Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 22.3710520524 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.056908496\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.747347165\) \(a_{7}=-0.824789287\) \(a_{8}=-0.353553391\) \(a_{9}=+0.117055569\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.193090885\) \(a_{12}=+0.528454248\) \(a_{13}=-0.400043352\) \(a_{14}=+0.583214098\) \(a_{15}=-0.472663849\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.023229091\) \(a_{18}=-0.082770787\) \(a_{19}=-0.706763069\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.871726805\) \(a_{22}=-0.843642655\) \(a_{23}=+0.656435248\) \(a_{24}=-0.373673582\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.282873367\) \(a_{27}=-0.933191471\) \(a_{28}=-0.412394644\) \(a_{29}=+0.516988136\) \(a_{30}=+0.334223813\)
\(a_{31}=-0.929411531\) \(a_{32}=-0.176776695\) \(a_{33}=+1.260987893\) \(a_{34}=+0.723532229\) \(a_{35}=+0.368856983\)
\(a_{36}=+0.058527785\) \(a_{37}=-0.082190538\) \(a_{38}=+0.499756959\) \(a_{39}=-0.422809218\) \(a_{40}=+0.158113883\)
\(a_{41}=+1.348400693\) \(a_{42}=+0.616403935\) \(a_{43}=+0.839240082\) \(a_{44}=+0.596545442\) \(a_{45}=-0.052348842\)
\(a_{46}=-0.464169816\) \(a_{47}=+1.736519782\) \(a_{48}=+0.264227124\) \(a_{49}=-0.319722632\) \(a_{50}=-0.141421356\)
\(a_{51}=-1.081459520\) \(a_{52}=-0.200021676\) \(a_{53}=-0.824536048\) \(a_{54}=+0.659866017\) \(a_{55}=-0.533566464\)
\(a_{56}=+0.291607049\) \(a_{57}=-0.746983893\) \(a_{58}=-0.365565817\) \(a_{59}=-1.476514742\) \(a_{60}=-0.236331924\)
\(a_{61}=-0.447356795\) \(a_{62}=+0.657193196\) \(a_{63}=-0.096546179\) \(a_{64}=+0.125000000\) \(a_{65}=+0.178904826\)
\(a_{66}=-0.891653090\) \(a_{67}=+1.582426113\) \(a_{68}=-0.511614546\) \(a_{69}=+0.693791991\) \(a_{70}=-0.260821274\)
\(a_{71}=+0.288301195\) \(a_{72}=-0.041385393\) \(a_{73}=+0.337920676\) \(a_{74}=+0.058117487\) \(a_{75}=+0.211381699\)
\(a_{76}=-0.353381535\) \(a_{77}=-0.984048580\) \(a_{78}=+0.298971265\) \(a_{79}=-1.352877380\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.103353563\) \(a_{82}=-0.953463274\) \(a_{83}=+1.157695968\) \(a_{84}=-0.435863402\) \(a_{85}=+0.457601961\)
\(a_{86}=-0.593432353\) \(a_{87}=+0.546409153\) \(a_{88}=-0.421821328\) \(a_{89}=+0.173056130\) \(a_{90}=+0.037016221\)
\(a_{91}=+0.329951471\) \(a_{92}=+0.328217624\) \(a_{93}=-0.982302944\) \(a_{94}=-1.227904913\) \(a_{95}=+0.316074053\)
\(a_{96}=-0.186836791\) \(a_{97}=-1.582576925\) \(a_{98}=+0.226078041\) \(a_{99}=+0.139657932\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

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