-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1363063560059404216718902095916', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.19568209498026, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, -1]]], 'bad_primes': [2, 3, 7], 'central_character': '4032.1', 'coefficient_field': '1.1.1.1', 'conductor': 4032, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[1], [1], [1, -2, 5], [1, -1], [1, -4, 11], [1, 2, 13], [1, -6, 17], [1, -8, 19], [1, 0, 23], [1, -6, 29], [1, 8, 31], [1, -2, 37], [1, 2, 41], [1, 4, 43], [1, 8, 47], [1, -6, 53], [1, 0, 59], [1, -6, 61], [1, 4, 67], [1, 8, 71], [1, -10, 73], [1, 16, 79], [1, 8, 83], [1, -6, 89], [1, 6, 97], [1, -2, 101], [1, -16, 103], [1, -12, 107], [1, -10, 109], [1, 2, 113]], 'euler_factors_factorization': [[1], [1], [[[1, -2, 5], 1]], [[[1, -1], 1]], [[[1, -4, 11], 1]], [[[1, 2, 13], 1]], [[[1, -6, 17], 1]], [[[1, -8, 19], 1]], [[[1, 0, 23], 1]], [[[1, -6, 29], 1]], [[[1, 8, 31], 1]], [[[1, -2, 37], 1]], [[[1, 2, 41], 1]], [[[1, 4, 43], 1]], [[[1, 8, 47], 1]], [[[1, -6, 53], 1]], [[[1, 0, 59], 1]], [[[1, -6, 61], 1]], [[[1, 4, 67], 1]], [[[1, 8, 71], 1]], [[[1, -10, 73], 1]], [[[1, 16, 79], 1]], [[[1, 8, 83], 1]], [[[1, -6, 89], 1]], [[[1, 6, 97], 1]], [[[1, -2, 101], 1]], [[[1, -16, 103], 1]], [[[1, -12, 107], 1]], [[[1, -10, 109], 1]], [[[1, 2, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 29, 'label': '2-4032-1.1-c1-0-29', 'leading_term': '2.85626283356353342445024575166000000000000000000000000000000000000000000000000000000000000', '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/4032/2/a/bk', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.8562628335635334, 2.84971147175415, 2.8299881471207624, 2.7968929775616744, 2.7501184028757577, 2.68928571579884, 2.61399274829506, 2.523869703265044, 2.418639800972112, 2.298181350366383, 2.162588008854673, 2.0122242948350926, 1.8477738009316935, 1.6702779698915282, 1.4811637046679142, 1.2822584720324572, 1.0757919219881373, 0.8643833893261469, 0.6510149791941624, 0.4389902761765038, 0.2318790644264747, 0.03344880927172504, -0.15241597157575384, -0.32180493091757545, -0.4708818024749064, -0.5959907112316818, -0.6937662384252509, -0.7612442769120021, -0.7959704486087049, -0.7961026627659816, -0.76050428719776, -0.6888243978272893, -0.5815616761688212, -0.4401087477137862, -0.26677410101300914, -0.06477919772598417, 0.161771026363033, 0.4079453696369962, 0.6680715869896713, 0.9358490586700916, 1.2044874126365768, 1.4668686565549913, 1.7157294303980335, 1.943859084795499, 2.1443084590208366, 2.3106035112429013, 2.436957376864183, 2.5184740304249367, 2.551336530843403, 2.5329728616009524, 2.4621926532142933, 2.339288603570531, 2.166097192331671, 1.9460143091248832, 1.6839626622970336, 1.386309276454634, 1.0607329841663777, 0.7160435226690401, 0.3619556052101321, 0.008823087791974632, -0.33265996952517135, -0.6517830088728637, -0.9381577777057, -1.182061494299421, -1.3747729031803904, -1.508889384342548, -1.5786133276835348, -1.579996466547152, -1.5111317898431333, -1.3722840124489273, -1.165951352483354, -0.8968534979306062, -0.5718430832750514, -0.1997406628428237, 0.2089040286604399, 0.6421188973458868, 1.0868759930607033, 1.5295067086420098, 1.956152399363122, 2.3532352558818515, 2.7079328690855, 3.0086391066674447, 3.2453937408669544, 3.410263763758833, 3.497660514447477, 3.5045786075684378, 3.4307451521224963, 3.27867081295712, 3.05359779626935, 2.7633437130903054, 2.4180443480926406, 2.0298024769807186, 1.6122538663163009, 1.1800652841079717, 0.7483825813057364, 0.3322495185881297, -0.05398012646988809, -0.39721363980004065, -0.6861500518743908, -0.9117477610571815, -1.067608354054266, -1.1502587342038078, -1.1593173828290773, -1.097535026402467, -0.97070499988017, -0.7874439892467322, -0.5588493841851215, -0.29804493879412225, -0.019631581977941088, 0.2609351986660259, 0.5280161779795939, 0.7664793819366835, 0.9623815332765854, 1.1036098293566567, 1.1804548365519254, 1.1860875244806346, 1.1169169788410136, 0.9728100101528101, 0.7571595461474583, 0.4767951348797398, 0.1417358269584839, -0.23520715148471213, -0.6389634990337132, -1.0528516978377755, -1.459314802300796, -1.840712573538928, -2.1801349348573313, -2.4621998008065598, -2.67379806700239, -2.804750006027266, -2.8483404834965245, -2.8017051934228796, -2.6660463389844464, -2.446663604687535, -2.1527945642732575, -1.7972674784231788, -1.3959783533907653, -0.967212733518449, -0.5308405658264482, -0.10741920390377124, 0.2827551463190505, 0.6206037911721628, 0.8891845403124261, 1.0745288408736258, 1.1663554357468648, 1.158623877300945, 1.0498980809812528, 0.8434985769199158, 0.5474318410915672, 0.17409561683688404, -0.2602300242173009, -0.7360855126127844, -1.2316982628481923, -1.72397395426299, -2.1895668658978287, -2.605978734007718, -2.952633213520227, -3.2118732153436214, -3.36983121371687, -3.417127993437366, -3.3493630255837137, -3.167369387054541, -2.8772174272512316, -2.4899636963211353, -2.0211543789066333, -1.4901049836799616, -0.9189896757242291, -0.33178378846647494, 0.2468888414107914, 0.7929464720945638, 1.2840179933015574, 1.70052970972367, 2.0266540836176254, 2.2510705406462463, 2.36749754867853, 2.374966575168846, 2.2778216602921955, 2.0854425505809924, 1.8117038893412452, 1.474197088515181, 1.0932544500304295, 0.6908261475263726, 0.2892691922957385, -0.08988701675033098, -0.42713187454249324, -0.7060562830769791, -0.9142667397857037, -1.0440790402506395, -1.0929511902591171, -1.0636288747665967, -0.9639922738502754, -0.8066093332113977, -0.6080169084202631, -0.38776660840396865, -0.16728579583865535, 0.03138472906773772, 0.18690699323669765, 0.2799425796107784, 0.2943562471100056, 0.21825688961315054, 0.0448142678967171, -0.22719847129137216, -0.5931718806061943, -1.0427554473704839, -1.5602813311864954, -2.1254984166148185, -2.714580647780169, -3.3013574828090095, -3.8587008408246337, -4.359992927911524, -4.780593454886365, -5.099223411294334, -5.299185899245997, -5.3693524552127725, -5.304855430704198, -5.107442747499735, -4.785469854182771, -4.353523976723853, -3.8316966442664078, -3.244540791399521, -2.6197673089836355, -1.9867516343121432, -1.3749328794300595, -0.8121953380776022, -0.3233244824190967, 0.07137345834725396, 0.3572074686631294, 0.5259254341273076, 0.5761748832135976, 0.5135704895389492, 0.350360470496159, 0.10470722788175812, -0.20037978237767137, -0.5384002300108276, -0.880931840719509, -1.199322441526057, -1.4664072418812604, -1.6581508842441715, -1.7551171049157241, -1.7436779375943205, -1.6168888123587786, -1.3749748699671076, -1.0253962593970871, -0.5824848238723744, -0.06666996392291094, 0.4966639153272491, 1.0786235994073232, 1.6484733904273412, 2.175424117108006, 2.630439154839677, 2.9879498321001385, 