-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1363663187576318389848651603727', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.397532625703008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '2304.1', 'coefficient_field': '1.1.1.1', 'conductor': 2304, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1], [1, -2, 5], [1, 0, 7], [1, 0, 11], [1, -4, 13], [1, -8, 17], [1, 0, 19], [1, 0, 23], [1, 10, 29], [1, 0, 31], [1, -12, 37], [1, 8, 41], [1, 0, 43], [1, 0, 47], [1, -14, 53], [1, 0, 59], [1, -12, 61], [1, 0, 67], [1, 0, 71], [1, -6, 73], [1, 0, 79], [1, 0, 83], [1, 16, 89], [1, -18, 97], [1, 2, 101], [1, 0, 103], [1, 0, 107], [1, -20, 109], [1, 16, 113]], 'euler_factors_factorization': [[1], [1], [[[1, -2, 5], 1]], [[[1, 0, 7], 1]], [[[1, 0, 11], 1]], [[[1, -4, 13], 1]], [[[1, -8, 17], 1]], [[[1, 0, 19], 1]], [[[1, 0, 23], 1]], [[[1, 10, 29], 1]], [[[1, 0, 31], 1]], [[[1, -12, 37], 1]], [[[1, 8, 41], 1]], [[[1, 0, 43], 1]], [[[1, 0, 47], 1]], [[[1, -14, 53], 1]], [[[1, 0, 59], 1]], [[[1, -12, 61], 1]], [[[1, 0, 67], 1]], [[[1, 0, 71], 1]], [[[1, -6, 73], 1]], [[[1, 0, 79], 1]], [[[1, 0, 83], 1]], [[[1, 16, 89], 1]], [[[1, -18, 97], 1]], [[[1, 2, 101], 1]], [[[1, 0, 103], 1]], [[[1, 0, 107], 1]], [[[1, -20, 109], 1]], [[[1, 16, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-48e2-1.1-c1-0-14', 'leading_term': '2.36929645963868895644455165941000000000000000000000000000000000000000000000000000000000000', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2304/2/a/n', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.369296459638689, 2.3632252835793217, 2.344879071874015, 2.3138728646125033, 2.269607611633362, 2.211330366873572, 2.1382118647600388, 2.0494359419040244, 1.9442949974134953, 1.8222859401992875, 1.6832016676214234, 1.5272138680450702, 1.3549436931465197, 1.1675175180144772, 0.9666055702987524, 0.754441678314655, 0.5338227997050048, 0.3080873911870507, 0.08107210552854337, -0.1429532172691468, -0.3593717462615425, -0.563325900949692, -0.7498418080712087, -0.9139694126827275, -1.0509349337542422, -1.1563016211022088, -1.2261340886859542, -1.2571609073458563, -1.246929676366389, -1.193948494501472, -1.0978076504760976, -0.959275478309664, -0.7803626948381588, -0.564350167585174, -0.31577595257314817, -0.04037858447321287, 0.2550050256104403, 0.5625871599725837, 0.8738206865604989, 1.1796308138062448, 1.4706819059660567, 1.737672261544462, 1.971648088642704, 2.1643264508870623, 2.30841578662375, 2.3979217979138077, 2.4284261311394992, 2.397325381479392, 2.3040185863052063, 2.1500325450742523, 1.9390760104688214, 1.6770160080313137, 1.371772204905982, 1.0331282832151198, 0.6724625773753663, 0.30240368394112543, -0.06357979271927595, -0.4116428871185426, -0.7280658348031626, -0.9997755270131065, -1.2148668947583563, -1.3631030552561396, -1.4363726921100273, -1.4290836966785674, -1.3384736099763006, -1.164819868643134, -0.9115362267113807, -0.5851459029513869, -0.19512685260033205, 0.24637009795545695, 0.724923900323948, 1.2243547178776388, 1.7273267289891523, 2.216019966207296, 2.6728446981889986, 3.0811687015466633, 3.4260258183189958, 3.6947736140533123, 3.8776688472040317, 3.968331872551731, 3.9640749973162848, 3.866075081067797, 3.6793771373509143, 3.412723103994774, 3.0782079866260394, 2.6907738827555296, 2.267560564928998, 1.8271389282597021, 1.3886602824437058, 0.9709598095228041, 0.5916561821321161, 0.26629107632332727, 0.007551937306187642, -0.17538121560584602, -0.27732889847458425, -0.2974159053352619, -0.2391649371228432, -0.11036931281855202, 0.07725514374596593, 0.3086276216003619, 0.5660466441694537, 0.8300881529292555, 1.0806151936025572, 1.2978497905779776, 1.463452668894853, 1.561554246512845, 1.5796810051370247, 1.5095250400525666, 1.3475112127863322, 1.0951256459906777, 0.7589809106195693, 0.3506066204802307, -0.11403139246536041, -0.6152653471610617, -1.130680908394633, -1.6362483129856442, -2.1075727965783915, -2.5211995849563014, -2.8559037043352027, -3.0938935542675954, -3.2218597844005363, -3.231807518945599, -3.1216201547004534, -2.8953163754707316, -2.562978031152477, -2.1403443035975758, -1.6480861708268006, -1.110793550394075, -0.5557245901307019, -0.011381353769975667, 0.49401230934958146, 0.9340473911478044, 1.2855945770163955, 1.5301129965634421, 1.6547254274953482, 1.6529940763106779, 1.5253467806314702, 1.279122550899489, 0.9282267669933908, 0.49240886830464486, -0.0038022826018932246, -0.5324493604678393, -1.0637098463992545, -1.5675835460951582, -2.0156071798189172, -2.3824953610607666, -2.647609752974693, -2.7961666523247994, -2.820107343406499, -2.7185745754099466, -2.497961407305247, -2.1715241250656523, -1.7585774595680517, -1.2833163026434051, -0.773331904523463, -0.2579105997913912, 0.23378189723113163, 0.6745187293023059, 1.0407187540299587, 1.3139332367182652, 1.482015703969785, 1.5398967796415308, 1.4899096785389077, 1.3416398469539688, 