Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 30.6522751725 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.055596263\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.039312495\) \(a_{7}=-1.617607508\) \(a_{8}=-0.353553391\) \(a_{9}=-0.996909056\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.007876967\) \(a_{12}=-0.027798131\) \(a_{13}=+0.567999193\) \(a_{14}=+1.143821238\) \(a_{15}=-0.024863405\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.396641399\) \(a_{18}=+0.704921153\) \(a_{19}=-0.518906068\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.089932932\) \(a_{22}=+0.005569857\) \(a_{23}=-0.933840272\) \(a_{24}=+0.019656247\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.401636081\) \(a_{27}=+0.111020681\) \(a_{28}=-0.808803754\) \(a_{29}=-0.935422072\) \(a_{30}=+0.017581082\)
\(a_{31}=-1.662009280\) \(a_{32}=-0.176776695\) \(a_{33}=+0.000437930\) \(a_{34}=-0.987574604\) \(a_{35}=-0.723416070\)
\(a_{36}=-0.498454528\) \(a_{37}=+0.725915838\) \(a_{38}=+0.366922000\) \(a_{39}=-0.031578632\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.004275643\) \(a_{42}=-0.063592186\) \(a_{43}=+0.963032370\) \(a_{44}=-0.003938483\) \(a_{45}=-0.445831283\)
\(a_{46}=+0.660324789\) \(a_{47}=-0.657265897\) \(a_{48}=-0.013899066\) \(a_{49}=+1.616654051\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.077648042\) \(a_{52}=+0.283999597\) \(a_{53}=+0.001048301\) \(a_{54}=-0.078503476\) \(a_{55}=-0.003522687\)
\(a_{56}=+0.571910619\) \(a_{57}=+0.028849238\) \(a_{58}=+0.661443291\) \(a_{59}=-1.152121945\) \(a_{60}=-0.012431702\)
\(a_{61}=-0.215483571\) \(a_{62}=+1.175218032\) \(a_{63}=+1.612607573\) \(a_{64}=+0.125000000\) \(a_{65}=+0.254016962\)
\(a_{66}=-0.000309663\) \(a_{67}=-1.683902866\) \(a_{68}=+0.698320699\) \(a_{69}=+0.051918029\) \(a_{70}=+0.511532409\)
\(a_{71}=-1.168571591\) \(a_{72}=+0.352460577\) \(a_{73}=-1.240422735\) \(a_{74}=-0.513300012\) \(a_{75}=-0.011119253\)
\(a_{76}=-0.259453034\) \(a_{77}=+0.012741841\) \(a_{78}=+0.022329465\) \(a_{79}=+0.757857172\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.990736721\) \(a_{82}=+0.710130117\) \(a_{83}=+0.158987876\) \(a_{84}=+0.044966466\) \(a_{85}=+0.624597022\)
\(a_{86}=-0.680966719\) \(a_{87}=+0.052005971\) \(a_{88}=+0.002784928\) \(a_{89}=+0.224127972\) \(a_{90}=+0.315250324\)
\(a_{91}=-0.918799760\) \(a_{92}=-0.466920136\) \(a_{93}=+0.092401505\) \(a_{94}=+0.464757173\) \(a_{95}=-0.232061848\)
\(a_{96}=+0.009828124\) \(a_{97}=+0.337130226\) \(a_{98}=-1.143147042\) \(a_{99}=+0.007852620\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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