Properties

Level $4$
Weight $0$
Character 4.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 4 = 2^{2} \)
Weight: \( 0 \)
Character: 4.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 6.62042287384 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.210250902\) \(a_{4}=+0.000000000\) \(a_{5}=+1.288528291\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.351110602\) \(a_{8}=+0.000000000\) \(a_{9}=+0.464707245\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.217644514\) \(a_{12}=+0.000000000\) \(a_{13}=-1.229189153\) \(a_{14}=+0.000000000\) \(a_{15}=+1.559442529\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.570261412\) \(a_{18}=+0.000000000\) \(a_{19}=-0.259179901\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.424931923\) \(a_{22}=+0.000000000\) \(a_{23}=+0.729976799\) \(a_{24}=+0.000000000\) \(a_{25}=+0.660305156\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.647838539\) \(a_{28}=+0.000000000\) \(a_{29}=-1.476441379\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.467636191\) \(a_{32}=+0.000000000\) \(a_{33}=+0.263404469\) \(a_{34}=+0.000000000\) \(a_{35}=-0.452415944\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.059884629\) \(a_{38}=+0.000000000\) \(a_{39}=-1.487627281\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.770721338\) \(a_{42}=+0.000000000\) \(a_{43}=+1.051167445\) \(a_{44}=+0.000000000\) \(a_{45}=+0.598788433\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.695126775\) \(a_{48}=+0.000000000\) \(a_{49}=-0.876721345\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.690159342\) \(a_{52}=+0.000000000\) \(a_{53}=-0.069271608\) \(a_{54}=+0.000000000\) \(a_{55}=+0.280441117\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.313672713\) \(a_{58}=+0.000000000\) \(a_{59}=+0.143036046\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.912999699\) \(a_{62}=+0.000000000\) \(a_{63}=-0.163163641\) \(a_{64}=+0.000000000\) \(a_{65}=-1.583844998\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.115132652\) \(a_{68}=+0.000000000\) \(a_{69}=+0.883455080\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.203760868\) \(a_{72}=+0.000000000\) \(a_{73}=-0.030113499\) \(a_{74}=+0.000000000\) \(a_{75}=+0.799134911\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.076417296\) \(a_{78}=+0.000000000\) \(a_{79}=+0.761449256\) \(a_{80}=+0.000000000\)
\(a_{81}=-1.248754421\) \(a_{82}=+0.000000000\) \(a_{83}=+0.461600923\) \(a_{84}=+0.000000000\) \(a_{85}=-0.734797912\)
\(a_{86}=+0.000000000\) \(a_{87}=-1.786864508\) \(a_{88}=+0.000000000\) \(a_{89}=+1.485172183\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.431581345\) \(a_{92}=+0.000000000\) \(a_{93}=+1.776208015\) \(a_{94}=+0.000000000\) \(a_{95}=-0.333960633\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.212839283\) \(a_{98}=+0.000000000\) \(a_{99}=+0.101140959\) \(a_{100}=+0.000000000\)

Showing 100 of 5000 available coefficients

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