-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '970736313102308788098928787673', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.447213595499958, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 359.95406846810107, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [11, [1, 5, 11]]], 'bad_primes': [2, 3, 11], 'central_character': '5645376.1', 'coefficient_field': '1.1.1.1', 'conductor': 5645376, 'conductor_radical': 66, 'degree': 4, 'euler_factors': [[1], [1], [1, 1, 4, 5, 25], [1, 0, -1, 0, 49], [1, 5, 11], [1, 0, 21, 0, 169], [1, 0, -10, 0, 289], [1, 0, 6, 0, 361], [1, -6, 19, -138, 529], [1, 0, -13, 0, 841], [1, 7, 54, 217, 961], [1, 10, 95, 370, 1369], [1, 0, 67, 0, 1681], [1, 0, 11, 0, 1849], [1, -7, 94, -329, 2209], [1, -8, 113, -424, 2809], [1, 1, 106, 59, 3481], [1, 0, -31, 0, 3721], [1, -9, 82, -603, 4489], [1, -12, 129, -852, 5041], [1, 0, 26, 0, 5329], [1, 0, -21, 0, 6241], [1, 0, 9, 0, 6889], [1, -8, 190, -712, 7921], [1, 1, 192, 97, 9409], [1, 0, 199, 0, 10201], [1, 5, 206, 515, 10609], [1, 0, 146, 0, 11449], [1, 0, 106, 0, 11881], [1, -17, 208, -1921, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 9, 'label': '4-2376e2-1.1-c1e2-0-9', 'load_key': 'Costa', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/2.0.11.1/46656.3/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.04296875', 'prec': 34}, 'plot_values': [-7.954815235568896e-75, 0.19525054305962503, 0.38688176442960714, 0.5712188090105575, 0.7444843027649556, 0.9027680366311601, 1.0420205957735023, 1.1580769599834573, 1.246714471305043, 1.3037475925766178, 1.325159617587478, 1.3072690095313824, 1.2469254284773053, 1.1417278700361095, 0.9902548051671567, 0.7922939308405098, 0.5490572706600938, 0.2633660659034675, -0.06021067154209118, -0.4152797703040216, -0.7936242130760511, -1.1852923463166802, -1.5787847602093468, -1.961343165822123, -2.319340242794691, -2.6387633703176814, -2.905778664112274, -3.1073551718124395, -3.231922837064503, -3.270032377389787, -3.2149809959028453, -3.0633653102575975, -2.815522431826394, -2.4758220765045635, -2.0527771272491813, -1.558947236806456, -1.0106197193212743, -0.4272638017557868, 0.16923223463931408, 0.7555171045932058, 1.3078873909329016, 1.8035013319669253, 2.2216320310541966, 2.544887981310356, 2.7603240887533764, 2.8603663321663086, 2.8434783281949607, 2.7145085678279792, 2.4846727763079666, 2.171146142049562, 1.7962640766204607, 1.38635634758718, 0.9702661964660665, 0.5776315239718438, 0.2370274070887917, -0.025913831489313036, -0.19027878471403525, -0.2414174702957944, -0.1721358299636477, 0.01656718923741118, 0.3152954845600759, 0.706628471725547, 1.1660750729033886, 1.6635708873938997, 2.165437628193182, 2.6366842850511065, 3.043496374625265, 3.3557361775605705, 3.5492656351459337, 3.6079063947642283, 3.5248691598082025, 3.303516663841662, 2.9573696707634305, 2.5093206256216525, 1.9900811070241096, 1.435952404564458, 0.8860682196643678, 0.3793094401616005, -0.048871693488903314, -0.36946097519631177, -0.5624688249765, -0.6188601293142559, -0.5416368930942649, -0.3459454692366463, -0.058156772061660957, 0.28604684606835423, 0.644457417195608, 0.9717981485937905, 1.2235817317014235, 1.3600531547812678, 1.3498779830585912, 1.1732439944428947, 0.8240809057184895, 0.3111679924266171, -0.34201169764865963, -1.0987059602984546, -1.9115382613410412, -2.7261720268949143, -3.485703901328759, -4.1354179900209225, -4.627486205674406, -4.925189405511067, -5.006262765296956, -4.865035906516771, -4.513139073859817, -3.9786730637507954, -3.3038816513012033, -2.5415079979968134, -1.7501471837518423, -0.9890123433746663, -0.31260050247022436, 0.23423220456156246, 0.6203019115303677, 0.8308253727011227, 0.8685533950272357, 0.7531684581525757, 0.5189760349765289, 0.21109244710049185, -0.11950920581085381, -0.4216062426542727, -0.6494164509883732, -0.7677752862087842, -0.756240014488523, -0.611655781450526, -0.3488659221627522, 0.0005650412017241652, 0.39154036341338255, 0.7702499831781815, 1.080152825420474, 1.2685140644972084, 1.2928065144141754, 1.1262736109841343, 0.7620145615002308, 0.215086408331663, -0.47768858237574796, -1.2602871143382397, -2.0622455339404047, -2.8051990851916964, -3.4105749029464167, -3.807666603604766, -3.941248929365308, -3.7779098371699726, -3.3103858670636392, -2.5593759642291447, -1.5725613286548838, -0.42084888135821547, 0.8078469528633319, 2.016697622190175, 3.1091266181350927, 3.9981117152505217, 4.614650932451106, 4.914489740188944, 4.882377542887535, 4.533376271059695, 3.9110566893218635, 3.082755106585571, 2.1323871947338198, 1.1515896776158718, 0.23015256956145388, -0.5532091563359526, -1.1387270941617549, -1.4912246211110747, -1.602915644391961, -1.4930604495117332, -1.2045438974797915, -0.7977991082856963, -0.34281164528063607, 0.08983261815850063, 0.4377768525176243, 0.6545327973358639, 0.7150040727289727, 0.6182212916407339, 0.3869561086519089, 0.06426521021056554, -0.29260245944727953, -0.6201683847864965, -0.8575475823524609, -0.9550027556573502, -0.8811203470067202, -0.6276598339823722, -0.21141104428888338, 0.3272326265969679, 0.9288597704552947, 1.5222502754737068, 2.0333238084603003, 2.3946995096734223, 2.5546354200922226, 2.4841691542528994, 2.1814878534336897, 1.6728927021608533, 1.0101510074460591, 0.264493991349972, -0.4820383000269303, -1.1468403553547812, -1.6572744124151226, -1.9601246741076734, -2.0287102114459183, -1.866668689210943, -1.5078341503178867, -1.012129813490477, -0.45791835914031903, 0.06827024920544288, 0.48334367273595935, 0.719084900874623, 0.7319042197745492, 0.5095677245636852, 0.07392661682012446, -0.5208280275044204, -1.1942835766652387, -1.8496167355740154, -2.385911493081318, -2.711436346731168, -2.7561651731980485, -2.4818799435354837, -1.8884675981172026, -1.015487114083094, 0.06132054688924642, 1.2382531053914012, 2.39564601890364, 3.412183648471671, 4.179724542699752, 4.616741395569825, 4.678623290024293, 4.363468770643246, 3.7125668162818197, 2.8054465054078426, 1.7500857689672524, 0.6695106100536267, -0.3134984366195073, -1.0916135055755138, -1.5861003066620147, -1.7561769299911842, -1.6033714183897467, -1.1703234838252814, -0.5342194914526043, 0.2042278826593837, 0.9347422083642266, 1.5524776009452992, 1.9719978221487369, 2.1383386785731804, 2.033661551745698, 1.6786240297606958, 1.1283355137809932, 0.46352791723308656, -0.22175332509756368, -0.8341411399892368, -1.294588125366729, -1.5496779307458317, -1.578966905620632, -1.3972948151546218, -1.0517396573780518, -0.613680234855751, -0.16715689250307417, 0.20472109547866565, 0.43326739167144035, 0.4755505844930438, 0.3218075731421738], 'positive_zeros': ['0.76577592668479485330664047736090', '1.62062139942700753657933883751617', '2.35827447095119636847007357982779', '2.53221676589038407628878917410607', '3.34611300254910108342742803321866', '3.61700667181298144495509723459832', '4.01758469059220763645795253920195', '4.74967620451416255578841827899776', '5.05469335715386464094979923950641', '5.37102962094917612787851385674325', '5.72903647953847466387316425753576', '6.24532243860152612139304346594525', '6.80077602362668751835955768063061', '7.16633413531286368640809197620786'], 'prelabel': '4-2376e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.355738229078537, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 