-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2804808722437925099109972363771', 'a10': [-4.675130870566646, 0.0], 'a2': [-1.4811943040920157, 0.0], 'a3': [0.8060634335253696, 0.0], 'a4': [0.19393656647463045, 0.0], 'a5': [3.1563251746586616, 0.0], 'a6': [-1.1939365664746304, 0.0], 'a7': [0.6751308705666461, 0.0], 'a8': [2.675130870566646, 0.0], 'a9': [-2.3502617411332922, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4870874523298106, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[61, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [61], 'central_character': '61.1', 'coefficient_field': 'CDF', 'conductor': 61, 'conductor_radical': 61, 'conjugate': '2804808722437925099109972363771', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4811943040920157, 0], [2.0, 0]], [[1.0, 0], [-0.8060634335253696, 0], [3.0, 0]], [[1.0, 0], [-3.1563251746586616, 0], [5.0, 0]], [[1.0, 0], [-0.6751308705666461, 0], [7.0, 0]], [[1.0, 0], [-2.5188056959079845, 0], [11.0, 0]], [[1.0, 0], [6.350261741133292, 0], [13.0, 0]], [[1.0, 0], [4.156325174658662, 0], [17.0, 0]], [[1.0, 0], [0.4181903005761087, 0], [19.0, 0]], [[1.0, 0], [-3.4811943040920155, 0], [23.0, 0]], [[1.0, 0], [2.1563251746586616, 0], [29.0, 0]], [[1.0, 0], [-6.730840649893432, 0], [31.0, 0]], [[1.0, 0], [2.4181903005761085, 0], [37.0, 0]], [[1.0, 0], [-7.7005234822665845, 0], [41.0, 0]], [[1.0, 0], [8.156325174658662, 0], [43.0, 0]], [[1.0, 0], [11.662912090450616, 0], [47.0, 0]], [[1.0, 0], [-2.9623886081840314, 0], [53.0, 0]], [[1.0, 0], [-15.249646345801416, 0], [59.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-12.212034953985448, 0], [67.0, 0]], [[1.0, 0], [2.730840649893432, 0], [71.0, 0]], [[1.0, 0], [-6.506586915791954, 0], [73.0, 0]], [[1.0, 0], [-6.705448038193494, 0], [79.0, 0]], [[1.0, 0], [3.2242537341014783, 0], [83.0, 0]], [[1.0, 0], [-1.738134874082553, 0], [89.0, 0]], [[1.0, 0], [10.625300698634646, 0], [97.0, 0]], [[1.0, 0], [6.544198307607923, 0], [101.0, 0]], [[1.0, 0], [-3.5818096994238915, 0], [103.0, 0]], [[1.0, 0], [-15.088396615215846, 0], [107.0, 0]], [[1.0, 0], [2.9247772163680623, 0], [109.0, 0]], [[1.0, 0], [-11.237427565685385, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-61-1.1-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/61/2/a/b/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6707920767205413, 0.6751243901823879, 0.6877247325193214, 0.7074488050825772, 0.7325189704427612, 0.7606585630792324, 0.7892041369631362, 0.8151798796012323, 0.8353417402805767, 0.846209394190493, 0.8441043518911008, 0.8252080797585514, 0.7856488428709324, 0.7216216000794996, 0.6295417792171422, 0.5062308025061927, 0.3491284896616166, 0.15652475472112218, -0.07219970266127705, -0.33633664716580175, -0.6336328257371228, -0.9601090038210726, -1.3099339734805395, -1.6753722096160544, -2.0468228494734726, -2.4129652459913493, -2.7610223677648054, -3.0771477549435224, -3.3469346797882866, -3.556037831280801, -3.6908886239210155, -3.739475650398762, -3.6921525209479116, -3.54242713059133, -3.287680103060269, -2.929756613363193, -2.4753757567256667, -1.9363057271432744, -1.3292616791224605, -0.6754963468948132, -7.098886810996472e-05, 0.6691847007731588, 1.3029915537385417, 1.8721621769344658, 2.3492844331409724, 2.710446661616371, 2.9368888907638273, 3.016456238666969, 2.9447315349458787, 2.7257350867410115, 2.3721008825855474, 1.9046699298662688, 1.3514814318195256, 0.7461887227823683, 0.12597599078868124, -0.4709001936563449, -1.0077781010592592, -1.4522680251431852, -1.7787224785938982, -1.970281804444643, -2.020296480865954, -1.9329661908456979, -1.7230929358500375, -1.414917602825471, -1.0400910693929786, -0.6349152010723303, -0.23706795017726864, 0.11790815350916625, 0.400031414260273, 0.5878823588133701, 0.6708604781579544, 0.6504269211689463, 0.5401468659890794, 0.36445472556929615, 0.15619208744795895, -0.046899433054195236, -0.20642401669011534, -0.2879076416443029, -0.2652289052257544, -0.12440820905768928, 0.133709984824128, 0.49226236178905725, 0.9189061473248418, 1.3681670292858712, 1.7854748729517893, 2.112568645792767, 2.2937734840708757, 2.28251567071088, 2.047364669504355, 1.5768892292193113, 0.8826934793164015, 0.00015655105330054722, -1.013376196949046, -2.0829314641006134, -3.1224677648758705, -4.043073557998257, -4.761993144372932, -5.21152029473163, -5.346751794513258, -5.151260186463794, -4.639927275208577, -3.8584637757734015, -2.879498757253211, -1.7955170388267943, -0.7093079850106876, 0.2770823349750672, 1.0736757464427638, 