Properties

Level $1$
Weight $0$
Character 1.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 23.2013961812 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.169942059\) \(a_{3}=+1.493045359\) \(a_{4}=-0.971119697\) \(a_{5}=-0.940001485\)
\(a_{6}=+0.253731203\) \(a_{7}=-0.605285723\) \(a_{8}=-0.334976140\) \(a_{9}=+1.229184445\) \(a_{10}=-0.159745788\)
\(a_{11}=-0.510896336\) \(a_{12}=-1.449925756\) \(a_{13}=-1.051883259\) \(a_{14}=-0.102863502\) \(a_{15}=-1.403464855\)
\(a_{16}=+0.914193162\) \(a_{17}=-0.800859558\) \(a_{18}=+0.208890136\) \(a_{19}=-0.395047759\) \(a_{20}=+0.912853957\)
\(a_{21}=-0.903719040\) \(a_{22}=-0.086822775\) \(a_{23}=+0.885833110\) \(a_{24}=-0.500134571\) \(a_{25}=-0.116397208\)
\(a_{26}=-0.178759207\) \(a_{27}=+0.342182772\) \(a_{28}=+0.587804888\) \(a_{29}=-0.933686369\) \(a_{30}=-0.238507707\)
\(a_{31}=+0.650236208\) \(a_{32}=+0.490336008\) \(a_{33}=-0.762791404\) \(a_{34}=-0.136099722\) \(a_{35}=+0.568969479\)
\(a_{36}=-1.193685225\) \(a_{37}=+1.732491266\) \(a_{38}=-0.067135230\) \(a_{39}=-1.570509419\) \(a_{40}=+0.314878069\)
\(a_{41}=+0.816638892\) \(a_{42}=-0.153579874\) \(a_{43}=-0.064530562\) \(a_{44}=+0.496141495\) \(a_{45}=-1.155435204\)
\(a_{46}=+0.150540303\) \(a_{47}=-0.032979290\) \(a_{48}=+1.364931857\) \(a_{49}=-0.633629194\) \(a_{50}=-0.019780781\)
\(a_{51}=-1.195719646\) \(a_{52}=+1.021504552\) \(a_{53}=-0.236060958\) \(a_{54}=+0.058151245\) \(a_{55}=+0.480243315\)
\(a_{56}=+0.202756274\) \(a_{57}=-0.589824224\) \(a_{58}=-0.158672581\) \(a_{59}=-1.167140347\) \(a_{60}=+1.362932358\)
\(a_{61}=+0.652678911\) \(a_{62}=+0.110502480\) \(a_{63}=-0.744007795\) \(a_{64}=-0.830864451\) \(a_{65}=+0.988771826\)
\(a_{66}=-0.129630342\) \(a_{67}=-1.129311940\) \(a_{68}=+0.777730491\) \(a_{69}=+1.322589015\) \(a_{70}=+0.096691845\)
\(a_{71}=-1.490858088\) \(a_{72}=-0.411747461\) \(a_{73}=+0.390140562\) \(a_{74}=+0.294423133\) \(a_{75}=-0.173786311\)
\(a_{76}=+0.383638659\) \(a_{77}=+0.309238258\) \(a_{78}=-0.266895604\) \(a_{79}=+0.580267307\) \(a_{80}=-0.859342930\)
\(a_{81}=-0.718290045\) \(a_{82}=+0.138781295\) \(a_{83}=+0.057014532\) \(a_{84}=+0.877619360\) \(a_{85}=+0.752809174\)
\(a_{86}=-0.010966457\) \(a_{87}=-1.394036101\) \(a_{88}=+0.171138083\) \(a_{89}=-0.091459795\) \(a_{90}=-0.196357038\)
\(a_{91}=+0.636689919\) \(a_{92}=-0.860249982\) \(a_{93}=+0.970832153\) \(a_{94}=-0.005604569\) \(a_{95}=+0.371345480\)
\(a_{96}=+0.732093902\) \(a_{97}=-1.741433171\) \(a_{98}=-0.107680249\) \(a_{99}=-0.627985830\) \(a_{100}=+0.113035621\)

Showing 100 of 5000 available coefficients

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