Properties

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

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Maass form invariants

Level: \( 4 = 2^{2} \)
Weight: \( 0 \)
Character: 4.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 8.04247759169 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.328064713\) \(a_{4}=+0.000000000\) \(a_{5}=-1.680010344\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.631110541\) \(a_{8}=+0.000000000\) \(a_{9}=-0.892373544\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.765556769\) \(a_{12}=+0.000000000\) \(a_{13}=-0.492991561\) \(a_{14}=+0.000000000\) \(a_{15}=-0.551152112\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.142481320\) \(a_{18}=+0.000000000\) \(a_{19}=-0.434566270\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.207045099\) \(a_{22}=+0.000000000\) \(a_{23}=-0.877014900\) \(a_{24}=+0.000000000\) \(a_{25}=+1.822434755\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.620820984\) \(a_{28}=+0.000000000\) \(a_{29}=-0.121983786\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.854200442\) \(a_{32}=+0.000000000\) \(a_{33}=+0.251152162\) \(a_{34}=+0.000000000\) \(a_{35}=+1.060272236\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.102132156\) \(a_{38}=+0.000000000\) \(a_{39}=-0.161733135\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.369559245\) \(a_{42}=+0.000000000\) \(a_{43}=-1.430297104\) \(a_{44}=+0.000000000\) \(a_{45}=+1.499196784\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.782097942\) \(a_{48}=+0.000000000\) \(a_{49}=-0.601699485\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.374807805\) \(a_{52}=+0.000000000\) \(a_{53}=-0.282498766\) \(a_{54}=+0.000000000\) \(a_{55}=-1.286143290\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.142565858\) \(a_{58}=+0.000000000\) \(a_{59}=+1.597499229\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.441880497\) \(a_{62}=+0.000000000\) \(a_{63}=+0.563186351\) \(a_{64}=+0.000000000\) \(a_{65}=+0.828230922\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.683950327\) \(a_{68}=+0.000000000\) \(a_{69}=-0.287717642\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.578126878\) \(a_{72}=+0.000000000\) \(a_{73}=+0.796704960\) \(a_{74}=+0.000000000\) \(a_{75}=+0.597876535\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.483150946\) \(a_{78}=+0.000000000\) \(a_{79}=+0.871802552\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.688704086\) \(a_{82}=+0.000000000\) \(a_{83}=-0.424918452\) \(a_{84}=+0.000000000\) \(a_{85}=-1.919380424\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.040018576\) \(a_{88}=+0.000000000\) \(a_{89}=+0.490525801\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.311132171\) \(a_{92}=+0.000000000\) \(a_{93}=-0.280233025\) \(a_{94}=+0.000000000\) \(a_{95}=+0.730075832\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.304547464\) \(a_{98}=+0.000000000\) \(a_{99}=-0.683162607\) \(a_{100}=+0.000000000\)

Showing 100 of 5000 available coefficients

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