-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3299611470382792013769953241646', 'a10': [-19.457513110645905, 0.0], 'a2': [0.0, -2.711871805402204], 'a3': [0.0, 0.0], 'a4': [-3.3542486889354093, 0.0], 'a5': [0.0, -7.17493838458198], 'a6': [0.0, 0.0], 'a7': [2.6457513110645907, 0.0], 'a8': [0.0, -1.7511947737775715], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.149876996409612, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.6457513110645907, 0]]]], 'bad_primes': [3, 7], 'central_character': '189.134', 'coefficient_field': 'CDF', 'conductor': 189, 'conductor_radical': 21, 'conjugate': '1115170718037762478345849479231', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.711871805402204], [-4.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 7.17493838458198], [-25.0, 0]], [[1.0, 0], [-2.6457513110645907, 0]], [[1.0, 0], [0, -2.711871805402204], [-121.0, 0]], [[1.0, 0], [-6.354248688935409, 0], [169.0, 0]], [[1.0, 0], [0, -6.38442064242904], [-289.0, 0]], [[1.0, 0], [30.520259177452136, 0], [361.0, 0]], [[1.0, 0], [0, 27.90923579617498], [-529.0, 0]], [[1.0, 0], [0, -37.00552824400622], [-841.0, 0]], [[1.0, 0], [-44.39476704383968, 0], [961.0, 0]], [[1.0, 0], [-71.206528843421, 0], [1369.0, 0]], [[1.0, 0], [0, 28.869912827799613], [-1681.0, 0]], [[1.0, 0], [4.686269665968859, 0], [1849.0, 0]], [[1.0, 0], [0, 65.70528178233414], [-2209.0, 0]], [[1.0, 0], [0, -36.044851212381595], [-2809.0, 0]], [[1.0, 0], [0, 101.75013299471573], [-3481.0, 0]], [[1.0, 0], [-45.542486889354095, 0], [3721.0, 0]], [[1.0, 0], [-93.85228015448558, 0], [4489.0, 0]], [[1.0, 0], [0, -80.84567629365104], [-5041.0, 0]], [[1.0, 0], [60.22875655532295, 0], [5329.0, 0]], [[1.0, 0], [-20.686269665968858, 0], [6241.0, 0]], [[1.0, 0], [0, 94.74535389960545], [-6889.0, 0]], [[1.0, 0], [0, -52.14592275532312], [-7921.0, 0]], [[1.0, 0], [-98.206528843421, 0], [9409.0, 0]], [[1.0, 0], [0, -21.074615990536387], [-10201.0, 0]], [[1.0, 0], [117.43528539874394, 0], [10609.0, 0]], [[1.0, 0], [0, -146.38079878651348], [-11449.0, 0]], [[1.0, 0], [-52.8967355782895, 0], [11881.0, 0]], [[1.0, 0], [0, -169.03645026135575], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-189-3.2-c2-0-14', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/189/3/b/a/134/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4399947075126016, 1.667444332480966, 1.901245113168627, 2.1406147721895157, 2.383429086111999, 2.62593407519256, 2.8625852172927546, 3.0860258138399725, 3.287210000990815, 3.4556726255982086, 3.5799459186504827, 3.648119184346192, 3.6485310870543617, 3.570574218796046, 3.4055790804140367, 3.147730675449024, 2.794957256361376, 2.3497192442676393, 1.8196188851451052, 1.2177496227457316, 0.5627099920175989, -0.12177888929069422, -0.8076900787683415, -1.4639483189589695, -2.0580967209641314, -2.558298825886054, -2.935559468935826, -3.16600889353698, -3.233064190236211, -3.1292651444761965, -2.8575821545846245, -2.432015014087269, -1.8773442444166775, -1.2279602542532935, -0.5257762701487102, 0.18267748048897614, 0.8497869610727722, 1.4307374544861988, 1.8874018462071207, 2.191851033830406, 2.3291027802287854, 2.2987674979550383, 2.1153352430464456, 1.8069731625188317, 1.4128568521618905, 0.9792275658794853, 0.5545311384473955, 0.18413302776732407, -0.09480329126953317, -0.2576573532045041, -0.2953388996867217, -0.21546880440747082, -0.041491943931984736, 0.190296417127265, 0.43555950519062336, 0.6480491766110722, 0.786323636235686, 0.8201771122570132, 0.735869581111989, 0.5393304358322812, 0.2567190050834772, -0.06795915939501652, -0.3780916570191443, -0.6120501416395884, -0.7122440156592239, -0.6344532718114119, -0.35610380669062847, 0.11782553637085724, 0.7523552932926918, 1.4842071884480463, 2.2278039153476894, 2.8850991601439504, 3.3581635293391017, 3.56294655315376, 3.4423162011975266, 2.9764113634900484, 2.1885636494598923, 1.1455463298045816, -0.04835961824429446, -1.2631197373628322, -2.3592650499703223, -3.2067415801644734, -3.70372092579869, -3.7926129648177715, -3.4707359293332836, -2.793716161834292, -1.8706459617304887, -0.8512005421714037, 0.09386216173170091, 0.7963094633581458, 1.1148712357322326, 0.95691767703025, 0.29401549556196716, -0.831237651839905, -2.3084925150773365, -3.9729458478745814, -5.6270161998764285, -7.067401651564087, -8.113583703799836, -8.633490940457257, -8.562358204248362, -7.911787773556289, -6.767504432447709, -5.27606942315359, -3.622593206487973, -2.0029654192506543, -0.5950429352820746, 0.4665698363338365, 1.1081030383827954, 1.3238085060721545, 1.1717728097375193, 0.7593420780377073, 