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: \( 28.8137386137 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.801389457\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.273774700\) \(a_{7}=-0.842306216\) \(a_{8}=+0.353553391\) \(a_{9}=+2.245003974\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.535472828\) \(a_{12}=+0.900694728\) \(a_{13}=-1.378833451\) \(a_{14}=-0.595600437\) \(a_{15}=+0.805605856\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.227497975\) \(a_{18}=+1.587457534\) \(a_{19}=-1.259529188\) \(a_{20}=+0.223606798\)
\(a_{21}=-1.517321537\) \(a_{22}=-1.085743249\) \(a_{23}=-1.444873681\) \(a_{24}=+0.636887350\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.974982483\) \(a_{27}=+2.242737033\) \(a_{28}=-0.421153108\) \(a_{29}=-1.259781134\) \(a_{30}=+0.569649364\)
\(a_{31}=-0.439046758\) \(a_{32}=+0.176776695\) \(a_{33}=-2.765984563\) \(a_{34}=+0.867972142\) \(a_{35}=-0.376690791\)
\(a_{36}=+1.122501987\) \(a_{37}=+1.446434929\) \(a_{38}=-0.890621630\) \(a_{39}=-2.483816040\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.447833110\) \(a_{42}=-1.072908348\) \(a_{43}=-0.780558263\) \(a_{44}=-0.767736414\) \(a_{45}=+1.003996299\)
\(a_{46}=-1.021679978\) \(a_{47}=+0.363179792\) \(a_{48}=+0.450347364\) \(a_{49}=-0.290520238\) \(a_{50}=+0.141421356\)
\(a_{51}=+2.211201910\) \(a_{52}=-0.689416725\) \(a_{53}=-0.584801077\) \(a_{54}=+1.585854564\) \(a_{55}=-0.686684324\)
\(a_{56}=-0.297800219\) \(a_{57}=-2.268902599\) \(a_{58}=-0.890799783\) \(a_{59}=+0.465543482\) \(a_{60}=+0.402802928\)
\(a_{61}=-0.384177219\) \(a_{62}=-0.310452940\) \(a_{63}=-1.890980803\) \(a_{64}=+0.125000000\) \(a_{65}=-0.616633065\)
\(a_{66}=-1.955846441\) \(a_{67}=-0.674788732\) \(a_{68}=+0.613748987\) \(a_{69}=-2.602780216\) \(a_{70}=-0.266360613\)
\(a_{71}=+0.252546951\) \(a_{72}=+0.793728767\) \(a_{73}=-1.468477422\) \(a_{74}=+1.022783947\) \(a_{75}=+0.360277891\)
\(a_{76}=-0.629764594\) \(a_{77}=+1.293338308\) \(a_{78}=-1.756323165\) \(a_{79}=+0.523484088\) \(a_{80}=+0.111803399\)
\(a_{81}=+1.795038871\) \(a_{82}=+0.316665829\) \(a_{83}=-1.065424217\) \(a_{84}=-0.758660768\) \(a_{85}=+0.548953783\)
\(a_{86}=-0.551938041\) \(a_{87}=-2.269356452\) \(a_{88}=-0.542871624\) \(a_{89}=-0.618295197\) \(a_{90}=+0.709932592\)
\(a_{91}=+1.161399986\) \(a_{92}=-0.722436841\) \(a_{93}=-0.790894201\) \(a_{94}=+0.256806894\) \(a_{95}=-0.563278577\)
\(a_{96}=+0.318443675\) \(a_{97}=-0.394523044\) \(a_{98}=-0.205428831\) \(a_{99}=-3.447142601\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

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