-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1365656344670259106140267810004,2187773446414311509898873905850', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 712.995438776321, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [11, [1, -2, 1]], [19, [1, -2, 1]]], 'bad_primes': [2, 11, 19], 'central_character': '3344.1', 'coefficient_field': '1.1.1.1', 'conductor': 11182336, 'conductor_radical': 418, 'degree': 4, 'euler_factors': [[1], [1, 1, 3, 3, 9], [1, 1, 7, 5, 25], [1, 1, 11, 7, 49], [1, -2, 1], [1, 7, 35, 91, 169], [1, -2, 22, -34, 289], [1, -2, 1], [1, -2, 34, -46, 529], [1, 15, 111, 435, 841], [1, -5, 39, -155, 961], [1, -16, 138, -592, 1369], [1, 11, 109, 451, 1681], [1, -1, 83, -43, 1849], [1, -8, 58, -376, 2209], [1, -6, 102, -318, 2809], [1, -8, 134, -472, 3481], [1, 4, 126, 244, 3721], [1, 7, 65, 469, 4489], [1, -15, 169, -1065, 5041], [1, 26, 302, 1898, 5329], [1, -2, 42, -158, 6241], [1, 11, 167, 913, 6889], [1, -6, 70, -534, 7921], [1, 0, -14, 0, 9409], [1, -2, 190, -202, 10201], [1, 9, 145, 927, 10609], [1, 0, 162, 0, 11449], [1, 8, 182, 872, 11881], [1, 8, 242, 904, 12769]], 'euler_factors_factorization': [[1], [[[1, 1, 3, 3, 9], 1]], [[[1, 1, 7, 5, 25], 1]], [[[1, 1, 11, 7, 49], 1]], [[[1, -1], 2]], [[[1, 7, 35, 91, 169], 1]], [[[1, -2, 22, -34, 289], 1]], [[[1, -1], 2]], [[[1, -2, 34, -46, 529], 1]], [[[1, 15, 111, 435, 841], 1]], [[[1, -5, 39, -155, 961], 1]], [[[1, -8, 37], 2]], [[[1, 11, 109, 451, 1681], 1]], [[[1, -1, 83, -43, 1849], 1]], [[[1, -8, 58, -376, 2209], 1]], [[[1, -6, 102, -318, 2809], 1]], [[[1, -4, 59], 2]], [[[1, 2, 61], 2]], [[[1, 7, 65, 469, 4489], 1]], [[[1, -15, 169, -1065, 5041], 1]], [[[1, 26, 302, 1898, 5329], 1]], [[[1, -2, 42, -158, 6241], 1]], [[[1, 11, 167, 913, 6889], 1]], [[[1, -6, 70, -534, 7921], 1]], [[[1, 0, -14, 0, 9409], 1]], [[[1, -2, 190, -202, 10201], 1]], [[[1, 9, 145, 927, 10609], 1]], [[[1, 0, 162, 0, 11449], 1]], [[[1, 8, 182, 872, 11881], 1]], [[[1, 4, 113], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 3, 'label': '4-3344e2-1.1-c1e2-0-3', 'load_key': 'CMFs-workshop', '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': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/3344/2/a/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.025390625', 'prec': 37}, 'plot_values': [1.8212936689529671e-121, 0.005379051843409631, 0.02148470297765068, 0.04822200804884313, 0.08543057068015723, 0.13288239034039534, 0.19027720322352093, 0.25723928141793795, 0.33331082548222857, 0.4179481270031049, 0.51051449302239, 0.6102761916098554, 0.7163965796921448, 0.8279328047201001, 0.9438322691666118, 1.0629320142833312, 1.1839578424724577, 1.3055288065176478, 1.4261591670597826, 1.544269694304697, 1.6581934268912997, 1.7661938438047442, 1.8664764656074393, 1.957212146782042, 2.036557095762123, 2.1026785148416156, 2.1537846681752355, 2.188150785340845, 2.204157829979094, 2.200318866481199, 2.175321369460526, 2.1280564326239757, 2.057656689250748, 1.963531334000305, 1.845391229169975, 1.7032909540872725, 1.5376351188804125, 1.3492242810646236, 1.1392419439546957, 0.90929493379723, 0.6613868520628058, 0.3979395235372252, 0.12176111522059985, -0.16396286753971015, -0.45570111368616506, -0.7496212986119501, -1.041620436211078, -1.3274026255489135, -1.6025128455294626, -1.862436510397129, -2.102645559893816, -2.318702705366399, -2.5063288687408365, -2.6614950089207503, -2.7805132144245883, -2.8601053824278098, -2.897510782729056, -2.890527838779181, -2.837623789076077, -2.7379504762060574, -2.5914387101185246, -2.3987906420636294, -2.161542804541101, -1.8820368545765445, -1.5634399992605779, -1.2096943206088613, -0.825488913901595, -0.4161885086031144, 0.012244560699519338, 0.45333803778746795, 0.9002378853598918, 1.3458027080566692, 1.78277995380338, 2.203893710417511, 2.602062729523402, 2.970468306110037, 3.302800562962789, 3.5932971525009663, 3.8369963800622076, 4.029742312463484, 