-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1838555684210822105976592313470', 'a10': [0, 0], 'a2': [1.0, 0], 'a3': [-1.618033988749895, 0.6180339887498949], 'a4': [1.0, 0], 'a5': [0, 0], 'a6': [-1.618033988749895, 0.6180339887498949], 'a7': [2.618033988749895, -0.38196601125010515], 'a8': [1.0, 0], 'a9': [2.23606797749979, -2.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.384292212234444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [1.618033988749895, -0.6180339887498949]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.618033988749895, 0.38196601125010515]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.1049', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '1102570158222085222274029320208', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.618033988749895, -0.6180339887498949]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.618033988749895, 0.38196601125010515]], [[1.0, 0], [0, 4.47213595499958], [-11.0, 0]], [[1.0, 0], [3.23606797749979, 0], [13.0, 0]], [[1.0, 0], [0, 0.7639320225002103], [-17.0, 0]], [[1.0, 0], [0, -0.4721359549995794], [-19.0, 0]], [[1.0, 0], [-4.0, 0], [23.0, 0]], [[1.0, 0], [0, 5.708203932499369], [-29.0, 0]], [[1.0, 0], [0, 7.23606797749979], [-31.0, 0]], [[1.0, 0], [0, 5.23606797749979], [-37.0, 0]], [[1.0, 0], [-6.47213595499958, 0], [41.0, 0]], [[1.0, 0], [0, -12.94427190999916], [-43.0, 0]], [[1.0, 0], [0, 2.4721359549995796], [-47.0, 0]], [[1.0, 0], [-8.47213595499958, 0], [53.0, 0]], [[1.0, 0], [-4.47213595499958, 0], [59.0, 0]], [[1.0, 0], [0, -2.76393202250021], [-61.0, 0]], [[1.0, 0], [0, -12.0], [-67.0, 0]], [[1.0, 0], [0, 2.76393202250021], [-71.0, 0]], [[1.0, 0], [-6.76393202250021, 0], [73.0, 0]], [[1.0, 0], [8.94427190999916, 0], [79.0, 0]], [[1.0, 0], [0, 16.65247584249853], [-83.0, 0]], [[1.0, 0], [-14.47213595499958, 0], [89.0, 0]], [[1.0, 0], [-5.23606797749979, 0], [97.0, 0]], [[1.0, 0], [3.5278640450004204, 0], [101.0, 0]], [[1.0, 0], [16.65247584249853, 0], [103.0, 0]], [[1.0, 0], [15.416407864998739, 0], [107.0, 0]], [[1.0, 0], [-4.47213595499958, 0], [109.0, 0]], [[1.0, 0], [14.94427190999916, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 29, 'label': '2-1050-105.104-c1-0-29', 'leading_term': '1.965733381112740454346345408699442066541849301864130089', '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/1050/2/d/d/1049/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.9657333811127404, 2.024838614359397, 2.0766758756051438, 2.1210278689212205, 2.157330002178426, 2.184698211030364, 2.2019767046081387, 2.2078016861127163, 2.2006766556657924, 2.1790550281326766, 2.1414262917149665, 2.0864025718870765, 2.0128030722255272, 1.9197343337443227, 1.8066645524209515, 1.673490336670086, 1.5205943169378342, 1.3488919922477578, 1.1598661646643986, 0.9555873145907153, 0.7387183389714378, 0.5125022315399542, 0.28073154048396926, 0.047698797554037525, -0.18187242984806473, -0.4029156650641235, -0.6101280065203297, -0.7980934714975955, -0.96142098987475, -1.0948941209247858, -1.1936288714270962, -1.2532353522573012, -1.269978455209823, -1.2409322938379426, -1.1641228617840422, -1.0386532467455631, -0.8648058208859536, -0.6441161264288809, -0.37941369857945234, -0.07482581876742278, 0.26425883772160064, 0.6312685214475543, 1.018569207437665, 1.4176268955088895, 1.819208854273355, 2.213619633077179, 2.590966073332864, 2.941444049529876, 3.255638329670727, 3.5248258335542495, 3.7412717502738353, 3.898507511855374, 3.9915795565286176, 4.017258188094875, 3.974196666824301, 3.8630319537902666, 3.6864202562378323, 3.4490026474750706, 3.157298501076519, 2.8195272062331265, 2.4453615212593647, 2.0456188629516117, 1.6318996969541482, 1.216184858473771, 0.8104059626997397, 0.42600493441378806, 0.07349998224406165, -0.23792403173752769, -0.5007829947774186, -0.7096017923117763, -0.8611481811327624, -0.9545795422889114, -0.9914929558005267, -0.9758728341963024, -0.9139346183522451, -0.8138676087344603, -0.6854846836722048, -0.5397912312023679, -0.3884898705975901, -0.24344124316813953, -0.11610410047298547, -0.016979925905729575, 0.044911759174328485, 0.06250153915363184, 0.03105737438217729, -0.05153052903379706, -0.1845847912343744, -0.3646083673267164, -0.58539106971599, -0.8382551360846318, -1.1124329947728342, -1.3955634897583842, -1.6742862750555325, -1.9349082233415, -2.1641108520506878, -2.3496642556806107, -2.481111098960225, -2.5503840584784454, -2.552321806351855, -2.48505222328292, -2.3502169270109636, -2.1530182234641293, -1.9020779539088946, -1.6091070572663841, -1.2883945550562166, -0.9561346059742473, -0.6296197461061785, -0.3263369029379531, -0.06300974389690694, 0.14536405760345736, 0.2864293551182705, 0.35129246614321874, 0.3351937384614813, 0.23799032677345944, 0.06441370717093757, -0.17592329725397698, -0.46878309381744804, -0.7958231919909211, -1.1353649848534728, -1.4633830536419987, -1.7546734415829661, -1.9841477650459478, -2.1281907467621126, -2.166012383041325, -2.080922981272261, -1.8614600495337696, -1.5023006219646313, -1.0049009907210862, -0.3778177046970236, 0.3633214034015677, 1.1962101661289202, 2.092616284643446, 3.0194688064381725, 3.940238141105398, 4.816548673412965, 5.609949390023995, 6.283756763753332, 6.804877190134629, 7.145514092200425, 7.2846677018040875, 7.2093435171372064, 6.915398267523951, 6.407969346042117, 5.701454292453697, 4.81902999021124, 3.791725572076401, 2.6570872857799768, 1.4574963897941087, 0.2382212020995796, -0.9546995002684818, -2.0766334578007943, -3.0864786972047047, -3.948621415925864, -4.634622539214758, -5.124540805988135, -5.4078189854167364, -5.483683061452902, -5.36103070141282, -5.057813577651133, -4.599946526701373, -4.019803447321092, -3.354383646862044, -2.6432515823731104, -1.9263663888072817, -1.2419243444120058, -0.6243369817861406, -0.10245982861291068, 0.30182788551172357, 0.5746129987515148, 0.7104538314606365, 0.7123765727552749, 0.5913688048526345, 0.36540695757904923, 0.05808299035396451, -0.30307982742325706, -0.6885131152393233, -1.0685703739340582, -1.4154489635466705, -1.7049446520999039, -1.9179275953008508, -2.041447113381389, -2.0693972392558195, -2.0027041746831142, -1.849028637363123, -1.622008534488151, -1.3400983069760584, -1.0250885721528225, -0.7004114793562287, -0.38935195068065487, -0.11329162551641227, 0.10988968751586473, 0.2671408938697463, 0.3511993309696471, 0.3611133063619054, 0.3022880859232418, 0.18604970606224433, 0.028755518030703205, -0.14948671065142938, -0.3264003525309873, -0.4793084527962378, -0.5869604458722528, -0.6312821464267059, -0.5989175778431377, -0.48244419386709214, -0.28116481449395836, -0.0014087480401046484, 0.3436908358792705, 0.7349385578390522, 1.148294699754893, 1.5564907266781913, 1.9309330737974195, 2.243762280587391, 2.4699201702160662, 2.5890737852897687, 2.5872517264594137, 2.458066145598272, 2.2034208878126034, 1.833641399573528, 1.3670026515520428, 0.8286746335766375, 0.24914787066324634, -0.3377592568298887, -0.897176786528276, -1.3955846875824622, -1.8031685315960964, -2.0959577233106432, -2.2575867203971294, -2.2805436548173557, -2.1668052288303543, -1.9277994112607961, -1.5836853594938116, -1.161989736705736, -0.695686560325366, -0.22085032867402754, 0.22595383987039333, 0.6103566648881762, 0.9027519769168211, 1.0805538896620912, 1.1299720389323304, 1.0471652561829021, 0.8386772598854566, 0.5211092061344559, 0.12003959999846837, -0.331741922323011, -0.7965682453872083, -1.234632783679704, -1.6069356774817687, -1.878222913319158, -2.0196997395814345, -2.0113126808747026, -1.8434230477546092, -1.5177372555029596, -1.047412585875612, -0.45631744078152586, 0.22251178051615036, 0.9491140219131657, 1.6793896639833579], 'positive_zeros': ['1.45036470134578584843213020944841', '2.45181275391618129208314372198343', '4.13897608242807353134322195402184', '5.07615583130982832862373006488910', '5.27831764470113514120003743645222', '6.76708913248062965026807378408077', '7.14341076757609441107859371446565', '8.032953152702273250427033985562939', '9.262296412539246462404144837987111', '10.38915026511409324821017334251469'], 'prelabel': '2-1050-105.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8955642303762565, 'root_angle': 0.19016120319734775, 'root_number': '0.82679580965139803427394882532727897955033044210951476899 + 0.5625021681228341622174102235764606998186474135599886088*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09508060159867388', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45036470134578584843213020945', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.45181275391618129208314372198', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.13897608242807353134322195402', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 8.384292212234444, 'bad_primes': [2, 3, 5, 7], 'central_character': '105.104', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/2/d/d/1049/2'], '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': '2-1050-105.104-c1-0-29', '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': '2-1050-105.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8955642303762565, 'root_angle': 0.09508060159867388, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45036470134578584843213020945', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1838555684210822105976592313470', 'Lhash_array': ['1838555684210822105976592313470'], 'label': '2-1050-105.104-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/2/d/d/1049/2'}