-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1369317622736594526682725498286', 'a10': [2.246979603717467, 1.0820883461285309], 'a2': [-0.6234898018587335, -0.7818314824680298], 'a3': [0.0, 0.0], 'a4': [-0.2225209339563144, 0.9749279121818236], 'a5': [-2.246979603717467, 1.0820883461285309], 'a6': [0.0, 0.0], 'a7': [-2.0685316697713625, 1.649598960703146], 'a8': [0.9009688679024191, -0.4338837391175581], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.042805458276933, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.6234898018587335, 0.7818314824680298]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.0685316697713625, -1.649598960703146]]]], 'bad_primes': [2, 3, 7], 'central_character': '882.253', 'coefficient_field': 'CDF', 'conductor': 882, 'conductor_radical': 42, 'conjugate': '515277077891104506698518316951', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.246979603717467, -1.0820883461285309], [3.1174490092936677, -3.909157412340149]], [[1.0, 0], [2.0685316697713625, -1.649598960703146]], [[1.0, 0], [1.554958132087371, 1.9498558243636472], [-2.4477302735194586, 10.72420703400006]], [[1.0, 0], [-0.9864264623160088, -1.236939659765209], [-2.8927721414320873, 12.674062858363706]], [[1.0, 0], [0.35689586789220945, 1.5636629649360596], [-15.316470754341125, 7.376023564998488]], [[1.0, 0], [-2.753020396282533, 0], [19.0, 0]], [[1.0, 0], [-0.8411663963029523, 3.6853907808338797], [-20.72228396175564, -9.979325999703837]], [[1.0, 0], [0.9118539999795806, 3.9950934081072353], [-26.128097169170154, 12.582628434409186]], [[1.0, 0], [-7.036835754392174, 0], [31.0, 0]], [[1.0, 0], [2.1871771321180002, 9.582649133614792], [-33.335848112389506, 16.053698347349652]], [[1.0, 0], [-4.405813207414515, 2.12172781589782], [25.563081876208074, -32.05509078118922]], [[1.0, 0], [-5.370469405576201, -2.5862817568078538], [26.81006147992554, 33.61875374612528]], [[1.0, 0], [7.713791735784419, 9.672788889664004], [-10.458483895946777, 45.82161187254571]], [[1.0, 0], [0.6527928111319818, -2.8600721789580055], [-47.75134999882821, -22.99583817323058]], [[1.0, 0], [-8.493959207434933, -4.090475167487177], [36.78589830966528, 46.12805746561376]], [[1.0, 0], [1.0772608679432578, 4.71978824727244], [-54.95910094204757, 26.466908086171046]], [[1.0, 0], [0.2958969432397724, 0], [67.0, 0]], [[1.0, 0], [0.48427052841074286, -2.12172781589782], [-63.96878962107176, -30.805745477346626]], [[1.0, 0], [-2.7714382734786196, 3.475273673222591], [-16.24402817881095, -71.16973758927313]], [[1.0, 0], [13.256668282741659, 0], [79.0, 0]], [[1.0, 0], [-5.603875471609676, 7.027037578599414], [-18.469237518374097, -80.91901671109136]], [[1.0, 0], [5.926919490217431, -7.43212196525271], [-19.804363122111983, -86.7685841841823]], [[1.0, 0], [-0.18060386785137073, 0], [97.0, 0]], [[1.0, 0], [-8.18598067906503, 3.9421605250865364], [62.97246998773208, -78.96497972927101]], [[1.0, 0], [-0.519614330249057, 0.25023307301661896], [64.21944959144956, -80.52864269420706]], [[1.0, 0], [-0.8019377358048383, 1.005598113974299], [-23.80973993332564, -104.31728660345513]], [[1.0, 0], [8.837281537643152, 11.081600540963386], [-24.25478180123827, 106.26714242781877]], [[1.0, 0], [9.063982829760155, -11.365874969774994], [-25.144865537063527, -110.16685407654607]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-882-49.8-c1-0-11', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/882/2/u/c/253/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5988219294530658, 0.720887279600755, 0.8131353555323881, 0.8700540222403776, 0.8823647469398085, 0.8379420090616083, 0.7234111259351698, 0.5261743548082006, 0.23664860382643077, -0.1494781840351858, -0.6291754136821627, -1.190417088195553, -1.8112070395619155, -2.4595385063704986, -3.0944999553315378, -3.668647316225633, -4.131626523394219, -4.434860377072838, -4.536929117506568, -4.409100275160176, -4.04032997886898, -3.440994882598257, -2.644646483174903, -1.7072231833842733, -0.7034105823240316, 0.2798103975445209, 1.1519813991034091, 1.8294938275407215, 2.246218537927524, 2.3630081906803326, 2.1746042679080997, 1.7126644048934434, 1.0440372095930348, 0.26401944291550755, -0.5149361083008328, -1.1778378416495465, -1.6232183789138948, -1.7783343958113886, -1.6110928364089385, -1.1365800914851958, -0.41674525316206057, 0.44721968354834496, 1.3290876037507402, 2.0965113624532496, 2.631815481765773, 2.851293694884573, 2.7196523151957384, 2.2568544766360947, 1.5357847928075614, 0.6707022231506348, -0.20187612116668321, -0.9467239418405563, -1.4537425664048544, -1.6576545482389642, -1.5496757794965235, -1.1786383092287822, -0.6409773831643502, -0.061181948056177826, 0.4336898036991769, 0.7404365388495754, 0.80164312123509, 0.6183406552829257, 0.25034267954183725, -0.19631730722475374, -0.5926600816891031, -0.8160972279757394, -0.7795801981169534, -0.4539920189530689, 0.12166212666016546, 0.8452826178227537, 1.5716634636479196, 2.143740995056494, 2.4285702683476527, 2.349969397249215, 1.9100030377251713, 1.1935440818262941, 0.3537132881580499, -0.41967174796051737, -0.9423651128657814, -1.079445494892855, -0.7803316092434941, -0.09620169057546184, 0.8254772741501725, 1.7695310134206583, 2.499513159516479, 2.8121425105776154, 2.5873465119625485, 1.8217767319435354, 0.6368568042177083, -0.7420277241877493, -2.0318790702002, -2.9543476810396374, -3.2999278820706204, -2.9789115173185516, -2.046346009488, -0.6939038304906188, 0.7907474642102329, 2.0885714447173704, 2.9230852711201636, 3.1260250777935723, 2.6785638762021167, 1.717325947458252, 0.5027659195893563, -0.6432768335788089, -1.4161740422963178, -1.6041423237862749, -1.142047399275952, -0.12954233925298567, 1.191607839134747, 2.495936162266605, 3.454170708150629, 3.814669126983513, 3.465782084896518, 2.463215401796065, 1.0153650535562992, -0.5695378856080469, -1.9606645843986634, -2.886002181426958, -3.196687788085113, -2.897662489637584, -2.137209590050661, -1.1591509338869141, -0.23165244917948385, 0.427109780735193, 0.7055533562998412, 0.6219843225142004, 0.3087484081742774, -0.03715780057345065, -0.22158242719417584, -0.11806137670147952, 0.289939655244595, 0.9025307002694403, 1.5349328038902, 1.977589641009127, 2.066330086783555, 1.7404759346671128, 1.0699436248544003, 0.24150801377984138, -0.49314011916722844, -0.8928381804837194, -0.8032575038713985, -0.21024055466279434, 0.7474849629068642, 1.8119645552567416, 2.6776400112664294, 3.080433699539326, 2.8776017951167003, 2.0935400140439477, 0.9163940540352556, -0.35493094550920223, -1.3983700272633373, -1.964664615100815, -1.952042595791663, -1.4357637218151762, -0.6422216983156539, 0.12541618568010185, 0.5873519052577212, 0.581351952633156, 0.12002176300404528, -0.6090810889617903, -1.3030321572039145, -1.6460504309432662, -1.4233558751071007, -0.6094448549275309, 0.5998963755296999, 1.8261286632294904, 2.6095615010538222, 2.546056971755734, 1.4182506002922561, -0.7197332338733817, -3.532700670092023, -6.476742902808505, -8.935561918709775, -10.38275305304606, -10.523097716516585, -9.371189977569735, -7.2438815986675005, -4.668673966868216, -2.235432508742702, -0.4357581421322207, 0.4623596189913863, 0.4684641456222822, -0.16136023812659633, -1.027247740012026, -1.724830036250118, -1.9752863005359418, -1.704829133478862, -1.0500574947487717, -0.2907789110762152, 0.2639111118953052, 0.3953558718194054, 0.05883821797882038, -0.5979415042204514, -1.287219035172501, -1.6853253742830212, -1.5514982351866557, -0.819044001714169, 0.3738098834804755, 1.7249128651280203, 2.867315843820088, 3.4922249138554187, 3.4528686695426325, 2.812827641691656, 1.8217592548296222, 0.8270036631536541, 0.15226039567052455, -0.013722180045613154, 0.3210014899057923, 0.9609890002079512, 1.600312366932682, 1.9387734495237197, 1.794892888076492, 1.1741365686448915, 0.26705195052370234, -0.6223132357791995, -1.19143653887276, -1.254962569558314, -0.8172302970467181, -0.0733712197049539, 0.66296239245093, 1.0794172666989392, 0.9876849353217293, 0.40203110315855217, -0.4583058026462167, -1.2469002005579068, -1.621687291493597, -1.3821252919176041, -0.5593678137657163, 0.577944358862735, 1.6096311810425405, 2.114749685140993, 1.8343803628601953, 0.7860877871372995, -0.7157764138592768, -2.1475961083782065, -2.9467400451796237, -2.708006505469015, -1.337428557023235, 0.8933222714151351, 3.4157061972462146, 5.537314765554262, 6.66279402275251, 6.487969754954929, 5.1000870563684835, 2.9486230609995547, 0.6957708096048419, -1.0023312146668728, -1.7082888919293875, -1.3370423945684946, -0.165574835020445, 1.281934248117336, 2.430086587800611, 2.8578065666620103, 2.43984841186997, 1.3753563998163612, 0.09674863535907485, -0.9037773785696398], 'positive_zeros': ['1.08020113940707389492009246056551', '3.08847445742321912692240746399894', '4.16642535793103971184828472065130', '5.06181995475910074901960166382800', '6.22010851617762449139509543896322', '7.13884702382727992863898920702477', '7.82050755284329378362659358241727', '8.476829618716224131686294771707541', '9.554005584950616143741115859220875', '10.13918358740378237426879688979446'], 'prelabel': '2-882-49.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6538284530611493, 'root_angle': 0.5306122448979592, 'root_number': '-0.09602302590768176 + 0.9953791129491982*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.265306122449', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08020113940707389492009246057', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08847445742321912692240746400', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16642535793103971184828472065', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.042805458276933, 'bad_primes': [2, 3, 7], 'central_character': '49.8', 'conductor': 882, 'conductor_radical': 42, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/2/u/c/253/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-882-49.8-c1-0-11', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-882-49.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6538284530611493, 'root_angle': 0.2653061224489796, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08020113940707389492009246057', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1369317622736594526682725498286', 'Lhash_array': ['1369317622736594526682725498286'], 'label': '2-882-49.8-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/2/u/c/253/1'}