-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1415507285965461704399468504898', 'a10': [-1.5901100316301644, 0.0], 'a2': [1.5901100316301644, 0.0], 'a3': [-1.5586001397577458, 0.0], 'a4': [0.5284499126908827, 0.0], 'a5': [-1.0, 0.0], 'a6': [-2.4783457175289683, 0.0], 'a7': [-1.6022754962195538, 0.0], 'a8': [-2.3399265558764717, 0.0], 'a9': [-0.5707656043471351, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 54.65760018356645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [1.0, 0]]], [37, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 37], 'central_character': '6845.1', 'coefficient_field': 'CDF', 'conductor': 6845, 'conductor_radical': 185, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.5901100316301644, 0], [2.0, 0]], [[1.0, 0], [1.5586001397577458, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.6022754962195538, 0], [7.0, 0]], [[1.0, 0], [-1.8429865350580077, 0], [11.0, 0]], [[1.0, 0], [-1.0423156916562524, 0], [13.0, 0]], [[1.0, 0], [-2.689325548668182, 0], [17.0, 0]], [[1.0, 0], [-5.627055888916878, 0], [19.0, 0]], [[1.0, 0], [0.7213502305890206, 0], [23.0, 0]], [[1.0, 0], [6.488636727264383, 0], [29.0, 0]], [[1.0, 0], [-5.9571104544255595, 0], [31.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [8.181645859110642, 0], [41.0, 0]], [[1.0, 0], [-8.155872593127505, 0], [43.0, 0]], [[1.0, 0], [1.5901100316301644, 0], [47.0, 0]], [[1.0, 0], [-2.753535794318218, 0], [53.0, 0]], [[1.0, 0], [0.9074843425010367, 0], [59.0, 0]], [[1.0, 0], [1.3237083988073766, 0], [61.0, 0]], [[1.0, 0], [-3.087433384922418, 0], [67.0, 0]], [[1.0, 0], [-10.320391607149043, 0], [71.0, 0]], [[1.0, 0], [11.927924480925663, 0], [73.0, 0]], [[1.0, 0], [-2.6075800040592187, 0], [79.0, 0]], [[1.0, 0], [-2.065712811418988, 0], [83.0, 0]], [[1.0, 0], [-3.8739214079174125, 0], [89.0, 0]], [[1.0, 0], [2.7055080188434437, 0], [97.0, 0]], [[1.0, 0], [-3.4704308540139546, 0], [101.0, 0]], [[1.0, 0], [19.61054173479043, 0], [103.0, 0]], [[1.0, 0], [-5.857894937387542, 0], [107.0, 0]], [[1.0, 0], [-18.795655866964793, 0], [109.0, 0]], [[1.0, 0], [16.88552101970533, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 278, 'label': '2-6845-1.1-c1-0-278', '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/6845/2/a/j/1/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-8.319636636124905e-61, 0.19791696946971205, 0.3941665123453199, 0.5870354191028347, 0.7747224156217889, 0.9553026384113017, 1.1267016620396393, 1.286681254207362, 1.4328383223800762, 1.5626177806823192, 1.6733393642123673, 1.7622377903947257, 1.8265151350954116, 1.8634038602982328, 1.870238593845912, 1.8445345074680133, 1.7840699528658213, 1.6869708846466012, 1.5517945147522527, 1.3776096013587085, 1.164070775611328, 0.9114843545979359, 0.6208631830868077, 0.29396819488964226, -0.06666540801640863, -0.45771919078694345, -0.875101233979873, -1.313975696676485, -1.7688128402531729, -2.233459649624997, -2.7012306363020144, -3.165017823764041, -3.617418315119164, -4.050877242558078, -4.457843316222945, -4.830933646376501, -5.163104027283092, -5.4478204639017775, -5.679227412315965, -5.852308009069445, -5.963031498087955, -6.008483138313735, -5.986972098407988, -5.898113220306987, -5.742879059592812, -5.523619280891639, -5.244045288801524, -4.909178891787481, -4.525264805540474, -4.099647876242832, -3.640617011694228, -3.157218914745887, -2.6590457821241626, -2.1560021245601724, -1.658056743432071, -1.1749866286863881, -0.7161200894253253, -0.29008676339506045, 0.09541774843557199, 0.43384502715277207, 0.7199775764408531, 0.950076643056973, 1.1219885201294977, 1.235204884033286, 1.290874064389612, 1.2917616588968752, 1.242160534659562, 1.1477519531306868, 1.0154212592202294, 0.853033225743997, 0.6691736801972628, 0.4728654009386107, 0.2732673968513232, 0.07936752688173748, -0.10032106981094979, -0.258049109068259, -0.38709546695310226, -0.4819968775764955, -0.5387342461105221, -0.554868159255428, -0.5296178575485065, -0.46387988693752674, -0.3601848065587896, -0.22259262023196588, -0.05652993686190267, 0.13142583979470113, 0.33380783042650786, 0.5425571103618582, 0.7493452256565913, 0.9459095293861968, 1.1243882819102526, 1.2776421668474, 1.3995491109992797, 1.4852600710519985, 1.5314047503180142, 1.5362380005111602, 1.499719890143826, 1.4235250056618889, 1.310979398762518, 1.1669265933624864, 0.997527097317628, 0.8099987998617094, 0.6123083473464941, 0.4128259531036974, 0.21995799792004886, 