-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '624573198657112907498861372590,808642345854041402506473271722,1035956904373331079664786611561,1054170440156629501583888392661,1097207346601660849851170375058,1506623510002779424363838178248', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 6, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': -5, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3332228787.247679, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -6, 15, -20, 15, -6, 1]], [11, [1]]], 'bad_primes': [2, 5, 11], 'central_character': '4840.1', 'coefficient_field': '1.1.1.1', 'conductor': 12855002631049216000000, 'conductor_radical': 110, 'degree': 12, 'euler_factors': [[1], [1, 2, 9, 18, 50, 82, 181, 246, 450, 486, 729, 486, 729], [1, -6, 15, -20, 15, -6, 1], [1, -4, 21, -56, 218, -636, 1993, -4452, 10682, -19208, 50421, -67228, 117649], [1], [1, 0, 46, -16, 935, -560, 13172, -7280, 158015, -35152, 1313806, 0, 4826809], [1, -8, 86, -488, 3247, -14352, 70772, -243984, 938383, -2397544, 7182806, -11358856, 24137569], [1, -12, 142, -1028, 6983, -36232, 176372, -688408, 2520863, -7051052, 18505582, -29713188, 47045881], [1, 8, 78, 464, 3647, 17448, 99796, 401304, 1929263, 5645488, 21827598, 51490744, 148035889], [1, -16, 158, -976, 3655, -5856, -10876, -169824, 3073855, -23803664, 111750398, -328178384, 594823321], [1, 4, 106, 580, 5471, 35008, 194684, 1085248, 5257631, 17278780, 97893226, 114516604, 887503681], [1, -8, 142, -872, 9911, -52016, 449252, -1924592, 13568159, -44169416, 266130862, -554751656, 2565726409], [1, -32, 597, -7760, 78494, -647040, 4497049, -26528640, 131948414, -534826960, 1686979317, -3707398432, 4750104241], [1, 4, 157, 160, 9938, -11060, 442193, -475580, 18375362, 12721120, 536751757, 588033772, 6321363049], [1, 6, 217, 1142, 22146, 96502, 1330941, 4535594, 48920514, 118565866, 1058890777, 1376070042, 10779215329], [1, -8, 142, -624, 8055, -33704, 443124, -1786312, 22626495, -92899248, 1120448302, -3345563944, 22164361129], [1, -4, 106, -804, 11415, -59440, 798588, -3506960, 39735615, -165124716, 1284440266, -2859697196, 42180533641], [1, -16, 245, -2240, 24374, -199632, 1856313, -12177552, 90695654, -508437440, 3392231045, -13513540816, 51520374361], [1, 2, 49, 458, 11018, 49970, 322277, 3347990, 49459802, 137749454, 987404929, 2700250214, 90458382169], [1, 28, 546, 7900, 98591, 1012032, 9200236, 71854272, 496997231, 2827496900, 13874777826, 50518421828, 128100283921], [1, -16, 246, -2768, 28991, -286368, 2601844, -20904864, 154493039, -1076799056, 6985967286, -33169145488, 151334226289], [1, 0, 342, -288, 55791, -50976, 5551220, -4027104, 348191631, -141995232, 13320927702, 0, 243087455521], [1, -12, 210, -1028, 22311, -168072, 2881772, -13949976, 153700479, -587797036, 9966247410, -47268487716, 326940373369], [1, -18, 253, -1798, 8058, 72934, -1088091, 6491126, 63827418, -1267534262, 15873786973, -100513070082, 496981290961], [1, 0, 342, 1080, 57231, 248616, 6595652, 24115752, 538486479, 985686840, 30277014102, 0, 832972004929], [1, -8, 229, -3000, 44766, -416072, 5881857, -42023272, 456657966, -3090903000, 23829831829, -84080804008, 1061520150601], [1, 0, 238, 632, 31679, 58456, 3774548, 6020968, 336082511, 690603464, 26787109678, 0, 1194052296529], [1, -32, 721, -10548, 126966, -1264856, 12922713, -135339592, 1453633734, -12921753564, 94508392321, -448816553824, 1500730351849], [1, 0, 277, 272, 55862, 52864, 6862457, 5762176, 663696422, 352247888, 39100810597, 0, 1677100110841], [1, -12, 610, -6364, 161679, -1392728, 23845596, -157378264, 2064479151, -9182596508, 99458890210, -221092221516, 2081951752609]], 'euler_factors_factorization': [[1], [[[1, 2, 9, 18, 50, 82, 181, 246, 450, 486, 729, 486, 729], 1]], [[[1, -1], 6]], [[[1, -4, 21, -56, 218, -636, 1993, -4452, 10682, -19208, 50421, -67228, 117649], 1]], [1], [[[1, 0, 46, -16, 935, -560, 13172, -7280, 158015, -35152, 1313806, 0, 4826809], 1]], [[[1, -8, 86, -488, 3247, -14352, 70772, -243984, 938383, -2397544, 7182806, -11358856, 24137569], 1]], [[[1, -12, 142, -1028, 6983, -36232, 176372, -688408, 2520863, -7051052, 18505582, -29713188, 47045881], 1]], [[[1, 8, 78, 464, 3647, 17448, 99796, 401304, 1929263, 5645488, 21827598, 51490744, 148035889], 1]], [[[1, -16, 158, -976, 3655, -5856, -10876, -169824, 3073855, -23803664, 111750398, -328178384, 594823321], 1]], [[[1, 4, 106, 580, 5471, 35008, 194684, 1085248, 5257631, 17278780, 97893226, 114516604, 887503681], 1]], [[[1, -8, 142, -872, 9911, -52016, 449252, -1924592, 13568159, -44169416, 266130862, -554751656, 2565726409], 1]], [[[1, -32, 597, -7760, 78494, -647040, 4497049, -26528640, 131948414, -534826960, 1686979317, -3707398432, 4750104241], 1]], [[[1, 4, 157, 160, 9938, -11060, 442193, -475580, 18375362, 12721120, 536751757, 588033772, 6321363049], 1]], [[[1, 6, 217, 1142, 22146, 96502, 1330941, 4535594, 48920514, 118565866, 1058890777, 1376070042, 10779215329], 1]], [[[1, -8, 142, -624, 8055, -33704, 443124, -1786312, 22626495, -92899248, 1120448302, -3345563944, 22164361129], 1]], [[[1, -4, 106, -804, 11415, -59440, 798588, -3506960, 39735615, -165124716, 1284440266, -2859697196, 42180533641], 1]], [[[1, -16, 245, -2240, 24374, -199632, 1856313, -12177552, 90695654, -508437440, 3392231045, -13513540816, 51520374361], 1]], [[[1, 2, 49, 458, 11018, 49970, 322277, 3347990, 49459802, 137749454, 987404929, 2700250214, 90458382169], 1]], [[[1, 28, 546, 7900, 98591, 1012032, 9200236, 71854272, 496997231, 2827496900, 13874777826, 50518421828, 128100283921], 1]], [[[1, -16, 246, -2768, 28991, -286368, 2601844, -20904864, 154493039, -1076799056, 6985967286, -33169145488, 151334226289], 1]], [[[1, 0, 342, -288, 55791, -50976, 5551220, -4027104, 348191631, -141995232, 13320927702, 0, 243087455521], 1]], [[[1, -12, 210, -1028, 22311, -168072, 2881772, -13949976, 153700479, -587797036, 9966247410, -47268487716, 326940373369], 1]], [[[1, -18, 253, -1798, 8058, 72934, -1088091, 6491126, 63827418, -1267534262, 15873786973, -100513070082, 496981290961], 1]], [[[1, 0, 342, 1080, 57231, 248616, 6595652, 24115752, 538486479, 985686840, 30277014102, 0, 832972004929], 1]], [[[1, -8, 229, -3000, 44766, -416072, 5881857, -42023272, 456657966, -3090903000, 23829831829, -84080804008, 1061520150601], 1]], [[[1, 0, 238, 632, 31679, 58456, 3774548, 6020968, 336082511, 690603464, 26787109678, 0, 1194052296529], 1]], [[[1, -32, 721, -10548, 126966, -1264856, 12922713, -135339592, 1453633734, -12921753564, 94508392321, -448816553824, 1500730351849], 1]], [[[1, 0, 277, 272, 55862, 52864, 6862457, 5762176, 663696422, 352247888, 39100810597, 0, 1677100110841], 1]], [[[1, -12, 610, -6364, 161679, -1392728, 23845596, -157378264, 2064479151, -9182596508, 99458890210, -221092221516, 2081951752609], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 2, 'label': '12-4840e6-1.1-c1e6-0-2', 'leading_term': '38.832933064789989464995871805871403929093649508960711343430017962555706816290082746522467', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4840/2/a/bd', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.008463541666666666', 'prec': 67}, 'plot_values': [38.83293306478999, 38.71776050107471, 38.58910952446771, 38.43338496662094, 38.237198066334905, 37.98745966809352, 37.67150920099396, 37.2800933145119, 36.81578385929489, 36.28422619352233, 35.69121706936436, 35.04264311318796, 34.34442311949217, 33.60175320188145, 32.81705549786234, 31.9922335253362, 31.12939325829983, 30.230838151782706, 29.29906269474176, 28.33690819488579, 27.34800912427024, 26.336225223710713, 25.30544922083499, 24.25958665308599, 23.202535790501415, 22.138134894726168, 21.07005389165998, 20.001891432830448, 18.93719211762088, 17.879428656370973, 16.831984366557418, 15.798149383430939, 14.781138816289648, 13.784028139080199, 12.809723821951886, 11.860949579555646, 10.940233760143993, 10.049902987088435, 9.192084621840634, 8.36867872070643, 7.581345536530984, 6.831500276312717, 6.120309476647032, 5.448694927071181, 4.817347129019265, 4.226702602971324, 3.676941195691464, 3.167992067072179, 2.6995413734483185, 2.271045439889276, 1.8817497118649282, 1.5306841925033157, 1.2166740167763854, 0.9383561157765934, 0.694197027158825, 0.48251363949643433, 0.30149600960545575, 0.149218054959585, 0.023657442510892832, -0.07728162147125617, -0.15574560129878057, -0.21390860594637684, -0.253950335574525, -0.27803766243384315, -0.28830326801553363, -0.28682459570736074, -0.2756042056493021, -0.2565520034259123, -0.23147018654857918, -0.20203815967761368, -0.16979907572576197, -0.1361488797559531, -0.10232780110950057, -0.06941471382580945, -0.03832453646383236, -0.00980560210139152, 0.015559491788706498, 0.037350021365032765, 0.05530077883824374, 0.06929322728746336, 0.07934452645152956, 0.08559561121295726, 0.08829664100005469, 0.08779065648935429, 0.08449597505491142, 0.07888770018345759, 0.07147885046799576, 0.0628008810222437, 0.0533840852177869, 0.04373848065806206, 0.03433554426494136, 0.025591222283869612, 0.017850548927043988, 0.011373623287815392, 0.006323983250642094, 0.0027595685115330863, 0.0006264221839075617, -0.00024468551639937695, -0.0001386237254873436, 0.0005468987325110848, 0.0013075052528134297, 0.0015415494852807064, 0.000562617198062099, -0.002385005687864721, -0.008107945160776914, -0.017442808446227115, -0.03123316369676602, -0.0503047964110692, -0.075439696071218, -0.10734911058527771, -0.14664577277824165, -0.19381709232152453, -0.2491992743119948, -0.31295285622846075, -0.38504034601906384, -0.46520635049241027, -0.5529604590839972, -0.6475649504835677, -0.7480265962486847, -0.853092990389795, -0.9612538988375297, -1.07074803255881, -1.1795757825615756, -1.28551690104347, -1.3861537489705174, -1.47890005093473, -1.5610348366077422, -1.629741955744742, -1.682155608647578, -1.7154053767805502, -1.7266654563989396, -1.7132069762775077, -1.672451927674412, -1.602028659593481, -1.4998279352013653, -1.3640516035912236, -1.1932614586222763, -0.986425867529555, -0.7429621956700011, -0.4627733023823599, -0.146273319794442, 0.20559195317880152, 0.5913299560643259, 1.0088944839202432, 1.4556874441477887, 1.9285747923962158, 2.4239277355648934, 2.9376470555716168, 3.4651986257831138, 4.0016612249417065, 4.541782456727375, 5.080054509842944, 5.610828399136591, 6.12836498357629, 6.626903655037081, 7.100744521021176, 7.544332429969822, 7.952362116233651, 8.319929333668126, 8.642558654868598, 8.916257454749891, 9.13758326930826, 9.3037044377469, 9.412479860916013, 9.462584832696406, 9.453462649459492, 9.38531413116809, 9.2591021795979, 9.076544746640312, 8.840124849796952, 8.55314103900054, 8.219566577644553, 7.843960090536105, 7.431396538514811, 6.987389782789268, 6.517832685463186, 6.028969873403508, 5.527206995867446, 5.0189817918089545, 4.510662498017513, 4.008447935528438, 3.5182875343150353, 3.0458265601686927, 2.5962488509071875, 2.17418162663863, 1.7836309333334772, 1.4279288645301746, 1.1097009796720312, 0.8308515411137463, 0.5925113382195978, 0.3950335987439435, 0.23801479963050762, 0.12032928083906334, 0.04017794905132818, -0.004854287239311591, -0.017738349058463946, -0.0019180452816830805, 0.03878280016040043, 0.10025829284995155, 0.17822015187891127, 0.26829531003182416, 0.36613135571577693, 0.4674985623846652, 0.568384607776604, 0.6650808929404445, 0.7542582062991043, 0.8330316289853008, 0.8990174980905641, 0.9503725581915622, 0.9858167589264216, 1.00464042674893, 1.0066969565537458, 0.9923839782996865, 0.9626051511897213, 0.91871789969809, 0.8624700995504411, 0.7959271638554187, 0.7213931630241687, 0.6413296678872585, 0.5582627516749672, 0.47469239870942137, 0.3930062489309976, 0.315398945703734, 0.24380036006400962, 0.17981486814430397, 0.12466744651007824, 0.07916681879859142, 0.043685355525043615, 0.018155614175440957, 0.0020840321732063776, -0.00541865561814248, -0.005591253750552273, 4.0712764070408186e-05, 0.009741987020609588, 0.021656439926616713, 0.03390531239365286, 0.04469205458387952, 0.05241095976506887, 0.05575587038360134, 0.053825388117607696, 