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: \( 31.097569992 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.781581305\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.259768222\) \(a_{7}=+1.142714020\) \(a_{8}=+0.353553391\) \(a_{9}=+2.174031946\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.008476527\) \(a_{12}=-0.890790652\) \(a_{13}=-0.602927298\) \(a_{14}=+0.808020833\) \(a_{15}=-0.796747381\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.884165628\) \(a_{18}=+1.537272732\) \(a_{19}=+1.164638450\) \(a_{20}=+0.223606798\)
\(a_{21}=-2.035837935\) \(a_{22}=+0.713100591\) \(a_{23}=-0.859120062\) \(a_{24}=-0.629884111\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.426333981\) \(a_{27}=-2.091633366\) \(a_{28}=+0.571357010\) \(a_{29}=-1.585567046\) \(a_{30}=-0.563385476\)
\(a_{31}=-0.803343235\) \(a_{32}=+0.176776695\) \(a_{33}=-1.796682927\) \(a_{34}=-0.625199511\) \(a_{35}=+0.511037246\)
\(a_{36}=+1.087015973\) \(a_{37}=+0.577096105\) \(a_{38}=+0.823523746\) \(a_{39}=+1.074164003\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.672313496\) \(a_{42}=-1.439554809\) \(a_{43}=+0.299718104\) \(a_{44}=+0.504238263\) \(a_{45}=+0.972256643\)
\(a_{46}=-0.607489622\) \(a_{47}=+1.016229330\) \(a_{48}=-0.445395326\) \(a_{49}=+0.305795332\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.575212953\) \(a_{52}=-0.301463649\) \(a_{53}=-0.874779846\) \(a_{54}=-1.479008137\) \(a_{55}=+0.451004414\)
\(a_{56}=+0.404010416\) \(a_{57}=-2.074898090\) \(a_{58}=-1.121165210\) \(a_{59}=-1.190196690\) \(a_{60}=-0.398373691\)
\(a_{61}=+0.739456516\) \(a_{62}=-0.568049449\) \(a_{63}=+2.484296785\) \(a_{64}=+0.125000000\) \(a_{65}=-0.269637285\)
\(a_{66}=-1.270446681\) \(a_{67}=-1.514448035\) \(a_{68}=-0.442082814\) \(a_{69}=+1.530592242\) \(a_{70}=+0.361357902\)
\(a_{71}=+1.124461419\) \(a_{72}=+0.768636366\) \(a_{73}=+1.363283470\) \(a_{74}=+0.408068569\) \(a_{75}=-0.356316261\)
\(a_{76}=+0.582319225\) \(a_{77}=+1.152400266\) \(a_{78}=+0.759548650\) \(a_{79}=-0.171158892\) \(a_{80}=+0.111803399\)
\(a_{81}=+1.552382956\) \(a_{82}=-1.182504213\) \(a_{83}=+1.670650905\) \(a_{84}=-1.017918968\) \(a_{85}=-0.395410889\)
\(a_{86}=+0.211932704\) \(a_{87}=+2.824816606\) \(a_{88}=+0.356550295\) \(a_{89}=-0.534736702\) \(a_{90}=+0.687489266\)
\(a_{91}=-0.688973477\) \(a_{92}=-0.429560031\) \(a_{93}=+1.431221288\) \(a_{94}=+0.718582651\) \(a_{95}=+0.520842149\)
\(a_{96}=-0.314942055\) \(a_{97}=-1.076831895\) \(a_{98}=+0.216229953\) \(a_{99}=+2.192460186\) \(a_{100}=+0.099975586\)

Showing 100 of 255 available coefficients

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