4.168418792181306, 4.25091942323546, 4.2763376376286795, 4.244899853362697, 4.158093952070449, 4.0185610353816905, 3.8301565452713895, 3.5977927117789585, 3.3274384474688197, 3.025906617697932, 2.7008043722654445, 2.36026938226718, 2.0128817247364648, 1.6673661323427102, 1.3324749818597443, 1.016684015448127, 0.7280561637380908, 0.47396284833855107, 0.26094163715526, 0.09447246142926516, -0.02115175685487698, -0.08297414082304616, -0.08946492614031533, -0.04058784911525376, 0.0621732110854537, 0.21582896095400703, 0.4159421752572157, 0.6567152736979776, 0.9311405931651542, 1.231146348520473, 1.5478370261626373, 1.8716751909698492, 2.192801359984435, 2.5012191687030274, 2.7871794988073035, 3.0413288426902274, 3.255138186949601, 3.4209736273557794, 3.5325444987910233, 3.5848636480267118, 3.574681619780635, 3.500320627402907, 3.362054801570458, 3.161822284741581, 2.9035111913916265, 2.592570074259208, 2.236172005619055, 1.8427499239984186, 1.4220334007905764, 0.9845371787080522, 0.5414880209055736, 0.10429685634241873, -0.31559012099327, -0.7072005948157327, -1.0602197066344485, -1.3654388036514262, -1.6149348966483525, -1.8024140438776444, -1.9233534125288216, -1.97520174575922, -1.9574540022659213, -1.871690715194604, -1.7215574068919306, -1.5126500917531605, -1.2523779234574304, -0.9497246293506209, -0.6149884690082108, -0.25946085126511537, 0.1049360741218855, 0.46601270801261535, 0.8117290324056203, 1.13056232776751, 1.4119151098602725, 1.6464493619998526, 1.8264234643729509, 1.9459499860353835, 2.0012183579242353, 1.9906277390920808, 1.914880446765539, 1.7769438559703197, 1.5820234361299335, 1.3373306834396708, 1.0519514120771598, 0.7364386381037941, 0.40258841689134856, 0.06291778400937478, -0.2696381364592034, -0.5822789468241356, -0.8626948244763533, -1.0995656473045172, -1.2829232123427097, -1.4045327784641872, -1.4581961856648111, -1.4399790822890945, -1.3483900275055218, -1.1844347000082596, -0.9516318096049369, -0.6558841910442038, -0.3053320962970941, 0.08995934152171003, 0.5182737047539379, 0.9667173838643018, 1.4215715544827532, 1.8688636756487584, 2.2947634219319166, 2.6861406758542015, 3.030991478597092, 3.318851463894287, 3.5412414389885494, 3.691825681705351, 3.766850974077952, 3.7649958753643955, 3.6877492221619597, 3.5389737048448877, 3.3251452596891995, 3.0547255155360187, 2.7381863796682313, 2.3873152917564804, 2.015003067549676, 1.6345827180575694, 1.2594336884435766, 0.9024171506964294, 0.575405373926173, 0.28884756224399893, 0.05135091672135726, -0.1306020244706463, -0.2529150678782505, -0.31399059248834693, -0.31477516219700546, -0.2586870239421241, -0.1514360175192572, -0.0007752152181137959, 0.18388165314384797, 0.39183594108259434, 0.6116472148715517, 0.8315512885451264, 1.0401056234596526, 1.226550997470607, 1.3814790307670102, 1.497057226357675, 1.567615150723132, 1.5896918289528097, 1.562433320201038, 1.48745754556512, 1.368985245959657, 1.2135400352917136, 1.0297907156378363, 0.8281166679675601, 0.6202041668307147, 0.4185173590438051, 0.235743429824688, 0.0842249766945084, -0.024628097806293155, -0.08086669958030465, -0.07651357462803339, -0.005961249496243105, 0.13368435599822484, 0.3424105770426031, 0.6171924897084782, 0.9520341691824007, 1.3381494398306037, 1.7642129755105782, 2.2168398021709845, 2.6809802379502807, 3.1406544776514993, 3.5794115946319196, 3.9812112962837047, 4.33087253544265, 4.614949135386853, 4.822101664253391, 4.943808508793864, 4.974596084455109, 4.9124679637233895, 4.758924336478086, 4.519066986276327, 4.201342214661622, 3.8173559642062362, 3.3813132092440794, 2.909617667604363, 2.4200579244001843, 1.9312728350523645, 1.4618116419035558, 1.0295466946492033, 0.6507763200373673, 0.3396729386639759, 0.10758900365579468, -0.03735992065423812, -0.09067861765985698, -0.05167156156709353, 0.07651926115411074, 0.28704910999599975, 0.5696513355378793, 0.9111004652025428, 1.2957447141135356, 