-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1953547914879158476294422805134', 'a10': [0.8090169943749475, 1.4012585384440734], 'a2': [0.0, 1.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.4012585384440734, -0.8090169943749475], 'a6': [0.0, 0.0], 'a7': [-0.30901699437494745, 0.5352331346596348], 'a8': [0.0, 1.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5794144796669158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [43, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [3, 43], 'central_character': '1161.1025', 'coefficient_field': 'CDF', 'conductor': 1161, 'conductor_radical': 129, 'conjugate': '2350337858894705089259250585474', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.4012585384440734, 0.8090169943749475], [0.5, -0.8660254037844386]], [[1.0, 0], [0.30901699437494745, -0.5352331346596348], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, -1.618033988749895], [-1.0, 0]], [[1.0, 0], [-0.8090169943749475, 1.4012585384440734], [-0.5, -0.8660254037844386]], [[1.0, 0], [1.4012585384440734, 0.8090169943749475], [0.5, 0.8660254037844386]], [[1.0, 0], [0.30901699437494745, 0.5352331346596348], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.5352331346596348, -0.30901699437494745], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, -0.6180339887498949], [-1.0, 0]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.5352331346596348, 0.30901699437494745], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0.6180339887498949], [-1.0, 0]], [[1.0, 0], [0.5, -0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.8660254037844386, 0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.8090169943749475, -1.4012585384440734], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.8660254037844386, 0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0.8660254037844386, 0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 1.0], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, -1.618033988749895], [-1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-1161-129.122-c0-0-3', 'leading_term': '1.3932918878172459443271291884036', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1161/1/i/c/1025/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.393291887817246, 1.3725445493530484, 1.3676086060169959, 1.375489644024463, 1.3924735948882476, 1.4145610826695802, 1.4378184895745048, 1.458605912962285, 1.473696369232302, 1.4803224634862469, 1.4761850802240066, 1.4594479148464128, 1.4287308593640031, 1.3831075023702701, 1.322107355306947, 1.245720995835789, 1.1544052628489356, 1.04908534776023, 0.9311507476356884, 0.8024423857364333, 0.6652286681170926, 0.5221687855818132, 0.37626216718365074, 0.2307836327534424, 0.08920446781044618, -0.04489965699988787, -0.16795229313286553, -0.27648902361931843, -0.367276488359101, -0.43743403585828067, -0.4845538955528303, -0.5068153629437486, -0.503088229828918, -0.4730205991849355, -0.41710632022348204, -0.3367275800488551, -0.2341687036831021, -0.1125979454954563, 0.023985005308138848, 0.17083695191872225, 0.3225944027664992, 0.47343050335744813, 0.6172426227042971, 0.7478660097060662, 0.8593074548753983, 0.9459915207296925, 1.0030107098078758, 1.0263699918392513, 1.013215476362001, 0.9620367520511286, 0.872832566429026, 0.7472301227545812, 0.5885493410159438, 0.40180496396137294, 0.19364136264919257, -0.027802737443412943, -0.2530996978545772, -0.4718057389030049, -0.6727951536077977, -0.8446470234397908, -0.9760725780171339, -1.0563686996015487, -1.0758808498596326, -1.02645702551185, -0.901873352022335, -0.6982117003752952, -0.4141703338053579, -0.05129009839181951, 0.3859189350411794, 0.8899622303185928, 1.4504647957835366, 2.0543976524028604, 2.686424853869848, 3.3293637665330253, 3.964745888125338, 4.573460261000335, 5.136456775355846, 5.635482615271657, 6.0538220142304136, 6.377007567532742, 6.593470766031249, 6.695100285815611, 6.677678946692245, 6.541174123955447, 6.28986167481554, 5.932269960170624, 5.480938069745128, 4.951990594592825, 4.364539881803911, 3.7399352578994156, 3.100886802653651, 2.470498473219118, 1.8712513162670166, 1.3239817994522707, 0.8469026392286398, 0.4547136759161157, 0.15784822116050062, -0.03810414158015797, -0.1327639889052172, -0.13109207903926284, -0.04326766854173095, 0.11568857976869468, 0.32653848931074414, 0.5666760062420153, 0.8111695636461705, 1.0339533165836046, 1.2091142758007696, 1.3122155244146918, 1.3215915860084202, 1.2195509598426424, 0.993423040550436, 0.6363921250038727, 