-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1001605382487170025293466074902,1092437667633634156914261729700', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6123.593669522886, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '9800.1', 'coefficient_field': '1.1.1.1', 'conductor': 96040000, 'conductor_radical': 70, 'degree': 4, 'euler_factors': [[1], [1, -1, 2, -3, 9], [1], [1], [1, 1, 18, 11, 121], [1, -1, -12, -13, 169], [1, -11, 60, -187, 289], [1, -6, 30, -114, 361], [1, -2, 30, -46, 529], [1, -5, 60, -145, 841], [1, -4, -2, -124, 961], [1, 0, 6, 0, 1369], [1, 6, 74, 246, 1681], [1, -6, 78, -258, 1849], [1, -9, 110, -423, 2209], [1, -18, 170, -954, 2809], [1, -8, 134, -472, 3481], [1, -22, 226, -1342, 3721], [1, -12, 102, -804, 4489], [1, 0, 142, 0, 5041], [1, -8, 94, -584, 5329], [1, 11, 150, 869, 6241], [1, -24, 310, -1992, 6889], [1, 2, 162, 178, 7921], [1, -15, 212, -1455, 9409], [1, 12, 238, 1212, 10201], [1, 3, 102, 309, 10609], [1, 22, 318, 2354, 11449], [1, 13, 256, 1417, 11881], [1, 0, 158, 0, 12769]], 'euler_factors_factorization': [[1], [[[1, -1, 2, -3, 9], 1]], [1], [1], [[[1, 1, 18, 11, 121], 1]], [[[1, -1, -12, -13, 169], 1]], [[[1, -11, 60, -187, 289], 1]], [[[1, -6, 30, -114, 361], 1]], [[[1, -2, 30, -46, 529], 1]], [[[1, -5, 60, -145, 841], 1]], [[[1, -4, -2, -124, 961], 1]], [[[1, 0, 6, 0, 1369], 1]], [[[1, 6, 74, 246, 1681], 1]], [[[1, -6, 78, -258, 1849], 1]], [[[1, -9, 110, -423, 2209], 1]], [[[1, -18, 170, -954, 2809], 1]], [[[1, -4, 59], 2]], [[[1, -22, 226, -1342, 3721], 1]], [[[1, -12, 102, -804, 4489], 1]], [[[1, 0, 71], 2]], [[[1, -8, 94, -584, 5329], 1]], [[[1, 11, 150, 869, 6241], 1]], [[[1, -12, 83], 2]], [[[1, 2, 162, 178, 7921], 1]], [[[1, -15, 212, -1455, 9409], 1]], [[[1, 6, 101], 2]], [[[1, 3, 102, 309, 10609], 1]], [[[1, 22, 318, 2354, 11449], 1]], [[[1, 13, 256, 1417, 11881], 1]], [[[1, 0, 158, 0, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 4, 'label': '4-9800e2-1.1-c1e2-0-4', 'leading_term': '6.82934043514454142123850653784637858835884623557245634213750000000000000000000000000000000', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/9800/2/a/by', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0234375', 'prec': 30}, 'plot_values': [6.829340435144541, 6.811622730907142, 6.777524777729613, 6.714296348867254, 6.623271469092134, 6.508430461783872, 6.3701976087015595, 6.208505200400531, 6.02444119369656, 5.819421666742971, 5.594788569712485, 5.352002796067006, 5.0927836031097256, 4.81901654478121, 4.532759104866079, 4.23620520558618, 3.9317272070357325, 3.6218076328300537, 3.309070015146381, 2.9962024986648657, 2.6859852826222297, 2.3812030627962817, 2.084663589178228, 1.7991045316655392, 1.5272021757765186, 1.2714773570459579, 1.0342939346878377, 0.8177694772372187, 0.6237650249220987, 0.45380621793088527, 0.3090675236111762, 0.1903091445125147, 0.09786044418412082, 0.03157705105133859, -0.009170606386639985, -0.02551701603110082, -0.01910139990565865, 0.007936841518678663, 0.05297642560596592, 0.11294187416298167, 0.18434553869034612, 0.26333486631913755, 0.3457621283297341, 0.4272453376110903, 0.503267305691764, 0.5692421830849115, 0.6206425838077856, 0.6530621454296852, 0.6623662921331406, 0.6447403975838131, 0.5968566308991344, 0.5158974417251438, 0.39972821077730863, 0.2468869773880264, 0.05675066383557668, -0.17051575396287194, -0.43381253381460266, -0.7312000952350762, -1.059784416177713, -1.415855593161216, -1.7948159932412218, -2.191357563090181, -2.5994399995051074, -3.0124975353394587, -3.423469783417919, -3.8250248578423496, -4.209640086895245, -4.569825475558598, -4.898245694876064, -5.187926499537301, -5.432403908953198, -5.625896592774925, -5.76346362683381, -5.841128210978709, -5.856022438311223, -5.806451964591432, -5.692005380531648, -5.513555329222147, -5.273311631760667, -4.974761340848911, -4.622648795737927, -4.222864506049708, -3.7823415656538995, -3.3089102513778186, -2.8111081737686208, -2.2980231797447237, -1.779023467305787, -1.2636149910555026, -0.7611065363797218, -0.28050870522680194, 0.1698434298571214, 0.5823249011242008, 0.9504125261551413, 1.2686335205679373, 1.5329409552196518, 1.7405649646438732, 1.8903424677175418, 1.982469611511779, 2.0187609210373885, 2.002312627116724, 1.9376743807197563, 1.830443762590239, 1.687344159224252, 1.5157796846148457, 1.3238245786569744, 1.1197737331728572, 0.9120605862905394, 0.7088404594285537, 0.5178638409000371, 0.34612726487999934, 0.1997356767252775, 0.08364862187966596, 0.0015679579577542626, -0.04420373225096885, -0.05281607575649677, -0.024896940947971378, 0.03748091858403966, 0.13087802397675039, 0.2506235764876686, 0.3909725254078404, 0.5453448148870068, 0.7065248530509162, 0.86699145714405, 1.0191163790009177, 1.1555579833548562, 1.2694142334877099, 1.354642496757548, 1.4061272357879475, 1.4200826253769199, 1.3940058133036755, 1.3270194028389728, 1.2196963871674174, 1.0743063330666978, 0.8945160597746245, 0.6855159524253975, 0.45361873564992655, 0.20625923654724873, -0.048470426147200735, -0.3019353912863525, -0.5454369280029032, -0.7704108567010521, -0.9688664515972415, -1.1336236430817392, -1.2586611633329752, -1.3393388434822766, -1.3726151954351948, -1.357200331522618, -1.2936207125402794, -1.1842559238522616, -1.0332501725197978, -0.8464017676994356, -0.6309440782641342, -0.3952782260381195, -0.14866718681974178, 0.0991730369400416, 0.3384070006475006, 0.5595907084876418, 0.7539664069469044, 0.9140163248458987, 1.033654686012374, 1.1087532354256129, 1.1371789513051747, 1.1192188668097485, 1.0574330579550733, 0.9569163416848532, 0.8249630349890446, 0.6711240436204121, 0.5067087197443622, 0.3446252672269217, 0.19877129374862856, 0.08367945895105906, 0.013867649878846302, 0.0033454903402898584, 0.06500390163171069, 0.21006626576846996, 0.44759333788502537, 0.7839807863128969, 1.2226387489338466, 1.7636416927733292, 2.4036141572194327, 3.1356278083916314, 3.949289800544885, 4.830956232401049, 5.763982245089296, 6.729283804560918, 7.70567501986222, 8.670766233188306, 9.601289787953373, 10.474278064684508, 11.2672686471966, 11.959667842495426, 12.53273255423106, 12.970998962047934, 13.26196160108571, 13.397437603511992, 13.37290101416542, 13.188662244902728, 12.848862600176844, 12.36237544285386, 11.741515532264929, 11.002609092274739, 10.164517331036704, 9.248871030372618, 8.278540325852774, 7.2775780394082545, 6.269782790088468, 5.2784362402007705, 4.325100754163208, 3.429262216189731, 2.6074767998367463, 1.8730384413118357, 1.2355451848929255, 0.7006972316769632, 0.2702980661084213, -0.05774282392904604, -0.289016957807547, -0.4323806540263941, -0.49926504962981344, -0.5032286009692549, -0.4591024651664655, -0.3824016458122999, -0.2884549449463805, -0.19178036930264042, -0.10534219246211457, -0.04001284325885929, -0.004070391821821766, -0.0028627452647477874, -0.03861188909188272, -0.11036681071308771, -0.21412403140921524, -0.3431073732954151, -0.4881575236568161, -0.6383172510410992, -0.7813959975925353, -0.904778531665439, -0.9960423797064468, -1.0438570033066845, -1.038527684111303, -0.9728208061770173, -0.842328847839502, -0.6460519826311597, -0.3865218081589132, -0.0699927306969442, 0.2936804709645254, 0.6913385744165361, 1.106829865392707, 1.5218220037567698, 1.916192814932538, 2.2693100263850012, 2.560354468236327, 2.769947444901854, 2.8802503165994975, 2.876764108260412, 2.748069450566213, 2.487594880656656, 2.0929089027234977, 1.5672579606185641, 0.9183909050985452, 0.15970495285358813, -0.6913390764922495, -1.612559970830319, -2.5789176568412895, -3.5623615741019807, -4.533779897767114, -5.463285065187191, -6.322033516984397, -7.0828081592743395, -7.721498322968808, -8.217791426281005, -8.556145190081649, -8.726386686690258, -8.724080851945741, -8.550857380502267, -8.214169938376001, -7.727226377242539, -7.10822679468575, -6.379850637554924, -5.5681427971336905, -4.701598282913376, -3.8099195577215084, -2.9228195836747575, -2.0688906924165655, -1.2743049140449825, -0.5620112759561897, 0.0494627964464833, 0.5463291500648637, 0.9204462307521717, 1.1690820039838934, 1.2953899924064638, 1.307645933588976, 1.219230507814223, 1.047460197409413, 0.8131062915215367, 0.5390095208886996, 0.24925309705164478, -0.03221569415546553, -0.28257265190443903, -0.4812730143668192, -0.6109784130955513, -0.6583243666451276, -0.6145724708633535, -0.47590166139729373, -0.24361692767858695, 0.07602743264963399, 0.4721535548831484, 0.9298029707825444, 1.4307924963326841, 1.9544480289561437, 2.478891322534816, 2.9817498755228535, 3.441698762168626, 3.838934524931886, 4.156752728209879, 4.381618141162207, 4.5045566676130315, 4.520731770318532, 4.430469321264587, 4.238346165694163, 3.95374044709465, 3.589533704976397, 3.162172811597419, 2.690163229353582, 2.1937233485443164, 1.6932883314717169, 1.208914551143613, 0.7590123595233801, 0.3597021512825393, 0.02395043188351652, -0.2389189691297642, -0.42358938987815176, -0.5289215465340317, -0.5578194017382162, -0.5169922142451693, -0.4164188355648806, -0.26870421925602184, -0.088315275726087, 0.10937430801350437, 0.3088630600752347, 0.4956238277808092, 0.6566874282776405, 0.7816916268254244, 0.863105808810128, 0.897035143764051, 0.8830026452921768, 0.8243677312038983, 0.7276787417915197, 0.6026483652187207, 0.4611826700237278, 0.3169541954338907, 0.18428297157228435, 0.07744058439174577, 0.009589425416660824, -0.007982410856545444, 0.033327680420366226, 0.138827904657857, 0.31010382912766604, 0.5447688021851063, 0.8364631017781381, 1.1751002379043078, 1.5472368686319342, 1.9368535689971162, 2.325947735113509, 2.6957781002579515, 3.0274719436638633, 3.3035650501528426, 3.508398196288289, 3.6297195713793005, 3.658678721287306, 3.5912414082548834, 3.427666291383603, 3.173517735950655, 2.8386161080255934, 2.437515955173334, 1.9880328185683431, 1.5111661898514888, 1.0294000298750008, 0.5661687691567946, 