-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '704105617790384797803028363181', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -0.5477811099284352], 'a4': [0, 0], 'a5': [3.3021868178743508, 3.7544057079459154], 'a6': [0, 0], 'a7': [-10.056592525820266, 0], 'a8': [0, 0], 'a9': [8.699935855605572, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.87747383811801, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-3.3021868178743508, -3.7544057079459154]]]], 'bad_primes': [2, 5], 'central_character': '1280.639', 'coefficient_field': 'CDF', 'conductor': 1280, 'conductor_radical': 10, 'conjugate': '1674043947040310650286436166244', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.5477811099284352], [-9.0, 0]], [[1.0, 0], [-3.3021868178743508, -3.7544057079459154]], [[1.0, 0], [10.056592525820266, 0], [49.0, 0]], [[1.0, 0], [-17.2087472714974, 0], [121.0, 0]], [[1.0, 0], [4.41324919603496, 0], [169.0, 0]], [[1.0, 0], [0, -27.01762283178366], [-289.0, 0]], [[1.0, 0], [4.826498392069921, 0], [361.0, 0]], [[1.0, 0], [15.265339797317669, 0], [529.0, 0]], [[1.0, 0], [0, 2.3822488794274816], [-841.0, 0]], [[1.0, 0], [0, 38.03524566356732], [-961.0, 0]], [[1.0, 0], [-16.569127972181377, 0], [1369.0, 0]], [[1.0, 0], [-13.31768697617809, 0], [1681.0, 0]], [[1.0, 0], [0, -59.79177404499316], [-1849.0, 0]], [[1.0, 0], [-62.43884140524775, 0], [2209.0, 0]], [[1.0, 0], [71.59524149788473, 0], [2809.0, 0]], [[1.0, 0], [68.82649839206992, 0], [3481.0, 0]], [[1.0, 0], [0, -40.9439287906703], [-3721.0, 0]], [[1.0, 0], [0, -51.00796937742913], [-4489.0, 0]], [[1.0, 0], [0, 40.452740206562126], [-5041.0, 0]], [[1.0, 0], [0, -35.844121223853584], [-5329.0, 0]], [[1.0, 0], [0, -126.79974342242228], [-6241.0, 0]], [[1.0, 0], [0, -75.14895203169841], [-6889.0, 0]], [[1.0, 0], [-106.52323153369677, 0], [7921.0, 0]], [[1.0, 0], [0, -85.43511737477847], [-9409.0, 0]], [[1.0, 0], [0, -83.28772929255175], [-10201.0, 0]], [[1.0, 0], [47.265339797317665, 0], [10609.0, 0]], [[1.0, 0], [0, 189.62844720790818], [-11449.0, 0]], [[1.0, 0], [0, -84.56167991124282], [-11881.0, 0]], [[1.0, 0], [0, -114.5584771972641], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 29, 'label': '2-1280-40.19-c2-0-29', 'leading_term': '1.829768131787011703166477053113745758261948168585955369', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1280/3/e/f/639/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.8297681317870118, 1.6773267102749003, 1.511219997637769, 1.3328998365295501, 1.1439144602889566, 0.9459281931488043, 0.7407413506689805, 0.5303083669013221, 0.31675221556068495, 0.10237332456673261, -0.110348605455174, -0.3187611924786736, -0.5200553632098273, -0.7112913717154289, -0.8894350949969442, -1.0514044616487825, -1.1941254753132058, -1.3145969058352616, -1.4099623449676297, -1.4775879673454972, -1.5151440089229535, -1.5206876825925282, -1.492745003579908, -1.4303888053524738, -1.3333101004424657, -1.2018798898174758, -1.0371985585197974, -0.8411301221315536, -0.6163188140577153, -0.3661858308603972, -0.09490448193578835, 0.19264748294269846, 0.49095897691935975, 0.7939800224047406, 1.095238693534713, 1.3879789060959322, 1.6653165859059578, 1.920410934702215, 2.1466467387016395, 2.3378229603631095, 2.488342250293594, 2.5933955448253263, 2.6491356047667356, 2.6528332281326352, 2.603009955604342, 2.499541397451766, 2.3437258529531833, 2.1383136681398573, 1.8874937762372928, 1.5968350693486957, 1.2731816320664826, 0.9245023908333645, 0.5596973513641299, 0.18836425702828266, -0.17946885561275228, -0.5336381655934, -0.8641571865115826, -1.1615388379094105, -1.4171158818446437, -1.623348538357691, -1.7741078723134314, -1.8649237367563862, -1.8931866866508156, -1.8582943479883915, -1.761734229625105, -1.6070968694198906, -1.400015464327936, -1.148030680144118, -0.8603820881453318, -0.5477305361797842, -0.2218186227451796, 0.10492081129612638, 0.4197957462364452, 0.7103110133371271, 0.9646330010636693, 1.172045605946847, 1.3233794943528676, 1.4113969386468737, 1.4311154207500496, 1.3800548619612794, 1.2583957128840517, 1.069038161921591, 0.8175563039289153, 0.5120451313393405, 0.16286252119376596, -0.21772717568952657, -0.6159969666415096, -1.0172733771688842, -1.406506176050328, -1.76886986179348, -2.090372861003835, -2.3584490778566902, -2.562506162266879, -2.69440569701202, -2.748852459229041, -2.7236729578360026, -2.619967502798951, -2.442124991735845, -2.1976952241227186, -1.8971196521074787, -1.5533277952195326, -1.181212806561958, -0.797005591537252, -0.41757215961494937, -0.05966326326821237, 0.2608513968013587, 0.5297302453400032, 0.7350536507153834, 0.8678311528122808, 0.9224915569382238, 0.8972296696574137, 0.7941891620033331, 0.6194679334496593, 