-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1062592528820671694994120227214', 'a10': [-1.8986644193336926, 0.0], 'a2': [-1.6809121646650085, 0.0], 'a3': [0.0, 0.0], 'a4': [0.8254657053188046, 0.0], 'a5': [1.1295441006651767, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.9089226555565926, 0.0], 'a8': [1.974288983745857, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.1', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1062592528820671694994120227214', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.6809121646650085, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.1295441006651767, 0], [5.0, 0]], [[1.0, 0], [3.9089226555565926, 0], [7.0, 0]], [[1.0, 0], [-1.8704558993348233, 0], [11.0, 0]], [[1.0, 0], [0.7325979468515602, 0], [13.0, 0]], [[1.0, 0], [1.8896434777947169, 0], [17.0, 0]], [[1.0, 0], [-2.74285618307446, 0], [19.0, 0]], [[1.0, 0], [-5.827699459385265, 0], [23.0, 0]], [[1.0, 0], [-5.319935263328435, 0], [29.0, 0]], [[1.0, 0], [-1.3406007671633275, 0], [31.0, 0]], [[1.0, 0], [-3.3961129470805123, 0], [37.0, 0]], [[1.0, 0], [1.796332379284849, 0], [41.0, 0]], [[1.0, 0], [-5.030152904403683, 0], [43.0, 0]], [[1.0, 0], [1.7086773446212542, 0], [47.0, 0]], [[1.0, 0], [2.844942653440345, 0], [53.0, 0]], [[1.0, 0], [-11.260045408621085, 0], [59.0, 0]], [[1.0, 0], [-5.2308939025918235, 0], [61.0, 0]], [[1.0, 0], [1.8890279873758096, 0], [67.0, 0]], [[1.0, 0], [-12.183867724869009, 0], [71.0, 0]], [[1.0, 0], [-9.887679147435371, 0], [73.0, 0]], [[1.0, 0], [-12.35287504113849, 0], [79.0, 0]], [[1.0, 0], [-11.683164098726776, 0], [83.0, 0]], [[1.0, 0], [-5.728732297029124, 0], [89.0, 0]], [[1.0, 0], [0.3433783583012457, 0], [97.0, 0]], [[1.0, 0], [-17.402253649951906, 0], [101.0, 0]], [[1.0, 0], [15.813002508045484, 0], [103.0, 0]], [[1.0, 0], [-16.52982155410854, 0], [107.0, 0]], [[1.0, 0], [4.718439893591352, 0], [109.0, 0]], [[1.0, 0], [19.94481452999199, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-3e6-1.1-c1-0-3', '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/729/2/a/d/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6961990031710072, 0.6839052386121311, 0.6457136512579226, 0.5780735574937645, 0.47622625855062123, 0.3356309328649316, 0.1535056890762904, -0.06973126591267184, -0.32926994351213235, -0.6150863597748978, -0.9116071486562446, -1.1979775431634077, -1.4490301488281796, -1.637004898880861, -1.7339948777027745, -1.7149941309421408, -1.561313061786841, -1.2640195498601012, -0.8269773362329809, -0.2690061937395545, 0.3753020738270739, 1.0564994846287583, 1.7131659082883708, 2.2767792809894516, 2.678322782490664, 2.8560933750390967, 2.763909871876896, 2.3787170744990442, 1.7064889278895956, 0.785383121399215, -0.3146887876573908, -1.4965410164723816, -2.644207934696817, -3.6348436330889458, -4.352845665396024, -4.704543426236111, -4.631495681887907, -4.12040246841331, -3.2078972101949135, -1.9790456123634284, -0.5591887581577758, 0.9002700257571946, 2.240559644274436, 3.3163123381027906, 4.015476728488866, 4.275330014884701, 4.091924032541693, 3.52114940822629, 2.6708255575668924, 1.6846467121997777, 0.7202064705415292, -0.07556157821198134, -0.5895730826068074, -0.7604912078129958, -0.5881415992750577, -0.13259527737491003, 0.49717301613250137, 1.1632723788777453, 1.724108757891076, 2.0603176320291916, 2.096625718995704, 1.8154713386461376, 1.2596709300333122, 0.5234741154399712, -0.26637684044986054, -0.9759245737861187, -1.4905724483345646, -1.7375247948364685, -1.6993832710688963, -1.415943173711357, -0.9736909255875309, -0.4851711339656784, -0.06269468603846375, 0.20773260591752524, 0.286234309845373, 0.18783440399154688, -0.022241144338269136, -0.24606783677387953, -0.3795679273241183, -0.34194192486516917, -0.10075672002548175, 0.3139478700361113, 0.810936600786788, 1.255376364692383, 1.4997324622211041, 1.421409724958375, 0.9583638928355004, 0.13364197151295534, -0.938279623670809, -2.066688991180598, -3.019768579725716, -3.5731155011258102, -3.56133038267381, -2.9207564889059823, -1.7125926951615948, -0.1194205465059249, 1.5860412487759072, 3.0946605193947234, 4.126123917156488, 4.491266496098212, 4.136864315789411, 3.1615201133339994, 1.7974590936927117, 