-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1415548293399244386780825791184', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 38.3281929702146, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '4800.1', 'coefficient_field': '1.1.1.1', 'conductor': 4800, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1, -4, 7], [1, 0, 11], [1, -4, 13], [1, 0, 17], [1, -8, 19], [1, 4, 23], [1, -6, 29], [1, 8, 31], [1, 4, 37], [1, -6, 41], [1, -4, 43], [1, -4, 47], [1, 12, 53], [1, 0, 59], [1, -6, 61], [1, -12, 67], [1, 16, 71], [1, 0, 73], [1, 8, 79], [1, 12, 83], [1, 10, 89], [1, 8, 97], [1, 14, 101], [1, -12, 103], [1, -12, 107], [1, -10, 109], [1, -8, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [1], [[[1, -4, 7], 1]], [[[1, 0, 11], 1]], [[[1, -4, 13], 1]], [[[1, 0, 17], 1]], [[[1, -8, 19], 1]], [[[1, 4, 23], 1]], [[[1, -6, 29], 1]], [[[1, 8, 31], 1]], [[[1, 4, 37], 1]], [[[1, -6, 41], 1]], [[[1, -4, 43], 1]], [[[1, -4, 47], 1]], [[[1, 12, 53], 1]], [[[1, 0, 59], 1]], [[[1, -6, 61], 1]], [[[1, -12, 67], 1]], [[[1, 16, 71], 1]], [[[1, 0, 73], 1]], [[[1, 8, 79], 1]], [[[1, 12, 83], 1]], [[[1, 10, 89], 1]], [[[1, 8, 97], 1]], [[[1, 14, 101], 1]], [[[1, -12, 103], 1]], [[[1, -12, 107], 1]], [[[1, -10, 109], 1]], [[[1, -8, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 40, 'label': '2-4800-1.1-c1-0-40', 'leading_term': '3.41151252156961245243853131175000000000000000000000000000000000000000000000000000000000000', '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/4800/2/a/cr', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [3.4115125215696125, 3.404017259408647, 3.381453686364099, 3.343597550738861, 3.29010481272189, 3.2205540239529684, 3.134501530903376, 3.03154590929942, 2.9113976561880865, 2.773950100520751, 2.6193476844259624, 2.448048138703413, 2.260875550860086, 2.059061839645156, 1.844274664453634, 1.6186302896710199, 1.384690388025623, 1.145442208951051, 0.904261968366941, 0.6648617459306909, 0.43122061256338, 0.20750115814183673, -0.0020469553373426703, -0.1931943331673776, -0.36184755158769827, -0.5041702762698955, -0.6167064678529185, -0.6965020298992833, -0.741221018346726, -0.7492523940013613, -0.7198032772418507, -0.6529747704705684, -0.5498166588810122, -0.412357689293199, -0.2436086605350557, -0.047536231932112406, 0.17099384216665328, 0.40630443132370386, 0.6520250800617265, 0.9012387090091554, 1.1466541969493493, 1.3808009982267007, 1.5962409246547482, 1.7857912885988798, 1.9427528061160364, 2.061135036180577, 2.1358717210410783, 2.163018225497584, 2.139923374455057, 2.065368375252429, 1.9396661910438204, 1.7647157001921205, 1.5440062189814725, 1.282569453882574, 0.9868776463318901, 0.6646885276655857, 0.3248396547101798, -0.023003320473913385, -0.36863795427644275, -0.7016475791891447, -1.0117452093307635, -1.2891275176009933, -1.5248266248959672, -1.7110468566195487, -1.84147349373028, -1.9115409087357749, -1.9186483477558522, -1.8623129948922343, -1.7442518108122826, -1.568385928672287, -1.3407640515614387, -1.069404241485531, -0.7640566184165317, -0.4358926831178472, -0.09713011343777003, 0.23939517052372528, 0.5606952525531292, 0.8541181802254413, 1.1078394240766172, 1.3113376625195408, 1.455835492888036, 1.5346862241748178, 1.543689261412772, 1.4813187301866937, 1.3488528631336552, 1.1503951950438596, 0.8927826733955655, 0.5853802416786016, 0.23976612396453045, -0.1306832573141572, -0.5112952618874456, -0.8866722748199556, -1.2413109754556864, -1.5602455417184982, -1.8296887515016529, -2.0376440266923264, -2.174461667472695, -2.233313886264427, -2.210565763932249, -2.1060228559366947, -1.9230407618497094, -1.668487377852184, -1.3525545742388465, -0.9884224373377373, -0.5917857186875639, -0.18025845819479894, 0.22732139765327178, 0.611660457782283, 0.9538204100089477, 1.2360367267681067, 1.442510223448462, 1.5601362185572396, 1.579137706645108, 1.4935721821366383, 1.3016864544073063, 1.0060998090736404, 0.6138029675703263, 0.13596818740114952, -0.4124258083586032, -1.0131419529599015, -1.6453857635114413, -2.286631394990321, -2.9135387710013103, -3.5029227661697466, -4.03273211238329, -4.482994278314489, -4.836683152902385, -5.080468980751325, -5.205314585649726, -5.2068883151463226, -5.085772088946939, -4.847452097757606, -4.502089668187927, -4.064080122480413, -3.551417627224068, -2.984893543388697, -2.3871641786672124, -1.7817306617771533, -1.191878531930473, -0.6396272763646217, -0.1447402695822759, 0.276156698897409, 0.6103048210428377, 0.8493530566571085, 0.9896826824788213, 1.0324984324146336, 0.983680564566503, 0.8534041864243989, 0.6555440504246332, 0.40689418495936097, 0.12624155967867148, -0.1666590392257947, -0.45215608276523533, -0.7117624723762749, -0.9291508256646628, -1.0910296900033167, -1.1878531561996235, -1.2143246173332565, -1.1696659230825315, -1.0576354050839794, -0.8862915770124152, -0.6675130525214004, -0.416298644048422, -0.14988397400153422, 0.11327844598191371, 0.35462044765596445, 0.5565801283761546, 0.7036816590619794, 0.7835114045034701, 0.7875334339153998, 0.711695392896581, 0.5567864811006701, 0.32852240283469963, 0.037346957039330456, -0.3020443745769655, -0.6714377495577316, -1.0500552077356047, -1.415680635573573, -1.745897506800569, -2.01937083414707, -2.2171017729303752, -2.3235832590703582, -2.3277890377680173, -2.2239363155455174, -2.011973695003234, -1.6977604663078099, -1.2929199867021806, -0.8143678881940096, -0.2835342242663717, 0.274683635679443, 0.8331845519915365, 1.3640774291371782, 1.8401692340114149, 2.2364453691523285, 2.531459299817783, 2.708551787334157, 2.7568281470164906, 2.6718342666866564, 2.4558880773965712, 2.1180419232829393, 1.6736718133635982, 1.1437107090398306, 0.5535635988177403, -0.06823906590860322, -0.6915770791521342, -1.2863808001365076, -1.8242841748949445, -2.2801963555517606, -2.6337010320472136, -2.8702011417953432, -2.9817401096238427, -2.967448499463104, -2.8335859728269464, -2.593171576127022, -2.2652192996019074, -1.8736191717450297, -1.4457254886366242, -1.0107318315838292, -0.5979261721318304, -0.2349277139493796, 0.05399041257096279, 0.24939215433477369, 0.3378924781524466, 0.3130187276978111, 0.17566383819828665, -0.06590056264931206, -0.3964572884973692, -0.7947024808247266, -1.2344839959810847, -1.686349667203768, -2.119316285260306, -2.5027556922800676, -2.8082859682103662, -3.0115539104775397, -3.0938000739356295, -3.043109345912144, -2.8552677677559495, -2.5341690893807165, -2.091741042567669, -1.5473899791187509, -0.9269916213348268, -0.26148344124856904, 0.4148610967514146, 1.0663760837241754, 1.6580499477449353, 2.157553551426549, 2.5371277133688785, 2.7752157611605774, 2.857741320828064, 2.7789524194554653, 2.541778898916037, 2.157679552771869, 1.6459865104958364, 1.0327852794083339, 0.3493975818308839, -0.3694411277065589, -1.087598403936892], 'positive_zeros': ['1.11667070811498633724375052576907', '1.78880168891016879906422911972826', '2.89117966658209599698824732349248', '3.77234879142134775989617790878176', '4.50188046792247165912627678050358', '5.35428782503707845302610895953052', '5.95456074589170255162775334423485', '7.12577752047617924306678684799539', '7.63913294562116664057387968365116', '8.305957288951370619438522439080020'], 'prelabel': '2-4800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.190976737980414, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1266597852054803578, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11667070811498633724375052577', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.78880168891016879906422911973', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.89117966658209599698824732349', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 38.3281929702146, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 4800, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 4, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 8, 0, 4, 0, -4, 0, 0, 0, 1, 0, 6, 0, -8, 0, 0, 0, 0, 0, -4, 0, 4, 0, 6, 0, 4, 0, 0, 0, 4, 0, 9, 0, 0, 0, -12, 0, 0, 0, 8, 0, 0, 0, 6, 0, 4, 0, 0, 0, 12, 0, -4, 0, -16, 0, 0, 0, 0, 0, 0, 0, -8, 0, 1, 0, -12, 0, 0, 0, 6, 0, -10, 0, 16, 0, -8, 0, 0, 0, -8, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -4, 13], 'euler17': [1, 0, 17], 'euler19': [1, -8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 8, 31], 'euler37': [1, 4, 37], 'euler41': [1, -6, 41], 'euler43': [1, -4, 43], 'euler47': [1, -4, 47], 'euler5': [1, 0, 0], 'euler53': [1, 12, 53], 'euler59': [1, 0, 59], 'euler61': [1, -6, 61], 'euler67': [1, -12, 67], 'euler7': [1, -4, 7], 'euler71': [1, 16, 71], 'euler73': [1, 0, 73], 'euler79': [1, 8, 79], 'euler83': [1, 12, 83], 'euler89': [1, 10, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, -4, 7], [1, 0, 11], [1, -4, 13], [1, 0, 17], [1, -8, 19], [1, 4, 23], [1, -6, 29], [1, 8, 31], [1, 4, 37], [1, -6, 41], [1, -4, 43], [1, -4, 47], [1, 12, 53], [1, 0, 59], [1, -6, 61], [1, -12, 67], [1, 16, 71], [1, 0, 73], [1, 8, 79], [1, 12, 83], [1, 10, 89], [1, 8, 97]], 'index': 40, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4800/cr', 'ModularForm/GL2/Q/holomorphic/4800/2/a/cr/1/1', 'ModularForm/GL2/Q/holomorphic/4800/2/a/cr'], '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': '2-4800-1.1-c1-0-40', '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': '2-4800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.190976737980414, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1266597852054803578, 'z1': {'__RealLiteral__': 0, 'data': '1.11667070811498633724375052577', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20019253
{'Lhash': '1415548293399244386780825791184', 'Lhash_array': ['1415548293399244386780825791184'], 'label': '2-4800-1.1-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4800/2/a/cr'}
-
id: 24567556
{'Lhash': '1415548293399244386780825791184', 'Lhash_array': ['1415548293399244386780825791184'], 'label': '2-4800-1.1-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4800/2/a/cr/1/1'}
-
id: 94607
{'Lhash': '1266597852054803578', 'Lhash_array': ['1266597852054803578'], 'label': '2-4800-1.1-c1-0-40', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4800/cr'}