-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '932104979307324687835302908403', 'a10': -1320, 'a2': -8, 'a3': 0, 'a4': 64, 'a5': 165, 'a6': 0, 'a7': -508, 'a8': -512, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.606374128427746, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 8]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '162.1', 'coefficient_field': '1.1.1.1', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1, 8], [1], [1, -165, 78125], [1, 508, 823543], [1, 3024, 19487171], [1, -5039, 62748517], [1, -3189, 410338673], [1, -1508, 893871739], [1, -75600, 3404825447], [1, -82665, 17249876309], [1, 174892, 27512614111], [1, 323569, 94931877133], [1, -308118, 194754273881], [1, -336680, 271818611107], [1, -383196, 506623120463], [1, 760206, 1174711139837], [1, -2225664, 2488651484819], [1, -2244815, 3142742836021], [1, -1473188, 6060711605323], [1, -5006892, 9095120158391], [1, 5898301, 11047398519097], [1, -7028768, 19203908986159], [1, -2651196, 27136050989627], [1, -6770901, 44231334895529], [1, -16176386, 80798284478113], [1, 2701614, 107213535210701], [1, -2068916, 122987386542487], [1, -9154500, 160578147647843], [1, -8686451, 182803912081669], [1, -24977553, 235260548044817]], 'euler_factors_factorization': [[[[1, 8], 1]], [1], [[[1, -165, 78125], 1]], [[[1, 508, 823543], 1]], [[[1, 3024, 19487171], 1]], [[[1, -5039, 62748517], 1]], [[[1, -3189, 410338673], 1]], [[[1, -1508, 893871739], 1]], [[[1, -75600, 3404825447], 1]], [[[1, -82665, 17249876309], 1]], [[[1, 174892, 27512614111], 1]], [[[1, 323569, 94931877133], 1]], [[[1, -308118, 194754273881], 1]], [[[1, -336680, 271818611107], 1]], [[[1, -383196, 506623120463], 1]], [[[1, 760206, 1174711139837], 1]], [[[1, -2225664, 2488651484819], 1]], [[[1, -2244815, 3142742836021], 1]], [[[1, -1473188, 6060711605323], 1]], [[[1, -5006892, 9095120158391], 1]], [[[1, 5898301, 11047398519097], 1]], [[[1, -7028768, 19203908986159], 1]], [[[1, -2651196, 27136050989627], 1]], [[[1, -6770901, 44231334895529], 1]], [[[1, -16176386, 80798284478113], 1]], [[[1, 2701614, 107213535210701], 1]], [[[1, -2068916, 122987386542487], 1]], [[[1, -9154500, 160578147647843], 1]], [[[1, -8686451, 182803912081669], 1]], [[[1, -24977553, 235260548044817], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-162-1.1-c7-0-3', 'leading_term': '1.420562673022654569893391027756000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/162/8/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [1.4205626730226546, 1.4048649002324545, 1.3580898441568137, 1.2811869725237186, 1.175721051802364, 1.0438458062072564, 0.8882674006961278, 0.7121981154608903, 0.5193006939375612, 0.3136239669599208, 0.09953048255436676, -0.11838299640557437, -0.3353711270102181, -0.5466306135588694, -0.7473945465171049, -0.9330290347141906, -1.0991305814329535, -1.24162253555375, -1.3568488457857797, -1.4416632645575818, -1.4935120938112694, -1.5105085431935874, -1.491496787170728, -1.4361038661699466, -1.344777682045291, -1.2188094931424347, -1.0603395210297208, -0.872344540256476, -0.65860663345227, -0.4236626541625127, -0.17273434469447396, 0.08836050027950237, 0.35331495963488324, 0.6154566419314026, 0.867886208968579, 1.1036284046687093, 1.3157927465769002, 1.4977405907022463, 1.6432548838411654, 1.7467085869363774, 1.8032275040188506, 1.8088430984618666, 1.7606308346968387, 1.6568296601100911, 1.49693844675671, 1.2817855507397842, 1.0135681198272222, 0.6958583841968267, 0.3335748937640222, -0.06708249360165996, -0.49873413212268114, -0.9529578644508568, -1.4204602419493233, -1.8912787960152404, -2.355011398964013, -2.8010677308379393, -3.218936928491012, -3.5984646713450354, -3.9301322891738004, -4.20532999367418, -4.416616066278345, -4.557953803518495, -4.624918245910477, -4.614865207047279, -4.527055878336825, -4.3627313044708425, -4.125132288640213, -3.8194617684104504, -3.452788367254342, -3.0338916283104953, -2.5730513233325243, -2.081785141704245, -1.5725409375433805, -1.058351480052816, -0.5524612454566911, -0.06793614190285382, 0.38273189018605813, 0.7880127654915786, 1.1377056997840398, 1.4232734284780322, 1.6381310095595067, 1.7778780789266866, 1.8404649276024596, 1.8262846861255255, 1.738186183494859, 1.5814046313640524, 1.3634100884989737, 1.0936765924316896, 0.783377801083555, 0.4450178563717065, 0.09200885106449803, -0.2617913625029316, -0.6025653436646893, -0.917029109794881, -1.192914119321014, -1.4194200728418418, -1.5876209251241378, -1.690807715320199, -1.7247537246455173, -1.6878900153015794, -1.5813825184026031, -1.4091054217579624, -1.1775095358676293, -0.8953884432037815, -0.5735494010980305, -0.22440000216069883, 0.1385346747794045, 0.5011464340792413, 0.849309236999024, 1.1694529029571785, 1.449121777439474, 1.677494876080507, 1.8458449794968708, 1.9479161118911545, 1.9802017434900727, 1.9421098240409524, 1.8360052514099472, 1.6671254371141304, 1.4433700481450684, 1.174971555407227, 0.8740586611754888, 0.5541297630750419, 0.22945809740560483, -0.08554613591767372, -0.3769887290948282, -0.6321301133821379, -0.8399801516774195, -0.9918207274553844, -1.0816303256473832, -1.1063886276350723, -1.0662441208850661, -0.9645336642237696, -0.8076496091450117, -0.6047571682643379, -0.36737192381407535, -0.1088143428601901, 0.15643543062677945, 0.4134537328105329, 0.6476274072393383, 0.8454097714238787, 0.9950413864487033, 1.0871990558429765, 1.1155388501714876, 1.0771030843596174, 0.9725669295078564, 0.8063074978349958, 0.5862864976944137, 0.3237465474837245, 0.032730543197452666, -0.2705573580267494, -0.5685220106491675, -0.8430441714044098, -1.0764033313648007, -1.2522116072741527, -1.356311718972065, -1.3775922889948897, -1.308676286200526, -1.1464433554601754, -0.8923538669616737, -0.5525515005780266, -0.1377316639680592, 0.33722545409609195, 0.8538464243763298, 1.3908581040011132, 1.925149452134942, 2.432858195019523, 2.89053105913883, 3.276300824702481, 3.571020729119087, 3.759297010731208, 3.8303637184258763, 3.7787502563323856, 3.6047012574331863, 3.31431990339032, 2.919419207533236, 2.437080413026652, 1.8889327997146337, 1.3001840594088567, 0.6984441962157215, 0.1123978712205634, -0.4296104533573758, -0.9010078875706921, -1.27836753560574, -1.5426535103934031, -1.6802689598567857, -1.6838481148074727, -1.5527453259226576, -1.293188837281306, -0.9180839327298064, -0.44646823828192067, 0.09735957624487983, 0.6849986706610991, 1.2853373350444692, 1.8661080283370086, 2.395527310088487, 2.8439356921143633, 3.1853507723658336, 3.398850014490907, 3.4697071516537092, 3.3902181123851536, 3.160168031612233, 2.7869095397469095, 2.2850431489572696, 1.6757120742122233, 0.9855450556211927, 0.24530049391245257, -0.5117176659232441, -1.251388383095301, -1.9405533682457992, -2.5487514498123858, -3.0498120202503385, -3.4232189669492303, -3.6551684467851544, -3.739260332274705, -3.676783272249435, -3.4765759722483858, -3.154471240275879, -2.732353193204594, -2.2368803876103573, -1.697947196394235, -1.1469713101822814, -0.6151058259396385, -0.13147929788185256, 0.27843400360604037, 0.5942185672669198, 0.8016146925601575, 0.8932438748833967, 0.868920201079187, 0.7355300840331961, 0.5064885914379796, 0.20080626342598645, -0.15817590218259753, -0.5443051704556962, -0.9302955566470252, -1.2894619971702619, -1.597402343949524, -1.833522224015782, -1.9823072880948955, -2.034262919572548, -1.9864621847770185, -1.8426674327750339, -1.6130179854855329, -1.3133041073391991, -0.9638741454830342, -0.5882456625429431, -0.21151096978532422, 0.14135861139824799, 0.4471981539550503, 0.6862125169044428, 0.84331328150862, 0.9091389631566442, 0.8806885122896256, 0.7615232626893237, 0.5615209069784352, 0.2961949467895118, -0.01437758007331724, -0.34695041143945826], 