-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2378069107202188799353611932102', 'a10': 2, 'a2': -1, 'a3': -1, 'a4': 1, 'a5': -2, 'a6': 1, 'a7': 1, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [7, [1, -1]], [11, [1, -1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '462.1', 'coefficient_field': '1.1.1.1', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, 2, 5], [1, -1], [1, -1], [1, -2, 13], [1, 6, 17], [1, 4, 19], [1, 4, 23], [1, -2, 29], [1, 4, 31], [1, 2, 37], [1, 6, 41], [1, 0, 43], [1, 8, 47], [1, 14, 53], [1, -12, 59], [1, 14, 61], [1, -4, 67], [1, -12, 71], [1, -6, 73], [1, 0, 79], [1, 0, 83], [1, 6, 89], [1, 14, 97], [1, -10, 101], [1, 4, 103], [1, -12, 107], [1, -10, 109], [1, 6, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, 1], 1]], [[[1, 2, 5], 1]], [[[1, -1], 1]], [[[1, -1], 1]], [[[1, -2, 13], 1]], [[[1, 6, 17], 1]], [[[1, 4, 19], 1]], [[[1, 4, 23], 1]], [[[1, -2, 29], 1]], [[[1, 4, 31], 1]], [[[1, 2, 37], 1]], [[[1, 6, 41], 1]], [[[1, 0, 43], 1]], [[[1, 8, 47], 1]], [[[1, 14, 53], 1]], [[[1, -12, 59], 1]], [[[1, 14, 61], 1]], [[[1, -4, 67], 1]], [[[1, -12, 71], 1]], [[[1, -6, 73], 1]], [[[1, 0, 79], 1]], [[[1, 0, 83], 1]], [[[1, 6, 89], 1]], [[[1, 14, 97], 1]], [[[1, -10, 101], 1]], [[[1, 4, 103], 1]], [[[1, -12, 107], 1]], [[[1, -10, 109], 1]], [[[1, 6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-462-1.1-c1-0-5', '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/462/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-7.51849605863036e-120, 0.15533359445760025, 0.31313388748205817, 0.4746135813793227, 0.638722667860868, 0.801528500696493, 0.9560080878817925, 1.0922109006103151, 1.1977458117917268, 1.2585653847754468, 1.2600320780369505, 1.188241586650816, 1.0315505256440247, 0.7822165650412817, 0.43801742894384293, 0.0036788941864678796, -0.5080815382136934, -1.0760927025702376, -1.6710264392205219, -2.2565815755669996, -2.79160805792277, -3.2331242922968304, -3.540064962893797, -3.6774767431558972, -3.620770582273654, -3.359558605978513, -2.900567777019122, -2.269145163547492, -1.508959342865101, -0.6796596480677064, 0.14752937908416672, 0.8960459834332917, 1.491563381203475, 1.870156181190729, 1.9861414757376317, 1.8185928319915579, 1.3755675802316938, 0.6952673238821921, -0.15633687807981497, -1.0914656390364994, -2.009651936835109, -2.809118534828464, -3.3991053354298986, -3.71157738491533, -3.7106802463601296, -3.398477688586019, -2.815908863413054, -2.0385034168848035, -1.1671223856708923, -0.3147502646794178, 0.408967024294171, 0.9132777250895978, 1.1396455159573606, 1.070695708257862, 0.7331902619947491, 0.1942809770624467, -0.4486767891213872, -1.0834036219495793, -1.600804926769974, -1.913042937706949, -1.9685480718561925, -1.761296491611361, -1.332518481553132, -0.7642170375263271, -0.16528033366764783, 0.34767256849901607, 0.6715155098868405, 0.7361662039346869, 0.5188272295518644, 0.05006210222445729, -0.5897878571296865, -1.2836171136604506, -1.8979879055561124, -2.3074616757583306, -2.4183891427903177, -2.1875988746169126, -1.6321833595358688, -0.8281269711875966, 0.10240341973921356, 1.0130570856599226, 1.7605982750696314, 2.2322717190630685, 2.3677499375062663, 2.1710324377440484, 1.7095205449508615, 1.1000211556897836, 0.48415175934257704, -0.002032104405753568, -0.25790706558453086, -0.2411676163600434, 0.021577948470094213, 0.4394152273329194, 0.8766816317908842, 1.1839147781809942, 1.2338975384509694, 0.9549798982867671, 0.353955015648741, -0.47742513153350713, -1.3749736283875396, -2.132266038021686, -2.543129852402952, -2.4479483059287706, -1.7738695536216136, -0.559670881427393, 1.0412356542435215, 2.781830292958988, 4.363639531310588, 5.492370813883425, 5.936049320577576, 5.5735685003862265, 4.423041432933185, 2.6432027085467635, 0.5066159381492517, -1.6505603529522255, -3.4923211103601837, -4.746985859779029, -5.2583280221459265, -5.012792497493332, -4.136998409305953, -2.866183085367822, -1.490658696049585, -0.29225440539373176, 0.5150553414594068, 0.8271466035914764, 0.665241964898782, 0.16199245031426898, -0.4778587471312492, -1.0322648786317354, -1.3185675232579213, -1.2382392691237691, -0.7989068522872239, -0.10862407998227226, 0.65564049455959, 1.2968253623521804, 1.651055109215306, 1.631420021599335, 1.25078915688652, 0.6176768594380563, -0.09371788817809422, -0.6913025681939595, -1.0178771389426902, -0.9945995377890592, -0.643155812595271, -0.08027551861485818, 0.5143140880417453, 0.9480835687011071, 1.0704454508561478, 0.8168610319588636, 0.22968434670236165, -0.5507518318893783, -1.323178044425008, -1.8809891496464588, -2.0712913970602456, -1.8407647245472651, -1.2547945171401387, -0.48333586573504767, 0.2438941129895534, 0.7015120035292707, 0.7345011102164669, 0.30748162497462156, -0.47763114028127296, -1.4022252122984997, -2.1860386605120006, -2.5629728912537697, -2.357490932530474, -1.5402654613439035, -0.24649681895146544, 