Properties

Level $12$
Weight $0$
Character 12.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 12 = 2^{2} \cdot 3 \)
Weight: \( 0 \)
Character: 12.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 12.4574662505 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=-1.274641286\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.576957040\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.544951081\) \(a_{12}=+0.000000000\) \(a_{13}=+0.812446251\) \(a_{14}=+0.000000000\) \(a_{15}=+0.735914490\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.016083764\) \(a_{18}=+0.000000000\) \(a_{19}=-0.898708528\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.333106302\) \(a_{22}=+0.000000000\) \(a_{23}=+1.573020479\) \(a_{24}=+0.000000000\) \(a_{25}=+0.624710409\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=+1.501959020\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.825294673\) \(a_{32}=+0.000000000\) \(a_{33}=-0.314627653\) \(a_{34}=+0.000000000\) \(a_{35}=-0.735413263\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.552339506\) \(a_{38}=+0.000000000\) \(a_{39}=-0.469066062\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.877229051\) \(a_{42}=+0.000000000\) \(a_{43}=-1.785619537\) \(a_{44}=+0.000000000\) \(a_{45}=-0.424880429\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.080496516\) \(a_{48}=+0.000000000\) \(a_{49}=-0.667120574\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.009285966\) \(a_{52}=+0.000000000\) \(a_{53}=+0.304909758\) \(a_{54}=+0.000000000\) \(a_{55}=-0.694617147\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.518869610\) \(a_{58}=+0.000000000\) \(a_{59}=-0.651189476\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.122544652\) \(a_{62}=+0.000000000\) \(a_{63}=+0.192319013\) \(a_{64}=+0.000000000\) \(a_{65}=-1.035577534\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.224412987\) \(a_{68}=+0.000000000\) \(a_{69}=-0.908183797\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.851578985\) \(a_{72}=+0.000000000\) \(a_{73}=+0.448811267\) \(a_{74}=+0.000000000\) \(a_{75}=-0.360676723\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.314413362\) \(a_{78}=+0.000000000\) \(a_{79}=+0.518199053\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=-1.142448380\) \(a_{84}=+0.000000000\) \(a_{85}=+0.020501030\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.867156444\) \(a_{88}=+0.000000000\) \(a_{89}=-1.335047436\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.468746584\) \(a_{92}=+0.000000000\) \(a_{93}=+1.053834371\) \(a_{94}=+0.000000000\) \(a_{95}=+1.145530993\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.269629790\) \(a_{98}=+0.000000000\) \(a_{99}=+0.181650360\) \(a_{100}=+0.000000000\)

Showing 100 of 190 available coefficients

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