782', '9.151661369503961962117148145249871', '9.617048099366130674806335954011222'], 'prelabel': '2-315-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.91974208472672, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c7-0', 'trace_hash': 201709590680152828, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33202535904229649704791322438', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.94298647854702915529021799917', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64173694804000630406893618966', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 98.4012830274984, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 315, 'conductor_radical': 105, 'degree': 2, 'dirichlet_coefficients': [1, -18, 0, 196, 125, 0, 343, -1224, 0, -2250, 8016, 0, -1786, -6174, 0, -3056, -8358, 0, -5884, 24500, 0, -144288, 77700, 0, 15625, 32148, 0, 67228, -155742, 0, -310000, 211680, 0, 150444, 42875, 0, -433618, 105912, 0, -153000, -357942, 0, -724492, 1571136, 0, -1398600, -175320, 0, 117649, -281250, 0, -350056, -132198, 0, 1002000, -419832, 0, 2803356, -2648628, 0, 835478, 5580000, 0, -3419072, -223250, 0, 3486308, -1638168, 0, -771750, 2872260, 0, 5951882, 7805124, 0, -1153264, 2749488, 0, -1680904, -382000, 0, 6442956, -3577524, 0, -1044750, 13040856, 0, -9811584, 6254826, 0, -612598, 15229200, 0, 3155760, -735500, 0, -5257054, -2117682, 0, 3062500], 'euler11': [1, -8016, 19487171], 'euler13': [1, 1786, 62748517], 'euler17': [1, 8358, 410338673], 'euler19': [1, 5884, 893871739], 'euler2': [1, 18, 128], 'euler23': [1, -77700, 3404825447], 'euler29': [1, 155742, 17249876309], 'euler3': [1, 0, 0], 'euler31': [1, 310000, 27512614111], 'euler37': [1, 433618, 94931877133], 'euler41': [1, 357942, 194754273881], 'euler43': [1, 724492, 271818611107], 'euler47': [1, 175320, 506623120463], 'euler5': [1, -125, 0], 'euler53': [1, 132198, 1174711139837], 'euler59': [1, 2648628, 2488651484819], 'euler61': [1, -835478, 3142742836021], 'euler67': [1, -3486308, 6060711605323], 'euler7': [1, -343, 0], 'euler71': [1, -2872260, 9095120158391], 'euler73': [1, -5951882, 11047398519097], 'euler79': [1, 1680904, 19203908986159], 'euler83': [1, 3577524, 27136050989627], 'euler89': [1, -6254826, 44231334895529], 'euler97': [1, 5257054, 80798284478113], 'euler_factors': [[1, 18, 128], [1, 0, 0], [1, -125, 0], [1, -343, 0], [1, -8016, 19487171], [1, 1786, 62748517], [1, 8358, 410338673], [1, 5884, 893871739], [1, -77700, 3404825447], [1, 155742, 17249876309], [1, 310000, 27512614111], [1, 433618, 94931877133], [1, 357942, 194754273881], [1, 724492, 271818611107], [1, 175320, 506623120463], [1, 132198, 1174711139837], [1, 2648628, 2488651484819], [1, -835478, 3142742836021], [1, -3486308, 6060711605323], [1, -2872260, 9095120158391], [1, -5951882, 11047398519097], [1, 1680904, 19203908986159], [1, 3577524, 27136050989627], [1, -6254826, 44231334895529], [1, 5257054, 80798284478113]], 'index': 59, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/315/8/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/315/8/a/a'], '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': '2-315-1.1-c7-0-59', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'prelabel': '2-315-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.91974208472672, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c7-0', 'trace_hash': 201709590680152828, 'z1': {'__RealLiteral__': 0, 'data': '1.33202535904229649704791322438', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20875921
{'Lhash': '1688542745909189930333339956293', 'Lhash_array': ['1688542745909189930333339956293'], 'label': '2-315-1.1-c7-0-59', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/315/8/a/a'}
-
id: 24591915
{'Lhash': '1688542745909189930333339956293', 'Lhash_array': ['1688542745909189930333339956293'], 'label': '2-315-1.1-c7-0-59', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/315/8/a/a/1/1'}