-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1708943960555540674729344230526', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.7210964310938708, 0.0], 'a4': [0.0, 0.0], 'a5': [3.1331102058626277, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.03782707487594079, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.62621853429843, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7, 13], 'central_character': '1456.1', 'coefficient_field': 'CDF', 'conductor': 1456, 'conductor_radical': 182, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.7210964310938708, 0], [3.0, 0]], [[1.0, 0], [-3.1331102058626277, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.354557718658011, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-5.31673064378207, 0], [17.0, 0]], [[1.0, 0], [-2.499648918298488, 0], [19.0, 0]], [[1.0, 0], [-2.8542066369564987, 0], [23.0, 0]], [[1.0, 0], [-3.625813300107184, 0], [29.0, 0]], [[1.0, 0], [-6.170937280738569, 0], [31.0, 0]], [[1.0, 0], [-9.796750580845753, 0], [37.0, 0]], [[1.0, 0], [-10.670586199037057, 0], [41.0, 0]], [[1.0, 0], [-0.4498408496446977, 0], [43.0, 0]], [[1.0, 0], [11.879350554651566, 0], [47.0, 0]], [[1.0, 0], [-5.89203371183244, 0], [53.0, 0]], [[1.0, 0], [-7.809433738026626, 0], [59.0, 0]], [[1.0, 0], [15.379701636353078, 0], [61.0, 0]], [[1.0, 0], [5.846558649499542, 0], [67.0, 0]], [[1.0, 0], [11.291364329420322, 0], [71.0, 0]], [[1.0, 0], [4.170937280738569, 0], [73.0, 0]], [[1.0, 0], [9.487667924520638, 0], [79.0, 0]], [[1.0, 0], [14.841523479775624, 0], [83.0, 0]], [[1.0, 0], [5.576005231453394, 0], [89.0, 0]], [[1.0, 0], [0.9796688553621703, 0], [97.0, 0]], [[1.0, 0], [17.062268829167984, 0], [101.0, 0]], [[1.0, 0], [3.191268425376398, 0], [103.0, 0]], [[1.0, 0], [-4.8996816992893955, 0], [107.0, 0]], [[1.0, 0], [2.1254622184056715, 0], [109.0, 0]], [[1.0, 0], [2.0301790874189845, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-1456-1.1-c1-0-17', 'leading_term': '3.01500491267715321106557914879', '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/1456/2/a/v/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [3.015004912677153, 3.011687846282134, 3.001571805375381, 2.984172933331821, 2.958719497399111, 2.9242010450262685, 2.8794319389880667, 2.823124985216186, 2.75397076054434, 2.6707185703826863, 2.5722555485533545, 2.457681081637111, 2.326374366215663, 2.1780534137945438, 2.0128241825249558, 1.8312187531779418, 1.6342216163973289, 1.4232832428732896, 1.2003202083324305, 0.9677012733745083, 0.7282189963394889, 0.4850466978812559, 0.24168090248770416, 0.0018697514619990946, -0.23047169517203364, -0.451357887270754, -0.6568390768376564, -0.8431151173102723, -1.0066539413755164, -1.1443114575555577, -1.2534492380909823, -1.3320460889959354, -1.3787994187585089, -1.393212273966503, -1.3756620039583616, -1.3274467641739214, -1.2508064760334952, -1.1489154310521001, -1.025844453346157, -0.8864914058297125, -0.7364798224058126, -0.5820265456346904, -0.42978041446844445, -0.2866352415677899, -0.15952150143737853, -0.055182272476815716, 0.020060010682619266, 0.06053858249363943, 0.06147108654796329, 0.019173564848957162, -0.06874888621210054, -0.20324317784373025, -0.38368886169766503, -0.6078253135294553, -0.8717312395818538, -1.1698607546433322, -1.4951384777309489, -1.8391140575844134, -2.1921743385504873, -2.5438090830333318, -2.88292386452125, -3.1981915275138504, -3.478431573573974, -3.713005072392917, -3.892211305303597, -4.007671409863239, -4.05268387906236, -4.022536931768259, -3.914763546126064, -3.7293263452755587, -3.468721529595253, -3.137993619401711, -2.744655837023153, -2.298514421641943, -1.8113989145660547, -1.2968043366013267, -0.7694550473120814, -0.2448037627545594, 0.2615174547600689, 0.7342745984247635, 1.1592157172930342, 1.5236383649825285, 1.8169168941168703, 2.0309665188079205, 2.1606226029527047, 2.203916168366562, 2.162230098600188, 2.0403248407181658, 1.8462274333514745, 1.5909832298955189, 1.2882755217368071, 0.9539241528874125, 0.6052798933652477, 0.26053653823708595, -0.06201283605537478, -0.34474553521217965, -0.5714725960156803, -0.7281626167943758, -0.8035933463659397, -0.7899002856470082, -0.682995007901915, -0.4828307376146192, -0.19349878202495205, 0.17685354446293308, 0.6162851106354429, 1.109496756524474, 1.638426031835609, 2.1829784858868937, 2.721866121039547, 3.233517758953285, 3.697021658550163, 4.093058035606606, 4.404778363223573, 