-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2102093009250247866124611427360', 'a10': [0.0, 0.0], 'a2': [1.9032119259115532, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.6222156349319639, 0.0], 'a5': [0.0, 0.0], 'a6': [-1.9032119259115532, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.7190037090204106, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.345022742820554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '3675.1', 'coefficient_field': 'CDF', 'conductor': 3675, 'conductor_radical': 105, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.9032119259115532, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, 0], [11.0, 0]], [[1.0, 0], [6.4286394867550705, 0], [13.0, 0]], [[1.0, 0], [-4.4286394867550705, 0], [17.0, 0]], [[1.0, 0], [-2.4286394867550705, 0], [19.0, 0]], [[1.0, 0], [1.3777843650680361, 0], [23.0, 0]], [[1.0, 0], [-0.7555687301360724, 0], [29.0, 0]], [[1.0, 0], [5.184208216891143, 0], [31.0, 0]], [[1.0, 0], [7.612847703646213, 0], [37.0, 0]], [[1.0, 0], [-8.235063338578177, 0], [41.0, 0]], [[1.0, 0], [10.101710243374068, 0], [43.0, 0]], [[1.0, 0], [-2.7555687301360723, 0], [47.0, 0]], [[1.0, 0], [9.184208216891143, 0], [53.0, 0]], [[1.0, 0], [14.101710243374068, 0], [59.0, 0]], [[1.0, 0], [6.857278973510141, 0], [61.0, 0]], [[1.0, 0], [2.7555687301360723, 0], [67.0, 0]], [[1.0, 0], [-2.0, 0], [71.0, 0]], [[1.0, 0], [1.5713605132449295, 0], [73.0, 0]], [[1.0, 0], [4.857278973510141, 0], [79.0, 0]], [[1.0, 0], [-11.612847703646214, 0], [83.0, 0]], [[1.0, 0], [4.622215634931964, 0], [89.0, 0]], [[1.0, 0], [11.939776947027216, 0], [97.0, 0]], [[1.0, 0], [1.4794946084421046, 0], [101.0, 0]], [[1.0, 0], [8.857278973510141, 0], [103.0, 0]], [[1.0, 0], [1.7649366614218231, 0], [107.0, 0]], [[1.0, 0], [-5.612847703646213, 0], [109.0, 0]], [[1.0, 0], [-11.285918460265211, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 116, 'label': '2-3675-1.1-c1-0-116', '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/3675/2/a/bi/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.773316267656134e-60, 0.2550694290010713, 0.5097200356091428, 0.7634831061964396, 1.015792722790371, 1.265943426717365, 1.513054923432854, 1.7560454480163488, 1.9936149086996662, 2.2242384192732216, 2.4461703634455736, 2.657458733672301, 2.8559691662817195, 3.0394178529798146, 3.2054123356276816, 3.3514990713145822, 3.475216572129627, 3.5741528646242506, 3.6460059673332728, 3.6886460445880487, 3.7001778587879715, 3.6790021120553136, 3.623874244857519, 3.533959248262788, 3.4088810531995444, 3.248765089663712, 3.0542726660576047, 2.8266259077335953, 2.5676221172575393, 2.2796365785419654, 1.9656130230881501, 1.629041207935682, 1.2739213189002063, 0.9047152051945793, 0.5262847671042097, 0.14381815027134667, -0.23725525955891438, -0.6113597076244853, -0.9728761435549209, -1.3162515239462338, -1.636112091772004, -1.9273781418272986, -2.185377593431516, -2.4059555631911684, -2.585577069683209, -2.721420014967919, -2.8114556796340295, -2.8545141413455357, -2.8503322820616703, -2.799582384252468, -2.703879726979952, -2.565768071497859, -2.3886824633084407, -2.176889361224589, -1.935404719508495, -1.6698912802541095, -1.3865369619689023, -1.0919168378363693, -0.7928417639127034, -0.49619722409243494, -0.20877638631914505, 0.06288830419038416, 0.312690449411717, 0.5351073003951259, 0.7253450354447946, 0.8794672926033573, 0.9945028552452768, 1.0685288492663898, 1.1007264015016502, 1.0914064194959843, 1.0420039659203648, 0.9550405958198522, 0.8340549767362687, 0.6835030925939619, 0.5086303116598124, 0.31531854492926514, 0.10991260144838738, -0.10096937059943896, -0.31063581401758267, -0.5125260223020939, -0.7004123678351315, -0.8685940157355797, -1.0120757292457985, -1.126725677766027, -1.2094066792755864, -1.2580760362254053, -1.2718500417330398, -1.251030317284535, -1.1970903633758898, -1.1126220235847026, -1.0012429381811037, -0.8674674493144181, -0.7165447672882196, -0.5542694668419528, -0.38677050498275867, -0.22028589178922203, -0.060930861342907386, 0.08553215353600624, 0.21391326889583048, 0.31979627970603247, 0.3997132778725399, 0.45128561667967004, 0.4733251250230075, 0.4658907844376126, 0.43029761792063714, 0.36907625325420795, 0.28588345740732324, 0.18536582795080317, 