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: \( 27.5213532352 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.573238615\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.112447693\) \(a_{7}=+1.166551097\) \(a_{8}=-0.353553391\) \(a_{9}=+1.475079741\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.414559160\) \(a_{12}=+0.786619308\) \(a_{13}=-0.937307760\) \(a_{14}=-0.824876191\) \(a_{15}=+0.703573698\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.945856322\) \(a_{18}=-1.043038888\) \(a_{19}=-0.018772711\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.835263232\) \(a_{22}=-0.293137593\) \(a_{23}=+0.908746533\) \(a_{24}=-0.556223847\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.662776673\) \(a_{27}=+0.747413794\) \(a_{28}=+0.583275548\) \(a_{29}=-0.793021317\) \(a_{30}=-0.497501733\)
\(a_{31}=-1.809203411\) \(a_{32}=-0.176776695\) \(a_{33}=+0.652200479\) \(a_{34}=-0.668821419\) \(a_{35}=+0.521697510\)
\(a_{36}=+0.737539870\) \(a_{37}=+1.614104019\) \(a_{38}=+0.013274311\) \(a_{39}=-1.474608763\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.731353325\) \(a_{42}=-1.297727077\) \(a_{43}=-0.244262168\) \(a_{44}=+0.207279580\) \(a_{45}=+0.659675715\)
\(a_{46}=-0.642580836\) \(a_{47}=-0.464139746\) \(a_{48}=+0.393309654\) \(a_{49}=+0.360841461\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.488057690\) \(a_{52}=-0.468653880\) \(a_{53}=+1.013905830\) \(a_{54}=-0.528501362\) \(a_{55}=+0.185396492\)
\(a_{56}=-0.412438096\) \(a_{57}=-0.029533954\) \(a_{58}=+0.560750751\) \(a_{59}=+1.451164997\) \(a_{60}=+0.351786849\)
\(a_{61}=+1.696225517\) \(a_{62}=+1.279300000\) \(a_{63}=+1.720755889\) \(a_{64}=+0.125000000\) \(a_{65}=-0.419176774\)
\(a_{66}=-0.461175381\) \(a_{67}=-1.100974961\) \(a_{68}=+0.472928161\) \(a_{69}=+1.429675138\) \(a_{70}=-0.368895847\)
\(a_{71}=+0.907815519\) \(a_{72}=-0.521519444\) \(a_{73}=+1.475559410\) \(a_{74}=-1.141343897\) \(a_{75}=+0.314647723\)
\(a_{76}=-0.009386355\) \(a_{77}=+0.483604443\) \(a_{78}=+1.042705856\) \(a_{79}=-1.276295958\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.299219499\) \(a_{82}=-1.224251677\) \(a_{83}=+0.333696682\) \(a_{84}=+0.917631616\) \(a_{85}=+0.422999806\)
\(a_{86}=+0.172719435\) \(a_{87}=-1.247611759\) \(a_{88}=-0.146568797\) \(a_{89}=-0.006961681\) \(a_{90}=-0.466461171\)
\(a_{91}=-1.093417396\) \(a_{92}=+0.454373267\) \(a_{93}=-2.846308669\) \(a_{94}=+0.328196362\) \(a_{95}=-0.008395412\)
\(a_{96}=-0.278111923\) \(a_{97}=+0.545427881\) \(a_{98}=-0.255153444\) \(a_{99}=+0.611507818\) \(a_{100}=+0.099975586\)

Showing 100 of 226 available coefficients

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