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: \( 31.604945484 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106783\) \(a_{3}=-0.309200310\) \(a_{4}=+0.500000003\) \(a_{5}=+0.761751321\)
\(a_{6}=-0.218637637\) \(a_{7}=+0.099189054\) \(a_{8}=+0.353553393\) \(a_{9}=-0.904395168\) \(a_{10}=+0.538639526\)
\(a_{11}=-1.348836671\) \(a_{12}=-0.154600156\) \(a_{13}=-0.184684019\) \(a_{14}=+0.070137253\) \(a_{15}=-0.235533745\)
\(a_{16}=+0.250000003\) \(a_{17}=+0.643430286\) \(a_{18}=-0.639503958\) \(a_{19}=+0.914722902\) \(a_{20}=+0.380875662\)
\(a_{21}=-0.030669286\) \(a_{22}=-0.953771559\) \(a_{23}=-1.232539456\) \(a_{24}=-0.109318819\) \(a_{25}=-0.419734925\)
\(a_{26}=-0.130591323\) \(a_{27}=+0.588839577\) \(a_{28}=+0.049594527\) \(a_{29}=-0.510545104\) \(a_{30}=-0.166547509\)
\(a_{31}=-1.614257420\) \(a_{32}=+0.176776698\) \(a_{33}=+0.417060717\) \(a_{34}=+0.454973920\) \(a_{35}=+0.075557393\)
\(a_{36}=-0.452197586\) \(a_{37}=+1.713420217\) \(a_{38}=+0.646806769\) \(a_{39}=+0.057104356\) \(a_{40}=+0.269319764\)
\(a_{41}=-1.668283998\) \(a_{42}=-0.021686460\) \(a_{43}=+0.024524562\) \(a_{44}=-0.674418339\) \(a_{45}=-0.688924214\)
\(a_{46}=-0.871537010\) \(a_{47}=-1.480373724\) \(a_{48}=-0.077300078\) \(a_{49}=-0.990161532\) \(a_{50}=-0.296797413\)
\(a_{51}=-0.198948844\) \(a_{52}=-0.092342010\) \(a_{53}=-1.115260562\) \(a_{54}=+0.416372459\) \(a_{55}=-1.027478115\)
\(a_{56}=+0.035068627\) \(a_{57}=-0.282832605\) \(a_{58}=-0.361009906\) \(a_{59}=+1.038960687\) \(a_{60}=-0.117766873\)
\(a_{61}=+0.099054165\) \(a_{62}=-1.141452371\) \(a_{63}=-0.089706101\) \(a_{64}=+0.125000002\) \(a_{65}=-0.140683296\)
\(a_{66}=+0.294906462\) \(a_{67}=+0.227281181\) \(a_{68}=+0.321715145\) \(a_{69}=+0.381101582\) \(a_{70}=+0.053427145\)
\(a_{71}=-1.562987815\) \(a_{72}=-0.319751981\) \(a_{73}=-0.123200705\) \(a_{74}=+1.211571058\) \(a_{75}=+0.129782169\)
\(a_{76}=+0.457361453\) \(a_{77}=-0.133789834\) \(a_{78}=+0.040378878\) \(a_{79}=-1.142754496\) \(a_{80}=+0.190437832\)
\(a_{81}=+0.722325788\) \(a_{82}=-1.179654931\) \(a_{83}=+0.541333692\) \(a_{84}=-0.015334643\) \(a_{85}=+0.490133870\)
\(a_{86}=+0.017341484\) \(a_{87}=+0.157860705\) \(a_{88}=-0.476885782\) \(a_{89}=+0.716102488\) \(a_{90}=-0.487142985\)
\(a_{91}=-0.018318633\) \(a_{92}=-0.616269731\) \(a_{93}=+0.499128895\) \(a_{94}=-1.046782302\) \(a_{95}=+0.696791379\)
\(a_{96}=-0.054659410\) \(a_{97}=+1.052337295\) \(a_{98}=-0.700149935\) \(a_{99}=+1.219881368\) \(a_{100}=-0.209867464\)

Showing 100 of 1228 available coefficients

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