0.04622105828864406, 0.03313501639050829, 0.015423666441257217, -0.005335657763061506, -0.026807724820435575, -0.04588452299383778, -0.05869432451618821, -0.0606360317810969, -0.046438894088241214, -0.010246526666046925, 0.054274131421439914, 0.15380047589001863, 0.2952006987422099, 0.4853637546904803, 0.7310232594848358, 1.0385650045085433, 1.4138273272819901, 1.8619008866031914, 2.3869317758243596, 2.9919437845760597, 3.678710294498694, 4.4475953981760314, 5.29742186293653, 6.225373619465051, 7.2269290497030605, 8.295858781142453, 9.424346554263625, 10.602986890505601, 11.820845297328079, 13.065579384066547, 14.323595647316598, 15.580300360253121, 16.820531918561382, 18.02867870208444, 19.18888950463603, 20.285351052564817, 21.30257510246316, 22.22578060730734, 23.04147655623503, 23.737495221744233, 24.30314880644768, 24.729448283820748, 25.009294821804744, 25.137749213549345, 25.112483221102455, 24.933516543461284, 24.6031188533012, 24.125778473027843, 23.50812916888908, 22.758943014135255, 21.889270180904365, 20.911867933216023, 19.84084204323407, 18.69137733307864, 17.47945027993236, 16.221612499293144, 14.934890188271474, 13.636148985091559, 12.341697208688949, 11.067001719390284, 9.826428451753241, 8.633061967151558, 7.49861488812923, 6.433051635087828, 5.444424090100044, 4.538814073693596, 3.7203218681765717, 2.991119949630581, 2.351562063689982, 1.8001978787960753, 1.3339168801452774, 0.9481514528627303, 0.6371043024333578, 0.3939976479428789, 0.2113304952081426, 0.08111289472684027, -0.004871798308641723, -0.05481013455078149, -0.07662178849832647, -0.07774893053821695, -0.0649778220879843, -0.04429127249990986, -0.020756478840064038, 0.0015456575492321482, 0.019549428115044606, 0.031192786782171245, 0.03536895210306133, 0.031843940616363406, 0.021142354461497682, 0.004408573047107491, -0.01674953131521634, -0.04042669080664573, -0.06458856465674823, -0.08723736200807984, -0.10656429251255171, -0.12108172266358408, -0.12972902643627332, -0.13194697214883855, -0.12771710437291692, -0.1175624121501549, -0.1025077444515836, -0.08400094386557155, -0.06379690358347759, -0.04380840051619609, -0.02592900220088631, -0.011834230449074612, -0.0027695574395619075, 0.0006658154097263598, -0.0012702015155115103, -0.0072671941548632666, -0.014792456586778649, -0.019955853777321807, -0.017418229696775152, -0.0003515644649354143, 0.039542443060046936, 0.11195122740544451, 0.22780966221507892, 0.39909262594020095, 0.6385423224496608, 0.9593350638875862, 1.374693061549005, 1.8974604514982336, 2.53968721647654, 3.3121484420868224, 4.223853680716337, 5.28156780747622, 6.489351845957628, 7.848185725164289, 9.355789904781979, 11.006289121718716, 12.789977294941057, 14.693204334445536, 16.698360736285416, 18.78408325742473, 20.925886274276394, 23.09627542308433, 25.265071190511552, 27.399922207349235, 29.46690596423755, 31.431412481652277, 33.25958238763948, 34.91859504729343, 36.37724578766227, 37.6067043260139, 38.581251949571445, 39.27925577655872, 39.68466164359953, 39.786715654148374, 39.58005627346649, 39.06495794111225, 38.2474494829839, 37.1395891530781, 35.76011909424656, 34.133155777635295, 32.287372749444934, 30.255367562068596, 28.07292645732391, 25.778430834000645, 23.412525210020824, 21.016253888036317, 18.629813565381117, 16.2915882748573, 14.037234225703092, 11.898966505963392, 9.905068028657826, 8.078671068174692, 6.437159381886459, 4.991905700551642, 3.748191768695949, 2.705356717414704, 1.8571379643438122, 1.1919240959451116, 0.69342011223967, 0.34153509039833785, 0.1134039172922805, -0.01548176887863156, -0.0700774917632642, -0.07455216631583673, -0.0510003028215005, -0.01819137724713913, 0.009595215460808715, 0.023612757064030234, 0.021536451811786796, 0.008162983636970758, -0.00412550809401217, 0.004847979776001103, 0.06299775183295192, 0.20564115004977992, 0.4748635772168073, 0.9186024618637152, 1.5894793754441505, 2.543402716326307, 3.8379754787270635, 5.53072483351109, 7.677129726911479, 10.328679204853582, 13.53093145715367, 17.32161406811961, 21.728836010441974, 26.76943562401647, 32.44745947844168, 38.75307511062507, 45.66177757139577, 53.13392168400655, 61.11462951135711, 69.53410829671131, 78.3084297609845, 87.34061323563694, 96.52209361436859, 105.73455301157439, 114.85206617602637, 123.74364525130034, 132.27631025672093, 140.31754953016912, 147.7380362802954, 154.41447356746733, 160.23237977147238, 165.0889894215446, 168.89644129267487, 171.5831863277194, 173.09552668077035, 173.39902486589693, 172.4795000686556, 170.3438602381379, 167.02091706903107, 162.55992840279197, 157.0293705237203, 150.51558103238528, 143.1209964153829, 134.96222364095073, 126.16800663325947, 116.87558440874767, 107.22755953608993, 97.36891366105968, 87.44399044113442, 77.59357923761878, 67.95207008628428, 58.64433957150366, 49.783318610773755, 41.46797997727498, 33.78167964938554, 26.790847753877145, 20.543965924949585, 15.071247277709888, 10.384818762103485, 6.479297782321382, 3.3327609230972848, 0.9080255112044036, -0.8457828010375353, -1.991009453510846, -2.5991971649853323, -2.7487411023236956, -2.522473334510066, -2.0052277347905005, -1.2813495110491053, -0.432321999959843, 0.46529545379536424, 1.3416796547519236, 2.135283460453512, 2.794134852804187, 3.2769586644346482, 3.553575973355193, 3.6049964918765087, 3.4232315073348, 3.0107993219347198, 2.3800018057443926, 1.5520024708263591, 0.5553177995913806, -0.5756947453318293, -1.8023825674070753, -3.0833892095063007, -4.376246379785022, -5.63900175203629, -6.831788164871178, -7.918133568376037, -8.866070590432626, -9.64903839629162, -10.246610553230246, -10.645128347383533, -10.837799234838853, -10.824572168768594, -10.611828912645581, -10.211876404593593, -9.642321426441319, -8.925399222160095, -8.086839933915543, -7.154773071526871, -6.158663003458198, -5.1282581842096, -4.0926147950340575, -3.079219667408031, -2.1130383000334247, -1.2157959763475141, -0.40544885979469547, 0.3041785917355933, 0.9035868959345617, 1.3876463605341127, 1.755486147748764, 2.0102021137017294, 2.158431007994216, 2.2098193571194154, 2.1764203830130744, 2.07205371761919, 1.911595196579645, 1.7102829263807793, 1.4830643915754238, 1.2440025028371453, 1.0057641043884384, 0.7792073415559768, 0.5730629156391418, 0.3937431662814973, 0.24527460356012354, 0.12934798723684715, 0.04547830183016617, -0.008736507299776564, -0.03727256646991043, -0.04527590657751432, -0.03861677236698013, -0.023423977040084577, -0.005621560372603718, 0.00950974883984351, 0.01772212234354784, 0.016126785700896634, 0.0034430841539181286, -0.019841340480318128, -0.05140815698964278, -0.08714898912308394, -0.12129675560496281, -0.14664588447241197, -0.15485484560098586, -0.13681898632380082, -0.08309580055233752, 0.015655533907541517, 0.1682216951400907, 0.38237948173525715, 0.6644611702674434, 1.0189580835578984, 1.4482084039430903, 1.9522638817815756, 2.5287120652274733, 3.1725836395776863, 3.8763669520763293, 4.630112587610382, 5.421707282377267, 6.237461344821871, 7.062334797791073, 7.880276262880331, 8.674664595385146, 9.428776141339608, 10.12639699455458, 10.752745323434493, 11.29458362222061, 11.740463460794283, 12.08103660310933, 12.309304427144468, 12.420953558324156, 12.414922497483317, 12.292931700666964, 12.059223313431408, 11.720385944902299, 11.2851193503689, 10.764077912608707, 10.169883639444274, 9.516273046493314, 8.817547548599407, 8.088169846663556, 7.342377626278994, 6.593904391714257, 5.855836846167745, 5.13999872743587, 4.456640581650654, 3.8142878510354086, 3.2196534676537096, 2.677645781706589, 2.19146154037771, 1.7625172005557346, 1.3905648149560874, 1.073891433453345, 0.8095476916258779, 0.5936025223588812, 0.42140644654220544, 0.2878036796033828, 0.18737829347115165, 0.11469035267728739, 0.0644825379340246, 0.03185256099566596, 0.012386421041715903, 0.002249710071566357, -0.0017545379626771663, -0.0021660698659861366, -0.0008833565222938349, 0.00078979485043246, 0.0020730630344582613, 0.002620749432420708, 0.002421511891403396, 0.0016936534821643389, 0.0007826856909536179, 6.714383630642167e-05, -0.00012232046503643043, 0.00043330007292472763, 0.0017973281115557353, 0.0038543041563015865, 0.006307731030069872, 0.008697366132106945, 0.01043359600627509, 0.010844672717928392, 0.009233137570688903, 0.00493700662292312, -0.0026089862035306144, -0.013816963793981098, -0.028900024695919225, -0.04783812569363333, -0.07035808779878336, -0.09592999029980291, -0.12378057597943133, -0.15292526103716533, -0.1822210017989942, -0.2104210243811093, -0.2362391608076374, -0.25842081961886, -0.2758151929710238, -0.2874476902059804, -0.2925905910222461, -0.2908011496670763, -0.2819512262589869, -0.26624390852288565, -0.2442125881167075, -0.21670356862819606, -0.1848399047241256, -0.14995584878169596, -0.11352763535214522, -0.0770980930207894, -0.04219623000867865, -0.010254186135829775, 0.017479029651454498, 0.040006472779759134, 0.05663611422558223, 0.06701870818681212, 0.07116786287197237, 0.06946362553116375, 0.06264022331981556, 0.051735039347941304, 0.038025865795367236, 0.02295747690337192, 0.008058332628522853, -0.005147856661647844, -0.015233941007330998, -0.02096317965837462, -0.02136671562055508, -0.01580526934898321, -0.004013190625059116, 0.013876715968378955, 0.03732839532874899, 0.06542840166041104, 0.09693416264370676, 0.13034100204058302, 0.16396524111514757, 0.19603961319118468, 0.22481978446151854, 0.24869280186855203, 0.2662770628051176, 0.2765105352159824, 0.278722454985721, 0.2726865273300806, 0.258655889789462, 0.23735730622680135, 0.209958420152755, 0.17801007464248422, 0.1433646348694157, 0.10807586867734935, 0.0742850406314045, 0.044086407959563416, 0.01939633398604708, 0.0018310564976311476, -0.007401428596943427, -0.007588864157659541, 0.001422321260905816, 0.01919641242040467, 0.04471547720538267, 0.07642306760957261, 0.11230332486829332, 0.14999184065452265, 0.18691248215108516, 0.22043830107675272, 0.24806401379516763, 0.26758022288209793, 0.2772394141051138, 0.27590198680349615, 0.2631497287913518, 0.23936748333533509, 0.20577976076702428, 0.1644362418252837, 0.11814387453140754, 0.07034237797608596, 0.02492512503426779, -0.013961221672841325, -0.04215564215360228, -0.05574774186654589, -0.05135266249751975, -0.02637815414585617, 0.020753070302033848, 0.09042335077196853, 0.18167885832311725, 0.29215124065243686, 0.41805401414509274, 0.5542871804514578, 0.6947113288739145, 0.8323799281629911, 0.9598484825428053, 1.0695649194587513, 1.1543115556498258, 1.2077336296710595, 1.2249956223268508, 1.2031030723207896, 1.1412444806437312, 1.0411129151975096, 0.9071391382918818, 0.7466627575720616, 0.5700223993247971, 0.3901540320314052, 0.22217479965157833, 0.08288084093846224, -0.00988960851911548, -0.03801841769898609, 0.01593522840683286, 0.16765217769901375, 0.4300626962669374, 0.8123907465216959, 1.319252625841191, 1.9497908870736873, 2.696784945461422, 3.5462932012936195, 4.477510887469824, 5.462835259346903, 6.468195178848304, 7.453602569903514, 8.37394276390116, 9.180429837171587, 9.822158429645253, 10.247784022170196, 10.407343028340474, 10.25419082040191, 9.747161893040879, 8.85260536255139, 7.546170935617593, 5.814381224096142, 3.6559249649551573, 1.0827276351950952, -1.8790584466580382, -5.189152133475737, -8.793649428803782, -12.62592258379306, -16.607987905656856, -20.65220555339194, -24.66319709664265, -28.540829270978165, -32.18325079269417, -35.489986942727356, -38.36510184897742, -40.72029255770817, -42.47785983954883, -43.5736931907416, -43.95972690034417, -43.60588713331746, -42.50150273328567, -40.656131663009106, -38.09979208484083, -34.88246482317577, -31.072916887728166, -26.75689843284313, -22.03475827337726, -17.018504407703944, -11.828309625197923, -6.588949590825196, -1.4260411482428887, 3.5378075803592477, 8.18677197039111, 12.415516687500958, 16.132838731578243, 19.264003628972073, 21.752770118814766, 23.56293264261316, 24.679194455193464, 25.107477636898473, 24.874678438063377, 24.02677602900774, 22.626747217626363, 