0.07298070256706983, -0.04521986358567989, -0.16283457286441538, -0.2733789306141992, -0.37056186872163593, -0.44856219104305445, -0.5022937116050653, -0.5276480054361468, -0.5217041785810235, -0.48289598773338804, -0.4111279832792081, -0.3078340773587634, -0.17597399908033998, -0.019965425016402708, 0.15444791620823936, 0.3403892628518779, 0.5300974633068753, 0.7152232582977772, 0.8871629453927667, 1.0374172132231112, 1.1579613844932761, 1.2416122464618689, 1.2823761394217552, 1.2757630629042007, 1.2190522690122103, 1.1114961416646663, 0.9544510838084577, 0.7514266009009947, 0.5080467030094215, 0.23192105222303686, -0.0675731601627668, -0.3795939435081149, -0.6922135252045378, -0.992861850964109, -1.2688195982919768, -1.5077430305839044, -1.6982009087333951, -1.8302022705730028, -1.8956932740143648, -1.8890015372195126, -1.807207526384913, -1.6504245320746174, -1.421971596052127, -1.1284273241844716, -0.7795567352273027, -0.38810800731721623, 0.030518975331634248, 0.4587251933194313, 0.8772739827730693, 1.2659444056943114, 1.6042550969497245, 1.872233497054246, 2.051202542752497, 2.1245550490965917, 2.0784852905757645, 1.9026477473279622, 1.5907146525584015, 1.1408068376696845, 0.5557763516165529, -0.15667568830652642, -0.9840567397954068, -1.9093202489914904, -2.911280265611463, -3.965193713845086, -5.043493939154534, -6.116652740781101, -7.154142385369082, -8.12546433155104, -9.001207800944432, -9.754099089308484, -10.360001754407518, -10.79882861940616, -11.055328905599804, -11.119717704907154, -10.988120305634432, -10.6628104180955, -10.152228877534114, -9.470777650581523, -8.638392621031455, -7.679907338816424, -6.624228329161495, -5.503350326634093, -4.351246588945678, -3.202674958233674, -2.091944319616588, -1.0516883625580111, -0.11169395225336289, 0.7021700870240009, 1.3688813609131598, 1.8730122121523425, 2.205267446164539, 2.3627890689810522, 2.3492147496770794, 2.174486498042374, 1.8544160882539347, 1.4100236439073832, 0.8666751114879258, 0.2530526884242537, -0.4000007262195694, -1.0607166382689837, -1.6976657460543891, -2.2810011411009845, -2.7836294070657916, -3.182261989366884, -3.4583041253375133, -3.5985453784452135, -3.5956241337402632, -3.448247937283644, -3.1611618948074907, -2.744868039430449, -2.2151091695973775, -1.592140681418137, -0.89982293022011, -0.1645742517648344, 0.5857693883375057, 1.323138334178297, 2.020405371650303, 2.6525033224636037, 3.1974362902884903, 3.6371417980030287, 3.958168006592338, 4.152138747007257, 4.215988837880514, 4.15196265871911, 3.967379717319544, 3.6741814942414104, 3.2882836773077364, 2.8287665580017967, 2.3169434455298052, 1.7753521325025365, 1.226717477262059, 0.6929339119163257, 0.19411511107610765, -0.2522457558873643, -0.6319676286183136, -0.934695080310219, -1.154212842161802, -1.2885503686744078, -1.339875904625495, -1.3141898800286906, -1.2208372595160186, -1.0718672234202107, -0.8812758266261775, -0.6641727082592537, -0.4359162421848345, -0.2112625622566269, -0.003572618692417108, 0.17588210827515768, 0.3184802107225223], 'positive_zeros': ['1.65825899413591127426315052973973', '2.84821970732624238087221305755914', '3.58698898384042368185291722638206', '4.51890590672999027272270943376301', '5.09155416546173539219780430690036', '5.67746706699558493605285790777573', '6.45840492919719691405433746094935', '7.21539296370568739724433809459059', '7.81846677711049997898068960151810'], 'prelabel': '2-3675-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.417104645732862, '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': '1.65825899413591127426315052974', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.84821970732624238087221305756', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58698898384042368185291722638', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 29.345022742820554, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 3675, 'conductor_radical': 105, 'degree': 2, 'index': 116, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3675/2/a/bi/1/3'], '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': '2-3675-1.1-c1-0-116', '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': '2-3675-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.417104645732862, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65825899413591127426315052974', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2102093009250247866124611427360', 'Lhash_array': ['2102093009250247866124611427360'], 'label': '2-3675-1.1-c1-0-116', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3675/2/a/bi/1/3'}