-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1735370767409949117799108551298,3433026738211724759757961869320,3573147322145751400925819233183,3837327928407403940793785170704,5294978977026278824343935608284,5726968426298915995654279788129', 'a10': -2, 'a2': 1, 'a3': -3, 'a4': 1, 'a5': -2, 'a6': -3, 'a7': -2, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.008890205012281008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 3, 6, 7, 6, 3, 1]], [19, [1, -4, 17, -136, 323, -1444, 6859]]], 'bad_primes': [3, 19], 'central_character': '57.1', 'coefficient_field': '1.1.1.1', 'conductor': 34296447249, 'conductor_radical': 57, 'degree': 12, 'euler_factors': [[1, -1, 0, 1, -2, -1, 11, -2, -8, 8, 0, -32, 64], [1, 3, 6, 7, 6, 3, 1], [1, 2, -3, -2, -2, -34, -31, -170, -50, -250, -1875, 6250, 15625], [1, 2, 25, 58, 346, 674, 3089, 4718, 16954, 19894, 60025, 33614, 117649], [1, 0, 18, -72, 279, -648, 5740, -7128, 33759, -95832, 263538, 0, 1771561], [1, -1, -17, 40, 61, -223, 854, -2899, 10309, 87880, -485537, -371293, 4826809], [1, 0, -51, 0, 1734, 0, -34391, 0, 501126, 0, -4259571, 0, 24137569], [1, -4, 17, -136, 323, -1444, 6859], [1, 14, 99, 382, 346, -7726, -57613, -177698, 183034, 4647794, 27704259, 90108802, 148035889], [1, 4, -39, -52, 886, -1916, -33907, -55564, 745126, -1268228, -27583959, 82044596, 594823321], [1, -30, 513, -6118, 56634, -421662, 2585865, -13071522, 54425274, -182261338, 473766273, -858874530, 887503681], [1, 6, 237, 1130, 22770, 84366, 1137381, 3121542, 31172130, 57237890, 444176157, 416063742, 2565726409], [1, -4, -75, 100, 3622, 2012, -174751, 82492, 6088582, 6892100, -211932075, -463424804, 4750104241], [1, -3, -99, 218, 6207, -6951, -285738, -298893, 11476743, 17332526, -338461299, -441025329, 6321363049], [1, -18, 75, -666, 15954, -93546, 218347, -4396662, 35242386, -69146118, 365976075, -4128210126, 10779215329], [1, -6, -51, 102, 1086, 11334, -107183, 600702, 3050574, 15185454, -402414531, -2509172958, 22164361129], [1, 0, -153, 72, 14382, -5508, -969077, -324972, 50063742, 14787288, -1853956233, 0, 42180533641], [1, 13, -25, -504, 6133, 34211, -181514, 2086871, 22820893, -114398424, -346146025, 10979751913, 51520374361], [1, 9, -39, -250, 375, -24519, -284658, -1642773, 1683375, -75190750, -785893719, 12151125963, 90458382169], [1, -18, 99, -234, 306, 55062, -871373, 3909402, 1542546, -83751174, 2515756419, -32476128318, 128100283921], [1, 19, 59, 252, 17041, 91889, -279578, 6707897, 90811489, 98032284, 1675496219, 39388360267, 151334226289], [1, 11, -119, -494, 21403, 27611, -1863994, 2181269, 133576123, -243561266, -4635059639, 33847620389, 243087455521], [1, 8, 354, 2296, 60391, 326864, 6327932, 27129712, 416033599, 1312822952, 16800245634, 31512325144, 326940373369], [1, -16, -87, 424, 39826, -163780, -2350663, -14576420, 315461746, 298906856, -5458574967, -89344951184, 496981290961], [1, -2, -19, -2166, 418, 14486, 2859997, 1405142, 3932962, -1976849718, -1682056339, -17174680514, 832972004929], [1, 22, 105, 74, 14458, 106174, -310999, 10723574, 147486058, 76242274, 10926342105, 231222211022, 1061520150601], [1, 18, 249, 1658, 25674, 358962, 5362977, 36973086, 272375466, 1811741366, 28025169369, 208669333374, 1194052296529], [1, 20, 510, 8236, 127255, 1515560, 18009860, 162164920, 1456942495, 10089454148, 66850596510, 280510346140, 1500730351849], [1, -18, 33, 2, 5802, 165606, -3625215, 18051054, 68933562, 2590058, 4658219313, -276952311882, 1677100110841], [1, 24, 702, 10896, 191295, 2234904, 28565332, 252544152, 2442645855, 15721805712, 114459247422, 442184443032, 2081951752609]], 'euler_factors_factorization': [[[[1, -1, 0, 1, -2, -1, 11, -2, -8, 8, 0, -32, 64], 1]], [[[1, 1, 1], 3]], [[[1, 2, -3, -2, -2, -34, -31, -170, -50, -250, -1875, 6250, 15625], 1]], [[[1, 1, 12, 17, 84, 49, 343], 2]], [[[1, 0, 9, -36, 99, 0, 1331], 2]], [[[1, -1, -17, 40, 61, -223, 854, -2899, 10309, 87880, -485537, -371293, 4826809], 1]], [[[1, 0, -17, 0, 289], 3]], [[[1, -4, 17, -136, 323, -1444, 6859], 1]], [[[1, 14, 99, 382, 346, -7726, -57613, -177698, 183034, 4647794, 27704259, 90108802, 148035889], 1]], [[[1, 4, -39, -52, 886, -1916, -33907, -55564, 745126, -1268228, -27583959, 82044596, 594823321], 1]], [[[1, -15, 144, -899, 4464, -14415, 29791], 2]], [[[1, 1, 37], 6]], [[[1, -4, -75, 100, 3622, 2012, -174751, 82492, 6088582, 6892100, -211932075, -463424804, 4750104241], 1]], [[[1, -3, -99, 218, 6207, -6951, -285738, -298893, 11476743, 17332526, -338461299, -441025329, 6321363049], 1]], [[[1, -6, -11, -282, 2209], 3]], [[[1, -6, -51, 102, 1086, 11334, -107183, 600702, 3050574, 15185454, -402414531, -2509172958, 22164361129], 1]], [[[1, 0, -153, 72, 14382, -5508, -969077, -324972, 50063742, 14787288, -1853956233, 0, 42180533641], 1]], [[[1, 13, -25, -504, 6133, 34211, -181514, 2086871, 22820893, -114398424, -346146025, 10979751913, 51520374361], 1]], [[[1, 9, -39, -250, 375, -24519, -284658, -1642773, 1683375, -75190750, -785893719, 12151125963, 90458382169], 1]], [[[1, -18, 99, -234, 306, 55062, -871373, 3909402, 1542546, -83751174, 2515756419, -32476128318, 128100283921], 1]], [[[1, 19, 59, 252, 17041, 91889, -279578, 6707897, 90811489, 98032284, 1675496219, 39388360267, 151334226289], 1]], [[[1, 11, -119, -494, 21403, 27611, -1863994, 2181269, 133576123, -243561266, -4635059639, 33847620389, 243087455521], 1]], [[[1, 4, 169, 472, 14027, 27556, 571787], 2]], [[[1, -16, -87, 424, 39826, -163780, -2350663, -14576420, 315461746, 298906856, -5458574967, -89344951184, 496981290961], 1]], [[[1, -2, -19, -2166, 418, 14486, 2859997, 1405142, 3932962, -1976849718, -1682056339, -17174680514, 832972004929], 1]], [[[1, 22, 105, 74, 14458, 106174, -310999, 10723574, 147486058, 76242274, 10926342105, 231222211022, 1061520150601], 1]], [[[1, 9, 84, 73, 8652, 95481, 1092727], 2]], [[[1, 10, 205, 2068, 21935, 114490, 1225043], 2]], [[[1, -18, 33, 2, 5802, 165606, -3625215, 18051054, 68933562, 2590058, 4658219313, -276952311882, 1677100110841], 1]], [[[1, 12, 279, 2100, 31527, 153228, 1442897], 2]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '12-57e6-1.1-c1e6-0-0', '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/57/2/e/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0208333333333', 'prec': 50}, 'plot_values': [0.3031892389303182, 0.30463432355796916, 0.30611305030690794, 0.3078053574802536, 0.30989397530310114, 0.31256605247966085, 0.31601569773560473, 0.3204062344449691, 0.3257460878490195, 0.33200621774924066, 0.33915915021021464, 0.3471776656775427, 0.3560334995960196, 0.3657073210096719, 0.37622356600565465, 0.38761990820027065, 0.3999364593038182, 0.4132157145886594, 0.4275024722421734, 0.4428392815763013, 0.4592518666937803, 0.47676006748613803, 0.4953812224995369, 0.5151292736542888, 0.5360137733154848, 0.558039700936906, 0.5812093656228865, 0.6055190462896881, 0.6309568743307933, 0.6575014253457202, 0.6851201816936254, 0.7137673040062927, 0.7433801192994021, 0.7738788070067779, 0.8051649187765582, 0.8371192295950843, 0.8695994694493816, 0.9024381693258874, 0.935441155771776, 0.9683848980560168, 1.0010139003112313, 1.0330382223078558, 1.0641309881721088, 1.0939262603942967, 1.122018145217318, 1.1479583719238255, 1.1712541443424491, 1.1913664316798014, 1.207708498730384, 1.2196457557252294, 1.226498915108861, 1.2275422545266252, 1.2220033057955475, 1.2090639253126776, 1.1878619769694263, 1.1574958836061826, 1.11703580430846, 1.0655238312121118, 1.001977494606615, 0.9253960277131591, 0.8347675766099426, 0.7290815499358705, 0.6073524966102198, 0.4686219244267137, 0.31196642667277785, 0.1365103913515621, -0.058560398258872715, -0.27397749185806464, -0.510351389057265, -0.7681714650286792, -1.0477956794268424, -1.349433874282854, -1.6731310330918867, -2.0187410566636443, -2.385879237978009, -2.7739317762961098, -3.1820509453581294, -3.609142668153084, -4.05385582886678, -4.51456231106349, -4.9893159310078, -5.475882182405634, -5.971750581098979, -6.474139489288389, -6.980004719672696, -7.4860419973077095, -7.988675404125357, -8.484113835570211, -8.9683897488406, -9.437391871127655, -9.88690235970463, -10.3126335036217, -10.710264379639371, -11.075514804892252, -11.40420571169302, -11.692315980601549, -11.936041130680978, -12.131857878247706, -12.276605649609515, -12.367544207392495, -12.402407598928804, -12.379457738129322, -12.297533677534366, -12.156111335415462, -11.955393592943448, -11.696299637338559, -11.380466793751918, -11.01025652783146, -10.588749594510642, -10.119753741745043, -9.607846222754459, -9.058255512682585, -8.476776677337664, -7.869698608938858, -7.243719773753484, -6.6058782719435465, -5.963512426385973, -5.324052690333758, -4.6948687883058415, -4.0831403278903835, -3.495725992139292, -2.939051543894437, -2.4190216496307375, -1.9408185043734774, -1.5087688714593164, -1.1262461377392203, -0.7955881893364504, -0.5180404576637287, -0.293719877294913, -0.12155195176816044, 0.000729517321119018, 0.07654589547774904, 0.11041096387546544, 0.10784260887033577, 0.07525466621312946, 0.01982151009665486, -0.05069089853878651, -0.12811375128899435, -0.20407879173651713, -0.2702321905149564, -0.31845850303697953, -0.34111196434766217, -0.3312395844463757, -0.2827917648687402, -0.19081555133462605, -0.051629252354922425, 0.13701828119109252, 0.37584333285607363, 0.66396021844509, 0.998852663159016, 1.3763886249084185, 1.7908776203589596, 2.235173879774636, 2.700842185077537, 3.178356082657288, 3.657329601405675, 4.126780288459322, 4.575430074883032, 4.992063651245736, 5.365831241233416, 5.686554773319977, 5.945033007066127, 6.133327723848139, 6.245055929580238, 6.275721815924068, 6.222802853778315, 6.085830394895676, 5.866444363977007, 5.5683886018703825, 5.19748970719325, 4.76165101341998, 4.270503116868877, 3.7350976097891713, 3.167602089274736, 2.580958581991203, 1.9885483232800578, 1.403874089029904, 0.8400092006250399, 0.3091702964662792, -0.17764251037801462, -0.6109678410843845, -0.9831486835729553, -1.28855563130699, -1.5238115270133599, -1.6878674348393046, -1.7819827698778492, -1.8096276053240143, -1.7763206838582069, -1.689429615111661, -1.5578420847715913, -1.3915772306158019, -1.201367641790818, -0.9982210536052541, -0.7929891508472777, -0.5959615139732505, -0.4164063114592642, -0.26218881592878157, -0.13946738764975794, -0.052465847381589964, -0.0033332614427468168, 0.007912752397699369, -0.01663286121686588, -0.07290078459215799, -0.1550811200176774, -0.2559378193223233, -0.3671865781320567, -0.4799111227516165, -0.5850349161523699, -0.6738064104552761, -0.738271125536594, -0.7717114139127217, -0.769025849386788, -0.7270136905368931, -0.6446070937807897, -0.5229971046808034, -0.36564527303988886, -0.1781834191553567, 0.031815622825846164, 0.2552251162760771, 0.4817414878935634, 0.700344829051152, 0.8998242179971007, 1.069330576674263, 1.1989655921925644, 1.28041769892074, 1.30733917082927, 1.2756926051295792, 1.1840317755089078, 1.03367084151073, 0.8287572227057551, 0.5762359308952542, 0.28548645485467117, -0.032075654811378196, -0.36346656557670864, -0.6946850551344044, -1.0113333231746278, -1.2993414175835425, -1.5456733283954882, -1.7389389132219437, -1.8699350972714817, -1.932094159966595, -1.9218609240922033, -1.8390450697566014, -1.686760100739531, -1.471242733994188, -1.2015611526643646, -0.8891888483795349, -0.5475031868952368, -0.19124856542253194, 0.16433627527478828, 0.5043109951206672, 0.8147625232211754, 1.0834792193895655, 1.300528337371565, 1.4587274344982866, 1.5540424273023936, 1.5857514929864889, 1.5564179813943175, 1.4716916437305976, 1.3399582871107003, 1.1718653851799412, 0.9796646101102595, 0.7764829332479686, 0.5755638998472836, 0.3895118876161334, 0.22958494538037266, 0.10507095149090528, 0.02275288096673663, -0.013446335122462641, -0.0026404826524086193, 0.05302299329006904, 0.1485495679981259, 0.2764730403173634, 0.42736540865873346, 0.5904606312590772, 0.754353876044594, 0.9077315445633903, 1.0401068343254742, 1.1425469326414759, 1.2081908084192798, 1.2326397883772986, 1.2141996426194814, 1.1539455763473532, 1.055626336733764, 0.925418941086057, 0.7713886647797688, 0.6028802646209334, 0.42985385617452976, 0.2621873311502722, 0.10899558949142935, -0.021999851126579907, -0.12502264705889862, -0.196604822701322, -0.2357670965842712, -0.24401176864529422, -0.2251279045674663, -0.18481315696005113, -0.13012448879247523, -0.06882457367146944, -0.008671347660268464, 0.04329855032172799, 0.08144524283739507, 0.10211582113674739, 0.10402892071166694, 0.08846451329407592, 0.059241327509287865, 0.02246876020196098, -0.013917905885196036, -0.040831477940216666, -0.0488756193229391, -0.029246991252738625, 0.02535244072324084, 0.11985902121102414, 0.25611625138558225, 0.4323534920050687, 0.6429707019055084, 0.8786173755237771, 1.1265851398237825, 1.371514755968512, 1.5964288186437146, 1.7841311417888739, 1.9185913528989396, 1.9863807621996528, 1.9780836167240792, 1.8895560931287254, 1.7229909994146047, 1.4877288726159759, 1.20020529251058, 0.8835108893073257, 0.5665059306780177, 0.28244414269317336, 0.06715948902976207, -0.0431833428974443, -0.014683046673149475, 0.18176183108363606, 0.5680278082915622, 1.1565848549456141, 1.9487070174638628, 2.9332772292192395, 4.086419959516755, 5.3718494801451495, 6.741973336598042, 8.139749726319565, 9.50142100448766, 10.760419804222556, 11.850750163204518, 12.71056356348685, 13.285811143473765, 13.533635318421217, 13.425706968998863, 12.951737326471575, 12.119505732185331, 10.954536991009169, 9.499176903546857, 7.810701541050913, 5.958894457589346, 4.023219214661245, 2.086926155726045, 0.23205041956651756, -1.465092610328122, -2.9380863092644915, -4.13395502375997, -5.016115309741271, -5.566850363505801, -5.787841675389302, -5.699334500783029, -5.338165442818548, -4.754862895419552, -4.010082534379982, -3.1698559839572145, -2.300633194821321, -1.4645429959994845, -0.7151327453973528, -0.09388638694693986, 0.3723329430002608, 0.6727487423628683, 0.8125927619866677, 0.8116505836877834, 0.7015936818005595, 0.5223360606041092, 0.31770657779684375, 0.13054276268357504, -0.002131758814756784, -0.053436796804562835, -0.010120400968008274, 0.12512903644901094, 0.3327949663396611, 0.5771853581399911, 0.8086983278901934, 0.9675606681646979, 0.9887988873260282, 0.8081194836854655, 0.3682309754243773, -0.37506988759124477, -1.4473557838040765, -2.8510640254314636, -4.562475015487911, -6.53068406377289, -8.67932037155551, -10.90972361402996, -13.105970982125038, -15.141678664429227, -16.888108825775646, -18.223603214340965, -19.04445725654837, -19.27210774918659, -18.859605303088255, -17.796768169212978, -16.113119112854577, -13.878691780889884, -11.2023922915967, -8.224436765180767, -5.1078114970230715, -2.0284007507787116, 0.8361856249604734, 3.318619923669105, 5.274698975187232, 6.594091460300318, 7.208434595940872, 7.096923796758891, 6.288929769407418, 4.863815496754633, 2.947882271621411, 0.7047458958876024, -1.6758871545529823, -3.9908518574326686, -6.0372891341500186, -7.626685512103282, -8.598911358784804, -8.834974552509289, -8.265964067355066, -6.878532479004545, -4.7167464335545395, -1.8802293554432037, 1.4816272663688663, 5.179943489689473, 8.999115264873268, 12.711210492413135, 16.091146226429824, 18.932228993462758, 21.06231379026227, 22.354712266575405, 22.73591416028735, 22.189962854928826, 20.758878584634218, 18.54004857448182, 15.681522768387353, 12.368369438859123, 8.808381227150738, 5.217448759055171, 1.8047806617596382, -1.2405304496884122, -3.760800155674355, -5.641597894207471, -6.818328422168116, -7.278376754857471, -7.0593952840064516, -6.24386516274051, -4.950560698583843, -3.3244104879208303, -1.5241709651660251, 0.2905562906847432, 1.9717653467349852, 3.394059525231596, 4.463288574846015, 5.121762274018804, 5.350635692102172, 5.1691292664539175, 4.630649585552516, 3.816120946436856, 2.824882373078997, 1.7649763298448637, 0.7433927196591552, -0.14321777669577648, -0.816593187344264, -1.2231296562792637, -1.3376044918825376, -1.1632531903937284, -0.7298325424061094, -0.08967112327007415, 0.6880504649178063, 1.5245334865397355, 2.3401730368290634, 3.06180145489758, 3.628715057851863, 3.997427026010078, 4.144679085719681, 4.0688802372760415, 3.790084131240194, 3.3455768095602876, 2.7847973733777587, 2.163807076317359, 1.5394629881437785, 0.96390239787414, 0.47961905430941065, 0.11516465974108493, -0.11684311461447174, -0.21981845815957424, -0.21164923816765108, -0.12173500292333149, 0.013059826655163583, 0.1534247015910242, 0.26266191159614094, 0.31122247353502974, 0.28029243233800616, 0.16409285362620618, -0.029301817833400544, -0.27891117923017855, -0.5533717403305481, -0.8147059534542417, -1.0229467032283195, -1.1411313760351567, -1.140113338754499, -1.0026611794242604, -0.7263940154111931, -0.3252381878246264, 0.1707824004381612, 0.7175891513983607, 1.2610765765068344, 1.7416779080380957, 2.0996827019171773, 2.280909227711195, 2.242133023974309, 1.955947963072809, 1.4145071755562246, 0.6301962757898526, -0.36487479156774066, -1.520814110087746, -2.7734030530139266, -4.049009259983114, -5.271327116379188, -6.367517841980032, -7.273561590797694, -7.938891740143392, -8.329894747058123, -8.43252685558, -8.254371229401826, -7.821726584612251, -7.176032521354844, -6.369759661228449, -5.461672205864524, -4.512171285254087, -3.579045621970243, -2.7118104738652313, -1.9482631393418022, -1.3127294111655943, -0.8156645081013401, -0.454573060949509, -0.21599068404927677, -0.07810351771445023, -0.014206824990864784, 0.003699180976033337, 0.0016202222725973231, 0.0008917535358526572, 0.016355492648796058, 0.055525643343798274, 0.11873447425684551, 0.2001526630460593, 0.2894872160024889, 0.37413167521005475, 0.44154365775041216, 0.4812545674428514, 0.48642623633387294, 0.4548178725792388, 0.3890585357415124, 0.2962550681601401, 0.18698244013539947, 0.07359699081204044, -0.03150853495046074, -0.11754711702496191, -0.176704910585011, -0.2050787639106991, -0.2030965326684258, -0.17519275562983674, -0.1289047014357227, -0.07357916996544361, -0.018871468136698086, 0.026747622145337564, 0.05728784517757683, 0.0701361990979987, 0.06633162552661087, 0.05022537944266725, 0.028587965320003426, 0.00929208362509395, -0.0002444689294736213, 0.005391849720336854, 0.028368314580712043, 0.06688503098343436, 0.11512942926297473, 0.16398679230891516, 0.20251693317767377, 0.2199694543686024, 0.20807740373894112, 0.16332270590128292, 0.08881704363611277, -0.004529149300410175, -0.09784684736215962, -0.16550114022418067, -0.17746508255480356, -0.10277691608339183, 0.08616088565843523, 0.40889394770416626, 0.8726199002631599, 1.4685565583251359, 2.1695359282202213, 2.9292938556916366, 3.6837386841369244, 4.354737253466449, 4.857245269779653, 5.106062735194011, 5.0235870399320826, 4.548082236077228, 3.6414356816047095, 2.296142434591422, 0.5409366416294081, -1.5601236253043136, -3.910540438652751, -6.386664474847165, -8.8456687056683, -11.135982376371075, -13.110681537333653, -14.640108542118575, -15.622542535085651, -15.992881476551025, -15.728512051430222, -14.852707228977925, -13.435903440506875, -11.586994503596573, -9.442904419815129, -7.156777836999552, -4.88493520190592, -2.774172059634999, -0.9501259723261031, 0.49526507011259246, 1.5106235229948113, 2.0873262581525127, 2.2575879777479626, 2.0887049907589677, 1.6742563876648404, 1.1229413236569368, 0.5459022805118028, 0.04438586822148295, -0.3009437197465982, -0.43794384501772965, -0.3471403966776115, -0.04197271423362001, 0.43464835102570504, 1.0170668060106016, 1.6260495535600819, 2.179637534579557, 2.6049909301225416, 2.8470235192576556, 2.8746876241401185, 2.684382320850042, 2.2998982866861986, 1.7692077546985725, 1.1583201071309066, 0.540754215405131, -0.012818288885960089, -0.4440942416173859, -0.7150283780390029, -0.8131482504799025, -0.7537821387582785, -0.5781486789776045, -0.347377422040738, -0.13361358697115516, -0.009296620924689167, -0.035893956468613014, -0.25329726019818627, -0.6714435040970866, -1.2656911538159379, -1.976574940111627, -2.714200204755199, -3.366975200042959, -3.813616279343401, -3.9375190292444513, -3.641771214903236, -2.863093395864823, -1.5830963750921176, 0.16508709681841247, 2.2975165441266086, 4.68404251116254, 7.157772742437097, 9.529182968616395, 11.603408327154431, 13.200397525038941, 14.17772520380757, 14.442733678078325, 13.961345385851546, 12.762524127217294, 10.93674597296086, 8.62918513355278, 6.027467835127303, 3.339475383015912, 0.7723345600175775, -1.4872272562048185, -3.2902519951557347, -4.539319623064598, -5.198153976290652, -5.292109727567683, -4.901414804677098, -4.148879033618889, -3.183243684010169, -2.1601655593903324, -1.2225112670047842, -0.4807475366183324, 0.001255454269712148, 0.2143294386985538, 0.20549561785072293, 0.07263655695380658, -0.04725914126191052, 0.004818089216976499, 0.38973388304930845, 1.2492409953372252, 2.68644531457958, 4.750066995022253, 7.425461671875281, 10.631980640976426, 14.22690810325313, 18.015935754698972, 21.769112233445366, 25.242433531813557, 28.20601792173859, 30.46202542476419, 31.8605212985394, 32.31211912308775, 31.795014015255916, 30.35800939374445, 28.120500758994698, 25.252198604858435, 21.9541505941987, 18.440368533521085, 14.91950996940716, 11.579147736801032, 8.573362237909446, 6.008915189635025, 3.941244885133401, 2.3769045175375516, 1.280399680169409, 0.5843537133973077, 0.20147071331808147, 0.03685459382710899, -1.5389606588707826e-05, 0.014325718371271562, 0.023653273600451243, -0.005224883581135741, -0.08324349134452738, -0.20282286226202972, -0.34366312797882054, -0.47950221217017125, -0.5847443465081207, -0.640017685234141, -0.6359033714930724, -0.5741781786861291, -0.4668917338524761, -0.3336153418828686, -0.197427339992706, -0.08035918295592347, 0.0009141695485822403, 0.038060919753398786, 0.032449437815941715, -0.005249026526076029, -0.057147810659113285, -0.10161745540111683, -0.11768582618958155, -0.08923163872896833, -0.008282044393488832, 0.1230325792690385, 0.292226949876305, 0.47804036943540446, 0.653900475509995, 0.7925991862363697, 0.8711286165242749, 0.8750403452205594, 0.8016266597813544, 0.6614231237670852, 0.4776700762393994, 0.2829165428941206, 0.1139472879680677, 0.0056734398422679, -0.015239554618783601, 0.06395335247631796, 0.23811843807359862, 0.48284726888953927, 0.756006633582314, 1.0021963120261874, 1.1597336800169442, 1.169543816058848, 0.9849778226132757, 0.5800611006376347, -0.044142584235485255, -0.8560126359698418, -1.7935118854928094, -2.7686123652577397, -3.676811827790238, -4.408216491724041, -4.859807317661404, -4.947993445514576, -4.61986323585953, -3.8622333941544045, -2.7070218474313164, -1.2277721017169985, 0.4669940121465377, 2.243736903801773, 3.9568426062581836, 5.4640007276015226, 6.644247335962535, 7.410076331401035, 7.715170816210428, 7.558124108703307, 6.981452099477433, 6.06711449357641, 4.929088575750748, 3.6952116767321024, 2.4913009089576086, 1.427704678115268, 0.5884268811105628, 0.023991564246964716, -0.2520827523974025, -0.26298432929031285, -0.06180667342373566, 0.2786820016714539, 0.6777550472733145, 1.058242689182493, 1.3564985915746226, 1.5304231628654987, 1.5632338027724602, 1.4628497669307297, 1.2574886878045815, 0.9885021197037612, 0.7018320618379361, 0.4391951218012413, 0.23079722402715774, 0.090927334439675, 0.017151810062275244, -0.006756790875645987, -0.004684220961283307, 6.342175573853771e-05, -0.0062901560783307645, -0.020062106431804335, -0.014860491610956827, 0.0596571229870256, 0.27443834918769505, 0.7132437691736062, 1.4609754924537421, 2.589413770337702, 4.142162942657692, 6.121639236366801, 8.482771213670658, 11.129814345164881, 13.918867512955558, 16.667031018969986, 19.167390977099945, 21.211031582696393, 22.617901111190747, 23.25285357045206, 23.03974998199793, 21.97200458920384, 20.11624061884813, 17.610553348417838, 14.657573946973288, 11.49479896242901, 8.367414661250155, 5.503177412662775, 3.0894798925286375, 1.2553959775636934, 0.059589930977452785, -0.5153808056641125, -0.5559424561891794, -0.2018520053141227, 0.3750596901190051, 0.9949873489858967, 1.4944766694703908, 1.7483079904968102, 1.684513363834645, 1.2910022193335198, 0.6134050685164998, -0.25516844451615933, -1.1910001786724451, -2.0613834159044155, -2.746582207102333, -3.1588773157562935, -3.255955156935541, -3.0467343864741387, -2.5887682522316373, -1.9765308883596902, -1.3231885760397246, -0.738611340426907, -0.3068982256092779, -0.06700180076224459, 0.00018574964503089087, -0.024172730168309856, -0.0027117729220396633, 0.24252476125646968, 0.906106354997383, 2.1699245995249408, 4.174575597785666, 6.993574110396212, 10.613345338138751, 14.922370843206908, 19.711420248746588, 24.68905273507637, 29.51922446541251, 33.8499920856663, 37.34577573677846, 39.72143705350375, 40.77229677512898, 40.402107598737864, 38.65029571030018, 35.67105158513211, 31.710137921030544, 27.078362039021112, 22.119483898080563, 17.178611951036633, 12.573152648381049, 8.551263408470007, 5.27171829701431, 2.798901856414618, 1.1089722341836215, 0.10578307491000513, -0.35663631850588595, -0.44856869298495144, -0.33679882483993495, -0.1608779142142203, -0.016828913378491357, 0.05011896497932645, 0.043449720843001784, 0.004711781952690843, -0.0030891426802950005, 0.08513973542786521, 0.3179216287538549, 0.7125551227515023, 1.247300580328803, 1.8618087473883138, 2.465400171455018, 2.9518480594963243, 3.218249469440949, 3.185111136089433, 2.8142915357318885, 2.1188879914962455, 1.1653231458953515, 0.06680516926749608, -1.0316435920780036, -1.9750079579927131, -2.6245871372502925, -2.8828290264410343, -2.712791227602109, -2.1497153487243694, -1.3024068957816857, -0.34321097273055995, 0.5140932868834295, 1.0445424130329017, 1.0452823332009735, 0.36836414576758636, -1.051327129279414, -3.177150506807481, -5.865917242207821, -8.879188179693289, -11.906303549265, -14.597639036632565, -16.604763964136666, -17.625085024550472, -17.44856503137343, -15.982078730891681, -13.262215126241886, -9.455265650785405, -4.842534033177844, 0.20673932655316232, 5.274631186255123, 9.947280141571314, 13.859938980155242, 16.733654858394985, 18.40129876606894, 18.821547117389386, 18.08112547747686, 16.37404144359765, 13.969884773454671, 11.176719209426379, 8.302463362693407, 5.619734955065205, 3.337445066068389, 1.5813614951608255, 0.38986645196279057, -0.2776331988218285, -0.5224269223916609, -0.48184404020439187, -0.302031187974739, -0.11173422901221736, -0.002780991712904144, -0.01936731253483888, -0.15698475912688095, -0.37053634939237906, -0.5899583943952117, -0.7399904825556434, -0.7599441275461943, -0.6199827899815601, -0.3310133501428917, 0.05371436174369816, 0.44616594593723335, 0.7389285941597881, 0.82508620525482, 0.61957109817841, 0.07851012695937044, -0.7870538630569454, -1.907368802422077, -3.160329406365367, -4.3863782227243915, -5.410643703177466, -6.069496176474277, -6.239063843244643, -5.8629257144228015, -4.964507742650774, -3.649698987413217, -2.0990388030298655, -0.5490463605183825, 0.735431748821262, 1.4964092108532756, 1.52019670141031, 0.6681140093134043, -1.1015572057484644, -3.722885060911323, -7.024530700254886, -10.746743122921005, -14.57116617851236, -18.156467100066234, -21.176386362592144, -23.355953178500805, -24.503602980203823, -24.537556206910377, -23.486567496434517, -21.48022957988533, -18.73008334030325, -15.50243720148238, -12.087367946584482, -8.766558385713276, -5.77760308504877, -3.2916961112288097, -1.402713017719181, -0.1266053106064138, 0.5898542651267286, 0.8530296942662109, 0.7998056518494586, 0.573548278996923, 0.3027828066049523, 0.0850914270725883, -0.02211545382407892, -0.003369963214714746, 0.12029646396640346, 0.3024375670985956, 0.48518833074694306, 0.6135505132133797, 0.6476330493119642, 0.5709011485166211, 0.3925748276867301, 0.1447492691664996, -0.12484490797661152, -0.3629801060933903, -0.5221528108764221, -0.57098054868022, -0.5008734675677567, -0.32842475027881174, -0.0933329376528755, 0.1478377662003062, 0.331128286620782, 0.39655945852036184, 0.29856172666695674, 0.013988497695164154, -0.45323507399128293, -1.0715336153087454, -1.785485555159114, -2.5243953995757122, -3.2123930961765135, -3.778539977175266, -4.166007494138271, -4.339046290903302, -4.287468245289532, -4.028482722213385, -3.6008001505463376, -3.0573438402996107, -2.4573384233949294, -1.858353089305682, -1.309544495457507, -0.8466565187037511, -0.4885419145088009, -0.23766072222063897, -0.08309290546571264, -0.004981867766878333, 0.020504055704353145, 0.016533526243771322, 0.0019012558599073798, -0.011007617146570652, -0.01649453277886715, -0.014376697635426906, -0.007895890499983042, -0.001329854727996976, 0.0020881140756318943, 0.0013955424594420023, -0.0019358794302015325, -0.004811089116206272, -0.003964001361237141, 0.002440704525666141, 0.01362409514447085, 0.02587147033331953, 0.03328019316337327, 0.029507394978268264, 0.010145367192546887, -0.024956307294222282, -0.0701202012575348, -0.11362181534211524, -0.13925472931461552, -0.12978825114796716, -0.07208113956714998, 0.03693973196124539, 0.18517993004208913, 0.3417816444750642, 0.45605084757519326, 0.45974990078855843, 0.27342423860802145, -0.18271318909949572, -0.9770063249438559, -2.1542717231943667, -3.724737597598668, -5.655848721519084, -7.868289052268663, -10.238455282037496, -12.609505965352396, -14.806244820177996, -16.652952037880166, -17.992453313142374, -18.704818227309378, -18.724929741711147, -18.050309076067542, -16.741110920417732, -14.913063623602973, -12.723842732022332, -10.35481172204391, -7.990320409812555, -5.795943199391525, -3.9009220113851755, -2.3865166713149386, -1.2813343559814832, -0.5638496043340335, -0.17175921818725887, -0.017249323466706632, -0.0034013066771611815, -0.03996339956663294, -0.05643869592689817, -0.010637317357821016, 