-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2338716081801269816050694991490', 'a10': [-4.714554966349793, 2.840360759469722], 'a2': [-1.3726077776832943, -0.3405112166189655], 'a3': [0.0, 0.0], 'a4': [1.7681042227133439, 0.9347766886391861], 'a5': [2.7520300586416617, -2.7520300586416617], 'a6': [0.0, 0.0], 'a7': [0.0, 0.11349232972547509], 'a8': [-2.1086116603354346, -1.885141073208433], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3726077776832943, 0.3405112166189655]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '432.109', 'coefficient_field': 'CDF', 'conductor': 432, 'conductor_radical': 6, 'conjugate': '1289581059125319037807284655414', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3726077776832943, 0.3405112166189655]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.7520300586416617, 2.7520300586416617], [0, -5.0]], [[1.0, 0], [0, -0.11349232972547509], [-7.0, 0]], [[1.0, 0], [-3.691886928196644, 3.691886928196644], [0, -11.0]], [[1.0, 0], [1.5362084454266878, 1.5362084454266878], [0, 13.0]], [[1.0, 0], [6.625460600611873, 0], [17.0, 0]], [[1.0, 0], [-3.2749596962343843, -3.2749596962343843], [0, 19.0]], [[1.0, 0], [0, -6.206208372936119], [-23.0, 0]], [[1.0, 0], [1.5186931285419334, 1.5186931285419334], [0, 29.0]], [[1.0, 0], [1.106680980594729, 0], [31.0, 0]], [[1.0, 0], [-2.6179417910385125, 2.6179417910385125], [0, -37.0]], [[1.0, 0], [0, 9.185505187286635], [-41.0, 0]], [[1.0, 0], [-3.188414326206554, 3.188414326206554], [0, -43.0]], [[1.0, 0], [-3.568684136268116, 0], [47.0, 0]], [[1.0, 0], [4.086243804164902, -4.086243804164902], [0, -53.0]], [[1.0, 0], [0.9427926388001079, -0.9427926388001079], [0, -59.0]], [[1.0, 0], [0.4372000986247154, 0.4372000986247154], [0, 61.0]], [[1.0, 0], [3.2676425661906756, 3.2676425661906756], [0, 67.0]], [[1.0, 0], [0, -7.725043675852424], [-71.0, 0]], [[1.0, 0], [0, -10.233378476449323], [-73.0, 0]], [[1.0, 0], [1.2540818963125095, 0], [79.0, 0]], [[1.0, 0], [-8.424004783148407, -8.424004783148407], [0, 83.0]], [[1.0, 0], [0, -0.36116278494240406], [-89.0, 0]], [[1.0, 0], [-13.728661760167826, 0], [97.0, 0]], [[1.0, 0], [-1.7736488308290375, 1.7736488308290375], [0, -101.0]], [[1.0, 0], [0, -1.3836400015438537], [-103.0, 0]], [[1.0, 0], [6.8089777623282, -6.8089777623282], [0, -107.0]], [[1.0, 0], [-2.4230716194502606, -2.4230716194502606], [0, 109.0]], [[1.0, 0], [-10.079387535794641, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-432-16.13-c1-0-21', '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/432/2/k/c/109/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1059623539757446, 1.1967810784819393, 1.2859645832659161, 1.3712744827762733, 1.4477327840605212, 1.5081210561631848, 1.543772205309441, 1.5455297860859951, 1.5048040343633706, 1.4146867767948959, 1.2710867578874823, 1.0738237916892943, 0.8275899118980423, 0.5426600958346435, 0.23522169371379564, -0.07280489795687578, -0.3545587580489688, -0.579705037497262, -0.7165736795446687, -0.7348900768716171, -0.6089305297726935, -0.3208490705132116, 0.13615199892481503, 0.7551852372577323, 1.5139656170065352, 2.3743807585188663, 3.2836184677966673, 4.176992093051891, 4.982427420457201, 5.626370628550695, 6.040667312166942, 6.1697748413557045, 5.977533400058866, 5.45266212224004, 4.6121867276675035, 3.502154384312521, 2.195246707657346, 0.7852435570626248, -0.6213162834364147, -1.9155341502743457, -2.9975212502352275, -3.787412163105804, -4.2346129004881385, -4.323979086301476, -4.077918942327094, -3.553888041192102, -2.8373378544024894, -2.0308224407057214, -1.2405652209225708, -0.562244925313109, -0.06799199010558257, 0.20346413495621313, 0.2519090135725966, 0.11505739433065602, -0.1378689420647336, -0.41762927292073676, -0.629899729440602, -0.6913946160727369, -0.544595091619351, -0.1685986145260898, 0.41588174335365163, 1.1484548158118435, 1.937884854413136, 2.6765883126294594, 3.258510690685268, 3.597388704184822, 3.6421829336905382, 3.3868124666246224, 2.8722124892715306, 2.1800420857293146, 1.4188782257455508, 0.7051734697516229, 0.14235132577576062, -0.19806896184140496, -0.28962682660149275, -0.15559192460326035, 0.136082662463646, 0.48689692113630195, 0.7885469103350403, 0.9463183032214423, 0.9004077861856012, 0.6405956672567589, 0.21078878447470378, -0.29815633860647145, -0.7665645994698436, -1.0718947140519917, -1.1174918939992327, -0.8581420900230522, -0.3166370467374757, 0.4129978488235703, 1.1774895379085826, 1.790332465896817, 2.0675951225241826, 1.8668779233807211, 1.1215867095409662, -0.13696022592198157, -1.7751299899325692, -3.57257569075336, -5.256189846803641, -6.546887143577372, -7.210713693101078, -7.104379387645277, -6.205881118855692, -4.623424472398266, -2.579935873294119, -0.37530620957591837, 1.6668672074158792, 3.2578640395080916, 4.196162147876629, 4.4028837896871895, 3.9330018871473746, 2.959849208417821, 1.736037638156907, 0.5389274287047345, -0.38782903786572615, -0.8841991551252677, -0.9044362254002837, -0.5219550035833459, 0.09245762580695974, 0.7140304322315194, 1.1190575766681305, 1.1390057321736153, 0.7012606080721775, -0.15285767196537242, -1.2769342723267374, -2.4530258552788946, -3.442023470202436, -4.038912946492513, -4.119866859643775, -3.670053440883765, -2.7856837463700588, -1.6500434850839922, -0.4895651220980381, 0.4791633540444819, 1.0983994743979573, 1.3022956338857024, 1.1261340664859898, 0.689981933201625, 0.16155998014473713, -0.2915445380315995, -0.5474743209052666, -0.5613125841646951, -0.37360816630064403, -0.09407448514528018, 0.13486312551153412, 0.18434958739464555, -0.018029470440073227, -0.46135116248910535, -1.0487979583911633, -1.621133264113419, -2.000517407845913, -2.042894453936103, -1.684158505289673, -0.9663179796055524, -0.03482168847424565, 0.8940998868529503, 1.5888004402430778, 1.8661662309185552, 1.6467434437695976, 0.985032176334732, 0.06486062222886194, -0.8411852399968437, -1.4394432562946067, -1.4931622607212773, -0.8902011723868483, 0.31849450846474436, 1.921642953400001, 3.5930421376803783, 4.969608898480771, 5.742699510612734, 5.738901991051203, 4.968293027874375, 3.6260093505785544, 2.0450060237109566, 0.6109509548452696, -0.33919193751769966, -0.6081966035476736, -0.1944526724214743, 0.7033808324337906, 1.7356765572605606, 2.4933511291288246, 2.618151800014103, 1.902637478837592, 0.3528777993108461, -1.8036480706427298, -4.168086474942546, -6.26584033458213, -7.66311650568331, -8.073922901448288, -7.429480022923721, -5.892064693812049, -3.810255930066412, -1.628290692365417, 0.22559895498945975, 1.4417806622141949, 1.8958183045440222, 1.6627197960863505, 0.9774303368917785, 0.1551770664529529, -0.5039452232940829, -0.7982464684315116, -0.6723342664361114, -0.21772212737924462, 0.3712170254185094, 0.8699769919173989, 1.1011954950516687, 0.9917947080024766, 0.5924046325982344, 0.053977931339580655, -0.4295698014402354, -0.6928911664678878, -0.6605679503575649, -0.37731440370835817, 0.0037501743842426067, 0.2716864689669713, 0.23106051778903364, -0.2261049352912226, -1.074119833383206, -2.1497771931747076, -3.1940645305555613, -3.9277607794007445, -4.137712923433938, -3.7462517350054703, -2.8406956294868646, -1.6520219018067641, -0.4878566402060733, 0.3601461720024244, 0.7055833037598666, 0.5245219621263694, -0.03848082237704299, -0.7185968102945814, -1.218621646202652, -1.3085855368497004, -0.9044464984361829, -0.099129665926007, 0.8659038363391279, 1.6809877119077627, 2.0752529207980115, 1.9150266343253781, 1.2595481793911605, 0.35246854773093594, -0.4520999023434771, -0.8084474252189517, -0.5063113154731531, 0.4357113453681414, 1.7439637327148363, 2.944790617357192, 3.4898057937727867, 2.9173924256602266, 1.0031042991108856, -2.147545302223999, -6.095128680825136, -10.15690156666243, -13.569562491952704, -15.679694563492317, -16.108296094095355, -14.842706569828456], 'positive_zeros': ['1.84492168534468760082327728716697', '2.71719715972749628879088700044975', '4.69412009688897322688233577480179', '6.27328371941254913429192786669702', '6.68644308186683613191994852763081', '7.41547461369417164796281304666445', '9.042271962772386921445126882049963', '9.447408644146220030661548130529466', '10.30254117755088387325839497065116', '11.05685827119729650738595485261323'], 'prelabel': '2-432-16.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': 0.4346100158385002, 'root_number': '0.2039868586190438 + 0.9789736265654628*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.217305007919', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84492168534468760082327728717', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71719715972749628879088700045', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.69412009688897322688233577480', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'bad_primes': [2, 3], 'central_character': '16.13', 'conductor': 432, 'conductor_radical': 6, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/432/2/k/c/109/2'], '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': '2-432-16.13-c1-0-21', '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': '2-432-16.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': 0.2173050079192501, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84492168534468760082327728717', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2338716081801269816050694991490', 'Lhash_array': ['2338716081801269816050694991490'], 'label': '2-432-16.13-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/432/2/k/c/109/2'}