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: \( 1.09199155992 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.650680501\) \(a_{3}=+1.278420601\) \(a_{4}=-0.576614885\) \(a_{5}=-1.112461457\)
\(a_{6}=-0.831843358\) \(a_{7}=+0.211139763\) \(a_{8}=+1.025872564\) \(a_{9}=+0.634359233\) \(a_{10}=+0.723856978\)
\(a_{11}=+0.661134713\) \(a_{12}=-0.737156348\) \(a_{13}=-0.129047529\) \(a_{14}=-0.137384527\) \(a_{15}=-1.422193644\)
\(a_{16}=-0.090900389\) \(a_{17}=+0.453168575\) \(a_{18}=-0.412765184\) \(a_{19}=+0.229415734\) \(a_{20}=+0.641461835\)
\(a_{21}=+0.269925422\) \(a_{22}=-0.430187466\) \(a_{23}=-1.676809218\) \(a_{24}=+1.311496620\) \(a_{25}=+0.237570493\)
\(a_{26}=+0.083968711\) \(a_{27}=-0.467442689\) \(a_{28}=-0.121746330\) \(a_{29}=-0.042861811\) \(a_{30}=+0.925393673\)
\(a_{31}=+1.773267901\) \(a_{32}=-0.966725453\) \(a_{33}=+0.845208237\) \(a_{34}=-0.294867956\) \(a_{35}=-0.234884848\)
\(a_{36}=-0.365780976\) \(a_{37}=-0.227298645\) \(a_{38}=-0.149276345\) \(a_{39}=-0.164977020\) \(a_{40}=-1.141243687\)
\(a_{41}=-0.183674027\) \(a_{42}=-0.175635209\) \(a_{43}=+0.230447058\) \(a_{44}=-0.381220116\) \(a_{45}=-0.705700196\)
\(a_{46}=+1.091067062\) \(a_{47}=+0.847227127\) \(a_{48}=-0.116208930\) \(a_{49}=-0.955420001\) \(a_{50}=-0.154582487\)
\(a_{51}=+0.579340042\) \(a_{52}=+0.074410726\) \(a_{53}=+0.341159929\) \(a_{54}=+0.304155843\) \(a_{55}=-0.735486885\)
\(a_{56}=+0.216602490\) \(a_{57}=+0.293289800\) \(a_{58}=+0.027889345\) \(a_{59}=+0.720018803\) \(a_{60}=+0.820058025\)
\(a_{61}=+1.142266743\) \(a_{62}=-1.153830847\) \(a_{63}=+0.133938458\) \(a_{64}=+0.719929792\) \(a_{65}=+0.143560402\)
\(a_{66}=-0.549960519\) \(a_{67}=+0.497495397\) \(a_{68}=-0.261303746\) \(a_{69}=-2.143667448\) \(a_{70}=+0.152834991\)
\(a_{71}=-1.051360391\) \(a_{72}=+0.650771733\) \(a_{73}=-1.524677592\) \(a_{74}=+0.147898796\) \(a_{75}=+0.303715012\)
\(a_{76}=-0.132284527\) \(a_{77}=+0.139591826\) \(a_{78}=+0.107347330\) \(a_{79}=+0.466228910\) \(a_{80}=+0.101123179\)
\(a_{81}=-1.231947597\) \(a_{82}=+0.119513108\) \(a_{83}=+0.854772976\) \(a_{84}=-0.155643016\) \(a_{85}=-0.504132573\)
\(a_{86}=-0.149947407\) \(a_{87}=-0.054795422\) \(a_{88}=+0.678239963\) \(a_{89}=+1.025479098\) \(a_{90}=+0.459185357\)
\(a_{91}=-0.027247065\) \(a_{92}=+0.966873154\) \(a_{93}=+2.266982215\) \(a_{94}=-0.551274172\) \(a_{95}=-0.255216161\)
\(a_{96}=-1.235881735\) \(a_{97}=-0.607144312\) \(a_{98}=+0.621673165\) \(a_{99}=+0.419396909\) \(a_{100}=-0.136986682\)

Showing 100 of 546 available coefficients

Rows: Cols: