-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3161230407108684249050742996160', 'a10': [-1.7660444431189781, 3.058878703906754], 'a2': [-0.766044443118978, 0.6427876096865394], 'a3': [-1.4396926207859084, -1.2080455471101075], 'a4': [0.17364817766693036, -0.984807753012208], 'a5': [3.3190778623577253, -1.2080455471101075], 'a6': [1.8793852415718169, 7.704816656998374e-61], 'a7': [0.8263518223330697, -0.3007674663608706], 'a8': [0.5, 0.8660254037844386], 'a9': [0.09239626545204768, 0.5240052604587699], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.766044443118978, -0.6427876096865394]]], [37, [[1.0, 0], [3.443563014047729, -5.0141673055735305]]]], 'bad_primes': [2, 37], 'central_character': '74.49', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '2015732682576302867009781060650', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.766044443118978, -0.6427876096865394]], [[1.0, 0], [1.4396926207859084, 1.2080455471101075], [0.520944533000791, 2.9544232590366244]], [[1.0, 0], [-3.3190778623577253, 1.2080455471101075], [3.83022221559489, -3.2139380484326967]], [[1.0, 0], [-0.8263518223330697, 0.3007674663608706], [5.362311101832846, -4.499513267805775]], [[1.0, 0], [1.6736481776669303, 2.8988436777141864], [-5.5, 9.526279441628825]], [[1.0, 0], [1.1133407984528387, -6.314069429304249], [-12.216004070216808, -4.446261863233693]], [[1.0, 0], [0.520944533000791, 2.9544232590366244], [-15.974774553360442, 5.814342436536369]], [[1.0, 0], [-3.553033419238747, -2.981349031643783], [3.2993153756716764, 18.711347307231954]], [[1.0, 0], [2.9187480877851173, -5.055419982538329], [-11.5, -19.91858428704209]], [[1.0, 0], [-1.6342853314536299, -2.8306652281422298], [-14.5, 25.11473670974872]], [[1.0, 0], [1.1206147584281831, 0], [31.0, 0]], [[1.0, 0], [3.443563014047729, -5.0141673055735305]], [[1.0, 0], [-1.490199820236374, 8.451343148104126], [-38.527397452222246, -14.022825876352417]], [[1.0, 0], [-5.61586701824112, 0], [43.0, 0]], [[1.0, 0], [-2.564177772475912, 4.441286181567069], [-23.5, -40.703193977868615]], [[1.0, 0], [0.25237387009353146, 0.09185657662061078], [40.60035548530583, 34.067743313386586]], [[1.0, 0], [7.159100257716242, 2.60569939793621], [45.196622144019706, 37.92446897150582]], [[1.0, 0], [-0.36958506180819073, 2.0960210418350798], [-57.32124986794041, -20.863228742865793]], [[1.0, 0], [8.017540966287267, -2.918146263738451], [51.32497768897153, -43.066769848998135]], [[1.0, 0], [-10.071918558999553, -8.451343148104126], [12.329020614352055, 69.92135046386677]], [[1.0, 0], [8.573977952239538, 0], [73.0, 0]], [[1.0, 0], [-10.883255634833636, 3.9611811029893658], [60.51751100639927, -50.780221165236604]], [[1.0, 0], [-0.724155377117396, -4.106889224824294], [-77.9944875252304, 28.387671896030504]], [[1.0, 0], [7.86958506180819, 2.8642947185241336], [68.17795543758905, 57.208097262102]], [[1.0, 0], [-8.532088886237956, 14.778011445657894], [-48.5, -84.00446416709055]], [[1.0, 0], [0.5432332394751211, -0.9409075711311408], [-50.5, -87.4685657822283]], [[1.0, 0], [5.607411011951033, 9.712320771620403], [-51.5, 89.20061658979718]], [[1.0, 0], [-1.666374217691586, 9.450477805473975], [-100.5471104240922, -36.596155335846554]], [[1.0, 0], [1.7018666706430658, -1.4280356956495022], [18.927651365695407, -107.34404507833068]], [[1.0, 0], [3.5471036327369414, -2.9763733499771576], [19.62224407636313, -111.28327609037952]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-74-37.12-c1-0-0', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/74/2/f/a/49/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6996824312872112, 0.7254679936511327, 0.7597565099968702, 0.8022882092569745, 0.8519327607915534, 0.9068244655491635, 0.9644916998017931, 1.0219544913359928, 1.0757912999841894, 1.1221913754184285, 1.157012375177525, 1.1758596860458848, 1.1741986336791963, 1.147505608888343, 1.0914595843246648, 1.0021713935524752, 0.87644424946249, 0.7120551572529346, 0.5080431500209183, 0.2649867993556716, -0.014749512267659928, -0.32682320182246366, -0.6647985663097731, -1.0201323288509092, -1.382280217504734, -1.7389406666557086, -2.076445118213008, -2.3802957307724366, -2.635840852603837, -2.82906686477531, -2.9474726545603644, -2.9809809340030005, -2.9228299280558687, -2.7703807673380196, -2.525771384495026, -2.1963478835166113, -1.7948100651819345, -1.3390195501024282, -0.8514367975503009, -0.3581767907756772, 0.11229882567376731, 0.530804485109612, 0.86928810344985, 1.102813396216665, 1.2115327135667449, 1.1824991835879404, 1.0111606279756058, 0.7023839808518927, 0.27087904748719943, -0.2590754841731774, -0.8546539932646168, -1.4762469442266057, -2.0798946490354595, -2.620256758457279, -3.053922401421002, -3.342816675143329, -3.457426803771115, -3.3795608244159827, -3.1043666877880383, -2.641381629447376, -2.014449491754927, -1.2604335150906663, -0.4267574249327328, 0.43208047692379287, 1.2587676426135346, 1.9978669570415324, 2.6005245412151505, 3.0287540207800623, 3.258867426277542, 3.283679655045458, 3.1132132012569804, 2.7737658294783625, 2.3053645432462107, 1.757799232718857, 1.1855908982441885, 0.6423837266557235, 