Properties

Level $20$
Weight $0$
Character 20.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 20 = 2^{2} \cdot 5 \)
Weight: \( 0 \)
Character: 20.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 9.77914502303 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.233942059\) \(a_{4}=+0.000000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.029441407\) \(a_{8}=+0.000000000\) \(a_{9}=-0.945271113\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.533893692\) \(a_{12}=+0.000000000\) \(a_{13}=-1.558913201\) \(a_{14}=+0.000000000\) \(a_{15}=+0.104622069\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.757264445\) \(a_{18}=+0.000000000\) \(a_{19}=+1.715093878\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.006887583\) \(a_{22}=+0.000000000\) \(a_{23}=+0.764638642\) \(a_{24}=+0.000000000\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.455080729\) \(a_{28}=+0.000000000\) \(a_{29}=+0.164088379\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.709363809\) \(a_{32}=+0.000000000\) \(a_{33}=+0.358842248\) \(a_{34}=+0.000000000\) \(a_{35}=-0.013166598\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.456592827\) \(a_{38}=+0.000000000\) \(a_{39}=-0.364695364\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.807712430\) \(a_{42}=+0.000000000\) \(a_{43}=-1.733417849\) \(a_{44}=+0.000000000\) \(a_{45}=-0.422738093\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.198433087\) \(a_{48}=+0.000000000\) \(a_{49}=-0.999133204\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.411098062\) \(a_{52}=+0.000000000\) \(a_{53}=+0.331224191\) \(a_{54}=+0.000000000\) \(a_{55}=+0.685978113\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.401232593\) \(a_{58}=+0.000000000\) \(a_{59}=-0.825800007\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.528755449\) \(a_{62}=+0.000000000\) \(a_{63}=+0.027830112\) \(a_{64}=+0.000000000\) \(a_{65}=-0.697167178\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.158012097\) \(a_{68}=+0.000000000\) \(a_{69}=+0.178881138\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.159738303\) \(a_{72}=+0.000000000\) \(a_{73}=-0.212288939\) \(a_{74}=+0.000000000\) \(a_{75}=+0.046788412\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.045159989\) \(a_{78}=+0.000000000\) \(a_{79}=+0.380118127\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.838808591\) \(a_{82}=+0.000000000\) \(a_{83}=+0.454882090\) \(a_{84}=+0.000000000\) \(a_{85}=-0.785872551\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.038387173\) \(a_{88}=+0.000000000\) \(a_{89}=+0.575952228\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.045896599\) \(a_{92}=+0.000000000\) \(a_{93}=-0.165950030\) \(a_{94}=+0.000000000\) \(a_{95}=+0.767013300\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.016102823\) \(a_{98}=+0.000000000\) \(a_{99}=-1.449945397\) \(a_{100}=+0.000000000\)

Showing 100 of 276 available coefficients

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