Formats: - HTML - YAML - JSON - 2026-09-09T08:00:20.069523
  • lfunc_lfunctions • Show schema
    {'Lhash': '816287563869628074086370844754', 'a10': [-19329.87968264429, 0.0], 'a2': [-30.92780749223086, 0.0], 'a3': [0.0, 0.0], 'a4': [444.5292762764913, 0.0], 'a5': [625.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2401.0, 0.0], 'a8': [2086.7215546821703, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 162.2362883916201, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 7}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-625.0, 0]]], [7, [[1.0, 0], [-2401.0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '315.1', 'coefficient_field': 'CDF', 'conductor': 315, 'conductor_radical': 105, 'degree': 2, 'euler_factors': [[[1.0, 0], [30.92780749223086, 0], [512.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-625.0, 0]], [[1.0, 0], [-2401.0, 0]], [[1.0, 0], [-51657.667223254975, 0], [2357947691.0, 0]], [[1.0, 0], [129921.26769403847, 0], [10604499373.0, 0]], [[1.0, 0], [-259512.58760157556, 0], [118587876497.0, 0]], [[1.0, 0], [-90316.42848365068, 0], [322687697779.0, 0]], [[1.0, 0], [751691.7746350704, 0], [1801152661463.0, 0]], [[1.0, 0], [-2205099.347921486, 0], [14507145975869.0, 0]], [[1.0, 0], [-3100316.7523045926, 0], [26439622160671.0, 0]], [[1.0, 0], [14252396.554081758, 0], [129961739795077.0, 0]], [[1.0, 0], [-14569138.708254926, 0], [327381934393961.0, 0]], [[1.0, 0], [-18909137.962194122, 0], [502592611936843.0, 0]], [[1.0, 0], [-14317547.473630408, 0], [1119130473102767.0, 0]], [[1.0, 0], [-34422002.008122824, 0], [3299763591802133.0, 0]], [[1.0, 0], [-36133048.52890704, 0], [8662995818654939.0, 0]], [[1.0, 0], [93300673.36910576, 0], [11694146092834140, 0]], [[1.0, 0], [-205761669.70896104, 0], [27206534396294948, 0]], [[1.0, 0], [-192396750.99046594, 0], [45848500718449030, 0]], [[1.0, 0], [-81166945.43632258, 0], [58871586708267910, 0]], [[1.0, 0], [-107122191.44934258, 0], [119851595982618320, 0]], [[1.0, 0], [354921627.166262, 0], [186940255267540400, 0]], [[1.0, 0], [442432831.6811176, 0], [350356403707485200, 0]], [[1.0, 0], [640462626.0437759, 0], [760231058654565200, 0]], [[1.0, 0], [575535996.044606, 0], [1093685272684361000, 0]], [[1.0, 0], [-597246065.0368562, 0], [1304773183829244700, 0]], [[1.0, 0], [1379165600.4710236, 0], [1838459212420154600, 0]], [[1.0, 0], [1979945393.822246, 0], [2171893279442309400, 0]], [[1.0, 0], [-2560211264.1952696, 0], [3004041937984268300, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 23, 'label': '2-315-1.1-c9-0-23', 'leading_term': '1.2522781950482474071988354045510', 'load_key': 'CMFs-workshop', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/315/10/a/e/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [1.2522781950482473, 1.238585372667154, 1.1978733860627744, 1.1312327153600001, 1.0404511467051163, 0.9279699159758628, 0.796823627435347, 0.6505652365971343, 0.4931777150370687, 0.3289743141040411, 0.162489608693189, -0.001636273851075588, -0.15877765580378395, -0.3044448285879634, -0.43440429929562685, -0.544794952091598, -0.6322373478548056, -0.69393347884229, -0.7277544464218575, -0.7323137378249942, -0.7070240401487472, -0.6521358430977109, -0.568756441700316, -0.4588483508485455, -0.3252065783212486, -0.17141466427743215, -0.0017798744486626922, 0.17875157798285626, 0.3646979206256788, 0.5501619849441042, 0.7289658577168167, 0.8947973172380124, 1.0413649780983723, 1.1625587509787232, 1.2526119713276538, 1.3062613718838034, 1.3189009763588995, 1.2867259813834064, 1.2068627755056862, 1.0774814201909941, 0.8978871888550528, 0.6685881242104158, 0.39133602747786334, 0.06913882879893189, -0.29375710242880465, -0.6919154768094965, -1.118789482579977, -1.5668313560649112, -2.027630648568839, -2.4920789444245277, -2.950558037397725, -3.393147866458108, -3.809849867052872, -4.190820829955815, -4.5266118949589815, -4.80840695797157, -5.028254552184919, -5.179287188867002, -5.255922219914378, -5.254038517770223, -5.171123660023135, -5.006386853030182, -4.760833523982605, -4.4372983422581225, -4.040434382641417, -3.5766571948725865, -3.0540436720366757, -2.4821867872492667, -1.8720084639127792, -1.2355340274935878, -0.5856328230827955, 0.06426936056424006, 0.700499476120703, 1.3094606277732972, 1.8779616948994766, 2.3935447280840365, 2.844801464134729, 3.2216703274004446, 3.51570554692562, 3.7203105249647517, 3.830928337228285, 3.8451832167573765, 3.7629680520924484, 3.5864742899553077, 3.3201621400113925, 2.9706705955852115, 2.5466684657236174, 2.0586493132084325, 1.5186748600013529, 0.9400730051170014, 0.3370980495428195, -0.2754380098295171, -0.8825532148556876, -1.4694917327220205, -2.0221171422266986, -2.527291614922407, -2.973229871699424, -3.3498173237080824, -3.648882671899334, -3.864416425076259, -3.9927282744954424, -4.032537995628349, -3.9849964870199113, -3.853635646234695, -3.644247960806692, -3.3646988900654, -3.0246772609533124, -2.635390926103021, -2.2092167658914454, -1.7593156925118836, -1.299224574458101, -0.8424378941909649, -0.4019924410263158, 0.009931601068804115, 0.3823801975796833, 0.7059534945016417, 0.9730814436583259, 1.1782377728405113, 1.3180850379606859, 1.3915457633948263, 1.3997971552612343, 1.3461894783455084, 1.2360908316593335, 1.0766636473112665, 0.8765806789633224, 0.6456904489327913, 0.39464400246427295, 0.13449629884697742, -0.12370341051728914, -0.36931735437421576, -0.5925063262263631, -0.7845838157451792, -0.9383240316866437, -1.0482122787339734, -1.1106282255920492, -1.123955064781103, -1.088610330361699, -1.0069971088788112, -0.8833774413261621, -0.7236727535988337, -0.5351990512531279, -0.32634725535526776, -0.10622133072719708, 0.11575133152132581, 0.33022155040862833, 0.5283156267805017, 0.7020118574088631, 0.8444805519044354, 0.9503731172830905, 1.016047692592098, 1.0397212828394364, 1.0215412695989778, 0.9635724558289318, 0.8696993078973994, 0.7454466489747403, 0.5977255877429551, 0.4345147860353338, 0.26449013424542733, 0.09661838040649157, -0.0602678694844974, -0.19789519132625108, -0.3089554326943659, -0.3874742681199434, -0.42912485399347955, -0.43147121933090815, -0.39412875089054356, -0.31883247740060056, -0.20940770210568105, -0.07164172427430564, 0.08694024220985354, 0.25738748555232976, 0.42971291857584903, 0.5933435007253256, 0.7376133381418494, 0.8522783454899232, 0.9280297108165824, 0.9569827145297712, 0.933117777210906, 0.8526519679030272, 0.7143215697664769, 0.5195596036599193, 0.2725563389080725, -0.019804379169679753, -0.3481348716559672, -0.7008557737996968, -1.0646213400168556, -1.424843286876483, -1.7662936401238076, -2.073762825914627, -2.332745919549783, -2.530127715007802, -2.654836242117379, -2.698434623178936, -2.655622760774933, -2.5246232591994233, -2.3074301204939394, -2.0099039825363265, -1.6417037881793255, -1.21605155213612, -0.7493340501053707, -0.260552490333595, 0.22936177435137492, 0.6983409918312243, 1.1240541223654201, 1.484824766205477, 1.760556259265406, 1.9336247335044345, 1.9897010426602109, 1.918464265002202, 1.7141729862754447, 1.3760656360201657, 0.9085676238317018, 0.32129065606623125, -0.3711818936723584, -1.1497206840390397, -1.991275168036858, -2.8696765493457757, -3.7565898717878627, -4.622579035609321, -5.438242779795584, -6.175375596466236, -6.808105374806142, -7.31395945204812, -7.674812733897748, -7.877675599823856, -7.915285299527448, -7.7864722551501915, -7.496281806375914, -7.055842098654741, -6.4819795888780884, -5.796594561096224, -5.025819623449551, -4.198993917252413, -3.34749425776328, -2.5034712393589333, -1.6985431391366737, -0.9625029906801842, -0.32209432031302004, 0.2000913045337612, 0.5865465056141164, 0.8255686551198523, 0.9117362212356879, 0.8461188162817908, 0.636210440638927, 0.2955875879786723, -0.15669390121288287, -0.6969376391904412, -1.2978448867435406, -1.9297067859981654, -2.561698161239947, -3.1632156511734624, -3.705200754865515, -4.16138890468864, -4.509428922427395, -4.731823040773593, -4.816645829355679, -4.758010486420928], 'positive_zeros': ['0.64393734655484929276314974562098', '1.52403001673730540192208067005498', '2.53119302362181091539746295290852', '4.15432693126029565040611968430976', '5.30570493406639795529939528095230', '6.61961823223409538749833207147956', '7.47171687350699000105467933957704', '8.348259107127932925727677664373895', '9.293202732492577720141946441711930', '9.870987127299659834033128014257150'], 'prelabel': '2-315-1.1-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.73720096377615, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64393734655484929276314974562', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.52403001673730540192208067005', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.53119302362181091539746295291', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 162.2362883916201, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 315, 'conductor_radical': 105, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/315/10/a/e/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': '2-315-1.1-c9-0-23', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-315-1.1-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.73720096377615, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '0.64393734655484929276314974562', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '816287563869628074086370844754', 'Lhash_array': ['816287563869628074086370844754'], 'factors': ['2-315-1.1-c9-0-23'], 'label': '2-315-1.1-c9-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/315/10/a/e/1/1'}