20.75210158826474, 18.491955522322744, 15.94378427137148, 13.209858918253156, 10.393277366972473, 7.594379351640629, 4.907409638354046, 2.4174625394942177, 0.19775968953622208, -1.6927156167188302, -3.2106459960166123, -4.3291893910603125, -5.038216247819818, -5.3439404612659045, -5.267986385702141, -4.8458196754650125, -4.1244453624654165, -3.159942755504453, -2.0148079075250087, -0.7551576098408822, 0.5521993399542835, 1.8429550381935844, 3.0577799695949968, 4.144437105577593, 5.059571202222465, 5.770061633939093, 6.254070723723021, 6.5019363185752574, 6.515479295184573, 6.307090032046263, 5.898564197191685, 5.3195938615827645, 4.606111074974764, 3.798574380485807, 2.9393088678280948, 2.0702537245404145, 1.2309878021213678, 0.45696543252976884, -0.22194090070063707, -0.7826032617183266, -1.2096377327729213, -1.4957511600198057, -1.6416143364539384, -1.6553422591434805, -1.5516368507820784, -1.3506701046568743, -1.0766089744713427, -0.7559653981807832, -0.415897954019262, -0.08254362014084878, 0.22053451757431522, 0.47373130405834446, 0.6625673661419514, 0.7784913651399248, 0.8193098543414578, 0.7892387916378268, 0.6985890590522267, 0.5631156840398321, 0.40298216382864055, 0.24146402806779993, 0.10346890452967523, 0.013946503674834432, -0.0037259815703851737, 0.07069066398209559, 0.25286927453284114, 0.5527359019453731, 0.973591107272034, 1.5115816872279413, 2.155559768220575, 2.887356611222594, 3.682451479905422, 4.511009077214858, 5.339244330208393, 6.131052626996336, 6.8498529082750395, 7.460585437530886, 7.931573405469594, 8.236320089199058, 8.355143252462362, 8.276539923614063, 7.998224569355903, 7.527763804101705, 6.88260920051056, 6.089746235662082, 5.18490805200562, 4.211345280444659, 3.218176008505343, 2.258343129524694, 1.3864189393737718, 0.6562872851864578, 0.11875829659311078, -0.18077925948078444, -0.20456485258179616, 0.07568018275459835, 0.6773685990240633, 1.6059775500733333, 2.8544069112579464, 4.4028192966511455, 6.219125622543006, 8.260499898651055, 10.474696242554135, 12.801710690947532, 15.175841837233879, 17.52798928370529, 19.78845944130687, 21.890739254579547, 23.773185022108887, 25.380860565198383, 26.66741257954498, 27.596624219512186, 28.144053288991707, 28.29916327671396, 28.0641100715429, 27.452879355487173, 26.490460219773674, 25.211647537164872, 23.659907134682673, 21.886546259611375, 19.94719956673008, 17.899244035300722, 15.799681940059953, 13.703146902589085, 11.660299108971614, 9.716647183579814, 7.910365535218162, 6.271232691529823, 4.820221054021964, 3.5694768773542096, 2.522716971611847, 1.6759473721670355, 1.0181382509840047, 0.5324447208190294, 0.19765456045680002, -0.010299572288057722, -0.11683978795835549, -0.14733988209120047, -0.12585520586438148, -0.07401498489373091, -0.01017048217126186, 0.051169816222695085, 0.09961019028232039, 0.12885590760208912, 0.13644513184233964, 0.1232424568941096, 0.09275080343078908, 0.050304315157953444, 0.002208109366247122, -0.045109948238106254, -0.08587713962694701, -0.11561824145941142, -0.13161442148260538, -0.13314461463866029, -0.12148994228471693, -0.09969787925534544, -0.07211822811029674, -0.04374176491771549, -0.019386035535771586, -0.0027850392619942826, 0.004350913154665964, 0.0032321969795131586, -0.00122759247355015, 0.0001915863268622814, 0.021375796287495592, 0.08093975152270831, 0.20195930434799536, 0.4113888027266894, 0.7391396110186811, 1.2168298372491781, 1.8762472661910894, 2.7475774852043346, 3.8575459734348083, 5.227801984929326, 6.873049489514752, 8.799288006415322, 11.0023109355737, 13.466507292829727, 16.164354840408468, 19.05732181340328, 22.095758217248505, 25.219435135738763, 28.358800814231234, 31.436716360133193, 34.37128476431163, 37.08071222764403, 39.48474802916516, 41.50694212245601, 43.077474745999424, 44.135904024070584, 44.63462190155708, 44.5438667351638, 43.85078950177631, 42.55947880716224, 40.69128737815069, 38.284577275262315, 35.3947028019734, 32.09472804236532, 28.470199421046352, 24.615445893006417, 20.630460946404888, 16.617580793806418, 12.678543680574656, 8.912011139321612, 5.408007560256821, 2.24439947593943, -0.5155439788327071, -2.825028949950932, -4.654889977644587, -5.994207805873647, -6.850997851102507, -7.251346973250912, -7.237690414123787, -6.866514882103609, -6.205641341366554, -5.33129953986206, -4.324577932948708, -3.2677063883972663, -2.240458661296362, -1.3167902980657393, -0.5618620058299519, -0.029500536074426386, 0.2399943459550227, 0.22124383461995134, -0.09556731641648603, -0.7047619274007827, -1.5859043179799217, -2.705086353792124, -4.0169010823659805, -5.466906370121186, -6.994411759343065, -8.535462763988171, -10.025875714832324, -11.404192064356387, -12.61446988564112, -13.608714774398308, -14.348860643226974, -14.808229989964342, -14.972435895813822, -14.839703976153851, -14.420500028781742, -13.736641360660105, -12.819925172850047, -11.710335224134138, -10.453917291681767, -9.100405156476041, -7.7007860711680785, -6.3049349925269915, -4.959389333829849, -3.7053642449724995, -2.5770765296048976, -1.6004543151158994, -0.792466573656734, -0.16086320573484605, 0.2956493327604635, 0.5867921549090782, 0.7296924686826667, 0.7474666649505518, 0.667562042960556, 0.5200178209667107, 0.3356716004588151, 0.1443913969872001, -0.02660249148690702, -0.15423472714820796, -0.22060592942376386, -0.21374541295435603, -0.1280500755654578, 0.03562679459767997, 0.27026625234933305, 0.5634768145624287, 0.8984804961469111, 1.255227525956611, 1.611657343855748, 1.945035421687759, 2.2334134240697074, 2.457330857474723, 2.6007165215818246, 2.65165829993537, 2.6030255102280546, 2.4528319119155126, 2.204456886244299, 1.866807448853715, 1.4533654121487973, 0.9812801792290011, 0.47043350747817814, -0.057605030929382794, -0.5806176780583123, -1.0767629815947726, -1.5259930334616705, -1.9110720415787263, -2.218328242037867, -2.4381958993334902, -2.565541240554343, -2.599836230775727, -2.5450460753988193, -2.409194089895498, -2.2037302680680386, -1.9427536606378506, -1.642164646932317, -1.3188203100889375, -0.989497656935627, -0.6699562908821489, -0.3741399098306151, -0.11352816293950324, 