-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2423200318143230157168533032953', 'a10': [0.0, 0.0], 'a2': [2.563852037391969, 0.0], 'a3': [-1.0, 0.0], 'a4': [4.573337269638951, 0.0], 'a5': [0.0, 0.0], 'a6': [-2.563852037391969, 0.0], 'a7': [-4.4494649924795615, 0.0], 'a8': [6.5976560016605115, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.14726671250135, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [47, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 47], 'central_character': '3525.1', 'coefficient_field': 'CDF', 'conductor': 3525, 'conductor_radical': 705, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.563852037391969, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.4494649924795615, 0], [7.0, 0]], [[1.0, 0], [5.412317284808023, 0], [11.0, 0]], [[1.0, 0], [-5.683518442740732, 0], [13.0, 0]], [[1.0, 0], [-0.38849088214166705, 0], [17.0, 0]], [[1.0, 0], [5.512946818802222, 0], [19.0, 0]], [[1.0, 0], [3.44228439886295, 0], [23.0, 0]], [[1.0, 0], [-1.3057970074311724, 0], [29.0, 0]], [[1.0, 0], [-3.6075162588871974, 0], [31.0, 0]], [[1.0, 0], [10.808944930677328, 0], [37.0, 0]], [[1.0, 0], [7.19470664472397, 0], [41.0, 0]], [[1.0, 0], [4.486975756354001, 0], [43.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.358961675808441, 0], [53.0, 0]], [[1.0, 0], [11.656406032821097, 0], [59.0, 0]], [[1.0, 0], [11.740024821229289, 0], [61.0, 0]], [[1.0, 0], [1.2442573230958838, 0], [67.0, 0]], [[1.0, 0], [-1.2519238679112505, 0], [71.0, 0]], [[1.0, 0], [4.039342691340318, 0], [73.0, 0]], [[1.0, 0], [-1.1874094124243424, 0], [79.0, 0]], [[1.0, 0], [-11.259397754702338, 0], [83.0, 0]], [[1.0, 0], [-5.7819925329298725, 0], [89.0, 0]], [[1.0, 0], [5.115446602037468, 0], [97.0, 0]], [[1.0, 0], [3.9151300062054015, 0], [101.0, 0]], [[1.0, 0], [-3.1967093256297643, 0], [103.0, 0]], [[1.0, 0], [0.33340567880841293, 0], [107.0, 0]], [[1.0, 0], [10.983692379195459, 0], [109.0, 0]], [[1.0, 0], [-9.815543554200003, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 137, 'label': '2-3525-1.1-c1-0-137', '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/3525/2/a/bg/1/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-3.1200156676307716e-60, 0.32392949334595855, 0.6477538693122497, 0.9713087818531467, 1.2943142633234115, 1.6163238021326647, 1.936681152474026, 2.2544866420182, 2.5685741868433243, 2.877499665266902, 3.179540792521186, 3.472708208189728, 3.7547671515860213, 4.0232688547536615, 4.275590615604181, 4.508983406470239, 4.720625806736176, 4.9076830053051905, 5.067369586769116, 5.197014786337274, 5.294128869409452, 5.356469262387042, 5.382105034853016, 5.369478314291697, 5.317461208611021, 5.225406824596341, 5.093193007430035, 4.921257492168185, 4.7106232561586, 4.4629129941799635, 4.180351806608326, 3.865757394796373, 3.522517295273858, 3.1545529521172306, 2.766270720297035, 2.362500206112436, 1.9484206769175862, 1.5294766031789653, 1.1112837226013605, 0.6995273291528952, 0.29985477949640144, -0.08223553427233643, -0.44150628319217705, -0.7730917474028939, -1.0726040842252986, -1.3362325588060149, -1.560833016088412, -1.7440049874293133, -1.8841540176250193, -1.980537067846668, -2.033289194047883, -2.0434301133828194, -2.012849745195728, -1.944272337976776, -1.8411993568726648, -1.7078318934745016, -1.5489739546146744, -1.3699185724820995, -1.1763192364327486, -0.9740496591098755, -0.7690553379083438, -0.5672007403674574, -0.3741162132516149, -0.1950488765222361, -0.034721804481573804, 0.10279429032069752, 0.214192873006019, 0.2970232540648648, 0.34975893678515774, 0.3718400660752073, 0.3636880985426214, 0.32669159901478706, 0.2631629199977189, 0.17626641344302701, 0.06991973155681494, -0.05132933370527365, -0.18244717429153404, -0.3180757805147177, -0.4527065030928984, -0.5808608788310387, -0.6972728492350672, -0.7970664881938766, -0.8759233299763416, -0.9302335610333664, -0.9572257109208261, -0.9550700446845686, -0.9229516098530854, -0.8611098073510881, -0.7708424120636609, -0.6544731341903672, -0.5152830503473488, -0.3574075027421408, -0.18570132179017598, -0.005576426830834132, 0.17718304427734735, 0.3566219766702453, 0.5268250290823823, 0.6821294920357759, 0.8173325638240783, 0.9278853381102196, 1.010066063972427, 1.0611257911268026, 1.0794003406929078, 1.0643836253469525, 1.0167586515741889, 0.9383840306339112, 0.8322354545861799, 0.7023033027030391, 0.5534492696200068, 0.3912265840373105, 0.22166994892284836, 