Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 23.0057216741 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.790243018\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.558786197\) \(a_{7}=+1.394915582\) \(a_{8}=+0.353553391\) \(a_{9}=-0.375515973\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.170009149\) \(a_{12}=+0.395121509\) \(a_{13}=+0.054637878\) \(a_{14}=+0.986354267\) \(a_{15}=-0.353407421\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.734532436\) \(a_{18}=-0.265529891\) \(a_{19}=-1.551378203\) \(a_{20}=-0.223606798\)
\(a_{21}=+1.102322299\) \(a_{22}=-0.120214622\) \(a_{23}=-1.080512576\) \(a_{24}=+0.279393098\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.038634814\) \(a_{27}=-1.086991893\) \(a_{28}=+0.697457791\) \(a_{29}=-0.216786141\) \(a_{30}=-0.249896784\)
\(a_{31}=+1.924365972\) \(a_{32}=+0.176776695\) \(a_{33}=-0.134348543\) \(a_{34}=-1.226499647\) \(a_{35}=-0.623825213\)
\(a_{36}=-0.187757986\) \(a_{37}=-1.297617474\) \(a_{38}=-1.096990047\) \(a_{39}=+0.043177202\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.597090861\) \(a_{42}=+0.779459573\) \(a_{43}=-1.333397384\) \(a_{44}=-0.085004575\) \(a_{45}=+0.167935848\)
\(a_{46}=-0.764037769\) \(a_{47}=-0.701749793\) \(a_{48}=+0.197560754\) \(a_{49}=+0.945789481\) \(a_{50}=+0.141421356\)
\(a_{51}=-1.370702147\) \(a_{52}=+0.027318939\) \(a_{53}=-0.081834952\) \(a_{54}=-0.768619339\) \(a_{55}=+0.076030403\)
\(a_{56}=+0.493177134\) \(a_{57}=-1.225965793\) \(a_{58}=-0.153290950\) \(a_{59}=+0.039522944\) \(a_{60}=-0.176703711\)
\(a_{61}=-0.224935119\) \(a_{62}=+1.360732229\) \(a_{63}=-0.523813082\) \(a_{64}=+0.125000000\) \(a_{65}=-0.024434802\)
\(a_{66}=-0.094998766\) \(a_{67}=-0.956099275\) \(a_{68}=-0.867266218\) \(a_{69}=-0.853867519\) \(a_{70}=-0.441111038\)
\(a_{71}=-0.096731997\) \(a_{72}=-0.132764945\) \(a_{73}=+0.431163774\) \(a_{74}=-0.917554115\) \(a_{75}=+0.158048604\)
\(a_{76}=-0.775689101\) \(a_{77}=-0.237148411\) \(a_{78}=+0.030530892\) \(a_{79}=-0.565890708\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.483471782\) \(a_{82}=+1.129313778\) \(a_{83}=+1.497460275\) \(a_{84}=+0.551161150\) \(a_{85}=+0.775706487\)
\(a_{86}=-0.942854332\) \(a_{87}=-0.171313734\) \(a_{88}=-0.060107311\) \(a_{89}=+0.268402909\) \(a_{90}=+0.118748577\)
\(a_{91}=+0.076215228\) \(a_{92}=-0.540256288\) \(a_{93}=+1.520716774\) \(a_{94}=-0.496212038\) \(a_{95}=+0.693797424\)
\(a_{96}=+0.139696549\) \(a_{97}=-0.257073663\) \(a_{98}=+0.668774155\) \(a_{99}=+0.063841151\) \(a_{100}=+0.099975586\)

Showing 100 of 210 available coefficients

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