-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1826725156849650436324407759212', 'a10': -1, 'a2': -1, 'a3': -1, 'a4': -1, 'a5': 1, 'a6': 1, 'a7': -1, 'a8': 3, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.222721433457888, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [5, [1, -1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [3, 5, 7, 11], 'central_character': '1155.1', 'coefficient_field': '1.1.1.1', 'conductor': 1155, 'conductor_radical': 1155, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, 1], [1, -1], [1, 1], [1, -1], [1, 2, 13], [1, 6, 17], [1, 4, 19], [1, -8, 23], [1, -6, 29], [1, -8, 31], [1, -6, 37], [1, 6, 41], [1, 4, 43], [1, 8, 47], [1, 10, 53], [1, 12, 59], [1, 10, 61], [1, 12, 67], [1, 8, 71], [1, 6, 73], [1, -8, 79], [1, 4, 83], [1, -10, 89], [1, 14, 97], [1, -6, 101], [1, -16, 103], [1, 12, 107], [1, 2, 109], [1, 14, 113]], 'euler_factors_factorization': [[[[1, 1, 2], 1]], [[[1, 1], 1]], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, -1], 1]], [[[1, 2, 13], 1]], [[[1, 6, 17], 1]], [[[1, 4, 19], 1]], [[[1, -8, 23], 1]], [[[1, -6, 29], 1]], [[[1, -8, 31], 1]], [[[1, -6, 37], 1]], [[[1, 6, 41], 1]], [[[1, 4, 43], 1]], [[[1, 8, 47], 1]], [[[1, 10, 53], 1]], [[[1, 12, 59], 1]], [[[1, 10, 61], 1]], [[[1, 12, 67], 1]], [[[1, 8, 71], 1]], [[[1, 6, 73], 1]], [[[1, -8, 79], 1]], [[[1, 4, 83], 1]], [[[1, -10, 89], 1]], [[[1, 14, 97], 1]], [[[1, -6, 101], 1]], [[[1, -16, 103], 1]], [[[1, 12, 107], 1]], [[[1, 2, 109], 1]], [[[1, 14, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 24, 'label': '2-1155-1.1-c1-0-24', '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/1155/2/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-9.091436382500262e-61, 0.08862202165386042, 0.1770120132414224, 0.2648901416727224, 0.35188406728003596, 0.43749012562105966, 0.5210426222670081, 0.6016927792043726, 0.67839817419602, 0.7499229063500588, 0.8148482558695567, 0.8715932920410598, 0.9184446960190457, 0.9535949620716123, 0.9751880789505527, 0.981371736125606, 0.9703550241906115, 0.9404704936311487, 0.8902393004691528, 0.818438007625327, 0.7241654384070276, 0.6069078070740012, 0.46660019560470783, 0.3036823200656149, 0.11914644797412756, -0.0854246980450975, -0.30783217474331925, -0.5452492003491198, -0.7942254982188724, -1.0507091366364232, -1.3100870360520656, -1.5672448707912596, -1.8166465734844943, -2.0524330670927733, -2.2685392148292443, -2.458827309252893, -2.6172347381583174, -2.737932789093905, -2.815492911001697, -2.8450561665814083, -2.8225011091033303, -2.744604928717397, -2.609192460602672, -2.415267552842977, -2.1631213743574387, -1.8544125165207366, -1.4922142145324178, -1.0810246878003376, -0.6267374669433535, -0.136569625040575, 0.3810529590335565, 0.9166528364148536, 1.4598988198171932, 1.9998410231095738, 2.5251782366749698, 3.024551335770435, 3.4868550991229403, 3.901559662857536, 4.259031906272346, 4.550846412748462, 4.770075316713099, 4.911546372919313, 4.972058993383146, 4.95054880336542, 4.848192469672311, 4.668446135659909, 4.417012724982018, 4.101735601613847, 3.7324185330040565, 3.3205745184421964, 2.879108726174001, 2.421943431726101, 1.9635953619325586, 1.5187181181207468, 1.1016242741051676, 0.7258032232701127, 0.4034517987419233, 0.14503504189359814, -0.04110580258489403, -0.14908195861182522, -0.17570799837241385, -0.12066276589698863, 0.013448931052327326, 0.22113973887367522, 0.49419036665638566, 0.8219054020820024, 1.1914681721659406, 1.5883843573238727, 1.9970001612906179, 2.401077329575565, 2.7844043613234284, 3.1314210247567877, 3.4278318936007386, 3.661184170571211, 3.8213856183666053, 3.9011400026832717, 3.896280046119543, 3.8059814319147316, 3.6328457730918613, 3.382845524323197, 3.0651293716172314, 2.6916924684699812, 2.276921753328307, 1.8370322259858147, 1.3894152217936213, 0.9519241539543819, 0.5421266689158568, 0.17655448434708557, -0.1300167965782327, -0.36522597401597406, -0.5196925306950536, -0.5874640043438908, -0.5663220858814518, -0.4579307619211607, -0.26781644370143226, -0.005177314375672505, 0.31747323093491087, 0.6848165255747571, 1.0793721201121305, 1.482248383101656, 1.8739682092395626, 2.235333595753137, 2.548290192177485, 2.7967520300372515, 2.9673475971555328, 3.050051249625864, 3.0386685754961342, 2.931150570027889, 2.729719099364526, 2.440794787436696, 2.0747277668642696, 1.6453412497319242, 1.1693071343608021, 0.6653814027020349, 0.15353443363878036, -0.34598284154182, -0.8135921193737297, -1.2313136765873316, -1.583619091461591, -1.8581676271540002, -2.0463883168621235, -2.14387698413812, -2.1505863552113214, -2.070797657384291, -1.9128731506433252, -1.688800352784242, -1.4135497052879085, -1.1042775011630013, -0.779414501147079, -0.4576873068243295, -0.15712383446775177, 0.10590414707843619, 0.3175496416557194, 0.46722244870401514, 0.5481434966600733, 0.5576894532905553, 0.4975065740979479, 0.3733851321878805, 0.1948988966067703, -0.025172715029292574, -0.27160971874052636, -0.5276627309522596, -0.7760600703463876, -1.0000542649370106, -1.1844481011865722, -1.3165403351138942, -1.3869345750996809, -1.3901615423814153, -1.3250746271405252, -1.1949909141706851, -1.0075640213423922, -0.7743904166637352, -0.5103665064720518, -0.2328288253970899, 0.039476778145810736, 0.28753980759870695, 0.49327824657272323, 0.6407101185508011, 0.717032773020657, 0.7135426459772091, 0.6263357438699716, 0.4567403320483092, 0.21144772578196006, -0.09767606576005153, -0.4540967210667003, -0.837416036707012, -1.2244361867641533, -1.5904290548648077, -1.9105420809406795, -2.1612618978489784, -2.321851212994376, -2.375673394578396, -2.3113232572807143, -2.1234915219428587, -1.813503965361313, -1.3894937133042489, -0.866185543215972, -0.264293327659533, 0.39044540492369023, 1.0685517330254979, 1.738338389032096, 2.3676109266982976, 2.9254421677492366, 3.3839182110157564, 3.719753277704485, 3.915675748618078, 3.961498789740621, 3.854805464828615, 3.601199356749336, 3.214096319240815, 2.714059670661974, 2.1277083686439333, 1.486253840873889, 0.8237445851956959, 0.1751169043073089, -0.42583606671231, -0.9484575230929123, -1.3670625105915442, -1.6625028926715664, -1.8233627716148264, -1.8467056067071772, -1.7383197461577682, -1.5124383703186128, -1.190941232378857, -0.8020772075383171, -0.37877659074288017, 0.04335155797500481, 0.42822063171788377, 0.7415354628899249, 0.9529915915383486, 1.038268936308259, 0.9806939697046662, 0.7724624163671195, 0.4153394037480993, -0.07921549874458106, -0.6905165896870751, -1.3896958381248885, -2.141268665446037, -2.9051351973160697, -3.6389022419367034, -4.300389622793615, -4.850170938296453, -5.253994324304794, -5.484933794336664, -5.525136072395415, -5.367050769484692, -5.014061986270741, -4.4804751672524175, -3.7908521243142603, -2.9787271808554245, -2.0847758557782905, -1.154541965072662, -0.2358572425860816, 0.6238922881284362, 