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: \( 12.153525187 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.079790118\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.763526914\) \(a_{7}=+0.513591083\) \(a_{8}=-0.353553391\) \(a_{9}=+0.165946698\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.124748807\) \(a_{12}=-0.539895059\) \(a_{13}=-0.117197472\) \(a_{14}=-0.363163737\) \(a_{15}=+0.482896821\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.615339626\) \(a_{18}=-0.117342036\) \(a_{19}=-1.365847361\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.554570576\) \(a_{22}=+0.795317509\) \(a_{23}=-1.230979415\) \(a_{24}=+0.381763457\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.082871127\) \(a_{27}=+0.900602513\) \(a_{28}=+0.256795541\) \(a_{29}=+0.332023117\) \(a_{30}=-0.341459617\)
\(a_{31}=+0.679125196\) \(a_{32}=-0.176776695\) \(a_{33}=+1.214492647\) \(a_{34}=+1.142217604\) \(a_{35}=-0.229684915\)
\(a_{36}=+0.082973349\) \(a_{37}=+0.936592697\) \(a_{38}=+0.965799931\) \(a_{39}=+0.126548672\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.741386954\) \(a_{42}=+0.392140615\) \(a_{43}=-0.197451909\) \(a_{44}=-0.562374404\) \(a_{45}=-0.074213620\)
\(a_{46}=+0.870433892\) \(a_{47}=+1.064283725\) \(a_{48}=-0.269947529\) \(a_{49}=-0.736224200\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.744227765\) \(a_{52}=-0.058598736\) \(a_{53}=-0.255223888\) \(a_{54}=-0.636822144\) \(a_{55}=+0.503002958\)
\(a_{56}=-0.181581869\) \(a_{57}=+1.474828483\) \(a_{58}=-0.234775798\) \(a_{59}=-1.324714032\) \(a_{60}=+0.241448410\)
\(a_{61}=-1.006458923\) \(a_{62}=-0.480214031\) \(a_{63}=+0.085228744\) \(a_{64}=+0.125000000\) \(a_{65}=+0.052412303\)
\(a_{66}=-0.858775986\) \(a_{67}=+1.905016695\) \(a_{68}=-0.807669813\) \(a_{69}=+1.329199407\) \(a_{70}=+0.162411761\)
\(a_{71}=+0.223620390\) \(a_{72}=-0.058671018\) \(a_{73}=+1.712842313\) \(a_{74}=-0.662271047\) \(a_{75}=-0.215958024\)
\(a_{76}=-0.682923681\) \(a_{77}=-0.577660960\) \(a_{78}=-0.089483424\) \(a_{79}=-1.559866937\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.138408398\) \(a_{82}=+0.524239742\) \(a_{83}=+1.290706110\) \(a_{84}=-0.277285288\) \(a_{85}=+0.722401842\)
\(a_{86}=+0.139619584\) \(a_{87}=-0.358515275\) \(a_{88}=+0.397658754\) \(a_{89}=+1.126622160\) \(a_{90}=+0.052476954\)
\(a_{91}=-0.060191527\) \(a_{92}=-0.615489708\) \(a_{93}=-0.733312636\) \(a_{94}=-0.752562239\) \(a_{95}=+0.610825509\)
\(a_{96}=+0.190881729\) \(a_{97}=+0.492290553\) \(a_{98}=+0.520589124\) \(a_{99}=-0.186648420\) \(a_{100}=+0.099975586\)

Showing 100 of 160 available coefficients

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