Properties

Level $31$
Weight $0$
Character 31.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 2.73466182125 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.619895974\) \(a_{3}=-1.130317605\) \(a_{4}=-0.615728982\) \(a_{5}=-0.250063790\)
\(a_{6}=-0.700679332\) \(a_{7}=+0.754975699\) \(a_{8}=-1.001583890\) \(a_{9}=+0.277617888\) \(a_{10}=-0.155013536\)
\(a_{11}=-0.317228861\) \(a_{12}=+0.695969308\) \(a_{13}=-0.732209773\) \(a_{14}=+0.468006396\) \(a_{15}=+0.282651504\)
\(a_{16}=-0.005148839\) \(a_{17}=+0.370707416\) \(a_{18}=+0.172094211\) \(a_{19}=-0.307579859\) \(a_{20}=+0.153971522\)
\(a_{21}=-0.853362324\) \(a_{22}=-0.196648894\) \(a_{23}=-1.878326446\) \(a_{24}=+1.132107904\) \(a_{25}=-0.937468101\)
\(a_{26}=-0.453893890\) \(a_{27}=+0.816521219\) \(a_{28}=-0.464860419\) \(a_{29}=+1.055464670\) \(a_{30}=+0.175214529\)
\(a_{31}=-0.179605302\) \(a_{32}=+0.998392146\) \(a_{33}=+0.358569366\) \(a_{34}=+0.229800034\) \(a_{35}=-0.188792084\)
\(a_{36}=-0.170937379\) \(a_{37}=+0.815737198\) \(a_{38}=-0.190667516\) \(a_{39}=+0.827629597\) \(a_{40}=+0.250459863\)
\(a_{41}=+0.495030474\) \(a_{42}=-0.528995869\) \(a_{43}=-0.829568205\) \(a_{44}=+0.195327004\) \(a_{45}=-0.069422181\)
\(a_{46}=-1.164367001\) \(a_{47}=-1.498650220\) \(a_{48}=+0.005819824\) \(a_{49}=-0.430011694\) \(a_{50}=-0.581132701\)
\(a_{51}=-0.419017118\) \(a_{52}=+0.450842778\) \(a_{53}=+1.836217013\) \(a_{54}=+0.506158216\) \(a_{55}=+0.079327451\)
\(a_{56}=-0.756171498\) \(a_{57}=+0.347662929\) \(a_{58}=+0.654278299\) \(a_{59}=-1.535184550\) \(a_{60}=-0.174036722\)
\(a_{61}=-0.207460613\) \(a_{62}=-0.111336604\) \(a_{63}=+0.209594759\) \(a_{64}=+0.624048111\) \(a_{65}=+0.183099151\)
\(a_{66}=+0.222275706\) \(a_{67}=-1.018802253\) \(a_{68}=-0.228255300\) \(a_{69}=+2.123105449\) \(a_{70}=-0.117031453\)
\(a_{71}=+0.541273241\) \(a_{72}=-0.278057604\) \(a_{73}=-0.772291361\) \(a_{74}=+0.505672205\) \(a_{75}=+1.059636699\)
\(a_{76}=+0.189385833\) \(a_{77}=-0.239500081\) \(a_{78}=+0.513044255\) \(a_{79}=-0.325851825\) \(a_{80}=+0.001287538\)
\(a_{81}=-1.200546196\) \(a_{82}=+0.306867398\) \(a_{83}=+0.755557888\) \(a_{84}=+0.525439915\) \(a_{85}=-0.092700501\)
\(a_{86}=-0.514245990\) \(a_{87}=-1.193010297\) \(a_{88}=+0.317731317\) \(a_{89}=+0.168185589\) \(a_{90}=-0.043034530\)
\(a_{91}=-0.552800585\) \(a_{92}=+1.156540030\) \(a_{93}=+0.203011035\) \(a_{94}=-0.929007237\) \(a_{95}=+0.076914585\)
\(a_{96}=-1.128500219\) \(a_{97}=-1.790066161\) \(a_{98}=-0.266562517\) \(a_{99}=-0.088068406\) \(a_{100}=+0.577226279\)

Showing 100 of 546 available coefficients

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