Formats: - HTML - YAML - JSON - 2026-03-11T12:43:58.470470
Query: /api/lfunc_lfunctions/?_offset=0
Show schema

{'Lhash': '2265857912875642606887454224207', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.14624566248161094, 0], 'a6': [0, 0], 'a7': [-0.08024021560339972, -2.644534270490727], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.1467615712352, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.08024021560339972, 2.644534270490727]]]], 'bad_primes': [2, 3, 7], 'central_character': '3024.289', 'coefficient_field': 'CDF', 'conductor': 3024, 'conductor_radical': 42, 'conjugate': '52341258438399943805061420003', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.14624566248161094, 0], [5.0, 0]], [[1.0, 0], [0.08024021560339972, 2.644534270490727]], [[1.0, 0], [-1.6640407426161252, 0], [11.0, 0]], [[1.0, 0], [-0.09994540418981711, -0.1731105180397706], [-6.5, 11.258330249197702]], [[1.0, 0], [3.1355517655842684, 5.430934967754251], [-8.5, 14.722431864335457]], [[1.0, 0], [3.4587883484468915, -5.990797152137262], [-9.5, -16.454482671904334]], [[1.0, 0], [6.18183582275064, 0], [23.0, 0]], [[1.0, 0], [-2.467572136892331, 4.273960312438822], [-14.5, -25.11473670974872]], [[1.0, 0], [1.258897540067257, -2.1804745009199658], [-15.5, -26.846787517317598]], [[1.0, 0], [3.5002275032436354, -6.062571873667934], [-18.5, -32.04293994002423]], [[1.0, 0], [1.15895213587744, 2.0073639828801952], [-20.5, 35.50704155516198]], [[1.0, 0], [-0.9409932683123771, 1.6298481502973299], [-21.5, -37.239092362730865]], [[1.0, 0], [-0.9058873892124755, -1.56904298405193], [-23.5, 40.703193977868615]], [[1.0, 0], [-2.6730682354306228, -4.629889995864324], [-26.5, 45.89934640057525]], [[1.0, 0], [-2.285492609772634, 3.958589320449391], [-29.5, -51.09549882328188]], [[1.0, 0], [-0.3391377556706569, -0.5874038235864578], [-30.5, 52.827549630850754]], [[1.0, 0], [3.0934178966119217, -5.357956965974697], [-33.5, -58.023702053557386]], [[1.0, 0], [-1.277492929992946, 0], [71.0, 0]], [[1.0, 0], [0.7786027286536745, 1.3485794849399284], [-36.5, 63.21985447626402]], [[1.0, 0], [-6.397871508307365, -11.081438512685683], [-39.5, 68.41600689897065]], [[1.0, 0], [-3.7568687624433483, 6.507087573920289], [-41.5, -71.88010851410841]], [[1.0, 0], [4.533939957311606, -7.853014364530368], [-44.5, -77.07626093681505]], [[1.0, 0], [3.98513971378321, -6.902464459533014], [-48.5, -84.00446416709055]], [[1.0, 0], [14.842998763688344, 0], [101.0, 0]], [[1.0, 0], [-0.2039483636274523, 0], [103.0, 0]], [[1.0, 0], [-3.4844449996076072, 6.035235775499693], [-53.5, -92.66471820493493]], [[1.0, 0], [-3.3305814704688523, -5.768736325599515], [-54.5, 94.39676901250381]], [[1.0, 0], [-0.019323375463873714, -0.033469068077159096], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23415179, 'index': 45, 'label': '2-3024-63.16-c1-0-45', 'leading_term': '0.1405907206944914849547417637615336524518717565151492080', '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/3024/2/t/i/289/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.1405907206944915, 0.31572508371560803, 0.49289294351660057, 0.6716022517175033, 0.8512723368281472, 1.031191923034436, 1.2104842803916966, 1.388081482078882, 1.562709133504211, 1.7328823241122298, 1.8969129931092625, 2.052928429177736, 2.1989002525598793, 2.332682948450884, 2.452060815373494, 2.554802039294743, 2.63871848358428, 2.7017296813499825, 2.7419294212727063, 2.757653227862167, 2.747544954117219, 2.710620634554829, 2.6463276973553, 2.5545976148328124, 2.435890090440387, 2.291226946113076, 2.1222139925957553, 1.9310493422970985, 1.7205168617896966, 1.493963759564911, 1.2552616617274581, 1.0087509390372928, 0.7591685055217262, 0.511559801710461, 0.2711761919566573, 0.043359530765900794, -0.16658382872495653, -0.35351681760677106, -0.5126100087856019, -0.6394809445178432, -0.7303305211029018, -0.7820723072320426, -0.792450574404115, -0.7601428451620561, -0.6848429272879419, -0.5673207053048045, -0.4094554060902903, -0.2142396397332907, 0.014247768507763055, 0.2709013078472539, 0.5496808966308541, 0.8437358020835581, 1.1455585360973939, 1.4471658352071133, 1.7403027915037048, 2.0166652182694245, 2.268134447370029, 2.487018002136321, 2.66628900487232, 2.799816794101899, 2.8825810702375807, 2.9108619803605795, 2.882398906652946, 2.796511343664512, 2.6541761326998334, 2.4580564530582594, 2.2124793255756017, 1.9233599300478192, 1.5980727316215897, 1.2452712008508606, 0.8746597397232548, 0.49672322830433707, 0.12242131739375205, -0.23714385537928326, -0.5710765206634948, -0.8690416555729146, -1.1216131333471506, -1.3206035733288592, -1.459363917361704, -1.5330412918643643, -1.538784687585929, -1.4758893886288837, -1.345872878995218, -1.152477102087154, -0.901594383673703, -0.6011169747031336, -0.26071293755892894, 0.10846611102848139, 0.4941371802817467, 0.8832872719407004, 1.262610975017284, 1.6189695046754684, 1.9398550592942427, 2.2138435863932, 2.4310188792151037, 2.58335140573493, 2.66501641090161, 2.6726376153719933, 2.6054452176710035, 2.465339823220879, 2.256857279917005, 1.9870330806374426, 1.665168864510206, 1.3025074632962692, 0.9118267408058942, 0.5069660034191806, 0.10230186423165727, -0.28780702141815173, -0.6495850914524148, -0.9703925843319298, -1.239243349230419, -1.4472660332266971, -1.5880885792665482, -1.658128510534421, -1.656774828012248, -1.5864513981531285, -1.4525563123924787, -1.2632766858819913, -1.0292835324079037, -0.7633164933447052, -0.4796730910171173, -0.1936216034990391, 0.07923958706082491, 0.32365042149761286, 0.5253577262810646, 0.6717555095414994, 0.752469023174004, 0.7598562771946638, 0.6894035329697543, 0.5399952443322931, 0.3140438231607427, 0.017470294306282805, -0.3404668517931059, -0.7474907601125687, -1.1887628601267222, -1.6474603749671501, -2.1054522828701088, -2.5440464388522472, -2.9447767599035015, -3.2901968553177268, -3.564645396863667, -3.754948962721226, -3.8510300791409713, -3.8463916791040056, -3.7384540818134675, -3.528726687012457, -3.2228036289254036, -2.8301803490855084, -2.3638960885905043, -1.8400153061519744, -1.276968627153106, -0.694780757234511, -0.11421851348318136, 0.4441035589062153, 0.9606198450191259, 1.4176715934187525, 1.8002861606801148, 2.0968405370928695, 2.2995768618843453, 2.4049439999824838, 2.4137469783101353, 2.331094832425896, 2.166146799990093, 1.9316663808272239, 1.643402107810642, 1.3193224823134215, 0.978739989122318, 0.641365029633091, 0.3263346749146832, 0.051263100682491625, -0.1686397197904244, -0.32133705852167144, -0.3985829840611273, -0.39635599621732603, -0.3150848546202453, -0.15965259539040083, 0.0608244981598565, 0.3334350621579165, 0.6421090817382068, 0.9684234728946639, 1.292538728580458, 1.5942213012520607, 1.853901294455448, 2.05371238048828, 2.1784608367809004, 2.2164732582344913, 2.1602777785164693, 2.007081307276268, 1.759015021766437, 1.4231316863818404, 1.0111507652291611, 0.5389601271002366, 0.02589576835176689, -0.5061672576622264, -1.0338692407914438, -1.533513854780932, -1.982252441704153, -2.359244300679207, -2.6467329689687653, -2.8309818307818557, -2.9030187430655707, -2.8591484551911837, -2.701202998031075, -2.4365133740934977, -2.0776001362738277, -1.6415950685629075, -1.1494204130623882, -0.6247651643237134, -0.09290916051434223, 0.42054558769847994, 0.8909711837962115, 1.2959702584869643, 1.6165262262395679, 1.8379858551303339, 1.9508207268838365, 1.9511252482617019, 1.8408223915385598, 1.627563603759745, 1.3243255371825275, 0.9487225554731141, 0.522069479504895, 0.06824289734158594, -0.3875992063105267, -0.8203714081978387, -1.2064155600400888, -1.5247826018899757, -1.7583710193198985, -1.8948585985039899, -1.927374823254914, -1.8548749933300817, -1.6821932108222186, -1.4197689259987476, -1.0830598031043137, -0.6916712620230214, -0.268249184030331, 0.16280398538323174, 0.5767189530537471, 0.9497776150680517, 1.260679470913704, 1.4917785014279494, 1.6301190540955486, 1.6682098654400788, 1.6044895284610683, 1.4434537329790047, 1.195433543706132, 0.8760337853750001, 0.5052601596681524, 0.10638190383972998, -0.2954074456709135, -0.6744562394111216, -1.0061646569772544, -1.2684516323179866, -1.4430933573348455, -1.5168542687471445, -1.4823423854512077, -1.3385359144454916, -1.0909463729473634], 'positive_zeros': ['1.78744672425327192745689331314005', '2.43451851104359993856837978129095', '3.67323064617030304609262186549800', '4.40335818833104457723619116593673', '5.39587464798286907303272622750711', '6.18013707017509222281774920819233', '6.65502655077854676351134359066625', '7.72891770147748721491304575744457', '8.592706509378418830162480865648165', '8.924749930112492297646466946003833'], 'prelabel': '2-3024-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.9139354463846185, 'root_angle': -0.4609585795401038, 'root_number': '-0.97006342659871239976484326202866314436614788104514385756 - 0.2428517003761030293198669712239206792048522538008995931*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4609585795401038', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78744672425327192745689331314', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.43451851104359993856837978129', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.67323064617030304609262186550', 'prec': 103}}