-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1744226519145628239216685950789', 'a10': [-0.655065549978268, 2.960076692698111e-61], 'a2': [-0.327532774989134, -0.567303407425205], 'a3': [0.997115999354784, 1.416248454131799], 'a4': [0.7854445626158346, -1.36042988897934], 'a5': [0.5, -0.8660254037844386], 'a6': [0.4768544035349127, -1.029535090288017], 'a7': [0.38859185210847114, 0.6730608312591632], 'a8': [-2.3391664487312998, 0.0], 'a9': [-1.011519367661421, 2.8243279853525936], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.997115999354784, -1.416248454131799]]], [5, [[1.0, 0], [-0.5, 0.8660254037844386]]], [13, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.391', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '1858502244599971381696731060125', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.327532774989134, 0.567303407425205], [-1.0, 1.7320508075688772]], [[1.0, 0], [-0.997115999354784, -1.416248454131799]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-0.38859185210847114, -0.6730608312591632], [-3.5, 6.06217782649107]], [[1.0, 0], [-2.033986683043183, -3.522968276949287], [-5.5, 9.526279441628825]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-5.291538679104049, 0], [17.0, 0]], [[1.0, 0], [-6.650416596075483, 0], [19.0, 0]], [[1.0, 0], [1.1528349628383943, -1.9967687283778772], [-11.5, -19.91858428704209]], [[1.0, 0], [3.1900801551441056, 5.525380908926798], [-14.5, 25.11473670974872]], [[1.0, 0], [-4.472586228252768, 7.746746588566646], [-15.5, -26.846787517317598]], [[1.0, 0], [2.805922295644757, 0], [37.0, 0]], [[1.0, 0], [3.8049318273746744, -6.590335244348829], [-20.5, -35.50704155516198]], [[1.0, 0], [4.421829071668606, 7.6588326145151475], [-21.5, 37.239092362730865]], [[1.0, 0], [-2.0439096207022147, -3.5401553091350686], [-23.5, 40.703193977868615]], [[1.0, 0], [4.780253938458363, 0], [53.0, 0]], [[1.0, 0], [-2.370493100906917, 4.1058144897622775], [-29.5, -51.09549882328188]], [[1.0, 0], [-7.182990451999793, -12.441304413145778], [-30.5, 52.827549630850754]], [[1.0, 0], [5.393534814825699, -9.341876331669706], [-33.5, -58.023702053557386]], [[1.0, 0], [-0.3077755050780636, 0], [71.0, 0]], [[1.0, 0], [7.506360651725031, 0], [73.0, 0]], [[1.0, 0], [3.809486352483348, 6.5982239132414], [-39.5, 68.41600689897065]], [[1.0, 0], [-6.264840239628812, -10.851021596339082], [-41.5, 71.88010851410841]], [[1.0, 0], [11.774313822682092, 0], [89.0, 0]], [[1.0, 0], [-3.0426778884174177, -5.270072693805354], [-48.5, 84.00446416709055]], [[1.0, 0], [4.676044404532677, 8.099146487098754], [-50.5, 87.4685657822283]], [[1.0, 0], [-1.1073333863926207, 1.9179576861493182], [-51.5, -89.20061658979718]], [[1.0, 0], [15.498494003188805, 0], [107.0, 0]], [[1.0, 0], [5.882779312086566, 0], [109.0, 0]], [[1.0, 0], [5.287904660959389, -9.158919538361939], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-585-9.4-c1-0-21', '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/585/2/i/e/391/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.8638505225297655, 1.8603270541469814, 1.8460907131984152, 1.8148164957871054, 1.7574555758602441, 1.66376193019199, 1.5239421816929042, 1.330229248425379, 1.0782805340196147, 0.7683415381002544, 0.4061066946187934, 0.003183842489118133, -0.4229468544198416, -0.8495810666620851, -1.2501120390328715, -1.596031483743805, -1.859533662672415, -2.016553094014434, -2.0499721419518777, -1.952653764871693, -1.7299017192279083, -1.4009395692353124, -0.9990419404165456, -0.5700521981627293, -0.16917827602567553, 0.14383800632974245, 0.3108530078097612, 0.2822015773908528, 0.02357958417842636, -0.47794054093491034, -1.2096532627558851, -2.1315157424699662, -3.177562852954921, -4.260666212735322, -5.280436584567324, -6.133610728726194, -6.725836756223451, -6.983445498053537, -6.863633547122153, -6.361534066912407, -5.512934814494899, -4.391905119412307, -3.103263365490582, -1.7705681290902806, -0.5210391661798273, 0.5306107261680538, 1.2971349422546599, 1.7302255003517777, 1.8266093311597644, 1.6276076925885101, 1.2119763429928243, 0.6829285302095724, 0.15125579338821704, -0.2827801557443375, -0.5457636182274689, -0.6027884866363356, -0.46229016429861375, -0.17298851758177583, 0.18672464972106304, 0.5251979995104029, 0.7567896670118235, 0.8203416887759228, 0.6931555972716018, 0.3974301487940248, -0.0025661909834031704, -0.41256356563763674, -0.7276961121486745, -0.8557004014681407, -0.7393130589459769, -0.3730774330760646, 0.18946076471315243, 0.8405279184773434, 1.434939808053387, 1.8165414950508685, 1.8496484922922731, 1.4494404643723904, 0.6049667965807662, -0.6105778370203809, -2.0454631119794344, -3.491060225312446, -4.71637570396309, -5.509484016188388, -5.71803355535963, -5.280673059190529, -4.242593474353639, -2.751233368836945, -1.0320486959861752, 0.6516558166352476, 2.0473555059737842, 2.960833310154866, 3.2928856200971603, 3.0573902991255415, 2.3765818887304078, 1.4540860126801196, 0.531035707015845, -0.16562191220588934, -0.47160204123609456, -0.3199707078944311, 0.2457022209192411, 1.0828275813429038, 1.9835405197133362, 2.723232889719032, 3.1128880210513077, 3.043161346125386, 2.5098598282991906, 1.614654047726298, 0.5406025189449261, -0.4919377657486455, -1.2786252133783576, -1.680845511501114, -1.6596052985086307, -1.2850005625316365, -0.7184754474820687, -0.17176250374669685, 0.14770089277647028, 0.09144781845651696, -0.38906890743094563, -1.2259974668518316, -2.247945278474243, -3.2197526333189286, -3.8998582433888465, -4.101189639176298, -3.740209246043327, -2.861334154656739, -1.6298867949272273, -0.294602353323982, 0.871456259031317, 1.636974266828129, 1.8687320863923196, 1.5636782172083423, 0.8482019957854302, -0.05553158755551337, -0.8877166386446912, -1.4184941440756949, -1.5072825261769607, -1.1381186423500311, -0.4215100419213538, 0.43779222471742585, 1.1984604158184995, 1.6500143437361114, 1.6714506244819303, 1.2647195855632367, 0.5534711670959853, -0.2529166224160156, -0.9202166285263951, -1.2580752824345076, -1.176923244509662, -0.7163561814039896, -0.03606580219142409, 0.6290174022903613, 1.0372860881417774, 1.0133763179728683, 0.5041970560060748, -0.39898553056670233, -1.4801663290660596, -2.4557885532969803, -3.054238251455344, -3.0952841669120206, -2.5462514067148225, -1.5376084115611528, -0.33182313618850484, 0.7472497366180751, 1.4053825183355817, 1.4636288613191417, 0.9134375917129954, -0.07599086334956796, -1.2020188391579654, -2.113517916821992, -2.513124428239907, -2.2475611901133052, -1.3591945549853384, -0.08233208498385976, 1.216721838419841, 2.1405112066813077, 2.374446124562033, 1.7815609652126219, 0.45016519286438655, -1.320665021119154, -3.0953194426681074, -4.415990272157402, -4.925633423700076, -4.465113458254634, -3.117046037751157, -1.1838361573359035, 0.8938674125813956, 2.6550795091011405, 3.739256380868413, 3.9759699512212334, 3.4189628971505543, 2.3166426183544404, 1.0297842730306401, -0.07756768959270133, -0.7408520083016404, -0.8612488486346891, -0.5174172575989424, 0.07792705934264191, 0.6600620260805116, 1.0048440727748664, 1.0013752385610273, 0.681790567084052, 0.20002193895396816, -0.231353320535505, -0.42307731103534924, -0.28079283376294606, 0.15910320213662332, 0.7421270731244041, 1.2526222941186422, 1.4948365123269698, 1.368981837937334, 0.914017343667513, 0.2997948588614239, -0.2313480943002031, -0.4552803670439782, -0.25812849016270545, 0.30374372788283804, 1.00025634864166, 1.4870622614481908, 1.4130283476829475, 0.5432779734616074, -1.1423681149279166, -3.4104210547131646, -5.811908081548619, -7.791428902881895, -8.837626551938337, -8.63086077536027, -7.142692362751071, -4.655069746336603, -1.6910402233091306, 1.1240200133427962, 3.2299158327556112, 4.277925327205188, 4.212399477780362, 3.264480805129513, 1.8624064380096441, 0.488956757287392, -0.46734990308313207, -0.8199745675899952, -0.6184001154709468, -0.10119924918884493, 0.4118625060770223, 0.64856286756636, 0.4875499666431977, -6.679312970890568e-05, -0.5846772726664705, -0.9742121514775103, -0.9362706929379583, -0.40054046799502263, 0.4977594197012815, 1.4519152837262452, 2.085872258798141, 2.0899440373196128, 1.3420211429941513, -0.03048762045746472, -1.67338454503233, -3.109466091983991, -3.891033013369242, -3.750511719249191], 'positive_zeros': ['1.37595211080371477162542160750447', '3.06168391522810254675223501587916', '3.50760815578544907697395060117717', '5.55827945872431379559704301606760', '6.53933769734545670732847322262569', '7.18622611285354470179050130131486', '7.999240408675441746105078934542947', '8.711326820384575597728632555722563', '9.566144245625156027828917665273755', '10.82504342839047041546153991826694'], 'prelabel': '2-585-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.05391521503338443, 'root_number': '0.9856895306312652 + 0.1685709026015943*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0269576075167', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37595211080371477162542160750', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.06168391522810254675223501588', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50760815578544907697395060118', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '9.4', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/i/e/391/4'], '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': '2-585-9.4-c1-0-21', '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': '2-585-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.026957607516692215, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37595211080371477162542160750', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1744226519145628239216685950789', 'Lhash_array': ['1744226519145628239216685950789'], 'label': '2-585-9.4-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/i/e/391/4'}