-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2494918386940769447828959814484', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 3, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [19, [1, -1]]], 'bad_primes': [5, 19], 'central_character': '475.1', 'coefficient_field': '1.1.1.1', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, 0, 3], [1], [1, -2, 7], [1, 4, 11], [1, 2, 13], [1, -4, 17], [1, -1], [1, 6, 23], [1, 6, 29], [1, 4, 31], [1, 10, 37], [1, 10, 41], [1, -2, 43], [1, 6, 47], [1, -10, 53], [1, 0, 59], [1, -2, 61], [1, -8, 67], [1, -4, 71], [1, -4, 73], [1, -4, 79], [1, 18, 83], [1, 2, 89], [1, -6, 97], [1, 6, 101], [1, -16, 103], [1, 4, 107], [1, -6, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, 1, 2], 1]], [[[1, 0, 3], 1]], [1], [[[1, -2, 7], 1]], [[[1, 4, 11], 1]], [[[1, 2, 13], 1]], [[[1, -4, 17], 1]], [[[1, -1], 1]], [[[1, 6, 23], 1]], [[[1, 6, 29], 1]], [[[1, 4, 31], 1]], [[[1, 10, 37], 1]], [[[1, 10, 41], 1]], [[[1, -2, 43], 1]], [[[1, 6, 47], 1]], [[[1, -10, 53], 1]], [[[1, 0, 59], 1]], [[[1, -2, 61], 1]], [[[1, -8, 67], 1]], [[[1, -4, 71], 1]], [[[1, -4, 73], 1]], [[[1, -4, 79], 1]], [[[1, 18, 83], 1]], [[[1, 2, 89], 1]], [[[1, -6, 97], 1]], [[[1, 6, 101], 1]], [[[1, -16, 103], 1]], [[[1, 4, 107], 1]], [[[1, -6, 109], 1]], [[[1, -6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-475-1.1-c1-0-17', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/475/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.8142715016570486e-121, 0.16755189914165244, 0.3380720373895952, 0.5132250047119076, 0.6923262649317763, 0.8717051319945391, 1.0444991807548496, 1.2008339678483062, 1.328336870740379, 1.412954568565766, 1.4400558143484394, 1.395791659895835, 1.268656448706842, 1.0511527983038425, 0.7414214364048692, 0.3446605637053423, -0.1258629347061785, -0.6484099069194363, -1.1931485235914272, -1.7234400880227543, -2.1980734906743873, -2.5743863817123716, -2.8120917835738535, -2.8775073275168617, -2.747776571654615, -2.4145955068771534, -1.8869292709788785, -1.1922378336051827, -0.37583248692795573, 0.5018435798648978, 1.3699885517990733, 2.153982349102008, 2.7831374515199, 3.1988655917353186, 3.362298680614256, 3.260341553723151, 2.9092052010589753, 2.35468220121649, 1.6687716070830585, 0.9427075224104258, 0.2769429176694089, -0.2308786169413562, -0.4985391761464079, -0.47079569927891735, -0.12819079814696202, 0.5083178374349505, 1.3778861359407526, 2.3857866564585204, 3.414428323500038, 4.338156811601191, 5.0399385613937895, 5.42760503185539, 5.447233543334529, 5.0915144766686, 4.401591924857737, 3.461794259077717, 2.3877639278090284, 1.3095831585522053, 0.3523899497870955, -0.3824814694306232, -0.832740558406545, -0.9841304898348824, -0.8714862080885117, -0.5714769770473741, -0.18809117101074804, 0.1667455207375643, 0.3940526978482098, 0.4264011656414105, 0.24073026818732937, -0.13719725140456893, -0.6377999634673351, -1.161471044713095, -1.5987524599252008, -1.8531178540068898, -1.8618927084426913, -1.610989113781623, -1.140156302362937, -0.5371996629566108, 0.07820534825748977, 0.5782967394911865, 0.8540575875279994, 0.8396340460261851, 0.529042289804595, -0.018851092097371517, -0.6888805895819418, -1.3307310820751193, -1.789022648313652, -1.936529711456102, -1.703679677214719, -1.0978084882282528, -0.2073948894268015, 0.8106234120106341, 1.7588697971553808, 2.4379341779240513, 2.687687017832594, 2.422943195500475, 1.655607229514649, 0.4978574405033381, -0.8553299119673979, -2.1616890682094714, -3.1785783827778866, -3.711892416486138, -3.6566861136654003, -3.020542934246079, -1.9240620939792559, -0.5775740296119697, 0.7616627266458187, 1.8431014508078953, 2.4760125383515454, 2.570415496396055, 2.156521783016599, 1.3778727296116098, 0.45910445708199804, -0.34499098023016295, -0.8080234868219497, -0.7850663780713617, -0.24801487099360953, 0.7052224065103407, 1.8703585712341335, 2.9812679350069136, 3.7696617879526086, 4.026417349435114, 3.6504284221788708, 2.6735022776031605, 1.255242898633203, -0.3511873589813201, -1.8546761244939314, -2.9902719819235837, -3.5768289713555386, -3.554693766335385, -2.9947028171725365, -2.0766783573366414, -1.0430197313548981, -0.13904670059028007, 0.44506690394184467, 0.6164605339040683, 0.39569242460168597, -0.09664028352236274, -0.6785664840650648, -1.159951489973246, -1.3957800762484207, -1.325128061032497, -0.9853722978425048, -0.4979673168575778, -0.02995422852990408, 0.257847760830528, 0.2611614135537654, -0.03352407413786032, -0.5411361371504713, -1.09961598007791, -1.5155751853481942, -1.621552707149742, -1.3286073234266529, -0.6586663947201703, 0.25379292290480177, 1.1928089297998652, 1.9175222772607459, 2.229392579422871, 2.031368083643041, 1.3616775322489985, 0.39124393452887546, -0.6165258492208214, -1.3742440035866568, -1.6495554948021243, -1.3330438422290645, -0.4754803204990529, 0.7174699715408804, 1.933626426165517, 2.8343005355421784, 3.145177274433146, 2.733437890553939, 1.6493481119098792, 0.11958699158536028, -1.5074712870354006, -2.8509821977262986, -3.5978372961345286, -3.586608823700706, -2.851785813844254, -1.6153280233251375, -0.22695285297082762, 0.9310830905369997, 1.5487056238074088, 1.4731204083918308, 0.7502093240716341, -0.38987437530390784, -1.5993749055187354, -2.5134263094545735, -2.856043696570568, -2.521356741077908, -1.6065475038758172, -0.38653367652092385, 0.762935378238088, 1.472195426558919, 1.4841811075955318, 0.7299896546454495, -0.6483359687706782, -2.334524720392437, -3.9238730168865676, -5.033526642788456, -5.405640698635938, -4.974039005041289, -3.87583420606237, -2.405713879824005, -0.9274093332471739, 0.23078188029257346, 0.8653444287799373, 0.9458658890374381, 0.6093651645692748, 0.10435985238942493, -0.29629162985199325, -0.3855448776813349, -0.08683193709620916, 0.5265620049515988, 1.2623408549504, 1.8789161365358629, 2.170179420066898, 2.0368389330780174, 1.5204975766686042, 0.7891605543546212, 0.07915799568235009, -0.3867915277910374, -0.47737144789343755, -0.199340229113436, 0.30371677242687695, 0.8012758494098962, 1.0583850491424875, 0.9230038826722645, 0.38769096819614157, -0.3972428733487596, -1.1663097245365461, -1.6255462189537777, -1.5560411099937153, -0.8997863688759974, 0.20258217932928405, 1.4381238813703, 2.407486944373499, 2.7458516268705444, 2.2415860316799114, 0.9141280379854367, -0.976003634374313, -2.9914756104402636, -4.6395107282089105, -5.51431191929785, -5.416615906135493, -4.412501194497332, -2.811992093703343, -1.0731479139225095, 0.3387943228284464, 1.0928417065954703, 1.0891304463295837, 0.4800814325029693, -0.39107933512859805, -1.11442634886839, -1.359292468832541, -0.9936234701503776, -0.13643227202178546, 0.8753613523554509], 'positive_zeros': ['1.96814357717464198506340057616878', '3.55403121637170592856879586722114', '5.06192463633366510578493432028307', '5.53012677110652044639814137101033', '7.30449183870349658498149256558808', '8.062630957458166067193418441089115', '8.585360868393304501131631040206576', '9.733312390315199950399079937400489', '10.37126018310212384850887592041663'], 'prelabel': '2-475-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 311833585263559080, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.96814357717464198506340057617', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.55403121637170592856879586722', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.06192463633366510578493432028', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, -1, 0, 0, 2, 3, -3, 0, -4, 0, -2, -2, 0, -1, 4, 3, 1, 0, 0, 4, -6, 0, 0, 2, 0, -2, -6, 0, -4, -5, 0, -4, 0, 3, -10, -1, 0, 0, -10, 0, 2, 4, 0, 6, -6, 0, -3, 0, 0, 2, 10, 0, 0, 6, 0, 6, 0, 0, 2, 4, -6, 7, 0, 0, 8, -4, 0, 0, 4, -9, 4, 10, 0, -1, -8, 0, 4, 0, 9, 10, -18, 0, 0, -2, 0, -12, -2, 0, -4, 6, 0, 6, 0, 0, 6, 3, 12, 0], 'euler11': [1, 4, 11], 'euler13': [1, 2, 13], 'euler17': [1, -4, 17], 'euler19': [1, -1, 0], 'euler2': [1, 1, 2], 'euler23': [1, 6, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 3], 'euler31': [1, 4, 31], 'euler37': [1, 10, 37], 'euler41': [1, 10, 41], 'euler43': [1, -2, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 0], 'euler53': [1, -10, 53], 'euler59': [1, 0, 59], 'euler61': [1, -2, 61], 'euler67': [1, -8, 67], 'euler7': [1, -2, 7], 'euler71': [1, -4, 71], 'euler73': [1, -4, 73], 'euler79': [1, -4, 79], 'euler83': [1, 18, 83], 'euler89': [1, 2, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 1, 2], [1, 0, 3], [1, 0, 0], [1, -2, 7], [1, 4, 11], [1, 2, 13], [1, -4, 17], [1, -1, 0], [1, 6, 23], [1, 6, 29], [1, 4, 31], [1, 10, 37], [1, 10, 41], [1, -2, 43], [1, 6, 47], [1, -10, 53], [1, 0, 59], [1, -2, 61], [1, -8, 67], [1, -4, 71], [1, -4, 73], [1, -4, 79], [1, 18, 83], [1, 2, 89], [1, -6, 97]], 'index': 17, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/475/a', 'ModularForm/GL2/Q/holomorphic/475/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/475/2/a/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-475-1.1-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': 1, 'prelabel': '2-475-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 311833585263559080, 'z1': {'__RealLiteral__': 0, 'data': '1.96814357717464198506340057617', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 10999579
{'Lhash': '2494918386940769447828959814484', 'Lhash_array': ['2494918386940769447828959814484'], 'label': '2-475-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/a/a'}
-
id: 24549478
{'Lhash': '2494918386940769447828959814484', 'Lhash_array': ['2494918386940769447828959814484'], 'label': '2-475-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/a/a/1/1'}
-
id: 34976
{'Lhash': '311833585263559080', 'Lhash_array': ['311833585263559080'], 'label': '2-475-1.1-c1-0-17', 'type': 'ECQ', 'url': 'EllipticCurve/Q/475/a'}