-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1437695341546280973725971787685', 'a10': 0, 'a2': -1, 'a3': -1, 'a4': 1, 'a5': 0, 'a6': 1, 'a7': -4, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.75736457606492, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1]], [19, [1, 1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '2850.1', 'coefficient_field': '1.1.1.1', 'conductor': 2850, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1], [1, 4, 7], [1, 4, 11], [1, -2, 13], [1, -2, 17], [1, 1], [1, -8, 23], [1, -6, 29], [1, -4, 31], [1, -10, 37], [1, 2, 41], [1, 12, 43], [1, 0, 47], [1, 6, 53], [1, 0, 59], [1, 10, 61], [1, -4, 67], [1, 8, 71], [1, 2, 73], [1, 12, 79], [1, -8, 83], [1, -6, 89], [1, 18, 97], [1, 10, 101], [1, 16, 103], [1, -12, 107], [1, -10, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, 1], 1]], [1], [[[1, 4, 7], 1]], [[[1, 4, 11], 1]], [[[1, -2, 13], 1]], [[[1, -2, 17], 1]], [[[1, 1], 1]], [[[1, -8, 23], 1]], [[[1, -6, 29], 1]], [[[1, -4, 31], 1]], [[[1, -10, 37], 1]], [[[1, 2, 41], 1]], [[[1, 12, 43], 1]], [[[1, 0, 47], 1]], [[[1, 6, 53], 1]], [[[1, 0, 59], 1]], [[[1, 10, 61], 1]], [[[1, -4, 67], 1]], [[[1, 8, 71], 1]], [[[1, 2, 73], 1]], [[[1, 12, 79], 1]], [[[1, -8, 83], 1]], [[[1, -6, 89], 1]], [[[1, 18, 97], 1]], [[[1, 10, 101], 1]], [[[1, 16, 103], 1]], [[[1, -12, 107], 1]], [[[1, -10, 109], 1]], [[[1, -6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 25, 'label': '2-2850-1.1-c1-0-25', '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/2850/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.43421055231956e-61, 0.09136071028801412, 0.18195770685121584, 0.270995466090931, 0.35761714601842787, 0.44087950388824254, 0.5197340384674921, 0.593015726072965, 0.6594402422615615, 0.7176100875790762, 0.7660296051886196, 0.8031285129309983, 0.8272932787179996, 0.8369054402349287, 0.8303857949304375, 0.8062432494665119, 0.7631270062071024, 0.6998806688062524, 0.6155967649304603, 0.509670111292984, 0.38184838758853, 0.23227824705970188, 0.0615452790845063, -0.12929383947574283, -0.3386886055757061, -0.5645828571384229, -0.804415180295974, -1.055132678562689, -1.31321895934425, -1.5747368742575496, -1.8353861821750797, -2.090575893891464, -2.3355106132977377, -2.5652897225672167, -2.7750177807063285, -2.959924030209593, -3.1154884511390186, -3.23757138231126, -3.322543362439405, -3.3674115469333508, -3.3699388447771894, -3.32875180927268, -3.243433319251848, -3.11459621375795, -2.943934300061563, -2.734247545314952, -2.4894387850032773, -2.2144799308829506, -1.9153464267586622, -1.5989195668333236, -1.2728572383138483, -0.9454346528635129, -0.6253576617844318, -0.3215522756208581, -0.04293499587812852, 0.20183052099934112, 0.4045841453908931, 0.557920323800215, 0.6554320397003982, 0.6919399596554683, 0.6636989998073922, 0.5685747586820339, 0.40618273315018805, 0.17798396748523218, -0.11266822602201303, -0.4605346087483843, -0.8585521125363796, -1.297952765125389, -1.7684387640173118, -2.2584111819869674, -2.7552479259363305, -3.2456247470315263, -3.71587137947181, -4.152353333768278, -4.541868552138426, -4.872047108274499, -5.131741454186471, -5.311394426657895, -5.403372357207537, -5.402251201037297, -5.305044616037272, -5.1113643702707545, -4.823505306705818, -4.446449302087056, -3.987785161832244, -3.4575441194530554, -2.867953469701059, -2.2331137622341535, -1.5686078133978185, -0.891052451157058, -0.21760628680019659, 