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: \( 9.93491995937 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.754396240\) \(a_{4}=+0.000000000\) \(a_{5}=-0.281387201\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.812409783\) \(a_{8}=+0.000000000\) \(a_{9}=+2.077906167\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.272302498\) \(a_{12}=+0.000000000\) \(a_{13}=+1.336836627\) \(a_{14}=+0.000000000\) \(a_{15}=-0.493664648\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.063944843\) \(a_{18}=+0.000000000\) \(a_{19}=-0.347938010\) \(a_{20}=+0.000000000\)
\(a_{21}=+1.425288668\) \(a_{22}=+0.000000000\) \(a_{23}=-1.148348886\) \(a_{24}=+0.000000000\) \(a_{25}=-0.920821243\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.891074527\) \(a_{28}=+0.000000000\) \(a_{29}=-0.733438403\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.233948736\) \(a_{32}=+0.000000000\) \(a_{33}=-0.477726478\) \(a_{34}=+0.000000000\) \(a_{35}=-0.228601715\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.525783700\) \(a_{38}=+0.000000000\) \(a_{39}=+2.345341153\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.676058894\) \(a_{42}=+0.000000000\) \(a_{43}=-1.254671764\) \(a_{44}=+0.000000000\) \(a_{45}=-0.584696201\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.389521320\) \(a_{48}=+0.000000000\) \(a_{49}=-0.339990345\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.112184592\) \(a_{52}=+0.000000000\) \(a_{53}=+0.586882831\) \(a_{54}=+0.000000000\) \(a_{55}=+0.076622438\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.610421138\) \(a_{58}=+0.000000000\) \(a_{59}=-1.877581756\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.920779265\) \(a_{62}=+0.000000000\) \(a_{63}=+1.688111305\) \(a_{64}=+0.000000000\) \(a_{65}=-0.376168727\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.000829906\) \(a_{68}=+0.000000000\) \(a_{69}=-2.014658967\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.186404239\) \(a_{72}=+0.000000000\) \(a_{73}=+1.526275122\) \(a_{74}=+0.000000000\) \(a_{75}=-1.615485327\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.221221213\) \(a_{78}=+0.000000000\) \(a_{79}=+0.566136416\) \(a_{80}=+0.000000000\)
\(a_{81}=+1.239787873\) \(a_{82}=+0.000000000\) \(a_{83}=+0.585056522\) \(a_{84}=+0.000000000\) \(a_{85}=-0.017993260\)
\(a_{86}=+0.000000000\) \(a_{87}=-1.286741576\) \(a_{88}=+0.000000000\) \(a_{89}=-1.840195630\) \(a_{90}=+0.000000000\)
\(a_{91}=+1.086059154\) \(a_{92}=+0.000000000\) \(a_{93}=+0.410438783\) \(a_{94}=+0.000000000\) \(a_{95}=+0.097905303\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.872100272\) \(a_{98}=+0.000000000\) \(a_{99}=-0.565819038\) \(a_{100}=+0.000000000\)

Showing 100 of 5000 available coefficients

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