-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2502844587414114148067762853497', 'a10': [0.0, 0.0], 'a2': [1.3660254037844386, 0.36602540378443865], 'a3': [4.371648007328276, -1.1713795531567386], 'a4': [1.7320508075688772, 1.0], 'a5': [0.0, 0.0], 'a6': [6.400536908343076, 2.3929298114967825e-60], 'a7': [-4.400125004702601, -5.44416200557909], 'a8': [2.0, 2.0], 'a9': [9.944947608363663, -5.741718178765486], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.536809252610393, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.3660254037844386, -0.36602540378443865]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [4.400125004702601, 5.44416200557909]]]], 'bad_primes': [2, 5, 7], 'central_character': '350.193', 'coefficient_field': 'CDF', 'conductor': 350, 'conductor_radical': 70, 'conjugate': '1988012816000206612468739884417', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3660254037844386, -0.36602540378443865]], [[1.0, 0], [-4.371648007328276, 1.1713795531567386], [7.794228634059948, -4.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.400125004702601, 5.44416200557909]], [[1.0, 0], [-3.2796294135778297, 5.680484774314123], [-60.5, -104.78907385791707]], [[1.0, 0], [-9.545784308416103, -9.545784308416103], [0, 169.0]], [[1.0, 0], [0.5506957037446057, 2.055224345884767], [-250.28134169370276, 144.5]], [[1.0, 0], [-23.508030972966996, 13.572368010360556], [180.5, -312.63517076618234]], [[1.0, 0], [-0.7976629006384006, 2.976918472495276], [-458.12743860196804, -264.5]], [[1.0, 0], [0, -52.61968848502756], [-841.0, 0]], [[1.0, 0], [19.33096224894694, -33.482208774372026], [-480.5, -832.2504130368455]], [[1.0, 0], [55.05860175380303, 14.752907876318318], [1185.5887777808964, 684.5]], [[1.0, 0], [75.47946090430142, 0], [1681.0, 0]], [[1.0, 0], [38.796231556522464, 38.796231556522464], [0, 1849.0]], [[1.0, 0], [16.94289439435551, 4.539834870413355], [1913.050116959825, 1104.5]], [[1.0, 0], [-54.568033666799096, 14.621460553573133], [2432.6653592304883, -1404.5]], [[1.0, 0], [67.7923519554296, 39.13993265046513], [1740.5, 3014.634430573631]], [[1.0, 0], [-48.20128167937449, -83.48706885861552], [-1860.5, 3222.4805274818964]], [[1.0, 0], [-6.109131425234874, -22.79958886909222], [-3887.5880375883453, 2244.5]], [[1.0, 0], [-117.05818893221479, 0], [5041.0, 0]], [[1.0, 0], [-23.671575230716176, 6.342779466642966], [4615.049376767273, -2664.5]], [[1.0, 0], [22.31713126146748, -12.884801741348461], [3120.5, -5404.864545018681]], [[1.0, 0], [31.859384841610094, 31.859384841610094], [0, 6889.0]], [[1.0, 0], [27.405167660746294, -15.822380926118699], [3960.5, -6859.787223376538]], [[1.0, 0], [-52.38497205708587, 52.38497205708587], [0, -9409.0]], [[1.0, 0], [-30.970912007013812, 53.64319315289291], [-5100.5, -8834.325144005059]], [[1.0, 0], [-26.445091249828675, 98.69442415515576], [-9187.66350874911, -5304.5]], [[1.0, 0], [72.64716015104378, 19.46574789488662], [9915.124847928038, 5724.5]], [[1.0, 0], [-47.57218220828154, -27.46581220388927], [5940.5, 10289.247822362915]], [[1.0, 0], [-59.0931739674525, -59.0931739674525], [0, 12769.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 22, 'label': '2-350-35.18-c2-0-22', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/350/3/p/g/193/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.859729028728221, 3.9175627864829616, 3.9422717888883914, 3.93117084672642, 3.880119606370901, 3.78414948423139, 3.638287875568582, 3.438485035562478, 3.1825475371210357, 2.870987189611585, 2.50770100974977, 2.100404991216869, 1.6607536349959338, 1.2040913280639953, 0.7488032201144221, 0.31526344723673666, -0.07558319570627658, -0.4039261780081541, -0.6529554963118108, -0.8107227803999487, -0.8717998562687385, -0.838523216776923, -0.721620971876897, -0.5400530641106926, -0.31995697085639585, -0.09267747928708273, 0.1080357317065649, 0.24946500201072214, 0.3036888046795095, 0.25127580549461853, 0.08445679755430092, -0.19068352054119353, -0.5534005487707345, -0.9691612640857321, -1.392314270709283, -1.77046596736401, -2.050236042387587, -2.1838393397042672, -2.1357558118558737, -1.8886380263669078, -1.4475934625664524, -0.8420833762686645, -0.12490367982126518, 0.6319586356097011, 1.3443998228392176, 1.925586177220699, 2.2966443751185253, 2.3973510873069226, 2.195373256635678, 1.69265746472902, 0.9278219334196752, -0.02614498304995978, -1.0689749687239065, -2.0844153863721364, -2.954485769009183, -3.5749089227090263, -3.869604654727101, -3.802097196222846, -3.3819744087412595, -2.6651350457956773, -1.747405455201916, -0.7520882438007311, 0.18702181171620474, 0.9448123870656032, 1.4233809221650005, 1.5670001945516916, 1.3709979730754394, 0.8828573072576904, 0.19501195283067976, -0.5698532597175305, -1.2788978779017666, -1.8114977315212202, -2.080218335555559, -2.046753843729897, -1.7298651251164057, -1.2035777899197941, -0.5855083005506583, -0.016914436397671866, 0.3623850340493887, 0.43999750380175745, 0.15324224732432504, -0.496448853909988, -1.4399922666545297, -2.549136345875313, -3.656001720234725, -4.58065087525773, -5.162049545630292, -5.286951235093375, -4.911381845393589, -4.070548078869053, -2.874974641603865, -1.4931548526324858, -0.12352571256845922, 