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: \( 28.0277820443 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.787145372\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.263702612\) \(a_{7}=+0.572505163\) \(a_{8}=-0.353553391\) \(a_{9}=+2.193888582\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.527872415\) \(a_{12}=+0.893572686\) \(a_{13}=+1.288920442\) \(a_{14}=-0.404822283\) \(a_{15}=-0.799235708\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.091572598\) \(a_{18}=-1.551313494\) \(a_{19}=+1.314293196\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.023149953\) \(a_{22}=+1.080368945\) \(a_{23}=+0.895894830\) \(a_{24}=-0.631851306\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.911404385\) \(a_{27}=+2.133652455\) \(a_{28}=+0.286252582\) \(a_{29}=-1.028786459\) \(a_{30}=+0.565144989\)
\(a_{31}=-0.356204844\) \(a_{32}=-0.176776695\) \(a_{33}=-2.730530116\) \(a_{34}=-0.771858386\) \(a_{35}=-0.256032092\)
\(a_{36}=+1.096944291\) \(a_{37}=-0.542876449\) \(a_{38}=-0.929345631\) \(a_{39}=+2.303488204\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.083027405\) \(a_{42}=-0.723476270\) \(a_{43}=-0.553714179\) \(a_{44}=-0.763936208\) \(a_{45}=-0.981136801\)
\(a_{46}=-0.633493309\) \(a_{47}=+1.490882842\) \(a_{48}=+0.446786343\) \(a_{49}=-0.672237838\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.950798916\) \(a_{52}=+0.644460221\) \(a_{53}=-1.569033856\) \(a_{54}=-1.508720119\) \(a_{55}=+0.683285316\)
\(a_{56}=-0.202411142\) \(a_{57}=+2.348833003\) \(a_{58}=+0.727461882\) \(a_{59}=+1.676225495\) \(a_{60}=-0.399617854\)
\(a_{61}=-0.111050908\) \(a_{62}=+0.251874861\) \(a_{63}=+1.256012541\) \(a_{64}=+0.125000000\) \(a_{65}=-0.576422745\)
\(a_{66}=+1.930776361\) \(a_{67}=+1.327397717\) \(a_{68}=+0.545786299\) \(a_{69}=+1.601094299\) \(a_{70}=+0.181042029\)
\(a_{71}=-0.185261564\) \(a_{72}=-0.775656747\) \(a_{73}=-0.290165835\) \(a_{74}=+0.383871618\) \(a_{75}=+0.357429074\)
\(a_{76}=+0.657146598\) \(a_{77}=-0.874714846\) \(a_{78}=-1.628812129\) \(a_{79}=+1.515970280\) \(a_{80}=-0.111803399\)
\(a_{81}=+1.619258529\) \(a_{82}=-0.058709241\) \(a_{83}=-0.504170051\) \(a_{84}=+0.511574976\) \(a_{85}=-0.488166106\)
\(a_{86}=+0.391535051\) \(a_{87}=-1.838590960\) \(a_{88}=+0.540184473\) \(a_{89}=-1.056359422\) \(a_{90}=+0.693768485\)
\(a_{91}=+0.737913608\) \(a_{92}=+0.447947415\) \(a_{93}=-0.636589838\) \(a_{94}=-1.054213367\) \(a_{95}=-0.587769786\)
\(a_{96}=-0.315925653\) \(a_{97}=-0.917027794\) \(a_{98}=+0.475343934\) \(a_{99}=-3.351981846\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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