1.7062339542754665, 2.1242088531997347, 2.5311703968130175, 2.9092018941001663, 3.2418402368464116, 3.5146753441603793, 3.7161106115935727, 3.837673206732454, 3.874591437631896, 3.82568940203998, 3.693736896610122, 3.484890241046262, 3.208789412890424, 2.8776150119536656, 2.505929424063297, 2.1095118571777176, 1.7049776389169167, 1.3085974676699366, 0.9357848130665715, 0.6000897350538583, 0.31270070452978366, 0.08174963681354921, -0.08801031727163852, -0.19550653351096167, -0.243375335689322, -0.23783594598979704, -0.18839076184074563, -0.10728845736557197, -0.008945662918403806, 0.09091219375303501, 0.17600966589099326, 0.23052717464947275, 0.23993127126942068, 0.191888889947925, 0.07706084955157982, -0.11031385747733465, -0.37177522886620973, -0.7045504458659662, -1.101188883230798, -1.549991234587133, -2.0350535851266085, -2.537100738341668, -3.034030224057994, -3.501945983491127, -3.916174273367621, -4.252296790384976, -4.487461138827395, -4.601257139984598, -4.577038329775944, -4.402532797232319, -4.070868869622892, -3.5808477358827293, -2.9374292154352264, -2.1516243245541427, -1.240314344964262, -0.22577111026671937, 0.8651970509225295, 2.0020040688820937, 3.1517301673727847, 4.279968186747943, 5.352710045315238, 6.337026886116556, 7.203192795455651, 7.9249585951407795, 8.48164863932598, 8.857884912996727, 9.045351243794007, 9.041960070174689, 8.85300854985453, 8.4898872067269, 7.970471484960943, 7.317529669161008, 6.558365926268426, 5.723104329636044, 4.843770021081246, 3.952625347967443, 3.080991551698031, 2.257808305383862, 1.5085244405329792, 0.8540490216840111, 0.30998031960969025, -0.11391388473630719, -0.41395568581711667, -0.5924955210490314, -0.6575824051863456, -0.6223940268736036, -0.5043314456771768, -0.3241341646150829, -0.1045025511175659, 0.13083580262936664, 0.3587867813858094, 0.5576028627833884, 0.7085743989066919, 0.7963098424829775, 0.8101947011523122, 0.7441149511713342, 0.5974763772228301, 0.3743479913315733, 0.08393963927115071, -0.26075337173153385, -0.6429972543556687, -1.0439908813662129, -1.4433223778298991, -1.8206898223541914, -2.156591038657472, -2.433795024574393, -2.6380575661793104, -2.759085773245496, -2.791069029535031, -2.7329873687888746, -2.58877986578509, -2.366988498545907, -2.080464935537571, -1.7454684499296413, -1.3809356293232358, -1.0072328711493974, -0.6451470454711083, -0.3145339821837344, -0.03327641628624375, 0.18391482518089566, 0.3263206032597088, 0.3880129570545329, 0.3682653374670452, 0.271755762195733, 0.10848815608177308, -0.10669006715928446, -0.3546376146835671, -0.6130095132443943, -0.8571980700326043, -1.0617811862361275, -1.2017246457855664, -1.253839827909446, -1.1980550964920216, -1.0185484915921277, -0.7048327366149667, -0.2523430036872363, 0.33694543764712037, 1.0545398585275125, 1.8854955571226635, 2.8089980879226357, 3.7991513939063, 4.826017094177523, 5.856948645895642, 6.857952516272425, 7.795236454376221, 8.636705048486116, 9.353361706788293, 9.92067110194458, 10.319563363038085, 10.537321296754422, 10.568111520831641, 10.413082020660317, 10.080464039956885, 9.58475055204497, 8.946439896950029, 8.190426439025696, 7.345453627054593, 6.4420703607563645, 5.5118724172928735, 4.585482254779391, 3.691702324812453, 2.8559320123728833, 2.0994196247780055, 1.4383693826304602, 0.8835088293924076, 0.4399486639327182, 0.1072183290601148, -0.12020168657185953, -0.25236613106826145, -0.30283454386156866, -0.28781866862918065, -0.2248941949972972, -0.13203620309323036, -0.02636037120618431, 0.07672562793901065, 0.16445955325755837, 0.22728531664542295, 0.25925159013905236, 0.25818269601066274, 0.22546949587452828, 0.16582087019765582, 0.08654937074923533, -0.0030445505907713143, -0.09266085126920746, -0.17183687751669216, -0.23093487657958706, -0.2619720585196382, -0.2593653787572846, -0.22050014346584096, -0.1460777377474713, -0.04027160162541191, 0.08955824821567489, 0.23312869261936148, 