-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3193644088492240668706488005434', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.4142135623730951, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.8284271247461903, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.088340583489558, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '512.1', 'coefficient_field': 'CDF', 'conductor': 512, 'conductor_radical': 2, 'conjugate': '3193644088492240668706488005434', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [3.0, 0]], [[1.0, 0], [2.8284271247461903, 0], [5.0, 0]], [[1.0, 0], [4.0, 0], [7.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [11.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [13.0, 0]], [[1.0, 0], [4.0, 0], [17.0, 0]], [[1.0, 0], [7.0710678118654755, 0], [19.0, 0]], [[1.0, 0], [4.0, 0], [23.0, 0]], [[1.0, 0], [-8.48528137423857, 0], [29.0, 0]], [[1.0, 0], [8.0, 0], [31.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [37.0, 0]], [[1.0, 0], [-2.0, 0], [41.0, 0]], [[1.0, 0], [-4.242640687119285, 0], [43.0, 0]], [[1.0, 0], [0, 0], [47.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [53.0, 0]], [[1.0, 0], [-4.242640687119285, 0], [59.0, 0]], [[1.0, 0], [8.48528137423857, 0], [61.0, 0]], [[1.0, 0], [-4.242640687119285, 0], [67.0, 0]], [[1.0, 0], [-4.0, 0], [71.0, 0]], [[1.0, 0], [4.0, 0], [73.0, 0]], [[1.0, 0], [-8.0, 0], [79.0, 0]], [[1.0, 0], [9.899494936611665, 0], [83.0, 0]], [[1.0, 0], [-12.0, 0], [89.0, 0]], [[1.0, 0], [4.0, 0], [97.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [101.0, 0]], [[1.0, 0], [12.0, 0], [103.0, 0]], [[1.0, 0], [9.899494936611665, 0], [107.0, 0]], [[1.0, 0], [14.142135623730951, 0], [109.0, 0]], [[1.0, 0], [-14.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-2e9-1.1-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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/512/2/a/c/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-7.263742309269153e-120, 0.2518801557435321, 0.5103080569851897, 0.7801643309267594, 1.0633278253150593, 1.357859058438895, 1.6577152013546534, 1.9529185789180217, 2.230097836579176, 2.4733544021182774, 2.6654300961301303, 2.7891473358559837, 2.829064463573563, 2.7732458880791486, 2.6150011817772416, 2.3544090360425707, 1.999419697668252, 1.566330370941666, 1.07945724464517, 0.5698875986478164, 0.07328439903762342, -0.37317200427802066, -0.7344955634969097, -0.9819272306752503, -1.096853163551529, -1.0741081603920983, -0.92415458901817, -0.6736852816621798, -0.36432957957415274, -0.04933995682804255, 0.2116136036573993, 0.3591399016090886, 0.34164840647984435, 0.12281953632324116, -0.3119747744284633, -0.9512950831544056, -1.7561510531653375, -2.661967735091385, -3.58414522423174, -4.426863983248663, -5.094282102353698, -5.50282557802885, -5.5929652974844295, -5.338770955987782, -4.753675364607355, -3.891281351624758, -2.840666227288468, -1.7164133224019027, -0.6444199650874884, 0.2547308271490272, 0.8825207795815331, 1.1768479037661503, 1.1216388634559036, 0.7499593921390216, 0.1397765196015795, -0.5973406454632928, -1.3331184797942306, -1.9425904550005664, -2.3240635056699444, -2.4156993807054596, -2.2057591075211653, -1.7344931690437935, -1.0870176461958312, -0.3780851393909891, 0.2688315251226978, 0.7445580008572437, 0.9751736509637121, 0.9368954297801683, 0.66180523426326, 0.23290396032894903, -0.23106380724695366, -0.5985679365728305, -0.7519294870447336, -0.612568803437333, -0.15976924586002317, 0.5611606904382647, 1.443582364198279, 2.336900603963323, 3.073881702874111, 3.5030129691670058, 3.519687129568832, 3.089861854760443, 2.2609985818326037, 1.15737263441878, -0.04013127117422896, -1.1264482821647135, -1.911020224603829, -2.2551841833648187, -2.1006056243756577, -1.482592382678569, -0.5249885382033402, 0.5829540233079561, 1.623538656670798, 2.394161077546905, 2.748502947110057, 2.6266517462813206, 2.067496488421659, 1.2003543144927458, 0.21719092429725406, -0.6689305786653528, -1.2703575007036194, -1.4661643413223324, -1.2290207984537653, -0.6313539149855294, 0.17094013871797983, 0.9739273142467131, 1.5724515974638973, 1.8077773911612944, 1.6050621816097634, 0.9917744274901712, 0.09242654348746779, -0.8995380715020397, -1.7664384707010936, -2.3172780282923418, -2.432823589827828, -2.0939152830442866, -1.3859086901286244, -0.47782064749788, 0.4190674179961188, 1.1032068721649275, 1.4325671049595128, 1.359639725993949, 0.9425035753403614, 0.32862797593780296, -0.28503243889157437, -0.7058878909449705, -0.7998102301739088, -0.5312162685970613, 0.022027922190429684, 0.6839394120513376, 1.2233694801605601, 1.4146254397072113, 1.1007402906090964, 0.24295765815829515, -1.057220880584435, -2.5706488613742735, -3.986459184229922, -4.981364564666635, -5.2960187312779725, -4.799682102900768, -3.5267104655442956, -1.674951638293946, 0.4345654015272874, 2.4275574493218723, 3.9593304632502595, 4.790361505705279, 4.83609399182169, 4.178877231198879, 3.0396322143487464, 1.7171748534520874, 0.5114381802247987, -0.3491386574560796, -0.7571748975037536, -0.7404684867128206, -0.43813049809050075, -0.04674195077481607, 0.24713547513580542, 0.3280215417033583, 0.1880334308201231, -0.07208343883723764, -0.2779080936295637, -0.24201875849380497, 0.16784341571265965, 0.974150693553456, 2.0661944113387047, 3.216923023191849, 4.137350599382837, 4.5545426856597695, 4.291517989287933, 3.3257766604249963, 1.8082805651599343, 0.03532889993400898, -1.62099397873446, -2.806025445788848, -3.274207523050389, -2.9536607555246874, -1.9650034153778704, -0.5882722731526708, 0.813596055838639, 1.8937399254612257, 2.4150681440899455, 2.312068093943, 1.70298024141732, 0.8487688168163524, 0.07076516411687248, -0.34893661562364287, -0.25495139842491416, 0.33214223520084124, 1.219779688211459, 2.0999500277106042, 2.6419233313242296, 2.5937639426263246, 1.862257313101114, 0.5469827309911929, -1.082257624644301, -2.6585533546056133, -3.82020749260709, -4.311988868665422, -4.055194256217007, -3.165708150370127, -1.914961211906676, -0.6460461213060996, 0.3290826976061039, 0.8196853882135532, 0.8060367505464353, 0.4340984207089197, -0.04238109419023833, -0.35311128080404475, -0.30597646571543813, 0.14580968840687292, 0.8863307967622261, 1.675490896324081, 2.2312354330525426, 2.3286344489730246, 1.8828561680294817, 0.9876035473829957, -0.10542110508103351, -1.061348986601995, -1.568481398216277, -1.4421553171620594, -0.6917733125277632, 0.47251852913011, 1.6981350462502915, 2.596956209533575, 2.8680834812786804, 2.3974431778943606, 1.3014120461311958, -0.10138572189019965, -1.3833862306949083, -2.1387474186095075, -2.1109628006552223, -1.277033098054932, 0.139253563487097, 1.7304040863105978, 3.0260348392026146, 3.6342878212950436, 3.3598609689359438, 2.2618039962778655, 0.6332044449453805, -1.0903424969391027, -2.4640117539194306, -3.1662635687963174, -3.0888437873446497, -2.3568251755937704, -1.274382392857169, -0.2162948980061061, 0.49743137974635193, 0.7017173569209126, 0.4287208883975405, -0.11989935504168375, -0.6586253100179452, -0.9295767663155606, -0.7992182277512807, -0.3053524043092417, 0.3624227487540212, 0.9414238743442219, 1.2046036438000611], 'positive_zeros': ['2.51934096660172210523376964460230', '3.64602790789663783204629244219703', '4.16725586767261259610490344282328', '6.08610173063719762075708845259890', '6.77474245661909789851894232305817', '7.945112543853197062870817498787194', '8.686721910286336691620343293808258', '9.281525011802992645370023439181689', '10.49574187132408215607831995199441'], 'prelabel': '2-2e9-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0219645356656377, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.51934096660172210523376964460', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.64602790789663783204629244220', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16725586767261259610490344282', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.088340583489558, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 512, 'conductor_radical': 2, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/512/2/a/c/1/2'], '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': '2-2e9-1.1-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': 1, 'prelabel': '2-2e9-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0219645356656377, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.51934096660172210523376964460', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3193644088492240668706488005434', 'Lhash_array': ['3193644088492240668706488005434'], 'factors': ['2-2e9-1.1-c1-0-14'], 'label': '2-2e9-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/512/2/a/c/1/2'}