3.227377125552357, 3.334367354183566, 3.3016660935500584, 3.1295758084894363, 2.825967505421442, 2.405843558720235], 'positive_zeros': ['1.07526755386223660246135627512485', '1.79239147115953487472752121747647', '2.99737772195369908741226640049682', '3.73233091133641602778161609627596', '4.86758911716003878330800803137167', '5.48790807221177914788155934026165', '6.11340833663381996666748371566839', '7.07204727903132066232126574118059', '7.58750440596713449607840635901580', '8.509354664621903192772158046209031'], 'prelabel': '2-4032-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.674123905501206, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 906952123743309320, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07526755386223660246135627512', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.79239147115953487472752121748', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99737772195369908741226640050', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 32.19568209498026, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 4032, 'conductor_radical': 42, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 4, 0, -2, 0, 0, 0, 6, 0, 8, 0, 0, 0, 0, 0, -1, 0, 0, 0, 6, 0, -8, 0, 0, 0, 2, 0, 2, 0, 0, 0, -2, 0, -4, 0, 0, 0, -8, 0, 1, 0, 0, 0, 6, 0, 8, 0, 0, 0, 0, 0, 6, 0, 0, 0, -4, 0, -4, 0, 0, 0, -8, 0, 10, 0, 0, 0, 4, 0, -16, 0, 0, 0, -8, 0, 12, 0, 0, 0, 6, 0, -2, 0, 0, 0, 16, 0, -6, 0, 0, 0], 'euler11': [1, -4, 11], 'euler13': [1, 2, 13], 'euler17': [1, -6, 17], 'euler19': [1, -8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, -2, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, -2, 5], 'euler53': [1, -6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -6, 61], 'euler67': [1, 4, 67], 'euler7': [1, -1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -10, 73], 'euler79': [1, 16, 79], 'euler83': [1, 8, 83], 'euler89': [1, -6, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -2, 5], [1, -1, 0], [1, -4, 11], [1, 2, 13], [1, -6, 17], [1, -8, 19], [1, 0, 23], [1, -6, 29], [1, 8, 31], [1, -2, 37], [1, 2, 41], [1, 4, 43], [1, 8, 47], [1, -6, 53], [1, 0, 59], [1, -6, 61], [1, 4, 67], [1, 8, 71], [1, -10, 73], [1, 16, 79], [1, 8, 83], [1, -6, 89], [1, 6, 97]], 'index': 29, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4032/bk', 'ModularForm/GL2/Q/holomorphic/4032/2/a/bk/1/1', 'ModularForm/GL2/Q/holomorphic/4032/2/a/bk'], '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': '2-4032-1.1-c1-0-29', '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': '2-4032-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.674123905501206, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 906952123743309320, 'z1': {'__RealLiteral__': 0, 'data': '1.07526755386223660246135627512', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20212459
{'Lhash': '1363063560059404216718902095916', 'Lhash_array': ['1363063560059404216718902095916'], 'label': '2-4032-1.1-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4032/2/a/bk'}
-
id: 24564177
{'Lhash': '1363063560059404216718902095916', 'Lhash_array': ['1363063560059404216718902095916'], 'label': '2-4032-1.1-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4032/2/a/bk/1/1'}
-
id: 37508
{'Lhash': '906952123743309320', 'Lhash_array': ['906952123743309320'], 'label': '2-4032-1.1-c1-0-29', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4032/bk'}