-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1346919765328379254166733321815,1784475060792349150003189722885', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5846.857224180202, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 2, 1]], [19, [1, -2, 1]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '9576.1', 'coefficient_field': '1.1.1.1', 'conductor': 91699776, 'conductor_radical': 798, 'degree': 4, 'euler_factors': [[1], [1], [1, -2, 6, -10, 25], [1, 2, 1], [1, 6, 26, 66, 121], [1, 6, 30, 78, 169], [1, -10, 54, -170, 289], [1, -2, 1], [1, 2, 42, 46, 529], [1, -8, 54, -232, 841], [1, 8, 58, 248, 961], [1, 0, -6, 0, 1369], [1, -4, 86, -164, 1681], [1, 8, 102, 344, 1849], [1, 4, 78, 188, 2209], [1, -8, 102, -424, 2809], [1, 16, 182, 944, 3481], [1, -8, 118, -488, 3721], [1, -6, 138, -402, 4489], [1, 12, 158, 852, 5041], [1, 0, 126, 0, 5329], [1, -18, 194, -1422, 6241], [1, -4, 170, -332, 6889], [1, 4, 102, 356, 7921], [1, 2, 190, 194, 9409], [1, 14, 126, 1414, 10201], [1, 24, 330, 2472, 10609], [1, 4, None, 428, 11449], [1, 0, 138, 0, 11881], [1, -4, 150, -452, 12769]], 'euler_factors_factorization': [[1], [1], [[[1, -2, 6, -10, 25], 1]], [[[1, 1], 2]], [[[1, 6, 26, 66, 121], 1]], [[[1, 6, 30, 78, 169], 1]], [[[1, -10, 54, -170, 289], 1]], [[[1, -1], 2]], [[[1, 2, 42, 46, 529], 1]], [[[1, -8, 54, -232, 841], 1]], [[[1, 8, 58, 248, 961], 1]], [[[1, 0, -6, 0, 1369], 1]], [[[1, -2, 41], 2]], [[[1, 4, 43], 2]], [[[1, 4, 78, 188, 2209], 1]], [[[1, -8, 102, -424, 2809], 1]], [[[1, 8, 59], 2]], [[[1, -8, 118, -488, 3721], 1]], [[[1, -6, 138, -402, 4489], 1]], [[[1, 12, 158, 852, 5041], 1]], [[[1, 0, 126, 0, 5329], 1]], [[[1, -18, 194, -1422, 6241], 1]], [[[1, -2, 83], 2]], [[[1, 4, 102, 356, 7921], 1]], [[[1, 2, 190, 194, 9409], 1]], [[[1, 14, 126, 1414, 10201], 1]], [[[1, 24, 330, 2472, 10609], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 14, 'label': '4-9576e2-1.1-c1e2-0-14', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/9576/2/a/bp', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0234375', 'prec': 30}, 'plot_values': [4.790468171583528e-121, 0.01038012491551622, 0.04143250333072248, 0.09289307720485845, 0.16432019162297026, 0.255094400726128, 0.3644145411461205, 0.49129928658466826, 0.6345809493224261, 0.7929107116278623, 0.9647512797964221, 1.148387433539161, 1.3419196232688, 1.5432808845608956, 1.7502342559880895, 1.9603962672651791, 2.17124153491359, 2.3801320317271757, 2.584332294345448, 2.7810426117447093, 2.9674278987277014, 3.140651901463495, 3.297921950788195, 3.436520373820834, 3.553866090533308, 3.647538739850592, 3.7153565222347367, 3.755388186746909, 3.766044794754666, 3.7460747479875893, 3.6946654296157657, 3.6114169378474927, 3.496448044154839, 3.350345257665007, 3.1742664204616893, 2.9698631509945868, 2.7393748486945846, 2.485524389562496, 2.2115954735286456, 1.9213035617078076, 1.6188504487609665, 1.3087746792531048, 0.9959789683628603, 0.6855665125924181, 0.38283933517683677, 0.09312878413444817, -0.17823412500216143, -0.4260843911400065, -0.6454763264636837, -0.8318352050605449, -0.9810265788028245, -1.089484033466873, -1.1542840160621666, -1.1732412311741969, -1.1449763377234656, -1.0689729537220638, -0.945624515193384, -0.7762502284150569, -0.5631076376766107, -0.3093689422980331, -0.019087523024597815, 0.30285951397131283, 0.6508594690973907, 1.0186450354897367, 1.3994413288694438, 1.7860563291612144, 2.1710857771382255, 2.5469962031253526, 2.9063809922999058, 3.242017813443413, 3.5471636904902684, 3.815569126239566, 4.041795398424433, 4.221170115948996, 4.350106794964059, 4.425990941893469, 4.447480760849454, 4.4143188535382345, 4.327593981582489, 4.1894806091513965, 4.0034450652301565, 3.773922739591246, 3.506457552318553, 3.207333825815215, 2.8836451778864554, 2.5429040646232233, 2.193044321757493, 1.8420352944690992, 1.4978303283183967, 1.1680136246845563, 0.8597140137392499, 0.5793108132592898, 0.33233722977372293, 0.12326650839048124, -0.044568493865785694, -0.16909536280761622, -0.24954095655072267, -0.28645402230897005, -0.2816815468322924, -0.23830119322719284, -0.1605219177929002, -0.0535441603829654, 0.07661860097434957, 0.2233248669586079, 0.37955489562377187, 0.5381076090029564, 0.6919032127533482, 0.8341562199817146, 0.9587034627758128, 1.0601194064950004, 1.1340363511806422, 1.177174599001195, 1.1876201702235283, 1.164752673872916, 1.109449241481718, 1.0239060231975117, 0.9117452127486767, 0.77774036982234, 0.6278156273624761, 0.46869865917025727, 0.3078160385717989, 0.15290870657699765, 0.011843096552363501, -0.10776929896760981, -0.19881118354117955, -0.2549929878044915, -0.2710979857572929, -0.2432310113033846, -0.1690196755738409, -0.047751082334832606, 0.11951919847698642, 0.32995415979635423, 0.5789585211816585, 0.8602829659402838, 1.166204454111511, 1.4877224538140335, 1.8149016964843876, 2.1371188007588935, 2.443550642512701, 2.7234182360788486, 2.9665823668516786, 3.163726970881165, 3.3070059175666464, 3.3901116160734293, 3.4089057302937436, 3.3613304386837766, 3.2479535766317973, 3.0716987778967026, 2.838243127945174, 2.5555660723970717, 2.2341548324798493, 1.8863973334672561, 1.526575664160447, 1.170151711745954, 0.8335588455806433, 0.5334468070722044, 0.2863126314842473, 0.10778054970886206, 0.01214057066565049, 0.011737685564352868, 0.11650634411144674, 0.3335305395105702, 0.6666712677343818, 1.1163361879167912, 1.6792930707013243, 2.3486573568155635, 3.11396735196278, 3.961364150606725, 4.873975601599133, 5.83223053974921, 6.8145617843531, 7.797770381291764, 8.758017927676956, 9.671140920521584, 10.513865068910533, 11.263967912545432, 11.901617961175955, 12.409296670272989, 12.773147808648298, 12.982596682742725, 13.031593012229326, 12.917902856259124, 12.644142245476523, 12.216760660530117, 11.646791120129572, 10.948587219541334, 10.140254465350202, 9.242239439254353, 8.277451324310427, 7.26982603347875, 6.244189577325656, 5.224927891590228, 4.235678489026042, 3.2982264396529932, 2.4321322340670317, 1.6539468050057422, 0.9768882704005454, 0.4104275957118677, -0.039885980801306696, -0.37246627183277625, -0.5896447745986237, -0.697386575941407, -0.7049935144778661, -0.6245854513216053, -0.47056494759850304, -0.2589844282267979, -0.006827365974823373, 0.26860655519056875, 0.5505162837365934, 0.8230726658175582, 1.07222445498737, 1.2859338641105498, 1.4548696640118177, 1.5723509252928813, 1.6348421496453205, 1.6416010418912617, 1.594924787919179, 1.499547406392417, 1.3626298180344432, 1.1929936090910063, 1.0008928644443222, 0.7971971293751023, 0.5930220375309583, 0.39898047961469096, 0.22477468656943672, 0.07862000903411592, -0.03309163453600654, -0.10612391250837504, -0.138564267954811, -0.13088612949740436, -0.08588298263615178, -0.008484938551912687, 0.09456271371531025, 0.21505847488256616, 0.34389337339784537, 0.47148229318133467, 0.5884659482238556, 0.6860972783418802, 0.7569893347461983, 0.7953471927301046, 0.7976404860106516, 0.7625998393520307, 0.6917016767850004, 0.5888926224675858, 0.46080532294072635, 0.3162265793572412, 0.16601151091343483, 0.022361620891830376, -0.10153754118097302, -0.1923233337872352, -0.23701297242125777, -0.2237710923806408, -0.14253442360035484, 0.014379842671518983, 0.251732814584661, 0.571005827239944, 0.970091774915239, 1.4432300767089832, 1.981050401000316, 2.570783802439556, 3.1967260581462345, 3.8406481670119925, 4.482679116066234, 5.101790170420716, 5.677026288724688, 6.187911000053139, 6.615894596800987, 6.944526330596482, 7.160947436139159, 7.255706422588644, 7.224114043134676, 7.065631731580283, 6.784926914003024, 6.390835316635912, 5.897005785887581, 5.320511931827406, 4.68204760864979, 4.004328462603912, 3.3118799394365177, 2.6294122438042864, 1.9813176520899969, 1.3902142043655188, 0.8763242767520747, 0.4563594782103207, 0.14297717211582808, -0.05587568062022394, -0.1372424194034186, -0.10331392288290323, 0.038695036809080346, 0.2768401230807603, 0.595042018595752, 0.9737038728509739, 1.3907577300577916, 1.8224169410526085, 2.2445708815866037, 2.633457546328708, 2.967236534666164, 3.226379350225965, 3.395215077286875, 