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: \( 19.32164295 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.506964207\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+1.065584610\) \(a_{7}=+1.930047321\) \(a_{8}=-0.353553391\) \(a_{9}=+1.270941121\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.410153783\) \(a_{12}=-0.753482103\) \(a_{13}=-1.560944217\) \(a_{14}=-1.364749549\) \(a_{15}=+0.673934881\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.530188113\) \(a_{18}=-0.898691085\) \(a_{19}=-0.341761823\) \(a_{20}=-0.223606798\)
\(a_{21}=-2.908512231\) \(a_{22}=+0.997129303\) \(a_{23}=+0.804289575\) \(a_{24}=+0.532792305\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.103754241\) \(a_{27}=-0.408298572\) \(a_{28}=+0.965023661\) \(a_{29}=+0.294872404\) \(a_{30}=-0.476543925\)
\(a_{31}=+0.033485360\) \(a_{32}=-0.176776695\) \(a_{33}=+2.125051277\) \(a_{34}=-0.374899610\) \(a_{35}=-0.863143402\)
\(a_{36}=+0.635470561\) \(a_{37}=+0.006953908\) \(a_{38}=+0.241662102\) \(a_{39}=+2.352287064\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.535008350\) \(a_{42}=+2.056628722\) \(a_{43}=-1.288619750\) \(a_{44}=-0.705076892\) \(a_{45}=-0.568382148\)
\(a_{46}=-0.568718613\) \(a_{47}=-0.298751568\) \(a_{48}=-0.376741052\) \(a_{49}=+2.725082663\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.798974510\) \(a_{52}=-0.780472108\) \(a_{53}=+1.266966395\) \(a_{54}=+0.288710689\) \(a_{55}=+0.630639944\)
\(a_{56}=-0.682374775\) \(a_{57}=+0.515022834\) \(a_{58}=-0.208506277\) \(a_{59}=+0.614795901\) \(a_{60}=+0.336967441\)
\(a_{61}=-0.145222761\) \(a_{62}=-0.023677725\) \(a_{63}=+2.452976507\) \(a_{64}=+0.125000000\) \(a_{65}=+0.698075476\)
\(a_{66}=-1.502638169\) \(a_{67}=-1.096359254\) \(a_{68}=+0.265094057\) \(a_{69}=-1.212035602\) \(a_{70}=+0.610334553\)
\(a_{71}=+1.798019012\) \(a_{72}=-0.449345543\) \(a_{73}=+0.704756093\) \(a_{74}=-0.004917156\) \(a_{75}=-0.301392841\)
\(a_{76}=-0.170880911\) \(a_{77}=-2.721663532\) \(a_{78}=-1.663318134\) \(a_{79}=+0.281497940\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.655649788\) \(a_{82}=-0.378308032\) \(a_{83}=+0.597255953\) \(a_{84}=-1.454256116\) \(a_{85}=-0.237107333\)
\(a_{86}=+0.911191764\) \(a_{87}=-0.444362159\) \(a_{88}=+0.498564651\) \(a_{89}=-0.187771699\) \(a_{90}=+0.401906871\)
\(a_{91}=-3.012696204\) \(a_{92}=+0.402144788\) \(a_{93}=-0.050461239\) \(a_{94}=+0.211249260\) \(a_{95}=+0.152840534\)
\(a_{96}=+0.266396152\) \(a_{97}=-1.044445457\) \(a_{98}=-1.926924430\) \(a_{99}=-1.792222430\) \(a_{100}=+0.099975586\)

Showing 100 of 126 available coefficients

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