-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1281661836723509323314993651323', 'a10': [-1.4811943040920157, 1.6751308705666461], 'a2': [0, 1.0], 'a3': [0, 0], 'a4': [-1.0, 0], 'a5': [1.6751308705666461, 1.4811943040920157], 'a6': [0, 0], 'a7': [0, -3.3502617411332922], 'a8': [0, -1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.654418745638953, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.6751308705666461, -1.4811943040920157]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '1710.1369', 'coefficient_field': 'CDF', 'conductor': 1710, 'conductor_radical': 570, 'conjugate': '1272719831872326630281027540251', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.6751308705666461, -1.4811943040920157]], [[1.0, 0], [0, 3.3502617411332922], [-7.0, 0]], [[1.0, 0], [-0.9623886081840313, 0], [11.0, 0]], [[1.0, 0], [0, -1.6121268670507392], [-13.0, 0]], [[1.0, 0], [0, -0.3878731329492609], [-17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0.9623886081840313], [-23.0, 0]], [[1.0, 0], [-6.962388608184031, 0], [29.0, 0]], [[1.0, 0], [-3.3502617411332922, 0], [31.0, 0]], [[1.0, 0], [0, 1.6121268670507392], [-37.0, 0]], [[1.0, 0], [-9.275038957501355, 0], [41.0, 0]], [[1.0, 0], [0, 6.186642342285509], [-43.0, 0]], [[1.0, 0], [0, 0.9623886081840313], [-47.0, 0]], [[1.0, 0], [0, -6.0], [-53.0, 0]], [[1.0, 0], [-10.312650349317323, 0], [59.0, 0]], [[1.0, 0], [-11.924777216368062, 0], [61.0, 0]], [[1.0, 0], [0, 7.224253734101478], [-67.0, 0]], [[1.0, 0], [7.224253734101478, 0], [71.0, 0]], [[1.0, 0], [0, -3.2242537341014783], [-73.0, 0]], [[1.0, 0], [-3.3502617411332922, 0], [79.0, 0]], [[1.0, 0], [0, -15.013173831583908], [-83.0, 0]], [[1.0, 0], [-4.649738258866708, 0], [89.0, 0]], [[1.0, 0], [0, 10.962388608184032], [-97.0, 0]], [[1.0, 0], [2.7249610424986455, 0], [101.0, 0]], [[1.0, 0], [0, 0.5745154752347703], [-103.0, 0]], [[1.0, 0], [0, 10.700523482266584], [-107.0, 0]], [[1.0, 0], [10.126008007031814, 0], [109.0, 0]], [[1.0, 0], [0, -20.55007791500271], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-1710-5.4-c1-0-27', 'leading_term': '1.9300825133309846630451421659548316899666827170781068080', '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/1710/2/d/f/1369/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.9300825133309847, 1.903681548281927, 1.8672282675180711, 1.8206834197028898, 1.7638187104152365, 1.6962758662056758, 1.617635939159249, 1.5274940372192949, 1.4255348176678349, 1.3116046005948387, 1.1857766761342028, 1.0484071384052216, 0.9001792714915757, 0.7421350847786211, 0.5756930401406362, 0.40265135633865207, 0.2251765551783065, 0.04577716918222954, -0.13273720547613652, -0.3073110320282978, -0.4747113163369428, -0.6316082543784761, -0.774666432323409, -0.9006445299722096, -1.0065010373638879, -1.0895030716910235, -1.1473350006222691, -1.1782032627180692, -1.180933549242339, -1.155056396108193, -1.1008772490583176, -1.0195272248858722, -0.9129911073085542, -0.784109593239865, -0.6365534425928805, -0.47476797446954017, -0.303887279467476, -0.12961855937718827, 0.04190186789432157, 0.2042781850117355, 0.35104641828438377, 0.47588246967795644, 0.5728207475710879, 0.6364763936320297, 0.662263381081802, 0.6466002747496671, 0.5870952372290024, 0.4827019718787275, 0.3338387361943027, 0.14246335003348215, -0.08790173946636128, -0.3521988073440458, -0.6439213210303774, -0.9552582231834406, -1.2772945172590757, -1.6002643331126611, -1.9138503135428717, -2.2075208987619463, -2.4708949953456103, -2.6941217012709595, -2.86826131767506, -2.9856529012290745, -3.0402531758292106, -3.0279317884331522, -2.9467086994054066, -2.79692095555739, -2.5813081892015615, -2.305008874568809, -1.9754625796671132, -1.6022170741228214, -1.196643062457071, -0.7715633558780199, -0.34080730508479207, 0.08129488787110221, 0.48045996181653505, 0.8430206517396527, 1.1564930807280918, 1.4101183575502034, 1.5953540363340977, 1.7062919477022476, 1.7399808582639982, 1.6966354381158761, 1.5797170433783925, 1.3958767308997155, 1.154756544098239, 0.8686512272414474, 0.5520388880279593, 0.22099545553046596, -0.1074862230352168, -0.41624643564350744, -0.6887471454583077, -0.9098650772235228, -1.0666535283321819, -1.1490367630812262, -1.1504021917282543, -1.068058569248864, -0.9035331196688192, -0.6626866660621905, -0.3556333090889766, 0.0035403407339718593, 0.39725226339222003, 0.8050849981599631, 1.2046058613172754, 1.5723162841932081, 1.8846917226861222, 2.119267669911418, 2.2557232436343484, 2.2769119044625756, 2.1697892819953757, 1.9261909301253153, 1.5434180687846066, 1.024596846041504, 0.378786100763585, -0.379180360054739, -1.2291188130740205, -2.146177149502703, -3.101749398630024, -4.064587810689644, -5.002066432671395, -5.8815413745985925, -6.671746634813911, -7.344160838260321, -7.874279820288032, -8.242732790131747, -8.436185801041553, -8.447985239425885, -8.278505661429234, -7.935180039741887, -7.432205694508127, -6.7899351283083815, -6.033976860507298, -5.194046331622968, -4.302620215097902, -3.39345828819332, -2.5000647395526543, -1.6541649382055073, -0.8842739452391778, -0.21442930401786314, 0.33684699929617784, 0.7573037375285726, 1.0413934202880075, 1.190360293270157, 1.211978732073381, 1.1199560659310168, 0.9330320481345711, 0.6738238747945013, 0.367479884436577, 0.04021600428944153, -0.2821840329972785, -0.5758211649368954, -0.8200047874960994, -0.998373270220006, -1.099747739622494, -1.1186705734854332, -1.0555979325068447, -0.916735539107938, -0.7135276739971762, -0.46182980039797383, -0.18081413690622652, 0.10832626045680012, 0.38379678817189017, 0.6246577740853007, 0.8122289536340127, 0.9313550693443793, 0.9714533182236096, 0.9272758863637875, 0.7993375691873461, 0.5939785345850785, 0.32305447788742325, 0.0032694192707351287, -0.3448111954996966, -0.6980090062498642, -1.0319676415919905, -1.3226860737432895, -1.5480550539975444, -1.6892996806591296, -1.7322356360467785, -1.6682570079838706, -1.494989340703359, -1.2165617468875343, -0.8434753612494482, -0.392070698008053, 0.11637798657211479, 0.656889056550761, 1.2022470887830279, 1.7246333387798491, 2.197311392406115, 2.596261352007926, 2.901657750059365, 3.0990950448486894, 3.1804795958199734, 3.1445275795589254, 2.99683314968324, 2.7494987160669444, 2.420347758849258, 2.0317682366515157, 1.6092595515076586, 1.1797764923009546, 0.7699781497519232, 0.4044973962396656, 0.10434651243091547, -0.11443322452317368, -0.24178532593991367, -0.27424423696262384, -0.21508964729769778, -0.07403503781278574, 0.1335317431350112, 0.3877070325181345, 0.6655519587945622, 0.9427945966176101, 1.1956362520328652, 1.4025353649743644, 1.5458420340887566, 1.6131645206604517, 1.5983658889018453, 1.5021132102508443, 1.3319319788623, 1.1017525827584311, 0.8309715528888986, 0.5430853986379037, 0.26398665371440644, 0.02003798671647235, -0.16394110698398415, -0.266630925246319, -0.2719677735333452, -0.17056665513296182, 0.03930235380340648, 0.35126795812022454, 0.7509900254517192, 1.2168787793259728, 1.7213673806745655, 2.2326639817528333, 2.716872954496676, 3.140345411887963, 3.4720986372780183, 3.686134315536402, 3.763487508971258, 3.69385232296834, 3.4766555037918394, 3.121484329575452, 2.6478178856102246, 2.084058348066253, 1.4659080113606244, 0.8341850594636592, 0.23221311474893716, -0.29704670674508393, -0.7139297464343802, -0.9848663455287854, -1.0848475008347866, -0.9993780395131061, -0.7257686429075245, -0.2736601651545661, 0.33527568993794304, 1.0684595072120635, 1.8842941815540302, 2.73471043074718, 3.568208489751658], 'positive_zeros': ['1.01105291670493219602777836254396', '2.21204272687266732311143998992442', '2.90840349330703420590720401256066', '4.26586968098719011463317028649260', '5.13683674287577788071854459082885', '5.80023459051981853608501175445874', '6.59277484829343264116401079694174', '8.048595097331937704988593062143312', '8.620451228864850096933132115179459', '9.294366095063741198714805488092004'], 'prelabel': '2-1710-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6951885940556477, 'root_angle': -0.26953360702095547, 'root_number': '0.6624102303670483693439429565788809575375432789865957954 - 0.7491412995590844545310588071817595635964987911003247935*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.13476680351047773', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01105291670493219602777836254', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21204272687266732311143998992', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.90840349330703420590720401256', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 13.654418745638953, 'bad_primes': [2, 3, 5, 19], 'central_character': '5.4', 'conductor': 1710, 'conductor_radical': 570, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1710/2/d/f/1369/6'], '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': '2-1710-5.4-c1-0-27', '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': '2-1710-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6951885940556477, 'root_angle': -0.13476680351047773, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01105291670493219602777836254', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1281661836723509323314993651323', 'Lhash_array': ['1281661836723509323314993651323'], 'label': '2-1710-5.4-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1710/2/d/f/1369/6'}