Properties

Level $68$
Weight $0$
Character 68.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 68 = 2^{2} \cdot 17 \)
Weight: \( 0 \)
Character: 68.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 5.50720744635 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.602225637\) \(a_{4}=+0.000000000\) \(a_{5}=+1.893152905\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.974963161\) \(a_{8}=+0.000000000\) \(a_{9}=+1.567126991\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.467074384\) \(a_{12}=+0.000000000\) \(a_{13}=-1.493479269\) \(a_{14}=+0.000000000\) \(a_{15}=-3.033258118\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.242535625\) \(a_{18}=+0.000000000\) \(a_{19}=+0.598423446\) \(a_{20}=+0.000000000\)
\(a_{21}=-1.562110972\) \(a_{22}=+0.000000000\) \(a_{23}=+0.257512198\) \(a_{24}=+0.000000000\) \(a_{25}=+2.584027921\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.908665404\) \(a_{28}=+0.000000000\) \(a_{29}=-0.037032757\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.328336645\) \(a_{32}=+0.000000000\) \(a_{33}=-2.350584188\) \(a_{34}=+0.000000000\) \(a_{35}=+1.845754341\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.066425066\) \(a_{38}=+0.000000000\) \(a_{39}=+2.392890773\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.835200983\) \(a_{42}=+0.000000000\) \(a_{43}=+0.030309030\) \(a_{44}=+0.000000000\) \(a_{45}=+2.966811015\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.341579488\) \(a_{48}=+0.000000000\) \(a_{49}=-0.049446834\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.388596796\) \(a_{52}=+0.000000000\) \(a_{53}=-0.164936414\) \(a_{54}=+0.000000000\) \(a_{55}=+2.777396131\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.958809387\) \(a_{58}=+0.000000000\) \(a_{59}=+0.236209281\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.408946362\) \(a_{62}=+0.000000000\) \(a_{63}=+1.527891086\) \(a_{64}=+0.000000000\) \(a_{65}=-2.827384616\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.018140941\) \(a_{68}=+0.000000000\) \(a_{69}=-0.412592645\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.070822715\) \(a_{72}=+0.000000000\) \(a_{73}=+1.644799819\) \(a_{74}=+0.000000000\) \(a_{75}=-4.140195781\)
\(a_{76}=+0.000000000\) \(a_{77}=+1.430343479\) \(a_{78}=+0.000000000\) \(a_{79}=-0.652475851\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.111239985\) \(a_{82}=+0.000000000\) \(a_{83}=+1.153079415\) \(a_{84}=+0.000000000\) \(a_{85}=+0.459157023\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.059334832\) \(a_{88}=+0.000000000\) \(a_{89}=+0.801211385\) \(a_{90}=+0.000000000\)
\(a_{91}=-1.456087270\) \(a_{92}=+0.000000000\) \(a_{93}=+0.526069389\) \(a_{94}=+0.000000000\) \(a_{95}=+1.132907085\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.922935325\) \(a_{98}=+0.000000000\) \(a_{99}=+2.299091864\) \(a_{100}=+0.000000000\)

Showing 100 of 676 available coefficients

Rows: Cols: