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: \( 22.5940390606 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.108560538\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.783870674\) \(a_{7}=+0.146344008\) \(a_{8}=+0.353553391\) \(a_{9}=+0.228906466\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.163325355\) \(a_{12}=-0.554280269\) \(a_{13}=+1.460541175\) \(a_{14}=+0.103480840\) \(a_{15}=-0.495763344\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.412258101\) \(a_{18}=+0.161861315\) \(a_{19}=-0.867925669\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.162231192\) \(a_{22}=-0.822595247\) \(a_{23}=+0.067876917\) \(a_{24}=-0.391935337\) \(a_{25}=+0.199951172\)
\(a_{26}=+1.032758569\) \(a_{27}=+0.854803863\) \(a_{28}=+0.073172004\) \(a_{29}=-0.226359995\) \(a_{30}=-0.350557622\)
\(a_{31}=+0.354441808\) \(a_{32}=+0.176776695\) \(a_{33}=+1.289616581\) \(a_{34}=+0.291510499\) \(a_{35}=+0.065447030\)
\(a_{36}=+0.114453233\) \(a_{37}=-0.934614163\) \(a_{38}=-0.613716126\) \(a_{39}=-1.619098311\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.777528834\) \(a_{42}=-0.114714776\) \(a_{43}=-1.098872265\) \(a_{44}=-0.581662677\) \(a_{45}=+0.102370084\)
\(a_{46}=+0.047996228\) \(a_{47}=+1.279926779\) \(a_{48}=-0.277140134\) \(a_{49}=-0.978583431\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.457013062\) \(a_{52}=+0.730270588\) \(a_{53}=-0.085583841\) \(a_{54}=+0.604437608\) \(a_{55}=-0.520254915\)
\(a_{56}=+0.051740420\) \(a_{57}=+0.962148147\) \(a_{58}=-0.160060687\) \(a_{59}=+0.914746393\) \(a_{60}=-0.247881672\)
\(a_{61}=-1.495643380\) \(a_{62}=+0.250628206\) \(a_{63}=+0.033499090\) \(a_{64}=+0.125000000\) \(a_{65}=+0.653173870\)
\(a_{66}=+0.911896630\) \(a_{67}=+1.370838337\) \(a_{68}=+0.206129051\) \(a_{69}=-0.075245671\) \(a_{70}=+0.046278039\)
\(a_{71}=+1.566947160\) \(a_{72}=+0.080930657\) \(a_{73}=+0.620681931\) \(a_{74}=-0.660872012\) \(a_{75}=-0.221712108\)
\(a_{76}=-0.433962835\) \(a_{77}=-0.170245694\) \(a_{78}=-1.144875395\) \(a_{79}=+1.403788311\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.176508296\) \(a_{82}=-0.549795911\) \(a_{83}=+0.778414701\) \(a_{84}=-0.081115596\) \(a_{85}=+0.184367428\)
\(a_{86}=-0.777020030\) \(a_{87}=+0.250933757\) \(a_{88}=-0.411297624\) \(a_{89}=-1.851460792\) \(a_{90}=+0.072386580\)
\(a_{91}=+0.213741449\) \(a_{92}=+0.033938458\) \(a_{93}=-0.392920202\) \(a_{94}=+0.905044905\) \(a_{95}=-0.388148159\)
\(a_{96}=-0.195967668\) \(a_{97}=+1.429835411\) \(a_{98}=-0.691962980\) \(a_{99}=-0.266292696\) \(a_{100}=+0.099975586\)

Showing 100 of 198 available coefficients

Rows: Cols: