-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2275730858005474926417393702080', 'a10': -1, 'a2': 1, 'a3': 1, 'a4': 1, 'a5': -1, 'a6': 1, 'a7': 0, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [5, [1, 1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.389', 'coefficient_field': '1.1.1.1', 'conductor': 1560, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1, 1], [1, 0, 1], [1, 0, -1], [1, 1], [1, 0, 1], [1, 0, 1], [1, 0, 1], [1, 0, 1], [1, 0, -1], [1, 0, -1], [1, 2, 1], [1, 2, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, -2, 1], [1, 0, 1], [1, 2, 1], [1, 2, 1], [1, -2, 1], [1, 0, 1], [1, 0, 1], [1, 0, -1], [1, 0, -1], [1, 0, 1], [1, 0, 1]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, 0, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, 1], 1]], [[[1, 0, 1], 1]], [[[1, 0, 1], 1]], [[[1, 0, 1], 1]], [[[1, 0, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, 1], 2]], [[[1, 1], 2]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 2]], [[[1, 0, 1], 1]], [[[1, 1], 2]], [[[1, 1], 2]], [[[1, -1], 2]], [[[1, 0, 1], 1]], [[[1, 0, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, 0, 1], 1]], [[[1, 0, 1], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-1560-1560.389-c0-0-6', 'leading_term': '2.43696717674108790394781001631000000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1560/1/y/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.436967176741088, 2.4505531895410733, 2.490377825434992, 2.5537891461712094, 2.6368025194638927, 2.7345868329783385, 2.8419166889982246, 2.953514533761231, 3.064269681669467, 3.1693588512926802, 3.26430366300975, 3.3449958588865822, 3.4077113366319653, 3.449125073384605, 3.4663324435281555, 3.456878241121141, 3.4187922751395905, 3.3506290967585706, 3.2515087936680245, 3.121155564044916, 2.9599307991464716, 2.7688575708637684, 2.5496336948920093, 2.3046309006116457, 2.0368780755914253, 1.7500270601105354, 1.4483000396003087, 1.13641821266411, 0.819512088378155, 0.5030144742987952, 0.19253793776744996, -0.10626076381968255, -0.3878261073686445, -0.6468552844198342, -0.8784514021733577, -1.0782736458663797, -1.2426793572633785, -1.3688528592369698, -1.454915911782501, -1.5000149342004263, -1.5043805791771572, -1.4693558974038161, -1.397390178465215, -1.2919965787609633, -1.1576728252579294, -0.9997855815095016, -0.8244204383163227, -0.6382008974595028, -0.44808109943197455, -0.2611183476290783, -0.0842326430281359, 0.07603859324797638, 0.21378172182039704, 0.32393471545046826, 0.40249225593125987, 0.44667904069721676, 0.45508293460004645, 0.4277406819854635, 0.36617034528446235, 0.27334642550882937, 0.15361569681943305, 0.012554084833592811, -0.1432326450966255, -0.3063591417554631, -0.4689539925915842, -0.6229865901944178, -0.7606154303390946, -0.8745443301756116, -0.9583719306608868, -1.0069192811678638, -1.0165203590936829, -0.9852610926561425, -0.9131538434658809, -0.802236349981533, -0.6565867858204362, -0.4822497694021098, -0.28707176529979694, -0.0804482080733222, 0.12701130091318744, 0.32388939780510684, 0.4984248880133979, 0.6390167963161663, 0.7347483810241299, 0.7759089649079768, 0.7544903320304909, 0.6646343300065795, 0.5030092659892227, 0.26909471055719475, -0.03464260429408493, -0.4026950710618234, -0.8265910881474905, -1.2951054321472761, -1.794600073020939, -2.3094862700069125, -2.822792781007542, -3.3168194128878343, -3.773850223163765, -4.1768967266132275, -4.510438704005821, -4.761128850124243, -4.918427673016421, -4.975136836971515, -4.927802524096706, -4.776965290526027, -4.527239150670033, -4.187209998108823, -3.7691516581864657, -3.288566502029524, -2.7635662302642157, -2.2141167297892386, -1.6611783886603249, -1.1257795117688054, -0.628065144114886, -0.18636637203948947, 