Properties

Level $19$
Weight $0$
Character 19.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more about

Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.86922836527 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.183746102\) \(a_{3}=-0.765926355\) \(a_{4}=+0.401254830\) \(a_{5}=-0.095658925\)
\(a_{6}=-0.906662333\) \(a_{7}=+1.719116071\) \(a_{8}=-0.708762261\) \(a_{9}=-0.413356825\) \(a_{10}=-0.113235881\)
\(a_{11}=-0.086304031\) \(a_{12}=-0.307331649\) \(a_{13}=+1.215172427\) \(a_{14}=+2.034996945\) \(a_{15}=+0.073267692\)
\(a_{16}=-1.240249393\) \(a_{17}=-0.991910033\) \(a_{18}=-0.489309521\) \(a_{19}=+0.229415725\) \(a_{20}=-0.038383609\)
\(a_{21}=-1.316716288\) \(a_{22}=-0.102162057\) \(a_{23}=-0.259715218\) \(a_{24}=+0.542859667\) \(a_{25}=-0.990849311\)
\(a_{26}=+1.438455623\) \(a_{27}=+1.082527221\) \(a_{28}=+0.689803620\) \(a_{29}=+0.486567628\) \(a_{30}=+0.086730334\)
\(a_{31}=+0.537506645\) \(a_{32}=-0.759378100\) \(a_{33}=+0.066102510\) \(a_{34}=-1.174169614\) \(a_{35}=-0.164448764\)
\(a_{36}=-0.165861414\) \(a_{37}=+1.292966067\) \(a_{38}=+0.271569913\) \(a_{39}=-0.930732563\) \(a_{40}=+0.067799464\)
\(a_{41}=-0.495921708\) \(a_{42}=-1.558657728\) \(a_{43}=-0.147899879\) \(a_{44}=-0.034629968\) \(a_{45}=+0.039541248\)
\(a_{46}=-0.307436806\) \(a_{47}=-0.042493877\) \(a_{48}=+0.949939743\) \(a_{49}=+1.955359985\) \(a_{50}=-1.172914273\)
\(a_{51}=+0.759729922\) \(a_{52}=+0.487593817\) \(a_{53}=-1.582601934\) \(a_{54}=+1.281437349\) \(a_{55}=+0.008255741\)
\(a_{56}=-1.218444477\) \(a_{57}=-0.175715584\) \(a_{58}=+0.575972501\) \(a_{59}=+0.876064697\) \(a_{60}=+0.029398910\)
\(a_{61}=+0.016753165\) \(a_{62}=+0.636271489\) \(a_{63}=-0.710608289\) \(a_{64}=+0.341338417\) \(a_{65}=-0.116242101\)
\(a_{66}=+0.078248667\) \(a_{67}=-0.779099340\) \(a_{68}=-0.398008693\) \(a_{69}=+0.198922769\) \(a_{70}=-0.194665607\)
\(a_{71}=+0.369785885\) \(a_{72}=+0.292971677\) \(a_{73}=-1.629680779\) \(a_{74}=+1.530543659\) \(a_{75}=+0.758917686\)
\(a_{76}=+0.092054150\) \(a_{77}=-0.148366714\) \(a_{78}=-1.101751076\) \(a_{79}=-0.438772936\) \(a_{80}=+0.118640903\)
\(a_{81}=-0.415779312\) \(a_{82}=-0.587045414\) \(a_{83}=-0.036739836\) \(a_{84}=-0.528338745\) \(a_{85}=+0.094885085\)
\(a_{86}=-0.175075944\) \(a_{87}=-0.372674947\) \(a_{88}=+0.061169042\) \(a_{89}=+0.212027509\) \(a_{90}=+0.046806767\)
\(a_{91}=+2.089022495\) \(a_{92}=-0.104211942\) \(a_{93}=-0.411690537\) \(a_{94}=-0.050302014\) \(a_{95}=-0.021945729\)
\(a_{96}=+0.581627771\) \(a_{97}=-0.844139898\) \(a_{98}=+2.314649909\) \(a_{99}=+0.035674262\) \(a_{100}=-0.397583039\)

Showing 100 of 1500 available coefficients

Rows: Cols: