-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1790835334715238638', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1435.518587377771, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [53, [1]]], 'bad_primes': [2, 53], 'central_character': '179776.1', 'coefficient_field': '1.1.1.1', 'conductor': 179776, 'conductor_radical': 106, 'degree': 2, 'euler_factors': [[1], [1, 2, 3], [1, -2, 5], [1, 0, 7], [1, 4, 11], [1, -2, 13], [1, -2, 17], [1, 2, 19], [1, 2, 23], [1, 2, 29], [1, -2, 31], [1, 10, 37], [1, 2, 41], [1, 4, 43], [1, -12, 47], [1], [1, 12, 59], [1, -10, 61], [1, -2, 67], [1, -6, 71], [1, 10, 73], [1, -10, 79], [1, -6, 83], [1, 10, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 5, 'label': '2-424e2-1.1-c1-0-5', 'leading_term': '0.971427613426', 'load_key': 'Cremona', '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': 'EllipticCurve/Q/179776/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.9714276134262443, 0.3827382358925272, -0.8836911977183342, -1.548595660666946, -0.5511245927773805, 1.548050446691107, 2.640993651187249, 1.44486451997364, -0.3895321704245683, 0.1328510152455272, 3.154421416016408, 4.941187055884403, 2.678296841334274, -0.9343562798750203, -0.678282268780335, 3.717568557627844, 6.605101548247808, 4.25004334840171, 0.02684573499804829, -1.014512669809762, 0.5544451970493567, 0.8640875701341492, -0.3399616944778223, -0.4830814466995364, 0.01026490806931366, -1.130744443623082, -2.308315530542035, -0.4602868987939144, 1.817696177840518, -0.336654438574606, -4.263217473358002, -2.970859291585731, 2.124507949580619, 2.852821313272841, -0.8724525428470398, -0.6561930789905358, 4.55184811238014, 6.171167259617885, 1.78780365433917, -1.100243296321865, 0.5174845858052937, 1.353728414514879, -0.1069679596469587, 0.05808157175877994, 0.9750212712685274, -1.089625867734115, -3.184177905335399, -1.22129900412729, 0.7524295332478665, -1.009021149440568, -1.700361460189735, 1.185201089411604, 1.809456284400147, -0.9227312313261318, -0.5462523977908204, 2.081388352399333, 0.3318180437080412, -1.90946926235599, 2.858644580677014, 7.87600042270495, 3.728021251114357, -2.628230979301867, -1.759438818034109, 0.8220876010864157, -0.9695913904492534, -1.595012333823966, 1.396061629658067, 1.938171825034422, -0.1490631451643452, -0.09040156927806876, 0.1409724536004579, -1.622989637576509, -1.332182576303058, 0.4800681694527452, -0.4846992776038172, 0.006271256490504356, 4.777619469687395, 4.239303274693227, -3.427290145500686, -3.780616856583374, 5.332226394085053, 8.13010778936516, 2.135806913102787, -0.3581269161004899, 0.7681091974715903, -1.401310664059317, -2.717973002953919, -0.2575683153978383, -0.2603747633489483, -2.063391162562229, -0.1620261554634403, 1.309830232896395, -0.9293004650799065, -1.187805325221488, 0.3538775117770839, -0.7955549754207778, -0.08052452154524457, 3.586165682832439, 1.268346962820522, -4.452687020362896, -2.537845361445325, 1.85505559877452, 0.1120822143224686, -0.4973415738313828, 2.750461748884225, 1.227304400165875, -0.9759864334788791, 4.213356845855288, 6.635999158906009, -0.2316741478311593, -4.025645409259743, -0.7717541291222142, 0.3726388808579305, -0.03494354460248362, 1.841084900528971, 1.616951476079676, -0.1951455722562615, 0.2060252754606688, -0.7591787306165843, -2.145903608790156, 0.737221904555013], 'positive_zeros': ['0.3301097551772842', '1.069941010715623', '1.929656012055265', '2.233801364931888', '3.171102939332251', '3.550124447910175', '4.502158542646264', '4.916280553655297', '5.427168025707606', '5.950540941993550', '6.012901065060300', '6.787425418770882', '7.229818445906361', '7.891884147767405', '8.438635618561909', '8.789293760960893', '9.602010245369537', '9.943648974741281', '10.47895625929035', '10.73872576853538', '11.15776290440204', '11.85431206660995', '12.14652636094171', '12.65762516985334', '13.16334263816642', '13.54661091233378', '14.02210379506884', '14.39159537797666', '15.12323878703881', '15.62682826210898', '15.90793526324127', '16.39107068204346', '16.97603027431826', '17.27236687960142', '17.52825276980749', '18.15620187235065', '18.42781788545312', '18.74953442842757', '19.39049382735262', '19.86257974568386'], 'prelabel': '2-424e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 37.88823811392885, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1790835334715238638, 'z1': {'__RealLiteral__': 0, 'data': '0.3301097551772842', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.069941010715623', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.929656012055265', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1435.518587377771, 'bad_primes': [2, 53], 'central_character': '1.1', 'conductor': 179776, 'conductor_radical': 106, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, 2, 0, 0, 0, 1, 0, -4, 0, 2, 0, -4, 0, 2, 0, -2, 0, 0, 0, -2, 0, -1, 0, 4, 0, -2, 0, 2, 0, 8, 0, 0, 0, -10, 0, -4, 0, -2, 0, -4, 0, 2, 0, 12, 0, -7, 0, -4, 0, 0, 0, -8, 0, 4, 0, -12, 0, 10, 0, 0, 0, 4, 0, 2, 0, 4, 0, 6, 0, -10, 0, 2, 0, 0, 0, 10, 0, -11, 0, 6, 0, 4, 0, 4, 0, -10, 0, 0, 0, -4, 0, -4, 0, 14, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, -2, 13], 'euler17': [1, -2, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 2, 23], 'euler29': [1, 2, 29], 'euler3': [1, 2, 3], 'euler31': [1, -2, 31], 'euler37': [1, 10, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, -12, 47], 'euler5': [1, -2, 5], 'euler53': [1, 0, 0], 'euler59': [1, 12, 59], 'euler61': [1, -10, 61], 'euler67': [1, -2, 67], 'euler7': [1, 0, 7], 'euler71': [1, -6, 71], 'euler73': [1, 10, 73], 'euler79': [1, -10, 79], 'euler83': [1, -6, 83], 'euler89': [1, 10, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 2, 3], [1, -2, 5], [1, 0, 7], [1, 4, 11], [1, -2, 13], [1, -2, 17], [1, 2, 19], [1, 2, 23], [1, 2, 29], [1, -2, 31], [1, 10, 37], [1, 2, 41], [1, 4, 43], [1, -12, 47], [1, 0, 0], [1, 12, 59], [1, -10, 61], [1, -2, 67], [1, -6, 71], [1, 10, 73], [1, -10, 79], [1, -6, 83], [1, 10, 89], [1, -14, 97]], 'index': 5, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/179776/g'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, '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': '2-424e2-1.1-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': '2-424e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 37.88823811392885, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1790835334715238638, 'z1': {'__RealLiteral__': 0, 'data': '0.3301097551772842', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1790835334715238638', 'Lhash_array': ['1790835334715238638'], 'label': '2-424e2-1.1-c1-0-5', 'type': 'ECQ', 'url': 'EllipticCurve/Q/179776/g'}