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: \( 18.6547712142 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.960694744\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.386420549\) \(a_{7}=+0.061581494\) \(a_{8}=-0.353553391\) \(a_{9}=+2.844323880\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.790624145\) \(a_{12}=+0.980347372\) \(a_{13}=-1.500931252\) \(a_{14}=-0.043544692\) \(a_{15}=-0.876849346\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.351555565\) \(a_{18}=-2.011240703\) \(a_{19}=+0.219278474\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.120742511\) \(a_{22}=+0.559055694\) \(a_{23}=+0.894961957\) \(a_{24}=-0.693210275\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.061318666\) \(a_{27}=+3.616156138\) \(a_{28}=+0.030790747\) \(a_{29}=+1.500591461\) \(a_{30}=+0.620026119\)
\(a_{31}=+0.147463261\) \(a_{32}=-0.176776695\) \(a_{33}=-1.550172605\) \(a_{34}=-0.248587324\) \(a_{35}=-0.027540081\)
\(a_{36}=+1.422161940\) \(a_{37}=+0.464326348\) \(a_{38}=-0.155053296\) \(a_{39}=-2.942868018\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.845928262\) \(a_{42}=-0.085377849\) \(a_{43}=+1.679428039\) \(a_{44}=-0.395312072\) \(a_{45}=-1.272020309\)
\(a_{46}=-0.632833669\) \(a_{47}=+0.975578671\) \(a_{48}=+0.490173686\) \(a_{49}=-0.996207720\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.689293149\) \(a_{52}=-0.750465626\) \(a_{53}=+0.564682168\) \(a_{54}=-2.557008527\) \(a_{55}=+0.353577866\)
\(a_{56}=-0.021772346\) \(a_{57}=+0.429938152\) \(a_{58}=-1.061078398\) \(a_{59}=-1.260939709\) \(a_{60}=-0.438424673\)
\(a_{61}=+0.892276420\) \(a_{62}=-0.104272272\) \(a_{63}=+0.175157714\) \(a_{64}=+0.125000000\) \(a_{65}=+0.671236862\)
\(a_{66}=+1.096137561\) \(a_{67}=-1.111122503\) \(a_{68}=+0.175777783\) \(a_{69}=+1.754747206\) \(a_{70}=+0.019473778\)
\(a_{71}=+0.248854044\) \(a_{72}=-1.005620352\) \(a_{73}=+0.636239658\) \(a_{74}=-0.328328309\) \(a_{75}=+0.392138949\)
\(a_{76}=+0.109639237\) \(a_{77}=-0.048687816\) \(a_{78}=+2.080921931\) \(a_{79}=+0.225037941\) \(a_{80}=-0.111803399\)
\(a_{81}=+4.245854454\) \(a_{82}=-0.598161611\) \(a_{83}=-1.917671676\) \(a_{84}=+0.060371256\) \(a_{85}=-0.157220428\)
\(a_{86}=-1.187534955\) \(a_{87}=+2.942201791\) \(a_{88}=+0.279527847\) \(a_{89}=+0.086745280\) \(a_{90}=+0.899454186\)
\(a_{91}=-0.092429589\) \(a_{92}=+0.447480979\) \(a_{93}=+0.289130441\) \(a_{94}=-0.689838294\) \(a_{95}=-0.098064315\)
\(a_{96}=-0.346605137\) \(a_{97}=+1.213275215\) \(a_{98}=+0.704425234\) \(a_{99}=-2.248791135\) \(a_{100}=+0.099975586\)

Showing 100 of 192 available coefficients

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