-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2476031538080323972157325649984', 'a10': [2.5303153229737565, 3.711290945813787], 'a2': [2.218668058452287, 0.8707630464222846], 'a3': [0.0, 0.0], 'a4': [2.6981559269221704, 2.503522839613619], 'a5': [1.5571249164009495, 1.0616297922419045], 'a6': [0.0, 0.0], 'a7': [0.0033335330735632177, -2.645749211009473], 'a8': [1.7380782212108112, 3.6091566152606367], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.0033335330735632177, 2.645749211009473]]]], 'bad_primes': [3, 7], 'central_character': '441.395', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '2835876854904024812636163607359', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.218668058452287, -0.8707630464222846], [1.4661037436596527, 1.3603454755418387]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.5571249164009495, -1.0616297922419045], [1.826705121831975, 4.6543687432210215]], [[1.0, 0], [-0.0033335330735632177, 2.645749211009473]], [[1.0, 0], [-0.09726572412565926, -0.6453159148618479], [-10.511300863647548, 3.2423069185199465]], [[1.0, 0], [-0.5318502412887903, 0.42413641429849586], [2.8927721414320873, -12.674062858363706]], [[1.0, 0], [5.580774034897482, 1.7214408091602798], [14.046059163371913, 9.576440987081574]], [[1.0, 0], [5.5866493601004175, -3.2254535119220265], [9.5, -16.454482671904334]], [[1.0, 0], [-2.208351391587261, -7.1592993732452035], [-19.00349180926788, 12.956361335463306]], [[1.0, 0], [-4.23402463424166, 0.9663884931728003], [26.128097169170154, -12.582628434409186]], [[1.0, 0], [2.432400579249363, 1.4043471292066214], [15.5, 26.846787517317598]], [[1.0, 0], [2.4294717368259082, -2.2542203438470416], [2.765013462697697, -36.89654049570367]], [[1.0, 0], [-3.4859240299516503, 1.67873253591597], [25.563081876208074, -32.05509078118922]], [[1.0, 0], [2.039307111526809, 0.9820785448650055], [26.81006147992554, 33.61875374612528]], [[1.0, 0], [-1.2663881399717891, 3.226704356945833], [-34.45343797600184, -31.96811867523321]], [[1.0, 0], [-6.960461797821682, 7.501593736930473], [-3.9606949600804855, -52.85180125060255]], [[1.0, 0], [1.5098104242068304, -1.0293713176718786], [21.555120437617305, -54.92155117000805]], [[1.0, 0], [6.856944098123982, 7.390028189949562], [-4.558535708771879, 60.82943162805199]], [[1.0, 0], [5.802623211635821, -10.050438219731737], [-33.5, -58.023702053557386]], [[1.0, 0], [-15.220010707115796, -3.473868124047392], [63.96878962107176, 30.805745477346626]], [[1.0, 0], [-8.216015628397574, 3.224548517197858], [53.51278664357732, -49.65260985727711]], [[1.0, 0], [-4.604800101026124, -7.975747733675546], [-39.5, 68.41600689897065]], [[1.0, 0], [5.98517721860355, -7.505174846011229], [-18.469237518374097, -80.91901671109136]], [[1.0, 0], [4.816476576195581, 0.7259670358792144], [85.04597971496652, 26.233210522570474]], [[1.0, 0], [0, 8.080548213419947], [-97.0, 0]], [[1.0, 0], [1.3905848307854052, -18.556064993523137], [-99.87191344873798, -15.053268883793619]], [[1.0, 0], [-5.510610591130668, 8.082581252653199], [-37.63012550973869, -95.87999611035303]], [[1.0, 0], [1.4711307356793515, -9.76031469574863], [-102.24629021911706, -31.53880366196675]], [[1.0, 0], [6.357673999033655, -0.9582651706385866], [104.15743583068934, -32.12831401078856]], [[1.0, 0], [10.020491986883783, 7.991075703049184], [25.144865537063527, 110.16685407654607]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-21e2-147.101-c1-0-14', '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/441/2/bg/a/395/17', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.4126381017844616, 3.327100526550771, 3.257934579521628, 3.195528005831815, 3.127614610506857, 3.0411374882071662, 2.9239448504139047, 2.766170744015644, 2.5612957089468082, 2.306926548372452, 2.0053129157468508, 1.6635790825697496, 1.2936216042137203, 0.9116183121054868, 0.5371113975075543, 0.1916634170169759, -0.10286563556369892, -0.3263159379194208, -0.4623403627666288, -0.5004253739801248, -0.43758405544869444, -0.2794800517755455, -0.04076671582784644, 0.25551552541526945, 0.5795501052423058, 0.8973141457324127, 1.1739276636715221, 1.3774739515285728, 1.4828741802901133, 1.4753296487755132, 1.3528316915463061, 1.1272939690428072, 0.8239885803006086, 0.47915983884576385, 0.13593014239206053, -0.16112687925145633, -0.37212592346020473, -0.46791324992488204, -0.4351093601656199, -0.27927517804526203, -0.025492643375972856, 0.28404844415745506, 0.5954571980110038, 0.8510745206217082, 0.9990036311007217, 1.002930093033926, 0.850697880410741, 0.5600961797787918, 0.18054617527367814, -0.21014482213552932, -0.514116409325126, -0.626234706797799, -0.4498802680833244, 0.08636354678384764, 1.0136436557220487, 2.3119707868546016, 3.905777557271087, 5.667365774143067, 7.428620425616772, 9.000094609320458, 10.195300890900432, 10.856992411663052, 10.88158090524641, 10.237769061405446, 8.976040838584833, 7.226822617146205, 5.186760235683568, 3.0944176942595334, 1.198496374696414, -0.2769125566047049, -1.1647679034177727, -1.380006449166549, -0.9327072081517208, 0.07303152148064103, 1.4547715237201644, 2.9798232602256376, 4.401435561131754, 5.497271331537705, 6.10380501411723, 6.140831614535323, 5.621883623146032, 4.648761202587294, 3.391179009157181, 2.055212822018174, 0.846283070899295, -0.06656869218831366, -0.5785951002160833, -0.6644218816864624, -0.37773528408093415, 0.16398427399647542, 0.8063186326770903, 1.390727262243959, 1.7865560357062924, 1.915725922820059, 1.7651966135592956, 1.3849466977244047, 0.8723473103281609, 0.34675958617230457, -0.07969172439648288, -0.32840997111241566, -0.3716397366289246, -0.23686102369178855, 0.002635563166806457, 0.24859808858005122, 0.40490857829789956, 0.40414609963930076, 0.22684333678133412, -0.09167499455888911, -0.4690028062872404, -0.7964190865966349, -0.9678129841116689, -0.9095408680902664, -0.6033694059887049, -0.09599898681153597, 0.5082600034401977, 1.0709370128638243, 1.45401433023456, 1.5574698605145658, 1.3501112716140562, 0.8850128671629917, 0.2941052753225786, -0.23864815363233008, -0.520628726085774, -0.4009876229906988, 0.18402860985083935, 1.1828187062730542, 2.426018931245956, 3.6531066027337573, 4.564306125430625, 4.887575964799136, 4.445924505958007, 3.2090096818777942, 1.3154696912922303, -0.9416316450256565, -3.165687225575527, -4.934615998513066, -5.890028163719653, -5.817843452794185, -4.701608555057925, -2.735111272283438, -0.28964603344231665, 2.158484141820227, 4.125316315218066, 5.220346897629117, 5.22891662432966, 4.157163765359484, 2.229125207809197, -0.16355873471773516, -2.547957018472559, -4.472452802046111, -5.602190828346013, -5.785760961571591, -5.07851072979786, -3.718342322173913, -2.0612089128615247, -0.4929770726365836, 0.6604664797570329, 1.2032764212054003, 1.1039447260397184, 0.48740086480176226, -0.41065486483661373, -1.3133693644013225, -1.9769903317565538, -2.2501866621849786, -2.1038071644365903, -1.6251323334254553, -0.9806523356245058, -0.3599070112255398, 0.08237662729464168, 0.2689532131090501, 0.21581578174498703, 0.017759807420272992, -0.19033435632517565, -0.2833560959294545, -0.19066807183532772, 0.0787608741152004, 0.4389015598017505, 0.7561520430899501, 0.896348149871833, 0.7740470533795701, 0.3877182960247403, -0.1714673993031912, -0.7414621829428196, -1.1362611916440948, -1.2040464651227751, -0.8783818800597645, -0.20556596696399954, 0.6620415528496104, 1.5066177209239588, 2.1084910668175487, 2.3139107074209866, 2.085659829781111, 1.5193435955991708, 0.8179962732234364, 0.23040980779289416, -0.029521572056573395, 0.14211311442625885, 0.6943418163251769, 1.4235766627567439, 2.026539407046594, 2.1917491990092364, 1.7044343151197106, 0.5333955986397679, -1.1288834542778472, -2.8899251603305833, -4.244135785133422, -4.703487816196233, -3.93821795488147, -1.8882383820770043, 1.1885260173597765, 4.749105075580564, 8.076360943618843, 10.442612309030858, 11.285148215728201, 10.347863307207696, 7.750882458024503, 3.968439272922107, -0.28049276364827436, -4.200953119075309, -7.106355215987407, -8.57076105958516, -8.510598809537237, -7.1771017221914, -5.065371143196751, -2.7684215603041307, -0.818479077281446, 0.4406501621315589, 0.9173073706117366, 0.7589513209771186, 0.2723716988534578, -0.1939822165146979, -0.36729400425840436, -0.13161150011027464, 0.4493384745662325, 1.1705382791590058, 1.7685621712234567, 2.018946233381487, 1.8149317138323677, 1.2021968386823607, 0.35990035467150766, -0.4633245297491931, -1.0349656846645452, -1.2158518723205904, -1.0028151545709392, -0.5231891139977017, 0.015527940550155946, 0.4020680196129297, 0.49639227136391767, 0.27685112664765776, -0.1566705400658974, -0.6239218998304246, -0.9341773746443225, -0.9589797661658053, -0.6808754412386198, -0.2000104677212738, 0.30412129355592293, 0.6418389448446145], 'positive_zeros': ['1.95324448048581853185673426346609', '2.76845210527343777903772239801819', '4.30376230873650264365394355560523', '5.01090145910447670146842791551705', '6.05643892068602598233346071397031', '6.60971805222273629035904245974384', '8.597684197346431220311796992575072', '9.117504430572554658806492461056355', '10.61378159793145420540994189214441', '11.09103454159140914708759085196811'], 'prelabel': '2-21e2-147.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': -0.28354653636874577, 'root_number': '0.6287997198200307 - 0.7775673040671469*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.141773268184', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.95324448048581853185673426347', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.76845210527343777903772239802', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.30376230873650264365394355561', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'bad_primes': [3, 7], 'central_character': '147.101', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/2/bg/a/395/17'], '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': '2-21e2-147.101-c1-0-14', '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': '2-21e2-147.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': -0.14177326818437289, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.95324448048581853185673426347', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2476031538080323972157325649984', 'Lhash_array': ['2476031538080323972157325649984'], 'label': '2-21e2-147.101-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/bg/a/395/17'}