-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '519173951206083099278610085273', 'a10': [0.0, 0.0], 'a2': [0.0, 1.0], 'a3': [0.0, 0.0], 'a4': [-1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, -1.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.247662531582506, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '2500.2499', 'coefficient_field': 'CDF', 'conductor': 2500, 'conductor_radical': 10, 'conjugate': '2125557604926748902578127669220', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, -1.618033988749895], [-1.0, 0]], [[1.0, 0], [0, -0.6180339887498949], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, -0.6180339887498949], [-1.0, 0]], [[1.0, 0], [1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, -1.618033988749895], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, -1.618033988749895], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [0, -0.6180339887498949], [-1.0, 0]], [[1.0, 0], [-0.6180339887498949, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-1.618033988749895, 0], [1.0, 0]], [[1.0, 0], [0, 0.6180339887498949], [-1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-50e2-20.19-c0-0-0', 'leading_term': '0.62735219989083288997711211651378', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2500/1/d/a/2499/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.6273521998908329, 0.5524099930926386, 0.480571300231423, 0.409673794268994, 0.33763009161384316, 0.26258067875877916, 0.18300286526741583, 0.09777326126996246, 0.006191505550974229, -0.09202306595544901, -0.19675090584336438, -0.30749995514930994, -0.4234368251444452, -0.5434192526067373, -0.6660292588583738, -0.7896073335840939, -0.9122883310591706, -1.0320398063362661, -1.1467033733488545, -1.254039426077898, -1.3517752819067197, -1.4376565142421316, -1.5095009574222886, -1.5652546018162974, -1.6030483582918114, -1.6212544647318263, -1.6185411381919161, -1.5939239494504536, -1.5468123166696233, -1.477049485772903, -1.384944390412708, -1.2712938665840883, -1.137393837380889, -0.9850382819957784, -0.8165050580892913, -0.6345279545310404, -0.4422547067567524, -0.2431911021269725, -0.04113172831982492, 0.15992163728096098, 0.3558525478836854, 0.5425314243747726, 0.7159237957074776, 0.872202547291307, 1.007861154901957, 1.1198246244955936, 1.205554685583256, 1.2631457102318235, 1.2914078618106926, 1.2899341250069427, 1.2591481357832526, 1.20033011749265, 1.1156187338288306, 1.0079872828835983, 0.8811933670829143, 0.739701964597362, 0.5885826782547842, 0.43338282357093666, 0.2799789106424048, 0.13440994527006828, 0.0026967912143792336, -0.10934743418534804, -0.19631034618044532, -0.2533706105506161, -0.2764792522733255, -0.2625255195276013, -0.20948098706200627, -0.11651592690029826, 0.015917453735548953, 0.18603951204980854, 0.39073900570532744, 0.6256126691037038, 0.8850495794172567, 1.162359885897998, 1.449945923083056, 1.739512149282221, 2.0223088011850052, 2.2894026912448173, 2.531967255065054, 2.7415828382567216, 2.910537349401003, 3.032116845125617, 3.1008753940450555, 3.1128737174077625, 3.0658766427777846, 2.959500336609579, 2.7953015914048214, 2.576803107590917, 2.3094506887404065, 2.000500506352069, 1.658837019114852, 1.2947246720233003, 0.9194990645771156, 0.5452057701203784, 0.18419731284921176, -0.151299131423948, -0.449629042043781, -0.7001573370848918, -0.8936983530418315, -1.0229125579614362, -1.0826539584284232, -1.0702532048388638, -0.9857230571125318, -0.8318751130331797, -0.6143394681527601, -0.34148219064637453, -0.02421905609930982, 0.32427222335976846, 0.6889351582231434, 1.053303080072416, 1.4000396001145945, 1.7115340693549406, 1.9705323970464868, 2.160781424112605, 2.267663625630983, 2.278798319743812, 2.1845858495283914, 1.9786724070793313, 1.6583152779400196, 1.2246312552933976, 0.6827147268508247, 0.04161635825033092, -0.6858217616255845, -1.4832733594592422, -2.331371006055349, -3.20827295725592, -4.090336719784485, -4.952877630761873, -5.77098680402994, -6.520379731022211, -7.178244782321961, -7.724059955912901, -8.140346534852672, -8.413329878993828, -8.533480360633876, -8.49591138964961, -8.300616436791126, -7.95253278467846, -7.4614262036588626, -6.841597619158506, -6.111419838886622, -5.292719258462893, -4.410023876425394, -3.489704647402317, -2.5590419305109857, -1.6452523272110644, -0.7745133713527879, 0.028975790393259204, 0.7438604714054973, 1.3523884535530921, 1.841029041426074, 2.2009275566321445, 2.428176111418278, 2.523888856365441, 2.4940778667391656, 2.3493340861237884, 2.10432593380692, 1.777135948330818, 1.3884628384541153, 0.9607222253950304, 0.5170839087296107, 0.08048644947461202, -0.32732891937121245, -0.6867236543833908, -0.980967573028584, -1.1969100580294632, -1.3254877897328794, -1.362047122494451, -1.3064673888836091, -1.163080273869502, -0.9403895557112769, -0.6506045459999199, -0.30900906137043205, 0.06680467527774153, 0.4578015379121598, 0.8444280750121443, 1.2075530100287857, 1.5293796871416676, 1.794287717168783, 1.9895643343761886, 2.105991122587713, 2.1382585840472133, 2.0851891990118627, 1.9497587798988718, 1.7389156296411437, 1.4632068052719212, 1.1362301891840956, 0.7739396186587424, 0.39383759097533766, 0.014095675538005573, -0.3473535687573754, -0.6737078554944905, -0.9501250270599588, -1.1644498854340954, -1.307801452048902, -1.3749910618977361, -1.3647501923720102, -1.2797565528727972, -1.1264572392713483, -0.9146981698187535, -0.6571790338714141, -0.3687620823304194, -0.06567078929241708, 0.23537969634514563, 0.5180746391984494, 0.7673672820410694, 0.9702758878755061, 1.1165677564022836, 1.199293483868025, 1.2151425061590833, 1.1646003476868254, 1.0518985146668705, 0.884759074771595, 0.6739470699295507, 0.432654420003744, 0.17574831924114642, -0.08107521480277084, -0.3221864459218834, -0.532916402679155, -0.7004010407471835, -0.8143276769611899, -0.8675412131767167, -0.856474995976928, -0.781380523508662, -0.64634112978228, -0.45906667219341757, -0.23047847813979228, 0.02589430052278358, 0.29467488662644736, 0.5595143279428128, 0.8040338024770904, 1.0127808939049918, 1.1721453659221004, 1.271181422168358, 1.3022879149029933, 1.26170526560149, 1.1497976266448762, 0.971100541868371, 0.7341274305764817, 0.45094191175330695, 0.1365165391220293, -0.19208883871034138, -0.5166848830124645, -0.8189938369430954, -1.0817151317158396, -1.2895542047656676, -1.4301540836469222, -1.4948736563964429, -1.4793642350182232, -1.3839066579772379, -1.213484227238206, -0.9775815418934461, -0.6897149654435916, -0.3667161675168635, -0.027805010488870865, 0.3064988675118101, 0.6155658850331122], 'positive_zeros': ['0.40955603311560012748092629782442', '1.94002225091826912362541592744902', '3.04799198685759782132689532728113', '3.44772444460552869119794460845191', '4.80072268899660433167958533506146', '5.38646890034592018374366773566819', '6.14759707981169934111053193585964', '7.46291817633939127720709648844785', '8.185448202910269074359029374343739', '8.776350118443228123755010972835300'], 'prelabel': '2-50e2-20.19-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1169881519436569, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.40955603311560012748092629782', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.94002225091826912362541592745', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.04799198685759782132689532728', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.247662531582506, 'bad_primes': [2, 5], 'central_character': '20.19', 'conductor': 2500, 'conductor_radical': 10, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2500/1/d/a/2499/4'], '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': '2-50e2-20.19-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-50e2-20.19-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1169881519436569, 'root_angle': 0.5, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.40955603311560012748092629782', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '519173951206083099278610085273', 'Lhash_array': ['519173951206083099278610085273'], 'label': '2-50e2-20.19-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2500/1/d/a/2499/4'}