1.0393326802442966, 1.8381461123171636, 2.1798260226167825, 2.0506729221710773, 1.5169353448463228, 0.7105374695467602, -0.19732085407515504, -1.0295660595073717, -1.637082420825003, -1.9262555556971823, -1.874735940853532, -1.5323131481286325, -1.006865318004174, -0.438483415932397, 0.03260063316496558, 0.2972900222365198, 0.30124439635039135, 0.05563039245309365, -0.36738011228426876, -0.8533149477247494, -1.2739870328555907, -1.5192692974379154, -1.5244803710644386, -1.2866561226057653, -0.8654502377795589, -0.3679820762649405, 0.07915800444244454, 0.364231631962715, 0.42258841014948484, 0.25843110280062304, -0.05020649509145983, -0.3658549904191793, -0.5233598488103668, -0.37253604714958044, 0.1779143301930306, 1.1259672618732894, 2.3606853745271166, 3.6711157766089983, 4.779998987934881, 5.396823653756321, 5.279838448394137, 4.293779178641382, 2.4500791196299496, -0.08062577218331207, -2.988336442902565, -5.8736022959257586, -8.31847370856775, -9.964417998341784, -10.581018886956322, -10.110723580029813, -8.679695042404672, -6.571986256448222, -4.172209193320123, -1.8888188752331228, -0.07445080863830791, 1.039608488482432, 1.380978572616036, 1.0383447239228478, 0.2289086896031449, -0.7602708714992109, -1.642621984449663, -2.1973120491807294, -2.314328164609552, -2.009616500284668, -1.4081254206554397, -0.7006120880076552, -0.08648006943943672, 0.2818960489676872, 0.33873298339377916, 0.11828062046539739, -0.26066950390342025, -0.6341460324063289, -0.8446984523548429, -0.7905806341144573, -0.4582972585589331, 0.07097306120808433, 0.643252032638591, 1.076086538626227, 1.2129506913644184, 0.9721614396864025, 0.37585880361420954, -0.4501733002920739, -1.3070731618131814, -1.9764619740666007, -2.282754007005018, -2.1468644719483456, -1.6156080241143724, -0.8571956803571017, -0.12228736516915474, 0.3203669044871328, 0.2572053267233965, -0.40762971688025945, -1.6180966724254509, -3.170896996748026, -4.759282697282375, -6.045731937783398, -6.7450526858083855, -6.696139647765324, -5.903144698657641, -4.534686412307153, -2.8808805654332743, -1.2794064899562134, -0.030362481989421604, 0.6771337380752593, 0.8067775314336583, 0.4742301845462643, -0.09559219438056242, -0.6404548356913515, -0.9409782892251664, -0.885641681820178, -0.5015187292424085, 0.05842096067664972, 0.5678358626075154, 0.8037937977666455, 0.6246262531609873, 0.024749273367947102, -0.851425536710562, -1.7426110008652143, -2.3429366789142856, -2.3934112452655483, -1.7658988790282273, -0.5139501168875166, 1.1265419086335897, 2.7898854399871755, 4.073899785259029, 4.649116814870547, 4.353324811541481, 3.2438820053537616, 1.591278611766916, -0.18639723116418835, -1.6316609250830918, -2.369529213903639, -2.2095562652425684, -1.1993238982270253, 0.38616840494920035, 2.1170052731682416, 3.5231751939679983, 4.220159569316508, 4.010652610343144, 2.9345200877744095, 1.253785681682654, -0.6221769890995317, -2.2492948019364167, -3.267036022626879, -3.48911486678922, -2.942247238705714, -1.8441727366378655, -0.5299862019416115, 0.6494777254195199, 1.4262242070871387, 1.6819062214022507, 1.4649708941074802, 0.9561865629047659, 0.39657876873008974, 0.0028625353214621467, -0.10177550712588886, 0.08008217905223981, 0.4334074901201024, 0.782697426926635, 0.9628266434273783, 0.8830494656722708, 0.5612849657149299, 0.11653711082286464, -0.2777419445865846], 'positive_zeros': ['1.97439624685500789754740566737732', '3.17944469145099210379524586026044', '3.79361858950352546202740580469796', '5.27072567359029689582640198880630', '6.37178241014992745800875083186434', '7.72361788973540412960950946993699', '8.532204219857420817267529563042282', '9.629293135533987631017566760112452', '10.03633451405913929864091522593660', '11.51200444167615258926302645496054'], 'prelabel': '2-350-35.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.088172477794981, 'root_angle': 0.09539425729793402, 'root_number': '0.9554280846202062 + 0.29522394062637275*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.047697128649', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.97439624685500789754740566738', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.17944469145099210379524586026', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79361858950352546202740580470', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.536809252610393, 'bad_primes': [2, 5, 7], 'central_character': '35.18', 'conductor': 350, 'conductor_radical': 70, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/350/3/p/g/193/5'], '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': '2-350-35.18-c2-0-22', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-350-35.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.088172477794981, 'root_angle': 0.04769712864896701, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.97439624685500789754740566738', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2502844587414114148067762853497', 'Lhash_array': ['2502844587414114148067762853497'], 'label': '2-350-35.18-c2-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/350/3/p/g/193/5'}