0.04177311684665863, -0.11436183271071008, -0.24211952137242632, -0.33650793082444463, -0.3941099131949139, -0.4132543786609476, -0.3941096823284706, -0.33869301386896183, -0.25079321463556203, -0.13580831002507338, -0.000502985774426324, 0.14730491859429606, 0.29911625509329187, 0.44616498243521463, 0.579856862864091, 0.6922123776372151, 0.7762928787306144, 0.8265890071567356, 0.8393513909344937, 0.812845583161265, 0.7475160633552442, 0.646047809712146, 0.5133183207996741, 0.3562378496774169, 0.1834808074548792, 0.005116569649752019, -0.1678469636306996, -0.3239889879683418, -0.4520484543235568, -0.5415184083262394, -0.5832344742724643, -0.5699289644724644, -0.4967223989527644, -0.3615258563596718, -0.1653305269326208, 0.08763497654732749, 0.3898937139532651, 0.7308639055247034, 1.0971579705349306, 1.4730310859062519, 1.840966000897642, 2.1823739016329506, 2.4783848022574766, 2.7106955680865115, 2.862439540130521, 2.919039074585813, 2.8690013214753893, 2.704618360095456, 2.4225354236382617, 2.024155336516799, 1.515853326182387, 0.9089838453334965, 0.219669663716094, -0.5316270904188327, -1.3207424434297936, -2.1206373746003924, -2.9023853507872133, -3.6362837095422487, -4.293045023996026, -4.845019336158177, -5.267394936159754, -5.539324414916212, -5.644924151123948, -5.574099228210355, -5.323151919357823, -4.895140124715958, -4.2999621850354215, -3.554155926733782, -2.680412133120571, -1.7068153453349824, -0.6658374001534887, 0.4068791725655201, 1.4739004062890915, 2.497486827318058, 3.441123897308187, 4.271031294074146, 4.957584740679226, 5.476586481916625, 5.810325867306778, 5.948379656418544, 5.888112305008441, 5.634849183203544, 5.201709875979221, 4.609103793184611, 3.883905586439412, 3.058342623362007, 2.16864030424965, 1.2534826634643996, 0.35235489364971206, -0.49615931292923293, -1.2560497427541022, -1.8954456113666451, -2.3880041710967603, -2.714058077792936, -2.861468116818097, -2.826141015476285, -2.612187235073503, -2.2317101434832067, -1.7042350447502073, -1.0558033729084688, -0.3177731298523177, 0.4746194108915584, 1.2838702947237697, 2.071916015729882, 2.8018596506060858, 3.43963448087222, 3.9555274842798465, 4.325491737825633, 4.532186899637142, 4.565700048138965, 4.423914623443027, 4.11251228322512, 3.6446103120031963, 3.040054922328877, 2.3244074724029886, 1.5276754557659853, 0.6828523426960593, -0.17566065392911193, -1.0136725149493016, -1.7987803462158893, -2.5018303015107675, -3.098191097531013, -3.568779884238842, -3.9007934281362346, -4.08811310366034, -4.131369255750543, -4.037668198680259, -3.8200025206940116, -3.496381552813751, -3.0887329783432955, -2.6216378613768545, -2.12096926240543, -1.6125086744834984, -1.1206145484721433, -0.6670131935357592, -0.26977457147446143, 0.057475609678900606, 0.30606993202261734, 0.4725176446745024, 0.5584224364414769, 0.5701116243786774, 0.5180049126851841, 0.4157652753097847, 0.2792863711433579, 0.12557954771365762, -0.028371555815961496, -0.1667198067301478, -0.27576080300210093, -0.34477740394665785, -0.3666737289866749, -0.3383628904893776, -0.26088788468068325], 'positive_zeros': ['1.11663835895365173972008984923843', '2.70662839328890433539137206657105', '3.44200191648198958649445079130337', '3.95210013147323619556854448634443', '4.93371050175323177841753347508575', '5.39078993307310357701513210394867', '6.09510141615696291017815874412623', '6.54733932664193599584220159333590', '7.37342197113652002162913845875176'], 'prelabel': '2-6845-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.393077855911329, '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': '1.11663835895365173972008984924', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.70662839328890433539137206657', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44200191648198958649445079130', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 54.65760018356645, 'bad_primes': [5, 37], 'central_character': '1.1', 'conductor': 6845, 'conductor_radical': 185, 'degree': 2, 'index': 278, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6845/2/a/j/1/6'], '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': '2-6845-1.1-c1-0-278', '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': '2-6845-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.393077855911329, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11663835895365173972008984924', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1415507285965461704399468504898', 'Lhash_array': ['1415507285965461704399468504898'], 'factors': ['2-6845-1.1-c1-0-278'], 'label': '2-6845-1.1-c1-0-278', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6845/2/a/j/1/6'}