648439994350923385, 'z1': {'__RealLiteral__': 0, 'data': '0.76577592668479485330664047736090', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.62062139942700753657933883751617', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.35827447095119636847007357982779', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 359.95406846810107, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 5645376, 'conductor_radical': 66, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 1, 0, 0, 0, 8, 0, 5, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], 'euler11': [1, 5, 11, 0, 0], 'euler13': [1, 0, 21, 0, 169], 'euler17': [1, 0, -10, 0, 289], 'euler19': [1, 0, 6, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -6, 19, -138, 529], 'euler29': [1, 0, -13, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 7, 54, 217, 961], 'euler37': [1, 10, 95, 370, 1369], 'euler41': [1, 0, 67, 0, 1681], 'euler43': [1, 0, 11, 0, 1849], 'euler47': [1, -7, 94, -329, 2209], 'euler5': [1, 1, 4, 5, 25], 'euler53': [1, -8, 113, -424, 2809], 'euler59': [1, 1, 106, 59, 3481], 'euler61': [1, 0, -31, 0, 3721], 'euler67': [1, -9, 82, -603, 4489], 'euler7': [1, 0, -1, 0, 49], 'euler71': [1, -12, 129, -852, 5041], 'euler73': [1, 0, 26, 0, 5329], 'euler79': [1, 0, -21, 0, 6241], 'euler83': [1, 0, 9, 0, 6889], 'euler89': [1, -8, 190, -712, 7921], 'euler97': [1, 1, 192, 97, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 1, 4, 5, 25], [1, 0, -1, 0, 49], [1, 5, 11, 0, 0], [1, 0, 21, 0, 169], [1, 0, -10, 0, 289], [1, 0, 6, 0, 361], [1, -6, 19, -138, 529], [1, 0, -13, 0, 841], [1, 7, 54, 217, 961], [1, 10, 95, 370, 1369], [1, 0, 67, 0, 1681], [1, 0, 11, 0, 1849], [1, -7, 94, -329, 2209], [1, -8, 113, -424, 2809], [1, 1, 106, 59, 3481], [1, 0, -31, 0, 3721], [1, -9, 82, -603, 4489], [1, -12, 129, -852, 5041], [1, 0, 26, 0, 5329], [1, 0, -21, 0, 6241], [1, 0, 9, 0, 6889], [1, -8, 190, -712, 7921], [1, 1, 192, 97, 9409]], 'index': 9, 'instance_types': ['ECNF', 'BMF', 'BMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.0.11.1/46656.3/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/46656.5/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/46656.3/b', 'EllipticCurve/2.0.11.1/46656.5/c'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-2376e2-1.1-c1e2-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-2376e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.355738229078537, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 648439994350923385, 'z1': {'__RealLiteral__': 0, 'data': '0.76577592668479485330664047736090', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9938645
{'Lhash': '970736313102308788098928787673', 'Lhash_array': ['970736313102308788098928787673'], 'factors': ['4-2376e2-1.1-c1e2-0-9'], 'label': '4-2376e2-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/46656.5/c'}
-
id: 9938515
{'Lhash': '970736313102308788098928787673', 'Lhash_array': ['970736313102308788098928787673'], 'factors': ['4-2376e2-1.1-c1e2-0-9'], 'label': '4-2376e2-1.1-c1e2-0-9', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/46656.3/b'}
-
id: 9938462
{'Lhash': '970736313102308788098928787673', 'Lhash_array': ['970736313102308788098928787673'], 'factors': ['4-2376e2-1.1-c1e2-0-9'], 'label': '4-2376e2-1.1-c1e2-0-9', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/46656.5/c'}
-
id: 9938290
{'Lhash': '970736313102308788098928787673', 'Lhash_array': ['970736313102308788098928787673'], 'factors': ['4-2376e2-1.1-c1e2-0-9'], 'label': '4-2376e2-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/46656.3/b'}