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: \( 10.7647106832 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.626430796\) \(a_{4}=+0.000000000\) \(a_{5}=-1.034052565\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.362850957\) \(a_{8}=+0.000000000\) \(a_{9}=+1.645277135\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.405885684\) \(a_{12}=+0.000000000\) \(a_{13}=-0.114274224\) \(a_{14}=+0.000000000\) \(a_{15}=+1.681814937\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.207940213\) \(a_{18}=+0.000000000\) \(a_{19}=+0.338286220\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.590151963\) \(a_{22}=+0.000000000\) \(a_{23}=-0.267766764\) \(a_{24}=+0.000000000\) \(a_{25}=+0.069264707\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.049498604\) \(a_{28}=+0.000000000\) \(a_{29}=+0.915405107\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.475639077\) \(a_{32}=+0.000000000\) \(a_{33}=-2.286575773\) \(a_{34}=+0.000000000\) \(a_{35}=+0.375206962\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.305862200\) \(a_{38}=+0.000000000\) \(a_{39}=+0.185859116\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.024197663\) \(a_{42}=+0.000000000\) \(a_{43}=+1.139094108\) \(a_{44}=+0.000000000\) \(a_{45}=-1.701303041\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.044314907\) \(a_{48}=+0.000000000\) \(a_{49}=-0.868339183\) \(a_{50}=+0.000000000\)
\(a_{51}=+1.964631162\) \(a_{52}=+0.000000000\) \(a_{53}=+0.823908912\) \(a_{54}=+0.000000000\) \(a_{55}=-1.453759698\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.550199124\) \(a_{58}=+0.000000000\) \(a_{59}=+0.582962511\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.232813695\) \(a_{62}=+0.000000000\) \(a_{63}=-0.596990372\) \(a_{64}=+0.000000000\) \(a_{65}=+0.118165530\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.751023831\) \(a_{68}=+0.000000000\) \(a_{69}=+0.435504112\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.253105206\) \(a_{72}=+0.000000000\) \(a_{73}=-0.957734537\) \(a_{74}=+0.000000000\) \(a_{75}=-0.112654253\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.510126965\) \(a_{78}=+0.000000000\) \(a_{79}=+1.847891570\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.061659716\) \(a_{82}=+0.000000000\) \(a_{83}=-0.704349913\) \(a_{84}=+0.000000000\) \(a_{85}=+1.249073675\)
\(a_{86}=+0.000000000\) \(a_{87}=-1.488843058\) \(a_{88}=+0.000000000\) \(a_{89}=+1.080102719\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.041464512\) \(a_{92}=+0.000000000\) \(a_{93}=-2.400024839\) \(a_{94}=+0.000000000\) \(a_{95}=-0.349805732\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.334499734\) \(a_{98}=+0.000000000\) \(a_{99}=+2.313071570\) \(a_{100}=+0.000000000\)

Showing 100 of 5000 available coefficients

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