Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 21.2395974784 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.674305845\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.183913017\) \(a_{7}=-1.689117430\) \(a_{8}=+0.353553391\) \(a_{9}=+1.803300064\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.248361620\) \(a_{12}=-0.837152923\) \(a_{13}=+1.378748743\) \(a_{14}=-1.194386389\) \(a_{15}=+0.748772337\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.214302494\) \(a_{18}=+1.275125704\) \(a_{19}=+0.370205175\) \(a_{20}=-0.223606798\)
\(a_{21}=+2.828099187\) \(a_{22}=-0.882724967\) \(a_{23}=-0.815952324\) \(a_{24}=-0.591956509\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.974922586\) \(a_{27}=-1.344969993\) \(a_{28}=-0.844558715\) \(a_{29}=-0.738262302\) \(a_{30}=+0.529461997\)
\(a_{31}=+0.265722619\) \(a_{32}=+0.176776695\) \(a_{33}=+2.090139157\) \(a_{34}=+0.858641528\) \(a_{35}=+0.755396279\)
\(a_{36}=+0.901650032\) \(a_{37}=+1.295824087\) \(a_{38}=+0.261774590\) \(a_{39}=-2.308447079\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.582600279\) \(a_{42}=+1.999768113\) \(a_{43}=+0.189487142\) \(a_{44}=-0.624180810\) \(a_{45}=-0.806460305\)
\(a_{46}=-0.576965421\) \(a_{47}=+0.351340974\) \(a_{48}=-0.418576461\) \(a_{49}=+1.853117693\) \(a_{50}=+0.141421356\)
\(a_{51}=-2.033113764\) \(a_{52}=+0.689374371\) \(a_{53}=-0.413492270\) \(a_{54}=-0.951037402\) \(a_{55}=+0.558284288\)
\(a_{56}=-0.597193195\) \(a_{57}=-0.619836689\) \(a_{58}=-0.522030280\) \(a_{59}=+0.601409483\) \(a_{60}=+0.374386169\)
\(a_{61}=-1.018484606\) \(a_{62}=+0.187894266\) \(a_{63}=-3.045985570\) \(a_{64}=+0.125000000\) \(a_{65}=-0.616595183\)
\(a_{66}=+1.477951572\) \(a_{67}=-0.819264025\) \(a_{68}=+0.607151247\) \(a_{69}=+1.366153745\) \(a_{70}=+0.534145832\)
\(a_{71}=+0.337844842\) \(a_{72}=+0.637562852\) \(a_{73}=-0.886938752\) \(a_{74}=+0.916285999\) \(a_{75}=-0.334861169\)
\(a_{76}=+0.185102588\) \(a_{77}=+2.108629371\) \(a_{78}=-1.632318584\) \(a_{79}=-1.370757571\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.448591057\) \(a_{82}=+1.119067389\) \(a_{83}=-0.708454990\) \(a_{84}=+1.414049593\) \(a_{85}=-0.543052585\)
\(a_{86}=+0.133987643\) \(a_{87}=+1.236076887\) \(a_{88}=-0.441362483\) \(a_{89}=+0.191741516\) \(a_{90}=-0.570253551\)
\(a_{91}=-2.328868533\) \(a_{92}=-0.407976162\) \(a_{93}=-0.444900935\) \(a_{94}=+0.248435585\) \(a_{95}=-0.165560787\)
\(a_{96}=-0.295978254\) \(a_{97}=-0.725378183\) \(a_{98}=+1.310352087\) \(a_{99}=-2.251170589\) \(a_{100}=+0.099975586\)

Showing 100 of 198 available coefficients

Rows: Cols: