-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2588807927438954518879941899629', 'a10': [4.002013946439463, -0.49741399842012357], 'a2': [1.302608882398979, 0.5506451665957698], 'a3': [-0.618109205827941, 1.6180052563792098], 'a4': [1.393579801009434, 1.4345505701154304], 'a5': [2.4695801500447594, -1.4258127644136982], 'a6': [-1.6961013157558158, 1.7672691721102902], 'a7': [-1.0203167421013688, -2.4410968325299285], 'a8': [1.0253610894554226, 2.6360262965742183], 'a9': [-2.235882019341504, -2.0002078880919747], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.302608882398979, -0.5506451665957698]]], [3, [[1.0, 0], [0.618109205827941, -1.6180052563792098]]], [7, [[1.0, 0], [1.0203167421013688, 2.4410968325299285]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': '3467539589354833690621909085092', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.302608882398979, -0.5506451665957698]], [[1.0, 0], [0.618109205827941, -1.6180052563792098]], [[1.0, 0], [-2.4695801500447594, 1.4258127644136982], [2.5, -4.330127018922194]], [[1.0, 0], [1.0203167421013688, 2.4410968325299285]], [[1.0, 0], [2.4262067903613596, -4.2023134305744865], [-5.5, -9.526279441628825]], [[1.0, 0], [2.7522113174524434, 0], [13.0, 0]], [[1.0, 0], [-1.7536630319108375, 3.037433470624852], [-8.5, -14.722431864335457]], [[1.0, 0], [3.1449267670134766, 5.447172946550671], [-9.5, 16.454482671904334]], [[1.0, 0], [-3.1586501126643323, 1.823647492822594], [11.5, -19.91858428704209]], [[1.0, 0], [-3.904273887244244, 0], [29.0, 0]], [[1.0, 0], [0.8580512461615736, 0.49539611794987837], [15.5, 26.846787517317598]], [[1.0, 0], [1.0651586051250779, -0.61496960739861], [18.5, -32.04293994002423]], [[1.0, 0], [2.106593798451668, 0], [41.0, 0]], [[1.0, 0], [0, -5.117683539903356], [-43.0, 0]], [[1.0, 0], [-5.612679277260173, -9.721445674803585], [-23.5, 40.703193977868615]], [[1.0, 0], [1.0041664096225407, -1.7392672407202614], [-26.5, -45.89934640057525]], [[1.0, 0], [0.8909962476687426, 0.5144169234384951], [29.5, 51.09549882328188]], [[1.0, 0], [1.2434746445574156, 2.1537612622970945], [-30.5, 52.827549630850754]], [[1.0, 0], [5.027772063026167, 2.9027855540122376], [33.5, 58.023702053557386]], [[1.0, 0], [0, 9.752770814403927], [-71.0, 0]], [[1.0, 0], [-0.2910187689225898, -0.16801976457669074], [36.5, 63.21985447626402]], [[1.0, 0], [2.8008190642626904, 4.8511609221105], [-39.5, 68.41600689897065]], [[1.0, 0], [0, -0.1381146039365881], [-83.0, 0]], [[1.0, 0], [-0.5809934812884153, -1.0063102284578531], [-44.5, 77.07626093681505]], [[1.0, 0], [0, -11.0953197110982], [-97.0, 0]], [[1.0, 0], [6.162559745333734, 3.557955527865583], [50.5, 87.4685657822283]], [[1.0, 0], [-1.5051879203264946, 0.8690206509814746], [51.5, -89.20061658979718]], [[1.0, 0], [-0.5320281330877119, -0.9214997575639335], [-53.5, 92.66471820493493]], [[1.0, 0], [-7.858740909850912, -4.537246179793948], [54.5, 94.39676901250381]], [[1.0, 0], [0, -16.812577504451276], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-168-168.101-c1-0-16', '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/168/2/ba/c/101/21', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.8049928810328781, 1.7518866326640459, 1.715568361885128, 1.6905250148897837, 1.670107997392834, 1.6472171077169269, 1.6148891136835484, 1.5667594275770307, 1.4974266332373296, 1.4027650193152854, 1.2802159095451264, 1.1290651273651995, 0.9506932559742226, 0.7487712756688591, 0.5293667140818713, 0.3009237493280734, 0.07408404783345567, -0.13867691893206413, -0.32361107434862535, -0.4664533619566281, -0.5533495958774317, -0.5719134455331839, -0.5123484914683186, -0.368552334150104, -0.13910516286448504, 0.17196258438450746, 0.5547276087096151, 0.9933483934672884, 1.4665258085768444, 1.9484835458125729, 2.4104576351639015, 2.8226328498383606, 3.1564098561095073, 3.3868359371052525, 3.4949901487829904, 3.470087090056759, 3.3110577065799953, 3.0273849064311666, 2.6390182692483175, 2.1752649696095863, 1.6726491547511888, 1.1718420292050211, 0.7138794094405537, 0.33598988003847263, 0.06744121060708144, -0.07413784726306835, -0.08549989146939796, 0.020825378325323662, 0.21678816426148595, 0.46088017883228666, 0.7019604565787063, 0.8845931212527085, 0.9554368118708157, 0.8700473954015919, 0.599333455429454, 0.13486017882689313, -0.5077530657849642, -1.2879477337316902, -2.1422196596603706, -2.98904460770695, -3.7364360382620405, -4.291482025839277, -4.570900361183371, -4.511433066731553, -4.0788116621711055, -3.274087480807786, -2.1363443240448343, -0.7411801342845233, 0.8051746585946763, 2.375695405117137, 3.8354209581653858, 5.055943744692109, 5.929843133366664, 6.38327217157089, 6.385037684483012, 5.9508743239807815, 5.142171744613158, 4.059107229681293, 2.8288761466594967, 1.5903985065176311, 0.4774109327543594, -0.3978558391782246, -0.9582192410170813, -1.1704299193508192, -1.0481230153062129, -0.6483686262715247, -0.06226294437253179, 0.5991224908552188, 1.2214069845615363, 1.703729918272822, 1.9732259840125654, 1.9949516414218826, 1.7757425308396193, 1.3614153582419006, 0.8277810653807025, 0.26694252141568525, -0.22885752310427618, -0.5831337229275245, -0.7480986193752718, -0.7124050836535095, -0.5023084444513402, -0.1759913367754798, 0.18799871330185522, 0.5061687824982102, 0.706570552116786, 0.7432915619615919, 0.6061427701691376, 0.3235276544680775, -0.04232337417357018, -0.4071611539230928, -0.6816068432480654, -0.790085315650405, -0.688203207957115, -0.3750559511103116, 0.10229745744651271, 0.6536286561871684, 1.1593585795272006, 1.4914120644930877, 1.5376378312420462, 1.2253995588388662, 0.5397888746281092, -0.46739594119743344, -1.6802967204491157, -2.933648330508585, -4.0376065213753805, -4.808909885169169, -5.103118426552429, -4.842149569235825, -4.031856460240449, -2.7659244892425234, -1.2146680572506363, 0.40000130460192707, 1.8395785977850396, 2.8880937332995567, 3.388526841887328, 3.269914520404372, 2.560033558094424, 1.3810425939077084, -0.07146669053789403, -1.5624729028754685, -2.858539229800404, -3.7683655756269423, -4.1753645495384895, -4.056145612344358, -3.481399171429201, -2.599013026402097, -1.6026907088814706, -0.6921990848478835, -0.03307028874373304, 0.27624473714017767, 0.2231957664089488, -0.11788522654540277, -0.6028765196825807, -1.0495934343816054, -1.277683352258125, -1.1484795070047813, -0.5965280233368269, 0.3538593733146277, 1.5906323684344001, 2.93437878730934, 4.172983785415523, 5.103473820068296, 5.572378428906847, 5.506190819502579, 4.925547659626169, 3.940167673338843, 2.7256703521621577, 1.4872660680251186, 0.41812346674881906, -0.3386479593116353, -0.7162802786244334, -0.7333833196259975, -0.4840622920177351, -0.11166859917790953, 0.2276005233118789, 0.4027692147449374, 0.33899129437686376, 0.03416070231435742, -0.4425633367573233, -0.9698426440705386, -1.4061947809603004, -1.6271806602910923, -1.558632990650013, -1.1976603438114735, -0.6160155015007848, 0.05536089816743794, 0.6572027746428779, 1.0408797824298144, 1.1059450171558565, 0.8268246267657281, 0.26160268669802567, -0.4599234819062954, -1.1666662867092383, -1.6881829908373105, -1.8979790837786084, -1.7472438626233973, -1.2799762430341648, -0.62469448238388, 0.0364335131300674, 0.5144750461752603, 0.665662594703031, 0.43546576419213406, -0.1169550754967237, -0.8215723413662692, -1.429033976505337, -1.6654335129210631, -1.2988054064218089, -0.20225412161368933, 1.6015580175594348, 3.9264033927344077, 6.444389685694072, 8.741190401073428, 10.39424559964042, 11.057852089813819, 10.536818228443314, 8.832234757067344, 6.148601558169579, 2.8598356554007536, -0.559289731392541, -3.622035897047979, -5.920126350149999, -7.196592502103832, -7.385928303466065, -6.613875622839382, -5.158280990054235, -3.381129381048603, -1.6480357013560745, -0.25372355286812986, 0.6301392830216319, 0.9743578974434257, 0.8767668472728661, 0.5183188424098534, 0.10372578601664391, -0.19718907361700963, -0.29233123122602406, -0.18416675708471683, 0.042271391280355286, 0.25512617337642096, 0.3238186476725922, 0.16504390844461875, -0.22685687700464793, -0.7739885553291572, -1.3351915626723747, -1.7466875781178302, -1.8712949995090824, -1.6417789978714477, -1.0853225365140344, -0.32125620392539767, 0.4683146358719059, 1.0875562620426897, 1.3823001736288532, 1.2861599066171683, 0.8437954036920976, 0.20369755062895134, -0.41883172139940694, -0.799418608254436, -0.7678201189242881], 'positive_zeros': ['2.04220936508282510792494909257646', '3.05980165506910829198654803910175', '5.54605547404688259267238303438255', '5.85772082438099811732812306021256', '6.90411658793784569598151997654272', '8.435832713694190833520774661384799', '10.06311036047444926015953799350531', '10.76203722127171045066827911920529', '11.93890205934456350909166738435337', '12.68525819489786157084355760486014'], 'prelabel': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.3349620454011873, 'root_number': '0.4955622386979539 - 0.8685724308177598*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.167481022701', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.04220936508282510792494909258', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.05980165506910829198654803910', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.54605547404688259267238303438', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/21'], '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': '2-168-168.101-c1-0-16', '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': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': -0.16748102270059365, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.04220936508282510792494909258', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2588807927438954518879941899629', 'Lhash_array': ['2588807927438954518879941899629'], 'label': '2-168-168.101-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/21'}