-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1584067077714626864729382579168', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.829735079150222, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [7, [1, 1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '3360.1', 'coefficient_field': '1.1.1.1', 'conductor': 3360, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, 1], [1, 2, 11], [1, 0, 13], [1, 6, 17], [1, -6, 19], [1, -8, 23], [1, -6, 29], [1, -6, 31], [1, 10, 37], [1, -2, 41], [1, -4, 43], [1, 8, 47], [1, 12, 53], [1, 12, 59], [1, 10, 61], [1, -4, 67], [1, -2, 71], [1, -4, 73], [1, 4, 79], [1, 12, 83], [1, -6, 89], [1, -16, 97], [1, 10, 101], [1, 0, 103], [1, -16, 107], [1, 14, 109], [1, 4, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, 1], 1]], [[[1, 1], 1]], [[[1, 2, 11], 1]], [[[1, 0, 13], 1]], [[[1, 6, 17], 1]], [[[1, -6, 19], 1]], [[[1, -8, 23], 1]], [[[1, -6, 29], 1]], [[[1, -6, 31], 1]], [[[1, 10, 37], 1]], [[[1, -2, 41], 1]], [[[1, -4, 43], 1]], [[[1, 8, 47], 1]], [[[1, 12, 53], 1]], [[[1, 12, 59], 1]], [[[1, 10, 61], 1]], [[[1, -4, 67], 1]], [[[1, -2, 71], 1]], [[[1, -4, 73], 1]], [[[1, 4, 79], 1]], [[[1, 12, 83], 1]], [[[1, -6, 89], 1]], [[[1, -16, 97], 1]], [[[1, 10, 101], 1]], [[[1, 0, 103], 1]], [[[1, -16, 107], 1]], [[[1, 14, 109], 1]], [[[1, 4, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-3360-1.1-c1-0-28', '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/3360/2/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-5.293209284196342e-61, 0.1345543752858945, 0.26825088745796055, 0.4001887325068318, 0.5293842583539317, 0.6547368877183217, 0.7750032289263564, 0.8887811564624342, 0.9945050040558341, 1.0904523812062188, 1.1747625522642868, 1.2454658358207535, 1.3005230996834662, 1.3378741350853058, 1.3554934755525283, 1.3514520610342073, 1.3239830187447104, 1.271549726143355, 1.1929142320688144, 1.087204038403878, 0.9539751903951974, 0.7932695955626998, 0.6056644973008211, 0.39231207848156, 0.15496727067892999, -0.10399799729489123, -0.38159565734437123, -0.6742387271235899, -0.9777758132260653, -1.2875433930821332, -1.598435910766819, -1.9049932108501648, -2.201504289494371, -2.48212577762935, -2.741013003851856, -2.972460933120966, -3.171051761069347, -3.331805483191091, -3.4503293736670817, -3.5229620197583276, -3.5469073826129422, -3.5203543097405947, -3.4425770209454774, -3.3140123369627905, -3.136309822691151, -2.9123515739657204, -2.6462390820050614, -2.343245450990817, -2.009732203921137, -1.653030966506401, -1.2812914397932615, -0.9032982261204021, -0.5282602228423217, -0.16557740418099898, 0.1754091677397521, 0.4856773675630428, 0.7567866045022444, 0.9811350067981688, 1.1522029182768672, 1.2647744063221942, 1.3151287348445946, 1.3011943000532582, 1.2226583606639247, 1.0810270066128471, 0.8796311794328717, 0.6235761502829991, 0.31963363485678586, -0.0239223748573788, -0.39753301478756975, -0.7906201755767216, -1.1918934450586594, -1.5896897121063482, -1.9723352487650996, -2.3285188460697235, -2.647663686607519, -2.920285146048176, -3.1383216665965397, -3.2954262631365348, -3.3872071167425597, -3.4114070714066647, -3.3680136508503695, -3.2592934071315884, -3.089746937505807, -2.8659836803551753, -2.5965185305325007, -2.29149529360499, -1.9623449141216291, -1.6213891486816472, -1.28140279491348, -0.9551496230527201, -0.6549086888953873, -0.3920086520753154, -0.1763880180092893, -0.016198824841635047, 0.08252980619191573, 0.11615363376518234, 0.0835885945110643, -0.013609718894423606, -0.17126805138686013, -0.38272074236921594, -0.6390359631666315, -0.9293365233817854, -1.2412048184811297, -1.5611577589992653, -1.8751742403306753, -2.1692550359449045, -2.4299930618431955, -2.6451308763400054, -2.804082125360448, -2.8983944614848802, -2.9221332570702403, -2.872168158188885, -2.748348105083228, -2.5535547542559747, -2.2936291183788433, -1.9771715027276322, -1.6152202463365615, -1.2208201421393634, -0.8084964763457796, -0.3936551604756295, 0.008066788337203855, 0.3814733251970564, 0.7124751847359756, 0.9887200721365278, 1.2001586584662614, 1.3395198603155456, 1.4026721882045463, 1.3888523916080036, 1.300748049027255, 1.1444269372429186, 0.9291127100175444, 0.6668133358289168, 0.37181557886645106, 0.06006524254616679, -0.25154137757643347, -0.5459246503801135, -0.8066137033270483, -1.0185277360025027, -1.168710373971442, -1.2469820801688076, -1.2464784913083158, -1.164046970245406, -1.0004795044679597, -0.7605671066037207, -0.4529687921056877, -0.08989667724421145, 0.3133726250016346, 0.7391417351848328, 1.1680650299092241, 1.5800168922542988, 1.9550172727285673, 2.274172463167749, 2.5205872028991476, 2.6802044906117604, 2.7425318129958405, 2.701216869482818, 2.554442118633626, 2.305115347575082, 1.9608426364920457, 1.5336801477489572, 1.0396716507283212, 0.4981891017577567, -0.06889657435266015, -0.6381786025009377, -1.1857682543984616, -1.6883911039573252, -2.124474151174009, -2.4751716927183076, -2.7252797139097464, -2.863992969978926, -2.885465657705922, -2.7891453742155776, -2.579860530227705, -2.2676530490303684, -1.867360486494319, -1.3979640522492183, -0.8817307815713178, -0.3431886995313056, 0.19201732342348754, 0.69833468424043, 1.1515187445968635, 1.529795540292175, 1.814913713893801, 1.993032606114572, 2.055400922929891, 1.998790305177875, 1.8256600040684312, 1.5440421369819726, 1.167151006242076, 0.7127340003397087, 0.2021949374568861, -0.3404673482288793, -0.8898524803244751, -1.420424074160758, -1.9077830464020291, -2.3298834230762866, -2.668127772787576, -2.9082851197408948, -3.041182992200599, -3.063136717152482, -2.976092612946318, -2.787476668311803, -2.509755850804934, -2.1597345357542315, -1.7576228599700903, -1.3259262960906044, -0.8882157117389788, -0.4678440459612642, -0.08667908606052827, 0.23607857156672926, 0.4849274735837408, 0.6488900571854267, 0.722084087315586, 0.7040083542510148, 0.5995258227117083, 0.41854414863084227, 0.17541039353726967, -0.11194707244443178, -0.4230819951042182, -0.7362395169615872, -1.0296430720493175, -1.2827856388751226, -1.4776511783942015, -1.5997953747586118, -1.6392221711454644, -1.5910036919416106, -1.4556053882496127, -1.2388948685000538, -0.9518309626734623, -0.609848099995307, -0.2319689951408055, 0.16030510725849242, 0.5442637528005122, 0.8973431181640448, 1.198489269125655, 1.4294482011850802, 1.5759051910444895, 1.628403739143686, 1.5829863503918546, 1.4415149549178559, 1.2116470643068111, 0.9064637662410748, 0.543766236636969, 0.14507739297039277, -0.26559656064446835, -0.6631747389272454, -1.0229990376495894, -1.3223324351402581, -1.5417684879734486, -1.6664660359606318, -1.687131962519858, -1.600688432669524, -1.4105786373204905, -1.1266857412987146, -0.7648622950444827, -0.3460905223240095, 0.10468372583858207], 'positive_zeros': ['1.24960858885676340498672394498817', '2.71557781749145545205368216765222', '3.39896233277134585610990366575410', '4.72916901985484185209248139883926', '4.92025339438886395369489047888324', '6.09270049536733414349274513765300', '6.76360727272757381454020390912369', '7.37497321130478871197915841208470', '8.220445638160044929496837312007423'], 'prelabel': '2-3360-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.179742761870537, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 137132694492993435, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24960858885676340498672394499', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71557781749145545205368216765', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39896233277134585610990366575', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 26.829735079150222, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 3360, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, -1, 0, 1, 0, -2, 0, 0, 0, 1, 0, -6, 0, 6, 0, 1, 0, 8, 0, 1, 0, -1, 0, 6, 0, 6, 0, 2, 0, 1, 0, -10, 0, 0, 0, 2, 0, 4, 0, -1, 0, -8, 0, 1, 0, 6, 0, -12, 0, 2, 0, -6, 0, -12, 0, -10, 0, -1, 0, 0, 0, 4, 0, -8, 0, 2, 0, 4, 0, -1, 0, 2, 0, -4, 0, 1, 0, -12, 0, 6, 0, -6, 0, 6, 0, 0, 0, -6, 0, -6, 0, 16, 0, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, 0, 13], 'euler17': [1, 6, 17], 'euler19': [1, -6, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -6, 31], 'euler37': [1, 10, 37], 'euler41': [1, -2, 41], 'euler43': [1, -4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 1, 0], 'euler53': [1, 12, 53], 'euler59': [1, 12, 59], 'euler61': [1, 10, 61], 'euler67': [1, -4, 67], 'euler7': [1, 1, 0], 'euler71': [1, -2, 71], 'euler73': [1, -4, 73], 'euler79': [1, 4, 79], 'euler83': [1, 12, 83], 'euler89': [1, -6, 89], 'euler97': [1, -16, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 1, 0], [1, 2, 11], [1, 0, 13], [1, 6, 17], [1, -6, 19], [1, -8, 23], [1, -6, 29], [1, -6, 31], [1, 10, 37], [1, -2, 41], [1, -4, 43], [1, 8, 47], [1, 12, 53], [1, 12, 59], [1, 10, 61], [1, -4, 67], [1, -2, 71], [1, -4, 73], [1, 4, 79], [1, 12, 83], [1, -6, 89], [1, -16, 97]], 'index': 28, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3360/b', 'ModularForm/GL2/Q/holomorphic/3360/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/3360/2/a/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-3360-1.1-c1-0-28', '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': '2-3360-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.179742761870537, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 137132694492993435, 'z1': {'__RealLiteral__': 0, 'data': '1.24960858885676340498672394499', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 19996293
{'Lhash': '1584067077714626864729382579168', 'Lhash_array': ['1584067077714626864729382579168'], 'label': '2-3360-1.1-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3360/2/a/b'}
-
id: 24561230
{'Lhash': '1584067077714626864729382579168', 'Lhash_array': ['1584067077714626864729382579168'], 'label': '2-3360-1.1-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3360/2/a/b/1/1'}
-
id: 26754
{'Lhash': '137132694492993435', 'Lhash_array': ['137132694492993435'], 'label': '2-3360-1.1-c1-0-28', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3360/b'}