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: \( 1.69106559844 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=+0.175592108\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.729592244\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.349458005\) \(a_{12}=+0.000000000\) \(a_{13}=-0.168401039\) \(a_{14}=+0.000000000\) \(a_{15}=-0.101378150\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.320314254\) \(a_{18}=+0.000000000\) \(a_{19}=+0.209429205\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.421230275\) \(a_{22}=+0.000000000\) \(a_{23}=+0.541969907\) \(a_{24}=+0.000000000\) \(a_{25}=-0.969167412\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=-1.136207551\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.543142452\) \(a_{32}=+0.000000000\) \(a_{33}=+0.779109946\) \(a_{34}=+0.000000000\) \(a_{35}=+0.128110634\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.263731702\) \(a_{38}=+0.000000000\) \(a_{39}=+0.097226372\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.616531319\) \(a_{42}=+0.000000000\) \(a_{43}=-0.843842325\) \(a_{44}=+0.000000000\) \(a_{45}=+0.058531004\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.234960988\) \(a_{48}=+0.000000000\) \(a_{49}=-0.467695157\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.762283969\) \(a_{52}=+0.000000000\) \(a_{53}=+1.133718359\) \(a_{54}=+0.000000000\) \(a_{55}=-0.236954116\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.120914076\) \(a_{58}=+0.000000000\) \(a_{59}=+1.191393589\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.486256143\) \(a_{62}=+0.000000000\) \(a_{63}=+0.243196238\) \(a_{64}=+0.000000000\) \(a_{65}=-0.029569539\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.215253401\) \(a_{68}=+0.000000000\) \(a_{69}=-0.312905271\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.192711120\) \(a_{72}=+0.000000000\) \(a_{73}=-1.342540822\) \(a_{74}=+0.000000000\) \(a_{75}=+0.559546417\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.984549434\) \(a_{78}=+0.000000000\) \(a_{79}=+1.521576508\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111189\) \(a_{82}=+0.000000000\) \(a_{83}=-0.710740110\) \(a_{84}=+0.000000000\) \(a_{85}=+0.231836860\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.655989832\) \(a_{88}=+0.000000000\) \(a_{89}=+1.205966991\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.122864173\) \(a_{92}=+0.000000000\) \(a_{93}=-0.313583028\) \(a_{94}=+0.000000000\) \(a_{95}=+0.036775414\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.714993725\) \(a_{98}=+0.000000000\) \(a_{99}=-0.449819591\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

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