0.10332218045865917, 0.27103642632115477, 0.3875574973908502, 0.45403055887838695, 0.47448588482774906, 0.45536411476623645, 0.4049193968836507, 0.33254484252081856, 0.2480707708425855, 0.1610642139740952, 0.08018305284182434, 0.012626517935327942, -0.036286772976368904, -0.06338797796544912, -0.06775412146717977, -0.05064351082783492, -0.015275992292813286, 0.03352493051389165, 0.08980395855950306, 0.14703217461025417, 0.1986826468974917, 0.23879679010620597, 0.26250702465390885, 0.26647748291192597, 0.24923445214472043, 0.21135721102725957, 0.15548572234953661, 0.0861882431926653, 0.009686790453426753, -0.06654966978307544, -0.1343241448457565, -0.18531628310029263, -0.21169607651193123, -0.20672231512692774, -0.16529584625795393, -0.08442929440436812, 0.036406343661563256, 0.19512485517917702, 0.3870336850037597, 0.6049901687441787, 0.8397177357481574, 1.0802695437878698, 1.314658785657652, 1.5307082873994888, 1.7167342472495695, 1.8622386076006636, 1.9585866153599734, 1.9996010412540102, 1.9820983830835903, 1.9063903190243086, 1.7761971879107221, 1.5984667299542124, 1.3830629440286657, 1.1422769840972318, 0.8902198689604894, 0.6421120199618937, 0.4132025935192502, 0.21780729089988857, 0.0684276977692392, -0.02504976246851128, -0.05603009327789958, -0.021754102330036346, 0.07635959082337496, 0.2326810963529534, 0.4375900560896822, 0.6779333944535708, 0.9376948401545142, 1.198857002470836, 1.4424803905909438, 1.6498522831336684, 1.803648054506837, 1.8890501853110166, 1.8947753293234448, 1.8139819272107134, 1.6448923084575824, 1.391132540847855, 1.061781017507908, 0.6711089236054909, 0.23802806281942596, -0.21474127343386443, -0.6618396204126883, -1.0765995434118256, -1.4324885520079642, -1.7046031443396177, -1.87114521967714, -1.914827260247768, -1.824047502949348, -1.5937946565930379, -1.2262421263627876, -0.7309871644615048, -0.12491211356047667, 0.5683578741276113, 1.3193946082828967, 2.094215633804642, 2.8558043634094252, 3.5658377859627746, 4.186569076298235, 4.682812158913528, 5.023691620913457, 5.184265201876638, 5.1469319211735645, 4.902526677596341, 4.4510505988449545, 3.8019485135231683, 2.9738202028168237, 1.9937866583850716, 0.8964692156913915, -0.2774039528041731, -1.4827653101666893, -2.6723820752616447, -3.79883486169623, -4.816538348704675, -5.683749302174436, -6.364431255755027, -6.829971888697689, -7.060682100044773, -7.046314095062038, -6.786377492407977, -6.290134061405608, -5.576178257317676, -4.671607863110388, -3.610626586650283, -2.4327696650916826, -1.1811593097771163, 0.0993219781298253, 1.3638943257567804, 2.5698534599823493, 3.6788537150022407, 4.65810724065543, 5.481345085844156, 6.129573645128573, 6.591494261582028, 6.863783093323644, 6.951410008141206, 6.866326724576708, 6.6262656548779875, 6.25355320339637, 5.773799253661143, 5.21466560141969, 4.6047975054104056, 3.9718996757283427, 3.3414048888040644, 2.7355229027958763, 2.1725343234946988, 1.6663919022544256, 1.226597242773939, 0.8580232460825085, 0.5612238846337396, 0.33301307267061103, 0.16719115692944245, 0.05536789536979993, -0.012187824852242308, -0.04573489436363766, -0.055267075467787356, -0.04983717624119312, -0.03704289790283044, -0.022695321712468353, -0.010676454837522414, -0.0029769107455579953, 9.51155878453492e-05, -0.0004354378720497447, -0.0026581873599043084, -0.004276266293548081, -0.0031074773163394754, 0.0024624794987314754, 0.013121983094410901, 0.02840915025126167, 0.04664912106183514, 0.06506859216881296, 0.0800903857271904, 0.08779433900975876, 0.08451700423021564, 0.06755107310368628, 0.03589452864737752, -0.009008949884494103, -0.0626018670937904, -0.116669366615964, -0.15897847743236543, -0.17315167062189307, -0.13881417297727214, -0.032036136893253755, 0.17396286714527004, 0.5078434216863059, 0.9989079795437755, 1.6756465545720118, 2.5641225794257028, 3.6863531613613443, 5.059026767238311, 6.691995788439458, 8.586912327925667, 10.7361459261784, 13.122004838164052, 15.716639910077996, 18.483338141411522, 21.376633187880696, 24.342977919601424, 27.322025170684157, 30.24825087973318, 33.05352074116488, 35.67150378186551, 38.03849811436429, 40.09497688640955, 41.78760679733243, 43.0711090552193, 43.91074505273352, 44.286253746881, 44.190155679905125, 43.62709256170397, 42.61358665334103, 41.17741098824243, 39.35736578752484, 37.20398883043301, 34.77502664635726, 32.13255084880424, 29.340842317376016, 26.464297289134027, 23.56589893193238, 20.706415993604256, 17.94072638737261, 15.315972099658627, 12.870659656331009, 10.634150465814995, 8.626711798637189, 6.860043399776826, 5.336948604907039, 4.052099829570879, 2.99327870359396, 2.1427666209898217, 1.4788431594989861, 0.9772778291048859, 0.6125488067116779, 0.3591635698154524, 0.19284048846379398, 0.0914552673056227, 0.03573250002863609, 0.009672175167165785, 0.00072179135291673, -0.0002671771020659317, 0.0007114470612179438, 0.000403679630931914, -0.0022351419125393067, -0.0066345354824133285, -0.011217155331920692, -0.013974896453353746, -0.012972284787908201, -0.0067458573018303394, 0.005421193254060031, 0.023358923428810626, 0.046002440508759714, 0.07150223658218045, 0.09743222460704201, 0.12106766606844489, 0.13970096095394988, 0.15095893085210985, 0.15308465145487027, 0.14516273045987482, 0.12726466345957554, 0.10049820103381639, 0.06695010082954451, 0.029516591548363492, -0.008333499796444484, -0.04285864022632089, -0.07038708473609658, -0.08767140159138269, -0.0922276011135661, -0.0826188091751741, -0.058622067573776845, -0.021312321861426956, 0.026956790144317167, 0.08268556371420221, 0.14148255252674685, 0.19846159706923516, 0.24865419429860872, 0.28744356480451805, 0.3110054559813011, 0.316716145131506, 0.3035153290593771, 0.27220434670142357, 0.22545979968674085, 0.16773587826400865, 0.10504102020488053, 0.044573495761295406, -0.005764634628056608, -0.037981386250241306, -0.04472228726162081, -0.019943917987242814, 0.040473182901808256, 0.13820638821335485, 0.272096929940385, 0.4379029582288031, 0.6283746513408377, 0.8335636523516595, 1.041349474309551, 1.2381747232352334, 1.4099591376377276, 1.5431889377451251, 1.6260934629723638, 1.649758721340812, 1.6091293104878497, 1.5038268485560429, 1.3387384654283399, 1.1243438535642003, 0.8764913424064184, 0.615769993466008, 0.3664843135565709, 0.15523424517735174, 0.009154561389822114, -0.04615281713553465, 0.011043950278453387, 0.19627725555135553, 0.5166520544052229, 0.9688410026383452, 1.537424566373841, 2.193685072688025, 2.895106048640437, 3.5855859704060533, 4.1964060358504485, 4.647979540691254, 4.852379526868419, 4.71663621389, 4.146564774542676, 3.051036473436937, 1.3465364731682046, -1.0381987380749147, -4.157689264660521, -8.045700854117342, -12.711879888698316, -18.13908806182667, -24.28167253582155, -31.06482011547805, -38.3853595427983, -46.11462692906774, -54.10116427497988, -62.17459380116938, -70.15064789856726, -77.83700304562758, -85.04037307793946, -91.57545839582292, -97.26996600221989, -101.97022751386811, -105.54690606073538, -107.89996229311718, -108.9634607892005, -108.71050568243594, -107.15160611831818, -104.33352178678679, -100.337669683534, -95.27729046655742, -89.29392632433529, -82.55309577791415, -75.2358483219752, -67.53180353633336, -59.63266655668605, -51.72583029426054, -43.98820918441056, -36.57989091135504, -29.63891620186663, -23.277949269933433, -17.582125776719057, -12.608041024106585, -8.383494961299819, -4.907533703230384, -2.1539539186031624, -0.07518850931806058, 1.3935766899127209, 2.3299284647441656, 2.8198843145740793, 2.953902361471428, 2.8212365143382105, 2.50571481528792, 2.0825606277455706, 1.616006829446902, 1.157823360548977, 0.7466495174840542, 0.40762339934101055, 0.15328744351031634, -0.014753080083629211, -0.1037135740008891, -0.12723936581551226, -0.10294362215861001, -0.04991788749087229, 0.013571560655390917, 0.07198850089272373, 0.11393060187042607, 0.1329672072164386, 0.12790397706359985, 0.10250461780897231, 0.06464343201640006, 0.02501710461652422, -0.004441134763091549, -0.012290566986688307, 0.010731459502612806, 0.07022259699104981, 0.16690935924911202, 0.29583985418182435, 0.44606025812031364, 0.6007540545949087, 0.737791203657186, 0.8314531494956658, 0.8547883440768156, 0.7823837772719903, 0.5933807904437551, 0.27427463418403925, -0.18050088652326887, -0.7691800412557425, -1.4823282420689925, -2.3022805146244814], 'positive_zeros': ['0.49270137886943292314371979562318', '0.63790633295046160347830288328701', '0.817225901353903119133286008739635', '0.831593847679191202559858382604070', '0.865543980655330629100108664434919', '1.18851638592805071124050620635654', '1.64060028833432289707609540997992', '1.65940070019316151238944338333606', '1.93978671001539915946718073738969', '1.96349845074531796692548607353639', '2.05453474023109268457619947334034', '2.10908648679711057998186919618122', '2.67387234298055596892021370119155', '2.73309333576716047461195451532394', '2.78639681382574888451728858589226', '2.93354658570206065776158624174940', '2.94222623190381881790941156852372', '2.98773988818005823291079902888137', '3.51097364398601086691112301382169', '3.55137170052535091085224908438400', '3.58484249415974404845911413849023', '3.59525854738450272153750697129973', '4.12574007100460366029484904263865', '4.19354326007236006951223042329175', '4.29528004026213863479368256958686', '4.51574649190889225540034690428172', '4.68709168257674743936001156552959', '4.73396522019000878514944113427764', '4.76649355437652656550760905107823', '4.84004779841242537761961877473743', '5.31016077688395636594594519498342', '5.33643936231355906727038274196451', '5.39251127004782612303600316894528', '5.40306800534211026700822669148330', '5.48186066150466241437288336019050', '5.69892837862409006563054551330095', '5.79403484126939722858293436855292', '5.84201025081897834015901059030248', '6.03570048975895808143592714952764', '6.05897262449374734894270936710320', '6.21743560879565320736733602745042', '6.25977211909793402478070581897293', '6.44798942102443997189781606414254', '6.46468283689716761283776442696465', '6.66402726467080909561336655769875', '6.89171087096223442330712643476638', '7.06787437405979055196473164010512', '7.16505506423472938895164201658765', '7.31804299957349209326078045868815', '7.41626189271841636915606257238532', '7.51818985496551099412146756378378', '7.52510753282090344793910428117637', '7.76365540053639755889120141249906', '7.78489251779758521758885491792892', '8.124442395360893535756045194898502', '8.168654679792975267223237787447102', '8.235409578052859359275200561210881', '8.330334470198394461013134919540549', '8.350977225963255218693537269304747', '8.361784753402884048797176767925000'], 'prelabel': '12-4840e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.216718956032975, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e6-0', 'trace_hash': 1912920511634028142, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49270137886943292314371979562', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.63790633295046160347830288329', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.817225901353903119133286008740', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3332228787.247679, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 12855002631049216000000, 'conductor_radical': 110, 'degree': 12, 'dirichlet_coefficients': [1, 0, -2, 0, 6, 0, 4, 0, -5, 0, 0, 0, 0, 0, -12, 0, 8, 0, 12, 0, -8, 0, -8, 0, 21, 0, 10, 0, 16, 0, -4, 0, 0, 0, 24, 0, 8, 0, 0, 0, 32, 0, -4, 0, -30, 0, -6, 0, -5, 0, -16, 0, 8, 0, 0, 0, -24, 0, 4, 0, 16, 0, -20, 0, 0, 0, -2, 0, 16, 0, -28, 0, 16, 0, -42, 0, 0, 0, 0, 0, 11, 0, 12, 0, 48, 0, -32, 0, 18, 0, 0, 0, 8, 0, 72, 0, 0, 0, 0, 0], 'euler11': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler13': [1, 0, 46, -16, 935, -560, 13172, -7280, 158015, -35152, 1313806, 0, 4826809], 'euler17': [1, -8, 86, -488, 3247, -14352, 70772, -243984, 938383, -2397544, 