0.38294013870427945, 0.09789739536834983, -0.21947976190473723, -0.550800777392501, -0.8762671979919964, -1.175564197990793, -1.4288023525468108, -1.617466871497491, -1.7253298000712343, -1.7392810749190741, -1.650036851677875, -1.4526881489631933, -1.1470594318322231, -0.7378550305862214, -0.23458090868255546, 0.3487601742181623, 0.9941911047092397, 1.6804806230457157, 2.384031273379309, 3.079896086926114, 3.7428776869920752, 4.348658314461285, 4.874906523926964, 5.302306211042246, 5.61545628796718, 5.8035946736821185, 5.86110811518099, 5.787799372857634, 5.588895032805242, 5.274790089215218, 4.8605388314180455, 4.365114784328803, 3.8104747873415623, 3.2204730786284124, 2.619679864549311, 2.032164779674972, 1.4803084923923626, 0.9837052488398045, 0.5582153107711587, 0.21521914909343873, -0.038884796404760176, -0.20290951912407693, -0.2808211426682806, -0.2813935758899627, -0.21759261786028058, -0.10572126549012513, 0.035628191303936796, 0.18675810472341914, 0.32811959471645846, 0.44156586774430634, 0.5115324535550042, 0.5260748588320495, 0.4777009101161687, 0.36394555094941555, 0.18764956978900413, -0.04308003184701111, -0.3152324289853408, -0.6115639475674818, -0.9115452491955979, -1.1925355763626793, -1.4311205625184331, -1.6045390868968146, -1.6921176750692208, -1.6766285221647204, -1.545489605272413, -1.2917325399433428, -0.9146755274980383, -0.42025436796550397, 0.1790167353481509, 0.864461998179997, 1.6120241332299934, 2.393371844598341, 3.177279024543007, 3.931202865806133, 4.6229749081280715, 5.222510593782705, 5.703439826704484, 6.044563621598239, 6.2310501709358945, 6.2552971879681945, 6.117405515875196, 5.825230746817062, 5.39400374813307, 4.845536150528542, 4.207051525340534, 3.5097056699693785, 2.7868787229560557, 2.0723365074964812, 1.3983675728439737, 0.7940052059723706, 0.2834399290291013, -0.11528221442029195, -0.3911964461867918, -0.5409332111184768, -0.5687764973532309, -0.4862611848763404, -0.3113322856685196, -0.067116123992664, 0.21962203014633333, 0.5202391908389795, 0.8060855253071192, 1.050367736456323, 1.229887181707814, 1.3265417147241887, 1.3284941151264853, 1.2309302062080514, 1.0363551744853554, 0.7544056668032895, 0.4011861565247222, -0.0018311079984480979, -0.42927451221248775, -0.8536169937448731, -1.2470834629396188, -1.5835975223092653, -1.8406389619436565, -2.00088748353209, -2.053540265247266, -1.995210677199025, -1.8303415423852338, -1.5710972213829613, -1.2367325459696594, -0.8524710777494477, -0.44795807489250533, -0.05538272343612941, 0.29261235711477757, 0.5651002384411383, 0.7349758175038089, 0.7808590238890738, 0.688666111154238, 0.45273969152842625, 0.07645537486524677, -0.42774404490296947, -1.0388990438010133, -1.728642380275296, -2.462803434593329, -3.2034111072231934, -3.9109708796372495, -4.546871859567318, -5.075769144872048, -5.46778649238181, -5.700394248590712, -5.759837273315126, -5.642015980203132, -5.352758841569481], 'positive_zeros': ['0.55544139502132270568153241794702', '1.77746726963888051164089044162963', '3.13530260843972310627578719396344', '4.14121809926537490557902071867441', '4.94742299875151339321667448423869', '6.10408194501076889409084691388747', '6.69825282823809636591205946860822', '7.46585113279592966112701620685548', '8.954341474498907764645717165663625', '9.302318631827747845895605566688074'], 'prelabel': '2-1280-40.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.90571535363143, 'root_angle': -0.4796290953163572, 'root_number': '0.0639534087500514735049396032941704507591630518248753745 - 0.9979528854155635135282987675251942769831817176226226353*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.23981454765817864', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55544139502132270568153241795', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.77746726963888051164089044163', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.13530260843972310627578719396', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 34.87747383811801, 'bad_primes': [2, 5], 'central_character': '40.19', 'conductor': 1280, 'conductor_radical': 10, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1280/3/e/f/639/3'], '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': '2-1280-40.19-c2-0-29', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1280-40.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.90571535363143, 'root_angle': -0.2398145476581786, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55544139502132270568153241795', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '704105617790384797803028363181', 'Lhash_array': ['704105617790384797803028363181'], 'label': '2-1280-40.19-c2-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1280/3/e/f/639/3'}