-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1525274155278225439104336608743', 'a10': [-3.146949601254041, 0.0], 'a2': [-1.0, 0.0], 'a3': [3.2960938535240034, 0.0], 'a4': [1.0, 0.0], 'a5': [3.146949601254041, 0.0], 'a6': [-3.2960938535240034, 0.0], 'a7': [1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [7.864234691238713, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.18173257964061, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [431, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7, 431], 'central_character': '6034.1', 'coefficient_field': 'CDF', 'conductor': 6034, 'conductor_radical': 6034, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.2960938535240034, 0], [3.0, 0]], [[1.0, 0], [-3.146949601254041, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.2628144562937385, 0], [11.0, 0]], [[1.0, 0], [-2.3233637569177157, 0], [13.0, 0]], [[1.0, 0], [2.6622059551838624, 0], [17.0, 0]], [[1.0, 0], [-1.7207803593071582, 0], [19.0, 0]], [[1.0, 0], [-0.41816187365312807, 0], [23.0, 0]], [[1.0, 0], [0.843223649320898, 0], [29.0, 0]], [[1.0, 0], [-3.4107859766864013, 0], [31.0, 0]], [[1.0, 0], [-1.578411010827403, 0], [37.0, 0]], [[1.0, 0], [1.8048554069115055, 0], [41.0, 0]], [[1.0, 0], [3.204191340233448, 0], [43.0, 0]], [[1.0, 0], [-7.379000655048247, 0], [47.0, 0]], [[1.0, 0], [-6.871659860577507, 0], [53.0, 0]], [[1.0, 0], [-9.124182440648903, 0], [59.0, 0]], [[1.0, 0], [11.771936424463783, 0], [61.0, 0]], [[1.0, 0], [5.917922937948552, 0], [67.0, 0]], [[1.0, 0], [7.232711338735386, 0], [71.0, 0]], [[1.0, 0], [-5.952428772347181, 0], [73.0, 0]], [[1.0, 0], [8.195132843297413, 0], [79.0, 0]], [[1.0, 0], [-13.596643646813936, 0], [83.0, 0]], [[1.0, 0], [5.785468402442322, 0], [89.0, 0]], [[1.0, 0], [10.653510665273052, 0], [97.0, 0]], [[1.0, 0], [-4.174526336978972, 0], [101.0, 0]], [[1.0, 0], [-4.537637157120172, 0], [103.0, 0]], [[1.0, 0], [-11.965389926802127, 0], [107.0, 0]], [[1.0, 0], [16.926422139138033, 0], [109.0, 0]], [[1.0, 0], [-14.104599740525954, 0], [113.0, 0]], [[1.0, 0], [12.58261023457179, 0], [127.0, 0]], [[1.0, 0], [-2.4182193170117157, 0], [131.0, 0]], [[1.0, 0], [-10.650908489593256, 0], [137.0, 0]], [[1.0, 0], [11.723545112069994, 0], [139.0, 0]], [[1.0, 0], [-15.67689704105909, 0], [149.0, 0]], [[1.0, 0], [-10.057392917951308, 0], [151.0, 0]], [[1.0, 0], [-1.5988729840012965, 0], [157.0, 0]], [[1.0, 0], [9.363943642495986, 0], [163.0, 0]], [[1.0, 0], [12.95603009436494, 0], [167.0, 0]], [[1.0, 0], [0.9257157532140307, 0], [173.0, 0]], [[1.0, 0], [10.697048993833272, 0], [179.0, 0]], [[1.0, 0], [-21.449453407305022, 0], [181.0, 0]], [[1.0, 0], [-1.7666900178373228, 0], [191.0, 0]], [[1.0, 0], [-5.331264819875963, 0], [193.0, 0]], [[1.0, 0], [7.995615428959391, 0], [197.0, 0]], [[1.0, 0], [13.734706029478627, 0], [199.0, 0]], [[1.0, 0], [8.926603041777096, 0], [211.0, 0]], [[1.0, 0], [-23.109527751732873, 0], [223.0, 0]], [[1.0, 0], [-3.8902199341962658, 0], [227.0, 0]], [[1.0, 0], [9.058739905605535, 0], [229.0, 0]], [[1.0, 0], [-11.207376447225565, 0], [233.0, 0]], [[1.0, 0], [16.27425513751138, 0], [239.0, 0]], [[1.0, 0], [-3.080911203279314, 0], [241.0, 0]], [[1.0, 0], [-25.888784038867616, 0], [251.0, 0]], [[1.0, 0], [29.44860125159275, 0], [257.0, 0]], [[1.0, 0], [-7.35366122596752, 0], [263.0, 0]], [[1.0, 0], [-10.610880171284991, 0], [269.0, 0]], [[1.0, 0], [13.847314975348405, 0], [271.0, 0]], [[1.0, 0], [30.595860705768654, 0], [277.0, 0]], [[1.0, 0], [18.539797027916045, 0], [281.0, 0]], [[1.0, 0], [-16.27752662474285, 0], [283.0, 0]], [[1.0, 0], [4.429776156866012, 0], [293.0, 0]], [[1.0, 0], [1.2106548263530623, 0], [307.0, 0]], [[1.0, 0], [-1.4626886497325606, 0], [311.0, 0]], [[1.0, 0], [17.630492505732413, 0], [313.0, 0]], [[1.0, 0], [15.162609015673917, 0], [317.0, 0]], [[1.0, 0], [-19.559728491466107, 0], [331.0, 0]], [[1.0, 0], [18.03861025383528, 0], [337.0, 0]], [[1.0, 0], [-18.193460338747727, 0], [347.0, 0]], [[1.0, 0], [22.18213633698278, 0], [349.0, 0]], [[1.0, 0], [27.13313954152364, 0], [353.0, 0]], [[1.0, 0], [12.068196475768865, 0], [359.0, 0]], [[1.0, 0], [-23.946863491183, 0], [367.0, 0]], [[1.0, 0], [2.562220545426584, 0], [373.0, 0]], [[1.0, 0], [-13.231174257309776, 0], [379.0, 0]], [[1.0, 0], [10.33492057544896, 0], [383.0, 0]], [[1.0, 0], [-15.417172390008986, 0], [389.0, 0]], [[1.0, 0], [4.675070375335636, 0], [397.0, 0]], [[1.0, 0], [-14.536704524530325, 0], [401.0, 0]], [[1.0, 0], [-16.113952843442572, 0], [409.0, 0]], [[1.0, 0], [22.2709592008013, 0], [419.0, 0]], [[1.0, 0], [10.12230530169499, 0], [421.0, 0]], [[1.0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 132, 'label': '2-6034-1.1-c1-0-132', 'leading_term': '4.28446183801163072309673094272', '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/6034/2/a/p/1/27', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [4.284461838011631, 4.2762057228321275, 4.2513435186843385, 4.209604055597212, 4.150569299003388, 4.073722614623916, 3.978511426780983, 3.8644200036655687, 3.7310476647594197, 3.578187649564932, 3.4059021444352813, 3.2145894437833915, 3.005039831301903, 2.7784774303066357, 2.5365859381226983, 2.281516799800764, 2.015878982809037, 1.742710090395746, 1.4654291062334563, 1.1877716059636263, 0.9137088080117898, 0.6473523667176404, 0.3928473295707108, 0.15425617568427571, -0.06456269153557573, -0.2600782276945584, -0.42920772022212145, -0.5694311494758135, -0.6788945446038912, -0.7564979887907478, -0.8019641314219285, -0.8158834317306302, -0.7997328930957576, -0.7558657461616778, -0.6874703919534809, -0.5984979053165331, -0.49355849903084276, -0.37778852747539404, -0.25669082698984785, -0.13595240397879838, -0.02124464318798772, 0.08198773305538738, 0.16874181947690506, 0.2346679601592259, 0.2762691700581877, 0.29108009312943167, 0.2778171993938304, 0.23649241781071512, 0.1684832442934233, 0.07655354924253086, -0.035179183400914735, -0.1613326584255949, -0.2954050530481945, -0.4299750157990989, -0.5569523108830742, -0.6678727244754156, -0.7542286194446193, -0.807824477118491, -0.8211449973128941, -0.7877219352338679, -0.7024849219070576, -0.5620811165250251, -0.3651487305926998, -0.11253028032324827, 0.19258712314264118, 0.5446150611737283, 0.9355986337063968, 1.3553476208361672, 1.7916652000814859, 2.2306715713246934, 2.6572158243335644, 3.0553653764185498, 3.408958479451734, 3.7022018192994337, 3.9202922763771304, 4.050039642040344, 4.080465631495896, 4.003354013140961, 3.813727166907181, 3.510225931678522, 3.0953722023565535, 2.5756973429754293, 1.9617239990505666, 1.2677941802976693, 0.5117423622038272, -0.2855813965587386, -1.1009269513338025, -1.909380583823329, -2.6851991181749217, -3.4027131077453134, -4.037266384694644, -4.566156265286713, -4.969537068643851, -5.23124947371308, -5.339539686652416, -5.287635430646714, -5.074150343789722, -4.703294348215679, -4.184874736155957, -3.5340808436648152, -2.771053933577376, -1.9202529265058246, -1.0096355150812366, -0.0696825736135107, 0.8676987590927098, 1.7703517586755202, 2.6070804051310414, 3.3488444120115552, 3.9698894548940626, 4.448764543984219, 4.769182128809796, 4.920682229597014, 4.899069466298815, 4.706601014735886, 4.3519138886091095, 3.8496910858527813, 3.2200775570107174, 2.4878681323828897, 1.681499959261759, 0.8318911468097058, -0.028825264180628002, -0.8686175849953043, -1.656864703452387, -2.3656006484889835, -2.9706392785657476, -3.4525288750884573, -3.797293845003174, -3.9969302741148325, -4.0496333023050886, -3.959746698346647, -3.7374380103481695, -3.398115630884729, -2.961616405092104, -2.451203407809865, -1.892422657579663, -1.3118743394961214, -0.7359582041474578, -0.1896539565729366, 0.30460444499562583, 0.7279065327242092, 1.0656486981522824, 1.308086793540792, 1.4506334922946942, 