-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2323895558066910583268139724331', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.19366152991567, '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': '2028.1', 'coefficient_field': '1.1.1.1', 'conductor': 2028, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 0, 5], [1, 2, 7], [1, 0, 11], [1], [1, 6, 17], [1, 2, 19], [1, 0, 23], [1, 6, 29], [1, 2, 31], [1, 2, 37], [1, -12, 41], [1, 4, 43], [1, 0, 47], [1, -6, 53], [1, 12, 59], [1, -2, 61], [1, -10, 67], [1, 12, 71], [1, 14, 73], [1, -8, 79], [1, 12, 83], [1, 0, 89], [1, -10, 97], [1, -18, 101], [1, 16, 103], [1, 12, 107], [1, 14, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, 0, 5], 1]], [[[1, 2, 7], 1]], [[[1, 0, 11], 1]], [1], [[[1, 6, 17], 1]], [[[1, 2, 19], 1]], [[[1, 0, 23], 1]], [[[1, 6, 29], 1]], [[[1, 2, 31], 1]], [[[1, 2, 37], 1]], [[[1, -12, 41], 1]], [[[1, 4, 43], 1]], [[[1, 0, 47], 1]], [[[1, -6, 53], 1]], [[[1, 12, 59], 1]], [[[1, -2, 61], 1]], [[[1, -10, 67], 1]], [[[1, 12, 71], 1]], [[[1, 14, 73], 1]], [[[1, -8, 79], 1]], [[[1, 12, 83], 1]], [[[1, 0, 89], 1]], [[[1, -10, 97], 1]], [[[1, -18, 101], 1]], [[[1, 16, 103], 1]], [[[1, 12, 107], 1]], [[[1, 14, 109], 1]], [[[1, -6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 23, 'label': '2-2028-1.1-c1-0-23', '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/2028/2/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.4524420423914188e-60, 0.1712389206685806, 0.3424343466782995, 0.5134986449637979, 0.684258246745275, 0.8544163426027057, 1.023521873207009, 1.190946167577443, 1.3558680901187248, 1.5172680870413817, 1.673931115514101, 1.8244581179138615, 1.9672854721475663, 2.100711695937873, 2.222930588824297, 2.332069938998435, 2.426234883878033, 2.5035549792285123, 2.562233992933515, 2.6006013926737017, 2.6171644424958695, 2.610659765287046, 2.580103172173973, 2.524836512483862, 2.4445702660029753, 2.3394205894292126, 2.2099395470187857, 2.05713730639866, 1.8824951681211204, 1.6879684242398239, 1.4759782080479262, 1.249391703718613, 1.011490328980879, 0.7659257826606601, 0.5166641569065491, 0.26791864471812266, 0.024071719149736884, -0.2104119878081495, -0.4310805312832457, -0.6335953169014922, -0.813835368254326, -0.9680027178013317, -1.092726222808481, -1.1851609507293202, -1.2430801917240673, -1.264957148330716, -1.250033430428891, -1.1983716521946453, -1.1108896888641007, -0.989374504160121, -0.8364739005497556, -0.6556650673237427, -0.4511993958885427, -0.22802368459957623, 0.008321449020349583, 0.2518244113365889, 0.4961444709350183, 0.7347696289495463, 0.9611868978114454, 1.1690607715513037, 1.3524151680903256, 1.5058137342465434, 1.624533147757702, 1.7047239448668086, 1.74355346057388, 1.739325700693609, 1.6915733744139783, 1.6011179015264474, 1.4700939623008888, 1.3019360663498682, 1.1013256598789047, 0.8740984426881918, 0.6271127960190658, 0.36808149398200984, 0.10537014525998238, -0.15223295418276478, -0.395769726105709, -0.6163811178222658, -0.8055841031133604, -0.955548518970138, -1.0593649745262916, -1.111294930763394, -1.1069942002021889, -1.0437015657556106, -0.9203849683264215, -0.7378387542330588, -0.49872678602450055, -0.20756777288687242, 0.12933907138568138, 0.5040480343705962, 0.9071585756620079, 1.3280606466816975, 1.7552276718193318, 2.1765493460405816, 2.5796947334670457, 2.952494735278411, 3.283331896044316, 3.5615247894116533, 3.777693910369027, 3.9240961325755817, 3.994915381219687, 3.986498224192306, 3.8975245797061717, 3.7291056423820983, 3.4848033910250815, 3.170568592927653, 2.794596980749671, 2.3671061564728855, 1.9000386716601807, 1.4066995381474163, 0.9013390308955849, 0.3986939502794099, -0.08649758329692947, -0.5399913107980349, -0.9485246404599142, -1.3002794795067776, -1.5853028909916118, -1.7958694272958162, -1.9267706824574418, -1.9755198933869336, -1.9424622391997441, -1.830784749086031, -1.6464233223407345, -1.3978681621278377, -1.0958727870746983, -0.7530755638623944, -0.3835462493320973, -0.0022731957070669193, 0.3753904794631833, 0.734301447215602, 1.0600998618130337, 1.3397601531893852, 1.5620972700987676, 1.7182079889216433, 1.801829007235293, 1.8095964282926218, 1.7411948193047966, 1.5993881683671103, 1.3899296201416265, 1.121351665136614, 0.8046433021704424, 0.45282539076525297, 0.08043976199844508, -0.29702852688840653, -0.6637733002574306, -1.004308988839434, -1.3041059489942128, -1.5501931309931039, -1.7317027195283972, -1.8403333221924458, -1.8707112638172667, -1.8206334564102662, -1.6911800132060448, -1.4866900802654084, -1.2146000578488405, -0.8851492410412861, -0.5109636757367897, -0.10653444987893256, 0.31238852359752123, 0.7294621519085569, 1.1284471405729, 1.4939063606693328, 1.8118740884024003, 2.0704663595868444, 2.2604047720223472, 2.3754294292999916, 2.4125812311465404, 2.372339203898681, 2.2586048073887866, 2.078531888684347, 1.8422078867426859, 1.5621987162468791, 1.2529761615316641, 0.9302522913452455, 