Formats: - HTML - YAML - JSON - 2025-12-09T00:29:03.087709
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '2002329322178249530004736504431', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.463710586481115, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.1830016886594454, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.7849724919853402, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.407033089703585, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 7, 17], 'central_character': '3808.1', 'coefficient_field': 'CDF', 'conductor': 3808, 'conductor_radical': 238, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.463710586481115, 0], [3.0, 0]], [[1.0, 0], [0.1830016886594454, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.931236065502095, 0], [11.0, 0]], [[1.0, 0], [2.195849077446364, 0], [13.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [7.890683057819539, 0], [19.0, 0]], [[1.0, 0], [-3.580090918291923, 0], [23.0, 0]], [[1.0, 0], [2.539537910609367, 0], [29.0, 0]], [[1.0, 0], [1.6249641264340557, 0], [31.0, 0]], [[1.0, 0], [9.29680478369907, 0], [37.0, 0]], [[1.0, 0], [0.8515938488339776, 0], [41.0, 0]], [[1.0, 0], [-0.2716764015746161, 0], [43.0, 0]], [[1.0, 0], [10.337357791381626, 0], [47.0, 0]], [[1.0, 0], [-13.00492081198108, 0], [53.0, 0]], [[1.0, 0], [-2.9531159505360667, 0], [59.0, 0]], [[1.0, 0], [-5.6228215487847875, 0], [61.0, 0]], [[1.0, 0], [4.2048815736934175, 0], [67.0, 0]], [[1.0, 0], [-6.042337706076044, 0], [71.0, 0]], [[1.0, 0], [13.938299455132443, 0], [73.0, 0]], [[1.0, 0], [1.7940049882323938, 0], [79.0, 0]], [[1.0, 0], [10.838372888454815, 0], [83.0, 0]], [[1.0, 0], [1.133416184729836, 0], [89.0, 0]], [[1.0, 0], [-6.873123373245144, 0], [97.0, 0]], [[1.0, 0], [-16.11915856614262, 0], [101.0, 0]], [[1.0, 0], [14.66459285941145, 0], [103.0, 0]], [[1.0, 0], [16.481347050921645, 0], [107.0, 0]], [[1.0, 0], [6.62607004587527, 0], [109.0, 0]], [[1.0, 0], [6.452535512584793, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 20144397, 'index': 79, 'label': '2-3808-1.1-c1-0-79', '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/3808/2/a/g/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-6.76388281665962e-61, 0.19640251402546224, 0.39214770463470283, 0.5865246216249734, 0.7787187258629157, 0.9677689600064322, 1.1525346736077822, 1.3316745073501461, 1.5036385490231294, 1.6666742947965978, 1.818846250198765, 1.958068423908722, 2.082148514290295, 2.1888422528770692, 2.275916128324346, 2.341216542950211, 2.3827433291419036, 2.3987254583202735, 2.3876967021158664, 2.3485689521843973, 2.280700875431864, 2.183959582734252, 2.0587730307888585, 1.9061709681037773, 1.7278123859764547, 1.5259976504282642, 1.3036637757094613, 1.0643616554279238, 0.8122144915608704, 0.5518571491340527, 0.28835670632292654, 0.027115053961503616, -0.22624499031639703, -0.46600796779679693, -0.6865057696357235, -0.8822660622940569, -1.0481653564109268, -1.1795824865659268, -1.272547928974952, -1.3238841655751006, -1.331332224391434, -1.2936596023342426, -1.2107450181586903, -1.0836358556768815, -0.9145747401765838, -0.7069924378908915, -0.4654651662876887, -0.19563543232866584, 0.09590334930798004, 0.4017569977107018, 0.7139127620094096, 1.0239496282422207, 1.3232716032515084, 1.6033577488629045, 1.8560217888538584, 2.073673347398787, 2.249572341666675, 2.3780677784633717, 2.4548122234266696, 2.476943540580047, 2.443226149004111, 2.3541450095360896, 2.2119468231154, 2.020624466505865, 1.7858424711309049, 1.514803315442459, 1.2160563888656493, 0.8992536253379197, 0.5748579195396478, 0.25381244776234024, -0.052819164480483786, -0.3342303349136486, -0.580253976813611, -0.7817364141694275, -0.9308889303372351, -1.0216032921536786, -1.0497182881865215, -1.0132255441330766, -0.9124046117382945, -0.7498795300432337, -0.5305916682888456, -0.26168659754165485, 0.047684095504586466, 0.386641857391273, 0.7429336115157008, 1.1033469955579556, 1.4541749305725467, 1.7817135984417731, 2.0727759618696333, 2.315201640789349, 2.498343344308952, 2.613510206630825, 2.654349318591744, 2.617148481943706, 2.501045706504126, 2.3081341527458394, 2.0434549939472033, 1.7148749027399923, 1.332849401263239, 0.9100779764419092, 0.46106146279760024, 0.00157653914778099, -0.4519139209474144, -0.8828926450737782, -1.2754374416658028, -1.6148623728009528, -1.8883241381703793, -2.085367796272153, -2.198387673050945, -2.222982117754439, -2.1581845811130145, -2.006558185099625, -1.7741463556537087, -1.4702779908439076, -1.1072317974981734, -0.6997705887879054, -0.26456222282676495, 0.1804907911916662, 0.6169864428487146, 1.0267930258717024, 1.3928211923830573, 1.6997649051767656, 1.9347784426752188, 2.088058591581245, 2.1533045763339946, 2.128033014204515, 2.0137310775539485, 1.8158378587047772, 1.5435513858127408, 1.2094665085994627, 0.8290566136774941, 0.42001948301941244, 0.0015142245756741965, -0.4066782472366905, -0.7850345105185311, -1.115168441137886, -1.3806714059163145, -1.5678737268960552, -1.666491152183252, -1.6701246883819951, -1.5765883656335917, -1.3880470663867626, -1.1109551286740489, -0.7557956504332296, -0.33662984773816584, 0.12952499159314884, 0.623461916474838, 1.1246606563429502, 1.612233593108688, 2.0658970018781186, 2.466921220448247, 2.7990136468033935, 3.049090965312697, 3.2079016974524635, 3.2704668819920855, 3.23631512763627, 3.109498068812878, 2.8983829353957056, 2.6152300052689803, 2.275573597624746, 1.8974354316640873, 1.5004080889633096, 1.1046534970355275, 0.7298663913721123, 0.39425530721838176, 0.11359361177721682, -0.09960964569420074, -0.23677463514275593, -0.2937147115060126, -0.27087255336036925, -0.1733129678743034, -0.010469274848880597, 0.2043469875022841, 0.4546507128194962, 0.721668245711244, 0.9853586649140851, 1.2255192225505787, 1.422917412420906, 1.5603896497150795, 1.623847180397374, 1.603133637487322, 1.4926854928348208, 1.2919562211957878, 1.0055768495105355, 0.6432391259913234, 0.2193021231419947, -0.24786207285928072, -0.7367536280194205, -1.2238182309316912, -1.684654467297691, -2.0952931266679253, -2.433481181723834, -2.6799016208224873, -2.8192624437329292, -2.841193911946605, -2.7409023419849863, -2.5195409140394833, -2.18427253712434, -1.7480160194384493, -1.2288837858600588, -0.6493362483120385, -0.03509374096047826, 0.586139209266743, 1.1860713972904717, 1.7372706672305362, 2.21458049500022, 2.596430476057417, 2.8659684255506854, 3.011950526975514, 3.0293383564166323, 2.9195670397354134, 2.690466463895482, 2.3558364135827614, 1.934695701670573, 1.4502437336817082, 0.9285894445071564, 0.39731620808227097, -0.11603867262893823, -0.5855055654960959, -0.9881198274721313, -1.305193246616129, -1.5233464737601403, -1.6352420487202755, -1.6399739858959148, -1.543088987503614, -1.3562351484169615, -1.0964553370221937, -0.7851630627872385, -0.446857372862337, -0.10764904484844988, 0.20631789648995935, 0.4704582581928413, 0.663258411672823, 0.7676202546208882, 0.7719557531018193, 0.670965015317151, 0.46604855284181496, 0.1653252183895031, -0.21674990368972863, -0.6601499465406708, -1.140382635469617, -1.6298775415341449, -2.099575857158409, -2.5206314205382503, -2.8661240214584898, -3.112684080348191, -3.2419318021038763, -3.2416437119893047, -3.106574579944191, -2.8388823048514027, -2.4481262546036775, -1.9508345158560074, -1.3696610318155618, -0.7321781741427409, -0.06937241815410705, 0.5860708928806112, 1.2015943498111055], 'positive_zeros': ['1.57955932164410891407881873258283', '2.42113203266858542590335413159490', '3.54568573677830076407064080663518', '4.15658600913587284926085669748053', '5.12908057576210545663525132330193', '5.92081311536896610999949599694071', '6.70330956014313623982826018323261', '7.34956039979808044182779091284350', '8.403804256208433685606302398244162'], 'prelabel': '2-3808-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.514257256394879, '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': '1.57955932164410891407881873258', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.42113203266858542590335413159', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54568573677830076407064080664', 'prec': 103}}