-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '2171070767568839077', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 162.89482012341207, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [17, [1, -1]]], 'bad_primes': [2, 3, 5, 17], 'central_character': '20400.1', 'coefficient_field': '1.1.1.1', 'conductor': 20400, 'conductor_radical': 510, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 1, 7], [1, 3, 11], [1, -2, 13], [1, -1], [1, 1, 19], [1, 2, 23], [1, -5, 29], [1, 6, 31], [1, 1, 37], [1, -5, 41], [1, -4, 43], [1, -13, 47], [1, 11, 53], [1, 4, 59], [1, 2, 61], [1, -8, 67], [1, 12, 71], [1, -13, 73], [1, 6, 79], [1, 4, 83], [1, 4, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 56, 'label': '2-20400-1.1-c1-0-56', 'leading_term': '3.88477094354', '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': 1, 'origin': 'EllipticCurve/Q/20400/n', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.8969060522633618, 1.343103189866519, 0.9505471916393858, -0.3098489853398178, -1.821481221434561, -2.509020171708967, -1.612587476993673, 0.4875857740493943, 2.26362993282761, 2.188199581181997, 0.2147726480913053, -1.903335673269385, -2.111128278639349, -0.1381314332225583, 2.036447780270746, 2.14427106222691, 0.1164027619778883, -1.743160311741385, -1.34741080701768, 0.7192580492512617, 1.926977032635127, 0.976338619580615, -0.5705677306224298, -0.461077755908342, 1.041579288289112, 1.383955771366827, -0.6358045957374048, -2.823308703764808, -2.393037609275572, -0.03700024294403198, 0.7009775013590978, -1.600250286811418, -3.872052352854896, -2.649401648148754, 0.8383442144502101, 2.083634420504897, -0.4054305089143842, -2.976923595006578, -2.122908369888123, 0.5831546694754804, 1.222794259000777, -0.4409446255267485, -1.056557479080169, 0.4884051295097612, 1.150739161220697, -1.017910425227792, -3.186367612706814, -2.063919957246453, 0.7205879215510201, 1.307004811367565, 0.04718887788264082, 0.6856300350785611, 3.438633772223168, 4.059922065627784, 1.172480442677196, -0.6184555240581084, 1.954491615567871, 4.886673724911117, 2.898784090787277, -1.995352290102183, -3.594230912107625, -1.136192924764628, 0.5401690082933281, -0.2430176709567222, 0.04935753713262685, 2.598582720912219, 3.530989461577819, 1.183355992306794, -0.3728765153854836, 1.465173199709817, 3.083585799690366, 1.364132894584617, -0.5874334364290471, 0.4311146691472551, 1.371988923167758, -1.090927583466257, -3.360347457374646, -0.9908470941447614, 2.476463265692183, 1.021902832080405, -3.122654602715736, -3.265056448544753, 0.006989940894124992, 0.5292056566611442, -1.890644979935683, -1.764882978673586, 1.16643850827397, 1.609458444535068, -0.8407517010969519, -1.08699957187971, 1.383254123608074, 1.792551729571693, -0.2852070724312412, -0.5813035578451576, 0.6097546130420674, -0.8127869474542168, -3.115616334002215, -0.850104876053705, 3.886076365130457, 3.868385803271124, -0.2257814872970905, -1.264257747588965, 0.860946769754724, -0.02815171912864709, -3.327375617073623, -2.704070488285433, 0.878688008572902, 0.6895199169887918, -2.550199538371094, -2.309390660618273, 0.8191143394042651, 0.9171465309991508, -1.26922775529692, -0.7824072847178262, 0.9397966721136216, -0.09597844481099493, -1.289447816474466, 0.5981074125314828, 1.416528681938356, -1.884141075699209], 'positive_zeros': ['0.9486062414980289', '1.946208774114015', '2.771977684208900', '3.513654094185229', '4.262039860227353', '4.917440231835465', '5.641471537266775', '6.084637920218701', '6.689269355841410', '7.504353637826127', '7.856316671766557', '8.687304725801129', '9.219848318357169', '9.940014342944272', '10.43980408219051', '10.93349121956892', '11.40959739378503', '12.17709347761909', '12.76499792206211', '12.88712991924200', '13.85007221896921', '14.10441887292806', '14.89430061068440', '15.61539454192281', '15.94174575382459', '16.24287964342511', '17.12441732439714', '17.34316797568229', '18.13645012471674', '18.44134027861993', '18.91835311959876', '19.55832599395132'], 'prelabel': '2-20400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.76302550821756, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2171070767568839077, 'z1': {'__RealLiteral__': 0, 'data': '0.9486062414980289', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.946208774114015', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.771977684208900', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 162.89482012341207, 'bad_primes': [2, 3, 5, 17], 'central_character': '1.1', 'conductor': 20400, 'conductor_radical': 510, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -1, 0, 1, 0, -3, 0, 2, 0, 0, 0, 1, 0, -1, 0, 1, 0, -2, 0, 0, 0, -1, 0, 5, 0, -6, 0, 3, 0, 0, 0, -1, 0, -2, 0, 5, 0, 4, 0, 0, 0, 13, 0, -6, 0, -1, 0, -11, 0, 0, 0, 1, 0, -4, 0, -2, 0, -1, 0, 0, 0, 8, 0, 2, 0, -12, 0, 13, 0, 0, 0, 3, 0, -6, 0, 1, 0, -4, 0, 0, 0, -5, 0, -4, 0, -2, 0, 6, 0, 0, 0, 10, 0, -3, 0], 'euler11': [1, 3, 11], 'euler13': [1, -2, 13], 'euler17': [1, -1, 0], 'euler19': [1, 1, 19], 'euler2': [1, 0, 0], 'euler23': [1, 2, 23], 'euler29': [1, -5, 29], 'euler3': [1, 1, 0], 'euler31': [1, 6, 31], 'euler37': [1, 1, 37], 'euler41': [1, -5, 41], 'euler43': [1, -4, 43], 'euler47': [1, -13, 47], 'euler5': [1, 0, 0], 'euler53': [1, 11, 53], 'euler59': [1, 4, 59], 'euler61': [1, 2, 61], 'euler67': [1, -8, 67], 'euler7': [1, 1, 7], 'euler71': [1, 12, 71], 'euler73': [1, -13, 73], 'euler79': [1, 6, 79], 'euler83': [1, 4, 83], 'euler89': [1, 4, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 1, 7], [1, 3, 11], [1, -2, 13], [1, -1, 0], [1, 1, 19], [1, 2, 23], [1, -5, 29], [1, 6, 31], [1, 1, 37], [1, -5, 41], [1, -4, 43], [1, -13, 47], [1, 11, 53], [1, 4, 59], [1, 2, 61], [1, -8, 67], [1, 12, 71], [1, -13, 73], [1, 6, 79], [1, 4, 83], [1, 4, 89], [1, -10, 97]], 'index': 56, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/20400/n'], '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': '2-20400-1.1-c1-0-56', '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': '2-20400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.76302550821756, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2171070767568839077, 'z1': {'__RealLiteral__': 0, 'data': '0.9486062414980289', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2171070767568839077', 'Lhash_array': ['2171070767568839077'], 'label': '2-20400-1.1-c1-0-56', 'type': 'ECQ', 'url': 'EllipticCurve/Q/20400/n'}