Properties

Level $12$
Weight $0$
Character 12.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more about

Maass form invariants

Level: \( 12 = 2^{2} \cdot 3 \)
Weight: \( 0 \)
Character: 12.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 4.9342604018 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=+0.633925451\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.525016755\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.381805546\) \(a_{12}=+0.000000000\) \(a_{13}=-1.133042417\) \(a_{14}=+0.000000000\) \(a_{15}=+0.365997030\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.717475778\) \(a_{18}=+0.000000000\) \(a_{19}=-1.026981521\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.880468832\) \(a_{22}=+0.000000000\) \(a_{23}=-1.275929375\) \(a_{24}=+0.000000000\) \(a_{25}=-0.598138519\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=+0.905417557\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.247477763\) \(a_{32}=+0.000000000\) \(a_{33}=+0.220435534\) \(a_{34}=+0.000000000\) \(a_{35}=+0.966746935\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.182544497\) \(a_{38}=+0.000000000\) \(a_{39}=-0.654162346\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.077389865\) \(a_{42}=+0.000000000\) \(a_{43}=-1.215828246\) \(a_{44}=+0.000000000\) \(a_{45}=+0.211308488\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.932392741\) \(a_{48}=+0.000000000\) \(a_{49}=+1.325676116\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.991585103\) \(a_{52}=+0.000000000\) \(a_{53}=+0.339930516\) \(a_{54}=+0.000000000\) \(a_{55}=+0.242036257\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.592928064\) \(a_{58}=+0.000000000\) \(a_{59}=-0.300658792\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.165546519\) \(a_{62}=+0.000000000\) \(a_{63}=+0.508338927\) \(a_{64}=+0.000000000\) \(a_{65}=-0.718264429\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.417937143\) \(a_{68}=+0.000000000\) \(a_{69}=-0.736658162\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.508816279\) \(a_{72}=+0.000000000\) \(a_{73}=-0.065620347\) \(a_{74}=+0.000000000\) \(a_{75}=-0.345335446\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.582259866\) \(a_{78}=+0.000000000\) \(a_{79}=+0.509716979\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111112\) \(a_{82}=+0.000000000\) \(a_{83}=+0.421709869\) \(a_{84}=+0.000000000\) \(a_{85}=+1.088751593\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.522743048\) \(a_{88}=+0.000000000\) \(a_{89}=-1.185851092\) \(a_{90}=+0.000000000\)
\(a_{91}=-1.727908666\) \(a_{92}=+0.000000000\) \(a_{93}=-0.142881382\) \(a_{94}=+0.000000000\) \(a_{95}=-0.651029715\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.722275906\) \(a_{98}=+0.000000000\) \(a_{99}=+0.127268502\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

Rows: Cols: