Properties

Level $53$
Weight $0$
Character 53.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 53 \)
Weight: \( 0 \)
Character: 53.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.89457785283 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.783275162\) \(a_{3}=+0.499989399\) \(a_{4}=+2.180070305\) \(a_{5}=-1.380638852\)
\(a_{6}=-0.891618677\) \(a_{7}=-0.964368468\) \(a_{8}=-2.104390064\) \(a_{9}=-0.750010601\) \(a_{10}=+2.462058972\)
\(a_{11}=+0.304968432\) \(a_{12}=+1.090012042\) \(a_{13}=-1.649974930\) \(a_{14}=+1.719734337\) \(a_{15}=-0.690304790\)
\(a_{16}=+1.572636229\) \(a_{17}=+1.077484701\) \(a_{18}=+1.337475276\) \(a_{19}=-1.088515047\) \(a_{20}=-3.009889762\)
\(a_{21}=-0.482174011\) \(a_{22}=-0.543842631\) \(a_{23}=+1.550403787\) \(a_{24}=-1.052172724\) \(a_{25}=+0.906163639\)
\(a_{26}=+2.942359311\) \(a_{27}=-0.874986749\) \(a_{28}=-2.102391060\) \(a_{29}=+0.448577196\) \(a_{30}=+1.231003387\)
\(a_{31}=+0.621824657\) \(a_{32}=-0.700053062\) \(a_{33}=+0.152480983\) \(a_{34}=-1.921451704\) \(a_{35}=+1.331444574\)
\(a_{36}=-1.635075839\) \(a_{37}=+0.187009168\) \(a_{38}=+1.941121847\) \(a_{39}=-0.824969974\) \(a_{40}=+2.905402682\)
\(a_{41}=-1.537639241\) \(a_{42}=+0.859848938\) \(a_{43}=+1.500523164\) \(a_{44}=+0.664852623\) \(a_{45}=+1.035493774\)
\(a_{46}=-2.764796565\) \(a_{47}=+0.089156707\) \(a_{48}=+0.786301443\) \(a_{49}=-0.069993458\) \(a_{50}=-1.615939110\)
\(a_{51}=+0.538730928\) \(a_{52}=-3.597061348\) \(a_{53}=+0.137360564\) \(a_{54}=+1.560342137\) \(a_{55}=-0.421051266\)
\(a_{56}=+2.029407423\) \(a_{57}=-0.544245984\) \(a_{58}=-0.799936572\) \(a_{59}=+1.142813619\) \(a_{60}=-1.504912974\)
\(a_{61}=-0.626583359\) \(a_{62}=-1.108884467\) \(a_{63}=+0.723286574\) \(a_{64}=-0.324248991\) \(a_{65}=+2.278019493\)
\(a_{66}=-0.271915550\) \(a_{67}=+0.562818986\) \(a_{68}=+2.348992399\) \(a_{69}=+0.775185458\) \(a_{70}=-2.374332040\)
\(a_{71}=+0.285619669\) \(a_{72}=+1.578314856\) \(a_{73}=-1.165844697\) \(a_{74}=-0.333488804\) \(a_{75}=+0.453072213\)
\(a_{76}=-2.373039330\) \(a_{77}=-0.294101940\) \(a_{78}=+1.471148464\) \(a_{79}=+0.615983175\) \(a_{80}=-2.171242677\)
\(a_{81}=+0.312526502\) \(a_{82}=+2.742033867\) \(a_{83}=-0.376431131\) \(a_{84}=-1.051173243\) \(a_{85}=-1.487617240\)
\(a_{86}=-2.675845688\) \(a_{87}=+0.224283843\) \(a_{88}=-0.641772539\) \(a_{89}=-1.578306692\) \(a_{90}=-1.846570329\)
\(a_{91}=+1.591183796\) \(a_{92}=+3.379989256\) \(a_{93}=+0.310905737\) \(a_{94}=-0.158990942\) \(a_{95}=+1.502846164\)
\(a_{96}=-0.350019110\) \(a_{97}=-0.733208200\) \(a_{98}=+0.124817595\) \(a_{99}=-0.228729557\) \(a_{100}=+1.975500440\)

Showing 100 of 546 available coefficients

Rows: Cols: