-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1322083795524877199483234066366', 'a10': [0.8815616842802567, 0.0], 'a2': [-0.9044204139327635, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.1820237148616888, 0.0], 'a5': [-0.9747255487598867, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [2.8778872053390785, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.888306657226465, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [127, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 127], 'central_character': '8001.1', 'coefficient_field': 'CDF', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9044204139327635, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.9747255487598867, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.9654420977588591, 0], [11.0, 0]], [[1.0, 0], [-2.7414102061076706, 0], [13.0, 0]], [[1.0, 0], [1.836823841131283, 0], [17.0, 0]], [[1.0, 0], [-2.0264040608981473, 0], [19.0, 0]], [[1.0, 0], [4.958438683914593, 0], [23.0, 0]], [[1.0, 0], [-5.224912464917119, 0], [29.0, 0]], [[1.0, 0], [1.182636960125846, 0], [31.0, 0]], [[1.0, 0], [0.4588760920222604, 0], [37.0, 0]], [[1.0, 0], [-4.632739725385035, 0], [41.0, 0]], [[1.0, 0], [9.800483970535982, 0], [43.0, 0]], [[1.0, 0], [1.05029970356571, 0], [47.0, 0]], [[1.0, 0], [-0.3545567156619674, 0], [53.0, 0]], [[1.0, 0], [-2.9997501429069353, 0], [59.0, 0]], [[1.0, 0], [-10.791772911207216, 0], [61.0, 0]], [[1.0, 0], [11.346604930931113, 0], [67.0, 0]], [[1.0, 0], [11.148221223311195, 0], [71.0, 0]], [[1.0, 0], [-15.241928528053705, 0], [73.0, 0]], [[1.0, 0], [10.839408511109552, 0], [79.0, 0]], [[1.0, 0], [-2.7828784989654003, 0], [83.0, 0]], [[1.0, 0], [-5.798642580492192, 0], [89.0, 0]], [[1.0, 0], [-14.07966181078294, 0], [97.0, 0]], [[1.0, 0], [18.690782294430186, 0], [101.0, 0]], [[1.0, 0], [11.20669447801431, 0], [103.0, 0]], [[1.0, 0], [0.8513472571506143, 0], [107.0, 0]], [[1.0, 0], [-5.233939651206195, 0], [109.0, 0]], [[1.0, 0], [-20.454904372673905, 0], [113.0, 0]], [[1.0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 182, 'label': '2-8001-1.1-c1-0-182', '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/8001/2/a/z/1/13', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-4.375557617246115e-61, 0.11577070461526341, 0.23017914542064752, 0.34184103588116577, 0.44933068755724254, 0.5511667207055028, 0.6458049398229174, 0.7316399465834827, 0.8070164805231154, 0.8702508693538848, 0.9196623817068463, 0.9536137390637742, 0.9705595807738623, 0.9691012944993264, 0.9480463236174614, 0.9064698375379233, 0.8437764935425033, 0.7597599234576554, 0.654657541247503, 0.5291982870244432, 0.3846409997666676, 0.222801247390294, 0.04606464142453589, -0.1426150733962609, -0.33973453585791014, -0.5412768797727481, -0.7427659752096535, -0.9393388265121683, -1.1258356013028412, -1.296906179143315, -1.4471315054374905, -1.5711574331014506, -1.6638381510611209, -1.7203857557960511, -1.7365220417018026, -1.708628189762063, -1.6338877428319163, -1.5104180889503616, -1.3373856481424649, -1.1151000863010825, -0.845083170851731, -0.5301083409166029, -0.17420768794575373, 0.21735617639102178, 0.6381549637756537, 1.0806968150558576, 1.5365650739389034, 1.9965919237417127, 2.4510638433798206, 2.8899546119856083, 3.3031804204569286, 3.6808705777276485, 4.013646374318106, 4.29289992860564, 4.511064331495137, 4.661866156669273, 4.740551443245349, 4.744076603796355, 4.671256371766307, 4.52286187585638, 4.3016632008811495, 4.012412338857079, 3.6617642128462444, 3.258135420289518, 2.811502433052808, 2.3331431404336374, 1.835327754617485, 1.330967137043863, 0.8332284689064892, 0.35512980116636383, -0.0908736947526546, -0.49329806094536915, -0.8420193110013036, -1.128628494116862, -1.346739504476083, -1.49223715336916, -1.5634546088679595, -1.5612713716990008, -1.4891254435615744, -1.3529361835831974, -1.1609374503831715, -0.9234238867908363, -0.6524165053492336, -0.3612569512398287, -0.06414282780858781, 0.22438085731355592, 0.4899568494617687, 0.7189584754227041, 0.8990202071965214, 1.0195357425272744, 1.0721038661325324, 1.0509036183605804, 0.9529823260968467, 0.7784427977048214, 0.5305193721529136, 0.21553643536689376, -0.15725265909380592, -0.575943758330795, -1.0263700180559292, -1.4925882683974137, -1.9574477200463696, -2.403221336807159, -2.8122770941416335, -3.167764037866328, -3.4542866771108036, -3.658540882151957, -3.7698851635295147, -3.780822994308604, -3.6873746682815987, -3.489320984061891, -3.190305685644382, -2.797788911211271, -2.3228497060808935, -1.7798417173427885, -1.1859122623544531, -0.5604007969774092, 0.07586185049979935, 0.7013275078746788, 1.2945483237359914, 1.835005923330763, 2.303918668716326, 2.6849937623823714, 2.9650924622768704, 3.134779582673692, 3.188732653943273, 3.1259914603770476, 2.950034969493963, 2.6686796618339956, 2.2938006820312817, 1.840884748150005, 1.3284310514271342, 0.777223127816416, 0.20950057637959646, -0.3519357424215531, -0.8846480099357819, -1.3674764039046732, -1.7814056931232531, -2.1103460140550174, -2.3417936062361315, -2.467342090321505, -2.483021067674553, -2.3894461516009478, -2.1917726977571124, -1.8994541298129728, -1.5258144711567527, -1.0874530967082783, -0.6035074188534945, -0.09480585048735647, 0.41705137926684893, 0.9106424116637007, 1.365662089984448, 1.7638058340417615, 2.089558697046066, 2.3308533977579295, 2.4795670184544263, 2.5318334467630814, 2.488157186216346, 2.353323473754368, 2.1361092853544115, 1.8488093225700033, 1.5065999902540328, 1.1267722572250343, 0.7278707383491426, 0.32878101346884314, -0.05219014740751533, -0.3981965093697762, -0.6946526624808277, -0.9299134197004975, -1.0957987979885535, -1.1879387187582522, -1.2059205892799363, -1.153232876276839, -1.037008162359471, -0.867579460576873, -0.6578732239186644, -0.4226710201236768, -0.17777879256612414, 0.060852385323864534, 0.2780074166023827, 0.4600431858435252, 0.5956346529888022, 0.6763907688287184, 0.6973066698521232, 0.6570271914940864, 0.557906746440958, 0.4058615352716285, 0.2100213192744393, -0.017801009729659503, -0.2637936768154714, -0.512946967540106, -0.7499269223542453, -0.9599733249131225, -1.129771612266666, -1.2482491645850622, -1.307250008264076, -1.3020481408769553, -1.231668166391459, -1.0989922890205421, -0.9106444167955624, -0.6766545492569681, -0.409919092659035, -0.12548456911858674, 0.16030730749835742, 0.43076663868993653, 0.6698417511358125, 0.8630890402616408, 0.998570075859447, 1.0676227593082028, 1.0654593503653371, 0.9915530067144854, 0.8497856683251562, 0.6483430955868005, 0.3993569457280443, 0.11830817885385772, -0.17677998122870783, -0.46631864231712017, -0.7302478568974257, -0.9491897293158752, -1.1055956869620462, -1.1848223063042214, -1.1760724907328977, -1.0731448422333363, -0.8749435000102498, -0.5857130858349618, -0.21497807049392656, 0.2228179153517766, 0.7089604389201873, 1.2213713246851166, 1.7357300975119332, 2.226752269115756, 2.669556633787408, 3.041047028905076, 3.3212313555171575, 3.4944022928216487, 3.550110088282556, 3.4838678285643634, 3.2975432244316476, 2.999407488125466, 2.6038304751327943, 2.130630897278039, 1.6041100013003724, 1.051815534402093, 0.5030990137638852, -0.012457688717257569, -0.4666614513317549, -0.8342833272373987, -1.094501502717998, -1.2321286188598286, -1.2385507230601827, -1.1123198819460276, -0.8593608309185525, -0.4927729867229073, -0.032231567382712926, 0.4969858001872759, 1.0652990376591542, 1.6403849448731356, 2.1889129281031936], 'positive_zeros': ['1.04294021971578570415275325449653', '1.99009102828662054218624590582023', '3.27135651639415773382733644526609', '3.94772018415713156151341274013614', '4.48101375066224783849435520801001', '5.43190056653648181437393730382462', '6.20482920371951429110836441366123', '6.89926990654265619693604834134614', '7.68086239325410809870628272130643'], 'prelabel': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, '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': '1.04294021971578570415275325450', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.99009102828662054218624590582', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27135651639415773382733644527', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 63.888306657226465, 'bad_primes': [3, 7, 127], 'central_character': '1.1', 'conductor': 8001, 'conductor_radical': 2667, 'degree': 2, 'index': 182, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8001/2/a/z/1/13'], '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': '2-8001-1.1-c1-0-182', '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': '2-8001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04294021971578570415275325450', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1322083795524877199483234066366', 'Lhash_array': ['1322083795524877199483234066366'], 'label': '2-8001-1.1-c1-0-182', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8001/2/a/z/1/13'}