0.37749667654500557, 0.5080924708579068, 0.6119881355509487, 0.6749923026115502, 0.6756233280318699, 0.6071464533279868], 'positive_zeros': ['1.07731290027739869936185854386829', '1.72584894135688654187460871474068', '2.53341398825740151331511385314199', '2.62687982149335497551463432781213', '3.33235690774399847798854618134481', '3.75051428546192640425754510788919', '4.19418652498217995583052543980109', '4.53935269492226908953650581988065', '5.18609395933032407836473225251852', '5.35753755528923034961581183437747', '5.88375961149779338106889285143957', '5.96821453965534371336900433130645', '6.74562287064492887547690602923654', '6.81706128950577403993615636275631', '7.50131396194742971695020905810862', '7.67019693490022117680034540986628', '7.83200400972601025979297758630414', '8.358895437090235206759436796859988'], 'prelabel': '4-3344e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.167395324137314, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 409839546386443881, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07731290027739869936185854387', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.72584894135688654187460871474', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.53341398825740151331511385314', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 712.995438776321, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 11182336, 'conductor_radical': 418, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, -1, 0, -2, 0, 2, 0, -7, 0, 1, 0, 2, 0, 2, 0, 1, 0, 2, 0, -6, 0, 2, 0, -15, 0, 5, 0, -2, 0, 1, 0, 16, 0, 7, 0, -11, 0, 1, 0, 2, 0, 8, 0, -10, 0, -2, 0, 6, 0, -2, 0, -2, 0, 8, 0, -4, 0, 2, 0, 7, 0, -7, 0, -2, 0, 15, 0, -26, 0, 6, 0, -2, 0, 2, 0, -2, 0, -11, 0, -2, 0, 15, 0, 6, 0, 7, 0, -5, 0, -2, 0, 0, 0, -4, 0], 'euler11': [1, -2, 1, 0, 0], 'euler13': [1, 7, 35, 91, 169], 'euler17': [1, -2, 22, -34, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -2, 34, -46, 529], 'euler29': [1, 15, 111, 435, 841], 'euler3': [1, 1, 3, 3, 9], 'euler31': [1, -5, 39, -155, 961], 'euler37': [1, -16, 138, -592, 1369], 'euler41': [1, 11, 109, 451, 1681], 'euler43': [1, -1, 83, -43, 1849], 'euler47': [1, -8, 58, -376, 2209], 'euler5': [1, 1, 7, 5, 25], 'euler53': [1, -6, 102, -318, 2809], 'euler59': [1, -8, 134, -472, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 7, 65, 469, 4489], 'euler7': [1, 1, 11, 7, 49], 'euler71': [1, -15, 169, -1065, 5041], 'euler73': [1, 26, 302, 1898, 5329], 'euler79': [1, -2, 42, -158, 6241], 'euler83': [1, 11, 167, 913, 6889], 'euler89': [1, -6, 70, -534, 7921], 'euler97': [1, 0, -14, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 1, 3, 3, 9], [1, 1, 7, 5, 25], [1, 1, 11, 7, 49], [1, -2, 1, 0, 0], [1, 7, 35, 91, 169], [1, -2, 22, -34, 289], [1, -2, 1, 0, 0], [1, -2, 34, -46, 529], [1, 15, 111, 435, 841], [1, -5, 39, -155, 961], [1, -16, 138, -592, 1369], [1, 11, 109, 451, 1681], [1, -1, 83, -43, 1849], [1, -8, 58, -376, 2209], [1, -6, 102, -318, 2809], [1, -8, 134, -472, 3481], [1, 4, 126, 244, 3721], [1, 7, 65, 469, 4489], [1, -15, 169, -1065, 5041], [1, 26, 302, 1898, 5329], [1, -2, 42, -158, 6241], [1, 11, 167, 913, 6889], [1, -6, 70, -534, 7921], [1, 0, -14, 0, 9409]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3344/2/a/j'], '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': '4-3344e2-1.1-c1e2-0-3', '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': 2, 'prelabel': '4-3344e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.167395324137314, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 409839546386443881, 'z1': {'__RealLiteral__': 0, 'data': '1.07731290027739869936185854387', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1365656344670259106140267810004,2187773446414311509898873905850', 'Lhash_array': ['1365656344670259106140267810004', '2187773446414311509898873905850'], 'label': '4-3344e2-1.1-c1e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3344/2/a/j'}