0.6102500860053636, 0.3089429125191066, 0.041297503174334636, -0.17944443768762008, -0.3424120139950746, -0.43964705538992344, -0.4665151626053485, -0.42196445741709304, -0.3086173168515289, -0.13268790571213393, 0.09627364498413567, 0.3658013975774288, 0.6610811657638642, 0.9656412311987309, 1.262135660520865, 1.5331846496421286, 1.7622328786531205, 1.9343851891642259, 2.0371791178006524, 2.06125596941043, 2.0008961348565633, 1.8543901038350716, 1.6242238596353469, 1.3170657595283854, 0.94355122653404, 0.5178711826393287, 0.05717968816580105, -0.4191547428697011, -0.8904216514632987, -1.3355258208176188, -1.7339850876387763, -2.0669218280077004, -2.3180004725868972, -2.4742649930405682, -2.5268341458146466, -2.4714182246165994, -2.3086289161841584, -2.044063234997109, -1.6881530081739045, -1.2557825043587405, -0.7656880206127927, -0.23966401317711095, 0.29838985460181944, 0.8235380702826086, 1.3109459766509457, 1.7370306525085517, 2.0805712090780992, 2.323724796505989, 2.4528983151207693, 2.459432038207069, 2.34005981649169, 2.097120871311149, 1.7385099145670524, 1.27736490105556, 0.7315045119409441, 0.12263985348234148, -0.5246037922934551, -1.183809592906788, -1.8279829900305793, -2.4307984878950193, -2.967818950610345, -3.4176277282282537, -3.762817705360244, -3.9907879920500844, -4.0943081589846315, -4.071821227088693, -3.9274695082579174, -3.6708412227945737, -3.3164498948362393, -2.882972130925989, -2.3922818133731867, -1.8683293339184583, -1.3359226844059413, -0.8194725561267765, -0.3417657668974258, 0.07716981558595727, 0.42105013278552855, 0.6781184047252333, 0.8416863285623877, 0.9104046472562894, 0.8882488473769433, 0.7842207305017279, 0.6117816705172914], 'positive_zeros': ['1.83323035357575148614764696337383', '2.74043286716224189352635232181261', '3.77836338617867858300845886261024', '4.44998746241878107130784883974878', '5.67824240643643493495071880885381', '6.44952092339185714604672088913844', '7.22174450219522200759702571931512', '7.985659136951548177101330183926506', '8.946160572584558004743809292840175'], 'prelabel': '2-2028-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.024134879687269, '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': 185029258416546996, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.83323035357575148614764696337', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.74043286716224189352635232181', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.77836338617867858300845886261', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 16.19366152991567, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 2028, 'conductor_radical': 78, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, -6, 0, -2, 0, -2, 0, 0, 0, -5, 0, 1, 0, -6, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 12, 0, -4, 0, 0, 0, 0, 0, -3, 0, -6, 0, 6, 0, 0, 0, -2, 0, -12, 0, 2, 0, -2, 0, 0, 0, 10, 0, 0, 0, -12, 0, -14, 0, -5, 0, 0, 0, 8, 0, 1, 0, -12, 0, 0, 0, -6, 0, 0, 0, 0, 0, -2, 0, 0, 0, 10, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 0, 0], 'euler17': [1, 6, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 2, 31], 'euler37': [1, 2, 37], 'euler41': [1, -12, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 5], 'euler53': [1, -6, 53], 'euler59': [1, 12, 59], 'euler61': [1, -2, 61], 'euler67': [1, -10, 67], 'euler7': [1, 2, 7], 'euler71': [1, 12, 71], 'euler73': [1, 14, 73], 'euler79': [1, -8, 79], 'euler83': [1, 12, 83], 'euler89': [1, 0, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 5], [1, 2, 7], [1, 0, 11], [1, 0, 0], [1, 6, 17], [1, 2, 19], [1, 0, 23], [1, 6, 29], [1, 2, 31], [1, 2, 37], [1, -12, 41], [1, 4, 43], [1, 0, 47], [1, -6, 53], [1, 12, 59], [1, -2, 61], [1, -10, 67], [1, 12, 71], [1, 14, 73], [1, -8, 79], [1, 12, 83], [1, 0, 89], [1, -10, 97]], 'index': 23, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2028/e', 'ModularForm/GL2/Q/holomorphic/2028/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/2028/2/a/e'], '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': '2-2028-1.1-c1-0-23', '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': '2-2028-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.024134879687269, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 185029258416546996, 'z1': {'__RealLiteral__': 0, 'data': '1.83323035357575148614764696337', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20600518
{'Lhash': '2323895558066910583268139724331', 'Lhash_array': ['2323895558066910583268139724331'], 'label': '2-2028-1.1-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2028/2/a/e'}
-
id: 24555528
{'Lhash': '2323895558066910583268139724331', 'Lhash_array': ['2323895558066910583268139724331'], 'label': '2-2028-1.1-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2028/2/a/e/1/1'}
-
id: 22831
{'Lhash': '185029258416546996', 'Lhash_array': ['185029258416546996'], 'label': '2-2028-1.1-c1-0-23', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2028/e'}