Properties

Level $6$
Weight $0$
Character 6.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.3088170303 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+0.800706300\)
\(a_{6}=-0.408248290\) \(a_{7}=-1.154488668\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.566184854\)
\(a_{11}=+0.161405162\) \(a_{12}=-0.288675135\) \(a_{13}=+0.118716280\) \(a_{14}=-0.816346766\) \(a_{15}=-0.462287998\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.745130432\) \(a_{18}=+0.235702259\) \(a_{19}=-0.660625376\) \(a_{20}=+0.400353153\)
\(a_{21}=+0.666544343\) \(a_{22}=+0.114130684\) \(a_{23}=-0.729119237\) \(a_{24}=-0.204124145\) \(a_{25}=-0.358869422\)
\(a_{26}=+0.083945087\) \(a_{27}=-0.192450090\) \(a_{28}=-0.577244334\) \(a_{29}=+0.425333511\) \(a_{30}=-0.326886978\)
\(a_{31}=+1.927383441\) \(a_{32}=+0.176776695\) \(a_{33}=-0.093187314\) \(a_{34}=+0.526886780\) \(a_{35}=-0.924406349\)
\(a_{36}=+0.166666667\) \(a_{37}=-1.652686184\) \(a_{38}=-0.467132678\) \(a_{39}=-0.068540876\) \(a_{40}=+0.283092427\)
\(a_{41}=+0.884721620\) \(a_{42}=+0.471318025\) \(a_{43}=-0.317464275\) \(a_{44}=+0.080702581\) \(a_{45}=+0.266902099\)
\(a_{46}=-0.515565156\) \(a_{47}=+1.049645355\) \(a_{48}=-0.144337569\) \(a_{49}=+0.332844097\) \(a_{50}=-0.253759000\)
\(a_{51}=-0.430201225\) \(a_{52}=+0.059358134\) \(a_{53}=-0.660150813\) \(a_{54}=-0.136082890\) \(a_{55}=+0.129238380\)
\(a_{56}=-0.408173343\) \(a_{57}=+0.381413290\) \(a_{58}=+0.300755381\) \(a_{59}=-1.394457421\) \(a_{60}=-0.231145561\)
\(a_{61}=+1.027285173\) \(a_{62}=+1.362872472\) \(a_{63}=-0.384860739\) \(a_{64}=+0.125000000\) \(a_{65}=+0.095056873\)
\(a_{66}=-0.065893382\) \(a_{67}=-0.109939639\) \(a_{68}=+0.372565215\) \(a_{69}=+0.420957187\) \(a_{70}=-0.653653999\)
\(a_{71}=+0.873450447\) \(a_{72}=+0.117851132\) \(a_{73}=-1.644096052\) \(a_{74}=-1.168625611\) \(a_{75}=+0.207193365\)
\(a_{76}=-0.330312684\) \(a_{77}=-0.186340418\) \(a_{78}=-0.048465725\) \(a_{79}=+0.505259174\) \(a_{80}=+0.200176561\)
\(a_{81}=+0.111111092\) \(a_{82}=+0.625592720\) \(a_{83}=+0.842732439\) \(a_{84}=+0.333272237\) \(a_{85}=+0.596630835\)
\(a_{86}=-0.224480794\) \(a_{87}=-0.245566469\) \(a_{88}=+0.057065848\) \(a_{89}=-0.472396723\) \(a_{90}=+0.188728469\)
\(a_{91}=-0.137053675\) \(a_{92}=-0.364558904\) \(a_{93}=-1.112772687\) \(a_{94}=+0.742214969\) \(a_{95}=-0.528977065\)
\(a_{96}=-0.102062744\) \(a_{97}=-0.624756957\) \(a_{98}=+0.235350588\) \(a_{99}=+0.053816937\) \(a_{100}=-0.179455121\)

Showing 100 of 1000 available coefficients

Rows: Cols: