Properties

Level $19$
Weight $0$
Character 19.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 5.54167292865 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.784378250\) \(a_{3}=+0.587080765\) \(a_{4}=+2.184005740\) \(a_{5}=-0.711865056\)
\(a_{6}=+1.047574147\) \(a_{7}=+1.750434133\) \(a_{8}=+2.112714091\) \(a_{9}=-0.655336176\) \(a_{10}=-1.270236524\)
\(a_{11}=+0.878381654\) \(a_{12}=+1.282187760\) \(a_{13}=-0.607593931\) \(a_{14}=+3.123436596\) \(a_{15}=-0.417922282\)
\(a_{16}=+1.585875333\) \(a_{17}=-0.055810191\) \(a_{18}=-1.169367619\) \(a_{19}=-0.229415734\) \(a_{20}=-1.554717370\)
\(a_{21}=+1.027646209\) \(a_{22}=+1.567365119\) \(a_{23}=-1.911192018\) \(a_{24}=+1.240333804\) \(a_{25}=-0.493248141\)
\(a_{26}=-1.084177395\) \(a_{27}=-0.971816028\) \(a_{28}=+3.822958195\) \(a_{29}=+0.580204793\) \(a_{30}=-0.745731430\)
\(a_{31}=+0.230492891\) \(a_{32}=+0.717087361\) \(a_{33}=+0.515680973\) \(a_{34}=-0.099586491\) \(a_{35}=-1.246072893\)
\(a_{36}=-1.431257970\) \(a_{37}=-0.391096830\) \(a_{38}=-0.409364446\) \(a_{39}=-0.356706710\) \(a_{40}=-1.503967336\)
\(a_{41}=+0.804866827\) \(a_{42}=+1.833709545\) \(a_{43}=+0.465017420\) \(a_{44}=+1.918390575\) \(a_{45}=+0.466510924\)
\(a_{46}=-3.410289469\) \(a_{47}=+0.402925684\) \(a_{48}=+0.931036903\) \(a_{49}=+2.064019654\) \(a_{50}=-0.880141256\)
\(a_{51}=-0.032765090\) \(a_{52}=-1.326988633\) \(a_{53}=-1.546668427\) \(a_{54}=-1.734087383\) \(a_{55}=-0.625289206\)
\(a_{56}=+3.698166859\) \(a_{57}=-0.134685564\) \(a_{58}=+1.035304814\) \(a_{59}=+0.098339269\) \(a_{60}=-0.912744662\)
\(a_{61}=+1.816698283\) \(a_{62}=+0.411286501\) \(a_{63}=-1.147122811\) \(a_{64}=-0.306320242\) \(a_{65}=+0.432524888\)
\(a_{66}=+0.920169912\) \(a_{67}=+0.122770389\) \(a_{68}=-0.121889778\) \(a_{69}=-1.122024071\) \(a_{70}=-2.223465368\)
\(a_{71}=+1.369714153\) \(a_{72}=-1.384537973\) \(a_{73}=+0.325330527\) \(a_{74}=-0.697864677\) \(a_{75}=-0.289576496\)
\(a_{76}=-0.501045280\) \(a_{77}=+1.537549229\) \(a_{78}=-0.636499694\) \(a_{79}=+0.358103831\) \(a_{80}=-1.128929234\)
\(a_{81}=+0.084801679\) \(a_{82}=+1.436186860\) \(a_{83}=-1.808337719\) \(a_{84}=+2.244385220\) \(a_{85}=+0.039729325\)
\(a_{86}=+0.829766970\) \(a_{87}=+0.340627074\) \(a_{88}=+1.855769298\) \(a_{89}=+0.017364266\) \(a_{90}=+0.832431946\)
\(a_{91}=-1.063553156\) \(a_{92}=-4.174054338\) \(a_{93}=+0.135317942\) \(a_{94}=+0.718971827\) \(a_{95}=+0.163313044\)
\(a_{96}=+0.420988196\) \(a_{97}=+1.424004351\) \(a_{98}=+3.682991779\) \(a_{99}=-0.575635274\) \(a_{100}=-1.077256772\)

Showing 100 of 546 available coefficients

Rows: Cols: