-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3008743459740295962999728710822', 'a10': [0.0, 0.0], 'a2': [0.0, -4.0], 'a3': [0.0, 0.0], 'a4': [-8.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, -6.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.199', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '346809522356606065933181774629', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 4.0], [-8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 6.0], [-343.0, 0]], [[1.0, 0], [32.0, 0], [1331.0, 0]], [[1.0, 0], [0, 38.0], [-2197.0, 0]], [[1.0, 0], [0, -26.0], [-4913.0, 0]], [[1.0, 0], [100.0, 0], [6859.0, 0]], [[1.0, 0], [0, -78.0], [-12167.0, 0]], [[1.0, 0], [50.0, 0], [24389.0, 0]], [[1.0, 0], [108.0, 0], [29791.0, 0]], [[1.0, 0], [0, 266.0], [-50653.0, 0]], [[1.0, 0], [22.0, 0], [68921.0, 0]], [[1.0, 0], [0, -442.0], [-79507.0, 0]], [[1.0, 0], [0, 514.0], [-103823.0, 0]], [[1.0, 0], [0, 2.0], [-148877.0, 0]], [[1.0, 0], [-500.0, 0], [205379.0, 0]], [[1.0, 0], [518.0, 0], [226981.0, 0]], [[1.0, 0], [0, 126.0], [-300763.0, 0]], [[1.0, 0], [412.0, 0], [357911.0, 0]], [[1.0, 0], [0, 878.0], [-389017.0, 0]], [[1.0, 0], [600.0, 0], [493039.0, 0]], [[1.0, 0], [0, 282.0], [-571787.0, 0]], [[1.0, 0], [150.0, 0], [704969.0, 0]], [[1.0, 0], [0, 386.0], [-912673.0, 0]], [[1.0, 0], [702.0, 0], [1030301.0, 0]], [[1.0, 0], [0, 598.0], [-1092727.0, 0]], [[1.0, 0], [0, 1194.0], [-1225043.0, 0]], [[1.0, 0], [-550.0, 0], [1295029.0, 0]], [[1.0, 0], [0, 1562.0], [-1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 20, 'label': '2-15e2-5.4-c3-0-20', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/225/4/b/c/199/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7089475847940504, 1.0677946877626914, 1.4400312857591384, 1.8185141083701213, 2.194956898900458, 2.55971199919772, 2.9016583403316525, 3.2082392681762637, 3.4656830640732013, 3.6594255702608893, 3.7747386159789538, 3.797550427115068, 3.7154253841426774, 3.5186511127540747, 3.2013620985617277, 2.7626124136561625, 2.207297706692472, 1.5468205094514784, 0.7993952490812171, -0.01009816129733999, -0.8507796510005764, -1.6869859785806356, -2.4800275070121054, -3.1904211061360943, -3.7804806000894082, -4.217093373789417, -4.474467132679212, -4.536600698166418, -4.399222987788346, -4.070959587536636, -3.573529123138995, -2.9408417560105002, -2.2169660855429627, -1.4530416233767356, -0.7033317286322558, -0.020723894457737764, 0.5479233178678715, 0.9661282341800591, 1.2113561499439864, 1.277377134581321, 1.1750704874787772, 0.9314787891592142, 0.587097807928653, 0.19159313482792448, -0.20166288743651425, -0.5416656567311858, -0.7857749563115246, -0.9048991383763502, -0.8871770136440209, -0.7396065663296865, -0.4872943633358866, -0.17028881129644724, 0.16171858291783708, 0.4562282431401563, 0.6654506907268877, 0.7534934099940862, 0.7021698687250966, 0.5144991689714596, 0.2152253246400628, -0.1519321457308718, -0.5301239037885018, -0.8576623526405724, -1.0776834678321003, -1.1478005955453565, -1.048250313605214, -0.7871270139539007, -0.4016249047822391, 0.045273331759324, 0.47256384033951543, 0.792640655861172, 0.9249128592825069, 0.8096820160713128, 0.42011620713135217, -0.22974936779847496, -1.0826256048053569, -2.0421071738367242, -2.983303137488428, -3.7689049577148737, -4.26868686057263, -4.379717806604006, -4.044218435337102, -3.2621086346662573, -2.095883262907936, -0.6664698181555004, 0.8599671225321937, 2.292893142979357, 3.4432609746916585, 4.150711861399424, 4.308031343883182, 3.8789531401187762, 2.9062292355620807, 1.508255765254522, -0.13572934526317731, -1.8100444091761925, -3.2931152144900335, -4.389613969565758, -4.959198011794312, -4.937244344051319, -4.3441393770191175, -3.2814624935927084, -1.9155185771809322, -0.4507775560788566, 0.902496177770026, 1.9611083534585156, 2.596838897897149, 2.754738542746258, 2.458806923265089, 1.8042333101239143, 0.9377465319595957, 0.029732053970949097, -0.7567616234536282, -1.294471734890417, -1.5126832429427486, -1.4066427201808405, -1.034143074166096, -0.5002685885773187, 0.06642569019888603, 0.5413788013725882, 0.8295369356510162, 0.8837658193004848, 0.7125082784171148, 0.3752858273587277, -0.032798308128988665, -0.4040610022226056, -0.6436337559674465, -0.6915957526493312, -0.5368658553748423, -0.21964951291384685, 0.17824384280617564, 0.5531643837249339, 0.8050683440068627, 0.8628182965549741, 0.7033497647535666, 0.35991695188505113, -0.08302385943363776, -0.5077231835774795, -0.7902449294655566, -0.8308272369936414, -0.5804524998995292, -0.057047318399989284, 0.6532516387951898, 1.4111362064293596, 2.0531285334121865, 2.4287931445542497, 2.4380929616667113, 2.060205901383648, 1.3664468717201232, 0.5130363417253665, -0.2862679443451977, -0.8030976769686626, -0.8445446618350156, -0.2997609977870835, 0.8274935420219611, 2.408545702850748, 4.205572458946842, 5.911791996014384, 7.209014434374782, 7.831311002330314, 7.6216282346256365, 6.569022940223527, 4.81776966710564, 2.6452303439733553, 0.4119219385263844, -1.5067323421635694, -2.793279578303829, -3.250684976126414, -2.8411537413168606, -1.6928993073501954, -0.07313369347643259, 1.6672437320339935, 3.1656700479482587, 4.121417610333295, 4.354995315047909, 3.8409732087753308, 2.707612408967362, 1.2040103614016586, -0.35738443148913457, -1.6696982384086105, -2.4964999868104307, -2.7183551103903976, -2.351300033376623, -1.5341460262925832, -0.48879750840318925, 0.5360744947945686, 1.324080113157065, 1.7387746076851516, 1.749055169673137, 1.4272024193539823, 0.9213887742799541, 0.41077296905731475, 0.05541671444660009, -0.045816028230247725, 0.12131725623870336, 0.4871978818472782, 0.9222573397836418, 1.2768349037374254, 1.4255978562501028, 1.3040608491654544, 0.9270485311117499, 0.3840265180744863, -0.18728563445840216, -0.6414725541167384, -0.8685198847187703, -0.8269420854789674, -0.5570726356513159, -0.17014401575544336, 0.18432835126596617, 0.36396124270061725, 0.278757664527115, -0.07727215987295895, -0.6182685828626435, -1.1862157650034348, -1.594139698639344, -1.6817253446930185, -1.3679705185906803, -0.6853110107361481, 0.21614090143509423, 1.0979333191113219, 1.6906840180733513, 1.7658086202699044, 1.2028415277686502, 0.03349064955146549, -1.55140728416688, -3.236753569904071, -4.653647901963452, -5.469282345460009, -5.473929601421406, -4.64211527321788, -3.1505399577732254, -1.3456782618555796, 0.33329230092271933, 1.458749544651831, 1.7208116561828777, 1.0086690388908175, -0.5543502763110337, -2.6323119587897605, -4.751051743203443, -6.408152248994222, -7.1919015363151955, -6.8798899504730775, -5.492661016794453, -3.2889547689887797, -0.703752674829074, 1.7552365043646985, 3.6265868601110345, 4.5999175261954, 4.580688744963218, 3.699964849020163, 2.2685064695436203, 0.6889100275438965, -0.65002007047415, -1.4686437540956472, -1.6572947025849454, -1.2883451463410474, -0.5789981220936953, 0.1823527211146683, 0.7239511981776944], 'positive_zeros': ['2.37348008922852876239774577557315', '4.37910657868203024511301877637141', '5.43477343017973845487129109245991', '6.43856895581418512275817067460740', '7.32488124350269556007860738420553', '8.362490277408615677388252496252497', '9.085699558658319960723887401630818', '10.42965859123453469199420682919955', '11.48999159216930931950021529862879', '12.66464164923169188111478288413766'], 'prelabel': '2-15e2-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.6475836176504333, 'root_number': '-0.4472135954999579 - 0.8944271909999159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.323791808825', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.37348008922852876239774577557', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.37910657868203024511301877637', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.43477343017973845487129109246', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/b/c/199/1'], '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': '2-15e2-5.4-c3-0-20', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-15e2-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.32379180882521663, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.37348008922852876239774577557', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3008743459740295962999728710822', 'Lhash_array': ['3008743459740295962999728710822'], 'label': '2-15e2-5.4-c3-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/b/c/199/1'}