-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '777386364003381236026206608957', 'a10': [7.606382098543529, 1.4660099875306736], 'a2': [0.09244115598230132, 1.9405786822263456], 'a3': [-0.9283679330160726, 0.3716624556603275], 'a4': [-1.7663564094458264, 0.1686665867108634], 'a5': [0.9400325758218718, -3.8748670535464926], 'a6': [-0.8070596433432314, -1.7672141130370649], 'a7': [-1.5892612469367466, 2.115241993008142], 'a8': [0.062377802106019974, 0.433847143214822], 'a9': [0.7237340381050702, -0.690079011482112], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.9283679330160726, -0.3716624556603275]]], [7, [[1.0, 0], [1.5892612469367466, -2.115241993008142]]], [23, [[1.0, 0], [-0.03909120411828081, -4.79567220290968]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.58', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': '2367544375094406902619834286741', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.09244115598230132, -1.9405786822263456], [-1.9909438451461692, 0.19011208660836532]], [[1.0, 0], [0.9283679330160726, -0.3716624556603275]], [[1.0, 0], [-0.9400325758218718, 3.8748670535464926], [-4.444177243274617, -2.291132608637052]], [[1.0, 0], [1.5892612469367466, -2.115241993008142]], [[1.0, 0], [0.1616037403800191, -3.3924800076012502], [-10.950191148303931, -1.0456164763460094]], [[1.0, 0], [2.4302830645368974, -2.804696168785074], [-1.850092897552707, -12.867678744452126]], [[1.0, 0], [1.6666019650689403, -2.340414983399761], [-5.5601553763961675, -16.065013918149365]], [[1.0, 0], [-2.815438947198259, -3.9537307857413224], [-6.214291303031011, 17.9550155555787]], [[1.0, 0], [-0.03909120411828081, -4.79567220290968]], [[1.0, 0], [-3.14457194641439, -6.885652093993468], [-18.990961284413267, 21.91673765627349]], [[1.0, 0], [-5.490090226942689, 4.317454675319418], [7.308527000792244, -30.12615861802979]], [[1.0, 0], [4.040110631090948, -3.8522377058309054], [1.760530885478465, -36.9580915497713]], [[1.0, 0], [-8.045927138013607, 2.3624973679725656], [34.49139484607843, -22.1662735156795]], [[1.0, 0], [-0.7927637838086464, 5.513793228318334], [-41.25819786542339, -12.114499944181476]], [[1.0, 0], [-1.8162435478045649, 3.1458261037166593], [-23.5, -40.703193977868615]], [[1.0, 0], [-1.1636327387828833, 3.362095998885145], [-41.660814021367734, -32.76242626969208]], [[1.0, 0], [-7.25656002835557, -1.398587309822647], [54.77370804794828, 21.928084883959322]], [[1.0, 0], [10.067238760448287, 4.03031443284703], [44.14777632440928, 42.094819700408834]], [[1.0, 0], [6.114119960208255, 3.1520479150894656], [38.863812941270275, 54.57658878737249]], [[1.0, 0], [1.0657822456856982, -0.6849366594610291], [29.494465923133937, -64.58387167017081]], [[1.0, 0], [10.864400158646236, -1.0374244300983042], [71.68079490017759, -13.815340838309945]], [[1.0, 0], [-1.622199130855153, -4.687036575601801], [-62.098194484680214, 48.83455991142781]], [[1.0, 0], [-4.293131856918971, -1.2605772508690953], [69.82404322498803, 44.8731878488146]], [[1.0, 0], [-3.1110071003682243, -2.446523025162826], [20.982545260339023, 86.4912295807952]], [[1.0, 0], [-10.181369991874613, 2.9895199640220698], [81.60159268462458, -52.442159293192965]], [[1.0, 0], [-0.21412160082995677, -0.8826212599954116], [-89.77238031414727, 46.28087869446845]], [[1.0, 0], [13.50098801515525, -6.960243076972351], [59.74586168583341, -83.90132306118458]], [[1.0, 0], [-5.512875361439493, -2.207022368734105], [77.4395420772425, 73.83845422858599]], [[1.0, 0], [-9.251949206510025, 12.992544712182601], [-35.65040800159896, -103.00508923989887]], [[1.0, 0], [15.490075530508369, -9.954867076847762], [46.94189646921317, -102.78841547506057]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-483-161.58-c1-0-4', '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/483/2/y/a/58/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9834501578457722, 0.7923626986085, 0.6007997571478458, 0.4036424488906176, 0.19694141436429455, -0.020945649379623305, -0.2486798863063922, -0.48171699829672526, -0.7124709543005201, -0.9308106757795, -1.1248537585398397, -1.282026326947803, -1.390342950064596, -1.4398301033254477, -1.4239794961722623, -1.34108260283315, -1.1952731638897085, -0.9970974543808518, -0.763448371014773, -0.5167422152851346, -0.2832866498801387, -0.09088104486877978, 0.03420154958033914, 0.07059017794022135, 0.005189251340361063, -0.16388197877205896, -0.4252411922107416, -0.7535115158302166, -1.1102348631398362, -1.446596158748326, -1.7079086400285226, -1.8395617459966662, -1.7938817776670404, -1.537137985407663, -1.0557812498388033, -0.36096345395875573, 0.5095226516303736, 1.4925122222909148, 2.5042158714875153, 3.448262466274123, 4.226358849259843, 4.750421098849887, 4.954668120185463, 4.805978946770221, 4.310854623880437, 3.517620244564016, 2.5130420437458185, 1.413267107041484, 0.34982956994124204, -0.5477115188257791, -1.1702633185394444, -1.4461781885901026, -1.354046628575714, -0.9290140988806084, -0.261116685731842, 0.5147672148408136, 1.2364791791817231, 1.737534931328413, 1.8723255445280906, 1.5398186295191232, 0.7019699528668795, -0.6063701382710915, -2.278124682037532, -4.1457298035613075, -6.002680305562724, -7.631948239846805, -8.837064665618653, -9.471016094602584, -9.458259478322619, -8.806124890658792, -7.603529674700648, -6.007014350528663, -4.216275994865825, -2.4432300806369955, -0.8798232186833452, 0.32990144157846457, 1.1087054449096836, 1.4528645264755595, 1.4257732933574427, 1.1399871566046504, 0.7314354470647316, 0.33102707071735327, 0.03933532135838963, -0.09063078616073521, -0.059276309659666536, 0.08597957063901487, 0.26758793776171014, 0.40118061210569156, 0.4198056953304942, 0.29333851995751425, 0.03835965016093156, -0.2840636981081082, -0.5824514006420076, -0.7577470747571408, -0.7295854165521423, -0.4595803591372603, 0.034378062175069356, 0.6769696364694148, 1.3486168268032759, 1.9107335763001052, 2.2376872102616336, 2.248088747238398, 1.9276549249525892, 1.337368195165609, 0.6037749938489081, -0.10762306397798509, -0.6307329361423181, -0.8405615172321098, -0.6883137944287283, -0.22076163624056083, 0.42220323443470337, 1.033161679652035, 1.3817803477328645, 1.2694222839992826, 0.5816018072523981, -0.6743507692748358, -2.3565712661701124, -4.2059844282848236, -5.892129843445633, -7.079213763792343, -7.498845097225045, -7.013460167849548, -5.655549996653932, -3.6324278444181566, -1.2935292086243133, 0.9344357916324914, 2.6316506786987315, 3.4709626694202034, 3.2865178846762837, 2.1097765374476025, 0.1643402809049055, -2.179892173426021, -4.483543929745447, -6.3287375050063845, -7.404088260243312, -7.564897501393414, -6.855468487327309, -5.48930420701278, -3.792782774984283, -2.1263718531206726, -0.8024714011930103, -0.01932735567157536, 0.17394450846414192, -0.12576650878198353, -0.714129811026119, -1.3419110890033255, -1.7843125349285816, -1.8987820209927755, -1.6566026848702298, -1.1410259799779128, -0.5139570334109077, 0.03825419900817971, 0.3638302513192308, 0.39228522577392844, 0.15549786052758002, -0.22271966634697368, -0.5652887375533665, -0.6973034797985237, -0.501846735493116, 0.04044624124134733, 0.8401246992915794, 1.71987230389162, 2.4621927579743654, 2.8704149489167503, 2.825449787779602, 2.321649808741733, 1.470943535195098, 0.47353149766522645, -0.4367752658211932, -1.056901105102171, -1.2697764470450024, -1.074220871189182, -0.5805131676018929, 0.027041535242256814, 0.5491672019038204, 0.8340731078397886, 0.8236688638490883, 0.5685216842596265, 0.2060137958038149, -0.09225027954075576, -0.18753112113429646, -0.03370428952388144, 0.29112778441477, 0.5942742799897273, 0.6201116091295169, 0.1310648098725213, -1.0052526090121987, -2.749973131502093, -4.871189405486954, -6.978206767732651, -8.60768683442105, -9.341654776694703, -8.92623703418877, -7.357269276617436, -4.905890001461787, -2.0724423763789748, 0.5235250549639088, 2.291057986056784, 2.8154792736176573, 1.9663972253636544, -0.06410624460811838, -2.8050768134847575, -5.622007439937553, -7.874065256131983, -9.071637570196879, -8.992292545520195, -7.724650838269009, -5.629656390847494, -3.231664370983028, -1.071071510879211, 0.439651088831631, 1.1165939320771507, 1.0351450272608964, 0.48504813314055567, -0.1339480978775196, -0.4427921482224552, -0.2004846039321125, 0.6263001680175275, 1.8602653429084357, 3.1754383488033446, 4.202646972856659, 4.644654691116055, 4.365339688122822, 3.426591887428718, 2.0637582441583033, 0.609912200749195, -0.6052305220717539, -1.3491045563171362, -1.5439821506526854, -1.2726818450927306, -0.734000732120329, -0.16588088888803326, 0.23600448445137276, 0.3765720031762322, 0.2783224770753801, 0.054180562335207176, -0.1507454599876447, -0.22460293322502423, -0.135629780210923, 0.057806415709002766, 0.2377522711761558, 0.2855970477324891, 0.14549919458064398, -0.1345011147633075, -0.4032429089005241, -0.4534495518930287, -0.10145857349352463, 0.7279589954353523, 1.9442106143857476, 3.2866675025592627, 4.38253415745803, 4.85413853926431, 4.443998230758602, 3.1165317756997797, 1.0993191320667626, -1.156046810180952, -3.0882051151861347], 'positive_zeros': ['0.61324971081417830872249843465760', '2.70673397278730621468226165241978', '3.00539474302339459165830888244701', '4.42947976325471285918044323037792', '6.04517206936340382255463320298825', '6.79276858657387956734355568529088', '7.57204761700046660914340730803020', '9.336381175966479156930795987558402', '10.27476114229929602295985342215699', '10.55952945726442430567161918872061'], 'prelabel': '2-483-161.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.9411395375001286, 'root_number': '-0.9829517728461965 - 0.18386356968828635*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.47056976875', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61324971081417830872249843466', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.70673397278730621468226165242', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.00539474302339459165830888245', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.58', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/y/a/58/14'], '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': '2-483-161.58-c1-0-4', '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': '2-483-161.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.4705697687500643, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61324971081417830872249843466', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '777386364003381236026206608957', 'Lhash_array': ['777386364003381236026206608957'], 'label': '2-483-161.58-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/y/a/58/14'}