-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1439985916369865335879980745471', 'a10': [0.0, 0.0], 'a2': [0.8660254037844386, 0.5], 'a3': [0.8660254037844386, 0.5], 'a4': [0.5, 0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.5, 0.8660254037844386], 'a7': [0.0, 0.0], 'a8': [3.9689140359382235e-80, 1.0], 'a9': [4.582907174078835e-80, 2.6459426906630975e-80], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8964470480054092, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [2, 5, 19], 'central_character': '3800.2899', 'coefficient_field': 'CDF', 'conductor': 3800, 'conductor_radical': 190, 'conjugate': '2329870528998600040787767329095', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [-0.8660254037844386, -0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-1.7320508075688772, -1.0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [1.7320508075688772, 1.0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.8660254037844386, 0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.8660254037844386, -0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 1.0], [-1.0, 0]], [[1.0, 0], [-1.0, -1.7320508075688772], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.8660254037844386, 0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 2.0], [-1.0, 0]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 1.0], [-1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-3800-760.619-c0-0-4', 'leading_term': '2.77859435750137794823368492327', '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/3800/1/bn/b/2899/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.778594357501378, 2.6961730463386013, 2.631953314983766, 2.581922305186885, 2.5413974355517683, 2.505427891621007, 2.469151112979858, 2.4280645141710075, 2.3782048679868977, 2.3162490552162875, 2.239558020816574, 2.146184771898965, 2.0348621494779136, 1.9049803929541573, 1.75655983109175, 1.5902207853633825, 1.4071507974406383, 1.2090682629467173, 0.9981811582415422, 0.7771395512429634, 0.5489808313293226, 0.3170669744577956, 0.08501361317128686, -0.14338883389028254, -0.3642612294030126, -0.5737277650762532, -0.7680123319548305, -0.9435371605295597, -1.097021341884328, -1.2255765763705722, -1.3267973140552047, -1.3988423613599321, -1.4405050390467422, -1.451269093871469, -1.4313477929085683, -1.381703965597553, -1.3040492002262798, -1.2008209412391502, -1.075136859841374, -0.9307265672999802, -0.7718414887749405, -0.6031444926849014, -0.4295816508659568, -0.25623926026950417, -0.08818995847482036, 0.0696676166867398, 0.21277066740612494, 0.3370502536461197, 0.43907996262185545, 0.5162096836652922, 0.5666791184928507, 0.5897060381395094, 0.5855448846910648, 0.5555121014182006, 0.5019755438590665, 0.4283064535184694, 0.33879373397331297, 0.23852161784641082, 0.13321320757146166, 0.029043763333569422, -0.0675710551842129, -0.15020556537272636, -0.21266557375228032, -0.2492327035794478, -0.2549026454326576, -0.2256081694029591, -0.15841780260841473, -0.05170149357974745, 0.09474463829772757, 0.27962124250549053, 0.5001016843697429, 0.7518645698320878, 1.0291844308274, 1.3250799904916968, 1.6315171635225176, 1.9396616672723714, 2.2401739140447443, 2.5235368177046027, 2.7804053701850857, 3.0019654128864026, 3.1802880225195227, 3.308665416073773, 3.38191430437775, 3.396633217835076, 3.3514014990985683, 3.246909389841499, 3.0860108921417653, 2.873693794880349, 2.61696433462414, 2.324647300801495, 2.007105871489417, 1.6758889408757751, 1.3433170268321746, 1.0220208795840864, 0.7244495071656986, 0.46236635803664056, 0.24635374098072152, 0.08534612547151453, -0.013787311144391863, -0.04659167037983097, -0.011289645651397612, 0.09105521315666312, 0.25648608578386034, 0.47821792581691236, 0.7468219046090225, 1.0505262384269247, 1.3756253330828472, 1.7069842546597378, 2.0286209529333434, 2.324344641344106, 2.578425475204844, 2.776268345543359, 2.9050623636589363, 2.954377553847801, 2.9166814535133705, 2.787750742837249, 2.5669566366297127, 2.2574074594137405, 1.8659374282726662, 1.4029369749882936, 0.8820266968059689, 0.31958394954112346, -0.265862116507129, -0.8543449393170519, -1.42525662263138, -1.9581934338323288, -2.433815179399591, -2.8346811269241914, -3.1460249730869876, -3.356432875556881, -3.45839176769588, -3.4486799744284173, -3.328578384289072, -3.103887871971941, -2.784747007939789, -2.385252983335635, -1.9228977268516754, -1.4178399803852288, -0.8920422138332572, -0.3683082941322721, 