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: \( 27.0752071997 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.821458000\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.287965303\) \(a_{7}=+0.213684097\) \(a_{8}=+0.353553391\) \(a_{9}=+2.317709244\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.080746280\) \(a_{12}=+0.910729000\) \(a_{13}=+0.601058147\) \(a_{14}=+0.151097474\) \(a_{15}=+0.814580781\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.680950010\) \(a_{18}=+1.638867923\) \(a_{19}=+1.739982562\) \(a_{20}=+0.223606798\)
\(a_{21}=+0.389216607\) \(a_{22}=+0.764203023\) \(a_{23}=-0.928998096\) \(a_{24}=+0.643982652\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.425012292\) \(a_{27}=+2.400152043\) \(a_{28}=+0.106842048\) \(a_{29}=-0.389189410\) \(a_{30}=+0.575995594\)
\(a_{31}=-1.539244464\) \(a_{32}=+0.176776695\) \(a_{33}=+1.968533957\) \(a_{34}=+0.481504370\) \(a_{35}=+0.095562433\)
\(a_{36}=+1.158854622\) \(a_{37}=-1.045146829\) \(a_{38}=+1.230353469\) \(a_{39}=+1.094802170\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.449332384\) \(a_{42}=+0.275217702\) \(a_{43}=-1.531323143\) \(a_{44}=+0.540373140\) \(a_{45}=+1.036511084\)
\(a_{46}=-0.656900854\) \(a_{47}=-0.282762481\) \(a_{48}=+0.455364500\) \(a_{49}=-0.954339107\) \(a_{50}=+0.141421356\)
\(a_{51}=+1.240321843\) \(a_{52}=+0.300529074\) \(a_{53}=+0.698068503\) \(a_{54}=+1.697163786\) \(a_{55}=+0.483324430\)
\(a_{56}=+0.075548737\) \(a_{57}=+3.169305157\) \(a_{58}=-0.275198471\) \(a_{59}=+1.185974858\) \(a_{60}=+0.407290391\)
\(a_{61}=-0.580133726\) \(a_{62}=-1.088410198\) \(a_{63}=+0.495257606\) \(a_{64}=+0.125000000\) \(a_{65}=+0.268801375\)
\(a_{66}=+1.391963710\) \(a_{67}=+0.189497421\) \(a_{68}=+0.340475005\) \(a_{69}=-1.692131014\) \(a_{70}=+0.067572844\)
\(a_{71}=-1.334835646\) \(a_{72}=+0.819433962\) \(a_{73}=+1.455269244\) \(a_{74}=-0.739030410\) \(a_{75}=+0.364291600\)
\(a_{76}=+0.869991281\) \(a_{77}=+0.230938292\) \(a_{78}=+0.774142039\) \(a_{79}=+0.921232833\) \(a_{80}=+0.111803399\)
\(a_{81}=+2.054066896\) \(a_{82}=-1.024832757\) \(a_{83}=+0.030702277\) \(a_{84}=+0.194608304\) \(a_{85}=+0.304530102\)
\(a_{86}=-1.082808979\) \(a_{87}=-0.708892165\) \(a_{88}=+0.382101512\) \(a_{89}=+1.620319562\) \(a_{90}=+0.732924016\)
\(a_{91}=+0.128436567\) \(a_{92}=-0.464499048\) \(a_{93}=-2.803669141\) \(a_{94}=-0.199943268\) \(a_{95}=+0.778143858\)
\(a_{96}=+0.321991326\) \(a_{97}=+1.139553352\) \(a_{98}=-0.674819654\) \(a_{99}=+2.504855643\) \(a_{100}=+0.099975586\)

Showing 100 of 226 available coefficients

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