4.6185895911524995, 4.724804725911894, 4.7181264781745895, 4.597937723582067, 4.368381056477685, 4.038219375515219, 3.6204797869752796, 3.1318936552612677, 2.5921558507282767, 2.023035619374085, 1.4473795268296146, 0.8880531603903018, 0.3668723328559459, -0.09642385590027029, -0.48510673949904876, -0.7862508617905722, -0.9913442503700539, -1.0966830842947255, -1.1035280295535752, -1.018011326369657, -0.8507963798902204, -0.616504487644578, -0.33293575764127503, -0.02012255656030695, 0.30073665676377104, 0.608408071861573, 0.8827583977148995, 1.1058351170440026, 1.262832328489588, 1.342888573376911, 1.339671281042629, 1.2517133804712324, 1.0824806875115884, 0.8401632214446343, 0.5371988637021166, 0.18955291247188574, -0.18420874238688983, -0.5640027234875793, -0.9294076153984894, -1.2608731636480848, -1.540889603486022, -1.755048386999234, -1.8929304367030624, -1.9487667171226275, -1.921827991640114, -1.816515519221572, -1.642141362143362, -1.412404996733332, -1.1445910262700296, -0.8585299332617529, -0.5753789454151689, -0.3162922783915293, -0.10105845477928004, 0.05321352624498349, 0.1332780513460583, 0.1307311631357071, 0.04271776233248447, -0.1276833900654068, -0.3714301890615696, -0.6738562092833698, -1.0153695131021951, -1.3724806784564008, -1.7191088083499204, -2.0280960491526905, -2.272846511588956, -2.4289954400903095, -2.476009751666784, -2.3986221061602877, -2.1880075840634396, -1.8426245941779305, -1.368659222911508, -0.7800339600611013, -0.09796640637400657, 0.6499102126413919, 1.4308266667508687, 2.2084947401967954, 2.944977327712737, 3.6027101656549534, 4.146562252908575, 4.545816964815114, 4.775957729889491, 4.820150979542506, 4.670334527090796, 4.327840802736195, 3.803510308999736, 3.117279795512713, 2.297260281540546, 1.3783503466187736, 0.40045821142320853, -0.5935697156483623, -1.56019749719942, -2.4574972911358772, -3.2473633821953, -3.8975137294072772, -4.383161693778405, -4.688259462231731, -4.806239770946471, -4.740212382021394, -4.502604584229903, -4.114268756029835, -3.6031126379408525, -3.002337342715894, -2.348392389713813, -1.6787745877246871, -1.0298072190175114, -0.434536999514031, 0.07912144499632502, 0.4898799236535944, 0.784119638487465, 0.9564219220153268, 1.0095593479781055, 0.9539551304920418, 0.8066536319534241, 0.5898769742755602, 0.32927002884868484, 0.051956583918027294, -0.2154581817063226, -0.4488005559281531, -0.6280242829192522, -0.7385727165936793, -0.7723135142016428, -0.7279821861662816, -0.6111053620569514, -0.4334114441213707, -0.21177287275044265, 0.03324202345622793, 0.2791010672180234, 0.5031963446551629, 0.6847481373257526, 0.8065818429872681, 0.8566426600268876, 0.8291302202992488, 0.7251614912712834, 0.5529034194946782, 0.32715471556147374, 0.06839626821032105, -0.19863089849735782, -0.4467252748390055, -0.6482774630773975, -0.7774296381803111, -0.8121844487952069, -0.7363057088750435, -0.5408643678964041, -0.2253051982765842], 'positive_zeros': ['1.34811907969582490950115101205033', '2.67697632614240162081736555123535', '2.88691224930538427592004375094583', '4.53967379799196774544207541729904', '5.49606750649498744656827555360859', '6.00865630296110725548163227901299', '7.36987299301824531663029701179113', '7.972427093838319773657585954798358', '8.701907357748347169391643993255789', '9.703217359900474251445418825828722'], 'prelabel': '2-1456-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4097241141034313, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34811907969582490950115101205', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.67697632614240162081736555124', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.88691224930538427592004375095', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 11.62621853429843, 'bad_primes': [2, 7, 13], 'central_character': '1.1', 'conductor': 1456, 'conductor_radical': 182, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1456/2/a/v/1/3'], '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': '2-1456-1.1-c1-0-17', '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': '2-1456-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4097241141034313, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34811907969582490950115101205', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1708943960555540674729344230526', 'Lhash_array': ['1708943960555540674729344230526'], 'label': '2-1456-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1456/2/a/v/1/3'}