Properties

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

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 5.12120997984 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.704867484\) \(a_{3}=+1.759327233\) \(a_{4}=+1.906573137\) \(a_{5}=-0.552474003\)
\(a_{6}=+2.999419793\) \(a_{7}=-1.246284854\) \(a_{8}=+1.545587062\) \(a_{9}=+2.095232314\) \(a_{10}=-0.941894963\)
\(a_{11}=+0.516965067\) \(a_{12}=+3.354286042\) \(a_{13}=-1.444022616\) \(a_{14}=-2.124750524\) \(a_{15}=-0.971982558\)
\(a_{16}=+0.728447989\) \(a_{17}=+0.713336725\) \(a_{18}=+3.572093442\) \(a_{19}=+0.229415734\) \(a_{20}=-1.053332092\)
\(a_{21}=-2.192622885\) \(a_{22}=+0.881356933\) \(a_{23}=+0.573092725\) \(a_{24}=+2.719193410\) \(a_{25}=-0.694772476\)
\(a_{26}=-2.461867204\) \(a_{27}=+1.926872036\) \(a_{28}=-2.376133224\) \(a_{29}=-0.329020558\) \(a_{30}=-1.657101459\)
\(a_{31}=-0.049077762\) \(a_{32}=-0.303679773\) \(a_{33}=+0.909510721\) \(a_{34}=+1.216144587\) \(a_{35}=+0.688539982\)
\(a_{36}=+3.994713644\) \(a_{37}=-0.197811620\) \(a_{38}=+0.391123425\) \(a_{39}=-2.540508314\) \(a_{40}=-0.853896671\)
\(a_{41}=+1.834448495\) \(a_{42}=-3.738131460\) \(a_{43}=-0.006457074\) \(a_{44}=+0.985631709\) \(a_{45}=-1.157561383\)
\(a_{46}=+0.977047153\) \(a_{47}=-0.397624391\) \(a_{48}=+1.281578385\) \(a_{49}=+0.553225938\) \(a_{50}=-1.184495004\)
\(a_{51}=+1.254992727\) \(a_{52}=-2.753134728\) \(a_{53}=+1.257788948\) \(a_{54}=+3.285061480\) \(a_{55}=-0.285609760\)
\(a_{56}=-1.926241747\) \(a_{57}=+0.403617348\) \(a_{58}=-0.560936450\) \(a_{59}=+0.525582316\) \(a_{60}=-1.853155835\)
\(a_{61}=+0.911496899\) \(a_{62}=-0.083671081\) \(a_{63}=-2.611256299\) \(a_{64}=-1.246181759\) \(a_{65}=+0.797784955\)
\(a_{66}=+1.550595254\) \(a_{67}=-1.080690552\) \(a_{68}=+1.360028637\) \(a_{69}=+1.008257639\) \(a_{70}=+1.173869426\)
\(a_{71}=+0.464680107\) \(a_{72}=+3.238363956\) \(a_{73}=+0.363834575\) \(a_{74}=-0.337242600\) \(a_{75}=-1.222332139\)
\(a_{76}=+0.437397875\) \(a_{77}=-0.644285733\) \(a_{78}=-4.331230016\) \(a_{79}=-0.533480065\) \(a_{80}=-0.402448576\)
\(a_{81}=+1.294766135\) \(a_{82}=+3.127491589\) \(a_{83}=+1.233487341\) \(a_{84}=-4.180395891\) \(a_{85}=-0.394099996\)
\(a_{86}=-0.011008455\) \(a_{87}=-0.578854827\) \(a_{88}=+0.799014519\) \(a_{89}=-0.062253618\) \(a_{90}=-1.973488762\)
\(a_{91}=+1.799663516\) \(a_{92}=+1.092643195\) \(a_{93}=-0.086343843\) \(a_{94}=-0.677896895\) \(a_{95}=-0.126746229\)
\(a_{96}=-0.534272094\) \(a_{97}=-0.193968851\) \(a_{98}=+0.943176913\) \(a_{99}=+1.083161913\) \(a_{100}=-1.324634540\)

Showing 100 of 546 available coefficients

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