Properties

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

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 29.3175625852 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+1.327606301\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.938759418\) \(a_{7}=+0.372929500\) \(a_{8}=+0.353553391\) \(a_{9}=+0.762538490\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.582219113\) \(a_{12}=+0.663803150\) \(a_{13}=-0.887836634\) \(a_{14}=+0.263700978\) \(a_{15}=-0.593723587\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.515691115\) \(a_{18}=+0.539196137\) \(a_{19}=+0.303805543\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.495103554\) \(a_{22}=+1.118797864\) \(a_{23}=+0.147493213\) \(a_{24}=+0.469379709\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.627795304\) \(a_{27}=-0.315255397\) \(a_{28}=+0.186464750\) \(a_{29}=+1.559085254\) \(a_{30}=-0.419825975\)
\(a_{31}=+0.297822595\) \(a_{32}=+0.176776695\) \(a_{33}=+2.100564064\) \(a_{34}=+0.364648684\) \(a_{35}=-0.166779143\)
\(a_{36}=+0.381269245\) \(a_{37}=-1.065625269\) \(a_{38}=+0.214822959\) \(a_{39}=-1.178697509\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.548580227\) \(a_{42}=+0.350091080\) \(a_{43}=+0.165825959\) \(a_{44}=+0.791109556\) \(a_{45}=-0.341017580\)
\(a_{46}=+0.104293451\) \(a_{47}=+0.383392167\) \(a_{48}=+0.331901575\) \(a_{49}=-0.860923588\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.684634773\) \(a_{52}=-0.443918317\) \(a_{53}=-1.402670907\) \(a_{54}=-0.222919229\) \(a_{55}=-0.707589898\)
\(a_{56}=+0.131850489\) \(a_{57}=+0.403334153\) \(a_{58}=+1.102439755\) \(a_{59}=+1.888688207\) \(a_{60}=-0.296861794\)
\(a_{61}=-0.594906503\) \(a_{62}=+0.210592376\) \(a_{63}=+0.284373098\) \(a_{64}=+0.125000000\) \(a_{65}=+0.397052613\)
\(a_{66}=+1.485323094\) \(a_{67}=+0.784948548\) \(a_{68}=+0.257845557\) \(a_{69}=+0.195812919\) \(a_{70}=-0.117930663\)
\(a_{71}=+1.454793477\) \(a_{72}=+0.269598069\) \(a_{73}=+1.320018968\) \(a_{74}=-0.753510854\) \(a_{75}=+0.265521260\)
\(a_{76}=+0.151902771\) \(a_{77}=+0.590056183\) \(a_{78}=-0.833465002\) \(a_{79}=+0.035454724\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.181073541\) \(a_{82}=+0.387904798\) \(a_{83}=-1.461679309\) \(a_{84}=+0.247551777\) \(a_{85}=-0.230624078\)
\(a_{86}=+0.117256660\) \(a_{87}=+2.069851407\) \(a_{88}=+0.559398932\) \(a_{89}=+0.389809152\) \(a_{90}=-0.241135843\)
\(a_{91}=-0.331100472\) \(a_{92}=+0.073746607\) \(a_{93}=+0.395391153\) \(a_{94}=+0.271099201\) \(a_{95}=-0.135865969\)
\(a_{96}=+0.234689855\) \(a_{97}=+1.347473042\) \(a_{98}=-0.608764907\) \(a_{99}=+1.206502973\) \(a_{100}=+0.099975586\)

Showing 100 of 246 available coefficients

Rows: Cols: