-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1949993371601513762557110382271', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.8793852415718169, -0.6840402866513374], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.9396926207859084, 0.3420201433256687], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.82', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1545005801644643949555393097982', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-1.8793852415718169, 0.6840402866513374]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.8682408883346517, 4.924038765061041]], [[1.0, 0], [-0.9396926207859084, -0.3420201433256687], [5.362311101832846, 4.499513267805775]], [[1.0, 0], [0, 0], [1.9101299543362338, -10.832885283134289]], [[1.0, 0], [-0.8682408883346517, 4.924038765061041], [-12.216004070216808, -4.446261863233693]], [[1.0, 0], [0, 0], [-8.5, -14.722431864335457]], [[1.0, 0], [-3.5, -6.06217782649107], [-9.5, 16.454482671904334]], [[1.0, 0], [0, 0], [17.619022191736494, -14.784115022790404]], [[1.0, 0], [0, 0], [-27.251086002791343, 9.918584156444393]], [[1.0, 0], [-3.7587704831436337, 1.3680805733026749], [23.747377736688318, -19.92641590028272]], [[1.0, 0], [5.5, -9.526279441628825], [-18.5, -32.04293994002423]], [[1.0, 0], [0, 0], [-38.527397452222246, -14.022825876352417]], [[1.0, 0], [-6.128355544951824, 5.142300877492315], [7.466871639678005, -42.34673337952495]], [[1.0, 0], [0, 0], [36.00408882659197, 30.211017655267348]], [[1.0, 0], [0, 0], [53.0, 0]], [[1.0, 0], [0, 0], [10.24524248234889, 58.10365742772028]], [[1.0, 0], [-0.9396926207859084, -0.3420201433256687], [46.728711030257664, 39.2100441908789]], [[1.0, 0], [-0.8682408883346517, 4.924038765061041], [-62.95940559265586, -22.915349602819806]], [[1.0, 0], [0, 0], [-35.5, -61.48780366869514]], [[1.0, 0], [-3.5, -6.06217782649107], [-36.5, 63.21985447626402]], [[1.0, 0], [-2.952019020337816, -16.741731801207536], [-74.23571704208676, 27.01959132272783]], [[1.0, 0], [0, 0], [-77.9944875252304, 28.387671896030504]], [[1.0, 0], [0, 0], [-44.5, 77.07626093681505]], [[1.0, 0], [14.554844419260583, -12.212964584044247], [16.843873233692243, -95.52635204218419]], [[1.0, 0], [0, 0], [77.37048875501678, 64.92154857834048]], [[1.0, 0], [9.958577760546714, 8.35623892592501], [17.885762299693827, 101.43519856025743]], [[1.0, 0], [0, 0], [107.0, 0]], [[1.0, 0], [-2.0, 0], [109.0, 0]], [[1.0, 0], [0, 0], [19.62224407636313, 111.28327609037952]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-3e6-27.13-c1-0-18', '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/729/2/e/f/82/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.0089474632616673, 2.063333923196554, 2.1040130935537475, 2.1251837543554313, 2.1175391352973834, 2.0699123549950724, 1.971199541877208, 1.8122857232047929, 1.587809559649363, 1.2976578849166478, 0.9480812076384999, 0.5523009184925781, 0.1304690428847842, -0.29114042996577905, -0.6817773831022359, -1.008683093461325, -1.2402556288685052, -1.349669582886843, -1.3185921495771349, -1.1405475502634161, -0.8234358581318169, -0.39072733903526863, 0.11905924445473354, 0.6548240437956303, 1.1573015370139197, 1.5651547128048091, 1.822196073202839, 1.8849310331024354, 1.7294419597448027, 1.3565703826701219, 0.7944412572545914, 0.09761867003893873, -0.6574248106387651, -1.3803410551580504, -1.9777094824167256, -2.365365411014792, -2.480619689183881, -2.2925525317706987, -1.8086472346637865, -1.076401726807025, -0.17919522861085058, 0.7734783613093487, 1.6603854488773553, 2.365664979747344, 2.79618150947017, 2.8963531656586694, 2.6578633665812057, 2.1223039401915735, 1.3758379213976322, 0.5362698131524033, -0.26573788723773506, -0.9084012395437896, -1.299863463761112, -1.394774236494681, -1.203162091693173, -0.7895525819906448, -0.2619557976565818, 0.2477771836074392, 0.6089914326019155, 0.7181711515673022, 0.5208250129992752, 0.024809007046338316, -0.6980373571025904, -1.5229622086690515, -2.294638160403957, -2.856971102071357, -3.0848329474675156, -2.9114197593539806, -2.3454214707194847, -1.473902607464075, -0.44946965368290615, 0.5365497229370377, 1.2901959062972201, 1.6533196499526996, 1.5365860761246082, 0.9399676300168781, -0.04408380229931147, -1.2461783565407119, -2.451734437717706, -3.442856323408783, -4.041843031557261, -4.147139290059053, -3.7538367437887463, -2.9539344834216257, -1.9158707187293849, -0.8474309407664913, 0.05000823739074175, 0.6257450180227162, 0.8124227049037435, 0.6393875080298159, 0.22329651152254174, -0.2622102611175909, -0.6309355496339479, -0.7322213705761029, -0.49106326149226603, 0.069868759994062, 0.8323485636217917, 1.6091833923827878, 2.189566201892381, 2.3925891724572903, 2.1158350029326174, 1.3666239021524262, 0.2672836539825957, -0.968070824568723, -2.080737627460671, -2.8278912844558497, -3.0418092389604245, -2.673066957115172, -1.8063346630484176, -0.6438513266333818, 0.540401697430663, 1.4653206381053956, 1.9105001709561364, 1.7703764030852192, 1.0808040198175008, 0.010832160059908204, -1.1788378538984547, -2.2006452570952915, -2.811944559481801, -2.875381708798947, -2.392151584532322, -1.4992871115001993, -0.4315025973805222, 0.542450818586357, 1.1919998525076605, 1.3860833865461484, 1.1268599444740022, 0.5463850617537721, -0.13305598866294485, -0.664154911393743, -0.8471829553083822, -0.5894182922360831, 0.06586445859899748, 0.9498218147478537, 1.8157986833426294, 2.4115343888687177, 2.5555023865571718, 2.1952308997903907, 1.4299270902381258, 0.4894476878025568, -0.3259902689342559, -0.7294512422279101, -0.5310436466791901, 0.3023018219856182, 1.6290879382373755, 3.1641241648027916, 4.5508627219022495, 5.455941821127612, 5.659778400621655, 5.117510987701459, 3.9724901209727665, 2.517751682361618, 1.1157613860088473, 0.0988803404067146, -0.3211572170230105, -0.10879679417722575, 0.5907251805154753, 1.4988618889030891, 2.289142233942015, 2.6850008908865934, 2.5408276245081827, 1.8820154094644095, 0.8921780946044723, -0.14817491174580133, -0.95225654405561, -1.3184812661135443, -1.1939175748701247, -0.6893946118018703, -0.04103478079152076, 0.47000392480118575, 0.6141772274608459, 0.29536310029551327, -0.4094106357973387, -1.2667493529270217, -1.95681786417101, -2.1757845092938406, -1.7389565478497226, -0.6513911456759642, 0.8780673954524482, 2.48624893242765, 3.7556710066514416, 4.335782109204355, 4.04853818700656, 2.9452927509046587, 1.2963749069007076, -0.4846757552072103, -1.9598585144106728, -2.7923915454887744, -2.840759457376433, -2.1922343209467146, -1.1259200538536815, -0.017640667937340437, 0.7825365798684166, 1.0606929244987215, 0.8019790198741849, 0.18626819500110944, -0.4811362165484723, -0.8799841218445865, -0.7893396356680439, -0.16693899670954404, 0.833358684976788, 1.9121751288827562, 2.726285884993951, 3.0067547081118584, 2.652867219043417, 1.7689650559210117, 0.63045815693184, -0.41045957479963785, -1.047755410059594, -1.1308707893889487, -0.7218075943644269, -0.07851576902493147, 0.43190739776159626, 0.4622586109888334, -0.18690112831947148, -1.4848938297108403, -3.1641438280932404, -4.7940268545268765, -5.913021875085459, -6.176404141524011, -5.470399398768545, -3.9539882374721276, -2.0132241641107322, -0.14214938118790288, 1.2107597585388723, 1.779795969066078, 1.5573731822685508, 0.7829284784263605, -0.14979782472028458, -0.8344225746884611, -0.993232253329608, -0.5693477884584361, 0.26155179185719835, 1.1627761557131104, 1.7648293971063604, 1.8036661290224214, 1.2189995419001147, 0.17719073420854928, -0.989397218064058, -1.9042731007421383, -2.2850993358628178, -2.0472227795852342, -1.3336414811668516, -0.45937656602082416, 0.21014729626149084, 0.4021525025730039, 0.047456895504793935, -0.683564675306263, -1.4361015563728718, -1.7997611562686353, -1.4658462249044764, -0.35569093377750527, 1.32862810102906, 3.153124439149313, 4.586682053144064, 5.176673076354195, 4.704360133968694], 'positive_zeros': ['1.53827353629654300169931148093872', '2.72184952383379176943349457570255', '3.89140524968830114346084977687790', '5.02359505910417287553351515004092', '6.20666735076104675126060596197266', '7.06161528353037875473470237816247', '7.62991530431921058117347079900421', '8.804880235518497228374776897339880', '9.495088441770129377999257989015186', '10.74184171131108221650325611893204'], 'prelabel': '2-3e6-27.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.14814814814814817, 'root_number': '0.8936326403234123 + 0.4487991802004622*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0740740740741', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.53827353629654300169931148094', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72184952383379176943349457570', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.89140524968830114346084977688', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.13', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/f/82/1'], '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': '2-3e6-27.13-c1-0-18', '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': '2-3e6-27.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.07407407407407408, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53827353629654300169931148094', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1949993371601513762557110382271', 'Lhash_array': ['1949993371601513762557110382271'], 'label': '2-3e6-27.13-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/f/82/1'}