Properties

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

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 10.5773733824 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.068062604\) \(a_{3}=+1.396818849\) \(a_{4}=+0.140757726\) \(a_{5}=-0.438358383\)
\(a_{6}=-1.491889978\) \(a_{7}=-0.377964473\) \(a_{8}=+0.917724541\) \(a_{9}=+0.951102898\) \(a_{10}=+0.468194196\)
\(a_{11}=+0.265066670\) \(a_{12}=+0.196613045\) \(a_{13}=-0.093927135\) \(a_{14}=+0.403689719\) \(a_{15}=-0.612307252\)
\(a_{16}=-1.120944989\) \(a_{17}=-1.399994582\) \(a_{18}=-1.015837438\) \(a_{19}=+1.331448465\) \(a_{20}=-0.061702329\)
\(a_{21}=-0.527947900\) \(a_{22}=-0.283107798\) \(a_{23}=-1.747390468\) \(a_{24}=+1.281894937\) \(a_{25}=-0.807841928\)
\(a_{26}=+0.100320060\) \(a_{27}=-0.068300394\) \(a_{28}=-0.053201420\) \(a_{29}=+0.052713225\) \(a_{30}=+0.653982478\)
\(a_{31}=-1.685053020\) \(a_{32}=+0.279514883\) \(a_{33}=+0.370250121\) \(a_{34}=+1.495281858\) \(a_{35}=+0.165683895\)
\(a_{36}=+0.133875081\) \(a_{37}=-1.338937926\) \(a_{38}=-1.422070315\) \(a_{39}=-0.131199192\) \(a_{40}=-0.402292246\)
\(a_{41}=+0.910443305\) \(a_{42}=+0.563881409\) \(a_{43}=+0.787814760\) \(a_{44}=+0.037310182\) \(a_{45}=-0.416923928\)
\(a_{46}=+1.866322414\) \(a_{47}=-0.488379708\) \(a_{48}=-1.565757089\) \(a_{49}=+0.142857143\) \(a_{50}=+0.862825753\)
\(a_{51}=-1.955538820\) \(a_{52}=-0.013220970\) \(a_{53}=+0.101831218\) \(a_{54}=+0.072949097\) \(a_{55}=-0.116194197\)
\(a_{56}=-0.346867272\) \(a_{57}=+1.859792313\) \(a_{58}=-0.056301025\) \(a_{59}=+0.222886838\) \(a_{60}=-0.086186977\)
\(a_{61}=-1.632383028\) \(a_{62}=+1.799742117\) \(a_{63}=-0.359483106\) \(a_{64}=+0.822405595\) \(a_{65}=+0.041173747\)
\(a_{66}=-0.395450309\) \(a_{67}=-0.280558440\) \(a_{68}=-0.197060054\) \(a_{69}=-2.440787943\) \(a_{70}=-0.176960773\)
\(a_{71}=+1.048092347\) \(a_{72}=+0.872850470\) \(a_{73}=-0.427549916\) \(a_{74}=+1.430069528\) \(a_{75}=-1.128408832\)
\(a_{76}=+0.187411658\) \(a_{77}=-0.100185784\) \(a_{78}=+0.140128951\) \(a_{79}=+1.126201380\) \(a_{80}=+0.491375633\)
\(a_{81}=-1.046506176\) \(a_{82}=-0.972410447\) \(a_{83}=+0.611208177\) \(a_{84}=-0.074312746\) \(a_{85}=+0.613699361\)
\(a_{86}=-0.841435484\) \(a_{87}=+0.073630827\) \(a_{88}=+0.243258188\) \(a_{89}=+0.896034619\) \(a_{90}=+0.445300857\)
\(a_{91}=+0.035501120\) \(a_{92}=-0.245958709\) \(a_{93}=-2.353713821\) \(a_{94}=+0.521620103\) \(a_{95}=-0.583651596\)
\(a_{96}=+0.390431657\) \(a_{97}=-1.141455551\) \(a_{98}=-0.152580372\) \(a_{99}=+0.252105678\) \(a_{100}=-0.113709993\)

Showing 100 of 1228 available coefficients

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