-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1949343372146182772008703786379', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.618033988749895, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.6180339887498949, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.38196601125010515, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.692473971915598, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.1', 'coefficient_field': 'CDF', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.618033988749895, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [7.0, 0]], [[1.0, 0], [-2.8541019662496847, 0], [11.0, 0]], [[1.0, 0], [7.0901699437494745, 0], [13.0, 0]], [[1.0, 0], [-6.0901699437494745, 0], [17.0, 0]], [[1.0, 0], [1.8541019662496845, 0], [19.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [9.23606797749979, 0], [29.0, 0]], [[1.0, 0], [9.090169943749475, 0], [31.0, 0]], [[1.0, 0], [-6.47213595499958, 0], [37.0, 0]], [[1.0, 0], [-3.326237921249264, 0], [41.0, 0]], [[1.0, 0], [0, 0], [43.0, 0]], [[1.0, 0], [-3.708203932499369, 0], [47.0, 0]], [[1.0, 0], [-0.4721359549995794, 0], [53.0, 0]], [[1.0, 0], [1.7082039324993692, 0], [59.0, 0]], [[1.0, 0], [9.326237921249264, 0], [61.0, 0]], [[1.0, 0], [14.47213595499958, 0], [67.0, 0]], [[1.0, 0], [-4.0901699437494745, 0], [71.0, 0]], [[1.0, 0], [-3.23606797749979, 0], [73.0, 0]], [[1.0, 0], [1.5278640450004206, 0], [79.0, 0]], [[1.0, 0], [-6.944271909999159, 0], [83.0, 0]], [[1.0, 0], [10.47213595499958, 0], [89.0, 0]], [[1.0, 0], [-12.381966011250105, 0], [97.0, 0]], [[1.0, 0], [0.2917960675006309, 0], [101.0, 0]], [[1.0, 0], [16.562305898749052, 0], [103.0, 0]], [[1.0, 0], [18.18033988749895, 0], [107.0, 0]], [[1.0, 0], [11.562305898749054, 0], [109.0, 0]], [[1.0, 0], [-1.0557280900008412, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 33, 'label': '2-1840-1.1-c1-0-33', '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/1840/2/a/l/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-8.277096492623901e-61, 0.14248915747759217, 0.2846060538850752, 0.42590637925761626, 0.565806954921131, 0.703528834791828, 0.8380540604124547, 0.9680986105282476, 1.0921028666764565, 1.208239833845649, 1.3144405023923267, 1.4084351326343592, 1.487808850325994, 1.5500696952363264, 1.5927270988229747, 1.6133786260673038, 1.6098026665841398, 1.5800545871416416, 1.5225636644445553, 1.436227917906934, 1.3205037785849865, 1.1754873869152023, 1.001984232992627, 0.8015638614802418, 0.576596478143044, 0.3302685313392911, 0.06657470932390953, -0.20971570303945486, -0.49311952870165565, -0.7775281240679031, -1.0563233159122325, -1.3225196815259335, -1.5689309855047435, -1.7883575407597812, -1.9737902261823872, -2.1186259104682086, -2.2168881447412665, -2.2634462403021027, -2.2542252853940665, -2.1863993165792985, -2.0585597812627725, -1.8708516360896772, -1.6250699403168207, -1.324710632015049, -0.9749703141158557, -0.5826913096917422, -0.15624994053262065, 0.29461210460948667, 0.7590113735625635, 1.225197125109135, 1.6808704001542247, 2.1135393188430087, 2.510900303493105, 2.8612332573424486, 3.153797407310111, 3.3792136264011887, 3.5298186575641903, 3.5999768195040396, 3.5863355205036367, 3.4880122504732958, 3.306702651037532, 3.0467017389005036, 2.714833312691815, 2.320285915803725, 1.8743573414765864, 1.3901134153368502, 0.8819705228174013, 0.3652149025177575, -0.14452506357816608, -0.6318346271464936, -1.0820755312633998, -1.4819336957435467, -1.8199290975763907, -2.086865791061115, -2.27620157605313, -2.384319360181228, -2.410685713283584, -2.3578863750377224, -2.2315334012038903, -2.040044031595654, -1.794297011920587, -1.5071777551091337, -1.1930291240881206, -0.8670294925773728, -0.54452383844889, -0.24033671317322122, 0.031902186069818025, 0.2603885877201473, 0.4357000275651395, 0.5512501039491203, 0.6036164974871269, 0.5927237900847147, 0.5218683907631274, 0.3975800248127341, 0.22932195882978754, 0.02904006357766949, -0.18942142322911237, -0.41101237488498, -0.6202461861062554, -0.8020098637799928, -0.9423752157340897, -1.0293700802917167, -1.0536690784610743, -1.0091659868988936, -0.893394482586599, -0.7077705515859666, -0.4576380313675349, -0.15210821889897294, 0.1963052089536261, 0.5722440491496553, 0.9582338081520935, 1.3355501936281053, 1.6851832903319872, 1.9888521901844824, 2.2300184041239843, 2.3948444860785627, 2.473045155964174, 2.4585818895316027, 2.3501583703530855, 2.1514831442643088, 1.8712769043332929, 1.5230145578974996, 1.1244059687800871, 0.6966333280113303, 0.263376738625766, -0.15032795044132133, -0.5193444814365945, -0.8197421229336183, -1.0300847228341758, -1.13263396312734, -1.1144001455533423, -0.9679797783086777, -0.6921286810926678, -0.2920318874994136, 0.2207532800365404, 0.8286877003070786, 1.5089634392952704, 2.234510392256992, 2.975250996005156, 3.6995426705643384, 4.375735774598806, 4.973766621875163, 5.466701084191856, 5.832144857757911, 6.05344170469633, 6.120590745286624, 6.030827751613404, 5.788832711939753, 5.406545810521465, 4.902595337589001, 4.3013627274705035, 3.631730683826531, 2.925578970840093, 2.216107797967649, 1.536079831972159, 0.9160779829020438, 0.3828767524466767, -0.041980064850860144, -0.34331301420450333, -0.5130851001255767, -0.5507772018121688, -0.4633363676569561, -0.2646971799075484, 0.02509860609914112, 0.38113501254214943, 0.775136854017374, 1.1771787826361682, 1.5574878380861181, 1.8882323601305597, 2.145189894081301, 2.309193018701212, 2.3672645868097595, 2.313372034040149, 2.1487531604137056, 1.8817917940540188, 1.5274494451010687, 1.106286749010144, 0.6431344438727097, 0.16549616098817466, -0.2982170529976471, -0.720509025444266, -1.0765615047400616, -1.3458246707757904, -1.513331881728227, -1.5706522837286887, -1.516417579840047, -1.356386372677487, -1.103039374754367, -0.7747295202054266, -0.3944406124388965, 0.011765361625373276, 0.41651053230570273, 0.7929561830279191, 1.1166260313937604, 1.3670738548255044, 1.5292804649736005, 1.5946818190659309, 1.5617537464109015, 1.436107906455327, 1.230086324516347, 0.9618760323308699, 0.654198686423937, 0.33266026617882344, 0.02387094288785544, -0.24653685425694516, -0.455854646205376, -0.5860706194748558, -0.6253403304401106, -0.5690451901577759, -0.42035483881406144, -0.1902422139822006, 0.10306291716239127, 0.4351574059226798, 0.7770226249603525, 1.096959789198666, 1.3627770725702202, 1.544082356061832, 1.6145245546273113, 1.5538262184705203, 1.3494607551955133, 0.9978486900929512, 0.5049776534371748, -0.11361163191654973, -0.8334886341731773, -1.6226163523992663, -2.4431820272890916, -3.2538631325703053, -4.012384052182896, -4.6781956632448995, -5.215098001486134, -5.593626368009998, -5.7930338953861265, -5.802728109192352, -5.6230539341476735, -5.265358675583252, -4.7513229084371345, -4.111591643386758, -3.3837891168708167, -2.610044602861923, -1.8341925805822958, -1.0988357344973547, -0.4424716420925298, 0.10311748199743351, 0.5150281109365354, 0.7807965752732934, 0.8992428569733476, 0.8805305029908099, 0.7454302684811873, 0.5238308595786094, 0.2525936130118162, -0.027104715156571174, -0.2727591408366938, -0.4436464020709538, -0.5038395482079252, -0.42491353836324297, -0.18814798080307027, 0.21393304444175726], 'positive_zeros': ['1.53776077713781743186760966495867', '2.71591056579124554536689308591022', '3.96757502714772256063808846325268', '5.03172832639205616633759214657672', '5.57439464092130833527045222896791', '6.29585942859912162290880847594083', '7.30237624592909503089433211277411', '7.82777677525183601533590119976772', '9.192606943682537249560077900761397'], 'prelabel': '2-1840-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.833076306560515, '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': '1.53776077713781743186760966496', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71591056579124554536689308591', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.96757502714772256063808846325', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.692473971915598, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/2/a/l/1/1'], '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': '2-1840-1.1-c1-0-33', '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': '2-1840-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.833076306560515, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53776077713781743186760966496', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1949343372146182772008703786379', 'Lhash_array': ['1949343372146182772008703786379'], 'label': '2-1840-1.1-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/2/a/l/1/1'}