0.14418418271771935, -0.21535683184615004, -0.4941630745557402, -0.6776406550105025, -0.7557968749028414, -0.7237665090472427, -0.5821207559885478, -0.3369142947326245, 0.0005861152358398481, 0.414449818353692, 0.8847964980705344, 1.388930756557269, 1.9022647841916427, 2.3999050132637314, 2.8574995140157227, 3.2530434276373263, 3.567377485173531, 3.7859284301833185, 3.898653860567246, 3.9014437576532686, 3.7954209009048148, 3.5877989512348085, 3.290583369231598, 2.9207962862050683, 2.498751266743695, 2.0476912346269627, 1.591903545921527, 1.1559451548148982, 0.7629013298896666, 0.4334638736619191, 0.18460826772488825, 0.028825361890552754, -0.02659724824247796, 0.020079385098787973, 0.16498593202738795, 0.39890103849215647, 0.7077604012064741, 1.0735621447636168, 1.4752270457681227, 1.8900573426143963, 2.29464963810707, 2.666688204415301, 2.9855964755787365, 3.23437055610972, 3.3997097638396276, 3.4735863009746497, 3.4527093855689173, 3.339586095306296, 3.141323073904365, 2.870049001017722, 2.5412100599999556, 2.173370721965714, 1.7862801246547746, 1.4002115774021004, 1.034138951782186, 0.7048829060862465, 0.4257241545868456, 0.20566966487868535, 0.04874440834374761, -0.04633884574837042, -0.08610836767338138, -0.08207650297164752, -0.04995372836459607, -0.00877037087906238, 0.020405860011784696, 0.015838201095673295, -0.04342518915599914, -0.17596700674120153, -0.39673517179815604, -0.7156022140568962, -1.1366015463904577, -1.6569944684466769, -2.267203635335223, -2.950669525315484, -3.6845120746792, -4.440303346141643, -5.1853151343095245, -5.884137464666088, -6.500228229002566, -6.998109915459443, -7.344861169049525, -7.512470604488636, -7.478919603792349, -7.230198179338517, -6.760724108647328, -6.074551439874103, -5.185033999688364, -4.114881005840107, -2.8951675903608174, -1.564091345473848, -0.1656146549615641, 1.2529889985129194, 2.6424493545048495, 3.9548524301166297, 5.144460514326094, 6.171491446872664, 7.0020543771068535, 7.61181435863238, 7.984806428309361, 8.116486054438361, 8.011397868683245, 7.685254345394752, 7.1616657298780115, 6.473100859702395, 5.657081501642871, 4.756114463473288, 3.813872727126506, 2.874395784235542, 1.9787937403233578, 1.1641482186989704, 0.4611788111981994, -0.10668862900921992, -0.5244420754711916, -0.7858530144146046, -0.8933720272847737, -0.8577021426029813, -0.6966993034604528, -0.43412525202847896, -0.09797058252202698, 0.2814273680000306, 0.6731242516681334, 1.0477379379231069, 1.3787571806683467, 1.6445817174214563, 1.8290179814089278, 1.922787407240993, 1.9230754585697103, 1.834275982529574, 1.6665556871236589, 1.4357036966824264, 1.1612851837856308, 0.865721814497922, 0.5718007946533027, 0.3021905826954575, 0.07746419309922525], 'positive_zeros': ['0.790127328703066710935470922176953', '0.861781367386999470685783872782951', '1.27184810507259228112262381138084', '2.10032276905432378676392079720180', '2.62557651961971797966650113411591', '2.70621060448665808695024167792331', '3.20649409371169983798220706737938', '3.59995048207000896712163475079659', '4.02038187091920110127114256359775', '4.02638693727193742410500773192314', '5.01092922542570892458922482269201', '5.28019561971392628105298986339603', '5.29175642791039600895899975567507', '5.67660600547981100308656020803514', '6.05145586863116930179918523653622', '6.65418378914650171822743020872739', '6.91128033461079658207999792441209', '7.09649512697186944939616124451960', '7.66594870202169498061069284533242', '7.86217499834449785748166201243656'], 