Properties

Level $7$
Weight $0$
Character 7.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 4.02170481942 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.799384968\) \(a_{3}=-0.838064010\) \(a_{4}=+2.237786264\) \(a_{5}=-0.251575775\)
\(a_{6}=-1.507999782\) \(a_{7}=-0.377964473\) \(a_{8}=+2.227253998\) \(a_{9}=-0.297648715\) \(a_{10}=-0.452681667\)
\(a_{11}=+0.929835353\) \(a_{12}=-1.875408131\) \(a_{13}=+0.444509654\) \(a_{14}=-0.680103591\) \(a_{15}=+0.210836603\)
\(a_{16}=+1.769901101\) \(a_{17}=+0.094372021\) \(a_{18}=-0.535584623\) \(a_{19}=-0.688105458\) \(a_{20}=-0.562972813\)
\(a_{21}=+0.316758422\) \(a_{22}=+1.673131757\) \(a_{23}=+0.098775289\) \(a_{24}=-1.866581417\) \(a_{25}=-0.936709630\)
\(a_{26}=+0.799843989\) \(a_{27}=+1.087512686\) \(a_{28}=-0.845803706\) \(a_{29}=-0.780856215\) \(a_{30}=+0.379376214\)
\(a_{31}=+1.663739667\) \(a_{32}=+0.957479438\) \(a_{33}=-0.779261545\) \(a_{34}=+0.169811595\) \(a_{35}=+0.095086705\)
\(a_{36}=-0.666074206\) \(a_{37}=-0.748625813\) \(a_{38}=-1.238166617\) \(a_{39}=-0.372527543\) \(a_{40}=-0.560323150\)
\(a_{41}=+0.037356916\) \(a_{42}=+0.569970343\) \(a_{43}=+1.854317265\) \(a_{44}=+2.080772781\) \(a_{45}=+0.074881206\)
\(a_{46}=+0.177734771\) \(a_{47}=-0.829688460\) \(a_{48}=-1.483290414\) \(a_{49}=+0.142857143\) \(a_{50}=-1.685501227\)
\(a_{51}=-0.079089794\) \(a_{52}=+0.994717598\) \(a_{53}=-0.503872062\) \(a_{54}=+1.956853980\) \(a_{55}=-0.233924049\)
\(a_{56}=-0.841822884\) \(a_{57}=+0.576676419\) \(a_{58}=-1.405060936\) \(a_{59}=-0.650062761\) \(a_{60}=+0.471807253\)
\(a_{61}=-0.917593843\) \(a_{62}=+2.993708148\) \(a_{63}=+0.112500640\) \(a_{64}=-0.047026993\) \(a_{65}=-0.111827861\)
\(a_{66}=-1.402191510\) \(a_{67}=+0.284911548\) \(a_{68}=+0.211184412\) \(a_{69}=-0.082780015\) \(a_{70}=+0.171097588\)
\(a_{71}=+0.867203175\) \(a_{72}=-0.662939290\) \(a_{73}=+1.677415966\) \(a_{74}=-1.347066035\) \(a_{75}=+0.785022628\)
\(a_{76}=-1.539832941\) \(a_{77}=-0.351444729\) \(a_{78}=-0.670320461\) \(a_{79}=+0.376566984\) \(a_{80}=-0.445264241\)
\(a_{81}=-0.613756528\) \(a_{82}=+0.067219473\) \(a_{83}=-1.407224623\) \(a_{84}=+0.708837646\) \(a_{85}=-0.023741714\)
\(a_{86}=+3.336630613\) \(a_{87}=+0.654407491\) \(a_{88}=+2.070979507\) \(a_{89}=-1.248390817\) \(a_{90}=+0.134740117\)
\(a_{91}=-0.168008857\) \(a_{92}=+0.221037986\) \(a_{93}=-1.394320337\) \(a_{94}=-1.492928944\) \(a_{95}=+0.173110664\)
\(a_{96}=-0.802429057\) \(a_{97}=+1.013518043\) \(a_{98}=+0.257054995\) \(a_{99}=-0.276764298\) \(a_{100}=-2.096155943\)

Showing 100 of 1228 available coefficients

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