-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1167008712867289069327183605050', 'a10': [-4.047500522600129, 0.0], 'a2': [1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-4.047500522600129, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.15363004511784759, 0.0], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.642188614702686, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1458.1', 'coefficient_field': 'CDF', 'conductor': 1458, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.047500522600129, 0], [5.0, 0]], [[1.0, 0], [0.15363004511784759, 0], [7.0, 0]], [[1.0, 0], [-0.22088964880682577, 0], [11.0, 0]], [[1.0, 0], [-0.5943178202890789, 0], [13.0, 0]], [[1.0, 0], [-5.5651041729276205, 0], [17.0, 0]], [[1.0, 0], [-3.8208189256944514, 0], [19.0, 0]], [[1.0, 0], [5.859045373522276, 0], [23.0, 0]], [[1.0, 0], [-0.7479478654069265, 0], [29.0, 0]], [[1.0, 0], [-5.083597640502859, 0], [31.0, 0]], [[1.0, 0], [-3.7477673739066213, 0], [37.0, 0]], [[1.0, 0], [-3.9744489708122988, 0], [41.0, 0]], [[1.0, 0], [-10.206922515816828, 0], [43.0, 0]], [[1.0, 0], [0.4757145843259097, 0], [47.0, 0]], [[1.0, 0], [-3.2995526571932023, 0], [53.0, 0]], [[1.0, 0], [-7.274001628005501, 0], [59.0, 0]], [[1.0, 0], [-3.369765553308496, 0], [61.0, 0]], [[1.0, 0], [-7.458117334427532, 0], [67.0, 0]], [[1.0, 0], [-2.8577733595795505, 0], [71.0, 0]], [[1.0, 0], [1.2778447376795632, 0], [73.0, 0]], [[1.0, 0], [3.30707959873539, 0], [79.0, 0]], [[1.0, 0], [8.271162972332965, 0], [83.0, 0]], [[1.0, 0], [4.957647954497808, 0], [89.0, 0]], [[1.0, 0], [-5.654071696130237, 0], [97.0, 0]], [[1.0, 0], [-15.79952655635694, 0], [101.0, 0]], [[1.0, 0], [-10.696845807031524, 0], [103.0, 0]], [[1.0, 0], [-1.8523636081756776, 0], [107.0, 0]], [[1.0, 0], [14.549455761454032, 0], [109.0, 0]], [[1.0, 0], [13.382260480448315, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-1458-1.1-c1-0-5', 'leading_term': '1.93713731308805331448622596351', '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/1458/2/a/g/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.9371373130880534, 1.9311131299753683, 1.9128854721630297, 1.881999661146971, 1.8377325737738786, 1.7791419350318574, 1.7051303370952609, 1.6145199070305927, 1.5061334063492142, 1.3788778040370542, 1.2318268668354468, 1.0642999002080467, 0.8759343296080729, 0.6667502643483098, 0.4372055139989471, 0.18823974370344823, -0.07869340612218621, -0.3616073082480172, -0.6579774150779862, -0.9647512390925426, -1.2783738971410532, -1.5948296178547987, -1.9096992924258018, -2.218233764339384, -2.5154421117440213, -2.796193689871142, -3.055332186743392, -3.2877994225872147, -3.488766113207882, -3.6537663427391456, -3.778832074868298, -3.860623696850049, -3.896552359250403, -3.884889766287353, -3.8248611037999045, -3.716716977356659, -3.561780580143834, -3.3624668218558993, -3.1222708224759175, -2.8457239985517493, -2.538316927420462, -2.206389242982492, -1.8569879646512302, -1.4976968525679333, -1.1364405755431337, -0.7812686280475852, -0.4401249911268241, -0.1206104509153112, 0.17025477965174943, 0.42625998903398704, 0.6422160658521426, 0.8141424559195615, 0.9394210527787211, 1.0169098147723334, 1.0470099467283354, 1.0316818399694023, 0.9744065997263224, 0.8800918592362174, 0.7549226266072999, 0.6061600637491663, 0.44189327619848595, 0.2707513111320228, 0.1015845267807782, -0.05687378207774226, -0.19635322926485846, -0.30938640468341877, -0.38962942334785866, -0.43214925839595264, -0.4336647733408098, -0.39272956286140487, -0.30984647383746655, -0.18750597054554563, -0.030143265489238402, 0.15598772912044423, 0.36302217673342546, 0.5817688360538247, 0.8020628254639389, 1.0131747845444625, 1.2042615627773572, 1.3648410228523702, 1.485271624479901, 1.5572162768335718, 1.5740696103024319, 1.53132838550414, 1.4268862565180447, 1.2612365219754282, 1.0375697748064978, 0.7617573986619404, 0.4422165145708978, 0.08965707628500706, -0.28328286313126805, -0.6625023708090483, -1.0329869276355355, -1.3794208143122688, -1.6868377786192468, -1.9412823011205218, -2.130452048618303, -2.2442916613927717, -2.275508949137091, -2.21998689794732, -2.0770685772835056, -1.8496969742089122, -1.5443977987251942, -1.171100163247734, -0.742797452229319, -0.2750583333745163, 0.21459463969011877, 0.7074143933877329, 1.1842361126447685, 1.6263259739974452, 2.0162329862419694, 2.33860345213242, 2.5809178371555914, 2.7341120901996203, 2.793049684294399, 2.7568167119100844, 2.628820058023948, 2.4166776720623906, 2.131899872264679, 1.7893709831335323, 1.4066509237379539, 1.003126105999142, 0.5990476471426462, 0.2145019610460731, -0.13163615960514294, -0.4227151689327293, -0.6452302057317024, -0.7896080630296715, -0.8508087105528156, -0.8287062165534326, -0.728221961793567, -0.5591948740792256, -0.33598649223695537, -0.07683236070358553, 0.19703513224693697, 0.46245454525717133, 0.6955445641376198, 0.8729961765300459, 0.9733830132647261, 0.9784217635684485, 0.874114767166319, 0.6517106635194078, 0.30842627033868925, -0.15211658751690438, -0.7197722140903957, -1.3780874912562295, -2.104853969733632, -2.87297832018108, -3.651636581102169, -4.407661626934675, -5.107099436930088, -5.716858889754107, -6.206372622320759, -6.549183479532039, -6.724372538496379, -6.7177506756581025, -6.522745970829006, -6.140933476537179, -5.582171363716716, -4.864327325243023, -4.0126003587728, -3.058464535256586, -2.0382819185171024, -0.9916502817587085, 0.040433400079883594, 1.017501439646869, 1.9015371901498057, 2.6587901246899985, 3.2613885257204274, 3.6886636110628133, 3.928113364198818, 3.975952965125513, 3.8372205676244544, 3.5254310671774887, 3.0617951355928055, 2.4740447779131416, 1.7949286172319348, 1.0604587458627495, 0.3080051761084626, -0.425657203296023, -1.106241297668725, -1.7036754401344931, -2.193570588890302, -2.5583465473622704, -2.7879563161558494, -2.880171021946806, -2.8404135492108105, -2.6811555213627085, -2.4209180594618727, -2.082940230261641, -1.6935988378455533, -1.2806779775331827, -0.8715956065975127, -0.49169669344094363, -0.16271807918402245, 0.09848076862797685, 0.2808437940727172, 0.3796456442898084, 0.39659005038273026, 0.33947654215920137, 0.2214604694791133, 0.05995759263405512, -0.12473233769203497, -0.3109900812326934, -0.4775239418353629, -0.6049879401646342, -0.6774611153112612, -0.6836865551152415, -0.617984117985528, -0.4807720046447717, -0.27865805054440856, -0.024090205755035475, 0.2654146997886328, 0.5684160887771047, 0.8609949617702375, 1.1184044165718003, 1.3168151521130933, 1.435037727766109, 1.4561031695249904, 1.368591310787009, 1.1676116316165652, 0.8553634048721855, 0.44122929435545793, -0.05861257800267091, -0.6220406994137239, -1.2222572504468712, -1.829392187086089, -2.4123422285095635, -2.940725131829041, -3.3868199584608374, -3.727363002679402, -3.9450768778416325, -4.029826554199628, -3.979319940697425, -3.79930039536941, -3.5032123886820523, -3.1113571705266385, -2.6495902789370795, -2.1476446511067264, -1.637189697034755, -1.1497560435246428, -0.7146662908826259, -0.35711316670262955, -0.09651768460263109, 0.05471822231129242, 0.09197650130739007, 0.018650017439283906, -0.1541861648279112, -0.4086382971404353, -0.7213333276342323, -1.065140927821824, -1.4111568473252702, -1.7308064681944673, -1.99791746530868, -2.190611238250003, -2.292874391718253, -2.2956933582219543], 'positive_zeros': ['0.920607549633297502688066905471037', '2.77743497290039679923071734923584', '3.66971535696760060573009989842678', '4.22882073575295506526928339401463', '5.22914393057585781223185579000370', '6.18543901643976412591477565943390', '7.24237314316451017356507497604542', '7.80951688380392884773945841640622', '8.361071058311211181955021397587963', '9.607034575970945175432462714346824'], 'prelabel': '2-1458-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4120651539357634, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.920607549633297502688066905471', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.77743497290039679923071734924', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.66971535696760060573009989843', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 11.642188614702686, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 1458, 'conductor_radical': 6, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1458/2/a/g/1/1'], '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': '2-1458-1.1-c1-0-5', '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': '2-1458-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4120651539357634, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.920607549633297502688066905471', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1167008712867289069327183605050', 'Lhash_array': ['1167008712867289069327183605050'], 'label': '2-1458-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1458/2/a/g/1/1'}