-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1437862298227867935063949753665', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.625896657683007, 0.0], 'a4': [0.0, 0.0], 'a5': [3.7884198409249255, 0.0], 'a6': [0.0, 0.0], 'a7': [2.9381449531881256, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.3564600585352269, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.26360354672649, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [503, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 503], 'central_character': '8048.1', 'coefficient_field': 'CDF', 'conductor': 8048, 'conductor_radical': 1006, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.625896657683007, 0], [3.0, 0]], [[1.0, 0], [-3.7884198409249255, 0], [5.0, 0]], [[1.0, 0], [-2.9381449531881256, 0], [7.0, 0]], [[1.0, 0], [-5.637412866299108, 0], [11.0, 0]], [[1.0, 0], [-2.5195855310707618, 0], [13.0, 0]], [[1.0, 0], [2.131868429082516, 0], [17.0, 0]], [[1.0, 0], [-5.045951958134898, 0], [19.0, 0]], [[1.0, 0], [-5.960888565221749, 0], [23.0, 0]], [[1.0, 0], [5.0848788884219704, 0], [29.0, 0]], [[1.0, 0], [-5.148665660661275, 0], [31.0, 0]], [[1.0, 0], [-6.067472590558526, 0], [37.0, 0]], [[1.0, 0], [-1.1288878208408417, 0], [41.0, 0]], [[1.0, 0], [11.208411490014841, 0], [43.0, 0]], [[1.0, 0], [-7.629617490948593, 0], [47.0, 0]], [[1.0, 0], [9.200598412560483, 0], [53.0, 0]], [[1.0, 0], [2.847906943992669, 0], [59.0, 0]], [[1.0, 0], [-4.624067374832782, 0], [61.0, 0]], [[1.0, 0], [4.872611313513668, 0], [67.0, 0]], [[1.0, 0], [-3.3475328698561184, 0], [71.0, 0]], [[1.0, 0], [4.28001417341312, 0], [73.0, 0]], [[1.0, 0], [-0.10968886239398012, 0], [79.0, 0]], [[1.0, 0], [-14.177309926594068, 0], [83.0, 0]], [[1.0, 0], [-5.062442850631809, 0], [89.0, 0]], [[1.0, 0], [-15.630868876861454, 0], [97.0, 0]], [[1.0, 0], [4.1835904084203355, 0], [101.0, 0]], [[1.0, 0], [6.746238341988975, 0], [103.0, 0]], [[1.0, 0], [6.5467204024940155, 0], [107.0, 0]], [[1.0, 0], [4.152972130448656, 0], [109.0, 0]], [[1.0, 0], [17.589406286179862, 0], [113.0, 0]], [[1.0, 0], [-1.4686953871384132, 0], [127.0, 0]], [[1.0, 0], [20.878181301992555, 0], [131.0, 0]], [[1.0, 0], [14.322728975978842, 0], [137.0, 0]], [[1.0, 0], [-16.39057580105612, 0], [139.0, 0]], [[1.0, 0], [21.886645746015173, 0], [149.0, 0]], [[1.0, 0], [19.829637386478275, 0], [151.0, 0]], [[1.0, 0], [-1.542080571211449, 0], [157.0, 0]], [[1.0, 0], [15.119427888246017, 0], [163.0, 0]], [[1.0, 0], [-13.480505262040843, 0], [167.0, 0]], [[1.0, 0], [-9.146121691698319, 0], [173.0, 0]], [[1.0, 0], [15.752252213473774, 0], [179.0, 0]], [[1.0, 0], [2.1747020071127725, 0], [181.0, 0]], [[1.0, 0], [6.851400772006347, 0], [191.0, 0]], [[1.0, 0], [7.1914835004503415, 0], [193.0, 0]], [[1.0, 0], [-0.4099159968658857, 0], [197.0, 0]], [[1.0, 0], [8.865636851215186, 0], [199.0, 0]], [[1.0, 0], [-19.458219936202582, 0], [211.0, 0]], [[1.0, 0], [17.509853232196097, 0], [223.0, 0]], [[1.0, 0], [-3.9312486325283085, 0], [227.0, 0]], [[1.0, 0], [14.573180644635853, 0], [229.0, 0]], [[1.0, 0], [19.16424427868341, 0], [233.0, 0]], [[1.0, 0], [19.155739974939255, 0], [239.0, 0]], [[1.0, 0], [-15.166328343177963, 0], [241.0, 0]], [[1.0, 0], [25.245587121415575, 0], [251.0, 0]], [[1.0, 0], [-6.765387325858379, 0], [257.0, 0]], [[1.0, 0], [28.65754491876387, 0], [263.0, 0]], [[1.0, 0], [-10.595652874062237, 0], [269.0, 0]], [[1.0, 0], [19.215991860343717, 0], [271.0, 0]], [[1.0, 0], [2.758500141417166, 0], [277.0, 0]], [[1.0, 0], [-10.650694436884379, 0], [281.0, 0]], [[1.0, 0], [-11.681522248583583, 0], [283.0, 0]], [[1.0, 0], [18.50367935041147, 0], [293.0, 0]], [[1.0, 0], [-27.641008655342016, 0], [307.0, 0]], [[1.0, 0], [12.338156412467121, 0], [311.0, 0]], [[1.0, 0], [11.286957372567949, 0], [313.0, 0]], [[1.0, 0], [14.800339352518087, 0], [317.0, 0]], [[1.0, 0], [-27.86120918739519, 0], [331.0, 0]], [[1.0, 0], [21.748494882706396, 0], [337.0, 0]], [[1.0, 0], [0.14670758258234576, 0], [347.0, 0]], [[1.0, 0], [14.947520270292337, 0], [349.0, 0]], [[1.0, 0], [-22.264619249218384, 0], [353.0, 0]], [[1.0, 0], [-11.138005964050032, 0], [359.0, 0]], [[1.0, 0], [31.270479805097647, 0], [367.0, 0]], [[1.0, 0], [9.486336262061414, 0], [373.0, 0]], [[1.0, 0], [4.532899089427033, 0], [379.0, 0]], [[1.0, 0], [-34.05911214300459, 0], [383.0, 0]], [[1.0, 0], [9.276772716215797, 0], [389.0, 0]], [[1.0, 0], [0.34388709350170654, 0], [397.0, 0]], [[1.0, 0], [-11.046358790983739, 0], [401.0, 0]], [[1.0, 0], [31.532643804576622, 0], [409.0, 0]], [[1.0, 0], [-22.122787710007714, 0], [419.0, 0]], [[1.0, 0], [-18.261860453975032, 0], [421.0, 0]], [[1.0, 0], [-22.05771431841809, 0], [431.0, 0]], [[1.0, 0], [-26.73817359116329, 0], [433.0, 0]], [[1.0, 0], [-38.27251024943243, 0], [439.0, 0]], [[1.0, 0], [-35.12802517109224, 0], [443.0, 0]], [[1.0, 0], [-36.094811067369335, 0], [449.0, 0]], [[1.0, 0], [20.23667604420912, 0], [457.0, 0]], [[1.0, 0], [30.633445319305572, 0], [461.0, 0]], [[1.0, 0], [-12.535871907648906, 0], [463.0, 0]], [[1.0, 0], [-14.384746959682705, 0], [467.0, 0]], [[1.0, 0], [-11.589337840607556, 0], [479.0, 0]], [[1.0, 0], [-2.9939311135810196, 0], [487.0, 0]], [[1.0, 0], [-38.772942149993526, 0], [491.0, 0]], [[1.0, 0], [20.427424277206857, 0], [499.0, 0]], [[1.0, 0], [-1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 158, 'label': '2-8048-1.1-c1-0-158', 'leading_term': '3.12148775203576224486614914478', '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/8048/2/a/w/1/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [3.1214877520357622, 3.1138989327517534, 3.091113750964384, 3.0530823581272744, 2.999742301334403, 2.931047934921954, 2.847008683081983, 2.7477335581174573, 2.633478994066739, 2.504696922442588, 2.3620800739175243, 2.2066017001261478, 2.039547231034145, 1.8625357756733023, 1.6775298051244731, 1.4868318036742643, 1.2930671234202495, 1.0991527227115114, 0.9082519076243225, 0.7237156280414458, 0.5490113055197092, 0.3876405870943523, 0.24304782320341312, 0.11852145212699756, 0.017090828386082037, -0.05857865289008054, -0.10628902220788573, -0.1244084841574647, -0.11196202418194633, -0.06871042593672327, 0.004785670327588481, 0.10711984979998866, 0.23601502404401517, 0.38832201025994423, 0.5600435159296717, 0.7463848173276398, 0.9418316872112078, 1.1402553153102868, 1.3350430953779446, 1.5192532488178738, 1.6857903449181955, 1.8275978917888926, 1.9378633422798133, 2.0102301182401363, 2.0390106368522263, 2.019393855182114, 1.9476405613824241, 1.821259556841722, 1.6391580112983148, 1.401759644340715, 1.1110849961750848, 0.7707888942380493, 0.386151287673243, -0.03598111251499689, -0.48730351382476894, -0.9582116016059485, -1.4380078823662308, -1.915152029015671, -2.377549782668164, -2.812873386032923, -3.2089050887692117, -3.553894035356464, -3.836915877385493, -4.048223795093269, -4.179579309578139, -4.224551349178949, -4.178772520427114, -4.040142431408607, -3.8089692140047275, -3.4880420665120373, -3.082629649249109, -2.600401457695936, -2.051271801541703, -1.4471686529520196, -0.801732303208673, -0.12995138697176284, 0.5522537019391753, 1.2284877691822342, 1.8823640576315055, 2.4979982424191887, 3.0604967432087706, 3.556422560981244, 3.9742220978824103, 4.304597290463112, 4.5408088720863935, 4.678898648122175, 4.717821262173765, 4.65947897400707, 4.508656359805263, 4.272855464304499, 3.9620356494204794, 3.5882660527317456, 3.165302045060609, 2.7081002144873754, 2.232289067300255, 1.7536147012707402, 1.287382069453982, 0.8479130344096963, 0.4480421634522481, 0.09867011793726885, -0.19160743898220967, -0.4167801984851848, -0.5736010060247391, -0.6616532535480412, -0.68330440355118, -0.64354682637237, -0.5497318360114062, -0.4112073775451214, -0.23887405156811828, -0.044677866183366, 0.15893889076017073, 0.3596051183462546, 0.5455819921731423, 0.7062928388374817, 0.83279792497735, 0.9181923372068941, 0.9579081959233432, 0.9499064259272345, 0.8947480487831219, 0.7955402750956749, 0.6577583362968764, 0.4889497586511033, 0.2983333874742364, 0.09631065587565277, -0.10608889120627868, -0.29780218895781324, -0.46833920755675723, -0.6083720373132928, -0.710277135371942, -0.7686028123260539, -0.7804368438625219, -0.745653171268979, -0.6670218549630333, -0.5501725589784491, -0.4034086132386994, -0.23737582630967138, -0.06459737879352635, 0.10110702155196552, 0.2452933329009906, 0.353627080137635, 0.4126453129484527, 0.41051043440852, 0.33771882091296346, 0.18772800428955827, -0.04253120239645125, -0.35228694762389273, -0.7367264118522246, -1.1869799921923114, -1.6902976948512094, -2.2304169731276615, -2.7881121319603483, -3.3419064699524155, -3.868919980321543, -4.345818102662553, -4.749821091643369, -5.059729375422595, -5.256918071258382, -5.326253776149419, -5.256888925135772, -5.0428933723054925, -4.683689255713843, -4.184263409960362, -3.5551412470922057, -2.8121167150020825, -1.9757441771972795, -1.0706093127441754, -0.12440686838199037, 0.8331372254575949, 1.7714537316241696, 2.66037618277549, 3.4713895418825396, 4.1788245793134395, 4.760942539681986, 5.200858797375281, 5.487260870781809, 5.61488511289913, 5.584727232356734, 5.403974033390955, 5.085656824667167, 4.648040209694425, 4.113772786595171, 3.508838011036038, 2.8613535128066236, 2.200274975553971, 1.5540658627944919, 0.949396498365519, 0.4099351255990102, -0.04471042948020909, -0.3998488280438085, -0.6463169792662288, -0.7808172827250223, -0.8059636208687607, -0.7300338313615086, -0.5664411106548765, -0.33295103289906625, -0.050683876061274995, 0.25704695497889496, 0.5660010272751598, 0.8523165105063338, 1.0937880501696355, 1.2710507637084898, 1.3686088584172353, 1.3756552348065032, 1.286639173874503, 1.1015522775397089, 0.8259175728340455, 0.4704823384639347, 0.050630944036288164, -0.41445103128377075, -0.9028167225883443, -1.3909461579755442, -1.8550187196169785, -2.272201126408573, -2.6218810808361073, -2.8867794150751136, -3.053879944777121, -3.1151259825955635, -3.067845077331642, -2.914878364137067, -2.66440714151496, -2.329486048369335, -1.9273085745774943, -1.47824568682713, -1.004711234065707, -0.5299177697879156, -0.07659290053018707, 0.3342711609820707, 0.6845636815830722, 0.9600315485670707, 1.151029235308271, 1.252999006815748, 1.2666530361741337, 1.1978461280601531, 1.0571455866656907, 0.8591224083727235, 0.6214044069780965, 0.3635461285733937, 0.10578163280704549, -0.13226628245468555, -0.3328435403739111, -0.4812132139676822, -0.5666248177374517, -0.5830441488176415, -0.529596832994695, -0.4106951417360262, -0.23583608290295358, -0.019078180453380385, 0.22177637683563575, 0.46624955479253116, 0.6924449755808957, 0.878422510278427, 1.0036091616608387, 1.0501618752961255, 1.0041992912245412, 0.8568257598501631, 0.6048819049548156, 0.2513710554759139], 'positive_zeros': ['1.13427335416320033793982701030438', '1.40368417998221175936412523970203', '2.48051555499139164784558997794940', '3.52457512648519812066820835945634', '4.65547124043865694774953665370566', '5.11974616894949560201035827226708', '5.78778287753331476678201157190062', '6.39281806537192007021453864786261', '6.74244908874708467760984571228275', '7.78733981410010232199658949484609'], 'prelabel': '2-8048-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.016458291959516, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13427335416320033793982701030', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.40368417998221175936412523970', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.48051555499139164784558997795', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 64.26360354672649, 'bad_primes': [2, 503], 'central_character': '1.1', 'conductor': 8048, 'conductor_radical': 1006, 'degree': 2, 'index': 158, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8048/2/a/w/1/7'], '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': '2-8048-1.1-c1-0-158', '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': '2-8048-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.016458291959516, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13427335416320033793982701030', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1437862298227867935063949753665', 'Lhash_array': ['1437862298227867935063949753665'], 'label': '2-8048-1.1-c1-0-158', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8048/2/a/w/1/7'}