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: \( 14.9703130686 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.987509128\) \(a_{4}=+0.000000000\) \(a_{5}=-0.117056027\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.494179834\) \(a_{8}=+0.000000000\) \(a_{9}=-0.024825722\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.476591579\) \(a_{12}=+0.000000000\) \(a_{13}=-1.583333623\) \(a_{14}=+0.000000000\) \(a_{15}=+0.115593895\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.173958592\) \(a_{18}=+0.000000000\) \(a_{19}=+0.830593146\) \(a_{20}=+0.000000000\)
\(a_{21}=+1.475516225\) \(a_{22}=+0.000000000\) \(a_{23}=+1.673995873\) \(a_{24}=+0.000000000\) \(a_{25}=-0.986297888\)
\(a_{26}=+0.000000000\) \(a_{27}=+1.012024755\) \(a_{28}=+0.000000000\) \(a_{29}=+0.658957111\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.114320273\) \(a_{32}=+0.000000000\) \(a_{33}=-0.470638534\) \(a_{34}=+0.000000000\) \(a_{35}=+0.174902755\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.358485366\) \(a_{38}=+0.000000000\) \(a_{39}=+1.563556405\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.682885100\) \(a_{42}=+0.000000000\) \(a_{43}=-0.972062381\) \(a_{44}=+0.000000000\) \(a_{45}=+0.002906000\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.488138642\) \(a_{48}=+0.000000000\) \(a_{49}=+1.232573376\) \(a_{50}=+0.000000000\)
\(a_{51}=-1.159294826\) \(a_{52}=+0.000000000\) \(a_{53}=+0.145847679\) \(a_{54}=+0.000000000\) \(a_{55}=-0.055787917\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.820218314\) \(a_{58}=+0.000000000\) \(a_{59}=+0.158883187\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.270231131\) \(a_{62}=+0.000000000\) \(a_{63}=+0.037094093\) \(a_{64}=+0.000000000\) \(a_{65}=+0.185338743\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.920899234\) \(a_{68}=+0.000000000\) \(a_{69}=-1.653086207\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.829322880\) \(a_{72}=+0.000000000\) \(a_{73}=-0.413944462\) \(a_{74}=+0.000000000\) \(a_{75}=+0.973978166\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.712113526\) \(a_{78}=+0.000000000\) \(a_{79}=+1.113467688\) \(a_{80}=+0.000000000\)
\(a_{81}=-0.974557962\) \(a_{82}=+0.000000000\) \(a_{83}=-0.307498489\) \(a_{84}=+0.000000000\) \(a_{85}=-0.137418929\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.650726162\) \(a_{88}=+0.000000000\) \(a_{89}=-0.334105442\) \(a_{90}=+0.000000000\)
\(a_{91}=+2.365785169\) \(a_{92}=+0.000000000\) \(a_{93}=+0.112892313\) \(a_{94}=+0.000000000\) \(a_{95}=-0.097225934\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.204607135\) \(a_{98}=+0.000000000\) \(a_{99}=-0.011831730\) \(a_{100}=+0.000000000\)

Showing 100 of 5000 available coefficients

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