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: \( 26.8887649597 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.915110413\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.647080779\) \(a_{7}=-1.778204906\) \(a_{8}=-0.353553391\) \(a_{9}=-0.162572932\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.431231944\) \(a_{12}=-0.457555207\) \(a_{13}=-0.677231313\) \(a_{14}=+1.257380748\) \(a_{15}=-0.409249818\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.143055447\) \(a_{18}=+0.114956423\) \(a_{19}=-1.138876176\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.627253826\) \(a_{22}=-0.304927032\) \(a_{23}=+1.680612992\) \(a_{24}=+0.323540389\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.478874854\) \(a_{27}=+1.063882596\) \(a_{28}=-0.889102453\) \(a_{29}=-0.472406028\) \(a_{30}=+0.289383322\)
\(a_{31}=+0.148603529\) \(a_{32}=-0.176776695\) \(a_{33}=-0.394624842\) \(a_{34}=+0.101155477\) \(a_{35}=-0.795237410\)
\(a_{36}=-0.081286466\) \(a_{37}=+0.355859930\) \(a_{38}=+0.805307067\) \(a_{39}=+0.619741427\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.656757572\) \(a_{42}=-1.150642215\) \(a_{43}=-1.453132969\) \(a_{44}=+0.215615972\) \(a_{45}=-0.072704825\)
\(a_{46}=-1.188372843\) \(a_{47}=+0.596327388\) \(a_{48}=-0.228777603\) \(a_{49}=+2.162012688\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.130911530\) \(a_{52}=-0.338615656\) \(a_{53}=+1.107281302\) \(a_{54}=-0.752278598\) \(a_{55}=+0.192852788\)
\(a_{56}=+0.628690374\) \(a_{57}=+1.042197448\) \(a_{58}=+0.334041506\) \(a_{59}=-0.386581753\) \(a_{60}=-0.204624909\)
\(a_{61}=+0.052118688\) \(a_{62}=-0.105078563\) \(a_{63}=+0.289087985\) \(a_{64}=+0.125000000\) \(a_{65}=-0.302867050\)
\(a_{66}=+0.279041902\) \(a_{67}=+1.356551003\) \(a_{68}=-0.071527724\) \(a_{69}=-1.537946450\) \(a_{70}=+0.562317765\)
\(a_{71}=-0.241706261\) \(a_{72}=+0.057478211\) \(a_{73}=+1.947254322\) \(a_{74}=-0.251630970\) \(a_{75}=-0.183022083\)
\(a_{76}=-0.569438088\) \(a_{77}=-0.766818758\) \(a_{78}=-0.438223365\) \(a_{79}=+0.682470306\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.810997110\) \(a_{82}=+1.171504514\) \(a_{83}=+1.018816207\) \(a_{84}=+0.813626913\) \(a_{85}=-0.063976341\)
\(a_{86}=+1.027520177\) \(a_{87}=+0.432303675\) \(a_{88}=-0.152463516\) \(a_{89}=+0.621357213\) \(a_{90}=+0.051410075\)
\(a_{91}=+1.204256043\) \(a_{92}=+0.840306496\) \(a_{93}=-0.135988637\) \(a_{94}=-0.421667140\) \(a_{95}=-0.509320910\)
\(a_{96}=+0.161770195\) \(a_{97}=+1.144999666\) \(a_{98}=-1.528773833\) \(a_{99}=-0.070106641\) \(a_{100}=+0.099975586\)

Showing 100 of 232 available coefficients

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