'prelabel': '4-9800e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.846094843537164, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1797289461461887395, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.790127328703066710935470922177', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '0.861781367386999470685783872783', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.27184810507259228112262381138', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6123.593669522886, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 96040000, 'conductor_radical': 70, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, 11, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 5, 0, 4, 0, -1, 0, 0, 0, 0, 0, 1, 0, -6, 0, 6, 0, 0, 0, 9, 0, 0, 0, 11, 0, 18, 0, 0, 0, 6, 0, 8, 0, 22, 0, 0, 0, 0, 0, 12, 0, 2, 0, 0, 0, 8, 0, 0, 0, 0, 0, -11, 0, -4, 0, 24, 0, 0, 0, 5, 0, -2, 0, 0, 0, 4, 0, 0, 0, 15, 0, 1, 0], 'euler11': [1, 1, 18, 11, 121], 'euler13': [1, -1, -12, -13, 169], 'euler17': [1, -11, 60, -187, 289], 'euler19': [1, -6, 30, -114, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -2, 30, -46, 529], 'euler29': [1, -5, 60, -145, 841], 'euler3': [1, -1, 2, -3, 9], 'euler31': [1, -4, -2, -124, 961], 'euler37': [1, 0, 6, 0, 1369], 'euler41': [1, 6, 74, 246, 1681], 'euler43': [1, -6, 78, -258, 1849], 'euler47': [1, -9, 110, -423, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, -18, 170, -954, 2809], 'euler59': [1, -8, 134, -472, 3481], 'euler61': [1, -22, 226, -1342, 3721], 'euler67': [1, -12, 102, -804, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -8, 94, -584, 5329], 'euler79': [1, 11, 150, 869, 6241], 'euler83': [1, -24, 310, -1992, 6889], 'euler89': [1, 2, 162, 178, 7921], 'euler97': [1, -15, 212, -1455, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -1, 2, -3, 9], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 1, 18, 11, 121], [1, -1, -12, -13, 169], [1, -11, 60, -187, 289], [1, -6, 30, -114, 361], [1, -2, 30, -46, 529], [1, -5, 60, -145, 841], [1, -4, -2, -124, 961], [1, 0, 6, 0, 1369], [1, 6, 74, 246, 1681], [1, -6, 78, -258, 1849], [1, -9, 110, -423, 2209], [1, -18, 170, -954, 2809], [1, -8, 134, -472, 3481], [1, -22, 226, -1342, 3721], [1, -12, 102, -804, 4489], [1, 0, 142, 0, 5041], [1, -8, 94, -584, 5329], [1, 11, 150, 869, 6241], [1, -24, 310, -1992, 6889], [1, 2, 162, 178, 7921], [1, -15, 212, -1455, 9409]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9800/2/a/by'], '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': '4-9800e2-1.1-c1e2-0-4', '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': 0, 'prelabel': '4-9800e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.846094843537164, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1797289461461887395, 'z1': {'__RealLiteral__': 0, 'data': '0.790127328703066710935470922177', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1001605382487170025293466074902,1092437667633634156914261729700', 'Lhash_array': ['1001605382487170025293466074902', '1092437667633634156914261729700'], 'label': '4-9800e2-1.1-c1e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9800/2/a/by'}