Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 28.0986176195 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.570497087\) \(a_{3}=+0.577350269\) \(a_{4}=-0.674533074\) \(a_{5}=+0.566001850\)
\(a_{6}=-0.329376647\) \(a_{7}=+1.680480975\) \(a_{8}=+0.955316241\) \(a_{9}=+0.333333333\) \(a_{10}=-0.322902407\)
\(a_{11}=+1.634702325\) \(a_{12}=-0.389441852\) \(a_{13}=-0.275258704\) \(a_{14}=-0.958709501\) \(a_{15}=+0.326781321\)
\(a_{16}=+0.129527941\) \(a_{17}=-0.723307980\) \(a_{18}=-0.190165696\) \(a_{19}=+1.838982741\) \(a_{20}=-0.381786968\)
\(a_{21}=+0.970226143\) \(a_{22}=-0.932592914\) \(a_{23}=+0.396136036\) \(a_{24}=+0.551552089\) \(a_{25}=-0.679641906\)
\(a_{26}=+0.157034289\) \(a_{27}=+0.192450090\) \(a_{28}=-1.133539997\) \(a_{29}=-0.531661477\) \(a_{30}=-0.186427791\)
\(a_{31}=-0.652570870\) \(a_{32}=-1.029211554\) \(a_{33}=+0.943795827\) \(a_{34}=+0.412645095\) \(a_{35}=+0.951155341\)
\(a_{36}=-0.224844358\) \(a_{37}=+0.431369541\) \(a_{38}=-1.049134297\) \(a_{39}=-0.158920687\) \(a_{40}=+0.540710760\)
\(a_{41}=-0.511152111\) \(a_{42}=-0.553511188\) \(a_{43}=-0.535623668\) \(a_{44}=-1.102660784\) \(a_{45}=+0.188667283\)
\(a_{46}=-0.225994455\) \(a_{47}=+0.141790589\) \(a_{48}=+0.074782992\) \(a_{49}=+1.824016307\) \(a_{50}=+0.387733727\)
\(a_{51}=-0.417602057\) \(a_{52}=+0.185671100\) \(a_{53}=+1.079759814\) \(a_{54}=-0.109792216\) \(a_{55}=+0.925244540\)
\(a_{56}=+1.605390767\) \(a_{57}=+1.061737181\) \(a_{58}=+0.303311324\) \(a_{59}=-0.247893328\) \(a_{60}=-0.220424809\)
\(a_{61}=+0.727044171\) \(a_{62}=+0.372289780\) \(a_{63}=+0.560160325\) \(a_{64}=+0.457634252\) \(a_{65}=-0.155796936\)
\(a_{66}=-0.538432770\) \(a_{67}=+1.326655424\) \(a_{68}=+0.487895155\) \(a_{69}=+0.228709247\) \(a_{70}=-0.542631351\)
\(a_{71}=-0.645386580\) \(a_{72}=+0.318438747\) \(a_{73}=+0.532631970\) \(a_{74}=-0.246095066\) \(a_{75}=-0.392391437\)
\(a_{76}=-1.240454681\) \(a_{77}=+2.747086156\) \(a_{78}=+0.090663789\) \(a_{79}=-0.707339535\) \(a_{80}=+0.073313055\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.291610790\) \(a_{83}=-0.773529649\) \(a_{84}=-0.654449623\) \(a_{85}=-0.409393655\)
\(a_{86}=+0.305571742\) \(a_{87}=-0.306954897\) \(a_{88}=+1.561657679\) \(a_{89}=+0.652140427\) \(a_{90}=-0.107634136\)
\(a_{91}=-0.462567016\) \(a_{92}=-0.267206858\) \(a_{93}=-0.376761967\) \(a_{94}=-0.080891118\) \(a_{95}=+1.040867634\)
\(a_{96}=-0.594215568\) \(a_{97}=-0.780606995\) \(a_{98}=-1.040595989\) \(a_{99}=+0.544900775\) \(a_{100}=+0.458440944\)

Showing 100 of 1228 available coefficients

Rows: Cols: