-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2197025094455924778544863854906', 'a10': [0, 0], 'a2': [0, 0], 'a3': [15.588457268119896, 0], 'a4': [0, 0], 'a5': [0, -195.23501110359052], 'a6': [0, 0], 'a7': [0, -277.509896465487], 'a8': [0, 0], 'a9': [243.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 88.3407681100228, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-15.588457268119896, 0]]]], 'bad_primes': [2, 3], 'central_character': '384.319', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '502522360708438555265101505938', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-15.588457268119896, 0]], [[1.0, 0], [0, 195.23501110359052], [-15625.0, 0]], [[1.0, 0], [0, 277.509896465487], [-117649.0, 0]], [[1.0, 0], [1753.2885949415727, 0], [1771561.0, 0]], [[1.0, 0], [0, 1246.748709740616], [-4826809.0, 0]], [[1.0, 0], [-6888.35478030956, 0], [24137569.0, 0]], [[1.0, 0], [-4401.674939634293, 0], [47045881.0, 0]], [[1.0, 0], [0, 12728.670304247911], [-148035889.0, 0]], [[1.0, 0], [0, 8278.436414499869], [-594823321.0, 0]], [[1.0, 0], [0, 43940.14887218998], [-887503681.0, 0]], [[1.0, 0], [0, -12186.363941601674], [-2565726409.0, 0]], [[1.0, 0], [54739.64521969044, 0], [4750104241.0, 0]], [[1.0, 0], [-45453.414429423785, 0], [6321363049.0, 0]], [[1.0, 0], [0, 152336.1635907019], [-10779215329.0, 0]], [[1.0, 0], [0, -272550.43521915056], [-22164361129.0, 0]], [[1.0, 0], [213174.53047170638, 0], [42180533641.0, 0]], [[1.0, 0], [0, 83964.83158115574], [-51520374361.0, 0]], [[1.0, 0], [373098.6914031859, 0], [90458382169.0, 0]], [[1.0, 0], [0, -667812.1488773096], [-128100283921.0, 0]], [[1.0, 0], [399457.0956061912, 0], [151334226289.0, 0]], [[1.0, 0], [0, -435376.24262118456], [-243087455521.0, 0]], [[1.0, 0], [-246583.14900782763, 0], [326940373369.0, 0]], [[1.0, 0], [-80967.48165176326, 0], [496981290961.0, 0]], [[1.0, 0], [-877030.4521969045, 0], [832972004929.0, 0]], [[1.0, 0], [0, -1804907.214819351], [-1061520150601.0, 0]], [[1.0, 0], [0, 826267.0539636391], [-1194052296529.0, 0]], [[1.0, 0], [1345866.215513445, 0], [1500730351849.0, 0]], [[1.0, 0], [0, -704622.2758621009], [-1677100110841.0, 0]], [[1.0, 0], [-2552725.1508951015, 0], [2081951752609.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 44, 'label': '2-384-8.3-c6-0-44', 'leading_term': '1.878414408448797631259023935282397267469844811182388638', 'load_key': 'CMFs-workshop', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/384/7/b/c/319/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.8784144084487977, 2.2021020616219644, 2.5179071220859712, 2.820275198641201, 3.103841074557244, 3.3635218639485798, 3.594606203100894, 3.792838160124358, 3.954494570266141, 4.076454538510214, 4.156259898269805, 4.192165477768802, 4.183178106879408, 4.129083399367353, 4.030459471018109, 3.888676904820839, 3.7058844514640663, 3.484980157235256, 3.2295678414599687, 2.9438991002549626, 2.6328012898574173, 2.301592237201308, 1.9559827326255648, 1.6019681733492968, 1.2457110393002773, 0.8934161867572566, 0.5512012310228387, 0.22496454739539287, -0.07974635981344348, -0.35786319741855666, -0.6049188937481145, -0.8171601900062131, -0.9916477464891037, -1.1263408005251996, -1.220163600402568, -1.2730511137919986, -1.2859718703185365, -1.2609262433868775, -1.2009190007139674, -1.1099055479336062, -0.9927119438493217, -0.8549294653139877, -0.7027852275427015, -0.5429911027967946, -0.38257390573811895, -0.22869050483073336, -0.08843215261737508, 0.03137711996172135, 0.1243827516678551, 0.1848969249593373, 0.20808507092349193, 0.19013579234007497, 0.128408546968388, 0.021553768304328237, -0.13039938129416562, -0.32599173360342576, -0.5623225562412288, -0.8350799364471894, -1.1386141799607035, -1.4660540447675243, -1.809464306991845, -2.1600418028881907, -2.508345748917893, -2.844556856045715, -3.1587585706459542, -3.441232738438836, -3.682761143422569, -3.8749237609316385, -4.010384217531633, -4.0831528983144745, -4.088818403721773, -4.024738643021392, -3.890183758976819, -3.686424295620447, -3.4167595241378628, -3.086482594772778, -2.7027811382998896, -2.2745740417505678, -1.8122873037579894, -1.3275740623129708, -0.8329860045076312, -0.34160533462522286, 0.1333517847907527, 0.5789479691164744, 0.9829401110008718, 1.334183593118398, 1.6230110024982831, 1.841571476022976, 1.9841176641077305, 2.0472286667426323, 2.02995914708792, 1.9339071169535595, 1.7631955508890642, 1.5243659386542685, 1.2261850314343092, 0.8793692646946265, 0.49623453060486405, 0.09028200147404887, -0.32426655127832615, -0.7329681592822725, -1.1216751713707387, -1.477050051484425, -1.7870590937576205, -2.041425881080436, -2.2320262609644863, -2.353208308909936, -2.4020231582933387, -2.3783556300630497, -2.2849471988473136, -2.1273078611954976, -1.913517780273224, -1.6539240050291648, -1.3607419241953278, -1.0475752348087353, -0.7288719017967725, -0.4193366900257755, -0.1333232111612423, 0.11577008225232213, 0.31607499935802885, 0.4577753550168994, 0.5335524427666755, 0.5389338815929534, 0.4725289818987448, 0.336138104309634, 0.13472848507226168, -0.12372551757917556, -0.428534060593825, -0.7667058798304806, -1.1234697919984695, -1.4828835953935362, -1.828505997829282, -2.14410380278663, -2.414364304748413, -2.6255818214597957, -2.7662876128443803, -2.8277941346489275, -2.804627619704259, -2.6948272789448406, -2.500094815538554, -2.225784240271156, -1.8807289078210159, -1.4769099662965877, -1.0289777045541284, -0.5536442590826969, -0.06897247302467059, 0.406408929119851, 0.8541295559706262, 1.2569039970125546, 1.5993229281789736, 1.8685714207114401, 2.0550396803639384, 2.1527956241221125, 2.1598944351227733, 2.0785072994320712, 1.9148596257776258, 1.6789778268024955, 1.384252799011388, 1.046837152639318, 0.6849015794603053, 0.3177830871015908, -0.034936211521157, -0.3543768149915124, -0.623290834381581, -0.8269269083769326, -0.9537877189915549, -0.9962410183989083, -0.9509513239429718, -0.8191074577638988, -0.606430554388711, -0.32295760717941574, 0.0173934172076308, 0.39745992861631046, 0.7976451863484922, 1.196866279734655, 1.5735953196343544, 1.906943885238589, 2.177737473185117, 2.369525990010219, 2.4694783193208494, 2.469113652632762, 2.3648294316086385, 2.1581951109181854, 1.8559920953336881, 1.46999260886069, 1.0164833151870503, 0.5155525744778159, -0.009827379599079894, -0.5348809815931291, -1.0342210821432047, -1.483093683174984, -1.8586135867039566, -2.140928147580876, -2.3142488147063074, -2.3676958140267774, -2.295909946022293, -2.099396655181293, -1.7845807487263614, -1.363564745326423, -0.8535990811006027, -0.2762874972236446, 0.34343492265333286, 0.978501177595611, 1.6010293517023049, 2.1836903142987274, 2.7010556831659334, 3.130855756495176, 3.455081019262402, 3.6608683496745877, 3.741123851419983, 3.6948477912687627, 3.5271427405867186, 3.248902886938002, 2.876199695591574, 2.4293957198906395, 1.9320334570441524, 1.4095588603940252, 0.8879487042455951, 0.39231686630724716, -0.054423644519277656, -0.4327685980479096, -0.7276327874206809, -0.9291056132018041, -1.0329089770679367, -1.0405310402948773, -0.9590277052445494, -0.8005026810195359, -0.5812956190682831, -0.3209249727962579, -0.040846931651225396, 0.23689688821559898, 0.49106306356819535, 0.7025386835083743, 0.8555418912825385, 0.9386170751025256, 0.9453624902226486, 0.8748433145662964, 0.7316613982453978, 0.5256732407696599, 0.2713688556497158, -0.013055077370305437, -0.3068752582378891, -0.588206180063318, -0.8354675904210225, -1.0288658428536086, -1.151797358476335, -1.19208527546622, -1.1429686453253047, -1.0037768559033504, -0.7802396283758097, -0.4844039786527853, -0.1341527587618752, 0.24765655120781896, 0.6343906764962262, 0.9971134569681536, 1.306251221294829, 1.533355478728555, 1.6528596835774096], 'positive_zeros': ['1.73314720480577978607540330196398', '2.91985305847968993221634815183281', '3.32261477761151924592233971145272', '5.10713096787248333238137887286120', '6.07614660951970506332105382332452', '7.28209675111874094546873344441888', '7.78413904783142336890477910347544', '9.008935957390723786448574366866796', '9.993593004250034060939826572779553', '10.62199978064500283318289320716436'], 'prelabel': '2-384-8.3-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.39897697145933, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.73314720480577978607540330196', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.91985305847968993221634815183', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.32261477761151924592233971145', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 88.3407681100228, 'bad_primes': [2, 3], 'central_character': '8.3', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/7/b/c/319/5'], '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': '2-384-8.3-c6-0-44', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-384-8.3-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.39897697145933, 'root_angle': 0.5, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '1.73314720480577978607540330196', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2197025094455924778544863854906', 'Lhash_array': ['2197025094455924778544863854906'], 'label': '2-384-8.3-c6-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/7/b/c/319/5'}