1.6128504390643466, 1.8573420179500186, 1.8049236131123534, 1.4890873872464758, 0.9755070035598093, 0.3545672700025146, -0.2692581255488371, -0.7899806002487836, -1.1131357073383474, -1.1676901730840683, -0.9153083514179574, -0.3557545850900958, 0.4723386008194835, 1.495536803081527, 2.614088988906465, 3.713833885875094, 4.680060117260853, 5.411563150555975, 5.833078523278069, 5.9044500251833325, 5.6252976300877, 5.0345348644002, 4.204773872028401, 3.23235596293419, 2.2243579669193525, 1.2843608957281083, 0.49895976814355514, -0.073092831567234, -0.40757740158322514, -0.5163903403610716, -0.4438162677879544, -0.25807066189587385, -0.03940557465201388, 0.1333974521758567, 0.19605807107154996, 0.10931164455361059, -0.13476646779155238, -0.5116659187560171, -0.9688010552530599, -1.4346802266875007, -1.8314481448326732, -2.0887805959182577, -2.156834821250277, -2.0160467019341826, -1.6820171284690313, -1.2044856406940068, -0.6603387797801938, -0.14159641458247915, 0.2597998239176017, 0.4679559735382505, 0.43707565784433255, 0.16111096537653755, -0.32284455096005726, -0.9383189554372604, -1.5801219226519467, -2.130471327250978, -2.4781655558038516, -2.5377447521635723, -2.265426686732054, -1.6689740474678956, -0.8095142649996306, 0.20542901864201266, 1.2370099468838212, 2.1361757067710907, 2.7676523591113824, 3.0329965805157815, 2.888875315460747, 2.357336272391865, 1.525996437929735, 0.5376347866085153, -0.4296130530903287, -1.1886745340087133, -1.5725994751245194, -1.4617012892731107, -0.8043683398944579, 0.37198981379011514, 1.9619098325570108, 3.794935158634191, 5.6589977655713, 7.3306389512003705, 8.607410829554906, 9.33736861495762, 9.44096663310719, 8.921858003363845, 7.864883501144282, 6.421626674759531, 4.785958424419251, 3.1636445038505254, 1.7410557352990914, 0.6581295867734772, -0.010042781114272639, -0.2601585018844396, -0.15534663065765292, 0.19116133946603697, 0.640104693568908, 1.0534677343032233, 1.31992835316191, 1.373889057768054, 1.204773666845822, 0.8551535804829882, 0.4084042044310562, -0.03141626848793853, -0.363304713578432, -0.5118432146994558, -0.44397132365258835, -0.17661553949530098, 0.2263718872644508, 0.6673571682418482, 1.0354915881380333, 1.2304978688499748, 1.1847578051991465, 0.8790509806305287, 0.34851238904774406, -0.32268028271111837, -1.0170866954874467, -1.6072621845837525, -1.9818722789620489, -2.069309225509749, -1.8538014634258524, -1.3803928931275802, -0.74734664230116, -0.08707982022084287, 0.46084702019289125, 0.7793784433407439, 0.8001817652932063, 0.5208194315229859, 0.008886745066206451, -0.6083652442510169, -1.1674854582123162, -1.5011755855753894, -1.47335017321972, -1.0098810352829317, -0.11856103658267392, 1.1062864436320212, 2.4962323740008343, 3.836531703182715, 4.9044621023501955, 5.511095856126282, 5.5384287544225295, 4.964410466881966, 3.8705517425748077, 2.4300467690573546, 0.8781251034409726, -0.5301053037487276, -1.5664625414557756, -2.0721761324100028, -1.9877375928677554, -1.3641196324526077, -0.352928365459985, 0.8228331931824485], 'positive_zeros': ['2.21260394775417123958667719120049', '5.00001310439645679527377361738839', '6.77572219622963771699791466067147', '8.331043809385276815054729206828224', '9.344546946873166470263184370971096', '9.941973882760487341597755345893775', '11.37502040003902649409728867531895', '13.08784591500517795037492903943899', '14.06973400813522684107601992760120', '14.80818074476872608703064148916597'], 'prelabel': '2-61-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6979165081367618, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.21260394775417123958667719120', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.00001310439645679527377361739', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.77572219622963771699791466067', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.4870874523298106, 'bad_primes': [61], 'central_character': '1.1', 'conductor': 61, 'conductor_radical': 61, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/61/2/a/b/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': '2-61-1.1-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': '2-61-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6979165081367618, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.21260394775417123958667719120', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2804808722437925099109972363771', 'Lhash_array': ['2804808722437925099109972363771'], 'label': '2-61-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/61/2/a/b/1/1'}