0.18366418979910418, 0.46980663487053004, 0.6638775243387689, 0.7621490371267006, 0.7655574097088154, 0.6796842365724166, 0.5145050895256674, 0.2839115096805927, 0.0050241626149556675, -0.302673775845138, -0.6183437226638412, -0.920891425230154, -1.190105060446055, -1.4077735826896596, -1.5587262553923211, -1.6317364029554042, -1.6202375894951462, -1.522808518907305, -1.3433936454170463, -1.0912393209592801, -0.7805396868616615, -0.42980173581750125, -0.06095424501574289, 0.30176020377214696, 0.6330579550476283, 0.9079889782141977, 1.103343115899598, 1.1990133401168446, 1.1792412162903727, 1.0336735401708508, 0.7581668443910681, 0.3552878940354169, -0.16552708478963973, -0.7881745561557557, -1.490448503770191, -2.2449497229106687, -3.020302190000806, -3.7826213649272598, -4.497163953693289, -5.130076688506934, -5.650153838683168, -6.030510014922064, -6.250076694839013, -6.294837832509954, -6.1587316904172535, -5.8441621406261985, -5.362082355622087, -4.7316360555248815, -3.9793651292400067, -3.1380162197085566, -2.2450014300860013, -1.3405883705339428, -0.4659111318425505, 0.3390945729258488, 1.0377226881971064, 1.598384903588915, 1.9962518511075047, 2.2145555499801066, 2.245478453112101, 2.0905761780566086, 1.7607060992111738, 1.27546106654258, 0.662135082072321, -0.04572577033595605, -0.8101100324151052, -1.5905683691909491, -2.3463705646281294, -3.0386724977968047, -3.632572155627497, -4.098939296687106, -4.415915697970565, -4.570001360607847, -4.5566656102803025, -4.380449369617297, -4.054554419013882, -3.599945457425965, -3.044019429602322, -2.4189221594587584, -1.759613242301906, -1.1017950860019752, -0.47982998693962126, 0.07523037008187164, 0.5373856817379711, 0.8870950527858806, 1.1122699390916024, 1.2087954797680938, 1.180553067335864, 1.0389481249367865, 0.8019779738666526, 0.49290342538677934, 0.13861247770828697, -0.23221636055765077, -0.5910313238438641, -0.9112808409575707, -1.1701222534309652, -1.3498561670453812, -1.4389952525801615, -1.4329007429945644, -1.3339487102608796, -1.1512195636051823, -0.8997360246312989, -0.5993049866206651, -0.27304512930161823, 0.05429686101818392, 0.35812456802588166, 0.6157415936558875, 0.8079520091643113, 0.920401275320351, 0.9445655406662744, 0.8783217765563109, 0.726060510448619, 0.49833497468779586, 0.21107308442004508, -0.11559047877417886, -0.458777849762003, -0.7945218908868028, -1.0994913631365375, -1.3526629784505646, -1.5368195158383908, -1.6397654473948902, -1.6551716917051098, -1.5829878213690227, -1.4293914401231758, -1.2062782916494506, -0.9303305349648231, -0.6217320500096291, -0.30262629055462037, 0.004567940785710804, 0.2788559163105178, 0.5022525476636079, 0.6611324832468183, 0.7472398109061004, 0.7582772587693236, 0.6980260354827831, 0.5759829030165801, 0.4065381476776635, 0.20775404882675427, -0.0001644951775130772, -0.19658984603939958, -0.36224746430292915, -0.48090592992223735, -0.5408429014522469, -0.535963076036891], 'positive_zeros': ['1.79523510468558883096740571807024', '2.95958092461933700766334004792233', '3.57911586414051145784750099108709', '4.53429545289116398773298304794718', '5.15016718629018384237631099508725', '6.64905614040384074345212568163969', '7.14942892068151733833520965736714', '7.978420059161413576508647063868793', '8.537353718068905978365648837869640', '9.759673132189673933585306688217459'], 