Formats: - HTML - YAML - JSON - 2026-10-12T04:14:37.825255
  • lfunc_lfunctions • Show schema
    {'Lhash': '1952628232337892348485945382634', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.1056294689830015, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.461637640603379, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.777583477316366, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.635718998299005, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [37, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 37], 'central_character': '2960.1', 'coefficient_field': 'CDF', 'conductor': 2960, 'conductor_radical': 370, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.1056294689830015, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.461637640603379, 0], [7.0, 0]], [[1.0, 0], [1.7149699734608754, 0], [11.0, 0]], [[1.0, 0], [-6.492553450777241, 0], [13.0, 0]], [[1.0, 0], [-3.329796801728977, 0], [17.0, 0]], [[1.0, 0], [0.734567512188855, 0], [19.0, 0]], [[1.0, 0], [-2.086031930255022, 0], [23.0, 0]], [[1.0, 0], [4.2112589379660035, 0], [29.0, 0]], [[1.0, 0], [7.4645912708235, 0], [31.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.7149699734608754, 0], [41.0, 0]], [[1.0, 0], [1.8188486323815354, 0], [43.0, 0]], [[1.0, 0], [-0.88227037606335, 0], [47.0, 0]], [[1.0, 0], [7.030655560252101, 0], [53.0, 0]], [[1.0, 0], [0.3878665520302574, 0], [59.0, 0]], [[1.0, 0], [11.822350252506219, 0], [61.0, 0]], [[1.0, 0], [12.108583099203122, 0], [67.0, 0]], [[1.0, 0], [13.748579163933098, 0], [71.0, 0]], [[1.0, 0], [-16.671854445139854, 0], [73.0, 0]], [[1.0, 0], [8.232531973971737, 0], [79.0, 0]], [[1.0, 0], [-4.802752713778239, 0], [83.0, 0]], [[1.0, 0], [1.5250593842851934, 0], [89.0, 0]], [[1.0, 0], [18.158836198183202, 0], [97.0, 0]], [[1.0, 0], [15.074874345537392, 0], [101.0, 0]], [[1.0, 0], [11.850572682381722, 0], [103.0, 0]], [[1.0, 0], [7.589818278534481, 0], [107.0, 0]], [[1.0, 0], [4.297290868221025, 0], [109.0, 0]], [[1.0, 0], [4.9373864961445095, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 59, 'label': '2-2960-1.1-c1-0-59', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/2960/2/a/w/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [-1.0647190201965547e-60, 0.17980769490297935, 0.3591390476862358, 0.5374671731618921, 0.7141671817675659, 0.8884746353973907, 1.0594523023038507, 1.2259670008102852, 1.3866776709796802, 1.5400351790640971, 1.6842937972231447, 1.8175338413517363, 1.9376945996540396, 2.042616432610164, 2.1300907498929025, 2.1979164475916138, 2.243961298484819, 2.266226713509771, 2.26291422515688, 2.2324919806729913, 2.17375947710293, 2.085908727236971, 1.9685800233847641, 1.8219104732406672, 1.6465735273668285, 1.4438078084121313, 1.2154336939517438, 0.9638563016538676, 0.6920537790017312, 0.40355010925427964, 0.10237200745112489, -0.20701011072946351, -0.5197566568130519, -0.8307479879284134, -1.1346867185561669, -1.4262113365073876, -1.7000187572282885, -1.9509930058517162, -2.1743368213205274, -2.3657026487704167, -2.5213192418395707, -2.6381099509517387, -2.7137987401356383, -2.747000064136742, -2.737288956673637, -2.685248033053032, -2.5924885950253937, -2.461643637113212, -2.296331281186849, -2.101087994404403, -1.881271854609541, -1.6429370922897217, -1.3926821307066726, -1.1374743340742726, -0.8844556235992436, -0.6407339974592781, -0.4131667579163941, -0.20814187248358285, -0.03136434464779586, 0.11234528473607937, 0.2192331642482492, 0.28676816752132606, 0.3137652904442764, 0.3004706855080031, 0.24860357342909195, 0.16135146035225292, 0.043316473069368214, -0.09958783184423335, -0.2602881712482599, -0.4307490172645216, -0.6022113996871754, -0.7654669043105112, -0.9111591973102827, -1.0301040454750583, -1.1136176871986503, -1.153842594990428, -1.1440592043334639, -1.078972103408599, -0.9549595086941036, -0.7702756039822694, -0.5251964908899615, -0.22210206736513138, 0.13451191941111204, 0.5380951602674164, 0.980178444886759, 1.4505820868434904, 1.9376927897655278, 2.4288019459079266, 2.910495803978769, 3.3690856235734197, 3.791063949307007, 4.163571581269797, 4.474858770558947, 4.714723694488047, 4.874911411632007, 4.949457286092442, 4.934960303050531, 4.83077374812437, 4.639103339798335, 4.365006010722245, 4.01628603021933, 3.6032889267407167, 3.138597568588136, 2.6366386455628628, 2.11321150859635, 1.5849547139797107, 1.0687685348088027, 0.5812140085898537, 0.13791066935856613, -0.24704412747092364, -0.5616115019824798, -0.7962812173772903, -0.9444559067607854, -1.0027323469787106, -0.9710663445462188, -0.8528120355085604, -0.6546311471386776, -0.386272847061469, -0.06023001615214383, 0.30871708644631035, 0.7040539612026407, 1.1081616749608039, 1.5029995797304345, 1.870814445748954, 2.194847796516909, 2.460012650856173, 2.6535114868131005, 2.7653690555610657, 2.788856649700063, 2.720788476891343, 2.5616757641554533, 2.315729932571844, 1.9907124099990143, 1.5976351341952646, 1.1503222641036106, 0.6648497788179943, 0.1588852221148739, -0.3490454170795175, -0.8403330440745609, -1.2970699896998656, -1.7028097319208744, -2.04326832320071, -2.306936061840973, -2.4855714213171316, -2.574554059588398, -2.573079685164195, -2.484186414937313, -2.314609728405729, -2.074470875283931, -1.7768112776575533, -1.4369927261420141, -1.0719896543263578, -0.6996051661604763, -0.33764650860688517, -0.0030981057525924323, 0.2886690509550917, 0.5246140014427232, 0.6946336959541393, 0.7920320995057428, 0.8138266461880125, 0.7608756105346726, 0.6378183409678729, 0.45282923017733, 0.21719535952764424, -0.055263487910583206, -0.34890573204151953, -0.6470762327468035, -0.9329729127430704, -1.1905292678807875, -1.4052687407058748, -1.5650875560588373, -1.660925408397633, -1.6872882614429745, -1.6425942778447011, -1.5293222468740069, -1.353951441385335, -1.1266921605309033, -0.8610168010618422, -0.5730116205258678, -0.28057888308613305, -0.002527312343170257, 0.2424047326230821, 0.4365445629542111, 0.5642481599001877, 0.6127806338405207, 0.5730670378142139, 0.440272041203577, 0.214174831729566, -0.1006846202943107, -0.49510058809896795, -0.9555384383710522, -1.4647014153723275, -2.0023033761394813, -2.546012361445639, -3.0725203144406343, -3.55868677768545, -3.9826994464197942, -4.3251923474527985, -4.570263324818195, -4.706336467882227, -4.726821979201798, -4.630535457084994, -4.421850226520662, -4.110569632189744, -3.71152045051728, -3.2438830598943076, -2.7302879754962484, -2.195721063390098, -1.666290503009683, -1.167916760128965, -0.725011978508298, -0.3592169623172427, -0.08826214014277026, 0.07498640346618787, 0.12324336179634829, 0.05524218013076814, -0.12413244419140537, -0.40402896455665815, -0.768125255739001, -1.1954152364855797, -1.661248708901885, -2.138573372643624, -2.59931655254201, -3.01583590268767, -3.3623637174275487, -3.616368801970725, -3.7597632357996114, -3.779888686038414, -3.670227864128801, -3.4308007337643254, -3.068221459814161, -2.59540998387947, -2.030970571477709, -1.3982677008024658, -0.7242462627561949, -0.03805728764931436, 0.630438508698895, 1.2522098101962553, 1.800553883496534, 2.2524748348136394, 2.5898658953639466, 2.8004308645665987, 2.8782936979718694, 2.824262042827202, 2.6457293964449144, 2.356220460827053, 1.9746040885882765, 1.5240168460749637, 1.030556597368357, 0.5218186880977912, 0.025356499895389024, -0.43284720997390247, -0.8298119870463629, -1.1468132984434292, -1.3703867943958568, -1.4930258453194198, -1.513532311993172], 'positive_zeros': ['1.54035207492217391474610803279094', '2.95541622176358851952492277817259', '3.36780371711373686603880504702143', '4.14573447902541874753868418281611', '5.50161858650883499758728825204414', '6.00083453941299709470696651655735', '6.92206813233682959022221625954639', '7.82081141380022946289323497595279', '8.318229365740873942860938157247018'], 'prelabel': '2-2960-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.861658050325938, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54035207492217391474610803279', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.95541622176358851952492277817', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.36780371711373686603880504702', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 23.635718998299005, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 2960, 'conductor_radical': 370, 'degree': 2, 'index': 59, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2960/2/a/w/1/4'], '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': '2-2960-1.1-c1-0-59', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-2960-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.861658050325938, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54035207492217391474610803279', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1952628232337892348485945382634', 'Lhash_array': ['1952628232337892348485945382634'], 'factors': ['2-2960-1.1-c1-0-59'], 'label': '2-2960-1.1-c1-0-59', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2960/2/a/w/1/4'}