-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1268358584989751342259678227948', 'a10': [-1.0, 0.0], 'a2': [-1.0, 0.0], 'a3': [-2.20277972023846, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [2.20277972023846, 0.0], 'a7': [4.442050823002687, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.8522384958938278, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.02001121053345, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [401, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 401], 'central_character': '4010.1', 'coefficient_field': 'CDF', 'conductor': 4010, 'conductor_radical': 4010, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [2.20277972023846, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.442050823002687, 0], [7.0, 0]], [[1.0, 0], [-0.34189898393314894, 0], [11.0, 0]], [[1.0, 0], [-6.108897792020106, 0], [13.0, 0]], [[1.0, 0], [-0.4864263551442321, 0], [17.0, 0]], [[1.0, 0], [-2.786517596789669, 0], [19.0, 0]], [[1.0, 0], [-3.3996584859100962, 0], [23.0, 0]], [[1.0, 0], [1.5991656023640206, 0], [29.0, 0]], [[1.0, 0], [-9.524437158377635, 0], [31.0, 0]], [[1.0, 0], [-9.08138074800741, 0], [37.0, 0]], [[1.0, 0], [-4.490733907612155, 0], [41.0, 0]], [[1.0, 0], [6.875953524044484, 0], [43.0, 0]], [[1.0, 0], [6.250772303339395, 0], [47.0, 0]], [[1.0, 0], [7.039934882882776, 0], [53.0, 0]], [[1.0, 0], [-12.894946475392278, 0], [59.0, 0]], [[1.0, 0], [-9.077765870174066, 0], [61.0, 0]], [[1.0, 0], [6.614851496117766, 0], [67.0, 0]], [[1.0, 0], [1.8401640928985277, 0], [71.0, 0]], [[1.0, 0], [-3.991128691272271, 0], [73.0, 0]], [[1.0, 0], [-5.130814863837643, 0], [79.0, 0]], [[1.0, 0], [-12.928106394862933, 0], [83.0, 0]], [[1.0, 0], [7.2511128663793105, 0], [89.0, 0]], [[1.0, 0], [-3.4005997484458987, 0], [97.0, 0]], [[1.0, 0], [16.634664909133676, 0], [101.0, 0]], [[1.0, 0], [16.355931736171087, 0], [103.0, 0]], [[1.0, 0], [8.63850303716454, 0], [107.0, 0]], [[1.0, 0], [19.53103089902467, 0], [109.0, 0]], [[1.0, 0], [17.143321774603553, 0], [113.0, 0]], [[1.0, 0], [4.4397681277319405, 0], [127.0, 0]], [[1.0, 0], [-1.7363484697384701, 0], [131.0, 0]], [[1.0, 0], [-3.8787720152331775, 0], [137.0, 0]], [[1.0, 0], [-9.97186578458209, 0], [139.0, 0]], [[1.0, 0], [3.0215193291717393, 0], [149.0, 0]], [[1.0, 0], [23.12971476155988, 0], [151.0, 0]], [[1.0, 0], [-10.163854838105417, 0], [157.0, 0]], [[1.0, 0], [21.060687737674044, 0], [163.0, 0]], [[1.0, 0], [4.965107009118863, 0], [167.0, 0]], [[1.0, 0], [21.17195895739733, 0], [173.0, 0]], [[1.0, 0], [-15.772213447756688, 0], [179.0, 0]], [[1.0, 0], [-19.039633457480686, 0], [181.0, 0]], [[1.0, 0], [-25.49273035180748, 0], [191.0, 0]], [[1.0, 0], [7.626975493663066, 0], [193.0, 0]], [[1.0, 0], [8.774566154151714, 0], [197.0, 0]], [[1.0, 0], [7.587875540755198, 0], [199.0, 0]], [[1.0, 0], [6.5949285151602695, 0], [211.0, 0]], [[1.0, 0], [-10.12842219821761, 0], [223.0, 0]], [[1.0, 0], [-19.016571483847773, 0], [227.0, 0]], [[1.0, 0], [11.765621272592796, 0], [229.0, 0]], [[1.0, 0], [25.525593431385285, 0], [233.0, 0]], [[1.0, 0], [-12.162658137574997, 0], [239.0, 0]], [[1.0, 0], [-8.545701461980745, 0], [241.0, 0]], [[1.0, 0], [0.5241246770952415, 0], [251.0, 0]], [[1.0, 0], [23.811335832096535, 0], [257.0, 0]], [[1.0, 0], [27.69457705354146, 0], [263.0, 0]], [[1.0, 0], [-21.389836410261747, 0], [269.0, 0]], [[1.0, 0], [-27.76439617408553, 0], [271.0, 0]], [[1.0, 0], [-29.283008814132923, 0], [277.0, 0]], [[1.0, 0], [-4.291943200215995, 0], [281.0, 0]], [[1.0, 0], [15.39401104153757, 0], [283.0, 0]], [[1.0, 0], [7.454254764699583, 0], [293.0, 0]], [[1.0, 0], [9.342230553256433, 0], [307.0, 0]], [[1.0, 0], [-1.0116866761992327, 0], [311.0, 0]], [[1.0, 0], [16.996990420771144, 0], [313.0, 0]], [[1.0, 0], [-26.31343958368741, 0], [317.0, 0]], [[1.0, 0], [-18.298202066494003, 0], [331.0, 0]], [[1.0, 0], [-2.1815392984887927, 0], [337.0, 0]], [[1.0, 0], [-21.99180522195489, 0], [347.0, 0]], [[1.0, 0], [27.270808152848197, 0], [349.0, 0]], [[1.0, 0], [-19.673416019673486, 0], [353.0, 0]], [[1.0, 0], [-9.435996150064629, 0], [359.0, 0]], [[1.0, 0], [14.390222097260837, 0], [367.0, 0]], [[1.0, 0], [20.190196345525596, 0], [373.0, 0]], [[1.0, 0], [-35.9146318054433, 0], [379.0, 0]], [[1.0, 0], [-19.205480852225474, 0], [383.0, 0]], [[1.0, 0], [-0.8126138764320578, 0], [389.0, 0]], [[1.0, 0], [8.107769676693426, 0], [397.0, 0]], [[1.0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 55, 'label': '2-4010-1.1-c1-0-55', 'leading_term': '1.4698728143045434650333605686290', '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/4010/2/a/m/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.4698728143045434, 1.4651418135375776, 1.450933086640155, 1.427204919922055, 1.3939055853685738, 1.3509986574878916, 1.2984958555313557, 1.2364951279150724, 1.1652214294097443, 1.0850675670000627, 0.996632575605635, 0.9007552870287857, 0.7985410311796665, 0.6913797221186901, 0.5809539085137926, 0.4692356961010062, 0.35847177533813784, 0.2511561132915566, 0.1499902001462838, 0.05783108271152033, -0.022372226966719772, -0.08765301022854662, -0.1351104300896655, -0.16200072821617303, -0.16583393260857143, -0.1444736198500633, -0.09623695066446145, -0.019991920813052164, 0.08475144327561455, 0.21775934802289823, 0.378005399035528, 0.5636180480149965, 0.7718475167485748, 0.9990550917354517, 1.2407272557973774, 1.4915165733385385, 1.7453105801996902, 1.9953291586376123, 2.234250019143271, 2.454360984702399, 2.6477368053091443, 2.80643725064554, 2.92272226965614, 2.9892791024158916, 2.9994554185670927, 2.947491874015501, 2.8287469584597487, 2.6399066827851234, 2.3791715551959833, 2.046413440289388, 1.6432953011380622, 1.1733474976819858, 0.6419952529685022, 0.0565330898027019, -0.5739565382888264, -1.238741578905273, -1.925635058458082, -2.6212436110052915, -3.311265441446229, -3.9808314051558953, -4.614881075375151, -5.1985640204056836, -5.717655095132828, -6.158971432210455, -6.510778057501065, -6.763168702902463, -6.908408486428275, -6.941225698994265, -6.859040988223575, -6.662123752478888, -6.353667525503507, -5.939778497085498, -5.42937401354995, -4.83399085241599, -4.16750617242273, -3.445777195808124, -2.686208768512108, -1.9072608460891662, -1.1279105492375732, -0.3670856089394185, 0.3569123266105175, 1.0269750117326846, 1.6277256810007015, 2.1460083876504075, 2.571310224589167, 2.89609990788785, 3.116068759961627, 3.2302633169723265, 3.241102504147288, 3.154276449282089, 2.978528391793233, 2.725325627934662, 2.408429836304985, 2.043381270964953, 1.6469150144432063, 1.2363305820425956, 0.8288385125120061, 0.4409090438238872, 0.08764846366917937, -0.21777181334905468, -0.46460997043411234, -0.6449514381068346, -0.7539921256061013, -0.7901942484838962, -0.7553067899252568, -0.654248130697845, -0.4948541343328806, -0.287500740879425, -0.044615655401344725, 0.21990123167079623, 0.49132472204585975, 0.7547911119814477, 0.9959952535751299, 1.201867161469591, 1.361197734743894, 1.4651848059257226, 1.5078736980302316, 1.4864706729633261, 1.401512937858169, 1.2568850327175352, 1.0596781988160087, 0.8198964313146551, 0.5500200351845843, 0.2644443034607561, -0.02118290250026323, -0.2906956741286851, -0.5281836784967049, -0.7187693164045286, -0.8493518801146687, -0.9092828954330369, -0.8909392569192811, -0.7901648268912109, -0.6065567224602078, -0.3435793381267236, -0.008496954730304783, 0.38787577705629056, 0.8315975060644483, 1.3061815096237759, 1.793310247914101, 2.2736517476973046, 2.727740801610804, 3.136884004914056, 3.4840455788370774, 3.7546709007036747, 3.9374067319385473, 4.024681260136255, 4.013113101904379, 3.9037261018054092, 3.7019557725726338, 3.4174431406618546, 3.063622119923136, 2.657116830400246, 2.216974993887359, 1.7637721727362377, 1.3186287140899495, 0.9021864240733576, 0.5335949186068681, 0.22955807800260455, 0.003488988742918964, -0.1351827683154553, -0.1815144569572074, -0.1353359728667596, -0.0013003569482948267, 0.21130711927089596, 0.4889953382196382, 0.8147111870643472, 1.168671512366782, 1.5293437456153496, 1.8745275317498273, 2.182483758895367, 2.433054110402969, 2.608713864844483, 2.6955032345688354, 2.6837879835231218, 2.5688081711399384, 2.3509842565605137, 2.0359619625841052, 1.6343906324903552, 1.1614436310556848, 0.6361029192231007, 0.08024254336048366, -0.4824432647626376, -1.0276129966587952, -1.5314914942150892, -1.972061234119887, -2.3301687772524615, -2.590487821750684, -2.7422874317335406, -2.7799640105969945, -2.7033079464081475, -2.5174899358660245, -2.232767044493182, -1.86392376863666, -1.4294778905422354, -0.9506939452779004, -0.4504579009219557, 0.04792544280410672, 0.5219462905689096, 0.9510479974598948, 1.3176654861263561, 1.608086433038971, 1.813087587227332, 1.9283112599984396, 1.954361819946777, 1.8966181205783363, 1.7647742649693183, 1.572137021240887, 1.3347226081420767, 1.0702076061125818, 0.7967976728339676, 0.5320829791763744, 0.29195046342880543, 0.08961999292937033, -0.06513556758782363, -0.16653719807863504, -0.21307825238177464, -0.20751577026070117, -0.15657340516017154, -0.07037290864794363, 0.038371501045491356, 0.15534596812075627, 0.265754302753748, 0.3554878621537194, 0.41227121519092924, 0.42670657834089437, 0.39314459885912323, 0.31031829444431513, 0.18169038888997402, 0.015481194542039136, -0.17563636248323006, -0.37516712702299143, -0.5637210492497662, -0.7201891230702105, -0.8231020821460506, -0.8520920384579416, -0.7893677768802853, -0.6211101640551641, -0.3386955131329709, 0.060338141174253374, 0.5716543153120949, 1.1838658891034286, 1.878701014067729, 2.6315964489725316, 3.412702020992697, 4.188254380535728, 4.922254338482159, 5.578361341000599, 6.121902398027697, 6.521882154043463, 6.752876585149324, 6.796695472365571, 6.643708384449667, 6.293745036643542, 5.756502802954266, 5.051420708943086, 4.207008970218208, 3.2596543893505365], 'positive_zeros': ['1.00055850149985688035798482302378', '1.38194892723015730939017018320503', '2.69609939214764003429919628549875', '4.03706589955170101305681355099858', '4.99026939542691117513936730978034', '5.49315949264124443319860206528991', '6.29304502840498102690650731022689', '6.80585837460640262495244794630569', '8.024407031640501050439330226071609', '8.226938696757724384368434042798611'], 'prelabel': '2-4010-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.658622730888979, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00055850149985688035798482302', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.38194892723015730939017018321', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.69609939214764003429919628550', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 32.02001121053345, 'bad_primes': [2, 5, 401], 'central_character': '1.1', 'conductor': 4010, 'conductor_radical': 4010, 'degree': 2, 'index': 55, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4010/2/a/m/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': '2-4010-1.1-c1-0-55', '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': '2-4010-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.658622730888979, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00055850149985688035798482302', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1268358584989751342259678227948', 'Lhash_array': ['1268358584989751342259678227948'], 'label': '2-4010-1.1-c1-0-55', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4010/2/a/m/1/4'}