'prelabel': '2-1560-1560.389-c0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.8823499417507114, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0-0', 'trace_hash': 2090690560820189285, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.79523510468558883096740571807', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95958092461933700766334004792', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57911586414051145784750099109', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.7785414197074838, 'bad_primes': [2, 3, 5, 13], 'central_character': '1560.389', 'conductor': 1560, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, -1, 1, 0, 1, 1, -1, 0, 1, -1, 0, -1, 1, 0, 1, 0, -1, 0, 0, 0, 1, 1, -1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, -1, -1, -2, 0, -2, 0, -1, 0, 0, 1, -1, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, -1, -2, -1, 1, -2, -2, 0, 0, -2, 0, 0, 2, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 1], 'euler11': [1, 0, -1], 'euler13': [1, 1, 0], 'euler17': [1, 0, 1], 'euler19': [1, 0, 1], 'euler2': [1, -1, 0], 'euler23': [1, 0, 1], 'euler29': [1, 0, 1], 'euler3': [1, -1, 0], 'euler31': [1, 0, -1], 'euler37': [1, 0, -1], 'euler41': [1, 2, 1], 'euler43': [1, 2, 1], 'euler47': [1, 0, -1], 'euler5': [1, 1, 0], 'euler53': [1, 0, -1], 'euler59': [1, 0, -1], 'euler61': [1, 0, -1], 'euler67': [1, 0, -1], 'euler7': [1, 0, 1], 'euler71': [1, -2, 1], 'euler73': [1, 0, 1], 'euler79': [1, 2, 1], 'euler83': [1, 2, 1], 'euler89': [1, -2, 1], 'euler97': [1, 0, 1], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, 1, 0], [1, 0, 1], [1, 0, -1], [1, 1, 0], [1, 0, 1], [1, 0, 1], [1, 0, 1], [1, 0, 1], [1, 0, -1], [1, 0, -1], [1, 2, 1], [1, 2, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, -2, 1], [1, 0, 1], [1, 2, 1], [1, 2, 1], [1, -2, 1], [1, 0, 1]], 'index': 6, 'instance_types': ['CMF', 'CMF', 'Artin', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1560/1/y/d/389/1', 'ModularForm/GL2/Q/holomorphic/1560/1/y/d', 'ArtinRepresentation/2.1560.4t3.c.a', 'ArtinRepresentation/2.1560.4t3.c'], 'is_instance_Artin': True, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-1560-1560.389-c0-0-6', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1560-1560.389-c0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.8823499417507114, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'trace_hash': 2090690560820189285, 'z1': {'__RealLiteral__': 0, 'data': '1.79523510468558883096740571807', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 24604845
{'Lhash': '2275730858005474926417393702080', 'Lhash_array': ['2275730858005474926417393702080'], 'label': '2-1560-1560.389-c0-0-6', 'type': 'Artin', 'url': 'ArtinRepresentation/2.1560.4t3.c'}
-
id: 24598503
{'Lhash': '2275730858005474926417393702080', 'Lhash_array': ['2275730858005474926417393702080'], 'label': '2-1560-1560.389-c0-0-6', 'type': 'Artin', 'url': 'ArtinRepresentation/2.1560.4t3.c.a'}
-
id: 19820498
{'Lhash': '2275730858005474926417393702080', 'Lhash_array': ['2275730858005474926417393702080'], 'label': '2-1560-1560.389-c0-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/1/y/d'}
-
id: 24546650
{'Lhash': '2275730858005474926417393702080', 'Lhash_array': ['2275730858005474926417393702080'], 'label': '2-1560-1560.389-c0-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1560/1/y/d/389/1'}