0.10883231246298976, 0.28637240005963993, 0.4874185245446177, 0.6689081105652092, 0.7902967246194627, 0.8234815684947789, 0.7601091514504792, 0.6121730952001406, 0.4084480562766119, 0.18782487549383428, -0.00927139087552953, -0.14969926173973133, -0.21526601558643788, -0.2069205433990018, -0.1440489927502332, -0.059690622122841513, 0.007245671241640662, 0.021177290719205065, -0.04133193255663493, -0.1851064736410037, -0.39417280608701155, -0.6342658261746128, -0.8596334661304679, -1.0230851687374107, -1.0876391673486117, -1.0356611946827308, -0.8742285440976891, -0.6354266851495114, -0.3709237933159193, -0.14144179327632525, -0.0025040930727317006, 0.010784355475352184, -0.10498252458156765, -0.31635100856528126, -0.5557850015411768, -0.7334009472102903, -0.7578512165601788, -0.5616844602541402, -0.12655492446471317, 0.49617041575778625, 1.1740887400299347, 1.6951947462621488, 1.7851763268171648, 1.1434896470401863, -0.5103691441637426, -3.385572023056213, -7.570360736754379, -12.992201668363613, -19.397100504657043, -26.354061919355154, -33.286354988740335, -39.52781169604071, -44.39895845833249, -47.297241931210834, -47.7946227082492, -45.70728376785011, -41.14172979467053, -34.50938519187187, -26.50293849516439, -18.034716472298523, -10.139948512500146, -3.853589339861944, -0.08538130169586212, 0.49603476161148635, -2.4433749173238604, -8.846581789179233, -18.266898749853908, -29.914712316088877, -42.73821442280122, -55.53465708387075, -67.07993250484091, -76.27383884577358, -82.30112548146381, -84.68787871542308, -83.32683622759806, -78.47121528483947, -70.68947254117144, -60.796112766846434, -49.765173908339996, -38.571381260160614, -28.07485592186527, -18.9412517450728, -11.592970429817735, -6.195139329678065, -2.6726724936891655, -0.75344919165846, -0.04073393497483291, -0.09221873107272432, -0.4922208483255921, -0.9082214396663756, -1.126511776682474, -1.0608438430286224, -0.7365155786279576, -0.25705112517918693, 0.23826702638131275, 0.6172047920887977, 0.7902836835592699, 0.7324227074899412, 0.4861391513104616, 0.14821845898662983, -0.1559447087010264, -0.304234275960216, -0.20903917016677903, 0.1595723071812549, 0.7641627319650611, 1.5053851259954139, 2.241572270725983, 2.819039921645448, 3.107676033859035, 3.031344164130548, 2.588382027826055, 1.858036518600926, 0.9905707599892103, 0.18178345142944088, -0.3650365409672867, -0.4810384539987408, -0.06854716887593688, 0.8730539379688215, 2.2375202567684616, 3.821784771862675, 5.358858427902628, 6.562768947007168, 7.178074534395062, 7.027470824739863, 6.049421189211026, 4.32062649623158, 2.057453634352277, -0.4194763100278242, -2.7346511670255165, -4.515730670517419, -5.4537044118579665, -5.357067694335231, -4.193781863429967, -2.102801369197129, 0.6241481029632673, 3.5843455317155235, 6.323476171216796, 8.404231776840017, 9.476972540779707, 9.338818439659663, 7.966318133987905, 5.51961361100953, 2.3183686674214865, -1.2059779295480892, -4.575161331641607, -7.341060567051186, -9.15485867599953, -9.818251776063436, -9.309524934984836, -7.781226400064533, -5.531615547687251, -2.950635765370223, -0.4518606075741751, 1.5978999903373268, 2.9399497097873555, 3.464818144153214, 3.224133417934074, 2.418554593903777, 1.3613345388602902, 0.4220443832959235, -0.040668623240703194, 0.25370167485947465, 1.4582392777080408, 3.5747118572842447, 6.449262636240275, 9.790602696683788, 13.208873256549825, 16.27616315492105, 18.612304268075466, 19.930885181789463, 20.071230621805498, 19.016364221347647, 16.891233994556565, 13.94705330263181, 10.534284443799802, 7.030030703296883, 3.7808063308972577, 1.0604800576579518, -0.9575277387858994, -2.2109129708161457, -2.743557752466129, -2.687734612010355, -2.230163045308914, -1.5735465734558827, -0.9012193537567232, -0.34998642604356006, 0.005515913826445882, 0.15392441846470004, 0.13652808336191963, 0.02824495235300397, -0.0854719282796522, -0.13105330781233743, -0.06435331254748387, 0.12068265299739381, 0.3931444734338955, 0.6943636173529159, 0.9526894610539063, 1.1008942858934871, 1.0935461128893786, 0.9173223387724627, 0.5937796884575136, 0.1748996724568022, -0.26760138986236476, -0.6564650895969033, -0.9235436134916913, -1.024829469996488, -0.9490230875841706, -0.7188954733355682, -0.38584318049457605, -0.018684445070901685, 0.3108757036380609, 0.5417042811505751, 0.6345550041468149, 0.5788551546598514, 0.3936389511181322, 0.12235359213544392, -0.17822680933316154, -0.45032207934826707, -0.646306078518245, -0.7371921561793746, -0.7168975438051165, -0.6019285804021961, -0.4265498522481868, -0.2324264441382272, -0.05848166963214421, 0.06724586596997255, 0.13244542584916003, 0.14123145422651054, 0.11081310587693234, 0.06470337731907727, 0.024526670759818972, 0.0030975637391162103, 0.0008323494737141822, 0.006769409006534875, 0.004399753246556512, -0.018737123876645105, -0.05991538429712518, -0.0914853861529145, -0.05561747211890141, 0.13398179267445745, 0.5826969419995424, 1.3985060657235961, 2.669978554301769, 4.442029770908733, 6.693646484019773, 9.324528460601309, 12.161693914624589, 14.969459894470438, 17.469996889856972, 19.374616642738577, 20.42112082328938, 20.418299335858404, 19.297399275283635, 17.113328121887772, 14.03776951105534, 10.342539109999464, 6.36953180616004, 2.4934278694783867, -0.9215282946504376, -3.584525497293764, -5.315758300052269, -6.063423533989019, -5.902586777565347, -5.01692734638885, -3.667794499797162, -2.1506913814389415, -0.7466617124006849, 0.32057657273831786, 0.9153289763464307, 1.0037108239890766, 0.6474277086086194, -0.015920087133669575, -0.8040514231940079, -1.5274063423594615, -2.025861271279493, -2.199576816007783, -2.028534717588857, -1.568662241050472, -0.9367398418765562, -0.28625599908980076, 