-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2252887274398823820407922245566', 'a10': [0.0, 0.0], 'a2': [1.4811943040920157, 0.0], 'a3': [0.0, 0.0], 'a4': [0.19393656647463045, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [4.481194304092016, 0.0], 'a8': [-2.675130870566646, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.13604686409738, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 19], 'central_character': '4275.1', 'coefficient_field': 'CDF', 'conductor': 4275, 'conductor_radical': 285, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4811943040920157, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.481194304092016, 0], [7.0, 0]], [[1.0, 0], [3.675130870566646, 0], [11.0, 0]], [[1.0, 0], [-2.8690674370412763, 0], [13.0, 0]], [[1.0, 0], [6.156325174658662, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [8.156325174658662, 0], [23.0, 0]], [[1.0, 0], [4.6375194787506775, 0], [29.0, 0]], [[1.0, 0], [2.8060634335253694, 0], [31.0, 0]], [[1.0, 0], [3.443582912276047, 0], [37.0, 0]], [[1.0, 0], [-5.599908086934708, 0], [41.0, 0]], [[1.0, 0], [10.14410639454263, 0], [43.0, 0]], [[1.0, 0], [3.8436748253413384, 0], [47.0, 0]], [[1.0, 0], [-3.8944600487412147, 0], [53.0, 0]], [[1.0, 0], [-9.536904083418802, 0], [59.0, 0]], [[1.0, 0], [9.894460048741214, 0], [61.0, 0]], [[1.0, 0], [-8.700523482266584, 0], [67.0, 0]], [[1.0, 0], [-2.0, 0], [71.0, 0]], [[1.0, 0], [3.0883966152158453, 0], [73.0, 0]], [[1.0, 0], [-4.962388608184031, 0], [79.0, 0]], [[1.0, 0], [6.730840649893432, 0], [83.0, 0]], [[1.0, 0], [11.473900079902895, 0], [89.0, 0]], [[1.0, 0], [-9.630225254561557, 0], [97.0, 0]], [[1.0, 0], [5.612126867050739, 0], [101.0, 0]], [[1.0, 0], [3.5369040834188015, 0], [103.0, 0]], [[1.0, 0], [-16.438658356349137, 0], [107.0, 0]], [[1.0, 0], [12.387873132949261, 0], [109.0, 0]], [[1.0, 0], [11.244721789874507, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 131, 'label': '2-4275-1.1-c1-0-131', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/4275/2/a/bd/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-2.148277246800697e-60, 0.29504585672284145, 0.5894937684659834, 0.8826690310592119, 1.1737483483114228, 1.4616974481188938, 1.745221926432702, 2.0227341255450093, 2.292337782768954, 2.5518311392957354, 2.7987282684605197, 3.0302976192679116, 3.2436161876752747, 3.435637308628495, 3.6032697736657773, 3.7434657850235658, 3.8533151247241277, 3.9301428222086545, 3.971607533292312, 3.9757977928068966, 3.941323277089575, 3.8673982193583307, 3.753914172497478, 3.6014994219163676, 3.4115625269005165, 3.186317720890001, 2.928790234864969, 2.642800025227698, 2.332922885919824, 2.0044284974880777, 1.6631956027472068, 1.3156051849623207, 0.9684132418430208, 0.628605475727593, 0.30323693323318013, -0.0007396993262649932, -0.27665283190226314, -0.5182929116964197, -0.7200903478530045, -0.8772849455099809, -0.9860812839072656, -1.0437845602927343, -1.048911697093629, -1.0012729788628028, -0.9020201457526501, -0.753657712386277, -0.5600152882126527, -0.32617982357760367, -0.058387963584344546, 0.2361199782854089, 0.5492815559606247, 0.8724250246298838, 1.196507989095488, 1.5123752301085487, 1.8110280883565717, 2.083897018049083, 2.3231084122275916, 2.5217365847393065, 2.6740318950006143, 2.77561643633676, 2.82363947993446, 2.8168859644655817, 2.7558327229920323, 2.6426488072143974, 2.4811381550487934, 2.2766248898389785, 2.035783667256188, 1.7664196204843354, 1.4772045121046196, 1.177377596880508, 0.8764213497483672, 0.5837235393140041, 0.3082380594355227, 0.058157412708843594, -0.15939027203341935, -0.33860733451398556, -0.4752444850698246, -0.5667607598594552, -0.6124177881451563, -0.6133030440232884, -0.5722794868412304, -0.4938619449666089, -0.3840236521349871, -0.2499393794414666, -0.09967448873714922, 0.05816816584953919, 0.21482936735807637, 0.3617869017342269, 0.49114430846245194, 0.5959977993583154, 0.6707645024020813, 0.7114563172442264, 0.7158855392921563, 0.6837909706361757, 0.6168764055963722, 0.5187570420064795, 0.3948133841841951, 0.2519564046130456, 0.0983119368171744, -0.05716370925813215, -0.20512127769161828, -0.33629053320776064, -0.4419656057575501, -0.5144811772473752, -0.5476564761829564, -0.5371845948202032, -0.4809462622055299, -0.3792298692250303, -0.2348431724445597, -0.05310657712498537, 0.15827695420264234, 0.3894747131601861, 0.6288932945789988, 0.8636516171895775, 