-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '1391933027275218640', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 259.0985844786507, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [13, [1]]], 'bad_primes': [2, 3, 13], 'central_character': '32448.1', 'coefficient_field': '1.1.1.1', 'conductor': 32448, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 2, 5], [1, -1, 7], [1, 2, 11], [1], [1, 4, 17], [1, 4, 19], [1, -6, 23], [1, 6, 29], [1, 1, 31], [1, 10, 37], [1, 4, 41], [1, 1, 43], [1, 10, 47], [1, 8, 53], [1, -2, 59], [1, -5, 61], [1, -7, 67], [1, -10, 71], [1, 7, 73], [1, -17, 79], [1, 12, 83], [1, 16, 89], [1, -13, 97]], 'gamma_factors': [[], [0]], 'index': 11, 'label': '2-32448-1.1-c1-0-11', 'leading_term': '1.05666205249', '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/32448/ci', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.056662052493299, 0.5265591781815265, -0.8964674754182831, -2.613726998350141, -3.63802764396322, -3.170104811404473, -1.392011855932782, 0.3786419566912267, 0.6598328089398299, -0.7653211364885777, -2.435729242873539, -2.564313886791776, -0.977500705863749, 0.5648138800705894, 0.3471785647479621, -1.159527151106829, -1.757406488348891, -0.354309231939595, 1.380411279208553, 1.089208115459096, -0.8020996399269532, -1.061968433575313, 2.158568192143467, 6.217160868233698, 6.668415688682866, 2.859483896840578, -1.028617352589548, -1.273238036916032, 0.8169318854875023, 1.331942948386356, -0.5023963426468814, -1.725095945802357, -0.6953116732431165, 0.4114175617311608, -0.3898019154816185, -1.235996988275299, 0.3752726110747314, 2.645408440308958, 1.671996199815556, -1.948074292949667, -3.143412161916378, 0.01090647959487066, 3.102441481376782, 2.223477051591315, -0.1090156269070917, 0.238618017476274, 1.708082739896056, -0.06062197612625024, -4.045301798489994, -4.88411633156398, -1.780227028491479, 0.2289312995196527, -0.9865645881390404, -1.33682971966081, 1.512633162628005, 3.430140736865299, 1.139624374955909, -1.681033323906401, -0.7458880177691044, 1.614589034520932, 1.348102910900086, -0.01589344853569229, 0.5962998257895025, 1.029494125284255, -1.545437303163728, -3.551604062820628, -0.6734775421886863, 3.216547412968488, 1.848274999842938, -2.112268369897927, -1.477023510506127, 2.525625716660033, 2.574553087552528, -1.432001514047711, -2.723293648726414, -0.1928139819845387, 0.7668132611198358, -0.7379519091217145, -0.4740595429889705, 1.237986734052968, 0.2206194415063526, -2.251729349343598, -1.60843897850323, 0.5410179984909425, -0.1166352272701709, -0.9672052535520527, 2.309664880249696, 5.395595504334332, 2.370841727890028, -2.261836792080402, -1.226759185394216, 2.096366282173972, 0.7739672936214758, -2.326565237501627, -1.180736800327717, 1.381028745164471, 0.6397950898335182, -0.0275365672434551, 2.58269518823453, 3.556271217250088, 0.1877323039182234, -1.420205811058457, 1.518389956491926, 2.748061958857543, -0.1555463678274922, -1.36011814395905, 0.5200236395325715, 0.2445868589648184, -1.914691483313612, -1.100323721636835, 0.6501597672054377, -1.00494799360561, -1.930703412837213, 1.806478632783753, 3.557947749470001, -1.272249849095281, -4.674747813279482, -1.282417972538268, 1.201447570981865, -1.862483563604014, -3.072784138347651], 'positive_zeros': ['0.3576115606910234', '1.682855964904129', '2.141412185025383', '3.134354880666772', '3.565466084827268', '4.293151550227792', '4.895738050407536', '5.361680628726776', '6.414039360638518', '6.903629877173823', '7.441828665007727', '8.115475652255809', '8.426741547911679', '8.963294093311753', '9.618899217721730', '10.24934267679741', '10.98120868857743', '11.21200878197656', '11.74584765820728', '12.67220187064692', '12.84735990557302', '13.38816891342007', '14.07972480051335', '14.56968845228492', '15.24295049332907', '15.35747129243273', '15.87947370657475', '16.53534513007605', '17.10628426486239', '17.59171610296990', '18.16300045662211', '18.76914633141289', '19.13385201054650', '19.56347735609724'], 'prelabel': '2-32448-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.096539518749076, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1391933027275218640, 'z1': {'__RealLiteral__': 0, 'data': '0.3576115606910234', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.682855964904129', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.141412185025383', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 259.0985844786507, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 32448, 'conductor_radical': 78, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -2, 0, 1, 0, 1, 0, -2, 0, 0, 0, -2, 0, -4, 0, -4, 0, 1, 0, 6, 0, -1, 0, 1, 0, -6, 0, -1, 0, -2, 0, -2, 0, -10, 0, 0, 0, -4, 0, -1, 0, -2, 0, -10, 0, -6, 0, -4, 0, -8, 0, 4, 0, -4, 0, 2, 0, 5, 0, 1, 0, 0, 0, 7, 0, 6, 0, 10, 0, -7, 0, -1, 0, -2, 0, 17, 0, 1, 0, -12, 0, 8, 0, -6, 0, -16, 0, 0, 0, -1, 0, 8, 0, 13, 0, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, 0, 0], 'euler17': [1, 4, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 1, 31], 'euler37': [1, 10, 37], 'euler41': [1, 4, 41], 'euler43': [1, 1, 43], 'euler47': [1, 10, 47], 'euler5': [1, 2, 5], 'euler53': [1, 8, 53], 'euler59': [1, -2, 59], 'euler61': [1, -5, 61], 'euler67': [1, -7, 67], 'euler7': [1, -1, 7], 'euler71': [1, -10, 71], 'euler73': [1, 7, 73], 'euler79': [1, -17, 79], 'euler83': [1, 12, 83], 'euler89': [1, 16, 89], 'euler97': [1, -13, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 2, 5], [1, -1, 7], [1, 2, 11], [1, 0, 0], [1, 4, 17], [1, 4, 19], [1, -6, 23], [1, 6, 29], [1, 1, 31], [1, 10, 37], [1, 4, 41], [1, 1, 43], [1, 10, 47], [1, 8, 53], [1, -2, 59], [1, -5, 61], [1, -7, 67], [1, -10, 71], [1, 7, 73], [1, -17, 79], [1, 12, 83], [1, 16, 89], [1, -13, 97]], 'index': 11, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32448/ci'], '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': '2-32448-1.1-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': 0, 'prelabel': '2-32448-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.096539518749076, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1391933027275218640, 'z1': {'__RealLiteral__': 0, 'data': '0.3576115606910234', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1391933027275218640', 'Lhash_array': ['1391933027275218640'], 'label': '2-32448-1.1-c1-0-11', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32448/ci'}