0.13073658637750774, 0.583678383037381, 0.9713118949208158, 1.2775568138740192, 1.490247768921317, 1.6017586775420085, 1.6094283894703911, 1.5157630348234894, 1.3284003208273338, 1.0598318352217067, 0.7268907231387941, 0.3500233814741823, -0.047625481587213477, -0.4412754759867744, -0.8056739045742385, -1.1163069755437507, -1.3506023615929155, -1.4890656544158483, -1.5162950463281346, -1.4218230876583053, -1.200741474425198, -0.8540742394277264, -0.3888760527395313, 0.18195491983192175, 0.8401465882290204, 1.5627881890095738, 2.3233012243090383, 3.0926040209780803, 3.840417555729611, 4.536652249808542, 5.152810289021262, 5.663335994123884, 6.0468480263090925, 6.2871917752182265, 6.3742579885106645, 6.304524245511146, 6.081288784665491, 5.714580866199438, 5.220747584488281, 4.62173306596477, 3.944081492512567, 3.217709580415576, 2.4745062742925827, 1.7468268272017782, 1.0659546015698296, 0.4606064668072692, -0.04444360577578857, -0.4295532420578638, -0.6811518600291676, -0.7923835012568426, -0.7634180407861436, -0.6014130651872946, -0.3201263722984064, 0.060803077804505536, 0.516870773617521, 1.019968307318328, 1.5398274905714953, 2.045573465897019, 2.5073072138475077, 2.8976358398413917, 3.1930712832379418, 3.3752245553783933, 3.431732986321596, 3.3568717307620566, 3.151817250643975, 2.8245487985068216, 2.3893931038588003, 1.8662364873601662, 1.2794464625055542, 0.6565605524349216, 0.02681267830422805, -0.580423649852504, -1.1371915048959291, -1.6184221946, -2.003243056823031, -2.276050980350437, -2.4272940633670883, -2.4539198732075875, -2.3594671702239154, -2.153797690464309, -1.8524845472337594, -1.4758928884951745, -1.0480055542483144, -0.5950606373048731, -0.14407824433437807, 0.2786402271888297, 0.6489556988861243, 0.9461968588601566, 1.154254588686241, 1.262404890887775, 1.265815700891045, 1.165711404016614, 0.9691888204967375, 0.688698706836185, 0.34122625938650186, -0.05277845235910514, -0.4706547865258287, -0.8888947146627806, -1.2845330625006455, -1.6364818944169215, -1.9267300251325812, -2.141337289212998, -2.2711660856734026, -2.3123090681727705, -2.266190681653693, -2.139340406882838, -1.9428558292571676, -1.6915927477283088, -1.4031362971521908, -1.0966204233859373, -0.7914721793894802, -0.5061616153809143, -0.25703722770163945, -0.05732103983143198, 0.08367323361035701, 0.16105018899720075, 0.1745400095492227], 'positive_zeros': ['1.13594859349304017073477690311898', '2.26224199376516917850708167907727', '3.01080050816064212321032002398473', '3.42188949055513843544158764581574', '4.96694254318839599471162262451899', '5.08583679416755380118742700207809', '6.17239023837203753593964451194206', '7.09569751583113792543885483726262', '7.71270432103438642481715771105015', '8.262057438386319443406924296114778'], 'prelabel': '2-3800-760.619-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3771154809983834, 'root_angle': -0.5486702390460434, 'root_number': '-0.15230697753240356606310011178134 - 0.98833323560170934653042967162502*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2743351195230217', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13594859349304017073477690312', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26224199376516917850708167908', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01080050816064212321032002398', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.8964470480054092, 'bad_primes': [2, 5, 19], 'central_character': '760.619', 'conductor': 3800, 'conductor_radical': 190, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3800/1/bn/b/2899/2'], 'is_instance_Artin': False, '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': '2-3800-760.619-c0-0-4', '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': '2-3800-760.619-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3771154809983834, 'root_angle': -0.2743351195230217, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13594859349304017073477690312', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1439985916369865335879980745471', 'Lhash_array': ['1439985916369865335879980745471'], 'label': '2-3800-760.619-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3800/1/bn/b/2899/2'}