7182806, -11358856, 24137569], 'euler19': [1, -12, 142, -1028, 6983, -36232, 176372, -688408, 2520863, -7051052, 18505582, -29713188, 47045881], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 8, 78, 464, 3647, 17448, 99796, 401304, 1929263, 5645488, 21827598, 51490744, 148035889], 'euler29': [1, -16, 158, -976, 3655, -5856, -10876, -169824, 3073855, -23803664, 111750398, -328178384, 594823321], 'euler3': [1, 2, 9, 18, 50, 82, 181, 246, 450, 486, 729, 486, 729], 'euler31': [1, 4, 106, 580, 5471, 35008, 194684, 1085248, 5257631, 17278780, 97893226, 114516604, 887503681], 'euler37': [1, -8, 142, -872, 9911, -52016, 449252, -1924592, 13568159, -44169416, 266130862, -554751656, 2565726409], 'euler41': [1, -32, 597, -7760, 78494, -647040, 4497049, -26528640, 131948414, -534826960, 1686979317, -3707398432, 4750104241], 'euler43': [1, 4, 157, 160, 9938, -11060, 442193, -475580, 18375362, 12721120, 536751757, 588033772, 6321363049], 'euler47': [1, 6, 217, 1142, 22146, 96502, 1330941, 4535594, 48920514, 118565866, 1058890777, 1376070042, 10779215329], 'euler5': [1, -6, 15, -20, 15, -6, 1, 0, 0, 0, 0, 0, 0], 'euler53': [1, -8, 142, -624, 8055, -33704, 443124, -1786312, 22626495, -92899248, 1120448302, -3345563944, 22164361129], 'euler59': [1, -4, 106, -804, 11415, -59440, 798588, -3506960, 39735615, -165124716, 1284440266, -2859697196, 42180533641], 'euler61': [1, -16, 245, -2240, 24374, -199632, 1856313, -12177552, 90695654, -508437440, 3392231045, -13513540816, 51520374361], 'euler67': [1, 2, 49, 458, 11018, 49970, 322277, 3347990, 49459802, 137749454, 987404929, 2700250214, 90458382169], 'euler7': [1, -4, 21, -56, 218, -636, 1993, -4452, 10682, -19208, 50421, -67228, 117649], 'euler71': [1, 28, 546, 7900, 98591, 1012032, 9200236, 71854272, 496997231, 2827496900, 13874777826, 50518421828, 128100283921], 'euler73': [1, -16, 246, -2768, 28991, -286368, 2601844, -20904864, 154493039, -1076799056, 6985967286, -33169145488, 151334226289], 'euler79': [1, 0, 342, -288, 55791, -50976, 5551220, -4027104, 348191631, -141995232, 13320927702, 0, 243087455521], 'euler83': [1, -12, 210, -1028, 22311, -168072, 2881772, -13949976, 153700479, -587797036, 9966247410, -47268487716, 326940373369], 'euler89': [1, -18, 253, -1798, 8058, 72934, -1088091, 6491126, 63827418, -1267534262, 15873786973, -100513070082, 496981290961], 'euler97': [1, 0, 342, 1080, 57231, 248616, 6595652, 24115752, 538486479, 985686840, 30277014102, 0, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 9, 18, 50, 82, 181, 246, 450, 486, 729, 486, 729], [1, -6, 15, -20, 15, -6, 1, 0, 0, 0, 0, 0, 0], [1, -4, 21, -56, 218, -636, 1993, -4452, 10682, -19208, 50421, -67228, 117649], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 46, -16, 935, -560, 13172, -7280, 158015, -35152, 1313806, 0, 4826809], [1, -8, 86, -488, 3247, -14352, 70772, -243984, 938383, -2397544, 7182806, -11358856, 24137569], [1, -12, 142, -1028, 6983, -36232, 176372, -688408, 2520863, -7051052, 18505582, -29713188, 47045881], [1, 8, 78, 464, 3647, 17448, 99796, 401304, 1929263, 5645488, 21827598, 51490744, 148035889], [1, -16, 158, -976, 3655, -5856, -10876, -169824, 3073855, -23803664, 111750398, -328178384, 594823321], [1, 4, 106, 580, 5471, 35008, 194684, 1085248, 5257631, 17278780, 97893226, 114516604, 887503681], [1, -8, 142, -872, 9911, -52016, 449252, -1924592, 13568159, -44169416, 266130862, -554751656, 2565726409], [1, -32, 597, -7760, 78494, -647040, 4497049, -26528640, 131948414, -534826960, 1686979317, -3707398432, 4750104241], [1, 4, 157, 160, 9938, -11060, 442193, -475580, 18375362, 12721120, 536751757, 588033772, 6321363049], [1, 6, 217, 1142, 22146, 96502, 1330941, 4535594, 48920514, 118565866, 1058890777, 1376070042, 10779215329], [1, -8, 142, -624, 8055, -33704, 443124, -1786312, 22626495, -92899248, 1120448302, -3345563944, 22164361129], [1, -4, 106, -804, 11415, -59440, 798588, -3506960, 39735615, -165124716, 1284440266, -2859697196, 42180533641], [1, -16, 245, -2240, 24374, -199632, 1856313, -12177552, 90695654, -508437440, 3392231045, -13513540816, 51520374361], [1, 2, 49, 458, 11018, 49970, 322277, 3347990, 49459802, 137749454, 987404929, 2700250214, 90458382169], [1, 28, 546, 7900, 98591, 1012032, 9200236, 71854272, 496997231, 2827496900, 13874777826, 50518421828, 128100283921], [1, -16, 246, -2768, 28991, -286368, 2601844, -20904864, 154493039, -1076799056, 6985967286, -33169145488, 151334226289], [1, 0, 342, -288, 55791, -50976, 5551220, -4027104, 348191631, -141995232, 13320927702, 0, 243087455521], [1, -12, 210, -1028, 22311, -168072, 2881772, -13949976, 153700479, -587797036, 9966247410, -47268487716, 326940373369], [1, -18, 253, -1798, 8058, 72934, -1088091, 6491126, 63827418, -1267534262, 15873786973, -100513070082, 496981290961], [1, 0, 342, 1080, 57231, 248616, 6595652, 24115752, 538486479, 985686840, 30277014102, 0, 832972004929]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4840/2/a/bd'], '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': '12-4840e6-1.1-c1e6-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-4840e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.216718956032975, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 1912920511634028142, 'z1': {'__RealLiteral__': 0, 'data': '0.49270137886943292314371979562', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '624573198657112907498861372590,808642345854041402506473271722,1035956904373331079664786611561,1054170440156629501583888392661,1097207346601660849851170375058,1506623510002779424363838178248', 'Lhash_array': ['624573198657112907498861372590', '808642345854041402506473271722', '1035956904373331079664786611561', '1054170440156629501583888392661', '1097207346601660849851170375058', '1506623510002779424363838178248'], 'factors': ['2-4840-1.1-c1-0-9', '2-4840-1.1-c1-0-18', '2-4840-1.1-c1-0-34', '2-4840-1.1-c1-0-35', '2-4840-1.1-c1-0-38', '2-4840-1.1-c1-0-66'], 'label': '12-4840e6-1.1-c1e6-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4840/2/a/bd'}