-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1935883325685889123895368899205', 'a10': [1.2282108452946385, 0.33687595970290884], 'a2': [0.5203180405687134, 0.23166051714472186], 'a3': [-1.625889883464084, 0.5970612086286861], 'a4': [-1.121196944580211, -1.2452153582390355], 'a5': [2.2105633092307926, -0.33676379835517933], 'a6': [-0.9842953467025001, -0.06599277305039548], 'a7': [1.5887164178523998, 2.751737554539183], 'a8': [-0.6469185862527567, -1.9910106828027985], 'a9': [2.287035826301705, -1.9415115578364393], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.625889883464084, -0.5970612086286861]]], [5, [[1.0, 0], [-2.2105633092307926, 0.33676379835517933]]]], 'bad_primes': [3, 5], 'central_character': '225.211', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '1907641131922482291421167435419', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5203180405687134, -0.23166051714472186], [1.3382612127177165, 1.4862896509547885]], [[1.0, 0], [1.625889883464084, -0.5970612086286861]], [[1.0, 0], [-2.2105633092307926, 0.33676379835517933]], [[1.0, 0], [-1.5887164178523998, -2.751737554539183], [-3.5, 6.06217782649107]], [[1.0, 0], [-1.73440307385276, -0.7722060003665483], [7.360436669947441, 8.174593080251336]], [[1.0, 0], [-5.02577385121486, 2.237618684434411], [8.698697882665156, -9.660882731206126]], [[1.0, 0], [-0.8887348820879594, -2.7352447155155026], [-13.753288904374106, 9.992349288972044]], [[1.0, 0], [1.3903859503905573, 4.279167949836787], [-15.371322893124, 11.16791979355699]], [[1.0, 0], [-0.3353807163695885, -3.190934366458519], [-22.49739481687753, 4.781968888808465]], [[1.0, 0], [1.7559708876240847, -0.37324313426603223], [26.492818271635425, -11.795362649198205]], [[1.0, 0], [7.355579419871161, 1.5634766705785899], [28.31990918692063, 12.608835935349806]], [[1.0, 0], [4.576186382464876, 3.3247940229397384], [11.433628791873055, 35.189091102920685]], [[1.0, 0], [0.9743455074750773, -0.43380656932940714], [27.434354860713185, -30.468937844573162]], [[1.0, 0], [3.6439190761733316, 6.311452978601656], [-21.5, 37.239092362730865]], [[1.0, 0], [-7.347302789711648, 1.5617174185296696], [42.936636509202245, -19.116622224562608]], [[1.0, 0], [0.9827098839920667, -3.024470031781787], [-42.877900701872214, -31.152618371501077]], [[1.0, 0], [12.07136689237198, -5.374518811367766], [39.478705775172635, -43.84554470316626]], [[1.0, 0], [-0.9582063747708838, -0.42662096449349907], [40.81696698789035, 45.33183435412105]], [[1.0, 0], [-12.706011018068002, -2.7007460145419517], [61.20754566205426, 27.251355086078615]], [[1.0, 0], [2.1045369567688943, -6.477098745224534], [-57.440206600621266, -41.73275291276559]], [[1.0, 0], [0.17373163254711665, -0.12622341950528057], [22.558240589371163, -69.42712568954622]], [[1.0, 0], [-4.793993495362095, 1.0189947740426182], [72.17009115376547, -32.13219480298822]], [[1.0, 0], [10.025071203685766, -11.133969540867172], [-8.675862451215238, -82.54531731556669]], [[1.0, 0], [2.150190197799162, -1.5622046220013504], [27.502512499370322, -84.64402995026867]], [[1.0, 0], [13.198962221651355, -2.8055260274467284], [88.61390939133229, -39.45345437835262]], [[1.0, 0], [6.608458683926028, 11.446186200279637], [-50.5, 87.4685657822283]], [[1.0, 0], [3.6581401278075454, 4.0627762069419235], [-10.766431716568308, 102.43575522293216]], [[1.0, 0], [-11.854506275601787, 0], [107.0, 0]], [[1.0, 0], [-3.147595202117489, -2.2868617752839855], [33.68285238686927, 103.66516027617173]], [[1.0, 0], [19.05677017275748, -8.484620730243739], [75.61175851855097, -83.97536527894555]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-15e2-225.211-c1-0-9', '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/225/2/q/a/211/18', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2557937321059711, 1.2536751516789753, 1.252818701996761, 1.2495225828515346, 1.2381876340879938, 1.21197653654926, 1.1634878272410105, 1.085383792919306, 0.9709709908307366, 0.8147552620375381, 0.6129862208841106, 0.36418596880205883, 0.06963541530483006, -0.2662251232084864, -0.6355344609897821, -1.0269445448805832, -1.4258017858407068, -1.8146156583417425, -2.1738353041441942, -2.4829291124464445, -2.7217313604783064, -2.871986260750612, -2.9189862637564126, -2.853171961759336, -2.671539556329869, -2.378692671068225, -1.9873818365629812, -1.5183996557437447, -0.9997432237095405, -0.4650164680725748, 0.048880045709419534, 0.5046417755042634, 0.8678233445182428, 1.1101886047240044, 1.2128131006910428, 1.1685836509090992, 0.9837567449239947, 0.6782963237314816, 0.28481185641741236, -0.15394628108610475, -0.5889165083050443, -0.9695942755077865, -1.2494948936355226, -1.3916426593651243, -1.3734471454135582, -1.1903268208812299, -0.857519406303606, -0.40967820672187477, 0.10191590296699964, 0.6144170380281057, 1.0603422879956494, 1.3756747695421458, 1.508228049019595, 1.4252298829153438, 1.1190786487546052, 0.6103602987068871, -0.05251508516117409, -0.7973117477269598, -1.5353955558094974, -2.1719046300416327, -2.61754501113301, -2.8005725682769462, -2.6773710988544765, -2.2400931451779806, -1.5201069135768561, -0.5864713053816795, 0.4607086740648899, 1.501489588406068, 2.410621747180629, 3.0736096699214346, 3.4021644077934337, 3.34685715371332, 2.905046760495645, 2.1227197174972114, 1.0896873713752908, -0.0714731322822829, -1.2214050242222676, -2.2227576220654264, -2.9591235576733372, -3.3513367023897453, -3.368621440515608, -3.032771420002505, -2.4145441280193163, -1.622643235271519, -0.7868416126132766, -0.0377811703380178, 0.5134012237247616, 0.7923506081269639, 0.7728172566570739, 0.4800785560010953, -0.01421677247844006, -0.605023821056469, -1.1725807138740914, -1.6036372087314217, -1.811553612232125, -1.7516981386253827, -1.4293193540563474, -0.898354621677938, -0.2512467959887362, 0.39850008734569575, 0.9378934623884455, 1.276147824535488, 1.3623428968931337, 1.1955107995194703, 0.8249468921106441, 0.34035049251199617, -0.14662626361470796, -0.5260823698366749, -0.714288312996767, -0.6739157196352606, -0.4257424961875717, -0.048957111518150145, 0.3307094094822379, 0.5634203152202684, 0.5044430058392125, 0.044769176542121494, -0.8628147702500202, -2.187622483436371, -3.818701722290429, -5.577509457204377, -7.2440721317924766, -8.592379098763622, -9.428765904064505, -9.626187490903135, -9.147783127470932, -8.054955924641286, -6.498022976442239, -4.690811139109743, -2.8737298588925095, -1.2722030620879412, -0.05838179337614578, 0.6764681447030799, 0.9335466038505041, 0.7998852573247622, 0.4250058185648073, -0.01417460076819651, -0.3527570972970487, -0.4732014001396345, -0.3290094208111669, 0.04837998294470831, 0.5610030786979727, 1.0715816784402952, 1.4404497635932052, 1.5637909892848998, 1.4042612559975314, 1.0065283606636382, 0.4934419031306739, 0.04280454632971186, -0.1508601852510858, 0.0784591770146497, 0.8259837195423069, 2.086572335858106, 3.7452114361239515, 5.590783392358852, 7.351312725541071, 8.744080628827264, 9.530482533154663, 9.564110268812515, 8.821650469307427, 7.409632771268392, 5.545131744763798, 3.514132668259638, 1.6161682754417561, 0.10690448847603694, -0.8491308755698604, -1.2056832497457506, -1.0362369867601604, -0.5100098920611345, 0.1516215317296839, 0.7280051892597079, 1.0491530739946766, 1.0313466122795112, 0.6905461159921614, 0.1311205253179754, -0.4866340381912702, -0.9916213981200276, -1.2481540531623696, -1.1915289359797658, -0.8440154165447036, -0.30731533962137314, 0.26640299798983136, 0.7172325953917588, 0.9226876334568899, 0.8331675327869575, 0.48793120832704423, 0.006728246841665733, -0.4414254452175574, -0.6847001302309541, -0.5981658667664289, -0.1434488222890135, 0.6128938643480015, 1.5083809081142547, 2.3201569613467248, 2.819224447478589, 2.830207669852973, 2.2813898150646956, 1.2315111611278016, -0.1348669881511546, -1.5439645366807315, -2.69374673289061, -3.3251077145217063, -3.2859306793062713, -2.5717680748859375, -1.3321408489471331, 0.16031048353805052, 1.5713757357002134, 2.5832001573022807, 2.9697661787252603, 2.6512516793175367, 1.7134490248732364, 0.3869033574859803, -1.0095611149130335, -2.1472341604051928, -2.7684315120767446, -2.7496621994592307, -2.1310789982840497, -1.1046684468307795, 0.035906371568564764, 0.9710857242731997, 1.4374747526745488, 1.2951783740019058, 0.5631672794251733, -0.5863038875715451, -1.8725750655214646, -2.9788871317305476, -3.633139028430462, -3.6760153372352415, -3.098881356653352, -2.041986445688907, -0.7541513614975155, 0.4746197682517943, 1.3890451047253234, 1.832397313905534, 1.7812770578452257, 1.3425953127933903, 0.7146500777112712, 0.12421339842306278, -0.24182180702605902, -0.29032724345054495, -0.045774577516872784, 0.36274858142542366, 0.747295299419808, 0.9258120028979595, 0.7862900698274737, 0.33055382861864485, -0.31643850207819746, -0.9359837536160773, -1.2765053540605606, -1.1290864778705967, -0.39587014226651995, 0.8692313454914569, 2.4608144507592264, 4.065197000689823, 5.336240739428147, 5.98378234229283, 5.850447200927291, 4.955206228900328], 'positive_zeros': ['1.52714267270283330888205751767721', '3.73762530490596195729281441676124', '4.83175221657701219981128042850844', '5.97562350673640946340988760026152', '6.99081139696808526970550767241310', '8.195787867845575138787315908297956', '9.367425557844263193112602085256973', '10.63215259580686615269060020341032', '11.24683070826857424988527378819718', '12.29717532518352056734643434561072'], 'prelabel': '2-15e2-225.211-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': -0.049181263230053986, 'root_number': '0.9880874438756767 - 0.15389348022327473*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.024590631615', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52714267270283330888205751768', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.73762530490596195729281441676', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.83175221657701219981128042851', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'bad_primes': [3, 5], 'central_character': '225.211', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/q/a/211/18'], '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': '2-15e2-225.211-c1-0-9', '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': '2-15e2-225.211-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': -0.024590631615026993, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52714267270283330888205751768', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1935883325685889123895368899205', 'Lhash_array': ['1935883325685889123895368899205'], 'label': '2-15e2-225.211-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/q/a/211/18'}