0.1480698355141278, -0.46523125907956725, -1.190546244046735, -2.0086365812785196, -2.8946903589226176, -3.819318832731818, -4.749808110163415, -5.651570512037979, -6.489728247383053, -7.230753276798171, -7.844082198124228, -8.30362406500232, -8.589082433644382, -8.687020586060461, -8.591610522875412, -8.30502144904229, -7.837421373516527, -7.206585212930364, -6.437123398480077, -5.559365322539756, -4.607950894323298, -3.6201999131987557, -2.6343419327280766, -1.6876979649922297, -0.8149091710643019, -0.04630627022429797, 0.5934932610111118, 1.0866847750326747, 1.4230134698368497, 1.6001091434782326, 1.6234011821386827, 1.505619753296243, 1.2659125917856757, 0.9286287485957544, 0.5218398984918374, 0.07568508633879036, -0.3793648425022136, -0.8142221347580071, -1.2027765952795966, -1.523277126182044, -1.7594207398195851, -1.9010872891798476, -1.9446799126706067, -1.8930555583279423, -1.7550554496252682, -1.5446703952792047, -1.279898840548143, -0.9813750185123311, -0.670859194849786, -0.36969080201236154, -0.09730757911269587, 0.13007056882081913, 0.3005052113441933, 0.40707958993834087, 0.4482661459736625, 0.4278973785066376, 0.3547431340932085, 0.24172462117046933, 0.10482088591151344, -0.038254569848157186, -0.16951246063660635, -0.2721765266617002, -0.33209389030578573, -0.33896245424381044, -0.28728230928405657, -0.17695633789801557, -0.013489035331211813, 0.19223951852080265, 0.42461748043675035, 0.6643255323714339, 0.8896760209477049, 1.078177064300843, 1.2082133114966829, 1.260723895568096, 1.2207552393889143, 1.0787721718323873, 0.8316251042462693, 0.48309301056012327, 0.04395028498952205, -0.4684616338253444, -1.0311419100878083, -1.6167663865849677, -2.1953690657722227, -2.7362588809037596, -3.2100417298789017, -3.590606650171157, -3.8569337879663625, -3.994590829681061, -3.9968034625385016, -3.8650131309867084, -3.608870106029805, -3.2456493697551583, -2.799118308424411, -2.2979257465961873, -1.7736184628872267, -1.2584212211418964, -0.7829371489188891, -0.37393520869063085, -0.05238948629504368, 0.16807914338804253, 0.28223404866454455, 0.2936372172113601, 0.21440081764948823, 0.0642776643982972, -0.13085851824290606, -0.34104523844086687, -0.5346368985629879, -0.6809130118183322, -0.7526975936227206, -0.7287914639181865, -0.5960267767298011, -0.35077503097606144, 0.00022505662131561268, 0.4398072982976051, 0.9411187948787904, 1.4691368034506962, 1.982878469356893, 2.4381660995868613, 2.7907649531136762, 2.999676825234663, 3.030353856429646, 2.8575948398610915, 2.4679014963085675, 1.8611041307688239, 1.0511129271188702, 0.06570986937593037, -1.0546370693694604, -2.2588859214896964, -3.48833922495543, -4.68018804025053, -5.771450672828676, -6.703040900752273, -7.423684458086585, -7.893406441354357, -8.086336380145509, -7.992620650631608, -7.619290994720417, -6.990009164553184, -6.143686179868796, -5.132054761377962, -4.016349347070828, -2.8633140656898486, -1.740810109519255, -0.7133261052649029, 0.16229435240984968], 'positive_zeros': ['1.54107757652419307287380007244190', '2.36441836502158253006420749800638', '3.42976903320511324576292803656152', '4.19540062594556646775632826385650', '6.04735708983201414059442426057209', '6.26970353906060181851784600810074', '7.01627413301465205729240159166070', '8.566613953841310767559214957257435', '9.197868698032742772079902862308183', '10.15004872775300703780860495784142'], 'prelabel': '2-1161-129.122-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7611928005879429, 'root_angle': -0.4029427582758795, 'root_number': '0.30021144619012749502297683707410 - 0.95387267891287890873004555995193*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.20147137913793978', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54107757652419307287380007244', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.36441836502158253006420749801', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42976903320511324576292803656', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.5794144796669158, 'bad_primes': [3, 43], 'central_character': '129.122', 'conductor': 1161, 'conductor_radical': 129, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1161/1/i/c/1025/4'], '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': '2-1161-129.122-c0-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1161-129.122-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7611928005879429, 'root_angle': -0.20147137913793975, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54107757652419307287380007244', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1953547914879158476294422805134', 'Lhash_array': ['1953547914879158476294422805134'], 'label': '2-1161-129.122-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1161/1/i/c/1025/4'}