-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '739308599446845979424745376725', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-0.27525512860841095, 0.15891862259789113], 'a6': [0, 0], 'a7': [1.255294939775204, 0.724744871391589], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.697224203915887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '2592.1727', 'coefficient_field': 'CDF', 'conductor': 2592, 'conductor_radical': 6, 'conjugate': '1458312117188512021412285378679', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.27525512860841095, -0.15891862259789113], [2.5, -4.330127018922194]], [[1.0, 0], [-1.255294939775204, -0.724744871391589], [3.5, 6.06217782649107]], [[1.0, 0], [0.5481881585886564, -0.9494897427831781], [-5.5, -9.526279441628825]], [[1.0, 0], [1.449489742783178, 2.510589879550408], [-6.5, 11.258330249197702]], [[1.0, 0], [0, -3.4641016151377544], [-17.0, 0]], [[1.0, 0], [0, 4.898979485566356], [-19.0, 0]], [[1.0, 0], [-1.4142135623730951, -2.449489742783178], [-11.5, 19.91858428704209]], [[1.0, 0], [-7.898979485566356, -4.5604779323150675], [14.5, 25.11473670974872]], [[1.0, 0], [6.451447362481836, -3.724744871391589], [15.5, -26.846787517317598]], [[1.0, 0], [-4.898979485566356, 0], [37.0, 0]], [[1.0, 0], [-8.449489742783179, 4.878315177510849], [20.5, -35.50704155516198]], [[1.0, 0], [-5.974691494688162, -3.449489742783178], [21.5, 37.239092362730865]], [[1.0, 0], [4.5604779323150675, -7.898979485566356], [-23.5, -40.703193977868615]], [[1.0, 0], [0, 4.417613350725102], [-53.0, 0]], [[1.0, 0], [-4.5604779323150675, -7.898979485566356], [-29.5, 51.09549882328188]], [[1.0, 0], [2.0, -3.4641016151377544], [-30.5, -52.827549630850754]], [[1.0, 0], [-4.417613350725102, 2.550510257216822], [33.5, -58.023702053557386]], [[1.0, 0], [7.563877720667073, 0], [71.0, 0]], [[1.0, 0], [-1.8989794855663562, 0], [73.0, 0]], [[1.0, 0], [1.7320508075688772, 1.0], [39.5, 68.41600689897065]], [[1.0, 0], [7.937093215649914, -13.74744871391589], [-41.5, -71.88010851410841]], [[1.0, 0], [0, -11.949382989376325], [-89.0, 0]], [[1.0, 0], [-2.5, 4.330127018922194], [-48.5, -84.00446416709055]], [[1.0, 0], [-13.623724356957945, -7.8656609248549305], [50.5, 87.4685657822283]], [[1.0, 0], [8.660254037844387, -5.0], [51.5, -89.20061658979718]], [[1.0, 0], [8.660254037844387, 0], [107.0, 0]], [[1.0, 0], [4.898979485566356, 0], [109.0, 0]], [[1.0, 0], [-12.24744871391589, 7.0710678118654755], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-2592-36.11-c1-0-13', 'leading_term': '1.587638774577065712983454798956495726153070810860913177', '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/2592/2/s/a/1727/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.5876387745770657, 1.4967836367692375, 1.396558255760025, 1.2870271337112082, 1.1682073804211657, 1.040111584683022, 0.9027940174986631, 0.7563976134714138, 0.6011992994640045, 0.43765150233200334, 0.2664180139597292, 0.08840276840228974, -0.09522954887394613, -0.2830418113293701, -0.4733221513675254, -0.6640912830979715, -0.8531194787436127, -1.0379530495175058, -1.2159500113598793, -1.3843244451339385, -1.540198883248212, -1.6806638674765126, -1.8028436267340708, -1.9039666224237413, -1.9814395086642091, -2.032922862876039, -2.0564068675056135, -2.050284975299715, -2.013423477725677, -1.9452248276837691, -1.845682551603163, -1.715425629213198, -1.5557503271057298, -1.3686376482231544, -1.1567548051296666, -0.9234394395790307, -0.6726656912639177, -0.40899165895853457, -0.1374882892171315, 0.13634973947589932, 0.4067100088987106, 0.6675835288628406, 0.9128988121033018, 1.1366660434713067, 1.3331280289074108, 1.4969141701884676, 1.6231933533490992, 1.7078213800528763, 1.7474784282909923, 1.7397920153446076, 1.6834410624644371, 1.5782369338397897, 1.425177744377484, 1.226472798961249, 0.9855347324259881, 0.7069377513650313, 0.396341317728299, 0.06037963655981511, -0.2934816118525499, -0.6571187536792196, -1.0219501855111506, -1.3791583480283511, -1.7199279830134444, -2.0356942186372375, -2.3183933605662115, -2.560708793511704, -2.756304147924606, -2.9000358823038694, -2.9881376885589486, -3.0183696533688416, -2.9901259007972696, -2.9044954892394323, -2.7642726179365678, -2.5739136839196752, -2.339440379212269, -2.0682897819408423, -1.7691142180506223, -1.451535491455414, -1.1258598349069826, -0.8027615554696903, -0.49294477200705267, -0.20679380576865294, 0.045976366753978454, 0.2566577043526811, 0.4178627549102934, 0.5238027298153445, 0.5705191261923744, 0.5560592201330578, 0.48058735349439624, 0.3464259005373878, 0.15802207381282463, -0.07816075823729259, -0.3538258987273832, -0.6590962155833525, -0.9828303197910114, -1.3129926840699342, -1.6370660347221946, -1.9424923668571, -2.217127381534985, -2.4496921010395543, -2.630204947850863, -2.75037771696049, -2.803959650901677, -2.787015239213236, -2.6981233808934006, -2.5384881164189808, -2.3119541775237424, -2.0249240182474866, -1.6861766605375539, -1.3065924772351538, -0.8987917992671981, -0.4766988217116478, -0.055045545219345855, 0.3511667179611952, 0.727228550343167, 1.059285141081071, 1.3348786090200564, 1.5434482087507955, 1.6767677358693511, 1.7293013594352635, 1.6984618417790736, 1.5847585753754871, 1.3918269565979438, 1.1263351795313195, 0.7977693969418437, 0.41810316814728093, 0.001361991304688356, -0.436901706586906, -0.880203676815813, -1.311770227992737, -1.7152025286176562, -2.0751359529915496, -2.3778671464723256, -2.6119221835331126, -2.768541036720607, -2.8420565229267845, -2.8301498525131015, -2.7339697367759817, -2.558107527331849, -2.3104268483469577, -2.0017523924324534, -1.6454287188755676, -1.2567657473383966, -0.8523929149922724, -0.4495484112311028, -0.06533330154773079, 0.2840374793496693, 0.5839544764182738, 0.8220712414248924, 0.9888699450446954, 1.078108443253033, 1.0871269044550096, 1.016997936239343, 0.8725108441219208, 0.6619879286345037, 0.3969382662682376, 0.09156188735349935, -0.2378756833148864, -0.5737722534909467, -0.8979896427064115, -1.1926907793920996, -1.4411754045057896, -1.628675884283018, -1.7430757143060704, -1.7755161362537932, -1.720860798809269, -1.5779944056700932, -1.3499385614921888, -1.0437762400149875, -0.6703850935656909, -0.2439887983133534, 0.21845563549252475, 0.6980085846806584, 1.1746035478260384, 1.627969280670464, 2.0385758445460187, 2.388560150428605, 2.6625867344896257, 2.8486017775009107, 2.93844271880693, 2.9282720528822157, 2.8188117734545113, 2.6153641012355053, 2.3276141792600726, 1.9692208744454804, 1.557212183709796, 1.1112114989444002, 0.6525296460540192, 0.20316473032681073, -0.21524298943422104, -0.5824510087384172, -0.8805985272639643, -1.0950856434267677, -1.2153033866961507, -1.2351768499029825, -1.1534923450584829, -0.9739897663703179, -0.7052127209276432, -0.36012093177595467, 0.04451865997864946, 0.4889343692527386, 0.9513080008573983, 1.408842675560211, 1.8388879265414804, 2.2200661413433336, 2.5333436034382317, 2.7629914419767756, 2.897386675650629, 2.929611038114026, 2.857815059857408, 2.6853264916433908, 2.420495020694835, 2.0762787093297277, 1.66959098855467, 1.2204396684374503, 0.7509006116699969, 0.2839778477926602, -0.15759152999120804, -0.5525257338740286, -0.8821175503520696, -1.1312250000227717, -1.2890799129955655, -1.3498698900650148, -1.3130605526355124, -1.1834383401308535, -0.9708687147633835, -0.6897797234394001, -0.35839564834874466, 0.0022408438057987877, 0.3694078197529233, 0.7199449256088062, 1.0315301777069816, 1.2839241188532098, 1.460113619456949, 1.5472921307034782, 1.537621208509151, 1.4287292450769455, 1.223917016405944, 0.9320551771316287, 0.5671753931195256, 0.14777351077875853, -0.3041408902492287, -0.7641999121878119, -1.2069772262838265, -1.6073632336117376, -1.9419412702985448, -2.1902896032915806, -2.3361370630117415, -2.3683072768773705, -2.2813972708872794, -2.076150153245116, -1.7594979586322466, -1.3442686417659218, -0.8485696912933745, -0.2948788688839012, 0.29111084900476125, 0.8818308850044695], 'positive_zeros': ['0.58321165099731734704477991769898', '1.95517149201855420227988544815522', '2.90334872275459936505021775243911', '4.15421614259401984489642084195204', '4.60528926279650340901308066109604', '5.69422979808710978224125865197037', '6.39859826071747023746501952247517', '7.37234151467112056412560086840895', '7.936250255852488793850859952487834', '8.659969098950145952107600235772586'], 'prelabel': '2-2592-36.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.549420205247685, 'root_angle': -0.3611111111111111, 'root_number': '0.4226182617406994361869784896477301815631293011948646235 - 0.9063077870366499632425526567543169832677126251758646809*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.18055555555555558', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58321165099731734704477991770', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95517149201855420227988544816', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.90334872275459936505021775244', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 20.697224203915887, 'bad_primes': [2, 3], 'central_character': '36.11', 'conductor': 2592, 'conductor_radical': 6, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2592/2/s/a/1727/4'], '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': '2-2592-36.11-c1-0-13', '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': '2-2592-36.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.549420205247685, 'root_angle': -0.18055555555555555, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58321165099731734704477991770', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '739308599446845979424745376725', 'Lhash_array': ['739308599446845979424745376725'], 'label': '2-2592-36.11-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2592/2/s/a/1727/4'}