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: \( 8.52250301688 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.922038550\) \(a_{4}=+0.000000000\) \(a_{5}=+0.863687734\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.802463187\) \(a_{8}=+0.000000000\) \(a_{9}=-0.149844913\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.636857974\) \(a_{12}=+0.000000000\) \(a_{13}=+0.177284955\) \(a_{14}=+0.000000000\) \(a_{15}=-0.796353385\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.461795306\) \(a_{18}=+0.000000000\) \(a_{19}=+0.992943361\) \(a_{20}=+0.000000000\)
\(a_{21}=-1.661940543\) \(a_{22}=+0.000000000\) \(a_{23}=+0.687278105\) \(a_{24}=+0.000000000\) \(a_{25}=-0.254043499\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.060201336\) \(a_{28}=+0.000000000\) \(a_{29}=-0.482551874\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.707065620\) \(a_{32}=+0.000000000\) \(a_{33}=-0.587207603\) \(a_{34}=+0.000000000\) \(a_{35}=+1.556765345\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.065227891\) \(a_{38}=+0.000000000\) \(a_{39}=-0.163463563\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.917470526\) \(a_{42}=+0.000000000\) \(a_{43}=+0.196330964\) \(a_{44}=+0.000000000\) \(a_{45}=-0.129419213\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.390820763\) \(a_{48}=+0.000000000\) \(a_{49}=+2.248873542\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.425793075\) \(a_{52}=+0.000000000\) \(a_{53}=-1.709251503\) \(a_{54}=+0.000000000\) \(a_{55}=+0.550046421\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.915532060\) \(a_{58}=+0.000000000\) \(a_{59}=+0.675841869\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.969414144\) \(a_{62}=+0.000000000\) \(a_{63}=-0.270089933\) \(a_{64}=+0.000000000\) \(a_{65}=+0.153118841\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.287771500\) \(a_{68}=+0.000000000\) \(a_{69}=-0.633696907\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.364834963\) \(a_{72}=+0.000000000\) \(a_{73}=+0.318935096\) \(a_{74}=+0.000000000\) \(a_{75}=+0.234237899\)
\(a_{76}=+0.000000000\) \(a_{77}=+1.147913054\) \(a_{78}=+0.000000000\) \(a_{79}=+1.025595727\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.827701589\) \(a_{82}=+0.000000000\) \(a_{83}=-1.022048332\) \(a_{84}=+0.000000000\) \(a_{85}=+0.398846942\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.444931430\) \(a_{88}=+0.000000000\) \(a_{89}=-1.846060134\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.319549605\) \(a_{92}=+0.000000000\) \(a_{93}=+0.651941759\) \(a_{94}=+0.000000000\) \(a_{95}=+0.857593004\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.181106932\) \(a_{98}=+0.000000000\) \(a_{99}=-0.095429930\) \(a_{100}=+0.000000000\)

Showing 100 of 5000 available coefficients

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