Properties

Level $28$
Weight $0$
Character 28.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 28 = 2^{2} \cdot 7 \)
Weight: \( 0 \)
Character: 28.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 6.50819078502 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.309280937\) \(a_{4}=+0.000000000\) \(a_{5}=+1.893177648\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.377964473\) \(a_{8}=+0.000000000\) \(a_{9}=-0.904345302\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.502265443\) \(a_{12}=+0.000000000\) \(a_{13}=-0.510094714\) \(a_{14}=+0.000000000\) \(a_{15}=-0.585523757\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.794418137\) \(a_{18}=+0.000000000\) \(a_{19}=+0.561023275\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.116897206\) \(a_{22}=+0.000000000\) \(a_{23}=+0.031061219\) \(a_{24}=+0.000000000\) \(a_{25}=+2.584121607\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.588977700\) \(a_{28}=+0.000000000\) \(a_{29}=+1.810249007\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.450342727\) \(a_{32}=+0.000000000\) \(a_{33}=-0.155341127\) \(a_{34}=+0.000000000\) \(a_{35}=+0.715553892\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.475528944\) \(a_{38}=+0.000000000\) \(a_{39}=+0.157762571\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.864248245\) \(a_{42}=+0.000000000\) \(a_{43}=+0.512010045\) \(a_{44}=+0.000000000\) \(a_{45}=-1.712086311\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.020995331\) \(a_{48}=+0.000000000\) \(a_{49}=+0.142857143\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.245698386\) \(a_{52}=+0.000000000\) \(a_{53}=+1.810041176\) \(a_{54}=+0.000000000\) \(a_{55}=+0.950877710\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.173513804\) \(a_{58}=+0.000000000\) \(a_{59}=-0.540774226\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.463688886\) \(a_{62}=+0.000000000\) \(a_{63}=-0.341810395\) \(a_{64}=+0.000000000\) \(a_{65}=-0.965699911\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.702238275\) \(a_{68}=+0.000000000\) \(a_{69}=-0.009606643\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.548246312\) \(a_{72}=+0.000000000\) \(a_{73}=+0.894578704\) \(a_{74}=+0.000000000\) \(a_{75}=-0.799219552\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.189838493\) \(a_{78}=+0.000000000\) \(a_{79}=-0.126635314\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.722185727\) \(a_{82}=+0.000000000\) \(a_{83}=-1.338770431\) \(a_{84}=+0.000000000\) \(a_{85}=+1.503974660\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.559875510\) \(a_{88}=+0.000000000\) \(a_{89}=+1.226047235\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.192797680\) \(a_{92}=+0.000000000\) \(a_{93}=+0.448563358\) \(a_{94}=+0.000000000\) \(a_{95}=+1.062116724\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.717003003\) \(a_{98}=+0.000000000\) \(a_{99}=-0.454221393\) \(a_{100}=+0.000000000\)

Showing 100 of 270 available coefficients

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