Properties

Level $2$
Weight $0$
Character 2.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 25.0524237851 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.591851386\) \(a_{4}=+0.500000000\) \(a_{5}=-1.499651612\)
\(a_{6}=-1.125608910\) \(a_{7}=-0.366714989\) \(a_{8}=-0.353553391\) \(a_{9}=+1.533990836\) \(a_{10}=+1.060413824\)
\(a_{11}=+0.856781780\) \(a_{12}=+0.795925693\) \(a_{13}=-0.530758800\) \(a_{14}=+0.259306655\) \(a_{15}=-2.387222497\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.047662944\) \(a_{18}=-1.084695322\) \(a_{19}=+1.182102164\) \(a_{20}=-0.749825806\)
\(a_{21}=-0.583755763\) \(a_{22}=-0.605836207\) \(a_{23}=-0.370802392\) \(a_{24}=-0.562804455\) \(a_{25}=+1.248954957\)
\(a_{26}=+0.375303147\) \(a_{27}=+0.850034052\) \(a_{28}=-0.183357494\) \(a_{29}=+1.341605854\) \(a_{30}=+1.688021216\)
\(a_{31}=+0.068795699\) \(a_{32}=-0.176776695\) \(a_{33}=+1.363869264\) \(a_{34}=-0.740809572\) \(a_{35}=+0.549944724\)
\(a_{36}=+0.766995418\) \(a_{37}=+0.869173205\) \(a_{38}=-0.835872456\) \(a_{39}=-0.844889131\) \(a_{40}=+0.530206912\)
\(a_{41}=+0.240058410\) \(a_{42}=+0.412777659\) \(a_{43}=+0.476813105\) \(a_{44}=+0.428390890\) \(a_{45}=-2.300451830\)
\(a_{46}=+0.262196886\) \(a_{47}=+1.319658020\) \(a_{48}=+0.397962847\) \(a_{49}=-0.865520117\) \(a_{50}=-0.883144519\)
\(a_{51}=+1.667723710\) \(a_{52}=-0.265379400\) \(a_{53}=+0.240825308\) \(a_{54}=-0.601064843\) \(a_{55}=-1.284874177\)
\(a_{56}=+0.129653328\) \(a_{57}=+1.881730968\) \(a_{58}=-0.948658597\) \(a_{59}=+1.601059795\) \(a_{60}=-1.193611249\)
\(a_{61}=-0.316504669\) \(a_{62}=-0.048645905\) \(a_{63}=-0.562537432\) \(a_{64}=+0.125000000\) \(a_{65}=+0.795953290\)
\(a_{66}=-0.964401205\) \(a_{67}=+1.201389983\) \(a_{68}=+0.523831472\) \(a_{69}=-0.590262301\) \(a_{70}=-0.388869644\)
\(a_{71}=+0.481031929\) \(a_{72}=-0.542347661\) \(a_{73}=-1.076729777\) \(a_{74}=-0.614598268\) \(a_{75}=+1.988150680\)
\(a_{76}=+0.591051082\) \(a_{77}=-0.314194721\) \(a_{78}=+0.597426834\) \(a_{79}=-1.041553220\) \(a_{80}=-0.374912903\)
\(a_{81}=-0.180862951\) \(a_{82}=-0.169746930\) \(a_{83}=+1.474419888\) \(a_{84}=-0.291877882\) \(a_{85}=-1.571129423\)
\(a_{86}=-0.337157780\) \(a_{87}=+2.135637138\) \(a_{88}=-0.302918103\) \(a_{89}=-1.300095511\) \(a_{90}=+1.626665089\)
\(a_{91}=+0.194637207\) \(a_{92}=-0.185401196\) \(a_{93}=+0.109512528\) \(a_{94}=-0.933139135\) \(a_{95}=-1.772741415\)
\(a_{96}=-0.281402227\) \(a_{97}=+1.326080945\) \(a_{98}=+0.612015144\) \(a_{99}=+1.314295399\) \(a_{100}=+0.624477478\)

Showing 100 of 1228 available coefficients

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