3.461885868735067, 3.419662414736154, 3.2663913041704933, 3.0054184411000198, 2.6445492394946237, 2.196490314656372, 1.6774354163690324, 1.107025562104081, 0.506745830524736, -0.10050557409232426, -0.6919861122304426, -1.2457672720799613, -1.7420486451359554, -2.1638387537181196, -2.4978391265496867, -2.734941823508632, -2.8705869982855563, -2.9049118871199253, -2.8425831669228834, -2.6925066177567434, -2.467233740386797, -2.18223521962351, -1.8550606127393796, -1.5042733825035752, -1.148587203791887, -0.8056362804050425, -0.49131269153264395, -0.21858676600193677, 0.0027737895652812177, 0.16712208533610307, 0.2727304127712944, 0.32228428752032284, 0.3221982282081527, 0.2826083843830428, 0.21630670784663517, 0.13826086539501695, 0.06434848046359533, 0.010538388876953646, -0.008350137770872679, 0.02041222111070587, 0.10646985837824102, 0.2555797076847519, 0.46903107904038394, 0.7432319652043992, 1.0696226402488653, 1.434841714806825, 1.8211017972030865, 2.207024475670778, 2.568337611928578, 2.8793437595141635, 3.11371473733689, 3.246434469812453, 3.2544259379420133, 3.1187118041725297, 2.824621938151601, 2.3638639169406352, 1.7341256619090366, 0.9407548566015045, -0.0043205721432959384, -1.0815392723398944, -2.265415751311468, -3.524235015766534, -4.822213651292505, -6.119923455566515, -7.376630460725351, -8.551288280011686, -9.604735509099244, -10.500986489944776, -11.208982962790618, -11.703846999280284, -11.967958315624267, -11.991834383016744, -11.774427250256295, -11.323360136167459, -10.654483933368779, -9.791316071671707, -8.764038684948552, -7.608131867358184, -6.36310463902549, -5.070462449293151, -3.7725164096428467, -2.5099451602924905, -1.3210157893951042, -0.23906953046402693, 0.7075890596711225, 1.4979478777896742, 2.1176002905954414, 2.5604668382872964, 2.827333250963004, 2.926873269845833, 2.8735820208561855, 2.6880742979758265, 2.3946971128745758, 2.0212166075637024, 1.5964505440097194, 1.1495672046253875, 0.7080681048425159, 0.29698188155948124, -0.06254749075739678, -0.3538906756977687, -0.5656073620100984, -0.6916800174641714, -0.7314647606817891, -0.6894141588262952, -0.5744562441865451, -0.39921703192825253, -0.1790807836247759, 0.0689597884107207, 0.3272640840029074, 0.5788544845069075, 0.8081195324955391, 1.0020432557929242, 1.1504509426300864, 1.2469407076606107, 1.2885898412113017, 1.2764492144565904, 1.2147589081215597, 1.1109743138042814, 0.9746537195944548, 0.8170984979277758, 0.6501472406701305, 0.48560387296932406, 0.3341873276061897, 0.20496863163210385, 0.10467984243929822, 0.0373724273323602, 0.004195895528120369, 0.0034268168518283705, 0.030709045245625226, 0.07950040578933988, 0.1416512739845636, 0.20819915166883884, 0.2700785319181366, 0.31909138444647495, 0.34850925492488055, 0.35398657444481446, 0.33384408043844827, 0.28968926305119447, 0.22625226015254196, 0.15153746035466156, 0.07619955351216005, 0.013161049436196623, -0.023361227780858567, -0.01870049363044574, 0.04114517641488025, 0.16841084195636197, 0.37256435101233404, 0.6592447590828281, 1.029614991833949, 1.4796689281608855, 2.000094422169453, 2.5762318239804185, 3.18847614352079, 3.8130538650129844, 4.422846039311045, 4.988985890372825, 5.481854200293856, 5.87332204145335, 6.1375889628553075, 6.253743134222659, 6.206104602842669, 5.98668552555351, 5.594772290088889, 5.038865568376274, 4.33537513055517, 3.5097092065946076, 2.5941363879517385, 1.6278618136799674, 0.65429260563228, -0.27984788026515406, -1.127472746863973, -1.842712835233855, -2.3836422461105835, -2.7141187077886344, -2.8058641919480545, -2.6400416467371284, -2.2083942857756584, -1.51405530697823, -0.571642577267457, 0.5930773569024218, 1.9440165342638653, 3.4364189988936817, 5.018276748306291, 6.633224452637564, 8.222062290745214, 9.726578232300279, 11.090644447369103, 12.26447595567793, 13.20482766684834, 13.879118536534227, 14.264419556054513, 14.35090792583729, 14.139570366488243, 13.644594038357006, 12.889967632941495, 11.910636374786927, 10.748406475403652, 9.451935427786147, 8.072502850318845, 