-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2262551602671586861947184780754', 'a10': -2, 'a2': -2, 'a3': 0, 'a4': 2, 'a5': 1, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -1]], [13, [1, 1]]], 'bad_primes': [3, 5, 13], 'central_character': '585.1', 'coefficient_field': '1.1.1.1', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'euler_factors': [[1, 2, 2], [1], [1, -1], [1, 1, 7], [1, 5, 11], [1, 1], [1, -7, 17], [1, 6, 19], [1, 3, 23], [1, 2, 29], [1, -2, 31], [1, -7, 37], [1, 9, 41], [1, 8, 43], [1, 10, 47], [1, 5, 53], [1, 0, 59], [1, -5, 61], [1, 4, 67], [1, 9, 71], [1, 6, 73], [1, 3, 79], [1, -4, 83], [1, 11, 89], [1, 11, 97], [1, 0, 101], [1, 4, 103], [1, -17, 107], [1, -4, 109], [1, 10, 113]], 'euler_factors_factorization': [[[[1, 2, 2], 1]], [1], [[[1, -1], 1]], [[[1, 1, 7], 1]], [[[1, 5, 11], 1]], [[[1, 1], 1]], [[[1, -7, 17], 1]], [[[1, 6, 19], 1]], [[[1, 3, 23], 1]], [[[1, 2, 29], 1]], [[[1, -2, 31], 1]], [[[1, -7, 37], 1]], [[[1, 9, 41], 1]], [[[1, 8, 43], 1]], [[[1, 10, 47], 1]], [[[1, 5, 53], 1]], [[[1, 0, 59], 1]], [[[1, -5, 61], 1]], [[[1, 4, 67], 1]], [[[1, 9, 71], 1]], [[[1, 6, 73], 1]], [[[1, 3, 79], 1]], [[[1, -4, 83], 1]], [[[1, 11, 89], 1]], [[[1, 11, 97], 1]], [[[1, 0, 101], 1]], [[[1, 4, 103], 1]], [[[1, -17, 107], 1]], [[[1, -4, 109], 1]], [[[1, 10, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-585-1.1-c1-0-11', '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/585/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.760001047746869e-120, 0.14712253449701634, 0.295470836281969, 0.44499377556094305, 0.5933673882713286, 0.7354511447379249, 0.8632354250583583, 0.9662413220646835, 1.0323169325100066, 1.0487812998541817, 1.0038649497593022, 0.8883727150035416, 0.6974542020206285, 0.43232011657433206, 0.10170021743504408, -0.27718832799840737, -0.6783956176106816, -1.0679204073789463, -1.4054562693523316, -1.647239409748419, -1.7499040760242377, -1.6751021493089562, -1.3944927110184548, -0.8945761717692896, -0.18075899557581623, 0.7199889533277036, 1.7584647443116748, 2.8649827259484555, 3.9537420010580426, 4.9297024532209175, 5.697515249652083, 6.171711060014726, 6.287059561180202, 6.007828483193277, 5.334634055434154, 4.307716707124895, 3.005803261078499, 1.5402091441553882, 0.044442005956850064, -1.339783314297572, -2.478611715387352, -3.262242368616981, -3.6190858008458195, -3.5258059366578394, -3.0115768042863134, -2.155583294591643, -1.0777090032187544, 0.07664104982874372, 1.1556910961070597, 2.0218024818304725, 2.570356185452085, 2.744111650199245, 2.540702911523165, 2.0119125333122736, 1.25463048581739, 0.3947632415957304, -0.4334208704651483, -1.1091643838503207, -1.5446442615264664, -1.698588522820224, -1.5816524202247682, -1.2525279265666753, -0.8054180830915224, -0.35111914411572526, 0.004790660948857198, 0.18251821110778543, 0.1433779598999188, -0.10320216629963856, -0.5024852403496022, -0.9665889731334155, -1.3936221680367684, -1.689882306599815, -1.7904285188899551, -1.6735278971863827, -1.3656317699004283, -0.9354815949788912, -0.4782980566514583, -0.09328205835753228, 0.14065536214423327, 0.18533138806119315, 0.054835967462827546, -0.18514578314504396, -0.43093951487812077, -0.5651413869904169, -0.4865716640718493, -0.1392121629120189, 0.46691812976457053, 1.248721539135844, 2.0598628058036867, 2.7168733718604017, 3.037054095611621, 2.880562032037612, 2.187399590445534, 1.000350004231171, -0.5326853506039118, -2.1793759747513937, -3.6640914366037425, -4.7220516271144914, -5.155551012209593, -4.87999670815253, -3.9488696802892496, -2.5506532755305966, -0.9765551638392169, 0.4357185519115811, 1.3712233247889132, 1.6056224403662855, 1.0566965044329324, -0.1925367068585627, -1.9054017684074815, -3.7367049675335346, -5.302765181919367, -6.261788246453734, -6.387233745438022, -5.61786986806801, -4.073011583469982, -2.0290061050887136, 0.1383072351310601, 2.032670768846013, 3.3205016123803737, 3.79945472065286, 3.437182106320847, 2.371894669093332, 0.875224208479331, -0.7133287890391714, -2.0645166057211957, -2.9314686964974417, -3.1990498254402073, -2.8995600665175525, -2.1923763856965808, -1.3141034570531702, -0.5129734828821538, 0.015210903385400423, 0.17325238897123987, -0.02030139728495762, -0.44619449153617596, -0.9261212913532837, -1.278417990156299, -1.3717169108462568, -1.161499536352549, -0.6996754449065403, -0.11522658290888187, 0.4276479653144782, 0.7809650074929569, 0.8583421597304942, 0.6605966262898747, 0.2737919710077119, -0.15968472437352213, -0.4881495409406793, -0.6011471690773422, -0.467463744510288, -0.14808992719003042, 0.22094743481047166, 0.47166131046498455, 0.4604831697964488, 0.12049311476145011, -0.5076065613844742, -1.277195335529108, -1.9719714772934158, -2.367858440723815, -2.303069134129515, -1.7350170864706769, -0.7652754355097554, 0.3777600327555304, 1.3966425995229337, 2.0087292425570364, 2.032754596662423, 1.4521771589265846, 0.4343941723817485, -0.7034233802707646, -1.5759141967733328, -1.838104823658329, -1.2911819827179944, 0.045551000576475244, 1.9197447592317383, 3.8962768487809116, 5.462628396517236, 6.162910726912245, 5.724505155503225, 4.141571857584302, 1.6902144094491398, -1.131750086320473, -3.7266001937851687, -5.548617253909653, -6.245318358752446, -5.749239519117702, -4.29449846451964, -2.352901719452132, -0.506682791399213, 0.7073083266777129, 0.9391482646301108, 0.11442575550467043, -1.5536995463314986, -3.630767378464341, -5.58532604644436, -6.934998392885037, -7.372751921194768, -6.838696847313347, -5.519559215441863, -3.7795886062284776, -2.046518343904026, -0.6883728692717768, 0.08208782600000555, 0.2486959222421109, -0.029667958050199103, -0.4922327356687179, -0.8742932004541465, -0.9967304272700922, -0.8183717072976244, -0.43613907000483915, -0.03606569143752471, 0.18524112423509886, 0.09969927411295944, -0.3008788019373564, -0.8990308924796617, -1.4929516165754153, -1.8695568690849433, -1.8827410382525305, -1.508407055114939, -0.8560697954418137, -0.13229312667773444, 0.43147689386112614, 0.6610892428486126, 0.5022275330787411, 0.04020387054967824, -0.5310729606086423, -0.980698056113012, -1.1275417889579473, -0.9104117104214564, -0.4148142396781294, 0.15548290707790488, 0.5539096472588428, 0.587456417038286, 0.19853206023403497, -0.49991300983416914, -1.253037075592733, -1.751155070965363, -1.7478077623341566, -1.1678155330641984, -0.16438829025131976, 0.9008832752563439, 1.5561632910862464, 1.3692044407769486, 0.10216911296572333, -2.1808994022165775, -5.094391051738335, -8.01322312459072, -10.237856411732768, -11.194848379596035, -10.611166264953743, -8.605731360163745, -5.665703992317975, -2.510668779917029, 0.11618629607632319, 1.6664020633703567, 1.946083811177132, 1.1666023050087282, -0.1304312533360295], 'positive_zeros': ['1.78483850539275904424541360816730', '3.02709857296590648239002053477262', '4.75380031772719504345197730312694', '5.86662536743360060967332495720319', '6.93279974611194334514178729187020', '7.997850874518894594264893149223458', '8.333107995317450905784282789603377', '9.664619125780354113128944873936397', '10.03210824623968341800708629458887'], 'prelabel': '2-585-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.161307131863703, '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': 995739043322927628, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78483850539275904424541360817', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.02709857296590648239002053477', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.75380031772719504345197730313', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'dirichlet_coefficients': [1, -2, 0, 2, 1, 0, -1, 0, 0, -2, -5, 0, -1, 2, 0, -4, 7, 0, -6, 2, 0, 10, -3, 0, 1, 2, 0, -2, -2, 0, 2, 8, 0, -14, -1, 0, 7, 12, 0, 0, -9, 0, -8, -10, 0, 6, -10, 0, -6, -2, 0, -2, -5, 0, -5, 0, 0, 4, 0, 0, 5, -4, 0, -8, -1, 0, -4, 14, 0, 2, -9, 0, -6, -14, 0, -12, 5, 0, -3, -4, 0, 18, 4, 0, 7, 16, 0, 0, -11, 0, 1, -6, 0, 20, -6, 0, -11, 12, 0, 2], 'euler11': [1, 5, 11], 'euler13': [1, 1, 0], 'euler17': [1, -7, 17], 'euler19': [1, 6, 19], 'euler2': [1, 2, 2], 'euler23': [1, 3, 23], 'euler29': [1, 2, 29], 'euler3': [1, 0, 0], 'euler31': [1, -2, 31], 'euler37': [1, -7, 37], 'euler41': [1, 9, 41], 'euler43': [1, 8, 43], 'euler47': [1, 10, 47], 'euler5': [1, -1, 0], 'euler53': [1, 5, 53], 'euler59': [1, 0, 59], 'euler61': [1, -5, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 7], 'euler71': [1, 9, 71], 'euler73': [1, 6, 73], 'euler79': [1, 3, 79], 'euler83': [1, -4, 83], 'euler89': [1, 11, 89], 'euler97': [1, 11, 97], 'euler_factors': [[1, 2, 2], [1, 0, 0], [1, -1, 0], [1, 1, 7], [1, 5, 11], [1, 1, 0], [1, -7, 17], [1, 6, 19], [1, 3, 23], [1, 2, 29], [1, -2, 31], [1, -7, 37], [1, 9, 41], [1, 8, 43], [1, 10, 47], [1, 5, 53], [1, 0, 59], [1, -5, 61], [1, 4, 67], [1, 9, 71], [1, 6, 73], [1, 3, 79], [1, -4, 83], [1, 11, 89], [1, 11, 97]], 'index': 11, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/585/c', 'ModularForm/GL2/Q/holomorphic/585/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/585/2/a/c'], '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': '2-585-1.1-c1-0-11', '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': '2-585-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 995739043322927628, 'z1': {'__RealLiteral__': 0, 'data': '1.78483850539275904424541360817', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 11908926
{'Lhash': '2262551602671586861947184780754', 'Lhash_array': ['2262551602671586861947184780754'], 'label': '2-585-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/a/c'}
-
id: 24549830
{'Lhash': '2262551602671586861947184780754', 'Lhash_array': ['2262551602671586861947184780754'], 'label': '2-585-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/a/c/1/1'}
-
id: 35006
{'Lhash': '995739043322927628', 'Lhash_array': ['995739043322927628'], 'label': '2-585-1.1-c1-0-11', 'type': 'ECQ', 'url': 'EllipticCurve/Q/585/c'}