Properties

Level $839$
Weight $0$
Character 839.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 839 \)
Weight: \( 0 \)
Character: 839.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.87559016784 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.774345311\) \(a_{3}=-0.972484020\) \(a_{4}=-0.400389294\) \(a_{5}=-1.388746168\)
\(a_{6}=-0.753038345\) \(a_{7}=+0.170949412\) \(a_{8}=-1.084384760\) \(a_{9}=-0.054274830\) \(a_{10}=-1.075369007\)
\(a_{11}=-0.815004883\) \(a_{12}=+0.389372074\) \(a_{13}=-0.328510159\) \(a_{14}=+0.132373940\) \(a_{15}=+1.350533551\)
\(a_{16}=-0.439299037\) \(a_{17}=+1.431840047\) \(a_{18}=-0.042027495\) \(a_{19}=-0.626395208\) \(a_{20}=+0.556039146\)
\(a_{21}=-0.166245507\) \(a_{22}=-0.631095137\) \(a_{23}=+1.094871930\) \(a_{24}=+1.054547033\) \(a_{25}=+0.928615919\)
\(a_{26}=-0.254380337\) \(a_{27}=+1.025265551\) \(a_{28}=-0.068446270\) \(a_{29}=-0.015988912\) \(a_{30}=+1.045779471\)
\(a_{31}=-1.098817570\) \(a_{32}=+0.744215568\) \(a_{33}=+0.792579240\) \(a_{34}=+1.108738777\) \(a_{35}=-0.237405617\)
\(a_{36}=+0.021730938\) \(a_{37}=-0.541306087\) \(a_{38}=-0.485046206\) \(a_{39}=+0.319470750\) \(a_{40}=+1.505935383\)
\(a_{41}=+0.379913318\) \(a_{42}=-0.128731649\) \(a_{43}=-0.731639530\) \(a_{44}=+0.326319399\) \(a_{45}=+0.075373810\)
\(a_{46}=+0.847809322\) \(a_{47}=+1.176386351\) \(a_{48}=+0.427211337\) \(a_{49}=-0.970776292\) \(a_{50}=+0.719069529\)
\(a_{51}=-1.392441788\) \(a_{52}=+0.131532072\) \(a_{53}=-0.587927749\) \(a_{54}=+0.793909573\) \(a_{55}=+1.131835055\)
\(a_{56}=-0.185375073\) \(a_{57}=+0.609159319\) \(a_{58}=-0.012380969\) \(a_{59}=+0.249059926\) \(a_{60}=-0.540739336\)
\(a_{61}=-0.563425886\) \(a_{62}=-0.850864046\) \(a_{63}=-0.009278354\) \(a_{64}=+1.015579025\) \(a_{65}=+0.456217435\)
\(a_{66}=+0.613730084\) \(a_{67}=+0.447670683\) \(a_{68}=-0.573293418\) \(a_{69}=-1.064745821\) \(a_{70}=-0.183833964\)
\(a_{71}=+0.506349839\) \(a_{72}=+0.058854703\) \(a_{73}=+1.275586295\) \(a_{74}=-0.419157531\) \(a_{75}=-0.903064092\)
\(a_{76}=+0.250802093\) \(a_{77}=-0.139324530\) \(a_{78}=+0.247380569\) \(a_{79}=+0.492629323\) \(a_{80}=+0.610075032\)
\(a_{81}=-0.942779371\) \(a_{82}=+0.294183950\) \(a_{83}=+1.629864804\) \(a_{84}=+0.066562715\) \(a_{85}=-1.988462567\)
\(a_{86}=-0.566541771\) \(a_{87}=+0.015548825\) \(a_{88}=+0.883778908\) \(a_{89}=-0.008295234\) \(a_{90}=+0.058365547\)
\(a_{91}=-0.056158394\) \(a_{92}=-0.438375024\) \(a_{93}=+1.068582500\) \(a_{94}=+0.910929467\) \(a_{95}=+0.869904141\)
\(a_{96}=-0.723737927\) \(a_{97}=+0.163531316\) \(a_{98}=-0.751716075\) \(a_{99}=+0.044234286\) \(a_{100}=-0.371807689\)

Showing 100 of 2292 available coefficients

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