-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '469195940982757230835879645772', 'a10': [0.3604154966650801, -0.62425795205909], 'a2': [-0.573576436351046, 0.8191520442889918], 'a3': [0.0, 0.0], 'a4': [-0.3420201433256687, -0.9396926207859084], 'a5': [-0.718088013775712, 0.06282456061922234], 'a6': [0.0, 0.0], 'a7': [-2.0708090204484066, -1.7376150852968426], 'a8': [0.9659258262890683, 0.25881904510252074], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.318036774617276, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.573576436351046, -0.8191520442889918]]], [3, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [-6.022230387547972, -0.8560030136008895]]]], 'bad_primes': [2, 3, 37], 'central_character': '666.17', 'coefficient_field': 'CDF', 'conductor': 666, 'conductor_radical': 222, 'conjugate': '2019326789950649672833087673925', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.573576436351046, -0.8191520442889918]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.718088013775712, -0.06282456061922234], [4.924038765061041, -0.8682408883346517]], [[1.0, 0], [2.0708090204484066, 1.7376150852968426], [1.2155372436685123, 6.893654271085456]], [[1.0, 0], [-2.1466612186708325, -3.718126297375606], [-5.5, 9.526279441628825]], [[1.0, 0], [-0.03509979468185405, -0.016367303059816637], [8.35623892592501, 9.958577760546714]], [[1.0, 0], [1.2622718818580525, -0.5886070451841315], [10.927389364671168, -13.022755533022627]], [[1.0, 0], [1.1599872419862276, -0.8122318110658474], [6.498382723187706, -17.854159794932258]], [[1.0, 0], [-1.2179277202766332, -4.545368132018931], [-19.91858428704209, 11.5]], [[1.0, 0], [2.185684618002496, -8.15708604370709], [-25.11473670974872, -14.5]], [[1.0, 0], [3.1999878705379294, -3.1999878705379294], [0, -31.0]], [[1.0, 0], [-6.022230387547972, -0.8560030136008895]], [[1.0, 0], [8.428831037287553, -3.0678436072317883], [31.4078221678781, -26.354291997148113]], [[1.0, 0], [0.6735461689479103, 0.6735461689479103], [0, 43.0]], [[1.0, 0], [-2.044395161687258, -1.1803320969301068], [23.5, 40.703193977868615]], [[1.0, 0], [0.3854519309938686, 0.4593637235343184], [-9.203353416347309, 52.194810909647025]], [[1.0, 0], [-0.273821989227548, 3.1297996585170273], [-58.10365742772028, -10.24524248234889]], [[1.0, 0], [4.736925221572723, -10.15836891959898], [-39.2100441908789, -46.728711030257664]], [[1.0, 0], [-5.481296121858043, 6.532354345297033], [-11.634427903684333, -65.98211945181794]], [[1.0, 0], [-0.7596031533645764, -0.13393853056940483], [66.71817607579949, 24.28343017612248]], [[1.0, 0], [0, -9.366281417641877], [-73.0, 0]], [[1.0, 0], [0.12402409150063864, 1.4176018526547582], [-77.79981248796443, 13.718206035687498]], [[1.0, 0], [2.8436973173189086, -7.812994167097386], [-63.581688778875176, -53.35137160398276]], [[1.0, 0], [10.67993226776907, 0.9343730006545067], [87.64789001808651, 15.4546878123568]], [[1.0, 0], [2.871613064109338, -0.7694464015027589], [84.00446416709055, -48.5]], [[1.0, 0], [3.3566611710306526, -5.813907692018735], [-50.5, -87.4685657822283]], [[1.0, 0], [-9.589368772967466, -2.569463618640859], [89.20061658979718, 51.5]], [[1.0, 0], [3.1851740739141206, 8.751193845111334], [-81.96675541373065, 68.77827423645971]], [[1.0, 0], [-5.932070519481475, 8.471874688251129], [-37.28019562249789, -102.42649566566402]], [[1.0, 0], [-1.8236472124955583, 2.604438131526345], [-38.64827619580057, -106.18526614880764]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-666-111.17-c1-0-1', '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/666/2/bs/a/17/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6027751854484092, 0.41096123792643446, 0.20812906048863308, -0.008736059635311632, -0.24101242707222242, -0.48711865710966745, -0.7417297476815651, -0.995557653351482, -1.2356612486809169, -1.4462444713640379, -1.6099042841682265, -1.7092747015946814, -1.7289744196649814, -1.657711229247317, -1.4903388443439636, -1.2296144108630613, -0.8873803802625596, -0.4849032803724344, -0.05215153116554426, 0.37411264011450546, 0.753419596602643, 1.045687959480976, 1.2159878432221922, 1.239469639938252, 1.1058353055730399, 0.822674106635352, 0.4170179743470819, -0.06539411191345097, -0.5634183920535212, -1.0063320021022986, -1.3217692246202606, -1.4449831966826556, -1.3283305501776612, -0.9496733037787038, -0.31835503001053284, 0.5224294202581853, 1.497682713144518, 2.5073353950195973, 3.4372515637947387, 4.17340376567559, 4.617489642408915, 4.701832350948112, 4.401264218285267, 3.7399008566215923, 2.791282602456847, 1.6712428627131364, 0.5239495382053506, -0.4973025830702107, -1.2519804305967628, -1.6336506212676623, -1.5873477267845544, -1.1199251994406987, -0.30126404869849804, 0.7444188839711241, 1.856309303944709, 2.8613337100478424, 3.6013636160248965, 3.9588293560835623, 3.8763075747494047, 3.3664658789681385, 2.510276874921316, 1.4434201195452867, 0.33293185118558466, -0.651957760494468, -1.3696188694084845, -1.730945477991976, -1.7146257565045955, -1.369660398358166, -0.8044021636085807, -0.1640158038978383, 0.39937771520430854, 0.7580015929382056, 0.8348192965972118, 0.6194891828861676, 0.17034034451210797, -0.39833906429621474, -0.9413115670332854, -1.3145920298831988, -1.408007595621682, -1.1709714701260885, -0.6255728539420582, 0.13630732280213706, 0.9716898936993604, 1.7172657575208057, 2.225623700970465, 2.398822781913126, 2.2114917449951204, 1.7177573552665244, 1.0398474836535245, 0.3404290670977281, -0.21533087211178636, -0.4992967888948773, -0.4520491205105824, -0.09875506823321642, 0.45527065328385635, 1.0490709150349682, 1.5054420996818079, 1.6761171795983474, 1.4817269326545606, 0.9362361318614035, 0.14884990736197212, -0.6983842064217778, -1.3930717322717894, -1.7455671899668552, -1.6399351816241876, -1.0697892777413731, -0.14900184831615443, 0.9070571619233514, 1.8270007975989184, 2.3460421382542544, 2.2713242765500974, 1.53401928018816, 0.21462302434127686, -1.4662432140695085, -3.1911030108987295, -4.614128619617187, -5.439416592220558, -5.490496659682671, -4.75394546115263, -3.38571786497916, -1.6776141209636786, 0.008934443193201063, 1.3262952842713243, 2.0211715658038156, 1.9924418608139103, 1.3118272106805537, 0.2020432483950541, -1.0222169048419962, -2.0356064657084474, -2.585048870114102, -2.5529910548715145, -1.98468922589148, -1.0725380831087123, -0.1017097519043029, 0.6283914156836359, 0.8858825674554195, 0.5694849649445626, -0.26396166713815655, -1.414858418640246, -2.59474731728244, -3.5039058047069522, -3.9113122904958644, -3.7150561074309416, -2.966758025206956, -1.8536693953160817, -0.6440177564856924, 0.3884979243684053, 1.039351016961942, 1.2256811813845068, 1.0019298741829499, 0.534782310511883, 0.04560009889127007, -0.2618397057677172, -0.2661246208491305, 0.03438835255649012, 0.523112070461005, 1.0053360119830623, 1.2745259297728242, 1.1840579381814527, 0.7015105229109025, -0.07241240744607616, -0.9275849197411916, -1.60480734337466, -1.8750492838776516, -1.6132516998868773, -0.843175325805127, 0.2619900963543148, 1.4252226325000366, 2.3450140184062422, 2.784958196199703, 2.645993878091768, 1.998144417462166, 1.0604804568012398, 0.1339173194818259, -0.4934926786706161, -0.639677409893194, -0.2903552775059467, 0.391427483809797, 1.1132525846016874, 1.5459361412774326, 1.4331704272924464, 0.6839043705881678, -0.5829720135056812, -2.058440136502724, -3.3249384673425633, -3.977476130405245, -3.7486404436616456, -2.599049356672447, -0.7438484788313767, 1.3956204829868937, 3.3032897077627164, 4.511576138127118, 4.734305539632187, 3.949339212773, 2.4052717261273227, 0.5491459199658106, -1.103924852083028, -2.120443924729294, -2.2725730989459145, -1.5992196566493615, -0.38610511069050224, 0.9283073234318412, 1.8912941978599807, 2.175463819142148, 1.6762031381042417, 0.537391818550365, -0.9012509305634313, -2.216921740819582, -3.0394716142619425, -3.1662553584923416, -2.6197020797561184, -1.630428321171085, -0.5533076535329337, 0.25423123098111367, 0.5504841689730735, 0.28504293680119974, -0.3926182033487165, -1.1928271065609457, -1.791788814031466, -1.9466850997224914, -1.5798715769836493, -0.803435401682355, 0.12357773398792574, 0.889360553257607, 1.2411173968949114, 1.0745559175213206, 0.4692964028984441, -0.34226578331876856, -1.061277857031669, -1.4326728147282743, -1.339270631961091, -0.8452081138398138, -0.1722531241640342, 0.3831376556265471, 0.562309971247298, 0.24530777851512908, -0.4976308775530279, -1.424542756536889, -2.2055290970075374, -2.543013806274927, -2.2852579370730752, -1.490927376298814, -0.4189883053218606, 0.5553673071069493, 1.0709924934857835, 0.9116005543120401, 0.08960413022224482, -1.1491782504175705, -2.4045028535365844, -3.2586944472028865, -3.4240150784394694, -2.847338352370221, -1.7327140783143729, -0.47086815453963177, 0.5018494793228149, 0.866034752410397, 0.544566193747623], 'positive_zeros': ['0.37013033472968230052093994491596', '2.26496537525727920077386230808527', '3.35865717576444763178224911109431', '4.30055058057090865988746054157035', '5.81106868250249339657426626622061', '6.53806300646348558735488404984717', '7.78957392239352592706749100533085', '8.658394967169801662284209003461525', '9.288835530146546485014084467335332', '10.10417864712527261371225338492002'], 'prelabel': '2-666-111.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': -0.794473851265982, 'root_number': '-0.798691104871362 - 0.6017412392377334*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.397236925633', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.37013033472968230052093994492', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26496537525727920077386230809', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35865717576444763178224911109', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.318036774617276, 'bad_primes': [2, 3, 37], 'central_character': '111.17', 'conductor': 666, 'conductor_radical': 222, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/666/2/bs/a/17/2'], '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': '2-666-111.17-c1-0-1', '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': '2-666-111.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': -0.397236925632991, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37013033472968230052093994492', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '469195940982757230835879645772', 'Lhash_array': ['469195940982757230835879645772'], 'label': '2-666-111.17-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/666/2/bs/a/17/2'}