'positive_zeros': ['0.73530117773738863068457326807461', '2.15609466215075861131496236119529', '3.43394493779649865361903169249635', '5.28366390603081500853263125855800', '6.34631407208950333116419438056371', '7.42642812979380193590689330433737', '8.628944445581923731139193937098633', '9.521022211319110619683944604418994', '10.41390497604905468566831904534028', '11.27121190862890214399060433074563'], 'prelabel': '2-162-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.113815722130265, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c7-0', 'trace_hash': 271228242337374110, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.73530117773738863068457326807', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.15609466215075861131496236120', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43394493779649865361903169250', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 50.606374128427746, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, -8, 0, 64, 165, 0, -508, -512, 0, -1320, -3024, 0, 5039, 4064, 0, 4096, 3189, 0, 1508, 10560, 0, 24192, 75600, 0, -50900, -40312, 0, -32512, 82665, 0, -174892, -32768, 0, -25512, -83820, 0, -323569, -12064, 0, -84480, 308118, 0, 336680, -193536, 0, -604800, 383196, 0, -565479, 407200, 0, 322496, -760206, 0, -498960, 260096, 0, -661320, 2225664, 0, 2244815, 1399136, 0, 262144, 831435, 0, 1473188, 204096, 0, 670560, 5006892, 0, -5898301, 2588552, 0, 96512, 1536192, 0, 7028768, 675840, 0, -2464944, 2651196, 0, 526185, -2693440, 0, 1548288, 6770901, 0, -2559812, 4838400, 0, -3065568, 248820, 0, 16176386, 4523832, 0, -3257600], 'euler11': [1, 3024, 19487171], 'euler13': [1, -5039, 62748517], 'euler17': [1, -3189, 410338673], 'euler19': [1, -1508, 893871739], 'euler2': [1, 8, 0], 'euler23': [1, -75600, 3404825447], 'euler29': [1, -82665, 17249876309], 'euler3': [1, 0, 0], 'euler31': [1, 174892, 27512614111], 'euler37': [1, 323569, 94931877133], 'euler41': [1, -308118, 194754273881], 'euler43': [1, -336680, 271818611107], 'euler47': [1, -383196, 506623120463], 'euler5': [1, -165, 78125], 'euler53': [1, 760206, 1174711139837], 'euler59': [1, -2225664, 2488651484819], 'euler61': [1, -2244815, 3142742836021], 'euler67': [1, -1473188, 6060711605323], 'euler7': [1, 508, 823543], 'euler71': [1, -5006892, 9095120158391], 'euler73': [1, 5898301, 11047398519097], 'euler79': [1, -7028768, 19203908986159], 'euler83': [1, -2651196, 27136050989627], 'euler89': [1, -6770901, 44231334895529], 'euler97': [1, -16176386, 80798284478113], 'euler_factors': [[1, 8, 0], [1, 0, 0], [1, -165, 78125], [1, 508, 823543], [1, 3024, 19487171], [1, -5039, 62748517], [1, -3189, 410338673], [1, -1508, 893871739], [1, -75600, 3404825447], [1, -82665, 17249876309], [1, 174892, 27512614111], [1, 323569, 94931877133], [1, -308118, 194754273881], [1, -336680, 271818611107], [1, -383196, 506623120463], [1, 760206, 1174711139837], [1, -2225664, 2488651484819], [1, -2244815, 3142742836021], [1, -1473188, 6060711605323], [1, -5006892, 9095120158391], [1, 5898301, 11047398519097], [1, -7028768, 19203908986159], [1, -2651196, 27136050989627], [1, -6770901, 44231334895529], [1, -16176386, 80798284478113]], 'index': 3, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/8/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/162/8/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': 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': '2-162-1.1-c7-0-3', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-162-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.113815722130265, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7-0', 'trace_hash': 271228242337374110, 'z1': {'__RealLiteral__': 0, 'data': '0.73530117773738863068457326807', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20521190
{'Lhash': '932104979307324687835302908403', 'Lhash_array': ['932104979307324687835302908403'], 'label': '2-162-1.1-c7-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/8/a/a'}
-
id: 24574551
{'Lhash': '932104979307324687835302908403', 'Lhash_array': ['932104979307324687835302908403'], 'label': '2-162-1.1-c7-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/8/a/a/1/1'}