-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3147477756366530712251067020990', 'a10': [-4.949891850599323, 1.7892800255561887], 'a2': [-1.081346185694727, -0.9114222000168007], 'a3': [-0.3166809768890286, -1.702854415056264], 'a4': [0.3386191466330699, 1.971125839091328], 'a5': [1.860878567454226, -3.2231362255467078], 'a6': [-1.2095775508378712, 2.1300051991741844], 'a7': [2.4642858405443335, 0.9629617313749844], 'a8': [1.4303633261597068, -2.4400944152178496], 'a9': [-2.799426317753221, 1.078523199319626], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.081346185694727, 0.9114222000168007]]], [3, [[1.0, 0], [0.3166809768890286, 1.702854415056264]]], [7, [[1.0, 0], [-2.4642858405443335, -0.9629617313749844]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.107', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': '1507684890109063907781371865857', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.081346185694727, 0.9114222000168007]], [[1.0, 0], [0.3166809768890286, 1.702854415056264]], [[1.0, 0], [-1.860878567454226, 3.2231362255467078], [-2.5, -4.330127018922194]], [[1.0, 0], [-2.4642858405443335, -0.9629617313749844]], [[1.0, 0], [2.269579992658392, -1.3103426197087116], [5.5, -9.526279441628825]], [[1.0, 0], [0, 3.5718217093398934], [-13.0, 0]], [[1.0, 0], [-0.18619196821462525, 0.10749798296966014], [8.5, -14.722431864335457]], [[1.0, 0], [1.1410257822211016, -1.976314627552969], [-9.5, -16.454482671904334]], [[1.0, 0], [2.3358629411319827, -4.045833293557863], [-11.5, -19.91858428704209]], [[1.0, 0], [-2.574151608273319, 0], [29.0, 0]], [[1.0, 0], [-4.2619615297069195, 2.4606446364521193], [15.5, -26.846787517317598]], [[1.0, 0], [-7.3110366247005985, -4.221028963326104], [18.5, 32.04293994002423]], [[1.0, 0], [0, 0.9094422919658944], [-41.0, 0]], [[1.0, 0], [-3.7354075181250725, 0], [43.0, 0]], [[1.0, 0], [0.5867281525269831, -1.0162429704077565], [-23.5, -40.703193977868615]], [[1.0, 0], [1.0617125262047398, 1.8389400384189123], [-26.5, 45.89934640057525]], [[1.0, 0], [6.791991205782294, -3.921357950991978], [29.5, -51.09549882328188]], [[1.0, 0], [0.3013008387611336, 0.17395612036580052], [30.5, 52.827549630850754]], [[1.0, 0], [4.9873573362838926, 8.63835630194508], [-33.5, 58.023702053557386]], [[1.0, 0], [-10.080763772444863, 0], [71.0, 0]], [[1.0, 0], [-4.4517300852338755, -7.710622689208002], [-36.5, 63.21985447626402]], [[1.0, 0], [9.70950420920097, 5.605784868879985], [39.5, 68.41600689897065]], [[1.0, 0], [0, -1.7393699147748416], [-83.0, 0]], [[1.0, 0], [-15.469405849491311, -8.93126563140738], [44.5, 77.07626093681505]], [[1.0, 0], [8.885528749861153, 0], [97.0, 0]], [[1.0, 0], [7.387211396952733, 12.795025465773994], [-50.5, 87.4685657822283]], [[1.0, 0], [-6.5015106887828935, -3.753648946308033], [51.5, 89.20061658979718]], [[1.0, 0], [-10.939581173159091, -6.315970135145163], [53.5, 92.66471820493493]], [[1.0, 0], [11.227484072562959, -6.48219095161646], [54.5, -94.39676901250381]], [[1.0, 0], [0, -7.1049771084283355], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 20, 'label': '2-168-168.107-c1-0-20', '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/168/2/v/a/107/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8648242021227089, 0.955751418106856, 1.0589466189915213, 1.1755008877377915, 1.304807455388992, 1.4445264907928994, 1.5906469644168157, 1.7375892995268256, 1.8783301905678478, 2.0045622365117093, 2.1069153588270573, 2.1752671385485804, 2.199161146534045, 2.1683403263447087, 2.073388698255656, 1.9064601157919578, 1.6620582433355124, 1.3378181823148787, 0.9352283650292841, 0.4602227987652593, -0.07643007828141782, -0.6590134015688557, -1.2670847641165033, -1.8760807384812368, -2.458322783856375, -2.9844124079475147, -3.4249665183655345, -3.7526046390941192, -3.9440616356651574, -3.982266930276171, -3.858208280903097, -3.572389224995547, -3.1356976992717365, -2.5695313243962743, -1.9050728020357122, -1.181675076183002, -0.4443962756045449, 0.25918740532037704, 0.8826751593933121, 1.3847482854492426, 1.732940051130936, 1.9068911165079998, 1.9007223860525397, 1.7242076343846644, 1.4025196558160593, 0.9744510519509844, 0.48916412412617155, 0.0016891828514273017, -0.4324509568071355, -0.7629799709133497, -0.9503724516166191, -0.9704985947231755, -0.8178277831030248, -0.5067270491879344, -0.07057496032515305, 0.44135243107259714, 0.9690034393535405, 1.4481998706250292, 1.818109146592423, 2.028680544021906, 2.0471280888078556, 1.8625970711105992, 1.4883221463369476, 0.9608606759944289, 0.3363379171279339, -0.31596997957183476, -0.9220134852631634, -1.4122970435961977, -1.7309521651030495, -1.8433115200151493, -1.7408702394788493, -1.442819069520153, -0.9937710636646527, -0.45782727969268866, 0.09033200894535089, 0.5761642030148397, 0.9362807579756245, 1.1281125946511212, 1.1366706846345356, 0.9771882069205647, 0.6929829025211782, 0.34857530102170986, 0.018844771598143448, -0.22431089778943106, -0.32583737363575027, -0.25969163769167836, -0.037189202626712464, 0.2901641655356847, 0.6343158006654044, 0.8807964746846143, 0.9043221954789219, 0.5879012712095312, -0.15723622612653687, -1.373919579802085, -3.0464613243296, -5.0955859787644195, -7.382241984232564, -9.720404739291014, -11.897603884072765, -13.700641459621316, -14.94301894835771, -15.490132533871623, -15.278430470067276, -14.325466851598852, -12.729046214945289, -10.655256483743264, -8.316890400018282, -5.94528478338572, -3.7597047127458487, -1.9388677049891845, -0.5989396913813598, 0.21864206468387332, 0.5477138388208728, 0.4863718490560674, 0.17637184770939146, -0.22349451384237146, -0.5654797384005269, -0.7376240633978715, -0.6809772462225686, -0.3964635380683382, 0.05957971171653206, 0.5901066240154986, 1.0793587749738094, 1.4178642952574552, 1.5256055404831812, 1.3688817899901065, 0.9676100257069402, 0.39166264101903386, -0.2530094990620044, -0.8456891254456861, -1.2753487538845705, -1.4632790578382577, -1.3792231055226989, -1.0476065158030174, -0.5424329235238454, 0.028265086109047842, 0.5453315003211223, 0.9040418089013083, 1.036914650041131, 0.9288108302788292, 0.6208356487896473, 0.2018376820621769, -0.21108054099661985, -0.499196088977183, -0.5703873425582769, -0.38278757905143196, 0.04159469818462336, 0.6168564970814291, 1.2075917015781676, 1.6554286372884308, 1.8126994510595493, 1.576404274732531, 0.9151744613436471, -0.11698710607095175, -1.3839540266922323, -2.688090496530349, -3.804963960349852, -4.525747702336822, -4.698960395484982, -4.262912892528945, -3.261761325822448, -1.8411589407210687, -0.22357085796710327, 1.3324555243879859, 2.581277882709348, 3.3376305318341757, 3.512808322056953, 3.131855722542262, 2.327815862608285, 1.3138083281391644, 0.33839282013735333, -0.36666878820449283, -0.635335258770421, -0.4024679922148159, 0.28240787211654717, 1.2659768573193304, 2.3245930964674155, 3.213349584163612, 3.7202688812741855, 3.7138393872977233, 3.1733903687839127, 2.1954021235260033, 0.9740382754527298, -0.24015274541330803, -1.194539168536531, -1.6898831062266861, -1.624752402811005, -1.0189343501579258, -0.010475068582134595, 1.173218012991313, 2.2639958031600615, 3.01065985417326, 3.2330061169354343, 2.8602846251133296, 1.9456282106390597, 0.6534164589052187, -0.7773526291574056, -2.0852152435748335, -3.0420160256156925, -3.4997286800691216, -3.4179940023131787, -2.866680541850981, -2.0036945013325282, -1.0340617621088104, -0.16058887601826716, 0.46184481482351497, 0.7575171241037975, 0.7396151485949963, 0.4970366138967914, 0.1625914685141887, -0.12838881900107874, -0.2777182810192255, -0.25161781154815716, -0.08831477741499999, 0.11592732160922416, 0.23836693998045974, 0.17005943176944768, -0.14659570790255144, -0.6940028599716792, -1.3767024944462192, -2.0417399306252655, -2.5175702479377993, -2.661611267659694, -2.4036208505519263, -1.7724850768138332, -0.8978026317763125, 0.016016980115687612, 0.7381228196744748, 1.0706652392883236, 0.9042070824654365, 0.2540750973733054, -0.7333305783418688, -1.8080838776429795, -2.6733694748835166, -3.058600152946327, -2.7913773773444808, -1.8498819013162024, -0.38117111452163605, 1.321352930815648, 2.8781575713009784, 3.908763191326311, 4.122369494591569, 3.392162808794039, 1.7946246070062188, -0.39702290407701185, -2.7653452240011807, -4.836209874713357, -6.181603214448113, -6.513990015023428, -5.750102538281264, -4.029103293392909, -1.6808577135613736, 0.8480586608843648, 3.092952310838201, 4.670843358812597, 5.358246957578021, 5.12940758502776], 'positive_zeros': ['2.48292215205030067080449501258464', '4.57771176980769641060157664816206', '5.87544951932867539235078281889577', '6.76805200593296253757888815066436', '8.064222955752319188805761027704446', '9.228849140898261695399617931767626', '10.25799557357893264773690195596735', '10.76584201224148666908589572308023', '11.47905773056194335280447355592246', '13.83272826996324416191002409090610'], 'prelabel': '2-168-168.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.7086460425274174, 'root_number': '-0.6095405293340066 + 0.7927549073321584*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.354323021264', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.48292215205030067080449501258', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.57771176980769641060157664816', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.87544951932867539235078281890', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.107', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/v/a/107/6'], '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': '2-168-168.107-c1-0-20', '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': '2-168-168.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.3543230212637087, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.48292215205030067080449501258', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3147477756366530712251067020990', 'Lhash_array': ['3147477756366530712251067020990'], 'label': '2-168-168.107-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/v/a/107/6'}