0.17534027090135534, -0.17984923382649068, -0.4027671208951081, -0.4904044118465681, -0.4573230747908957, -0.33374571313963697, -0.16171087811506335, 0.010331140728898352, 0.13389912655962474, 0.16710327244984075, 0.08070053599284448, -0.1372051532139689, -0.4784871668352443, -0.9148041165403158, -1.400068389054453, -1.875427744625985, -2.2762834827624006, -2.5405765932350284, -2.6173581332095597, -2.4745551890076274, -2.1048710216349598, -1.5289237944908565, -0.7950215413191092, 0.02463688099127227, 0.8410980266951086, 1.5584428228752274, 2.085154287241599, 2.3457140149767293, 2.2909593154815333, 1.9057991944389323, 1.2131419147181972, 0.2733083853034076, -0.8212511192464163, -1.9555192249607927, -3.004754817073289, -3.8491386197864896, -4.388431207511345, -4.5547647943151865, -4.321847995081761, -3.709259376695938, -2.781099508035461, -1.6389910051090733, -0.41016877497075116, 0.7679143965417186, 1.7645269075558685, 2.4719348626859303, 2.818837700453913, 2.7791177863128183, 2.3746614040537373, 1.6718049038860283, 0.771842643903062, -0.2031217976696215, -1.1270172235629177, -1.8869608524238572, -2.3982739556458736, -2.6151860704840706, -2.5356696812321213, -2.199707037414093, -1.6812743561928014, -1.0752893205475686, -0.48155687240432765, 0.011761696622125024, 0.342525865903808, 0.48451581465708027, 0.4512151929301739, 0.29279906336198663, 0.0867447458862515, -0.07646077332656645, -0.11019937219260251, 0.051618400758857416, 0.4409556992768239, 1.0475262786149129, 1.817712448328878, 2.6609561105631836, 3.4628106818880067, 4.102691935704124, 4.473506838568653, 4.499926346091512, 4.152186711237989, 3.452953258010189, 2.4758696471381554, 1.3357747436024865, 0.1719758475321839, -0.8728179301683088, -1.674490376023214, -2.1467815433575095, -2.2545350421739956, -2.018597591765835, -1.5114240826747811, -0.8440303594177281, -0.1464567624640764, 0.4549122226063632, 0.85920362284036, 1.0081836289189638, 0.8955191648433501, 0.5663870432241395, 0.10735942319158706, -0.3717246399654911, -0.7606654361208866, -0.9723660498660022, -0.9623897388103904, -0.7407196469651476, -0.3731420123438679, 0.02848417651202036, 0.32575505169021624, 0.3798365721341302, 0.07957490906641339, -0.6335790658719693, -1.7486715054132806, -3.1799652229843214, -4.7749056530484, -6.334615918205826, -7.64389191070432, -8.505816282549027, -8.77507555747281, -8.38406705720306, -7.356958132264045, -5.808848338788376, -3.9297505788546503, -1.9557970148103296, -0.13239992473102002, 1.3243798775999165, 2.2615835128809727, 2.6123329358902194, 2.404015297639056, 1.7502765354991192, 0.828339313910037, -0.15418134711807469, -0.9968864741948643, -1.5417618188293505, -1.6995363353332331, -1.4625495403187776, -0.9020196764353704, -0.1505735795887619, 0.6263053226528915, 1.2641744674035427, 1.6321819217420972, 1.6579326042671056, 1.3399390982653039, 0.7454599674277244, -0.005510877367446587, -0.7665488286595047, -1.3957864403362457, -1.7850751083443985, -1.8812588377769452, -1.6952057915936096, -1.2968621060802312, -0.7975800698204069, -0.32370225311198986, 0.012727019654624323, 0.13961424016985058, 0.041093562664421386, -0.23928105916217365, -0.6092625958483252, -0.9502806789856978, -1.1465074950960192, -1.1140370848003427, -0.8233818166872767, -0.3097873439882851, 0.3315625628336255, 0.9650615361542616, 1.4451656576776075, 1.6514332499313942, 1.520352007700558, 1.066495336641006, 0.3875219481837563, -0.34919384410312343, -0.9365984129363555, -1.169226791901069, -0.8875360984121685, -0.0160406648926524, 1.4131742807487044, 3.2573072733255004, 5.281800104073254, 7.198600649121389, 8.716809830508064, 9.5959856758551, 9.691517053792564, 8.982806994409414, 7.578299825737721, 5.696000252389584], 'positive_zeros': ['2.49377108056394432966295850797814', '4.96917904069463441676932877451128', '6.06633479311166729227181358383295', '7.81205207965268755664204507915485', '9.556268847832162792380504731987237', '10.36678143118228997176234470288085', '10.80560483297321943769679328476215', '12.37130676594942482871804590782608', '13.40741425438717766319729073543760', '14.79219508229132085500120868294549'], 'prelabel': '2-74-37.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.1570168944659723, 'root_number': '0.8807829838304243 + 0.4735201531030908*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.078508447233', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.49377108056394432966295850798', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.96917904069463441676932877451', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.06633479311166729227181358383', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'bad_primes': [2, 37], 'central_character': '37.12', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/f/a/49/1'], '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': '2-74-37.12-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-74-37.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.07850844723298615, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.49377108056394432966295850798', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3161230407108684249050742996160', 'Lhash_array': ['3161230407108684249050742996160'], 'label': '2-74-37.12-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/f/a/49/1'}