0.36084557123206046, -0.8191615504467203, -1.4768338329832078, -1.473947591572194, -0.8358259261275703, 0.25029060017063565, 1.4755339169848238, 2.480087328696741, 2.938355731481712, 2.63868494337762, 1.5383665085730662, -0.2199221562259835, -2.3351170029655455, -4.412655437145917, -6.052380578808548, -6.938730323364063, -6.911640897822983, -6.001100027222714, -4.4171030812841945, -2.4977342139234873, -0.6284497511494032, 0.8472764654321823, 1.703830784112926, 1.8774588823069454, 1.4684236927134922, 0.7023186151155938, -0.1378870973622823, -0.7901135993400716, -1.080584716044653, -0.9627780116676019, -0.5185989493684047, 0.07679829545199976, 0.6149627261355325, 0.92056780103836, 0.9046080204095516, 0.588997354616097, 0.09596083382858418, -0.39374988441988, -0.7004126188767794, -0.703947495276949, -0.3832424614508663, 0.17616524234848302, 0.8085686896898894, 1.3205252535801952, 1.5527306905797462, 1.4315600338265364, 0.9934285625903772, 0.3734826388286524, -0.23856013750233138, -0.6618275709114989, -0.7865819309313319, -0.6145175537448793, -0.2624616505496344, 0.07382228888679335, 0.18605400074333328, -0.07016566845345443, -0.713865421894599, -1.6138966608396037, -2.512249272321877, -3.0922314372552586, -3.073594305454132, -2.3067081420801867, -0.8360512823693507, 1.0893560304679788, 3.0660957258581094, 4.636458480468624, 5.4119122404111515, 5.184577860919125, 3.9929390625244854, 2.1199955186960318, 0.02129636436535885, -1.7987806084970728, -2.927845424644226, -3.1622829583809597, -2.5646359048068903, -1.4429036646345792, -0.2560237319548336, 0.5277919327854408, 0.5781964923744314, -0.18911280384257956, -1.576943266386013, -3.156436929639701, -4.389201455877858, -4.78661826160411, -4.0593030517846485, -2.2118702799940313, 0.4460298641899787, 3.3766346113766246, 5.95690767100192, 7.64554333544724, 8.12533082703115, 7.379860235493884, 5.683748578282658, 3.5118630527565613, 1.3972069293594414, -0.2182995873649174, -1.09538364310841, -1.2399972128405108, -0.8684170714188986, -0.3111221747290424, 0.10966153520829279, 0.187229637488478, -0.11180871473473229, -0.6551841473541486, -1.2110448703424321, -1.545665229660092, -1.5161047588279397, -1.124325450892681, -0.5141735848480498, 0.08617959618431931, 0.45384556129684345, 0.4588526155124771, 0.11671232658679363, -0.4141520034388384, -0.8897684249057697, -1.0720115118244669, -0.8203197132040839, -0.1493694432792379, 0.7696028086484815, 1.6655949655073456, 2.262902189923746, 2.379890273186008, 1.9947353626147897, 1.2528655364661467, 0.4121043714150985, -0.2550634342356093, -0.565794698556107, -0.49765883316665827, -0.1970312363898875, 0.08102141642632826, 0.08132714734591516, -0.3343241345374041, -1.107541987075934, -1.9759245001114636, -2.547698046019079, -2.4378543155417707, -1.420377150031365, 0.45867804967193265, 2.852757506045266, 5.189579267713667, 6.832160177030825, 7.277396982886438, 6.327006972362454, 4.171082951874384, 1.3510940717737334, -1.391466712143545, -3.3356274149631697, -4.000537608770146, -3.2921584891005886, -1.527751662638747, 0.6711063915919546, 2.582304351846626, 3.616296034949028, 3.5009174402630956], 'positive_zeros': ['0.838237704166559149232616522113444', '2.42874296961364628202601194986679', '3.71568342102786692878602136319618', '5.04755137468847749112526420927478', '6.36122113288789111001909320414249', '6.90343064278603609270608316095033', '7.957456576376682828174837836455914', '9.022859919991342779309901007511129', '9.488115242187539971656109339633441', '10.03475684192351090769091152165240'], 'prelabel': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.838237704166559149232616522113', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.42874296961364628202601194987', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.71568342102786692878602136320', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/a/d/1/1'], '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': '2-3e6-1.1-c1-0-3', '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': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.838237704166559149232616522113', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1062592528820671694994120227214', 'Lhash_array': ['1062592528820671694994120227214'], 'label': '2-3e6-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/a/d/1/1'}