1.1113023225433902, 0.8206808571244435, 0.49569174745185296, 0.16466074335683661, -0.143578382268454, -0.40164144951739267, -0.5854796429629446, -0.6760677841016094, -0.6607801190152084, -0.5343570903046971, -0.2993917697285363, 0.033704918651600746, 0.4472672486661752, 0.9174380843255137, 1.4156707977275464, 1.910577403825521, 2.370005618061563, 2.7632098632955984, 3.0629722320226245, 3.2475298536161246, 3.3021752116850673, 3.2204152441367606, 3.0046024457785445, 2.6659850123242625, 2.2241611704145594, 1.7059627423124333, 1.1438320256978014, 0.5737915537959457, 0.03313574356978303, -0.44200530013651196, -0.8190681071590928, -1.0712619267466703, -1.1794266354083576, -1.133411539714714, -0.9328745125429346, -0.5874387190765554, -0.11618699470252095, 0.45348113240217636, 1.0875607983105768, 1.7476126008904218, 2.3932508100277627, 2.9847831819098016, 3.4858239259340937, 3.865700952179582, 4.101490573905132, 4.179536723037467, 4.096345977225077, 3.858792052059469, 3.4836110193585728, 2.9962180816147774, 2.4289247717336573, 1.8186785084624215, 1.2044813671726418, 0.6246690952931839, 0.11424291122950259, -0.29755554587609223, -0.5892516502188734, -0.7485818294196401, -0.7732680149627766, -0.671064066670701, -0.4590683096302695, -0.16234993954344162, 0.1880122014928594, 0.5573358731558719, 0.910009988758366, 1.2122392915805589, 1.4346539492964117, 1.5545870013061869, 1.5578455253379606, 1.4398376256785193, 1.2059643814430943, 0.8712403740729765, 0.45916436739659405, -8.116020173769738e-05, -0.4719709479833911, -0.9203448268354665, -1.3102787014301707, -1.610899520120774, -1.7979262525322777, -1.8557366451321207, -1.7787928102608375, -1.5723052489195972, -1.2520713867983488, -0.8434869747141664, -0.37979211091603726, 0.10032664408026716, 0.5556052004573031, 0.9453300712225249, 1.2324904631318132, 1.3867133478521476, 1.3867531858580868, 1.2223383496101303, 0.8952223467154458], 'positive_zeros': ['1.07574057656802494464390490749068', '2.05899636987229362790422468605165', '3.27092596459393225052086143179252', '4.01100966495944443006006263062719', '5.39262958273976329743454417116471', '5.71994566936884971110657383523823', '6.54863571929054381318876237423095', '7.55985426853550376471644781915656', '8.202694220619429288756420575978432', '9.112200135449134934371783246206760'], 'prelabel': '2-48e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.289234503463644, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 726375266439705038, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07574057656802494464390490749', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.05899636987229362790422468605', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27092596459393225052086143179', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 18.397532625703008, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 2304, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -7, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -4, 13], 'euler17': [1, -8, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 10, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, -12, 37], 'euler41': [1, 8, 41], 'euler43': [1, 0, 43], 'euler47': [1, 0, 47], 'euler5': [1, -2, 5], 'euler53': [1, -14, 53], 'euler59': [1, 0, 59], 'euler61': [1, -12, 61], 'euler67': [1, 0, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, -6, 73], 'euler79': [1, 0, 79], 'euler83': [1, 0, 83], 'euler89': [1, 16, 89], 'euler97': [1, -18, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -2, 5], [1, 0, 7], [1, 0, 11], [1, -4, 13], [1, -8, 17], [1, 0, 19], [1, 0, 23], [1, 10, 29], [1, 0, 31], [1, -12, 37], [1, 8, 41], [1, 0, 43], [1, 0, 47], [1, -14, 53], [1, 0, 59], [1, -12, 61], [1, 0, 67], [1, 0, 71], [1, -6, 73], [1, 0, 79], [1, 0, 83], [1, 16, 89], [1, -18, 97]], 'index': 14, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2304/n', 'ModularForm/GL2/Q/holomorphic/2304/2/a/n/1/1', 'ModularForm/GL2/Q/holomorphic/2304/2/a/n'], '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': '2-48e2-1.1-c1-0-14', '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': '2-48e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.289234503463644, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 726375266439705038, 'z1': {'__RealLiteral__': 0, 'data': '1.07574057656802494464390490749', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20604791
{'Lhash': '1363663187576318389848651603727', 'Lhash_array': ['1363663187576318389848651603727'], 'label': '2-48e2-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2304/2/a/n'}
-
id: 24556634
{'Lhash': '1363663187576318389848651603727', 'Lhash_array': ['1363663187576318389848651603727'], 'label': '2-48e2-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2304/2/a/n/1/1'}
-
id: 24737
{'Lhash': '726375266439705038', 'Lhash_array': ['726375266439705038'], 'label': '2-48e2-1.1-c1-0-14', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2304/n'}