0.2225181083757182, 0.45363368104527196, 0.32421920456321374, -0.18068722546373797, -1.0077805754332527, -2.0466824387700364, -3.150326060428492, -4.160737517509533, -4.937028212346346, -5.3798631826627785, -5.445081219366488, -5.14649102852822, -4.548626748320303, -3.75206224565569, -2.8742587847196135, -2.0258764949221097, -1.292869302961858, -0.7261979200676786, -0.33958328981662234, -0.11474851917896861, -0.012100597527937506, 0.015779529843419186, 0.011169437532253851, 0.0022263105452797337, -0.000291742263612711, -0.00043280528778407974, -0.009873440848108964, -0.038664325215193134, -0.08700061501600573, -0.14076930276062855, -0.17262416199813171, -0.1489477712989112, -0.04130410925949382, 0.16126188869436572, 0.44244179871361505, 0.7548236211825152, 1.024642411289541, 1.166539286753686, 1.108066100074249, 0.8164485946934993, 0.32346062657709973, -0.25686767915604697, -0.7232626313424831, -0.799081296353191, -0.1645204179389928, 1.4947791765050409, 4.4319237697076534, 8.78250804616244, 14.516703301740966, 21.409199881497493, 29.039584838030407, 36.823904365506955, 44.071829836850625, 50.06476995833102, 54.145488559155936, 55.811927421192806, 54.80875023207246, 51.16441784530963, 45.19587171663124, 37.479000730285456, 28.783879884133626, 19.983524627736625, 11.94685944830595, 5.424334730717451, 0.9568803082839342, -1.1852633429267319, -1.0278372968985756, 1.123196923287536, 4.745325004791884, 9.184368880708737, 13.74575620505023, 17.785060228016956, 20.785876356117072, 22.421862722761997, 22.60084272676949, 21.43236946140908, 19.179413797564944, 16.201208135717835, 12.890674900526873, 9.61798274844699, 6.685301632385444, 4.284515200231699, 2.4909198104396153, 1.2796244162809123, 0.5548835554140935, 0.18516341780079337, 0.03642411223802874, -0.002010419184250529, -0.0028129374744828486, -3.63762551916204e-05, -0.00013202251663358352, 0.0003107563703801588, -0.003944243188703989, -0.04054490704612191, -0.164913519591047, -0.455722415109181, -1.00115069026039, -1.8775879749992748, -3.120484595248949, -4.699524708361307, -6.505334480266971, -8.35244653298726, -10.00126368746231, -11.21678234449358, -11.884172118434131, -11.986929165533242, -11.578342535397589, -10.760179160116849], 'positive_zeros': ['1.36896615447309439343496612575250', '2.70818058035363871303248431600592', '2.81871623103593173270887540884614', '3.02711798323333465484932043093883', '3.72131723958425200607757363456176', '4.14833953162062799113937923518159', '4.17700190894317738548401858802772', '4.51778149694231630428310060810944', '4.83128594404653082423649151181685', '5.17781613996977954792779011068177', '5.57222427665717340383168612318156', '5.60571460097962418484689675050732', '6.03785838530267181462580340343559', '6.23236419385355723520457615136014', '6.38751472088923433339225279723544', '6.47121470790871871560557699886252', '6.90563790575456069500084841087403', '6.94008622201490174816918985161359', '7.46105943233515286424869484117499', '7.77450293761169913236384536453540', '7.957880378968913562745530172827729', '8.002195579321495856740009216699461', '8.178099061397265020894718182557140', '8.618678728878695840298435504181120', '8.818723326978585894456721069922364', '9.032811416233504471939533376053552', '9.386965400084828628150560135319468', '9.600768409773439544157499173348012', '9.850478153649958921899851704352914', '9.981722622473345269012849564949814', '10.32137139330550745859504170294782', '10.41478192402783261517544584764729', '10.53892121203741385623123343820777', '10.74316328484034785040043227968063', '10.95113834603095607726545469876383', '11.47038008537841220191263069047725', '11.51030442507292996928342453108547', '11.51545091123422372035104233252228', '11.82677434114662715527895155892498', '12.00794958446947199983094699605232', '12.16506371133357347652857568165609', '12.17509903695284885953826405021882', '12.39486437786918420430776271375547', '12.49214142205402292838886570007225', '12.79734605495329255649767817502439', '13.17967328770234491298212002194808', '13.35633797664994695896872278125737', '13.43961616221065116784361556092426', '13.70781247855639843511033799716920', '13.87997974762801974695047236036611', '13.88484499280457131580449180338669', '14.14405732213462761781038565335111', '14.46507060263240882713199873838176', '14.70826039606738999426689963433025', '14.78147888604863489333849665196832', '14.81197389192486419983691683027734', '15.45886773406256492697656751290618', '15.51868418320865219810418344003606', '15.79132543079098679276192599946752', '15.85185809122776284486672892594355'], 'prelabel': '12-57e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.6746460490666928, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e6-0', 'trace_hash': 608500418467347334, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36896615447309439343496612575', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.70818058035363871303248431601', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81871623103593173270887540885', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.008890205012281008, 'bad_primes': [3, 19], 'central_character': '1.1', 'conductor': 34296447249, 'conductor_radical': 57, 'degree': 12, 'dirichlet_coefficients': [1, 1, -3, 1, -2, -3, -2, 0, 3, -2, 0, -3, 1, -2, 6, 1, 0, 3, 4, -2, 6, 0, -14, 0, 7, 1, 2, -2, -4, 6, 30, 3, 0, 0, 4, 3, -6, 4, -3, 0, 4, 6, 3, 0, -6, -14, 18, -3, -21, 7, 0, 1, 6, 2, 0, 0, -12, -4, 0, 6, -13, 30, -6, -5, -2, 0, -9, 0, 42, 4, 18, 0, -19, -6, -21, 4, 0, -3, -11, -2, -9, 4, -8, 6, 0, 3, 12, 0, 16, -6, -2, -14, -90, 18, -8, -9, 2, -21, 0, 7], 'euler11': [1, 0, 18, -72, 279, -648, 5740, -7128, 33759, -95832, 263538, 0, 1771561], 'euler13': [1, -1, -17, 40, 61, -223, 854, -2899, 10309, 87880, -485537, -371293, 4826809], 'euler17': [1, 0, -51, 0, 1734, 0, -34391, 0, 