Properties

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

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 5.54519770971 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.602784283\) \(a_{3}=-1.137012437\) \(a_{4}=+1.568917456\) \(a_{5}=-0.242095070\)
\(a_{6}=+1.822385664\) \(a_{7}=+0.791123215\) \(a_{8}=-0.911851957\) \(a_{9}=+0.292797283\) \(a_{10}=+0.388026172\)
\(a_{11}=+0.919673514\) \(a_{12}=-1.783878661\) \(a_{13}=-0.935480886\) \(a_{14}=-1.267999855\) \(a_{15}=+0.275265105\)
\(a_{16}=-0.107415471\) \(a_{17}=+1.506137895\) \(a_{18}=-0.469290883\) \(a_{19}=+0.229415734\) \(a_{20}=-0.379827181\)
\(a_{21}=-0.899516935\) \(a_{22}=-1.474038253\) \(a_{23}=+0.328070022\) \(a_{24}=+1.036787016\) \(a_{25}=-0.941389977\)
\(a_{26}=+1.499374061\) \(a_{27}=+0.804098285\) \(a_{28}=+1.241207022\) \(a_{29}=-1.864406215\) \(a_{30}=-0.441190584\)
\(a_{31}=-0.536917443\) \(a_{32}=+1.084015786\) \(a_{33}=-1.045680224\) \(a_{34}=-2.414014146\) \(a_{35}=-0.191527030\)
\(a_{36}=+0.459374768\) \(a_{37}=+0.911210590\) \(a_{38}=-0.367703932\) \(a_{39}=+1.063653403\) \(a_{40}=+0.220754863\)
\(a_{41}=+0.892755880\) \(a_{42}=+1.441731605\) \(a_{43}=-1.601945727\) \(a_{44}=+1.442891830\) \(a_{45}=-0.070884779\)
\(a_{46}=-0.525825476\) \(a_{47}=+0.465395178\) \(a_{48}=+0.122132727\) \(a_{49}=-0.374124059\) \(a_{50}=+1.508845059\)
\(a_{51}=-1.712497519\) \(a_{52}=-1.467692293\) \(a_{53}=-0.718224332\) \(a_{54}=-1.288796093\) \(a_{55}=-0.222648423\)
\(a_{56}=-0.721387252\) \(a_{57}=-0.260848543\) \(a_{58}=+2.988240977\) \(a_{59}=-1.393145863\) \(a_{60}=+0.431868229\)
\(a_{61}=+0.606211096\) \(a_{62}=+0.860562839\) \(a_{63}=+0.231638728\) \(a_{64}=-1.630027993\) \(a_{65}=+0.226475310\)
\(a_{66}=+1.675999827\) \(a_{67}=-0.768697519\) \(a_{68}=+2.363006036\) \(a_{69}=-0.373019696\) \(a_{70}=+0.306976513\)
\(a_{71}=-0.407197534\) \(a_{72}=-0.266987775\) \(a_{73}=+0.287001279\) \(a_{74}=-1.460474012\) \(a_{75}=+1.070372113\)
\(a_{76}=+0.359934350\) \(a_{77}=+0.727575067\) \(a_{78}=-1.704806956\) \(a_{79}=-0.760396055\) \(a_{80}=+0.026004756\)
\(a_{81}=-1.207067034\) \(a_{82}=-1.430895093\) \(a_{83}=+1.274136798\) \(a_{84}=-1.411267822\) \(a_{85}=-0.364628559\)
\(a_{86}=+2.567573433\) \(a_{87}=+2.119853054\) \(a_{88}=-0.838606094\) \(a_{89}=+0.088720823\) \(a_{90}=+0.113613009\)
\(a_{91}=-0.740080646\) \(a_{92}=+0.514714785\) \(a_{93}=+0.610481811\) \(a_{94}=-0.745928076\) \(a_{95}=-0.055540418\)
\(a_{96}=-1.232539432\) \(a_{97}=-1.401879701\) \(a_{98}=+0.599640161\) \(a_{99}=+0.269277906\) \(a_{100}=-1.476963169\)

Showing 100 of 546 available coefficients

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