-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1809144392571748153596103682209', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.650678796170963, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '1960.1', 'coefficient_field': '1.1.1.1', 'conductor': 1960, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1, 1], [1], [1, 2, 11], [1, -4, 13], [1, 0, 17], [1, -6, 19], [1, -3, 23], [1, 3, 29], [1, 0, 31], [1, 12, 37], [1, 7, 41], [1, 9, 43], [1, 0, 47], [1, 6, 53], [1, 10, 59], [1, -5, 61], [1, -11, 67], [1, 10, 71], [1, 8, 73], [1, -6, 79], [1, 3, 83], [1, -17, 89], [1, 2, 97], [1, 17, 101], [1, 15, 103], [1, 1, 107], [1, 5, 109], [1, 18, 113]], 'euler_factors_factorization': [[1], [[[1, 1, 3], 1]], [[[1, 1], 1]], [1], [[[1, 2, 11], 1]], [[[1, -4, 13], 1]], [[[1, 0, 17], 1]], [[[1, -6, 19], 1]], [[[1, -3, 23], 1]], [[[1, 3, 29], 1]], [[[1, 0, 31], 1]], [[[1, 12, 37], 1]], [[[1, 7, 41], 1]], [[[1, 9, 43], 1]], [[[1, 0, 47], 1]], [[[1, 6, 53], 1]], [[[1, 10, 59], 1]], [[[1, -5, 61], 1]], [[[1, -11, 67], 1]], [[[1, 10, 71], 1]], [[[1, 8, 73], 1]], [[[1, -6, 79], 1]], [[[1, 3, 83], 1]], [[[1, -17, 89], 1]], [[[1, 2, 97], 1]], [[[1, 17, 101], 1]], [[[1, 15, 103], 1]], [[[1, 1, 107], 1]], [[[1, 5, 109], 1]], [[[1, 18, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-1960-1.1-c1-0-28', '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/1960/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-7.717997463753564e-61, 0.12180441319626603, 0.24326068279219837, 0.36398379968548966, 0.48351706875771683, 0.6013012189948373, 0.7166490372140825, 0.8287267374652797, 0.9365428619587731, 1.0389451067656779, 1.1346251126364562, 1.222130977373774, 1.29988703450475, 1.3662202947237625, 1.4193928462022485, 1.457639440108349, 1.4792094331424708, 1.482412208093578, 1.465665139474427, 1.4275431116497281, 1.3668285325186857, 1.2825607203183023, 1.174083479687402, 1.0410896318371252, 0.883661228802149, 0.7023041693444866, 0.49797594960430125, 0.2721053296504463, 0.026602781252692758, -0.23613929512786488, -0.5132574338531879, -0.8014396962420135, -1.0969604002170368, -1.3957271227109498, -1.6933398066491634, -1.985161477196812, -2.2663997285478485, -2.5321977914906366, -2.7777336430059982, -2.9983252827746587, -3.18953998879983, -3.3473050867662333, -3.4680175365686714, -3.5486494655232286, -3.5868466711684035, -3.5810170860965598, -3.5304062501389684, -3.435156976684286, -3.2963506328357544, -3.116027777779287, -2.897186317560162, -2.6437558318547003, -2.360547300596892, -2.0531780937450885, -1.727972771395017, -1.391840956527869, -1.052134269265765, -0.7164850280683825, -0.39263010702101553, -0.08822396576713311, 0.18935458365828897, 0.43319686335400376, 0.6370547372660258, 0.7955214268746056, 0.9041971970044085, 0.9598345166519406, 0.9604576161005134, 0.9054518525843964, 0.7956189576753496, 0.6331950597819953, 0.4218293380893315, 0.16652224751726566, -0.1264765700115953, -0.4498093372520167, -0.7951875471094203, -1.153601871227061, -1.5155595381026612, -1.8713430651572642, -2.211283289515338, -2.5260388839590684, -2.8068740027344066, -3.0459254063809995, -3.23645038854647, -3.3730470858580195, -3.451839300390331, -3.4706187993599857, -3.428939164458595, -3.328156619464173, -3.171414835153191, -2.9635724513915243, -2.7110739155727654, -2.421766155311206, -2.1046655173011724, -1.7696812461911593, -1.4273034789927548, -1.0882652253399079, -0.7631890293445617, -0.46222990901799804, -0.19472669746873122, 0.03112596914537153, 0.2085730809393153, 0.33255091129123204, 0.39988488744898487, 0.4094252410224567, 0.362113949137274, 0.2609787296994624, 0.11105234495940983, -0.08078188585110097, -0.30601475339847223, -0.5547997168740684, -0.8162965259241245, -1.0790587731815824, -1.3314522730010834, -1.562089610476268, -1.7602651487642795, -1.9163742816238032, -2.022300812484893, -2.0717570505824594, -2.0605625349254804, -1.986849200430875, -1.8511832358046714, -1.656596775156514, -1.4085258193617067, -1.114654285219719, -0.7846677025366415, -0.42992368357592753, -0.06304973333582106, 0.3025178889214688, 0.6530378417432374, 0.9749913474550718, 1.2556137730491954, 1.4834093753921014, 1.648628511449944, 1.7436875133023928, 1.7635131467378649, 1.7057960697109298, 1.5711409081207701, 1.363104364942705, 1.0881170400598814, 0.7552892036685429, 0.3761054591264852, -0.035982136705663186, -0.4660485486234601, -0.8982599496245632, -1.3164864162645797, -1.7049393875051908, -2.048808504735724, -2.3348718158544512, -2.552053751316819, -2.691906779797308, -2.748995195599989, -2.7211630040290906, -2.6096722358591147, -2.419203079072507, -2.1577127718181552, -1.836156034276376, -1.468075689101368, -1.0690777814891925, -0.6562107131300493, -0.24727241388176904, 0.13992682178327193, 0.48831568962661487, 0.7822959855995485, 1.008428056280359, 1.1560375451689198, 1.2177160854456965, 1.189692528422902, 1.0720563402414993, 0.868820756250477, 0.5878199162019047, 0.24044124070938883, -0.15879854823005934, -0.592818423846704, -1.042657310521685, -1.4882502351187223, -1.909264484181811, -2.285960658494844, -2.600041777763024, -2.8354534412029757, -2.979099537354258, -3.021441088538726, -2.9569504089119927, -2.7843986762383266, -2.5069620281451805, -2.1321391001561145, -1.671481188486676, -1.140144579773428, -0.5562826642164477, 0.059697135871145675, 0.685980185405696, 1.3002586863435546, 1.8806729425829247, 2.4067381003613506, 2.860214786611355, 3.2258841430161485, 3.492191680034814, 3.651730002864283, 3.7015375570156897, 3.64319879778207, 3.482740237159114, 3.230326250607296, 2.8997678950386034, 2.5078668534156536, 2.0736245506609756, 1.6173530869621886, 1.1597295710527937, 0.7208384444663875, 0.3192472930866117, -0.028839631883744995, -0.31030938711903766, -0.5157144519969286, -0.6396648601850269, -0.681018908488252, -0.6428627428507881, -0.5322794518204613, -0.3599187185359146, -0.1393880790563864, 0.11350409508899537, 0.3816160947029151, 0.6474071754609306, 0.8938912291628578, 1.1055609690419341, 1.2692348060562924, 1.3747820618155526, 1.4156879332929941, 1.38942743935223, 1.297627075445418, 1.1460036243668736, 0.9440809903993226, 0.7046974686880406, 0.44332694105547027, 0.177247526137095, -0.07540032943512294, -0.2966179152931314, -0.46956206677990325, -0.5795149633016238, -0.6147575919827365, -0.567298740762412, -0.4334181608338894, -0.2139915973084009, 0.08542370046413893, 0.4547521461362577, 0.8798078824838315, 1.342930990615855, 1.8238227469683663, 2.3005397899181785, 2.7505979159988168, 3.152129501623779, 3.4850346401000074, 3.7320652556175546, 3.8797838091347767, 3.919343683429505, 3.8470466981274183, 3.6646440751725873, 3.379360025828378, 3.0036313215668065, 2.5545710191678404], 'positive_zeros': ['1.42716328319966679433068843179588', '3.01165179487227605482580787316791', '3.63504624826388638450776523592310', '5.01968135180339698653294960296276', '5.41340289830795980497616333726969', '6.40713018566319065782761915503450', '7.15583529024822094542501370686371', '8.106170928651121440047566664439655', '8.664044103642081964361887443344979'], 'prelabel': '2-1960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9560938811118933, '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': 1593290053591338410, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.42716328319966679433068843180', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.01165179487227605482580787317', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.63504624826388638450776523592', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 15.650678796170963, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 1960, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 0, 0, -2, 0, -2, 0, 4, 0, 1, 0, 0, 0, 6, 0, 0, 0, 3, 0, 1, 0, 5, 0, -3, 0, 0, 0, 2, 0, 0, 0, -12, 0, -4, 0, -7, 0, -9, 0, 2, 0, 0, 0, 0, 0, 0, 0, -6, 0, 2, 0, -6, 0, -10, 0, 5, 0, 0, 0, -4, 0, 11, 0, -3, 0, -10, 0, -8, 0, -1, 0, 0, 0, 6, 0, 1, 0, -3, 0, 0, 0, 3, 0, 17, 0, 0, 0, 0, 0, -6, 0, -2, 0, 4, 0], 'euler11': [1, 2, 11], 'euler13': [1, -4, 13], 'euler17': [1, 0, 17], 'euler19': [1, -6, 19], 'euler2': [1, 0, 0], 'euler23': [1, -3, 23], 'euler29': [1, 3, 29], 'euler3': [1, 1, 3], 'euler31': [1, 0, 31], 'euler37': [1, 12, 37], 'euler41': [1, 7, 41], 'euler43': [1, 9, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, 6, 53], 'euler59': [1, 10, 59], 'euler61': [1, -5, 61], 'euler67': [1, -11, 67], 'euler7': [1, 0, 0], 'euler71': [1, 10, 71], 'euler73': [1, 8, 73], 'euler79': [1, -6, 79], 'euler83': [1, 3, 83], 'euler89': [1, -17, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, 1, 0], [1, 0, 0], [1, 2, 11], [1, -4, 13], [1, 0, 17], [1, -6, 19], [1, -3, 23], [1, 3, 29], [1, 0, 31], [1, 12, 37], [1, 7, 41], [1, 9, 43], [1, 0, 47], [1, 6, 53], [1, 10, 59], [1, -5, 61], [1, -11, 67], [1, 10, 71], [1, 8, 73], [1, -6, 79], [1, 3, 83], [1, -17, 89], [1, 2, 97]], 'index': 28, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1960/c', 'ModularForm/GL2/Q/holomorphic/1960/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/1960/2/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': '2-1960-1.1-c1-0-28', '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': '2-1960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9560938811118933, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1593290053591338410, 'z1': {'__RealLiteral__': 0, 'data': '1.42716328319966679433068843180', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20609162
{'Lhash': '1809144392571748153596103682209', 'Lhash_array': ['1809144392571748153596103682209'], 'label': '2-1960-1.1-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1960/2/a/c'}
-
id: 24555264
{'Lhash': '1809144392571748153596103682209', 'Lhash_array': ['1809144392571748153596103682209'], 'label': '2-1960-1.1-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1960/2/a/c/1/1'}
-
id: 36460
{'Lhash': '1593290053591338410', 'Lhash_array': ['1593290053591338410'], 'label': '2-1960-1.1-c1-0-28', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1960/c'}