Properties

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

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.3253059439 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.786445924\) \(a_{3}=+1.045161256\) \(a_{4}=+2.191389039\) \(a_{5}=-1.288677478\)
\(a_{6}=-1.867124065\) \(a_{7}=+1.706649973\) \(a_{8}=-2.128352092\) \(a_{9}=+0.092362050\) \(a_{10}=+2.302152628\)
\(a_{11}=+0.681700946\) \(a_{12}=+2.290354919\) \(a_{13}=+0.574209074\) \(a_{14}=-3.048837888\) \(a_{15}=-1.346875771\)
\(a_{16}=+1.610796880\) \(a_{17}=+1.169710497\) \(a_{18}=-0.164999808\) \(a_{19}=+0.534609253\) \(a_{20}=-2.823993700\)
\(a_{21}=+1.783724429\) \(a_{22}=-1.217821876\) \(a_{23}=+0.986734653\) \(a_{24}=-2.224471145\) \(a_{25}=+0.660689642\)
\(a_{26}=-1.025793460\) \(a_{27}=-0.948628019\) \(a_{28}=+3.739934044\) \(a_{29}=-0.034554966\) \(a_{30}=+2.406120731\)
\(a_{31}=-0.179605302\) \(a_{32}=-0.749249429\) \(a_{33}=+0.712487417\) \(a_{34}=-2.089624549\) \(a_{35}=-2.199321383\)
\(a_{36}=+0.202401185\) \(a_{37}=+0.792141312\) \(a_{38}=-0.955050521\) \(a_{39}=+0.600141077\) \(a_{40}=+2.742759406\)
\(a_{41}=+0.942390704\) \(a_{42}=-3.186527235\) \(a_{43}=+0.141252891\) \(a_{44}=+1.493871981\) \(a_{45}=-0.119024894\)
\(a_{46}=-1.762748098\) \(a_{47}=-0.833414984\) \(a_{48}=+1.683542490\) \(a_{49}=+1.912654130\) \(a_{50}=-1.180286318\)
\(a_{51}=+1.222536091\) \(a_{52}=+1.258315470\) \(a_{53}=-1.082899919\) \(a_{54}=+1.694672658\) \(a_{55}=-0.878492656\)
\(a_{56}=-3.632352040\) \(a_{57}=+0.558752878\) \(a_{58}=+0.061730578\) \(a_{59}=-0.050797941\) \(a_{60}=-2.951528801\)
\(a_{61}=+0.154603511\) \(a_{62}=+0.320855160\) \(a_{63}=+0.157629691\) \(a_{64}=-0.272303292\) \(a_{65}=-0.739970301\)
\(a_{66}=-1.272820241\) \(a_{67}=-0.848664731\) \(a_{68}=+2.563290761\) \(a_{69}=+1.031296829\) \(a_{70}=+3.928968720\)
\(a_{71}=+0.969459198\) \(a_{72}=-0.196578963\) \(a_{73}=-0.711486546\) \(a_{74}=-1.415117619\) \(a_{75}=+0.690527216\)
\(a_{76}=+1.171536857\) \(a_{77}=+1.163424901\) \(a_{78}=-1.072119580\) \(a_{79}=+0.317540272\) \(a_{80}=-2.075797661\)
\(a_{81}=-1.083831302\) \(a_{82}=-1.683530031\) \(a_{83}=+0.386525402\) \(a_{84}=+3.908834161\) \(a_{85}=-1.507379573\)
\(a_{86}=-0.252340651\) \(a_{87}=-0.036115512\) \(a_{88}=-1.450899634\) \(a_{89}=+1.888367805\) \(a_{90}=+0.212631537\)
\(a_{91}=+0.979973901\) \(a_{92}=+2.162319502\) \(a_{93}=-0.187716503\) \(a_{94}=+1.488850801\) \(a_{95}=-0.688938904\)
\(a_{96}=-0.783086474\) \(a_{97}=-1.833640608\) \(a_{98}=-3.416853175\) \(a_{99}=+0.062963297\) \(a_{100}=+1.447828040\)

Showing 100 of 546 available coefficients

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