501126, 0, -4259571, 0, 24137569], 'euler19': [1, -4, 17, -136, 323, -1444, 6859, 0, 0, 0, 0, 0, 0], 'euler2': [1, -1, 0, 1, -2, -1, 11, -2, -8, 8, 0, -32, 64], 'euler23': [1, 14, 99, 382, 346, -7726, -57613, -177698, 183034, 4647794, 27704259, 90108802, 148035889], 'euler29': [1, 4, -39, -52, 886, -1916, -33907, -55564, 745126, -1268228, -27583959, 82044596, 594823321], 'euler3': [1, 3, 6, 7, 6, 3, 1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -30, 513, -6118, 56634, -421662, 2585865, -13071522, 54425274, -182261338, 473766273, -858874530, 887503681], 'euler37': [1, 6, 237, 1130, 22770, 84366, 1137381, 3121542, 31172130, 57237890, 444176157, 416063742, 2565726409], 'euler41': [1, -4, -75, 100, 3622, 2012, -174751, 82492, 6088582, 6892100, -211932075, -463424804, 4750104241], 'euler43': [1, -3, -99, 218, 6207, -6951, -285738, -298893, 11476743, 17332526, -338461299, -441025329, 6321363049], 'euler47': [1, -18, 75, -666, 15954, -93546, 218347, -4396662, 35242386, -69146118, 365976075, -4128210126, 10779215329], 'euler5': [1, 2, -3, -2, -2, -34, -31, -170, -50, -250, -1875, 6250, 15625], 'euler53': [1, -6, -51, 102, 1086, 11334, -107183, 600702, 3050574, 15185454, -402414531, -2509172958, 22164361129], 'euler59': [1, 0, -153, 72, 14382, -5508, -969077, -324972, 50063742, 14787288, -1853956233, 0, 42180533641], 'euler61': [1, 13, -25, -504, 6133, 34211, -181514, 2086871, 22820893, -114398424, -346146025, 10979751913, 51520374361], 'euler67': [1, 9, -39, -250, 375, -24519, -284658, -1642773, 1683375, -75190750, -785893719, 12151125963, 90458382169], 'euler7': [1, 2, 25, 58, 346, 674, 3089, 4718, 16954, 19894, 60025, 33614, 117649], 'euler71': [1, -18, 99, -234, 306, 55062, -871373, 3909402, 1542546, -83751174, 2515756419, -32476128318, 128100283921], 'euler73': [1, 19, 59, 252, 17041, 91889, -279578, 6707897, 90811489, 98032284, 1675496219, 39388360267, 151334226289], 'euler79': [1, 11, -119, -494, 21403, 27611, -1863994, 2181269, 133576123, -243561266, -4635059639, 33847620389, 243087455521], 'euler83': [1, 8, 354, 2296, 60391, 326864, 6327932, 27129712, 416033599, 1312822952, 16800245634, 31512325144, 326940373369], 'euler89': [1, -16, -87, 424, 39826, -163780, -2350663, -14576420, 315461746, 298906856, -5458574967, -89344951184, 496981290961], 'euler97': [1, -2, -19, -2166, 418, 14486, 2859997, 1405142, 3932962, -1976849718, -1682056339, -17174680514, 832972004929], 'euler_factors': [[1, -1, 0, 1, -2, -1, 11, -2, -8, 8, 0, -32, 64], [1, 3, 6, 7, 6, 3, 1, 0, 0, 0, 0, 0, 0], [1, 2, -3, -2, -2, -34, -31, -170, -50, -250, -1875, 6250, 15625], [1, 2, 25, 58, 346, 674, 3089, 4718, 16954, 19894, 60025, 33614, 117649], [1, 0, 18, -72, 279, -648, 5740, -7128, 33759, -95832, 263538, 0, 1771561], [1, -1, -17, 40, 61, -223, 854, -2899, 10309, 87880, -485537, -371293, 4826809], [1, 0, -51, 0, 1734, 0, -34391, 0, 501126, 0, -4259571, 0, 24137569], [1, -4, 17, -136, 323, -1444, 6859, 0, 0, 0, 0, 0, 0], [1, 14, 99, 382, 346, -7726, -57613, -177698, 183034, 4647794, 27704259, 90108802, 148035889], [1, 4, -39, -52, 886, -1916, -33907, -55564, 745126, -1268228, -27583959, 82044596, 594823321], [1, -30, 513, -6118, 56634, -421662, 2585865, -13071522, 54425274, -182261338, 473766273, -858874530, 887503681], [1, 6, 237, 1130, 22770, 84366, 1137381, 3121542, 31172130, 57237890, 444176157, 416063742, 2565726409], [1, -4, -75, 100, 3622, 2012, -174751, 82492, 6088582, 6892100, -211932075, -463424804, 4750104241], [1, -3, -99, 218, 6207, -6951, -285738, -298893, 11476743, 17332526, -338461299, -441025329, 6321363049], [1, -18, 75, -666, 15954, -93546, 218347, -4396662, 35242386, -69146118, 365976075, -4128210126, 10779215329], [1, -6, -51, 102, 1086, 11334, -107183, 600702, 3050574, 15185454, -402414531, -2509172958, 22164361129], [1, 0, -153, 72, 14382, -5508, -969077, -324972, 50063742, 14787288, -1853956233, 0, 42180533641], [1, 13, -25, -504, 6133, 34211, -181514, 2086871, 22820893, -114398424, -346146025, 10979751913, 51520374361], [1, 9, -39, -250, 375, -24519, -284658, -1642773, 1683375, -75190750, -785893719, 12151125963, 90458382169], [1, -18, 99, -234, 306, 55062, -871373, 3909402, 1542546, -83751174, 2515756419, -32476128318, 128100283921], [1, 19, 59, 252, 17041, 91889, -279578, 6707897, 90811489, 98032284, 1675496219, 39388360267, 151334226289], [1, 11, -119, -494, 21403, 27611, -1863994, 2181269, 133576123, -243561266, -4635059639, 33847620389, 243087455521], [1, 8, 354, 2296, 60391, 326864, 6327932, 27129712, 416033599, 1312822952, 16800245634, 31512325144, 326940373369], [1, -16, -87, 424, 39826, -163780, -2350663, -14576420, 315461746, 298906856, -5458574967, -89344951184, 496981290961], [1, -2, -19, -2166, 418, 14486, 2859997, 1405142, 3932962, -1976849718, -1682056339, -17174680514, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/57/2/e/b'], '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': '12-57e6-1.1-c1e6-0-0', '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': '12-57e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.6746460490666928, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 608500418467347334, 'z1': {'__RealLiteral__': 0, 'data': '1.36896615447309439343496612575', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1735370767409949117799108551298,3433026738211724759757961869320,3573147322145751400925819233183,3837327928407403940793785170704,5294978977026278824343935608284,5726968426298915995654279788129', 'Lhash_array': ['1735370767409949117799108551298', '3433026738211724759757961869320', '3573147322145751400925819233183', '3837327928407403940793785170704', '5294978977026278824343935608284', '5726968426298915995654279788129'], 'factors': ['2-57-19.11-c1-0-0', '2-57-19.11-c1-0-2', '2-57-19.7-c1-0-0', '2-57-19.7-c1-0-2', '2-57-19.7-c1-0-3', '2-57-19.11-c1-0-3'], 'label': '12-57e6-1.1-c1e6-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/57/2/e/b'}