Properties

Level $14$
Weight $0$
Character 14.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 14 = 2 \cdot 7 \)
Weight: \( 0 \)
Character: 14.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.84665998673 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.138295004\) \(a_{4}=+0.500000000\) \(a_{5}=+0.296620585\)
\(a_{6}=+0.097789335\) \(a_{7}=+0.377964473\) \(a_{8}=+0.353553391\) \(a_{9}=-0.980874492\) \(a_{10}=+0.209742427\)
\(a_{11}=-1.077010646\) \(a_{12}=+0.069147502\) \(a_{13}=+0.541316643\) \(a_{14}=+0.267261242\) \(a_{15}=+0.041021145\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.929771505\) \(a_{18}=-0.693583005\) \(a_{19}=-0.952601234\) \(a_{20}=+0.148310293\)
\(a_{21}=+0.052270598\) \(a_{22}=-0.761561532\) \(a_{23}=-0.412436491\) \(a_{24}=+0.048894667\) \(a_{25}=-0.912016228\)
\(a_{26}=+0.382768669\) \(a_{27}=-0.273945045\) \(a_{28}=+0.188982237\) \(a_{29}=+1.632193110\) \(a_{30}=+0.029006330\)
\(a_{31}=-0.378071536\) \(a_{32}=+0.176776695\) \(a_{33}=-0.148945191\) \(a_{34}=+1.364554517\) \(a_{35}=+0.112112043\)
\(a_{36}=-0.490437246\) \(a_{37}=-0.693722579\) \(a_{38}=-0.673590793\) \(a_{39}=+0.074861387\) \(a_{40}=+0.104871214\)
\(a_{41}=-0.135343518\) \(a_{42}=+0.036960894\) \(a_{43}=+0.934674841\) \(a_{44}=-0.538505323\) \(a_{45}=-0.290947566\)
\(a_{46}=-0.291636640\) \(a_{47}=-0.520367400\) \(a_{48}=+0.034573751\) \(a_{49}=+0.142857143\) \(a_{50}=-0.644892860\)
\(a_{51}=+0.266877758\) \(a_{52}=+0.270658322\) \(a_{53}=+0.590399608\) \(a_{54}=-0.193708399\) \(a_{55}=-0.319463528\)
\(a_{56}=+0.133630621\) \(a_{57}=-0.131739991\) \(a_{58}=+1.154134817\) \(a_{59}=+1.441333089\) \(a_{60}=+0.020510572\)
\(a_{61}=-0.356061560\) \(a_{62}=-0.267336947\) \(a_{63}=-0.370735710\) \(a_{64}=+0.125000000\) \(a_{65}=+0.160565660\)
\(a_{66}=-0.105320155\) \(a_{67}=-1.330745080\) \(a_{68}=+0.964885752\) \(a_{69}=-0.057037906\) \(a_{70}=+0.079275186\)
\(a_{71}=-1.153382900\) \(a_{72}=-0.346791502\) \(a_{73}=+0.423784110\) \(a_{74}=-0.490535940\) \(a_{75}=-0.126127288\)
\(a_{76}=-0.476300617\) \(a_{77}=-0.407071761\) \(a_{78}=+0.052934995\) \(a_{79}=-0.655569920\) \(a_{80}=+0.074155146\)
\(a_{81}=+0.942989261\) \(a_{82}=-0.095702320\) \(a_{83}=+1.165629700\) \(a_{84}=+0.026135299\) \(a_{85}=+0.572409953\)
\(a_{86}=+0.660914918\) \(a_{87}=+0.225724152\) \(a_{88}=-0.380780766\) \(a_{89}=+1.131843000\) \(a_{90}=-0.205730997\)
\(a_{91}=+0.204598460\) \(a_{92}=-0.206218246\) \(a_{93}=-0.052285405\) \(a_{94}=-0.367955317\) \(a_{95}=-0.282561136\)
\(a_{96}=+0.024447334\) \(a_{97}=-0.455698000\) \(a_{98}=+0.101015254\) \(a_{99}=+1.056412271\) \(a_{100}=-0.456008114\)

Showing 100 of 166 available coefficients

Rows: Cols: