-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1946318701217679706517587781147', 'a10': [-31651.514692345518, -80646.74418381829], 'a2': [-7.491884492022691, -32.82409064285612], 'a3': [195.48746366576756, 181.38585886089294], 'a4': [-559.9965329225861, 269.68011687573204], 'a5': [2544.473041950563, -383.517603151821], 'a6': [4489.256375159843, -7775.620129979337], 'a7': [-1789.3642456797213, -3099.269786764436], 'a8': [2299.635479803664, 2883.651682755737], 'a9': [3843.606223709434, 51289.36064718853], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.14654095504655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [-17253330.125803556, 14314859.814433476]]]], 'bad_primes': [43], 'central_character': '43.10', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '1801474993650140530748034440678', 'degree': 2, 'euler_factors': [[[1.0, 0], [7.491884492022691, 32.82409064285612], [-461.2960603660386, 222.14847442818976]], [[1.0, 0], [-195.48746366576756, -181.38585886089294], [1470.9124320615886, 19627.96233991717]], [[1.0, 0], [-2544.473041950563, 383.517603151821], [1866353.136301056, -575693.7000212973]], [[1.0, 0], [1789.3642456797213, 3099.269786764436], [-20176803.5, 34947248.79633355]], [[1.0, 0], [5522.292046221876, 2659.3956871031473], [1470156338.6548483, 1843517738.836598]], [[1.0, 0], [-50255.571440921725, 128049.10770313838], [-7773648115.195869, -7212891371.223408]], [[1.0, 0], [-520273.40063691715, -78418.59760595347], [113319349876.45862, 34954390219.892006]], [[1.0, 0], [-745.7336720068961, 9951.124289053954], [-319083542807.49316, -48094105744.154655]], [[1.0, 0], [671630.8498675791, -457910.15999937465], [658034958379.1511, -1676645729856.548]], [[1.0, 0], [1323484.5619258033, -1228014.213558403], [1084120376448.6084, -14466581053398.244]], [[1.0, 0], [-187959.31182404145, -57977.769358212514], [21845441007410.824, 14893969490729.416]], [[1.0, 0], [2346477.845057125, -4064218.846473673], [-64980869897538.5, -112550168182559.7]], [[1.0, 0], [111046.76298544132, 486527.6577223084], [-294960930802631.06, 142045697814390.9]], [[1.0, 0], [-17253330.125803556, 14314859.814433476]], [[1.0, 0], [27770146.648771323, -13373397.786611218], [697766436928914.9, -874971436861083.9]], [[1.0, 0], [34070127.443235055, 86809268.96965042], [-2418897877566464.5, 2244409236232859.2]], [[1.0, 0], [-4631112.917797376, 5807231.918155307], [-1927697920426743.5, -8445796426721127.0]], [[1.0, 0], [82565057.6235398, -25467947.40569395], [9662156934415462.0, -6587547056019807.0]], [[1.0, 0], [9279982.683616467, -123832763.02438702], [-26902659885810710, -4054923541223837.0]], [[1.0, 0], [-120992172.33975545, -82491066.34350236], [16750338218141566, 42679165733499144]], [[1.0, 0], [122820363.40178554, -312941182.25004876], [-43155926834087720, -40042848308280660]], [[1.0, 0], [35014153.66700161, 60646293.135270916], [-59925797991309160, 103794526805056430]], [[1.0, 0], [144012632.71063617, 133624195.54278226], [13970062771213334, 186417532398810400]], [[1.0, 0], [-264082723.62334976, -245032958.8225825], [26182166837663410, 349376736143846800]], [[1.0, 0], [620032758.7690418, 298592039.4523817], [473996312127390100, 594372575606138500]], [[1.0, 0], [754416575.6080804, 514352512.1143371], [399568097856944450, 1018082909620649700]], [[1.0, 0], [1501354211.745733, 226292736.9547672], [1246805772186227200, 384588647366259800]], [[1.0, 0], [567808208.3909199, -2487730306.0166883], [-1656394515298959600, -797677557299977700]], [[1.0, 0], [-1005566639.0933553, 685583726.0722277], [793481715525942300, -2021758438689617000]], [[1.0, 0], [1866052031.8535874, -2339955235.959299], [-668462217684196100, -2928724334705642000]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-43-43.10-c9-0-18', 'load_key': 'CMFs-workshop', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/43/10/g/a/10/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.4014117643772495, 3.455638363026087, 3.434070443185687, 3.335769559543377, 3.1624635017414615, 2.9185771134231, 2.6111831249425164, 2.2498703934314537, 1.8465282759553707, 1.4150475473205675, 0.9709403622926456, 0.5308842687459215, 0.11219818072599382, -0.2677385481367105, -0.5921093630085837, -0.8453079658116122, -1.0135885406587504, -1.0856943160321932, -1.0534376969487138, -0.9122037785580568, -0.6613488092863152, -0.30446634334382056, 0.15050340393839573, 0.6913409941747721, 1.3018057655101583, 1.9620902868510008, 2.6494678547126274, 3.339119234684147, 4.005113863016436, 4.6215097361869395, 5.163525923037143, 5.608732792698219, 5.9381984364885465, 6.1375261107230985, 6.197717479939583, 6.115800476001804, 5.895168966041742, 5.545594124355151, 5.082884097663851, 4.528188569550987, 3.906967162448955, 3.247663951614969, 2.5801531441311716, 1.9340414757916156, 1.3369293324510363, 0.8127433319672569, 0.38025666736848596, 0.05190885705141941, -0.16697685564518905, -0.27850225431958564, -0.2919827149554539, -0.22320536902319865, -0.09318677541818621, 0.07349870485813882, 0.2507094718087964, 0.41290224431847083, 0.5373040460053788, 0.6059093710784718, 0.6071228192082923, 0.5368845239046398, 0.3991482846147616, 0.20562912234442723, -0.02520473256996833, -0.26985471934528876, -0.5021210779103391, -0.6958654197173367, -0.827979660754125, -0.8812958565000751, -0.8471540642918798, -0.7273525587768809, -0.5352382405284688, -0.2957542860006494, -0.04434385924726385, 0.17529255929790893, 0.3144807616148343, 0.32368420604690734, 0.15713305046735163, -0.2224155083499244, -0.8392179727023712, -1.700827535095656, -2.7955278987386594, -4.091252093225468, -5.536207923128045, -7.061288858945611, -8.584187580352937, -10.01496341175117, -11.262660602163951, -12.242447990530147, -12.882666736220918, -13.131142977316234, -12.960153353290611, -12.369524393005518, -11.387496592003611, -10.0691790754199, -8.49264401318404, -6.752940231906477, -4.954519393115368, -3.2027425194499775, -1.5952491208521362, -0.21401043369864778, 0.8811557342578047, 1.6569578553960567, 2.1084405059934275, 2.258035385664723, 2.151942367358942, 1.85421369757609, 1.4391668891593687, 0.9829428595349833, 0.5551314366910468, 0.2113910964782721, -0.012110735857965862, -0.10180864482671621, -0.06704955255683355, 0.06242474946940202, 0.2415137004970017, 0.4166955288184388, 0.5340076980784956, 0.5470687569742324, 0.42411683985024906, 0.15314370444972417, -0.25557454154956444, -0.7699315657113037, -1.33943566509048, -1.9012629894844257, -2.3881854212149443, -2.7373718628080472, -2.898916131014349, -2.8429450414525097, -2.5643124483044866, -2.084175018801814, -1.4481404237440145, -0.7211298874904383, 0.02045373419314081, 0.6982748968146344, 1.2420858179582837, 1.5988649107129655, 1.7397936376742085, 1.6640461192955351, 1.3987726394892683, 0.9951683222472749, 0.5210652246605676, 0.05099490541060991, -0.34493428083624933, -0.6117768537959882, -0.7185278240933864, -0.6635739350654889, -0.4758749442468021, -0.21150835512251617, 0.05413049499717481, 0.2375315224498196, 0.26018805779678333, 0.06178251521988154, -0.38851847438357795, -1.0844498001287777, -1.9800683187123576, -2.9929053763591393, -4.012755564428645, -4.915183439103588, -5.578095703672802, -5.89919109374132, -5.81185155804465, -5.297126795158352, -4.389893877547094, -3.1779992953840552, -1.7941218204825264, -0.4011065243502345, 0.8275290094620513, 1.729465296265867, 2.1749445730948804, 2.0847029174205285, 1.4419186058820475, 0.2963710278998519, -1.239969467754208, -3.0055339578648512, -4.808400235980708, -6.449709216347598, -7.7481512210737415, -8.562232322544322, -8.807309655022149, -8.465098578004614, -7.584405969060167, -6.273082361284597, -4.68242975882305, -2.986366465084716, -1.358374332762762, 0.05047344358311996, 1.1293273499050507, 1.8188251685161585, 2.1144479020027056, 2.061843052422042, 1.7452211590226048, 1.2709668732245156, 0.7492811028447536, 0.276878843432776, -0.07652284063510775, -0.2759294977737142, -0.3220678342703626, -0.24591794134672063, -0.09817182133815623, 0.064118725898273, 0.19098682856821628, 0.2504127661303237, 0.2344652312214992, 0.15952165289284068, 0.06054225678999591, -0.019428638183151818, -0.04235951740954235, 0.011858661914357865, 0.13556863286909862, 0.2889856921776183, 0.40278269736481503, 0.3877954315722574, 0.15062227831359543, -0.3873639131683273, -1.2709443986216054, -2.4955781876533227, -3.998820198082964, -5.66094689666687, -7.315626347338789, -8.769741329687692, -9.829789015413635, -10.330941677397744, -10.164117125255176, -9.296437999929617, -7.781291140163084, -5.75572757284857, -3.4249382272389695, -1.0356759267392939, 1.1575926199413173, 2.9286697716993784, 4.112075301180211, 4.62669510035586, 4.486671527212689, 3.797588999038406, 2.7384014592332946, 1.531920375168591, 0.4086234551198955, -0.4302898379003057, -0.8444974655074536, -0.7755796237489824, -0.25401754309135716, 0.6088967446296106, 1.6427132725560092, 2.6491759999458524, 3.4377401347191863, 3.8590207167866732, 3.8303388905634166, 3.3489696777510307, 2.4909166377924175, 1.3956472289077462, 0.23974650005919707, -0.7955739994878005, -1.5571039956176462, -1.9464262513567936, -1.9360364714105713, -1.5719836668985692, -0.962764830757628], 'positive_zeros': ['1.53537473249116282534632879173730', '2.71134883698807041420447560219261', '5.89967005320784323215320329985852', '6.57199055314005697354240190214014', '7.73693728055422751137025950491081', '9.023078123616035874090121587340196', '9.561125664777237710574911410059904', '12.39691734031341414165464730768340', '13.74065448517302168936187546948298', '14.07329400956624634996029350769977'], 'prelabel': '2-43-43.10-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.706011151181705, 'root_angle': 0.31735290236562513, 'root_number': '0.5428297034736844 + 0.8398427906618428*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.15867645118281257', 'prec': 64}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.53537473249116282534632879173730', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.71134883698807041420447560219261', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '5.89967005320784323215320329985852', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 22.14654095504655, 'bad_primes': [43], 'central_character': '43.10', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/10/g/a/10/6'], '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': '2-43-43.10-c9-0-18', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-43-43.10-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.706011151181705, 'root_angle': 0.15867645118281257, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53537473249116282534632879173730', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1946318701217679706517587781147', 'Lhash_array': ['1946318701217679706517587781147'], 'label': '2-43-43.10-c9-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/10/g/a/10/6'}