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: \( 29.5185335504 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.034985315\) \(a_{4}=+0.500000000\) \(a_{5}=-0.206473753\)
\(a_{6}=+0.731845135\) \(a_{7}=+0.911580113\) \(a_{8}=-0.353553391\) \(a_{9}=+0.071194603\) \(a_{10}=+0.145998991\)
\(a_{11}=+1.520392773\) \(a_{12}=-0.517492658\) \(a_{13}=-1.367502921\) \(a_{14}=-0.644584479\) \(a_{15}=+0.213697302\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.960310985\) \(a_{18}=-0.050342186\) \(a_{19}=-0.019525609\) \(a_{20}=-0.103236877\)
\(a_{21}=-0.943472030\) \(a_{22}=-1.075080040\) \(a_{23}=-0.305083144\) \(a_{24}=+0.365922567\) \(a_{25}=-0.957368589\)
\(a_{26}=+0.966970589\) \(a_{27}=+0.961299947\) \(a_{28}=+0.455790056\) \(a_{29}=-1.797758275\) \(a_{30}=-0.151106812\)
\(a_{31}=+0.055089509\) \(a_{32}=-0.176776695\) \(a_{33}=-1.573584193\) \(a_{34}=+0.679042409\) \(a_{35}=-0.188217367\)
\(a_{36}=+0.035597301\) \(a_{37}=+1.675081483\) \(a_{38}=+0.013806690\) \(a_{39}=+1.415345442\) \(a_{40}=+0.072999495\)
\(a_{41}=+0.556575214\) \(a_{42}=+0.667135471\) \(a_{43}=+1.239678238\) \(a_{44}=+0.760196387\) \(a_{45}=-0.014699817\)
\(a_{46}=+0.215726360\) \(a_{47}=+0.637996658\) \(a_{48}=-0.258746329\) \(a_{49}=-0.169021698\) \(a_{50}=+0.676961822\)
\(a_{51}=+0.993907767\) \(a_{52}=-0.683751461\) \(a_{53}=+0.739971743\) \(a_{54}=-0.679741711\) \(a_{55}=-0.313921202\)
\(a_{56}=-0.322292240\) \(a_{57}=+0.020208718\) \(a_{58}=+1.271207067\) \(a_{59}=+0.600843678\) \(a_{60}=+0.106848651\)
\(a_{61}=-1.738279995\) \(a_{62}=-0.038954165\) \(a_{63}=+0.064899584\) \(a_{64}=+0.125000000\) \(a_{65}=+0.282353460\)
\(a_{66}=+1.112692054\) \(a_{67}=-0.683654439\) \(a_{68}=-0.480155492\) \(a_{69}=+0.315756574\) \(a_{70}=+0.133089777\)
\(a_{71}=-0.264942212\) \(a_{72}=-0.025171093\) \(a_{73}=+0.080691285\) \(a_{74}=-1.184461476\) \(a_{75}=+0.990862431\)
\(a_{76}=-0.009762804\) \(a_{77}=+1.385959816\) \(a_{78}=-1.000800360\) \(a_{79}=+0.307136654\) \(a_{80}=-0.051618438\)
\(a_{81}=-1.066125931\) \(a_{82}=-0.393558108\) \(a_{83}=+1.171122038\) \(a_{84}=-0.471736015\) \(a_{85}=+0.198279013\)
\(a_{86}=-0.876584888\) \(a_{87}=+1.860653415\) \(a_{88}=-0.537540020\) \(a_{89}=+0.603940352\) \(a_{90}=+0.010394340\)
\(a_{91}=-1.246588467\) \(a_{92}=-0.152541572\) \(a_{93}=-0.057016833\) \(a_{94}=-0.451131763\) \(a_{95}=+0.004031526\)
\(a_{96}=+0.182961284\) \(a_{97}=+1.629954382\) \(a_{98}=+0.119516389\) \(a_{99}=+0.108243759\) \(a_{100}=-0.478684295\)

Showing 100 of 1228 available coefficients

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