6.663146694486073, 5.274861324287248, 3.955297006481899, 2.745984719308325, 1.6811933662651262, 0.7862078234492679, 0.07656107754261514, -0.4417230561009817, -0.7718839224590951, -0.926575777906734, -0.9262852820854764, -0.7957590723494394, -0.5673043706174108, -0.2782384616985916], 'positive_zeros': ['1.06253234533701804970516112835826', '1.40770261180097262244541817007713', '2.19628579670689065891934734060257', '2.37727265390168097453209292552835', '2.86150048264250425115867151696106', '3.03080944469916260484713513206021', '3.71236298188686259298093930437002', '3.71769567864192478583617791018172', '4.63827208955850708369141916845312', '4.82872440384361548174008013630625', '5.28906491480325043859367010864923', '5.41620808211978932750062680225927', '5.79296642442226513235641897268461', '5.92794714347534419531652616140076', '6.67153638661439331718921644210204', '6.74501910984697976146392828345649', '7.21485225397475412147114786576746', '7.66372358086910743812149147043717'], 'prelabel': '4-9576e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.744412214413165, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 82591092214390151, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06253234533701804970516112836', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.40770261180097262244541817008', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.19628579670689065891934734060', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5846.857224180202, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 91699776, 'conductor_radical': 798, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, -2, 0, 0, 0, -6, 0, -6, 0, 0, 0, 10, 0, 2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 8, 0, -8, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, -8, 0, 0, 0, -4, 0, 3, 0, 0, 0, 8, 0, -12, 0, 0, 0, -16, 0, 8, 0, 0, 0, -12, 0, 6, 0, 0, 0, -12, 0, 0, 0, 0, 0, 12, 0, 18, 0, 0, 0, 4, 0, 20, 0, 0, 0, -4, 0, 12, 0, 0, 0, 4, 0, -2, 0, 0, 0], 'euler11': [1, 6, 26, 66, 121], 'euler13': [1, 6, 30, 78, 169], 'euler17': [1, -10, 54, -170, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 2, 42, 46, 529], 'euler29': [1, -8, 54, -232, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 8, 58, 248, 961], 'euler37': [1, 0, -6, 0, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 4, 78, 188, 2209], 'euler5': [1, -2, 6, -10, 25], 'euler53': [1, -8, 102, -424, 2809], 'euler59': [1, 16, 182, 944, 3481], 'euler61': [1, -8, 118, -488, 3721], 'euler67': [1, -6, 138, -402, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, 12, 158, 852, 5041], 'euler73': [1, 0, 126, 0, 5329], 'euler79': [1, -18, 194, -1422, 6241], 'euler83': [1, -4, 170, -332, 6889], 'euler89': [1, 4, 102, 356, 7921], 'euler97': [1, 2, 190, 194, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -2, 6, -10, 25], [1, 2, 1, 0, 0], [1, 6, 26, 66, 121], [1, 6, 30, 78, 169], [1, -10, 54, -170, 289], [1, -2, 1, 0, 0], [1, 2, 42, 46, 529], [1, -8, 54, -232, 841], [1, 8, 58, 248, 961], [1, 0, -6, 0, 1369], [1, -4, 86, -164, 1681], [1, 8, 102, 344, 1849], [1, 4, 78, 188, 2209], [1, -8, 102, -424, 2809], [1, 16, 182, 944, 3481], [1, -8, 118, -488, 3721], [1, -6, 138, -402, 4489], [1, 12, 158, 852, 5041], [1, 0, 126, 0, 5329], [1, -18, 194, -1422, 6241], [1, -4, 170, -332, 6889], [1, 4, 102, 356, 7921], [1, 2, 190, 194, 9409]], 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9576/2/a/bp'], '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': '4-9576e2-1.1-c1e2-0-14', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-9576e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.744412214413165, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 82591092214390151, 'z1': {'__RealLiteral__': 0, 'data': '1.06253234533701804970516112836', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1346919765328379254166733321815,1784475060792349150003189722885', 'Lhash_array': ['1346919765328379254166733321815', '1784475060792349150003189722885'], 'label': '4-9576e2-1.1-c1e2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9576/2/a/bp'}