-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1297996736961662889630088106666', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.965330172255797, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [13, [1, -1]]], 'bad_primes': [2, 3, 13], 'central_character': '1248.1', 'coefficient_field': '1.1.1.1', 'conductor': 1248, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 0, 5], [1, -2, 7], [1, -4, 11], [1, -1], [1, 6, 17], [1, -6, 19], [1, 0, 23], [1, 2, 29], [1, 6, 31], [1, -10, 37], [1, -8, 41], [1, -12, 43], [1, -12, 47], [1, 6, 53], [1, 0, 59], [1, -2, 61], [1, -2, 67], [1, 8, 71], [1, -14, 73], [1, -4, 79], [1, -8, 83], [1, -4, 89], [1, -14, 97], [1, 18, 101], [1, -4, 103], [1, 4, 107], [1, 2, 109], [1, 10, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, 0, 5], 1]], [[[1, -2, 7], 1]], [[[1, -4, 11], 1]], [[[1, -1], 1]], [[[1, 6, 17], 1]], [[[1, -6, 19], 1]], [[[1, 0, 23], 1]], [[[1, 2, 29], 1]], [[[1, 6, 31], 1]], [[[1, -10, 37], 1]], [[[1, -8, 41], 1]], [[[1, -12, 43], 1]], [[[1, -12, 47], 1]], [[[1, 6, 53], 1]], [[[1, 0, 59], 1]], [[[1, -2, 61], 1]], [[[1, -2, 67], 1]], [[[1, 8, 71], 1]], [[[1, -14, 73], 1]], [[[1, -4, 79], 1]], [[[1, -8, 83], 1]], [[[1, -4, 89], 1]], [[[1, -14, 97], 1]], [[[1, 18, 101], 1]], [[[1, -4, 103], 1]], [[[1, 4, 107], 1]], [[[1, 2, 109], 1]], [[[1, 10, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-1248-1.1-c1-0-5', 'leading_term': '1.586183076912566556872531386720000000000000000000000000000000000000000000000000000000000000', '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/1248/2/a/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.5861830769125667, 1.58222881522439, 1.5702578310704145, 1.5499536384885826, 1.52081517915398, 1.482194384008361, 1.4333449656434334, 1.3734793378761712, 1.3018304472440987, 1.2177154893236215, 1.1205988541581766, 1.010152081481879, 0.886309016451126, 0.7493146876148278, 0.5997666650137914, 0.4386478087045338, 0.2673494128645549, 0.0876838191848466, -0.09811435511644426, -0.2873991307710112, -0.4771368351289419, -0.6639429433944598, -0.8441322556591406, -1.0137822623181114, -1.1688091889715864, -1.3050558088372162, -1.4183896782296568, -1.5048100034257523, -1.5605609017787963, -1.5822483942597299, -1.5669580795781324, -1.5123701108849277, -1.4168678436737872, -1.2796363657496577, -1.1007470731266755, -0.8812245330314715, -0.6230920871123475, -0.32939300077414285, -0.00418445990290546, 0.3474976494484338, 0.7197044787204081, 1.1056708931733583, 1.4979425351060034, 1.8885316813361075, 2.2690992251524955, 2.6311590353293357, 2.9662999059744144, 3.266419352415176, 3.5239626722306907, 3.7321600183058043, 3.8852537612554134, 3.978708186246408, 4.009393602523957, 3.975737263412357, 3.8778341114559347, 3.7175112783161435, 3.4983414710833682, 3.225601842676778, 2.9061766386054306, 2.5484037882850723, 2.161867608132312, 1.757141838091342, 1.3454892678983241, 0.9385261440583773, 0.5478613009026768, 0.1847214480517113, -0.1404248044196141, -0.41823086124067954, -0.6408104003244594, -0.8020366085287671, -0.8977897916567879, -0.9261420530656547, -0.8874695497498419, -0.7844851256712472, -0.622186826275951, -0.40772083094041506, -0.15016059751965577, 0.13979262504494008, 0.4501794264319136, 0.7682103515524168, 1.0807379922553184, 1.3747561324273287, 1.637907187942151, 1.8589780287141848, 2.0283638853440986, 2.1384804861322744, 2.1841058676457425, 2.16263544382624, 2.0742368574821968, 1.921894788744082, 1.711340136172503, 1.45086266311, 1.1510111319032268, 0.8241899276751059, 0.48416598385123844, 0.145504241829426, -0.1770463091201544, -0.46919095862089616, -0.7177248892695918, -0.9111380916116085, -1.040161900011343, -1.0982310326464502, -1.081837826392924, -0.990759338416276, -0.8281430119067007, -0.6004424894834672, -0.3172016708415875, 0.009308023188275597, 0.3645853042218116, 0.7325130709829006, 1.0960643047651284, 1.438070109281968, 1.7420162519173596, 1.992832044504999, 2.177634491131104, 2.286391439394468, 2.312470033318877, 2.253041030442416, 2.1093153771867836, 1.886596617652078, 1.594140948088984, 1.2448256644436237, 0.8546359756798448, 0.44198923137293183, 0.026924087357568766, -0.36981043217798887, -0.7277250305948115, -1.0275742587795993, -1.2523074114313524, -1.3879390953957067, -1.424294843186118, -1.3555919179632994, -1.180822369249597, -0.9039141809900325, -0.5336566290900407, -0.08338726749129997, 0.4295502468348587, 0.9845565812409771, 1.5587034922515424, 2.127795284872064, 2.66751541409823, 3.154603052372753, 3.568001472164706, 3.8899200066910917, 4.1067542505030525, 4.209814988618749, 4.19582488573861, 4.067152863221968, 3.8317688419070177, 3.5029155197750543, 3.0985083851959114, 2.640289487914386, 2.152773837127884, 1.66203893305821, 1.194417198252723, 0.7751573977638164, 0.4271241051291351, 0.1696036345179751, 0.017280557591837137, -0.02055890661373769, 0.05944863433894001, 0.25452296949766035, 0.555839066716834, 0.9489443881761668, 1.4144765348275372, 1.9291464831699972, 2.466937719384679, 3.0004590558347632, 3.5023795844067296, 3.9468686721884167, 4.310962532301361, 4.575781875627954, 4.727532395384804, 4.758231039267842, 4.666115633277633, 4.455712679134293, 4.137557124807522, 3.7275775549871377, 3.2461794511003976, 2.7170768134204226, 2.165937469386623, 1.6189188879027283, 1.1011785390411255, 0.6354452751450057, 0.24073562467326431, -0.06870866362135955, -0.28419766455951384, -0.4030369161696006, -0.42860894479473943, -0.3700852733802085, -0.2417836118478071, -0.062206514032905266, 0.14718245243749217, 0.36337226702801473, 0.5633224059551885, 0.7254922243386379, 0.8312867364193074, 0.8663274581921518, 0.8214663461789709, 0.6934754503131008, 0.48536391185308225, 0.20629630216481176, -0.1288892932598267, -0.5005400542086591, -0.885376647145822, -1.257941906045563, -1.5922232923346293, -1.8633498060701446, -2.0492573232993982, -2.132216137618275, -2.1001209436263766, -1.9474563593485594, -1.6758696792491232, -1.2943058386372888, -0.8186861935135932, -0.27114107454979985, 0.32116558968157427, 0.9275547563721226, 1.5156060310034605, 2.053080934594218, 2.509878261618987, 2.859899657117819, 3.0827067060420528, 3.1648615783830705, 3.1008610894643804, 2.8935979323434755, 2.55431142402296, 2.1020216534164518, 1.5624734730709962, 0.9666482773079044, 0.34892991839119764, -0.25496545371130025, -0.810168986355782, -1.2848124466500503, -1.6520190228401985, -1.89160353801254, -1.9913705511835895, -1.947922809837788, -1.7669225394469779, -1.4627822741645349, -1.0577982040130052, -0.5807750173359526, -0.06522460607818593, 0.4527504445464415, 0.9367558858116459, 1.3524411984309495, 1.6697210633324162, 1.8647382465362208, 1.9214383908598227, 1.8326510485061676, 1.6006023753433376, 1.2368212954952555, 0.7614403046702242, 0.20193184715375123, -0.40864125962625714, -1.0337500953733056, -1.6357615657680888], 'positive_zeros': ['1.02393888089349693967293608434390', '2.22728463189050631057902889298842', '3.84092207155881713644722109377886', '4.48413639840570454203249914551663', '5.59232004512023197121827602220448', '6.26794152529161447517798404710298', '7.26948453317897544910090398161271', '7.920126496569155684931452044744870', '9.269820194810572915186635399883487', '9.342068647681432314010660944254909'], 'prelabel': '2-1248-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.1567911195161136, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1037025418527821627, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.02393888089349693967293608434', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22728463189050631057902889299', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84092207155881713644722109378', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.965330172255797, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 1248, 'conductor_radical': 78, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 2, 0, 1, 0, 4, 0, 1, 0, 0, 0, -6, 0, 6, 0, -2, 0, 0, 0, -5, 0, -1, 0, -2, 0, -6, 0, -4, 0, 0, 0, 10, 0, -1, 0, 8, 0, 12, 0, 0, 0, 12, 0, -3, 0, 6, 0, -6, 0, 0, 0, -6, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, -8, 0, 14, 0, 5, 0, 8, 0, 4, 0, 1, 0, 8, 0, 0, 0, 2, 0, 4, 0, 2, 0, 6, 0, 0, 0, 14, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, -1, 0], 'euler17': [1, 6, 17], 'euler19': [1, -6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 6, 31], 'euler37': [1, -10, 37], 'euler41': [1, -8, 41], 'euler43': [1, -12, 43], 'euler47': [1, -12, 47], 'euler5': [1, 0, 5], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -2, 61], 'euler67': [1, -2, 67], 'euler7': [1, -2, 7], 'euler71': [1, 8, 71], 'euler73': [1, -14, 73], 'euler79': [1, -4, 79], 'euler83': [1, -8, 83], 'euler89': [1, -4, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 5], [1, -2, 7], [1, -4, 11], [1, -1, 0], [1, 6, 17], [1, -6, 19], [1, 0, 23], [1, 2, 29], [1, 6, 31], [1, -10, 37], [1, -8, 41], [1, -12, 43], [1, -12, 47], [1, 6, 53], [1, 0, 59], [1, -2, 61], [1, -2, 67], [1, 8, 71], [1, -14, 73], [1, -4, 79], [1, -8, 83], [1, -4, 89], [1, -14, 97]], 'index': 5, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1248/d', 'ModularForm/GL2/Q/holomorphic/1248/2/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/1248/2/a/d'], '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': '2-1248-1.1-c1-0-5', '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': '2-1248-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.1567911195161136, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1037025418527821627, 'z1': {'__RealLiteral__': 0, 'data': '1.02393888089349693967293608434', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20639794
{'Lhash': '1297996736961662889630088106666', 'Lhash_array': ['1297996736961662889630088106666'], 'label': '2-1248-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1248/2/a/d'}
-
id: 24552367
{'Lhash': '1297996736961662889630088106666', 'Lhash_array': ['1297996736961662889630088106666'], 'label': '2-1248-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1248/2/a/d/1/1'}
-
id: 37889
{'Lhash': '1037025418527821627', 'Lhash_array': ['1037025418527821627'], 'label': '2-1248-1.1-c1-0-5', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1248/d'}