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: \( 21.6514464961 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.407671501\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.995374064\) \(a_{7}=-0.886152580\) \(a_{8}=-0.353553391\) \(a_{9}=+0.981539056\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.419932675\) \(a_{12}=+0.703835751\) \(a_{13}=-1.644448453\) \(a_{14}=+0.626604499\) \(a_{15}=+0.629529833\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.692225006\) \(a_{18}=-0.694052922\) \(a_{19}=+1.547080030\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.247411733\) \(a_{22}=+0.296937242\) \(a_{23}=-0.105619770\) \(a_{24}=-0.497687032\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.162800652\) \(a_{27}=-0.025986945\) \(a_{28}=-0.443076290\) \(a_{29}=-0.601297358\) \(a_{30}=-0.445144814\)
\(a_{31}=+0.217779866\) \(a_{32}=-0.176776695\) \(a_{33}=-0.591127259\) \(a_{34}=-1.196583777\) \(a_{35}=-0.396299481\)
\(a_{36}=+0.490769528\) \(a_{37}=+0.360614003\) \(a_{38}=-1.093950780\) \(a_{39}=-2.314843223\) \(a_{40}=-0.158113883\)
\(a_{41}=-1.134209592\) \(a_{42}=+0.882053295\) \(a_{43}=-1.684566336\) \(a_{44}=-0.209966337\) \(a_{45}=+0.438957610\)
\(a_{46}=+0.074684456\) \(a_{47}=+0.566785150\) \(a_{48}=+0.351917875\) \(a_{49}=-0.214733605\) \(a_{50}=-0.141421356\)
\(a_{51}=+2.382096915\) \(a_{52}=-0.822224226\) \(a_{53}=+0.242387432\) \(a_{54}=+0.018375545\) \(a_{55}=-0.187799601\)
\(a_{56}=+0.313302249\) \(a_{57}=+2.177780469\) \(a_{58}=+0.425181439\) \(a_{59}=-1.458932616\) \(a_{60}=+0.314764917\)
\(a_{61}=-0.403143547\) \(a_{62}=-0.153993620\) \(a_{63}=-0.869793367\) \(a_{64}=+0.125000000\) \(a_{65}=-0.735419705\)
\(a_{66}=+0.417990093\) \(a_{67}=+0.160256396\) \(a_{68}=+0.846112503\) \(a_{69}=-0.148677940\) \(a_{70}=+0.280226051\)
\(a_{71}=-0.751948105\) \(a_{72}=-0.347026461\) \(a_{73}=+1.646699663\) \(a_{74}=-0.254992607\) \(a_{75}=+0.281534300\)
\(a_{76}=+0.773540015\) \(a_{77}=+0.372124423\) \(a_{78}=+1.636841340\) \(a_{79}=+0.128324120\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.018120138\) \(a_{82}=+0.802007294\) \(a_{83}=-1.194113340\) \(a_{84}=-0.623705866\) \(a_{85}=+0.756786029\)
\(a_{86}=+1.191168280\) \(a_{87}=-0.846429154\) \(a_{88}=+0.148468621\) \(a_{89}=-0.672825788\) \(a_{90}=-0.310389903\)
\(a_{91}=+1.457232239\) \(a_{92}=-0.052809885\) \(a_{93}=+0.306562511\) \(a_{94}=-0.400777623\) \(a_{95}=+0.691875223\)
\(a_{96}=-0.248843516\) \(a_{97}=-1.776728365\) \(a_{98}=+0.151839588\) \(a_{99}=-0.412180321\) \(a_{100}=+0.099975586\)

Showing 100 of 196 available coefficients

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