Properties

Level $6$
Weight $0$
Character 6.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 12.6353414748 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+1.780222044\)
\(a_{6}=-0.408248290\) \(a_{7}=-1.015212109\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+1.258807079\)
\(a_{11}=-0.622580837\) \(a_{12}=-0.288675135\) \(a_{13}=+1.223378630\) \(a_{14}=-0.717863366\) \(a_{15}=-1.027811676\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.933368901\) \(a_{18}=+0.235702260\) \(a_{19}=+1.127308810\) \(a_{20}=+0.890111022\)
\(a_{21}=+0.586132984\) \(a_{22}=-0.440231132\) \(a_{23}=+0.067751079\) \(a_{24}=-0.204124145\) \(a_{25}=+2.169190526\)
\(a_{26}=+0.865059326\) \(a_{27}=-0.192450090\) \(a_{28}=-0.507606054\) \(a_{29}=+0.616570733\) \(a_{30}=-0.726772606\)
\(a_{31}=+0.255666418\) \(a_{32}=+0.176776695\) \(a_{33}=+0.359447214\) \(a_{34}=+0.659991483\) \(a_{35}=-1.807302975\)
\(a_{36}=+0.166666667\) \(a_{37}=+1.301506220\) \(a_{38}=+0.797127704\) \(a_{39}=-0.706317982\) \(a_{40}=+0.629403540\)
\(a_{41}=-1.142962234\) \(a_{42}=+0.414458608\) \(a_{43}=-0.600769686\) \(a_{44}=-0.311290419\) \(a_{45}=+0.593407348\)
\(a_{46}=+0.047907247\) \(a_{47}=-0.611391339\) \(a_{48}=-0.144337567\) \(a_{49}=+0.030655626\) \(a_{50}=+1.533849331\)
\(a_{51}=-0.538880786\) \(a_{52}=+0.611689315\) \(a_{53}=+0.520648515\) \(a_{54}=-0.136082763\) \(a_{55}=-1.108332130\)
\(a_{56}=-0.358931683\) \(a_{57}=-0.650852045\) \(a_{58}=+0.435981347\) \(a_{59}=+0.817318585\) \(a_{60}=-0.513905838\)
\(a_{61}=-1.071070666\) \(a_{62}=+0.180783457\) \(a_{63}=-0.338404036\) \(a_{64}=+0.125000000\) \(a_{65}=+2.177885606\)
\(a_{66}=+0.254167562\) \(a_{67}=+0.166985374\) \(a_{68}=+0.466684450\) \(a_{69}=-0.039116103\) \(a_{70}=-1.277956190\)
\(a_{71}=-0.725323119\) \(a_{72}=+0.117851130\) \(a_{73}=-0.966229916\) \(a_{74}=+0.920303873\) \(a_{75}=-1.252382739\)
\(a_{76}=+0.563654402\) \(a_{77}=+0.632051617\) \(a_{78}=-0.499442237\) \(a_{79}=+0.523084308\) \(a_{80}=+0.445055511\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.808196346\) \(a_{83}=-0.045919815\) \(a_{84}=+0.293066492\) \(a_{85}=+1.661603892\)
\(a_{86}=-0.424808319\) \(a_{87}=-0.355977279\) \(a_{88}=-0.220115566\) \(a_{89}=-0.019178163\) \(a_{90}=+0.419602360\)
\(a_{91}=-1.241988799\) \(a_{92}=+0.033875539\) \(a_{93}=-0.147609075\) \(a_{94}=-0.432318962\) \(a_{95}=+2.006859994\)
\(a_{96}=-0.102062073\) \(a_{97}=-1.527477112\) \(a_{98}=+0.021676801\) \(a_{99}=-0.207526946\) \(a_{100}=+1.084595263\)

Showing 100 of 1000 available coefficients

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