1.3804882897331654, 1.9954251056502876, 2.4381223911188625], 'positive_zeros': ['1.44103206082241001703888146306777', '2.88681565469918806050213132342504', '4.55506539008696734138729210412723', '4.80002762182347396606928725837140', '6.30171642528183805525931295511562', '6.73930780627269621365845974322784', '7.86931166885158693607339542171889', '8.822830716811895429813830368216330', '9.310116363210925935025690188215354'], 'prelabel': '2-1155-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.036893385263613, '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': 993314052577958824, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.44103206082241001703888146307', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.88681565469918806050213132343', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.55506539008696734138729210413', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.222721433457888, 'bad_primes': [3, 5, 7, 11], 'central_character': '1.1', 'conductor': 1155, 'conductor_radical': 1155, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, -1, 1, 1, -1, 3, 1, -1, 1, 1, -2, 1, -1, -1, -6, -1, -4, -1, 1, -1, 8, -3, 1, 2, -1, 1, 6, 1, 8, -5, -1, 6, -1, -1, 6, 4, 2, 3, -6, -1, -4, -1, 1, -8, -8, 1, 1, -1, 6, 2, -10, 1, 1, -3, 4, -6, -12, 1, -10, -8, -1, 7, -2, 1, -12, 6, -8, 1, -8, 3, -6, -6, -1, 4, -1, -2, 8, -1, 1, 6, -4, -1, -6, 4, -6, 3, 10, -1, 2, -8, -8, 8, -4, 5, -14, -1, 1, -1], 'euler11': [1, -1, 0], 'euler13': [1, 2, 13], 'euler17': [1, 6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 1, 2], 'euler23': [1, -8, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -6, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, -1, 0], 'euler53': [1, 10, 53], 'euler59': [1, 12, 59], 'euler61': [1, 10, 61], 'euler67': [1, 12, 67], 'euler7': [1, 1, 0], 'euler71': [1, 8, 71], 'euler73': [1, 6, 73], 'euler79': [1, -8, 79], 'euler83': [1, 4, 83], 'euler89': [1, -10, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 1, 2], [1, 1, 0], [1, -1, 0], [1, 1, 0], [1, -1, 0], [1, 2, 13], [1, 6, 17], [1, 4, 19], [1, -8, 23], [1, -6, 29], [1, -8, 31], [1, -6, 37], [1, 6, 41], [1, 4, 43], [1, 8, 47], [1, 10, 53], [1, 12, 59], [1, 10, 61], [1, 12, 67], [1, 8, 71], [1, 6, 73], [1, -8, 79], [1, 4, 83], [1, -10, 89], [1, 14, 97]], 'index': 24, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1155/e', 'ModularForm/GL2/Q/holomorphic/1155/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/1155/2/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': '2-1155-1.1-c1-0-24', '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': '2-1155-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.036893385263613, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 993314052577958824, 'z1': {'__RealLiteral__': 0, 'data': '1.44103206082241001703888146307', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20575458
{'Lhash': '1826725156849650436324407759212', 'Lhash_array': ['1826725156849650436324407759212'], 'label': '2-1155-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1155/2/a/e'}
-
id: 24552005
{'Lhash': '1826725156849650436324407759212', 'Lhash_array': ['1826725156849650436324407759212'], 'label': '2-1155-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1155/2/a/e/1/1'}
-
id: 37506
{'Lhash': '993314052577958824', 'Lhash_array': ['993314052577958824'], 'label': '2-1155-1.1-c1-0-24', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1155/e'}