-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1740317111415209735010092510735', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896257, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1637633450242784, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [3, [1, 1]], [13, [1, -6, 13]]], 'bad_primes': [2, 3, 13], 'central_character': '18252.1', 'coefficient_field': '1.1.1.1', 'conductor': 18252, 'conductor_radical': 78, 'degree': 4, 'euler_factors': [[1, 0, -1], [1, 1], [1, 0, 6, 0, 25], [1, 0, -10, 0, 49], [1, 0, 22, 0, 121], [1, -6, 13], [1, 0, 30, 0, 289], [1, 0, -2, 0, 361], [1, 0, 30, 0, 529], [1, 0, -42, 0, 841], [1, 0, 38, 0, 961], [1, 0, -10, 0, 1369], [1, 0, -18, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, -50, 0, 2209], [1, 0, 70, 0, 2809], [1, 0, 102, 0, 3481], [1, 4, 126, 244, 3721], [1, 0, -130, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, -130, 0, 5329], [1, 0, 158, 0, 6241], [1, 0, 150, 0, 6889], [1, 0, 142, 0, 7921], [1, 0, -50, 0, 9409], [1, 0, 198, 0, 10201], [1, 32, 462, 3296, 10609], [1, 0, 150, 0, 11449], [1, 0, -202, 0, 11881], [1, 0, 30, 0, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 2, 'label': '4-18252-1.1-c1e2-0-2', 'leading_term': '1.11228273597', 'load_key': 'Costa', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/2.2.13.1/108.2/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.1122827359683454, 1.114067693213486, 1.1192975309788096, 1.1275974476597945, 1.1383439510022966, 1.1506672323807323, 1.1634556806297152, 1.1753636607466098, 1.1848239110633407, 1.1900660693495877, 1.1891429069438264, 1.1799658139822848, 1.160350922906013, 1.1280769688385333, 1.0809555550786185, 1.0169139161628913, 0.9340895531423785, 0.8309352681235026, 0.7063321703533001, 0.5597071983690103, 0.3911506484352346, 0.20152817732456374, -0.007419172624374156, -0.23299411719386626, -0.4714891064413959, -0.7181669168911666, -0.9672833278772835, -1.2121585277677198, -1.445302513111918, -1.6585977734320745, -1.8435400027206765, -1.9915344924413287, -2.0942423323647095, -2.1439667159687192, -2.1340657060564974, -2.059373998237651, -1.916612796489047, -1.7047641823098123, -1.4253846210721293, -1.0828317973346568, -0.6843800598415674, -0.240202579163106, 0.23679701909626172, 0.7313142923493243, 1.2261374557097164, 1.7027976697607106, 2.1423585540176107, 2.5263163744137103, 2.8375716855860786, 3.06142362531378, 3.186530391564144, 3.2057745029885893, 3.1169699951933523, 2.923351334545293, 2.63379091887484, 2.2627036803917746, 1.8296132798970524, 1.3583740901265626, 0.876065648067526, 0.4116002036566802, -0.0058921929776880886, -0.34881474279618596, -0.5928867038806397, -0.7188411558538542, -0.7139157745356037, -0.5730180123250201, -0.2994586229870531, 0.09483074208447219, 0.589649806614772, 1.1574683583973704, 1.7649256840636285, 2.3748209286693807, 2.94848185175666, 3.448361814528428, 3.840685857373135, 4.097949649865317, 4.2010724726067314, 4.141018793737204, 3.9197327705178284, 3.5502750762327744, 3.056109307756432, 2.4695519709812674, 1.829470601360786, 1.1783830619903382, 0.559171216218054, 0.01166792462733164, -0.4305976303594133, -0.7432088820302934, -0.9129609971054042, -0.9390350063376943, -0.8331036963809693, -0.6183159267783086, -0.32720679699900557, 0.0013161080118187917, 0.32566505193490863, 0.6056200739508047, 0.8063581940515706, 0.9020715195780702, 0.8788012513617893, 0.7361721359210049, 0.48780455270349676, 0.16030226347930862, -0.20914744403660876, -0.5763808845824423, -0.8947580158826745, -1.1201311537912797, -1.2157855327376923, -1.1568297610890907, -0.9335424731248155, -0.5532637451132618, -0.04055101210058665, 0.564511466683465, 1.2097687730586082, 1.835941333825649, 2.382607801553733, 2.794633026134582, 3.0283666221595262, 3.0569238445349796, 2.8739216321435093, 2.4951768315058134, 1.9580705073082627, 1.3185238524787835, 0.6457932182824302, 0.015545939742859923, -0.4981043027042102, -0.8307707846869372, -0.9352761696375366, -0.7875749992088165, -0.3903781613337172, 0.22603640110572867, 1.0060491561552967, 1.873848649296028, 2.741054468951939, 3.516058380088666, 4.114096410367111, 4.466935804311836, 4.531055687548884, 4.293325984176752, 3.7734373305450966, 3.0226820064839584, 2.119095665303875, 1.1593958351710791, 0.2485453901207037, -0.5119213369753003, -1.0354864744709913, -1.2607932675404292, -1.1591183772403884, -0.7382240545995519, -0.04204840137681441, 0.8538226711230805, 1.8504504611110593, 2.836686418559543, 3.7018759972913213, 4.3486177411044435, 4.704035002350525, 4.728172929431746, 4.4184668845094714, 3.809702873724359, 2.9694489129804498, 1.989508652838181, 0.974461022406391, 0.028733601432698912, -0.7561407792282596, -1.312446144030092, -1.6039742296379182, -1.6294932747089366, -1.4215618161544388, -1.0408785139498704, -0.5669652143273264, -0.08648516290641144, 0.31917048539837023, 0.5852867104335786, 0.6726131062931855, 0.5722947630237798, 0.30624974592661447, -0.0770485142442204, -0.5107554569435314, -0.9205884056571226, -1.2368697538935454, -1.4058553884284128, -1.3986048515263108, -1.2159937669407146, -0.8890313676086029, -0.47434832670261445, -0.04546076176414302, 0.31891562644763993, 0.547735487549146, 0.5896770347590586, 0.42244394787664363, 0.0577488121714421, -0.45896644302038353, -1.0542267595605594, -1.6369474155814316, -2.1121286985985805, -2.3957973171938693, -2.428895754854179, -2.1878946164096678, -1.6903271637628192, -0.9941673593944179, -0.1908919260910684, 0.606952598477078, 1.2819659945261306, 1.7295236956066296, 1.8741362519860016, 1.681950653677087, 1.1673092151087692, 0.39213179257917974, -0.5420368595047244, -1.508331378884663, -2.373209049006157, -3.016668435075924, -3.3509365720240045, -3.3346517725175917, -2.9801766535864567, -2.3526782721466346, -1.5608647106801599, -0.7405802731451003, -0.033628274170805605, 0.43497928922494067, 0.5777956478164383, 0.360388828018602, -0.19114165556265894, -0.9920130763727855, -1.9099655095440673, -2.7843381247493837, -3.4502426859154367, -3.7641815401240626, -3.627135857810773, -3.001452897169256, -1.918755869638986, -0.47745712562304016, 1.1699329257910749, 2.8378967819049534, 4.334244396129343, 5.487666883161498, 6.172250011445103, 6.325134976719552, 5.954580066817925, 5.137196418242783, 4.004860523742832, 2.723463144078714, 1.4669642949232613, 0.3909666328522551, -0.38993324677960495, -0.8174168691283948, -0.8950021593085994, -0.6832027267477689, -0.28536581424325247, 0.17316085224985986, 0.5687721992617393, 0.8020426320932336, 0.8149224114805653, 0.5997322649363037, 0.19848975852396003, -0.3071448528655535, -0.8133135404757084, -1.2154621498174856], 'positive_zeros': ['1.37286813188261880910767163756035', '2.59439103665810412476981586961605', '3.74904387488260970946838288229485', '4.17395035154105580618519439241070', '5.31396272181510219841318127340234', '5.81225327835322207959592349923365', '6.34006998241373302303396063950506', '6.87944639643402688270762012934841', '7.68916893113167905967774177447938', '8.041746957490896078081456984785710', '8.893772573450384569097262787010337', '9.253220401756145526066424253393762', '10.06454957650976622915451112659827', '10.57457186614303466943177704363271', '10.92591047448404489455298703811967'], 'prelabel': '4-18252-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.0386426891785907, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 961461683509547509, 'z1': {'__RealLiteral__': 0, 'data': '1.37286813188261880910767163756035', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.59439103665810412476981586961605', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.74904387488260970946838288229485', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.1637633450242784, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 18252, 'conductor_radical': 78, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 1, 0, 0, 0, 0, 1, 0, 0, -1, 6, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -6, 0, 0, 0, 8, 0, 0, 0, 0, -1, 10, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, -6, 13, 0, 0], 'euler17': [1, 0, 30, 0, 289], 'euler19': [1, 0, -2, 0, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 0, 30, 0, 529], 'euler29': [1, 0, -42, 0, 841], 'euler3': [1, 1, 0, 0, 0], 'euler31': [1, 0, 38, 0, 961], 'euler37': [1, 0, -10, 0, 1369], 'euler41': [1, 0, -18, 0, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, 0, 6, 0, 25], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 0, 102, 0, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 0, -130, 0, 4489], 'euler7': [1, 0, -10, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, -130, 0, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, 150, 0, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, 0, -50, 0, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 1, 0, 0, 0], [1, 0, 6, 0, 25], [1, 0, -10, 0, 49], [1, 0, 22, 0, 121], [1, -6, 13, 0, 0], [1, 0, 30, 0, 289], [1, 0, -2, 0, 361], [1, 0, 30, 0, 529], [1, 0, -42, 0, 841], [1, 0, 38, 0, 961], [1, 0, -10, 0, 1369], [1, 0, -18, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, -50, 0, 2209], [1, 0, 70, 0, 2809], [1, 0, 102, 0, 3481], [1, 4, 126, 244, 3721], [1, 0, -130, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, -130, 0, 5329], [1, 0, 158, 0, 6241], [1, 0, 150, 0, 6889], [1, 0, 142, 0, 7921], [1, 0, -50, 0, 9409]], 'index': 2, 'instance_types': ['ECNF', 'HMF', 'HMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.2.13.1/108.1/a', 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-108.2-a', 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-108.1-a', 'EllipticCurve/2.2.13.1/108.2/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-18252-1.1-c1e2-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-18252-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.0386426891785907, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 961461683509547509, 'z1': {'__RealLiteral__': 0, 'data': '1.37286813188261880910767163756035', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9518752
{'Lhash': '1740317111415209735010092510735', 'Lhash_array': ['1740317111415209735010092510735'], 'label': '4-18252-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.13.1/108.2/a'}
-
id: 9518750
{'Lhash': '1740317111415209735010092510735', 'Lhash_array': ['1740317111415209735010092510735'], 'label': '4-18252-1.1-c1e2-0-2', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-108.1-a'}
-
id: 9517925
{'Lhash': '1740317111415209735010092510735', 'Lhash_array': ['1740317111415209735010092510735'], 'label': '4-18252-1.1-c1e2-0-2', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-108.2-a'}
-
id: 9517924
{'Lhash': '1740317111415209735010092510735', 'Lhash_array': ['1740317111415209735010092510735'], 'label': '4-18252-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.13.1/108.1/a'}