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: \( 24.8561990173 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.883828925\) \(a_{4}=+0.500000000\) \(a_{5}=+1.449410586\)
\(a_{6}=+0.624961427\) \(a_{7}=+1.730299700\) \(a_{8}=-0.353553391\) \(a_{9}=-0.218846431\) \(a_{10}=-1.024888054\)
\(a_{11}=+0.466978313\) \(a_{12}=-0.441914463\) \(a_{13}=+0.203469736\) \(a_{14}=-1.223506652\) \(a_{15}=-1.281031000\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.504623336\) \(a_{18}=+0.154747795\) \(a_{19}=-0.694165200\) \(a_{20}=+0.724705293\)
\(a_{21}=-1.529288925\) \(a_{22}=-0.330203532\) \(a_{23}=-0.506405813\) \(a_{24}=+0.312480713\) \(a_{25}=+1.100791046\)
\(a_{26}=-0.143874830\) \(a_{27}=+1.077251731\) \(a_{28}=+0.865149850\) \(a_{29}=+0.423067044\) \(a_{30}=+0.905825707\)
\(a_{31}=+1.488557627\) \(a_{32}=-0.176776695\) \(a_{33}=-0.412728941\) \(a_{34}=-0.356822583\) \(a_{35}=+2.507914702\)
\(a_{36}=-0.109423215\) \(a_{37}=-1.055353062\) \(a_{38}=+0.490848920\) \(a_{39}=-0.179832438\) \(a_{40}=-0.512444027\)
\(a_{41}=+0.799848188\) \(a_{42}=+1.081370569\) \(a_{43}=-1.169459018\) \(a_{44}=+0.233489157\) \(a_{45}=-0.317198333\)
\(a_{46}=+0.358082984\) \(a_{47}=-0.749134071\) \(a_{48}=-0.220957231\) \(a_{49}=+1.993937053\) \(a_{50}=-0.778376813\)
\(a_{51}=-0.446000701\) \(a_{52}=+0.101734868\) \(a_{53}=+0.127057799\) \(a_{54}=-0.761732004\) \(a_{55}=+0.676843311\)
\(a_{56}=-0.611753326\) \(a_{57}=+0.613523283\) \(a_{58}=-0.299153575\) \(a_{59}=+1.233063915\) \(a_{60}=-0.640515500\)
\(a_{61}=+0.235871053\) \(a_{62}=-1.052569192\) \(a_{63}=-0.378669913\) \(a_{64}=+0.125000000\) \(a_{65}=+0.294911189\)
\(a_{66}=+0.291843433\) \(a_{67}=+0.868615914\) \(a_{68}=+0.252311668\) \(a_{69}=+0.447576105\) \(a_{70}=-1.773363493\)
\(a_{71}=-1.023036565\) \(a_{72}=+0.077373898\) \(a_{73}=+1.349606171\) \(a_{74}=+0.746247307\) \(a_{75}=-0.972910967\)
\(a_{76}=-0.347082600\) \(a_{77}=+0.808012436\) \(a_{78}=+0.127160736\) \(a_{79}=-0.071295126\) \(a_{80}=+0.362352646\)
\(a_{81}=-0.733259809\) \(a_{82}=-0.565578078\) \(a_{83}=+0.260409761\) \(a_{84}=-0.764644462\) \(a_{85}=+0.731406405\)
\(a_{86}=+0.826932402\) \(a_{87}=-0.373918891\) \(a_{88}=-0.165101766\) \(a_{89}=+0.350111071\) \(a_{90}=+0.224293092\)
\(a_{91}=+0.352063623\) \(a_{92}=-0.253202906\) \(a_{93}=-1.315630287\) \(a_{94}=+0.529717781\) \(a_{95}=-1.006130389\)
\(a_{96}=+0.156240357\) \(a_{97}=+1.836321137\) \(a_{98}=-1.409926411\) \(a_{99}=-0.102196537\) \(a_{100}=+0.550395523\)

Showing 100 of 1228 available coefficients

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