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: \( 27.299702759 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.724768977\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.512489058\) \(a_{7}=-0.514916311\) \(a_{8}=-0.353553391\) \(a_{9}=-0.474709930\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.793333250\) \(a_{12}=+0.362384489\) \(a_{13}=-0.314645565\) \(a_{14}=+0.364100815\) \(a_{15}=-0.324126540\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.097225507\) \(a_{18}=+0.335670610\) \(a_{19}=+0.155888614\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.373195368\) \(a_{22}=+0.560971321\) \(a_{23}=+1.535386130\) \(a_{24}=-0.256244529\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.222488012\) \(a_{27}=-1.068824007\) \(a_{28}=-0.257458155\) \(a_{29}=+1.478971194\) \(a_{30}=+0.229192075\)
\(a_{31}=+1.927674013\) \(a_{32}=-0.176776695\) \(a_{33}=-0.574983328\) \(a_{34}=-0.068748816\) \(a_{35}=+0.230277575\)
\(a_{36}=-0.237354965\) \(a_{37}=+0.911571066\) \(a_{38}=-0.110229896\) \(a_{39}=-0.228045344\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.285829238\) \(a_{42}=+0.263888975\) \(a_{43}=-0.170469708\) \(a_{44}=-0.396666625\) \(a_{45}=+0.212296735\)
\(a_{46}=-1.085681944\) \(a_{47}=+0.483360718\) \(a_{48}=+0.181192244\) \(a_{49}=-0.734861193\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.070466032\) \(a_{52}=-0.157322782\) \(a_{53}=-0.347892971\) \(a_{54}=+0.755772704\) \(a_{55}=+0.354789415\)
\(a_{56}=+0.182050407\) \(a_{57}=+0.112983231\) \(a_{58}=-1.045790560\) \(a_{59}=-1.530966762\) \(a_{60}=-0.162063270\)
\(a_{61}=-0.663284190\) \(a_{62}=-1.363071367\) \(a_{63}=+0.244435886\) \(a_{64}=+0.125000000\) \(a_{65}=+0.140713774\)
\(a_{66}=+0.406574611\) \(a_{67}=-0.393188954\) \(a_{68}=+0.048612754\) \(a_{69}=+1.112800235\) \(a_{70}=-0.162830835\)
\(a_{71}=-1.540853397\) \(a_{72}=+0.167835305\) \(a_{73}=-0.450469784\) \(a_{74}=-0.644578082\) \(a_{75}=+0.144953795\)
\(a_{76}=+0.077944307\) \(a_{77}=+0.408500230\) \(a_{78}=+0.161252409\) \(a_{79}=+0.769741210\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.299940553\) \(a_{82}=-0.202111793\) \(a_{83}=+0.465080608\) \(a_{84}=-0.186597684\) \(a_{85}=-0.043480569\)
\(a_{86}=+0.120540286\) \(a_{87}=+1.071912439\) \(a_{88}=+0.280485661\) \(a_{89}=+0.944423934\) \(a_{90}=-0.150116461\)
\(a_{91}=+0.162016133\) \(a_{92}=+0.767693065\) \(a_{93}=+1.397118323\) \(a_{94}=-0.341787641\) \(a_{95}=-0.069715508\)
\(a_{96}=-0.128122265\) \(a_{97}=+0.414736742\) \(a_{98}=+0.519625333\) \(a_{99}=+0.376603172\) \(a_{100}=+0.099975586\)

Showing 100 of 228 available coefficients

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