1.4938891459736985, 1.4434086952263676, 1.3092208963387815, 1.1051289852966049, 0.8478332237785897, 0.5559249363194116, 0.2488081437911464, -0.05439164693754327, -0.335871734040842, -0.5800929110595369, -0.7745660934540182, -0.9104434481050642, -0.9828839465418926, -0.991176316529196, -0.9386163913127266, -0.832150057456521, -0.6818065663129744, -0.4999591120588745, -0.3004595740430733, -0.09770157082385172, 0.0943299723520817, 0.26296395056090693, 0.3976470505768241, 0.4905970503079156, 0.5372653108939928, 0.5365802211943379, 0.4909570707789039, 0.4060745503116893, 0.29043291705588686, 0.15472290451605003, 0.011046816937667911, -0.12795686451945318, -0.25002728605299884, -0.34417222119369606, -0.4014757941876625, -0.4157671056149321, -0.3841022847377049, -0.3070240825621513, -0.1885772873599217, -0.03607414565079021, 0.14037936986052918, 0.32856923859345905, 0.5150287986697409, 0.686009011975435, 0.8284993102111694, 0.9312292857402537, 0.9855804565265501, 0.9863409323518569, 0.9322439594759838, 0.8262436497555924, 0.675497055865871, 0.49104023757365106, 0.28716597739030497, 0.08053111388034058, -0.11095922873348467, -0.26942620433577485, -0.3783727193650586, -0.42403282647595175, -0.3966241589922129, -0.29141431825806857, -0.10951970763582383, 0.14163156817349584, 0.4482230581991769, 0.7903878361944756, 1.14296432087251, 1.476647326680004, 1.759485733721528, 1.9586541579144474, 2.042405448399113, 1.9820951495152217, 1.7541593991753528, 1.3419249221769411, 0.7371342490077836, -0.058918954021091735, -1.034730970567137, -2.168467532717452, -3.4284145383663995, -4.774000555583936, -6.157358247773877, -7.525359206718624, -8.822026818588599, -9.991206598141071, -10.979354566621483, -11.73829303874144, -12.227780513382386, -12.417748624815857, -12.290074165643373, -11.839777359348725, -11.075567648130907, -10.019693629017077, -8.707092416828242, -7.1838733905897945, -5.505209633561528, -3.732745081744374, -1.9316543042445466, -0.16751311810053576, 1.4968495087371771, 3.0043454587631166, 4.306302381915848, 5.364672184726813, 6.153652262696292, 6.660632512830432, 6.886420387472221, 6.844738483196733, 6.561031835437798, 6.070662590990848, 5.4166055463695315, 4.646786930015184, 3.811228946259815, 2.959172701561626, 2.136351537322742, 1.3825755119801768, 0.7297665027518786, 0.20055347264494186], 'positive_zeros': ['1.20322915084299504149175918770662', '2.04117581154431352376306226047251', '2.52388222844128850789058557749638', '3.21894289708719948978544865308883', '4.29842809868791268028321441119983', '5.23421754139134466506513283948217', '6.09203970699223323983966679437630', '6.97578199678981155707897643732373', '7.60788941211081337591961163307579', '8.251824503709500556548704964443667'], 'prelabel': '2-6034-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.9413062588853265, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.20322915084299504149175918771', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.04117581154431352376306226047', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.52388222844128850789058557750', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 48.18173257964061, 'bad_primes': [2, 7, 431], 'central_character': '1.1', 'conductor': 6034, 'conductor_radical': 6034, 'degree': 2, 'index': 132, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6034/2/a/p/1/27'], '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': '2-6034-1.1-c1-0-132', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-6034-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.9413062588853265, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20322915084299504149175918771', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1525274155278225439104336608743', 'Lhash_array': ['1525274155278225439104336608743'], 'label': '2-6034-1.1-c1-0-132', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6034/2/a/p/1/27'}