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: \( 11.972776694 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.634119476\) \(a_{4}=+0.000000000\) \(a_{5}=+0.998786365\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.456457343\) \(a_{8}=+0.000000000\) \(a_{9}=-0.597892490\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.882033978\) \(a_{12}=+0.000000000\) \(a_{13}=+1.038889191\) \(a_{14}=+0.000000000\) \(a_{15}=+0.633349886\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.265715162\) \(a_{18}=+0.000000000\) \(a_{19}=-0.484171655\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.289448490\) \(a_{22}=+0.000000000\) \(a_{23}=+1.037859598\) \(a_{24}=+0.000000000\) \(a_{25}=-0.002425798\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.013254749\) \(a_{28}=+0.000000000\) \(a_{29}=+0.534335230\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.291167511\) \(a_{32}=+0.000000000\) \(a_{33}=+1.193434400\) \(a_{34}=+0.000000000\) \(a_{35}=-0.455903370\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.336462068\) \(a_{38}=+0.000000000\) \(a_{39}=+0.658779869\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.212122107\) \(a_{42}=+0.000000000\) \(a_{43}=+0.933927726\) \(a_{44}=+0.000000000\) \(a_{45}=-0.597166866\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.287683603\) \(a_{48}=+0.000000000\) \(a_{49}=-0.791646694\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.802614635\) \(a_{52}=+0.000000000\) \(a_{53}=-0.812745044\) \(a_{54}=+0.000000000\) \(a_{55}=+1.879749875\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.307022676\) \(a_{58}=+0.000000000\) \(a_{59}=-0.178255625\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.680564363\) \(a_{62}=+0.000000000\) \(a_{63}=+0.272912416\) \(a_{64}=+0.000000000\) \(a_{65}=+1.037628358\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.546686069\) \(a_{68}=+0.000000000\) \(a_{69}=+0.658126985\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.934223585\) \(a_{72}=+0.000000000\) \(a_{73}=-1.096027012\) \(a_{74}=+0.000000000\) \(a_{75}=-0.001538246\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.859068229\) \(a_{78}=+0.000000000\) \(a_{79}=-0.032338793\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.044632080\) \(a_{82}=+0.000000000\) \(a_{83}=+0.545180895\) \(a_{84}=+0.000000000\) \(a_{85}=+1.264179045\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.338832376\) \(a_{88}=+0.000000000\) \(a_{89}=-1.080635703\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.474208600\) \(a_{92}=+0.000000000\) \(a_{93}=-0.184634990\) \(a_{94}=+0.000000000\) \(a_{95}=-0.483584047\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.948068265\) \(a_{98}=+0.000000000\) \(a_{99}=-1.125253981\) \(a_{100}=+0.000000000\)

Showing 100 of 5000 available coefficients

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