0.43455119354005545, 1.0487523951885098, 1.609368435051752, 2.102311838050576, 2.5154972070537935, 2.8392429035523032, 3.0665983740000473, 3.193583978629382, 3.2193329664702492, 3.146128508501391, 2.979332344108954, 2.7272054888011796, 2.400625452733212, 2.012708379117242, 1.5783482735089571, 1.113688905230476, 0.6355468745722967, 0.16080662177752233, -0.2941903058585803, -0.7142387005584986, -1.0858229988227488, -1.3976086685782325, -1.6408518756610044, -1.8097104414157532, -1.9014426726231277, -1.91648484716465, -1.8584028213912103, -1.7337182102826463, -1.5516146825216177, -1.3235349016561055, -1.0626833208637008, -0.7834541977954976, -0.5008076479737381, -0.22961913443680315, 0.01597063621925727, 0.22317797075813586, 0.3811438408605178, 0.4814220088587848, 0.5183656532979916, 0.48939447737847197, 0.39512910792036793, 0.23938509770219016, 0.029024807678161842, -0.2263283814934091, -0.5147029629298032, -0.822302948173954, -1.1341207139920366, -1.4346131462925202, -1.7084118751340742, -1.9410363234361074, -2.119577574538954, -2.2333217667133227, -2.2742838500415687, -2.2376260319932175, -2.121939967714555, -1.9293775345350614, -1.6656216289026597, -1.339695555198818, -0.9636169246131555, -0.5519092147962311, -0.12099092007848372, 0.31153177753466094, 0.7276379620352795, 1.109696113766888, 1.4412629049185803, 1.7078397469583184, 1.8975514939137814, 2.001714718149033, 2.015267579329922, 1.9370393198102123, 1.7698445859865966, 1.520395778904381, 1.1990351141183044, 0.8192966243560146, 0.3973165593594686, -0.04888187792930983, -0.500197148160679, -0.9373141084335554, -1.341584412573838, -1.695880824534805, -1.9853843934028965, -2.1982661555006957, -2.326229666692925, -2.364887035276508, -2.313948941513242, -2.1772180341163843, -1.9623846644717358, -1.6806336908161357, -1.3460805712549424, -0.9750636841464068, -0.5853273128497483, -0.1951356068140226, 0.1776382461781479, 0.5164016674676528, 0.8066657693699794, 1.0367594017610646, 1.1983968352331478, 1.2870688969299011, 1.302236190693025, 1.247313094444204, 1.1294420351616627, 0.9590685458352795, 0.7493382374041275, 0.5153465068766119, 0.27328002241257693, 0.03949531446371404, -0.17041621192882297, -0.34252610244338644, -0.4653800364471027, -0.5306768239379681, -0.5337761286699892, -0.4740045116976056, -0.3547398782423897, -0.18326617990962632, 0.02959733348144671, 0.270075560760035, 0.5221971449792832, 0.7686951833689598, 0.992001446233308, 1.1752803515164048, 1.3034456078383894, 1.3641021658565555, 1.3483589920584718, 1.2514641170816234, 1.0732221593269031, 0.8181656707510668, 0.49546464026513026, 0.1185726510180157, -0.2953772304591094, -0.7263995464103895, -1.1526661917915508, -1.5516473532514983, -1.9013236374588833, -2.1814039496962163, -2.374481744747439, -2.4670640229395935, -2.450412880666935, -2.3211483382867777, -2.081573152061983, -1.7396947829374096, -1.3089359022908957, -0.8075419062537887, -0.25771095717726417, 0.31551187685450066, 0.8855206752913262, 1.4255478142753197, 1.9101011823582463, 2.316360486356033, 2.625454030394106, 2.82354210612444, 2.9026421279715318, 2.861143488493763, 2.703976174729676, 2.4424156596966564, 2.0935264915045857, 1.6792672684195487, 1.22529918714655, 0.7595579739435443, 0.31066372186978575, -0.09374593200045925, -0.42866745142786356, -0.67327459984288, -0.8122636689679772, -0.836920045389878, -0.7458389710258793, -0.5452509701619981], 'positive_zeros': ['1.13414164856423095138492661576659', '2.75056461237209541081175930756122', '3.23152712333822717439104363251611', '4.58700919259485571170731352211609', '5.50198314718409406405972989252789', '6.34412577628387629359364040514422', '6.76011464101421078127674608335489', '7.68210243280282842646408090808335', '8.424191733926246675640608898571209'], 'prelabel': '2-2850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.770467961957707, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 745544897139724238, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13414164856423095138492661577', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.75056461237209541081175930756', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.23152712333822717439104363252', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 22.75736457606492, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 2850, 'conductor_radical': 570, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, -4, -1, 1, 0, -4, -1, 2, 4, 0, 1, 2, -1, -1, 0, 4, 4, 8, 1, 0, -2, -1, -4, 6, 0, 4, -1, 4, -2, 0, 1, 10, 1, -2, 0, -2, -4, -12, -4, 0, -8, 0, -1, 9, 0, -2, 2, -6, 1, 0, 4, 1, -6, 0, 0, -10, -4, -4, 1, 0, -4, 4, 2, -8, 0, -8, -1, -2, -10, 0, -1, 16, 2, -12, 0, 1, 2, 8, 4, 0, 12, -6, 4, 6, 0, -8, 8, -4, 0, 0, 1, -18, -9, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, -2, 13], 'euler17': [1, -2, 17], 'euler19': [1, 1, 0], 'euler2': [1, 1, 0], 'euler23': [1, -8, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -4, 31], 'euler37': [1, -10, 37], 'euler41': [1, 2, 41], 'euler43': [1, 12, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, 10, 61], 'euler67': [1, -4, 67], 'euler7': [1, 4, 7], 'euler71': [1, 8, 71], 'euler73': [1, 2, 73], 'euler79': [1, 12, 79], 'euler83': [1, -8, 83], 'euler89': [1, -6, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 0, 0], [1, 4, 7], [1, 4, 11], [1, -2, 13], [1, -2, 17], [1, 1, 0], [1, -8, 23], [1, -6, 29], [1, -4, 31], [1, -10, 37], [1, 2, 41], [1, 12, 43], [1, 0, 47], [1, 6, 53], [1, 0, 59], [1, 10, 61], [1, -4, 67], [1, 8, 71], [1, 2, 73], [1, 12, 79], [1, -8, 83], [1, -6, 89], [1, 18, 97]], 'index': 25, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2850/a', 'ModularForm/GL2/Q/holomorphic/2850/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/2850/2/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': '2-2850-1.1-c1-0-25', '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': '2-2850-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.770467961957707, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 745544897139724238, 'z1': {'__RealLiteral__': 0, 'data': '1.13414164856423095138492661577', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20030325
{'Lhash': '1437695341546280973725971787685', 'Lhash_array': ['1437695341546280973725971787685'], 'factors': ['2-2850-1.1-c1-0-25'], 'label': '2-2850-1.1-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2850/2/a/a'}
-
id: 24559035
{'Lhash': '1437695341546280973725971787685', 'Lhash_array': ['1437695341546280973725971787685'], 'factors': ['2-2850-1.1-c1-0-25'], 'label': '2-2850-1.1-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2850/2/a/a/1/1'}
-
id: 100271
{'Lhash': '745544897139724238', 'Lhash_array': ['745544897139724238'], 'factors': ['2-2850-1.1-c1-0-25'], 'label': '2-2850-1.1-c1-0-25', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2850/a'}