1.2500817863537508, 2.6025262809414196, 3.4792450306457243, 3.65261754437835, 3.0635234208431843, 1.843324599667715, 0.2858449867343216, -1.2246668440167598, -2.311383089030626, -2.702781042511384, -2.304149279383745, -1.222943589294853, 0.25950083597879714, 1.7627751782638434, 2.9086778950079517, 3.4213792323333663, 3.1989327237560325, 2.3363835476595662, 1.0941715122589122, -0.17909394451096095, -1.1474550038233036, -1.5832055183654048, -1.4298699869316451, -0.8144822258583778, -0.005712067972278918, 0.6698590732404626, 0.9287122675997475, 0.6188025526079688, -0.23091191662504612, -1.4148707065525277, -2.6084697679909747, -3.4622608230099803, -3.705268154876425, -3.2269494141071067, -2.1133932944246103, -0.6267097562651311, 0.8666945513419106, 1.9981280244893949, 2.499095908939588, 2.2743235161874367, 1.4242301114279912, 0.21091006616572816, -1.0214399495531175, -1.9472197953265176, -2.3508380253983074, -2.1817632147530923, -1.557746669030612, -0.7169988915595318, 0.06408526692151127, 0.5606391043292099, 0.6677038429372777, 0.4259418495589262, -0.0024204356303285175, -0.39809196585190865, -0.567030541029814, -0.4121327295867231, 0.030494948064756673, 0.60350085364793, 1.0848721501000937, 1.2700518761797486, 1.0512090075086202, 0.4654326281920061, -0.30658247334248984, -0.9933721536437154, -1.3213638310646993, -1.1106001257401246, -0.344929925931034, 0.8088738645785079, 2.0425954204876526, 2.9982065299337815, 3.3817871775256267, 3.062966877693166, 2.126056589034264, 0.8533773319392737, -0.35722875457507436, -1.1168940909710934, -1.1734406549325969, -0.5006282591256854, 0.6821067895956556, 1.9692088452851042, 2.892294390361924, 3.0702853614448498, 2.339269774695916, 0.8195822575058961, -1.1039454769043093, -2.8858146799060367, -3.9782578330003866, -3.996569973669422, -2.8402902375319767, -0.7318200899619614], 'positive_zeros': ['1.87596574858564202101556695192438', '3.72716170584453900058590617218931', '4.72832473817225769292057457440268', '6.17569848665337782312463950998811', '6.91394332771191655575545668717976', '8.036862420200993690310137538450254', '8.635812633514396852158410641487839', '9.736475583363369767193155110475435', '10.87433876808485933510030987852768'], 'prelabel': '2-462-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 2123292645045813547, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.87596574858564202101556695192', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.72716170584453900058590617219', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.72832473817225769292057457440', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, -2, 1, 1, -1, 1, 2, 1, -1, 2, -1, 2, 1, -6, -1, -4, -2, -1, -1, -4, 1, -1, -2, -1, 1, 2, -2, -4, -1, -1, 6, -2, 1, -2, 4, -2, 2, -6, 1, 0, 1, -2, 4, -8, -1, 1, 1, 6, 2, -14, 1, -2, -1, 4, -2, 12, 2, -14, 4, 1, 1, -4, 1, 4, -6, 4, 2, 12, -1, 6, 2, 1, -4, 1, 2, 0, -2, 1, 6, 0, -1, 12, 0, -2, -1, -6, 2, 2, -4, 4, 8, 8, 1, -14, -1, 1, -1], 'euler11': [1, -1, 0], 'euler13': [1, -2, 13], 'euler17': [1, 6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 4, 23], 'euler29': [1, -2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 0, 43], 'euler47': [1, 8, 47], 'euler5': [1, 2, 5], 'euler53': [1, 14, 53], 'euler59': [1, -12, 59], 'euler61': [1, 14, 61], 'euler67': [1, -4, 67], 'euler7': [1, -1, 0], 'euler71': [1, -12, 71], 'euler73': [1, -6, 73], 'euler79': [1, 0, 79], 'euler83': [1, 0, 83], 'euler89': [1, 6, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 2, 5], [1, -1, 0], [1, -1, 0], [1, -2, 13], [1, 6, 17], [1, 4, 19], [1, 4, 23], [1, -2, 29], [1, 4, 31], [1, 2, 37], [1, 6, 41], [1, 0, 43], [1, 8, 47], [1, 14, 53], [1, -12, 59], [1, 14, 61], [1, -4, 67], [1, -12, 71], [1, -6, 73], [1, 0, 79], [1, 0, 83], [1, 6, 89], [1, 14, 97]], 'index': 5, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/462/a', 'ModularForm/GL2/Q/holomorphic/462/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/462/2/a/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-462-1.1-c1-0-5', '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': '2-462-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2123292645045813547, 'z1': {'__RealLiteral__': 0, 'data': '1.87596574858564202101556695192', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 10913267
{'Lhash': '2378069107202188799353611932102', 'Lhash_array': ['2378069107202188799353611932102'], 'label': '2-462-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/2/a/a'}
-
id: 24549426
{'Lhash': '2378069107202188799353611932102', 'Lhash_array': ['2378069107202188799353611932102'], 'label': '2-462-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/2/a/a/1/1'}
-
id: 94505
{'Lhash': '2123292645045813547', 'Lhash_array': ['2123292645045813547'], 'label': '2-462-1.1-c1-0-5', 'type': 'ECQ', 'url': 'EllipticCurve/Q/462/a'}