Properties

Level $12$
Weight $0$
Character 12.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 12 = 2^{2} \cdot 3 \)
Weight: \( 0 \)
Character: 12.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 8.89214384141 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=+0.343565880\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.612809279\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.198056447\) \(a_{12}=+0.000000000\) \(a_{13}=-1.011481733\) \(a_{14}=+0.000000000\) \(a_{15}=+0.198357854\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.775491318\) \(a_{18}=+0.000000000\) \(a_{19}=-0.773633245\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.931155872\) \(a_{22}=+0.000000000\) \(a_{23}=-1.316070810\) \(a_{24}=+0.000000000\) \(a_{25}=-0.881962486\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=+0.167923537\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.366817559\) \(a_{32}=+0.000000000\) \(a_{33}=+0.691698212\) \(a_{34}=+0.000000000\) \(a_{35}=-0.554106240\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.614544102\) \(a_{38}=+0.000000000\) \(a_{39}=-0.583979251\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.292407392\) \(a_{42}=+0.000000000\) \(a_{43}=+0.586848967\) \(a_{44}=+0.000000000\) \(a_{45}=+0.114521960\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.841152414\) \(a_{48}=+0.000000000\) \(a_{49}=+1.601153773\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.447730122\) \(a_{52}=+0.000000000\) \(a_{53}=-1.282780446\) \(a_{54}=+0.000000000\) \(a_{55}=+0.411611324\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.446657346\) \(a_{58}=+0.000000000\) \(a_{59}=-0.673129037\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.972668781\) \(a_{62}=+0.000000000\) \(a_{63}=-0.537603093\) \(a_{64}=+0.000000000\) \(a_{65}=-0.347510612\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.857812185\) \(a_{68}=+0.000000000\) \(a_{69}=-0.759833837\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.981405386\) \(a_{72}=+0.000000000\) \(a_{73}=-0.690682823\) \(a_{74}=+0.000000000\) \(a_{75}=-0.509201279\)
\(a_{76}=+0.000000000\) \(a_{77}=-1.932236555\) \(a_{78}=+0.000000000\) \(a_{79}=+1.138275975\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=-1.424954155\) \(a_{84}=+0.000000000\) \(a_{85}=-0.266432355\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.096950698\) \(a_{88}=+0.000000000\) \(a_{89}=+0.682869551\) \(a_{90}=+0.000000000\)
\(a_{91}=+1.631327136\) \(a_{92}=+0.000000000\) \(a_{93}=-0.211782224\) \(a_{94}=+0.000000000\) \(a_{95}=-0.265793993\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.115634468\) \(a_{98}=+0.000000000\) \(a_{99}=+0.399352150\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

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