Properties

Level $22$
Weight $0$
Character 22.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 22 = 2 \cdot 11 \)
Weight: \( 0 \)
Character: 22.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.04598060261 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.175908977\) \(a_{4}=+0.500000000\) \(a_{5}=-0.627502628\)
\(a_{6}=-0.831493213\) \(a_{7}=+1.005945314\) \(a_{8}=+0.353553390\) \(a_{9}=+0.382761923\) \(a_{10}=-0.443711364\)
\(a_{11}=-0.301511344\) \(a_{12}=-0.587954484\) \(a_{13}=+0.472536170\) \(a_{14}=+0.711310750\) \(a_{15}=+0.737885976\)
\(a_{16}=+0.249999993\) \(a_{17}=+0.612929850\) \(a_{18}=+0.270653559\) \(a_{19}=-1.720052378\) \(a_{20}=-0.313751321\)
\(a_{21}=-1.182900127\) \(a_{22}=-0.213200692\) \(a_{23}=+0.037025340\) \(a_{24}=-0.415746620\) \(a_{25}=-0.606240437\)
\(a_{26}=+0.334133477\) \(a_{27}=+0.725815779\) \(a_{28}=+0.502972657\) \(a_{29}=+0.159012445\) \(a_{30}=+0.521764289\)
\(a_{31}=+0.682712912\) \(a_{32}=+0.176776617\) \(a_{33}=+0.354550005\) \(a_{34}=+0.433406835\) \(a_{35}=-0.631233272\)
\(a_{36}=+0.191380981\) \(a_{37}=+0.558673032\) \(a_{38}=-1.216260666\) \(a_{39}=-0.555659509\) \(a_{40}=-0.221855727\)
\(a_{41}=+1.285195436\) \(a_{42}=-0.836436675\) \(a_{43}=+0.744792454\) \(a_{44}=-0.150755630\) \(a_{45}=-0.240184157\)
\(a_{46}=+0.026180805\) \(a_{47}=-1.074898413\) \(a_{48}=-0.293977299\) \(a_{49}=+0.011925930\) \(a_{50}=-0.428676741\)
\(a_{51}=-0.720749627\) \(a_{52}=+0.236268079\) \(a_{53}=-0.713314467\) \(a_{54}=+0.513229293\) \(a_{55}=+0.189199109\)
\(a_{56}=+0.355655422\) \(a_{57}=+2.022625063\) \(a_{58}=+0.112438753\) \(a_{59}=-1.493536364\) \(a_{60}=+0.368942936\)
\(a_{61}=-0.319209247\) \(a_{62}=+0.482750945\) \(a_{63}=+0.385037450\) \(a_{64}=+0.124999986\) \(a_{65}=-0.296517620\)
\(a_{66}=+0.250704631\) \(a_{67}=+0.881955070\) \(a_{68}=+0.306464997\) \(a_{69}=-0.043538320\) \(a_{70}=-0.446349356\)
\(a_{71}=+0.013653424\) \(a_{72}=+0.135326677\) \(a_{73}=-0.227030906\) \(a_{74}=+0.395041541\) \(a_{75}=+0.712883637\)
\(a_{76}=-0.860026231\) \(a_{77}=-0.303303965\) \(a_{78}=-0.392910527\) \(a_{79}=-0.642614436\) \(a_{80}=-0.156875682\)
\(a_{81}=-1.236255448\) \(a_{82}=+0.908770420\) \(a_{83}=+0.762373572\) \(a_{84}=-0.591450006\) \(a_{85}=-0.384615096\)
\(a_{86}=+0.526647767\) \(a_{87}=-0.186984103\) \(a_{88}=-0.106600373\) \(a_{89}=+0.784057437\) \(a_{90}=-0.169835985\)
\(a_{91}=+0.475345491\) \(a_{92}=+0.018512717\) \(a_{93}=-0.802808231\) \(a_{94}=-0.760067900\) \(a_{95}=+1.079337356\)
\(a_{96}=-0.207873264\) \(a_{97}=-1.619321532\) \(a_{98}=+0.008433001\) \(a_{99}=-0.115407056\) \(a_{100}=-0.303120218\)

Showing 100 of 1500 available coefficients

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