1.0801401852608483, 1.2646439874050743, 1.4040024047442758, 1.4862765550191404, 1.5013928208125873, 1.441731036111397, 1.302627012558379, 1.0827617843249036, 0.7844140770018608, 0.4135579283618352, -0.02020609393327664, -0.5038902836429229, -1.0215261365265014, -1.5547259520628083, -2.0833801949367685, -2.5864639010028374, -3.0429191700155216, -3.4325758579174233, -3.737069257483946, -3.940712064881965, -4.031278419043026, -4.00066032833705, -3.845361325541038, -3.56679857894096, -3.1713926992648913, -2.6704337944381558, -2.0797225352768294, -1.4189956432108548, -0.7111557939631961, 0.018664069921546938, 0.7441631200695881, 1.4390154848967014, 2.078041975150551, 2.6383560888555255, 3.1004292213806695, 3.449022203604233, 3.673935141921952, 3.77053489097325, 3.7400290759228194, 3.5894669971079827, 3.3314604912788446, 2.9836313017785567, 2.5678050786157445, 2.108985115426694, 1.6341506671334287, 1.1709345534739226, 0.7462421870879236, 0.38487872257196715, 0.10825238793783445, -0.06677993305900705, -0.12886415025898473, -0.07284526899315436, 0.09983224717749649, 0.38104710207952713, 0.7562583616485935, 1.205092340317436, 1.7022376623011717, 2.2186110018862544, 2.722741519432586, 3.1823097923602908, 3.5657677758150577, 3.8439605652099047, 3.991668855464255, 3.98899319161899, 3.8225073683860806, 3.486118436597396, 2.9815842817572062, 2.318656035237362, 1.514830882924488, 0.5947202466990298, -0.41094215056949557, -1.4666091763095779, -2.5334861984978403, -3.571280082558959, -4.540046912343537, -5.402047817917087, -6.123520616272131, -6.676278040532761, -7.039051068119376, -7.198507928407081, -7.14989520827715, -6.897266300903084, -6.4532833068986575, -5.83860032001629, -5.080857665106023, -4.213336949061139, -3.2733446356938978, -2.3004062783965664, -1.3343637272778524, -0.4134729767403543, 0.42739950270510835, 1.158389157714864, 1.7559717373227803, 2.203959494390303, 2.494105326528826, 2.626286046210025, 2.608258665835644, 2.4550066686255723, 2.187715435538378, 1.8324360744712014, 1.4185137207018514, 0.9768689899294869, 0.5382289398306905, 0.13140617895979803, -0.2182784979148491, -0.49034320743562987, -0.6701886120301913, -0.7497825872652918, -0.7279512568811418, -0.6102645241634886, -0.40852766607560254, -0.1399132807325761, 0.1742114347364513, 0.5096896627904169, 0.8411266303839174, 1.1434942943930817, 1.3936928347616735, 1.571975904737054, 1.6631552803400707, 1.6575142646216312, 1.5513771226864344, 1.3473028800538973, 1.0538947440826443, 0.6852398206180549, 0.2600162739382659, -0.19967475445259325, -0.6696785313513393, -1.1252714363072882, -1.542668274158839, -1.9004585081396237, -2.1808825699594423, -2.3708697783448565, -2.4627746680125107, -2.454767751619153, -2.3508587095202462, -2.1605533478388557, -1.8981689113428588, -1.5818540084047308, -1.2323781163179754, -0.8717701817312901, -0.5218952664869496, -0.20306188850887663, 0.0672495901858837], 'positive_zeros': ['1.77721469464315417380654339946425', '2.44789917193775925686595693432207', '3.71983181297957502588035087982698', '4.29779687760289000978172683034530', '5.00855040844894080549152045213590', '5.54851664747922271800707779699124', '6.29464459542632045769713364697557', '7.26042420277940743411015818509380', '8.254060194464370458530843892727623'], 'prelabel': '2-4275-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.842606170545588, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.77721469464315417380654339946', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44789917193775925686595693432', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.71983181297957502588035087983', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 34.13604686409738, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 4275, 'conductor_radical': 285, 'degree': 2, 'index': 131, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4275/2/a/bd/1/3'], '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': '2-4275-1.1-c1-0-131', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4275-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.842606170545588, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77721469464315417380654339946', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2252887274398823820407922245566', 'Lhash_array': ['2252887274398823820407922245566'], 'label': '2-4275-1.1-c1-0-131', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4275/2/a/bd/1/3'}