-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1095682118833149783019134385670', 'a10': [1.724744871391589, 2.987345747344081], 'a2': [1.0, 0.0], 'a3': [-0.724744871391589, 1.5731321849709863], 'a4': [1.0, 0.0], 'a5': [1.724744871391589, 2.987345747344081], 'a6': [-0.724744871391589, 1.5731321849709863], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [-1.949489742783178, -2.2802389661575337], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.042805458276933, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0.724744871391589, -1.5731321849709863]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '882.373', 'coefficient_field': 'CDF', 'conductor': 882, 'conductor_radical': 42, 'conjugate': '2812318327176245980895810376593', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.724744871391589, -1.5731321849709863]], [[1.0, 0], [-1.724744871391589, -2.987345747344081], [-2.5, 4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, -1.7320508075688772], [-5.5, -9.526279441628825]], [[1.0, 0], [2.449489742783178, -4.242640687119285], [-6.5, -11.258330249197702]], [[1.0, 0], [-1.0, -1.7320508075688772], [-8.5, 14.722431864335457]], [[1.0, 0], [-3.724744871391589, 6.451447362481836], [-9.5, -16.454482671904334]], [[1.0, 0], [-0.5, -0.8660254037844386], [-11.5, 19.91858428704209]], [[1.0, 0], [1.449489742783178, 2.510589879550408], [-14.5, 25.11473670974872]], [[1.0, 0], [6.0, 0], [31.0, 0]], [[1.0, 0], [-3.898979485566356, 6.753230566669693], [-18.5, -32.04293994002423]], [[1.0, 0], [4.898979485566356, -8.48528137423857], [-20.5, -35.50704155516198]], [[1.0, 0], [-1.449489742783178, -2.510589879550408], [-21.5, 37.239092362730865]], [[1.0, 0], [-9.797958971132712, 0], [47.0, 0]], [[1.0, 0], [-0.5505102572168219, -0.9535117355873467], [-26.5, 45.89934640057525]], [[1.0, 0], [-2.0, 0], [59.0, 0]], [[1.0, 0], [11.449489742783179, 0], [61.0, 0]], [[1.0, 0], [3.101020514433644, 0], [67.0, 0]], [[1.0, 0], [-9.898979485566356, 0], [71.0, 0]], [[1.0, 0], [-1.449489742783178, -2.510589879550408], [-36.5, 63.21985447626402]], [[1.0, 0], [-7.898979485566356, 0], [79.0, 0]], [[1.0, 0], [-1.0, -1.7320508075688772], [-41.5, 71.88010851410841]], [[1.0, 0], [3.550510257216822, -6.149664158293978], [-44.5, -77.07626093681505]], [[1.0, 0], [3.449489742783178, 5.974691494688162], [-48.5, 84.00446416709055]], [[1.0, 0], [-3.623724356957945, 6.27647469887602], [-50.5, -87.4685657822283]], [[1.0, 0], [-7.0, -12.12435565298214], [-51.5, 89.20061658979718]], [[1.0, 0], [-6.0, 10.392304845413264], [-53.5, -92.66471820493493]], [[1.0, 0], [-8.348469228349535, -14.459972868926732], [-54.5, 94.39676901250381]], [[1.0, 0], [-7.949489742783178, 13.76892012874811], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-882-63.58-c1-0-12', '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/e/n/373/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.156982323870802, 1.866361288730595, 1.5756999023625342, 1.2777673411670611, 0.9670917089259355, 0.6422147045482333, 0.3071189767608365, -0.028257156310207324, -0.3483671883109475, -0.6331832744841784, -0.8600189576627906, -1.0059444317758515, -1.0506378907995528, -0.979439967892496, -0.786297967032911, -0.47622414071043956, -0.06686746071623546, 0.4111732723368644, 0.9155764658938202, 1.3951931061100196, 1.7945327551909895, 2.059524947355059, 2.144002413313736, 2.0161509983633152, 1.6640458074916942, 1.0993789382748005, 0.3586045408516963, -0.4990127311402275, -1.3965767443401251, -2.247632692816433, -2.966316653566877, -3.478339797767635, -3.731278741153856, -3.702565511401133, -3.403745766024018, -2.880009437812143, -2.2046559428848522, -1.468952773513072, -0.7686603922609708, -0.18918552358546523, 0.2082506732580475, 0.39699408696683003, 0.3898356697994092, 0.23712895149712412, 0.018001550413434184, -0.17422927017263679, -0.25014865800925484, -0.142688878980982, 0.17758031523450363, 0.6935333511232932, 1.3412144818211291, 2.0189912357075563, 2.605125503793436, 2.980978501896344, 3.055672640982522, 2.7873441820073688, 2.1963511207185693, 1.3670008685618342, 0.43638595302942007, -0.42857070435819977, -1.0622289590630958, -1.3338501991619554, -1.1770317577318803, -0.6085285574584972, 0.268335973962934, 1.2776831826114332, 2.20107487833272, 2.8185975795011777, 2.9534292163931557, 2.5109541912056756, 1.5039508720879589, 0.05766841134817175, -1.6076106207309824, -3.2143609949117895, -4.479379859124768, -5.169245258392653, -5.148398817720912, -4.409537466465056, -3.079233783423252, -1.3966436277704144, 0.3311922408646946, 1.7888048652272968, 2.714402507044829, 2.951587258497322, 2.479571892865326, 1.415247176088158, -0.013475392456176103, -1.517269545942154, -2.807004160494875, -3.653662466921691, -3.9332535929499373, -3.6468896925873517, -2.9120385790724934, -1.9277843229205702, -0.9230941627451299, -0.10107296848078676, 0.4070360570233714, 0.5670148172632143, 0.44039355095151983, 0.15806014562054557, -0.12332420122823118, -0.26966691175935475, -0.20890936196680004, 0.04951040797883939, 0.42070863974568506, 0.7741744288643659, 0.978677605469552, 0.9489311712899833, 0.6796891735803535, 0.2560767664881516, -0.16454059397596954, -0.39563615190272394, -0.2784002208097767, 0.2635751912015875, 1.1883025632638982, 2.3303584775366177, 3.4310169144736067, 4.197996454942279, 4.3804303851443125, 3.8393589259272605, 2.593973303038287, 0.8293377134653995, -1.1388624445860691, -2.9353885971342026, -4.214964568882009, -4.747012060631615, -4.472737773953901, -3.518467905998826, -2.1606621024308947, -0.7512763860133447, 0.376612004817128, 0.9970369622583599, 1.0485589134332907, 0.6444750441360224, 0.03265114484306592, -0.48371889720083006, -0.6415477686990586, -0.3014145054082003, 0.5059029326849713, 1.584651425899404, 2.6307250386114265, 3.3239050754095905, 3.428758785712667, 2.8737809924394107, 1.7839175029580645, 0.45480890844898303, -0.7257711278565795, -1.387758434562541, -1.2882948839884512, -0.38832793760660295, 1.127422796270159, 2.894681654145307, 4.466680598334374, 5.4367803469804725, 5.551228602504595, 4.778973772455617, 3.3177790598419894, 1.534651906116779, -0.14177884341603567, -1.3448142543570354, -1.872187307445408, -1.7369385620983822, -1.1519018341670038, -0.4534649622003245, 0.010992964020199168, -0.003592980152705051, -0.5615650467821323, -1.52751161506918, -2.6121741846409217, -3.46813909389723, -3.804254073420548, -3.4817399024767095, -2.5609140077182952, -1.2834520132265805, 0.003952780769312593, 0.9596038861417955, 1.3546024171378008, 1.1433322277797138, 0.4738563275139231, -0.3646990916129317, -1.0398810525150581, -1.2860233280227262, -0.9900963125161848, -0.22505425056325956, 0.7796571691879292, 1.7194149162379568, 2.3190051071957054, 2.4242548473487626, 2.0493483973901534, 1.3642448832785732, 0.6278486573587653, 0.09183024907216698, -0.08959764608347962, 0.08908897889106897, 0.49120436319442906, 0.8993435256901624, 1.1083319045193132, 1.0134680220797716, 0.6584616040477359, 0.22153567360627596, -0.058885147979312706, 0.006285130536457593, 0.4530031416888509, 1.1085187354046633, 1.6121738202412552, 1.5148188599004244, 0.4301634755452423, -1.8103258345587594, -5.053576913613476, -8.814146418653586, -12.370385480457294, -14.94637118356854, -15.92825232098989, -15.048885166660572, -12.481072411914317, -8.806166078250877, -4.863196040826141, -1.5216476736194497, 0.5540854564985854, 1.0772444131102543, 0.19665103616024135, -1.5750504352166117, -3.5367408395689637, -5.019375173653594, -5.580722100468071, -5.1143190694123115, -3.843289104564635, -2.209118524170253, -0.7001066333607534, 0.31783456307033386, 0.7098279496167841, 0.5866321294235416, 0.2272870864771651, -0.05472218927867704, -0.047183008554018385, 0.27607281014463936, 0.7526253766696636, 1.1095678815234904, 1.0890498687681958, 0.5696871570840638, -0.36594173065107627, -1.4462880297664638, -2.3044406835100095, -2.6152798759814306, -2.223249249147325, -1.2103546364155866, 0.12381107046091645, 1.3646955171783557, 2.1307058521285835, 2.2109239192579553, 1.6401311737225164, 0.6819820397161872, -0.2738968627669627, -0.8618988517817019, -0.8799671999912602, -0.3646162902322344, 0.4280270416607762], 'positive_zeros': ['0.864340788097194765073690537969849', '2.01837700243424224814722347537813', '3.30374751120496943846137109414232', '4.92680244568265268925859438189875', '5.51021321876497266921793463478048', '5.94105885439756850034183886156152', '7.31034161089436904541696375998462', '7.964892383204558731544363354834304', '8.879497509456085088645711759211340', '9.975181730277029025981319197484666'], 'prelabel': '2-882-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6538284530611493, 'root_angle': -0.694740586468614, 'root_number': '-0.574338292343343 - 0.8186180586501453*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.347370293234', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.864340788097194765073690537970', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.01837700243424224814722347538', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30374751120496943846137109414', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.042805458276933, 'bad_primes': [2, 3, 7], 'central_character': '63.58', 'conductor': 882, 'conductor_radical': 42, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/2/e/n/373/1'], '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': '2-882-63.58-c1-0-12', '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': '2-882-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6538284530611493, 'root_angle': -0.347370293234307, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.864340788097194765073690537970', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1095682118833149783019134385670', 'Lhash_array': ['1095682118833149783019134385670'], 'label': '2-882-63.58-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/2/e/n/373/1'}