-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1571629430847206966059085126241', 'a10': [-1.0, -2.0], 'a2': [0.0, 1.0], 'a3': [0.0, 1.0], 'a4': [-1.0, 0.0], 'a5': [-2.0, 1.0], 'a6': [-1.0, 0.0], 'a7': [0.0, 3.0], 'a8': [0.0, -1.0], 'a9': [2.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8783544222340847, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [2.0, -1.0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 11], 'central_character': '110.89', 'coefficient_field': 'CDF', 'conductor': 110, 'conductor_radical': 110, 'conjugate': '4243617019696223861684879072392', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -1.0], [-3.0, 0]], [[1.0, 0], [2.0, -1.0]], [[1.0, 0], [0, -3.0], [-7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 4.0], [-13.0, 0]], [[1.0, 0], [0, -3.0], [-17.0, 0]], [[1.0, 0], [-5.0, 0], [19.0, 0]], [[1.0, 0], [0, 4.0], [-23.0, 0]], [[1.0, 0], [5.0, 0], [29.0, 0]], [[1.0, 0], [-7.0, 0], [31.0, 0]], [[1.0, 0], [0, 7.0], [-37.0, 0]], [[1.0, 0], [8.0, 0], [41.0, 0]], [[1.0, 0], [0, -6.0], [-43.0, 0]], [[1.0, 0], [0, -8.0], [-47.0, 0]], [[1.0, 0], [0, 9.0], [-53.0, 0]], [[1.0, 0], [0, 0], [59.0, 0]], [[1.0, 0], [13.0, 0], [61.0, 0]], [[1.0, 0], [0, 12.0], [-67.0, 0]], [[1.0, 0], [3.0, 0], [71.0, 0]], [[1.0, 0], [0, -6.0], [-73.0, 0]], [[1.0, 0], [0, 0], [79.0, 0]], [[1.0, 0], [0, 4.0], [-83.0, 0]], [[1.0, 0], [-15.0, 0], [89.0, 0]], [[1.0, 0], [0, 12.0], [-97.0, 0]], [[1.0, 0], [-2.0, 0], [101.0, 0]], [[1.0, 0], [0, 4.0], [-103.0, 0]], [[1.0, 0], [0, 12.0], [-107.0, 0]], [[1.0, 0], [-10.0, 0], [109.0, 0]], [[1.0, 0], [0, -6.0], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-110-5.4-c1-0-0', '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/110/2/b/a/89/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9044366572954894, 0.8297784291451161, 0.7632550765434807, 0.700021429997787, 0.6350803433973233, 0.5636534090500676, 0.4814613074600533, 0.38492189492814693, 0.27129903204694356, 0.13883327403373352, -0.013129054214372054, -0.1840074165911336, -0.3718697896163587, -0.5733440014912342, -0.7835783693454853, -0.996272771079139, -1.2037994749670444, -1.3974291659855116, -1.5676717107596134, -1.7047333709950019, -1.7990826155350075, -1.8421057970082517, -1.8268223804386807, -1.748617994118493, -1.6059433677603943, -1.4009194119839345, -1.139784500075309, -0.8331205853825165, -0.49580106212598263, -0.14661583561594904, 0.19245200052044795, 0.4972986951924881, 0.7430929508363266, 0.9059287876519921, 0.9646449247474639, 0.9026878775086284, 0.7098725985623818, 0.3838806547601557, -0.06866537580231641, -0.6316991325109372, -1.2798977836731777, -1.9796328649983557, -2.6906994062409555, -3.3687694452438666, -3.968442718913676, -4.446696031919072, -4.766471038674393, -4.900095583966722, -4.832213315784224, -4.5619054494555105, -4.103730377491882, -3.487481247916576, -2.7565650938082564, -1.9650323470039588, -1.1734220033271765, -0.44372208821645337, 0.1661373159954362, 0.6077550780855567, 0.8471489687615686, 0.868531749646851, 0.6765113679683595, 0.2963808058178484, -0.22766090217985469, -0.8363056130305188, -1.4606779106603176, -2.0291379865612234, -2.474687848311302, -2.742209877478946, -2.7947329337284232, -2.6179778956831408, -2.2225828705149024, -1.6436382810945598, -0.9374526096236341, -0.17579021914230175, 0.5618636558460264, 1.1971884051213346, 1.6620578104114427, 1.9066368199796933, 1.905527174205077, 1.661134838166766, 1.2037400129416682, 0.5881430983248446, -0.1128083260513527, -0.8170901012989343, -1.4437038234009876, -1.9229234896578384, -2.2052382751101924, -2.2677618310131957, -2.117171344828272, -1.7886768980346315, -1.3410510977570742, -0.8483014733884406, -0.3890665389290158, -0.035185996309303316, 0.1589248907938389, 0.16451481689665468, -0.016949613880611565, -0.3537255998464316, -0.7884055036284098, -1.2466752095979539, -1.6490408168154982, -1.923831497573539, -2.0195023908254632, -1.9142647949846558, -1.6213791948888838, -1.1890313988976775, -0.6945000461559362, -0.23320513112887473, 0.09592986847749728, 0.20669986201327864, 0.04094136420147626, -0.41953782903062203, -1.1465362863876751, -2.0659187179367247, -3.0653306880529367, -4.008419005797011, -4.753737761584525, -5.175674460750068, -5.184259031073885, -4.740718115246029, -3.8661352134532647, -2.6415220250217315, -1.1988703583414768, 0.29584934534209967, 1.6654660984987737, 2.746877938608812, 3.415000226551648, 3.60164152122372, 3.306223553262455, 2.5964529957430886, 1.598594104334062, 0.478643362848585, -0.5827985670345615, -1.4180796220462566, -1.8981194785404776, -1.9519786515199986, -1.5771694405041985, -0.8389809274818606, 0.14111181908057618, 1.2060624389306387, 2.189466301194578, 2.9429724201300553, 3.3602630598090175, 3.3935373581997017, 3.0597196504782596, 2.43540196369946, 1.641514868628967, 0.8205493769761796, 0.11049169984000186, -0.3797702133809945, -0.5890774135235315, -0.5132766053407566, -0.20349371508536793, 0.2461733331783317, 0.7191039909647453, 1.1007301887031382, 1.3023919885396655, 1.2797244490479336, 1.041849368409577, 0.649418984504415, 0.20175464396432416, -0.18447847134813428, -0.4008531538612365, -0.37183925752158936, -0.07340087497055897, 0.4585317216210792, 1.1318486938770451, 1.8140136816409125, 2.3570411558682443, 2.626974419665417, 2.5320445120864545, 2.0437336320321036, 1.2061827841340826, 0.1315691895025327, -1.0181728913101995, -2.060141327268704, -2.8243840289553646, -3.1863430022983112, -3.0913001237693556, -2.565709205191365, -1.7127984091165305, -0.6929437707191682, 0.30756958888164904, 1.1133080211929933, 1.5945813930039758, 1.6932598814861248, 1.4339886890895768, 0.918152856613651, 0.3014649200078907, -0.24050124631377656, -0.5518490724678068, -0.5327066061860346, -0.1645273210663647, 0.4814388555412017, 1.2549306289522293, 1.9551626064048593, 2.3716731435595815, 2.3293993916894475, 1.728670708035278, 0.5715522639901394, -1.0314677231032419, -2.8765544106961936, -4.701017861909006, -6.230781256984463, -7.231535005963333, -7.553304507925577, -7.159301581725714, -6.133003300217365, -4.6617987701077555, -3.0003598158108047, -1.4211120959049135, -0.16190238817191344, 0.6184256562678909, 0.8674802715491258, 0.6443084269654453, 0.10119963182817575, -0.5534830487561427, -1.1032049974357572, -1.3714109781809967, -1.2594824998754972, -0.7663879434684397, 0.01397778518652638, 0.9167821599420564, 1.7458409396942818, 2.3196217672452533, 2.51312117593715, 2.2861030050553506, 1.691386320144501, 0.8615111631649619, -0.022873979712710303, -0.7753284552097629, -1.2466069380573537, -1.3581830832602964, -1.1184631053119802, -0.6179960649810832, -0.005030644480383738, 0.552496067123933, 0.9091628307472839, 0.9780512792183532, 0.751601046826944, 0.3021141363992108, -0.2382851049003878, -0.7132844373942021, -0.9846654398422351, -0.9704458569491654, -0.668918802961014, -0.1619711158250659, 0.40383363542316425, 0.8542842748215491, 1.0337594654208953, 0.8490688934511411, 0.2994192959031479, -0.5159508785724037, -1.415650570563249, -2.176413937520964, -2.5868673505903086, -2.50204379788023], 'positive_zeros': ['1.23979701549011126191742279765473', '3.67809253555074976153314280702964', '4.73295666042138592083941452173730', '6.96274046055113740750404610805355', '7.69900240295976557573366582432828', '9.153928025466994275930952749671081', '10.23030438801077257222125559895337', '11.64126003200319204649037279643384', '11.99190237894301110032142643339436', '13.45559146327761817173452832323148'], 'prelabel': '2-110-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9372056456477866, 'root_angle': -0.32379180882521663, 'root_number': '-0.4472135954999579 - 0.8944271909999159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.323791808825', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23979701549011126191742279765', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.67809253555074976153314280703', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.73295666042138592083941452174', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.8783544222340847, 'bad_primes': [2, 5, 11], 'central_character': '5.4', 'conductor': 110, 'conductor_radical': 110, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/110/2/b/a/89/2'], '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': '2-110-5.4-c1-0-0', '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': '2-110-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9372056456477866, 'root_angle': -0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23979701549011126191742279765', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1571629430847206966059085126241', 'Lhash_array': ['1571629430847206966059085126241'], 'factors': ['2-110-5.4-c1-0-0'], 'label': '2-110-5.4-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/110/2/b/a/89/2'}