Properties

Level $76$
Weight $0$
Character 76.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 76 = 2^{2} \cdot 19 \)
Weight: \( 0 \)
Character: 76.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 2.02831755396 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.770822742\) \(a_{4}=+0.000000000\) \(a_{5}=+1.841571394\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.074582206\) \(a_{8}=+0.000000000\) \(a_{9}=+2.135813184\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.121273251\) \(a_{12}=+0.000000000\) \(a_{13}=+0.528752294\) \(a_{14}=+0.000000000\) \(a_{15}=-3.261096506\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.225643220\) \(a_{18}=+0.000000000\) \(a_{19}=-0.229415734\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.132071866\) \(a_{22}=+0.000000000\) \(a_{23}=+0.596375569\) \(a_{24}=+0.000000000\) \(a_{25}=+2.391385200\)
\(a_{26}=+0.000000000\) \(a_{27}=-2.011323817\) \(a_{28}=+0.000000000\) \(a_{29}=+0.463125740\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.334132737\) \(a_{32}=+0.000000000\) \(a_{33}=-1.985576174\) \(a_{34}=+0.000000000\) \(a_{35}=-0.137348456\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.253196914\) \(a_{38}=+0.000000000\) \(a_{39}=-0.936326587\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.701275983\) \(a_{42}=+0.000000000\) \(a_{43}=+0.616307437\) \(a_{44}=+0.000000000\) \(a_{45}=+3.933252463\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.124971686\) \(a_{48}=+0.000000000\) \(a_{49}=-0.994437495\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.399574146\) \(a_{52}=+0.000000000\) \(a_{53}=-1.595072832\) \(a_{54}=+0.000000000\) \(a_{55}=+2.064904745\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.406254599\) \(a_{58}=+0.000000000\) \(a_{59}=+0.464140266\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.948394705\) \(a_{62}=+0.000000000\) \(a_{63}=-0.159293658\) \(a_{64}=+0.000000000\) \(a_{65}=+0.973735099\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.395716332\) \(a_{68}=+0.000000000\) \(a_{69}=-1.056075420\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.295054624\) \(a_{72}=+0.000000000\) \(a_{73}=+0.593705980\) \(a_{74}=+0.000000000\) \(a_{75}=-4.234719297\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.083627032\) \(a_{78}=+0.000000000\) \(a_{79}=+0.858331933\) \(a_{80}=+0.000000000\)
\(a_{81}=+1.425884772\) \(a_{82}=+0.000000000\) \(a_{83}=-0.515482477\) \(a_{84}=+0.000000000\) \(a_{85}=-0.415538100\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.820113593\) \(a_{88}=+0.000000000\) \(a_{89}=+0.092988297\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.039435512\) \(a_{92}=+0.000000000\) \(a_{93}=-2.362512591\) \(a_{94}=+0.000000000\) \(a_{95}=-0.422485453\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.885182126\) \(a_{98}=+0.000000000\) \(a_{99}=+2.394830193\) \(a_{100}=+0.000000000\)

Showing 100 of 606 available coefficients

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