-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1616792665534162093217565572752', 'a10': [-2.3622101161622884, 0.0], 'a2': [-1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [2.3622101161622884, 0.0], 'a6': [-1.0, 0.0], 'a7': [-4.260269112346257, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.15181298389669, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]], [103, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 13, 103], 'central_character': '8034.1', 'coefficient_field': 'CDF', 'conductor': 8034, 'conductor_radical': 8034, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.3622101161622884, 0], [5.0, 0]], [[1.0, 0], [4.260269112346257, 0], [7.0, 0]], [[1.0, 0], [1.6669494989469271, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.266603909246002, 0], [17.0, 0]], [[1.0, 0], [4.502571634977649, 0], [19.0, 0]], [[1.0, 0], [-8.718518391371763, 0], [23.0, 0]], [[1.0, 0], [-7.704791602756026, 0], [29.0, 0]], [[1.0, 0], [7.02641556945107, 0], [31.0, 0]], [[1.0, 0], [-1.4273395703422245, 0], [37.0, 0]], [[1.0, 0], [2.889007337654028, 0], [41.0, 0]], [[1.0, 0], [2.8722054323226365, 0], [43.0, 0]], [[1.0, 0], [-2.3231812863048282, 0], [47.0, 0]], [[1.0, 0], [3.142220829891601, 0], [53.0, 0]], [[1.0, 0], [-13.927063849318666, 0], [59.0, 0]], [[1.0, 0], [4.277007368846325, 0], [61.0, 0]], [[1.0, 0], [9.627611859186121, 0], [67.0, 0]], [[1.0, 0], [7.378359806545973, 0], [71.0, 0]], [[1.0, 0], [5.928782809381462, 0], [73.0, 0]], [[1.0, 0], [-5.4255972780079365, 0], [79.0, 0]], [[1.0, 0], [13.77427770170423, 0], [83.0, 0]], [[1.0, 0], [11.404166132016844, 0], [89.0, 0]], [[1.0, 0], [-8.923346169696627, 0], [97.0, 0]], [[1.0, 0], [-8.264686768835373, 0], [101.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.4721829231455026, 0], [107.0, 0]], [[1.0, 0], [12.02915554406516, 0], [109.0, 0]], [[1.0, 0], [-15.05600611023837, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 148, 'label': '2-8034-1.1-c1-0-148', '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/8034/2/a/bb/1/12', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.1634701551939125e-61, 0.17719497178792448, 0.3531009847640005, 0.5263952322845651, 0.6956902422540239, 0.8595088944394537, 1.0162676544086031, 1.1642698350716025, 1.3017100400688444, 1.4266902625801312, 1.5372474615561895, 1.6313918530345004, 1.7071546587984325, 1.7626436553915383, 1.7961045602011325, 1.8059860689971812, 1.7910062103028732, 1.7502175968830536, 1.6830691269155134, 1.5894617137973923, 1.4697957036740434, 1.325007775320886, 1.1565953105588858, 0.966626477396107, 0.7577345839119022, 0.5330956380082437, 0.2963884835683788, 0.05173737149999381, -0.19636264416742194, -0.44313653124894464, -0.6836347903525843, -0.9128515350486512, -1.1258524613662806, -1.3179095026040106, -1.484638501562458, -1.6221358498884655, -1.7271097636442743, -1.7970017041600879, -1.830093429790344, -1.8255952900346575, -1.783711657034113, -1.705679834206868, -1.5937793857250997, -1.451309585708706, -1.2825335783127092, -1.0925888490394133, -0.8873647073935093, -0.6733486397274001, -0.4574445723552284, -0.24676724852638648, -0.04841802583546467, 0.1307516008923744, 0.2843815958944793, 0.4068422820344031, 0.4934622947304575, 0.5407371682286847, 0.5465102441350995, 0.5101180056129979, 0.43249266225034333, 0.31621583590286595, 0.16551851079594676, -0.013776016075730013, -0.21436765526171705, -0.42765302436073765, -0.6439543635785319, -0.8527991922737289, -1.0432439541851706, -1.2042329352426755, -1.324981967284734, -1.3953749313899353, -1.4063599184652833, -1.350331156498234, -1.2214825263794375, -1.0161187001781902, -0.7329106693379153, -0.37308368905279005, 0.05947256717294041, 0.558179608832881, 1.1138367965387619, 1.714781394014551, 2.347141082239493, 2.9951746390552785, 3.6416930965929564, 4.268550409453953, 4.857189628972845, 5.389227911096329, 5.8470615079339305, 6.214470313651284, 6.477200644136877, 6.623504794528118, 6.644616580762278, 6.535143543068288, 6.29335875166643, 5.921378156655134, 5.425213082153585, 4.81469166626928, 4.103247653516287, 3.3075797925525103, 2.4471900001806555, 1.5438132326573635, 0.6207564644970204, -0.2978318752283919, -1.1877373943920626, -2.02547311821116, -2.78906226355668, -3.4587815176089385, -4.017836651956214, -4.452944149330662, -4.754795456088472, -4.918384417445693, -4.943183277905542, -4.833158168681387, -4.5966210540143395, -4.245921437477857, -3.796987486378071, -3.2687323562501027, -2.682347128401556, -2.06050666396963, -1.4265186039595898, -0.8034485160625793, -0.21325565889523948, 0.32402609293880924, 0.7910289823773369, 1.1736833575802257, 1.461714614843661, 1.6489840886892337, 1.7336591576208942, 1.7182048480906735, 1.6091966835293432, 1.416962125214242, 1.155065358392049, 0.8396570616944645, 0.488716846632366, 0.12122098248534038, -0.24372841090340247, -0.5877744997886042, -0.894138647263528, -1.1483779049716403, -1.3390329407181472, -1.4581368838947364, -1.5015615950455785, -1.4691850379860416, -1.364871444477632, -1.1962644588829, -0.9744020496682284, -0.7131702794243784, -0.4286206440660583, -0.1381822579942229, 0.14019464971358406, 0.3889239190093156, 0.5916556074616087, 0.7340936310356886, 0.8047196343403701, 0.7953879307423855, 0.7017621821897437, 0.523571791128289, 0.26467442334128755, -0.06707971991602098, -0.4601767441253289, -0.8999465033754542, -1.36922534810279, -1.8491431433265793, -2.31999721287239, -2.7621713194166206, -3.1570552572776203, -3.4879202681252197, -3.7407073370409196, -3.9046894254005355, -3.9729746764506886, -3.942825315085743, -3.8157759902335053, -3.5975452373884718, -3.297744078041283, -2.9293960009479747, -2.5082921635329507, -2.0522141106082303, -1.5800631829170002, -1.1109407054591756, -0.6632257265277484, -0.2536973563736432, 0.1032534141004065, 0.3962820651249573, 0.6175854043481289, 0.7632077709492388, 0.8331433372489337, 0.8312300509237855, 0.764841876010435, 0.6443968357401959, 0.48270834786030337, 0.29421592296815563, 0.09413798494957828, -0.1024060192370514, -0.28125519708571384, -0.43000028496039544, -0.5386655430432334, -0.6002408342577173, -0.6110335187649778, -0.5708198660394805, -0.4827870251529276, -0.3532685859212814, -0.1912887457115142, -0.007941392955027184, 0.18435962261273944, 0.37271473114386744, 0.5446074827512086, 0.6887552524771957, 0.7958892627062694, 0.8594146234356445, 0.8759072810075393, 0.8454136094860749, 0.7715294290462905, 0.6612479091441505, 0.5245794203828974, 0.37396017666497094, 0.22347966776608308, 0.08796864588842308, -0.01800091884322529, -0.08114557502714764, -0.09046775960862223, -0.038158530926657865, 0.07965319096003572, 0.2623567856709307, 0.5045632184185367, 0.7960842361507438, 1.1222012310533827, 1.4642212063116018, 1.800300557922409, 2.1065012099008613, 2.35802894836915, 2.5305914755123444, 2.601804520937808, 2.5525689231619384, 2.3683403496856847, 2.0402164571915695, 1.5657737579759858, 0.9495979622597385, 0.2034665790127552, -0.6538396624354879, -1.5971003812201963, -2.5955774913008747, -3.614258813363234, -4.615368000424013, -5.560069326423506, -6.410283295645498, -7.130520740176102, -7.689639653699907, -8.062430773181747, -8.230944891357256, -8.185486795557837, -7.925217030637731, -7.458322564026623, -6.80173985766851, -5.980437627061934, -5.02629039225093, -3.9765964699002843, -2.8723140351378493, -1.7561051316509007], 'positive_zeros': ['1.27542452568797168325844931754269', '2.35586675860125948721941227045239', '2.85598512775288158305526742245878', '3.55647449882894083703299596161528', '4.71907560699107651661473100261909', '5.64297144781018032057047606364534', '6.24979056765980520282641875256236', '6.91345284210374282668694304399292', '7.35061125294277680483254012075157'], 'prelabel': '2-8034-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.009482691403777, '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': '1.27542452568797168325844931754', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.35586675860125948721941227045', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.85598512775288158305526742246', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 64.15181298389669, 'bad_primes': [2, 3, 13, 103], 'central_character': '1.1', 'conductor': 8034, 'conductor_radical': 8034, 'degree': 2, 'index': 148, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8034/2/a/bb/1/12'], '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': '2-8034-1.1-c1-0-148', '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': '2-8034-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.009482691403777, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27542452568797168325844931754', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1616792665534162093217565572752', 'Lhash_array': ['1616792665534162093217565572752'], 'label': '2-8034-1.1-c1-0-148', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8034/2/a/bb/1/12'}