0.05106271570692092, -0.11431005535549156, -0.26841315326505394, -0.40570739620267476, -0.5213803117191023, -0.6115514678707081, -0.6734432818178038, -0.7055092024964422, -0.7075126029672468, -0.6805514847464906, -0.6270261346785678, -0.5505491150902305, -0.4557993290968073, -0.3483242953529718, -0.23429709508271712, -0.12023662173901647, -0.012701674817389076, 0.08202899538272788, 0.15827744580590897, 0.21127420819785614, 0.23743886808265766, 0.23462002488893205, 0.20228215198198657, 0.14162849104104297, 0.055651259279441166, -0.05089694117798779, -0.17161362849035686, -0.2986387038128275, -0.4229248806292715, -0.5345792281030171, -0.6232654261048884, -0.6786532339763923, -0.690898972454299, -0.6511386382037775, -0.5519737278878003, -0.38792903817450325, -0.15586169898039604, 0.14469847014948894, 0.5112955082140327, 0.938396486911666, 1.4173557626793336, 1.936502820086759, 2.481357738653564, 3.034973444598902, 3.5783988260867603, 4.091251688773329, 4.552385611188093, 4.940630231872747, 5.235580561087045, 5.418407743372105, 5.472661464591393, 5.385033029096796, 5.146048123204486, 4.750659481587847, 4.198712088550252, 3.495257132995252, 2.650695602097995, 1.6807380050358995, 0.6061730822398392, -0.5475547425245986, -1.750952220489088, -2.971254294136587, -4.173350179141719, -5.320831028206622, -6.377126120295341, -7.306690012617228, -8.076199866966913, -8.655720386810389, -9.019793594744497, -9.148412100811587, -9.027837556627258, -8.651230589303893, -8.019064529282057, -7.139302493000394, -6.027325605495558, -4.705609053763651, -3.203151917566053, -1.5546759756838293, 0.20038243152479882, 2.0190552465946596, 3.8561609193119133, 5.665712962291973, 7.402369691998845, 9.022873732339123, 10.4874295270676, 11.760968772392195, 12.814257312057649, 13.62480252279642, 14.177527369463329, 14.465185865857483, 14.488504316356723, 14.256043062220527, 13.783784106595407, 13.09446051687789, 12.216653473955038, 11.183691843620323, 10.032396809390528, 8.801720102388604, 7.5313284330545684, 6.260188689220018, 5.0252082203416775, 3.859982075341242, 2.7936944919158204, 1.8502154295171884, 1.047424761663901, 0.3967872346125371, -0.09680914292701404, -0.4349495491101993, -0.6253328692979888, -0.6811760394091765, -0.6204115901878564, -0.46471608695384, -0.2384138074333053, 0.032695307499686445, 0.3225318604532923, 0.605905520545996, 0.8596060198227895, 1.0633709512321041, 1.2006908468912685, 1.2594198618757961, 1.232169570709577, 1.11647347964511, 0.9147204044167256, 0.6338653765433011, 0.28493673934350405, -0.11763288025972285, -0.5568163984517169, -1.0139016666174256, -1.4694552854690752, -1.9042939553729068, -2.300416969753606, -2.6418561474185815, -2.915404241022157, -3.111189410640273, -3.2230713847561856, -3.24884404606617, -3.1902389248969003, -3.052733977429509, -2.8451815818969073, -2.579278433811634, -2.268907532513497, -1.929388359766983, -1.5766753714953299, -1.2265468660269025, -0.8938260715517333, -0.591673936578095], 'positive_zeros': ['1.91156799650231233859437154184585', '3.01108706317753123568515569384285', '3.49635718241382694524558806584921', '4.36080756102071648217345175072756', '5.21736125240025380919448953295082', '5.95900144614382541038203248917018', '6.35356759120967320685393239642301', '6.91624318577252188254848753959682', '7.946830967099318201351386824475677'], 'prelabel': '2-3525-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3053997693389086, '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': '1.91156799650231233859437154185', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.01108706317753123568515569384', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.49635718241382694524558806585', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 28.14726671250135, 'bad_primes': [3, 5, 47], 'central_character': '1.1', 'conductor': 3525, 'conductor_radical': 705, 'degree': 2, 'index': 137, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3525/2/a/bg/1/10'], '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': '2-3525-1.1-c1-0-137', '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': '2-3525-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3053997693389086, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91156799650231233859437154185', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2423200318143230157168533032953', 'Lhash_array': ['2423200318143230157168533032953'], 'label': '2-3525-1.1-c1-0-137', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3525/2/a/bg/1/10'}