0.22095007023113178, -0.30754065837918165, -0.7132917427369937, -0.9253156285359603, -0.9243466469619387, -0.7421470503997104, -0.45067161754034396, -0.14347751822162386, 0.08672136350436253, 0.1696981907982248, 0.07405809559561051, -0.18514557095596437, -0.5491731381856062, -0.9282372747523053, -1.221424734849555, -1.339705857968545, -1.2270724362754895, -0.8751052802542468, -0.3275400237864537, 0.3265557460619618, 0.9699611081852078, 1.481507059848541, 1.7623024280315305, 1.7583045652063953, 1.4740879725575353, 0.9743372268920673, 0.3721052124556183, -0.1942660035845394, -0.5910666167671724, -0.719726562813993, -0.5411576509743193, -0.08813065729202896, 0.5378357939483754, 1.1854121885527302, 1.685101186825783, 1.8874718234179044, 1.7000144891044127, 1.1144024507626484, 0.21746466845565637, -0.8177638068504646, -1.7605096896351633, -2.365638725592735, -2.4238539924310696, -1.808658855681566, -0.5100769929374345, 1.3527124975347378, 3.5437326511706977, 5.746508028788907, 7.618271944243789, 8.852091777464345, 9.234874315518045, 8.68958279919461, 7.292800362224797, 5.263507154575751, 2.9246666652178255, 0.6447624691470162, -1.2293857886429143, -2.4352867987790896, -2.8404991879481933, -2.4624085712532495, -1.4583942465825404, -0.08885231052731185, 1.338838499873779, 2.533432001663418, 3.2767262204442704, 3.46255179958135, 3.1102128401123785, 2.350472766656622, 1.388239038576038, 0.45114621115444486, -0.26386599412226586, -0.6337783354581693, -0.6330102683324402, -0.3325593596035018, 0.12406644652043707, 0.5614873125681941, 0.8192292709566373, 0.7929774830347384, 0.4602497256437665, -0.11552418456541437, -0.8030586989887233, -1.438395628297984, -1.8679533944134654, -1.9882891768676842, -1.7723633395804066, -1.275639992304665, -0.6206101961911572, 0.03605196196274694, 0.5449429887932542, 0.8029550708356268, 0.7794418559590964, 0.5224714241493101, 0.14341548103596685, -0.21601684326622742, -0.42532460418009443, -0.40381586746926973, -0.14526147281658822, 0.27885152268248614, 0.7391967825473258, 1.0869152583750863, 1.2002270098663903, 1.0263250534203545, 0.6060624917158642, 0.07294291327319458, -0.375508159838871, -0.5284036027390809, -0.2221121619039772, 0.6049107936204311, 1.878528148205043, 3.3875906371875097, 4.81827232880393, 5.818445003279603, 6.078306668333389, 5.40835567348841, 3.7952004883509693, 1.420010987642286, -1.3672014440633264, -4.113774063412126, -6.357270446877372, -7.724173936245456, -8.011329169326459, -7.230488979428345, -5.604697138553704, -3.5166112526748816, -1.420480481516899, 0.2615578440830127, 1.2342036177493163, 1.3921292598782757, 0.8365778966745242, -0.15809716226093584, -1.2191284828099171, -1.9722890038805974, -2.1367465339090463, -1.5942312307476394, -0.4156615186818346, 1.1606608777788685, 2.792804804277001, 4.123846924468812, 4.872257333209032, 4.900884198655202, 4.247376535032659, 3.109242822326946, 1.7886943455459166, 0.6127864610323811, -0.1495795312346744], 'positive_zeros': ['2.60293449140380309263588697660676', '4.34240232919681319874182734348092', '5.95181494010663835341818846768503', '6.52410439288956774032694763610207', '7.59914572549747203251965824758326', '8.347952608025344022939181259991936', '9.745073113974419101645705576084507', '10.98640995386590556495198412568452', '11.53764317046855470659468613966807', '13.31423876686308478108256872919085'], 'prelabel': '2-189-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.269334042491235, 'root_angle': -1.0, 'root_number': '-1.0 - 1.2246467991473532e-16*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.5', 'prec': 14}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.60293449140380309263588697661', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.34240232919681319874182734348', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.95181494010663835341818846769', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.149876996409612, 'bad_primes': [3, 7], 'central_character': '3.2', 'conductor': 189, 'conductor_radical': 21, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/189/3/b/a/134/2'], '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': '2-189-3.2-c2-0-14', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-189-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.269334042491235, 'root_angle': -0.5, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.60293449140380309263588697661', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3299611470382792013769953241646', 'Lhash_array': ['3299611470382792013769953241646'], 'label': '2-189-3.2-c2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/189/3/b/a/134/2'}